%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SCT117+1 : TPTP v8.1.2. Released v5.2.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n015.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 14:20:42 EDT 2023 % Result : Theorem 191.20s 26.55s % Output : Proof 194.86s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SCT117+1 : TPTP v8.1.2. Released v5.2.0. % 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.33 % Computer : n015.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 300 % 0.13/0.33 % DateTime : Thu Aug 24 15:35:51 EDT 2023 % 0.13/0.33 % CPUTime : % 0.19/0.60 ________ _____ % 0.19/0.60 ___ __ \_________(_)________________________________ % 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.60 % 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.60 (2023-06-19) % 0.19/0.60 % 0.19/0.60 (c) Philipp Rümmer, 2009-2023 % 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.60 Amanda Stjerna. % 0.19/0.60 Free software under BSD-3-Clause. % 0.19/0.60 % 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.60 % 0.19/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.61 Running up to 7 provers in parallel. % 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 13.19/2.54 Prover 1: Preprocessing ... % 13.19/2.55 Prover 0: Preprocessing ... % 13.19/2.55 Prover 3: Preprocessing ... % 13.19/2.55 Prover 2: Preprocessing ... % 13.19/2.55 Prover 5: Preprocessing ... % 13.19/2.55 Prover 6: Preprocessing ... % 13.19/2.56 Prover 4: Preprocessing ... % 37.91/5.85 Prover 6: Proving ... % 37.91/5.86 Prover 3: Warning: ignoring some quantifiers % 38.45/5.91 Prover 1: Warning: ignoring some quantifiers % 39.32/6.02 Prover 3: Constructing countermodel ... % 40.22/6.17 Prover 1: Constructing countermodel ... % 43.24/6.58 Prover 5: Proving ... % 44.17/6.65 Prover 4: Warning: ignoring some quantifiers % 45.53/6.87 Prover 4: Constructing countermodel ... % 47.81/7.19 Prover 0: Proving ... % 51.84/7.75 Prover 2: Proving ... % 99.35/13.96 Prover 5: stopped % 99.35/13.97 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 102.26/14.48 Prover 7: Preprocessing ... % 106.29/14.89 Prover 2: stopped % 106.29/14.89 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 108.62/15.28 Prover 8: Preprocessing ... % 110.94/15.48 Prover 7: Warning: ignoring some quantifiers % 111.70/15.60 Prover 7: Constructing countermodel ... % 113.29/15.97 Prover 1: stopped % 113.29/15.99 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 114.68/16.05 Prover 8: Warning: ignoring some quantifiers % 116.02/16.15 Prover 8: Constructing countermodel ... % 117.59/16.39 Prover 9: Preprocessing ... % 128.41/17.81 Prover 9: Warning: ignoring some quantifiers % 128.41/17.86 Prover 9: Constructing countermodel ... % 129.03/17.87 Prover 6: stopped % 129.03/17.87 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 133.18/18.44 Prover 10: Preprocessing ... % 138.02/19.11 Prover 10: Warning: ignoring some quantifiers % 138.23/19.20 Prover 10: Constructing countermodel ... % 191.20/26.54 Prover 8: Found proof (size 3527) % 191.20/26.54 Prover 8: proved (11598ms) % 191.20/26.54 Prover 3: stopped % 191.20/26.54 Prover 9: stopped % 191.20/26.54 Prover 0: stopped % 191.20/26.55 Prover 10: stopped % 191.20/26.55 Prover 4: stopped % 191.20/26.55 Prover 7: stopped % 191.20/26.55 % 191.20/26.55 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 191.20/26.55 % 191.94/26.61 % SZS output start Proof for theBenchmark % 191.96/26.63 Assumptions after simplification: % 191.96/26.63 --------------------------------- % 191.96/26.63 % 191.96/26.63 (conj_0) % 191.96/26.64 ~ (v_x = v_y) & $i(v_x) & $i(v_y) % 191.96/26.64 % 191.96/26.64 (conj_1) % 191.96/26.67 $i(v_L) & $i(tc_Arrow__Order__Mirabelle_Oalt) & ? [v0: $i] : % 191.96/26.67 (tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt) = % 191.96/26.67 v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = v1 | ~ % 191.96/26.67 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 191.96/26.67 tc_Arrow__Order__Mirabelle_Oalt, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) % 191.96/26.67 | ? [v4: any] : ? [v5: $i] : ? [v6: any] : % 191.96/26.67 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 191.96/26.67 tc_Arrow__Order__Mirabelle_Oalt, v2, v1) = v5 & c_member(v0, v5, v_L) % 191.96/26.67 = v6 & c_member(v0, v3, v_L) = v4 & $i(v5) & (v6 = 0 | v4 = 0))) & ! % 191.96/26.67 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 191.96/26.67 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 191.96/26.67 tc_Arrow__Order__Mirabelle_Oalt, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) % 191.96/26.67 | ? [v4: int] : ( ~ (v4 = 0) & c_member(v0, v3, v_L) = v4) | ! [v4: $i] % 191.96/26.67 : ! [v5: $i] : ( ~ % 191.96/26.67 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 191.96/26.67 tc_Arrow__Order__Mirabelle_Oalt, v1, v4) = v5) | ~ $i(v4) | ? [v6: % 191.96/26.67 $i] : ? [v7: any] : ? [v8: any] : % 191.96/26.67 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 191.96/26.67 tc_Arrow__Order__Mirabelle_Oalt, v2, v4) = v6 & c_member(v0, v6, % 191.96/26.67 v_L) = v7 & c_member(v0, v5, v_L) = v8 & $i(v6) & ( ~ (v7 = 0) | v8 % 191.96/26.67 = 0)))) & ! [v1: $i] : ! [v2: $i] : ( ~ % 191.96/26.67 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 191.96/26.67 tc_Arrow__Order__Mirabelle_Oalt, v1, v1) = v2) | ~ $i(v1) | ? [v3: % 191.96/26.67 int] : ( ~ (v3 = 0) & c_member(v0, v2, v_L) = v3))) % 191.96/26.67 % 191.96/26.67 (conj_2) % 191.96/26.68 $i(v_L) & $i(v_x) & $i(v_y) & $i(tc_Arrow__Order__Mirabelle_Oalt) & ? [v0: % 191.96/26.68 $i] : (tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 191.96/26.68 tc_Arrow__Order__Mirabelle_Oalt) = v0 & $i(v0) & ( ? [v1: $i] : ? [v2: % 191.96/26.68 $i] : ? [v3: $i] : ? [v4: any] : ? [v5: $i] : ? [v6: any] : ? [v7: % 191.96/26.68 $i] : ? [v8: any] : ? [v9: $i] : ? [v10: any] : ? [v11: $i] : ? % 191.96/26.68 [v12: any] : ? [v13: $i] : ? [v14: any] : ( ~ (v2 = v1) & % 191.96/26.68 c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 191.96/26.68 tc_Arrow__Order__Mirabelle_Oalt, v2, v1) = v9 & % 191.96/26.68 c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 191.96/26.68 tc_Arrow__Order__Mirabelle_Oalt, v2, v_x) = v11 & % 191.96/26.68 c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 191.96/26.68 tc_Arrow__Order__Mirabelle_Oalt, v1, v2) = v3 & % 191.96/26.68 c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 191.96/26.68 tc_Arrow__Order__Mirabelle_Oalt, v1, v_x) = v5 & % 191.96/26.68 c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 191.96/26.68 tc_Arrow__Order__Mirabelle_Oalt, v_x, v2) = v7 & % 191.96/26.68 c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 191.96/26.68 tc_Arrow__Order__Mirabelle_Oalt, v_x, v1) = v13 & c_member(v0, v13, % 191.96/26.68 v_L) = v14 & c_member(v0, v11, v_L) = v12 & c_member(v0, v9, v_L) = % 191.96/26.68 v10 & c_member(v0, v7, v_L) = v8 & c_member(v0, v5, v_L) = v6 & % 191.96/26.68 c_member(v0, v3, v_L) = v4 & $i(v13) & $i(v11) & $i(v9) & $i(v7) & % 191.96/26.68 $i(v5) & $i(v3) & $i(v2) & $i(v1) & ( ~ (v14 = 0) | ~ (v2 = v_y) | v1 = % 191.96/26.68 v_y) & ( ~ (v12 = 0) | ~ (v1 = v_y) | v2 = v_y) & ( ~ (v10 = 0) | v2 % 191.96/26.68 = v_y | v1 = v_y) & ( ~ (v8 = 0) | ~ (v1 = v_y) | v2 = v_y) & ( ~ (v6 % 191.96/26.68 = 0) | ~ (v2 = v_y) | v1 = v_y) & ( ~ (v4 = 0) | v2 = v_y | v1 = % 191.96/26.68 v_y) & ( ~ (v2 = v_x) | ~ (v1 = v_y)) & ( ~ (v2 = v_y) | ~ (v1 = % 191.96/26.68 v_x))) | ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: any] : ? % 191.96/26.68 [v5: $i] : ? [v6: any] : ? [v7: $i] : ? [v8: any] : ? [v9: $i] : ? % 191.96/26.68 [v10: any] : (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 191.96/26.68 tc_Arrow__Order__Mirabelle_Oalt, v2, v_x) = v7 & % 191.96/26.68 c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 191.96/26.68 tc_Arrow__Order__Mirabelle_Oalt, v1, v2) = v3 & % 191.96/26.68 c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 191.96/26.68 tc_Arrow__Order__Mirabelle_Oalt, v1, v_x) = v5 & % 191.96/26.68 c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 191.96/26.68 tc_Arrow__Order__Mirabelle_Oalt, v_x, v2) = v9 & c_member(v0, v9, v_L) % 191.96/26.68 = v10 & c_member(v0, v7, v_L) = v8 & c_member(v0, v5, v_L) = v6 & % 191.96/26.68 c_member(v0, v3, v_L) = v4 & $i(v9) & $i(v7) & $i(v5) & $i(v3) & $i(v2) % 191.96/26.68 & $i(v1) & ((v10 = 0 & v1 = v_y & ~ (v2 = v_y) & ? [v11: $i] : ? % 191.96/26.68 [v12: $i] : ? [v13: any] : ? [v14: $i] : ? [v15: any] : % 191.96/26.68 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 191.96/26.68 tc_Arrow__Order__Mirabelle_Oalt, v2, v11) = v12 & % 191.96/26.68 c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 191.96/26.68 tc_Arrow__Order__Mirabelle_Oalt, v_x, v11) = v14 & c_member(v0, % 191.96/26.68 v14, v_L) = v15 & c_member(v0, v12, v_L) = v13 & $i(v14) & % 191.96/26.68 $i(v12) & $i(v11) & ((v13 = 0 & ~ (v15 = 0) & ~ (v11 = v_y)) | % 191.96/26.68 (v11 = v_y & v8 = 0) | (v11 = v_y & v2 = v_x)))) | ( ~ (v1 = % 191.96/26.68 v_y) & ((v6 = 0 & v2 = v_y & ? [v11: $i] : ? [v12: $i] : ? % 191.96/26.68 [v13: $i] : ? [v14: int] : ( ~ (v14 = 0) & ~ (v11 = v_y) & % 191.96/26.68 c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 191.96/26.68 tc_Arrow__Order__Mirabelle_Oalt, v1, v11) = v13 & % 191.96/26.68 c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 191.96/26.68 tc_Arrow__Order__Mirabelle_Oalt, v_x, v11) = v12 & % 191.96/26.68 c_member(v0, v13, v_L) = v14 & c_member(v0, v12, v_L) = 0 & % 191.96/26.68 $i(v13) & $i(v12) & $i(v11))) | (v4 = 0 & ~ (v2 = v_y) & ? % 191.96/26.68 [v11: $i] : ? [v12: $i] : ? [v13: any] : ? [v14: $i] : ? % 191.96/26.68 [v15: any] : % 191.96/26.68 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 191.96/26.68 tc_Arrow__Order__Mirabelle_Oalt, v2, v11) = v12 & % 191.96/26.68 c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 191.96/26.68 tc_Arrow__Order__Mirabelle_Oalt, v1, v11) = v14 & % 191.96/26.68 c_member(v0, v14, v_L) = v15 & c_member(v0, v12, v_L) = v13 & % 191.96/26.68 $i(v14) & $i(v12) & $i(v11) & ((v13 = 0 & ~ (v15 = 0) & ~ % 191.96/26.68 (v11 = v_y)) | (v11 = v_y & v8 = 0 & ~ (v6 = 0) & ~ (v1 % 191.96/26.68 = v_x)) | (v11 = v_y & v2 = v_x & ~ (v6 = 0) & ~ (v1 = % 191.96/26.68 v_x))))))))))) % 191.96/26.68 % 191.96/26.68 (fact_Lin__irrefl) % 191.96/26.68 $i(c_Arrow__Order__Mirabelle_OLin) & $i(tc_HOL_Obool) & % 191.96/26.68 $i(tc_Arrow__Order__Mirabelle_Oalt) & ? [v0: $i] : ? [v1: $i] : (tc_fun(v0, % 191.96/26.68 tc_HOL_Obool) = v1 & tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 191.96/26.68 tc_Arrow__Order__Mirabelle_Oalt) = v0 & $i(v1) & $i(v0) & ! [v2: $i] : ! % 191.96/26.68 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 191.96/26.68 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 191.96/26.68 tc_Arrow__Order__Mirabelle_Oalt, v2, v3) = v5) | ~ (c_member(v0, v5, % 191.96/26.68 v4) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v6: any] : ? [v7: % 191.96/26.68 $i] : ? [v8: any] : % 191.96/26.68 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 191.96/26.68 tc_Arrow__Order__Mirabelle_Oalt, v3, v2) = v7 & c_member(v1, v4, % 191.96/26.68 c_Arrow__Order__Mirabelle_OLin) = v6 & c_member(v0, v7, v4) = v8 & % 191.96/26.68 $i(v7) & ( ~ (v8 = 0) | ~ (v6 = 0))))) % 191.96/26.68 % 191.96/26.68 (fact_antisymD) % 191.96/26.69 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 191.96/26.69 $i] : (v1 = v0 | ~ (tc_prod(v3, v3) = v4) | ~ (c_Product__Type_OPair(v3, % 191.96/26.69 v3, v0, v1) = v5) | ~ (c_member(v4, v5, v2) = 0) | ~ $i(v3) | ~ % 191.96/26.69 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: $i] : ? [v8: any] : % 191.96/26.69 (c_Relation_Oantisym(v3, v2) = v6 & c_Product__Type_OPair(v3, v3, v1, v0) = % 191.96/26.69 v7 & c_member(v4, v7, v2) = v8 & $i(v7) & ( ~ (v8 = 0) | ~ (v6 = 0)))) % 191.96/26.69 % 191.96/26.69 (fact_below__Lin) % 191.96/26.69 $i(c_Arrow__Order__Mirabelle_OLin) & $i(tc_HOL_Obool) & % 191.96/26.69 $i(tc_Arrow__Order__Mirabelle_Oalt) & ? [v0: $i] : ? [v1: $i] : (tc_fun(v0, % 191.96/26.69 tc_HOL_Obool) = v1 & tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 191.96/26.69 tc_Arrow__Order__Mirabelle_Oalt) = v0 & $i(v1) & $i(v0) & ! [v2: $i] : ! % 191.96/26.69 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v4 = v3 | ~ % 191.96/26.69 (c_Arrow__Order__Mirabelle_Obelow(v2, v4, v3) = v5) | ~ $i(v4) | ~ % 191.96/26.69 $i(v3) | ~ $i(v2) | ? [v6: any] : ? [v7: any] : (c_member(v1, v5, % 191.96/26.69 c_Arrow__Order__Mirabelle_OLin) = v7 & c_member(v1, v2, % 191.96/26.69 c_Arrow__Order__Mirabelle_OLin) = v6 & ( ~ (v6 = 0) | v7 = 0)))) % 191.96/26.69 % 191.96/26.69 (fact_converse__in__Lin) % 191.96/26.69 $i(c_Arrow__Order__Mirabelle_OLin) & $i(tc_HOL_Obool) & % 191.96/26.69 $i(tc_Arrow__Order__Mirabelle_Oalt) & ? [v0: $i] : ? [v1: $i] : (tc_fun(v0, % 191.96/26.69 tc_HOL_Obool) = v1 & tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 191.96/26.69 tc_Arrow__Order__Mirabelle_Oalt) = v0 & $i(v1) & $i(v0) & ! [v2: $i] : ! % 191.96/26.69 [v3: int] : (v3 = 0 | ~ (c_member(v1, v2, c_Arrow__Order__Mirabelle_OLin) = % 191.96/26.69 v3) | ~ $i(v2) | ? [v4: $i] : ? [v5: int] : ( ~ (v5 = 0) & % 191.96/26.69 c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt, % 191.96/26.69 tc_Arrow__Order__Mirabelle_Oalt, v2) = v4 & c_member(v1, v4, % 191.96/26.69 c_Arrow__Order__Mirabelle_OLin) = v5 & $i(v4))) & ! [v2: $i] : ( ~ % 191.96/26.69 (c_member(v1, v2, c_Arrow__Order__Mirabelle_OLin) = 0) | ~ $i(v2) | ? % 191.96/26.69 [v3: $i] : (c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt, % 191.96/26.69 tc_Arrow__Order__Mirabelle_Oalt, v2) = v3 & c_member(v1, v3, % 191.96/26.69 c_Arrow__Order__Mirabelle_OLin) = 0 & $i(v3)))) % 191.96/26.69 % 191.96/26.69 (fact_in__above) % 191.96/26.69 $i(c_Arrow__Order__Mirabelle_OLin) & $i(tc_HOL_Obool) & % 191.96/26.69 $i(tc_Arrow__Order__Mirabelle_Oalt) & ? [v0: $i] : ? [v1: $i] : (tc_fun(v0, % 191.96/26.69 tc_HOL_Obool) = v1 & tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 191.96/26.69 tc_Arrow__Order__Mirabelle_Oalt) = v0 & $i(v1) & $i(v0) & ! [v2: $i] : ! % 191.96/26.69 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: % 191.96/26.69 $i] : ! [v9: any] : (v6 = v5 | ~ (c_Arrow__Order__Mirabelle_Oabove(v4, % 191.96/26.69 v6, v5) = v8) | ~ % 191.96/26.69 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 191.96/26.69 tc_Arrow__Order__Mirabelle_Oalt, v3, v2) = v7) | ~ (c_member(v0, v7, % 191.96/26.69 v8) = v9) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) % 191.96/26.69 | ? [v10: any] : ? [v11: $i] : ? [v12: any] : ? [v13: $i] : ? [v14: % 191.96/26.69 any] : ? [v15: any] : % 191.96/26.69 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 191.96/26.69 tc_Arrow__Order__Mirabelle_Oalt, v6, v2) = v11 & % 191.96/26.69 c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 191.96/26.69 tc_Arrow__Order__Mirabelle_Oalt, v3, v6) = v13 & c_member(v1, v4, % 191.96/26.69 c_Arrow__Order__Mirabelle_OLin) = v10 & c_member(v0, v13, v4) = v14 & % 191.96/26.69 c_member(v0, v11, v4) = v12 & c_member(v0, v7, v4) = v15 & $i(v13) & % 191.96/26.69 $i(v11) & ( ~ (v10 = 0) | (( ~ (v9 = 0) | ( ~ (v3 = v2) & ( ~ (v5 = v3) % 191.96/26.69 | v12 = 0) & (v5 = v3 | (( ~ (v5 = v2) | v14 = 0 | v6 = v3) & % 191.96/26.69 (v15 = 0 | v5 = v2))))) & (v9 = 0 | v3 = v2 | (v5 = v3 & ~ % 191.96/26.69 (v12 = 0)) | ( ~ (v5 = v3) & ((v5 = v2 & ~ (v14 = 0) & ~ (v6 = % 191.96/26.69 v3)) | ( ~ (v15 = 0) & ~ (v5 = v2)))))))))) % 191.96/26.69 % 191.96/26.70 (fact_in__below) % 191.96/26.70 $i(c_Arrow__Order__Mirabelle_OLin) & $i(tc_HOL_Obool) & % 191.96/26.70 $i(tc_Arrow__Order__Mirabelle_Oalt) & ? [v0: $i] : ? [v1: $i] : (tc_fun(v0, % 191.96/26.70 tc_HOL_Obool) = v1 & tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 191.96/26.70 tc_Arrow__Order__Mirabelle_Oalt) = v0 & $i(v1) & $i(v0) & ! [v2: $i] : ! % 191.96/26.70 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: % 191.96/26.70 $i] : ! [v9: any] : (v6 = v5 | ~ (c_Arrow__Order__Mirabelle_Obelow(v4, % 191.96/26.70 v6, v5) = v8) | ~ % 191.96/26.70 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 191.96/26.70 tc_Arrow__Order__Mirabelle_Oalt, v3, v2) = v7) | ~ (c_member(v0, v7, % 191.96/26.70 v8) = v9) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) % 191.96/26.70 | ? [v10: any] : ? [v11: $i] : ? [v12: any] : ? [v13: $i] : ? [v14: % 191.96/26.70 any] : ? [v15: any] : % 191.96/26.70 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 191.96/26.70 tc_Arrow__Order__Mirabelle_Oalt, v5, v2) = v13 & % 191.96/26.70 c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 191.96/26.70 tc_Arrow__Order__Mirabelle_Oalt, v3, v5) = v11 & c_member(v1, v4, % 191.96/26.70 c_Arrow__Order__Mirabelle_OLin) = v10 & c_member(v0, v13, v4) = v14 & % 191.96/26.70 c_member(v0, v11, v4) = v12 & c_member(v0, v7, v4) = v15 & $i(v13) & % 191.96/26.70 $i(v11) & ( ~ (v10 = 0) | (( ~ (v9 = 0) | ( ~ (v3 = v2) & ( ~ (v6 = v2) % 191.96/26.70 | v12 = 0) & (v6 = v2 | (( ~ (v6 = v3) | v14 = 0 | v5 = v2) & % 191.96/26.70 (v15 = 0 | v6 = v3))))) & (v9 = 0 | v3 = v2 | (v6 = v2 & ~ % 191.96/26.70 (v12 = 0)) | ( ~ (v6 = v2) & ((v6 = v3 & ~ (v14 = 0) & ~ (v5 = % 191.96/26.70 v2)) | ( ~ (v15 = 0) & ~ (v6 = v3)))))))))) % 191.96/26.70 % 191.96/26.70 (fact_in__mkbot) % 191.96/26.70 $i(tc_Arrow__Order__Mirabelle_Oalt) & ? [v0: $i] : % 191.96/26.70 (tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt) = % 191.96/26.70 v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 191.96/26.70 [v5: $i] : ! [v6: $i] : ! [v7: int] : (v7 = 0 | v3 = v1 | ~ % 191.96/26.70 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 191.96/26.70 tc_Arrow__Order__Mirabelle_Oalt, v4, v3) = v5) | ~ % 191.96/26.70 (c_Arrow__Order__Mirabelle_Omkbot(v2, v1) = v6) | ~ (c_member(v0, v5, v6) % 191.96/26.70 = v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ( ~ (v4 = v1) & % 191.96/26.70 ? [v8: int] : ( ~ (v8 = 0) & c_member(v0, v5, v2) = v8))) & ! [v1: $i] % 191.96/26.70 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ % 191.96/26.70 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 191.96/26.70 tc_Arrow__Order__Mirabelle_Oalt, v4, v3) = v5) | ~ % 191.96/26.70 (c_Arrow__Order__Mirabelle_Omkbot(v2, v1) = v6) | ~ (c_member(v0, v5, v6) % 191.96/26.70 = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ( ~ (v3 = v1) & % 191.96/26.70 (v4 = v1 | c_member(v0, v5, v2) = 0)))) % 191.96/26.70 % 191.96/26.70 (fact_in__mktop) % 191.96/26.70 $i(tc_Arrow__Order__Mirabelle_Oalt) & ? [v0: $i] : % 191.96/26.70 (tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt) = % 191.96/26.70 v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 191.96/26.70 [v5: $i] : ! [v6: $i] : ! [v7: int] : (v7 = 0 | v4 = v1 | ~ % 191.96/26.70 (c_Arrow__Order__Mirabelle_Omktop(v2, v1) = v6) | ~ % 191.96/26.70 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 191.96/26.70 tc_Arrow__Order__Mirabelle_Oalt, v4, v3) = v5) | ~ (c_member(v0, v5, % 191.96/26.70 v6) = v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ( ~ (v3 = % 191.96/26.70 v1) & ? [v8: int] : ( ~ (v8 = 0) & c_member(v0, v5, v2) = v8))) & ! % 191.96/26.70 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: % 191.96/26.70 $i] : ( ~ (c_Arrow__Order__Mirabelle_Omktop(v2, v1) = v6) | ~ % 191.96/26.71 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 191.96/26.71 tc_Arrow__Order__Mirabelle_Oalt, v4, v3) = v5) | ~ (c_member(v0, v5, % 191.96/26.71 v6) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ( ~ (v4 = % 191.96/26.71 v1) & (v3 = v1 | c_member(v0, v5, v2) = 0)))) % 191.96/26.71 % 191.96/26.71 (fact_linear__alt) % 191.96/26.71 $i(c_Arrow__Order__Mirabelle_OLin) & $i(tc_HOL_Obool) & % 191.96/26.71 $i(tc_Arrow__Order__Mirabelle_Oalt) & ? [v0: $i] : ? [v1: $i] : (tc_fun(v0, % 191.96/26.71 tc_HOL_Obool) = v1 & tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 191.96/26.71 tc_Arrow__Order__Mirabelle_Oalt) = v0 & $i(v1) & $i(v0) & ? [v2: $i] : % 191.96/26.71 (c_member(v1, v2, c_Arrow__Order__Mirabelle_OLin) = 0 & $i(v2))) % 191.96/26.71 % 191.96/26.71 (fact_mem__def) % 191.96/26.71 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 191.96/26.71 (c_member(v2, v1, v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 191.96/26.71 $i] : ? [v5: int] : ( ~ (v5 = 0) & hBOOL(v4) = v5 & hAPP(v0, v1) = v4 & % 191.96/26.71 $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (c_member(v2, v1, % 191.96/26.71 v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (hBOOL(v3) % 191.96/26.71 = 0 & hAPP(v0, v1) = v3 & $i(v3))) % 191.96/26.71 % 191.96/26.71 (fact_mkbot__Lin) % 192.36/26.71 $i(c_Arrow__Order__Mirabelle_OLin) & $i(tc_HOL_Obool) & % 192.36/26.71 $i(tc_Arrow__Order__Mirabelle_Oalt) & ? [v0: $i] : ? [v1: $i] : (tc_fun(v0, % 192.36/26.71 tc_HOL_Obool) = v1 & tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 192.36/26.71 tc_Arrow__Order__Mirabelle_Oalt) = v0 & $i(v1) & $i(v0) & ! [v2: $i] : ! % 192.36/26.71 [v3: $i] : ! [v4: $i] : ( ~ (c_Arrow__Order__Mirabelle_Omkbot(v3, v2) = v4) % 192.36/26.71 | ~ $i(v3) | ~ $i(v2) | ? [v5: any] : ? [v6: any] : (c_member(v1, v4, % 192.36/26.71 c_Arrow__Order__Mirabelle_OLin) = v6 & c_member(v1, v3, % 192.36/26.71 c_Arrow__Order__Mirabelle_OLin) = v5 & ( ~ (v5 = 0) | v6 = 0)))) % 192.36/26.71 % 192.36/26.71 (fact_mktop__Lin) % 192.36/26.71 $i(c_Arrow__Order__Mirabelle_OLin) & $i(tc_HOL_Obool) & % 192.36/26.71 $i(tc_Arrow__Order__Mirabelle_Oalt) & ? [v0: $i] : ? [v1: $i] : (tc_fun(v0, % 192.36/26.71 tc_HOL_Obool) = v1 & tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 192.36/26.71 tc_Arrow__Order__Mirabelle_Oalt) = v0 & $i(v1) & $i(v0) & ! [v2: $i] : ! % 192.36/26.71 [v3: $i] : ! [v4: $i] : ( ~ (c_Arrow__Order__Mirabelle_Omktop(v3, v2) = v4) % 192.36/26.71 | ~ $i(v3) | ~ $i(v2) | ? [v5: any] : ? [v6: any] : (c_member(v1, v4, % 192.36/26.71 c_Arrow__Order__Mirabelle_OLin) = v6 & c_member(v1, v3, % 192.36/26.71 c_Arrow__Order__Mirabelle_OLin) = v5 & ( ~ (v5 = 0) | v6 = 0)))) % 192.36/26.71 % 192.36/26.71 (fact_notin__Lin__iff) % 192.36/26.71 $i(c_Arrow__Order__Mirabelle_OLin) & $i(tc_HOL_Obool) & % 192.36/26.71 $i(tc_Arrow__Order__Mirabelle_Oalt) & ? [v0: $i] : ? [v1: $i] : (tc_fun(v0, % 192.36/26.71 tc_HOL_Obool) = v1 & tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 192.36/26.71 tc_Arrow__Order__Mirabelle_Oalt) = v0 & $i(v1) & $i(v0) & ! [v2: $i] : ! % 192.36/26.71 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: any] : (v3 = v2 | ~ % 192.36/26.71 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.36/26.71 tc_Arrow__Order__Mirabelle_Oalt, v2, v3) = v5) | ~ (c_member(v0, v5, % 192.36/26.71 v4) = v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v7: any] : ? [v8: % 192.36/26.71 $i] : ? [v9: any] : % 192.36/26.71 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.36/26.71 tc_Arrow__Order__Mirabelle_Oalt, v3, v2) = v8 & c_member(v1, v4, % 192.36/26.71 c_Arrow__Order__Mirabelle_OLin) = v7 & c_member(v0, v8, v4) = v9 & % 192.36/26.71 $i(v8) & ( ~ (v7 = 0) | (( ~ (v9 = 0) | ~ (v6 = 0)) & (v9 = 0 | v6 = % 192.36/26.71 0)))))) % 192.36/26.71 % 192.36/26.71 (fact_single__valuedD) % 192.36/26.72 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 192.36/26.72 $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : (v1 = v0 | ~ (tc_prod(v5, % 192.36/26.72 v4) = v6) | ~ (c_Product__Type_OPair(v5, v4, v2, v1) = v7) | ~ % 192.36/26.72 (c_Product__Type_OPair(v5, v4, v2, v0) = v8) | ~ (c_member(v6, v8, v3) = 0) % 192.36/26.72 | ~ (c_member(v6, v7, v3) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ % 192.36/26.72 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v9: int] : ( ~ (v9 = 0) & % 192.36/26.72 c_Relation_Osingle__valued(v5, v4, v3) = v9)) % 192.36/26.72 % 192.36/26.72 (fact_transD) % 192.36/26.72 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 192.36/26.72 $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: int] : (v8 = 0 | ~ (tc_prod(v4, % 192.36/26.72 v4) = v5) | ~ (c_Product__Type_OPair(v4, v4, v2, v0) = v7) | ~ % 192.36/26.72 (c_Product__Type_OPair(v4, v4, v1, v0) = v6) | ~ (c_member(v5, v7, v3) = % 192.36/26.72 v8) | ~ (c_member(v5, v6, v3) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | % 192.36/26.72 ~ $i(v1) | ~ $i(v0) | ? [v9: any] : ? [v10: $i] : ? [v11: any] : % 192.36/26.72 (c_Relation_Otrans(v4, v3) = v9 & c_Product__Type_OPair(v4, v4, v2, v1) = % 192.36/26.72 v10 & c_member(v5, v10, v3) = v11 & $i(v10) & ( ~ (v11 = 0) | ~ (v9 = % 192.36/26.72 0)))) % 192.36/26.72 % 192.36/26.72 (fact_wf__asym) % 192.36/26.72 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 192.36/26.72 $i] : ( ~ (tc_prod(v3, v3) = v4) | ~ (c_Product__Type_OPair(v3, v3, v0, v1) % 192.36/26.72 = v5) | ~ (c_member(v4, v5, v2) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) % 192.36/26.72 | ~ $i(v0) | ? [v6: any] : ? [v7: $i] : ? [v8: any] : % 192.36/26.72 (c_Wellfounded_Owf(v3, v2) = v6 & c_Product__Type_OPair(v3, v3, v1, v0) = v7 % 192.36/26.72 & c_member(v4, v7, v2) = v8 & $i(v7) & ( ~ (v8 = 0) | ~ (v6 = 0)))) % 192.36/26.72 % 192.36/26.72 (fact_wf__not__sym) % 192.36/26.72 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 192.36/26.72 $i] : ( ~ (tc_prod(v3, v3) = v4) | ~ (c_Product__Type_OPair(v3, v3, v0, v1) % 192.36/26.72 = v5) | ~ (c_member(v4, v5, v2) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) % 192.36/26.72 | ~ $i(v0) | ? [v6: any] : ? [v7: $i] : ? [v8: any] : % 192.36/26.72 (c_Wellfounded_Owf(v3, v2) = v6 & c_Product__Type_OPair(v3, v3, v1, v0) = v7 % 192.36/26.72 & c_member(v4, v7, v2) = v8 & $i(v7) & ( ~ (v8 = 0) | ~ (v6 = 0)))) % 192.36/26.72 % 192.36/26.72 (function-axioms) % 192.36/26.76 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 192.36/26.76 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v1 = v0 | % 192.36/26.76 ~ (c_Nitpick_Ofold__graph_H(v7, v6, v5, v4, v3, v2) = v1) | ~ % 192.36/26.76 (c_Nitpick_Ofold__graph_H(v7, v6, v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! % 192.36/26.76 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] % 192.36/26.76 : ! [v7: $i] : (v1 = v0 | ~ (c_Product__Type_Ocurry(v7, v6, v5, v4, v3, v2) % 192.36/26.76 = v1) | ~ (c_Product__Type_Ocurry(v7, v6, v5, v4, v3, v2) = v0)) & ! % 192.36/26.76 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 192.36/26.76 $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v1 = v0 | ~ % 192.36/26.76 (c_Recdef_Owfrec__rel(v7, v6, v5, v4, v3, v2) = v1) | ~ % 192.36/26.76 (c_Recdef_Owfrec__rel(v7, v6, v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 192.36/26.76 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : % 192.36/26.76 (v1 = v0 | ~ (c_Nitpick_Owf__wfrec_H(v6, v5, v4, v3, v2) = v1) | ~ % 192.36/26.76 (c_Nitpick_Owf__wfrec_H(v6, v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 192.36/26.76 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : % 192.36/26.76 (v1 = v0 | ~ (c_Recdef_Ocut(v6, v5, v4, v3, v2) = v1) | ~ (c_Recdef_Ocut(v6, % 192.36/26.76 v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 192.36/26.76 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ % 192.36/26.76 (c_Product__Type_Ointernal__split(v6, v5, v4, v3, v2) = v1) | ~ % 192.36/26.76 (c_Product__Type_Ointernal__split(v6, v5, v4, v3, v2) = v0)) & ! [v0: $i] : % 192.36/26.76 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: % 192.36/26.76 $i] : (v1 = v0 | ~ (c_Product__Type_Oprod_Oprod__rec(v6, v5, v4, v3, v2) = % 192.36/26.76 v1) | ~ (c_Product__Type_Oprod_Oprod__rec(v6, v5, v4, v3, v2) = v0)) & ! % 192.36/26.76 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] % 192.36/26.76 : (v1 = v0 | ~ (c_Relation_OImage(v5, v4, v3, v2) = v1) | ~ % 192.36/26.76 (c_Relation_OImage(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 192.36/26.76 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ % 192.36/26.76 (c_Recdef_Owfrec(v5, v4, v3, v2) = v1) | ~ (c_Recdef_Owfrec(v5, v4, v3, v2) % 192.36/26.76 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 192.36/26.76 $i] : ! [v5: $i] : (v1 = v0 | ~ (c_Product__Type_OSigma(v5, v4, v3, v2) = % 192.36/26.76 v1) | ~ (c_Product__Type_OSigma(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! % 192.36/26.76 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | % 192.36/26.76 ~ (c_Nitpick_Owf__wfrec(v5, v4, v3, v2) = v1) | ~ (c_Nitpick_Owf__wfrec(v5, % 192.36/26.76 v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 192.36/26.76 $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ % 192.36/26.76 (c_Wellfounded_Olex__prod(v5, v4, v3, v2) = v1) | ~ % 192.36/26.76 (c_Wellfounded_Olex__prod(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 192.36/26.76 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ % 192.36/26.76 (c_Recdef_Osame__fst(v5, v4, v3, v2) = v1) | ~ (c_Recdef_Osame__fst(v5, v4, % 192.36/26.76 v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 192.36/26.76 ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (c_Product__Type_OPair(v5, v4, v3, % 192.36/26.76 v2) = v1) | ~ (c_Product__Type_OPair(v5, v4, v3, v2) = v0)) & ! [v0: % 192.36/26.76 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 192.36/26.76 : ! [v4: $i] : (v1 = v0 | ~ (c_Equiv__Relations_Oequiv(v4, v3, v2) = v1) | % 192.36/26.76 ~ (c_Equiv__Relations_Oequiv(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 192.36/26.76 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 192.36/26.76 (c_Lattices_Osemilattice__inf__class_Oinf(v4, v3, v2) = v1) | ~ % 192.36/26.76 (c_Lattices_Osemilattice__inf__class_Oinf(v4, v3, v2) = v0)) & ! [v0: % 192.36/26.76 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 192.36/26.76 : ! [v4: $i] : (v1 = v0 | ~ (c_Orderings_Oord__class_Oless__eq(v4, v3, v2) = % 192.36/26.76 v1) | ~ (c_Orderings_Oord__class_Oless__eq(v4, v3, v2) = v0)) & ! [v0: % 192.36/26.76 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 192.36/26.76 (c_Wellfounded_Omlex__prod(v4, v3, v2) = v1) | ~ % 192.36/26.76 (c_Wellfounded_Omlex__prod(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : % 192.36/26.76 ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = % 192.36/26.76 v0 | ~ (c_Orderings_Oord__class_Oless(v4, v3, v2) = v1) | ~ % 192.36/26.76 (c_Orderings_Oord__class_Oless(v4, v3, v2) = v0)) & ! [v0: % 192.36/26.76 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 192.36/26.76 : ! [v4: $i] : (v1 = v0 | ~ (c_Order__Relation_Opartial__order__on(v4, v3, % 192.36/26.76 v2) = v1) | ~ (c_Order__Relation_Opartial__order__on(v4, v3, v2) = v0)) % 192.36/26.76 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 192.36/26.76 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (c_Order__Relation_Owell__order__on(v4, % 192.36/26.76 v3, v2) = v1) | ~ (c_Order__Relation_Owell__order__on(v4, v3, v2) = % 192.36/26.76 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 192.36/26.76 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 192.36/26.76 (c_Order__Relation_Opreorder__on(v4, v3, v2) = v1) | ~ % 192.36/26.76 (c_Order__Relation_Opreorder__on(v4, v3, v2) = v0)) & ! [v0: % 192.36/26.76 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 192.36/26.76 : ! [v4: $i] : (v1 = v0 | ~ (c_Order__Relation_Olinear__order__on(v4, v3, % 192.36/26.76 v2) = v1) | ~ (c_Order__Relation_Olinear__order__on(v4, v3, v2) = v0)) % 192.36/26.76 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 192.36/26.76 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 192.36/26.76 (c_Order__Relation_Ostrict__linear__order__on(v4, v3, v2) = v1) | ~ % 192.36/26.76 (c_Order__Relation_Ostrict__linear__order__on(v4, v3, v2) = v0)) & ! [v0: % 192.36/26.76 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 192.36/26.76 (c_Groups_Ominus__class_Ominus(v4, v3, v2) = v1) | ~ % 192.36/26.76 (c_Groups_Ominus__class_Ominus(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 192.36/26.76 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 192.36/26.76 (c_Lattices_Osemilattice__sup__class_Osup(v4, v3, v2) = v1) | ~ % 192.36/26.76 (c_Lattices_Osemilattice__sup__class_Osup(v4, v3, v2) = v0)) & ! [v0: $i] : % 192.36/26.76 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 192.36/26.76 (c_Set_Oinsert(v4, v3, v2) = v1) | ~ (c_Set_Oinsert(v4, v3, v2) = v0)) & ! % 192.36/26.76 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 192.36/26.76 $i] : ! [v4: $i] : (v1 = v0 | ~ (c_Relation_Orefl__on(v4, v3, v2) = v1) | % 192.36/26.76 ~ (c_Relation_Orefl__on(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 192.36/26.76 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 192.36/26.76 (c_Relation_Oinv__image(v4, v3, v2) = v1) | ~ (c_Relation_Oinv__image(v4, % 192.36/26.76 v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] % 192.36/26.76 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 192.36/26.76 (c_Relation_Ototal__on(v4, v3, v2) = v1) | ~ (c_Relation_Ototal__on(v4, v3, % 192.36/26.76 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! % 192.36/26.76 [v4: $i] : (v1 = v0 | ~ (c_Relation_ODomain(v4, v3, v2) = v1) | ~ % 192.36/26.76 (c_Relation_ODomain(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 192.36/26.76 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | % 192.36/26.76 ~ (c_Relation_Osingle__valued(v4, v3, v2) = v1) | ~ % 192.36/26.76 (c_Relation_Osingle__valued(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 192.36/26.76 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 192.36/26.76 (c_Relation_Oconverse(v4, v3, v2) = v1) | ~ (c_Relation_Oconverse(v4, v3, % 192.36/26.76 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! % 192.36/26.76 [v4: $i] : (v1 = v0 | ~ (c_Relation_ORange(v4, v3, v2) = v1) | ~ % 192.36/26.76 (c_Relation_ORange(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 192.36/26.76 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 192.36/26.76 (c_Arrow__Order__Mirabelle_Obelow(v4, v3, v2) = v1) | ~ % 192.36/26.76 (c_Arrow__Order__Mirabelle_Obelow(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 192.36/26.76 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 192.36/26.76 (c_Arrow__Order__Mirabelle_Oabove(v4, v3, v2) = v1) | ~ % 192.36/26.76 (c_Arrow__Order__Mirabelle_Oabove(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 192.36/26.76 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 192.36/26.76 (c_FunDef_Oin__rel(v4, v3, v2) = v1) | ~ (c_FunDef_Oin__rel(v4, v3, v2) = % 192.36/26.76 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 192.36/26.76 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (c_member(v4, v3, v2) = v1) % 192.36/26.76 | ~ (c_member(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 192.36/26.76 : ! [v3: $i] : (v1 = v0 | ~ (c_Set_Othe__elem(v3, v2) = v1) | ~ % 192.36/26.76 (c_Set_Othe__elem(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 192.36/26.76 ! [v3: $i] : (v1 = v0 | ~ (c_Relation_OField(v3, v2) = v1) | ~ % 192.36/26.76 (c_Relation_OField(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 192.36/26.76 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 192.36/26.76 (c_Wellfounded_OwfP(v3, v2) = v1) | ~ (c_Wellfounded_OwfP(v3, v2) = v0)) & % 192.36/26.76 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 192.36/26.76 $i] : (v1 = v0 | ~ (c_Wellfounded_Owf(v3, v2) = v1) | ~ % 192.36/26.76 (c_Wellfounded_Owf(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 192.36/26.76 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 192.36/26.76 (c_Relation_Otrans(v3, v2) = v1) | ~ (c_Relation_Otrans(v3, v2) = v0)) & ! % 192.36/26.76 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 192.36/26.76 $i] : (v1 = v0 | ~ (c_Wellfounded_Oacyclic(v3, v2) = v1) | ~ % 192.36/26.76 (c_Wellfounded_Oacyclic(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 192.36/26.76 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 192.36/26.76 (c_Relation_Oantisym(v3, v2) = v1) | ~ (c_Relation_Oantisym(v3, v2) = v0)) % 192.36/26.76 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 192.36/26.76 (c_Transitive__Closure_Otrancl(v3, v2) = v1) | ~ % 192.36/26.76 (c_Transitive__Closure_Otrancl(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 192.36/26.76 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (c_Relation_OId__on(v3, v2) = v1) | % 192.36/26.76 ~ (c_Relation_OId__on(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 192.36/26.76 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 192.36/26.76 (c_Relation_Oirrefl(v3, v2) = v1) | ~ (c_Relation_Oirrefl(v3, v2) = v0)) & % 192.36/26.76 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 192.36/26.76 (c_Transitive__Closure_Ortrancl(v3, v2) = v1) | ~ % 192.36/26.76 (c_Transitive__Closure_Ortrancl(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 192.36/26.76 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (c_Wellfounded_Oacc(v3, v2) = v1) | % 192.36/26.76 ~ (c_Wellfounded_Oacc(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 192.36/26.76 $i] : ! [v3: $i] : (v1 = v0 | ~ (tc_fun(v3, v2) = v1) | ~ (tc_fun(v3, v2) % 192.36/26.76 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 192.36/26.76 $i] : ! [v3: $i] : (v1 = v0 | ~ (c_Nitpick_Orefl_H(v3, v2) = v1) | ~ % 192.36/26.76 (c_Nitpick_Orefl_H(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 192.36/26.76 : ! [v3: $i] : (v1 = v0 | ~ (c_Arrow__Order__Mirabelle_Omktop(v3, v2) = v1) % 192.36/26.76 | ~ (c_Arrow__Order__Mirabelle_Omktop(v3, v2) = v0)) & ! [v0: $i] : ! % 192.36/26.76 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tc_prod(v3, v2) = v1) | % 192.36/26.76 ~ (tc_prod(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 192.36/26.76 [v3: $i] : (v1 = v0 | ~ (c_Arrow__Order__Mirabelle_Omkbot(v3, v2) = v1) | ~ % 192.36/26.76 (c_Arrow__Order__Mirabelle_Omkbot(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 192.36/26.76 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP(v3, v2) = v1) | ~ (hAPP(v3, % 192.36/26.76 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 192.36/26.76 ! [v2: $i] : (v1 = v0 | ~ (class_Lattices_Obounded__lattice(v2) = v1) | ~ % 192.36/26.76 (class_Lattices_Obounded__lattice(v2) = v0)) & ! [v0: MultipleValueBool] : % 192.36/26.76 ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ % 192.36/26.76 (class_Lattices_Osemilattice__inf(v2) = v1) | ~ % 192.36/26.76 (class_Lattices_Osemilattice__inf(v2) = v0)) & ! [v0: MultipleValueBool] : % 192.36/26.76 ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ % 192.36/26.76 (class_Orderings_Oord(v2) = v1) | ~ (class_Orderings_Oord(v2) = v0)) & ! % 192.36/26.76 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 % 192.36/26.76 | ~ (class_Orderings_Oorder(v2) = v1) | ~ (class_Orderings_Oorder(v2) = % 192.36/26.76 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 192.36/26.76 $i] : (v1 = v0 | ~ (class_Orderings_Olinorder(v2) = v1) | ~ % 192.36/26.76 (class_Orderings_Olinorder(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 192.36/26.76 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ % 192.36/26.76 (class_Orderings_Opreorder(v2) = v1) | ~ (class_Orderings_Opreorder(v2) = % 192.36/26.76 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 192.36/26.76 $i] : (v1 = v0 | ~ (class_Orderings_Obot(v2) = v1) | ~ % 192.36/26.76 (class_Orderings_Obot(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 192.36/26.76 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ % 192.36/26.76 (class_Groups_Oab__group__add(v2) = v1) | ~ % 192.36/26.76 (class_Groups_Oab__group__add(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 192.36/26.76 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ % 192.36/26.76 (class_Lattices_Obounded__lattice__bot(v2) = v1) | ~ % 192.36/26.76 (class_Lattices_Obounded__lattice__bot(v2) = v0)) & ! [v0: $i] : ! [v1: % 192.36/26.76 $i] : ! [v2: $i] : (v1 = v0 | ~ (c_Orderings_Obot__class_Obot(v2) = v1) | % 192.36/26.76 ~ (c_Orderings_Obot__class_Obot(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 192.36/26.76 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ % 192.36/26.76 (class_Groups_Oordered__ab__group__add(v2) = v1) | ~ % 192.36/26.76 (class_Groups_Oordered__ab__group__add(v2) = v0)) & ! [v0: $i] : ! [v1: % 192.36/26.76 $i] : ! [v2: $i] : (v1 = v0 | ~ (c_Wellfounded_Omeasure(v2) = v1) | ~ % 192.36/26.76 (c_Wellfounded_Omeasure(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 192.36/26.76 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ % 192.36/26.76 (class_Lattices_Osemilattice__sup(v2) = v1) | ~ % 192.36/26.76 (class_Lattices_Osemilattice__sup(v2) = v0)) & ! [v0: MultipleValueBool] : % 192.36/26.76 ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ % 192.36/26.76 (class_Lattices_Olattice(v2) = v1) | ~ (class_Lattices_Olattice(v2) = v0)) % 192.36/26.76 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 % 192.36/26.76 = v0 | ~ (class_Groups_Ominus(v2) = v1) | ~ (class_Groups_Ominus(v2) = % 192.36/26.76 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 192.36/26.76 (c_Relation_OId(v2) = v1) | ~ (c_Relation_OId(v2) = v0)) & ! [v0: $i] : ! % 192.36/26.76 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (c_fequal(v2) = v1) | ~ (c_fequal(v2) % 192.36/26.76 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 192.36/26.76 $i] : (v1 = v0 | ~ (hBOOL(v2) = v1) | ~ (hBOOL(v2) = v0)) & ? [v0: $i] : % 192.36/26.76 ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: % 192.36/26.76 MultipleValueBool] : (c_Nitpick_Ofold__graph_H(v5, v4, v3, v2, v1, v0) = v6) % 192.36/26.76 & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? % 192.36/26.76 [v5: $i] : ? [v6: MultipleValueBool] : (c_Recdef_Owfrec__rel(v5, v4, v3, v2, % 192.36/26.76 v1, v0) = v6) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? % 192.36/26.76 [v4: $i] : ? [v5: $i] : ? [v6: $i] : (c_Product__Type_Ocurry(v5, v4, v3, v2, % 192.36/26.76 v1, v0) = v6 & $i(v6)) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 192.36/26.76 $i] : ? [v4: $i] : ? [v5: $i] : (c_Nitpick_Owf__wfrec_H(v4, v3, v2, v1, % 192.36/26.76 v0) = v5 & $i(v5)) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] % 192.36/26.76 : ? [v4: $i] : ? [v5: $i] : (c_Recdef_Ocut(v4, v3, v2, v1, v0) = v5 & % 192.36/26.76 $i(v5)) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: % 192.36/26.76 $i] : ? [v5: $i] : (c_Product__Type_Ointernal__split(v4, v3, v2, v1, v0) = % 192.36/26.76 v5 & $i(v5)) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? % 192.36/26.76 [v4: $i] : ? [v5: $i] : (c_Product__Type_Oprod_Oprod__rec(v4, v3, v2, v1, v0) % 192.36/26.76 = v5 & $i(v5)) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? % 192.36/26.76 [v4: $i] : (c_Relation_OImage(v3, v2, v1, v0) = v4 & $i(v4)) & ? [v0: $i] : % 192.36/26.76 ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : (c_Recdef_Owfrec(v3, % 192.36/26.76 v2, v1, v0) = v4 & $i(v4)) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? % 192.36/26.76 [v3: $i] : ? [v4: $i] : (c_Product__Type_OSigma(v3, v2, v1, v0) = v4 & % 192.36/26.76 $i(v4)) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: % 192.36/26.76 $i] : (c_Nitpick_Owf__wfrec(v3, v2, v1, v0) = v4 & $i(v4)) & ? [v0: $i] : % 192.36/26.76 ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 192.36/26.76 (c_Wellfounded_Olex__prod(v3, v2, v1, v0) = v4 & $i(v4)) & ? [v0: $i] : ? % 192.36/26.76 [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : (c_Recdef_Osame__fst(v3, % 192.36/26.76 v2, v1, v0) = v4 & $i(v4)) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? % 192.36/26.76 [v3: $i] : ? [v4: $i] : (c_Product__Type_OPair(v3, v2, v1, v0) = v4 & $i(v4)) % 192.36/26.76 & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: MultipleValueBool] : % 192.36/26.76 (c_Equiv__Relations_Oequiv(v2, v1, v0) = v3) & ? [v0: $i] : ? [v1: $i] : ? % 192.36/26.76 [v2: $i] : ? [v3: MultipleValueBool] : (c_Orderings_Oord__class_Oless__eq(v2, % 192.36/26.76 v1, v0) = v3) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 192.36/26.76 MultipleValueBool] : (c_Orderings_Oord__class_Oless(v2, v1, v0) = v3) & ? % 192.36/26.76 [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: MultipleValueBool] : % 192.36/26.76 (c_Order__Relation_Opartial__order__on(v2, v1, v0) = v3) & ? [v0: $i] : ? % 192.36/26.76 [v1: $i] : ? [v2: $i] : ? [v3: MultipleValueBool] : % 192.36/26.76 (c_Order__Relation_Owell__order__on(v2, v1, v0) = v3) & ? [v0: $i] : ? [v1: % 192.36/26.76 $i] : ? [v2: $i] : ? [v3: MultipleValueBool] : % 192.36/26.76 (c_Order__Relation_Opreorder__on(v2, v1, v0) = v3) & ? [v0: $i] : ? [v1: $i] % 192.36/26.76 : ? [v2: $i] : ? [v3: MultipleValueBool] : % 192.36/26.76 (c_Order__Relation_Olinear__order__on(v2, v1, v0) = v3) & ? [v0: $i] : ? % 192.36/26.76 [v1: $i] : ? [v2: $i] : ? [v3: MultipleValueBool] : % 192.36/26.76 (c_Order__Relation_Ostrict__linear__order__on(v2, v1, v0) = v3) & ? [v0: $i] % 192.36/26.76 : ? [v1: $i] : ? [v2: $i] : ? [v3: MultipleValueBool] : % 192.36/26.76 (c_Relation_Orefl__on(v2, v1, v0) = v3) & ? [v0: $i] : ? [v1: $i] : ? [v2: % 192.36/26.76 $i] : ? [v3: MultipleValueBool] : (c_Relation_Ototal__on(v2, v1, v0) = v3) % 192.36/26.76 & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: MultipleValueBool] : % 192.36/26.76 (c_Relation_Osingle__valued(v2, v1, v0) = v3) & ? [v0: $i] : ? [v1: $i] : ? % 192.36/26.76 [v2: $i] : ? [v3: MultipleValueBool] : (c_member(v2, v1, v0) = v3) & ? [v0: % 192.36/26.76 $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 192.36/26.76 (c_Lattices_Osemilattice__inf__class_Oinf(v2, v1, v0) = v3 & $i(v3)) & ? [v0: % 192.36/26.76 $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 192.36/26.76 (c_Wellfounded_Omlex__prod(v2, v1, v0) = v3 & $i(v3)) & ? [v0: $i] : ? [v1: % 192.36/26.76 $i] : ? [v2: $i] : ? [v3: $i] : (c_Groups_Ominus__class_Ominus(v2, v1, v0) % 192.36/26.76 = v3 & $i(v3)) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 192.36/26.76 (c_Lattices_Osemilattice__sup__class_Osup(v2, v1, v0) = v3 & $i(v3)) & ? [v0: % 192.36/26.76 $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (c_Set_Oinsert(v2, v1, v0) = % 192.36/26.76 v3 & $i(v3)) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 192.36/26.76 (c_Relation_Oinv__image(v2, v1, v0) = v3 & $i(v3)) & ? [v0: $i] : ? [v1: $i] % 192.36/26.76 : ? [v2: $i] : ? [v3: $i] : (c_Relation_ODomain(v2, v1, v0) = v3 & $i(v3)) & % 192.36/26.76 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 192.36/26.76 (c_Relation_Oconverse(v2, v1, v0) = v3 & $i(v3)) & ? [v0: $i] : ? [v1: $i] : % 192.36/26.76 ? [v2: $i] : ? [v3: $i] : (c_Relation_ORange(v2, v1, v0) = v3 & $i(v3)) & ? % 192.36/26.76 [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 192.36/26.76 (c_Arrow__Order__Mirabelle_Obelow(v2, v1, v0) = v3 & $i(v3)) & ? [v0: $i] : % 192.36/26.76 ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (c_Arrow__Order__Mirabelle_Oabove(v2, % 192.36/26.76 v1, v0) = v3 & $i(v3)) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 192.36/26.76 $i] : (c_FunDef_Oin__rel(v2, v1, v0) = v3 & $i(v3)) & ? [v0: $i] : ? [v1: % 192.36/26.76 $i] : ? [v2: MultipleValueBool] : (c_Wellfounded_OwfP(v1, v0) = v2) & ? % 192.36/26.76 [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : (c_Wellfounded_Owf(v1, % 192.36/26.76 v0) = v2) & ? [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : % 192.36/26.76 (c_Relation_Otrans(v1, v0) = v2) & ? [v0: $i] : ? [v1: $i] : ? [v2: % 192.36/26.76 MultipleValueBool] : (c_Wellfounded_Oacyclic(v1, v0) = v2) & ? [v0: $i] : % 192.36/26.76 ? [v1: $i] : ? [v2: MultipleValueBool] : (c_Relation_Oantisym(v1, v0) = v2) & % 192.36/26.76 ? [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : % 192.36/26.76 (c_Relation_Oirrefl(v1, v0) = v2) & ? [v0: $i] : ? [v1: $i] : ? [v2: % 192.36/26.76 MultipleValueBool] : (c_Nitpick_Orefl_H(v1, v0) = v2) & ? [v0: $i] : ? % 192.36/26.76 [v1: $i] : ? [v2: $i] : (c_Set_Othe__elem(v1, v0) = v2 & $i(v2)) & ? [v0: % 192.36/26.76 $i] : ? [v1: $i] : ? [v2: $i] : (c_Relation_OField(v1, v0) = v2 & $i(v2)) % 192.36/26.76 & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Transitive__Closure_Otrancl(v1, % 192.36/26.76 v0) = v2 & $i(v2)) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 192.36/26.76 (c_Relation_OId__on(v1, v0) = v2 & $i(v2)) & ? [v0: $i] : ? [v1: $i] : ? % 192.36/26.76 [v2: $i] : (c_Transitive__Closure_Ortrancl(v1, v0) = v2 & $i(v2)) & ? [v0: % 192.36/26.76 $i] : ? [v1: $i] : ? [v2: $i] : (c_Wellfounded_Oacc(v1, v0) = v2 & $i(v2)) % 192.36/26.76 & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (tc_fun(v1, v0) = v2 & $i(v2)) & % 192.36/26.76 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Arrow__Order__Mirabelle_Omktop(v1, % 192.36/26.76 v0) = v2 & $i(v2)) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 192.36/26.76 (tc_prod(v1, v0) = v2 & $i(v2)) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 192.36/26.76 (c_Arrow__Order__Mirabelle_Omkbot(v1, v0) = v2 & $i(v2)) & ? [v0: $i] : ? % 192.36/26.76 [v1: $i] : ? [v2: $i] : (hAPP(v1, v0) = v2 & $i(v2)) & ? [v0: $i] : ? [v1: % 192.36/26.76 MultipleValueBool] : (class_Lattices_Obounded__lattice(v0) = v1) & ? [v0: % 192.36/26.76 $i] : ? [v1: MultipleValueBool] : (class_Lattices_Osemilattice__inf(v0) = % 192.36/26.76 v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : (class_Orderings_Oord(v0) = % 192.36/26.76 v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : (class_Orderings_Oorder(v0) % 192.36/26.76 = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : % 192.36/26.76 (class_Orderings_Olinorder(v0) = v1) & ? [v0: $i] : ? [v1: % 192.36/26.76 MultipleValueBool] : (class_Orderings_Opreorder(v0) = v1) & ? [v0: $i] : ? % 192.36/26.76 [v1: MultipleValueBool] : (class_Orderings_Obot(v0) = v1) & ? [v0: $i] : ? % 192.36/26.76 [v1: MultipleValueBool] : (class_Groups_Oab__group__add(v0) = v1) & ? [v0: % 192.36/26.76 $i] : ? [v1: MultipleValueBool] : % 192.36/26.76 (class_Lattices_Obounded__lattice__bot(v0) = v1) & ? [v0: $i] : ? [v1: % 192.36/26.76 MultipleValueBool] : (class_Groups_Oordered__ab__group__add(v0) = v1) & ? % 192.36/26.76 [v0: $i] : ? [v1: MultipleValueBool] : (class_Lattices_Osemilattice__sup(v0) % 192.36/26.76 = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : % 192.36/26.76 (class_Lattices_Olattice(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] % 192.36/26.76 : (class_Groups_Ominus(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : % 192.36/26.76 (hBOOL(v0) = v1) & ? [v0: $i] : ? [v1: $i] : % 192.36/26.76 (c_Orderings_Obot__class_Obot(v0) = v1 & $i(v1)) & ? [v0: $i] : ? [v1: $i] : % 192.36/26.76 (c_Wellfounded_Omeasure(v0) = v1 & $i(v1)) & ? [v0: $i] : ? [v1: $i] : % 192.36/26.76 (c_Relation_OId(v0) = v1 & $i(v1)) & ? [v0: $i] : ? [v1: $i] : (c_fequal(v0) % 192.36/26.76 = v1 & $i(v1)) % 192.36/26.76 % 192.36/26.76 Further assumptions not needed in the proof: % 192.36/26.76 -------------------------------------------- % 192.36/26.77 arity_HOL__Obool__Groups_Ominus, arity_HOL__Obool__Lattices_Obounded__lattice, % 192.36/26.77 arity_HOL__Obool__Lattices_Obounded__lattice__bot, % 192.36/26.77 arity_HOL__Obool__Lattices_Olattice, % 192.36/26.77 arity_HOL__Obool__Lattices_Osemilattice__inf, % 192.36/26.77 arity_HOL__Obool__Lattices_Osemilattice__sup, arity_HOL__Obool__Orderings_Obot, % 192.36/26.77 arity_HOL__Obool__Orderings_Oord, arity_HOL__Obool__Orderings_Oorder, % 192.36/26.77 arity_HOL__Obool__Orderings_Opreorder, arity_Nat__Onat__Groups_Ominus, % 192.36/26.77 arity_Nat__Onat__Lattices_Olattice, arity_Nat__Onat__Lattices_Osemilattice__inf, % 192.36/26.77 arity_Nat__Onat__Lattices_Osemilattice__sup, arity_Nat__Onat__Orderings_Obot, % 192.36/26.77 arity_Nat__Onat__Orderings_Olinorder, arity_Nat__Onat__Orderings_Oord, % 192.36/26.77 arity_Nat__Onat__Orderings_Oorder, arity_Nat__Onat__Orderings_Opreorder, % 192.36/26.77 arity_fun__Groups_Ominus, arity_fun__Lattices_Obounded__lattice, % 192.36/26.77 arity_fun__Lattices_Obounded__lattice__bot, arity_fun__Lattices_Olattice, % 192.36/26.77 arity_fun__Lattices_Osemilattice__inf, arity_fun__Lattices_Osemilattice__sup, % 192.36/26.77 arity_fun__Orderings_Obot, arity_fun__Orderings_Oord, % 192.36/26.77 arity_fun__Orderings_Oorder, arity_fun__Orderings_Opreorder, fact_DiffD1, % 192.36/26.77 fact_DiffD2, fact_DiffE, fact_DiffI, fact_Diff__cancel, fact_Diff__empty, % 192.36/26.77 fact_Diff__idemp, fact_Diff__iff, fact_Diff__insert, fact_Diff__insert2, % 192.36/26.77 fact_Diff__insert__absorb, fact_Diff__mono, fact_Diff__partition, % 192.36/26.77 fact_Diff__subset, fact_Diff__subset__conv, fact_DomainE, fact_DomainI, % 192.36/26.77 fact_Domain__Diff__subset, fact_Domain__Id__on, fact_Domain__Un__eq, % 192.36/26.77 fact_Domain__converse, fact_Domain__empty, fact_Domain__empty__iff, % 192.36/26.77 fact_Domain__iff, fact_Domain__insert, fact_Domain__mono, fact_Field__Un, % 192.36/26.77 fact_Field__converse, fact_Field__def, fact_Field__empty, fact_Field__insert, % 192.36/26.77 fact_IdE, fact_IdI, fact_Id__onE, fact_Id__on__empty, fact_Id__on__eqI, % 192.36/26.77 fact_Id__on__iff, fact_ImageE, fact_Image__Id, fact_Image__Int__subset, % 192.36/26.77 fact_Image__Un, fact_Image__closed__trancl, fact_Image__empty, fact_Image__iff, % 192.36/26.77 fact_Image__mono, fact_Image__singleton__iff, fact_IntE, fact_IntI, % 192.36/26.77 fact_Nitpick_Orefl_H__def, fact_Nitpick_Owf__wfrec_H__def, % 192.36/26.77 fact_Not__Domain__rtrancl, fact_Pair__eq, fact_Pair__inject, % 192.36/26.77 fact_Partial__order__eq__Image1__Image1__iff, fact_RangeE, fact_RangeI, % 192.36/26.77 fact_Range__Diff__subset, fact_Range__Id__on, fact_Range__Un__eq, % 192.36/26.77 fact_Range__converse, fact_Range__def, fact_Range__empty, % 192.36/26.77 fact_Range__empty__iff, fact_Range__iff, fact_Range__insert, % 192.36/26.77 fact_Refl__antisym__eq__Image1__Image1__iff, fact_SigmaD1, fact_SigmaD2, % 192.36/26.77 fact_SigmaE, fact_SigmaE2, fact_SigmaI, fact_Sigma__empty1, % 192.36/26.77 fact_Transitive__Closure_Otrancl__into__trancl, fact_UnCI, fact_UnE, fact_UnI1, % 192.36/26.77 fact_UnI2, fact_Un__Diff, fact_Un__Diff__cancel, fact_Un__Diff__cancel2, % 192.36/26.77 fact_Un__Image, fact_Un__Int__assoc__eq, fact_Un__absorb, fact_Un__absorb1, % 192.36/26.77 fact_Un__absorb2, fact_Un__assoc, fact_Un__commute, fact_Un__empty, % 192.36/26.77 fact_Un__empty__left, fact_Un__empty__right, fact_Un__iff, % 192.36/26.77 fact_Un__insert__left, fact_Un__insert__right, fact_Un__least, % 192.36/26.77 fact_Un__left__absorb, fact_Un__left__commute, fact_Un__mono, fact_Un__upper1, % 192.36/26.77 fact_Un__upper2, fact_acc_OaccI, fact_acc_Osimps, fact_acc__downward, % 192.36/26.77 fact_acc__downwards, fact_acc__downwards__aux, fact_acc__subset, fact_acc__wfD, % 192.36/26.77 fact_acc__wfI, fact_acyclicI, fact_acyclic__converse, fact_acyclic__def, % 192.36/26.77 fact_acyclic__impl__antisym__rtrancl, fact_acyclic__insert, % 192.36/26.77 fact_acyclic__subset, fact_all__not__in__conv, fact_antisymI, fact_antisym__Id, % 192.36/26.77 fact_antisym__Id__on, fact_antisym__converse, fact_antisym__def, % 192.36/26.77 fact_antisym__empty, fact_antisym__reflcl, fact_antisym__subset, fact_ball__Un, % 192.36/26.77 fact_bex__Un, fact_bot__apply, fact_bot__least, fact_converseD, fact_converseE, % 192.36/26.77 fact_converseI, fact_converse__Id, fact_converse__Id__on, fact_converse__Un, % 192.36/26.77 fact_converse__converse, fact_converse__iff, fact_converse__inv__image, % 192.36/26.77 fact_converse__rtranclE, fact_converse__rtranclE2, % 192.36/26.77 fact_converse__rtrancl__induct, fact_converse__rtrancl__induct2, % 192.36/26.77 fact_converse__rtrancl__into__rtrancl, fact_converse__tranclE, fact_curryD, % 192.36/26.77 fact_curryE, fact_curryI, fact_curry__conv, fact_cut__apply, fact_cuts__eq, % 192.36/26.77 fact_def__wfrec, fact_diff__eq__diff__eq, fact_diff__eq__diff__less, % 192.36/26.77 fact_diff__eq__diff__less__eq, fact_diff__single__insert, fact_distrib__inf__le, % 192.36/26.77 fact_distrib__sup__le, fact_double__diff, fact_doubleton__eq__iff, fact_emptyE, % 192.36/26.77 fact_empty__Diff, fact_empty__iff, fact_empty__not__insert, fact_empty__subsetI, % 192.36/26.77 fact_eq__mem, fact_eq__mem__trans, fact_eqelem__imp__iff, fact_eqset__imp__iff, % 192.36/26.77 fact_equalityCE, fact_equalityD1, fact_equalityD2, fact_equalityE, % 192.36/26.77 fact_equalityI, fact_equals0D, fact_ex__in__conv, fact_ext, % 192.36/26.77 fact_fold__graph_H_Oequations_I1_J, fact_fold__graph_H_Oequations_I2_J, % 192.36/26.77 fact_fold__graph_H_Ointros_I1_J, fact_fold__graph_H_Ointros_I2_J, % 192.36/26.77 fact_in__inv__image, fact_in__lex__prod, fact_in__measure, fact_in__mono, % 192.36/26.77 fact_in__rel__def, fact_in__rtrancl__UnI, fact_inf1E, fact_inf1I, fact_inf__le1, % 192.36/26.77 fact_inf__le2, fact_inf__sup__aci_I5_J, fact_inf__sup__aci_I6_J, % 192.36/26.77 fact_inf__sup__aci_I7_J, fact_inf__sup__aci_I8_J, fact_inf__sup__ord_I1_J, % 192.36/26.77 fact_inf__sup__ord_I2_J, fact_inf__sup__ord_I3_J, fact_inf__sup__ord_I4_J, % 192.36/26.77 fact_insertCI, fact_insertE, fact_insertI1, fact_insertI2, fact_insert__Diff, % 192.36/26.77 fact_insert__Diff1, fact_insert__Diff__if, fact_insert__Diff__single, % 192.36/26.77 fact_insert__absorb, fact_insert__absorb2, fact_insert__code, % 192.36/26.77 fact_insert__commute, fact_insert__ident, fact_insert__iff, fact_insert__is__Un, % 192.36/26.77 fact_insert__mono, fact_insert__not__empty, fact_insert__subset, % 192.36/26.77 fact_internal__split__conv, fact_irrefl__def, fact_irrefl__diff__Id, % 192.36/26.77 fact_irrefl__tranclI, fact_irrefl__trancl__rD, fact_leD, fact_leI, % 192.36/26.77 fact_le__funD, fact_le__funE, fact_le__fun__def, fact_le__iff__inf, % 192.36/26.77 fact_le__iff__sup, fact_le__supE, fact_le__supI, fact_le__supI1, fact_le__supI2, % 192.36/26.77 fact_le__sup__iff, fact_less__by__empty, fact_less__eq, fact_less__fun__def, % 192.36/26.77 fact_less__imp__neq, fact_less__le__not__le, fact_less__supI1, fact_less__supI2, % 192.36/26.77 fact_less__than__def, fact_less__than__iff, fact_linear__order__on__converse, % 192.36/26.77 fact_linear__order__on__def, fact_linorder__antisym__conv1, % 192.36/26.77 fact_linorder__antisym__conv2, fact_linorder__antisym__conv3, % 192.36/26.77 fact_linorder__cases, fact_linorder__le__cases, fact_linorder__le__less__linear, % 192.36/26.77 fact_linorder__less__linear, fact_linorder__linear, fact_linorder__neqE, % 192.36/26.77 fact_linorder__neq__iff, fact_linorder__not__le, fact_linorder__not__less, % 192.36/26.77 fact_lnear__order__on__empty, fact_measure__def, fact_mem__Sigma__iff, % 192.36/26.77 fact_minus__apply, fact_mlex__leq, fact_mlex__less, fact_mono__Field, % 192.36/26.77 fact_not__acc__down, fact_not__leE, fact_not__less__iff__gr__or__eq, % 192.36/26.77 fact_not__psubset__empty, fact_ord__eq__le__trans, fact_ord__eq__less__trans, % 192.36/26.77 fact_ord__le__eq__trans, fact_ord__less__eq__trans, fact_order__antisym, % 192.36/26.77 fact_order__antisym__conv, fact_order__eq__iff, fact_order__eq__refl, % 192.36/26.77 fact_order__le__imp__less__or__eq, fact_order__le__less, % 192.36/26.77 fact_order__le__less__trans, fact_order__le__neq__trans, fact_order__less__asym, % 192.36/26.77 fact_order__less__asym_H, fact_order__less__imp__le, % 192.36/26.77 fact_order__less__imp__not__eq, fact_order__less__imp__not__eq2, % 192.36/26.77 fact_order__less__imp__not__less, fact_order__less__irrefl, % 192.36/26.77 fact_order__less__le, fact_order__less__le__trans, fact_order__less__not__sym, % 192.36/26.77 fact_order__less__trans, fact_order__neq__le__trans, fact_order__refl, % 192.36/26.77 fact_order__trans, fact_pair__in__Id__conv, fact_partial__order__on__converse, % 192.36/26.77 fact_partial__order__on__def, fact_partial__order__on__empty, % 192.36/26.77 fact_pred__nat__trancl__eq__le, fact_predicate1D, fact_preorder__on__converse, % 192.36/26.77 fact_preorder__on__def, fact_preorder__on__empty, fact_prod_Orecs, % 192.36/26.77 fact_psubsetD, fact_psubset__eq, fact_psubset__imp__subset, % 192.36/26.77 fact_psubset__insert__iff, fact_psubset__subset__trans, fact_psubset__trans, % 192.36/26.77 fact_r__into__rtrancl, fact_r__into__trancl_H, fact_r__r__into__trancl, % 192.36/26.77 fact_refl__onD, fact_refl__onD1, fact_refl__onD2, fact_refl__on__Id__on, % 192.36/26.77 fact_refl__on__Un, fact_refl__on__converse, fact_refl__on__empty, % 192.36/26.77 fact_reflcl__trancl, fact_rev__ImageI, fact_rev__predicate1D, fact_rtranclD, % 192.36/26.77 fact_rtranclE, fact_rtrancl_Ortrancl__into__rtrancl, % 192.36/26.77 fact_rtrancl_Ortrancl__refl, fact_rtrancl__Un__rtrancl, % 192.36/26.77 fact_rtrancl__Un__separatorE, fact_rtrancl__Un__separator__converseE, % 192.36/26.77 fact_rtrancl__Un__subset, fact_rtrancl__converse, fact_rtrancl__converseD, % 192.36/26.77 fact_rtrancl__converseI, fact_rtrancl__empty, fact_rtrancl__eq__or__trancl, % 192.36/26.77 fact_rtrancl__idemp, fact_rtrancl__induct, fact_rtrancl__induct2, % 192.36/26.77 fact_rtrancl__into__trancl1, fact_rtrancl__into__trancl2, fact_rtrancl__mono, % 192.36/26.77 fact_rtrancl__r__diff__Id, fact_rtrancl__reflcl, fact_rtrancl__reflcl__absorb, % 192.36/26.77 fact_rtrancl__subset, fact_rtrancl__subset__rtrancl, % 192.36/26.77 fact_rtrancl__trancl__absorb, fact_rtrancl__trancl__trancl, fact_rtrancl__trans, % 192.36/26.77 fact_same__fstI, fact_set__eq__subset, fact_set__mp, fact_set__rev__mp, % 192.36/26.77 fact_single__valuedI, fact_single__valued__Id, fact_single__valued__Id__on, % 192.36/26.77 fact_single__valued__confluent, fact_single__valued__def, % 192.36/26.77 fact_single__valued__subset, fact_singletonE, fact_singleton__iff, % 192.36/26.77 fact_singleton__inject, fact_split__paired__All, % 192.36/26.77 fact_strict__linear__order__on__def, fact_strict__linear__order__on__diff__Id, % 192.36/26.77 fact_subsetD, fact_subset__Image1__Image1__iff, fact_subset__Image__Image__iff, % 192.36/26.77 fact_subset__Un__eq, fact_subset__empty, fact_subset__equiv__class, % 192.36/26.77 fact_subset__iff__psubset__eq, fact_subset__insert, fact_subset__insertI, % 192.36/26.77 fact_subset__insertI2, fact_subset__insert__iff, fact_subset__psubset__trans, % 192.36/26.77 fact_subset__refl, fact_subset__singletonD, fact_subset__trans, fact_sup1CI, % 192.36/26.77 fact_sup1E, fact_sup1I1, fact_sup1I2, fact_sup_Oassoc, fact_sup_Ocommute, % 192.36/26.77 fact_sup_Oidem, fact_sup_Oleft__commute, fact_sup_Oleft__idem, % 192.36/26.77 fact_sup__absorb1, fact_sup__absorb2, fact_sup__apply, fact_sup__assoc, % 192.36/26.77 fact_sup__bot__left, fact_sup__bot__right, fact_sup__commute, % 192.36/26.77 fact_sup__eq__bot__iff, fact_sup__ge1, fact_sup__ge2, fact_sup__idem, % 192.36/26.77 fact_sup__least, fact_sup__left__commute, fact_sup__left__idem, fact_sup__mono, % 192.36/26.77 fact_termination__basic__simps_I5_J, fact_tfl__cut__apply, fact_tfl__wfrec, % 192.36/26.77 fact_the__elem__eq, fact_total__on__converse, fact_total__on__def, % 192.36/26.77 fact_total__on__diff__Id, fact_total__on__empty, fact_tranclD, fact_tranclD2, % 192.36/26.77 fact_tranclE, fact_trancl_Or__into__trancl, fact_trancl__converse, % 192.36/26.77 fact_trancl__converseD, fact_trancl__converseI, fact_trancl__domain, % 192.36/26.77 fact_trancl__empty, fact_trancl__id, fact_trancl__into__rtrancl, % 192.36/26.77 fact_trancl__into__trancl2, fact_trancl__mono, fact_trancl__range, % 192.36/26.77 fact_trancl__reflcl, fact_trancl__rtrancl__absorb, fact_trancl__rtrancl__trancl, % 192.36/26.77 fact_trancl__trans, fact_transI, fact_trans__Id, fact_trans__Id__on, % 192.36/26.77 fact_trans__converse, fact_trans__def, fact_trans__diff__Id, % 192.36/26.77 fact_trans__inv__image, fact_trans__less__than, fact_trans__lex__prod, % 192.36/26.77 fact_trans__reflclI, fact_trans__rtrancl, fact_trans__trancl, % 192.36/26.77 fact_well__order__on__def, fact_well__order__on__empty, fact_wfE__pf, % 192.36/26.77 fact_wfP__subset, fact_wf__acc__iff, fact_wf__acyclic, % 192.36/26.77 fact_wf__converse__trancl, fact_wf__empty, fact_wf__eq__minimal, % 192.36/26.77 fact_wf__in__rel, fact_wf__insert, fact_wf__inv__image, fact_wf__irrefl, % 192.36/26.77 fact_wf__less__than, fact_wf__lex__prod, fact_wf__measure, fact_wf__mlex, % 192.36/26.77 fact_wf__not__refl, fact_wf__pred__nat, fact_wf__same__fst, fact_wf__subset, % 192.36/26.77 fact_wf__trancl, fact_wfrec, fact_wfrec__rel_Oequations, % 192.36/26.77 fact_wfrec__rel_Ointros, fact_wfrec__rel_Osimps, fact_xt1_I10_J, fact_xt1_I11_J, % 192.36/26.77 fact_xt1_I12_J, fact_xt1_I1_J, fact_xt1_I2_J, fact_xt1_I3_J, fact_xt1_I4_J, % 192.36/26.77 fact_xt1_I5_J, fact_xt1_I6_J, fact_xt1_I7_J, fact_xt1_I8_J, fact_xt1_I9_J, % 192.36/26.77 help_c__fequal__1, help_c__fequal__2 % 192.36/26.77 % 192.36/26.77 Those formulas are unsatisfiable: % 192.36/26.77 --------------------------------- % 192.36/26.77 % 192.36/26.77 Begin of proof % 192.36/26.77 | % 192.36/26.77 | ALPHA: (fact_in__mkbot) implies: % 192.36/26.77 | (1) ? [v0: $i] : (tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 192.36/26.77 | tc_Arrow__Order__Mirabelle_Oalt) = v0 & $i(v0) & ! [v1: $i] : ! % 192.36/26.77 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! % 192.36/26.77 | [v7: int] : (v7 = 0 | v3 = v1 | ~ % 192.36/26.77 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.36/26.77 | tc_Arrow__Order__Mirabelle_Oalt, v4, v3) = v5) | ~ % 192.36/26.77 | (c_Arrow__Order__Mirabelle_Omkbot(v2, v1) = v6) | ~ (c_member(v0, % 192.36/26.77 | v5, v6) = v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 192.36/26.77 | ( ~ (v4 = v1) & ? [v8: int] : ( ~ (v8 = 0) & c_member(v0, v5, v2) % 192.36/26.77 | = v8))) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] % 192.36/26.77 | : ! [v5: $i] : ! [v6: $i] : ( ~ % 192.36/26.77 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.36/26.77 | tc_Arrow__Order__Mirabelle_Oalt, v4, v3) = v5) | ~ % 192.36/26.77 | (c_Arrow__Order__Mirabelle_Omkbot(v2, v1) = v6) | ~ (c_member(v0, % 192.36/26.77 | v5, v6) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 192.36/26.77 | ( ~ (v3 = v1) & (v4 = v1 | c_member(v0, v5, v2) = 0)))) % 192.36/26.77 | % 192.36/26.77 | ALPHA: (fact_in__mktop) implies: % 192.36/26.77 | (2) ? [v0: $i] : (tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 192.36/26.77 | tc_Arrow__Order__Mirabelle_Oalt) = v0 & $i(v0) & ! [v1: $i] : ! % 192.36/26.77 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! % 192.36/26.77 | [v7: int] : (v7 = 0 | v4 = v1 | ~ % 192.36/26.77 | (c_Arrow__Order__Mirabelle_Omktop(v2, v1) = v6) | ~ % 192.36/26.77 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.36/26.77 | tc_Arrow__Order__Mirabelle_Oalt, v4, v3) = v5) | ~ % 192.36/26.77 | (c_member(v0, v5, v6) = v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | % 192.36/26.77 | ~ $i(v1) | ( ~ (v3 = v1) & ? [v8: int] : ( ~ (v8 = 0) & % 192.36/26.77 | c_member(v0, v5, v2) = v8))) & ! [v1: $i] : ! [v2: $i] : ! % 192.36/26.77 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ % 192.36/26.77 | (c_Arrow__Order__Mirabelle_Omktop(v2, v1) = v6) | ~ % 192.36/26.77 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.36/26.77 | tc_Arrow__Order__Mirabelle_Oalt, v4, v3) = v5) | ~ % 192.36/26.77 | (c_member(v0, v5, v6) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 192.36/26.77 | $i(v1) | ( ~ (v4 = v1) & (v3 = v1 | c_member(v0, v5, v2) = 0)))) % 192.36/26.77 | % 192.36/26.78 | ALPHA: (fact_mem__def) implies: % 192.36/26.78 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 192.36/26.78 | (c_member(v2, v1, v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 192.36/26.78 | [v4: $i] : ? [v5: int] : ( ~ (v5 = 0) & hBOOL(v4) = v5 & hAPP(v0, % 192.36/26.78 | v1) = v4 & $i(v4))) % 192.36/26.78 | % 192.36/26.78 | ALPHA: (fact_Lin__irrefl) implies: % 192.36/26.78 | (4) ? [v0: $i] : ? [v1: $i] : (tc_fun(v0, tc_HOL_Obool) = v1 & % 192.36/26.78 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 192.36/26.78 | tc_Arrow__Order__Mirabelle_Oalt) = v0 & $i(v1) & $i(v0) & ! [v2: % 192.36/26.78 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 192.36/26.78 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.36/26.78 | tc_Arrow__Order__Mirabelle_Oalt, v2, v3) = v5) | ~ % 192.36/26.78 | (c_member(v0, v5, v4) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? % 192.36/26.78 | [v6: any] : ? [v7: $i] : ? [v8: any] : % 192.36/26.78 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.36/26.78 | tc_Arrow__Order__Mirabelle_Oalt, v3, v2) = v7 & c_member(v1, % 192.36/26.78 | v4, c_Arrow__Order__Mirabelle_OLin) = v6 & c_member(v0, v7, v4) % 192.36/26.78 | = v8 & $i(v7) & ( ~ (v8 = 0) | ~ (v6 = 0))))) % 192.36/26.78 | % 192.36/26.78 | ALPHA: (fact_notin__Lin__iff) implies: % 192.36/26.78 | (5) ? [v0: $i] : ? [v1: $i] : (tc_fun(v0, tc_HOL_Obool) = v1 & % 192.36/26.78 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 192.36/26.78 | tc_Arrow__Order__Mirabelle_Oalt) = v0 & $i(v1) & $i(v0) & ! [v2: % 192.36/26.78 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: any] : (v3 % 192.36/26.78 | = v2 | ~ (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.36/26.78 | tc_Arrow__Order__Mirabelle_Oalt, v2, v3) = v5) | ~ % 192.36/26.78 | (c_member(v0, v5, v4) = v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | % 192.36/26.78 | ? [v7: any] : ? [v8: $i] : ? [v9: any] : % 192.36/26.78 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.36/26.78 | tc_Arrow__Order__Mirabelle_Oalt, v3, v2) = v8 & c_member(v1, % 192.36/26.78 | v4, c_Arrow__Order__Mirabelle_OLin) = v7 & c_member(v0, v8, v4) % 192.36/26.78 | = v9 & $i(v8) & ( ~ (v7 = 0) | (( ~ (v9 = 0) | ~ (v6 = 0)) & (v9 % 192.36/26.78 | = 0 | v6 = 0)))))) % 192.36/26.78 | % 192.36/26.78 | ALPHA: (fact_mkbot__Lin) implies: % 192.36/26.78 | (6) ? [v0: $i] : ? [v1: $i] : (tc_fun(v0, tc_HOL_Obool) = v1 & % 192.36/26.78 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 192.36/26.78 | tc_Arrow__Order__Mirabelle_Oalt) = v0 & $i(v1) & $i(v0) & ! [v2: % 192.36/26.78 | $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 192.36/26.78 | (c_Arrow__Order__Mirabelle_Omkbot(v3, v2) = v4) | ~ $i(v3) | ~ % 192.36/26.78 | $i(v2) | ? [v5: any] : ? [v6: any] : (c_member(v1, v4, % 192.36/26.78 | c_Arrow__Order__Mirabelle_OLin) = v6 & c_member(v1, v3, % 192.36/26.78 | c_Arrow__Order__Mirabelle_OLin) = v5 & ( ~ (v5 = 0) | v6 = % 192.36/26.78 | 0)))) % 192.36/26.78 | % 192.36/26.78 | ALPHA: (fact_mktop__Lin) implies: % 192.36/26.78 | (7) ? [v0: $i] : ? [v1: $i] : (tc_fun(v0, tc_HOL_Obool) = v1 & % 192.36/26.78 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 192.36/26.78 | tc_Arrow__Order__Mirabelle_Oalt) = v0 & $i(v1) & $i(v0) & ! [v2: % 192.36/26.78 | $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 192.36/26.78 | (c_Arrow__Order__Mirabelle_Omktop(v3, v2) = v4) | ~ $i(v3) | ~ % 192.36/26.78 | $i(v2) | ? [v5: any] : ? [v6: any] : (c_member(v1, v4, % 192.36/26.78 | c_Arrow__Order__Mirabelle_OLin) = v6 & c_member(v1, v3, % 192.36/26.78 | c_Arrow__Order__Mirabelle_OLin) = v5 & ( ~ (v5 = 0) | v6 = % 192.36/26.78 | 0)))) % 192.36/26.78 | % 192.36/26.78 | ALPHA: (fact_in__above) implies: % 192.74/26.78 | (8) ? [v0: $i] : ? [v1: $i] : (tc_fun(v0, tc_HOL_Obool) = v1 & % 192.74/26.78 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.78 | tc_Arrow__Order__Mirabelle_Oalt) = v0 & $i(v1) & $i(v0) & ! [v2: % 192.74/26.78 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! % 192.74/26.78 | [v7: $i] : ! [v8: $i] : ! [v9: any] : (v6 = v5 | ~ % 192.74/26.78 | (c_Arrow__Order__Mirabelle_Oabove(v4, v6, v5) = v8) | ~ % 192.74/26.78 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.78 | tc_Arrow__Order__Mirabelle_Oalt, v3, v2) = v7) | ~ % 192.74/26.78 | (c_member(v0, v7, v8) = v9) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | % 192.74/26.78 | ~ $i(v3) | ~ $i(v2) | ? [v10: any] : ? [v11: $i] : ? [v12: any] % 192.74/26.78 | : ? [v13: $i] : ? [v14: any] : ? [v15: any] : % 192.74/26.78 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.78 | tc_Arrow__Order__Mirabelle_Oalt, v6, v2) = v11 & % 192.74/26.78 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.78 | tc_Arrow__Order__Mirabelle_Oalt, v3, v6) = v13 & c_member(v1, % 192.74/26.78 | v4, c_Arrow__Order__Mirabelle_OLin) = v10 & c_member(v0, v13, % 192.74/26.78 | v4) = v14 & c_member(v0, v11, v4) = v12 & c_member(v0, v7, v4) % 192.74/26.78 | = v15 & $i(v13) & $i(v11) & ( ~ (v10 = 0) | (( ~ (v9 = 0) | ( ~ % 192.74/26.78 | (v3 = v2) & ( ~ (v5 = v3) | v12 = 0) & (v5 = v3 | (( ~ % 192.74/26.78 | (v5 = v2) | v14 = 0 | v6 = v3) & (v15 = 0 | v5 = % 192.74/26.78 | v2))))) & (v9 = 0 | v3 = v2 | (v5 = v3 & ~ (v12 = % 192.74/26.78 | 0)) | ( ~ (v5 = v3) & ((v5 = v2 & ~ (v14 = 0) & ~ (v6 % 192.74/26.78 | = v3)) | ( ~ (v15 = 0) & ~ (v5 = v2)))))))))) % 192.74/26.78 | % 192.74/26.78 | ALPHA: (fact_in__below) implies: % 192.74/26.79 | (9) ? [v0: $i] : ? [v1: $i] : (tc_fun(v0, tc_HOL_Obool) = v1 & % 192.74/26.79 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.79 | tc_Arrow__Order__Mirabelle_Oalt) = v0 & $i(v1) & $i(v0) & ! [v2: % 192.74/26.79 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! % 192.74/26.79 | [v7: $i] : ! [v8: $i] : ! [v9: any] : (v6 = v5 | ~ % 192.74/26.79 | (c_Arrow__Order__Mirabelle_Obelow(v4, v6, v5) = v8) | ~ % 192.74/26.79 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.79 | tc_Arrow__Order__Mirabelle_Oalt, v3, v2) = v7) | ~ % 192.74/26.79 | (c_member(v0, v7, v8) = v9) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | % 192.74/26.79 | ~ $i(v3) | ~ $i(v2) | ? [v10: any] : ? [v11: $i] : ? [v12: any] % 192.74/26.79 | : ? [v13: $i] : ? [v14: any] : ? [v15: any] : % 192.74/26.79 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.79 | tc_Arrow__Order__Mirabelle_Oalt, v5, v2) = v13 & % 192.74/26.79 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.79 | tc_Arrow__Order__Mirabelle_Oalt, v3, v5) = v11 & c_member(v1, % 192.74/26.79 | v4, c_Arrow__Order__Mirabelle_OLin) = v10 & c_member(v0, v13, % 192.74/26.79 | v4) = v14 & c_member(v0, v11, v4) = v12 & c_member(v0, v7, v4) % 192.74/26.79 | = v15 & $i(v13) & $i(v11) & ( ~ (v10 = 0) | (( ~ (v9 = 0) | ( ~ % 192.74/26.79 | (v3 = v2) & ( ~ (v6 = v2) | v12 = 0) & (v6 = v2 | (( ~ % 192.74/26.79 | (v6 = v3) | v14 = 0 | v5 = v2) & (v15 = 0 | v6 = % 192.74/26.79 | v3))))) & (v9 = 0 | v3 = v2 | (v6 = v2 & ~ (v12 = % 192.74/26.79 | 0)) | ( ~ (v6 = v2) & ((v6 = v3 & ~ (v14 = 0) & ~ (v5 % 192.74/26.79 | = v2)) | ( ~ (v15 = 0) & ~ (v6 = v3)))))))))) % 192.74/26.79 | % 192.74/26.79 | ALPHA: (fact_below__Lin) implies: % 192.74/26.79 | (10) ? [v0: $i] : ? [v1: $i] : (tc_fun(v0, tc_HOL_Obool) = v1 & % 192.74/26.79 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.79 | tc_Arrow__Order__Mirabelle_Oalt) = v0 & $i(v1) & $i(v0) & ! [v2: % 192.74/26.79 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v4 = v3 | ~ % 192.74/26.79 | (c_Arrow__Order__Mirabelle_Obelow(v2, v4, v3) = v5) | ~ $i(v4) | % 192.74/26.79 | ~ $i(v3) | ~ $i(v2) | ? [v6: any] : ? [v7: any] : (c_member(v1, % 192.74/26.79 | v5, c_Arrow__Order__Mirabelle_OLin) = v7 & c_member(v1, v2, % 192.74/26.79 | c_Arrow__Order__Mirabelle_OLin) = v6 & ( ~ (v6 = 0) | v7 = % 192.74/26.79 | 0)))) % 192.74/26.79 | % 192.74/26.79 | ALPHA: (fact_linear__alt) implies: % 192.74/26.79 | (11) ? [v0: $i] : ? [v1: $i] : (tc_fun(v0, tc_HOL_Obool) = v1 & % 192.74/26.79 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.79 | tc_Arrow__Order__Mirabelle_Oalt) = v0 & $i(v1) & $i(v0) & ? [v2: % 192.74/26.79 | $i] : (c_member(v1, v2, c_Arrow__Order__Mirabelle_OLin) = 0 & % 192.74/26.79 | $i(v2))) % 192.74/26.79 | % 192.74/26.79 | ALPHA: (fact_converse__in__Lin) implies: % 192.74/26.79 | (12) ? [v0: $i] : ? [v1: $i] : (tc_fun(v0, tc_HOL_Obool) = v1 & % 192.74/26.79 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.79 | tc_Arrow__Order__Mirabelle_Oalt) = v0 & $i(v1) & $i(v0) & ! [v2: % 192.74/26.79 | $i] : ! [v3: int] : (v3 = 0 | ~ (c_member(v1, v2, % 192.74/26.79 | c_Arrow__Order__Mirabelle_OLin) = v3) | ~ $i(v2) | ? [v4: % 192.74/26.79 | $i] : ? [v5: int] : ( ~ (v5 = 0) & % 192.74/26.79 | c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.79 | tc_Arrow__Order__Mirabelle_Oalt, v2) = v4 & c_member(v1, v4, % 192.74/26.79 | c_Arrow__Order__Mirabelle_OLin) = v5 & $i(v4))) & ! [v2: $i] % 192.74/26.79 | : ( ~ (c_member(v1, v2, c_Arrow__Order__Mirabelle_OLin) = 0) | ~ % 192.74/26.79 | $i(v2) | ? [v3: $i] : % 192.74/26.79 | (c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.79 | tc_Arrow__Order__Mirabelle_Oalt, v2) = v3 & c_member(v1, v3, % 192.74/26.79 | c_Arrow__Order__Mirabelle_OLin) = 0 & $i(v3)))) % 192.74/26.79 | % 192.74/26.79 | ALPHA: (conj_0) implies: % 192.74/26.79 | (13) ~ (v_x = v_y) % 192.74/26.79 | % 192.74/26.79 | ALPHA: (conj_1) implies: % 192.74/26.79 | (14) ? [v0: $i] : (tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.79 | tc_Arrow__Order__Mirabelle_Oalt) = v0 & $i(v0) & ! [v1: $i] : ! % 192.74/26.79 | [v2: $i] : ! [v3: $i] : (v2 = v1 | ~ % 192.74/26.79 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.79 | tc_Arrow__Order__Mirabelle_Oalt, v1, v2) = v3) | ~ $i(v2) | % 192.74/26.79 | ~ $i(v1) | ? [v4: any] : ? [v5: $i] : ? [v6: any] : % 192.74/26.79 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.79 | tc_Arrow__Order__Mirabelle_Oalt, v2, v1) = v5 & c_member(v0, % 192.74/26.79 | v5, v_L) = v6 & c_member(v0, v3, v_L) = v4 & $i(v5) & (v6 = 0 % 192.74/26.79 | | v4 = 0))) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 192.74/26.79 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.79 | tc_Arrow__Order__Mirabelle_Oalt, v1, v2) = v3) | ~ $i(v2) | % 192.74/26.79 | ~ $i(v1) | ? [v4: int] : ( ~ (v4 = 0) & c_member(v0, v3, v_L) = % 192.74/26.79 | v4) | ! [v4: $i] : ! [v5: $i] : ( ~ % 192.74/26.79 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.79 | tc_Arrow__Order__Mirabelle_Oalt, v1, v4) = v5) | ~ $i(v4) | % 192.74/26.79 | ? [v6: $i] : ? [v7: any] : ? [v8: any] : % 192.74/26.79 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.79 | tc_Arrow__Order__Mirabelle_Oalt, v2, v4) = v6 & c_member(v0, % 192.74/26.79 | v6, v_L) = v7 & c_member(v0, v5, v_L) = v8 & $i(v6) & ( ~ % 192.74/26.79 | (v7 = 0) | v8 = 0)))) & ! [v1: $i] : ! [v2: $i] : ( ~ % 192.74/26.79 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.79 | tc_Arrow__Order__Mirabelle_Oalt, v1, v1) = v2) | ~ $i(v1) | % 192.74/26.79 | ? [v3: int] : ( ~ (v3 = 0) & c_member(v0, v2, v_L) = v3))) % 192.74/26.79 | % 192.74/26.79 | ALPHA: (conj_2) implies: % 192.74/26.79 | (15) $i(tc_Arrow__Order__Mirabelle_Oalt) % 192.74/26.79 | (16) $i(v_x) % 192.74/26.80 | (17) $i(v_L) % 192.74/26.80 | (18) ? [v0: $i] : (tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.80 | tc_Arrow__Order__Mirabelle_Oalt) = v0 & $i(v0) & ( ? [v1: $i] : ? % 192.74/26.80 | [v2: $i] : ? [v3: $i] : ? [v4: any] : ? [v5: $i] : ? [v6: any] % 192.74/26.80 | : ? [v7: $i] : ? [v8: any] : ? [v9: $i] : ? [v10: any] : ? % 192.74/26.80 | [v11: $i] : ? [v12: any] : ? [v13: $i] : ? [v14: any] : ( ~ (v2 % 192.74/26.80 | = v1) & c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.80 | tc_Arrow__Order__Mirabelle_Oalt, v2, v1) = v9 & % 192.74/26.80 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.80 | tc_Arrow__Order__Mirabelle_Oalt, v2, v_x) = v11 & % 192.74/26.80 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.80 | tc_Arrow__Order__Mirabelle_Oalt, v1, v2) = v3 & % 192.74/26.80 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.80 | tc_Arrow__Order__Mirabelle_Oalt, v1, v_x) = v5 & % 192.74/26.80 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.80 | tc_Arrow__Order__Mirabelle_Oalt, v_x, v2) = v7 & % 192.74/26.80 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.80 | tc_Arrow__Order__Mirabelle_Oalt, v_x, v1) = v13 & c_member(v0, % 192.74/26.80 | v13, v_L) = v14 & c_member(v0, v11, v_L) = v12 & c_member(v0, % 192.74/26.80 | v9, v_L) = v10 & c_member(v0, v7, v_L) = v8 & c_member(v0, v5, % 192.74/26.80 | v_L) = v6 & c_member(v0, v3, v_L) = v4 & $i(v13) & $i(v11) & % 192.74/26.80 | $i(v9) & $i(v7) & $i(v5) & $i(v3) & $i(v2) & $i(v1) & ( ~ (v14 = % 192.74/26.80 | 0) | ~ (v2 = v_y) | v1 = v_y) & ( ~ (v12 = 0) | ~ (v1 = % 192.74/26.80 | v_y) | v2 = v_y) & ( ~ (v10 = 0) | v2 = v_y | v1 = v_y) & ( % 192.74/26.80 | ~ (v8 = 0) | ~ (v1 = v_y) | v2 = v_y) & ( ~ (v6 = 0) | ~ (v2 % 192.74/26.80 | = v_y) | v1 = v_y) & ( ~ (v4 = 0) | v2 = v_y | v1 = v_y) & ( % 192.74/26.80 | ~ (v2 = v_x) | ~ (v1 = v_y)) & ( ~ (v2 = v_y) | ~ (v1 = % 192.74/26.80 | v_x))) | ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: % 192.74/26.80 | any] : ? [v5: $i] : ? [v6: any] : ? [v7: $i] : ? [v8: any] : % 192.74/26.80 | ? [v9: $i] : ? [v10: any] : % 192.74/26.80 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.80 | tc_Arrow__Order__Mirabelle_Oalt, v2, v_x) = v7 & % 192.74/26.80 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.80 | tc_Arrow__Order__Mirabelle_Oalt, v1, v2) = v3 & % 192.74/26.80 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.80 | tc_Arrow__Order__Mirabelle_Oalt, v1, v_x) = v5 & % 192.74/26.80 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.80 | tc_Arrow__Order__Mirabelle_Oalt, v_x, v2) = v9 & c_member(v0, % 192.74/26.80 | v9, v_L) = v10 & c_member(v0, v7, v_L) = v8 & c_member(v0, v5, % 192.74/26.80 | v_L) = v6 & c_member(v0, v3, v_L) = v4 & $i(v9) & $i(v7) & % 192.74/26.80 | $i(v5) & $i(v3) & $i(v2) & $i(v1) & ((v10 = 0 & v1 = v_y & ~ % 192.74/26.80 | (v2 = v_y) & ? [v11: $i] : ? [v12: $i] : ? [v13: any] : % 192.74/26.80 | ? [v14: $i] : ? [v15: any] : % 192.74/26.80 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.80 | tc_Arrow__Order__Mirabelle_Oalt, v2, v11) = v12 & % 192.74/26.80 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.80 | tc_Arrow__Order__Mirabelle_Oalt, v_x, v11) = v14 & % 192.74/26.80 | c_member(v0, v14, v_L) = v15 & c_member(v0, v12, v_L) = % 192.74/26.80 | v13 & $i(v14) & $i(v12) & $i(v11) & ((v13 = 0 & ~ (v15 = % 192.74/26.80 | 0) & ~ (v11 = v_y)) | (v11 = v_y & v8 = 0) | (v11 = % 192.74/26.80 | v_y & v2 = v_x)))) | ( ~ (v1 = v_y) & ((v6 = 0 & v2 = % 192.74/26.80 | v_y & ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? % 192.74/26.80 | [v14: int] : ( ~ (v14 = 0) & ~ (v11 = v_y) & % 192.74/26.80 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.80 | tc_Arrow__Order__Mirabelle_Oalt, v1, v11) = v13 & % 192.74/26.80 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.80 | tc_Arrow__Order__Mirabelle_Oalt, v_x, v11) = v12 & % 192.74/26.80 | c_member(v0, v13, v_L) = v14 & c_member(v0, v12, v_L) % 192.74/26.80 | = 0 & $i(v13) & $i(v12) & $i(v11))) | (v4 = 0 & ~ (v2 % 192.74/26.80 | = v_y) & ? [v11: $i] : ? [v12: $i] : ? [v13: any] : % 192.74/26.80 | ? [v14: $i] : ? [v15: any] : % 192.74/26.80 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.80 | tc_Arrow__Order__Mirabelle_Oalt, v2, v11) = v12 & % 192.74/26.80 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.80 | tc_Arrow__Order__Mirabelle_Oalt, v1, v11) = v14 & % 192.74/26.80 | c_member(v0, v14, v_L) = v15 & c_member(v0, v12, v_L) % 192.74/26.80 | = v13 & $i(v14) & $i(v12) & $i(v11) & ((v13 = 0 & ~ % 192.74/26.80 | (v15 = 0) & ~ (v11 = v_y)) | (v11 = v_y & v8 = 0 % 192.74/26.80 | & ~ (v6 = 0) & ~ (v1 = v_x)) | (v11 = v_y & v2 = % 192.74/26.80 | v_x & ~ (v6 = 0) & ~ (v1 = v_x))))))))))) % 192.74/26.80 | % 192.74/26.80 | ALPHA: (function-axioms) implies: % 192.74/26.80 | (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 192.74/26.80 | (tc_prod(v3, v2) = v1) | ~ (tc_prod(v3, v2) = v0)) % 192.74/26.80 | (20) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 192.74/26.80 | : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (c_member(v4, v3, v2) = % 192.74/26.80 | v1) | ~ (c_member(v4, v3, v2) = v0)) % 192.74/26.80 | (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 192.74/26.80 | ! [v5: $i] : (v1 = v0 | ~ (c_Product__Type_OPair(v5, v4, v3, v2) = % 192.74/26.80 | v1) | ~ (c_Product__Type_OPair(v5, v4, v3, v2) = v0)) % 192.74/26.80 | % 192.74/26.80 | DELTA: instantiating (11) with fresh symbols all_622_0, all_622_1 gives: % 192.74/26.80 | (22) tc_fun(all_622_1, tc_HOL_Obool) = all_622_0 & % 192.74/26.80 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.80 | tc_Arrow__Order__Mirabelle_Oalt) = all_622_1 & $i(all_622_0) & % 192.74/26.80 | $i(all_622_1) & ? [v0: $i] : (c_member(all_622_0, v0, % 192.74/26.80 | c_Arrow__Order__Mirabelle_OLin) = 0 & $i(v0)) % 192.74/26.80 | % 192.74/26.80 | ALPHA: (22) implies: % 192.74/26.80 | (23) tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.80 | tc_Arrow__Order__Mirabelle_Oalt) = all_622_1 % 192.74/26.80 | % 192.74/26.80 | DELTA: instantiating (6) with fresh symbols all_633_0, all_633_1 gives: % 192.74/26.81 | (24) tc_fun(all_633_1, tc_HOL_Obool) = all_633_0 & % 192.74/26.81 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.81 | tc_Arrow__Order__Mirabelle_Oalt) = all_633_1 & $i(all_633_0) & % 192.74/26.81 | $i(all_633_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 192.74/26.81 | (c_Arrow__Order__Mirabelle_Omkbot(v1, v0) = v2) | ~ $i(v1) | ~ % 192.74/26.81 | $i(v0) | ? [v3: any] : ? [v4: any] : (c_member(all_633_0, v2, % 192.74/26.81 | c_Arrow__Order__Mirabelle_OLin) = v4 & c_member(all_633_0, v1, % 192.74/26.81 | c_Arrow__Order__Mirabelle_OLin) = v3 & ( ~ (v3 = 0) | v4 = 0))) % 192.74/26.81 | % 192.74/26.81 | ALPHA: (24) implies: % 192.74/26.81 | (25) $i(all_633_1) % 192.74/26.81 | (26) tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.81 | tc_Arrow__Order__Mirabelle_Oalt) = all_633_1 % 192.74/26.81 | % 192.74/26.81 | DELTA: instantiating (7) with fresh symbols all_636_0, all_636_1 gives: % 192.74/26.81 | (27) tc_fun(all_636_1, tc_HOL_Obool) = all_636_0 & % 192.74/26.81 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.81 | tc_Arrow__Order__Mirabelle_Oalt) = all_636_1 & $i(all_636_0) & % 192.74/26.81 | $i(all_636_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 192.74/26.81 | (c_Arrow__Order__Mirabelle_Omktop(v1, v0) = v2) | ~ $i(v1) | ~ % 192.74/26.81 | $i(v0) | ? [v3: any] : ? [v4: any] : (c_member(all_636_0, v2, % 192.74/26.81 | c_Arrow__Order__Mirabelle_OLin) = v4 & c_member(all_636_0, v1, % 192.74/26.81 | c_Arrow__Order__Mirabelle_OLin) = v3 & ( ~ (v3 = 0) | v4 = 0))) % 192.74/26.81 | % 192.74/26.81 | ALPHA: (27) implies: % 192.74/26.81 | (28) tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.81 | tc_Arrow__Order__Mirabelle_Oalt) = all_636_1 % 192.74/26.81 | % 192.74/26.81 | DELTA: instantiating (10) with fresh symbols all_640_0, all_640_1 gives: % 192.74/26.81 | (29) tc_fun(all_640_1, tc_HOL_Obool) = all_640_0 & % 192.74/26.81 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.81 | tc_Arrow__Order__Mirabelle_Oalt) = all_640_1 & $i(all_640_0) & % 192.74/26.81 | $i(all_640_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 192.74/26.81 | : (v2 = v1 | ~ (c_Arrow__Order__Mirabelle_Obelow(v0, v2, v1) = v3) | % 192.74/26.81 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : % 192.74/26.81 | (c_member(all_640_0, v3, c_Arrow__Order__Mirabelle_OLin) = v5 & % 192.74/26.81 | c_member(all_640_0, v0, c_Arrow__Order__Mirabelle_OLin) = v4 & ( ~ % 192.74/26.81 | (v4 = 0) | v5 = 0))) % 192.74/26.81 | % 192.74/26.81 | ALPHA: (29) implies: % 192.74/26.81 | (30) tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.81 | tc_Arrow__Order__Mirabelle_Oalt) = all_640_1 % 192.74/26.81 | % 192.74/26.81 | DELTA: instantiating (4) with fresh symbols all_644_0, all_644_1 gives: % 192.74/26.81 | (31) tc_fun(all_644_1, tc_HOL_Obool) = all_644_0 & % 192.74/26.81 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.81 | tc_Arrow__Order__Mirabelle_Oalt) = all_644_1 & $i(all_644_0) & % 192.74/26.81 | $i(all_644_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 192.74/26.81 | : ( ~ (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.81 | tc_Arrow__Order__Mirabelle_Oalt, v0, v1) = v3) | ~ % 192.74/26.81 | (c_member(all_644_1, v3, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 192.74/26.81 | $i(v0) | ? [v4: any] : ? [v5: $i] : ? [v6: any] : % 192.74/26.81 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.81 | tc_Arrow__Order__Mirabelle_Oalt, v1, v0) = v5 & % 192.74/26.81 | c_member(all_644_0, v2, c_Arrow__Order__Mirabelle_OLin) = v4 & % 192.74/26.81 | c_member(all_644_1, v5, v2) = v6 & $i(v5) & ( ~ (v6 = 0) | ~ (v4 % 192.74/26.81 | = 0)))) % 192.74/26.81 | % 192.74/26.81 | ALPHA: (31) implies: % 192.74/26.81 | (32) tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.81 | tc_Arrow__Order__Mirabelle_Oalt) = all_644_1 % 192.74/26.81 | % 192.74/26.81 | DELTA: instantiating (12) with fresh symbols all_647_0, all_647_1 gives: % 192.74/26.81 | (33) tc_fun(all_647_1, tc_HOL_Obool) = all_647_0 & % 192.74/26.81 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.81 | tc_Arrow__Order__Mirabelle_Oalt) = all_647_1 & $i(all_647_0) & % 192.74/26.81 | $i(all_647_1) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ % 192.74/26.81 | (c_member(all_647_0, v0, c_Arrow__Order__Mirabelle_OLin) = v1) | ~ % 192.74/26.81 | $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 192.74/26.81 | c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.81 | tc_Arrow__Order__Mirabelle_Oalt, v0) = v2 & c_member(all_647_0, % 192.74/26.81 | v2, c_Arrow__Order__Mirabelle_OLin) = v3 & $i(v2))) & ! [v0: % 192.74/26.81 | $i] : ( ~ (c_member(all_647_0, v0, c_Arrow__Order__Mirabelle_OLin) = % 192.74/26.81 | 0) | ~ $i(v0) | ? [v1: $i] : % 192.74/26.81 | (c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.81 | tc_Arrow__Order__Mirabelle_Oalt, v0) = v1 & c_member(all_647_0, % 192.74/26.81 | v1, c_Arrow__Order__Mirabelle_OLin) = 0 & $i(v1))) % 192.74/26.81 | % 192.74/26.81 | ALPHA: (33) implies: % 192.74/26.81 | (34) tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.81 | tc_Arrow__Order__Mirabelle_Oalt) = all_647_1 % 192.74/26.81 | % 192.74/26.81 | DELTA: instantiating (5) with fresh symbols all_659_0, all_659_1 gives: % 192.74/26.81 | (35) tc_fun(all_659_1, tc_HOL_Obool) = all_659_0 & % 192.74/26.81 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.81 | tc_Arrow__Order__Mirabelle_Oalt) = all_659_1 & $i(all_659_0) & % 192.74/26.81 | $i(all_659_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 192.74/26.81 | : ! [v4: any] : (v1 = v0 | ~ % 192.74/26.81 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.81 | tc_Arrow__Order__Mirabelle_Oalt, v0, v1) = v3) | ~ % 192.74/26.81 | (c_member(all_659_1, v3, v2) = v4) | ~ $i(v2) | ~ $i(v1) | ~ % 192.74/26.81 | $i(v0) | ? [v5: any] : ? [v6: $i] : ? [v7: any] : % 192.74/26.81 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.81 | tc_Arrow__Order__Mirabelle_Oalt, v1, v0) = v6 & % 192.74/26.81 | c_member(all_659_0, v2, c_Arrow__Order__Mirabelle_OLin) = v5 & % 192.74/26.81 | c_member(all_659_1, v6, v2) = v7 & $i(v6) & ( ~ (v5 = 0) | (( ~ % 192.74/26.81 | (v7 = 0) | ~ (v4 = 0)) & (v7 = 0 | v4 = 0))))) % 192.74/26.81 | % 192.74/26.81 | ALPHA: (35) implies: % 192.74/26.81 | (36) tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.81 | tc_Arrow__Order__Mirabelle_Oalt) = all_659_1 % 192.74/26.81 | % 192.74/26.81 | DELTA: instantiating (2) with fresh symbol all_668_0 gives: % 192.74/26.81 | (37) tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.81 | tc_Arrow__Order__Mirabelle_Oalt) = all_668_0 & $i(all_668_0) & ! % 192.74/26.81 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 192.74/26.81 | [v5: $i] : ! [v6: int] : (v6 = 0 | v3 = v0 | ~ % 192.74/26.81 | (c_Arrow__Order__Mirabelle_Omktop(v1, v0) = v5) | ~ % 192.74/26.81 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.81 | tc_Arrow__Order__Mirabelle_Oalt, v3, v2) = v4) | ~ % 192.74/26.81 | (c_member(all_668_0, v4, v5) = v6) | ~ $i(v3) | ~ $i(v2) | ~ % 192.74/26.81 | $i(v1) | ~ $i(v0) | ( ~ (v2 = v0) & ? [v7: int] : ( ~ (v7 = 0) & % 192.74/26.81 | c_member(all_668_0, v4, v1) = v7))) & ! [v0: $i] : ! [v1: $i] % 192.74/26.81 | : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 192.74/26.81 | (c_Arrow__Order__Mirabelle_Omktop(v1, v0) = v5) | ~ % 192.74/26.81 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.81 | tc_Arrow__Order__Mirabelle_Oalt, v3, v2) = v4) | ~ % 192.74/26.81 | (c_member(all_668_0, v4, v5) = 0) | ~ $i(v3) | ~ $i(v2) | ~ % 192.74/26.81 | $i(v1) | ~ $i(v0) | ( ~ (v3 = v0) & (v2 = v0 | c_member(all_668_0, % 192.74/26.81 | v4, v1) = 0))) % 192.74/26.81 | % 192.74/26.81 | ALPHA: (37) implies: % 192.74/26.81 | (38) tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.81 | tc_Arrow__Order__Mirabelle_Oalt) = all_668_0 % 192.74/26.81 | % 192.74/26.81 | DELTA: instantiating (1) with fresh symbol all_673_0 gives: % 192.74/26.82 | (39) tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.82 | tc_Arrow__Order__Mirabelle_Oalt) = all_673_0 & $i(all_673_0) & ! % 192.74/26.82 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 192.74/26.82 | [v5: $i] : ! [v6: int] : (v6 = 0 | v2 = v0 | ~ % 192.74/26.82 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.82 | tc_Arrow__Order__Mirabelle_Oalt, v3, v2) = v4) | ~ % 192.74/26.82 | (c_Arrow__Order__Mirabelle_Omkbot(v1, v0) = v5) | ~ % 192.74/26.82 | (c_member(all_673_0, v4, v5) = v6) | ~ $i(v3) | ~ $i(v2) | ~ % 192.74/26.82 | $i(v1) | ~ $i(v0) | ( ~ (v3 = v0) & ? [v7: int] : ( ~ (v7 = 0) & % 192.74/26.82 | c_member(all_673_0, v4, v1) = v7))) & ! [v0: $i] : ! [v1: $i] % 192.74/26.82 | : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 192.74/26.82 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.82 | tc_Arrow__Order__Mirabelle_Oalt, v3, v2) = v4) | ~ % 192.74/26.82 | (c_Arrow__Order__Mirabelle_Omkbot(v1, v0) = v5) | ~ % 192.74/26.82 | (c_member(all_673_0, v4, v5) = 0) | ~ $i(v3) | ~ $i(v2) | ~ % 192.74/26.82 | $i(v1) | ~ $i(v0) | ( ~ (v2 = v0) & (v3 = v0 | c_member(all_673_0, % 192.74/26.82 | v4, v1) = 0))) % 192.74/26.82 | % 192.74/26.82 | ALPHA: (39) implies: % 192.74/26.82 | (40) tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.82 | tc_Arrow__Order__Mirabelle_Oalt) = all_673_0 % 192.74/26.82 | % 192.74/26.82 | DELTA: instantiating (14) with fresh symbol all_676_0 gives: % 192.74/26.82 | (41) tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.82 | tc_Arrow__Order__Mirabelle_Oalt) = all_676_0 & $i(all_676_0) & ! % 192.74/26.82 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 192.74/26.82 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.82 | tc_Arrow__Order__Mirabelle_Oalt, v0, v1) = v2) | ~ $i(v1) | ~ % 192.74/26.82 | $i(v0) | ? [v3: any] : ? [v4: $i] : ? [v5: any] : % 192.74/26.82 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.82 | tc_Arrow__Order__Mirabelle_Oalt, v1, v0) = v4 & % 192.74/26.82 | c_member(all_676_0, v4, v_L) = v5 & c_member(all_676_0, v2, v_L) = % 192.74/26.82 | v3 & $i(v4) & (v5 = 0 | v3 = 0))) & ! [v0: $i] : ! [v1: $i] : ! % 192.74/26.82 | [v2: $i] : ( ~ (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.82 | tc_Arrow__Order__Mirabelle_Oalt, v0, v1) = v2) | ~ $i(v1) | ~ % 192.74/26.82 | $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & c_member(all_676_0, v2, v_L) % 192.74/26.82 | = v3) | ! [v3: $i] : ! [v4: $i] : ( ~ % 192.74/26.82 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.82 | tc_Arrow__Order__Mirabelle_Oalt, v0, v3) = v4) | ~ $i(v3) | % 192.74/26.82 | ? [v5: $i] : ? [v6: any] : ? [v7: any] : % 192.74/26.82 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.82 | tc_Arrow__Order__Mirabelle_Oalt, v1, v3) = v5 & % 192.74/26.82 | c_member(all_676_0, v5, v_L) = v6 & c_member(all_676_0, v4, v_L) % 192.74/26.82 | = v7 & $i(v5) & ( ~ (v6 = 0) | v7 = 0)))) & ! [v0: $i] : ! % 192.74/26.82 | [v1: $i] : ( ~ (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.82 | tc_Arrow__Order__Mirabelle_Oalt, v0, v0) = v1) | ~ $i(v0) | ? % 192.74/26.82 | [v2: int] : ( ~ (v2 = 0) & c_member(all_676_0, v1, v_L) = v2)) % 192.74/26.82 | % 192.74/26.82 | ALPHA: (41) implies: % 192.74/26.82 | (42) tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.82 | tc_Arrow__Order__Mirabelle_Oalt) = all_676_0 % 192.74/26.82 | (43) ! [v0: $i] : ! [v1: $i] : ( ~ % 192.74/26.82 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.82 | tc_Arrow__Order__Mirabelle_Oalt, v0, v0) = v1) | ~ $i(v0) | ? % 192.74/26.82 | [v2: int] : ( ~ (v2 = 0) & c_member(all_676_0, v1, v_L) = v2)) % 192.74/26.82 | (44) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 192.74/26.82 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.82 | tc_Arrow__Order__Mirabelle_Oalt, v0, v1) = v2) | ~ $i(v1) | ~ % 192.74/26.82 | $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & c_member(all_676_0, v2, v_L) % 192.74/26.82 | = v3) | ! [v3: $i] : ! [v4: $i] : ( ~ % 192.74/26.82 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.82 | tc_Arrow__Order__Mirabelle_Oalt, v0, v3) = v4) | ~ $i(v3) | % 192.74/26.82 | ? [v5: $i] : ? [v6: any] : ? [v7: any] : % 192.74/26.82 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.82 | tc_Arrow__Order__Mirabelle_Oalt, v1, v3) = v5 & % 192.74/26.82 | c_member(all_676_0, v5, v_L) = v6 & c_member(all_676_0, v4, v_L) % 192.74/26.82 | = v7 & $i(v5) & ( ~ (v6 = 0) | v7 = 0)))) % 192.74/26.82 | (45) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 192.74/26.82 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.82 | tc_Arrow__Order__Mirabelle_Oalt, v0, v1) = v2) | ~ $i(v1) | ~ % 192.74/26.82 | $i(v0) | ? [v3: any] : ? [v4: $i] : ? [v5: any] : % 192.74/26.82 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.82 | tc_Arrow__Order__Mirabelle_Oalt, v1, v0) = v4 & % 192.74/26.82 | c_member(all_676_0, v4, v_L) = v5 & c_member(all_676_0, v2, v_L) = % 192.74/26.82 | v3 & $i(v4) & (v5 = 0 | v3 = 0))) % 192.74/26.82 | % 192.74/26.82 | DELTA: instantiating (8) with fresh symbols all_679_0, all_679_1 gives: % 192.74/26.82 | (46) tc_fun(all_679_1, tc_HOL_Obool) = all_679_0 & % 192.74/26.82 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.82 | tc_Arrow__Order__Mirabelle_Oalt) = all_679_1 & $i(all_679_0) & % 192.74/26.82 | $i(all_679_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 192.74/26.82 | : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: any] : (v4 = v3 | % 192.74/26.82 | ~ (c_Arrow__Order__Mirabelle_Oabove(v2, v4, v3) = v6) | ~ % 192.74/26.82 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.82 | tc_Arrow__Order__Mirabelle_Oalt, v1, v0) = v5) | ~ % 192.74/26.82 | (c_member(all_679_1, v5, v6) = v7) | ~ $i(v4) | ~ $i(v3) | ~ % 192.74/26.82 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v8: any] : ? [v9: $i] : ? % 192.74/26.82 | [v10: any] : ? [v11: $i] : ? [v12: any] : ? [v13: any] : % 192.74/26.82 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.82 | tc_Arrow__Order__Mirabelle_Oalt, v4, v0) = v9 & % 192.74/26.82 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.82 | tc_Arrow__Order__Mirabelle_Oalt, v1, v4) = v11 & % 192.74/26.82 | c_member(all_679_0, v2, c_Arrow__Order__Mirabelle_OLin) = v8 & % 192.74/26.82 | c_member(all_679_1, v11, v2) = v12 & c_member(all_679_1, v9, v2) = % 192.74/26.82 | v10 & c_member(all_679_1, v5, v2) = v13 & $i(v11) & $i(v9) & ( ~ % 192.74/26.82 | (v8 = 0) | (( ~ (v7 = 0) | ( ~ (v1 = v0) & ( ~ (v3 = v1) | v10 = % 192.74/26.82 | 0) & (v3 = v1 | (( ~ (v3 = v0) | v12 = 0 | v4 = v1) & % 192.74/26.82 | (v13 = 0 | v3 = v0))))) & (v7 = 0 | v1 = v0 | (v3 = v1 % 192.74/26.82 | & ~ (v10 = 0)) | ( ~ (v3 = v1) & ((v3 = v0 & ~ (v12 = 0) % 192.74/26.82 | & ~ (v4 = v1)) | ( ~ (v13 = 0) & ~ (v3 = v0))))))))) % 192.74/26.82 | % 192.74/26.82 | ALPHA: (46) implies: % 192.74/26.82 | (47) tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.82 | tc_Arrow__Order__Mirabelle_Oalt) = all_679_1 % 192.74/26.82 | % 192.74/26.82 | DELTA: instantiating (9) with fresh symbols all_682_0, all_682_1 gives: % 192.74/26.83 | (48) tc_fun(all_682_1, tc_HOL_Obool) = all_682_0 & % 192.74/26.83 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.83 | tc_Arrow__Order__Mirabelle_Oalt) = all_682_1 & $i(all_682_0) & % 192.74/26.83 | $i(all_682_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 192.74/26.83 | : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: any] : (v4 = v3 | % 192.74/26.83 | ~ (c_Arrow__Order__Mirabelle_Obelow(v2, v4, v3) = v6) | ~ % 192.74/26.83 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.83 | tc_Arrow__Order__Mirabelle_Oalt, v1, v0) = v5) | ~ % 192.74/26.83 | (c_member(all_682_1, v5, v6) = v7) | ~ $i(v4) | ~ $i(v3) | ~ % 192.74/26.83 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v8: any] : ? [v9: $i] : ? % 192.74/26.83 | [v10: any] : ? [v11: $i] : ? [v12: any] : ? [v13: any] : % 192.74/26.83 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.83 | tc_Arrow__Order__Mirabelle_Oalt, v3, v0) = v11 & % 192.74/26.83 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.83 | tc_Arrow__Order__Mirabelle_Oalt, v1, v3) = v9 & % 192.74/26.83 | c_member(all_682_0, v2, c_Arrow__Order__Mirabelle_OLin) = v8 & % 192.74/26.83 | c_member(all_682_1, v11, v2) = v12 & c_member(all_682_1, v9, v2) = % 192.74/26.83 | v10 & c_member(all_682_1, v5, v2) = v13 & $i(v11) & $i(v9) & ( ~ % 192.74/26.83 | (v8 = 0) | (( ~ (v7 = 0) | ( ~ (v1 = v0) & ( ~ (v4 = v0) | v10 = % 192.74/26.83 | 0) & (v4 = v0 | (( ~ (v4 = v1) | v12 = 0 | v3 = v0) & % 192.74/26.83 | (v13 = 0 | v4 = v1))))) & (v7 = 0 | v1 = v0 | (v4 = v0 % 192.74/26.83 | & ~ (v10 = 0)) | ( ~ (v4 = v0) & ((v4 = v1 & ~ (v12 = 0) % 192.74/26.83 | & ~ (v3 = v0)) | ( ~ (v13 = 0) & ~ (v4 = v1))))))))) % 192.74/26.83 | % 192.74/26.83 | ALPHA: (48) implies: % 192.74/26.83 | (49) tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.83 | tc_Arrow__Order__Mirabelle_Oalt) = all_682_1 % 192.74/26.83 | % 192.74/26.83 | DELTA: instantiating (18) with fresh symbol all_685_0 gives: % 192.74/26.83 | (50) tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.83 | tc_Arrow__Order__Mirabelle_Oalt) = all_685_0 & $i(all_685_0) & ( ? % 192.74/26.83 | [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] : ? [v4: $i] : % 192.74/26.83 | ? [v5: any] : ? [v6: $i] : ? [v7: any] : ? [v8: $i] : ? [v9: % 192.74/26.83 | any] : ? [v10: $i] : ? [v11: any] : ? [v12: $i] : ? [v13: any] % 192.74/26.83 | : ( ~ (v1 = v0) & % 192.74/26.83 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.83 | tc_Arrow__Order__Mirabelle_Oalt, v1, v0) = v8 & % 192.74/26.83 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.83 | tc_Arrow__Order__Mirabelle_Oalt, v1, v_x) = v10 & % 192.74/26.83 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.83 | tc_Arrow__Order__Mirabelle_Oalt, v0, v1) = v2 & % 192.74/26.83 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.83 | tc_Arrow__Order__Mirabelle_Oalt, v0, v_x) = v4 & % 192.74/26.83 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.83 | tc_Arrow__Order__Mirabelle_Oalt, v_x, v1) = v6 & % 192.74/26.83 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.83 | tc_Arrow__Order__Mirabelle_Oalt, v_x, v0) = v12 & % 192.74/26.83 | c_member(all_685_0, v12, v_L) = v13 & c_member(all_685_0, v10, % 192.74/26.83 | v_L) = v11 & c_member(all_685_0, v8, v_L) = v9 & % 192.74/26.83 | c_member(all_685_0, v6, v_L) = v7 & c_member(all_685_0, v4, v_L) = % 192.74/26.83 | v5 & c_member(all_685_0, v2, v_L) = v3 & $i(v12) & $i(v10) & % 192.74/26.83 | $i(v8) & $i(v6) & $i(v4) & $i(v2) & $i(v1) & $i(v0) & ( ~ (v13 = % 192.74/26.83 | 0) | ~ (v1 = v_y) | v0 = v_y) & ( ~ (v11 = 0) | ~ (v0 = v_y) % 192.74/26.83 | | v1 = v_y) & ( ~ (v9 = 0) | v1 = v_y | v0 = v_y) & ( ~ (v7 = 0) % 192.74/26.83 | | ~ (v0 = v_y) | v1 = v_y) & ( ~ (v5 = 0) | ~ (v1 = v_y) | v0 % 192.74/26.83 | = v_y) & ( ~ (v3 = 0) | v1 = v_y | v0 = v_y) & ( ~ (v1 = v_x) | % 192.74/26.83 | ~ (v0 = v_y)) & ( ~ (v1 = v_y) | ~ (v0 = v_x))) | ? [v0: $i] : % 192.74/26.83 | ? [v1: $i] : ? [v2: $i] : ? [v3: any] : ? [v4: $i] : ? [v5: % 192.74/26.83 | any] : ? [v6: $i] : ? [v7: any] : ? [v8: $i] : ? [v9: any] : % 192.74/26.83 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.83 | tc_Arrow__Order__Mirabelle_Oalt, v1, v_x) = v6 & % 192.74/26.83 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.83 | tc_Arrow__Order__Mirabelle_Oalt, v0, v1) = v2 & % 192.74/26.83 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.83 | tc_Arrow__Order__Mirabelle_Oalt, v0, v_x) = v4 & % 192.74/26.83 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.83 | tc_Arrow__Order__Mirabelle_Oalt, v_x, v1) = v8 & % 192.74/26.83 | c_member(all_685_0, v8, v_L) = v9 & c_member(all_685_0, v6, v_L) = % 192.74/26.83 | v7 & c_member(all_685_0, v4, v_L) = v5 & c_member(all_685_0, v2, % 192.74/26.83 | v_L) = v3 & $i(v8) & $i(v6) & $i(v4) & $i(v2) & $i(v1) & $i(v0) % 192.74/26.83 | & ((v9 = 0 & v0 = v_y & ~ (v1 = v_y) & ? [v10: $i] : ? [v11: % 192.74/26.83 | $i] : ? [v12: any] : ? [v13: $i] : ? [v14: any] : % 192.74/26.83 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.83 | tc_Arrow__Order__Mirabelle_Oalt, v1, v10) = v11 & % 192.74/26.83 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.83 | tc_Arrow__Order__Mirabelle_Oalt, v_x, v10) = v13 & % 192.74/26.83 | c_member(all_685_0, v13, v_L) = v14 & c_member(all_685_0, % 192.74/26.83 | v11, v_L) = v12 & $i(v13) & $i(v11) & $i(v10) & ((v12 = 0 % 192.74/26.83 | & ~ (v14 = 0) & ~ (v10 = v_y)) | (v10 = v_y & v7 = 0) % 192.74/26.83 | | (v10 = v_y & v1 = v_x)))) | ( ~ (v0 = v_y) & ((v5 = 0 & % 192.74/26.83 | v1 = v_y & ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? % 192.74/26.83 | [v13: int] : ( ~ (v13 = 0) & ~ (v10 = v_y) & % 192.74/26.83 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.83 | tc_Arrow__Order__Mirabelle_Oalt, v0, v10) = v12 & % 192.74/26.83 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.83 | tc_Arrow__Order__Mirabelle_Oalt, v_x, v10) = v11 & % 192.74/26.83 | c_member(all_685_0, v12, v_L) = v13 & % 192.74/26.83 | c_member(all_685_0, v11, v_L) = 0 & $i(v12) & $i(v11) & % 192.74/26.83 | $i(v10))) | (v3 = 0 & ~ (v1 = v_y) & ? [v10: $i] : ? % 192.74/26.83 | [v11: $i] : ? [v12: any] : ? [v13: $i] : ? [v14: any] : % 192.74/26.83 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.83 | tc_Arrow__Order__Mirabelle_Oalt, v1, v10) = v11 & % 192.74/26.83 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.83 | tc_Arrow__Order__Mirabelle_Oalt, v0, v10) = v13 & % 192.74/26.83 | c_member(all_685_0, v13, v_L) = v14 & % 192.74/26.83 | c_member(all_685_0, v11, v_L) = v12 & $i(v13) & $i(v11) % 192.74/26.83 | & $i(v10) & ((v12 = 0 & ~ (v14 = 0) & ~ (v10 = v_y)) | % 192.74/26.83 | (v10 = v_y & v7 = 0 & ~ (v5 = 0) & ~ (v0 = v_x)) | % 192.74/26.83 | (v10 = v_y & v1 = v_x & ~ (v5 = 0) & ~ (v0 = % 192.74/26.83 | v_x)))))))))) % 192.74/26.83 | % 192.74/26.83 | ALPHA: (50) implies: % 192.74/26.83 | (51) tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.83 | tc_Arrow__Order__Mirabelle_Oalt) = all_685_0 % 192.74/26.84 | (52) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] : ? [v4: $i] : % 192.74/26.84 | ? [v5: any] : ? [v6: $i] : ? [v7: any] : ? [v8: $i] : ? [v9: any] % 192.74/26.84 | : ? [v10: $i] : ? [v11: any] : ? [v12: $i] : ? [v13: any] : ( ~ % 192.74/26.84 | (v1 = v0) & c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.84 | tc_Arrow__Order__Mirabelle_Oalt, v1, v0) = v8 & % 192.74/26.84 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.84 | tc_Arrow__Order__Mirabelle_Oalt, v1, v_x) = v10 & % 192.74/26.84 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.84 | tc_Arrow__Order__Mirabelle_Oalt, v0, v1) = v2 & % 192.74/26.84 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.84 | tc_Arrow__Order__Mirabelle_Oalt, v0, v_x) = v4 & % 192.74/26.84 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.84 | tc_Arrow__Order__Mirabelle_Oalt, v_x, v1) = v6 & % 192.74/26.84 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.84 | tc_Arrow__Order__Mirabelle_Oalt, v_x, v0) = v12 & % 192.74/26.84 | c_member(all_685_0, v12, v_L) = v13 & c_member(all_685_0, v10, v_L) % 192.74/26.84 | = v11 & c_member(all_685_0, v8, v_L) = v9 & c_member(all_685_0, v6, % 192.74/26.84 | v_L) = v7 & c_member(all_685_0, v4, v_L) = v5 & % 192.74/26.84 | c_member(all_685_0, v2, v_L) = v3 & $i(v12) & $i(v10) & $i(v8) & % 192.74/26.84 | $i(v6) & $i(v4) & $i(v2) & $i(v1) & $i(v0) & ( ~ (v13 = 0) | ~ (v1 % 192.74/26.84 | = v_y) | v0 = v_y) & ( ~ (v11 = 0) | ~ (v0 = v_y) | v1 = v_y) & % 192.74/26.84 | ( ~ (v9 = 0) | v1 = v_y | v0 = v_y) & ( ~ (v7 = 0) | ~ (v0 = v_y) | % 192.74/26.84 | v1 = v_y) & ( ~ (v5 = 0) | ~ (v1 = v_y) | v0 = v_y) & ( ~ (v3 = % 192.74/26.84 | 0) | v1 = v_y | v0 = v_y) & ( ~ (v1 = v_x) | ~ (v0 = v_y)) & ( % 192.74/26.84 | ~ (v1 = v_y) | ~ (v0 = v_x))) | ? [v0: $i] : ? [v1: $i] : ? % 192.74/26.84 | [v2: $i] : ? [v3: any] : ? [v4: $i] : ? [v5: any] : ? [v6: $i] : % 192.74/26.84 | ? [v7: any] : ? [v8: $i] : ? [v9: any] : % 192.74/26.84 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.84 | tc_Arrow__Order__Mirabelle_Oalt, v1, v_x) = v6 & % 192.74/26.84 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.84 | tc_Arrow__Order__Mirabelle_Oalt, v0, v1) = v2 & % 192.74/26.84 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.84 | tc_Arrow__Order__Mirabelle_Oalt, v0, v_x) = v4 & % 192.74/26.84 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.84 | tc_Arrow__Order__Mirabelle_Oalt, v_x, v1) = v8 & % 192.74/26.84 | c_member(all_685_0, v8, v_L) = v9 & c_member(all_685_0, v6, v_L) = % 192.74/26.84 | v7 & c_member(all_685_0, v4, v_L) = v5 & c_member(all_685_0, v2, % 192.74/26.84 | v_L) = v3 & $i(v8) & $i(v6) & $i(v4) & $i(v2) & $i(v1) & $i(v0) & % 192.74/26.84 | ((v9 = 0 & v0 = v_y & ~ (v1 = v_y) & ? [v10: $i] : ? [v11: $i] : % 192.74/26.84 | ? [v12: any] : ? [v13: $i] : ? [v14: any] : % 192.74/26.84 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.84 | tc_Arrow__Order__Mirabelle_Oalt, v1, v10) = v11 & % 192.74/26.84 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.84 | tc_Arrow__Order__Mirabelle_Oalt, v_x, v10) = v13 & % 192.74/26.84 | c_member(all_685_0, v13, v_L) = v14 & c_member(all_685_0, v11, % 192.74/26.84 | v_L) = v12 & $i(v13) & $i(v11) & $i(v10) & ((v12 = 0 & ~ % 192.74/26.84 | (v14 = 0) & ~ (v10 = v_y)) | (v10 = v_y & v7 = 0) | (v10 % 192.74/26.84 | = v_y & v1 = v_x)))) | ( ~ (v0 = v_y) & ((v5 = 0 & v1 = % 192.74/26.84 | v_y & ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: % 192.74/26.84 | int] : ( ~ (v13 = 0) & ~ (v10 = v_y) & % 192.74/26.84 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.84 | tc_Arrow__Order__Mirabelle_Oalt, v0, v10) = v12 & % 192.74/26.84 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.84 | tc_Arrow__Order__Mirabelle_Oalt, v_x, v10) = v11 & % 192.74/26.84 | c_member(all_685_0, v12, v_L) = v13 & c_member(all_685_0, % 192.74/26.84 | v11, v_L) = 0 & $i(v12) & $i(v11) & $i(v10))) | (v3 = 0 % 192.74/26.84 | & ~ (v1 = v_y) & ? [v10: $i] : ? [v11: $i] : ? [v12: % 192.74/26.84 | any] : ? [v13: $i] : ? [v14: any] : % 192.74/26.84 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.84 | tc_Arrow__Order__Mirabelle_Oalt, v1, v10) = v11 & % 192.74/26.84 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.84 | tc_Arrow__Order__Mirabelle_Oalt, v0, v10) = v13 & % 192.74/26.84 | c_member(all_685_0, v13, v_L) = v14 & c_member(all_685_0, % 192.74/26.84 | v11, v_L) = v12 & $i(v13) & $i(v11) & $i(v10) & ((v12 = % 192.74/26.84 | 0 & ~ (v14 = 0) & ~ (v10 = v_y)) | (v10 = v_y & v7 = % 192.74/26.84 | 0 & ~ (v5 = 0) & ~ (v0 = v_x)) | (v10 = v_y & v1 = % 192.74/26.84 | v_x & ~ (v5 = 0) & ~ (v0 = v_x))))))))) % 192.74/26.84 | % 192.74/26.84 | GROUND_INST: instantiating (19) with all_622_1, all_640_1, % 192.74/26.84 | tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.84 | simplifying with (23), (30) gives: % 192.74/26.84 | (53) all_640_1 = all_622_1 % 192.74/26.84 | % 192.74/26.84 | GROUND_INST: instantiating (19) with all_640_1, all_668_0, % 192.74/26.84 | tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.84 | simplifying with (30), (38) gives: % 192.74/26.84 | (54) all_668_0 = all_640_1 % 192.74/26.84 | % 192.74/26.84 | GROUND_INST: instantiating (19) with all_636_1, all_668_0, % 192.74/26.84 | tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.84 | simplifying with (28), (38) gives: % 192.74/26.84 | (55) all_668_0 = all_636_1 % 192.74/26.84 | % 192.74/26.84 | GROUND_INST: instantiating (19) with all_644_1, all_673_0, % 192.74/26.84 | tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.84 | simplifying with (32), (40) gives: % 192.74/26.84 | (56) all_673_0 = all_644_1 % 192.74/26.84 | % 192.74/26.84 | GROUND_INST: instantiating (19) with all_640_1, all_673_0, % 192.74/26.84 | tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.84 | simplifying with (30), (40) gives: % 192.74/26.84 | (57) all_673_0 = all_640_1 % 192.74/26.84 | % 192.74/26.84 | GROUND_INST: instantiating (19) with all_633_1, all_673_0, % 192.74/26.84 | tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.84 | simplifying with (26), (40) gives: % 192.74/26.84 | (58) all_673_0 = all_633_1 % 192.74/26.84 | % 192.74/26.84 | GROUND_INST: instantiating (19) with all_668_0, all_676_0, % 192.74/26.84 | tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.84 | simplifying with (38), (42) gives: % 192.74/26.84 | (59) all_676_0 = all_668_0 % 192.74/26.84 | % 192.74/26.84 | GROUND_INST: instantiating (19) with all_679_1, all_682_1, % 192.74/26.84 | tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.84 | simplifying with (47), (49) gives: % 192.74/26.84 | (60) all_682_1 = all_679_1 % 192.74/26.84 | % 192.74/26.84 | GROUND_INST: instantiating (19) with all_668_0, all_682_1, % 192.74/26.84 | tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.84 | simplifying with (38), (49) gives: % 192.74/26.84 | (61) all_682_1 = all_668_0 % 192.74/26.84 | % 192.74/26.84 | GROUND_INST: instantiating (19) with all_647_1, all_682_1, % 192.74/26.84 | tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.84 | simplifying with (34), (49) gives: % 192.74/26.84 | (62) all_682_1 = all_647_1 % 192.74/26.84 | % 192.74/26.84 | GROUND_INST: instantiating (19) with all_676_0, all_685_0, % 192.74/26.84 | tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.84 | simplifying with (42), (51) gives: % 192.74/26.84 | (63) all_685_0 = all_676_0 % 192.74/26.84 | % 192.74/26.84 | GROUND_INST: instantiating (19) with all_659_1, all_685_0, % 192.74/26.84 | tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.84 | simplifying with (36), (51) gives: % 192.74/26.84 | (64) all_685_0 = all_659_1 % 192.74/26.84 | % 192.74/26.84 | COMBINE_EQS: (63), (64) imply: % 192.74/26.84 | (65) all_676_0 = all_659_1 % 192.74/26.84 | % 192.74/26.84 | SIMP: (65) implies: % 192.74/26.84 | (66) all_676_0 = all_659_1 % 192.74/26.84 | % 192.74/26.84 | COMBINE_EQS: (60), (61) imply: % 192.74/26.84 | (67) all_679_1 = all_668_0 % 192.74/26.84 | % 192.74/26.84 | COMBINE_EQS: (60), (62) imply: % 192.74/26.84 | (68) all_679_1 = all_647_1 % 192.74/26.84 | % 192.74/26.84 | COMBINE_EQS: (67), (68) imply: % 192.74/26.84 | (69) all_668_0 = all_647_1 % 192.74/26.84 | % 192.74/26.84 | SIMP: (69) implies: % 192.74/26.84 | (70) all_668_0 = all_647_1 % 192.74/26.84 | % 192.74/26.84 | COMBINE_EQS: (59), (66) imply: % 192.74/26.84 | (71) all_668_0 = all_659_1 % 192.74/26.84 | % 192.74/26.84 | SIMP: (71) implies: % 192.74/26.84 | (72) all_668_0 = all_659_1 % 192.74/26.84 | % 192.74/26.84 | COMBINE_EQS: (56), (58) imply: % 192.74/26.84 | (73) all_644_1 = all_633_1 % 192.74/26.84 | % 192.74/26.84 | COMBINE_EQS: (56), (57) imply: % 192.74/26.84 | (74) all_644_1 = all_640_1 % 192.74/26.84 | % 192.74/26.84 | COMBINE_EQS: (54), (72) imply: % 192.74/26.84 | (75) all_659_1 = all_640_1 % 192.74/26.84 | % 192.74/26.84 | COMBINE_EQS: (70), (72) imply: % 192.74/26.84 | (76) all_659_1 = all_647_1 % 192.74/26.84 | % 192.74/26.84 | COMBINE_EQS: (55), (72) imply: % 192.74/26.84 | (77) all_659_1 = all_636_1 % 192.74/26.84 | % 192.74/26.84 | COMBINE_EQS: (76), (77) imply: % 192.74/26.84 | (78) all_647_1 = all_636_1 % 192.74/26.84 | % 192.74/26.84 | COMBINE_EQS: (75), (76) imply: % 192.74/26.84 | (79) all_647_1 = all_640_1 % 192.74/26.84 | % 192.74/26.84 | COMBINE_EQS: (78), (79) imply: % 192.74/26.84 | (80) all_640_1 = all_636_1 % 192.74/26.84 | % 192.74/26.84 | SIMP: (80) implies: % 192.74/26.84 | (81) all_640_1 = all_636_1 % 192.74/26.84 | % 192.74/26.84 | COMBINE_EQS: (73), (74) imply: % 192.74/26.85 | (82) all_640_1 = all_633_1 % 192.74/26.85 | % 192.74/26.85 | SIMP: (82) implies: % 192.74/26.85 | (83) all_640_1 = all_633_1 % 192.74/26.85 | % 192.74/26.85 | COMBINE_EQS: (53), (81) imply: % 192.74/26.85 | (84) all_636_1 = all_622_1 % 192.74/26.85 | % 192.74/26.85 | COMBINE_EQS: (81), (83) imply: % 192.74/26.85 | (85) all_636_1 = all_633_1 % 192.74/26.85 | % 192.74/26.85 | COMBINE_EQS: (84), (85) imply: % 192.74/26.85 | (86) all_633_1 = all_622_1 % 192.74/26.85 | % 192.74/26.85 | COMBINE_EQS: (78), (84) imply: % 192.74/26.85 | (87) all_647_1 = all_622_1 % 192.74/26.85 | % 192.74/26.85 | COMBINE_EQS: (76), (87) imply: % 192.74/26.85 | (88) all_659_1 = all_622_1 % 192.74/26.85 | % 192.74/26.85 | COMBINE_EQS: (66), (88) imply: % 192.74/26.85 | (89) all_676_0 = all_622_1 % 192.74/26.85 | % 192.74/26.85 | COMBINE_EQS: (64), (88) imply: % 192.74/26.85 | (90) all_685_0 = all_622_1 % 192.74/26.85 | % 192.74/26.85 | REDUCE: (25), (86) imply: % 192.74/26.85 | (91) $i(all_622_1) % 192.74/26.85 | % 192.74/26.85 | BETA: splitting (52) gives: % 192.74/26.85 | % 192.74/26.85 | Case 1: % 192.74/26.85 | | % 192.74/26.85 | | (92) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] : ? [v4: $i] % 192.74/26.85 | | : ? [v5: any] : ? [v6: $i] : ? [v7: any] : ? [v8: $i] : ? [v9: % 192.74/26.85 | | any] : ? [v10: $i] : ? [v11: any] : ? [v12: $i] : ? [v13: any] % 192.74/26.85 | | : ( ~ (v1 = v0) & % 192.74/26.85 | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.85 | | tc_Arrow__Order__Mirabelle_Oalt, v1, v0) = v8 & % 192.74/26.85 | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.85 | | tc_Arrow__Order__Mirabelle_Oalt, v1, v_x) = v10 & % 192.74/26.85 | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.85 | | tc_Arrow__Order__Mirabelle_Oalt, v0, v1) = v2 & % 192.74/26.85 | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.85 | | tc_Arrow__Order__Mirabelle_Oalt, v0, v_x) = v4 & % 192.74/26.85 | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.85 | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v1) = v6 & % 192.74/26.85 | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.85 | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v0) = v12 & % 192.74/26.85 | | c_member(all_685_0, v12, v_L) = v13 & c_member(all_685_0, v10, % 192.74/26.85 | | v_L) = v11 & c_member(all_685_0, v8, v_L) = v9 & % 192.74/26.85 | | c_member(all_685_0, v6, v_L) = v7 & c_member(all_685_0, v4, v_L) = % 192.74/26.85 | | v5 & c_member(all_685_0, v2, v_L) = v3 & $i(v12) & $i(v10) & % 192.74/26.85 | | $i(v8) & $i(v6) & $i(v4) & $i(v2) & $i(v1) & $i(v0) & ( ~ (v13 = % 192.74/26.85 | | 0) | ~ (v1 = v_y) | v0 = v_y) & ( ~ (v11 = 0) | ~ (v0 = v_y) % 192.74/26.85 | | | v1 = v_y) & ( ~ (v9 = 0) | v1 = v_y | v0 = v_y) & ( ~ (v7 = 0) % 192.74/26.85 | | | ~ (v0 = v_y) | v1 = v_y) & ( ~ (v5 = 0) | ~ (v1 = v_y) | v0 % 192.74/26.85 | | = v_y) & ( ~ (v3 = 0) | v1 = v_y | v0 = v_y) & ( ~ (v1 = v_x) | % 192.74/26.85 | | ~ (v0 = v_y)) & ( ~ (v1 = v_y) | ~ (v0 = v_x))) % 192.74/26.85 | | % 192.74/26.85 | | DELTA: instantiating (92) with fresh symbols all_872_0, all_872_1, % 192.74/26.85 | | all_872_2, all_872_3, all_872_4, all_872_5, all_872_6, all_872_7, % 192.74/26.85 | | all_872_8, all_872_9, all_872_10, all_872_11, all_872_12, all_872_13 % 192.74/26.85 | | gives: % 192.74/26.85 | | (93) ~ (all_872_12 = all_872_13) & % 192.74/26.85 | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.85 | | tc_Arrow__Order__Mirabelle_Oalt, all_872_12, all_872_13) = % 192.74/26.85 | | all_872_5 & c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.85 | | tc_Arrow__Order__Mirabelle_Oalt, all_872_12, v_x) = all_872_3 & % 192.74/26.85 | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.85 | | tc_Arrow__Order__Mirabelle_Oalt, all_872_13, all_872_12) = % 192.74/26.85 | | all_872_11 & c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.85 | | tc_Arrow__Order__Mirabelle_Oalt, all_872_13, v_x) = all_872_9 & % 192.74/26.85 | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.85 | | tc_Arrow__Order__Mirabelle_Oalt, v_x, all_872_12) = all_872_7 & % 192.74/26.85 | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.85 | | tc_Arrow__Order__Mirabelle_Oalt, v_x, all_872_13) = all_872_1 & % 192.74/26.85 | | c_member(all_685_0, all_872_1, v_L) = all_872_0 & % 192.74/26.85 | | c_member(all_685_0, all_872_3, v_L) = all_872_2 & % 192.74/26.85 | | c_member(all_685_0, all_872_5, v_L) = all_872_4 & % 192.74/26.85 | | c_member(all_685_0, all_872_7, v_L) = all_872_6 & % 192.74/26.85 | | c_member(all_685_0, all_872_9, v_L) = all_872_8 & % 192.74/26.85 | | c_member(all_685_0, all_872_11, v_L) = all_872_10 & $i(all_872_1) & % 192.74/26.85 | | $i(all_872_3) & $i(all_872_5) & $i(all_872_7) & $i(all_872_9) & % 192.74/26.85 | | $i(all_872_11) & $i(all_872_12) & $i(all_872_13) & ( ~ (all_872_0 = % 192.74/26.85 | | 0) | ~ (all_872_12 = v_y) | all_872_13 = v_y) & ( ~ (all_872_2 % 192.74/26.85 | | = 0) | ~ (all_872_13 = v_y) | all_872_12 = v_y) & ( ~ % 192.74/26.85 | | (all_872_4 = 0) | all_872_12 = v_y | all_872_13 = v_y) & ( ~ % 192.74/26.85 | | (all_872_6 = 0) | ~ (all_872_13 = v_y) | all_872_12 = v_y) & ( ~ % 192.74/26.85 | | (all_872_8 = 0) | ~ (all_872_12 = v_y) | all_872_13 = v_y) & ( ~ % 192.74/26.85 | | (all_872_10 = 0) | all_872_12 = v_y | all_872_13 = v_y) & ( ~ % 192.74/26.85 | | (all_872_12 = v_x) | ~ (all_872_13 = v_y)) & ( ~ (all_872_12 = % 192.74/26.85 | | v_y) | ~ (all_872_13 = v_x)) % 192.74/26.85 | | % 192.74/26.85 | | ALPHA: (93) implies: % 192.74/26.85 | | (94) ~ (all_872_12 = all_872_13) % 192.74/26.85 | | (95) $i(all_872_13) % 192.74/26.85 | | (96) $i(all_872_12) % 192.74/26.85 | | (97) $i(all_872_11) % 192.74/26.85 | | (98) c_member(all_685_0, all_872_11, v_L) = all_872_10 % 192.74/26.85 | | (99) c_member(all_685_0, all_872_9, v_L) = all_872_8 % 192.74/26.85 | | (100) c_member(all_685_0, all_872_7, v_L) = all_872_6 % 192.74/26.85 | | (101) c_member(all_685_0, all_872_5, v_L) = all_872_4 % 192.74/26.85 | | (102) c_member(all_685_0, all_872_3, v_L) = all_872_2 % 192.74/26.85 | | (103) c_member(all_685_0, all_872_1, v_L) = all_872_0 % 192.74/26.85 | | (104) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.85 | | tc_Arrow__Order__Mirabelle_Oalt, v_x, all_872_13) = all_872_1 % 192.74/26.85 | | (105) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.85 | | tc_Arrow__Order__Mirabelle_Oalt, v_x, all_872_12) = all_872_7 % 192.74/26.85 | | (106) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.85 | | tc_Arrow__Order__Mirabelle_Oalt, all_872_13, v_x) = all_872_9 % 192.74/26.85 | | (107) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.85 | | tc_Arrow__Order__Mirabelle_Oalt, all_872_13, all_872_12) = % 192.74/26.85 | | all_872_11 % 192.74/26.85 | | (108) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.85 | | tc_Arrow__Order__Mirabelle_Oalt, all_872_12, v_x) = all_872_3 % 192.74/26.85 | | (109) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.85 | | tc_Arrow__Order__Mirabelle_Oalt, all_872_12, all_872_13) = % 192.74/26.85 | | all_872_5 % 192.74/26.85 | | (110) ~ (all_872_12 = v_y) | ~ (all_872_13 = v_x) % 192.74/26.85 | | (111) ~ (all_872_12 = v_x) | ~ (all_872_13 = v_y) % 192.74/26.85 | | (112) ~ (all_872_10 = 0) | all_872_12 = v_y | all_872_13 = v_y % 192.74/26.85 | | (113) ~ (all_872_8 = 0) | ~ (all_872_12 = v_y) | all_872_13 = v_y % 192.74/26.85 | | (114) ~ (all_872_6 = 0) | ~ (all_872_13 = v_y) | all_872_12 = v_y % 192.74/26.85 | | (115) ~ (all_872_4 = 0) | all_872_12 = v_y | all_872_13 = v_y % 192.74/26.85 | | (116) ~ (all_872_2 = 0) | ~ (all_872_13 = v_y) | all_872_12 = v_y % 192.74/26.85 | | (117) ~ (all_872_0 = 0) | ~ (all_872_12 = v_y) | all_872_13 = v_y % 192.74/26.85 | | % 192.74/26.85 | | REDUCE: (90), (103) imply: % 192.74/26.85 | | (118) c_member(all_622_1, all_872_1, v_L) = all_872_0 % 192.74/26.85 | | % 192.74/26.85 | | REDUCE: (90), (102) imply: % 192.74/26.85 | | (119) c_member(all_622_1, all_872_3, v_L) = all_872_2 % 192.74/26.85 | | % 192.74/26.85 | | REDUCE: (90), (101) imply: % 192.74/26.85 | | (120) c_member(all_622_1, all_872_5, v_L) = all_872_4 % 192.74/26.85 | | % 192.74/26.86 | | REDUCE: (90), (100) imply: % 192.74/26.86 | | (121) c_member(all_622_1, all_872_7, v_L) = all_872_6 % 192.74/26.86 | | % 192.74/26.86 | | REDUCE: (90), (99) imply: % 192.74/26.86 | | (122) c_member(all_622_1, all_872_9, v_L) = all_872_8 % 192.74/26.86 | | % 192.74/26.86 | | REDUCE: (90), (98) imply: % 192.74/26.86 | | (123) c_member(all_622_1, all_872_11, v_L) = all_872_10 % 192.74/26.86 | | % 192.74/26.86 | | GROUND_INST: instantiating (3) with v_L, all_872_11, all_622_1, all_872_10, % 192.74/26.86 | | simplifying with (17), (91), (97), (123) gives: % 192.74/26.86 | | (124) all_872_10 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 192.74/26.86 | | hBOOL(v0) = v1 & hAPP(v_L, all_872_11) = v0 & $i(v0)) % 192.74/26.86 | | % 192.74/26.86 | | GROUND_INST: instantiating (45) with v_x, all_872_13, all_872_1, simplifying % 192.74/26.86 | | with (16), (95), (104) gives: % 192.74/26.86 | | (125) all_872_13 = v_x | ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 192.74/26.86 | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.86 | | tc_Arrow__Order__Mirabelle_Oalt, all_872_13, v_x) = v1 & % 192.74/26.86 | | c_member(all_676_0, v1, v_L) = v2 & c_member(all_676_0, % 192.74/26.86 | | all_872_1, v_L) = v0 & $i(v1) & (v2 = 0 | v0 = 0)) % 192.74/26.86 | | % 192.74/26.86 | | GROUND_INST: instantiating (45) with v_x, all_872_12, all_872_7, simplifying % 192.74/26.86 | | with (16), (96), (105) gives: % 192.74/26.86 | | (126) all_872_12 = v_x | ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 192.74/26.86 | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.86 | | tc_Arrow__Order__Mirabelle_Oalt, all_872_12, v_x) = v1 & % 192.74/26.86 | | c_member(all_676_0, v1, v_L) = v2 & c_member(all_676_0, % 192.74/26.86 | | all_872_7, v_L) = v0 & $i(v1) & (v2 = 0 | v0 = 0)) % 192.74/26.86 | | % 192.74/26.86 | | GROUND_INST: instantiating (45) with all_872_13, v_x, all_872_9, simplifying % 192.74/26.86 | | with (16), (95), (106) gives: % 192.74/26.86 | | (127) all_872_13 = v_x | ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 192.74/26.86 | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.86 | | tc_Arrow__Order__Mirabelle_Oalt, v_x, all_872_13) = v1 & % 192.74/26.86 | | c_member(all_676_0, v1, v_L) = v2 & c_member(all_676_0, % 192.74/26.86 | | all_872_9, v_L) = v0 & $i(v1) & (v2 = 0 | v0 = 0)) % 192.74/26.86 | | % 192.74/26.86 | | GROUND_INST: instantiating (45) with all_872_13, all_872_12, all_872_11, % 192.74/26.86 | | simplifying with (95), (96), (107) gives: % 192.74/26.86 | | (128) all_872_12 = all_872_13 | ? [v0: any] : ? [v1: $i] : ? [v2: any] % 192.74/26.86 | | : (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.86 | | tc_Arrow__Order__Mirabelle_Oalt, all_872_12, all_872_13) = v1 & % 192.74/26.86 | | c_member(all_676_0, v1, v_L) = v2 & c_member(all_676_0, % 192.74/26.86 | | all_872_11, v_L) = v0 & $i(v1) & (v2 = 0 | v0 = 0)) % 192.74/26.86 | | % 192.74/26.86 | | GROUND_INST: instantiating (45) with all_872_12, v_x, all_872_3, simplifying % 192.74/26.86 | | with (16), (96), (108) gives: % 192.74/26.86 | | (129) all_872_12 = v_x | ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 192.74/26.86 | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.86 | | tc_Arrow__Order__Mirabelle_Oalt, v_x, all_872_12) = v1 & % 192.74/26.86 | | c_member(all_676_0, v1, v_L) = v2 & c_member(all_676_0, % 192.74/26.86 | | all_872_3, v_L) = v0 & $i(v1) & (v2 = 0 | v0 = 0)) % 192.74/26.86 | | % 192.74/26.86 | | GROUND_INST: instantiating (45) with all_872_12, all_872_13, all_872_5, % 192.74/26.86 | | simplifying with (95), (96), (109) gives: % 192.74/26.86 | | (130) all_872_12 = all_872_13 | ? [v0: any] : ? [v1: $i] : ? [v2: any] % 192.74/26.86 | | : (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.86 | | tc_Arrow__Order__Mirabelle_Oalt, all_872_13, all_872_12) = v1 & % 192.74/26.86 | | c_member(all_676_0, v1, v_L) = v2 & c_member(all_676_0, % 192.74/26.86 | | all_872_5, v_L) = v0 & $i(v1) & (v2 = 0 | v0 = 0)) % 192.74/26.86 | | % 192.74/26.86 | | BETA: splitting (110) gives: % 192.74/26.86 | | % 192.74/26.86 | | Case 1: % 192.74/26.86 | | | % 192.74/26.86 | | | (131) ~ (all_872_12 = v_y) % 192.74/26.86 | | | % 192.74/26.86 | | | REF_CLOSE: (20), (21), (89), (94), (105), (106), (107), (109), (111), % 192.74/26.86 | | | (112), (114), (115), (116), (119), (120), (121), (122), (123), % 192.74/26.86 | | | (124), (126), (128), (129), (130), (131) are inconsistent by % 192.74/26.86 | | | sub-proof #19. % 192.74/26.86 | | | % 192.74/26.86 | | Case 2: % 192.74/26.86 | | | % 192.74/26.86 | | | (132) all_872_12 = v_y % 192.74/26.86 | | | (133) ~ (all_872_13 = v_x) % 192.74/26.86 | | | % 192.74/26.86 | | | REDUCE: (94), (132) imply: % 192.74/26.86 | | | (134) ~ (all_872_13 = v_y) % 192.74/26.86 | | | % 192.74/26.86 | | | SIMP: (134) implies: % 192.74/26.86 | | | (135) ~ (all_872_13 = v_y) % 192.74/26.86 | | | % 192.74/26.86 | | | BETA: splitting (117) gives: % 192.74/26.86 | | | % 192.74/26.86 | | | Case 1: % 192.74/26.86 | | | | % 192.74/26.86 | | | | (136) ~ (all_872_0 = 0) % 192.74/26.86 | | | | % 192.74/26.86 | | | | BETA: splitting (127) gives: % 192.74/26.86 | | | | % 192.74/26.86 | | | | Case 1: % 192.74/26.86 | | | | | % 192.74/26.86 | | | | | (137) all_872_13 = v_x % 192.74/26.86 | | | | | % 192.74/26.86 | | | | | REDUCE: (133), (137) imply: % 192.74/26.86 | | | | | (138) $false % 192.74/26.86 | | | | | % 192.74/26.86 | | | | | CLOSE: (138) is inconsistent. % 192.74/26.86 | | | | | % 192.74/26.86 | | | | Case 2: % 192.74/26.86 | | | | | % 192.74/26.86 | | | | | (139) ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 192.74/26.86 | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.86 | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, all_872_13) = v1 & % 192.74/26.86 | | | | | c_member(all_676_0, v1, v_L) = v2 & c_member(all_676_0, % 192.74/26.86 | | | | | all_872_9, v_L) = v0 & $i(v1) & (v2 = 0 | v0 = 0)) % 192.74/26.86 | | | | | % 192.74/26.86 | | | | | DELTA: instantiating (139) with fresh symbols all_1164_0, all_1164_1, % 192.74/26.86 | | | | | all_1164_2 gives: % 192.74/26.87 | | | | | (140) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.87 | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, all_872_13) = % 192.74/26.87 | | | | | all_1164_1 & c_member(all_676_0, all_1164_1, v_L) = % 192.74/26.87 | | | | | all_1164_0 & c_member(all_676_0, all_872_9, v_L) = all_1164_2 % 192.74/26.87 | | | | | & $i(all_1164_1) & (all_1164_0 = 0 | all_1164_2 = 0) % 192.74/26.87 | | | | | % 192.74/26.87 | | | | | ALPHA: (140) implies: % 192.74/26.87 | | | | | (141) c_member(all_676_0, all_872_9, v_L) = all_1164_2 % 192.74/26.87 | | | | | % 192.74/26.87 | | | | | REDUCE: (89), (141) imply: % 192.74/26.87 | | | | | (142) c_member(all_622_1, all_872_9, v_L) = all_1164_2 % 192.74/26.87 | | | | | % 192.74/26.87 | | | | | BETA: splitting (113) gives: % 192.74/26.87 | | | | | % 192.74/26.87 | | | | | Case 1: % 192.74/26.87 | | | | | | % 192.74/26.87 | | | | | | (143) ~ (all_872_8 = 0) % 192.74/26.87 | | | | | | % 192.74/26.87 | | | | | | BETA: splitting (125) gives: % 192.74/26.87 | | | | | | % 192.74/26.87 | | | | | | Case 1: % 192.74/26.87 | | | | | | | % 192.74/26.87 | | | | | | | (144) all_872_13 = v_x % 192.74/26.87 | | | | | | | % 192.74/26.87 | | | | | | | REDUCE: (133), (144) imply: % 192.74/26.87 | | | | | | | (145) $false % 192.74/26.87 | | | | | | | % 192.74/26.87 | | | | | | | CLOSE: (145) is inconsistent. % 192.74/26.87 | | | | | | | % 192.74/26.87 | | | | | | Case 2: % 192.74/26.87 | | | | | | | % 192.74/26.87 | | | | | | | (146) ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 192.74/26.87 | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.87 | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_13, v_x) = % 192.74/26.87 | | | | | | | v1 & c_member(all_676_0, v1, v_L) = v2 & % 192.74/26.87 | | | | | | | c_member(all_676_0, all_872_1, v_L) = v0 & $i(v1) & (v2 % 192.74/26.87 | | | | | | | = 0 | v0 = 0)) % 192.74/26.87 | | | | | | | % 192.74/26.87 | | | | | | | DELTA: instantiating (146) with fresh symbols all_1174_0, % 192.74/26.87 | | | | | | | all_1174_1, all_1174_2 gives: % 192.74/26.87 | | | | | | | (147) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.87 | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_13, v_x) = % 192.74/26.87 | | | | | | | all_1174_1 & c_member(all_676_0, all_1174_1, v_L) = % 192.74/26.87 | | | | | | | all_1174_0 & c_member(all_676_0, all_872_1, v_L) = % 192.74/26.87 | | | | | | | all_1174_2 & $i(all_1174_1) & (all_1174_0 = 0 | % 192.74/26.87 | | | | | | | all_1174_2 = 0) % 192.74/26.87 | | | | | | | % 192.74/26.87 | | | | | | | ALPHA: (147) implies: % 192.74/26.87 | | | | | | | (148) c_member(all_676_0, all_872_1, v_L) = all_1174_2 % 192.74/26.87 | | | | | | | (149) c_member(all_676_0, all_1174_1, v_L) = all_1174_0 % 192.74/26.87 | | | | | | | (150) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.87 | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_13, v_x) = % 192.74/26.87 | | | | | | | all_1174_1 % 192.74/26.87 | | | | | | | (151) all_1174_0 = 0 | all_1174_2 = 0 % 192.74/26.87 | | | | | | | % 192.74/26.87 | | | | | | | REDUCE: (89), (149) imply: % 192.74/26.87 | | | | | | | (152) c_member(all_622_1, all_1174_1, v_L) = all_1174_0 % 192.74/26.87 | | | | | | | % 192.74/26.87 | | | | | | | REDUCE: (89), (148) imply: % 192.74/26.87 | | | | | | | (153) c_member(all_622_1, all_872_1, v_L) = all_1174_2 % 192.74/26.87 | | | | | | | % 192.74/26.87 | | | | | | | GROUND_INST: instantiating (20) with all_872_8, all_1164_2, v_L, % 192.74/26.87 | | | | | | | all_872_9, all_622_1, simplifying with (122), (142) % 192.74/26.87 | | | | | | | gives: % 192.74/26.87 | | | | | | | (154) all_1164_2 = all_872_8 % 192.74/26.87 | | | | | | | % 192.74/26.87 | | | | | | | GROUND_INST: instantiating (20) with all_872_0, all_1174_2, v_L, % 192.74/26.87 | | | | | | | all_872_1, all_622_1, simplifying with (118), (153) % 192.74/26.87 | | | | | | | gives: % 192.74/26.87 | | | | | | | (155) all_1174_2 = all_872_0 % 192.74/26.87 | | | | | | | % 192.74/26.87 | | | | | | | GROUND_INST: instantiating (21) with all_872_9, all_1174_1, v_x, % 192.74/26.87 | | | | | | | all_872_13, tc_Arrow__Order__Mirabelle_Oalt, % 192.74/26.87 | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with % 192.74/26.87 | | | | | | | (106), (150) gives: % 192.74/26.87 | | | | | | | (156) all_1174_1 = all_872_9 % 192.74/26.87 | | | | | | | % 192.74/26.87 | | | | | | | REDUCE: (152), (156) imply: % 192.74/26.87 | | | | | | | (157) c_member(all_622_1, all_872_9, v_L) = all_1174_0 % 192.74/26.87 | | | | | | | % 192.74/26.87 | | | | | | | BETA: splitting (151) gives: % 192.74/26.87 | | | | | | | % 192.74/26.87 | | | | | | | Case 1: % 192.74/26.87 | | | | | | | | % 192.74/26.87 | | | | | | | | (158) all_1174_0 = 0 % 192.74/26.87 | | | | | | | | % 192.74/26.87 | | | | | | | | REDUCE: (157), (158) imply: % 192.74/26.87 | | | | | | | | (159) c_member(all_622_1, all_872_9, v_L) = 0 % 192.74/26.87 | | | | | | | | % 192.74/26.87 | | | | | | | | GROUND_INST: instantiating (20) with all_872_8, 0, v_L, % 192.74/26.87 | | | | | | | | all_872_9, all_622_1, simplifying with (122), (159) % 192.74/26.87 | | | | | | | | gives: % 192.74/26.87 | | | | | | | | (160) all_872_8 = 0 % 192.74/26.87 | | | | | | | | % 192.74/26.87 | | | | | | | | REDUCE: (143), (160) imply: % 192.74/26.87 | | | | | | | | (161) $false % 192.74/26.87 | | | | | | | | % 192.74/26.87 | | | | | | | | CLOSE: (161) is inconsistent. % 192.74/26.87 | | | | | | | | % 192.74/26.87 | | | | | | | Case 2: % 192.74/26.87 | | | | | | | | % 192.74/26.87 | | | | | | | | (162) all_1174_2 = 0 % 192.74/26.87 | | | | | | | | % 192.74/26.87 | | | | | | | | COMBINE_EQS: (155), (162) imply: % 192.74/26.87 | | | | | | | | (163) all_872_0 = 0 % 192.74/26.87 | | | | | | | | % 192.74/26.87 | | | | | | | | REDUCE: (136), (163) imply: % 192.74/26.87 | | | | | | | | (164) $false % 192.74/26.87 | | | | | | | | % 192.74/26.87 | | | | | | | | CLOSE: (164) is inconsistent. % 192.74/26.87 | | | | | | | | % 192.74/26.87 | | | | | | | End of split % 192.74/26.87 | | | | | | | % 192.74/26.87 | | | | | | End of split % 192.74/26.87 | | | | | | % 192.74/26.87 | | | | | Case 2: % 192.74/26.87 | | | | | | % 192.74/26.87 | | | | | | (165) ~ (all_872_12 = v_y) | all_872_13 = v_y % 192.74/26.87 | | | | | | % 192.74/26.87 | | | | | | REF_CLOSE: (20), (21), (89), (94), (105), (106), (107), (109), % 192.74/26.87 | | | | | | (111), (112), (114), (115), (116), (119), (120), (121), % 192.74/26.87 | | | | | | (122), (123), (124), (126), (128), (129), (130), (135), % 192.74/26.87 | | | | | | (165) are inconsistent by sub-proof #18. % 192.74/26.87 | | | | | | % 192.74/26.87 | | | | | End of split % 192.74/26.87 | | | | | % 192.74/26.87 | | | | End of split % 192.74/26.87 | | | | % 192.74/26.87 | | | Case 2: % 193.11/26.87 | | | | % 193.11/26.87 | | | | (166) ~ (all_872_12 = v_y) | all_872_13 = v_y % 193.11/26.87 | | | | % 193.11/26.87 | | | | REF_CLOSE: (20), (21), (89), (94), (105), (106), (107), (109), (111), % 193.11/26.87 | | | | (112), (114), (115), (116), (119), (120), (121), (122), % 193.11/26.87 | | | | (123), (124), (126), (128), (129), (130), (135), (166) are % 193.11/26.87 | | | | inconsistent by sub-proof #18. % 193.11/26.87 | | | | % 193.11/26.87 | | | End of split % 193.11/26.87 | | | % 193.11/26.87 | | End of split % 193.11/26.87 | | % 193.11/26.87 | Case 2: % 193.11/26.87 | | % 193.11/26.88 | | (167) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] : ? [v4: % 193.11/26.88 | | $i] : ? [v5: any] : ? [v6: $i] : ? [v7: any] : ? [v8: $i] : % 193.11/26.88 | | ? [v9: any] : % 193.11/26.88 | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.11/26.88 | | tc_Arrow__Order__Mirabelle_Oalt, v1, v_x) = v6 & % 193.11/26.88 | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.11/26.88 | | tc_Arrow__Order__Mirabelle_Oalt, v0, v1) = v2 & % 193.11/26.88 | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.11/26.88 | | tc_Arrow__Order__Mirabelle_Oalt, v0, v_x) = v4 & % 193.11/26.88 | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.11/26.88 | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v1) = v8 & % 193.11/26.88 | | c_member(all_685_0, v8, v_L) = v9 & c_member(all_685_0, v6, v_L) % 193.11/26.88 | | = v7 & c_member(all_685_0, v4, v_L) = v5 & c_member(all_685_0, % 193.11/26.88 | | v2, v_L) = v3 & $i(v8) & $i(v6) & $i(v4) & $i(v2) & $i(v1) & % 193.11/26.88 | | $i(v0) & ((v9 = 0 & v0 = v_y & ~ (v1 = v_y) & ? [v10: $i] : ? % 193.11/26.88 | | [v11: $i] : ? [v12: any] : ? [v13: $i] : ? [v14: any] : % 193.11/26.88 | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.11/26.88 | | tc_Arrow__Order__Mirabelle_Oalt, v1, v10) = v11 & % 193.11/26.88 | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.11/26.88 | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v10) = v13 & % 193.11/26.88 | | c_member(all_685_0, v13, v_L) = v14 & c_member(all_685_0, % 193.11/26.88 | | v11, v_L) = v12 & $i(v13) & $i(v11) & $i(v10) & ((v12 = 0 % 193.11/26.88 | | & ~ (v14 = 0) & ~ (v10 = v_y)) | (v10 = v_y & v7 = 0) % 193.11/26.88 | | | (v10 = v_y & v1 = v_x)))) | ( ~ (v0 = v_y) & ((v5 = 0 & % 193.11/26.88 | | v1 = v_y & ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : % 193.11/26.88 | | ? [v13: int] : ( ~ (v13 = 0) & ~ (v10 = v_y) & % 193.11/26.88 | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.11/26.88 | | tc_Arrow__Order__Mirabelle_Oalt, v0, v10) = v12 & % 193.11/26.88 | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.11/26.88 | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v10) = v11 & % 193.11/26.88 | | c_member(all_685_0, v12, v_L) = v13 & % 193.11/26.88 | | c_member(all_685_0, v11, v_L) = 0 & $i(v12) & $i(v11) & % 193.11/26.88 | | $i(v10))) | (v3 = 0 & ~ (v1 = v_y) & ? [v10: $i] : ? % 193.11/26.88 | | [v11: $i] : ? [v12: any] : ? [v13: $i] : ? [v14: any] % 193.11/26.88 | | : (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.11/26.88 | | tc_Arrow__Order__Mirabelle_Oalt, v1, v10) = v11 & % 193.11/26.88 | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.11/26.88 | | tc_Arrow__Order__Mirabelle_Oalt, v0, v10) = v13 & % 193.11/26.88 | | c_member(all_685_0, v13, v_L) = v14 & % 193.11/26.88 | | c_member(all_685_0, v11, v_L) = v12 & $i(v13) & $i(v11) % 193.11/26.88 | | & $i(v10) & ((v12 = 0 & ~ (v14 = 0) & ~ (v10 = v_y)) % 193.11/26.88 | | | (v10 = v_y & v7 = 0 & ~ (v5 = 0) & ~ (v0 = v_x)) % 193.11/26.88 | | | (v10 = v_y & v1 = v_x & ~ (v5 = 0) & ~ (v0 = % 193.11/26.88 | | v_x))))))))) % 193.11/26.88 | | % 193.11/26.88 | | DELTA: instantiating (167) with fresh symbols all_872_0, all_872_1, % 193.11/26.88 | | all_872_2, all_872_3, all_872_4, all_872_5, all_872_6, all_872_7, % 193.11/26.88 | | all_872_8, all_872_9 gives: % 193.11/26.88 | | (168) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.11/26.88 | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v_x) = all_872_3 & % 193.11/26.88 | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.11/26.88 | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, all_872_8) = % 193.11/26.88 | | all_872_7 & c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.11/26.88 | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v_x) = all_872_5 & % 193.11/26.88 | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.11/26.88 | | tc_Arrow__Order__Mirabelle_Oalt, v_x, all_872_8) = all_872_1 & % 193.11/26.88 | | c_member(all_685_0, all_872_1, v_L) = all_872_0 & % 193.11/26.88 | | c_member(all_685_0, all_872_3, v_L) = all_872_2 & % 193.11/26.88 | | c_member(all_685_0, all_872_5, v_L) = all_872_4 & % 193.11/26.88 | | c_member(all_685_0, all_872_7, v_L) = all_872_6 & $i(all_872_1) & % 193.11/26.88 | | $i(all_872_3) & $i(all_872_5) & $i(all_872_7) & $i(all_872_8) & % 193.11/26.88 | | $i(all_872_9) & ((all_872_0 = 0 & all_872_9 = v_y & ~ (all_872_8 = % 193.11/26.88 | | v_y) & ? [v0: $i] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] % 193.11/26.88 | | : ? [v4: any] : % 193.11/26.88 | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.11/26.88 | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v0) = v1 & % 193.11/26.88 | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.11/26.88 | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v0) = v3 & % 193.11/26.88 | | c_member(all_685_0, v3, v_L) = v4 & c_member(all_685_0, v1, % 193.11/26.88 | | v_L) = v2 & $i(v3) & $i(v1) & $i(v0) & ((v2 = 0 & ~ (v4 = % 193.11/26.88 | | 0) & ~ (v0 = v_y)) | (v0 = v_y & all_872_2 = 0) | (v0 % 193.11/26.88 | | = v_y & all_872_8 = v_x)))) | ( ~ (all_872_9 = v_y) & % 193.11/26.88 | | ((all_872_4 = 0 & all_872_8 = v_y & ? [v0: $i] : ? [v1: $i] : % 193.11/26.88 | | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & ~ (v0 = v_y) & % 193.11/26.88 | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.11/26.88 | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v0) = v2 & % 193.11/26.88 | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.11/26.88 | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v0) = v1 & % 193.11/26.88 | | c_member(all_685_0, v2, v_L) = v3 & c_member(all_685_0, % 193.11/26.88 | | v1, v_L) = 0 & $i(v2) & $i(v1) & $i(v0))) | (all_872_6 % 193.11/26.88 | | = 0 & ~ (all_872_8 = v_y) & ? [v0: $i] : ? [v1: $i] : ? % 193.11/26.88 | | [v2: any] : ? [v3: $i] : ? [v4: any] : % 193.11/26.88 | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.11/26.88 | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v0) = v1 & % 193.11/26.88 | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.11/26.88 | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v0) = v3 & % 193.11/26.88 | | c_member(all_685_0, v3, v_L) = v4 & c_member(all_685_0, % 193.11/26.88 | | v1, v_L) = v2 & $i(v3) & $i(v1) & $i(v0) & ((v2 = 0 & % 193.11/26.88 | | ~ (v4 = 0) & ~ (v0 = v_y)) | (v0 = v_y & all_872_2 = % 193.11/26.88 | | 0 & ~ (all_872_4 = 0) & ~ (all_872_9 = v_x)) | (v0 % 193.11/26.88 | | = v_y & all_872_8 = v_x & ~ (all_872_4 = 0) & ~ % 193.11/26.88 | | (all_872_9 = v_x)))))))) % 193.11/26.88 | | % 193.11/26.88 | | ALPHA: (168) implies: % 193.11/26.88 | | (169) $i(all_872_9) % 193.11/26.88 | | (170) $i(all_872_8) % 193.11/26.88 | | (171) $i(all_872_7) % 193.11/26.88 | | (172) $i(all_872_5) % 193.11/26.88 | | (173) $i(all_872_3) % 193.11/26.88 | | (174) $i(all_872_1) % 193.11/26.88 | | (175) c_member(all_685_0, all_872_7, v_L) = all_872_6 % 193.11/26.88 | | (176) c_member(all_685_0, all_872_5, v_L) = all_872_4 % 193.11/26.88 | | (177) c_member(all_685_0, all_872_3, v_L) = all_872_2 % 193.11/26.88 | | (178) c_member(all_685_0, all_872_1, v_L) = all_872_0 % 193.11/26.88 | | (179) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.11/26.88 | | tc_Arrow__Order__Mirabelle_Oalt, v_x, all_872_8) = all_872_1 % 193.11/26.88 | | (180) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.11/26.88 | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v_x) = all_872_5 % 193.11/26.88 | | (181) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.11/26.88 | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, all_872_8) = % 193.11/26.88 | | all_872_7 % 193.11/26.88 | | (182) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.11/26.88 | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v_x) = all_872_3 % 193.16/26.89 | | (183) (all_872_0 = 0 & all_872_9 = v_y & ~ (all_872_8 = v_y) & ? [v0: % 193.16/26.89 | | $i] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ? [v4: any] : % 193.16/26.89 | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.16/26.89 | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v0) = v1 & % 193.16/26.89 | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.16/26.89 | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v0) = v3 & % 193.16/26.89 | | c_member(all_685_0, v3, v_L) = v4 & c_member(all_685_0, v1, % 193.16/26.89 | | v_L) = v2 & $i(v3) & $i(v1) & $i(v0) & ((v2 = 0 & ~ (v4 = 0) % 193.16/26.89 | | & ~ (v0 = v_y)) | (v0 = v_y & all_872_2 = 0) | (v0 = v_y & % 193.16/26.89 | | all_872_8 = v_x)))) | ( ~ (all_872_9 = v_y) & ((all_872_4 = % 193.16/26.89 | | 0 & all_872_8 = v_y & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] % 193.16/26.89 | | : ? [v3: int] : ( ~ (v3 = 0) & ~ (v0 = v_y) & % 193.16/26.89 | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.16/26.89 | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v0) = v2 & % 193.16/26.89 | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.16/26.89 | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v0) = v1 & % 193.16/26.89 | | c_member(all_685_0, v2, v_L) = v3 & c_member(all_685_0, v1, % 193.16/26.89 | | v_L) = 0 & $i(v2) & $i(v1) & $i(v0))) | (all_872_6 = 0 & % 193.16/26.89 | | ~ (all_872_8 = v_y) & ? [v0: $i] : ? [v1: $i] : ? [v2: % 193.16/26.89 | | any] : ? [v3: $i] : ? [v4: any] : % 193.16/26.89 | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.16/26.89 | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v0) = v1 & % 193.16/26.89 | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.16/26.89 | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v0) = v3 & % 193.16/26.89 | | c_member(all_685_0, v3, v_L) = v4 & c_member(all_685_0, v1, % 193.16/26.89 | | v_L) = v2 & $i(v3) & $i(v1) & $i(v0) & ((v2 = 0 & ~ (v4 % 193.16/26.89 | | = 0) & ~ (v0 = v_y)) | (v0 = v_y & all_872_2 = 0 & % 193.16/26.89 | | ~ (all_872_4 = 0) & ~ (all_872_9 = v_x)) | (v0 = v_y & % 193.16/26.89 | | all_872_8 = v_x & ~ (all_872_4 = 0) & ~ (all_872_9 = % 193.16/26.89 | | v_x))))))) % 193.16/26.89 | | % 193.16/26.89 | | REDUCE: (90), (178) imply: % 193.16/26.89 | | (184) c_member(all_622_1, all_872_1, v_L) = all_872_0 % 193.16/26.89 | | % 193.16/26.89 | | REDUCE: (90), (177) imply: % 193.16/26.89 | | (185) c_member(all_622_1, all_872_3, v_L) = all_872_2 % 193.16/26.89 | | % 193.16/26.89 | | REDUCE: (90), (176) imply: % 193.16/26.89 | | (186) c_member(all_622_1, all_872_5, v_L) = all_872_4 % 193.16/26.89 | | % 193.16/26.89 | | REDUCE: (90), (175) imply: % 193.16/26.89 | | (187) c_member(all_622_1, all_872_7, v_L) = all_872_6 % 193.16/26.89 | | % 193.16/26.89 | | GROUND_INST: instantiating (3) with v_L, all_872_7, all_622_1, all_872_6, % 193.16/26.89 | | simplifying with (17), (91), (171), (187) gives: % 193.16/26.89 | | (188) all_872_6 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 193.16/26.89 | | hBOOL(v0) = v1 & hAPP(v_L, all_872_7) = v0 & $i(v0)) % 193.16/26.89 | | % 193.16/26.89 | | GROUND_INST: instantiating (3) with v_L, all_872_5, all_622_1, all_872_4, % 193.16/26.89 | | simplifying with (17), (91), (172), (186) gives: % 193.16/26.89 | | (189) all_872_4 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 193.16/26.89 | | hBOOL(v0) = v1 & hAPP(v_L, all_872_5) = v0 & $i(v0)) % 193.16/26.89 | | % 193.16/26.89 | | GROUND_INST: instantiating (3) with v_L, all_872_3, all_622_1, all_872_2, % 193.16/26.89 | | simplifying with (17), (91), (173), (185) gives: % 193.16/26.89 | | (190) all_872_2 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 193.16/26.89 | | hBOOL(v0) = v1 & hAPP(v_L, all_872_3) = v0 & $i(v0)) % 193.16/26.89 | | % 193.16/26.89 | | GROUND_INST: instantiating (3) with v_L, all_872_1, all_622_1, all_872_0, % 193.16/26.89 | | simplifying with (17), (91), (174), (184) gives: % 193.16/26.89 | | (191) all_872_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 193.16/26.89 | | hBOOL(v0) = v1 & hAPP(v_L, all_872_1) = v0 & $i(v0)) % 193.16/26.89 | | % 193.16/26.89 | | GROUND_INST: instantiating (45) with v_x, all_872_8, all_872_1, simplifying % 193.16/26.89 | | with (16), (170), (179) gives: % 193.16/26.89 | | (192) all_872_8 = v_x | ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 193.16/26.89 | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.16/26.89 | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v_x) = v1 & % 193.16/26.89 | | c_member(all_676_0, v1, v_L) = v2 & c_member(all_676_0, % 193.16/26.89 | | all_872_1, v_L) = v0 & $i(v1) & (v2 = 0 | v0 = 0)) % 193.16/26.89 | | % 193.16/26.89 | | GROUND_INST: instantiating (44) with v_x, all_872_8, all_872_1, simplifying % 193.16/26.89 | | with (16), (170), (179) gives: % 193.16/26.89 | | (193) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_676_0, all_872_1, v_L) = % 193.16/26.89 | | v0) | ! [v0: $i] : ! [v1: $i] : ( ~ % 193.16/26.89 | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.16/26.89 | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v0) = v1) | ~ $i(v0) | % 193.16/26.89 | | ? [v2: $i] : ? [v3: any] : ? [v4: any] : % 193.16/26.89 | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.16/26.89 | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v0) = v2 & % 193.16/26.89 | | c_member(all_676_0, v2, v_L) = v3 & c_member(all_676_0, v1, % 193.16/26.89 | | v_L) = v4 & $i(v2) & ( ~ (v3 = 0) | v4 = 0))) % 193.16/26.89 | | % 193.16/26.89 | | GROUND_INST: instantiating (45) with all_872_9, v_x, all_872_5, simplifying % 193.16/26.89 | | with (16), (169), (180) gives: % 193.16/26.89 | | (194) all_872_9 = v_x | ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 193.16/26.89 | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.16/26.89 | | tc_Arrow__Order__Mirabelle_Oalt, v_x, all_872_9) = v1 & % 193.16/26.89 | | c_member(all_676_0, v1, v_L) = v2 & c_member(all_676_0, % 193.16/26.89 | | all_872_5, v_L) = v0 & $i(v1) & (v2 = 0 | v0 = 0)) % 193.16/26.89 | | % 193.16/26.89 | | GROUND_INST: instantiating (44) with all_872_9, v_x, all_872_5, simplifying % 193.16/26.89 | | with (16), (169), (180) gives: % 193.16/26.89 | | (195) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_676_0, all_872_5, v_L) = % 193.16/26.89 | | v0) | ! [v0: $i] : ! [v1: $i] : ( ~ % 193.16/26.89 | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.16/26.89 | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v0) = v1) | ~ % 193.16/26.89 | | $i(v0) | ? [v2: $i] : ? [v3: any] : ? [v4: any] : % 193.16/26.89 | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.16/26.89 | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v0) = v2 & % 193.16/26.89 | | c_member(all_676_0, v2, v_L) = v3 & c_member(all_676_0, v1, % 193.16/26.89 | | v_L) = v4 & $i(v2) & ( ~ (v3 = 0) | v4 = 0))) % 193.16/26.89 | | % 193.16/26.89 | | GROUND_INST: instantiating (45) with all_872_9, all_872_8, all_872_7, % 193.16/26.89 | | simplifying with (169), (170), (181) gives: % 193.16/26.89 | | (196) all_872_8 = all_872_9 | ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 193.16/26.89 | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.16/26.89 | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, all_872_9) = v1 & % 193.16/26.89 | | c_member(all_676_0, v1, v_L) = v2 & c_member(all_676_0, % 193.16/26.89 | | all_872_7, v_L) = v0 & $i(v1) & (v2 = 0 | v0 = 0)) % 193.16/26.89 | | % 193.16/26.89 | | GROUND_INST: instantiating (44) with all_872_9, all_872_8, all_872_7, % 193.16/26.89 | | simplifying with (169), (170), (181) gives: % 193.16/26.89 | | (197) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_676_0, all_872_7, v_L) = % 193.16/26.89 | | v0) | ! [v0: $i] : ! [v1: $i] : ( ~ % 193.16/26.89 | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.16/26.89 | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v0) = v1) | ~ % 193.16/26.89 | | $i(v0) | ? [v2: $i] : ? [v3: any] : ? [v4: any] : % 193.16/26.89 | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.16/26.89 | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v0) = v2 & % 193.16/26.89 | | c_member(all_676_0, v2, v_L) = v3 & c_member(all_676_0, v1, % 193.16/26.89 | | v_L) = v4 & $i(v2) & ( ~ (v3 = 0) | v4 = 0))) % 193.16/26.89 | | % 193.16/26.89 | | GROUND_INST: instantiating (45) with all_872_8, v_x, all_872_3, simplifying % 193.16/26.89 | | with (16), (170), (182) gives: % 193.16/26.89 | | (198) all_872_8 = v_x | ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 193.16/26.89 | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.16/26.89 | | tc_Arrow__Order__Mirabelle_Oalt, v_x, all_872_8) = v1 & % 193.16/26.89 | | c_member(all_676_0, v1, v_L) = v2 & c_member(all_676_0, % 193.16/26.89 | | all_872_3, v_L) = v0 & $i(v1) & (v2 = 0 | v0 = 0)) % 193.16/26.89 | | % 193.16/26.89 | | GROUND_INST: instantiating (44) with all_872_8, v_x, all_872_3, simplifying % 193.16/26.89 | | with (16), (170), (182) gives: % 193.16/26.90 | | (199) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_676_0, all_872_3, v_L) = % 193.16/26.90 | | v0) | ! [v0: $i] : ! [v1: $i] : ( ~ % 193.16/26.90 | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.16/26.90 | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v0) = v1) | ~ % 193.16/26.90 | | $i(v0) | ? [v2: $i] : ? [v3: any] : ? [v4: any] : % 193.16/26.90 | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.16/26.90 | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v0) = v2 & % 193.16/26.90 | | c_member(all_676_0, v2, v_L) = v3 & c_member(all_676_0, v1, % 193.16/26.90 | | v_L) = v4 & $i(v2) & ( ~ (v3 = 0) | v4 = 0))) % 193.16/26.90 | | % 193.16/26.90 | | BETA: splitting (183) gives: % 193.16/26.90 | | % 193.16/26.90 | | Case 1: % 193.16/26.90 | | | % 193.16/26.90 | | | (200) all_872_0 = 0 & all_872_9 = v_y & ~ (all_872_8 = v_y) & ? [v0: % 193.16/26.90 | | | $i] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ? [v4: any] : % 193.16/26.90 | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.16/26.90 | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v0) = v1 & % 193.16/26.90 | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.16/26.90 | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v0) = v3 & % 193.16/26.90 | | | c_member(all_685_0, v3, v_L) = v4 & c_member(all_685_0, v1, % 193.16/26.90 | | | v_L) = v2 & $i(v3) & $i(v1) & $i(v0) & ((v2 = 0 & ~ (v4 = 0) % 193.16/26.90 | | | & ~ (v0 = v_y)) | (v0 = v_y & all_872_2 = 0) | (v0 = v_y & % 193.16/26.90 | | | all_872_8 = v_x))) % 193.16/26.90 | | | % 193.16/26.90 | | | ALPHA: (200) implies: % 193.16/26.90 | | | (201) all_872_9 = v_y % 193.16/26.90 | | | (202) all_872_0 = 0 % 193.16/26.90 | | | (203) ~ (all_872_8 = v_y) % 193.16/26.90 | | | (204) ? [v0: $i] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ? [v4: % 193.16/26.90 | | | any] : (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.16/26.90 | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v0) = v1 & % 193.16/26.90 | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.16/26.90 | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v0) = v3 & % 193.16/26.90 | | | c_member(all_685_0, v3, v_L) = v4 & c_member(all_685_0, v1, % 193.16/26.90 | | | v_L) = v2 & $i(v3) & $i(v1) & $i(v0) & ((v2 = 0 & ~ (v4 = 0) % 193.16/26.90 | | | & ~ (v0 = v_y)) | (v0 = v_y & all_872_2 = 0) | (v0 = v_y & % 193.16/26.90 | | | all_872_8 = v_x))) % 193.16/26.90 | | | % 193.16/26.90 | | | DELTA: instantiating (204) with fresh symbols all_1080_0, all_1080_1, % 193.16/26.90 | | | all_1080_2, all_1080_3, all_1080_4 gives: % 193.16/26.90 | | | (205) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.16/26.90 | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, all_1080_4) = % 193.16/26.90 | | | all_1080_3 & % 193.16/26.90 | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.16/26.90 | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, all_1080_4) = all_1080_1 % 193.16/26.90 | | | & c_member(all_685_0, all_1080_1, v_L) = all_1080_0 & % 193.16/26.90 | | | c_member(all_685_0, all_1080_3, v_L) = all_1080_2 & % 193.16/26.90 | | | $i(all_1080_1) & $i(all_1080_3) & $i(all_1080_4) & ((all_1080_2 = % 193.16/26.90 | | | 0 & ~ (all_1080_0 = 0) & ~ (all_1080_4 = v_y)) | % 193.16/26.90 | | | (all_1080_4 = v_y & all_872_2 = 0) | (all_1080_4 = v_y & % 193.16/26.90 | | | all_872_8 = v_x)) % 193.16/26.90 | | | % 193.16/26.90 | | | ALPHA: (205) implies: % 193.16/26.90 | | | (206) $i(all_1080_4) % 193.16/26.90 | | | (207) c_member(all_685_0, all_1080_3, v_L) = all_1080_2 % 193.16/26.90 | | | (208) c_member(all_685_0, all_1080_1, v_L) = all_1080_0 % 193.16/26.90 | | | (209) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.16/26.90 | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, all_1080_4) = all_1080_1 % 193.16/26.90 | | | (210) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.16/26.90 | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, all_1080_4) = % 193.16/26.90 | | | all_1080_3 % 193.16/26.90 | | | (211) (all_1080_2 = 0 & ~ (all_1080_0 = 0) & ~ (all_1080_4 = v_y)) | % 193.16/26.90 | | | (all_1080_4 = v_y & all_872_2 = 0) | (all_1080_4 = v_y & % 193.16/26.90 | | | all_872_8 = v_x) % 193.16/26.90 | | | % 193.16/26.90 | | | REDUCE: (181), (201) imply: % 193.16/26.90 | | | (212) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.16/26.90 | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, all_872_8) = all_872_7 % 193.16/26.90 | | | % 193.16/26.90 | | | REDUCE: (180), (201) imply: % 193.16/26.90 | | | (213) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.16/26.90 | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v_x) = all_872_5 % 193.16/26.90 | | | % 193.16/26.90 | | | REDUCE: (90), (208) imply: % 193.16/26.90 | | | (214) c_member(all_622_1, all_1080_1, v_L) = all_1080_0 % 193.16/26.90 | | | % 193.16/26.90 | | | REDUCE: (90), (207) imply: % 193.16/26.90 | | | (215) c_member(all_622_1, all_1080_3, v_L) = all_1080_2 % 193.16/26.90 | | | % 193.16/26.90 | | | REDUCE: (184), (202) imply: % 193.16/26.90 | | | (216) c_member(all_622_1, all_872_1, v_L) = 0 % 193.16/26.90 | | | % 193.16/26.90 | | | REDUCE: (169), (201) imply: % 193.16/26.90 | | | (217) $i(v_y) % 193.16/26.90 | | | % 193.16/26.90 | | | BETA: splitting (193) gives: % 193.16/26.90 | | | % 193.16/26.90 | | | Case 1: % 193.16/26.90 | | | | % 193.16/26.90 | | | | (218) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_676_0, all_872_1, % 193.16/26.90 | | | | v_L) = v0) % 193.16/26.90 | | | | % 193.16/26.90 | | | | DELTA: instantiating (218) with fresh symbol all_1151_0 gives: % 193.16/26.90 | | | | (219) ~ (all_1151_0 = 0) & c_member(all_676_0, all_872_1, v_L) = % 193.16/26.90 | | | | all_1151_0 % 193.16/26.90 | | | | % 193.16/26.90 | | | | REF_CLOSE: (20), (89), (216), (219) are inconsistent by sub-proof #17. % 193.16/26.90 | | | | % 193.16/26.90 | | | Case 2: % 193.16/26.90 | | | | % 193.16/26.90 | | | | (220) ! [v0: $i] : ! [v1: $i] : ( ~ % 193.16/26.90 | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.16/26.90 | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v0) = v1) | ~ % 193.16/26.90 | | | | $i(v0) | ? [v2: $i] : ? [v3: any] : ? [v4: any] : % 193.16/26.90 | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.16/26.90 | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v0) = v2 & % 193.16/26.90 | | | | c_member(all_676_0, v2, v_L) = v3 & c_member(all_676_0, v1, % 193.16/26.90 | | | | v_L) = v4 & $i(v2) & ( ~ (v3 = 0) | v4 = 0))) % 193.16/26.90 | | | | % 193.16/26.90 | | | | GROUND_INST: instantiating (220) with all_872_8, all_872_1, simplifying % 193.16/26.90 | | | | with (170), (179) gives: % 193.16/26.90 | | | | (221) ? [v0: $i] : ? [v1: any] : ? [v2: any] : % 193.16/26.90 | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.16/26.90 | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, all_872_8) = v0 % 193.16/26.90 | | | | & c_member(all_676_0, v0, v_L) = v1 & c_member(all_676_0, % 193.16/26.90 | | | | all_872_1, v_L) = v2 & $i(v0) & ( ~ (v1 = 0) | v2 = 0)) % 193.16/26.90 | | | | % 193.16/26.90 | | | | DELTA: instantiating (221) with fresh symbols all_1086_0, all_1086_1, % 193.16/26.90 | | | | all_1086_2 gives: % 193.16/26.90 | | | | (222) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.16/26.90 | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, all_872_8) = % 193.16/26.90 | | | | all_1086_2 & c_member(all_676_0, all_1086_2, v_L) = all_1086_1 % 193.16/26.90 | | | | & c_member(all_676_0, all_872_1, v_L) = all_1086_0 & % 193.16/26.90 | | | | $i(all_1086_2) & ( ~ (all_1086_1 = 0) | all_1086_0 = 0) % 193.16/26.90 | | | | % 193.16/26.90 | | | | ALPHA: (222) implies: % 193.16/26.90 | | | | (223) c_member(all_676_0, all_872_1, v_L) = all_1086_0 % 193.16/26.90 | | | | (224) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.16/26.90 | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, all_872_8) = % 193.16/26.90 | | | | all_1086_2 % 193.16/26.90 | | | | % 193.16/26.90 | | | | REDUCE: (89), (223) imply: % 193.16/26.90 | | | | (225) c_member(all_622_1, all_872_1, v_L) = all_1086_0 % 193.16/26.90 | | | | % 193.16/26.90 | | | | BETA: splitting (194) gives: % 193.16/26.90 | | | | % 193.16/26.90 | | | | Case 1: % 193.16/26.90 | | | | | % 193.16/26.90 | | | | | (226) all_872_9 = v_x % 193.16/26.90 | | | | | % 193.16/26.90 | | | | | COMBINE_EQS: (201), (226) imply: % 193.16/26.90 | | | | | (227) v_x = v_y % 193.16/26.90 | | | | | % 193.16/26.90 | | | | | SIMP: (227) implies: % 193.16/26.90 | | | | | (228) v_x = v_y % 193.16/26.90 | | | | | % 193.16/26.90 | | | | | REDUCE: (13), (228) imply: % 193.16/26.90 | | | | | (229) $false % 193.16/26.90 | | | | | % 193.16/26.90 | | | | | CLOSE: (229) is inconsistent. % 193.16/26.90 | | | | | % 193.16/26.90 | | | | Case 2: % 193.16/26.90 | | | | | % 193.16/26.90 | | | | | (230) ~ (all_872_9 = v_x) % 193.16/26.90 | | | | | (231) ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 193.16/26.90 | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.16/26.90 | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, all_872_9) = v1 & % 193.16/26.90 | | | | | c_member(all_676_0, v1, v_L) = v2 & c_member(all_676_0, % 193.16/26.90 | | | | | all_872_5, v_L) = v0 & $i(v1) & (v2 = 0 | v0 = 0)) % 193.16/26.90 | | | | | % 193.16/26.90 | | | | | DELTA: instantiating (231) with fresh symbols all_1091_0, all_1091_1, % 193.16/26.90 | | | | | all_1091_2 gives: % 193.16/26.90 | | | | | (232) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.16/26.90 | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, all_872_9) = % 193.16/26.90 | | | | | all_1091_1 & c_member(all_676_0, all_1091_1, v_L) = % 193.16/26.90 | | | | | all_1091_0 & c_member(all_676_0, all_872_5, v_L) = all_1091_2 % 193.16/26.90 | | | | | & $i(all_1091_1) & (all_1091_0 = 0 | all_1091_2 = 0) % 193.16/26.91 | | | | | % 193.16/26.91 | | | | | ALPHA: (232) implies: % 193.16/26.91 | | | | | (233) c_member(all_676_0, all_872_5, v_L) = all_1091_2 % 193.16/26.91 | | | | | (234) c_member(all_676_0, all_1091_1, v_L) = all_1091_0 % 193.16/26.91 | | | | | (235) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.16/26.91 | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, all_872_9) = % 193.16/26.91 | | | | | all_1091_1 % 193.16/26.91 | | | | | (236) all_1091_0 = 0 | all_1091_2 = 0 % 193.16/26.91 | | | | | % 193.16/26.91 | | | | | REDUCE: (201), (230) imply: % 193.16/26.91 | | | | | (237) ~ (v_x = v_y) % 193.16/26.91 | | | | | % 193.16/26.91 | | | | | REDUCE: (201), (235) imply: % 193.16/26.91 | | | | | (238) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.16/26.91 | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v_y) = all_1091_1 % 193.16/26.91 | | | | | % 193.16/26.91 | | | | | REDUCE: (89), (234) imply: % 193.16/26.91 | | | | | (239) c_member(all_622_1, all_1091_1, v_L) = all_1091_0 % 193.16/26.91 | | | | | % 193.16/26.91 | | | | | REDUCE: (89), (233) imply: % 193.16/26.91 | | | | | (240) c_member(all_622_1, all_872_5, v_L) = all_1091_2 % 193.16/26.91 | | | | | % 193.16/26.91 | | | | | BETA: splitting (196) gives: % 193.16/26.91 | | | | | % 193.16/26.91 | | | | | Case 1: % 193.16/26.91 | | | | | | % 193.16/26.91 | | | | | | (241) all_872_8 = all_872_9 % 193.16/26.91 | | | | | | % 193.16/26.91 | | | | | | COMBINE_EQS: (201), (241) imply: % 193.16/26.91 | | | | | | (242) all_872_8 = v_y % 193.16/26.91 | | | | | | % 193.16/26.91 | | | | | | REDUCE: (203), (242) imply: % 193.16/26.91 | | | | | | (243) $false % 193.16/26.91 | | | | | | % 193.16/26.91 | | | | | | CLOSE: (243) is inconsistent. % 193.16/26.91 | | | | | | % 193.16/26.91 | | | | | Case 2: % 193.16/26.91 | | | | | | % 193.16/26.91 | | | | | | (244) ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 193.16/26.91 | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.16/26.91 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, all_872_9) % 193.16/26.91 | | | | | | = v1 & c_member(all_676_0, v1, v_L) = v2 & % 193.16/26.91 | | | | | | c_member(all_676_0, all_872_7, v_L) = v0 & $i(v1) & (v2 = % 193.16/26.91 | | | | | | 0 | v0 = 0)) % 193.16/26.91 | | | | | | % 193.16/26.91 | | | | | | DELTA: instantiating (244) with fresh symbols all_1096_0, % 193.16/26.91 | | | | | | all_1096_1, all_1096_2 gives: % 193.16/26.91 | | | | | | (245) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.16/26.91 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, all_872_9) = % 193.16/26.91 | | | | | | all_1096_1 & c_member(all_676_0, all_1096_1, v_L) = % 193.16/26.91 | | | | | | all_1096_0 & c_member(all_676_0, all_872_7, v_L) = % 193.16/26.91 | | | | | | all_1096_2 & $i(all_1096_1) & (all_1096_0 = 0 | all_1096_2 % 193.16/26.91 | | | | | | = 0) % 193.16/26.91 | | | | | | % 193.16/26.91 | | | | | | ALPHA: (245) implies: % 193.16/26.91 | | | | | | (246) c_member(all_676_0, all_872_7, v_L) = all_1096_2 % 193.16/26.91 | | | | | | (247) c_member(all_676_0, all_1096_1, v_L) = all_1096_0 % 193.16/26.91 | | | | | | (248) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.16/26.91 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, all_872_9) = % 193.16/26.91 | | | | | | all_1096_1 % 193.16/26.91 | | | | | | (249) all_1096_0 = 0 | all_1096_2 = 0 % 193.16/26.91 | | | | | | % 193.16/26.91 | | | | | | REDUCE: (201), (248) imply: % 193.16/26.91 | | | | | | (250) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.16/26.91 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v_y) = % 193.16/26.91 | | | | | | all_1096_1 % 193.16/26.91 | | | | | | % 193.16/26.91 | | | | | | REDUCE: (89), (247) imply: % 193.16/26.91 | | | | | | (251) c_member(all_622_1, all_1096_1, v_L) = all_1096_0 % 193.16/26.91 | | | | | | % 193.16/26.91 | | | | | | REDUCE: (89), (246) imply: % 193.16/26.91 | | | | | | (252) c_member(all_622_1, all_872_7, v_L) = all_1096_2 % 193.16/26.91 | | | | | | % 193.16/26.91 | | | | | | GROUND_INST: instantiating (20) with all_872_6, all_1096_2, v_L, % 193.16/26.91 | | | | | | all_872_7, all_622_1, simplifying with (187), (252) % 193.16/26.91 | | | | | | gives: % 193.16/26.91 | | | | | | (253) all_1096_2 = all_872_6 % 193.16/26.91 | | | | | | % 193.16/26.91 | | | | | | GROUND_INST: instantiating (20) with all_872_4, all_1091_2, v_L, % 193.16/26.91 | | | | | | all_872_5, all_622_1, simplifying with (186), (240) % 193.16/26.91 | | | | | | gives: % 193.16/26.91 | | | | | | (254) all_1091_2 = all_872_4 % 193.16/26.91 | | | | | | % 193.16/26.91 | | | | | | GROUND_INST: instantiating (20) with 0, all_1086_0, v_L, all_872_1, % 193.16/26.91 | | | | | | all_622_1, simplifying with (216), (225) gives: % 193.16/26.91 | | | | | | (255) all_1086_0 = 0 % 193.16/26.91 | | | | | | % 193.16/26.91 | | | | | | BETA: splitting (189) gives: % 193.16/26.91 | | | | | | % 193.16/26.91 | | | | | | Case 1: % 193.16/26.91 | | | | | | | % 193.16/26.91 | | | | | | | (256) all_872_4 = 0 % 193.16/26.91 | | | | | | | % 193.16/26.91 | | | | | | | REDUCE: (186), (256) imply: % 193.16/26.91 | | | | | | | (257) c_member(all_622_1, all_872_5, v_L) = 0 % 193.27/26.91 | | | | | | | % 193.27/26.91 | | | | | | | BETA: splitting (190) gives: % 193.27/26.91 | | | | | | | % 193.27/26.91 | | | | | | | Case 1: % 193.27/26.91 | | | | | | | | % 193.27/26.91 | | | | | | | | (258) all_872_2 = 0 % 193.27/26.91 | | | | | | | | % 193.27/26.91 | | | | | | | | REDUCE: (185), (258) imply: % 193.27/26.91 | | | | | | | | (259) c_member(all_622_1, all_872_3, v_L) = 0 % 193.27/26.91 | | | | | | | | % 193.27/26.91 | | | | | | | | BETA: splitting (199) gives: % 193.27/26.91 | | | | | | | | % 193.27/26.91 | | | | | | | | Case 1: % 193.27/26.91 | | | | | | | | | % 193.27/26.91 | | | | | | | | | (260) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_676_0, % 193.27/26.91 | | | | | | | | | all_872_3, v_L) = v0) % 193.27/26.91 | | | | | | | | | % 193.27/26.91 | | | | | | | | | DELTA: instantiating (260) with fresh symbol all_1198_0 gives: % 193.27/26.91 | | | | | | | | | (261) ~ (all_1198_0 = 0) & c_member(all_676_0, all_872_3, % 193.27/26.91 | | | | | | | | | v_L) = all_1198_0 % 193.27/26.91 | | | | | | | | | % 193.27/26.91 | | | | | | | | | REF_CLOSE: (20), (89), (259), (261) are inconsistent by % 193.27/26.91 | | | | | | | | | sub-proof #16. % 193.27/26.91 | | | | | | | | | % 193.27/26.91 | | | | | | | | Case 2: % 193.27/26.91 | | | | | | | | | % 193.27/26.91 | | | | | | | | | (262) ! [v0: $i] : ! [v1: $i] : ( ~ % 193.27/26.91 | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.27/26.91 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v0) % 193.27/26.91 | | | | | | | | | = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: any] : % 193.27/26.91 | | | | | | | | | ? [v4: any] : % 193.27/26.91 | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.27/26.91 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v0) = v2 % 193.27/26.91 | | | | | | | | | & c_member(all_676_0, v2, v_L) = v3 & % 193.27/26.91 | | | | | | | | | c_member(all_676_0, v1, v_L) = v4 & $i(v2) & ( ~ % 193.27/26.91 | | | | | | | | | (v3 = 0) | v4 = 0))) % 193.27/26.91 | | | | | | | | | % 193.27/26.91 | | | | | | | | | GROUND_INST: instantiating (262) with v_x, all_872_3, % 193.27/26.91 | | | | | | | | | simplifying with (16), (182) gives: % 193.27/26.91 | | | | | | | | | (263) ? [v0: $i] : ? [v1: any] : ? [v2: any] : % 193.27/26.91 | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.27/26.91 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v_x) = v0 & % 193.27/26.91 | | | | | | | | | c_member(all_676_0, v0, v_L) = v1 & % 193.27/26.91 | | | | | | | | | c_member(all_676_0, all_872_3, v_L) = v2 & $i(v0) & % 193.27/26.91 | | | | | | | | | ( ~ (v1 = 0) | v2 = 0)) % 193.27/26.91 | | | | | | | | | % 193.27/26.91 | | | | | | | | | DELTA: instantiating (263) with fresh symbols all_1199_0, % 193.27/26.91 | | | | | | | | | all_1199_1, all_1199_2 gives: % 193.27/26.91 | | | | | | | | | (264) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.27/26.91 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v_x) = % 193.27/26.91 | | | | | | | | | all_1199_2 & c_member(all_676_0, all_1199_2, v_L) = % 193.27/26.91 | | | | | | | | | all_1199_1 & c_member(all_676_0, all_872_3, v_L) = % 193.27/26.91 | | | | | | | | | all_1199_0 & $i(all_1199_2) & ( ~ (all_1199_1 = 0) | % 193.27/26.91 | | | | | | | | | all_1199_0 = 0) % 193.27/26.91 | | | | | | | | | % 193.27/26.91 | | | | | | | | | ALPHA: (264) implies: % 193.27/26.91 | | | | | | | | | (265) c_member(all_676_0, all_872_3, v_L) = all_1199_0 % 193.27/26.91 | | | | | | | | | % 193.27/26.91 | | | | | | | | | REDUCE: (89), (265) imply: % 193.27/26.91 | | | | | | | | | (266) c_member(all_622_1, all_872_3, v_L) = all_1199_0 % 193.27/26.91 | | | | | | | | | % 193.27/26.91 | | | | | | | | | GROUND_INST: instantiating (20) with 0, all_1199_0, v_L, % 193.27/26.91 | | | | | | | | | all_872_3, all_622_1, simplifying with (259), % 193.27/26.91 | | | | | | | | | (266) gives: % 193.27/26.91 | | | | | | | | | (267) all_1199_0 = 0 % 193.27/26.91 | | | | | | | | | % 193.27/26.91 | | | | | | | | | GROUND_INST: instantiating (fact_wf__not__sym) with all_872_8, % 193.27/26.91 | | | | | | | | | v_x, v_L, tc_Arrow__Order__Mirabelle_Oalt, % 193.27/26.91 | | | | | | | | | all_622_1, all_872_3, simplifying with (15), (16), % 193.27/26.91 | | | | | | | | | (17), (23), (170), (182), (259) gives: % 193.27/26.91 | | | | | | | | | (268) ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 193.27/26.91 | | | | | | | | | (c_Wellfounded_Owf(tc_Arrow__Order__Mirabelle_Oalt, % 193.27/26.91 | | | | | | | | | v_L) = v0 & % 193.27/26.91 | | | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.27/26.91 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, all_872_8) % 193.27/26.91 | | | | | | | | | = v1 & c_member(all_622_1, v1, v_L) = v2 & $i(v1) & % 193.27/26.91 | | | | | | | | | ( ~ (v2 = 0) | ~ (v0 = 0))) % 193.27/26.91 | | | | | | | | | % 193.27/26.91 | | | | | | | | | GROUND_INST: instantiating (44) with v_y, v_x, all_872_5, % 193.27/26.91 | | | | | | | | | simplifying with (16), (213), (217) gives: % 193.27/26.91 | | | | | | | | | (269) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_676_0, % 193.27/26.91 | | | | | | | | | all_872_5, v_L) = v0) | ! [v0: $i] : ! [v1: $i] % 193.27/26.91 | | | | | | | | | : ( ~ % 193.27/26.91 | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.27/26.91 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = v1) % 193.27/26.91 | | | | | | | | | | ~ $i(v0) | ? [v2: $i] : ? [v3: any] : ? [v4: % 193.27/26.91 | | | | | | | | | any] : % 193.27/26.91 | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.27/26.91 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v0) = v2 % 193.27/26.91 | | | | | | | | | & c_member(all_676_0, v2, v_L) = v3 & % 193.27/26.91 | | | | | | | | | c_member(all_676_0, v1, v_L) = v4 & $i(v2) & ( ~ % 193.27/26.91 | | | | | | | | | (v3 = 0) | v4 = 0))) % 193.27/26.91 | | | | | | | | | % 193.27/26.91 | | | | | | | | | GROUND_INST: instantiating (43) with all_872_8, all_1086_2, % 193.27/26.91 | | | | | | | | | simplifying with (170), (224) gives: % 193.27/26.92 | | | | | | | | | (270) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_676_0, % 193.27/26.92 | | | | | | | | | all_1086_2, v_L) = v0) % 193.27/26.92 | | | | | | | | | % 193.27/26.92 | | | | | | | | | GROUND_INST: instantiating (262) with all_872_8, all_1086_2, % 193.27/26.92 | | | | | | | | | simplifying with (170), (224) gives: % 193.27/26.92 | | | | | | | | | (271) ? [v0: $i] : ? [v1: any] : ? [v2: any] : % 193.27/26.92 | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.27/26.92 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, all_872_8) % 193.27/26.92 | | | | | | | | | = v0 & c_member(all_676_0, v0, v_L) = v1 & % 193.27/26.92 | | | | | | | | | c_member(all_676_0, all_1086_2, v_L) = v2 & $i(v0) % 193.27/26.92 | | | | | | | | | & ( ~ (v1 = 0) | v2 = 0)) % 193.27/26.92 | | | | | | | | | % 193.27/26.92 | | | | | | | | | DELTA: instantiating (270) with fresh symbol all_1230_0 gives: % 193.27/26.92 | | | | | | | | | (272) ~ (all_1230_0 = 0) & c_member(all_676_0, all_1086_2, % 193.27/26.92 | | | | | | | | | v_L) = all_1230_0 % 193.27/26.92 | | | | | | | | | % 193.27/26.92 | | | | | | | | | ALPHA: (272) implies: % 193.27/26.92 | | | | | | | | | (273) ~ (all_1230_0 = 0) % 193.27/26.92 | | | | | | | | | (274) c_member(all_676_0, all_1086_2, v_L) = all_1230_0 % 193.27/26.92 | | | | | | | | | % 193.27/26.92 | | | | | | | | | DELTA: instantiating (271) with fresh symbols all_1258_0, % 193.27/26.92 | | | | | | | | | all_1258_1, all_1258_2 gives: % 193.27/26.92 | | | | | | | | | (275) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.27/26.92 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, all_872_8) = % 193.27/26.92 | | | | | | | | | all_1258_2 & c_member(all_676_0, all_1258_2, v_L) = % 193.27/26.92 | | | | | | | | | all_1258_1 & c_member(all_676_0, all_1086_2, v_L) = % 193.27/26.92 | | | | | | | | | all_1258_0 & $i(all_1258_2) & ( ~ (all_1258_1 = 0) | % 193.27/26.92 | | | | | | | | | all_1258_0 = 0) % 193.27/26.92 | | | | | | | | | % 193.27/26.92 | | | | | | | | | ALPHA: (275) implies: % 193.27/26.92 | | | | | | | | | (276) c_member(all_676_0, all_1086_2, v_L) = all_1258_0 % 193.27/26.92 | | | | | | | | | (277) c_member(all_676_0, all_1258_2, v_L) = all_1258_1 % 193.27/26.92 | | | | | | | | | (278) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.27/26.92 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, all_872_8) = % 193.27/26.92 | | | | | | | | | all_1258_2 % 193.27/26.92 | | | | | | | | | (279) ~ (all_1258_1 = 0) | all_1258_0 = 0 % 193.27/26.92 | | | | | | | | | % 193.27/26.92 | | | | | | | | | DELTA: instantiating (268) with fresh symbols all_1266_0, % 193.27/26.92 | | | | | | | | | all_1266_1, all_1266_2 gives: % 193.27/26.92 | | | | | | | | | (280) c_Wellfounded_Owf(tc_Arrow__Order__Mirabelle_Oalt, % 193.27/26.92 | | | | | | | | | v_L) = all_1266_2 & % 193.27/26.92 | | | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.27/26.92 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, all_872_8) = % 193.27/26.92 | | | | | | | | | all_1266_1 & c_member(all_622_1, all_1266_1, v_L) = % 193.27/26.92 | | | | | | | | | all_1266_0 & $i(all_1266_1) & ( ~ (all_1266_0 = 0) | % 193.27/26.92 | | | | | | | | | ~ (all_1266_2 = 0)) % 193.27/26.92 | | | | | | | | | % 193.27/26.92 | | | | | | | | | ALPHA: (280) implies: % 193.27/26.92 | | | | | | | | | (281) c_member(all_622_1, all_1266_1, v_L) = all_1266_0 % 193.27/26.92 | | | | | | | | | (282) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.27/26.92 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, all_872_8) = % 193.27/26.92 | | | | | | | | | all_1266_1 % 193.27/26.92 | | | | | | | | | % 193.27/26.92 | | | | | | | | | REDUCE: (89), (277) imply: % 193.27/26.92 | | | | | | | | | (283) c_member(all_622_1, all_1258_2, v_L) = all_1258_1 % 193.27/26.92 | | | | | | | | | % 193.27/26.92 | | | | | | | | | REDUCE: (89), (276) imply: % 193.27/26.92 | | | | | | | | | (284) c_member(all_622_1, all_1086_2, v_L) = all_1258_0 % 193.27/26.92 | | | | | | | | | % 193.27/26.92 | | | | | | | | | REDUCE: (89), (274) imply: % 193.27/26.92 | | | | | | | | | (285) c_member(all_622_1, all_1086_2, v_L) = all_1230_0 % 193.27/26.92 | | | | | | | | | % 193.27/26.92 | | | | | | | | | BETA: splitting (269) gives: % 193.27/26.92 | | | | | | | | | % 193.27/26.92 | | | | | | | | | Case 1: % 193.27/26.92 | | | | | | | | | | % 193.27/26.92 | | | | | | | | | | (286) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_676_0, % 193.27/26.92 | | | | | | | | | | all_872_5, v_L) = v0) % 193.27/26.92 | | | | | | | | | | % 193.27/26.92 | | | | | | | | | | DELTA: instantiating (286) with fresh symbol all_1124_0 % 193.27/26.92 | | | | | | | | | | gives: % 193.27/26.92 | | | | | | | | | | (287) ~ (all_1124_0 = 0) & c_member(all_676_0, % 193.27/26.92 | | | | | | | | | | all_872_5, v_L) = all_1124_0 % 193.27/26.92 | | | | | | | | | | % 193.27/26.92 | | | | | | | | | | REF_CLOSE: (20), (89), (257), (287) are inconsistent by % 193.27/26.92 | | | | | | | | | | sub-proof #15. % 193.27/26.92 | | | | | | | | | | % 193.27/26.92 | | | | | | | | | Case 2: % 193.27/26.92 | | | | | | | | | | % 193.27/26.92 | | | | | | | | | | (288) ! [v0: $i] : ! [v1: $i] : ( ~ % 193.27/26.92 | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.27/26.92 | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = % 193.27/26.92 | | | | | | | | | | v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: any] : % 193.27/26.92 | | | | | | | | | | ? [v4: any] : % 193.27/26.92 | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.27/26.92 | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v0) = % 193.27/26.92 | | | | | | | | | | v2 & c_member(all_676_0, v2, v_L) = v3 & % 193.27/26.92 | | | | | | | | | | c_member(all_676_0, v1, v_L) = v4 & $i(v2) & ( % 193.27/26.92 | | | | | | | | | | ~ (v3 = 0) | v4 = 0))) % 193.27/26.92 | | | | | | | | | | % 193.27/26.92 | | | | | | | | | | GROUND_INST: instantiating (288) with all_872_8, all_872_7, % 193.27/26.92 | | | | | | | | | | simplifying with (170), (212) gives: % 193.27/26.92 | | | | | | | | | | (289) ? [v0: $i] : ? [v1: any] : ? [v2: any] : % 193.27/26.92 | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.27/26.92 | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, % 193.27/26.92 | | | | | | | | | | all_872_8) = v0 & c_member(all_676_0, v0, v_L) % 193.27/26.92 | | | | | | | | | | = v1 & c_member(all_676_0, all_872_7, v_L) = v2 & % 193.27/26.92 | | | | | | | | | | $i(v0) & ( ~ (v1 = 0) | v2 = 0)) % 193.27/26.92 | | | | | | | | | | % 193.27/26.92 | | | | | | | | | | DELTA: instantiating (289) with fresh symbols all_1288_0, % 193.27/26.92 | | | | | | | | | | all_1288_1, all_1288_2 gives: % 193.27/26.92 | | | | | | | | | | (290) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.27/26.92 | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, all_872_8) % 193.27/26.92 | | | | | | | | | | = all_1288_2 & c_member(all_676_0, all_1288_2, v_L) % 193.27/26.92 | | | | | | | | | | = all_1288_1 & c_member(all_676_0, all_872_7, v_L) % 193.27/26.92 | | | | | | | | | | = all_1288_0 & $i(all_1288_2) & ( ~ (all_1288_1 = % 193.27/26.92 | | | | | | | | | | 0) | all_1288_0 = 0) % 193.27/26.92 | | | | | | | | | | % 193.27/26.92 | | | | | | | | | | ALPHA: (290) implies: % 193.27/26.92 | | | | | | | | | | (291) c_member(all_676_0, all_1288_2, v_L) = all_1288_1 % 193.27/26.92 | | | | | | | | | | (292) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.27/26.92 | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, all_872_8) % 193.27/26.92 | | | | | | | | | | = all_1288_2 % 193.27/26.92 | | | | | | | | | | % 193.27/26.92 | | | | | | | | | | REDUCE: (89), (291) imply: % 193.27/26.92 | | | | | | | | | | (293) c_member(all_622_1, all_1288_2, v_L) = all_1288_1 % 193.27/26.92 | | | | | | | | | | % 193.27/26.92 | | | | | | | | | | GROUND_INST: instantiating (20) with all_1230_0, all_1258_0, % 193.27/26.92 | | | | | | | | | | v_L, all_1086_2, all_622_1, simplifying with % 193.27/26.92 | | | | | | | | | | (284), (285) gives: % 193.27/26.92 | | | | | | | | | | (294) all_1258_0 = all_1230_0 % 193.27/26.92 | | | | | | | | | | % 193.27/26.92 | | | | | | | | | | GROUND_INST: instantiating (21) with all_872_1, all_1288_2, % 193.27/26.92 | | | | | | | | | | all_872_8, v_x, tc_Arrow__Order__Mirabelle_Oalt, % 193.27/26.92 | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with % 193.27/26.92 | | | | | | | | | | (179), (292) gives: % 193.27/26.92 | | | | | | | | | | (295) all_1288_2 = all_872_1 % 193.27/26.92 | | | | | | | | | | % 193.27/26.92 | | | | | | | | | | GROUND_INST: instantiating (21) with all_1266_1, all_1288_2, % 193.27/26.92 | | | | | | | | | | all_872_8, v_x, tc_Arrow__Order__Mirabelle_Oalt, % 193.27/26.92 | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with % 193.27/26.92 | | | | | | | | | | (282), (292) gives: % 193.27/26.92 | | | | | | | | | | (296) all_1288_2 = all_1266_1 % 193.27/26.92 | | | | | | | | | | % 193.27/26.92 | | | | | | | | | | GROUND_INST: instantiating (21) with all_1258_2, all_1288_2, % 193.27/26.92 | | | | | | | | | | all_872_8, v_x, tc_Arrow__Order__Mirabelle_Oalt, % 193.27/26.92 | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with % 193.27/26.92 | | | | | | | | | | (278), (292) gives: % 193.27/26.92 | | | | | | | | | | (297) all_1288_2 = all_1258_2 % 193.27/26.92 | | | | | | | | | | % 193.27/26.92 | | | | | | | | | | COMBINE_EQS: (296), (297) imply: % 193.27/26.92 | | | | | | | | | | (298) all_1266_1 = all_1258_2 % 193.27/26.92 | | | | | | | | | | % 193.27/26.92 | | | | | | | | | | COMBINE_EQS: (295), (296) imply: % 193.27/26.92 | | | | | | | | | | (299) all_1266_1 = all_872_1 % 193.27/26.92 | | | | | | | | | | % 193.27/26.92 | | | | | | | | | | COMBINE_EQS: (298), (299) imply: % 193.27/26.92 | | | | | | | | | | (300) all_1258_2 = all_872_1 % 193.27/26.92 | | | | | | | | | | % 193.27/26.92 | | | | | | | | | | SIMP: (300) implies: % 193.27/26.92 | | | | | | | | | | (301) all_1258_2 = all_872_1 % 193.27/26.92 | | | | | | | | | | % 193.27/26.92 | | | | | | | | | | REDUCE: (293), (295) imply: % 193.32/26.92 | | | | | | | | | | (302) c_member(all_622_1, all_872_1, v_L) = all_1288_1 % 193.32/26.92 | | | | | | | | | | % 193.32/26.92 | | | | | | | | | | REDUCE: (281), (299) imply: % 193.32/26.92 | | | | | | | | | | (303) c_member(all_622_1, all_872_1, v_L) = all_1266_0 % 193.32/26.92 | | | | | | | | | | % 193.32/26.92 | | | | | | | | | | REDUCE: (283), (301) imply: % 193.32/26.92 | | | | | | | | | | (304) c_member(all_622_1, all_872_1, v_L) = all_1258_1 % 193.32/26.92 | | | | | | | | | | % 193.32/26.92 | | | | | | | | | | BETA: splitting (279) gives: % 193.32/26.92 | | | | | | | | | | % 193.32/26.92 | | | | | | | | | | Case 1: % 193.32/26.92 | | | | | | | | | | | % 193.32/26.92 | | | | | | | | | | | (305) ~ (all_1258_1 = 0) % 193.32/26.92 | | | | | | | | | | | % 193.32/26.92 | | | | | | | | | | | GROUND_INST: instantiating (20) with 0, all_1266_0, v_L, % 193.32/26.92 | | | | | | | | | | | all_872_1, all_622_1, simplifying with (216), % 193.32/26.92 | | | | | | | | | | | (303) gives: % 193.32/26.92 | | | | | | | | | | | (306) all_1266_0 = 0 % 193.32/26.92 | | | | | | | | | | | % 193.32/26.92 | | | | | | | | | | | GROUND_INST: instantiating (20) with all_1266_0, all_1288_1, % 193.32/26.92 | | | | | | | | | | | v_L, all_872_1, all_622_1, simplifying with (302), % 193.32/26.92 | | | | | | | | | | | (303) gives: % 193.32/26.92 | | | | | | | | | | | (307) all_1288_1 = all_1266_0 % 193.32/26.92 | | | | | | | | | | | % 193.32/26.92 | | | | | | | | | | | GROUND_INST: instantiating (20) with all_1258_1, all_1288_1, % 193.32/26.92 | | | | | | | | | | | v_L, all_872_1, all_622_1, simplifying with (302), % 193.32/26.92 | | | | | | | | | | | (304) gives: % 193.32/26.92 | | | | | | | | | | | (308) all_1288_1 = all_1258_1 % 193.32/26.92 | | | | | | | | | | | % 193.32/26.92 | | | | | | | | | | | COMBINE_EQS: (307), (308) imply: % 193.32/26.92 | | | | | | | | | | | (309) all_1266_0 = all_1258_1 % 193.32/26.92 | | | | | | | | | | | % 193.32/26.92 | | | | | | | | | | | SIMP: (309) implies: % 193.32/26.92 | | | | | | | | | | | (310) all_1266_0 = all_1258_1 % 193.32/26.92 | | | | | | | | | | | % 193.32/26.92 | | | | | | | | | | | COMBINE_EQS: (306), (310) imply: % 193.32/26.92 | | | | | | | | | | | (311) all_1258_1 = 0 % 193.32/26.92 | | | | | | | | | | | % 193.32/26.92 | | | | | | | | | | | REDUCE: (305), (311) imply: % 193.32/26.92 | | | | | | | | | | | (312) $false % 193.32/26.92 | | | | | | | | | | | % 193.32/26.92 | | | | | | | | | | | CLOSE: (312) is inconsistent. % 193.32/26.92 | | | | | | | | | | | % 193.32/26.92 | | | | | | | | | | Case 2: % 193.32/26.92 | | | | | | | | | | | % 193.32/26.92 | | | | | | | | | | | (313) all_1258_0 = 0 % 193.32/26.92 | | | | | | | | | | | % 193.32/26.92 | | | | | | | | | | | COMBINE_EQS: (294), (313) imply: % 193.32/26.92 | | | | | | | | | | | (314) all_1230_0 = 0 % 193.32/26.92 | | | | | | | | | | | % 193.32/26.92 | | | | | | | | | | | REDUCE: (273), (314) imply: % 193.32/26.92 | | | | | | | | | | | (315) $false % 193.32/26.92 | | | | | | | | | | | % 193.32/26.92 | | | | | | | | | | | CLOSE: (315) is inconsistent. % 193.32/26.92 | | | | | | | | | | | % 193.32/26.92 | | | | | | | | | | End of split % 193.32/26.92 | | | | | | | | | | % 193.32/26.92 | | | | | | | | | End of split % 193.32/26.92 | | | | | | | | | % 193.32/26.92 | | | | | | | | End of split % 193.32/26.92 | | | | | | | | % 193.32/26.92 | | | | | | | Case 2: % 193.32/26.92 | | | | | | | | % 193.32/26.92 | | | | | | | | (316) ~ (all_872_2 = 0) % 193.32/26.92 | | | | | | | | % 193.32/26.92 | | | | | | | | BETA: splitting (188) gives: % 193.32/26.92 | | | | | | | | % 193.32/26.92 | | | | | | | | Case 1: % 193.32/26.92 | | | | | | | | | % 193.32/26.92 | | | | | | | | | (317) all_872_6 = 0 % 193.32/26.92 | | | | | | | | | % 193.32/26.92 | | | | | | | | | REDUCE: (187), (317) imply: % 193.32/26.93 | | | | | | | | | (318) c_member(all_622_1, all_872_7, v_L) = 0 % 193.32/26.93 | | | | | | | | | % 193.32/26.93 | | | | | | | | | GROUND_INST: instantiating (fact_wf__not__sym) with v_x, % 193.32/26.93 | | | | | | | | | all_872_8, v_L, tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.93 | | | | | | | | | all_622_1, all_872_1, simplifying with (15), (16), % 193.32/26.93 | | | | | | | | | (17), (23), (170), (179), (216) gives: % 193.32/26.93 | | | | | | | | | (319) ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 193.32/26.93 | | | | | | | | | (c_Wellfounded_Owf(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.93 | | | | | | | | | v_L) = v0 & % 193.32/26.93 | | | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.93 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v_x) % 193.32/26.93 | | | | | | | | | = v1 & c_member(all_622_1, v1, v_L) = v2 & $i(v1) & % 193.32/26.93 | | | | | | | | | ( ~ (v2 = 0) | ~ (v0 = 0))) % 193.32/26.93 | | | | | | | | | % 193.32/26.93 | | | | | | | | | GROUND_INST: instantiating (fact_antisymD) with v_y, v_x, v_L, % 193.32/26.93 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_622_1, % 193.32/26.93 | | | | | | | | | all_872_5, simplifying with (15), (16), (17), % 193.32/26.93 | | | | | | | | | (23), (213), (217), (257) gives: % 193.32/26.93 | | | | | | | | | (320) v_x = v_y | ? [v0: any] : ? [v1: $i] : ? [v2: any] % 193.32/26.93 | | | | | | | | | : % 193.32/26.93 | | | | | | | | | (c_Relation_Oantisym(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.93 | | | | | | | | | v_L) = v0 & % 193.32/26.93 | | | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.93 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v_y) = v1 & % 193.32/26.93 | | | | | | | | | c_member(all_622_1, v1, v_L) = v2 & $i(v1) & ( ~ % 193.32/26.93 | | | | | | | | | (v2 = 0) | ~ (v0 = 0))) % 193.32/26.93 | | | | | | | | | % 193.32/26.93 | | | | | | | | | GROUND_INST: instantiating (44) with v_y, v_x, all_872_5, % 193.32/26.93 | | | | | | | | | simplifying with (16), (213), (217) gives: % 193.32/26.93 | | | | | | | | | (321) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_676_0, % 193.32/26.93 | | | | | | | | | all_872_5, v_L) = v0) | ! [v0: $i] : ! [v1: $i] % 193.32/26.93 | | | | | | | | | : ( ~ % 193.32/26.93 | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.93 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = v1) % 193.32/26.93 | | | | | | | | | | ~ $i(v0) | ? [v2: $i] : ? [v3: any] : ? [v4: % 193.32/26.93 | | | | | | | | | any] : % 193.32/26.93 | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.93 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v0) = v2 % 193.32/26.93 | | | | | | | | | & c_member(all_676_0, v2, v_L) = v3 & % 193.32/26.93 | | | | | | | | | c_member(all_676_0, v1, v_L) = v4 & $i(v2) & ( ~ % 193.32/26.93 | | | | | | | | | (v3 = 0) | v4 = 0))) % 193.32/26.93 | | | | | | | | | % 193.32/26.93 | | | | | | | | | GROUND_INST: instantiating (44) with v_y, all_872_8, all_872_7, % 193.32/26.93 | | | | | | | | | simplifying with (170), (212), (217) gives: % 193.32/26.93 | | | | | | | | | (322) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_676_0, % 193.32/26.93 | | | | | | | | | all_872_7, v_L) = v0) | ! [v0: $i] : ! [v1: $i] % 193.32/26.93 | | | | | | | | | : ( ~ % 193.32/26.93 | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.93 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = v1) % 193.32/26.93 | | | | | | | | | | ~ $i(v0) | ? [v2: $i] : ? [v3: any] : ? [v4: % 193.32/26.93 | | | | | | | | | any] : % 193.32/26.93 | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.93 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v0) % 193.32/26.93 | | | | | | | | | = v2 & c_member(all_676_0, v2, v_L) = v3 & % 193.32/26.93 | | | | | | | | | c_member(all_676_0, v1, v_L) = v4 & $i(v2) & ( ~ % 193.32/26.93 | | | | | | | | | (v3 = 0) | v4 = 0))) % 193.32/26.93 | | | | | | | | | % 193.32/26.93 | | | | | | | | | GROUND_INST: instantiating (220) with all_1080_4, all_1080_1, % 193.32/26.93 | | | | | | | | | simplifying with (206), (209) gives: % 193.32/26.93 | | | | | | | | | (323) ? [v0: $i] : ? [v1: any] : ? [v2: any] : % 193.32/26.93 | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.93 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, % 193.32/26.93 | | | | | | | | | all_1080_4) = v0 & c_member(all_676_0, v0, v_L) = % 193.32/26.93 | | | | | | | | | v1 & c_member(all_676_0, all_1080_1, v_L) = v2 & % 193.32/26.93 | | | | | | | | | $i(v0) & ( ~ (v1 = 0) | v2 = 0)) % 193.32/26.93 | | | | | | | | | % 193.32/26.93 | | | | | | | | | DELTA: instantiating (323) with fresh symbols all_1230_0, % 193.32/26.93 | | | | | | | | | all_1230_1, all_1230_2 gives: % 193.32/26.93 | | | | | | | | | (324) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.93 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, % 193.32/26.93 | | | | | | | | | all_1080_4) = all_1230_2 & c_member(all_676_0, % 193.32/26.93 | | | | | | | | | all_1230_2, v_L) = all_1230_1 & c_member(all_676_0, % 193.32/26.93 | | | | | | | | | all_1080_1, v_L) = all_1230_0 & $i(all_1230_2) & ( % 193.32/26.93 | | | | | | | | | ~ (all_1230_1 = 0) | all_1230_0 = 0) % 193.32/26.93 | | | | | | | | | % 193.32/26.93 | | | | | | | | | ALPHA: (324) implies: % 193.32/26.93 | | | | | | | | | (325) c_member(all_676_0, all_1080_1, v_L) = all_1230_0 % 193.32/26.93 | | | | | | | | | (326) c_member(all_676_0, all_1230_2, v_L) = all_1230_1 % 193.32/26.93 | | | | | | | | | (327) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.93 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, % 193.32/26.93 | | | | | | | | | all_1080_4) = all_1230_2 % 193.32/26.93 | | | | | | | | | (328) ~ (all_1230_1 = 0) | all_1230_0 = 0 % 193.32/26.93 | | | | | | | | | % 193.32/26.93 | | | | | | | | | DELTA: instantiating (319) with fresh symbols all_1242_0, % 193.32/26.93 | | | | | | | | | all_1242_1, all_1242_2 gives: % 193.32/26.93 | | | | | | | | | (329) c_Wellfounded_Owf(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.93 | | | | | | | | | v_L) = all_1242_2 & % 193.32/26.93 | | | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.93 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v_x) = % 193.32/26.93 | | | | | | | | | all_1242_1 & c_member(all_622_1, all_1242_1, v_L) = % 193.32/26.93 | | | | | | | | | all_1242_0 & $i(all_1242_1) & ( ~ (all_1242_0 = 0) | % 193.32/26.93 | | | | | | | | | ~ (all_1242_2 = 0)) % 193.32/26.93 | | | | | | | | | % 193.32/26.93 | | | | | | | | | ALPHA: (329) implies: % 193.32/26.93 | | | | | | | | | (330) c_member(all_622_1, all_1242_1, v_L) = all_1242_0 % 193.32/26.93 | | | | | | | | | (331) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.93 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v_x) = % 193.32/26.93 | | | | | | | | | all_1242_1 % 193.32/26.93 | | | | | | | | | % 193.32/26.93 | | | | | | | | | REDUCE: (89), (326) imply: % 193.32/26.93 | | | | | | | | | (332) c_member(all_622_1, all_1230_2, v_L) = all_1230_1 % 193.32/26.93 | | | | | | | | | % 193.32/26.93 | | | | | | | | | REDUCE: (89), (325) imply: % 193.32/26.93 | | | | | | | | | (333) c_member(all_622_1, all_1080_1, v_L) = all_1230_0 % 193.32/26.93 | | | | | | | | | % 193.32/26.93 | | | | | | | | | BETA: splitting (321) gives: % 193.32/26.93 | | | | | | | | | % 193.32/26.93 | | | | | | | | | Case 1: % 193.32/26.93 | | | | | | | | | | % 193.32/26.93 | | | | | | | | | | (334) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_676_0, % 193.32/26.93 | | | | | | | | | | all_872_5, v_L) = v0) % 193.32/26.93 | | | | | | | | | | % 193.32/26.93 | | | | | | | | | | DELTA: instantiating (334) with fresh symbol all_1124_0 % 193.32/26.93 | | | | | | | | | | gives: % 193.32/26.93 | | | | | | | | | | (335) ~ (all_1124_0 = 0) & c_member(all_676_0, % 193.32/26.93 | | | | | | | | | | all_872_5, v_L) = all_1124_0 % 193.32/26.93 | | | | | | | | | | % 193.32/26.93 | | | | | | | | | | REF_CLOSE: (20), (89), (257), (335) are inconsistent by % 193.32/26.93 | | | | | | | | | | sub-proof #15. % 193.32/26.93 | | | | | | | | | | % 193.32/26.93 | | | | | | | | | Case 2: % 193.32/26.93 | | | | | | | | | | % 193.32/26.93 | | | | | | | | | | (336) ! [v0: $i] : ! [v1: $i] : ( ~ % 193.32/26.93 | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.93 | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = % 193.32/26.93 | | | | | | | | | | v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: any] : % 193.32/26.93 | | | | | | | | | | ? [v4: any] : % 193.32/26.93 | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.93 | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v0) = % 193.32/26.93 | | | | | | | | | | v2 & c_member(all_676_0, v2, v_L) = v3 & % 193.32/26.93 | | | | | | | | | | c_member(all_676_0, v1, v_L) = v4 & $i(v2) & ( % 193.32/26.93 | | | | | | | | | | ~ (v3 = 0) | v4 = 0))) % 193.32/26.93 | | | | | | | | | | % 193.32/26.93 | | | | | | | | | | GROUND_INST: instantiating (336) with v_x, all_872_5, % 193.32/26.93 | | | | | | | | | | simplifying with (16), (213) gives: % 193.32/26.93 | | | | | | | | | | (337) ? [v0: $i] : ? [v1: any] : ? [v2: any] : % 193.32/26.93 | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.93 | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v_x) = v0 % 193.32/26.93 | | | | | | | | | | & c_member(all_676_0, v0, v_L) = v1 & % 193.32/26.93 | | | | | | | | | | c_member(all_676_0, all_872_5, v_L) = v2 & $i(v0) % 193.32/26.93 | | | | | | | | | | & ( ~ (v1 = 0) | v2 = 0)) % 193.32/26.93 | | | | | | | | | | % 193.32/26.93 | | | | | | | | | | BETA: splitting (322) gives: % 193.32/26.93 | | | | | | | | | | % 193.32/26.93 | | | | | | | | | | Case 1: % 193.32/26.93 | | | | | | | | | | | % 193.32/26.93 | | | | | | | | | | | (338) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_676_0, % 193.32/26.93 | | | | | | | | | | | all_872_7, v_L) = v0) % 193.32/26.93 | | | | | | | | | | | % 193.32/26.93 | | | | | | | | | | | DELTA: instantiating (338) with fresh symbol all_1123_0 % 193.32/26.93 | | | | | | | | | | | gives: % 193.32/26.93 | | | | | | | | | | | (339) ~ (all_1123_0 = 0) & c_member(all_676_0, % 193.32/26.93 | | | | | | | | | | | all_872_7, v_L) = all_1123_0 % 193.32/26.93 | | | | | | | | | | | % 193.32/26.93 | | | | | | | | | | | REF_CLOSE: (20), (89), (318), (339) are inconsistent by % 193.32/26.93 | | | | | | | | | | | sub-proof #14. % 193.32/26.93 | | | | | | | | | | | % 193.32/26.93 | | | | | | | | | | Case 2: % 193.32/26.93 | | | | | | | | | | | % 193.32/26.93 | | | | | | | | | | | % 193.32/26.93 | | | | | | | | | | | DELTA: instantiating (337) with fresh symbols all_1252_0, % 193.32/26.93 | | | | | | | | | | | all_1252_1, all_1252_2 gives: % 193.32/26.93 | | | | | | | | | | | (340) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.93 | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v_x) = % 193.32/26.93 | | | | | | | | | | | all_1252_2 & c_member(all_676_0, all_1252_2, v_L) % 193.32/26.93 | | | | | | | | | | | = all_1252_1 & c_member(all_676_0, all_872_5, v_L) % 193.32/26.93 | | | | | | | | | | | = all_1252_0 & $i(all_1252_2) & ( ~ (all_1252_1 = % 193.32/26.93 | | | | | | | | | | | 0) | all_1252_0 = 0) % 193.32/26.93 | | | | | | | | | | | % 193.32/26.93 | | | | | | | | | | | ALPHA: (340) implies: % 193.32/26.93 | | | | | | | | | | | (341) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.93 | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v_x) = % 193.32/26.93 | | | | | | | | | | | all_1252_2 % 193.32/26.93 | | | | | | | | | | | % 193.32/26.93 | | | | | | | | | | | BETA: splitting (320) gives: % 193.32/26.93 | | | | | | | | | | | % 193.32/26.93 | | | | | | | | | | | Case 1: % 193.32/26.93 | | | | | | | | | | | | % 193.32/26.93 | | | | | | | | | | | | (342) v_x = v_y % 193.32/26.94 | | | | | | | | | | | | % 193.32/26.94 | | | | | | | | | | | | REDUCE: (13), (342) imply: % 193.32/26.94 | | | | | | | | | | | | (343) $false % 193.32/26.94 | | | | | | | | | | | | % 193.32/26.94 | | | | | | | | | | | | CLOSE: (343) is inconsistent. % 193.32/26.94 | | | | | | | | | | | | % 193.32/26.94 | | | | | | | | | | | Case 2: % 193.32/26.94 | | | | | | | | | | | | % 193.32/26.94 | | | | | | | | | | | | % 193.32/26.94 | | | | | | | | | | | | GROUND_INST: instantiating (20) with all_1080_0, all_1230_0, % 193.32/26.94 | | | | | | | | | | | | v_L, all_1080_1, all_622_1, simplifying with % 193.32/26.94 | | | | | | | | | | | | (214), (333) gives: % 193.32/26.94 | | | | | | | | | | | | (344) all_1230_0 = all_1080_0 % 193.32/26.94 | | | | | | | | | | | | % 193.32/26.94 | | | | | | | | | | | | GROUND_INST: instantiating (21) with all_872_3, all_1242_1, % 193.32/26.94 | | | | | | | | | | | | v_x, all_872_8, tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.94 | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with % 193.32/26.94 | | | | | | | | | | | | (182), (331) gives: % 193.32/26.94 | | | | | | | | | | | | (345) all_1242_1 = all_872_3 % 193.32/26.94 | | | | | | | | | | | | % 193.32/26.94 | | | | | | | | | | | | GROUND_INST: instantiating (21) with all_1080_3, all_1230_2, % 193.32/26.94 | | | | | | | | | | | | all_1080_4, all_872_8, % 193.32/26.94 | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.94 | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with % 193.32/26.94 | | | | | | | | | | | | (210), (327) gives: % 193.32/26.94 | | | | | | | | | | | | (346) all_1230_2 = all_1080_3 % 193.32/26.94 | | | | | | | | | | | | % 193.32/26.94 | | | | | | | | | | | | REDUCE: (330), (345) imply: % 193.32/26.94 | | | | | | | | | | | | (347) c_member(all_622_1, all_872_3, v_L) = all_1242_0 % 193.32/26.94 | | | | | | | | | | | | % 193.32/26.94 | | | | | | | | | | | | REDUCE: (332), (346) imply: % 193.32/26.94 | | | | | | | | | | | | (348) c_member(all_622_1, all_1080_3, v_L) = all_1230_1 % 193.32/26.94 | | | | | | | | | | | | % 193.32/26.94 | | | | | | | | | | | | GROUND_INST: instantiating (20) with all_872_2, all_1242_0, % 193.32/26.94 | | | | | | | | | | | | v_L, all_872_3, all_622_1, simplifying with (185), % 193.32/26.94 | | | | | | | | | | | | (347) gives: % 193.32/26.94 | | | | | | | | | | | | (349) all_1242_0 = all_872_2 % 193.32/26.94 | | | | | | | | | | | | % 193.32/26.94 | | | | | | | | | | | | GROUND_INST: instantiating (20) with all_1080_2, all_1230_1, % 193.32/26.94 | | | | | | | | | | | | v_L, all_1080_3, all_622_1, simplifying with % 193.32/26.94 | | | | | | | | | | | | (215), (348) gives: % 193.32/26.94 | | | | | | | | | | | | (350) all_1230_1 = all_1080_2 % 193.32/26.94 | | | | | | | | | | | | % 193.32/26.94 | | | | | | | | | | | | BETA: splitting (211) gives: % 193.32/26.94 | | | | | | | | | | | | % 193.32/26.94 | | | | | | | | | | | | Case 1: % 193.32/26.94 | | | | | | | | | | | | | % 193.32/26.94 | | | | | | | | | | | | | (351) all_1080_2 = 0 & ~ (all_1080_0 = 0) & ~ % 193.32/26.94 | | | | | | | | | | | | | (all_1080_4 = v_y) % 193.32/26.94 | | | | | | | | | | | | | % 193.32/26.94 | | | | | | | | | | | | | ALPHA: (351) implies: % 193.32/26.94 | | | | | | | | | | | | | (352) all_1080_2 = 0 % 193.32/26.94 | | | | | | | | | | | | | (353) ~ (all_1080_0 = 0) % 193.32/26.94 | | | | | | | | | | | | | % 193.32/26.94 | | | | | | | | | | | | | COMBINE_EQS: (350), (352) imply: % 193.32/26.94 | | | | | | | | | | | | | (354) all_1230_1 = 0 % 193.32/26.94 | | | | | | | | | | | | | % 193.32/26.94 | | | | | | | | | | | | | BETA: splitting (328) gives: % 193.32/26.94 | | | | | | | | | | | | | % 193.32/26.94 | | | | | | | | | | | | | Case 1: % 193.32/26.94 | | | | | | | | | | | | | | % 193.32/26.94 | | | | | | | | | | | | | | (355) ~ (all_1230_1 = 0) % 193.32/26.94 | | | | | | | | | | | | | | % 193.32/26.94 | | | | | | | | | | | | | | REDUCE: (354), (355) imply: % 193.32/26.94 | | | | | | | | | | | | | | (356) $false % 193.32/26.94 | | | | | | | | | | | | | | % 193.32/26.94 | | | | | | | | | | | | | | CLOSE: (356) is inconsistent. % 193.32/26.94 | | | | | | | | | | | | | | % 193.32/26.94 | | | | | | | | | | | | | Case 2: % 193.32/26.94 | | | | | | | | | | | | | | % 193.32/26.94 | | | | | | | | | | | | | | (357) all_1230_0 = 0 % 193.32/26.94 | | | | | | | | | | | | | | % 193.32/26.94 | | | | | | | | | | | | | | COMBINE_EQS: (344), (357) imply: % 193.32/26.94 | | | | | | | | | | | | | | (358) all_1080_0 = 0 % 193.32/26.94 | | | | | | | | | | | | | | % 193.32/26.94 | | | | | | | | | | | | | | SIMP: (358) implies: % 193.32/26.94 | | | | | | | | | | | | | | (359) all_1080_0 = 0 % 193.32/26.94 | | | | | | | | | | | | | | % 193.32/26.94 | | | | | | | | | | | | | | REDUCE: (353), (359) imply: % 193.32/26.94 | | | | | | | | | | | | | | (360) $false % 193.32/26.94 | | | | | | | | | | | | | | % 193.32/26.94 | | | | | | | | | | | | | | CLOSE: (360) is inconsistent. % 193.32/26.94 | | | | | | | | | | | | | | % 193.32/26.94 | | | | | | | | | | | | | End of split % 193.32/26.94 | | | | | | | | | | | | | % 193.32/26.94 | | | | | | | | | | | | Case 2: % 193.32/26.94 | | | | | | | | | | | | | % 193.32/26.94 | | | | | | | | | | | | | (361) (all_1080_4 = v_y & all_872_2 = 0) | (all_1080_4 = % 193.32/26.94 | | | | | | | | | | | | | v_y & all_872_8 = v_x) % 193.32/26.94 | | | | | | | | | | | | | % 193.32/26.94 | | | | | | | | | | | | | BETA: splitting (361) gives: % 193.32/26.94 | | | | | | | | | | | | | % 193.32/26.94 | | | | | | | | | | | | | Case 1: % 193.32/26.94 | | | | | | | | | | | | | | % 193.32/26.94 | | | | | | | | | | | | | | (362) all_1080_4 = v_y & all_872_2 = 0 % 193.32/26.94 | | | | | | | | | | | | | | % 193.32/26.94 | | | | | | | | | | | | | | ALPHA: (362) implies: % 193.32/26.94 | | | | | | | | | | | | | | (363) all_872_2 = 0 % 193.32/26.94 | | | | | | | | | | | | | | % 193.32/26.94 | | | | | | | | | | | | | | REDUCE: (316), (363) imply: % 193.32/26.94 | | | | | | | | | | | | | | (364) $false % 193.32/26.94 | | | | | | | | | | | | | | % 193.32/26.94 | | | | | | | | | | | | | | CLOSE: (364) is inconsistent. % 193.32/26.94 | | | | | | | | | | | | | | % 193.32/26.94 | | | | | | | | | | | | | Case 2: % 193.32/26.94 | | | | | | | | | | | | | | % 193.32/26.94 | | | | | | | | | | | | | | (365) all_1080_4 = v_y & all_872_8 = v_x % 193.32/26.94 | | | | | | | | | | | | | | % 193.32/26.94 | | | | | | | | | | | | | | ALPHA: (365) implies: % 193.32/26.94 | | | | | | | | | | | | | | (366) all_872_8 = v_x % 193.32/26.94 | | | | | | | | | | | | | | % 193.32/26.94 | | | | | | | | | | | | | | REDUCE: (224), (366) imply: % 193.32/26.94 | | | | | | | | | | | | | | (367) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.94 | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v_x) = % 193.32/26.94 | | | | | | | | | | | | | | all_1086_2 % 193.32/26.94 | | | | | | | | | | | | | | % 193.32/26.94 | | | | | | | | | | | | | | REDUCE: (182), (366) imply: % 193.32/26.94 | | | | | | | | | | | | | | (368) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.94 | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v_x) = % 193.32/26.94 | | | | | | | | | | | | | | all_872_3 % 193.32/26.94 | | | | | | | | | | | | | | % 193.32/26.94 | | | | | | | | | | | | | | REDUCE: (179), (366) imply: % 193.32/26.94 | | | | | | | | | | | | | | (369) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.94 | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v_x) = % 193.32/26.94 | | | | | | | | | | | | | | all_872_1 % 193.32/26.94 | | | | | | | | | | | | | | % 193.32/26.94 | | | | | | | | | | | | | | GROUND_INST: instantiating (21) with all_1252_2, all_872_3, % 193.32/26.94 | | | | | | | | | | | | | | v_x, v_x, tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.94 | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with % 193.32/26.94 | | | | | | | | | | | | | | (341), (368) gives: % 193.32/26.94 | | | | | | | | | | | | | | (370) all_1252_2 = all_872_3 % 193.32/26.94 | | | | | | | | | | | | | | % 193.32/26.94 | | | | | | | | | | | | | | GROUND_INST: instantiating (21) with all_1252_2, all_872_1, % 193.32/26.94 | | | | | | | | | | | | | | v_x, v_x, tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.94 | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with % 193.32/26.94 | | | | | | | | | | | | | | (341), (369) gives: % 193.32/26.94 | | | | | | | | | | | | | | (371) all_1252_2 = all_872_1 % 193.32/26.94 | | | | | | | | | | | | | | % 193.32/26.94 | | | | | | | | | | | | | | GROUND_INST: instantiating (21) with all_1252_2, all_1086_2, % 193.32/26.94 | | | | | | | | | | | | | | v_x, v_x, tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.94 | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with % 193.32/26.94 | | | | | | | | | | | | | | (341), (367) gives: % 193.32/26.94 | | | | | | | | | | | | | | (372) all_1252_2 = all_1086_2 % 193.32/26.94 | | | | | | | | | | | | | | % 193.32/26.94 | | | | | | | | | | | | | | COMBINE_EQS: (371), (372) imply: % 193.32/26.94 | | | | | | | | | | | | | | (373) all_1086_2 = all_872_1 % 193.32/26.94 | | | | | | | | | | | | | | % 193.32/26.94 | | | | | | | | | | | | | | COMBINE_EQS: (370), (372) imply: % 193.32/26.94 | | | | | | | | | | | | | | (374) all_1086_2 = all_872_3 % 193.32/26.94 | | | | | | | | | | | | | | % 193.32/26.94 | | | | | | | | | | | | | | COMBINE_EQS: (373), (374) imply: % 193.32/26.94 | | | | | | | | | | | | | | (375) all_872_1 = all_872_3 % 193.32/26.94 | | | | | | | | | | | | | | % 193.32/26.94 | | | | | | | | | | | | | | SIMP: (375) implies: % 193.32/26.94 | | | | | | | | | | | | | | (376) all_872_1 = all_872_3 % 193.32/26.94 | | | | | | | | | | | | | | % 193.32/26.94 | | | | | | | | | | | | | | REDUCE: (216), (376) imply: % 193.32/26.94 | | | | | | | | | | | | | | (377) c_member(all_622_1, all_872_3, v_L) = 0 % 193.32/26.94 | | | | | | | | | | | | | | % 193.32/26.94 | | | | | | | | | | | | | | REF_CLOSE: (20), (185), (316), (377) are inconsistent by % 193.32/26.94 | | | | | | | | | | | | | | sub-proof #13. % 193.32/26.94 | | | | | | | | | | | | | | % 193.32/26.94 | | | | | | | | | | | | | End of split % 193.32/26.94 | | | | | | | | | | | | | % 193.32/26.94 | | | | | | | | | | | | End of split % 193.32/26.94 | | | | | | | | | | | | % 193.32/26.94 | | | | | | | | | | | End of split % 193.32/26.94 | | | | | | | | | | | % 193.32/26.94 | | | | | | | | | | End of split % 193.32/26.94 | | | | | | | | | | % 193.32/26.94 | | | | | | | | | End of split % 193.32/26.94 | | | | | | | | | % 193.32/26.94 | | | | | | | | Case 2: % 193.32/26.94 | | | | | | | | | % 193.32/26.94 | | | | | | | | | (378) ~ (all_872_6 = 0) % 193.32/26.94 | | | | | | | | | % 193.32/26.94 | | | | | | | | | BETA: splitting (249) gives: % 193.32/26.94 | | | | | | | | | % 193.32/26.94 | | | | | | | | | Case 1: % 193.32/26.94 | | | | | | | | | | % 193.32/26.94 | | | | | | | | | | (379) all_1096_0 = 0 % 193.32/26.94 | | | | | | | | | | % 193.32/26.94 | | | | | | | | | | REDUCE: (251), (379) imply: % 193.32/26.94 | | | | | | | | | | (380) c_member(all_622_1, all_1096_1, v_L) = 0 % 193.32/26.94 | | | | | | | | | | % 193.32/26.94 | | | | | | | | | | GROUND_INST: instantiating (fact_transD) with v_x, v_y, % 193.32/26.94 | | | | | | | | | | all_872_8, v_L, tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.94 | | | | | | | | | | all_622_1, all_872_5, all_872_3, all_872_2, % 193.32/26.94 | | | | | | | | | | simplifying with (15), (16), (17), (23), (170), % 193.32/26.94 | | | | | | | | | | (182), (185), (213), (217), (257) gives: % 193.32/26.94 | | | | | | | | | | (381) all_872_2 = 0 | ? [v0: any] : ? [v1: $i] : ? % 193.32/26.94 | | | | | | | | | | [v2: any] : % 193.32/26.94 | | | | | | | | | | (c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.94 | | | | | | | | | | v_L) = v0 & % 193.32/26.94 | | | | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.94 | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, % 193.32/26.94 | | | | | | | | | | v_y) = v1 & c_member(all_622_1, v1, v_L) = v2 & % 193.32/26.94 | | | | | | | | | | $i(v1) & ( ~ (v2 = 0) | ~ (v0 = 0))) % 193.32/26.94 | | | | | | | | | | % 193.32/26.94 | | | | | | | | | | GROUND_INST: instantiating (44) with v_y, v_x, all_872_5, % 193.32/26.94 | | | | | | | | | | simplifying with (16), (213), (217) gives: % 193.32/26.94 | | | | | | | | | | (382) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_676_0, % 193.32/26.94 | | | | | | | | | | all_872_5, v_L) = v0) | ! [v0: $i] : ! [v1: % 193.32/26.94 | | | | | | | | | | $i] : ( ~ % 193.32/26.94 | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.94 | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = % 193.32/26.94 | | | | | | | | | | v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: any] : % 193.32/26.94 | | | | | | | | | | ? [v4: any] : % 193.32/26.94 | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.94 | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v0) = % 193.32/26.94 | | | | | | | | | | v2 & c_member(all_676_0, v2, v_L) = v3 & % 193.32/26.94 | | | | | | | | | | c_member(all_676_0, v1, v_L) = v4 & $i(v2) & ( % 193.32/26.94 | | | | | | | | | | ~ (v3 = 0) | v4 = 0))) % 193.32/26.94 | | | | | | | | | | % 193.32/26.94 | | | | | | | | | | GROUND_INST: instantiating (fact_transD) with all_872_8, v_x, % 193.32/26.94 | | | | | | | | | | v_y, v_L, tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.94 | | | | | | | | | | all_622_1, all_872_1, all_872_7, all_872_6, % 193.32/26.94 | | | | | | | | | | simplifying with (15), (16), (17), (23), (170), % 193.32/26.94 | | | | | | | | | | (179), (187), (212), (216), (217) gives: % 193.32/26.94 | | | | | | | | | | (383) all_872_6 = 0 | ? [v0: any] : ? [v1: $i] : ? % 193.32/26.94 | | | | | | | | | | [v2: any] : % 193.32/26.94 | | | | | | | | | | (c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.94 | | | | | | | | | | v_L) = v0 & % 193.32/26.94 | | | | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.94 | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v_x) = v1 % 193.32/26.94 | | | | | | | | | | & c_member(all_622_1, v1, v_L) = v2 & $i(v1) & ( % 193.32/26.94 | | | | | | | | | | ~ (v2 = 0) | ~ (v0 = 0))) % 193.32/26.94 | | | | | | | | | | % 193.32/26.94 | | | | | | | | | | GROUND_INST: instantiating (44) with all_872_8, v_y, % 193.32/26.94 | | | | | | | | | | all_1096_1, simplifying with (170), (217), (250) % 193.32/26.94 | | | | | | | | | | gives: % 193.32/26.94 | | | | | | | | | | (384) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_676_0, % 193.32/26.94 | | | | | | | | | | all_1096_1, v_L) = v0) | ! [v0: $i] : ! [v1: % 193.32/26.94 | | | | | | | | | | $i] : ( ~ % 193.32/26.94 | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.94 | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, % 193.32/26.94 | | | | | | | | | | v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: % 193.32/26.95 | | | | | | | | | | any] : ? [v4: any] : % 193.32/26.95 | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.95 | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = % 193.32/26.95 | | | | | | | | | | v2 & c_member(all_676_0, v2, v_L) = v3 & % 193.32/26.95 | | | | | | | | | | c_member(all_676_0, v1, v_L) = v4 & $i(v2) & ( % 193.32/26.95 | | | | | | | | | | ~ (v3 = 0) | v4 = 0))) % 193.32/26.95 | | | | | | | | | | % 193.32/26.95 | | | | | | | | | | BETA: splitting (384) gives: % 193.32/26.95 | | | | | | | | | | % 193.32/26.95 | | | | | | | | | | Case 1: % 193.32/26.95 | | | | | | | | | | | % 193.32/26.95 | | | | | | | | | | | (385) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_676_0, % 193.32/26.95 | | | | | | | | | | | all_1096_1, v_L) = v0) % 193.32/26.95 | | | | | | | | | | | % 193.32/26.95 | | | | | | | | | | | DELTA: instantiating (385) with fresh symbol all_1265_0 % 193.32/26.95 | | | | | | | | | | | gives: % 193.32/26.95 | | | | | | | | | | | (386) ~ (all_1265_0 = 0) & c_member(all_676_0, % 193.32/26.95 | | | | | | | | | | | all_1096_1, v_L) = all_1265_0 % 193.32/26.95 | | | | | | | | | | | % 193.32/26.95 | | | | | | | | | | | ALPHA: (386) implies: % 193.32/26.95 | | | | | | | | | | | (387) ~ (all_1265_0 = 0) % 193.32/26.95 | | | | | | | | | | | (388) c_member(all_676_0, all_1096_1, v_L) = all_1265_0 % 193.32/26.95 | | | | | | | | | | | % 193.32/26.95 | | | | | | | | | | | REDUCE: (89), (388) imply: % 193.32/26.95 | | | | | | | | | | | (389) c_member(all_622_1, all_1096_1, v_L) = all_1265_0 % 193.32/26.95 | | | | | | | | | | | % 193.32/26.95 | | | | | | | | | | | GROUND_INST: instantiating (20) with 0, all_1265_0, v_L, % 193.32/26.95 | | | | | | | | | | | all_1096_1, all_622_1, simplifying with (380), % 193.32/26.95 | | | | | | | | | | | (389) gives: % 193.32/26.95 | | | | | | | | | | | (390) all_1265_0 = 0 % 193.32/26.95 | | | | | | | | | | | % 193.32/26.95 | | | | | | | | | | | REDUCE: (387), (390) imply: % 193.32/26.95 | | | | | | | | | | | (391) $false % 193.32/26.95 | | | | | | | | | | | % 193.32/26.95 | | | | | | | | | | | CLOSE: (391) is inconsistent. % 193.32/26.95 | | | | | | | | | | | % 193.32/26.95 | | | | | | | | | | Case 2: % 193.32/26.95 | | | | | | | | | | | % 193.32/26.95 | | | | | | | | | | | (392) ! [v0: $i] : ! [v1: $i] : ( ~ % 193.32/26.95 | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.95 | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, % 193.32/26.95 | | | | | | | | | | | v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? % 193.32/26.95 | | | | | | | | | | | [v3: any] : ? [v4: any] : % 193.32/26.95 | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.95 | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = % 193.32/26.95 | | | | | | | | | | | v2 & c_member(all_676_0, v2, v_L) = v3 & % 193.32/26.95 | | | | | | | | | | | c_member(all_676_0, v1, v_L) = v4 & $i(v2) & ( % 193.32/26.95 | | | | | | | | | | | ~ (v3 = 0) | v4 = 0))) % 193.32/26.95 | | | | | | | | | | | % 193.32/26.95 | | | | | | | | | | | GROUND_INST: instantiating (392) with v_x, all_872_3, % 193.32/26.95 | | | | | | | | | | | simplifying with (16), (182) gives: % 193.32/26.95 | | | | | | | | | | | (393) ? [v0: $i] : ? [v1: any] : ? [v2: any] : % 193.32/26.95 | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.95 | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v_x) = % 193.32/26.95 | | | | | | | | | | | v0 & c_member(all_676_0, v0, v_L) = v1 & % 193.32/26.95 | | | | | | | | | | | c_member(all_676_0, all_872_3, v_L) = v2 & % 193.32/26.95 | | | | | | | | | | | $i(v0) & ( ~ (v1 = 0) | v2 = 0)) % 193.32/26.95 | | | | | | | | | | | % 193.32/26.95 | | | | | | | | | | | BETA: splitting (382) gives: % 193.32/26.95 | | | | | | | | | | | % 193.32/26.95 | | | | | | | | | | | Case 1: % 193.32/26.95 | | | | | | | | | | | | % 193.32/26.95 | | | | | | | | | | | | (394) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_676_0, % 193.32/26.95 | | | | | | | | | | | | all_872_5, v_L) = v0) % 193.32/26.95 | | | | | | | | | | | | % 193.32/26.95 | | | | | | | | | | | | DELTA: instantiating (394) with fresh symbol all_1124_0 % 193.32/26.95 | | | | | | | | | | | | gives: % 193.32/26.95 | | | | | | | | | | | | (395) ~ (all_1124_0 = 0) & c_member(all_676_0, % 193.32/26.95 | | | | | | | | | | | | all_872_5, v_L) = all_1124_0 % 193.32/26.95 | | | | | | | | | | | | % 193.32/26.95 | | | | | | | | | | | | REF_CLOSE: (20), (89), (257), (395) are inconsistent by % 193.32/26.95 | | | | | | | | | | | | sub-proof #15. % 193.32/26.95 | | | | | | | | | | | | % 193.32/26.95 | | | | | | | | | | | Case 2: % 193.32/26.95 | | | | | | | | | | | | % 193.32/26.95 | | | | | | | | | | | | (396) ! [v0: $i] : ! [v1: $i] : ( ~ % 193.32/26.95 | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.95 | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = % 193.32/26.95 | | | | | | | | | | | | v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: any] : % 193.32/26.95 | | | | | | | | | | | | ? [v4: any] : % 193.32/26.95 | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.95 | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v0) = % 193.32/26.95 | | | | | | | | | | | | v2 & c_member(all_676_0, v2, v_L) = v3 & % 193.32/26.95 | | | | | | | | | | | | c_member(all_676_0, v1, v_L) = v4 & $i(v2) & ( % 193.32/26.95 | | | | | | | | | | | | ~ (v3 = 0) | v4 = 0))) % 193.32/26.95 | | | | | | | | | | | | % 193.32/26.95 | | | | | | | | | | | | GROUND_INST: instantiating (396) with v_x, all_872_5, % 193.32/26.95 | | | | | | | | | | | | simplifying with (16), (213) gives: % 193.32/26.95 | | | | | | | | | | | | (397) ? [v0: $i] : ? [v1: any] : ? [v2: any] : % 193.32/26.95 | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.95 | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v_x) = % 193.32/26.95 | | | | | | | | | | | | v0 & c_member(all_676_0, v0, v_L) = v1 & % 193.32/26.95 | | | | | | | | | | | | c_member(all_676_0, all_872_5, v_L) = v2 & % 193.32/26.95 | | | | | | | | | | | | $i(v0) & ( ~ (v1 = 0) | v2 = 0)) % 193.32/26.95 | | | | | | | | | | | | % 193.32/26.95 | | | | | | | | | | | | DELTA: instantiating (393) with fresh symbols all_1270_0, % 193.32/26.95 | | | | | | | | | | | | all_1270_1, all_1270_2 gives: % 193.32/26.95 | | | | | | | | | | | | (398) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.95 | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v_x) = % 193.32/26.95 | | | | | | | | | | | | all_1270_2 & c_member(all_676_0, all_1270_2, v_L) % 193.32/26.95 | | | | | | | | | | | | = all_1270_1 & c_member(all_676_0, all_872_3, v_L) % 193.32/26.95 | | | | | | | | | | | | = all_1270_0 & $i(all_1270_2) & ( ~ (all_1270_1 = % 193.32/26.95 | | | | | | | | | | | | 0) | all_1270_0 = 0) % 193.32/26.95 | | | | | | | | | | | | % 193.32/26.95 | | | | | | | | | | | | ALPHA: (398) implies: % 193.32/26.95 | | | | | | | | | | | | (399) c_member(all_676_0, all_872_3, v_L) = all_1270_0 % 193.32/26.95 | | | | | | | | | | | | (400) c_member(all_676_0, all_1270_2, v_L) = all_1270_1 % 193.32/26.95 | | | | | | | | | | | | (401) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.95 | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v_x) = % 193.32/26.95 | | | | | | | | | | | | all_1270_2 % 193.32/26.95 | | | | | | | | | | | | (402) ~ (all_1270_1 = 0) | all_1270_0 = 0 % 193.32/26.95 | | | | | | | | | | | | % 193.32/26.95 | | | | | | | | | | | | DELTA: instantiating (397) with fresh symbols all_1276_0, % 193.32/26.95 | | | | | | | | | | | | all_1276_1, all_1276_2 gives: % 193.32/26.95 | | | | | | | | | | | | (403) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.95 | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v_x) = % 193.32/26.95 | | | | | | | | | | | | all_1276_2 & c_member(all_676_0, all_1276_2, v_L) % 193.32/26.95 | | | | | | | | | | | | = all_1276_1 & c_member(all_676_0, all_872_5, v_L) % 193.32/26.95 | | | | | | | | | | | | = all_1276_0 & $i(all_1276_2) & ( ~ (all_1276_1 = % 193.32/26.95 | | | | | | | | | | | | 0) | all_1276_0 = 0) % 193.32/26.95 | | | | | | | | | | | | % 193.32/26.95 | | | | | | | | | | | | ALPHA: (403) implies: % 193.32/26.95 | | | | | | | | | | | | (404) c_member(all_676_0, all_872_5, v_L) = all_1276_0 % 193.32/26.95 | | | | | | | | | | | | % 193.32/26.95 | | | | | | | | | | | | REDUCE: (89), (400) imply: % 193.32/26.95 | | | | | | | | | | | | (405) c_member(all_622_1, all_1270_2, v_L) = all_1270_1 % 193.32/26.95 | | | | | | | | | | | | % 193.32/26.95 | | | | | | | | | | | | REDUCE: (89), (399) imply: % 193.32/26.95 | | | | | | | | | | | | (406) c_member(all_622_1, all_872_3, v_L) = all_1270_0 % 193.32/26.95 | | | | | | | | | | | | % 193.32/26.95 | | | | | | | | | | | | REDUCE: (89), (404) imply: % 193.32/26.95 | | | | | | | | | | | | (407) c_member(all_622_1, all_872_5, v_L) = all_1276_0 % 193.32/26.95 | | | | | | | | | | | | % 193.32/26.95 | | | | | | | | | | | | BETA: splitting (383) gives: % 193.32/26.95 | | | | | | | | | | | | % 193.32/26.95 | | | | | | | | | | | | Case 1: % 193.32/26.95 | | | | | | | | | | | | | % 193.32/26.95 | | | | | | | | | | | | | (408) all_872_6 = 0 % 193.32/26.95 | | | | | | | | | | | | | % 193.32/26.95 | | | | | | | | | | | | | REDUCE: (378), (408) imply: % 193.32/26.95 | | | | | | | | | | | | | (409) $false % 193.32/26.95 | | | | | | | | | | | | | % 193.32/26.95 | | | | | | | | | | | | | CLOSE: (409) is inconsistent. % 193.32/26.95 | | | | | | | | | | | | | % 193.32/26.95 | | | | | | | | | | | | Case 2: % 193.32/26.95 | | | | | | | | | | | | | % 193.32/26.95 | | | | | | | | | | | | | (410) ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 193.32/26.95 | | | | | | | | | | | | | (c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.95 | | | | | | | | | | | | | v_L) = v0 & % 193.32/26.95 | | | | | | | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.95 | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v_x) = % 193.32/26.95 | | | | | | | | | | | | | v1 & c_member(all_622_1, v1, v_L) = v2 & $i(v1) % 193.32/26.95 | | | | | | | | | | | | | & ( ~ (v2 = 0) | ~ (v0 = 0))) % 193.32/26.95 | | | | | | | | | | | | | % 193.32/26.95 | | | | | | | | | | | | | DELTA: instantiating (410) with fresh symbols all_1281_0, % 193.32/26.95 | | | | | | | | | | | | | all_1281_1, all_1281_2 gives: % 193.32/26.95 | | | | | | | | | | | | | (411) c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.95 | | | | | | | | | | | | | v_L) = all_1281_2 & % 193.32/26.95 | | | | | | | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.95 | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v_x) = % 193.32/26.95 | | | | | | | | | | | | | all_1281_1 & c_member(all_622_1, all_1281_1, v_L) % 193.32/26.95 | | | | | | | | | | | | | = all_1281_0 & $i(all_1281_1) & ( ~ (all_1281_0 = % 193.32/26.95 | | | | | | | | | | | | | 0) | ~ (all_1281_2 = 0)) % 193.32/26.95 | | | | | | | | | | | | | % 193.32/26.95 | | | | | | | | | | | | | ALPHA: (411) implies: % 193.32/26.95 | | | | | | | | | | | | | (412) c_member(all_622_1, all_1281_1, v_L) = all_1281_0 % 193.32/26.95 | | | | | | | | | | | | | (413) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.95 | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v_x) = % 193.32/26.95 | | | | | | | | | | | | | all_1281_1 % 193.32/26.95 | | | | | | | | | | | | | % 193.32/26.95 | | | | | | | | | | | | | BETA: splitting (381) gives: % 193.32/26.95 | | | | | | | | | | | | | % 193.32/26.95 | | | | | | | | | | | | | Case 1: % 193.32/26.95 | | | | | | | | | | | | | | % 193.32/26.95 | | | | | | | | | | | | | | (414) all_872_2 = 0 % 193.32/26.95 | | | | | | | | | | | | | | % 193.32/26.95 | | | | | | | | | | | | | | REDUCE: (316), (414) imply: % 193.32/26.95 | | | | | | | | | | | | | | (415) $false % 193.32/26.95 | | | | | | | | | | | | | | % 193.32/26.95 | | | | | | | | | | | | | | CLOSE: (415) is inconsistent. % 193.32/26.95 | | | | | | | | | | | | | | % 193.32/26.95 | | | | | | | | | | | | | Case 2: % 193.32/26.95 | | | | | | | | | | | | | | % 193.32/26.95 | | | | | | | | | | | | | | % 193.32/26.95 | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with 0, all_1276_0, v_L, % 193.32/26.95 | | | | | | | | | | | | | | all_872_5, all_622_1, simplifying with (257), % 193.32/26.95 | | | | | | | | | | | | | | (407) gives: % 193.32/26.95 | | | | | | | | | | | | | | (416) all_1276_0 = 0 % 193.32/26.95 | | | | | | | | | | | | | | % 193.32/26.95 | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with all_872_2, all_1270_0, % 193.32/26.95 | | | | | | | | | | | | | | v_L, all_872_3, all_622_1, simplifying with (185), % 193.32/26.95 | | | | | | | | | | | | | | (406) gives: % 193.32/26.95 | | | | | | | | | | | | | | (417) all_1270_0 = all_872_2 % 193.32/26.95 | | | | | | | | | | | | | | % 193.32/26.95 | | | | | | | | | | | | | | GROUND_INST: instantiating (21) with all_872_5, all_1281_1, % 193.32/26.95 | | | | | | | | | | | | | | v_x, v_y, tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.95 | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with % 193.32/26.95 | | | | | | | | | | | | | | (213), (413) gives: % 193.32/26.95 | | | | | | | | | | | | | | (418) all_1281_1 = all_872_5 % 193.32/26.95 | | | | | | | | | | | | | | % 193.32/26.95 | | | | | | | | | | | | | | GROUND_INST: instantiating (21) with all_1270_2, all_1281_1, % 193.32/26.95 | | | | | | | | | | | | | | v_x, v_y, tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.95 | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with % 193.32/26.95 | | | | | | | | | | | | | | (401), (413) gives: % 193.32/26.95 | | | | | | | | | | | | | | (419) all_1281_1 = all_1270_2 % 193.32/26.95 | | | | | | | | | | | | | | % 193.32/26.95 | | | | | | | | | | | | | | COMBINE_EQS: (418), (419) imply: % 193.32/26.95 | | | | | | | | | | | | | | (420) all_1270_2 = all_872_5 % 193.32/26.95 | | | | | | | | | | | | | | % 193.32/26.95 | | | | | | | | | | | | | | REDUCE: (412), (418) imply: % 193.32/26.95 | | | | | | | | | | | | | | (421) c_member(all_622_1, all_872_5, v_L) = all_1281_0 % 193.32/26.95 | | | | | | | | | | | | | | % 193.32/26.95 | | | | | | | | | | | | | | REDUCE: (405), (420) imply: % 193.32/26.95 | | | | | | | | | | | | | | (422) c_member(all_622_1, all_872_5, v_L) = all_1270_1 % 193.32/26.95 | | | | | | | | | | | | | | % 193.32/26.95 | | | | | | | | | | | | | | BETA: splitting (402) gives: % 193.32/26.95 | | | | | | | | | | | | | | % 193.32/26.95 | | | | | | | | | | | | | | Case 1: % 193.32/26.95 | | | | | | | | | | | | | | | % 193.32/26.95 | | | | | | | | | | | | | | | (423) ~ (all_1270_1 = 0) % 193.32/26.95 | | | | | | | | | | | | | | | % 193.32/26.95 | | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with 0, all_1281_0, v_L, % 193.32/26.95 | | | | | | | | | | | | | | | all_872_5, all_622_1, simplifying with (257), % 193.32/26.95 | | | | | | | | | | | | | | | (421) gives: % 193.32/26.95 | | | | | | | | | | | | | | | (424) all_1281_0 = 0 % 193.32/26.95 | | | | | | | | | | | | | | | % 193.32/26.95 | | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with all_1270_1, all_1281_0, % 193.32/26.95 | | | | | | | | | | | | | | | v_L, all_872_5, all_622_1, simplifying with (421), % 193.32/26.95 | | | | | | | | | | | | | | | (422) gives: % 193.32/26.95 | | | | | | | | | | | | | | | (425) all_1281_0 = all_1270_1 % 193.32/26.95 | | | | | | | | | | | | | | | % 193.32/26.95 | | | | | | | | | | | | | | | COMBINE_EQS: (424), (425) imply: % 193.32/26.95 | | | | | | | | | | | | | | | (426) all_1270_1 = 0 % 193.32/26.95 | | | | | | | | | | | | | | | % 193.32/26.95 | | | | | | | | | | | | | | | SIMP: (426) implies: % 193.32/26.95 | | | | | | | | | | | | | | | (427) all_1270_1 = 0 % 193.32/26.95 | | | | | | | | | | | | | | | % 193.32/26.95 | | | | | | | | | | | | | | | REDUCE: (423), (427) imply: % 193.32/26.95 | | | | | | | | | | | | | | | (428) $false % 193.32/26.95 | | | | | | | | | | | | | | | % 193.32/26.95 | | | | | | | | | | | | | | | CLOSE: (428) is inconsistent. % 193.32/26.95 | | | | | | | | | | | | | | | % 193.32/26.95 | | | | | | | | | | | | | | Case 2: % 193.32/26.95 | | | | | | | | | | | | | | | % 193.32/26.95 | | | | | | | | | | | | | | | (429) all_1270_0 = 0 % 193.32/26.95 | | | | | | | | | | | | | | | % 193.32/26.95 | | | | | | | | | | | | | | | COMBINE_EQS: (417), (429) imply: % 193.32/26.95 | | | | | | | | | | | | | | | (430) all_872_2 = 0 % 193.32/26.95 | | | | | | | | | | | | | | | % 193.32/26.95 | | | | | | | | | | | | | | | REDUCE: (316), (430) imply: % 193.32/26.95 | | | | | | | | | | | | | | | (431) $false % 193.32/26.95 | | | | | | | | | | | | | | | % 193.32/26.95 | | | | | | | | | | | | | | | CLOSE: (431) is inconsistent. % 193.32/26.95 | | | | | | | | | | | | | | | % 193.32/26.95 | | | | | | | | | | | | | | End of split % 193.32/26.95 | | | | | | | | | | | | | | % 193.32/26.96 | | | | | | | | | | | | | End of split % 193.32/26.96 | | | | | | | | | | | | | % 193.32/26.96 | | | | | | | | | | | | End of split % 193.32/26.96 | | | | | | | | | | | | % 193.32/26.96 | | | | | | | | | | | End of split % 193.32/26.96 | | | | | | | | | | | % 193.32/26.96 | | | | | | | | | | End of split % 193.32/26.96 | | | | | | | | | | % 193.32/26.96 | | | | | | | | | Case 2: % 193.32/26.96 | | | | | | | | | | % 193.32/26.96 | | | | | | | | | | (432) all_1096_2 = 0 % 193.32/26.96 | | | | | | | | | | % 193.32/26.96 | | | | | | | | | | COMBINE_EQS: (253), (432) imply: % 193.32/26.96 | | | | | | | | | | (433) all_872_6 = 0 % 193.32/26.96 | | | | | | | | | | % 193.32/26.96 | | | | | | | | | | REDUCE: (378), (433) imply: % 193.32/26.96 | | | | | | | | | | (434) $false % 193.32/26.96 | | | | | | | | | | % 193.32/26.96 | | | | | | | | | | CLOSE: (434) is inconsistent. % 193.32/26.96 | | | | | | | | | | % 193.32/26.96 | | | | | | | | | End of split % 193.32/26.96 | | | | | | | | | % 193.32/26.96 | | | | | | | | End of split % 193.32/26.96 | | | | | | | | % 193.32/26.96 | | | | | | | End of split % 193.32/26.96 | | | | | | | % 193.32/26.96 | | | | | | Case 2: % 193.32/26.96 | | | | | | | % 193.32/26.96 | | | | | | | (435) ~ (all_872_4 = 0) % 193.32/26.96 | | | | | | | % 193.32/26.96 | | | | | | | BETA: splitting (236) gives: % 193.32/26.96 | | | | | | | % 193.32/26.96 | | | | | | | Case 1: % 193.32/26.96 | | | | | | | | % 193.32/26.96 | | | | | | | | (436) all_1091_0 = 0 % 193.32/26.96 | | | | | | | | % 193.32/26.96 | | | | | | | | REDUCE: (239), (436) imply: % 193.32/26.96 | | | | | | | | (437) c_member(all_622_1, all_1091_1, v_L) = 0 % 193.32/26.96 | | | | | | | | % 193.32/26.96 | | | | | | | | BETA: splitting (188) gives: % 193.32/26.96 | | | | | | | | % 193.32/26.96 | | | | | | | | Case 1: % 193.32/26.96 | | | | | | | | | % 193.32/26.96 | | | | | | | | | (438) all_872_6 = 0 % 193.32/26.96 | | | | | | | | | % 193.32/26.96 | | | | | | | | | REDUCE: (187), (438) imply: % 193.32/26.96 | | | | | | | | | (439) c_member(all_622_1, all_872_7, v_L) = 0 % 193.32/26.96 | | | | | | | | | % 193.32/26.96 | | | | | | | | | GROUND_INST: instantiating (fact_wf__not__sym) with v_x, % 193.32/26.96 | | | | | | | | | all_872_8, v_L, tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.96 | | | | | | | | | all_622_1, all_872_1, simplifying with (15), (16), % 193.32/26.96 | | | | | | | | | (17), (23), (170), (179), (216) gives: % 193.32/26.96 | | | | | | | | | (440) ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 193.32/26.96 | | | | | | | | | (c_Wellfounded_Owf(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.96 | | | | | | | | | v_L) = v0 & % 193.32/26.96 | | | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.96 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v_x) % 193.32/26.96 | | | | | | | | | = v1 & c_member(all_622_1, v1, v_L) = v2 & $i(v1) & % 193.32/26.96 | | | | | | | | | ( ~ (v2 = 0) | ~ (v0 = 0))) % 193.32/26.96 | | | | | | | | | % 193.32/26.96 | | | | | | | | | GROUND_INST: instantiating (44) with v_y, all_872_8, all_872_7, % 193.32/26.96 | | | | | | | | | simplifying with (170), (212), (217) gives: % 193.32/26.96 | | | | | | | | | (441) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_676_0, % 193.32/26.96 | | | | | | | | | all_872_7, v_L) = v0) | ! [v0: $i] : ! [v1: $i] % 193.32/26.96 | | | | | | | | | : ( ~ % 193.32/26.96 | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.96 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = v1) % 193.32/26.96 | | | | | | | | | | ~ $i(v0) | ? [v2: $i] : ? [v3: any] : ? [v4: % 193.32/26.96 | | | | | | | | | any] : % 193.32/26.96 | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.96 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v0) % 193.32/26.96 | | | | | | | | | = v2 & c_member(all_676_0, v2, v_L) = v3 & % 193.32/26.96 | | | | | | | | | c_member(all_676_0, v1, v_L) = v4 & $i(v2) & ( ~ % 193.32/26.96 | | | | | | | | | (v3 = 0) | v4 = 0))) % 193.32/26.96 | | | | | | | | | % 193.32/26.96 | | | | | | | | | GROUND_INST: instantiating (220) with v_y, all_1091_1, % 193.32/26.96 | | | | | | | | | simplifying with (217), (238) gives: % 193.32/26.96 | | | | | | | | | (442) ? [v0: $i] : ? [v1: any] : ? [v2: any] : % 193.32/26.96 | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.96 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v_y) % 193.32/26.96 | | | | | | | | | = v0 & c_member(all_676_0, v0, v_L) = v1 & % 193.32/26.96 | | | | | | | | | c_member(all_676_0, all_1091_1, v_L) = v2 & $i(v0) % 193.32/26.96 | | | | | | | | | & ( ~ (v1 = 0) | v2 = 0)) % 193.32/26.96 | | | | | | | | | % 193.32/26.96 | | | | | | | | | GROUND_INST: instantiating (44) with v_x, v_y, all_1091_1, % 193.32/26.96 | | | | | | | | | simplifying with (16), (217), (238) gives: % 193.32/26.96 | | | | | | | | | (443) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_676_0, % 193.32/26.96 | | | | | | | | | all_1091_1, v_L) = v0) | ! [v0: $i] : ! [v1: % 193.32/26.96 | | | | | | | | | $i] : ( ~ % 193.32/26.96 | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.96 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v0) = v1) % 193.32/26.96 | | | | | | | | | | ~ $i(v0) | ? [v2: $i] : ? [v3: any] : ? [v4: % 193.32/26.96 | | | | | | | | | any] : % 193.32/26.96 | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.96 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = v2 % 193.32/26.96 | | | | | | | | | & c_member(all_676_0, v2, v_L) = v3 & % 193.32/26.96 | | | | | | | | | c_member(all_676_0, v1, v_L) = v4 & $i(v2) & ( ~ % 193.32/26.96 | | | | | | | | | (v3 = 0) | v4 = 0))) % 193.32/26.96 | | | | | | | | | % 193.32/26.96 | | | | | | | | | GROUND_INST: instantiating (220) with all_1080_4, all_1080_1, % 193.32/26.96 | | | | | | | | | simplifying with (206), (209) gives: % 193.32/26.96 | | | | | | | | | (444) ? [v0: $i] : ? [v1: any] : ? [v2: any] : % 193.32/26.96 | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.96 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, % 193.32/26.96 | | | | | | | | | all_1080_4) = v0 & c_member(all_676_0, v0, v_L) = % 193.32/26.96 | | | | | | | | | v1 & c_member(all_676_0, all_1080_1, v_L) = v2 & % 193.32/26.96 | | | | | | | | | $i(v0) & ( ~ (v1 = 0) | v2 = 0)) % 193.32/26.96 | | | | | | | | | % 193.32/26.96 | | | | | | | | | DELTA: instantiating (440) with fresh symbols all_1237_0, % 193.32/26.96 | | | | | | | | | all_1237_1, all_1237_2 gives: % 193.32/26.96 | | | | | | | | | (445) c_Wellfounded_Owf(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.96 | | | | | | | | | v_L) = all_1237_2 & % 193.32/26.96 | | | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.96 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v_x) = % 193.32/26.96 | | | | | | | | | all_1237_1 & c_member(all_622_1, all_1237_1, v_L) = % 193.32/26.96 | | | | | | | | | all_1237_0 & $i(all_1237_1) & ( ~ (all_1237_0 = 0) | % 193.32/26.96 | | | | | | | | | ~ (all_1237_2 = 0)) % 193.32/26.96 | | | | | | | | | % 193.32/26.96 | | | | | | | | | ALPHA: (445) implies: % 193.32/26.96 | | | | | | | | | (446) c_member(all_622_1, all_1237_1, v_L) = all_1237_0 % 193.32/26.96 | | | | | | | | | (447) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.96 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v_x) = % 193.32/26.96 | | | | | | | | | all_1237_1 % 193.32/26.96 | | | | | | | | | % 193.32/26.96 | | | | | | | | | DELTA: instantiating (444) with fresh symbols all_1241_0, % 193.32/26.96 | | | | | | | | | all_1241_1, all_1241_2 gives: % 193.32/26.96 | | | | | | | | | (448) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.96 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, % 193.32/26.96 | | | | | | | | | all_1080_4) = all_1241_2 & c_member(all_676_0, % 193.32/26.96 | | | | | | | | | all_1241_2, v_L) = all_1241_1 & c_member(all_676_0, % 193.32/26.96 | | | | | | | | | all_1080_1, v_L) = all_1241_0 & $i(all_1241_2) & ( % 193.32/26.96 | | | | | | | | | ~ (all_1241_1 = 0) | all_1241_0 = 0) % 193.32/26.96 | | | | | | | | | % 193.32/26.96 | | | | | | | | | ALPHA: (448) implies: % 193.32/26.96 | | | | | | | | | (449) c_member(all_676_0, all_1080_1, v_L) = all_1241_0 % 193.32/26.96 | | | | | | | | | (450) c_member(all_676_0, all_1241_2, v_L) = all_1241_1 % 193.32/26.96 | | | | | | | | | (451) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.96 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, % 193.32/26.96 | | | | | | | | | all_1080_4) = all_1241_2 % 193.32/26.96 | | | | | | | | | (452) ~ (all_1241_1 = 0) | all_1241_0 = 0 % 193.32/26.96 | | | | | | | | | % 193.32/26.96 | | | | | | | | | DELTA: instantiating (442) with fresh symbols all_1243_0, % 193.32/26.96 | | | | | | | | | all_1243_1, all_1243_2 gives: % 193.32/26.96 | | | | | | | | | (453) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.96 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v_y) = % 193.32/26.96 | | | | | | | | | all_1243_2 & c_member(all_676_0, all_1243_2, v_L) = % 193.32/26.96 | | | | | | | | | all_1243_1 & c_member(all_676_0, all_1091_1, v_L) = % 193.32/26.96 | | | | | | | | | all_1243_0 & $i(all_1243_2) & ( ~ (all_1243_1 = 0) | % 193.32/26.96 | | | | | | | | | all_1243_0 = 0) % 193.32/26.96 | | | | | | | | | % 193.32/26.96 | | | | | | | | | ALPHA: (453) implies: % 193.32/26.96 | | | | | | | | | (454) c_member(all_676_0, all_1091_1, v_L) = all_1243_0 % 193.32/26.96 | | | | | | | | | % 193.32/26.96 | | | | | | | | | REDUCE: (89), (450) imply: % 193.32/26.96 | | | | | | | | | (455) c_member(all_622_1, all_1241_2, v_L) = all_1241_1 % 193.32/26.96 | | | | | | | | | % 193.32/26.96 | | | | | | | | | REDUCE: (89), (454) imply: % 193.32/26.96 | | | | | | | | | (456) c_member(all_622_1, all_1091_1, v_L) = all_1243_0 % 193.32/26.96 | | | | | | | | | % 193.32/26.96 | | | | | | | | | REDUCE: (89), (449) imply: % 193.32/26.96 | | | | | | | | | (457) c_member(all_622_1, all_1080_1, v_L) = all_1241_0 % 193.32/26.96 | | | | | | | | | % 193.32/26.96 | | | | | | | | | BETA: splitting (441) gives: % 193.32/26.96 | | | | | | | | | % 193.32/26.96 | | | | | | | | | Case 1: % 193.32/26.96 | | | | | | | | | | % 193.32/26.96 | | | | | | | | | | (458) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_676_0, % 193.32/26.96 | | | | | | | | | | all_872_7, v_L) = v0) % 193.32/26.96 | | | | | | | | | | % 193.32/26.96 | | | | | | | | | | DELTA: instantiating (458) with fresh symbol all_1123_0 % 193.32/26.96 | | | | | | | | | | gives: % 193.32/26.96 | | | | | | | | | | (459) ~ (all_1123_0 = 0) & c_member(all_676_0, % 193.32/26.96 | | | | | | | | | | all_872_7, v_L) = all_1123_0 % 193.32/26.96 | | | | | | | | | | % 193.32/26.96 | | | | | | | | | | REF_CLOSE: (20), (89), (439), (459) are inconsistent by % 193.32/26.96 | | | | | | | | | | sub-proof #14. % 193.32/26.96 | | | | | | | | | | % 193.32/26.96 | | | | | | | | | Case 2: % 193.32/26.96 | | | | | | | | | | % 193.32/26.96 | | | | | | | | | | (460) ! [v0: $i] : ! [v1: $i] : ( ~ % 193.32/26.96 | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.96 | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = % 193.32/26.96 | | | | | | | | | | v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: any] : % 193.32/26.96 | | | | | | | | | | ? [v4: any] : % 193.32/26.96 | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.96 | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, % 193.32/26.96 | | | | | | | | | | v0) = v2 & c_member(all_676_0, v2, v_L) = v3 % 193.32/26.96 | | | | | | | | | | & c_member(all_676_0, v1, v_L) = v4 & $i(v2) & % 193.32/26.96 | | | | | | | | | | ( ~ (v3 = 0) | v4 = 0))) % 193.32/26.96 | | | | | | | | | | % 193.32/26.96 | | | | | | | | | | GROUND_INST: instantiating (460) with v_x, all_872_5, % 193.32/26.96 | | | | | | | | | | simplifying with (16), (213) gives: % 193.32/26.96 | | | | | | | | | | (461) ? [v0: $i] : ? [v1: any] : ? [v2: any] : % 193.32/26.96 | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.96 | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, % 193.32/26.96 | | | | | | | | | | v_x) = v0 & c_member(all_676_0, v0, v_L) = v1 & % 193.32/26.96 | | | | | | | | | | c_member(all_676_0, all_872_5, v_L) = v2 & $i(v0) % 193.32/26.96 | | | | | | | | | | & ( ~ (v1 = 0) | v2 = 0)) % 193.32/26.96 | | | | | | | | | | % 193.32/26.96 | | | | | | | | | | DELTA: instantiating (461) with fresh symbols all_1253_0, % 193.32/26.96 | | | | | | | | | | all_1253_1, all_1253_2 gives: % 193.32/26.96 | | | | | | | | | | (462) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.96 | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v_x) % 193.32/26.96 | | | | | | | | | | = all_1253_2 & c_member(all_676_0, all_1253_2, v_L) % 193.32/26.96 | | | | | | | | | | = all_1253_1 & c_member(all_676_0, all_872_5, v_L) % 193.32/26.96 | | | | | | | | | | = all_1253_0 & $i(all_1253_2) & ( ~ (all_1253_1 = % 193.32/26.96 | | | | | | | | | | 0) | all_1253_0 = 0) % 193.32/26.96 | | | | | | | | | | % 193.32/26.96 | | | | | | | | | | ALPHA: (462) implies: % 193.32/26.96 | | | | | | | | | | (463) c_member(all_676_0, all_872_5, v_L) = all_1253_0 % 193.32/26.96 | | | | | | | | | | (464) c_member(all_676_0, all_1253_2, v_L) = all_1253_1 % 193.32/26.96 | | | | | | | | | | (465) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.96 | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v_x) % 193.32/26.96 | | | | | | | | | | = all_1253_2 % 193.32/26.96 | | | | | | | | | | (466) ~ (all_1253_1 = 0) | all_1253_0 = 0 % 193.32/26.96 | | | | | | | | | | % 193.32/26.96 | | | | | | | | | | REDUCE: (89), (464) imply: % 193.32/26.96 | | | | | | | | | | (467) c_member(all_622_1, all_1253_2, v_L) = all_1253_1 % 193.32/26.96 | | | | | | | | | | % 193.32/26.96 | | | | | | | | | | REDUCE: (89), (463) imply: % 193.32/26.97 | | | | | | | | | | (468) c_member(all_622_1, all_872_5, v_L) = all_1253_0 % 193.32/26.97 | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | GROUND_INST: instantiating (20) with all_872_4, all_1253_0, % 193.32/26.97 | | | | | | | | | | v_L, all_872_5, all_622_1, simplifying with (186), % 193.32/26.97 | | | | | | | | | | (468) gives: % 193.32/26.97 | | | | | | | | | | (469) all_1253_0 = all_872_4 % 193.32/26.97 | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | GROUND_INST: instantiating (20) with all_1080_0, all_1241_0, % 193.32/26.97 | | | | | | | | | | v_L, all_1080_1, all_622_1, simplifying with % 193.32/26.97 | | | | | | | | | | (214), (457) gives: % 193.32/26.97 | | | | | | | | | | (470) all_1241_0 = all_1080_0 % 193.32/26.97 | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | GROUND_INST: instantiating (20) with 0, all_1243_0, v_L, % 193.32/26.97 | | | | | | | | | | all_1091_1, all_622_1, simplifying with (437), % 193.32/26.97 | | | | | | | | | | (456) gives: % 193.32/26.97 | | | | | | | | | | (471) all_1243_0 = 0 % 193.32/26.97 | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | GROUND_INST: instantiating (21) with all_872_3, all_1253_2, % 193.32/26.97 | | | | | | | | | | v_x, all_872_8, tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.97 | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with % 193.32/26.97 | | | | | | | | | | (182), (465) gives: % 193.32/26.97 | | | | | | | | | | (472) all_1253_2 = all_872_3 % 193.32/26.97 | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | GROUND_INST: instantiating (21) with all_1237_1, all_1253_2, % 193.32/26.97 | | | | | | | | | | v_x, all_872_8, tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.97 | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with % 193.32/26.97 | | | | | | | | | | (447), (465) gives: % 193.32/26.97 | | | | | | | | | | (473) all_1253_2 = all_1237_1 % 193.32/26.97 | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | GROUND_INST: instantiating (21) with all_1080_3, all_1241_2, % 193.32/26.97 | | | | | | | | | | all_1080_4, all_872_8, % 193.32/26.97 | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.97 | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with % 193.32/26.97 | | | | | | | | | | (210), (451) gives: % 193.32/26.97 | | | | | | | | | | (474) all_1241_2 = all_1080_3 % 193.32/26.97 | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | COMBINE_EQS: (472), (473) imply: % 193.32/26.97 | | | | | | | | | | (475) all_1237_1 = all_872_3 % 193.32/26.97 | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | REDUCE: (467), (472) imply: % 193.32/26.97 | | | | | | | | | | (476) c_member(all_622_1, all_872_3, v_L) = all_1253_1 % 193.32/26.97 | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | REDUCE: (455), (474) imply: % 193.32/26.97 | | | | | | | | | | (477) c_member(all_622_1, all_1080_3, v_L) = all_1241_1 % 193.32/26.97 | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | REDUCE: (446), (475) imply: % 193.32/26.97 | | | | | | | | | | (478) c_member(all_622_1, all_872_3, v_L) = all_1237_0 % 193.32/26.97 | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | BETA: splitting (466) gives: % 193.32/26.97 | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | Case 1: % 193.32/26.97 | | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | | (479) ~ (all_1253_1 = 0) % 193.32/26.97 | | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | | BETA: splitting (443) gives: % 193.32/26.97 | | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | | Case 1: % 193.32/26.97 | | | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | | | (480) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_676_0, % 193.32/26.97 | | | | | | | | | | | | all_1091_1, v_L) = v0) % 193.32/26.97 | | | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | | | DELTA: instantiating (480) with fresh symbol all_1285_0 % 193.32/26.97 | | | | | | | | | | | | gives: % 193.32/26.97 | | | | | | | | | | | | (481) ~ (all_1285_0 = 0) & c_member(all_676_0, % 193.32/26.97 | | | | | | | | | | | | all_1091_1, v_L) = all_1285_0 % 193.32/26.97 | | | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | | | ALPHA: (481) implies: % 193.32/26.97 | | | | | | | | | | | | (482) ~ (all_1285_0 = 0) % 193.32/26.97 | | | | | | | | | | | | (483) c_member(all_676_0, all_1091_1, v_L) = all_1285_0 % 193.32/26.97 | | | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | | | REDUCE: (89), (483) imply: % 193.32/26.97 | | | | | | | | | | | | (484) c_member(all_622_1, all_1091_1, v_L) = all_1285_0 % 193.32/26.97 | | | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | | | GROUND_INST: instantiating (20) with 0, all_1285_0, v_L, % 193.32/26.97 | | | | | | | | | | | | all_1091_1, all_622_1, simplifying with (437), % 193.32/26.97 | | | | | | | | | | | | (484) gives: % 193.32/26.97 | | | | | | | | | | | | (485) all_1285_0 = 0 % 193.32/26.97 | | | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | | | REDUCE: (482), (485) imply: % 193.32/26.97 | | | | | | | | | | | | (486) $false % 193.32/26.97 | | | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | | | CLOSE: (486) is inconsistent. % 193.32/26.97 | | | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | | Case 2: % 193.32/26.97 | | | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | | | GROUND_INST: instantiating (20) with all_872_2, all_1253_1, % 193.32/26.97 | | | | | | | | | | | | v_L, all_872_3, all_622_1, simplifying with (185), % 193.32/26.97 | | | | | | | | | | | | (476) gives: % 193.32/26.97 | | | | | | | | | | | | (487) all_1253_1 = all_872_2 % 193.32/26.97 | | | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | | | GROUND_INST: instantiating (20) with all_1237_0, all_1253_1, % 193.32/26.97 | | | | | | | | | | | | v_L, all_872_3, all_622_1, simplifying with (476), % 193.32/26.97 | | | | | | | | | | | | (478) gives: % 193.32/26.97 | | | | | | | | | | | | (488) all_1253_1 = all_1237_0 % 193.32/26.97 | | | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | | | GROUND_INST: instantiating (20) with all_1080_2, all_1241_1, % 193.32/26.97 | | | | | | | | | | | | v_L, all_1080_3, all_622_1, simplifying with % 193.32/26.97 | | | | | | | | | | | | (215), (477) gives: % 193.32/26.97 | | | | | | | | | | | | (489) all_1241_1 = all_1080_2 % 193.32/26.97 | | | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | | | COMBINE_EQS: (487), (488) imply: % 193.32/26.97 | | | | | | | | | | | | (490) all_1237_0 = all_872_2 % 193.32/26.97 | | | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | | | SIMP: (490) implies: % 193.32/26.97 | | | | | | | | | | | | (491) all_1237_0 = all_872_2 % 193.32/26.97 | | | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | | | REDUCE: (479), (487) imply: % 193.32/26.97 | | | | | | | | | | | | (492) ~ (all_872_2 = 0) % 193.32/26.97 | | | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | | | BETA: splitting (211) gives: % 193.32/26.97 | | | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | | | Case 1: % 193.32/26.97 | | | | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | | | | (493) all_1080_2 = 0 & ~ (all_1080_0 = 0) & ~ % 193.32/26.97 | | | | | | | | | | | | | (all_1080_4 = v_y) % 193.32/26.97 | | | | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | | | | ALPHA: (493) implies: % 193.32/26.97 | | | | | | | | | | | | | (494) all_1080_2 = 0 % 193.32/26.97 | | | | | | | | | | | | | (495) ~ (all_1080_0 = 0) % 193.32/26.97 | | | | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | | | | COMBINE_EQS: (489), (494) imply: % 193.32/26.97 | | | | | | | | | | | | | (496) all_1241_1 = 0 % 193.32/26.97 | | | | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | | | | BETA: splitting (452) gives: % 193.32/26.97 | | | | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | | | | Case 1: % 193.32/26.97 | | | | | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | | | | | (497) ~ (all_1241_1 = 0) % 193.32/26.97 | | | | | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | | | | | REDUCE: (496), (497) imply: % 193.32/26.97 | | | | | | | | | | | | | | (498) $false % 193.32/26.97 | | | | | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | | | | | CLOSE: (498) is inconsistent. % 193.32/26.97 | | | | | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | | | | Case 2: % 193.32/26.97 | | | | | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | | | | | (499) all_1241_0 = 0 % 193.32/26.97 | | | | | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | | | | | COMBINE_EQS: (470), (499) imply: % 193.32/26.97 | | | | | | | | | | | | | | (500) all_1080_0 = 0 % 193.32/26.97 | | | | | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | | | | | SIMP: (500) implies: % 193.32/26.97 | | | | | | | | | | | | | | (501) all_1080_0 = 0 % 193.32/26.97 | | | | | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | | | | | REDUCE: (495), (501) imply: % 193.32/26.97 | | | | | | | | | | | | | | (502) $false % 193.32/26.97 | | | | | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | | | | | CLOSE: (502) is inconsistent. % 193.32/26.97 | | | | | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | | | | End of split % 193.32/26.97 | | | | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | | | Case 2: % 193.32/26.97 | | | | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | | | | (503) (all_1080_4 = v_y & all_872_2 = 0) | (all_1080_4 = % 193.32/26.97 | | | | | | | | | | | | | v_y & all_872_8 = v_x) % 193.32/26.97 | | | | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | | | | BETA: splitting (503) gives: % 193.32/26.97 | | | | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | | | | Case 1: % 193.32/26.97 | | | | | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | | | | | (504) all_1080_4 = v_y & all_872_2 = 0 % 193.32/26.97 | | | | | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | | | | | ALPHA: (504) implies: % 193.32/26.97 | | | | | | | | | | | | | | (505) all_872_2 = 0 % 193.32/26.97 | | | | | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | | | | | REDUCE: (492), (505) imply: % 193.32/26.97 | | | | | | | | | | | | | | (506) $false % 193.32/26.97 | | | | | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | | | | | CLOSE: (506) is inconsistent. % 193.32/26.97 | | | | | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | | | | Case 2: % 193.32/26.97 | | | | | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | | | | | (507) all_1080_4 = v_y & all_872_8 = v_x % 193.32/26.97 | | | | | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | | | | | ALPHA: (507) implies: % 193.32/26.97 | | | | | | | | | | | | | | (508) all_872_8 = v_x % 193.32/26.97 | | | | | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | | | | | REDUCE: (224), (508) imply: % 193.32/26.97 | | | | | | | | | | | | | | (509) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.97 | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v_x) = % 193.32/26.97 | | | | | | | | | | | | | | all_1086_2 % 193.32/26.97 | | | | | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | | | | | REDUCE: (182), (508) imply: % 193.32/26.97 | | | | | | | | | | | | | | (510) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.97 | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v_x) = % 193.32/26.97 | | | | | | | | | | | | | | all_872_3 % 193.32/26.97 | | | | | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | | | | | REDUCE: (179), (508) imply: % 193.32/26.97 | | | | | | | | | | | | | | (511) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.97 | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v_x) = % 193.32/26.97 | | | | | | | | | | | | | | all_872_1 % 193.32/26.97 | | | | | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | | | | | GROUND_INST: instantiating (21) with all_872_1, all_1086_2, % 193.32/26.97 | | | | | | | | | | | | | | v_x, v_x, tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.97 | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with % 193.32/26.97 | | | | | | | | | | | | | | (509), (511) gives: % 193.32/26.97 | | | | | | | | | | | | | | (512) all_1086_2 = all_872_1 % 193.32/26.97 | | | | | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | | | | | GROUND_INST: instantiating (21) with all_872_3, all_1086_2, % 193.32/26.97 | | | | | | | | | | | | | | v_x, v_x, tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.97 | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with % 193.32/26.97 | | | | | | | | | | | | | | (509), (510) gives: % 193.32/26.97 | | | | | | | | | | | | | | (513) all_1086_2 = all_872_3 % 193.32/26.97 | | | | | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | | | | | COMBINE_EQS: (512), (513) imply: % 193.32/26.97 | | | | | | | | | | | | | | (514) all_872_1 = all_872_3 % 193.32/26.97 | | | | | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | | | | | SIMP: (514) implies: % 193.32/26.97 | | | | | | | | | | | | | | (515) all_872_1 = all_872_3 % 193.32/26.97 | | | | | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | | | | | REDUCE: (216), (515) imply: % 193.32/26.97 | | | | | | | | | | | | | | (516) c_member(all_622_1, all_872_3, v_L) = 0 % 193.32/26.97 | | | | | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | | | | | REF_CLOSE: (20), (185), (492), (516) are inconsistent by % 193.32/26.97 | | | | | | | | | | | | | | sub-proof #13. % 193.32/26.97 | | | | | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | | | | End of split % 193.32/26.97 | | | | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | | | End of split % 193.32/26.97 | | | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | | End of split % 193.32/26.97 | | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | Case 2: % 193.32/26.97 | | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | | (517) all_1253_0 = 0 % 193.32/26.97 | | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | | COMBINE_EQS: (469), (517) imply: % 193.32/26.97 | | | | | | | | | | | (518) all_872_4 = 0 % 193.32/26.97 | | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | | REDUCE: (435), (518) imply: % 193.32/26.97 | | | | | | | | | | | (519) $false % 193.32/26.97 | | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | | CLOSE: (519) is inconsistent. % 193.32/26.97 | | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | End of split % 193.32/26.97 | | | | | | | | | | % 193.32/26.97 | | | | | | | | | End of split % 193.32/26.97 | | | | | | | | | % 193.32/26.97 | | | | | | | | Case 2: % 193.32/26.97 | | | | | | | | | % 193.32/26.97 | | | | | | | | | (520) ~ (all_872_6 = 0) % 193.32/26.97 | | | | | | | | | % 193.32/26.97 | | | | | | | | | BETA: splitting (249) gives: % 193.32/26.97 | | | | | | | | | % 193.32/26.97 | | | | | | | | | Case 1: % 193.32/26.97 | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | (521) all_1096_0 = 0 % 193.32/26.97 | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | REDUCE: (251), (521) imply: % 193.32/26.97 | | | | | | | | | | (522) c_member(all_622_1, all_1096_1, v_L) = 0 % 193.32/26.97 | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | BETA: splitting (199) gives: % 193.32/26.97 | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | Case 1: % 193.32/26.97 | | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | | (523) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_676_0, % 193.32/26.97 | | | | | | | | | | | all_872_3, v_L) = v0) % 193.32/26.97 | | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | | DELTA: instantiating (523) with fresh symbol all_1197_0 % 193.32/26.97 | | | | | | | | | | | gives: % 193.32/26.97 | | | | | | | | | | | (524) ~ (all_1197_0 = 0) & c_member(all_676_0, % 193.32/26.97 | | | | | | | | | | | all_872_3, v_L) = all_1197_0 % 193.32/26.97 | | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | | ALPHA: (524) implies: % 193.32/26.97 | | | | | | | | | | | (525) ~ (all_1197_0 = 0) % 193.32/26.97 | | | | | | | | | | | (526) c_member(all_676_0, all_872_3, v_L) = all_1197_0 % 193.32/26.97 | | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | | REDUCE: (89), (526) imply: % 193.32/26.97 | | | | | | | | | | | (527) c_member(all_622_1, all_872_3, v_L) = all_1197_0 % 193.32/26.97 | | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | | GROUND_INST: instantiating (20) with all_872_2, all_1197_0, % 193.32/26.97 | | | | | | | | | | | v_L, all_872_3, all_622_1, simplifying with (185), % 193.32/26.97 | | | | | | | | | | | (527) gives: % 193.32/26.97 | | | | | | | | | | | (528) all_1197_0 = all_872_2 % 193.32/26.97 | | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | | REDUCE: (525), (528) imply: % 193.32/26.97 | | | | | | | | | | | (529) ~ (all_872_2 = 0) % 193.32/26.97 | | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | | GROUND_INST: instantiating (fact_wf__not__sym) with v_x, % 193.32/26.97 | | | | | | | | | | | all_872_8, v_L, tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.97 | | | | | | | | | | | all_622_1, all_872_1, simplifying with (15), (16), % 193.32/26.97 | | | | | | | | | | | (17), (23), (170), (179), (216) gives: % 193.32/26.97 | | | | | | | | | | | (530) ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 193.32/26.97 | | | | | | | | | | | (c_Wellfounded_Owf(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.97 | | | | | | | | | | | v_L) = v0 & % 193.32/26.97 | | | | | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.97 | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, % 193.32/26.97 | | | | | | | | | | | v_x) = v1 & c_member(all_622_1, v1, v_L) = v2 % 193.32/26.97 | | | | | | | | | | | & $i(v1) & ( ~ (v2 = 0) | ~ (v0 = 0))) % 193.32/26.97 | | | | | | | | | | | % 193.32/26.97 | | | | | | | | | | | GROUND_INST: instantiating (44) with v_x, v_y, all_1091_1, % 193.32/26.97 | | | | | | | | | | | simplifying with (16), (217), (238) gives: % 193.32/26.98 | | | | | | | | | | | (531) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_676_0, % 193.32/26.98 | | | | | | | | | | | all_1091_1, v_L) = v0) | ! [v0: $i] : ! [v1: % 193.32/26.98 | | | | | | | | | | | $i] : ( ~ % 193.32/26.98 | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.98 | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v0) = % 193.32/26.98 | | | | | | | | | | | v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: any] : % 193.32/26.98 | | | | | | | | | | | ? [v4: any] : % 193.32/26.98 | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.98 | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = % 193.32/26.98 | | | | | | | | | | | v2 & c_member(all_676_0, v2, v_L) = v3 & % 193.32/26.98 | | | | | | | | | | | c_member(all_676_0, v1, v_L) = v4 & $i(v2) & ( % 193.32/26.98 | | | | | | | | | | | ~ (v3 = 0) | v4 = 0))) % 193.32/26.98 | | | | | | | | | | | % 193.32/26.98 | | | | | | | | | | | GROUND_INST: instantiating (220) with all_1080_4, all_1080_1, % 193.32/26.98 | | | | | | | | | | | simplifying with (206), (209) gives: % 193.32/26.98 | | | | | | | | | | | (532) ? [v0: $i] : ? [v1: any] : ? [v2: any] : % 193.32/26.98 | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.98 | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, % 193.32/26.98 | | | | | | | | | | | all_1080_4) = v0 & c_member(all_676_0, v0, % 193.32/26.98 | | | | | | | | | | | v_L) = v1 & c_member(all_676_0, all_1080_1, % 193.32/26.98 | | | | | | | | | | | v_L) = v2 & $i(v0) & ( ~ (v1 = 0) | v2 = 0)) % 193.32/26.98 | | | | | | | | | | | % 193.32/26.98 | | | | | | | | | | | GROUND_INST: instantiating (44) with all_872_8, v_y, % 193.32/26.98 | | | | | | | | | | | all_1096_1, simplifying with (170), (217), (250) % 193.32/26.98 | | | | | | | | | | | gives: % 193.32/26.98 | | | | | | | | | | | (533) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_676_0, % 193.32/26.98 | | | | | | | | | | | all_1096_1, v_L) = v0) | ! [v0: $i] : ! [v1: % 193.32/26.98 | | | | | | | | | | | $i] : ( ~ % 193.32/26.98 | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.98 | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, % 193.32/26.98 | | | | | | | | | | | v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? % 193.32/26.98 | | | | | | | | | | | [v3: any] : ? [v4: any] : % 193.32/26.98 | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.98 | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = % 193.32/26.98 | | | | | | | | | | | v2 & c_member(all_676_0, v2, v_L) = v3 & % 193.32/26.98 | | | | | | | | | | | c_member(all_676_0, v1, v_L) = v4 & $i(v2) & ( % 193.32/26.98 | | | | | | | | | | | ~ (v3 = 0) | v4 = 0))) % 193.32/26.98 | | | | | | | | | | | % 193.32/26.98 | | | | | | | | | | | DELTA: instantiating (532) with fresh symbols all_1252_0, % 193.32/26.98 | | | | | | | | | | | all_1252_1, all_1252_2 gives: % 193.32/26.98 | | | | | | | | | | | (534) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.98 | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, % 193.32/26.98 | | | | | | | | | | | all_1080_4) = all_1252_2 & c_member(all_676_0, % 193.32/26.98 | | | | | | | | | | | all_1252_2, v_L) = all_1252_1 & % 193.32/26.98 | | | | | | | | | | | c_member(all_676_0, all_1080_1, v_L) = all_1252_0 % 193.32/26.98 | | | | | | | | | | | & $i(all_1252_2) & ( ~ (all_1252_1 = 0) | % 193.32/26.98 | | | | | | | | | | | all_1252_0 = 0) % 193.32/26.98 | | | | | | | | | | | % 193.32/26.98 | | | | | | | | | | | ALPHA: (534) implies: % 193.32/26.98 | | | | | | | | | | | (535) c_member(all_676_0, all_1080_1, v_L) = all_1252_0 % 193.32/26.98 | | | | | | | | | | | (536) c_member(all_676_0, all_1252_2, v_L) = all_1252_1 % 193.32/26.98 | | | | | | | | | | | (537) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.98 | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, % 193.32/26.98 | | | | | | | | | | | all_1080_4) = all_1252_2 % 193.32/26.98 | | | | | | | | | | | (538) ~ (all_1252_1 = 0) | all_1252_0 = 0 % 193.32/26.98 | | | | | | | | | | | % 193.32/26.98 | | | | | | | | | | | DELTA: instantiating (530) with fresh symbols all_1264_0, % 193.32/26.98 | | | | | | | | | | | all_1264_1, all_1264_2 gives: % 193.32/26.98 | | | | | | | | | | | (539) c_Wellfounded_Owf(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.98 | | | | | | | | | | | v_L) = all_1264_2 & % 193.32/26.98 | | | | | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.98 | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v_x) % 193.32/26.98 | | | | | | | | | | | = all_1264_1 & c_member(all_622_1, all_1264_1, % 193.32/26.98 | | | | | | | | | | | v_L) = all_1264_0 & $i(all_1264_1) & ( ~ % 193.32/26.98 | | | | | | | | | | | (all_1264_0 = 0) | ~ (all_1264_2 = 0)) % 193.32/26.98 | | | | | | | | | | | % 193.32/26.98 | | | | | | | | | | | ALPHA: (539) implies: % 193.32/26.98 | | | | | | | | | | | (540) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.98 | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v_x) % 193.32/26.98 | | | | | | | | | | | = all_1264_1 % 193.32/26.98 | | | | | | | | | | | % 193.32/26.98 | | | | | | | | | | | REDUCE: (89), (536) imply: % 193.32/26.98 | | | | | | | | | | | (541) c_member(all_622_1, all_1252_2, v_L) = all_1252_1 % 193.32/26.98 | | | | | | | | | | | % 193.32/26.98 | | | | | | | | | | | REDUCE: (89), (535) imply: % 193.32/26.98 | | | | | | | | | | | (542) c_member(all_622_1, all_1080_1, v_L) = all_1252_0 % 193.32/26.98 | | | | | | | | | | | % 193.32/26.98 | | | | | | | | | | | BETA: splitting (531) gives: % 193.32/26.98 | | | | | | | | | | | % 193.32/26.98 | | | | | | | | | | | Case 1: % 193.32/26.98 | | | | | | | | | | | | % 193.32/26.98 | | | | | | | | | | | | (543) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_676_0, % 193.32/26.98 | | | | | | | | | | | | all_1091_1, v_L) = v0) % 193.32/26.98 | | | | | | | | | | | | % 193.32/26.98 | | | | | | | | | | | | DELTA: instantiating (543) with fresh symbol all_1271_0 % 193.32/26.98 | | | | | | | | | | | | gives: % 193.32/26.98 | | | | | | | | | | | | (544) ~ (all_1271_0 = 0) & c_member(all_676_0, % 193.32/26.98 | | | | | | | | | | | | all_1091_1, v_L) = all_1271_0 % 193.32/26.98 | | | | | | | | | | | | % 193.32/26.98 | | | | | | | | | | | | ALPHA: (544) implies: % 193.32/26.98 | | | | | | | | | | | | (545) ~ (all_1271_0 = 0) % 193.32/26.98 | | | | | | | | | | | | (546) c_member(all_676_0, all_1091_1, v_L) = all_1271_0 % 193.32/26.98 | | | | | | | | | | | | % 193.32/26.98 | | | | | | | | | | | | REDUCE: (89), (546) imply: % 193.32/26.98 | | | | | | | | | | | | (547) c_member(all_622_1, all_1091_1, v_L) = all_1271_0 % 193.32/26.98 | | | | | | | | | | | | % 193.32/26.98 | | | | | | | | | | | | GROUND_INST: instantiating (20) with 0, all_1271_0, v_L, % 193.32/26.98 | | | | | | | | | | | | all_1091_1, all_622_1, simplifying with (437), % 193.32/26.98 | | | | | | | | | | | | (547) gives: % 193.32/26.98 | | | | | | | | | | | | (548) all_1271_0 = 0 % 193.32/26.98 | | | | | | | | | | | | % 193.32/26.98 | | | | | | | | | | | | REDUCE: (545), (548) imply: % 193.32/26.98 | | | | | | | | | | | | (549) $false % 193.32/26.98 | | | | | | | | | | | | % 193.32/26.98 | | | | | | | | | | | | CLOSE: (549) is inconsistent. % 193.32/26.98 | | | | | | | | | | | | % 193.32/26.98 | | | | | | | | | | | Case 2: % 193.32/26.98 | | | | | | | | | | | | % 193.32/26.98 | | | | | | | | | | | | (550) ! [v0: $i] : ! [v1: $i] : ( ~ % 193.32/26.98 | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.98 | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v0) = % 193.32/26.98 | | | | | | | | | | | | v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: any] : % 193.32/26.98 | | | | | | | | | | | | ? [v4: any] : % 193.32/26.98 | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.98 | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = % 193.32/26.98 | | | | | | | | | | | | v2 & c_member(all_676_0, v2, v_L) = v3 & % 193.32/26.98 | | | | | | | | | | | | c_member(all_676_0, v1, v_L) = v4 & $i(v2) & ( % 193.32/26.98 | | | | | | | | | | | | ~ (v3 = 0) | v4 = 0))) % 193.32/26.98 | | | | | | | | | | | | % 193.32/26.98 | | | | | | | | | | | | GROUND_INST: instantiating (550) with all_1080_4, all_1080_1, % 193.32/26.98 | | | | | | | | | | | | simplifying with (206), (209) gives: % 193.32/26.98 | | | | | | | | | | | | (551) ? [v0: $i] : ? [v1: any] : ? [v2: any] : % 193.32/26.98 | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.98 | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, % 193.32/26.98 | | | | | | | | | | | | all_1080_4) = v0 & c_member(all_676_0, v0, % 193.32/26.98 | | | | | | | | | | | | v_L) = v1 & c_member(all_676_0, all_1080_1, % 193.32/26.98 | | | | | | | | | | | | v_L) = v2 & $i(v0) & ( ~ (v1 = 0) | v2 = 0)) % 193.32/26.98 | | | | | | | | | | | | % 193.32/26.98 | | | | | | | | | | | | BETA: splitting (533) gives: % 193.32/26.98 | | | | | | | | | | | | % 193.32/26.98 | | | | | | | | | | | | Case 1: % 193.32/26.98 | | | | | | | | | | | | | % 193.32/26.98 | | | | | | | | | | | | | (552) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_676_0, % 193.32/26.98 | | | | | | | | | | | | | all_1096_1, v_L) = v0) % 193.32/26.98 | | | | | | | | | | | | | % 193.32/26.98 | | | | | | | | | | | | | DELTA: instantiating (552) with fresh symbol all_1271_0 % 193.32/26.98 | | | | | | | | | | | | | gives: % 193.32/26.98 | | | | | | | | | | | | | (553) ~ (all_1271_0 = 0) & c_member(all_676_0, % 193.32/26.98 | | | | | | | | | | | | | all_1096_1, v_L) = all_1271_0 % 193.32/26.98 | | | | | | | | | | | | | % 193.32/26.98 | | | | | | | | | | | | | ALPHA: (553) implies: % 193.32/26.98 | | | | | | | | | | | | | (554) ~ (all_1271_0 = 0) % 193.32/26.98 | | | | | | | | | | | | | (555) c_member(all_676_0, all_1096_1, v_L) = all_1271_0 % 193.32/26.98 | | | | | | | | | | | | | % 193.32/26.98 | | | | | | | | | | | | | REDUCE: (89), (555) imply: % 193.32/26.98 | | | | | | | | | | | | | (556) c_member(all_622_1, all_1096_1, v_L) = all_1271_0 % 193.32/26.98 | | | | | | | | | | | | | % 193.32/26.98 | | | | | | | | | | | | | GROUND_INST: instantiating (20) with 0, all_1271_0, v_L, % 193.32/26.98 | | | | | | | | | | | | | all_1096_1, all_622_1, simplifying with (522), % 193.32/26.98 | | | | | | | | | | | | | (556) gives: % 193.32/26.98 | | | | | | | | | | | | | (557) all_1271_0 = 0 % 193.32/26.98 | | | | | | | | | | | | | % 193.32/26.98 | | | | | | | | | | | | | REDUCE: (554), (557) imply: % 193.32/26.98 | | | | | | | | | | | | | (558) $false % 193.32/26.98 | | | | | | | | | | | | | % 193.32/26.98 | | | | | | | | | | | | | CLOSE: (558) is inconsistent. % 193.32/26.98 | | | | | | | | | | | | | % 193.32/26.98 | | | | | | | | | | | | Case 2: % 193.32/26.98 | | | | | | | | | | | | | % 193.32/26.98 | | | | | | | | | | | | | (559) ! [v0: $i] : ! [v1: $i] : ( ~ % 193.32/26.98 | | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.98 | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, % 193.32/26.98 | | | | | | | | | | | | | v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? % 193.32/26.98 | | | | | | | | | | | | | [v3: any] : ? [v4: any] : % 193.32/26.98 | | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.98 | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = % 193.32/26.98 | | | | | | | | | | | | | v2 & c_member(all_676_0, v2, v_L) = v3 & % 193.32/26.98 | | | | | | | | | | | | | c_member(all_676_0, v1, v_L) = v4 & $i(v2) & ( % 193.32/26.98 | | | | | | | | | | | | | ~ (v3 = 0) | v4 = 0))) % 193.32/26.98 | | | | | | | | | | | | | % 193.32/26.98 | | | | | | | | | | | | | GROUND_INST: instantiating (559) with v_x, all_872_3, % 193.32/26.98 | | | | | | | | | | | | | simplifying with (16), (182) gives: % 193.32/26.98 | | | | | | | | | | | | | (560) ? [v0: $i] : ? [v1: any] : ? [v2: any] : % 193.32/26.98 | | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.98 | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v_x) = % 193.32/26.98 | | | | | | | | | | | | | v0 & c_member(all_676_0, v0, v_L) = v1 & % 193.32/26.98 | | | | | | | | | | | | | c_member(all_676_0, all_872_3, v_L) = v2 & % 193.32/26.98 | | | | | | | | | | | | | $i(v0) & ( ~ (v1 = 0) | v2 = 0)) % 193.32/26.98 | | | | | | | | | | | | | % 193.32/26.98 | | | | | | | | | | | | | GROUND_INST: instantiating (559) with all_1080_4, all_1080_3, % 193.32/26.98 | | | | | | | | | | | | | simplifying with (206), (210) gives: % 193.32/26.98 | | | | | | | | | | | | | (561) ? [v0: $i] : ? [v1: any] : ? [v2: any] : % 193.32/26.98 | | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.98 | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, % 193.32/26.98 | | | | | | | | | | | | | all_1080_4) = v0 & c_member(all_676_0, v0, % 193.32/26.98 | | | | | | | | | | | | | v_L) = v1 & c_member(all_676_0, all_1080_3, % 193.32/26.98 | | | | | | | | | | | | | v_L) = v2 & $i(v0) & ( ~ (v1 = 0) | v2 = 0)) % 193.32/26.98 | | | | | | | | | | | | | % 193.32/26.98 | | | | | | | | | | | | | DELTA: instantiating (551) with fresh symbols all_1272_0, % 193.32/26.98 | | | | | | | | | | | | | all_1272_1, all_1272_2 gives: % 193.32/26.98 | | | | | | | | | | | | | (562) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.98 | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, % 193.32/26.98 | | | | | | | | | | | | | all_1080_4) = all_1272_2 & c_member(all_676_0, % 193.32/26.98 | | | | | | | | | | | | | all_1272_2, v_L) = all_1272_1 & % 193.32/26.98 | | | | | | | | | | | | | c_member(all_676_0, all_1080_1, v_L) = all_1272_0 % 193.32/26.98 | | | | | | | | | | | | | & $i(all_1272_2) & ( ~ (all_1272_1 = 0) | % 193.32/26.98 | | | | | | | | | | | | | all_1272_0 = 0) % 193.32/26.98 | | | | | | | | | | | | | % 193.32/26.98 | | | | | | | | | | | | | ALPHA: (562) implies: % 193.32/26.98 | | | | | | | | | | | | | (563) c_member(all_676_0, all_1080_1, v_L) = all_1272_0 % 193.32/26.98 | | | | | | | | | | | | | % 193.32/26.98 | | | | | | | | | | | | | DELTA: instantiating (561) with fresh symbols all_1276_0, % 193.32/26.98 | | | | | | | | | | | | | all_1276_1, all_1276_2 gives: % 193.32/26.98 | | | | | | | | | | | | | (564) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.98 | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, % 193.32/26.98 | | | | | | | | | | | | | all_1080_4) = all_1276_2 & c_member(all_676_0, % 193.32/26.98 | | | | | | | | | | | | | all_1276_2, v_L) = all_1276_1 & % 193.32/26.98 | | | | | | | | | | | | | c_member(all_676_0, all_1080_3, v_L) = all_1276_0 % 193.32/26.98 | | | | | | | | | | | | | & $i(all_1276_2) & ( ~ (all_1276_1 = 0) | % 193.32/26.98 | | | | | | | | | | | | | all_1276_0 = 0) % 193.32/26.98 | | | | | | | | | | | | | % 193.32/26.98 | | | | | | | | | | | | | ALPHA: (564) implies: % 193.32/26.98 | | | | | | | | | | | | | (565) c_member(all_676_0, all_1080_3, v_L) = all_1276_0 % 193.32/26.98 | | | | | | | | | | | | | % 193.32/26.98 | | | | | | | | | | | | | DELTA: instantiating (560) with fresh symbols all_1280_0, % 193.32/26.98 | | | | | | | | | | | | | all_1280_1, all_1280_2 gives: % 193.32/26.99 | | | | | | | | | | | | | (566) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.99 | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v_x) = % 193.32/26.99 | | | | | | | | | | | | | all_1280_2 & c_member(all_676_0, all_1280_2, v_L) % 193.32/26.99 | | | | | | | | | | | | | = all_1280_1 & c_member(all_676_0, all_872_3, v_L) % 193.32/26.99 | | | | | | | | | | | | | = all_1280_0 & $i(all_1280_2) & ( ~ (all_1280_1 = % 193.32/26.99 | | | | | | | | | | | | | 0) | all_1280_0 = 0) % 193.32/26.99 | | | | | | | | | | | | | % 193.32/26.99 | | | | | | | | | | | | | ALPHA: (566) implies: % 193.32/26.99 | | | | | | | | | | | | | (567) c_member(all_676_0, all_872_3, v_L) = all_1280_0 % 193.32/26.99 | | | | | | | | | | | | | (568) ~ (all_1280_1 = 0) | all_1280_0 = 0 % 193.32/26.99 | | | | | | | | | | | | | % 193.32/26.99 | | | | | | | | | | | | | REDUCE: (89), (563) imply: % 193.32/26.99 | | | | | | | | | | | | | (569) c_member(all_622_1, all_1080_1, v_L) = all_1272_0 % 193.32/26.99 | | | | | | | | | | | | | % 193.32/26.99 | | | | | | | | | | | | | REDUCE: (89), (565) imply: % 193.32/26.99 | | | | | | | | | | | | | (570) c_member(all_622_1, all_1080_3, v_L) = all_1276_0 % 193.32/26.99 | | | | | | | | | | | | | % 193.32/26.99 | | | | | | | | | | | | | REDUCE: (89), (567) imply: % 193.32/26.99 | | | | | | | | | | | | | (571) c_member(all_622_1, all_872_3, v_L) = all_1280_0 % 193.32/26.99 | | | | | | | | | | | | | % 193.32/26.99 | | | | | | | | | | | | | GROUND_INST: instantiating (20) with all_872_2, all_1280_0, % 193.32/26.99 | | | | | | | | | | | | | v_L, all_872_3, all_622_1, simplifying with (185), % 193.32/26.99 | | | | | | | | | | | | | (571) gives: % 193.32/26.99 | | | | | | | | | | | | | (572) all_1280_0 = all_872_2 % 193.32/26.99 | | | | | | | | | | | | | % 193.32/26.99 | | | | | | | | | | | | | GROUND_INST: instantiating (20) with all_1080_2, all_1276_0, % 193.32/26.99 | | | | | | | | | | | | | v_L, all_1080_3, all_622_1, simplifying with % 193.32/26.99 | | | | | | | | | | | | | (215), (570) gives: % 193.32/26.99 | | | | | | | | | | | | | (573) all_1276_0 = all_1080_2 % 193.32/26.99 | | | | | | | | | | | | | % 193.32/26.99 | | | | | | | | | | | | | GROUND_INST: instantiating (20) with all_1080_0, all_1272_0, % 193.32/26.99 | | | | | | | | | | | | | v_L, all_1080_1, all_622_1, simplifying with % 193.32/26.99 | | | | | | | | | | | | | (214), (569) gives: % 193.32/26.99 | | | | | | | | | | | | | (574) all_1272_0 = all_1080_0 % 193.32/26.99 | | | | | | | | | | | | | % 193.32/26.99 | | | | | | | | | | | | | GROUND_INST: instantiating (20) with all_1252_0, all_1272_0, % 193.32/26.99 | | | | | | | | | | | | | v_L, all_1080_1, all_622_1, simplifying with % 193.32/26.99 | | | | | | | | | | | | | (542), (569) gives: % 193.32/26.99 | | | | | | | | | | | | | (575) all_1272_0 = all_1252_0 % 193.32/26.99 | | | | | | | | | | | | | % 193.32/26.99 | | | | | | | | | | | | | GROUND_INST: instantiating (21) with all_872_3, all_1264_1, % 193.32/26.99 | | | | | | | | | | | | | v_x, all_872_8, tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.99 | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with % 193.32/26.99 | | | | | | | | | | | | | (182), (540) gives: % 193.32/26.99 | | | | | | | | | | | | | (576) all_1264_1 = all_872_3 % 193.32/26.99 | | | | | | | | | | | | | % 193.32/26.99 | | | | | | | | | | | | | GROUND_INST: instantiating (21) with all_1080_3, all_1252_2, % 193.32/26.99 | | | | | | | | | | | | | all_1080_4, all_872_8, % 193.32/26.99 | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.99 | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with % 193.32/26.99 | | | | | | | | | | | | | (210), (537) gives: % 193.32/26.99 | | | | | | | | | | | | | (577) all_1252_2 = all_1080_3 % 193.32/26.99 | | | | | | | | | | | | | % 193.32/26.99 | | | | | | | | | | | | | COMBINE_EQS: (574), (575) imply: % 193.32/26.99 | | | | | | | | | | | | | (578) all_1252_0 = all_1080_0 % 193.32/26.99 | | | | | | | | | | | | | % 193.32/26.99 | | | | | | | | | | | | | SIMP: (578) implies: % 193.32/26.99 | | | | | | | | | | | | | (579) all_1252_0 = all_1080_0 % 193.32/26.99 | | | | | | | | | | | | | % 193.32/26.99 | | | | | | | | | | | | | REDUCE: (541), (577) imply: % 193.32/26.99 | | | | | | | | | | | | | (580) c_member(all_622_1, all_1080_3, v_L) = all_1252_1 % 193.32/26.99 | | | | | | | | | | | | | % 193.32/26.99 | | | | | | | | | | | | | BETA: splitting (568) gives: % 193.32/26.99 | | | | | | | | | | | | | % 193.32/26.99 | | | | | | | | | | | | | Case 1: % 193.32/26.99 | | | | | | | | | | | | | | % 193.32/26.99 | | | | | | | | | | | | | | % 193.32/26.99 | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with all_1080_2, all_1252_1, % 193.32/26.99 | | | | | | | | | | | | | | v_L, all_1080_3, all_622_1, simplifying with % 193.32/26.99 | | | | | | | | | | | | | | (215), (580) gives: % 193.32/26.99 | | | | | | | | | | | | | | (581) all_1252_1 = all_1080_2 % 193.32/26.99 | | | | | | | | | | | | | | % 193.32/26.99 | | | | | | | | | | | | | | BETA: splitting (211) gives: % 193.32/26.99 | | | | | | | | | | | | | | % 193.32/26.99 | | | | | | | | | | | | | | Case 1: % 193.32/26.99 | | | | | | | | | | | | | | | % 193.32/26.99 | | | | | | | | | | | | | | | (582) all_1080_2 = 0 & ~ (all_1080_0 = 0) & ~ % 193.32/26.99 | | | | | | | | | | | | | | | (all_1080_4 = v_y) % 193.32/26.99 | | | | | | | | | | | | | | | % 193.32/26.99 | | | | | | | | | | | | | | | ALPHA: (582) implies: % 193.32/26.99 | | | | | | | | | | | | | | | (583) all_1080_2 = 0 % 193.32/26.99 | | | | | | | | | | | | | | | (584) ~ (all_1080_0 = 0) % 193.32/26.99 | | | | | | | | | | | | | | | % 193.32/26.99 | | | | | | | | | | | | | | | COMBINE_EQS: (581), (583) imply: % 193.32/26.99 | | | | | | | | | | | | | | | (585) all_1252_1 = 0 % 193.32/26.99 | | | | | | | | | | | | | | | % 193.32/26.99 | | | | | | | | | | | | | | | BETA: splitting (538) gives: % 193.32/26.99 | | | | | | | | | | | | | | | % 193.32/26.99 | | | | | | | | | | | | | | | Case 1: % 193.32/26.99 | | | | | | | | | | | | | | | | % 193.32/26.99 | | | | | | | | | | | | | | | | (586) ~ (all_1252_1 = 0) % 193.32/26.99 | | | | | | | | | | | | | | | | % 193.32/26.99 | | | | | | | | | | | | | | | | REDUCE: (585), (586) imply: % 193.32/26.99 | | | | | | | | | | | | | | | | (587) $false % 193.32/26.99 | | | | | | | | | | | | | | | | % 193.32/26.99 | | | | | | | | | | | | | | | | CLOSE: (587) is inconsistent. % 193.32/26.99 | | | | | | | | | | | | | | | | % 193.32/26.99 | | | | | | | | | | | | | | | Case 2: % 193.32/26.99 | | | | | | | | | | | | | | | | % 193.32/26.99 | | | | | | | | | | | | | | | | (588) all_1252_0 = 0 % 193.32/26.99 | | | | | | | | | | | | | | | | % 193.32/26.99 | | | | | | | | | | | | | | | | COMBINE_EQS: (579), (588) imply: % 193.32/26.99 | | | | | | | | | | | | | | | | (589) all_1080_0 = 0 % 193.32/26.99 | | | | | | | | | | | | | | | | % 193.32/26.99 | | | | | | | | | | | | | | | | SIMP: (589) implies: % 193.32/26.99 | | | | | | | | | | | | | | | | (590) all_1080_0 = 0 % 193.32/26.99 | | | | | | | | | | | | | | | | % 193.32/26.99 | | | | | | | | | | | | | | | | REDUCE: (584), (590) imply: % 193.32/26.99 | | | | | | | | | | | | | | | | (591) $false % 193.32/26.99 | | | | | | | | | | | | | | | | % 193.32/26.99 | | | | | | | | | | | | | | | | CLOSE: (591) is inconsistent. % 193.32/26.99 | | | | | | | | | | | | | | | | % 193.32/26.99 | | | | | | | | | | | | | | | End of split % 193.32/26.99 | | | | | | | | | | | | | | | % 193.32/26.99 | | | | | | | | | | | | | | Case 2: % 193.32/26.99 | | | | | | | | | | | | | | | % 193.32/26.99 | | | | | | | | | | | | | | | (592) (all_1080_4 = v_y & all_872_2 = 0) | (all_1080_4 = % 193.32/26.99 | | | | | | | | | | | | | | | v_y & all_872_8 = v_x) % 193.32/26.99 | | | | | | | | | | | | | | | % 193.32/26.99 | | | | | | | | | | | | | | | BETA: splitting (592) gives: % 193.32/26.99 | | | | | | | | | | | | | | | % 193.32/26.99 | | | | | | | | | | | | | | | Case 1: % 193.32/26.99 | | | | | | | | | | | | | | | | % 193.32/26.99 | | | | | | | | | | | | | | | | (593) all_1080_4 = v_y & all_872_2 = 0 % 193.32/26.99 | | | | | | | | | | | | | | | | % 193.32/26.99 | | | | | | | | | | | | | | | | ALPHA: (593) implies: % 193.32/26.99 | | | | | | | | | | | | | | | | (594) all_872_2 = 0 % 193.32/26.99 | | | | | | | | | | | | | | | | % 193.32/26.99 | | | | | | | | | | | | | | | | REDUCE: (529), (594) imply: % 193.32/26.99 | | | | | | | | | | | | | | | | (595) $false % 193.32/26.99 | | | | | | | | | | | | | | | | % 193.32/26.99 | | | | | | | | | | | | | | | | CLOSE: (595) is inconsistent. % 193.32/26.99 | | | | | | | | | | | | | | | | % 193.32/26.99 | | | | | | | | | | | | | | | Case 2: % 193.32/26.99 | | | | | | | | | | | | | | | | % 193.32/26.99 | | | | | | | | | | | | | | | | (596) all_1080_4 = v_y & all_872_8 = v_x % 193.32/26.99 | | | | | | | | | | | | | | | | % 193.32/26.99 | | | | | | | | | | | | | | | | ALPHA: (596) implies: % 193.32/26.99 | | | | | | | | | | | | | | | | (597) all_872_8 = v_x % 193.32/26.99 | | | | | | | | | | | | | | | | % 193.32/26.99 | | | | | | | | | | | | | | | | REDUCE: (224), (597) imply: % 193.32/26.99 | | | | | | | | | | | | | | | | (598) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.99 | | | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v_x) = % 193.32/26.99 | | | | | | | | | | | | | | | | all_1086_2 % 193.32/26.99 | | | | | | | | | | | | | | | | % 193.32/26.99 | | | | | | | | | | | | | | | | REDUCE: (182), (597) imply: % 193.32/26.99 | | | | | | | | | | | | | | | | (599) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.99 | | | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v_x) = % 193.32/26.99 | | | | | | | | | | | | | | | | all_872_3 % 193.32/26.99 | | | | | | | | | | | | | | | | % 193.32/26.99 | | | | | | | | | | | | | | | | REDUCE: (179), (597) imply: % 193.32/26.99 | | | | | | | | | | | | | | | | (600) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.99 | | | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v_x) = % 193.32/26.99 | | | | | | | | | | | | | | | | all_872_1 % 193.32/26.99 | | | | | | | | | | | | | | | | % 193.32/26.99 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (21) with all_872_1, all_1086_2, % 193.32/26.99 | | | | | | | | | | | | | | | | v_x, v_x, tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.99 | | | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with % 193.32/26.99 | | | | | | | | | | | | | | | | (598), (600) gives: % 193.32/26.99 | | | | | | | | | | | | | | | | (601) all_1086_2 = all_872_1 % 193.32/26.99 | | | | | | | | | | | | | | | | % 193.32/26.99 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (21) with all_872_3, all_1086_2, % 193.32/26.99 | | | | | | | | | | | | | | | | v_x, v_x, tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.99 | | | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with % 193.32/26.99 | | | | | | | | | | | | | | | | (598), (599) gives: % 193.32/26.99 | | | | | | | | | | | | | | | | (602) all_1086_2 = all_872_3 % 193.32/26.99 | | | | | | | | | | | | | | | | % 193.32/26.99 | | | | | | | | | | | | | | | | COMBINE_EQS: (601), (602) imply: % 193.32/26.99 | | | | | | | | | | | | | | | | (603) all_872_1 = all_872_3 % 193.32/26.99 | | | | | | | | | | | | | | | | % 193.32/26.99 | | | | | | | | | | | | | | | | SIMP: (603) implies: % 193.32/26.99 | | | | | | | | | | | | | | | | (604) all_872_1 = all_872_3 % 193.32/26.99 | | | | | | | | | | | | | | | | % 193.32/26.99 | | | | | | | | | | | | | | | | REDUCE: (216), (604) imply: % 193.32/26.99 | | | | | | | | | | | | | | | | (605) c_member(all_622_1, all_872_3, v_L) = 0 % 193.32/26.99 | | | | | | | | | | | | | | | | % 193.32/26.99 | | | | | | | | | | | | | | | | DELTA: instantiating (523) with fresh symbol all_1198_0 % 193.32/26.99 | | | | | | | | | | | | | | | | gives: % 193.32/26.99 | | | | | | | | | | | | | | | | (606) ~ (all_1198_0 = 0) & c_member(all_676_0, % 193.32/26.99 | | | | | | | | | | | | | | | | all_872_3, v_L) = all_1198_0 % 193.32/26.99 | | | | | | | | | | | | | | | | % 193.32/26.99 | | | | | | | | | | | | | | | | REF_CLOSE: (20), (89), (605), (606) are inconsistent by % 193.32/26.99 | | | | | | | | | | | | | | | | sub-proof #16. % 193.32/26.99 | | | | | | | | | | | | | | | | % 193.32/26.99 | | | | | | | | | | | | | | | End of split % 193.32/26.99 | | | | | | | | | | | | | | | % 193.32/26.99 | | | | | | | | | | | | | | End of split % 193.32/26.99 | | | | | | | | | | | | | | % 193.32/26.99 | | | | | | | | | | | | | Case 2: % 193.32/26.99 | | | | | | | | | | | | | | % 193.32/26.99 | | | | | | | | | | | | | | (607) all_1280_0 = 0 % 193.32/26.99 | | | | | | | | | | | | | | % 193.32/26.99 | | | | | | | | | | | | | | COMBINE_EQS: (572), (607) imply: % 193.32/26.99 | | | | | | | | | | | | | | (608) all_872_2 = 0 % 193.32/26.99 | | | | | | | | | | | | | | % 193.32/26.99 | | | | | | | | | | | | | | SIMP: (608) implies: % 193.32/26.99 | | | | | | | | | | | | | | (609) all_872_2 = 0 % 193.32/26.99 | | | | | | | | | | | | | | % 193.32/26.99 | | | | | | | | | | | | | | REDUCE: (529), (609) imply: % 193.32/26.99 | | | | | | | | | | | | | | (610) $false % 193.32/26.99 | | | | | | | | | | | | | | % 193.32/26.99 | | | | | | | | | | | | | | CLOSE: (610) is inconsistent. % 193.32/26.99 | | | | | | | | | | | | | | % 193.32/26.99 | | | | | | | | | | | | | End of split % 193.32/26.99 | | | | | | | | | | | | | % 193.32/26.99 | | | | | | | | | | | | End of split % 193.32/26.99 | | | | | | | | | | | | % 193.32/26.99 | | | | | | | | | | | End of split % 193.32/26.99 | | | | | | | | | | | % 193.32/26.99 | | | | | | | | | | Case 2: % 193.32/26.99 | | | | | | | | | | | % 193.32/26.99 | | | | | | | | | | | (611) ! [v0: $i] : ! [v1: $i] : ( ~ % 193.32/26.99 | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.99 | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, % 193.32/26.99 | | | | | | | | | | | v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? % 193.32/26.99 | | | | | | | | | | | [v3: any] : ? [v4: any] : % 193.32/26.99 | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.99 | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v0) = % 193.32/26.99 | | | | | | | | | | | v2 & c_member(all_676_0, v2, v_L) = v3 & % 193.32/26.99 | | | | | | | | | | | c_member(all_676_0, v1, v_L) = v4 & $i(v2) & ( % 193.32/26.99 | | | | | | | | | | | ~ (v3 = 0) | v4 = 0))) % 193.32/26.99 | | | | | | | | | | | % 193.32/26.99 | | | | | | | | | | | GROUND_INST: instantiating (44) with all_872_8, v_y, % 193.32/26.99 | | | | | | | | | | | all_1096_1, simplifying with (170), (217), (250) % 193.32/26.99 | | | | | | | | | | | gives: % 193.32/26.99 | | | | | | | | | | | (612) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_676_0, % 193.32/26.99 | | | | | | | | | | | all_1096_1, v_L) = v0) | ! [v0: $i] : ! [v1: % 193.32/26.99 | | | | | | | | | | | $i] : ( ~ % 193.32/26.99 | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.99 | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, % 193.32/26.99 | | | | | | | | | | | v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? % 193.32/26.99 | | | | | | | | | | | [v3: any] : ? [v4: any] : % 193.32/26.99 | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.99 | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = % 193.32/26.99 | | | | | | | | | | | v2 & c_member(all_676_0, v2, v_L) = v3 & % 193.32/26.99 | | | | | | | | | | | c_member(all_676_0, v1, v_L) = v4 & $i(v2) & ( % 193.32/26.99 | | | | | | | | | | | ~ (v3 = 0) | v4 = 0))) % 193.32/26.99 | | | | | | | | | | | % 193.32/26.99 | | | | | | | | | | | GROUND_INST: instantiating (43) with all_872_8, all_1086_2, % 193.32/26.99 | | | | | | | | | | | simplifying with (170), (224) gives: % 193.32/26.99 | | | | | | | | | | | (613) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_676_0, % 193.32/26.99 | | | | | | | | | | | all_1086_2, v_L) = v0) % 193.32/26.99 | | | | | | | | | | | % 193.32/26.99 | | | | | | | | | | | GROUND_INST: instantiating (611) with all_872_8, all_1086_2, % 193.32/26.99 | | | | | | | | | | | simplifying with (170), (224) gives: % 193.32/26.99 | | | | | | | | | | | (614) ? [v0: $i] : ? [v1: any] : ? [v2: any] : % 193.32/26.99 | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.99 | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, % 193.32/26.99 | | | | | | | | | | | all_872_8) = v0 & c_member(all_676_0, v0, v_L) % 193.32/26.99 | | | | | | | | | | | = v1 & c_member(all_676_0, all_1086_2, v_L) = v2 % 193.32/26.99 | | | | | | | | | | | & $i(v0) & ( ~ (v1 = 0) | v2 = 0)) % 193.32/26.99 | | | | | | | | | | | % 193.32/26.99 | | | | | | | | | | | DELTA: instantiating (613) with fresh symbol all_1239_0 % 193.32/26.99 | | | | | | | | | | | gives: % 193.32/26.99 | | | | | | | | | | | (615) ~ (all_1239_0 = 0) & c_member(all_676_0, % 193.32/26.99 | | | | | | | | | | | all_1086_2, v_L) = all_1239_0 % 193.32/26.99 | | | | | | | | | | | % 193.32/26.99 | | | | | | | | | | | ALPHA: (615) implies: % 193.32/26.99 | | | | | | | | | | | (616) ~ (all_1239_0 = 0) % 193.32/26.99 | | | | | | | | | | | (617) c_member(all_676_0, all_1086_2, v_L) = all_1239_0 % 193.32/26.99 | | | | | | | | | | | % 193.32/26.99 | | | | | | | | | | | DELTA: instantiating (614) with fresh symbols all_1273_0, % 193.32/26.99 | | | | | | | | | | | all_1273_1, all_1273_2 gives: % 193.32/26.99 | | | | | | | | | | | (618) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.99 | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, all_872_8) % 193.32/26.99 | | | | | | | | | | | = all_1273_2 & c_member(all_676_0, all_1273_2, % 193.32/26.99 | | | | | | | | | | | v_L) = all_1273_1 & c_member(all_676_0, % 193.32/26.99 | | | | | | | | | | | all_1086_2, v_L) = all_1273_0 & $i(all_1273_2) & % 193.32/26.99 | | | | | | | | | | | ( ~ (all_1273_1 = 0) | all_1273_0 = 0) % 193.32/26.99 | | | | | | | | | | | % 193.32/26.99 | | | | | | | | | | | ALPHA: (618) implies: % 193.32/26.99 | | | | | | | | | | | (619) c_member(all_676_0, all_1086_2, v_L) = all_1273_0 % 193.32/26.99 | | | | | | | | | | | (620) c_member(all_676_0, all_1273_2, v_L) = all_1273_1 % 193.32/26.99 | | | | | | | | | | | (621) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/26.99 | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, all_872_8) % 193.32/26.99 | | | | | | | | | | | = all_1273_2 % 193.32/26.99 | | | | | | | | | | | (622) ~ (all_1273_1 = 0) | all_1273_0 = 0 % 193.32/26.99 | | | | | | | | | | | % 193.32/26.99 | | | | | | | | | | | REDUCE: (89), (620) imply: % 193.32/26.99 | | | | | | | | | | | (623) c_member(all_622_1, all_1273_2, v_L) = all_1273_1 % 193.32/26.99 | | | | | | | | | | | % 193.32/26.99 | | | | | | | | | | | REDUCE: (89), (619) imply: % 193.32/26.99 | | | | | | | | | | | (624) c_member(all_622_1, all_1086_2, v_L) = all_1273_0 % 193.32/26.99 | | | | | | | | | | | % 193.32/26.99 | | | | | | | | | | | REDUCE: (89), (617) imply: % 193.32/26.99 | | | | | | | | | | | (625) c_member(all_622_1, all_1086_2, v_L) = all_1239_0 % 193.32/26.99 | | | | | | | | | | | % 193.32/26.99 | | | | | | | | | | | BETA: splitting (612) gives: % 193.32/26.99 | | | | | | | | | | | % 193.32/26.99 | | | | | | | | | | | Case 1: % 193.32/26.99 | | | | | | | | | | | | % 193.32/27.00 | | | | | | | | | | | | (626) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_676_0, % 193.32/27.00 | | | | | | | | | | | | all_1096_1, v_L) = v0) % 193.32/27.00 | | | | | | | | | | | | % 193.32/27.00 | | | | | | | | | | | | DELTA: instantiating (626) with fresh symbol all_1280_0 % 193.32/27.00 | | | | | | | | | | | | gives: % 193.32/27.00 | | | | | | | | | | | | (627) ~ (all_1280_0 = 0) & c_member(all_676_0, % 193.32/27.00 | | | | | | | | | | | | all_1096_1, v_L) = all_1280_0 % 193.32/27.00 | | | | | | | | | | | | % 193.32/27.00 | | | | | | | | | | | | ALPHA: (627) implies: % 193.32/27.00 | | | | | | | | | | | | (628) ~ (all_1280_0 = 0) % 193.32/27.00 | | | | | | | | | | | | (629) c_member(all_676_0, all_1096_1, v_L) = all_1280_0 % 193.32/27.00 | | | | | | | | | | | | % 193.32/27.00 | | | | | | | | | | | | REDUCE: (89), (629) imply: % 193.32/27.00 | | | | | | | | | | | | (630) c_member(all_622_1, all_1096_1, v_L) = all_1280_0 % 193.32/27.00 | | | | | | | | | | | | % 193.32/27.00 | | | | | | | | | | | | GROUND_INST: instantiating (20) with 0, all_1280_0, v_L, % 193.32/27.00 | | | | | | | | | | | | all_1096_1, all_622_1, simplifying with (522), % 193.32/27.00 | | | | | | | | | | | | (630) gives: % 193.32/27.00 | | | | | | | | | | | | (631) all_1280_0 = 0 % 193.32/27.00 | | | | | | | | | | | | % 193.32/27.00 | | | | | | | | | | | | REDUCE: (628), (631) imply: % 193.32/27.00 | | | | | | | | | | | | (632) $false % 193.32/27.00 | | | | | | | | | | | | % 193.32/27.00 | | | | | | | | | | | | CLOSE: (632) is inconsistent. % 193.32/27.00 | | | | | | | | | | | | % 193.32/27.00 | | | | | | | | | | | Case 2: % 193.32/27.00 | | | | | | | | | | | | % 193.32/27.00 | | | | | | | | | | | | (633) ! [v0: $i] : ! [v1: $i] : ( ~ % 193.32/27.00 | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.00 | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, % 193.32/27.00 | | | | | | | | | | | | v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? % 193.32/27.00 | | | | | | | | | | | | [v3: any] : ? [v4: any] : % 193.32/27.00 | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.00 | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = % 193.32/27.00 | | | | | | | | | | | | v2 & c_member(all_676_0, v2, v_L) = v3 & % 193.32/27.00 | | | | | | | | | | | | c_member(all_676_0, v1, v_L) = v4 & $i(v2) & ( % 193.32/27.00 | | | | | | | | | | | | ~ (v3 = 0) | v4 = 0))) % 193.32/27.00 | | | | | | | | | | | | % 193.32/27.00 | | | | | | | | | | | | GROUND_INST: instantiating (633) with all_872_8, all_1086_2, % 193.32/27.00 | | | | | | | | | | | | simplifying with (170), (224) gives: % 193.32/27.00 | | | | | | | | | | | | (634) ? [v0: $i] : ? [v1: any] : ? [v2: any] : % 193.32/27.00 | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.00 | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, % 193.32/27.00 | | | | | | | | | | | | all_872_8) = v0 & c_member(all_676_0, v0, v_L) % 193.32/27.00 | | | | | | | | | | | | = v1 & c_member(all_676_0, all_1086_2, v_L) = v2 % 193.32/27.00 | | | | | | | | | | | | & $i(v0) & ( ~ (v1 = 0) | v2 = 0)) % 193.32/27.00 | | | | | | | | | | | | % 193.32/27.00 | | | | | | | | | | | | DELTA: instantiating (634) with fresh symbols all_1283_0, % 193.32/27.00 | | | | | | | | | | | | all_1283_1, all_1283_2 gives: % 193.32/27.00 | | | | | | | | | | | | (635) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.00 | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, all_872_8) % 193.32/27.00 | | | | | | | | | | | | = all_1283_2 & c_member(all_676_0, all_1283_2, % 193.32/27.00 | | | | | | | | | | | | v_L) = all_1283_1 & c_member(all_676_0, % 193.32/27.00 | | | | | | | | | | | | all_1086_2, v_L) = all_1283_0 & $i(all_1283_2) & % 193.32/27.00 | | | | | | | | | | | | ( ~ (all_1283_1 = 0) | all_1283_0 = 0) % 193.32/27.00 | | | | | | | | | | | | % 193.32/27.00 | | | | | | | | | | | | ALPHA: (635) implies: % 193.32/27.00 | | | | | | | | | | | | (636) c_member(all_676_0, all_1086_2, v_L) = all_1283_0 % 193.32/27.00 | | | | | | | | | | | | % 193.32/27.00 | | | | | | | | | | | | REDUCE: (89), (636) imply: % 193.32/27.00 | | | | | | | | | | | | (637) c_member(all_622_1, all_1086_2, v_L) = all_1283_0 % 193.32/27.00 | | | | | | | | | | | | % 193.32/27.00 | | | | | | | | | | | | GROUND_INST: instantiating (20) with all_1273_0, all_1283_0, % 193.32/27.00 | | | | | | | | | | | | v_L, all_1086_2, all_622_1, simplifying with % 193.32/27.00 | | | | | | | | | | | | (624), (637) gives: % 193.32/27.00 | | | | | | | | | | | | (638) all_1283_0 = all_1273_0 % 193.32/27.00 | | | | | | | | | | | | % 193.32/27.00 | | | | | | | | | | | | GROUND_INST: instantiating (20) with all_1239_0, all_1283_0, % 193.32/27.00 | | | | | | | | | | | | v_L, all_1086_2, all_622_1, simplifying with % 193.32/27.00 | | | | | | | | | | | | (625), (637) gives: % 193.32/27.00 | | | | | | | | | | | | (639) all_1283_0 = all_1239_0 % 193.32/27.00 | | | | | | | | | | | | % 193.32/27.00 | | | | | | | | | | | | GROUND_INST: instantiating (21) with all_872_1, all_1273_2, % 193.32/27.00 | | | | | | | | | | | | all_872_8, v_x, tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.00 | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with % 193.32/27.00 | | | | | | | | | | | | (179), (621) gives: % 193.32/27.00 | | | | | | | | | | | | (640) all_1273_2 = all_872_1 % 193.32/27.00 | | | | | | | | | | | | % 193.32/27.00 | | | | | | | | | | | | COMBINE_EQS: (638), (639) imply: % 193.32/27.00 | | | | | | | | | | | | (641) all_1273_0 = all_1239_0 % 193.32/27.00 | | | | | | | | | | | | % 193.32/27.00 | | | | | | | | | | | | REDUCE: (623), (640) imply: % 193.32/27.00 | | | | | | | | | | | | (642) c_member(all_622_1, all_872_1, v_L) = all_1273_1 % 193.32/27.00 | | | | | | | | | | | | % 193.32/27.00 | | | | | | | | | | | | BETA: splitting (622) gives: % 193.32/27.00 | | | | | | | | | | | | % 193.32/27.00 | | | | | | | | | | | | Case 1: % 193.32/27.00 | | | | | | | | | | | | | % 193.32/27.00 | | | | | | | | | | | | | (643) ~ (all_1273_1 = 0) % 193.32/27.00 | | | | | | | | | | | | | % 193.32/27.00 | | | | | | | | | | | | | GROUND_INST: instantiating (20) with 0, all_1273_1, v_L, % 193.32/27.00 | | | | | | | | | | | | | all_872_1, all_622_1, simplifying with (216), % 193.32/27.00 | | | | | | | | | | | | | (642) gives: % 193.32/27.00 | | | | | | | | | | | | | (644) all_1273_1 = 0 % 193.32/27.00 | | | | | | | | | | | | | % 193.32/27.00 | | | | | | | | | | | | | REDUCE: (643), (644) imply: % 193.32/27.00 | | | | | | | | | | | | | (645) $false % 193.32/27.00 | | | | | | | | | | | | | % 193.32/27.00 | | | | | | | | | | | | | CLOSE: (645) is inconsistent. % 193.32/27.00 | | | | | | | | | | | | | % 193.32/27.00 | | | | | | | | | | | | Case 2: % 193.32/27.00 | | | | | | | | | | | | | % 193.32/27.00 | | | | | | | | | | | | | (646) all_1273_0 = 0 % 193.32/27.00 | | | | | | | | | | | | | % 193.32/27.00 | | | | | | | | | | | | | COMBINE_EQS: (641), (646) imply: % 193.32/27.00 | | | | | | | | | | | | | (647) all_1239_0 = 0 % 193.32/27.00 | | | | | | | | | | | | | % 193.32/27.00 | | | | | | | | | | | | | REDUCE: (616), (647) imply: % 193.32/27.00 | | | | | | | | | | | | | (648) $false % 193.32/27.00 | | | | | | | | | | | | | % 193.32/27.00 | | | | | | | | | | | | | CLOSE: (648) is inconsistent. % 193.32/27.00 | | | | | | | | | | | | | % 193.32/27.00 | | | | | | | | | | | | End of split % 193.32/27.00 | | | | | | | | | | | | % 193.32/27.00 | | | | | | | | | | | End of split % 193.32/27.00 | | | | | | | | | | | % 193.32/27.00 | | | | | | | | | | End of split % 193.32/27.00 | | | | | | | | | | % 193.32/27.00 | | | | | | | | | Case 2: % 193.32/27.00 | | | | | | | | | | % 193.32/27.00 | | | | | | | | | | (649) all_1096_2 = 0 % 193.32/27.00 | | | | | | | | | | % 193.32/27.00 | | | | | | | | | | COMBINE_EQS: (253), (649) imply: % 193.32/27.00 | | | | | | | | | | (650) all_872_6 = 0 % 193.32/27.00 | | | | | | | | | | % 193.32/27.00 | | | | | | | | | | REDUCE: (520), (650) imply: % 193.32/27.00 | | | | | | | | | | (651) $false % 193.32/27.00 | | | | | | | | | | % 193.32/27.00 | | | | | | | | | | CLOSE: (651) is inconsistent. % 193.32/27.00 | | | | | | | | | | % 193.32/27.00 | | | | | | | | | End of split % 193.32/27.00 | | | | | | | | | % 193.32/27.00 | | | | | | | | End of split % 193.32/27.00 | | | | | | | | % 193.32/27.00 | | | | | | | Case 2: % 193.32/27.00 | | | | | | | | % 193.32/27.00 | | | | | | | | (652) all_1091_2 = 0 % 193.32/27.00 | | | | | | | | % 193.32/27.00 | | | | | | | | COMBINE_EQS: (254), (652) imply: % 193.32/27.00 | | | | | | | | (653) all_872_4 = 0 % 193.32/27.00 | | | | | | | | % 193.32/27.00 | | | | | | | | REDUCE: (435), (653) imply: % 193.32/27.00 | | | | | | | | (654) $false % 193.32/27.00 | | | | | | | | % 193.32/27.00 | | | | | | | | CLOSE: (654) is inconsistent. % 193.32/27.00 | | | | | | | | % 193.32/27.00 | | | | | | | End of split % 193.32/27.00 | | | | | | | % 193.32/27.00 | | | | | | End of split % 193.32/27.00 | | | | | | % 193.32/27.00 | | | | | End of split % 193.32/27.00 | | | | | % 193.32/27.00 | | | | End of split % 193.32/27.00 | | | | % 193.32/27.00 | | | End of split % 193.32/27.00 | | | % 193.32/27.00 | | Case 2: % 193.32/27.00 | | | % 193.32/27.00 | | | (655) ~ (all_872_9 = v_y) & ((all_872_4 = 0 & all_872_8 = v_y & ? % 193.32/27.00 | | | [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 % 193.32/27.00 | | | = 0) & ~ (v0 = v_y) & % 193.32/27.00 | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.00 | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v0) = v2 & % 193.32/27.00 | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.00 | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v0) = v1 & % 193.32/27.00 | | | c_member(all_685_0, v2, v_L) = v3 & c_member(all_685_0, v1, % 193.32/27.00 | | | v_L) = 0 & $i(v2) & $i(v1) & $i(v0))) | (all_872_6 = 0 & % 193.32/27.00 | | | ~ (all_872_8 = v_y) & ? [v0: $i] : ? [v1: $i] : ? [v2: % 193.32/27.00 | | | any] : ? [v3: $i] : ? [v4: any] : % 193.32/27.00 | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.00 | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v0) = v1 & % 193.32/27.00 | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.00 | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v0) = v3 & % 193.32/27.00 | | | c_member(all_685_0, v3, v_L) = v4 & c_member(all_685_0, v1, % 193.32/27.00 | | | v_L) = v2 & $i(v3) & $i(v1) & $i(v0) & ((v2 = 0 & ~ (v4 % 193.32/27.00 | | | = 0) & ~ (v0 = v_y)) | (v0 = v_y & all_872_2 = 0 & % 193.32/27.00 | | | ~ (all_872_4 = 0) & ~ (all_872_9 = v_x)) | (v0 = v_y & % 193.32/27.00 | | | all_872_8 = v_x & ~ (all_872_4 = 0) & ~ (all_872_9 = % 193.32/27.00 | | | v_x)))))) % 193.32/27.00 | | | % 193.32/27.00 | | | ALPHA: (655) implies: % 193.32/27.00 | | | (656) ~ (all_872_9 = v_y) % 193.32/27.00 | | | (657) (all_872_4 = 0 & all_872_8 = v_y & ? [v0: $i] : ? [v1: $i] : ? % 193.32/27.00 | | | [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & ~ (v0 = v_y) & % 193.32/27.00 | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.00 | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v0) = v2 & % 193.32/27.00 | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.00 | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v0) = v1 & % 193.32/27.00 | | | c_member(all_685_0, v2, v_L) = v3 & c_member(all_685_0, v1, % 193.32/27.00 | | | v_L) = 0 & $i(v2) & $i(v1) & $i(v0))) | (all_872_6 = 0 & ~ % 193.32/27.00 | | | (all_872_8 = v_y) & ? [v0: $i] : ? [v1: $i] : ? [v2: any] : % 193.32/27.00 | | | ? [v3: $i] : ? [v4: any] : % 193.32/27.00 | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.00 | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v0) = v1 & % 193.32/27.00 | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.00 | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v0) = v3 & % 193.32/27.00 | | | c_member(all_685_0, v3, v_L) = v4 & c_member(all_685_0, v1, % 193.32/27.00 | | | v_L) = v2 & $i(v3) & $i(v1) & $i(v0) & ((v2 = 0 & ~ (v4 = % 193.32/27.00 | | | 0) & ~ (v0 = v_y)) | (v0 = v_y & all_872_2 = 0 & ~ % 193.32/27.00 | | | (all_872_4 = 0) & ~ (all_872_9 = v_x)) | (v0 = v_y & % 193.32/27.00 | | | all_872_8 = v_x & ~ (all_872_4 = 0) & ~ (all_872_9 = % 193.32/27.00 | | | v_x))))) % 193.32/27.00 | | | % 193.32/27.00 | | | BETA: splitting (199) gives: % 193.32/27.00 | | | % 193.32/27.00 | | | Case 1: % 193.32/27.00 | | | | % 193.32/27.00 | | | | (658) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_676_0, all_872_3, % 193.32/27.00 | | | | v_L) = v0) % 193.32/27.00 | | | | % 193.32/27.00 | | | | DELTA: instantiating (658) with fresh symbol all_1091_0 gives: % 193.32/27.00 | | | | (659) ~ (all_1091_0 = 0) & c_member(all_676_0, all_872_3, v_L) = % 193.32/27.00 | | | | all_1091_0 % 193.32/27.00 | | | | % 193.32/27.00 | | | | ALPHA: (659) implies: % 193.32/27.00 | | | | (660) ~ (all_1091_0 = 0) % 193.32/27.00 | | | | (661) c_member(all_676_0, all_872_3, v_L) = all_1091_0 % 193.32/27.00 | | | | % 193.32/27.00 | | | | REDUCE: (89), (661) imply: % 193.32/27.00 | | | | (662) c_member(all_622_1, all_872_3, v_L) = all_1091_0 % 193.32/27.00 | | | | % 193.32/27.00 | | | | GROUND_INST: instantiating (20) with all_872_2, all_1091_0, v_L, % 193.32/27.00 | | | | all_872_3, all_622_1, simplifying with (185), (662) gives: % 193.32/27.00 | | | | (663) all_1091_0 = all_872_2 % 193.32/27.00 | | | | % 193.32/27.00 | | | | REDUCE: (660), (663) imply: % 193.32/27.00 | | | | (664) ~ (all_872_2 = 0) % 193.32/27.00 | | | | % 193.32/27.00 | | | | BETA: splitting (194) gives: % 193.32/27.00 | | | | % 193.32/27.00 | | | | Case 1: % 193.32/27.00 | | | | | % 193.32/27.00 | | | | | (665) all_872_9 = v_x % 193.32/27.00 | | | | | % 193.32/27.00 | | | | | REDUCE: (181), (665) imply: % 193.32/27.00 | | | | | (666) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.00 | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, all_872_8) = % 193.32/27.00 | | | | | all_872_7 % 193.32/27.00 | | | | | % 193.32/27.00 | | | | | REF_CLOSE: (20), (21), (44), (89), (90), (170), (179), (184), (187), % 193.32/27.00 | | | | | (193), (657), (665), (666) are inconsistent by sub-proof % 193.32/27.00 | | | | | #12. % 193.32/27.00 | | | | | % 193.32/27.00 | | | | Case 2: % 193.32/27.00 | | | | | % 193.32/27.00 | | | | | (667) ~ (all_872_9 = v_x) % 193.32/27.01 | | | | | (668) ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 193.32/27.01 | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.01 | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, all_872_9) = v1 & % 193.32/27.01 | | | | | c_member(all_676_0, v1, v_L) = v2 & c_member(all_676_0, % 193.32/27.01 | | | | | all_872_5, v_L) = v0 & $i(v1) & (v2 = 0 | v0 = 0)) % 193.32/27.01 | | | | | % 193.32/27.01 | | | | | DELTA: instantiating (668) with fresh symbols all_1109_0, all_1109_1, % 193.32/27.01 | | | | | all_1109_2 gives: % 193.32/27.01 | | | | | (669) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.01 | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, all_872_9) = % 193.32/27.01 | | | | | all_1109_1 & c_member(all_676_0, all_1109_1, v_L) = % 193.32/27.01 | | | | | all_1109_0 & c_member(all_676_0, all_872_5, v_L) = all_1109_2 % 193.32/27.01 | | | | | & $i(all_1109_1) & (all_1109_0 = 0 | all_1109_2 = 0) % 193.32/27.01 | | | | | % 193.32/27.01 | | | | | ALPHA: (669) implies: % 193.32/27.01 | | | | | (670) c_member(all_676_0, all_872_5, v_L) = all_1109_2 % 193.32/27.01 | | | | | (671) c_member(all_676_0, all_1109_1, v_L) = all_1109_0 % 193.32/27.01 | | | | | (672) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.01 | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, all_872_9) = % 193.32/27.01 | | | | | all_1109_1 % 193.32/27.01 | | | | | (673) all_1109_0 = 0 | all_1109_2 = 0 % 193.32/27.01 | | | | | % 193.32/27.01 | | | | | REDUCE: (89), (671) imply: % 193.32/27.01 | | | | | (674) c_member(all_622_1, all_1109_1, v_L) = all_1109_0 % 193.32/27.01 | | | | | % 193.32/27.01 | | | | | REDUCE: (89), (670) imply: % 193.32/27.01 | | | | | (675) c_member(all_622_1, all_872_5, v_L) = all_1109_2 % 193.32/27.01 | | | | | % 193.32/27.01 | | | | | GROUND_INST: instantiating (20) with all_872_4, all_1109_2, v_L, % 193.32/27.01 | | | | | all_872_5, all_622_1, simplifying with (186), (675) % 193.32/27.01 | | | | | gives: % 193.32/27.01 | | | | | (676) all_1109_2 = all_872_4 % 193.32/27.01 | | | | | % 193.32/27.01 | | | | | BETA: splitting (189) gives: % 193.32/27.01 | | | | | % 193.32/27.01 | | | | | Case 1: % 193.32/27.01 | | | | | | % 193.32/27.01 | | | | | | (677) all_872_4 = 0 % 193.32/27.01 | | | | | | % 193.32/27.01 | | | | | | REDUCE: (186), (677) imply: % 193.32/27.01 | | | | | | (678) c_member(all_622_1, all_872_5, v_L) = 0 % 193.32/27.01 | | | | | | % 193.32/27.01 | | | | | | BETA: splitting (195) gives: % 193.32/27.01 | | | | | | % 193.32/27.01 | | | | | | Case 1: % 193.32/27.01 | | | | | | | % 193.32/27.01 | | | | | | | (679) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_676_0, % 193.32/27.01 | | | | | | | all_872_5, v_L) = v0) % 193.32/27.01 | | | | | | | % 193.32/27.01 | | | | | | | DELTA: instantiating (679) with fresh symbol all_1124_0 gives: % 193.32/27.01 | | | | | | | (680) ~ (all_1124_0 = 0) & c_member(all_676_0, all_872_5, v_L) % 193.32/27.01 | | | | | | | = all_1124_0 % 193.32/27.01 | | | | | | | % 193.32/27.01 | | | | | | | REF_CLOSE: (20), (89), (678), (680) are inconsistent by sub-proof % 193.32/27.01 | | | | | | | #15. % 193.32/27.01 | | | | | | | % 193.32/27.01 | | | | | | Case 2: % 193.32/27.01 | | | | | | | % 193.32/27.01 | | | | | | | (681) ! [v0: $i] : ! [v1: $i] : ( ~ % 193.32/27.01 | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.01 | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v0) = % 193.32/27.01 | | | | | | | v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: any] : ? % 193.32/27.01 | | | | | | | [v4: any] : % 193.32/27.01 | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.01 | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v0) = v2 & % 193.32/27.01 | | | | | | | c_member(all_676_0, v2, v_L) = v3 & % 193.32/27.01 | | | | | | | c_member(all_676_0, v1, v_L) = v4 & $i(v2) & ( ~ (v3 % 193.32/27.01 | | | | | | | = 0) | v4 = 0))) % 193.32/27.01 | | | | | | | % 193.32/27.01 | | | | | | | GROUND_INST: instantiating (681) with v_x, all_872_5, simplifying % 193.32/27.01 | | | | | | | with (16), (180) gives: % 193.32/27.01 | | | | | | | (682) ? [v0: $i] : ? [v1: any] : ? [v2: any] : % 193.32/27.01 | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.01 | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v_x) = v0 & % 193.32/27.01 | | | | | | | c_member(all_676_0, v0, v_L) = v1 & c_member(all_676_0, % 193.32/27.01 | | | | | | | all_872_5, v_L) = v2 & $i(v0) & ( ~ (v1 = 0) | v2 = % 193.32/27.01 | | | | | | | 0)) % 193.32/27.01 | | | | | | | % 193.32/27.01 | | | | | | | GROUND_INST: instantiating (681) with all_872_8, all_872_7, % 193.32/27.01 | | | | | | | simplifying with (170), (181) gives: % 193.32/27.01 | | | | | | | (683) ? [v0: $i] : ? [v1: any] : ? [v2: any] : % 193.32/27.01 | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.01 | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, all_872_8) = v0 % 193.32/27.01 | | | | | | | & c_member(all_676_0, v0, v_L) = v1 & % 193.32/27.01 | | | | | | | c_member(all_676_0, all_872_7, v_L) = v2 & $i(v0) & ( ~ % 193.32/27.01 | | | | | | | (v1 = 0) | v2 = 0)) % 193.32/27.01 | | | | | | | % 193.32/27.01 | | | | | | | DELTA: instantiating (683) with fresh symbols all_1125_0, % 193.32/27.01 | | | | | | | all_1125_1, all_1125_2 gives: % 193.32/27.01 | | | | | | | (684) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.01 | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, all_872_8) = % 193.32/27.01 | | | | | | | all_1125_2 & c_member(all_676_0, all_1125_2, v_L) = % 193.32/27.01 | | | | | | | all_1125_1 & c_member(all_676_0, all_872_7, v_L) = % 193.32/27.01 | | | | | | | all_1125_0 & $i(all_1125_2) & ( ~ (all_1125_1 = 0) | % 193.32/27.01 | | | | | | | all_1125_0 = 0) % 193.32/27.01 | | | | | | | % 193.32/27.01 | | | | | | | ALPHA: (684) implies: % 193.32/27.01 | | | | | | | (685) c_member(all_676_0, all_872_7, v_L) = all_1125_0 % 193.32/27.01 | | | | | | | (686) c_member(all_676_0, all_1125_2, v_L) = all_1125_1 % 193.32/27.01 | | | | | | | (687) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.01 | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, all_872_8) = % 193.32/27.01 | | | | | | | all_1125_2 % 193.32/27.01 | | | | | | | (688) ~ (all_1125_1 = 0) | all_1125_0 = 0 % 193.32/27.01 | | | | | | | % 193.32/27.01 | | | | | | | DELTA: instantiating (682) with fresh symbols all_1127_0, % 193.32/27.01 | | | | | | | all_1127_1, all_1127_2 gives: % 193.32/27.01 | | | | | | | (689) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.01 | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v_x) = all_1127_2 % 193.32/27.01 | | | | | | | & c_member(all_676_0, all_1127_2, v_L) = all_1127_1 & % 193.32/27.01 | | | | | | | c_member(all_676_0, all_872_5, v_L) = all_1127_0 & % 193.32/27.01 | | | | | | | $i(all_1127_2) & ( ~ (all_1127_1 = 0) | all_1127_0 = 0) % 193.32/27.01 | | | | | | | % 193.32/27.01 | | | | | | | ALPHA: (689) implies: % 193.32/27.01 | | | | | | | (690) c_member(all_676_0, all_872_5, v_L) = all_1127_0 % 193.32/27.01 | | | | | | | % 193.32/27.01 | | | | | | | REDUCE: (89), (686) imply: % 193.32/27.01 | | | | | | | (691) c_member(all_622_1, all_1125_2, v_L) = all_1125_1 % 193.32/27.01 | | | | | | | % 193.32/27.01 | | | | | | | REDUCE: (89), (690) imply: % 193.32/27.01 | | | | | | | (692) c_member(all_622_1, all_872_5, v_L) = all_1127_0 % 193.32/27.01 | | | | | | | % 193.32/27.01 | | | | | | | REDUCE: (89), (685) imply: % 193.32/27.01 | | | | | | | (693) c_member(all_622_1, all_872_7, v_L) = all_1125_0 % 193.32/27.01 | | | | | | | % 193.32/27.01 | | | | | | | GROUND_INST: instantiating (20) with all_872_6, all_1125_0, v_L, % 193.32/27.01 | | | | | | | all_872_7, all_622_1, simplifying with (187), (693) % 193.32/27.01 | | | | | | | gives: % 193.32/27.01 | | | | | | | (694) all_1125_0 = all_872_6 % 193.32/27.01 | | | | | | | % 193.32/27.01 | | | | | | | GROUND_INST: instantiating (20) with 0, all_1127_0, v_L, % 193.32/27.01 | | | | | | | all_872_5, all_622_1, simplifying with (678), (692) % 193.32/27.01 | | | | | | | gives: % 193.32/27.01 | | | | | | | (695) all_1127_0 = 0 % 193.32/27.01 | | | | | | | % 193.32/27.01 | | | | | | | GROUND_INST: instantiating (21) with all_872_1, all_1125_2, % 193.32/27.01 | | | | | | | all_872_8, v_x, tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.01 | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with % 193.32/27.01 | | | | | | | (179), (687) gives: % 193.32/27.01 | | | | | | | (696) all_1125_2 = all_872_1 % 193.32/27.01 | | | | | | | % 193.32/27.01 | | | | | | | REDUCE: (691), (696) imply: % 193.32/27.01 | | | | | | | (697) c_member(all_622_1, all_872_1, v_L) = all_1125_1 % 193.32/27.01 | | | | | | | % 193.32/27.01 | | | | | | | GROUND_INST: instantiating (20) with all_872_0, all_1125_1, v_L, % 193.32/27.01 | | | | | | | all_872_1, all_622_1, simplifying with (184), (697) % 193.32/27.01 | | | | | | | gives: % 193.32/27.01 | | | | | | | (698) all_1125_1 = all_872_0 % 193.32/27.01 | | | | | | | % 193.32/27.01 | | | | | | | BETA: splitting (193) gives: % 193.32/27.01 | | | | | | | % 193.32/27.01 | | | | | | | Case 1: % 193.32/27.01 | | | | | | | | % 193.32/27.01 | | | | | | | | (699) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_676_0, % 193.32/27.01 | | | | | | | | all_872_1, v_L) = v0) % 193.32/27.01 | | | | | | | | % 193.32/27.01 | | | | | | | | DELTA: instantiating (699) with fresh symbol all_1142_0 gives: % 193.32/27.01 | | | | | | | | (700) ~ (all_1142_0 = 0) & c_member(all_676_0, all_872_1, % 193.32/27.01 | | | | | | | | v_L) = all_1142_0 % 193.32/27.01 | | | | | | | | % 193.32/27.01 | | | | | | | | ALPHA: (700) implies: % 193.32/27.01 | | | | | | | | (701) ~ (all_1142_0 = 0) % 193.32/27.01 | | | | | | | | (702) c_member(all_676_0, all_872_1, v_L) = all_1142_0 % 193.32/27.01 | | | | | | | | % 193.32/27.01 | | | | | | | | REDUCE: (89), (702) imply: % 193.32/27.01 | | | | | | | | (703) c_member(all_622_1, all_872_1, v_L) = all_1142_0 % 193.32/27.01 | | | | | | | | % 193.32/27.01 | | | | | | | | GROUND_INST: instantiating (20) with all_872_0, all_1142_0, v_L, % 193.32/27.01 | | | | | | | | all_872_1, all_622_1, simplifying with (184), (703) % 193.32/27.01 | | | | | | | | gives: % 193.32/27.01 | | | | | | | | (704) all_1142_0 = all_872_0 % 193.32/27.01 | | | | | | | | % 193.32/27.01 | | | | | | | | REDUCE: (701), (704) imply: % 193.32/27.01 | | | | | | | | (705) ~ (all_872_0 = 0) % 193.32/27.01 | | | | | | | | % 193.32/27.01 | | | | | | | | BETA: splitting (192) gives: % 193.32/27.01 | | | | | | | | % 193.32/27.01 | | | | | | | | Case 1: % 193.32/27.01 | | | | | | | | | % 193.32/27.01 | | | | | | | | | (706) all_872_8 = v_x % 193.32/27.01 | | | | | | | | | % 193.32/27.01 | | | | | | | | | BETA: splitting (657) gives: % 193.32/27.01 | | | | | | | | | % 193.32/27.01 | | | | | | | | | Case 1: % 193.32/27.01 | | | | | | | | | | % 193.32/27.01 | | | | | | | | | | (707) all_872_4 = 0 & all_872_8 = v_y & ? [v0: $i] : ? % 193.32/27.01 | | | | | | | | | | [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = % 193.32/27.01 | | | | | | | | | | 0) & ~ (v0 = v_y) & % 193.32/27.01 | | | | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.01 | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v0) % 193.32/27.01 | | | | | | | | | | = v2 & % 193.32/27.01 | | | | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.01 | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v0) = v1 % 193.32/27.01 | | | | | | | | | | & c_member(all_685_0, v2, v_L) = v3 & % 193.32/27.01 | | | | | | | | | | c_member(all_685_0, v1, v_L) = 0 & $i(v2) & % 193.32/27.01 | | | | | | | | | | $i(v1) & $i(v0)) % 193.32/27.01 | | | | | | | | | | % 193.32/27.01 | | | | | | | | | | ALPHA: (707) implies: % 193.32/27.01 | | | | | | | | | | (708) all_872_8 = v_y % 193.32/27.01 | | | | | | | | | | % 193.32/27.01 | | | | | | | | | | COMBINE_EQS: (706), (708) imply: % 193.32/27.01 | | | | | | | | | | (709) v_x = v_y % 193.32/27.01 | | | | | | | | | | % 193.32/27.01 | | | | | | | | | | REDUCE: (13), (709) imply: % 193.32/27.01 | | | | | | | | | | (710) $false % 193.32/27.01 | | | | | | | | | | % 193.32/27.01 | | | | | | | | | | CLOSE: (710) is inconsistent. % 193.32/27.01 | | | | | | | | | | % 193.32/27.01 | | | | | | | | | Case 2: % 193.32/27.01 | | | | | | | | | | % 193.32/27.02 | | | | | | | | | | (711) all_872_6 = 0 & ~ (all_872_8 = v_y) & ? [v0: $i] % 193.32/27.02 | | | | | | | | | | : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ? % 193.32/27.02 | | | | | | | | | | [v4: any] : % 193.32/27.02 | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.02 | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v0) % 193.32/27.02 | | | | | | | | | | = v1 & % 193.32/27.02 | | | | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.02 | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v0) % 193.32/27.02 | | | | | | | | | | = v3 & c_member(all_685_0, v3, v_L) = v4 & % 193.32/27.02 | | | | | | | | | | c_member(all_685_0, v1, v_L) = v2 & $i(v3) & % 193.32/27.02 | | | | | | | | | | $i(v1) & $i(v0) & ((v2 = 0 & ~ (v4 = 0) & ~ (v0 % 193.32/27.02 | | | | | | | | | | = v_y)) | (v0 = v_y & all_872_2 = 0 & ~ % 193.32/27.02 | | | | | | | | | | (all_872_4 = 0) & ~ (all_872_9 = v_x)) | (v0 % 193.32/27.02 | | | | | | | | | | = v_y & all_872_8 = v_x & ~ (all_872_4 = 0) % 193.32/27.02 | | | | | | | | | | & ~ (all_872_9 = v_x)))) % 193.32/27.02 | | | | | | | | | | % 193.32/27.02 | | | | | | | | | | ALPHA: (711) implies: % 193.32/27.02 | | | | | | | | | | (712) all_872_6 = 0 % 193.32/27.02 | | | | | | | | | | (713) ~ (all_872_8 = v_y) % 193.32/27.02 | | | | | | | | | | % 193.32/27.02 | | | | | | | | | | REDUCE: (187), (712) imply: % 193.32/27.02 | | | | | | | | | | (714) c_member(all_622_1, all_872_7, v_L) = 0 % 193.32/27.02 | | | | | | | | | | % 193.32/27.02 | | | | | | | | | | BETA: splitting (197) gives: % 193.32/27.02 | | | | | | | | | | % 193.32/27.02 | | | | | | | | | | Case 1: % 193.32/27.02 | | | | | | | | | | | % 193.32/27.02 | | | | | | | | | | | (715) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_676_0, % 193.32/27.02 | | | | | | | | | | | all_872_7, v_L) = v0) % 193.32/27.02 | | | | | | | | | | | % 193.32/27.02 | | | | | | | | | | | DELTA: instantiating (715) with fresh symbol all_1123_0 % 193.32/27.02 | | | | | | | | | | | gives: % 193.32/27.02 | | | | | | | | | | | (716) ~ (all_1123_0 = 0) & c_member(all_676_0, % 193.32/27.02 | | | | | | | | | | | all_872_7, v_L) = all_1123_0 % 193.32/27.02 | | | | | | | | | | | % 193.32/27.02 | | | | | | | | | | | REF_CLOSE: (20), (89), (714), (716) are inconsistent by % 193.32/27.02 | | | | | | | | | | | sub-proof #14. % 193.32/27.02 | | | | | | | | | | | % 193.32/27.02 | | | | | | | | | | Case 2: % 193.32/27.02 | | | | | | | | | | | % 193.32/27.02 | | | | | | | | | | | (717) ! [v0: $i] : ! [v1: $i] : ( ~ % 193.32/27.02 | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.02 | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, % 193.32/27.02 | | | | | | | | | | | v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? % 193.32/27.02 | | | | | | | | | | | [v3: any] : ? [v4: any] : % 193.32/27.02 | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.02 | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, % 193.32/27.02 | | | | | | | | | | | v0) = v2 & c_member(all_676_0, v2, v_L) = v3 % 193.32/27.02 | | | | | | | | | | | & c_member(all_676_0, v1, v_L) = v4 & $i(v2) & % 193.32/27.02 | | | | | | | | | | | ( ~ (v3 = 0) | v4 = 0))) % 193.32/27.02 | | | | | | | | | | | % 193.32/27.02 | | | | | | | | | | | REF_CLOSE: (3), (13), (17), (20), (21), (44), (89), (90), % 193.32/27.02 | | | | | | | | | | | (91), (170), (180), (181), (182), (184), (185), % 193.32/27.02 | | | | | | | | | | | (186), (192), (198), (657), (664), (681), (705), % 193.32/27.02 | | | | | | | | | | | (714), (717) are inconsistent by sub-proof #7. % 193.32/27.02 | | | | | | | | | | | % 193.32/27.02 | | | | | | | | | | End of split % 193.32/27.02 | | | | | | | | | | % 193.32/27.02 | | | | | | | | | End of split % 193.32/27.02 | | | | | | | | | % 193.32/27.02 | | | | | | | | Case 2: % 193.32/27.02 | | | | | | | | | % 193.32/27.02 | | | | | | | | | (718) ~ (all_872_8 = v_x) % 193.32/27.02 | | | | | | | | | (719) ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 193.32/27.02 | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.02 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v_x) % 193.32/27.02 | | | | | | | | | = v1 & c_member(all_676_0, v1, v_L) = v2 & % 193.32/27.02 | | | | | | | | | c_member(all_676_0, all_872_1, v_L) = v0 & $i(v1) & % 193.32/27.02 | | | | | | | | | (v2 = 0 | v0 = 0)) % 193.32/27.02 | | | | | | | | | % 193.32/27.02 | | | | | | | | | DELTA: instantiating (719) with fresh symbols all_1201_0, % 193.32/27.02 | | | | | | | | | all_1201_1, all_1201_2 gives: % 193.32/27.02 | | | | | | | | | (720) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.02 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v_x) = % 193.32/27.02 | | | | | | | | | all_1201_1 & c_member(all_676_0, all_1201_1, v_L) = % 193.32/27.02 | | | | | | | | | all_1201_0 & c_member(all_676_0, all_872_1, v_L) = % 193.32/27.02 | | | | | | | | | all_1201_2 & $i(all_1201_1) & (all_1201_0 = 0 | % 193.32/27.02 | | | | | | | | | all_1201_2 = 0) % 193.32/27.02 | | | | | | | | | % 193.32/27.02 | | | | | | | | | REF_CLOSE: (20), (21), (89), (182), (184), (185), (198), % 193.32/27.02 | | | | | | | | | (664), (705), (718), (720) are inconsistent by % 193.32/27.02 | | | | | | | | | sub-proof #9. % 193.32/27.02 | | | | | | | | | % 193.32/27.02 | | | | | | | | End of split % 193.32/27.02 | | | | | | | | % 193.32/27.02 | | | | | | | Case 2: % 193.32/27.02 | | | | | | | | % 193.32/27.02 | | | | | | | | (721) ! [v0: $i] : ! [v1: $i] : ( ~ % 193.32/27.02 | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.02 | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v0) = v1) | % 193.32/27.02 | | | | | | | | ~ $i(v0) | ? [v2: $i] : ? [v3: any] : ? [v4: any] % 193.32/27.02 | | | | | | | | : % 193.32/27.02 | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.02 | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v0) = % 193.32/27.02 | | | | | | | | v2 & c_member(all_676_0, v2, v_L) = v3 & % 193.32/27.02 | | | | | | | | c_member(all_676_0, v1, v_L) = v4 & $i(v2) & ( ~ % 193.32/27.02 | | | | | | | | (v3 = 0) | v4 = 0))) % 193.32/27.02 | | | | | | | | % 193.32/27.02 | | | | | | | | GROUND_INST: instantiating (721) with all_872_8, all_872_1, % 193.32/27.02 | | | | | | | | simplifying with (170), (179) gives: % 193.32/27.02 | | | | | | | | (722) ? [v0: $i] : ? [v1: any] : ? [v2: any] : % 193.32/27.02 | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.02 | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, % 193.32/27.02 | | | | | | | | all_872_8) = v0 & c_member(all_676_0, v0, v_L) = v1 % 193.32/27.02 | | | | | | | | & c_member(all_676_0, all_872_1, v_L) = v2 & $i(v0) & % 193.32/27.02 | | | | | | | | ( ~ (v1 = 0) | v2 = 0)) % 193.32/27.02 | | | | | | | | % 193.32/27.02 | | | | | | | | DELTA: instantiating (722) with fresh symbols all_1143_0, % 193.32/27.02 | | | | | | | | all_1143_1, all_1143_2 gives: % 193.32/27.02 | | | | | | | | (723) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.02 | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, % 193.32/27.02 | | | | | | | | all_872_8) = all_1143_2 & c_member(all_676_0, % 193.32/27.02 | | | | | | | | all_1143_2, v_L) = all_1143_1 & c_member(all_676_0, % 193.32/27.02 | | | | | | | | all_872_1, v_L) = all_1143_0 & $i(all_1143_2) & ( ~ % 193.32/27.02 | | | | | | | | (all_1143_1 = 0) | all_1143_0 = 0) % 193.32/27.02 | | | | | | | | % 193.32/27.02 | | | | | | | | ALPHA: (723) implies: % 193.32/27.02 | | | | | | | | (724) c_member(all_676_0, all_872_1, v_L) = all_1143_0 % 193.32/27.02 | | | | | | | | % 193.32/27.02 | | | | | | | | REDUCE: (89), (724) imply: % 193.32/27.02 | | | | | | | | (725) c_member(all_622_1, all_872_1, v_L) = all_1143_0 % 193.32/27.02 | | | | | | | | % 193.32/27.02 | | | | | | | | GROUND_INST: instantiating (20) with all_872_0, all_1143_0, v_L, % 193.32/27.02 | | | | | | | | all_872_1, all_622_1, simplifying with (184), (725) % 193.32/27.02 | | | | | | | | gives: % 193.32/27.02 | | | | | | | | (726) all_1143_0 = all_872_0 % 193.32/27.02 | | | | | | | | % 193.32/27.02 | | | | | | | | BETA: splitting (197) gives: % 193.32/27.02 | | | | | | | | % 193.32/27.02 | | | | | | | | Case 1: % 193.32/27.02 | | | | | | | | | % 193.32/27.02 | | | | | | | | | (727) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_676_0, % 193.32/27.02 | | | | | | | | | all_872_7, v_L) = v0) % 193.32/27.02 | | | | | | | | | % 193.32/27.02 | | | | | | | | | DELTA: instantiating (727) with fresh symbol all_1154_0 gives: % 193.32/27.02 | | | | | | | | | (728) ~ (all_1154_0 = 0) & c_member(all_676_0, all_872_7, % 193.32/27.02 | | | | | | | | | v_L) = all_1154_0 % 193.32/27.02 | | | | | | | | | % 193.32/27.02 | | | | | | | | | ALPHA: (728) implies: % 193.32/27.02 | | | | | | | | | (729) ~ (all_1154_0 = 0) % 193.32/27.02 | | | | | | | | | (730) c_member(all_676_0, all_872_7, v_L) = all_1154_0 % 193.32/27.02 | | | | | | | | | % 193.32/27.02 | | | | | | | | | REDUCE: (89), (730) imply: % 193.32/27.02 | | | | | | | | | (731) c_member(all_622_1, all_872_7, v_L) = all_1154_0 % 193.32/27.02 | | | | | | | | | % 193.32/27.02 | | | | | | | | | GROUND_INST: instantiating (20) with all_872_6, all_1154_0, % 193.32/27.02 | | | | | | | | | v_L, all_872_7, all_622_1, simplifying with (187), % 193.32/27.02 | | | | | | | | | (731) gives: % 193.32/27.02 | | | | | | | | | (732) all_1154_0 = all_872_6 % 193.32/27.02 | | | | | | | | | % 193.32/27.02 | | | | | | | | | REDUCE: (729), (732) imply: % 193.32/27.02 | | | | | | | | | (733) ~ (all_872_6 = 0) % 193.32/27.02 | | | | | | | | | % 193.32/27.02 | | | | | | | | | BETA: splitting (688) gives: % 193.32/27.02 | | | | | | | | | % 193.32/27.02 | | | | | | | | | Case 1: % 193.32/27.02 | | | | | | | | | | % 193.32/27.02 | | | | | | | | | | (734) ~ (all_1125_1 = 0) % 193.32/27.02 | | | | | | | | | | % 193.32/27.02 | | | | | | | | | | REDUCE: (698), (734) imply: % 193.32/27.02 | | | | | | | | | | (735) ~ (all_872_0 = 0) % 193.32/27.02 | | | | | | | | | | % 193.32/27.02 | | | | | | | | | | BETA: splitting (192) gives: % 193.32/27.02 | | | | | | | | | | % 193.32/27.02 | | | | | | | | | | Case 1: % 193.32/27.02 | | | | | | | | | | | % 193.32/27.02 | | | | | | | | | | | (736) all_872_8 = v_x % 193.32/27.02 | | | | | | | | | | | % 193.32/27.02 | | | | | | | | | | | BETA: splitting (657) gives: % 193.32/27.02 | | | | | | | | | | | % 193.32/27.02 | | | | | | | | | | | Case 1: % 193.32/27.02 | | | | | | | | | | | | % 193.32/27.02 | | | | | | | | | | | | (737) all_872_4 = 0 & all_872_8 = v_y & ? [v0: $i] : ? % 193.32/27.02 | | | | | | | | | | | | [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = % 193.32/27.02 | | | | | | | | | | | | 0) & ~ (v0 = v_y) & % 193.32/27.02 | | | | | | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.02 | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, % 193.32/27.02 | | | | | | | | | | | | v0) = v2 & % 193.32/27.02 | | | | | | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.02 | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v0) = v1 % 193.32/27.02 | | | | | | | | | | | | & c_member(all_685_0, v2, v_L) = v3 & % 193.32/27.02 | | | | | | | | | | | | c_member(all_685_0, v1, v_L) = 0 & $i(v2) & % 193.32/27.02 | | | | | | | | | | | | $i(v1) & $i(v0)) % 193.32/27.02 | | | | | | | | | | | | % 193.32/27.02 | | | | | | | | | | | | ALPHA: (737) implies: % 193.32/27.02 | | | | | | | | | | | | (738) all_872_8 = v_y % 193.32/27.02 | | | | | | | | | | | | % 193.32/27.02 | | | | | | | | | | | | COMBINE_EQS: (736), (738) imply: % 193.32/27.02 | | | | | | | | | | | | (739) v_x = v_y % 193.32/27.02 | | | | | | | | | | | | % 193.32/27.02 | | | | | | | | | | | | REDUCE: (13), (739) imply: % 193.32/27.02 | | | | | | | | | | | | (740) $false % 193.32/27.02 | | | | | | | | | | | | % 193.32/27.02 | | | | | | | | | | | | CLOSE: (740) is inconsistent. % 193.32/27.02 | | | | | | | | | | | | % 193.32/27.02 | | | | | | | | | | | Case 2: % 193.32/27.02 | | | | | | | | | | | | % 193.32/27.02 | | | | | | | | | | | | (741) all_872_6 = 0 & ~ (all_872_8 = v_y) & ? [v0: $i] % 193.32/27.02 | | | | | | | | | | | | : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ? % 193.32/27.02 | | | | | | | | | | | | [v4: any] : % 193.32/27.02 | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.02 | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, % 193.32/27.02 | | | | | | | | | | | | v0) = v1 & % 193.32/27.02 | | | | | | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.02 | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, % 193.32/27.02 | | | | | | | | | | | | v0) = v3 & c_member(all_685_0, v3, v_L) = v4 & % 193.32/27.02 | | | | | | | | | | | | c_member(all_685_0, v1, v_L) = v2 & $i(v3) & % 193.32/27.02 | | | | | | | | | | | | $i(v1) & $i(v0) & ((v2 = 0 & ~ (v4 = 0) & ~ % 193.32/27.02 | | | | | | | | | | | | (v0 = v_y)) | (v0 = v_y & all_872_2 = 0 & ~ % 193.32/27.02 | | | | | | | | | | | | (all_872_4 = 0) & ~ (all_872_9 = v_x)) | % 193.32/27.02 | | | | | | | | | | | | (v0 = v_y & all_872_8 = v_x & ~ (all_872_4 = % 193.32/27.02 | | | | | | | | | | | | 0) & ~ (all_872_9 = v_x)))) % 193.32/27.02 | | | | | | | | | | | | % 193.32/27.02 | | | | | | | | | | | | ALPHA: (741) implies: % 193.32/27.02 | | | | | | | | | | | | (742) all_872_6 = 0 % 193.32/27.02 | | | | | | | | | | | | % 193.32/27.02 | | | | | | | | | | | | REDUCE: (733), (742) imply: % 193.32/27.02 | | | | | | | | | | | | (743) $false % 193.32/27.02 | | | | | | | | | | | | % 193.32/27.02 | | | | | | | | | | | | CLOSE: (743) is inconsistent. % 193.32/27.02 | | | | | | | | | | | | % 193.32/27.02 | | | | | | | | | | | End of split % 193.32/27.02 | | | | | | | | | | | % 193.32/27.02 | | | | | | | | | | Case 2: % 193.32/27.02 | | | | | | | | | | | % 193.32/27.02 | | | | | | | | | | | (744) ~ (all_872_8 = v_x) % 193.32/27.02 | | | | | | | | | | | (745) ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 193.32/27.02 | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.02 | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, % 193.32/27.02 | | | | | | | | | | | v_x) = v1 & c_member(all_676_0, v1, v_L) = v2 % 193.32/27.02 | | | | | | | | | | | & c_member(all_676_0, all_872_1, v_L) = v0 & % 193.32/27.02 | | | | | | | | | | | $i(v1) & (v2 = 0 | v0 = 0)) % 193.32/27.02 | | | | | | | | | | | % 193.32/27.02 | | | | | | | | | | | DELTA: instantiating (745) with fresh symbols all_1201_0, % 193.32/27.02 | | | | | | | | | | | all_1201_1, all_1201_2 gives: % 193.32/27.03 | | | | | | | | | | | (746) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.03 | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v_x) % 193.32/27.03 | | | | | | | | | | | = all_1201_1 & c_member(all_676_0, all_1201_1, % 193.32/27.03 | | | | | | | | | | | v_L) = all_1201_0 & c_member(all_676_0, % 193.32/27.03 | | | | | | | | | | | all_872_1, v_L) = all_1201_2 & $i(all_1201_1) & % 193.32/27.03 | | | | | | | | | | | (all_1201_0 = 0 | all_1201_2 = 0) % 193.32/27.03 | | | | | | | | | | | % 193.32/27.03 | | | | | | | | | | | REF_CLOSE: (20), (21), (89), (182), (184), (185), (198), % 193.32/27.03 | | | | | | | | | | | (664), (735), (744), (746) are inconsistent by % 193.32/27.03 | | | | | | | | | | | sub-proof #9. % 193.32/27.03 | | | | | | | | | | | % 193.32/27.03 | | | | | | | | | | End of split % 193.32/27.03 | | | | | | | | | | % 193.32/27.03 | | | | | | | | | Case 2: % 193.32/27.03 | | | | | | | | | | % 193.32/27.03 | | | | | | | | | | (747) all_1125_0 = 0 % 193.32/27.03 | | | | | | | | | | % 193.32/27.03 | | | | | | | | | | COMBINE_EQS: (694), (747) imply: % 193.32/27.03 | | | | | | | | | | (748) all_872_6 = 0 % 193.32/27.03 | | | | | | | | | | % 193.32/27.03 | | | | | | | | | | REDUCE: (733), (748) imply: % 193.32/27.03 | | | | | | | | | | (749) $false % 193.32/27.03 | | | | | | | | | | % 193.32/27.03 | | | | | | | | | | CLOSE: (749) is inconsistent. % 193.32/27.03 | | | | | | | | | | % 193.32/27.03 | | | | | | | | | End of split % 193.32/27.03 | | | | | | | | | % 193.32/27.03 | | | | | | | | Case 2: % 193.32/27.03 | | | | | | | | | % 193.32/27.03 | | | | | | | | | (750) ! [v0: $i] : ! [v1: $i] : ( ~ % 193.32/27.03 | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.03 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v0) % 193.32/27.03 | | | | | | | | | = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: any] : % 193.32/27.03 | | | | | | | | | ? [v4: any] : % 193.32/27.03 | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.03 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v0) % 193.32/27.03 | | | | | | | | | = v2 & c_member(all_676_0, v2, v_L) = v3 & % 193.32/27.03 | | | | | | | | | c_member(all_676_0, v1, v_L) = v4 & $i(v2) & ( ~ % 193.32/27.03 | | | | | | | | | (v3 = 0) | v4 = 0))) % 193.32/27.03 | | | | | | | | | % 193.32/27.03 | | | | | | | | | GROUND_INST: instantiating (750) with all_872_8, all_872_7, % 193.32/27.03 | | | | | | | | | simplifying with (170), (181) gives: % 193.32/27.03 | | | | | | | | | (751) ? [v0: $i] : ? [v1: any] : ? [v2: any] : % 193.32/27.03 | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.03 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, % 193.32/27.03 | | | | | | | | | all_872_8) = v0 & c_member(all_676_0, v0, v_L) = % 193.32/27.03 | | | | | | | | | v1 & c_member(all_676_0, all_872_7, v_L) = v2 & % 193.32/27.03 | | | | | | | | | $i(v0) & ( ~ (v1 = 0) | v2 = 0)) % 193.32/27.03 | | | | | | | | | % 193.32/27.03 | | | | | | | | | DELTA: instantiating (751) with fresh symbols all_1155_0, % 193.32/27.03 | | | | | | | | | all_1155_1, all_1155_2 gives: % 193.32/27.03 | | | | | | | | | (752) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.03 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, % 193.32/27.03 | | | | | | | | | all_872_8) = all_1155_2 & c_member(all_676_0, % 193.32/27.03 | | | | | | | | | all_1155_2, v_L) = all_1155_1 & c_member(all_676_0, % 193.32/27.03 | | | | | | | | | all_872_7, v_L) = all_1155_0 & $i(all_1155_2) & ( ~ % 193.32/27.03 | | | | | | | | | (all_1155_1 = 0) | all_1155_0 = 0) % 193.32/27.03 | | | | | | | | | % 193.32/27.03 | | | | | | | | | ALPHA: (752) implies: % 193.32/27.03 | | | | | | | | | (753) c_member(all_676_0, all_872_7, v_L) = all_1155_0 % 193.32/27.03 | | | | | | | | | % 193.32/27.03 | | | | | | | | | REDUCE: (89), (753) imply: % 193.32/27.03 | | | | | | | | | (754) c_member(all_622_1, all_872_7, v_L) = all_1155_0 % 193.32/27.03 | | | | | | | | | % 193.32/27.03 | | | | | | | | | GROUND_INST: instantiating (20) with all_872_6, all_1155_0, % 193.32/27.03 | | | | | | | | | v_L, all_872_7, all_622_1, simplifying with (187), % 193.32/27.03 | | | | | | | | | (754) gives: % 193.32/27.03 | | | | | | | | | (755) all_1155_0 = all_872_6 % 193.32/27.03 | | | | | | | | | % 193.32/27.03 | | | | | | | | | BETA: splitting (191) gives: % 193.32/27.03 | | | | | | | | | % 193.32/27.03 | | | | | | | | | Case 1: % 193.32/27.03 | | | | | | | | | | % 193.32/27.03 | | | | | | | | | | (756) all_872_0 = 0 % 193.32/27.03 | | | | | | | | | | % 193.32/27.03 | | | | | | | | | | COMBINE_EQS: (698), (756) imply: % 193.32/27.03 | | | | | | | | | | (757) all_1125_1 = 0 % 193.32/27.03 | | | | | | | | | | % 193.32/27.03 | | | | | | | | | | REDUCE: (184), (756) imply: % 193.32/27.03 | | | | | | | | | | (758) c_member(all_622_1, all_872_1, v_L) = 0 % 193.32/27.03 | | | | | | | | | | % 193.32/27.03 | | | | | | | | | | BETA: splitting (688) gives: % 193.32/27.03 | | | | | | | | | | % 193.32/27.03 | | | | | | | | | | Case 1: % 193.32/27.03 | | | | | | | | | | | % 193.32/27.03 | | | | | | | | | | | (759) ~ (all_1125_1 = 0) % 193.32/27.03 | | | | | | | | | | | % 193.32/27.03 | | | | | | | | | | | REDUCE: (757), (759) imply: % 193.32/27.03 | | | | | | | | | | | (760) $false % 193.32/27.03 | | | | | | | | | | | % 193.32/27.03 | | | | | | | | | | | CLOSE: (760) is inconsistent. % 193.32/27.03 | | | | | | | | | | | % 193.32/27.03 | | | | | | | | | | Case 2: % 193.32/27.03 | | | | | | | | | | | % 193.32/27.03 | | | | | | | | | | | (761) all_1125_0 = 0 % 193.32/27.03 | | | | | | | | | | | % 193.32/27.03 | | | | | | | | | | | COMBINE_EQS: (694), (761) imply: % 193.32/27.03 | | | | | | | | | | | (762) all_872_6 = 0 % 193.32/27.03 | | | | | | | | | | | % 193.32/27.03 | | | | | | | | | | | REDUCE: (187), (762) imply: % 193.32/27.03 | | | | | | | | | | | (763) c_member(all_622_1, all_872_7, v_L) = 0 % 193.32/27.03 | | | | | | | | | | | % 193.32/27.03 | | | | | | | | | | | BETA: splitting (196) gives: % 193.32/27.03 | | | | | | | | | | | % 193.32/27.03 | | | | | | | | | | | Case 1: % 193.32/27.03 | | | | | | | | | | | | % 193.32/27.03 | | | | | | | | | | | | (764) all_872_8 = all_872_9 % 193.32/27.03 | | | | | | | | | | | | % 193.32/27.03 | | | | | | | | | | | | REDUCE: (182), (764) imply: % 193.32/27.03 | | | | | | | | | | | | (765) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.03 | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v_x) % 193.32/27.03 | | | | | | | | | | | | = all_872_3 % 193.32/27.03 | | | | | | | | | | | | % 193.32/27.03 | | | | | | | | | | | | REF_CLOSE: (20), (21), (90), (180), (185), (186), (656), % 193.32/27.03 | | | | | | | | | | | | (657), (764), (765) are inconsistent by sub-proof % 193.32/27.03 | | | | | | | | | | | | #5. % 193.32/27.03 | | | | | | | | | | | | % 193.32/27.03 | | | | | | | | | | | Case 2: % 193.32/27.03 | | | | | | | | | | | | % 193.32/27.03 | | | | | | | | | | | | (766) ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 193.32/27.03 | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.03 | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, % 193.32/27.03 | | | | | | | | | | | | all_872_9) = v1 & c_member(all_676_0, v1, v_L) % 193.32/27.03 | | | | | | | | | | | | = v2 & c_member(all_676_0, all_872_7, v_L) = v0 % 193.32/27.03 | | | | | | | | | | | | & $i(v1) & (v2 = 0 | v0 = 0)) % 193.32/27.03 | | | | | | | | | | | | % 193.32/27.03 | | | | | | | | | | | | DELTA: instantiating (766) with fresh symbols all_1181_0, % 193.32/27.03 | | | | | | | | | | | | all_1181_1, all_1181_2 gives: % 193.32/27.03 | | | | | | | | | | | | (767) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.03 | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, % 193.32/27.03 | | | | | | | | | | | | all_872_9) = all_1181_1 & c_member(all_676_0, % 193.32/27.03 | | | | | | | | | | | | all_1181_1, v_L) = all_1181_0 & % 193.32/27.03 | | | | | | | | | | | | c_member(all_676_0, all_872_7, v_L) = all_1181_2 & % 193.32/27.03 | | | | | | | | | | | | $i(all_1181_1) & (all_1181_0 = 0 | all_1181_2 = 0) % 193.32/27.03 | | | | | | | | | | | | % 193.32/27.03 | | | | | | | | | | | | ALPHA: (767) implies: % 193.32/27.03 | | | | | | | | | | | | (768) c_member(all_676_0, all_872_7, v_L) = all_1181_2 % 193.32/27.03 | | | | | | | | | | | | % 193.32/27.03 | | | | | | | | | | | | REDUCE: (89), (768) imply: % 193.32/27.03 | | | | | | | | | | | | (769) c_member(all_622_1, all_872_7, v_L) = all_1181_2 % 193.32/27.03 | | | | | | | | | | | | % 193.32/27.03 | | | | | | | | | | | | GROUND_INST: instantiating (20) with 0, all_1181_2, v_L, % 193.32/27.03 | | | | | | | | | | | | all_872_7, all_622_1, simplifying with (763), % 193.32/27.03 | | | | | | | | | | | | (769) gives: % 193.32/27.03 | | | | | | | | | | | | (770) all_1181_2 = 0 % 193.32/27.03 | | | | | | | | | | | | % 193.32/27.03 | | | | | | | | | | | | GROUND_INST: instantiating (fact_single__valuedD) with v_x, % 193.32/27.03 | | | | | | | | | | | | all_872_8, all_872_9, v_L, % 193.32/27.03 | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.03 | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_622_1, % 193.32/27.03 | | | | | | | | | | | | all_872_7, all_872_5, simplifying with (15), (16), % 193.32/27.03 | | | | | | | | | | | | (17), (23), (169), (170), (180), (181), (678), % 193.32/27.03 | | | | | | | | | | | | (763) gives: % 193.32/27.03 | | | | | | | | | | | | (771) all_872_8 = v_x | ? [v0: int] : ( ~ (v0 = 0) & % 193.32/27.03 | | | | | | | | | | | | c_Relation_Osingle__valued(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.03 | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_L) = v0) % 193.32/27.03 | | | | | | | | | | | | % 193.32/27.03 | | | | | | | | | | | | BETA: splitting (657) gives: % 193.32/27.03 | | | | | | | | | | | | % 193.32/27.03 | | | | | | | | | | | | Case 1: % 193.32/27.03 | | | | | | | | | | | | | % 193.32/27.03 | | | | | | | | | | | | | (772) all_872_4 = 0 & all_872_8 = v_y & ? [v0: $i] : ? % 193.32/27.03 | | | | | | | | | | | | | [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = % 193.32/27.03 | | | | | | | | | | | | | 0) & ~ (v0 = v_y) & % 193.32/27.03 | | | | | | | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.03 | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, % 193.32/27.03 | | | | | | | | | | | | | v0) = v2 & % 193.32/27.03 | | | | | | | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.03 | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v0) = v1 % 193.32/27.03 | | | | | | | | | | | | | & c_member(all_685_0, v2, v_L) = v3 & % 193.32/27.03 | | | | | | | | | | | | | c_member(all_685_0, v1, v_L) = 0 & $i(v2) & % 193.32/27.03 | | | | | | | | | | | | | $i(v1) & $i(v0)) % 193.32/27.03 | | | | | | | | | | | | | % 193.32/27.03 | | | | | | | | | | | | | ALPHA: (772) implies: % 193.32/27.03 | | | | | | | | | | | | | (773) all_872_8 = v_y % 193.32/27.03 | | | | | | | | | | | | | (774) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 193.32/27.03 | | | | | | | | | | | | | int] : ( ~ (v3 = 0) & ~ (v0 = v_y) & % 193.32/27.03 | | | | | | | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.03 | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, % 193.32/27.03 | | | | | | | | | | | | | v0) = v2 & % 193.32/27.03 | | | | | | | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.03 | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v0) = v1 % 193.32/27.03 | | | | | | | | | | | | | & c_member(all_685_0, v2, v_L) = v3 & % 193.32/27.03 | | | | | | | | | | | | | c_member(all_685_0, v1, v_L) = 0 & $i(v2) & % 193.32/27.03 | | | | | | | | | | | | | $i(v1) & $i(v0)) % 193.32/27.03 | | | | | | | | | | | | | % 193.32/27.03 | | | | | | | | | | | | | DELTA: instantiating (774) with fresh symbols all_1325_0, % 193.32/27.03 | | | | | | | | | | | | | all_1325_1, all_1325_2, all_1325_3 gives: % 193.32/27.03 | | | | | | | | | | | | | (775) ~ (all_1325_0 = 0) & ~ (all_1325_3 = v_y) & % 193.32/27.03 | | | | | | | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.03 | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, % 193.32/27.03 | | | | | | | | | | | | | all_1325_3) = all_1325_1 & % 193.32/27.03 | | | | | | | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.03 | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, % 193.32/27.03 | | | | | | | | | | | | | all_1325_3) = all_1325_2 & c_member(all_685_0, % 193.32/27.03 | | | | | | | | | | | | | all_1325_1, v_L) = all_1325_0 & % 193.32/27.03 | | | | | | | | | | | | | c_member(all_685_0, all_1325_2, v_L) = 0 & % 193.32/27.03 | | | | | | | | | | | | | $i(all_1325_1) & $i(all_1325_2) & $i(all_1325_3) % 193.32/27.03 | | | | | | | | | | | | | % 193.32/27.03 | | | | | | | | | | | | | ALPHA: (775) implies: % 193.32/27.03 | | | | | | | | | | | | | (776) ~ (all_1325_0 = 0) % 193.32/27.03 | | | | | | | | | | | | | (777) $i(all_1325_3) % 193.32/27.03 | | | | | | | | | | | | | (778) c_member(all_685_0, all_1325_2, v_L) = 0 % 193.32/27.03 | | | | | | | | | | | | | (779) c_member(all_685_0, all_1325_1, v_L) = all_1325_0 % 193.32/27.03 | | | | | | | | | | | | | (780) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.03 | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, % 193.32/27.03 | | | | | | | | | | | | | all_1325_3) = all_1325_2 % 193.32/27.03 | | | | | | | | | | | | | (781) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.03 | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, % 193.32/27.03 | | | | | | | | | | | | | all_1325_3) = all_1325_1 % 193.32/27.03 | | | | | | | | | | | | | % 193.32/27.03 | | | | | | | | | | | | | REDUCE: (181), (773) imply: % 193.32/27.03 | | | | | | | | | | | | | (782) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.03 | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v_y) % 193.32/27.03 | | | | | | | | | | | | | = all_872_7 % 193.32/27.03 | | | | | | | | | | | | | % 193.32/27.03 | | | | | | | | | | | | | REDUCE: (179), (773) imply: % 193.32/27.03 | | | | | | | | | | | | | (783) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.03 | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v_y) = % 193.32/27.03 | | | | | | | | | | | | | all_872_1 % 193.32/27.03 | | | | | | | | | | | | | % 193.32/27.03 | | | | | | | | | | | | | REDUCE: (90), (779) imply: % 193.32/27.03 | | | | | | | | | | | | | (784) c_member(all_622_1, all_1325_1, v_L) = all_1325_0 % 193.32/27.03 | | | | | | | | | | | | | % 193.32/27.03 | | | | | | | | | | | | | REDUCE: (90), (778) imply: % 193.32/27.03 | | | | | | | | | | | | | (785) c_member(all_622_1, all_1325_2, v_L) = 0 % 193.32/27.03 | | | | | | | | | | | | | % 193.32/27.03 | | | | | | | | | | | | | REDUCE: (170), (773) imply: % 193.32/27.03 | | | | | | | | | | | | | (786) $i(v_y) % 193.32/27.03 | | | | | | | | | | | | | % 193.32/27.03 | | | | | | | | | | | | | BETA: splitting (771) gives: % 193.32/27.03 | | | | | | | | | | | | | % 193.32/27.03 | | | | | | | | | | | | | Case 1: % 193.32/27.03 | | | | | | | | | | | | | | % 193.32/27.03 | | | | | | | | | | | | | | (787) all_872_8 = v_x % 193.32/27.03 | | | | | | | | | | | | | | % 193.32/27.03 | | | | | | | | | | | | | | COMBINE_EQS: (773), (787) imply: % 193.32/27.03 | | | | | | | | | | | | | | (788) v_x = v_y % 193.32/27.03 | | | | | | | | | | | | | | % 193.32/27.03 | | | | | | | | | | | | | | REDUCE: (13), (788) imply: % 193.32/27.03 | | | | | | | | | | | | | | (789) $false % 193.32/27.03 | | | | | | | | | | | | | | % 193.32/27.03 | | | | | | | | | | | | | | CLOSE: (789) is inconsistent. % 193.32/27.03 | | | | | | | | | | | | | | % 193.32/27.03 | | | | | | | | | | | | | Case 2: % 193.32/27.03 | | | | | | | | | | | | | | % 193.32/27.03 | | | | | | | | | | | | | | % 193.32/27.03 | | | | | | | | | | | | | | GROUND_INST: instantiating (44) with v_x, v_y, all_872_1, % 193.32/27.03 | | | | | | | | | | | | | | simplifying with (16), (783), (786) gives: % 193.32/27.03 | | | | | | | | | | | | | | (790) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_676_0, % 193.32/27.03 | | | | | | | | | | | | | | all_872_1, v_L) = v0) | ! [v0: $i] : ! [v1: % 193.32/27.03 | | | | | | | | | | | | | | $i] : ( ~ % 193.32/27.03 | | | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.03 | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v0) = % 193.32/27.03 | | | | | | | | | | | | | | v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: any] : % 193.32/27.03 | | | | | | | | | | | | | | ? [v4: any] : % 193.32/27.03 | | | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.03 | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = % 193.32/27.03 | | | | | | | | | | | | | | v2 & c_member(all_676_0, v2, v_L) = v3 & % 193.32/27.03 | | | | | | | | | | | | | | c_member(all_676_0, v1, v_L) = v4 & $i(v2) & ( % 193.32/27.03 | | | | | | | | | | | | | | ~ (v3 = 0) | v4 = 0))) % 193.32/27.03 | | | | | | | | | | | | | | % 193.32/27.03 | | | | | | | | | | | | | | GROUND_INST: instantiating (721) with all_1325_3, all_1325_2, % 193.32/27.03 | | | | | | | | | | | | | | simplifying with (777), (780) gives: % 193.32/27.04 | | | | | | | | | | | | | | (791) ? [v0: $i] : ? [v1: any] : ? [v2: any] : % 193.32/27.04 | | | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.04 | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, % 193.32/27.04 | | | | | | | | | | | | | | all_1325_3) = v0 & c_member(all_676_0, v0, % 193.32/27.04 | | | | | | | | | | | | | | v_L) = v1 & c_member(all_676_0, all_1325_2, % 193.32/27.04 | | | | | | | | | | | | | | v_L) = v2 & $i(v0) & ( ~ (v1 = 0) | v2 = 0)) % 193.32/27.04 | | | | | | | | | | | | | | % 193.32/27.04 | | | | | | | | | | | | | | GROUND_INST: instantiating (44) with v_x, all_1325_3, % 193.32/27.04 | | | | | | | | | | | | | | all_1325_2, simplifying with (16), (777), (780) % 193.32/27.04 | | | | | | | | | | | | | | gives: % 193.32/27.04 | | | | | | | | | | | | | | (792) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_676_0, % 193.32/27.04 | | | | | | | | | | | | | | all_1325_2, v_L) = v0) | ! [v0: $i] : ! [v1: % 193.32/27.04 | | | | | | | | | | | | | | $i] : ( ~ % 193.32/27.04 | | | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.04 | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v0) = % 193.32/27.04 | | | | | | | | | | | | | | v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: any] : % 193.32/27.04 | | | | | | | | | | | | | | ? [v4: any] : % 193.32/27.04 | | | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.04 | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_1325_3, % 193.32/27.04 | | | | | | | | | | | | | | v0) = v2 & c_member(all_676_0, v2, v_L) = v3 % 193.32/27.04 | | | | | | | | | | | | | | & c_member(all_676_0, v1, v_L) = v4 & $i(v2) & % 193.32/27.04 | | | | | | | | | | | | | | ( ~ (v3 = 0) | v4 = 0))) % 193.32/27.04 | | | | | | | | | | | | | | % 193.32/27.04 | | | | | | | | | | | | | | GROUND_INST: instantiating (44) with all_872_9, v_y, all_872_7, % 193.32/27.04 | | | | | | | | | | | | | | simplifying with (169), (782), (786) gives: % 193.32/27.04 | | | | | | | | | | | | | | (793) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_676_0, % 193.32/27.04 | | | | | | | | | | | | | | all_872_7, v_L) = v0) | ! [v0: $i] : ! [v1: % 193.32/27.04 | | | | | | | | | | | | | | $i] : ( ~ % 193.32/27.04 | | | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.04 | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, % 193.32/27.04 | | | | | | | | | | | | | | v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? % 193.32/27.04 | | | | | | | | | | | | | | [v3: any] : ? [v4: any] : % 193.32/27.04 | | | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.04 | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = % 193.32/27.04 | | | | | | | | | | | | | | v2 & c_member(all_676_0, v2, v_L) = v3 & % 193.32/27.04 | | | | | | | | | | | | | | c_member(all_676_0, v1, v_L) = v4 & $i(v2) & ( % 193.32/27.04 | | | | | | | | | | | | | | ~ (v3 = 0) | v4 = 0))) % 193.32/27.04 | | | | | | | | | | | | | | % 193.32/27.04 | | | | | | | | | | | | | | GROUND_INST: instantiating (750) with all_1325_3, all_1325_1, % 193.32/27.04 | | | | | | | | | | | | | | simplifying with (777), (781) gives: % 193.32/27.04 | | | | | | | | | | | | | | (794) ? [v0: $i] : ? [v1: any] : ? [v2: any] : % 193.32/27.04 | | | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.04 | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, % 193.32/27.04 | | | | | | | | | | | | | | all_1325_3) = v0 & c_member(all_676_0, v0, % 193.32/27.04 | | | | | | | | | | | | | | v_L) = v1 & c_member(all_676_0, all_1325_1, % 193.32/27.04 | | | | | | | | | | | | | | v_L) = v2 & $i(v0) & ( ~ (v1 = 0) | v2 = 0)) % 193.32/27.04 | | | | | | | | | | | | | | % 193.32/27.04 | | | | | | | | | | | | | | GROUND_INST: instantiating (681) with all_1325_3, all_1325_1, % 193.32/27.04 | | | | | | | | | | | | | | simplifying with (777), (781) gives: % 193.32/27.04 | | | | | | | | | | | | | | (795) ? [v0: $i] : ? [v1: any] : ? [v2: any] : % 193.32/27.04 | | | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.04 | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, % 193.32/27.04 | | | | | | | | | | | | | | all_1325_3) = v0 & c_member(all_676_0, v0, % 193.32/27.04 | | | | | | | | | | | | | | v_L) = v1 & c_member(all_676_0, all_1325_1, % 193.32/27.04 | | | | | | | | | | | | | | v_L) = v2 & $i(v0) & ( ~ (v1 = 0) | v2 = 0)) % 193.32/27.04 | | | | | | | | | | | | | | % 193.32/27.04 | | | | | | | | | | | | | | DELTA: instantiating (795) with fresh symbols all_1358_0, % 193.32/27.04 | | | | | | | | | | | | | | all_1358_1, all_1358_2 gives: % 193.32/27.04 | | | | | | | | | | | | | | (796) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.04 | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, % 193.32/27.04 | | | | | | | | | | | | | | all_1325_3) = all_1358_2 & c_member(all_676_0, % 193.32/27.04 | | | | | | | | | | | | | | all_1358_2, v_L) = all_1358_1 & % 193.32/27.04 | | | | | | | | | | | | | | c_member(all_676_0, all_1325_1, v_L) = all_1358_0 % 193.32/27.04 | | | | | | | | | | | | | | & $i(all_1358_2) & ( ~ (all_1358_1 = 0) | % 193.32/27.04 | | | | | | | | | | | | | | all_1358_0 = 0) % 193.32/27.04 | | | | | | | | | | | | | | % 193.32/27.04 | | | | | | | | | | | | | | ALPHA: (796) implies: % 193.32/27.04 | | | | | | | | | | | | | | (797) c_member(all_676_0, all_1325_1, v_L) = all_1358_0 % 193.32/27.04 | | | | | | | | | | | | | | (798) c_member(all_676_0, all_1358_2, v_L) = all_1358_1 % 193.32/27.04 | | | | | | | | | | | | | | (799) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.04 | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, % 193.32/27.04 | | | | | | | | | | | | | | all_1325_3) = all_1358_2 % 193.32/27.04 | | | | | | | | | | | | | | (800) ~ (all_1358_1 = 0) | all_1358_0 = 0 % 193.32/27.04 | | | | | | | | | | | | | | % 193.32/27.04 | | | | | | | | | | | | | | DELTA: instantiating (791) with fresh symbols all_1360_0, % 193.32/27.04 | | | | | | | | | | | | | | all_1360_1, all_1360_2 gives: % 193.32/27.04 | | | | | | | | | | | | | | (801) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.04 | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, % 193.32/27.04 | | | | | | | | | | | | | | all_1325_3) = all_1360_2 & c_member(all_676_0, % 193.32/27.04 | | | | | | | | | | | | | | all_1360_2, v_L) = all_1360_1 & % 193.32/27.04 | | | | | | | | | | | | | | c_member(all_676_0, all_1325_2, v_L) = all_1360_0 % 193.32/27.04 | | | | | | | | | | | | | | & $i(all_1360_2) & ( ~ (all_1360_1 = 0) | % 193.32/27.04 | | | | | | | | | | | | | | all_1360_0 = 0) % 193.32/27.04 | | | | | | | | | | | | | | % 193.32/27.04 | | | | | | | | | | | | | | ALPHA: (801) implies: % 193.32/27.04 | | | | | | | | | | | | | | (802) c_member(all_676_0, all_1325_2, v_L) = all_1360_0 % 193.32/27.04 | | | | | | | | | | | | | | % 193.32/27.04 | | | | | | | | | | | | | | DELTA: instantiating (794) with fresh symbols all_1364_0, % 193.32/27.04 | | | | | | | | | | | | | | all_1364_1, all_1364_2 gives: % 193.32/27.04 | | | | | | | | | | | | | | (803) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.04 | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, % 193.32/27.04 | | | | | | | | | | | | | | all_1325_3) = all_1364_2 & c_member(all_676_0, % 193.32/27.04 | | | | | | | | | | | | | | all_1364_2, v_L) = all_1364_1 & % 193.32/27.04 | | | | | | | | | | | | | | c_member(all_676_0, all_1325_1, v_L) = all_1364_0 % 193.32/27.04 | | | | | | | | | | | | | | & $i(all_1364_2) & ( ~ (all_1364_1 = 0) | % 193.32/27.04 | | | | | | | | | | | | | | all_1364_0 = 0) % 193.32/27.04 | | | | | | | | | | | | | | % 193.32/27.04 | | | | | | | | | | | | | | ALPHA: (803) implies: % 193.32/27.04 | | | | | | | | | | | | | | (804) c_member(all_676_0, all_1325_1, v_L) = all_1364_0 % 193.32/27.04 | | | | | | | | | | | | | | % 193.32/27.04 | | | | | | | | | | | | | | REDUCE: (89), (798) imply: % 193.32/27.04 | | | | | | | | | | | | | | (805) c_member(all_622_1, all_1358_2, v_L) = all_1358_1 % 193.32/27.04 | | | | | | | | | | | | | | % 193.32/27.04 | | | | | | | | | | | | | | REDUCE: (89), (804) imply: % 193.32/27.04 | | | | | | | | | | | | | | (806) c_member(all_622_1, all_1325_1, v_L) = all_1364_0 % 193.32/27.04 | | | | | | | | | | | | | | % 193.32/27.04 | | | | | | | | | | | | | | REDUCE: (89), (797) imply: % 193.32/27.04 | | | | | | | | | | | | | | (807) c_member(all_622_1, all_1325_1, v_L) = all_1358_0 % 193.32/27.04 | | | | | | | | | | | | | | % 193.32/27.04 | | | | | | | | | | | | | | REDUCE: (89), (802) imply: % 193.32/27.04 | | | | | | | | | | | | | | (808) c_member(all_622_1, all_1325_2, v_L) = all_1360_0 % 193.32/27.04 | | | | | | | | | | | | | | % 193.32/27.04 | | | | | | | | | | | | | | BETA: splitting (793) gives: % 193.32/27.04 | | | | | | | | | | | | | | % 193.32/27.04 | | | | | | | | | | | | | | Case 1: % 193.32/27.04 | | | | | | | | | | | | | | | % 193.32/27.04 | | | | | | | | | | | | | | | (809) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_676_0, % 193.32/27.04 | | | | | | | | | | | | | | | all_872_7, v_L) = v0) % 193.32/27.04 | | | | | | | | | | | | | | | % 193.32/27.04 | | | | | | | | | | | | | | | DELTA: instantiating (809) with fresh symbol all_1123_0 % 193.32/27.04 | | | | | | | | | | | | | | | gives: % 193.32/27.04 | | | | | | | | | | | | | | | (810) ~ (all_1123_0 = 0) & c_member(all_676_0, % 193.32/27.04 | | | | | | | | | | | | | | | all_872_7, v_L) = all_1123_0 % 193.32/27.04 | | | | | | | | | | | | | | | % 193.32/27.04 | | | | | | | | | | | | | | | REF_CLOSE: (20), (89), (763), (810) are inconsistent by % 193.32/27.04 | | | | | | | | | | | | | | | sub-proof #14. % 193.32/27.04 | | | | | | | | | | | | | | | % 193.32/27.04 | | | | | | | | | | | | | | Case 2: % 193.32/27.04 | | | | | | | | | | | | | | | % 193.32/27.04 | | | | | | | | | | | | | | | (811) ! [v0: $i] : ! [v1: $i] : ( ~ % 193.32/27.04 | | | | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.04 | | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, % 193.32/27.04 | | | | | | | | | | | | | | | v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? % 193.32/27.04 | | | | | | | | | | | | | | | [v3: any] : ? [v4: any] : % 193.32/27.04 | | | | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.04 | | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = % 193.32/27.04 | | | | | | | | | | | | | | | v2 & c_member(all_676_0, v2, v_L) = v3 & % 193.32/27.04 | | | | | | | | | | | | | | | c_member(all_676_0, v1, v_L) = v4 & $i(v2) & ( % 193.32/27.04 | | | | | | | | | | | | | | | ~ (v3 = 0) | v4 = 0))) % 193.32/27.04 | | | | | | | | | | | | | | | % 193.32/27.04 | | | | | | | | | | | | | | | GROUND_INST: instantiating (811) with all_1325_3, all_1325_1, % 193.32/27.04 | | | | | | | | | | | | | | | simplifying with (777), (781) gives: % 193.32/27.04 | | | | | | | | | | | | | | | (812) ? [v0: $i] : ? [v1: any] : ? [v2: any] : % 193.32/27.04 | | | | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.04 | | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, % 193.32/27.04 | | | | | | | | | | | | | | | all_1325_3) = v0 & c_member(all_676_0, v0, % 193.32/27.04 | | | | | | | | | | | | | | | v_L) = v1 & c_member(all_676_0, all_1325_1, % 193.32/27.04 | | | | | | | | | | | | | | | v_L) = v2 & $i(v0) & ( ~ (v1 = 0) | v2 = 0)) % 193.32/27.04 | | | | | | | | | | | | | | | % 193.32/27.04 | | | | | | | | | | | | | | | BETA: splitting (790) gives: % 193.32/27.04 | | | | | | | | | | | | | | | % 193.32/27.04 | | | | | | | | | | | | | | | Case 1: % 193.32/27.04 | | | | | | | | | | | | | | | | % 193.32/27.04 | | | | | | | | | | | | | | | | (813) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_676_0, % 193.32/27.04 | | | | | | | | | | | | | | | | all_872_1, v_L) = v0) % 193.32/27.04 | | | | | | | | | | | | | | | | % 193.32/27.04 | | | | | | | | | | | | | | | | DELTA: instantiating (813) with fresh symbol all_1151_0 % 193.32/27.04 | | | | | | | | | | | | | | | | gives: % 193.32/27.04 | | | | | | | | | | | | | | | | (814) ~ (all_1151_0 = 0) & c_member(all_676_0, % 193.32/27.04 | | | | | | | | | | | | | | | | all_872_1, v_L) = all_1151_0 % 193.32/27.04 | | | | | | | | | | | | | | | | % 193.32/27.04 | | | | | | | | | | | | | | | | REF_CLOSE: (20), (89), (758), (814) are inconsistent by % 193.32/27.04 | | | | | | | | | | | | | | | | sub-proof #17. % 193.32/27.04 | | | | | | | | | | | | | | | | % 193.32/27.04 | | | | | | | | | | | | | | | Case 2: % 193.32/27.04 | | | | | | | | | | | | | | | | % 193.32/27.04 | | | | | | | | | | | | | | | | (815) ! [v0: $i] : ! [v1: $i] : ( ~ % 193.32/27.04 | | | | | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.04 | | | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v0) = % 193.32/27.04 | | | | | | | | | | | | | | | | v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: any] : % 193.32/27.04 | | | | | | | | | | | | | | | | ? [v4: any] : % 193.32/27.04 | | | | | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.04 | | | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = % 193.32/27.04 | | | | | | | | | | | | | | | | v2 & c_member(all_676_0, v2, v_L) = v3 & % 193.32/27.04 | | | | | | | | | | | | | | | | c_member(all_676_0, v1, v_L) = v4 & $i(v2) & ( % 193.32/27.04 | | | | | | | | | | | | | | | | ~ (v3 = 0) | v4 = 0))) % 193.32/27.04 | | | | | | | | | | | | | | | | % 193.32/27.04 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (815) with all_1325_3, all_1325_2, % 193.32/27.04 | | | | | | | | | | | | | | | | simplifying with (777), (780) gives: % 193.32/27.04 | | | | | | | | | | | | | | | | (816) ? [v0: $i] : ? [v1: any] : ? [v2: any] : % 193.32/27.04 | | | | | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.04 | | | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, % 193.32/27.04 | | | | | | | | | | | | | | | | all_1325_3) = v0 & c_member(all_676_0, v0, % 193.32/27.04 | | | | | | | | | | | | | | | | v_L) = v1 & c_member(all_676_0, all_1325_2, % 193.32/27.04 | | | | | | | | | | | | | | | | v_L) = v2 & $i(v0) & ( ~ (v1 = 0) | v2 = 0)) % 193.32/27.04 | | | | | | | | | | | | | | | | % 193.32/27.04 | | | | | | | | | | | | | | | | DELTA: instantiating (812) with fresh symbols all_1424_0, % 193.32/27.04 | | | | | | | | | | | | | | | | all_1424_1, all_1424_2 gives: % 193.32/27.04 | | | | | | | | | | | | | | | | (817) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.04 | | | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, % 193.32/27.04 | | | | | | | | | | | | | | | | all_1325_3) = all_1424_2 & c_member(all_676_0, % 193.32/27.04 | | | | | | | | | | | | | | | | all_1424_2, v_L) = all_1424_1 & % 193.32/27.04 | | | | | | | | | | | | | | | | c_member(all_676_0, all_1325_1, v_L) = all_1424_0 % 193.32/27.04 | | | | | | | | | | | | | | | | & $i(all_1424_2) & ( ~ (all_1424_1 = 0) | % 193.32/27.04 | | | | | | | | | | | | | | | | all_1424_0 = 0) % 193.32/27.04 | | | | | | | | | | | | | | | | % 193.32/27.04 | | | | | | | | | | | | | | | | ALPHA: (817) implies: % 193.32/27.04 | | | | | | | | | | | | | | | | (818) c_member(all_676_0, all_1325_1, v_L) = all_1424_0 % 193.32/27.04 | | | | | | | | | | | | | | | | % 193.32/27.04 | | | | | | | | | | | | | | | | DELTA: instantiating (816) with fresh symbols all_1426_0, % 193.32/27.04 | | | | | | | | | | | | | | | | all_1426_1, all_1426_2 gives: % 193.32/27.04 | | | | | | | | | | | | | | | | (819) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.04 | | | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, % 193.32/27.04 | | | | | | | | | | | | | | | | all_1325_3) = all_1426_2 & c_member(all_676_0, % 193.32/27.04 | | | | | | | | | | | | | | | | all_1426_2, v_L) = all_1426_1 & % 193.32/27.04 | | | | | | | | | | | | | | | | c_member(all_676_0, all_1325_2, v_L) = all_1426_0 % 193.32/27.04 | | | | | | | | | | | | | | | | & $i(all_1426_2) & ( ~ (all_1426_1 = 0) | % 193.32/27.04 | | | | | | | | | | | | | | | | all_1426_0 = 0) % 193.32/27.04 | | | | | | | | | | | | | | | | % 193.32/27.04 | | | | | | | | | | | | | | | | ALPHA: (819) implies: % 193.32/27.04 | | | | | | | | | | | | | | | | (820) c_member(all_676_0, all_1325_2, v_L) = all_1426_0 % 193.32/27.04 | | | | | | | | | | | | | | | | % 193.32/27.04 | | | | | | | | | | | | | | | | REDUCE: (89), (818) imply: % 193.32/27.04 | | | | | | | | | | | | | | | | (821) c_member(all_622_1, all_1325_1, v_L) = all_1424_0 % 193.32/27.04 | | | | | | | | | | | | | | | | % 193.32/27.04 | | | | | | | | | | | | | | | | REDUCE: (89), (820) imply: % 193.32/27.05 | | | | | | | | | | | | | | | | (822) c_member(all_622_1, all_1325_2, v_L) = all_1426_0 % 193.32/27.05 | | | | | | | | | | | | | | | | % 193.32/27.05 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with 0, all_1426_0, v_L, % 193.32/27.05 | | | | | | | | | | | | | | | | all_1325_2, all_622_1, simplifying with (785), % 193.32/27.05 | | | | | | | | | | | | | | | | (822) gives: % 193.32/27.05 | | | | | | | | | | | | | | | | (823) all_1426_0 = 0 % 193.32/27.05 | | | | | | | | | | | | | | | | % 193.32/27.05 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with all_1360_0, all_1426_0, % 193.32/27.05 | | | | | | | | | | | | | | | | v_L, all_1325_2, all_622_1, simplifying with % 193.32/27.05 | | | | | | | | | | | | | | | | (808), (822) gives: % 193.32/27.05 | | | | | | | | | | | | | | | | (824) all_1426_0 = all_1360_0 % 193.32/27.05 | | | | | | | | | | | | | | | | % 193.32/27.05 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with all_1358_0, all_1364_0, % 193.32/27.05 | | | | | | | | | | | | | | | | v_L, all_1325_1, all_622_1, simplifying with % 193.32/27.05 | | | | | | | | | | | | | | | | (806), (807) gives: % 193.32/27.05 | | | | | | | | | | | | | | | | (825) all_1364_0 = all_1358_0 % 193.32/27.05 | | | | | | | | | | | | | | | | % 193.32/27.05 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with all_1325_0, all_1424_0, % 193.32/27.05 | | | | | | | | | | | | | | | | v_L, all_1325_1, all_622_1, simplifying with % 193.32/27.05 | | | | | | | | | | | | | | | | (784), (821) gives: % 193.32/27.05 | | | | | | | | | | | | | | | | (826) all_1424_0 = all_1325_0 % 193.32/27.05 | | | | | | | | | | | | | | | | % 193.32/27.05 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with all_1364_0, all_1424_0, % 193.32/27.05 | | | | | | | | | | | | | | | | v_L, all_1325_1, all_622_1, simplifying with % 193.32/27.05 | | | | | | | | | | | | | | | | (806), (821) gives: % 193.32/27.05 | | | | | | | | | | | | | | | | (827) all_1424_0 = all_1364_0 % 193.32/27.05 | | | | | | | | | | | | | | | | % 193.32/27.05 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (21) with all_1325_2, all_1358_2, % 193.32/27.05 | | | | | | | | | | | | | | | | all_1325_3, v_x, tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.05 | | | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with % 193.32/27.05 | | | | | | | | | | | | | | | | (780), (799) gives: % 193.32/27.05 | | | | | | | | | | | | | | | | (828) all_1358_2 = all_1325_2 % 193.32/27.05 | | | | | | | | | | | | | | | | % 193.32/27.05 | | | | | | | | | | | | | | | | COMBINE_EQS: (823), (824) imply: % 193.32/27.05 | | | | | | | | | | | | | | | | (829) all_1360_0 = 0 % 193.32/27.05 | | | | | | | | | | | | | | | | % 193.32/27.05 | | | | | | | | | | | | | | | | COMBINE_EQS: (826), (827) imply: % 193.32/27.05 | | | | | | | | | | | | | | | | (830) all_1364_0 = all_1325_0 % 193.32/27.05 | | | | | | | | | | | | | | | | % 193.32/27.05 | | | | | | | | | | | | | | | | SIMP: (830) implies: % 193.32/27.05 | | | | | | | | | | | | | | | | (831) all_1364_0 = all_1325_0 % 193.32/27.05 | | | | | | | | | | | | | | | | % 193.32/27.05 | | | | | | | | | | | | | | | | COMBINE_EQS: (825), (831) imply: % 193.32/27.05 | | | | | | | | | | | | | | | | (832) all_1358_0 = all_1325_0 % 193.32/27.05 | | | | | | | | | | | | | | | | % 193.32/27.05 | | | | | | | | | | | | | | | | REDUCE: (805), (828) imply: % 193.32/27.05 | | | | | | | | | | | | | | | | (833) c_member(all_622_1, all_1325_2, v_L) = all_1358_1 % 193.32/27.05 | | | | | | | | | | | | | | | | % 193.32/27.05 | | | | | | | | | | | | | | | | BETA: splitting (800) gives: % 193.32/27.05 | | | | | | | | | | | | | | | | % 193.32/27.05 | | | | | | | | | | | | | | | | Case 1: % 193.32/27.05 | | | | | | | | | | | | | | | | | % 193.32/27.05 | | | | | | | | | | | | | | | | | (834) ~ (all_1358_1 = 0) % 193.32/27.05 | | | | | | | | | | | | | | | | | % 193.32/27.05 | | | | | | | | | | | | | | | | | BETA: splitting (792) gives: % 193.32/27.05 | | | | | | | | | | | | | | | | | % 193.32/27.05 | | | | | | | | | | | | | | | | | Case 1: % 193.32/27.05 | | | | | | | | | | | | | | | | | | % 193.32/27.05 | | | | | | | | | | | | | | | | | | (835) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_676_0, % 193.32/27.05 | | | | | | | | | | | | | | | | | | all_1325_2, v_L) = v0) % 193.32/27.05 | | | | | | | | | | | | | | | | | | % 193.32/27.05 | | | | | | | | | | | | | | | | | | DELTA: instantiating (835) with fresh symbol all_1449_0 % 193.32/27.05 | | | | | | | | | | | | | | | | | | gives: % 193.32/27.05 | | | | | | | | | | | | | | | | | | (836) ~ (all_1449_0 = 0) & c_member(all_676_0, % 193.32/27.05 | | | | | | | | | | | | | | | | | | all_1325_2, v_L) = all_1449_0 % 193.32/27.05 | | | | | | | | | | | | | | | | | | % 193.32/27.05 | | | | | | | | | | | | | | | | | | ALPHA: (836) implies: % 193.32/27.05 | | | | | | | | | | | | | | | | | | (837) c_member(all_676_0, all_1325_2, v_L) = all_1449_0 % 193.32/27.05 | | | | | | | | | | | | | | | | | | % 193.32/27.05 | | | | | | | | | | | | | | | | | | REDUCE: (89), (837) imply: % 193.32/27.05 | | | | | | | | | | | | | | | | | | (838) c_member(all_622_1, all_1325_2, v_L) = all_1449_0 % 193.32/27.05 | | | | | | | | | | | | | | | | | | % 193.32/27.05 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with 0, all_1449_0, v_L, % 193.32/27.05 | | | | | | | | | | | | | | | | | | all_1325_2, all_622_1, simplifying with (785), % 193.32/27.05 | | | | | | | | | | | | | | | | | | (838) gives: % 193.32/27.05 | | | | | | | | | | | | | | | | | | (839) all_1449_0 = 0 % 193.32/27.05 | | | | | | | | | | | | | | | | | | % 193.32/27.05 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with all_1358_1, all_1449_0, % 193.32/27.05 | | | | | | | | | | | | | | | | | | v_L, all_1325_2, all_622_1, simplifying with % 193.32/27.05 | | | | | | | | | | | | | | | | | | (833), (838) gives: % 193.32/27.05 | | | | | | | | | | | | | | | | | | (840) all_1449_0 = all_1358_1 % 193.32/27.05 | | | | | | | | | | | | | | | | | | % 193.32/27.05 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (839), (840) imply: % 193.32/27.05 | | | | | | | | | | | | | | | | | | (841) all_1358_1 = 0 % 193.32/27.05 | | | | | | | | | | | | | | | | | | % 193.32/27.05 | | | | | | | | | | | | | | | | | | REDUCE: (834), (841) imply: % 193.32/27.05 | | | | | | | | | | | | | | | | | | (842) $false % 193.32/27.05 | | | | | | | | | | | | | | | | | | % 193.32/27.05 | | | | | | | | | | | | | | | | | | CLOSE: (842) is inconsistent. % 193.32/27.05 | | | | | | | | | | | | | | | | | | % 193.32/27.05 | | | | | | | | | | | | | | | | | Case 2: % 193.32/27.05 | | | | | | | | | | | | | | | | | | % 193.32/27.05 | | | | | | | | | | | | | | | | | | (843) ! [v0: $i] : ! [v1: $i] : ( ~ % 193.32/27.05 | | | | | | | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.05 | | | | | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v0) = % 193.32/27.05 | | | | | | | | | | | | | | | | | | v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: any] : % 193.32/27.05 | | | | | | | | | | | | | | | | | | ? [v4: any] : % 193.32/27.05 | | | | | | | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.05 | | | | | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_1325_3, % 193.32/27.05 | | | | | | | | | | | | | | | | | | v0) = v2 & c_member(all_676_0, v2, v_L) = v3 % 193.32/27.05 | | | | | | | | | | | | | | | | | | & c_member(all_676_0, v1, v_L) = v4 & $i(v2) & % 193.32/27.05 | | | | | | | | | | | | | | | | | | ( ~ (v3 = 0) | v4 = 0))) % 193.32/27.05 | | | | | | | | | | | | | | | | | | % 193.32/27.05 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (843) with all_1325_3, all_1325_2, % 193.32/27.05 | | | | | | | | | | | | | | | | | | simplifying with (777), (780) gives: % 193.32/27.05 | | | | | | | | | | | | | | | | | | (844) ? [v0: $i] : ? [v1: any] : ? [v2: any] : % 193.32/27.05 | | | | | | | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.05 | | | | | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_1325_3, % 193.32/27.05 | | | | | | | | | | | | | | | | | | all_1325_3) = v0 & c_member(all_676_0, v0, % 193.32/27.05 | | | | | | | | | | | | | | | | | | v_L) = v1 & c_member(all_676_0, all_1325_2, % 193.32/27.05 | | | | | | | | | | | | | | | | | | v_L) = v2 & $i(v0) & ( ~ (v1 = 0) | v2 = 0)) % 193.32/27.05 | | | | | | | | | | | | | | | | | | % 193.32/27.05 | | | | | | | | | | | | | | | | | | DELTA: instantiating (844) with fresh symbols all_1450_0, % 193.32/27.05 | | | | | | | | | | | | | | | | | | all_1450_1, all_1450_2 gives: % 193.32/27.05 | | | | | | | | | | | | | | | | | | (845) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.05 | | | | | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_1325_3, % 193.32/27.05 | | | | | | | | | | | | | | | | | | all_1325_3) = all_1450_2 & c_member(all_676_0, % 193.32/27.05 | | | | | | | | | | | | | | | | | | all_1450_2, v_L) = all_1450_1 & % 193.32/27.05 | | | | | | | | | | | | | | | | | | c_member(all_676_0, all_1325_2, v_L) = all_1450_0 % 193.32/27.05 | | | | | | | | | | | | | | | | | | & $i(all_1450_2) & ( ~ (all_1450_1 = 0) | % 193.32/27.05 | | | | | | | | | | | | | | | | | | all_1450_0 = 0) % 193.32/27.05 | | | | | | | | | | | | | | | | | | % 193.32/27.05 | | | | | | | | | | | | | | | | | | ALPHA: (845) implies: % 193.32/27.05 | | | | | | | | | | | | | | | | | | (846) c_member(all_676_0, all_1325_2, v_L) = all_1450_0 % 193.32/27.05 | | | | | | | | | | | | | | | | | | % 193.32/27.05 | | | | | | | | | | | | | | | | | | REDUCE: (89), (846) imply: % 193.32/27.05 | | | | | | | | | | | | | | | | | | (847) c_member(all_622_1, all_1325_2, v_L) = all_1450_0 % 193.32/27.05 | | | | | | | | | | | | | | | | | | % 193.32/27.05 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with 0, all_1450_0, v_L, % 193.32/27.05 | | | | | | | | | | | | | | | | | | all_1325_2, all_622_1, simplifying with (785), % 193.32/27.05 | | | | | | | | | | | | | | | | | | (847) gives: % 193.32/27.05 | | | | | | | | | | | | | | | | | | (848) all_1450_0 = 0 % 193.32/27.05 | | | | | | | | | | | | | | | | | | % 193.32/27.05 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with all_1358_1, all_1450_0, % 193.32/27.05 | | | | | | | | | | | | | | | | | | v_L, all_1325_2, all_622_1, simplifying with % 193.32/27.05 | | | | | | | | | | | | | | | | | | (833), (847) gives: % 193.32/27.05 | | | | | | | | | | | | | | | | | | (849) all_1450_0 = all_1358_1 % 193.32/27.05 | | | | | | | | | | | | | | | | | | % 193.32/27.05 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (848), (849) imply: % 193.32/27.05 | | | | | | | | | | | | | | | | | | (850) all_1358_1 = 0 % 193.32/27.05 | | | | | | | | | | | | | | | | | | % 193.32/27.05 | | | | | | | | | | | | | | | | | | REDUCE: (834), (850) imply: % 193.32/27.05 | | | | | | | | | | | | | | | | | | (851) $false % 193.32/27.05 | | | | | | | | | | | | | | | | | | % 193.32/27.05 | | | | | | | | | | | | | | | | | | CLOSE: (851) is inconsistent. % 193.32/27.05 | | | | | | | | | | | | | | | | | | % 193.32/27.05 | | | | | | | | | | | | | | | | | End of split % 193.32/27.05 | | | | | | | | | | | | | | | | | % 193.32/27.05 | | | | | | | | | | | | | | | | Case 2: % 193.32/27.05 | | | | | | | | | | | | | | | | | % 193.32/27.05 | | | | | | | | | | | | | | | | | (852) all_1358_0 = 0 % 193.32/27.05 | | | | | | | | | | | | | | | | | % 193.32/27.05 | | | | | | | | | | | | | | | | | COMBINE_EQS: (832), (852) imply: % 193.32/27.05 | | | | | | | | | | | | | | | | | (853) all_1325_0 = 0 % 193.32/27.05 | | | | | | | | | | | | | | | | | % 193.32/27.05 | | | | | | | | | | | | | | | | | REDUCE: (776), (853) imply: % 193.32/27.05 | | | | | | | | | | | | | | | | | (854) $false % 193.32/27.05 | | | | | | | | | | | | | | | | | % 193.32/27.05 | | | | | | | | | | | | | | | | | CLOSE: (854) is inconsistent. % 193.32/27.05 | | | | | | | | | | | | | | | | | % 193.32/27.05 | | | | | | | | | | | | | | | | End of split % 193.32/27.05 | | | | | | | | | | | | | | | | % 193.32/27.05 | | | | | | | | | | | | | | | End of split % 193.32/27.05 | | | | | | | | | | | | | | | % 193.32/27.05 | | | | | | | | | | | | | | End of split % 193.32/27.05 | | | | | | | | | | | | | | % 193.32/27.05 | | | | | | | | | | | | | End of split % 193.32/27.05 | | | | | | | | | | | | | % 193.32/27.05 | | | | | | | | | | | | Case 2: % 193.32/27.05 | | | | | | | | | | | | | % 193.32/27.05 | | | | | | | | | | | | | (855) all_872_6 = 0 & ~ (all_872_8 = v_y) & ? [v0: $i] % 193.32/27.05 | | | | | | | | | | | | | : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ? % 193.32/27.05 | | | | | | | | | | | | | [v4: any] : % 193.32/27.05 | | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.05 | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, % 193.32/27.05 | | | | | | | | | | | | | v0) = v1 & % 193.32/27.05 | | | | | | | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.05 | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, % 193.32/27.05 | | | | | | | | | | | | | v0) = v3 & c_member(all_685_0, v3, v_L) = v4 & % 193.32/27.05 | | | | | | | | | | | | | c_member(all_685_0, v1, v_L) = v2 & $i(v3) & % 193.32/27.05 | | | | | | | | | | | | | $i(v1) & $i(v0) & ((v2 = 0 & ~ (v4 = 0) & ~ % 193.32/27.05 | | | | | | | | | | | | | (v0 = v_y)) | (v0 = v_y & all_872_2 = 0 & ~ % 193.32/27.05 | | | | | | | | | | | | | (all_872_4 = 0) & ~ (all_872_9 = v_x)) | % 193.32/27.05 | | | | | | | | | | | | | (v0 = v_y & all_872_8 = v_x & ~ (all_872_4 = % 193.32/27.05 | | | | | | | | | | | | | 0) & ~ (all_872_9 = v_x)))) % 193.32/27.05 | | | | | | | | | | | | | % 193.32/27.05 | | | | | | | | | | | | | ALPHA: (855) implies: % 193.32/27.05 | | | | | | | | | | | | | (856) ? [v0: $i] : ? [v1: $i] : ? [v2: any] : ? [v3: % 193.32/27.05 | | | | | | | | | | | | | $i] : ? [v4: any] : % 193.32/27.05 | | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.05 | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, % 193.32/27.05 | | | | | | | | | | | | | v0) = v1 & % 193.32/27.05 | | | | | | | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.05 | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, % 193.32/27.05 | | | | | | | | | | | | | v0) = v3 & c_member(all_685_0, v3, v_L) = v4 & % 193.32/27.05 | | | | | | | | | | | | | c_member(all_685_0, v1, v_L) = v2 & $i(v3) & % 193.32/27.05 | | | | | | | | | | | | | $i(v1) & $i(v0) & ((v2 = 0 & ~ (v4 = 0) & ~ % 193.32/27.05 | | | | | | | | | | | | | (v0 = v_y)) | (v0 = v_y & all_872_2 = 0 & ~ % 193.32/27.05 | | | | | | | | | | | | | (all_872_4 = 0) & ~ (all_872_9 = v_x)) | % 193.32/27.05 | | | | | | | | | | | | | (v0 = v_y & all_872_8 = v_x & ~ (all_872_4 = % 193.32/27.05 | | | | | | | | | | | | | 0) & ~ (all_872_9 = v_x)))) % 193.32/27.05 | | | | | | | | | | | | | % 193.32/27.05 | | | | | | | | | | | | | DELTA: instantiating (856) with fresh symbols all_1325_0, % 193.32/27.05 | | | | | | | | | | | | | all_1325_1, all_1325_2, all_1325_3, all_1325_4 % 193.32/27.05 | | | | | | | | | | | | | gives: % 193.32/27.05 | | | | | | | | | | | | | (857) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.05 | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, % 193.32/27.05 | | | | | | | | | | | | | all_1325_4) = all_1325_3 & % 193.32/27.05 | | | | | | | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.05 | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, % 193.32/27.05 | | | | | | | | | | | | | all_1325_4) = all_1325_1 & c_member(all_685_0, % 193.32/27.05 | | | | | | | | | | | | | all_1325_1, v_L) = all_1325_0 & % 193.32/27.05 | | | | | | | | | | | | | c_member(all_685_0, all_1325_3, v_L) = all_1325_2 % 193.32/27.05 | | | | | | | | | | | | | & $i(all_1325_1) & $i(all_1325_3) & $i(all_1325_4) % 193.32/27.05 | | | | | | | | | | | | | & ((all_1325_2 = 0 & ~ (all_1325_0 = 0) & ~ % 193.32/27.05 | | | | | | | | | | | | | (all_1325_4 = v_y)) | (all_1325_4 = v_y & % 193.32/27.05 | | | | | | | | | | | | | all_872_2 = 0 & ~ (all_872_4 = 0) & ~ % 193.32/27.05 | | | | | | | | | | | | | (all_872_9 = v_x)) | (all_1325_4 = v_y & % 193.32/27.05 | | | | | | | | | | | | | all_872_8 = v_x & ~ (all_872_4 = 0) & ~ % 193.32/27.05 | | | | | | | | | | | | | (all_872_9 = v_x))) % 193.32/27.05 | | | | | | | | | | | | | % 193.32/27.05 | | | | | | | | | | | | | ALPHA: (857) implies: % 193.32/27.05 | | | | | | | | | | | | | (858) $i(all_1325_4) % 193.32/27.05 | | | | | | | | | | | | | (859) $i(all_1325_1) % 193.32/27.05 | | | | | | | | | | | | | (860) c_member(all_685_0, all_1325_3, v_L) = all_1325_2 % 193.32/27.05 | | | | | | | | | | | | | (861) c_member(all_685_0, all_1325_1, v_L) = all_1325_0 % 193.32/27.05 | | | | | | | | | | | | | (862) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.05 | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, % 193.32/27.05 | | | | | | | | | | | | | all_1325_4) = all_1325_1 % 193.32/27.05 | | | | | | | | | | | | | (863) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.05 | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, % 193.32/27.05 | | | | | | | | | | | | | all_1325_4) = all_1325_3 % 193.32/27.05 | | | | | | | | | | | | | (864) (all_1325_2 = 0 & ~ (all_1325_0 = 0) & ~ % 193.32/27.05 | | | | | | | | | | | | | (all_1325_4 = v_y)) | (all_1325_4 = v_y & % 193.32/27.05 | | | | | | | | | | | | | all_872_2 = 0 & ~ (all_872_4 = 0) & ~ % 193.32/27.05 | | | | | | | | | | | | | (all_872_9 = v_x)) | (all_1325_4 = v_y & % 193.32/27.05 | | | | | | | | | | | | | all_872_8 = v_x & ~ (all_872_4 = 0) & ~ % 193.32/27.05 | | | | | | | | | | | | | (all_872_9 = v_x)) % 193.32/27.05 | | | | | | | | | | | | | % 193.32/27.05 | | | | | | | | | | | | | REDUCE: (90), (861) imply: % 193.32/27.05 | | | | | | | | | | | | | (865) c_member(all_622_1, all_1325_1, v_L) = all_1325_0 % 193.32/27.05 | | | | | | | | | | | | | % 193.32/27.05 | | | | | | | | | | | | | REDUCE: (90), (860) imply: % 193.32/27.05 | | | | | | | | | | | | | (866) c_member(all_622_1, all_1325_3, v_L) = all_1325_2 % 193.32/27.05 | | | | | | | | | | | | | % 193.32/27.05 | | | | | | | | | | | | | BETA: splitting (864) gives: % 193.32/27.05 | | | | | | | | | | | | | % 193.32/27.05 | | | | | | | | | | | | | Case 1: % 193.32/27.05 | | | | | | | | | | | | | | % 193.32/27.05 | | | | | | | | | | | | | | (867) all_1325_2 = 0 & ~ (all_1325_0 = 0) & ~ % 193.32/27.05 | | | | | | | | | | | | | | (all_1325_4 = v_y) % 193.32/27.05 | | | | | | | | | | | | | | % 193.32/27.05 | | | | | | | | | | | | | | ALPHA: (867) implies: % 193.32/27.05 | | | | | | | | | | | | | | (868) all_1325_2 = 0 % 193.32/27.05 | | | | | | | | | | | | | | (869) ~ (all_1325_0 = 0) % 193.32/27.05 | | | | | | | | | | | | | | % 193.32/27.05 | | | | | | | | | | | | | | REDUCE: (866), (868) imply: % 193.32/27.06 | | | | | | | | | | | | | | (870) c_member(all_622_1, all_1325_3, v_L) = 0 % 193.32/27.06 | | | | | | | | | | | | | | % 193.32/27.06 | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with v_L, all_1325_1, all_622_1, % 193.32/27.06 | | | | | | | | | | | | | | all_1325_0, simplifying with (17), (91), (859), % 193.32/27.06 | | | | | | | | | | | | | | (865) gives: % 193.32/27.06 | | | | | | | | | | | | | | (871) all_1325_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ % 193.32/27.06 | | | | | | | | | | | | | | (v1 = 0) & hBOOL(v0) = v1 & hAPP(v_L, % 193.32/27.06 | | | | | | | | | | | | | | all_1325_1) = v0 & $i(v0)) % 193.32/27.06 | | | | | | | | | | | | | | % 193.32/27.06 | | | | | | | | | | | | | | GROUND_INST: instantiating (750) with all_1325_4, all_1325_1, % 193.32/27.06 | | | | | | | | | | | | | | simplifying with (858), (862) gives: % 193.32/27.06 | | | | | | | | | | | | | | (872) ? [v0: $i] : ? [v1: any] : ? [v2: any] : % 193.32/27.06 | | | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.06 | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, % 193.32/27.06 | | | | | | | | | | | | | | all_1325_4) = v0 & c_member(all_676_0, v0, % 193.32/27.06 | | | | | | | | | | | | | | v_L) = v1 & c_member(all_676_0, all_1325_1, % 193.32/27.06 | | | | | | | | | | | | | | v_L) = v2 & $i(v0) & ( ~ (v1 = 0) | v2 = 0)) % 193.32/27.06 | | | | | | | | | | | | | | % 193.32/27.06 | | | | | | | | | | | | | | GROUND_INST: instantiating (44) with all_872_8, all_1325_4, % 193.32/27.06 | | | | | | | | | | | | | | all_1325_3, simplifying with (170), (858), (863) % 193.32/27.06 | | | | | | | | | | | | | | gives: % 193.32/27.06 | | | | | | | | | | | | | | (873) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_676_0, % 193.32/27.06 | | | | | | | | | | | | | | all_1325_3, v_L) = v0) | ! [v0: $i] : ! [v1: % 193.32/27.06 | | | | | | | | | | | | | | $i] : ( ~ % 193.32/27.06 | | | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.06 | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, % 193.32/27.06 | | | | | | | | | | | | | | v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? % 193.32/27.06 | | | | | | | | | | | | | | [v3: any] : ? [v4: any] : % 193.32/27.06 | | | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.06 | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_1325_4, % 193.32/27.06 | | | | | | | | | | | | | | v0) = v2 & c_member(all_676_0, v2, v_L) = v3 % 193.32/27.06 | | | | | | | | | | | | | | & c_member(all_676_0, v1, v_L) = v4 & $i(v2) & % 193.32/27.06 | | | | | | | | | | | | | | ( ~ (v3 = 0) | v4 = 0))) % 193.32/27.06 | | | | | | | | | | | | | | % 193.32/27.06 | | | | | | | | | | | | | | DELTA: instantiating (872) with fresh symbols all_1366_0, % 193.32/27.06 | | | | | | | | | | | | | | all_1366_1, all_1366_2 gives: % 193.32/27.06 | | | | | | | | | | | | | | (874) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.06 | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, % 193.32/27.06 | | | | | | | | | | | | | | all_1325_4) = all_1366_2 & c_member(all_676_0, % 193.32/27.06 | | | | | | | | | | | | | | all_1366_2, v_L) = all_1366_1 & % 193.32/27.06 | | | | | | | | | | | | | | c_member(all_676_0, all_1325_1, v_L) = all_1366_0 % 193.32/27.06 | | | | | | | | | | | | | | & $i(all_1366_2) & ( ~ (all_1366_1 = 0) | % 193.32/27.06 | | | | | | | | | | | | | | all_1366_0 = 0) % 193.32/27.06 | | | | | | | | | | | | | | % 193.32/27.06 | | | | | | | | | | | | | | ALPHA: (874) implies: % 193.32/27.06 | | | | | | | | | | | | | | (875) c_member(all_676_0, all_1325_1, v_L) = all_1366_0 % 193.32/27.06 | | | | | | | | | | | | | | (876) c_member(all_676_0, all_1366_2, v_L) = all_1366_1 % 193.32/27.06 | | | | | | | | | | | | | | (877) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.06 | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, % 193.32/27.06 | | | | | | | | | | | | | | all_1325_4) = all_1366_2 % 193.32/27.06 | | | | | | | | | | | | | | (878) ~ (all_1366_1 = 0) | all_1366_0 = 0 % 193.32/27.06 | | | | | | | | | | | | | | % 193.32/27.06 | | | | | | | | | | | | | | REDUCE: (89), (876) imply: % 193.32/27.06 | | | | | | | | | | | | | | (879) c_member(all_622_1, all_1366_2, v_L) = all_1366_1 % 193.32/27.06 | | | | | | | | | | | | | | % 193.32/27.06 | | | | | | | | | | | | | | REDUCE: (89), (875) imply: % 193.32/27.06 | | | | | | | | | | | | | | (880) c_member(all_622_1, all_1325_1, v_L) = all_1366_0 % 193.32/27.06 | | | | | | | | | | | | | | % 193.32/27.06 | | | | | | | | | | | | | | BETA: splitting (873) gives: % 193.32/27.06 | | | | | | | | | | | | | | % 193.32/27.06 | | | | | | | | | | | | | | Case 1: % 193.32/27.06 | | | | | | | | | | | | | | | % 193.32/27.06 | | | | | | | | | | | | | | | (881) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_676_0, % 193.32/27.06 | | | | | | | | | | | | | | | all_1325_3, v_L) = v0) % 193.32/27.06 | | | | | | | | | | | | | | | % 193.32/27.06 | | | | | | | | | | | | | | | DELTA: instantiating (881) with fresh symbol all_1392_0 % 193.32/27.06 | | | | | | | | | | | | | | | gives: % 193.32/27.06 | | | | | | | | | | | | | | | (882) ~ (all_1392_0 = 0) & c_member(all_676_0, % 193.32/27.06 | | | | | | | | | | | | | | | all_1325_3, v_L) = all_1392_0 % 193.32/27.06 | | | | | | | | | | | | | | | % 193.32/27.06 | | | | | | | | | | | | | | | ALPHA: (882) implies: % 193.32/27.06 | | | | | | | | | | | | | | | (883) ~ (all_1392_0 = 0) % 193.32/27.06 | | | | | | | | | | | | | | | (884) c_member(all_676_0, all_1325_3, v_L) = all_1392_0 % 193.32/27.06 | | | | | | | | | | | | | | | % 193.32/27.06 | | | | | | | | | | | | | | | REDUCE: (89), (884) imply: % 193.32/27.06 | | | | | | | | | | | | | | | (885) c_member(all_622_1, all_1325_3, v_L) = all_1392_0 % 193.32/27.06 | | | | | | | | | | | | | | | % 193.32/27.06 | | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with 0, all_1392_0, v_L, % 193.32/27.06 | | | | | | | | | | | | | | | all_1325_3, all_622_1, simplifying with (870), % 193.32/27.06 | | | | | | | | | | | | | | | (885) gives: % 193.32/27.06 | | | | | | | | | | | | | | | (886) all_1392_0 = 0 % 193.32/27.06 | | | | | | | | | | | | | | | % 193.32/27.06 | | | | | | | | | | | | | | | REDUCE: (883), (886) imply: % 193.32/27.06 | | | | | | | | | | | | | | | (887) $false % 193.32/27.06 | | | | | | | | | | | | | | | % 193.32/27.06 | | | | | | | | | | | | | | | CLOSE: (887) is inconsistent. % 193.32/27.06 | | | | | | | | | | | | | | | % 193.32/27.06 | | | | | | | | | | | | | | Case 2: % 193.32/27.06 | | | | | | | | | | | | | | | % 193.32/27.06 | | | | | | | | | | | | | | | (888) ! [v0: $i] : ! [v1: $i] : ( ~ % 193.32/27.06 | | | | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.06 | | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, % 193.32/27.06 | | | | | | | | | | | | | | | v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? % 193.32/27.06 | | | | | | | | | | | | | | | [v3: any] : ? [v4: any] : % 193.32/27.06 | | | | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.06 | | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_1325_4, % 193.32/27.06 | | | | | | | | | | | | | | | v0) = v2 & c_member(all_676_0, v2, v_L) = v3 % 193.32/27.06 | | | | | | | | | | | | | | | & c_member(all_676_0, v1, v_L) = v4 & $i(v2) & % 193.32/27.06 | | | | | | | | | | | | | | | ( ~ (v3 = 0) | v4 = 0))) % 193.32/27.06 | | | | | | | | | | | | | | | % 193.32/27.06 | | | | | | | | | | | | | | | GROUND_INST: instantiating (888) with all_1325_4, all_1325_3, % 193.32/27.06 | | | | | | | | | | | | | | | simplifying with (858), (863) gives: % 193.32/27.06 | | | | | | | | | | | | | | | (889) ? [v0: $i] : ? [v1: any] : ? [v2: any] : % 193.32/27.06 | | | | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.06 | | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_1325_4, % 193.32/27.06 | | | | | | | | | | | | | | | all_1325_4) = v0 & c_member(all_676_0, v0, % 193.32/27.06 | | | | | | | | | | | | | | | v_L) = v1 & c_member(all_676_0, all_1325_3, % 193.32/27.06 | | | | | | | | | | | | | | | v_L) = v2 & $i(v0) & ( ~ (v1 = 0) | v2 = 0)) % 193.32/27.06 | | | | | | | | | | | | | | | % 193.32/27.06 | | | | | | | | | | | | | | | DELTA: instantiating (889) with fresh symbols all_1395_0, % 193.32/27.06 | | | | | | | | | | | | | | | all_1395_1, all_1395_2 gives: % 193.32/27.06 | | | | | | | | | | | | | | | (890) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.06 | | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_1325_4, % 193.32/27.06 | | | | | | | | | | | | | | | all_1325_4) = all_1395_2 & c_member(all_676_0, % 193.32/27.06 | | | | | | | | | | | | | | | all_1395_2, v_L) = all_1395_1 & % 193.32/27.06 | | | | | | | | | | | | | | | c_member(all_676_0, all_1325_3, v_L) = all_1395_0 % 193.32/27.06 | | | | | | | | | | | | | | | & $i(all_1395_2) & ( ~ (all_1395_1 = 0) | % 193.32/27.06 | | | | | | | | | | | | | | | all_1395_0 = 0) % 193.32/27.06 | | | | | | | | | | | | | | | % 193.32/27.06 | | | | | | | | | | | | | | | ALPHA: (890) implies: % 193.32/27.06 | | | | | | | | | | | | | | | (891) c_member(all_676_0, all_1325_3, v_L) = all_1395_0 % 193.32/27.06 | | | | | | | | | | | | | | | % 193.32/27.06 | | | | | | | | | | | | | | | REDUCE: (89), (891) imply: % 193.32/27.06 | | | | | | | | | | | | | | | (892) c_member(all_622_1, all_1325_3, v_L) = all_1395_0 % 193.32/27.06 | | | | | | | | | | | | | | | % 193.32/27.06 | | | | | | | | | | | | | | | BETA: splitting (871) gives: % 193.32/27.06 | | | | | | | | | | | | | | | % 193.32/27.06 | | | | | | | | | | | | | | | Case 1: % 193.32/27.06 | | | | | | | | | | | | | | | | % 193.32/27.06 | | | | | | | | | | | | | | | | (893) all_1325_0 = 0 % 193.32/27.06 | | | | | | | | | | | | | | | | % 193.32/27.06 | | | | | | | | | | | | | | | | REDUCE: (869), (893) imply: % 193.32/27.06 | | | | | | | | | | | | | | | | (894) $false % 193.32/27.06 | | | | | | | | | | | | | | | | % 193.32/27.06 | | | | | | | | | | | | | | | | CLOSE: (894) is inconsistent. % 193.32/27.06 | | | | | | | | | | | | | | | | % 193.32/27.06 | | | | | | | | | | | | | | | Case 2: % 193.32/27.06 | | | | | | | | | | | | | | | | % 193.32/27.06 | | | | | | | | | | | | | | | | % 193.32/27.06 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with 0, all_1395_0, v_L, % 193.32/27.06 | | | | | | | | | | | | | | | | all_1325_3, all_622_1, simplifying with (870), % 193.32/27.06 | | | | | | | | | | | | | | | | (892) gives: % 193.32/27.06 | | | | | | | | | | | | | | | | (895) all_1395_0 = 0 % 193.32/27.06 | | | | | | | | | | | | | | | | % 193.32/27.06 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with all_1325_0, all_1366_0, % 193.32/27.06 | | | | | | | | | | | | | | | | v_L, all_1325_1, all_622_1, simplifying with % 193.32/27.06 | | | | | | | | | | | | | | | | (865), (880) gives: % 193.32/27.06 | | | | | | | | | | | | | | | | (896) all_1366_0 = all_1325_0 % 193.32/27.06 | | | | | | | | | | | | | | | | % 193.32/27.06 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (21) with all_1325_3, all_1366_2, % 193.32/27.06 | | | | | | | | | | | | | | | | all_1325_4, all_872_8, % 193.32/27.06 | | | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.06 | | | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with % 193.32/27.06 | | | | | | | | | | | | | | | | (863), (877) gives: % 193.32/27.06 | | | | | | | | | | | | | | | | (897) all_1366_2 = all_1325_3 % 193.32/27.06 | | | | | | | | | | | | | | | | % 193.32/27.06 | | | | | | | | | | | | | | | | REDUCE: (879), (897) imply: % 193.32/27.06 | | | | | | | | | | | | | | | | (898) c_member(all_622_1, all_1325_3, v_L) = all_1366_1 % 193.32/27.06 | | | | | | | | | | | | | | | | % 193.32/27.06 | | | | | | | | | | | | | | | | BETA: splitting (878) gives: % 193.32/27.06 | | | | | | | | | | | | | | | | % 193.32/27.06 | | | | | | | | | | | | | | | | Case 1: % 193.32/27.06 | | | | | | | | | | | | | | | | | % 193.32/27.06 | | | | | | | | | | | | | | | | | (899) ~ (all_1366_1 = 0) % 193.32/27.06 | | | | | | | | | | | | | | | | | % 193.32/27.06 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with 0, all_1366_1, v_L, % 193.32/27.06 | | | | | | | | | | | | | | | | | all_1325_3, all_622_1, simplifying with (870), % 193.32/27.06 | | | | | | | | | | | | | | | | | (898) gives: % 193.32/27.06 | | | | | | | | | | | | | | | | | (900) all_1366_1 = 0 % 193.32/27.06 | | | | | | | | | | | | | | | | | % 193.32/27.06 | | | | | | | | | | | | | | | | | REDUCE: (899), (900) imply: % 193.32/27.06 | | | | | | | | | | | | | | | | | (901) $false % 193.32/27.06 | | | | | | | | | | | | | | | | | % 193.32/27.06 | | | | | | | | | | | | | | | | | CLOSE: (901) is inconsistent. % 193.32/27.06 | | | | | | | | | | | | | | | | | % 193.32/27.06 | | | | | | | | | | | | | | | | Case 2: % 193.32/27.06 | | | | | | | | | | | | | | | | | % 193.32/27.06 | | | | | | | | | | | | | | | | | (902) all_1366_0 = 0 % 193.32/27.06 | | | | | | | | | | | | | | | | | % 193.32/27.06 | | | | | | | | | | | | | | | | | COMBINE_EQS: (896), (902) imply: % 193.32/27.06 | | | | | | | | | | | | | | | | | (903) all_1325_0 = 0 % 193.32/27.06 | | | | | | | | | | | | | | | | | % 193.32/27.06 | | | | | | | | | | | | | | | | | REDUCE: (869), (903) imply: % 193.32/27.06 | | | | | | | | | | | | | | | | | (904) $false % 193.32/27.06 | | | | | | | | | | | | | | | | | % 193.32/27.06 | | | | | | | | | | | | | | | | | CLOSE: (904) is inconsistent. % 193.32/27.06 | | | | | | | | | | | | | | | | | % 193.32/27.06 | | | | | | | | | | | | | | | | End of split % 193.32/27.06 | | | | | | | | | | | | | | | | % 193.32/27.06 | | | | | | | | | | | | | | | End of split % 193.32/27.06 | | | | | | | | | | | | | | | % 193.32/27.06 | | | | | | | | | | | | | | End of split % 193.32/27.06 | | | | | | | | | | | | | | % 193.32/27.06 | | | | | | | | | | | | | Case 2: % 193.32/27.06 | | | | | | | | | | | | | | % 193.32/27.06 | | | | | | | | | | | | | | (905) (all_1325_4 = v_y & all_872_2 = 0 & ~ (all_872_4 % 193.32/27.06 | | | | | | | | | | | | | | = 0) & ~ (all_872_9 = v_x)) | (all_1325_4 = % 193.32/27.06 | | | | | | | | | | | | | | v_y & all_872_8 = v_x & ~ (all_872_4 = 0) & ~ % 193.32/27.06 | | | | | | | | | | | | | | (all_872_9 = v_x)) % 193.32/27.06 | | | | | | | | | | | | | | % 193.32/27.06 | | | | | | | | | | | | | | BETA: splitting (905) gives: % 193.32/27.06 | | | | | | | | | | | | | | % 193.32/27.06 | | | | | | | | | | | | | | Case 1: % 193.32/27.06 | | | | | | | | | | | | | | | % 193.32/27.06 | | | | | | | | | | | | | | | (906) all_1325_4 = v_y & all_872_2 = 0 & ~ (all_872_4 = % 193.32/27.06 | | | | | | | | | | | | | | | 0) & ~ (all_872_9 = v_x) % 193.32/27.06 | | | | | | | | | | | | | | | % 193.32/27.06 | | | | | | | | | | | | | | | ALPHA: (906) implies: % 193.32/27.06 | | | | | | | | | | | | | | | (907) ~ (all_872_4 = 0) % 193.32/27.06 | | | | | | | | | | | | | | | % 193.32/27.06 | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (17), (20), (21), (23), (44), (45), % 193.32/27.06 | | | | | | | | | | | | | | | (89), (90), (169), (170), (180), (181), (182), % 193.32/27.06 | | | | | | | | | | | | | | | (184), (185), (186), (187), (191), (192), (193), % 193.32/27.06 | | | | | | | | | | | | | | | (196), (197), (198), (664), (667), (672), (673), % 193.32/27.06 | | | | | | | | | | | | | | | (674), (676), (762), (856), (907), % 193.32/27.06 | | | | | | | | | | | | | | | (fact_antisymD), (fact_wf__not__sym) are % 193.32/27.06 | | | | | | | | | | | | | | | inconsistent by sub-proof #3. % 193.32/27.06 | | | | | | | | | | | | | | | % 193.32/27.06 | | | | | | | | | | | | | | Case 2: % 193.32/27.06 | | | | | | | | | | | | | | | % 193.32/27.06 | | | | | | | | | | | | | | | (908) all_1325_4 = v_y & all_872_8 = v_x & ~ (all_872_4 % 193.32/27.06 | | | | | | | | | | | | | | | = 0) & ~ (all_872_9 = v_x) % 193.32/27.06 | | | | | | | | | | | | | | | % 193.32/27.06 | | | | | | | | | | | | | | | ALPHA: (908) implies: % 193.32/27.06 | | | | | | | | | | | | | | | (909) ~ (all_872_4 = 0) % 193.32/27.06 | | | | | | | | | | | | | | | % 193.32/27.06 | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (17), (20), (21), (23), (44), (45), % 193.32/27.06 | | | | | | | | | | | | | | | (89), (90), (169), (170), (180), (181), (182), % 193.32/27.06 | | | | | | | | | | | | | | | (184), (185), (186), (187), (191), (192), (193), % 193.32/27.06 | | | | | | | | | | | | | | | (196), (197), (198), (664), (667), (672), (673), % 193.32/27.06 | | | | | | | | | | | | | | | (674), (676), (762), (856), (909), % 193.32/27.06 | | | | | | | | | | | | | | | (fact_antisymD), (fact_wf__not__sym) are % 193.32/27.06 | | | | | | | | | | | | | | | inconsistent by sub-proof #3. % 193.32/27.06 | | | | | | | | | | | | | | | % 193.32/27.06 | | | | | | | | | | | | | | End of split % 193.32/27.06 | | | | | | | | | | | | | | % 193.32/27.06 | | | | | | | | | | | | | End of split % 193.32/27.06 | | | | | | | | | | | | | % 193.32/27.06 | | | | | | | | | | | | End of split % 193.32/27.06 | | | | | | | | | | | | % 193.32/27.06 | | | | | | | | | | | End of split % 193.32/27.06 | | | | | | | | | | | % 193.32/27.06 | | | | | | | | | | End of split % 193.32/27.06 | | | | | | | | | | % 193.32/27.06 | | | | | | | | | Case 2: % 193.32/27.06 | | | | | | | | | | % 193.32/27.06 | | | | | | | | | | (910) ~ (all_872_0 = 0) % 193.32/27.06 | | | | | | | | | | % 193.32/27.07 | | | | | | | | | | REF_CLOSE: (3), (13), (17), (20), (21), (44), (89), (90), % 193.32/27.07 | | | | | | | | | | (91), (170), (180), (181), (182), (184), (185), % 193.32/27.07 | | | | | | | | | | (186), (187), (192), (198), (657), (664), (681), % 193.32/27.07 | | | | | | | | | | (750), (910) are inconsistent by sub-proof #2. % 193.32/27.07 | | | | | | | | | | % 193.32/27.07 | | | | | | | | | End of split % 193.32/27.07 | | | | | | | | | % 193.32/27.07 | | | | | | | | End of split % 193.32/27.07 | | | | | | | | % 193.32/27.07 | | | | | | | End of split % 193.32/27.07 | | | | | | | % 193.32/27.07 | | | | | | End of split % 193.32/27.07 | | | | | | % 193.32/27.07 | | | | | Case 2: % 193.32/27.07 | | | | | | % 193.32/27.07 | | | | | | (911) ~ (all_872_4 = 0) % 193.32/27.07 | | | | | | % 193.32/27.07 | | | | | | BETA: splitting (657) gives: % 193.32/27.07 | | | | | | % 193.32/27.07 | | | | | | Case 1: % 193.32/27.07 | | | | | | | % 193.32/27.07 | | | | | | | (912) all_872_4 = 0 & all_872_8 = v_y & ? [v0: $i] : ? [v1: % 193.32/27.07 | | | | | | | $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & ~ % 193.32/27.07 | | | | | | | (v0 = v_y) & % 193.32/27.07 | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.07 | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v0) = v2 % 193.32/27.07 | | | | | | | & % 193.32/27.07 | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.07 | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v0) = v1 & % 193.32/27.07 | | | | | | | c_member(all_685_0, v2, v_L) = v3 & c_member(all_685_0, % 193.32/27.07 | | | | | | | v1, v_L) = 0 & $i(v2) & $i(v1) & $i(v0)) % 193.32/27.07 | | | | | | | % 193.32/27.07 | | | | | | | ALPHA: (912) implies: % 193.32/27.07 | | | | | | | (913) all_872_4 = 0 % 193.32/27.07 | | | | | | | % 193.32/27.07 | | | | | | | REDUCE: (911), (913) imply: % 193.32/27.07 | | | | | | | (914) $false % 193.32/27.07 | | | | | | | % 193.32/27.07 | | | | | | | CLOSE: (914) is inconsistent. % 193.32/27.07 | | | | | | | % 193.32/27.07 | | | | | | Case 2: % 193.32/27.07 | | | | | | | % 193.32/27.07 | | | | | | | (915) all_872_6 = 0 & ~ (all_872_8 = v_y) & ? [v0: $i] : ? % 193.32/27.07 | | | | | | | [v1: $i] : ? [v2: any] : ? [v3: $i] : ? [v4: any] : % 193.32/27.07 | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.07 | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v0) = v1 % 193.32/27.07 | | | | | | | & % 193.32/27.07 | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.07 | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v0) = v3 % 193.32/27.07 | | | | | | | & c_member(all_685_0, v3, v_L) = v4 & % 193.32/27.07 | | | | | | | c_member(all_685_0, v1, v_L) = v2 & $i(v3) & $i(v1) & % 193.32/27.07 | | | | | | | $i(v0) & ((v2 = 0 & ~ (v4 = 0) & ~ (v0 = v_y)) | (v0 % 193.32/27.07 | | | | | | | = v_y & all_872_2 = 0 & ~ (all_872_4 = 0) & ~ % 193.32/27.07 | | | | | | | (all_872_9 = v_x)) | (v0 = v_y & all_872_8 = v_x & % 193.32/27.07 | | | | | | | ~ (all_872_4 = 0) & ~ (all_872_9 = v_x)))) % 193.32/27.07 | | | | | | | % 193.32/27.07 | | | | | | | ALPHA: (915) implies: % 193.32/27.07 | | | | | | | (916) all_872_6 = 0 % 193.32/27.07 | | | | | | | (917) ? [v0: $i] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : % 193.32/27.07 | | | | | | | ? [v4: any] : % 193.32/27.07 | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.07 | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v0) = v1 % 193.32/27.07 | | | | | | | & % 193.32/27.07 | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.07 | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v0) = v3 % 193.32/27.07 | | | | | | | & c_member(all_685_0, v3, v_L) = v4 & % 193.32/27.07 | | | | | | | c_member(all_685_0, v1, v_L) = v2 & $i(v3) & $i(v1) & % 193.32/27.07 | | | | | | | $i(v0) & ((v2 = 0 & ~ (v4 = 0) & ~ (v0 = v_y)) | (v0 % 193.32/27.07 | | | | | | | = v_y & all_872_2 = 0 & ~ (all_872_4 = 0) & ~ % 193.32/27.07 | | | | | | | (all_872_9 = v_x)) | (v0 = v_y & all_872_8 = v_x & % 193.32/27.07 | | | | | | | ~ (all_872_4 = 0) & ~ (all_872_9 = v_x)))) % 193.32/27.07 | | | | | | | % 193.32/27.07 | | | | | | | REF_CLOSE: (15), (16), (17), (20), (21), (23), (44), (45), (89), % 193.32/27.07 | | | | | | | (90), (169), (170), (180), (181), (182), (184), (185), % 193.32/27.07 | | | | | | | (186), (187), (191), (192), (193), (196), (197), (198), % 193.32/27.07 | | | | | | | (664), (667), (672), (673), (674), (676), (911), (916), % 193.32/27.07 | | | | | | | (917), (fact_antisymD), (fact_wf__not__sym) are % 193.32/27.07 | | | | | | | inconsistent by sub-proof #3. % 193.32/27.07 | | | | | | | % 193.32/27.07 | | | | | | End of split % 193.32/27.07 | | | | | | % 193.32/27.07 | | | | | End of split % 193.32/27.07 | | | | | % 193.32/27.07 | | | | End of split % 193.32/27.07 | | | | % 193.32/27.07 | | | Case 2: % 193.32/27.07 | | | | % 193.32/27.07 | | | | (918) ! [v0: $i] : ! [v1: $i] : ( ~ % 193.32/27.07 | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.07 | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v0) = v1) | % 193.32/27.07 | | | | ~ $i(v0) | ? [v2: $i] : ? [v3: any] : ? [v4: any] : % 193.32/27.07 | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.07 | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v0) = v2 & % 193.32/27.07 | | | | c_member(all_676_0, v2, v_L) = v3 & c_member(all_676_0, v1, % 193.32/27.07 | | | | v_L) = v4 & $i(v2) & ( ~ (v3 = 0) | v4 = 0))) % 193.32/27.07 | | | | % 193.32/27.07 | | | | GROUND_INST: instantiating (918) with v_x, all_872_3, simplifying with % 193.32/27.07 | | | | (16), (182) gives: % 193.32/27.07 | | | | (919) ? [v0: $i] : ? [v1: any] : ? [v2: any] : % 193.32/27.07 | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.07 | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v_x) = v0 & % 193.32/27.07 | | | | c_member(all_676_0, v0, v_L) = v1 & c_member(all_676_0, % 193.32/27.07 | | | | all_872_3, v_L) = v2 & $i(v0) & ( ~ (v1 = 0) | v2 = 0)) % 193.32/27.07 | | | | % 193.32/27.07 | | | | DELTA: instantiating (919) with fresh symbols all_1092_0, all_1092_1, % 193.32/27.07 | | | | all_1092_2 gives: % 193.32/27.07 | | | | (920) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.07 | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v_x) = all_1092_2 & % 193.32/27.07 | | | | c_member(all_676_0, all_1092_2, v_L) = all_1092_1 & % 193.32/27.07 | | | | c_member(all_676_0, all_872_3, v_L) = all_1092_0 & % 193.32/27.07 | | | | $i(all_1092_2) & ( ~ (all_1092_1 = 0) | all_1092_0 = 0) % 193.32/27.07 | | | | % 193.32/27.07 | | | | ALPHA: (920) implies: % 193.32/27.07 | | | | (921) c_member(all_676_0, all_872_3, v_L) = all_1092_0 % 193.32/27.07 | | | | (922) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.07 | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v_x) = all_1092_2 % 193.32/27.07 | | | | (923) ~ (all_1092_1 = 0) | all_1092_0 = 0 % 193.32/27.07 | | | | % 193.32/27.07 | | | | REDUCE: (89), (921) imply: % 193.32/27.07 | | | | (924) c_member(all_622_1, all_872_3, v_L) = all_1092_0 % 193.32/27.07 | | | | % 193.32/27.07 | | | | GROUND_INST: instantiating (20) with all_872_2, all_1092_0, v_L, % 193.32/27.07 | | | | all_872_3, all_622_1, simplifying with (185), (924) gives: % 193.32/27.07 | | | | (925) all_1092_0 = all_872_2 % 193.32/27.07 | | | | % 193.32/27.07 | | | | BETA: splitting (195) gives: % 193.32/27.07 | | | | % 193.32/27.07 | | | | Case 1: % 193.32/27.07 | | | | | % 193.32/27.07 | | | | | (926) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_676_0, all_872_5, % 193.32/27.07 | | | | | v_L) = v0) % 193.32/27.07 | | | | | % 193.32/27.07 | | | | | DELTA: instantiating (926) with fresh symbol all_1103_0 gives: % 193.32/27.07 | | | | | (927) ~ (all_1103_0 = 0) & c_member(all_676_0, all_872_5, v_L) = % 193.32/27.07 | | | | | all_1103_0 % 193.32/27.07 | | | | | % 193.32/27.07 | | | | | ALPHA: (927) implies: % 193.32/27.07 | | | | | (928) ~ (all_1103_0 = 0) % 193.32/27.07 | | | | | (929) c_member(all_676_0, all_872_5, v_L) = all_1103_0 % 193.32/27.07 | | | | | % 193.32/27.07 | | | | | REDUCE: (89), (929) imply: % 193.32/27.07 | | | | | (930) c_member(all_622_1, all_872_5, v_L) = all_1103_0 % 193.32/27.07 | | | | | % 193.32/27.07 | | | | | GROUND_INST: instantiating (20) with all_872_4, all_1103_0, v_L, % 193.32/27.07 | | | | | all_872_5, all_622_1, simplifying with (186), (930) % 193.32/27.07 | | | | | gives: % 193.32/27.07 | | | | | (931) all_1103_0 = all_872_4 % 193.32/27.07 | | | | | % 193.32/27.07 | | | | | REDUCE: (928), (931) imply: % 193.32/27.07 | | | | | (932) ~ (all_872_4 = 0) % 193.32/27.07 | | | | | % 193.32/27.07 | | | | | BETA: splitting (657) gives: % 193.32/27.07 | | | | | % 193.32/27.07 | | | | | Case 1: % 193.32/27.07 | | | | | | % 193.32/27.07 | | | | | | (933) all_872_4 = 0 & all_872_8 = v_y & ? [v0: $i] : ? [v1: $i] % 193.32/27.07 | | | | | | : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & ~ (v0 = v_y) % 193.32/27.07 | | | | | | & c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.07 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v0) = v2 & % 193.32/27.07 | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.07 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v0) = v1 & % 193.32/27.07 | | | | | | c_member(all_685_0, v2, v_L) = v3 & c_member(all_685_0, % 193.32/27.07 | | | | | | v1, v_L) = 0 & $i(v2) & $i(v1) & $i(v0)) % 193.32/27.07 | | | | | | % 193.32/27.07 | | | | | | ALPHA: (933) implies: % 193.32/27.07 | | | | | | (934) all_872_4 = 0 % 193.32/27.07 | | | | | | % 193.32/27.07 | | | | | | REDUCE: (932), (934) imply: % 193.32/27.07 | | | | | | (935) $false % 193.32/27.07 | | | | | | % 193.32/27.07 | | | | | | CLOSE: (935) is inconsistent. % 193.32/27.07 | | | | | | % 193.32/27.07 | | | | | Case 2: % 193.32/27.07 | | | | | | % 193.32/27.07 | | | | | | (936) all_872_6 = 0 & ~ (all_872_8 = v_y) & ? [v0: $i] : ? % 193.32/27.07 | | | | | | [v1: $i] : ? [v2: any] : ? [v3: $i] : ? [v4: any] : % 193.32/27.07 | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.07 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v0) = v1 & % 193.32/27.07 | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.07 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v0) = v3 & % 193.32/27.07 | | | | | | c_member(all_685_0, v3, v_L) = v4 & c_member(all_685_0, % 193.32/27.07 | | | | | | v1, v_L) = v2 & $i(v3) & $i(v1) & $i(v0) & ((v2 = 0 & % 193.32/27.07 | | | | | | ~ (v4 = 0) & ~ (v0 = v_y)) | (v0 = v_y & all_872_2 = % 193.32/27.07 | | | | | | 0 & ~ (all_872_4 = 0) & ~ (all_872_9 = v_x)) | (v0 % 193.32/27.07 | | | | | | = v_y & all_872_8 = v_x & ~ (all_872_4 = 0) & ~ % 193.32/27.07 | | | | | | (all_872_9 = v_x)))) % 193.32/27.07 | | | | | | % 193.32/27.07 | | | | | | ALPHA: (936) implies: % 193.32/27.07 | | | | | | (937) all_872_6 = 0 % 193.32/27.08 | | | | | | (938) ? [v0: $i] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ? % 193.32/27.08 | | | | | | [v4: any] : % 193.32/27.08 | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.08 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v0) = v1 & % 193.32/27.08 | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.08 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v0) = v3 & % 193.32/27.08 | | | | | | c_member(all_685_0, v3, v_L) = v4 & c_member(all_685_0, % 193.32/27.08 | | | | | | v1, v_L) = v2 & $i(v3) & $i(v1) & $i(v0) & ((v2 = 0 & % 193.32/27.08 | | | | | | ~ (v4 = 0) & ~ (v0 = v_y)) | (v0 = v_y & all_872_2 = % 193.32/27.08 | | | | | | 0 & ~ (all_872_4 = 0) & ~ (all_872_9 = v_x)) | (v0 % 193.32/27.08 | | | | | | = v_y & all_872_8 = v_x & ~ (all_872_4 = 0) & ~ % 193.32/27.08 | | | | | | (all_872_9 = v_x)))) % 193.32/27.08 | | | | | | % 193.32/27.08 | | | | | | DELTA: instantiating (938) with fresh symbols all_1113_0, % 193.32/27.08 | | | | | | all_1113_1, all_1113_2, all_1113_3, all_1113_4 gives: % 193.32/27.08 | | | | | | (939) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.08 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, all_1113_4) = % 193.32/27.08 | | | | | | all_1113_3 & % 193.32/27.08 | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.08 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, all_1113_4) = % 193.32/27.08 | | | | | | all_1113_1 & c_member(all_685_0, all_1113_1, v_L) = % 193.32/27.08 | | | | | | all_1113_0 & c_member(all_685_0, all_1113_3, v_L) = % 193.32/27.08 | | | | | | all_1113_2 & $i(all_1113_1) & $i(all_1113_3) & % 193.32/27.08 | | | | | | $i(all_1113_4) & ((all_1113_2 = 0 & ~ (all_1113_0 = 0) & % 193.32/27.08 | | | | | | ~ (all_1113_4 = v_y)) | (all_1113_4 = v_y & all_872_2 = % 193.32/27.08 | | | | | | 0 & ~ (all_872_4 = 0) & ~ (all_872_9 = v_x)) | % 193.32/27.08 | | | | | | (all_1113_4 = v_y & all_872_8 = v_x & ~ (all_872_4 = 0) % 193.32/27.08 | | | | | | & ~ (all_872_9 = v_x))) % 193.32/27.08 | | | | | | % 193.32/27.08 | | | | | | ALPHA: (939) implies: % 193.32/27.08 | | | | | | (940) c_member(all_685_0, all_1113_3, v_L) = all_1113_2 % 193.32/27.08 | | | | | | (941) c_member(all_685_0, all_1113_1, v_L) = all_1113_0 % 193.32/27.08 | | | | | | (942) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.08 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, all_1113_4) = % 193.32/27.08 | | | | | | all_1113_1 % 193.32/27.08 | | | | | | (943) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.08 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, all_1113_4) = % 193.32/27.08 | | | | | | all_1113_3 % 193.32/27.08 | | | | | | (944) (all_1113_2 = 0 & ~ (all_1113_0 = 0) & ~ (all_1113_4 = % 193.32/27.08 | | | | | | v_y)) | (all_1113_4 = v_y & all_872_2 = 0 & ~ % 193.32/27.08 | | | | | | (all_872_4 = 0) & ~ (all_872_9 = v_x)) | (all_1113_4 = % 193.32/27.08 | | | | | | v_y & all_872_8 = v_x & ~ (all_872_4 = 0) & ~ % 193.32/27.08 | | | | | | (all_872_9 = v_x)) % 193.32/27.08 | | | | | | % 193.32/27.08 | | | | | | REDUCE: (90), (941) imply: % 193.32/27.08 | | | | | | (945) c_member(all_622_1, all_1113_1, v_L) = all_1113_0 % 193.32/27.08 | | | | | | % 193.32/27.08 | | | | | | REDUCE: (90), (940) imply: % 193.32/27.08 | | | | | | (946) c_member(all_622_1, all_1113_3, v_L) = all_1113_2 % 193.32/27.08 | | | | | | % 193.32/27.08 | | | | | | REDUCE: (187), (937) imply: % 193.32/27.08 | | | | | | (947) c_member(all_622_1, all_872_7, v_L) = 0 % 193.32/27.08 | | | | | | % 193.32/27.08 | | | | | | BETA: splitting (197) gives: % 193.32/27.08 | | | | | | % 193.32/27.08 | | | | | | Case 1: % 193.32/27.08 | | | | | | | % 193.32/27.08 | | | | | | | (948) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_676_0, % 193.32/27.08 | | | | | | | all_872_7, v_L) = v0) % 193.32/27.08 | | | | | | | % 193.32/27.08 | | | | | | | DELTA: instantiating (948) with fresh symbol all_1123_0 gives: % 193.32/27.08 | | | | | | | (949) ~ (all_1123_0 = 0) & c_member(all_676_0, all_872_7, v_L) % 193.32/27.08 | | | | | | | = all_1123_0 % 193.32/27.08 | | | | | | | % 193.32/27.08 | | | | | | | REF_CLOSE: (20), (89), (947), (949) are inconsistent by sub-proof % 193.32/27.08 | | | | | | | #14. % 193.32/27.08 | | | | | | | % 193.32/27.08 | | | | | | Case 2: % 193.32/27.08 | | | | | | | % 193.32/27.08 | | | | | | | (950) ! [v0: $i] : ! [v1: $i] : ( ~ % 193.32/27.08 | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.08 | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v0) = % 193.32/27.08 | | | | | | | v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: any] : ? % 193.32/27.08 | | | | | | | [v4: any] : % 193.32/27.08 | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.08 | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v0) = % 193.32/27.08 | | | | | | | v2 & c_member(all_676_0, v2, v_L) = v3 & % 193.32/27.08 | | | | | | | c_member(all_676_0, v1, v_L) = v4 & $i(v2) & ( ~ (v3 % 193.32/27.08 | | | | | | | = 0) | v4 = 0))) % 193.32/27.08 | | | | | | | % 193.32/27.08 | | | | | | | GROUND_INST: instantiating (950) with v_x, all_872_5, simplifying % 193.32/27.08 | | | | | | | with (16), (180) gives: % 193.32/27.08 | | | | | | | (951) ? [v0: $i] : ? [v1: any] : ? [v2: any] : % 193.32/27.08 | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.08 | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v_x) = v0 % 193.32/27.08 | | | | | | | & c_member(all_676_0, v0, v_L) = v1 & % 193.32/27.08 | | | | | | | c_member(all_676_0, all_872_5, v_L) = v2 & $i(v0) & ( ~ % 193.32/27.08 | | | | | | | (v1 = 0) | v2 = 0)) % 193.32/27.08 | | | | | | | % 193.32/27.08 | | | | | | | GROUND_INST: instantiating (950) with all_872_8, all_872_7, % 193.32/27.08 | | | | | | | simplifying with (170), (181) gives: % 193.32/27.08 | | | | | | | (952) ? [v0: $i] : ? [v1: any] : ? [v2: any] : % 193.32/27.08 | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.08 | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, % 193.32/27.08 | | | | | | | all_872_8) = v0 & c_member(all_676_0, v0, v_L) = v1 & % 193.32/27.08 | | | | | | | c_member(all_676_0, all_872_7, v_L) = v2 & $i(v0) & ( ~ % 193.32/27.08 | | | | | | | (v1 = 0) | v2 = 0)) % 193.32/27.08 | | | | | | | % 193.32/27.08 | | | | | | | DELTA: instantiating (952) with fresh symbols all_1124_0, % 193.32/27.08 | | | | | | | all_1124_1, all_1124_2 gives: % 193.32/27.08 | | | | | | | (953) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.08 | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, all_872_8) % 193.32/27.08 | | | | | | | = all_1124_2 & c_member(all_676_0, all_1124_2, v_L) = % 193.32/27.08 | | | | | | | all_1124_1 & c_member(all_676_0, all_872_7, v_L) = % 193.32/27.08 | | | | | | | all_1124_0 & $i(all_1124_2) & ( ~ (all_1124_1 = 0) | % 193.32/27.08 | | | | | | | all_1124_0 = 0) % 193.32/27.08 | | | | | | | % 193.32/27.08 | | | | | | | ALPHA: (953) implies: % 193.32/27.08 | | | | | | | (954) c_member(all_676_0, all_872_7, v_L) = all_1124_0 % 193.32/27.08 | | | | | | | (955) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.08 | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, all_872_8) % 193.32/27.08 | | | | | | | = all_1124_2 % 193.32/27.08 | | | | | | | % 193.32/27.08 | | | | | | | DELTA: instantiating (951) with fresh symbols all_1126_0, % 193.32/27.08 | | | | | | | all_1126_1, all_1126_2 gives: % 193.32/27.08 | | | | | | | (956) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.08 | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v_x) = % 193.32/27.08 | | | | | | | all_1126_2 & c_member(all_676_0, all_1126_2, v_L) = % 193.32/27.08 | | | | | | | all_1126_1 & c_member(all_676_0, all_872_5, v_L) = % 193.32/27.08 | | | | | | | all_1126_0 & $i(all_1126_2) & ( ~ (all_1126_1 = 0) | % 193.32/27.08 | | | | | | | all_1126_0 = 0) % 193.32/27.08 | | | | | | | % 193.32/27.08 | | | | | | | ALPHA: (956) implies: % 193.32/27.08 | | | | | | | (957) c_member(all_676_0, all_872_5, v_L) = all_1126_0 % 193.32/27.08 | | | | | | | (958) c_member(all_676_0, all_1126_2, v_L) = all_1126_1 % 193.32/27.08 | | | | | | | (959) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.08 | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v_x) = % 193.32/27.08 | | | | | | | all_1126_2 % 193.32/27.08 | | | | | | | (960) ~ (all_1126_1 = 0) | all_1126_0 = 0 % 193.32/27.08 | | | | | | | % 193.32/27.08 | | | | | | | REDUCE: (89), (958) imply: % 193.32/27.08 | | | | | | | (961) c_member(all_622_1, all_1126_2, v_L) = all_1126_1 % 193.32/27.08 | | | | | | | % 193.32/27.08 | | | | | | | REDUCE: (89), (957) imply: % 193.32/27.08 | | | | | | | (962) c_member(all_622_1, all_872_5, v_L) = all_1126_0 % 193.32/27.08 | | | | | | | % 193.32/27.08 | | | | | | | REDUCE: (89), (954) imply: % 193.32/27.08 | | | | | | | (963) c_member(all_622_1, all_872_7, v_L) = all_1124_0 % 193.32/27.08 | | | | | | | % 193.32/27.08 | | | | | | | GROUND_INST: instantiating (20) with 0, all_1124_0, v_L, % 193.32/27.08 | | | | | | | all_872_7, all_622_1, simplifying with (947), (963) % 193.32/27.08 | | | | | | | gives: % 193.32/27.08 | | | | | | | (964) all_1124_0 = 0 % 193.32/27.08 | | | | | | | % 193.32/27.08 | | | | | | | GROUND_INST: instantiating (20) with all_872_4, all_1126_0, v_L, % 193.32/27.08 | | | | | | | all_872_5, all_622_1, simplifying with (186), (962) % 193.32/27.08 | | | | | | | gives: % 193.32/27.08 | | | | | | | (965) all_1126_0 = all_872_4 % 193.32/27.08 | | | | | | | % 193.32/27.08 | | | | | | | GROUND_INST: instantiating (21) with all_872_3, all_1126_2, v_x, % 193.32/27.08 | | | | | | | all_872_8, tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.08 | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with % 193.32/27.08 | | | | | | | (182), (959) gives: % 193.32/27.08 | | | | | | | (966) all_1126_2 = all_872_3 % 193.32/27.08 | | | | | | | % 193.32/27.08 | | | | | | | REDUCE: (961), (966) imply: % 193.32/27.08 | | | | | | | (967) c_member(all_622_1, all_872_3, v_L) = all_1126_1 % 193.32/27.08 | | | | | | | % 193.32/27.08 | | | | | | | BETA: splitting (960) gives: % 193.32/27.08 | | | | | | | % 193.32/27.08 | | | | | | | Case 1: % 193.32/27.08 | | | | | | | | % 193.32/27.08 | | | | | | | | (968) ~ (all_1126_1 = 0) % 193.32/27.08 | | | | | | | | % 193.32/27.08 | | | | | | | | GROUND_INST: instantiating (20) with all_872_2, all_1126_1, v_L, % 193.32/27.08 | | | | | | | | all_872_3, all_622_1, simplifying with (185), (967) % 193.32/27.08 | | | | | | | | gives: % 193.32/27.08 | | | | | | | | (969) all_1126_1 = all_872_2 % 193.32/27.08 | | | | | | | | % 193.32/27.08 | | | | | | | | REDUCE: (968), (969) imply: % 193.32/27.08 | | | | | | | | (970) ~ (all_872_2 = 0) % 193.32/27.08 | | | | | | | | % 193.32/27.08 | | | | | | | | BETA: splitting (196) gives: % 193.32/27.08 | | | | | | | | % 193.32/27.08 | | | | | | | | Case 1: % 193.32/27.08 | | | | | | | | | % 193.32/27.08 | | | | | | | | | (971) all_872_8 = all_872_9 % 193.32/27.08 | | | | | | | | | % 193.32/27.08 | | | | | | | | | REDUCE: (943), (971) imply: % 193.32/27.08 | | | | | | | | | (972) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.08 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, % 193.32/27.08 | | | | | | | | | all_1113_4) = all_1113_3 % 193.32/27.08 | | | | | | | | | % 193.32/27.08 | | | | | | | | | BETA: splitting (944) gives: % 193.32/27.08 | | | | | | | | | % 193.32/27.08 | | | | | | | | | Case 1: % 193.32/27.08 | | | | | | | | | | % 193.32/27.08 | | | | | | | | | | (973) all_1113_2 = 0 & ~ (all_1113_0 = 0) & ~ % 193.32/27.08 | | | | | | | | | | (all_1113_4 = v_y) % 193.32/27.08 | | | | | | | | | | % 193.32/27.08 | | | | | | | | | | ALPHA: (973) implies: % 193.32/27.08 | | | | | | | | | | (974) all_1113_2 = 0 % 193.32/27.08 | | | | | | | | | | (975) ~ (all_1113_0 = 0) % 193.32/27.08 | | | | | | | | | | % 193.32/27.08 | | | | | | | | | | REDUCE: (946), (974) imply: % 193.32/27.08 | | | | | | | | | | (976) c_member(all_622_1, all_1113_3, v_L) = 0 % 193.32/27.08 | | | | | | | | | | % 193.32/27.08 | | | | | | | | | | GROUND_INST: instantiating (21) with all_1113_1, all_1113_3, % 193.32/27.08 | | | | | | | | | | all_1113_4, all_872_9, % 193.32/27.08 | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.08 | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with % 193.32/27.08 | | | | | | | | | | (942), (972) gives: % 193.32/27.08 | | | | | | | | | | (977) all_1113_1 = all_1113_3 % 193.32/27.08 | | | | | | | | | | % 193.32/27.08 | | | | | | | | | | REDUCE: (945), (977) imply: % 193.32/27.08 | | | | | | | | | | (978) c_member(all_622_1, all_1113_3, v_L) = all_1113_0 % 193.32/27.08 | | | | | | | | | | % 193.32/27.08 | | | | | | | | | | GROUND_INST: instantiating (20) with 0, all_1113_0, v_L, % 193.32/27.08 | | | | | | | | | | all_1113_3, all_622_1, simplifying with (976), % 193.32/27.08 | | | | | | | | | | (978) gives: % 193.32/27.08 | | | | | | | | | | (979) all_1113_0 = 0 % 193.32/27.08 | | | | | | | | | | % 193.32/27.08 | | | | | | | | | | REDUCE: (975), (979) imply: % 193.32/27.08 | | | | | | | | | | (980) $false % 193.32/27.08 | | | | | | | | | | % 193.32/27.08 | | | | | | | | | | CLOSE: (980) is inconsistent. % 193.32/27.08 | | | | | | | | | | % 193.32/27.08 | | | | | | | | | Case 2: % 193.32/27.08 | | | | | | | | | | % 193.32/27.08 | | | | | | | | | | (981) (all_1113_4 = v_y & all_872_2 = 0 & ~ (all_872_4 = % 193.32/27.08 | | | | | | | | | | 0) & ~ (all_872_9 = v_x)) | (all_1113_4 = v_y % 193.32/27.08 | | | | | | | | | | & all_872_8 = v_x & ~ (all_872_4 = 0) & ~ % 193.32/27.08 | | | | | | | | | | (all_872_9 = v_x)) % 193.32/27.08 | | | | | | | | | | % 193.32/27.08 | | | | | | | | | | BETA: splitting (981) gives: % 193.32/27.08 | | | | | | | | | | % 193.32/27.08 | | | | | | | | | | Case 1: % 193.32/27.08 | | | | | | | | | | | % 193.32/27.08 | | | | | | | | | | | (982) all_1113_4 = v_y & all_872_2 = 0 & ~ (all_872_4 = % 193.32/27.08 | | | | | | | | | | | 0) & ~ (all_872_9 = v_x) % 193.32/27.08 | | | | | | | | | | | % 193.32/27.08 | | | | | | | | | | | ALPHA: (982) implies: % 193.32/27.08 | | | | | | | | | | | (983) all_872_2 = 0 % 193.32/27.08 | | | | | | | | | | | % 193.32/27.08 | | | | | | | | | | | REDUCE: (970), (983) imply: % 193.32/27.08 | | | | | | | | | | | (984) $false % 193.32/27.08 | | | | | | | | | | | % 193.32/27.08 | | | | | | | | | | | CLOSE: (984) is inconsistent. % 193.32/27.08 | | | | | | | | | | | % 193.32/27.08 | | | | | | | | | | Case 2: % 193.32/27.08 | | | | | | | | | | | % 193.32/27.08 | | | | | | | | | | | (985) all_1113_4 = v_y & all_872_8 = v_x & ~ (all_872_4 % 193.32/27.08 | | | | | | | | | | | = 0) & ~ (all_872_9 = v_x) % 193.32/27.08 | | | | | | | | | | | % 193.32/27.08 | | | | | | | | | | | ALPHA: (985) implies: % 193.32/27.08 | | | | | | | | | | | (986) all_872_8 = v_x % 193.32/27.08 | | | | | | | | | | | (987) ~ (all_872_9 = v_x) % 193.32/27.08 | | | | | | | | | | | % 193.32/27.08 | | | | | | | | | | | COMBINE_EQS: (971), (986) imply: % 193.32/27.08 | | | | | | | | | | | (988) all_872_9 = v_x % 193.32/27.08 | | | | | | | | | | | % 193.32/27.08 | | | | | | | | | | | REDUCE: (987), (988) imply: % 193.32/27.08 | | | | | | | | | | | (989) $false % 193.32/27.08 | | | | | | | | | | | % 193.32/27.08 | | | | | | | | | | | CLOSE: (989) is inconsistent. % 193.32/27.08 | | | | | | | | | | | % 193.32/27.08 | | | | | | | | | | End of split % 193.32/27.08 | | | | | | | | | | % 193.32/27.08 | | | | | | | | | End of split % 193.32/27.08 | | | | | | | | | % 193.32/27.08 | | | | | | | | Case 2: % 193.32/27.08 | | | | | | | | | % 193.32/27.08 | | | | | | | | | (990) ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 193.32/27.08 | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.08 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, % 193.32/27.08 | | | | | | | | | all_872_9) = v1 & c_member(all_676_0, v1, v_L) = % 193.32/27.08 | | | | | | | | | v2 & c_member(all_676_0, all_872_7, v_L) = v0 & % 193.32/27.08 | | | | | | | | | $i(v1) & (v2 = 0 | v0 = 0)) % 193.32/27.08 | | | | | | | | | % 193.32/27.08 | | | | | | | | | DELTA: instantiating (990) with fresh symbols all_1183_0, % 193.32/27.08 | | | | | | | | | all_1183_1, all_1183_2 gives: % 193.32/27.09 | | | | | | | | | (991) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.09 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, % 193.32/27.09 | | | | | | | | | all_872_9) = all_1183_1 & c_member(all_676_0, % 193.32/27.09 | | | | | | | | | all_1183_1, v_L) = all_1183_0 & c_member(all_676_0, % 193.32/27.09 | | | | | | | | | all_872_7, v_L) = all_1183_2 & $i(all_1183_1) & % 193.32/27.09 | | | | | | | | | (all_1183_0 = 0 | all_1183_2 = 0) % 193.32/27.09 | | | | | | | | | % 193.32/27.09 | | | | | | | | | ALPHA: (991) implies: % 193.32/27.09 | | | | | | | | | (992) c_member(all_676_0, all_872_7, v_L) = all_1183_2 % 193.32/27.09 | | | | | | | | | % 193.32/27.09 | | | | | | | | | REDUCE: (89), (992) imply: % 193.32/27.09 | | | | | | | | | (993) c_member(all_622_1, all_872_7, v_L) = all_1183_2 % 193.32/27.09 | | | | | | | | | % 193.32/27.09 | | | | | | | | | GROUND_INST: instantiating (20) with 0, all_1183_2, v_L, % 193.32/27.09 | | | | | | | | | all_872_7, all_622_1, simplifying with (947), % 193.32/27.09 | | | | | | | | | (993) gives: % 193.32/27.09 | | | | | | | | | (994) all_1183_2 = 0 % 193.32/27.09 | | | | | | | | | % 193.32/27.09 | | | | | | | | | BETA: splitting (191) gives: % 193.32/27.09 | | | | | | | | | % 193.32/27.09 | | | | | | | | | Case 1: % 193.32/27.09 | | | | | | | | | | % 193.32/27.09 | | | | | | | | | | (995) all_872_0 = 0 % 193.32/27.09 | | | | | | | | | | % 193.32/27.09 | | | | | | | | | | REDUCE: (184), (995) imply: % 193.32/27.09 | | | | | | | | | | (996) c_member(all_622_1, all_872_1, v_L) = 0 % 193.32/27.09 | | | | | | | | | | % 193.32/27.09 | | | | | | | | | | GROUND_INST: instantiating (43) with all_872_8, all_1124_2, % 193.32/27.09 | | | | | | | | | | simplifying with (170), (955) gives: % 193.32/27.09 | | | | | | | | | | (997) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_676_0, % 193.32/27.09 | | | | | | | | | | all_1124_2, v_L) = v0) % 193.32/27.09 | | | | | | | | | | % 193.32/27.09 | | | | | | | | | | GROUND_INST: instantiating (918) with all_872_8, all_1124_2, % 193.32/27.09 | | | | | | | | | | simplifying with (170), (955) gives: % 193.32/27.09 | | | | | | | | | | (998) ? [v0: $i] : ? [v1: any] : ? [v2: any] : % 193.32/27.09 | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.09 | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, % 193.32/27.09 | | | | | | | | | | all_872_8) = v0 & c_member(all_676_0, v0, v_L) % 193.32/27.09 | | | | | | | | | | = v1 & c_member(all_676_0, all_1124_2, v_L) = v2 % 193.32/27.09 | | | | | | | | | | & $i(v0) & ( ~ (v1 = 0) | v2 = 0)) % 193.32/27.09 | | | | | | | | | | % 193.32/27.09 | | | | | | | | | | DELTA: instantiating (997) with fresh symbol all_1220_0 % 193.32/27.09 | | | | | | | | | | gives: % 193.32/27.09 | | | | | | | | | | (999) ~ (all_1220_0 = 0) & c_member(all_676_0, % 193.32/27.09 | | | | | | | | | | all_1124_2, v_L) = all_1220_0 % 193.32/27.09 | | | | | | | | | | % 193.32/27.09 | | | | | | | | | | ALPHA: (999) implies: % 193.32/27.09 | | | | | | | | | | (1000) ~ (all_1220_0 = 0) % 193.32/27.09 | | | | | | | | | | (1001) c_member(all_676_0, all_1124_2, v_L) = all_1220_0 % 193.32/27.09 | | | | | | | | | | % 193.32/27.09 | | | | | | | | | | DELTA: instantiating (998) with fresh symbols all_1252_0, % 193.32/27.09 | | | | | | | | | | all_1252_1, all_1252_2 gives: % 193.32/27.09 | | | | | | | | | | (1002) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.09 | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, all_872_8) % 193.32/27.09 | | | | | | | | | | = all_1252_2 & c_member(all_676_0, all_1252_2, % 193.32/27.09 | | | | | | | | | | v_L) = all_1252_1 & c_member(all_676_0, % 193.32/27.09 | | | | | | | | | | all_1124_2, v_L) = all_1252_0 & $i(all_1252_2) & % 193.32/27.09 | | | | | | | | | | ( ~ (all_1252_1 = 0) | all_1252_0 = 0) % 193.32/27.09 | | | | | | | | | | % 193.32/27.09 | | | | | | | | | | ALPHA: (1002) implies: % 193.32/27.09 | | | | | | | | | | (1003) c_member(all_676_0, all_1124_2, v_L) = all_1252_0 % 193.32/27.09 | | | | | | | | | | (1004) c_member(all_676_0, all_1252_2, v_L) = all_1252_1 % 193.32/27.09 | | | | | | | | | | (1005) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.09 | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, all_872_8) % 193.32/27.09 | | | | | | | | | | = all_1252_2 % 193.32/27.09 | | | | | | | | | | (1006) ~ (all_1252_1 = 0) | all_1252_0 = 0 % 193.32/27.09 | | | | | | | | | | % 193.32/27.09 | | | | | | | | | | REDUCE: (89), (1004) imply: % 193.32/27.09 | | | | | | | | | | (1007) c_member(all_622_1, all_1252_2, v_L) = all_1252_1 % 193.32/27.09 | | | | | | | | | | % 193.32/27.09 | | | | | | | | | | REDUCE: (89), (1003) imply: % 193.32/27.09 | | | | | | | | | | (1008) c_member(all_622_1, all_1124_2, v_L) = all_1252_0 % 193.32/27.09 | | | | | | | | | | % 193.32/27.09 | | | | | | | | | | REDUCE: (89), (1001) imply: % 193.32/27.09 | | | | | | | | | | (1009) c_member(all_622_1, all_1124_2, v_L) = all_1220_0 % 193.32/27.09 | | | | | | | | | | % 193.32/27.09 | | | | | | | | | | GROUND_INST: instantiating (20) with all_1220_0, all_1252_0, % 193.32/27.09 | | | | | | | | | | v_L, all_1124_2, all_622_1, simplifying with % 193.32/27.09 | | | | | | | | | | (1008), (1009) gives: % 193.32/27.09 | | | | | | | | | | (1010) all_1252_0 = all_1220_0 % 193.32/27.09 | | | | | | | | | | % 193.32/27.09 | | | | | | | | | | GROUND_INST: instantiating (21) with all_872_1, all_1252_2, % 193.32/27.09 | | | | | | | | | | all_872_8, v_x, tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.09 | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with % 193.32/27.09 | | | | | | | | | | (179), (1005) gives: % 193.32/27.09 | | | | | | | | | | (1011) all_1252_2 = all_872_1 % 193.32/27.09 | | | | | | | | | | % 193.32/27.09 | | | | | | | | | | REDUCE: (1007), (1011) imply: % 193.32/27.09 | | | | | | | | | | (1012) c_member(all_622_1, all_872_1, v_L) = all_1252_1 % 193.32/27.09 | | | | | | | | | | % 193.32/27.09 | | | | | | | | | | BETA: splitting (1006) gives: % 193.32/27.09 | | | | | | | | | | % 193.32/27.09 | | | | | | | | | | Case 1: % 193.32/27.09 | | | | | | | | | | | % 193.32/27.09 | | | | | | | | | | | (1013) ~ (all_1252_1 = 0) % 193.32/27.09 | | | | | | | | | | | % 193.32/27.09 | | | | | | | | | | | GROUND_INST: instantiating (20) with 0, all_1252_1, v_L, % 193.32/27.09 | | | | | | | | | | | all_872_1, all_622_1, simplifying with (996), % 193.32/27.09 | | | | | | | | | | | (1012) gives: % 193.32/27.09 | | | | | | | | | | | (1014) all_1252_1 = 0 % 193.32/27.09 | | | | | | | | | | | % 193.32/27.09 | | | | | | | | | | | REDUCE: (1013), (1014) imply: % 193.32/27.09 | | | | | | | | | | | (1015) $false % 193.32/27.09 | | | | | | | | | | | % 193.32/27.09 | | | | | | | | | | | CLOSE: (1015) is inconsistent. % 193.32/27.09 | | | | | | | | | | | % 193.32/27.09 | | | | | | | | | | Case 2: % 193.32/27.09 | | | | | | | | | | | % 193.32/27.09 | | | | | | | | | | | (1016) all_1252_0 = 0 % 193.32/27.09 | | | | | | | | | | | % 193.32/27.09 | | | | | | | | | | | COMBINE_EQS: (1010), (1016) imply: % 193.32/27.09 | | | | | | | | | | | (1017) all_1220_0 = 0 % 193.32/27.09 | | | | | | | | | | | % 193.32/27.09 | | | | | | | | | | | REDUCE: (1000), (1017) imply: % 193.32/27.09 | | | | | | | | | | | (1018) $false % 193.32/27.09 | | | | | | | | | | | % 193.32/27.09 | | | | | | | | | | | CLOSE: (1018) is inconsistent. % 193.32/27.09 | | | | | | | | | | | % 193.32/27.09 | | | | | | | | | | End of split % 193.32/27.09 | | | | | | | | | | % 193.32/27.09 | | | | | | | | | Case 2: % 193.32/27.09 | | | | | | | | | | % 193.32/27.09 | | | | | | | | | | (1019) ~ (all_872_0 = 0) % 193.32/27.09 | | | | | | | | | | % 193.32/27.09 | | | | | | | | | | REF_CLOSE: (20), (21), (89), (180), (181), (182), (184), % 193.32/27.09 | | | | | | | | | | (185), (186), (192), (198), (932), (947), (970), % 193.32/27.09 | | | | | | | | | | (1019) are inconsistent by sub-proof #4. % 193.32/27.09 | | | | | | | | | | % 193.32/27.09 | | | | | | | | | End of split % 193.32/27.09 | | | | | | | | | % 193.32/27.09 | | | | | | | | End of split % 193.32/27.09 | | | | | | | | % 193.32/27.09 | | | | | | | Case 2: % 193.32/27.09 | | | | | | | | % 193.32/27.09 | | | | | | | | (1020) all_1126_0 = 0 % 193.32/27.09 | | | | | | | | % 193.32/27.09 | | | | | | | | COMBINE_EQS: (965), (1020) imply: % 193.32/27.09 | | | | | | | | (1021) all_872_4 = 0 % 193.32/27.09 | | | | | | | | % 193.32/27.09 | | | | | | | | REDUCE: (932), (1021) imply: % 193.32/27.09 | | | | | | | | (1022) $false % 193.32/27.09 | | | | | | | | % 193.32/27.09 | | | | | | | | CLOSE: (1022) is inconsistent. % 193.32/27.09 | | | | | | | | % 193.32/27.09 | | | | | | | End of split % 193.32/27.09 | | | | | | | % 193.32/27.09 | | | | | | End of split % 193.32/27.09 | | | | | | % 193.32/27.09 | | | | | End of split % 193.32/27.09 | | | | | % 193.32/27.09 | | | | Case 2: % 193.32/27.09 | | | | | % 193.32/27.09 | | | | | (1023) ! [v0: $i] : ! [v1: $i] : ( ~ % 193.32/27.09 | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.09 | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v0) = v1) % 193.32/27.09 | | | | | | ~ $i(v0) | ? [v2: $i] : ? [v3: any] : ? [v4: any] : % 193.32/27.09 | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.09 | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v0) = v2 & % 193.32/27.09 | | | | | c_member(all_676_0, v2, v_L) = v3 & c_member(all_676_0, % 193.32/27.09 | | | | | v1, v_L) = v4 & $i(v2) & ( ~ (v3 = 0) | v4 = 0))) % 193.32/27.09 | | | | | % 193.32/27.09 | | | | | GROUND_INST: instantiating (1023) with v_x, all_872_5, simplifying % 193.32/27.09 | | | | | with (16), (180) gives: % 193.32/27.09 | | | | | (1024) ? [v0: $i] : ? [v1: any] : ? [v2: any] : % 193.32/27.09 | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.09 | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v_x) = v0 & % 193.32/27.09 | | | | | c_member(all_676_0, v0, v_L) = v1 & c_member(all_676_0, % 193.32/27.09 | | | | | all_872_5, v_L) = v2 & $i(v0) & ( ~ (v1 = 0) | v2 = 0)) % 193.32/27.09 | | | | | % 193.32/27.09 | | | | | GROUND_INST: instantiating (1023) with all_872_8, all_872_7, % 193.32/27.09 | | | | | simplifying with (170), (181) gives: % 193.32/27.09 | | | | | (1025) ? [v0: $i] : ? [v1: any] : ? [v2: any] : % 193.32/27.09 | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.09 | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, all_872_8) = v0 & % 193.32/27.09 | | | | | c_member(all_676_0, v0, v_L) = v1 & c_member(all_676_0, % 193.32/27.09 | | | | | all_872_7, v_L) = v2 & $i(v0) & ( ~ (v1 = 0) | v2 = 0)) % 193.32/27.09 | | | | | % 193.32/27.09 | | | | | DELTA: instantiating (1025) with fresh symbols all_1104_0, all_1104_1, % 193.32/27.09 | | | | | all_1104_2 gives: % 193.32/27.09 | | | | | (1026) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.09 | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, all_872_8) = % 193.32/27.09 | | | | | all_1104_2 & c_member(all_676_0, all_1104_2, v_L) = % 193.32/27.09 | | | | | all_1104_1 & c_member(all_676_0, all_872_7, v_L) = % 193.32/27.09 | | | | | all_1104_0 & $i(all_1104_2) & ( ~ (all_1104_1 = 0) | % 193.32/27.09 | | | | | all_1104_0 = 0) % 193.32/27.09 | | | | | % 193.32/27.09 | | | | | ALPHA: (1026) implies: % 193.32/27.09 | | | | | (1027) c_member(all_676_0, all_872_7, v_L) = all_1104_0 % 193.32/27.09 | | | | | (1028) c_member(all_676_0, all_1104_2, v_L) = all_1104_1 % 193.32/27.09 | | | | | (1029) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.09 | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, all_872_8) = % 193.32/27.09 | | | | | all_1104_2 % 193.32/27.09 | | | | | (1030) ~ (all_1104_1 = 0) | all_1104_0 = 0 % 193.32/27.09 | | | | | % 193.32/27.09 | | | | | DELTA: instantiating (1024) with fresh symbols all_1106_0, all_1106_1, % 193.32/27.09 | | | | | all_1106_2 gives: % 193.32/27.09 | | | | | (1031) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.09 | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v_x) = all_1106_2 & % 193.32/27.09 | | | | | c_member(all_676_0, all_1106_2, v_L) = all_1106_1 & % 193.32/27.09 | | | | | c_member(all_676_0, all_872_5, v_L) = all_1106_0 & % 193.32/27.09 | | | | | $i(all_1106_2) & ( ~ (all_1106_1 = 0) | all_1106_0 = 0) % 193.32/27.09 | | | | | % 193.32/27.09 | | | | | ALPHA: (1031) implies: % 193.32/27.09 | | | | | (1032) c_member(all_676_0, all_872_5, v_L) = all_1106_0 % 193.32/27.09 | | | | | (1033) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.09 | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v_x) = all_1106_2 % 193.32/27.09 | | | | | % 193.32/27.09 | | | | | REDUCE: (89), (1028) imply: % 193.32/27.09 | | | | | (1034) c_member(all_622_1, all_1104_2, v_L) = all_1104_1 % 193.32/27.09 | | | | | % 193.32/27.09 | | | | | REDUCE: (89), (1032) imply: % 193.32/27.09 | | | | | (1035) c_member(all_622_1, all_872_5, v_L) = all_1106_0 % 193.32/27.09 | | | | | % 193.32/27.09 | | | | | REDUCE: (89), (1027) imply: % 193.32/27.09 | | | | | (1036) c_member(all_622_1, all_872_7, v_L) = all_1104_0 % 193.32/27.09 | | | | | % 193.32/27.09 | | | | | GROUND_INST: instantiating (20) with all_872_6, all_1104_0, v_L, % 193.32/27.09 | | | | | all_872_7, all_622_1, simplifying with (187), (1036) % 193.32/27.09 | | | | | gives: % 193.32/27.09 | | | | | (1037) all_1104_0 = all_872_6 % 193.32/27.09 | | | | | % 193.32/27.09 | | | | | GROUND_INST: instantiating (20) with all_872_4, all_1106_0, v_L, % 193.32/27.09 | | | | | all_872_5, all_622_1, simplifying with (186), (1035) % 193.32/27.09 | | | | | gives: % 193.32/27.09 | | | | | (1038) all_1106_0 = all_872_4 % 193.32/27.09 | | | | | % 193.32/27.09 | | | | | GROUND_INST: instantiating (21) with all_1092_2, all_1106_2, v_x, v_x, % 193.32/27.09 | | | | | tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.09 | | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with (922), % 193.32/27.09 | | | | | (1033) gives: % 193.32/27.09 | | | | | (1039) all_1106_2 = all_1092_2 % 193.32/27.09 | | | | | % 193.32/27.09 | | | | | GROUND_INST: instantiating (21) with all_872_1, all_1104_2, all_872_8, % 193.32/27.09 | | | | | v_x, tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.09 | | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with (179), % 193.32/27.09 | | | | | (1029) gives: % 193.32/27.09 | | | | | (1040) all_1104_2 = all_872_1 % 193.32/27.09 | | | | | % 193.32/27.09 | | | | | REDUCE: (1034), (1040) imply: % 193.32/27.09 | | | | | (1041) c_member(all_622_1, all_872_1, v_L) = all_1104_1 % 193.32/27.09 | | | | | % 193.32/27.09 | | | | | GROUND_INST: instantiating (20) with all_872_0, all_1104_1, v_L, % 193.32/27.09 | | | | | all_872_1, all_622_1, simplifying with (184), (1041) % 193.32/27.09 | | | | | gives: % 193.32/27.09 | | | | | (1042) all_1104_1 = all_872_0 % 193.32/27.09 | | | | | % 193.32/27.09 | | | | | BETA: splitting (194) gives: % 193.32/27.09 | | | | | % 193.32/27.09 | | | | | Case 1: % 193.32/27.09 | | | | | | % 193.32/27.09 | | | | | | (1043) all_872_9 = v_x % 193.32/27.09 | | | | | | % 193.32/27.09 | | | | | | REDUCE: (181), (1043) imply: % 193.32/27.09 | | | | | | (1044) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.09 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, all_872_8) = % 193.32/27.09 | | | | | | all_872_7 % 193.32/27.09 | | | | | | % 193.32/27.09 | | | | | | REF_CLOSE: (20), (21), (44), (89), (90), (170), (179), (184), (187), % 193.32/27.09 | | | | | | (193), (657), (1043), (1044) are inconsistent by % 193.32/27.09 | | | | | | sub-proof #12. % 193.32/27.09 | | | | | | % 193.32/27.09 | | | | | Case 2: % 193.32/27.09 | | | | | | % 193.32/27.09 | | | | | | (1045) ~ (all_872_9 = v_x) % 193.32/27.10 | | | | | | (1046) ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 193.32/27.10 | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.10 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, all_872_9) = v1 % 193.32/27.10 | | | | | | & c_member(all_676_0, v1, v_L) = v2 & % 193.32/27.10 | | | | | | c_member(all_676_0, all_872_5, v_L) = v0 & $i(v1) & (v2 % 193.32/27.10 | | | | | | = 0 | v0 = 0)) % 193.32/27.10 | | | | | | % 193.32/27.10 | | | | | | DELTA: instantiating (1046) with fresh symbols all_1122_0, % 193.32/27.10 | | | | | | all_1122_1, all_1122_2 gives: % 193.32/27.10 | | | | | | (1047) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.10 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, all_872_9) = % 193.32/27.10 | | | | | | all_1122_1 & c_member(all_676_0, all_1122_1, v_L) = % 193.32/27.10 | | | | | | all_1122_0 & c_member(all_676_0, all_872_5, v_L) = % 193.32/27.10 | | | | | | all_1122_2 & $i(all_1122_1) & (all_1122_0 = 0 | all_1122_2 % 193.32/27.10 | | | | | | = 0) % 193.32/27.10 | | | | | | % 193.32/27.10 | | | | | | ALPHA: (1047) implies: % 193.32/27.10 | | | | | | (1048) c_member(all_676_0, all_872_5, v_L) = all_1122_2 % 193.32/27.10 | | | | | | % 193.32/27.10 | | | | | | REDUCE: (89), (1048) imply: % 193.32/27.10 | | | | | | (1049) c_member(all_622_1, all_872_5, v_L) = all_1122_2 % 193.32/27.10 | | | | | | % 193.32/27.10 | | | | | | GROUND_INST: instantiating (20) with all_872_4, all_1122_2, v_L, % 193.32/27.10 | | | | | | all_872_5, all_622_1, simplifying with (186), (1049) % 193.32/27.10 | | | | | | gives: % 193.32/27.10 | | | | | | (1050) all_1122_2 = all_872_4 % 193.32/27.10 | | | | | | % 193.32/27.10 | | | | | | BETA: splitting (197) gives: % 193.32/27.10 | | | | | | % 193.32/27.10 | | | | | | Case 1: % 193.32/27.10 | | | | | | | % 193.32/27.10 | | | | | | | (1051) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_676_0, % 193.32/27.10 | | | | | | | all_872_7, v_L) = v0) % 193.32/27.10 | | | | | | | % 193.32/27.10 | | | | | | | DELTA: instantiating (1051) with fresh symbol all_1133_0 gives: % 193.32/27.10 | | | | | | | (1052) ~ (all_1133_0 = 0) & c_member(all_676_0, all_872_7, % 193.32/27.10 | | | | | | | v_L) = all_1133_0 % 193.32/27.10 | | | | | | | % 193.32/27.10 | | | | | | | ALPHA: (1052) implies: % 193.32/27.10 | | | | | | | (1053) ~ (all_1133_0 = 0) % 193.32/27.10 | | | | | | | (1054) c_member(all_676_0, all_872_7, v_L) = all_1133_0 % 193.32/27.10 | | | | | | | % 193.32/27.10 | | | | | | | REDUCE: (89), (1054) imply: % 193.32/27.10 | | | | | | | (1055) c_member(all_622_1, all_872_7, v_L) = all_1133_0 % 193.32/27.10 | | | | | | | % 193.32/27.10 | | | | | | | GROUND_INST: instantiating (20) with all_872_6, all_1133_0, v_L, % 193.32/27.10 | | | | | | | all_872_7, all_622_1, simplifying with (187), (1055) % 193.32/27.10 | | | | | | | gives: % 193.32/27.10 | | | | | | | (1056) all_1133_0 = all_872_6 % 193.32/27.10 | | | | | | | % 193.32/27.10 | | | | | | | REDUCE: (1053), (1056) imply: % 193.32/27.10 | | | | | | | (1057) ~ (all_872_6 = 0) % 193.32/27.10 | | | | | | | % 193.32/27.10 | | | | | | | BETA: splitting (657) gives: % 193.32/27.10 | | | | | | | % 193.32/27.10 | | | | | | | Case 1: % 193.32/27.10 | | | | | | | | % 193.32/27.10 | | | | | | | | (1058) all_872_4 = 0 & all_872_8 = v_y & ? [v0: $i] : ? % 193.32/27.10 | | | | | | | | [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 193.32/27.10 | | | | | | | | ~ (v0 = v_y) & % 193.32/27.10 | | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.10 | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v0) = % 193.32/27.10 | | | | | | | | v2 & % 193.32/27.10 | | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.10 | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v0) = v1 & % 193.32/27.10 | | | | | | | | c_member(all_685_0, v2, v_L) = v3 & % 193.32/27.10 | | | | | | | | c_member(all_685_0, v1, v_L) = 0 & $i(v2) & $i(v1) & % 193.32/27.10 | | | | | | | | $i(v0)) % 193.32/27.10 | | | | | | | | % 193.32/27.10 | | | | | | | | ALPHA: (1058) implies: % 193.32/27.10 | | | | | | | | (1059) all_872_8 = v_y % 193.32/27.10 | | | | | | | | (1060) all_872_4 = 0 % 193.32/27.10 | | | | | | | | (1061) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] % 193.32/27.10 | | | | | | | | : ( ~ (v3 = 0) & ~ (v0 = v_y) & % 193.32/27.10 | | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.10 | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v0) = % 193.32/27.10 | | | | | | | | v2 & % 193.32/27.10 | | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.10 | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v0) = v1 & % 193.32/27.10 | | | | | | | | c_member(all_685_0, v2, v_L) = v3 & % 193.32/27.10 | | | | | | | | c_member(all_685_0, v1, v_L) = 0 & $i(v2) & $i(v1) & % 193.32/27.10 | | | | | | | | $i(v0)) % 193.32/27.10 | | | | | | | | % 193.32/27.10 | | | | | | | | DELTA: instantiating (1061) with fresh symbols all_1143_0, % 193.32/27.10 | | | | | | | | all_1143_1, all_1143_2, all_1143_3 gives: % 193.32/27.10 | | | | | | | | (1062) ~ (all_1143_0 = 0) & ~ (all_1143_3 = v_y) & % 193.32/27.10 | | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.10 | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, % 193.32/27.10 | | | | | | | | all_1143_3) = all_1143_1 & % 193.32/27.10 | | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.10 | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, all_1143_3) = % 193.32/27.10 | | | | | | | | all_1143_2 & c_member(all_685_0, all_1143_1, v_L) = % 193.32/27.10 | | | | | | | | all_1143_0 & c_member(all_685_0, all_1143_2, v_L) = 0 % 193.32/27.10 | | | | | | | | & $i(all_1143_1) & $i(all_1143_2) & $i(all_1143_3) % 193.32/27.10 | | | | | | | | % 193.32/27.10 | | | | | | | | ALPHA: (1062) implies: % 193.32/27.10 | | | | | | | | (1063) ~ (all_1143_0 = 0) % 193.32/27.10 | | | | | | | | (1064) $i(all_1143_3) % 193.32/27.10 | | | | | | | | (1065) c_member(all_685_0, all_1143_2, v_L) = 0 % 193.32/27.10 | | | | | | | | (1066) c_member(all_685_0, all_1143_1, v_L) = all_1143_0 % 193.32/27.10 | | | | | | | | (1067) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.10 | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, all_1143_3) = % 193.32/27.10 | | | | | | | | all_1143_2 % 193.32/27.10 | | | | | | | | (1068) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.10 | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, % 193.32/27.10 | | | | | | | | all_1143_3) = all_1143_1 % 193.32/27.10 | | | | | | | | % 193.32/27.10 | | | | | | | | REDUCE: (182), (1059) imply: % 193.32/27.10 | | | | | | | | (1069) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.10 | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v_x) = % 193.32/27.10 | | | | | | | | all_872_3 % 193.32/27.10 | | | | | | | | % 193.32/27.10 | | | | | | | | REDUCE: (90), (1066) imply: % 193.32/27.10 | | | | | | | | (1070) c_member(all_622_1, all_1143_1, v_L) = all_1143_0 % 193.32/27.10 | | | | | | | | % 193.32/27.10 | | | | | | | | REDUCE: (90), (1065) imply: % 193.32/27.10 | | | | | | | | (1071) c_member(all_622_1, all_1143_2, v_L) = 0 % 193.32/27.10 | | | | | | | | % 193.32/27.10 | | | | | | | | REDUCE: (186), (1060) imply: % 193.32/27.10 | | | | | | | | (1072) c_member(all_622_1, all_872_5, v_L) = 0 % 193.32/27.10 | | | | | | | | % 193.32/27.10 | | | | | | | | REDUCE: (170), (1059) imply: % 193.32/27.10 | | | | | | | | (1073) $i(v_y) % 193.32/27.10 | | | | | | | | % 193.32/27.10 | | | | | | | | BETA: splitting (1030) gives: % 193.32/27.10 | | | | | | | | % 193.32/27.10 | | | | | | | | Case 1: % 193.32/27.10 | | | | | | | | | % 193.32/27.10 | | | | | | | | | (1074) ~ (all_1104_1 = 0) % 193.32/27.10 | | | | | | | | | % 193.32/27.10 | | | | | | | | | REDUCE: (1042), (1074) imply: % 193.32/27.10 | | | | | | | | | (1075) ~ (all_872_0 = 0) % 193.32/27.10 | | | | | | | | | % 193.32/27.10 | | | | | | | | | BETA: splitting (192) gives: % 193.32/27.10 | | | | | | | | | % 193.32/27.10 | | | | | | | | | Case 1: % 193.32/27.10 | | | | | | | | | | % 193.32/27.10 | | | | | | | | | | (1076) all_872_8 = v_x % 193.32/27.10 | | | | | | | | | | % 193.32/27.10 | | | | | | | | | | COMBINE_EQS: (1059), (1076) imply: % 193.32/27.10 | | | | | | | | | | (1077) v_x = v_y % 193.32/27.10 | | | | | | | | | | % 193.32/27.10 | | | | | | | | | | REDUCE: (13), (1077) imply: % 193.32/27.10 | | | | | | | | | | (1078) $false % 193.32/27.10 | | | | | | | | | | % 193.32/27.10 | | | | | | | | | | CLOSE: (1078) is inconsistent. % 193.32/27.10 | | | | | | | | | | % 193.32/27.10 | | | | | | | | | Case 2: % 193.32/27.10 | | | | | | | | | | % 193.32/27.10 | | | | | | | | | | (1079) ~ (all_872_8 = v_x) % 193.32/27.10 | | | | | | | | | | (1080) ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 193.32/27.10 | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.10 | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, % 193.32/27.10 | | | | | | | | | | v_x) = v1 & c_member(all_676_0, v1, v_L) = v2 % 193.32/27.10 | | | | | | | | | | & c_member(all_676_0, all_872_1, v_L) = v0 & % 193.32/27.10 | | | | | | | | | | $i(v1) & (v2 = 0 | v0 = 0)) % 193.32/27.10 | | | | | | | | | | % 193.32/27.10 | | | | | | | | | | DELTA: instantiating (1080) with fresh symbols all_1163_0, % 193.32/27.10 | | | | | | | | | | all_1163_1, all_1163_2 gives: % 193.32/27.10 | | | | | | | | | | (1081) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.10 | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v_x) % 193.32/27.10 | | | | | | | | | | = all_1163_1 & c_member(all_676_0, all_1163_1, % 193.32/27.10 | | | | | | | | | | v_L) = all_1163_0 & c_member(all_676_0, % 193.32/27.10 | | | | | | | | | | all_872_1, v_L) = all_1163_2 & $i(all_1163_1) & % 193.32/27.10 | | | | | | | | | | (all_1163_0 = 0 | all_1163_2 = 0) % 193.32/27.10 | | | | | | | | | | % 193.32/27.10 | | | | | | | | | | ALPHA: (1081) implies: % 193.32/27.10 | | | | | | | | | | (1082) c_member(all_676_0, all_872_1, v_L) = all_1163_2 % 193.32/27.10 | | | | | | | | | | (1083) c_member(all_676_0, all_1163_1, v_L) = all_1163_0 % 193.32/27.10 | | | | | | | | | | (1084) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.10 | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v_x) % 193.32/27.10 | | | | | | | | | | = all_1163_1 % 193.32/27.10 | | | | | | | | | | (1085) all_1163_0 = 0 | all_1163_2 = 0 % 193.32/27.10 | | | | | | | | | | % 193.32/27.10 | | | | | | | | | | REDUCE: (1059), (1079) imply: % 193.32/27.10 | | | | | | | | | | (1086) ~ (v_x = v_y) % 193.32/27.10 | | | | | | | | | | % 193.32/27.10 | | | | | | | | | | REDUCE: (1059), (1084) imply: % 193.32/27.10 | | | | | | | | | | (1087) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.10 | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v_x) = % 193.32/27.10 | | | | | | | | | | all_1163_1 % 193.32/27.10 | | | | | | | | | | % 193.32/27.10 | | | | | | | | | | REDUCE: (89), (1083) imply: % 193.32/27.10 | | | | | | | | | | (1088) c_member(all_622_1, all_1163_1, v_L) = all_1163_0 % 193.32/27.10 | | | | | | | | | | % 193.32/27.10 | | | | | | | | | | REDUCE: (89), (1082) imply: % 193.32/27.10 | | | | | | | | | | (1089) c_member(all_622_1, all_872_1, v_L) = all_1163_2 % 193.32/27.10 | | | | | | | | | | % 193.32/27.10 | | | | | | | | | | BETA: splitting (198) gives: % 193.32/27.10 | | | | | | | | | | % 193.32/27.10 | | | | | | | | | | Case 1: % 193.32/27.10 | | | | | | | | | | | % 193.32/27.10 | | | | | | | | | | | (1090) all_872_8 = v_x % 193.32/27.10 | | | | | | | | | | | % 193.32/27.10 | | | | | | | | | | | COMBINE_EQS: (1059), (1090) imply: % 193.32/27.10 | | | | | | | | | | | (1091) v_x = v_y % 193.32/27.10 | | | | | | | | | | | % 193.32/27.10 | | | | | | | | | | | REDUCE: (13), (1091) imply: % 193.32/27.10 | | | | | | | | | | | (1092) $false % 193.32/27.10 | | | | | | | | | | | % 193.32/27.10 | | | | | | | | | | | CLOSE: (1092) is inconsistent. % 193.32/27.10 | | | | | | | | | | | % 193.32/27.10 | | | | | | | | | | Case 2: % 193.32/27.10 | | | | | | | | | | | % 193.32/27.10 | | | | | | | | | | | (1093) ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 193.32/27.10 | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.10 | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, % 193.32/27.10 | | | | | | | | | | | all_872_8) = v1 & c_member(all_676_0, v1, v_L) % 193.32/27.10 | | | | | | | | | | | = v2 & c_member(all_676_0, all_872_3, v_L) = v0 % 193.32/27.10 | | | | | | | | | | | & $i(v1) & (v2 = 0 | v0 = 0)) % 193.32/27.10 | | | | | | | | | | | % 193.32/27.10 | | | | | | | | | | | DELTA: instantiating (1093) with fresh symbols all_1174_0, % 193.32/27.10 | | | | | | | | | | | all_1174_1, all_1174_2 gives: % 193.32/27.10 | | | | | | | | | | | (1094) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.10 | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, all_872_8) % 193.32/27.10 | | | | | | | | | | | = all_1174_1 & c_member(all_676_0, all_1174_1, % 193.32/27.10 | | | | | | | | | | | v_L) = all_1174_0 & c_member(all_676_0, % 193.32/27.10 | | | | | | | | | | | all_872_3, v_L) = all_1174_2 & $i(all_1174_1) & % 193.32/27.10 | | | | | | | | | | | (all_1174_0 = 0 | all_1174_2 = 0) % 193.32/27.10 | | | | | | | | | | | % 193.32/27.10 | | | | | | | | | | | ALPHA: (1094) implies: % 193.32/27.10 | | | | | | | | | | | (1095) c_member(all_676_0, all_872_3, v_L) = all_1174_2 % 193.32/27.10 | | | | | | | | | | | % 193.32/27.10 | | | | | | | | | | | REDUCE: (89), (1095) imply: % 193.32/27.10 | | | | | | | | | | | (1096) c_member(all_622_1, all_872_3, v_L) = all_1174_2 % 193.32/27.10 | | | | | | | | | | | % 193.32/27.10 | | | | | | | | | | | GROUND_INST: instantiating (20) with all_872_2, all_1174_2, % 193.32/27.10 | | | | | | | | | | | v_L, all_872_3, all_622_1, simplifying with (185), % 193.32/27.10 | | | | | | | | | | | (1096) gives: % 193.32/27.10 | | | | | | | | | | | (1097) all_1174_2 = all_872_2 % 193.32/27.10 | | | | | | | | | | | % 193.32/27.10 | | | | | | | | | | | GROUND_INST: instantiating (20) with all_872_0, all_1163_2, % 193.32/27.10 | | | | | | | | | | | v_L, all_872_1, all_622_1, simplifying with (184), % 193.32/27.10 | | | | | | | | | | | (1089) gives: % 193.32/27.10 | | | | | | | | | | | (1098) all_1163_2 = all_872_0 % 193.32/27.10 | | | | | | | | | | | % 193.32/27.10 | | | | | | | | | | | GROUND_INST: instantiating (21) with all_872_3, all_1163_1, % 193.32/27.10 | | | | | | | | | | | v_x, v_y, tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.10 | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with % 193.32/27.10 | | | | | | | | | | | (1069), (1087) gives: % 193.32/27.10 | | | | | | | | | | | (1099) all_1163_1 = all_872_3 % 193.32/27.10 | | | | | | | | | | | % 193.32/27.10 | | | | | | | | | | | REDUCE: (1088), (1099) imply: % 193.32/27.10 | | | | | | | | | | | (1100) c_member(all_622_1, all_872_3, v_L) = all_1163_0 % 193.32/27.10 | | | | | | | | | | | % 193.32/27.10 | | | | | | | | | | | BETA: splitting (1085) gives: % 193.32/27.10 | | | | | | | | | | | % 193.32/27.10 | | | | | | | | | | | Case 1: % 193.32/27.10 | | | | | | | | | | | | % 193.32/27.10 | | | | | | | | | | | | (1101) all_1163_0 = 0 % 193.32/27.10 | | | | | | | | | | | | % 193.32/27.10 | | | | | | | | | | | | REDUCE: (1100), (1101) imply: % 193.32/27.10 | | | | | | | | | | | | (1102) c_member(all_622_1, all_872_3, v_L) = 0 % 193.32/27.10 | | | | | | | | | | | | % 193.32/27.10 | | | | | | | | | | | | GROUND_INST: instantiating (20) with all_872_2, 0, v_L, % 193.32/27.10 | | | | | | | | | | | | all_872_3, all_622_1, simplifying with (185), % 193.32/27.10 | | | | | | | | | | | | (1102) gives: % 193.32/27.10 | | | | | | | | | | | | (1103) all_872_2 = 0 % 193.32/27.10 | | | | | | | | | | | | % 193.32/27.10 | | | | | | | | | | | | GROUND_INST: instantiating (fact_antisymD) with all_872_9, v_x, % 193.32/27.10 | | | | | | | | | | | | v_L, tc_Arrow__Order__Mirabelle_Oalt, all_622_1, % 193.32/27.10 | | | | | | | | | | | | all_872_5, simplifying with (15), (16), (17), % 193.32/27.10 | | | | | | | | | | | | (23), (169), (180), (1072) gives: % 193.32/27.11 | | | | | | | | | | | | (1104) all_872_9 = v_x | ? [v0: any] : ? [v1: $i] : ? % 193.32/27.11 | | | | | | | | | | | | [v2: any] : % 193.32/27.11 | | | | | | | | | | | | (c_Relation_Oantisym(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.11 | | | | | | | | | | | | v_L) = v0 & % 193.32/27.11 | | | | | | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.11 | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, % 193.32/27.11 | | | | | | | | | | | | all_872_9) = v1 & c_member(all_622_1, v1, v_L) % 193.32/27.11 | | | | | | | | | | | | = v2 & $i(v1) & ( ~ (v2 = 0) | ~ (v0 = 0))) % 193.32/27.11 | | | | | | | | | | | | % 193.32/27.11 | | | | | | | | | | | | GROUND_INST: instantiating (44) with v_y, v_x, all_872_3, % 193.32/27.11 | | | | | | | | | | | | simplifying with (16), (1069), (1073) gives: % 193.32/27.11 | | | | | | | | | | | | (1105) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_676_0, % 193.32/27.11 | | | | | | | | | | | | all_872_3, v_L) = v0) | ! [v0: $i] : ! [v1: % 193.32/27.11 | | | | | | | | | | | | $i] : ( ~ % 193.32/27.11 | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.11 | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = % 193.32/27.11 | | | | | | | | | | | | v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: any] : % 193.32/27.11 | | | | | | | | | | | | ? [v4: any] : % 193.32/27.11 | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.11 | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v0) = % 193.32/27.11 | | | | | | | | | | | | v2 & c_member(all_676_0, v2, v_L) = v3 & % 193.32/27.11 | | | | | | | | | | | | c_member(all_676_0, v1, v_L) = v4 & $i(v2) & ( % 193.32/27.11 | | | | | | | | | | | | ~ (v3 = 0) | v4 = 0))) % 193.32/27.11 | | | | | | | | | | | | % 193.32/27.11 | | | | | | | | | | | | GROUND_INST: instantiating (44) with v_x, all_1143_3, % 193.32/27.11 | | | | | | | | | | | | all_1143_2, simplifying with (16), (1064), (1067) % 193.32/27.11 | | | | | | | | | | | | gives: % 193.32/27.11 | | | | | | | | | | | | (1106) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_676_0, % 193.32/27.11 | | | | | | | | | | | | all_1143_2, v_L) = v0) | ! [v0: $i] : ! [v1: % 193.32/27.11 | | | | | | | | | | | | $i] : ( ~ % 193.32/27.11 | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.11 | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v0) = % 193.32/27.11 | | | | | | | | | | | | v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: any] : % 193.32/27.11 | | | | | | | | | | | | ? [v4: any] : % 193.32/27.11 | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.11 | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_1143_3, % 193.32/27.11 | | | | | | | | | | | | v0) = v2 & c_member(all_676_0, v2, v_L) = v3 % 193.32/27.11 | | | | | | | | | | | | & c_member(all_676_0, v1, v_L) = v4 & $i(v2) & % 193.32/27.11 | | | | | | | | | | | | ( ~ (v3 = 0) | v4 = 0))) % 193.32/27.11 | | | | | | | | | | | | % 193.32/27.11 | | | | | | | | | | | | GROUND_INST: instantiating (1023) with all_1143_3, all_1143_1, % 193.32/27.11 | | | | | | | | | | | | simplifying with (1064), (1068) gives: % 193.32/27.11 | | | | | | | | | | | | (1107) ? [v0: $i] : ? [v1: any] : ? [v2: any] : % 193.32/27.11 | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.11 | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, % 193.32/27.11 | | | | | | | | | | | | all_1143_3) = v0 & c_member(all_676_0, v0, % 193.32/27.11 | | | | | | | | | | | | v_L) = v1 & c_member(all_676_0, all_1143_1, % 193.32/27.11 | | | | | | | | | | | | v_L) = v2 & $i(v0) & ( ~ (v1 = 0) | v2 = 0)) % 193.32/27.11 | | | | | | | | | | | | % 193.32/27.11 | | | | | | | | | | | | DELTA: instantiating (1107) with fresh symbols % 193.32/27.11 | | | | | | | | | | | | all_1249_0, all_1249_1, all_1249_2 gives: % 193.32/27.11 | | | | | | | | | | | | (1108) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.11 | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, % 193.32/27.11 | | | | | | | | | | | | all_1143_3) = all_1249_2 & c_member(all_676_0, % 193.32/27.11 | | | | | | | | | | | | all_1249_2, v_L) = all_1249_1 & % 193.32/27.11 | | | | | | | | | | | | c_member(all_676_0, all_1143_1, v_L) = all_1249_0 % 193.32/27.11 | | | | | | | | | | | | & $i(all_1249_2) & ( ~ (all_1249_1 = 0) | % 193.32/27.11 | | | | | | | | | | | | all_1249_0 = 0) % 193.32/27.11 | | | | | | | | | | | | % 193.32/27.11 | | | | | | | | | | | | ALPHA: (1108) implies: % 193.32/27.11 | | | | | | | | | | | | (1109) c_member(all_676_0, all_1143_1, v_L) = all_1249_0 % 193.32/27.11 | | | | | | | | | | | | (1110) c_member(all_676_0, all_1249_2, v_L) = all_1249_1 % 193.32/27.11 | | | | | | | | | | | | (1111) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.11 | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, % 193.32/27.11 | | | | | | | | | | | | all_1143_3) = all_1249_2 % 193.32/27.11 | | | | | | | | | | | | (1112) ~ (all_1249_1 = 0) | all_1249_0 = 0 % 193.32/27.11 | | | | | | | | | | | | % 193.32/27.11 | | | | | | | | | | | | REDUCE: (89), (1110) imply: % 193.32/27.11 | | | | | | | | | | | | (1113) c_member(all_622_1, all_1249_2, v_L) = all_1249_1 % 193.32/27.11 | | | | | | | | | | | | % 193.32/27.11 | | | | | | | | | | | | REDUCE: (89), (1109) imply: % 193.32/27.11 | | | | | | | | | | | | (1114) c_member(all_622_1, all_1143_1, v_L) = all_1249_0 % 193.32/27.11 | | | | | | | | | | | | % 193.32/27.11 | | | | | | | | | | | | BETA: splitting (1106) gives: % 193.32/27.11 | | | | | | | | | | | | % 193.32/27.11 | | | | | | | | | | | | Case 1: % 193.32/27.11 | | | | | | | | | | | | | % 193.32/27.11 | | | | | | | | | | | | | (1115) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_676_0, % 193.32/27.11 | | | | | | | | | | | | | all_1143_2, v_L) = v0) % 193.32/27.11 | | | | | | | | | | | | | % 193.32/27.11 | | | | | | | | | | | | | DELTA: instantiating (1115) with fresh symbol all_1263_0 % 193.32/27.11 | | | | | | | | | | | | | gives: % 193.32/27.11 | | | | | | | | | | | | | (1116) ~ (all_1263_0 = 0) & c_member(all_676_0, % 193.32/27.11 | | | | | | | | | | | | | all_1143_2, v_L) = all_1263_0 % 193.32/27.11 | | | | | | | | | | | | | % 193.32/27.11 | | | | | | | | | | | | | ALPHA: (1116) implies: % 193.32/27.11 | | | | | | | | | | | | | (1117) ~ (all_1263_0 = 0) % 193.32/27.11 | | | | | | | | | | | | | (1118) c_member(all_676_0, all_1143_2, v_L) = all_1263_0 % 193.32/27.11 | | | | | | | | | | | | | % 193.32/27.11 | | | | | | | | | | | | | REDUCE: (89), (1118) imply: % 193.32/27.11 | | | | | | | | | | | | | (1119) c_member(all_622_1, all_1143_2, v_L) = all_1263_0 % 193.32/27.11 | | | | | | | | | | | | | % 193.32/27.11 | | | | | | | | | | | | | GROUND_INST: instantiating (20) with 0, all_1263_0, v_L, % 193.32/27.11 | | | | | | | | | | | | | all_1143_2, all_622_1, simplifying with (1071), % 193.32/27.11 | | | | | | | | | | | | | (1119) gives: % 193.32/27.11 | | | | | | | | | | | | | (1120) all_1263_0 = 0 % 193.32/27.11 | | | | | | | | | | | | | % 193.32/27.11 | | | | | | | | | | | | | REDUCE: (1117), (1120) imply: % 193.32/27.11 | | | | | | | | | | | | | (1121) $false % 193.32/27.11 | | | | | | | | | | | | | % 193.32/27.11 | | | | | | | | | | | | | CLOSE: (1121) is inconsistent. % 193.32/27.11 | | | | | | | | | | | | | % 193.32/27.11 | | | | | | | | | | | | Case 2: % 193.32/27.11 | | | | | | | | | | | | | % 193.32/27.11 | | | | | | | | | | | | | (1122) ! [v0: $i] : ! [v1: $i] : ( ~ % 193.32/27.11 | | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.11 | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v0) = % 193.32/27.11 | | | | | | | | | | | | | v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: any] : % 193.32/27.11 | | | | | | | | | | | | | ? [v4: any] : % 193.32/27.11 | | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.11 | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_1143_3, % 193.32/27.11 | | | | | | | | | | | | | v0) = v2 & c_member(all_676_0, v2, v_L) = v3 % 193.32/27.11 | | | | | | | | | | | | | & c_member(all_676_0, v1, v_L) = v4 & $i(v2) & % 193.32/27.11 | | | | | | | | | | | | | ( ~ (v3 = 0) | v4 = 0))) % 193.32/27.11 | | | | | | | | | | | | | % 193.32/27.11 | | | | | | | | | | | | | GROUND_INST: instantiating (1122) with all_1143_3, all_1143_2, % 193.32/27.11 | | | | | | | | | | | | | simplifying with (1064), (1067) gives: % 193.32/27.11 | | | | | | | | | | | | | (1123) ? [v0: $i] : ? [v1: any] : ? [v2: any] : % 193.32/27.11 | | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.11 | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_1143_3, % 193.32/27.11 | | | | | | | | | | | | | all_1143_3) = v0 & c_member(all_676_0, v0, % 193.32/27.11 | | | | | | | | | | | | | v_L) = v1 & c_member(all_676_0, all_1143_2, % 193.32/27.11 | | | | | | | | | | | | | v_L) = v2 & $i(v0) & ( ~ (v1 = 0) | v2 = 0)) % 193.32/27.11 | | | | | | | | | | | | | % 193.32/27.11 | | | | | | | | | | | | | BETA: splitting (1105) gives: % 193.32/27.11 | | | | | | | | | | | | | % 193.32/27.11 | | | | | | | | | | | | | Case 1: % 193.32/27.11 | | | | | | | | | | | | | | % 193.32/27.11 | | | | | | | | | | | | | | (1124) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_676_0, % 193.32/27.11 | | | | | | | | | | | | | | all_872_3, v_L) = v0) % 193.32/27.11 | | | | | | | | | | | | | | % 193.32/27.11 | | | | | | | | | | | | | | DELTA: instantiating (1124) with fresh symbol all_1264_0 % 193.32/27.11 | | | | | | | | | | | | | | gives: % 193.32/27.11 | | | | | | | | | | | | | | (1125) ~ (all_1264_0 = 0) & c_member(all_676_0, % 193.32/27.11 | | | | | | | | | | | | | | all_872_3, v_L) = all_1264_0 % 193.32/27.11 | | | | | | | | | | | | | | % 193.32/27.11 | | | | | | | | | | | | | | ALPHA: (1125) implies: % 193.32/27.11 | | | | | | | | | | | | | | (1126) ~ (all_1264_0 = 0) % 193.32/27.11 | | | | | | | | | | | | | | (1127) c_member(all_676_0, all_872_3, v_L) = all_1264_0 % 193.32/27.11 | | | | | | | | | | | | | | % 193.32/27.11 | | | | | | | | | | | | | | REDUCE: (89), (1127) imply: % 193.32/27.11 | | | | | | | | | | | | | | (1128) c_member(all_622_1, all_872_3, v_L) = all_1264_0 % 193.32/27.11 | | | | | | | | | | | | | | % 193.32/27.11 | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with 0, all_1264_0, v_L, % 193.32/27.11 | | | | | | | | | | | | | | all_872_3, all_622_1, simplifying with (1102), % 193.32/27.11 | | | | | | | | | | | | | | (1128) gives: % 193.32/27.11 | | | | | | | | | | | | | | (1129) all_1264_0 = 0 % 193.32/27.11 | | | | | | | | | | | | | | % 193.32/27.11 | | | | | | | | | | | | | | REDUCE: (1126), (1129) imply: % 193.32/27.11 | | | | | | | | | | | | | | (1130) $false % 193.32/27.11 | | | | | | | | | | | | | | % 193.32/27.11 | | | | | | | | | | | | | | CLOSE: (1130) is inconsistent. % 193.32/27.11 | | | | | | | | | | | | | | % 193.32/27.11 | | | | | | | | | | | | | Case 2: % 193.32/27.11 | | | | | | | | | | | | | | % 193.32/27.11 | | | | | | | | | | | | | | % 193.32/27.11 | | | | | | | | | | | | | | DELTA: instantiating (1123) with fresh symbols % 193.32/27.11 | | | | | | | | | | | | | | all_1267_0, all_1267_1, all_1267_2 gives: % 193.32/27.11 | | | | | | | | | | | | | | (1131) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.11 | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_1143_3, % 193.32/27.11 | | | | | | | | | | | | | | all_1143_3) = all_1267_2 & c_member(all_676_0, % 193.32/27.11 | | | | | | | | | | | | | | all_1267_2, v_L) = all_1267_1 & % 193.32/27.11 | | | | | | | | | | | | | | c_member(all_676_0, all_1143_2, v_L) = all_1267_0 % 193.32/27.11 | | | | | | | | | | | | | | & $i(all_1267_2) & ( ~ (all_1267_1 = 0) | % 193.32/27.11 | | | | | | | | | | | | | | all_1267_0 = 0) % 193.32/27.11 | | | | | | | | | | | | | | % 193.32/27.11 | | | | | | | | | | | | | | ALPHA: (1131) implies: % 193.32/27.11 | | | | | | | | | | | | | | (1132) c_member(all_676_0, all_1143_2, v_L) = all_1267_0 % 193.32/27.11 | | | | | | | | | | | | | | % 193.32/27.11 | | | | | | | | | | | | | | REDUCE: (89), (1132) imply: % 193.32/27.11 | | | | | | | | | | | | | | (1133) c_member(all_622_1, all_1143_2, v_L) = all_1267_0 % 193.32/27.11 | | | | | | | | | | | | | | % 193.32/27.11 | | | | | | | | | | | | | | BETA: splitting (1104) gives: % 193.32/27.11 | | | | | | | | | | | | | | % 193.32/27.11 | | | | | | | | | | | | | | Case 1: % 193.32/27.11 | | | | | | | | | | | | | | | % 193.32/27.11 | | | | | | | | | | | | | | | (1134) all_872_9 = v_x % 193.32/27.11 | | | | | | | | | | | | | | | % 193.32/27.11 | | | | | | | | | | | | | | | REDUCE: (1045), (1134) imply: % 193.32/27.11 | | | | | | | | | | | | | | | (1135) $false % 193.32/27.11 | | | | | | | | | | | | | | | % 193.32/27.11 | | | | | | | | | | | | | | | CLOSE: (1135) is inconsistent. % 193.32/27.11 | | | | | | | | | | | | | | | % 193.32/27.11 | | | | | | | | | | | | | | Case 2: % 193.32/27.11 | | | | | | | | | | | | | | | % 193.32/27.11 | | | | | | | | | | | | | | | % 193.32/27.11 | | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with 0, all_1267_0, v_L, % 193.32/27.11 | | | | | | | | | | | | | | | all_1143_2, all_622_1, simplifying with (1071), % 193.32/27.11 | | | | | | | | | | | | | | | (1133) gives: % 193.32/27.11 | | | | | | | | | | | | | | | (1136) all_1267_0 = 0 % 193.32/27.11 | | | | | | | | | | | | | | | % 193.32/27.11 | | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with all_1143_0, all_1249_0, % 193.32/27.11 | | | | | | | | | | | | | | | v_L, all_1143_1, all_622_1, simplifying with % 193.32/27.11 | | | | | | | | | | | | | | | (1070), (1114) gives: % 193.32/27.11 | | | | | | | | | | | | | | | (1137) all_1249_0 = all_1143_0 % 193.32/27.11 | | | | | | | | | | | | | | | % 193.32/27.11 | | | | | | | | | | | | | | | GROUND_INST: instantiating (21) with all_1143_2, all_1249_2, % 193.32/27.11 | | | | | | | | | | | | | | | all_1143_3, v_x, tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.11 | | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with % 193.32/27.11 | | | | | | | | | | | | | | | (1067), (1111) gives: % 193.32/27.11 | | | | | | | | | | | | | | | (1138) all_1249_2 = all_1143_2 % 193.32/27.11 | | | | | | | | | | | | | | | % 193.32/27.11 | | | | | | | | | | | | | | | REDUCE: (1113), (1138) imply: % 193.32/27.11 | | | | | | | | | | | | | | | (1139) c_member(all_622_1, all_1143_2, v_L) = all_1249_1 % 193.32/27.11 | | | | | | | | | | | | | | | % 193.32/27.11 | | | | | | | | | | | | | | | BETA: splitting (1112) gives: % 193.32/27.11 | | | | | | | | | | | | | | | % 193.32/27.11 | | | | | | | | | | | | | | | Case 1: % 193.32/27.11 | | | | | | | | | | | | | | | | % 193.32/27.11 | | | | | | | | | | | | | | | | (1140) ~ (all_1249_1 = 0) % 193.32/27.11 | | | | | | | | | | | | | | | | % 193.32/27.11 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with 0, all_1249_1, v_L, % 193.32/27.11 | | | | | | | | | | | | | | | | all_1143_2, all_622_1, simplifying with (1071), % 193.32/27.11 | | | | | | | | | | | | | | | | (1139) gives: % 193.32/27.11 | | | | | | | | | | | | | | | | (1141) all_1249_1 = 0 % 193.32/27.11 | | | | | | | | | | | | | | | | % 193.32/27.11 | | | | | | | | | | | | | | | | REDUCE: (1140), (1141) imply: % 193.32/27.11 | | | | | | | | | | | | | | | | (1142) $false % 193.32/27.11 | | | | | | | | | | | | | | | | % 193.32/27.11 | | | | | | | | | | | | | | | | CLOSE: (1142) is inconsistent. % 193.32/27.11 | | | | | | | | | | | | | | | | % 193.32/27.11 | | | | | | | | | | | | | | | Case 2: % 193.32/27.11 | | | | | | | | | | | | | | | | % 193.32/27.11 | | | | | | | | | | | | | | | | (1143) all_1249_0 = 0 % 193.32/27.11 | | | | | | | | | | | | | | | | % 193.32/27.11 | | | | | | | | | | | | | | | | COMBINE_EQS: (1137), (1143) imply: % 193.32/27.11 | | | | | | | | | | | | | | | | (1144) all_1143_0 = 0 % 193.32/27.11 | | | | | | | | | | | | | | | | % 193.32/27.11 | | | | | | | | | | | | | | | | REDUCE: (1063), (1144) imply: % 193.32/27.11 | | | | | | | | | | | | | | | | (1145) $false % 193.32/27.11 | | | | | | | | | | | | | | | | % 193.32/27.11 | | | | | | | | | | | | | | | | CLOSE: (1145) is inconsistent. % 193.32/27.11 | | | | | | | | | | | | | | | | % 193.32/27.11 | | | | | | | | | | | | | | | End of split % 193.32/27.11 | | | | | | | | | | | | | | | % 193.32/27.11 | | | | | | | | | | | | | | End of split % 193.32/27.11 | | | | | | | | | | | | | | % 193.32/27.11 | | | | | | | | | | | | | End of split % 193.32/27.11 | | | | | | | | | | | | | % 193.32/27.11 | | | | | | | | | | | | End of split % 193.32/27.11 | | | | | | | | | | | | % 193.32/27.11 | | | | | | | | | | | Case 2: % 193.32/27.11 | | | | | | | | | | | | % 193.32/27.11 | | | | | | | | | | | | (1146) all_1163_2 = 0 % 193.32/27.11 | | | | | | | | | | | | % 193.32/27.11 | | | | | | | | | | | | COMBINE_EQS: (1098), (1146) imply: % 193.32/27.11 | | | | | | | | | | | | (1147) all_872_0 = 0 % 193.32/27.11 | | | | | | | | | | | | % 193.32/27.11 | | | | | | | | | | | | REDUCE: (1075), (1147) imply: % 193.32/27.11 | | | | | | | | | | | | (1148) $false % 193.32/27.11 | | | | | | | | | | | | % 193.32/27.11 | | | | | | | | | | | | CLOSE: (1148) is inconsistent. % 193.32/27.11 | | | | | | | | | | | | % 193.32/27.11 | | | | | | | | | | | End of split % 193.32/27.11 | | | | | | | | | | | % 193.32/27.11 | | | | | | | | | | End of split % 193.32/27.11 | | | | | | | | | | % 193.32/27.11 | | | | | | | | | End of split % 193.32/27.11 | | | | | | | | | % 193.32/27.11 | | | | | | | | Case 2: % 193.32/27.11 | | | | | | | | | % 193.32/27.11 | | | | | | | | | (1149) all_1104_0 = 0 % 193.32/27.11 | | | | | | | | | % 193.32/27.11 | | | | | | | | | COMBINE_EQS: (1037), (1149) imply: % 193.32/27.11 | | | | | | | | | (1150) all_872_6 = 0 % 193.32/27.11 | | | | | | | | | % 193.32/27.11 | | | | | | | | | SIMP: (1150) implies: % 193.32/27.11 | | | | | | | | | (1151) all_872_6 = 0 % 193.32/27.11 | | | | | | | | | % 193.32/27.11 | | | | | | | | | REDUCE: (1057), (1151) imply: % 193.32/27.11 | | | | | | | | | (1152) $false % 193.32/27.11 | | | | | | | | | % 193.32/27.11 | | | | | | | | | CLOSE: (1152) is inconsistent. % 193.32/27.11 | | | | | | | | | % 193.32/27.11 | | | | | | | | End of split % 193.32/27.11 | | | | | | | | % 193.32/27.11 | | | | | | | Case 2: % 193.32/27.11 | | | | | | | | % 193.32/27.12 | | | | | | | | (1153) all_872_6 = 0 & ~ (all_872_8 = v_y) & ? [v0: $i] : % 193.32/27.12 | | | | | | | | ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ? [v4: any] % 193.32/27.12 | | | | | | | | : % 193.32/27.12 | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.12 | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v0) = % 193.32/27.12 | | | | | | | | v1 & % 193.32/27.12 | | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.12 | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v0) = % 193.32/27.12 | | | | | | | | v3 & c_member(all_685_0, v3, v_L) = v4 & % 193.32/27.12 | | | | | | | | c_member(all_685_0, v1, v_L) = v2 & $i(v3) & $i(v1) % 193.32/27.12 | | | | | | | | & $i(v0) & ((v2 = 0 & ~ (v4 = 0) & ~ (v0 = v_y)) | % 193.32/27.12 | | | | | | | | (v0 = v_y & all_872_2 = 0 & ~ (all_872_4 = 0) & % 193.32/27.12 | | | | | | | | ~ (all_872_9 = v_x)) | (v0 = v_y & all_872_8 = % 193.32/27.12 | | | | | | | | v_x & ~ (all_872_4 = 0) & ~ (all_872_9 = % 193.32/27.12 | | | | | | | | v_x)))) % 193.32/27.12 | | | | | | | | % 193.32/27.12 | | | | | | | | ALPHA: (1153) implies: % 193.32/27.12 | | | | | | | | (1154) all_872_6 = 0 % 193.32/27.12 | | | | | | | | % 193.32/27.12 | | | | | | | | REDUCE: (1057), (1154) imply: % 193.32/27.12 | | | | | | | | (1155) $false % 193.32/27.12 | | | | | | | | % 193.32/27.12 | | | | | | | | CLOSE: (1155) is inconsistent. % 193.32/27.12 | | | | | | | | % 193.32/27.12 | | | | | | | End of split % 193.32/27.12 | | | | | | | % 193.32/27.12 | | | | | | Case 2: % 193.32/27.12 | | | | | | | % 193.32/27.12 | | | | | | | (1156) ! [v0: $i] : ! [v1: $i] : ( ~ % 193.32/27.12 | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.12 | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v0) = % 193.32/27.12 | | | | | | | v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: any] : ? % 193.32/27.12 | | | | | | | [v4: any] : % 193.32/27.12 | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.12 | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v0) = % 193.32/27.12 | | | | | | | v2 & c_member(all_676_0, v2, v_L) = v3 & % 193.32/27.12 | | | | | | | c_member(all_676_0, v1, v_L) = v4 & $i(v2) & ( ~ (v3 % 193.32/27.12 | | | | | | | = 0) | v4 = 0))) % 193.32/27.12 | | | | | | | % 193.32/27.12 | | | | | | | GROUND_INST: instantiating (1156) with v_x, all_872_5, simplifying % 193.32/27.12 | | | | | | | with (16), (180) gives: % 193.32/27.12 | | | | | | | (1157) ? [v0: $i] : ? [v1: any] : ? [v2: any] : % 193.32/27.12 | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.12 | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v_x) = % 193.32/27.12 | | | | | | | v0 & c_member(all_676_0, v0, v_L) = v1 & % 193.32/27.12 | | | | | | | c_member(all_676_0, all_872_5, v_L) = v2 & $i(v0) & ( % 193.32/27.12 | | | | | | | ~ (v1 = 0) | v2 = 0)) % 193.32/27.12 | | | | | | | % 193.32/27.12 | | | | | | | GROUND_INST: instantiating (1156) with all_872_8, all_872_7, % 193.32/27.12 | | | | | | | simplifying with (170), (181) gives: % 193.32/27.12 | | | | | | | (1158) ? [v0: $i] : ? [v1: any] : ? [v2: any] : % 193.32/27.12 | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.12 | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, % 193.32/27.12 | | | | | | | all_872_8) = v0 & c_member(all_676_0, v0, v_L) = v1 % 193.32/27.12 | | | | | | | & c_member(all_676_0, all_872_7, v_L) = v2 & $i(v0) & % 193.32/27.12 | | | | | | | ( ~ (v1 = 0) | v2 = 0)) % 193.32/27.12 | | | | | | | % 193.32/27.12 | | | | | | | DELTA: instantiating (1158) with fresh symbols all_1134_0, % 193.32/27.12 | | | | | | | all_1134_1, all_1134_2 gives: % 193.32/27.12 | | | | | | | (1159) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.12 | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, all_872_8) % 193.32/27.12 | | | | | | | = all_1134_2 & c_member(all_676_0, all_1134_2, v_L) = % 193.32/27.12 | | | | | | | all_1134_1 & c_member(all_676_0, all_872_7, v_L) = % 193.32/27.12 | | | | | | | all_1134_0 & $i(all_1134_2) & ( ~ (all_1134_1 = 0) | % 193.32/27.12 | | | | | | | all_1134_0 = 0) % 193.32/27.12 | | | | | | | % 193.32/27.12 | | | | | | | ALPHA: (1159) implies: % 193.32/27.12 | | | | | | | (1160) $i(all_1134_2) % 193.32/27.12 | | | | | | | (1161) c_member(all_676_0, all_872_7, v_L) = all_1134_0 % 193.32/27.12 | | | | | | | (1162) c_member(all_676_0, all_1134_2, v_L) = all_1134_1 % 193.32/27.12 | | | | | | | (1163) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.12 | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, all_872_8) % 193.32/27.12 | | | | | | | = all_1134_2 % 193.32/27.12 | | | | | | | % 193.32/27.12 | | | | | | | DELTA: instantiating (1157) with fresh symbols all_1136_0, % 193.32/27.12 | | | | | | | all_1136_1, all_1136_2 gives: % 193.32/27.12 | | | | | | | (1164) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.12 | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v_x) = % 193.32/27.12 | | | | | | | all_1136_2 & c_member(all_676_0, all_1136_2, v_L) = % 193.32/27.12 | | | | | | | all_1136_1 & c_member(all_676_0, all_872_5, v_L) = % 193.32/27.12 | | | | | | | all_1136_0 & $i(all_1136_2) & ( ~ (all_1136_1 = 0) | % 193.32/27.12 | | | | | | | all_1136_0 = 0) % 193.32/27.12 | | | | | | | % 193.32/27.12 | | | | | | | ALPHA: (1164) implies: % 193.32/27.12 | | | | | | | (1165) c_member(all_676_0, all_872_5, v_L) = all_1136_0 % 193.32/27.12 | | | | | | | (1166) c_member(all_676_0, all_1136_2, v_L) = all_1136_1 % 193.32/27.12 | | | | | | | (1167) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.12 | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v_x) = % 193.32/27.12 | | | | | | | all_1136_2 % 193.32/27.12 | | | | | | | (1168) ~ (all_1136_1 = 0) | all_1136_0 = 0 % 193.32/27.12 | | | | | | | % 193.32/27.12 | | | | | | | REDUCE: (89), (1166) imply: % 193.32/27.12 | | | | | | | (1169) c_member(all_622_1, all_1136_2, v_L) = all_1136_1 % 193.32/27.12 | | | | | | | % 193.32/27.12 | | | | | | | REDUCE: (89), (1162) imply: % 193.32/27.12 | | | | | | | (1170) c_member(all_622_1, all_1134_2, v_L) = all_1134_1 % 193.32/27.12 | | | | | | | % 193.32/27.12 | | | | | | | REDUCE: (89), (1165) imply: % 193.32/27.12 | | | | | | | (1171) c_member(all_622_1, all_872_5, v_L) = all_1136_0 % 193.32/27.12 | | | | | | | % 193.32/27.12 | | | | | | | REDUCE: (89), (1161) imply: % 193.32/27.12 | | | | | | | (1172) c_member(all_622_1, all_872_7, v_L) = all_1134_0 % 193.32/27.12 | | | | | | | % 193.32/27.12 | | | | | | | GROUND_INST: instantiating (20) with all_872_6, all_1134_0, v_L, % 193.32/27.12 | | | | | | | all_872_7, all_622_1, simplifying with (187), (1172) % 193.32/27.12 | | | | | | | gives: % 193.32/27.12 | | | | | | | (1173) all_1134_0 = all_872_6 % 193.32/27.12 | | | | | | | % 193.32/27.12 | | | | | | | GROUND_INST: instantiating (20) with all_872_4, all_1136_0, v_L, % 193.32/27.12 | | | | | | | all_872_5, all_622_1, simplifying with (186), (1171) % 193.32/27.12 | | | | | | | gives: % 193.32/27.12 | | | | | | | (1174) all_1136_0 = all_872_4 % 193.32/27.12 | | | | | | | % 193.32/27.12 | | | | | | | GROUND_INST: instantiating (21) with all_872_3, all_1136_2, v_x, % 193.32/27.12 | | | | | | | all_872_8, tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.12 | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with % 193.32/27.12 | | | | | | | (182), (1167) gives: % 193.32/27.12 | | | | | | | (1175) all_1136_2 = all_872_3 % 193.32/27.12 | | | | | | | % 193.32/27.12 | | | | | | | REDUCE: (1169), (1175) imply: % 193.32/27.12 | | | | | | | (1176) c_member(all_622_1, all_872_3, v_L) = all_1136_1 % 193.32/27.12 | | | | | | | % 193.32/27.12 | | | | | | | GROUND_INST: instantiating (20) with all_872_2, all_1136_1, v_L, % 193.32/27.12 | | | | | | | all_872_3, all_622_1, simplifying with (185), (1176) % 193.32/27.12 | | | | | | | gives: % 193.32/27.12 | | | | | | | (1177) all_1136_1 = all_872_2 % 193.32/27.12 | | | | | | | % 193.32/27.12 | | | | | | | BETA: splitting (196) gives: % 193.32/27.12 | | | | | | | % 193.32/27.12 | | | | | | | Case 1: % 193.32/27.12 | | | | | | | | % 193.32/27.12 | | | | | | | | (1178) all_872_8 = all_872_9 % 193.32/27.12 | | | | | | | | % 193.32/27.12 | | | | | | | | REDUCE: (182), (1178) imply: % 193.32/27.12 | | | | | | | | (1179) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.12 | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v_x) = % 193.32/27.12 | | | | | | | | all_872_3 % 193.32/27.12 | | | | | | | | % 193.32/27.12 | | | | | | | | REF_CLOSE: (20), (21), (90), (180), (185), (186), (656), (657), % 193.32/27.12 | | | | | | | | (1178), (1179) are inconsistent by sub-proof #5. % 193.32/27.12 | | | | | | | | % 193.32/27.12 | | | | | | | Case 2: % 193.32/27.12 | | | | | | | | % 193.32/27.12 | | | | | | | | (1180) ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 193.32/27.12 | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.12 | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, % 193.32/27.12 | | | | | | | | all_872_9) = v1 & c_member(all_676_0, v1, v_L) = % 193.32/27.12 | | | | | | | | v2 & c_member(all_676_0, all_872_7, v_L) = v0 & % 193.32/27.12 | | | | | | | | $i(v1) & (v2 = 0 | v0 = 0)) % 193.32/27.12 | | | | | | | | % 193.32/27.12 | | | | | | | | DELTA: instantiating (1180) with fresh symbols all_1152_0, % 193.32/27.12 | | | | | | | | all_1152_1, all_1152_2 gives: % 193.32/27.12 | | | | | | | | (1181) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.12 | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, % 193.32/27.12 | | | | | | | | all_872_9) = all_1152_1 & c_member(all_676_0, % 193.32/27.12 | | | | | | | | all_1152_1, v_L) = all_1152_0 & c_member(all_676_0, % 193.32/27.12 | | | | | | | | all_872_7, v_L) = all_1152_2 & $i(all_1152_1) & % 193.32/27.12 | | | | | | | | (all_1152_0 = 0 | all_1152_2 = 0) % 193.32/27.12 | | | | | | | | % 193.32/27.12 | | | | | | | | ALPHA: (1181) implies: % 193.32/27.12 | | | | | | | | (1182) c_member(all_676_0, all_872_7, v_L) = all_1152_2 % 193.32/27.12 | | | | | | | | (1183) c_member(all_676_0, all_1152_1, v_L) = all_1152_0 % 193.32/27.12 | | | | | | | | (1184) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.12 | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, % 193.32/27.12 | | | | | | | | all_872_9) = all_1152_1 % 193.32/27.12 | | | | | | | | (1185) all_1152_0 = 0 | all_1152_2 = 0 % 193.32/27.12 | | | | | | | | % 193.32/27.12 | | | | | | | | REDUCE: (89), (1183) imply: % 193.32/27.12 | | | | | | | | (1186) c_member(all_622_1, all_1152_1, v_L) = all_1152_0 % 193.32/27.12 | | | | | | | | % 193.32/27.12 | | | | | | | | REDUCE: (89), (1182) imply: % 193.32/27.12 | | | | | | | | (1187) c_member(all_622_1, all_872_7, v_L) = all_1152_2 % 193.32/27.12 | | | | | | | | % 193.32/27.12 | | | | | | | | GROUND_INST: instantiating (20) with all_872_6, all_1152_2, v_L, % 193.32/27.12 | | | | | | | | all_872_7, all_622_1, simplifying with (187), % 193.32/27.12 | | | | | | | | (1187) gives: % 193.32/27.12 | | | | | | | | (1188) all_1152_2 = all_872_6 % 193.32/27.12 | | | | | | | | % 193.32/27.12 | | | | | | | | BETA: splitting (193) gives: % 193.32/27.12 | | | | | | | | % 193.32/27.12 | | | | | | | | Case 1: % 193.32/27.12 | | | | | | | | | % 193.32/27.12 | | | | | | | | | (1189) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_676_0, % 193.32/27.12 | | | | | | | | | all_872_1, v_L) = v0) % 193.32/27.12 | | | | | | | | | % 193.32/27.12 | | | | | | | | | DELTA: instantiating (1189) with fresh symbol all_1163_0 % 193.32/27.12 | | | | | | | | | gives: % 193.32/27.12 | | | | | | | | | (1190) ~ (all_1163_0 = 0) & c_member(all_676_0, all_872_1, % 193.32/27.12 | | | | | | | | | v_L) = all_1163_0 % 193.32/27.12 | | | | | | | | | % 193.32/27.12 | | | | | | | | | ALPHA: (1190) implies: % 193.32/27.12 | | | | | | | | | (1191) ~ (all_1163_0 = 0) % 193.32/27.12 | | | | | | | | | (1192) c_member(all_676_0, all_872_1, v_L) = all_1163_0 % 193.32/27.12 | | | | | | | | | % 193.32/27.12 | | | | | | | | | REDUCE: (89), (1192) imply: % 193.32/27.12 | | | | | | | | | (1193) c_member(all_622_1, all_872_1, v_L) = all_1163_0 % 193.32/27.12 | | | | | | | | | % 193.32/27.12 | | | | | | | | | GROUND_INST: instantiating (20) with all_872_0, all_1163_0, % 193.32/27.12 | | | | | | | | | v_L, all_872_1, all_622_1, simplifying with (184), % 193.32/27.12 | | | | | | | | | (1193) gives: % 193.32/27.12 | | | | | | | | | (1194) all_1163_0 = all_872_0 % 193.32/27.12 | | | | | | | | | % 193.32/27.12 | | | | | | | | | REDUCE: (1191), (1194) imply: % 193.32/27.12 | | | | | | | | | (1195) ~ (all_872_0 = 0) % 193.32/27.12 | | | | | | | | | % 193.32/27.12 | | | | | | | | | BETA: splitting (190) gives: % 193.32/27.12 | | | | | | | | | % 193.32/27.12 | | | | | | | | | Case 1: % 193.32/27.12 | | | | | | | | | | % 193.32/27.12 | | | | | | | | | | (1196) all_872_2 = 0 % 193.32/27.12 | | | | | | | | | | % 193.32/27.12 | | | | | | | | | | REDUCE: (185), (1196) imply: % 193.32/27.12 | | | | | | | | | | (1197) c_member(all_622_1, all_872_3, v_L) = 0 % 193.32/27.12 | | | | | | | | | | % 193.32/27.12 | | | | | | | | | | BETA: splitting (188) gives: % 193.32/27.12 | | | | | | | | | | % 193.32/27.12 | | | | | | | | | | Case 1: % 193.32/27.12 | | | | | | | | | | | % 193.32/27.12 | | | | | | | | | | | (1198) all_872_6 = 0 % 193.32/27.12 | | | | | | | | | | | % 193.32/27.12 | | | | | | | | | | | REDUCE: (187), (1198) imply: % 193.32/27.12 | | | | | | | | | | | (1199) c_member(all_622_1, all_872_7, v_L) = 0 % 193.32/27.12 | | | | | | | | | | | % 193.32/27.12 | | | | | | | | | | | GROUND_INST: instantiating (43) with all_872_8, all_1134_2, % 193.32/27.12 | | | | | | | | | | | simplifying with (170), (1163) gives: % 193.32/27.12 | | | | | | | | | | | (1200) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_676_0, % 193.32/27.12 | | | | | | | | | | | all_1134_2, v_L) = v0) % 193.32/27.12 | | | | | | | | | | | % 193.32/27.12 | | | | | | | | | | | DELTA: instantiating (1200) with fresh symbol all_1214_0 % 193.32/27.12 | | | | | | | | | | | gives: % 193.32/27.12 | | | | | | | | | | | (1201) ~ (all_1214_0 = 0) & c_member(all_676_0, % 193.32/27.12 | | | | | | | | | | | all_1134_2, v_L) = all_1214_0 % 193.32/27.12 | | | | | | | | | | | % 193.32/27.12 | | | | | | | | | | | ALPHA: (1201) implies: % 193.32/27.12 | | | | | | | | | | | (1202) ~ (all_1214_0 = 0) % 193.32/27.12 | | | | | | | | | | | (1203) c_member(all_676_0, all_1134_2, v_L) = all_1214_0 % 193.32/27.12 | | | | | | | | | | | % 193.32/27.12 | | | | | | | | | | | REDUCE: (89), (1203) imply: % 193.32/27.12 | | | | | | | | | | | (1204) c_member(all_622_1, all_1134_2, v_L) = all_1214_0 % 193.32/27.12 | | | | | | | | | | | % 193.32/27.12 | | | | | | | | | | | BETA: splitting (657) gives: % 193.32/27.12 | | | | | | | | | | | % 193.32/27.12 | | | | | | | | | | | Case 1: % 193.32/27.12 | | | | | | | | | | | | % 193.32/27.12 | | | | | | | | | | | | (1205) all_872_4 = 0 & all_872_8 = v_y & ? [v0: $i] : ? % 193.32/27.12 | | | | | | | | | | | | [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = % 193.32/27.12 | | | | | | | | | | | | 0) & ~ (v0 = v_y) & % 193.32/27.12 | | | | | | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.12 | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, % 193.32/27.12 | | | | | | | | | | | | v0) = v2 & % 193.32/27.12 | | | | | | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.12 | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v0) = v1 % 193.32/27.12 | | | | | | | | | | | | & c_member(all_685_0, v2, v_L) = v3 & % 193.32/27.12 | | | | | | | | | | | | c_member(all_685_0, v1, v_L) = 0 & $i(v2) & % 193.32/27.12 | | | | | | | | | | | | $i(v1) & $i(v0)) % 193.32/27.12 | | | | | | | | | | | | % 193.32/27.12 | | | | | | | | | | | | ALPHA: (1205) implies: % 193.32/27.13 | | | | | | | | | | | | (1206) all_872_8 = v_y % 193.32/27.13 | | | | | | | | | | | | (1207) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 193.32/27.13 | | | | | | | | | | | | int] : ( ~ (v3 = 0) & ~ (v0 = v_y) & % 193.32/27.13 | | | | | | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.13 | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, % 193.32/27.13 | | | | | | | | | | | | v0) = v2 & % 193.32/27.13 | | | | | | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.13 | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v0) = v1 % 193.32/27.13 | | | | | | | | | | | | & c_member(all_685_0, v2, v_L) = v3 & % 193.32/27.13 | | | | | | | | | | | | c_member(all_685_0, v1, v_L) = 0 & $i(v2) & % 193.32/27.13 | | | | | | | | | | | | $i(v1) & $i(v0)) % 193.32/27.13 | | | | | | | | | | | | % 193.32/27.13 | | | | | | | | | | | | DELTA: instantiating (1207) with fresh symbols % 193.32/27.13 | | | | | | | | | | | | all_1341_0, all_1341_1, all_1341_2, all_1341_3 % 193.32/27.13 | | | | | | | | | | | | gives: % 193.32/27.13 | | | | | | | | | | | | (1208) ~ (all_1341_0 = 0) & ~ (all_1341_3 = v_y) & % 193.32/27.13 | | | | | | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.13 | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, % 193.32/27.13 | | | | | | | | | | | | all_1341_3) = all_1341_1 & % 193.32/27.13 | | | | | | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.13 | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, % 193.32/27.13 | | | | | | | | | | | | all_1341_3) = all_1341_2 & c_member(all_685_0, % 193.32/27.13 | | | | | | | | | | | | all_1341_1, v_L) = all_1341_0 & % 193.32/27.13 | | | | | | | | | | | | c_member(all_685_0, all_1341_2, v_L) = 0 & % 193.32/27.13 | | | | | | | | | | | | $i(all_1341_1) & $i(all_1341_2) & $i(all_1341_3) % 193.32/27.13 | | | | | | | | | | | | % 193.32/27.13 | | | | | | | | | | | | ALPHA: (1208) implies: % 193.32/27.13 | | | | | | | | | | | | (1209) ~ (all_1341_0 = 0) % 193.32/27.13 | | | | | | | | | | | | (1210) $i(all_1341_3) % 193.32/27.13 | | | | | | | | | | | | (1211) c_member(all_685_0, all_1341_2, v_L) = 0 % 193.32/27.13 | | | | | | | | | | | | (1212) c_member(all_685_0, all_1341_1, v_L) = all_1341_0 % 193.32/27.13 | | | | | | | | | | | | (1213) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.13 | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, % 193.32/27.13 | | | | | | | | | | | | all_1341_3) = all_1341_2 % 193.32/27.13 | | | | | | | | | | | | (1214) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.13 | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, % 193.32/27.13 | | | | | | | | | | | | all_1341_3) = all_1341_1 % 193.32/27.13 | | | | | | | | | | | | % 193.32/27.13 | | | | | | | | | | | | REDUCE: (181), (1206) imply: % 193.32/27.13 | | | | | | | | | | | | (1215) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 193.32/27.13 | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v_y) % 193.32/27.13 | | | | | | | | | | | | = all_872_7 % 193.32/27.13 | | | | | | | | | | | | % 194.05/27.13 | | | | | | | | | | | | REDUCE: (90), (1212) imply: % 194.05/27.13 | | | | | | | | | | | | (1216) c_member(all_622_1, all_1341_1, v_L) = all_1341_0 % 194.05/27.13 | | | | | | | | | | | | % 194.05/27.13 | | | | | | | | | | | | REDUCE: (90), (1211) imply: % 194.05/27.13 | | | | | | | | | | | | (1217) c_member(all_622_1, all_1341_2, v_L) = 0 % 194.05/27.13 | | | | | | | | | | | | % 194.05/27.13 | | | | | | | | | | | | REDUCE: (170), (1206) imply: % 194.05/27.13 | | | | | | | | | | | | (1218) $i(v_y) % 194.05/27.13 | | | | | | | | | | | | % 194.05/27.13 | | | | | | | | | | | | GROUND_INST: instantiating (44) with v_x, all_1341_3, % 194.05/27.13 | | | | | | | | | | | | all_1341_2, simplifying with (16), (1210), (1213) % 194.05/27.13 | | | | | | | | | | | | gives: % 194.05/27.13 | | | | | | | | | | | | (1219) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_676_0, % 194.05/27.13 | | | | | | | | | | | | all_1341_2, v_L) = v0) | ! [v0: $i] : ! [v1: % 194.05/27.13 | | | | | | | | | | | | $i] : ( ~ % 194.05/27.13 | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.13 | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v0) = % 194.05/27.13 | | | | | | | | | | | | v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: any] : % 194.05/27.13 | | | | | | | | | | | | ? [v4: any] : % 194.05/27.13 | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.13 | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_1341_3, % 194.05/27.13 | | | | | | | | | | | | v0) = v2 & c_member(all_676_0, v2, v_L) = v3 % 194.05/27.13 | | | | | | | | | | | | & c_member(all_676_0, v1, v_L) = v4 & $i(v2) & % 194.05/27.13 | | | | | | | | | | | | ( ~ (v3 = 0) | v4 = 0))) % 194.05/27.13 | | | | | | | | | | | | % 194.05/27.13 | | | | | | | | | | | | GROUND_INST: instantiating (44) with all_872_9, v_y, all_872_7, % 194.05/27.13 | | | | | | | | | | | | simplifying with (169), (1215), (1218) gives: % 194.05/27.13 | | | | | | | | | | | | (1220) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_676_0, % 194.05/27.13 | | | | | | | | | | | | all_872_7, v_L) = v0) | ! [v0: $i] : ! [v1: % 194.05/27.13 | | | | | | | | | | | | $i] : ( ~ % 194.05/27.13 | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.13 | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, % 194.05/27.13 | | | | | | | | | | | | v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? % 194.05/27.13 | | | | | | | | | | | | [v3: any] : ? [v4: any] : % 194.05/27.13 | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.13 | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = % 194.05/27.13 | | | | | | | | | | | | v2 & c_member(all_676_0, v2, v_L) = v3 & % 194.05/27.13 | | | | | | | | | | | | c_member(all_676_0, v1, v_L) = v4 & $i(v2) & ( % 194.05/27.13 | | | | | | | | | | | | ~ (v3 = 0) | v4 = 0))) % 194.05/27.13 | | | | | | | | | | | | % 194.05/27.13 | | | | | | | | | | | | GROUND_INST: instantiating (1156) with all_1341_3, all_1341_1, % 194.05/27.13 | | | | | | | | | | | | simplifying with (1210), (1214) gives: % 194.05/27.13 | | | | | | | | | | | | (1221) ? [v0: $i] : ? [v1: any] : ? [v2: any] : % 194.05/27.13 | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.13 | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, % 194.05/27.13 | | | | | | | | | | | | all_1341_3) = v0 & c_member(all_676_0, v0, % 194.05/27.13 | | | | | | | | | | | | v_L) = v1 & c_member(all_676_0, all_1341_1, % 194.05/27.13 | | | | | | | | | | | | v_L) = v2 & $i(v0) & ( ~ (v1 = 0) | v2 = 0)) % 194.05/27.13 | | | | | | | | | | | | % 194.05/27.13 | | | | | | | | | | | | GROUND_INST: instantiating (1023) with all_1341_3, all_1341_1, % 194.05/27.13 | | | | | | | | | | | | simplifying with (1210), (1214) gives: % 194.05/27.13 | | | | | | | | | | | | (1222) ? [v0: $i] : ? [v1: any] : ? [v2: any] : % 194.05/27.13 | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.13 | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, % 194.05/27.13 | | | | | | | | | | | | all_1341_3) = v0 & c_member(all_676_0, v0, % 194.05/27.13 | | | | | | | | | | | | v_L) = v1 & c_member(all_676_0, all_1341_1, % 194.05/27.13 | | | | | | | | | | | | v_L) = v2 & $i(v0) & ( ~ (v1 = 0) | v2 = 0)) % 194.05/27.13 | | | | | | | | | | | | % 194.05/27.13 | | | | | | | | | | | | DELTA: instantiating (1222) with fresh symbols % 194.05/27.13 | | | | | | | | | | | | all_1390_0, all_1390_1, all_1390_2 gives: % 194.05/27.13 | | | | | | | | | | | | (1223) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.13 | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, % 194.05/27.13 | | | | | | | | | | | | all_1341_3) = all_1390_2 & c_member(all_676_0, % 194.05/27.13 | | | | | | | | | | | | all_1390_2, v_L) = all_1390_1 & % 194.05/27.13 | | | | | | | | | | | | c_member(all_676_0, all_1341_1, v_L) = all_1390_0 % 194.05/27.13 | | | | | | | | | | | | & $i(all_1390_2) & ( ~ (all_1390_1 = 0) | % 194.05/27.13 | | | | | | | | | | | | all_1390_0 = 0) % 194.05/27.13 | | | | | | | | | | | | % 194.05/27.13 | | | | | | | | | | | | ALPHA: (1223) implies: % 194.05/27.13 | | | | | | | | | | | | (1224) c_member(all_676_0, all_1341_1, v_L) = all_1390_0 % 194.05/27.13 | | | | | | | | | | | | (1225) c_member(all_676_0, all_1390_2, v_L) = all_1390_1 % 194.05/27.13 | | | | | | | | | | | | (1226) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.13 | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, % 194.05/27.13 | | | | | | | | | | | | all_1341_3) = all_1390_2 % 194.05/27.13 | | | | | | | | | | | | (1227) ~ (all_1390_1 = 0) | all_1390_0 = 0 % 194.05/27.13 | | | | | | | | | | | | % 194.05/27.13 | | | | | | | | | | | | DELTA: instantiating (1221) with fresh symbols % 194.05/27.13 | | | | | | | | | | | | all_1394_0, all_1394_1, all_1394_2 gives: % 194.05/27.13 | | | | | | | | | | | | (1228) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.13 | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, % 194.05/27.13 | | | | | | | | | | | | all_1341_3) = all_1394_2 & c_member(all_676_0, % 194.05/27.13 | | | | | | | | | | | | all_1394_2, v_L) = all_1394_1 & % 194.05/27.13 | | | | | | | | | | | | c_member(all_676_0, all_1341_1, v_L) = all_1394_0 % 194.05/27.13 | | | | | | | | | | | | & $i(all_1394_2) & ( ~ (all_1394_1 = 0) | % 194.05/27.13 | | | | | | | | | | | | all_1394_0 = 0) % 194.05/27.13 | | | | | | | | | | | | % 194.05/27.13 | | | | | | | | | | | | ALPHA: (1228) implies: % 194.05/27.13 | | | | | | | | | | | | (1229) c_member(all_676_0, all_1341_1, v_L) = all_1394_0 % 194.05/27.13 | | | | | | | | | | | | % 194.05/27.13 | | | | | | | | | | | | REDUCE: (89), (1225) imply: % 194.05/27.13 | | | | | | | | | | | | (1230) c_member(all_622_1, all_1390_2, v_L) = all_1390_1 % 194.05/27.13 | | | | | | | | | | | | % 194.05/27.13 | | | | | | | | | | | | REDUCE: (89), (1229) imply: % 194.05/27.13 | | | | | | | | | | | | (1231) c_member(all_622_1, all_1341_1, v_L) = all_1394_0 % 194.05/27.13 | | | | | | | | | | | | % 194.05/27.13 | | | | | | | | | | | | REDUCE: (89), (1224) imply: % 194.05/27.13 | | | | | | | | | | | | (1232) c_member(all_622_1, all_1341_1, v_L) = all_1390_0 % 194.05/27.13 | | | | | | | | | | | | % 194.05/27.13 | | | | | | | | | | | | BETA: splitting (1220) gives: % 194.05/27.13 | | | | | | | | | | | | % 194.05/27.13 | | | | | | | | | | | | Case 1: % 194.05/27.13 | | | | | | | | | | | | | % 194.05/27.13 | | | | | | | | | | | | | (1233) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_676_0, % 194.05/27.13 | | | | | | | | | | | | | all_872_7, v_L) = v0) % 194.05/27.13 | | | | | | | | | | | | | % 194.05/27.13 | | | | | | | | | | | | | DELTA: instantiating (1233) with fresh symbol all_1123_0 % 194.05/27.13 | | | | | | | | | | | | | gives: % 194.05/27.13 | | | | | | | | | | | | | (1234) ~ (all_1123_0 = 0) & c_member(all_676_0, % 194.05/27.13 | | | | | | | | | | | | | all_872_7, v_L) = all_1123_0 % 194.05/27.13 | | | | | | | | | | | | | % 194.05/27.13 | | | | | | | | | | | | | REF_CLOSE: (20), (89), (1199), (1234) are inconsistent by % 194.05/27.13 | | | | | | | | | | | | | sub-proof #14. % 194.05/27.13 | | | | | | | | | | | | | % 194.05/27.13 | | | | | | | | | | | | Case 2: % 194.05/27.13 | | | | | | | | | | | | | % 194.05/27.13 | | | | | | | | | | | | | (1235) ! [v0: $i] : ! [v1: $i] : ( ~ % 194.05/27.13 | | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.13 | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, % 194.05/27.13 | | | | | | | | | | | | | v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? % 194.05/27.13 | | | | | | | | | | | | | [v3: any] : ? [v4: any] : % 194.05/27.13 | | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.13 | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = % 194.05/27.13 | | | | | | | | | | | | | v2 & c_member(all_676_0, v2, v_L) = v3 & % 194.05/27.13 | | | | | | | | | | | | | c_member(all_676_0, v1, v_L) = v4 & $i(v2) & ( % 194.05/27.13 | | | | | | | | | | | | | ~ (v3 = 0) | v4 = 0))) % 194.05/27.13 | | | | | | | | | | | | | % 194.05/27.13 | | | | | | | | | | | | | GROUND_INST: instantiating (1235) with all_1341_3, all_1341_1, % 194.05/27.13 | | | | | | | | | | | | | simplifying with (1210), (1214) gives: % 194.05/27.13 | | | | | | | | | | | | | (1236) ? [v0: $i] : ? [v1: any] : ? [v2: any] : % 194.05/27.13 | | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.13 | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, % 194.05/27.13 | | | | | | | | | | | | | all_1341_3) = v0 & c_member(all_676_0, v0, % 194.05/27.13 | | | | | | | | | | | | | v_L) = v1 & c_member(all_676_0, all_1341_1, % 194.05/27.13 | | | | | | | | | | | | | v_L) = v2 & $i(v0) & ( ~ (v1 = 0) | v2 = 0)) % 194.05/27.13 | | | | | | | | | | | | | % 194.05/27.13 | | | | | | | | | | | | | BETA: splitting (1219) gives: % 194.05/27.13 | | | | | | | | | | | | | % 194.05/27.13 | | | | | | | | | | | | | Case 1: % 194.05/27.13 | | | | | | | | | | | | | | % 194.05/27.13 | | | | | | | | | | | | | | (1237) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_676_0, % 194.05/27.13 | | | | | | | | | | | | | | all_1341_2, v_L) = v0) % 194.05/27.13 | | | | | | | | | | | | | | % 194.05/27.13 | | | | | | | | | | | | | | DELTA: instantiating (1237) with fresh symbol all_1447_0 % 194.05/27.13 | | | | | | | | | | | | | | gives: % 194.05/27.13 | | | | | | | | | | | | | | (1238) ~ (all_1447_0 = 0) & c_member(all_676_0, % 194.05/27.13 | | | | | | | | | | | | | | all_1341_2, v_L) = all_1447_0 % 194.05/27.13 | | | | | | | | | | | | | | % 194.05/27.13 | | | | | | | | | | | | | | ALPHA: (1238) implies: % 194.05/27.13 | | | | | | | | | | | | | | (1239) ~ (all_1447_0 = 0) % 194.05/27.13 | | | | | | | | | | | | | | (1240) c_member(all_676_0, all_1341_2, v_L) = all_1447_0 % 194.05/27.13 | | | | | | | | | | | | | | % 194.05/27.13 | | | | | | | | | | | | | | REDUCE: (89), (1240) imply: % 194.05/27.13 | | | | | | | | | | | | | | (1241) c_member(all_622_1, all_1341_2, v_L) = all_1447_0 % 194.05/27.13 | | | | | | | | | | | | | | % 194.05/27.13 | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with 0, all_1447_0, v_L, % 194.05/27.13 | | | | | | | | | | | | | | all_1341_2, all_622_1, simplifying with (1217), % 194.05/27.13 | | | | | | | | | | | | | | (1241) gives: % 194.05/27.13 | | | | | | | | | | | | | | (1242) all_1447_0 = 0 % 194.05/27.13 | | | | | | | | | | | | | | % 194.05/27.13 | | | | | | | | | | | | | | REDUCE: (1239), (1242) imply: % 194.05/27.13 | | | | | | | | | | | | | | (1243) $false % 194.05/27.13 | | | | | | | | | | | | | | % 194.05/27.13 | | | | | | | | | | | | | | CLOSE: (1243) is inconsistent. % 194.05/27.13 | | | | | | | | | | | | | | % 194.05/27.13 | | | | | | | | | | | | | Case 2: % 194.05/27.13 | | | | | | | | | | | | | | % 194.05/27.13 | | | | | | | | | | | | | | (1244) ! [v0: $i] : ! [v1: $i] : ( ~ % 194.05/27.13 | | | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.13 | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v0) = % 194.05/27.13 | | | | | | | | | | | | | | v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: any] : % 194.05/27.13 | | | | | | | | | | | | | | ? [v4: any] : % 194.05/27.13 | | | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.13 | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_1341_3, % 194.05/27.13 | | | | | | | | | | | | | | v0) = v2 & c_member(all_676_0, v2, v_L) = v3 % 194.05/27.13 | | | | | | | | | | | | | | & c_member(all_676_0, v1, v_L) = v4 & $i(v2) & % 194.05/27.13 | | | | | | | | | | | | | | ( ~ (v3 = 0) | v4 = 0))) % 194.05/27.13 | | | | | | | | | | | | | | % 194.05/27.13 | | | | | | | | | | | | | | GROUND_INST: instantiating (1244) with all_1341_3, all_1341_2, % 194.05/27.13 | | | | | | | | | | | | | | simplifying with (1210), (1213) gives: % 194.05/27.14 | | | | | | | | | | | | | | (1245) ? [v0: $i] : ? [v1: any] : ? [v2: any] : % 194.05/27.14 | | | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.14 | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_1341_3, % 194.05/27.14 | | | | | | | | | | | | | | all_1341_3) = v0 & c_member(all_676_0, v0, % 194.05/27.14 | | | | | | | | | | | | | | v_L) = v1 & c_member(all_676_0, all_1341_2, % 194.05/27.14 | | | | | | | | | | | | | | v_L) = v2 & $i(v0) & ( ~ (v1 = 0) | v2 = 0)) % 194.05/27.14 | | | | | | | | | | | | | | % 194.05/27.14 | | | | | | | | | | | | | | DELTA: instantiating (1236) with fresh symbols % 194.05/27.14 | | | | | | | | | | | | | | all_1448_0, all_1448_1, all_1448_2 gives: % 194.05/27.14 | | | | | | | | | | | | | | (1246) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.14 | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, % 194.05/27.14 | | | | | | | | | | | | | | all_1341_3) = all_1448_2 & c_member(all_676_0, % 194.05/27.14 | | | | | | | | | | | | | | all_1448_2, v_L) = all_1448_1 & % 194.05/27.14 | | | | | | | | | | | | | | c_member(all_676_0, all_1341_1, v_L) = all_1448_0 % 194.05/27.14 | | | | | | | | | | | | | | & $i(all_1448_2) & ( ~ (all_1448_1 = 0) | % 194.05/27.14 | | | | | | | | | | | | | | all_1448_0 = 0) % 194.05/27.14 | | | | | | | | | | | | | | % 194.05/27.14 | | | | | | | | | | | | | | ALPHA: (1246) implies: % 194.05/27.14 | | | | | | | | | | | | | | (1247) c_member(all_676_0, all_1341_1, v_L) = all_1448_0 % 194.05/27.14 | | | | | | | | | | | | | | % 194.05/27.14 | | | | | | | | | | | | | | DELTA: instantiating (1245) with fresh symbols % 194.05/27.14 | | | | | | | | | | | | | | all_1450_0, all_1450_1, all_1450_2 gives: % 194.05/27.14 | | | | | | | | | | | | | | (1248) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.14 | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_1341_3, % 194.05/27.14 | | | | | | | | | | | | | | all_1341_3) = all_1450_2 & c_member(all_676_0, % 194.05/27.14 | | | | | | | | | | | | | | all_1450_2, v_L) = all_1450_1 & % 194.05/27.14 | | | | | | | | | | | | | | c_member(all_676_0, all_1341_2, v_L) = all_1450_0 % 194.05/27.14 | | | | | | | | | | | | | | & $i(all_1450_2) & ( ~ (all_1450_1 = 0) | % 194.05/27.14 | | | | | | | | | | | | | | all_1450_0 = 0) % 194.05/27.14 | | | | | | | | | | | | | | % 194.05/27.14 | | | | | | | | | | | | | | ALPHA: (1248) implies: % 194.05/27.14 | | | | | | | | | | | | | | (1249) c_member(all_676_0, all_1341_2, v_L) = all_1450_0 % 194.05/27.14 | | | | | | | | | | | | | | % 194.05/27.14 | | | | | | | | | | | | | | REDUCE: (89), (1247) imply: % 194.05/27.14 | | | | | | | | | | | | | | (1250) c_member(all_622_1, all_1341_1, v_L) = all_1448_0 % 194.05/27.14 | | | | | | | | | | | | | | % 194.05/27.14 | | | | | | | | | | | | | | REDUCE: (89), (1249) imply: % 194.05/27.14 | | | | | | | | | | | | | | (1251) c_member(all_622_1, all_1341_2, v_L) = all_1450_0 % 194.05/27.14 | | | | | | | | | | | | | | % 194.05/27.14 | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with 0, all_1450_0, v_L, % 194.05/27.14 | | | | | | | | | | | | | | all_1341_2, all_622_1, simplifying with (1217), % 194.05/27.14 | | | | | | | | | | | | | | (1251) gives: % 194.05/27.14 | | | | | | | | | | | | | | (1252) all_1450_0 = 0 % 194.05/27.14 | | | | | | | | | | | | | | % 194.05/27.14 | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with all_1341_0, all_1394_0, % 194.05/27.14 | | | | | | | | | | | | | | v_L, all_1341_1, all_622_1, simplifying with % 194.05/27.14 | | | | | | | | | | | | | | (1216), (1231) gives: % 194.05/27.14 | | | | | | | | | | | | | | (1253) all_1394_0 = all_1341_0 % 194.05/27.14 | | | | | | | | | | | | | | % 194.05/27.14 | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with all_1394_0, all_1448_0, % 194.05/27.14 | | | | | | | | | | | | | | v_L, all_1341_1, all_622_1, simplifying with % 194.05/27.14 | | | | | | | | | | | | | | (1231), (1250) gives: % 194.05/27.14 | | | | | | | | | | | | | | (1254) all_1448_0 = all_1394_0 % 194.05/27.14 | | | | | | | | | | | | | | % 194.05/27.14 | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with all_1390_0, all_1448_0, % 194.05/27.14 | | | | | | | | | | | | | | v_L, all_1341_1, all_622_1, simplifying with % 194.05/27.14 | | | | | | | | | | | | | | (1232), (1250) gives: % 194.05/27.14 | | | | | | | | | | | | | | (1255) all_1448_0 = all_1390_0 % 194.05/27.14 | | | | | | | | | | | | | | % 194.05/27.14 | | | | | | | | | | | | | | GROUND_INST: instantiating (21) with all_1341_2, all_1390_2, % 194.05/27.14 | | | | | | | | | | | | | | all_1341_3, v_x, tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.14 | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with % 194.05/27.14 | | | | | | | | | | | | | | (1213), (1226) gives: % 194.05/27.14 | | | | | | | | | | | | | | (1256) all_1390_2 = all_1341_2 % 194.05/27.14 | | | | | | | | | | | | | | % 194.05/27.14 | | | | | | | | | | | | | | COMBINE_EQS: (1254), (1255) imply: % 194.05/27.14 | | | | | | | | | | | | | | (1257) all_1394_0 = all_1390_0 % 194.05/27.14 | | | | | | | | | | | | | | % 194.05/27.14 | | | | | | | | | | | | | | SIMP: (1257) implies: % 194.05/27.14 | | | | | | | | | | | | | | (1258) all_1394_0 = all_1390_0 % 194.05/27.14 | | | | | | | | | | | | | | % 194.05/27.14 | | | | | | | | | | | | | | COMBINE_EQS: (1253), (1258) imply: % 194.05/27.14 | | | | | | | | | | | | | | (1259) all_1390_0 = all_1341_0 % 194.05/27.14 | | | | | | | | | | | | | | % 194.05/27.14 | | | | | | | | | | | | | | REDUCE: (1230), (1256) imply: % 194.05/27.14 | | | | | | | | | | | | | | (1260) c_member(all_622_1, all_1341_2, v_L) = all_1390_1 % 194.05/27.14 | | | | | | | | | | | | | | % 194.05/27.14 | | | | | | | | | | | | | | BETA: splitting (1227) gives: % 194.05/27.14 | | | | | | | | | | | | | | % 194.05/27.14 | | | | | | | | | | | | | | Case 1: % 194.05/27.14 | | | | | | | | | | | | | | | % 194.05/27.14 | | | | | | | | | | | | | | | (1261) ~ (all_1390_1 = 0) % 194.05/27.14 | | | | | | | | | | | | | | | % 194.05/27.14 | | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with 0, all_1390_1, v_L, % 194.05/27.14 | | | | | | | | | | | | | | | all_1341_2, all_622_1, simplifying with (1217), % 194.05/27.14 | | | | | | | | | | | | | | | (1260) gives: % 194.05/27.14 | | | | | | | | | | | | | | | (1262) all_1390_1 = 0 % 194.05/27.14 | | | | | | | | | | | | | | | % 194.05/27.14 | | | | | | | | | | | | | | | REDUCE: (1261), (1262) imply: % 194.05/27.14 | | | | | | | | | | | | | | | (1263) $false % 194.05/27.14 | | | | | | | | | | | | | | | % 194.05/27.14 | | | | | | | | | | | | | | | CLOSE: (1263) is inconsistent. % 194.05/27.14 | | | | | | | | | | | | | | | % 194.05/27.14 | | | | | | | | | | | | | | Case 2: % 194.05/27.14 | | | | | | | | | | | | | | | % 194.05/27.14 | | | | | | | | | | | | | | | (1264) all_1390_0 = 0 % 194.05/27.14 | | | | | | | | | | | | | | | % 194.05/27.14 | | | | | | | | | | | | | | | COMBINE_EQS: (1259), (1264) imply: % 194.05/27.14 | | | | | | | | | | | | | | | (1265) all_1341_0 = 0 % 194.05/27.14 | | | | | | | | | | | | | | | % 194.05/27.14 | | | | | | | | | | | | | | | SIMP: (1265) implies: % 194.05/27.14 | | | | | | | | | | | | | | | (1266) all_1341_0 = 0 % 194.05/27.14 | | | | | | | | | | | | | | | % 194.05/27.14 | | | | | | | | | | | | | | | REDUCE: (1209), (1266) imply: % 194.05/27.14 | | | | | | | | | | | | | | | (1267) $false % 194.05/27.14 | | | | | | | | | | | | | | | % 194.05/27.14 | | | | | | | | | | | | | | | CLOSE: (1267) is inconsistent. % 194.05/27.14 | | | | | | | | | | | | | | | % 194.05/27.14 | | | | | | | | | | | | | | End of split % 194.05/27.14 | | | | | | | | | | | | | | % 194.05/27.14 | | | | | | | | | | | | | End of split % 194.05/27.14 | | | | | | | | | | | | | % 194.05/27.14 | | | | | | | | | | | | End of split % 194.05/27.14 | | | | | | | | | | | | % 194.05/27.14 | | | | | | | | | | | Case 2: % 194.05/27.14 | | | | | | | | | | | | % 194.05/27.14 | | | | | | | | | | | | (1268) all_872_6 = 0 & ~ (all_872_8 = v_y) & ? [v0: $i] % 194.05/27.14 | | | | | | | | | | | | : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ? % 194.05/27.14 | | | | | | | | | | | | [v4: any] : % 194.05/27.14 | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.14 | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, % 194.05/27.14 | | | | | | | | | | | | v0) = v1 & % 194.05/27.14 | | | | | | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.14 | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, % 194.05/27.14 | | | | | | | | | | | | v0) = v3 & c_member(all_685_0, v3, v_L) = v4 & % 194.05/27.14 | | | | | | | | | | | | c_member(all_685_0, v1, v_L) = v2 & $i(v3) & % 194.05/27.14 | | | | | | | | | | | | $i(v1) & $i(v0) & ((v2 = 0 & ~ (v4 = 0) & ~ % 194.05/27.14 | | | | | | | | | | | | (v0 = v_y)) | (v0 = v_y & all_872_2 = 0 & ~ % 194.05/27.14 | | | | | | | | | | | | (all_872_4 = 0) & ~ (all_872_9 = v_x)) | % 194.05/27.14 | | | | | | | | | | | | (v0 = v_y & all_872_8 = v_x & ~ (all_872_4 = % 194.05/27.14 | | | | | | | | | | | | 0) & ~ (all_872_9 = v_x)))) % 194.05/27.14 | | | | | | | | | | | | % 194.05/27.14 | | | | | | | | | | | | ALPHA: (1268) implies: % 194.05/27.14 | | | | | | | | | | | | (1269) ? [v0: $i] : ? [v1: $i] : ? [v2: any] : ? [v3: % 194.05/27.14 | | | | | | | | | | | | $i] : ? [v4: any] : % 194.05/27.14 | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.14 | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, % 194.05/27.14 | | | | | | | | | | | | v0) = v1 & % 194.05/27.14 | | | | | | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.14 | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, % 194.05/27.14 | | | | | | | | | | | | v0) = v3 & c_member(all_685_0, v3, v_L) = v4 & % 194.05/27.14 | | | | | | | | | | | | c_member(all_685_0, v1, v_L) = v2 & $i(v3) & % 194.05/27.14 | | | | | | | | | | | | $i(v1) & $i(v0) & ((v2 = 0 & ~ (v4 = 0) & ~ % 194.05/27.14 | | | | | | | | | | | | (v0 = v_y)) | (v0 = v_y & all_872_2 = 0 & ~ % 194.05/27.14 | | | | | | | | | | | | (all_872_4 = 0) & ~ (all_872_9 = v_x)) | % 194.05/27.14 | | | | | | | | | | | | (v0 = v_y & all_872_8 = v_x & ~ (all_872_4 = % 194.05/27.14 | | | | | | | | | | | | 0) & ~ (all_872_9 = v_x)))) % 194.05/27.14 | | | | | | | | | | | | % 194.05/27.14 | | | | | | | | | | | | DELTA: instantiating (1269) with fresh symbols % 194.05/27.14 | | | | | | | | | | | | all_1341_0, all_1341_1, all_1341_2, all_1341_3, % 194.05/27.14 | | | | | | | | | | | | all_1341_4 gives: % 194.05/27.14 | | | | | | | | | | | | (1270) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.14 | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, % 194.05/27.14 | | | | | | | | | | | | all_1341_4) = all_1341_3 & % 194.05/27.14 | | | | | | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.14 | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, % 194.05/27.14 | | | | | | | | | | | | all_1341_4) = all_1341_1 & c_member(all_685_0, % 194.05/27.14 | | | | | | | | | | | | all_1341_1, v_L) = all_1341_0 & % 194.05/27.14 | | | | | | | | | | | | c_member(all_685_0, all_1341_3, v_L) = all_1341_2 % 194.05/27.14 | | | | | | | | | | | | & $i(all_1341_1) & $i(all_1341_3) & $i(all_1341_4) % 194.05/27.14 | | | | | | | | | | | | & ((all_1341_2 = 0 & ~ (all_1341_0 = 0) & ~ % 194.05/27.14 | | | | | | | | | | | | (all_1341_4 = v_y)) | (all_1341_4 = v_y & % 194.05/27.14 | | | | | | | | | | | | all_872_2 = 0 & ~ (all_872_4 = 0) & ~ % 194.05/27.14 | | | | | | | | | | | | (all_872_9 = v_x)) | (all_1341_4 = v_y & % 194.05/27.14 | | | | | | | | | | | | all_872_8 = v_x & ~ (all_872_4 = 0) & ~ % 194.05/27.14 | | | | | | | | | | | | (all_872_9 = v_x))) % 194.05/27.14 | | | | | | | | | | | | % 194.05/27.14 | | | | | | | | | | | | ALPHA: (1270) implies: % 194.05/27.14 | | | | | | | | | | | | (1271) $i(all_1341_4) % 194.05/27.14 | | | | | | | | | | | | (1272) c_member(all_685_0, all_1341_3, v_L) = all_1341_2 % 194.05/27.14 | | | | | | | | | | | | (1273) c_member(all_685_0, all_1341_1, v_L) = all_1341_0 % 194.05/27.14 | | | | | | | | | | | | (1274) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.14 | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, % 194.05/27.14 | | | | | | | | | | | | all_1341_4) = all_1341_1 % 194.05/27.14 | | | | | | | | | | | | (1275) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.14 | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, % 194.05/27.14 | | | | | | | | | | | | all_1341_4) = all_1341_3 % 194.05/27.14 | | | | | | | | | | | | (1276) (all_1341_2 = 0 & ~ (all_1341_0 = 0) & ~ % 194.05/27.14 | | | | | | | | | | | | (all_1341_4 = v_y)) | (all_1341_4 = v_y & % 194.05/27.14 | | | | | | | | | | | | all_872_2 = 0 & ~ (all_872_4 = 0) & ~ % 194.05/27.14 | | | | | | | | | | | | (all_872_9 = v_x)) | (all_1341_4 = v_y & % 194.05/27.14 | | | | | | | | | | | | all_872_8 = v_x & ~ (all_872_4 = 0) & ~ % 194.05/27.14 | | | | | | | | | | | | (all_872_9 = v_x)) % 194.05/27.14 | | | | | | | | | | | | % 194.05/27.14 | | | | | | | | | | | | REDUCE: (90), (1273) imply: % 194.05/27.14 | | | | | | | | | | | | (1277) c_member(all_622_1, all_1341_1, v_L) = all_1341_0 % 194.05/27.14 | | | | | | | | | | | | % 194.05/27.14 | | | | | | | | | | | | REDUCE: (90), (1272) imply: % 194.05/27.14 | | | | | | | | | | | | (1278) c_member(all_622_1, all_1341_3, v_L) = all_1341_2 % 194.05/27.14 | | | | | | | | | | | | % 194.05/27.14 | | | | | | | | | | | | BETA: splitting (1276) gives: % 194.05/27.14 | | | | | | | | | | | | % 194.05/27.14 | | | | | | | | | | | | Case 1: % 194.05/27.14 | | | | | | | | | | | | | % 194.05/27.14 | | | | | | | | | | | | | (1279) all_1341_2 = 0 & ~ (all_1341_0 = 0) & ~ % 194.05/27.14 | | | | | | | | | | | | | (all_1341_4 = v_y) % 194.05/27.14 | | | | | | | | | | | | | % 194.05/27.14 | | | | | | | | | | | | | ALPHA: (1279) implies: % 194.05/27.14 | | | | | | | | | | | | | (1280) all_1341_2 = 0 % 194.05/27.14 | | | | | | | | | | | | | (1281) ~ (all_1341_0 = 0) % 194.05/27.14 | | | | | | | | | | | | | % 194.05/27.14 | | | | | | | | | | | | | REDUCE: (1278), (1280) imply: % 194.05/27.14 | | | | | | | | | | | | | (1282) c_member(all_622_1, all_1341_3, v_L) = 0 % 194.05/27.14 | | | | | | | | | | | | | % 194.05/27.14 | | | | | | | | | | | | | GROUND_INST: instantiating (3) with v_L, all_1134_2, all_622_1, % 194.05/27.14 | | | | | | | | | | | | | all_1214_0, simplifying with (17), (91), (1160), % 194.05/27.14 | | | | | | | | | | | | | (1204) gives: % 194.05/27.14 | | | | | | | | | | | | | (1283) all_1214_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ % 194.05/27.14 | | | | | | | | | | | | | (v1 = 0) & hBOOL(v0) = v1 & hAPP(v_L, % 194.05/27.14 | | | | | | | | | | | | | all_1134_2) = v0 & $i(v0)) % 194.05/27.14 | | | | | | | | | | | | | % 194.05/27.14 | | | | | | | | | | | | | GROUND_INST: instantiating (1156) with all_1341_4, all_1341_1, % 194.05/27.14 | | | | | | | | | | | | | simplifying with (1271), (1274) gives: % 194.05/27.14 | | | | | | | | | | | | | (1284) ? [v0: $i] : ? [v1: any] : ? [v2: any] : % 194.05/27.14 | | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.14 | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, % 194.05/27.14 | | | | | | | | | | | | | all_1341_4) = v0 & c_member(all_676_0, v0, % 194.05/27.14 | | | | | | | | | | | | | v_L) = v1 & c_member(all_676_0, all_1341_1, % 194.05/27.14 | | | | | | | | | | | | | v_L) = v2 & $i(v0) & ( ~ (v1 = 0) | v2 = 0)) % 194.05/27.14 | | | | | | | | | | | | | % 194.05/27.14 | | | | | | | | | | | | | GROUND_INST: instantiating (918) with all_1341_4, all_1341_3, % 194.05/27.14 | | | | | | | | | | | | | simplifying with (1271), (1275) gives: % 194.05/27.14 | | | | | | | | | | | | | (1285) ? [v0: $i] : ? [v1: any] : ? [v2: any] : % 194.05/27.14 | | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.14 | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, % 194.05/27.14 | | | | | | | | | | | | | all_1341_4) = v0 & c_member(all_676_0, v0, % 194.05/27.14 | | | | | | | | | | | | | v_L) = v1 & c_member(all_676_0, all_1341_3, % 194.05/27.14 | | | | | | | | | | | | | v_L) = v2 & $i(v0) & ( ~ (v1 = 0) | v2 = 0)) % 194.05/27.14 | | | | | | | | | | | | | % 194.05/27.14 | | | | | | | | | | | | | GROUND_INST: instantiating (44) with all_872_8, all_1341_4, % 194.05/27.14 | | | | | | | | | | | | | all_1341_3, simplifying with (170), (1271), (1275) % 194.05/27.14 | | | | | | | | | | | | | gives: % 194.05/27.14 | | | | | | | | | | | | | (1286) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_676_0, % 194.05/27.14 | | | | | | | | | | | | | all_1341_3, v_L) = v0) | ! [v0: $i] : ! [v1: % 194.05/27.14 | | | | | | | | | | | | | $i] : ( ~ % 194.05/27.14 | | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.14 | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, % 194.05/27.14 | | | | | | | | | | | | | v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? % 194.05/27.14 | | | | | | | | | | | | | [v3: any] : ? [v4: any] : % 194.05/27.14 | | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.14 | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_1341_4, % 194.05/27.14 | | | | | | | | | | | | | v0) = v2 & c_member(all_676_0, v2, v_L) = v3 % 194.05/27.14 | | | | | | | | | | | | | & c_member(all_676_0, v1, v_L) = v4 & $i(v2) & % 194.05/27.14 | | | | | | | | | | | | | ( ~ (v3 = 0) | v4 = 0))) % 194.05/27.14 | | | | | | | | | | | | | % 194.05/27.14 | | | | | | | | | | | | | DELTA: instantiating (1285) with fresh symbols % 194.05/27.14 | | | | | | | | | | | | | all_1376_0, all_1376_1, all_1376_2 gives: % 194.05/27.14 | | | | | | | | | | | | | (1287) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.14 | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, % 194.05/27.14 | | | | | | | | | | | | | all_1341_4) = all_1376_2 & c_member(all_676_0, % 194.05/27.14 | | | | | | | | | | | | | all_1376_2, v_L) = all_1376_1 & % 194.05/27.14 | | | | | | | | | | | | | c_member(all_676_0, all_1341_3, v_L) = all_1376_0 % 194.05/27.14 | | | | | | | | | | | | | & $i(all_1376_2) & ( ~ (all_1376_1 = 0) | % 194.05/27.14 | | | | | | | | | | | | | all_1376_0 = 0) % 194.05/27.14 | | | | | | | | | | | | | % 194.05/27.14 | | | | | | | | | | | | | ALPHA: (1287) implies: % 194.05/27.14 | | | | | | | | | | | | | (1288) c_member(all_676_0, all_1341_3, v_L) = all_1376_0 % 194.05/27.14 | | | | | | | | | | | | | % 194.05/27.14 | | | | | | | | | | | | | DELTA: instantiating (1284) with fresh symbols % 194.05/27.14 | | | | | | | | | | | | | all_1382_0, all_1382_1, all_1382_2 gives: % 194.05/27.14 | | | | | | | | | | | | | (1289) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.15 | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, % 194.05/27.15 | | | | | | | | | | | | | all_1341_4) = all_1382_2 & c_member(all_676_0, % 194.05/27.15 | | | | | | | | | | | | | all_1382_2, v_L) = all_1382_1 & % 194.05/27.15 | | | | | | | | | | | | | c_member(all_676_0, all_1341_1, v_L) = all_1382_0 % 194.05/27.15 | | | | | | | | | | | | | & $i(all_1382_2) & ( ~ (all_1382_1 = 0) | % 194.05/27.15 | | | | | | | | | | | | | all_1382_0 = 0) % 194.05/27.15 | | | | | | | | | | | | | % 194.05/27.15 | | | | | | | | | | | | | ALPHA: (1289) implies: % 194.05/27.15 | | | | | | | | | | | | | (1290) c_member(all_676_0, all_1341_1, v_L) = all_1382_0 % 194.05/27.15 | | | | | | | | | | | | | (1291) c_member(all_676_0, all_1382_2, v_L) = all_1382_1 % 194.05/27.15 | | | | | | | | | | | | | (1292) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.15 | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, % 194.05/27.15 | | | | | | | | | | | | | all_1341_4) = all_1382_2 % 194.05/27.15 | | | | | | | | | | | | | (1293) ~ (all_1382_1 = 0) | all_1382_0 = 0 % 194.05/27.15 | | | | | | | | | | | | | % 194.05/27.15 | | | | | | | | | | | | | REDUCE: (89), (1291) imply: % 194.05/27.15 | | | | | | | | | | | | | (1294) c_member(all_622_1, all_1382_2, v_L) = all_1382_1 % 194.05/27.15 | | | | | | | | | | | | | % 194.05/27.15 | | | | | | | | | | | | | REDUCE: (89), (1290) imply: % 194.05/27.15 | | | | | | | | | | | | | (1295) c_member(all_622_1, all_1341_1, v_L) = all_1382_0 % 194.05/27.15 | | | | | | | | | | | | | % 194.05/27.15 | | | | | | | | | | | | | REDUCE: (89), (1288) imply: % 194.05/27.15 | | | | | | | | | | | | | (1296) c_member(all_622_1, all_1341_3, v_L) = all_1376_0 % 194.05/27.15 | | | | | | | | | | | | | % 194.05/27.15 | | | | | | | | | | | | | BETA: splitting (1283) gives: % 194.05/27.15 | | | | | | | | | | | | | % 194.05/27.15 | | | | | | | | | | | | | Case 1: % 194.05/27.15 | | | | | | | | | | | | | | % 194.05/27.15 | | | | | | | | | | | | | | (1297) all_1214_0 = 0 % 194.05/27.15 | | | | | | | | | | | | | | % 194.05/27.15 | | | | | | | | | | | | | | REDUCE: (1202), (1297) imply: % 194.05/27.15 | | | | | | | | | | | | | | (1298) $false % 194.05/27.15 | | | | | | | | | | | | | | % 194.05/27.15 | | | | | | | | | | | | | | CLOSE: (1298) is inconsistent. % 194.05/27.15 | | | | | | | | | | | | | | % 194.05/27.15 | | | | | | | | | | | | | Case 2: % 194.05/27.15 | | | | | | | | | | | | | | % 194.05/27.15 | | | | | | | | | | | | | | % 194.05/27.15 | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with 0, all_1376_0, v_L, % 194.05/27.15 | | | | | | | | | | | | | | all_1341_3, all_622_1, simplifying with (1282), % 194.05/27.15 | | | | | | | | | | | | | | (1296) gives: % 194.05/27.15 | | | | | | | | | | | | | | (1299) all_1376_0 = 0 % 194.05/27.15 | | | | | | | | | | | | | | % 194.05/27.15 | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with all_1341_0, all_1382_0, % 194.05/27.15 | | | | | | | | | | | | | | v_L, all_1341_1, all_622_1, simplifying with % 194.05/27.15 | | | | | | | | | | | | | | (1277), (1295) gives: % 194.05/27.15 | | | | | | | | | | | | | | (1300) all_1382_0 = all_1341_0 % 194.05/27.15 | | | | | | | | | | | | | | % 194.05/27.15 | | | | | | | | | | | | | | GROUND_INST: instantiating (21) with all_1341_3, all_1382_2, % 194.05/27.15 | | | | | | | | | | | | | | all_1341_4, all_872_8, % 194.05/27.15 | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.15 | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with % 194.05/27.15 | | | | | | | | | | | | | | (1275), (1292) gives: % 194.05/27.15 | | | | | | | | | | | | | | (1301) all_1382_2 = all_1341_3 % 194.05/27.15 | | | | | | | | | | | | | | % 194.05/27.15 | | | | | | | | | | | | | | REDUCE: (1294), (1301) imply: % 194.05/27.15 | | | | | | | | | | | | | | (1302) c_member(all_622_1, all_1341_3, v_L) = all_1382_1 % 194.05/27.15 | | | | | | | | | | | | | | % 194.05/27.15 | | | | | | | | | | | | | | BETA: splitting (1293) gives: % 194.05/27.15 | | | | | | | | | | | | | | % 194.05/27.15 | | | | | | | | | | | | | | Case 1: % 194.05/27.15 | | | | | | | | | | | | | | | % 194.05/27.15 | | | | | | | | | | | | | | | (1303) ~ (all_1382_1 = 0) % 194.05/27.15 | | | | | | | | | | | | | | | % 194.05/27.15 | | | | | | | | | | | | | | | BETA: splitting (1286) gives: % 194.05/27.15 | | | | | | | | | | | | | | | % 194.05/27.15 | | | | | | | | | | | | | | | Case 1: % 194.05/27.15 | | | | | | | | | | | | | | | | % 194.05/27.15 | | | | | | | | | | | | | | | | (1304) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_676_0, % 194.05/27.15 | | | | | | | | | | | | | | | | all_1341_3, v_L) = v0) % 194.05/27.15 | | | | | | | | | | | | | | | | % 194.05/27.15 | | | | | | | | | | | | | | | | DELTA: instantiating (1304) with fresh symbol all_1446_0 % 194.05/27.15 | | | | | | | | | | | | | | | | gives: % 194.05/27.15 | | | | | | | | | | | | | | | | (1305) ~ (all_1446_0 = 0) & c_member(all_676_0, % 194.05/27.15 | | | | | | | | | | | | | | | | all_1341_3, v_L) = all_1446_0 % 194.05/27.15 | | | | | | | | | | | | | | | | % 194.05/27.15 | | | | | | | | | | | | | | | | ALPHA: (1305) implies: % 194.05/27.15 | | | | | | | | | | | | | | | | (1306) c_member(all_676_0, all_1341_3, v_L) = all_1446_0 % 194.05/27.15 | | | | | | | | | | | | | | | | % 194.05/27.15 | | | | | | | | | | | | | | | | REDUCE: (89), (1306) imply: % 194.05/27.15 | | | | | | | | | | | | | | | | (1307) c_member(all_622_1, all_1341_3, v_L) = all_1446_0 % 194.05/27.15 | | | | | | | | | | | | | | | | % 194.05/27.15 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with 0, all_1446_0, v_L, % 194.05/27.15 | | | | | | | | | | | | | | | | all_1341_3, all_622_1, simplifying with (1282), % 194.05/27.15 | | | | | | | | | | | | | | | | (1307) gives: % 194.05/27.15 | | | | | | | | | | | | | | | | (1308) all_1446_0 = 0 % 194.05/27.15 | | | | | | | | | | | | | | | | % 194.05/27.15 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with all_1382_1, all_1446_0, % 194.05/27.15 | | | | | | | | | | | | | | | | v_L, all_1341_3, all_622_1, simplifying with % 194.05/27.15 | | | | | | | | | | | | | | | | (1302), (1307) gives: % 194.05/27.15 | | | | | | | | | | | | | | | | (1309) all_1446_0 = all_1382_1 % 194.05/27.15 | | | | | | | | | | | | | | | | % 194.05/27.15 | | | | | | | | | | | | | | | | COMBINE_EQS: (1308), (1309) imply: % 194.05/27.15 | | | | | | | | | | | | | | | | (1310) all_1382_1 = 0 % 194.05/27.15 | | | | | | | | | | | | | | | | % 194.05/27.15 | | | | | | | | | | | | | | | | REDUCE: (1303), (1310) imply: % 194.05/27.15 | | | | | | | | | | | | | | | | (1311) $false % 194.05/27.15 | | | | | | | | | | | | | | | | % 194.05/27.15 | | | | | | | | | | | | | | | | CLOSE: (1311) is inconsistent. % 194.05/27.15 | | | | | | | | | | | | | | | | % 194.05/27.15 | | | | | | | | | | | | | | | Case 2: % 194.05/27.15 | | | | | | | | | | | | | | | | % 194.05/27.15 | | | | | | | | | | | | | | | | (1312) ! [v0: $i] : ! [v1: $i] : ( ~ % 194.05/27.15 | | | | | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.15 | | | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, % 194.05/27.15 | | | | | | | | | | | | | | | | v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? % 194.05/27.15 | | | | | | | | | | | | | | | | [v3: any] : ? [v4: any] : % 194.05/27.15 | | | | | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.15 | | | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_1341_4, % 194.05/27.15 | | | | | | | | | | | | | | | | v0) = v2 & c_member(all_676_0, v2, v_L) = v3 % 194.05/27.15 | | | | | | | | | | | | | | | | & c_member(all_676_0, v1, v_L) = v4 & $i(v2) & % 194.05/27.15 | | | | | | | | | | | | | | | | ( ~ (v3 = 0) | v4 = 0))) % 194.05/27.15 | | | | | | | | | | | | | | | | % 194.05/27.15 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1312) with all_1341_4, all_1341_3, % 194.05/27.15 | | | | | | | | | | | | | | | | simplifying with (1271), (1275) gives: % 194.05/27.15 | | | | | | | | | | | | | | | | (1313) ? [v0: $i] : ? [v1: any] : ? [v2: any] : % 194.05/27.15 | | | | | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.15 | | | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_1341_4, % 194.05/27.15 | | | | | | | | | | | | | | | | all_1341_4) = v0 & c_member(all_676_0, v0, % 194.05/27.15 | | | | | | | | | | | | | | | | v_L) = v1 & c_member(all_676_0, all_1341_3, % 194.05/27.15 | | | | | | | | | | | | | | | | v_L) = v2 & $i(v0) & ( ~ (v1 = 0) | v2 = 0)) % 194.05/27.15 | | | | | | | | | | | | | | | | % 194.05/27.15 | | | | | | | | | | | | | | | | DELTA: instantiating (1313) with fresh symbols % 194.05/27.15 | | | | | | | | | | | | | | | | all_1447_0, all_1447_1, all_1447_2 gives: % 194.05/27.15 | | | | | | | | | | | | | | | | (1314) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.15 | | | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_1341_4, % 194.05/27.15 | | | | | | | | | | | | | | | | all_1341_4) = all_1447_2 & c_member(all_676_0, % 194.05/27.15 | | | | | | | | | | | | | | | | all_1447_2, v_L) = all_1447_1 & % 194.05/27.15 | | | | | | | | | | | | | | | | c_member(all_676_0, all_1341_3, v_L) = all_1447_0 % 194.05/27.15 | | | | | | | | | | | | | | | | & $i(all_1447_2) & ( ~ (all_1447_1 = 0) | % 194.05/27.15 | | | | | | | | | | | | | | | | all_1447_0 = 0) % 194.05/27.15 | | | | | | | | | | | | | | | | % 194.05/27.15 | | | | | | | | | | | | | | | | ALPHA: (1314) implies: % 194.05/27.15 | | | | | | | | | | | | | | | | (1315) c_member(all_676_0, all_1341_3, v_L) = all_1447_0 % 194.05/27.15 | | | | | | | | | | | | | | | | % 194.05/27.15 | | | | | | | | | | | | | | | | REDUCE: (89), (1315) imply: % 194.05/27.15 | | | | | | | | | | | | | | | | (1316) c_member(all_622_1, all_1341_3, v_L) = all_1447_0 % 194.05/27.15 | | | | | | | | | | | | | | | | % 194.05/27.15 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with 0, all_1447_0, v_L, % 194.05/27.15 | | | | | | | | | | | | | | | | all_1341_3, all_622_1, simplifying with (1282), % 194.05/27.15 | | | | | | | | | | | | | | | | (1316) gives: % 194.05/27.15 | | | | | | | | | | | | | | | | (1317) all_1447_0 = 0 % 194.05/27.15 | | | | | | | | | | | | | | | | % 194.05/27.15 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with all_1382_1, all_1447_0, % 194.05/27.15 | | | | | | | | | | | | | | | | v_L, all_1341_3, all_622_1, simplifying with % 194.05/27.15 | | | | | | | | | | | | | | | | (1302), (1316) gives: % 194.05/27.15 | | | | | | | | | | | | | | | | (1318) all_1447_0 = all_1382_1 % 194.05/27.15 | | | | | | | | | | | | | | | | % 194.05/27.15 | | | | | | | | | | | | | | | | COMBINE_EQS: (1317), (1318) imply: % 194.05/27.15 | | | | | | | | | | | | | | | | (1319) all_1382_1 = 0 % 194.05/27.15 | | | | | | | | | | | | | | | | % 194.05/27.15 | | | | | | | | | | | | | | | | REDUCE: (1303), (1319) imply: % 194.05/27.15 | | | | | | | | | | | | | | | | (1320) $false % 194.05/27.15 | | | | | | | | | | | | | | | | % 194.05/27.15 | | | | | | | | | | | | | | | | CLOSE: (1320) is inconsistent. % 194.05/27.15 | | | | | | | | | | | | | | | | % 194.05/27.15 | | | | | | | | | | | | | | | End of split % 194.05/27.15 | | | | | | | | | | | | | | | % 194.05/27.15 | | | | | | | | | | | | | | Case 2: % 194.05/27.15 | | | | | | | | | | | | | | | % 194.05/27.15 | | | | | | | | | | | | | | | (1321) all_1382_0 = 0 % 194.05/27.15 | | | | | | | | | | | | | | | % 194.05/27.15 | | | | | | | | | | | | | | | COMBINE_EQS: (1300), (1321) imply: % 194.05/27.15 | | | | | | | | | | | | | | | (1322) all_1341_0 = 0 % 194.05/27.15 | | | | | | | | | | | | | | | % 194.05/27.15 | | | | | | | | | | | | | | | REDUCE: (1281), (1322) imply: % 194.05/27.15 | | | | | | | | | | | | | | | (1323) $false % 194.05/27.15 | | | | | | | | | | | | | | | % 194.05/27.15 | | | | | | | | | | | | | | | CLOSE: (1323) is inconsistent. % 194.05/27.15 | | | | | | | | | | | | | | | % 194.05/27.15 | | | | | | | | | | | | | | End of split % 194.05/27.15 | | | | | | | | | | | | | | % 194.05/27.15 | | | | | | | | | | | | | End of split % 194.05/27.15 | | | | | | | | | | | | | % 194.05/27.15 | | | | | | | | | | | | Case 2: % 194.05/27.15 | | | | | | | | | | | | | % 194.05/27.15 | | | | | | | | | | | | | (1324) (all_1341_4 = v_y & all_872_2 = 0 & ~ (all_872_4 % 194.05/27.15 | | | | | | | | | | | | | = 0) & ~ (all_872_9 = v_x)) | (all_1341_4 = % 194.05/27.15 | | | | | | | | | | | | | v_y & all_872_8 = v_x & ~ (all_872_4 = 0) & ~ % 194.05/27.15 | | | | | | | | | | | | | (all_872_9 = v_x)) % 194.05/27.15 | | | | | | | | | | | | | % 194.05/27.15 | | | | | | | | | | | | | BETA: splitting (1324) gives: % 194.05/27.15 | | | | | | | | | | | | | % 194.05/27.15 | | | | | | | | | | | | | Case 1: % 194.05/27.15 | | | | | | | | | | | | | | % 194.05/27.15 | | | | | | | | | | | | | | (1325) all_1341_4 = v_y & all_872_2 = 0 & ~ (all_872_4 = % 194.05/27.15 | | | | | | | | | | | | | | 0) & ~ (all_872_9 = v_x) % 194.05/27.15 | | | | | | | | | | | | | | % 194.05/27.15 | | | | | | | | | | | | | | ALPHA: (1325) implies: % 194.05/27.15 | | | | | | | | | | | | | | (1326) ~ (all_872_4 = 0) % 194.05/27.15 | | | | | | | | | | | | | | % 194.05/27.15 | | | | | | | | | | | | | | REF_CLOSE: (20), (21), (89), (180), (181), (182), (184), % 194.05/27.15 | | | | | | | | | | | | | | (185), (186), (192), (198), (1168), (1174), % 194.05/27.15 | | | | | | | | | | | | | | (1177), (1195), (1199), (1326) are inconsistent by % 194.05/27.15 | | | | | | | | | | | | | | sub-proof #1. % 194.05/27.15 | | | | | | | | | | | | | | % 194.05/27.15 | | | | | | | | | | | | | Case 2: % 194.05/27.15 | | | | | | | | | | | | | | % 194.05/27.15 | | | | | | | | | | | | | | (1327) all_1341_4 = v_y & all_872_8 = v_x & ~ (all_872_4 % 194.05/27.15 | | | | | | | | | | | | | | = 0) & ~ (all_872_9 = v_x) % 194.05/27.15 | | | | | | | | | | | | | | % 194.05/27.15 | | | | | | | | | | | | | | ALPHA: (1327) implies: % 194.05/27.15 | | | | | | | | | | | | | | (1328) ~ (all_872_4 = 0) % 194.05/27.15 | | | | | | | | | | | | | | % 194.05/27.15 | | | | | | | | | | | | | | REF_CLOSE: (20), (21), (89), (180), (181), (182), (184), % 194.05/27.15 | | | | | | | | | | | | | | (185), (186), (192), (198), (1168), (1174), % 194.05/27.15 | | | | | | | | | | | | | | (1177), (1195), (1199), (1328) are inconsistent by % 194.05/27.15 | | | | | | | | | | | | | | sub-proof #1. % 194.05/27.15 | | | | | | | | | | | | | | % 194.05/27.15 | | | | | | | | | | | | | End of split % 194.05/27.15 | | | | | | | | | | | | | % 194.05/27.15 | | | | | | | | | | | | End of split % 194.05/27.15 | | | | | | | | | | | | % 194.05/27.15 | | | | | | | | | | | End of split % 194.05/27.15 | | | | | | | | | | | % 194.05/27.15 | | | | | | | | | | Case 2: % 194.05/27.15 | | | | | | | | | | | % 194.05/27.15 | | | | | | | | | | | (1329) ~ (all_872_6 = 0) % 194.05/27.15 | | | | | | | | | | | % 194.05/27.15 | | | | | | | | | | | BETA: splitting (657) gives: % 194.05/27.15 | | | | | | | | | | | % 194.05/27.15 | | | | | | | | | | | Case 1: % 194.05/27.15 | | | | | | | | | | | | % 194.05/27.15 | | | | | | | | | | | | (1330) all_872_4 = 0 & all_872_8 = v_y & ? [v0: $i] : ? % 194.05/27.15 | | | | | | | | | | | | [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = % 194.05/27.15 | | | | | | | | | | | | 0) & ~ (v0 = v_y) & % 194.05/27.15 | | | | | | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.15 | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, % 194.05/27.15 | | | | | | | | | | | | v0) = v2 & % 194.05/27.15 | | | | | | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.15 | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v0) = v1 % 194.05/27.15 | | | | | | | | | | | | & c_member(all_685_0, v2, v_L) = v3 & % 194.05/27.15 | | | | | | | | | | | | c_member(all_685_0, v1, v_L) = 0 & $i(v2) & % 194.05/27.15 | | | | | | | | | | | | $i(v1) & $i(v0)) % 194.05/27.15 | | | | | | | | | | | | % 194.05/27.15 | | | | | | | | | | | | ALPHA: (1330) implies: % 194.05/27.15 | | | | | | | | | | | | (1331) all_872_8 = v_y % 194.05/27.15 | | | | | | | | | | | | (1332) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 194.05/27.15 | | | | | | | | | | | | int] : ( ~ (v3 = 0) & ~ (v0 = v_y) & % 194.05/27.15 | | | | | | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.15 | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, % 194.05/27.15 | | | | | | | | | | | | v0) = v2 & % 194.05/27.15 | | | | | | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.15 | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v0) = v1 % 194.05/27.15 | | | | | | | | | | | | & c_member(all_685_0, v2, v_L) = v3 & % 194.05/27.15 | | | | | | | | | | | | c_member(all_685_0, v1, v_L) = 0 & $i(v2) & % 194.05/27.15 | | | | | | | | | | | | $i(v1) & $i(v0)) % 194.05/27.15 | | | | | | | | | | | | % 194.05/27.15 | | | | | | | | | | | | DELTA: instantiating (1332) with fresh symbols % 194.05/27.15 | | | | | | | | | | | | all_1197_0, all_1197_1, all_1197_2, all_1197_3 % 194.05/27.15 | | | | | | | | | | | | gives: % 194.05/27.15 | | | | | | | | | | | | (1333) ~ (all_1197_0 = 0) & ~ (all_1197_3 = v_y) & % 194.05/27.15 | | | | | | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.15 | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, % 194.05/27.15 | | | | | | | | | | | | all_1197_3) = all_1197_1 & % 194.05/27.15 | | | | | | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.15 | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, % 194.05/27.15 | | | | | | | | | | | | all_1197_3) = all_1197_2 & c_member(all_685_0, % 194.05/27.15 | | | | | | | | | | | | all_1197_1, v_L) = all_1197_0 & % 194.05/27.15 | | | | | | | | | | | | c_member(all_685_0, all_1197_2, v_L) = 0 & % 194.05/27.15 | | | | | | | | | | | | $i(all_1197_1) & $i(all_1197_2) & $i(all_1197_3) % 194.05/27.15 | | | | | | | | | | | | % 194.05/27.15 | | | | | | | | | | | | ALPHA: (1333) implies: % 194.05/27.15 | | | | | | | | | | | | (1334) ~ (all_1197_0 = 0) % 194.05/27.15 | | | | | | | | | | | | (1335) $i(all_1197_3) % 194.05/27.15 | | | | | | | | | | | | (1336) c_member(all_685_0, all_1197_2, v_L) = 0 % 194.05/27.15 | | | | | | | | | | | | (1337) c_member(all_685_0, all_1197_1, v_L) = all_1197_0 % 194.05/27.15 | | | | | | | | | | | | (1338) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.15 | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, % 194.05/27.15 | | | | | | | | | | | | all_1197_3) = all_1197_2 % 194.05/27.15 | | | | | | | | | | | | (1339) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.15 | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, % 194.05/27.15 | | | | | | | | | | | | all_1197_3) = all_1197_1 % 194.05/27.15 | | | | | | | | | | | | % 194.05/27.15 | | | | | | | | | | | | REDUCE: (1184), (1331) imply: % 194.05/27.15 | | | | | | | | | | | | (1340) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.15 | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, all_872_9) % 194.05/27.15 | | | | | | | | | | | | = all_1152_1 % 194.05/27.15 | | | | | | | | | | | | % 194.05/27.15 | | | | | | | | | | | | REDUCE: (182), (1331) imply: % 194.05/27.15 | | | | | | | | | | | | (1341) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.15 | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v_x) = % 194.05/27.15 | | | | | | | | | | | | all_872_3 % 194.05/27.15 | | | | | | | | | | | | % 194.05/27.15 | | | | | | | | | | | | REDUCE: (90), (1337) imply: % 194.05/27.15 | | | | | | | | | | | | (1342) c_member(all_622_1, all_1197_1, v_L) = all_1197_0 % 194.05/27.15 | | | | | | | | | | | | % 194.05/27.15 | | | | | | | | | | | | REDUCE: (90), (1336) imply: % 194.05/27.15 | | | | | | | | | | | | (1343) c_member(all_622_1, all_1197_2, v_L) = 0 % 194.05/27.15 | | | | | | | | | | | | % 194.05/27.15 | | | | | | | | | | | | REDUCE: (170), (1331) imply: % 194.05/27.15 | | | | | | | | | | | | (1344) $i(v_y) % 194.05/27.15 | | | | | | | | | | | | % 194.05/27.15 | | | | | | | | | | | | BETA: splitting (1185) gives: % 194.05/27.15 | | | | | | | | | | | | % 194.05/27.15 | | | | | | | | | | | | Case 1: % 194.05/27.15 | | | | | | | | | | | | | % 194.05/27.15 | | | | | | | | | | | | | (1345) all_1152_0 = 0 % 194.05/27.15 | | | | | | | | | | | | | % 194.05/27.15 | | | | | | | | | | | | | REDUCE: (1186), (1345) imply: % 194.05/27.15 | | | | | | | | | | | | | (1346) c_member(all_622_1, all_1152_1, v_L) = 0 % 194.05/27.15 | | | | | | | | | | | | | % 194.05/27.15 | | | | | | | | | | | | | GROUND_INST: instantiating (44) with v_y, v_x, all_872_3, % 194.05/27.15 | | | | | | | | | | | | | simplifying with (16), (1341), (1344) gives: % 194.05/27.16 | | | | | | | | | | | | | (1347) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_676_0, % 194.05/27.16 | | | | | | | | | | | | | all_872_3, v_L) = v0) | ! [v0: $i] : ! [v1: % 194.05/27.16 | | | | | | | | | | | | | $i] : ( ~ % 194.05/27.16 | | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.16 | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = % 194.05/27.16 | | | | | | | | | | | | | v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: any] : % 194.05/27.16 | | | | | | | | | | | | | ? [v4: any] : % 194.05/27.16 | | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.16 | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v0) = % 194.05/27.16 | | | | | | | | | | | | | v2 & c_member(all_676_0, v2, v_L) = v3 & % 194.05/27.16 | | | | | | | | | | | | | c_member(all_676_0, v1, v_L) = v4 & $i(v2) & ( % 194.05/27.16 | | | | | | | | | | | | | ~ (v3 = 0) | v4 = 0))) % 194.05/27.16 | | | | | | | | | | | | | % 194.05/27.16 | | | | | | | | | | | | | GROUND_INST: instantiating (fact_single__valuedD) with % 194.05/27.16 | | | | | | | | | | | | | all_872_9, v_x, v_y, v_L, % 194.05/27.16 | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.16 | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_622_1, % 194.05/27.16 | | | | | | | | | | | | | all_872_3, all_1152_1, simplifying with (15), % 194.05/27.16 | | | | | | | | | | | | | (16), (17), (23), (169), (1197), (1340), (1341), % 194.05/27.16 | | | | | | | | | | | | | (1344), (1346) gives: % 194.05/27.16 | | | | | | | | | | | | | (1348) all_872_9 = v_x | ? [v0: int] : ( ~ (v0 = 0) & % 194.05/27.16 | | | | | | | | | | | | | c_Relation_Osingle__valued(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.16 | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_L) = v0) % 194.05/27.16 | | | | | | | | | | | | | % 194.05/27.16 | | | | | | | | | | | | | GROUND_INST: instantiating (44) with v_x, all_1197_3, % 194.05/27.16 | | | | | | | | | | | | | all_1197_2, simplifying with (16), (1335), (1338) % 194.05/27.16 | | | | | | | | | | | | | gives: % 194.05/27.16 | | | | | | | | | | | | | (1349) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_676_0, % 194.05/27.16 | | | | | | | | | | | | | all_1197_2, v_L) = v0) | ! [v0: $i] : ! [v1: % 194.05/27.16 | | | | | | | | | | | | | $i] : ( ~ % 194.05/27.16 | | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.16 | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v0) = % 194.05/27.16 | | | | | | | | | | | | | v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: any] : % 194.05/27.16 | | | | | | | | | | | | | ? [v4: any] : % 194.05/27.16 | | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.16 | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_1197_3, % 194.05/27.16 | | | | | | | | | | | | | v0) = v2 & c_member(all_676_0, v2, v_L) = v3 % 194.05/27.16 | | | | | | | | | | | | | & c_member(all_676_0, v1, v_L) = v4 & $i(v2) & % 194.05/27.16 | | | | | | | | | | | | | ( ~ (v3 = 0) | v4 = 0))) % 194.05/27.16 | | | | | | | | | | | | | % 194.05/27.16 | | | | | | | | | | | | | GROUND_INST: instantiating (1156) with all_1197_3, all_1197_1, % 194.05/27.16 | | | | | | | | | | | | | simplifying with (1335), (1339) gives: % 194.05/27.16 | | | | | | | | | | | | | (1350) ? [v0: $i] : ? [v1: any] : ? [v2: any] : % 194.05/27.16 | | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.16 | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, % 194.05/27.16 | | | | | | | | | | | | | all_1197_3) = v0 & c_member(all_676_0, v0, % 194.05/27.16 | | | | | | | | | | | | | v_L) = v1 & c_member(all_676_0, all_1197_1, % 194.05/27.16 | | | | | | | | | | | | | v_L) = v2 & $i(v0) & ( ~ (v1 = 0) | v2 = 0)) % 194.05/27.16 | | | | | | | | | | | | | % 194.05/27.16 | | | | | | | | | | | | | GROUND_INST: instantiating (1023) with all_1197_3, all_1197_1, % 194.05/27.16 | | | | | | | | | | | | | simplifying with (1335), (1339) gives: % 194.05/27.16 | | | | | | | | | | | | | (1351) ? [v0: $i] : ? [v1: any] : ? [v2: any] : % 194.05/27.16 | | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.16 | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, % 194.05/27.16 | | | | | | | | | | | | | all_1197_3) = v0 & c_member(all_676_0, v0, % 194.05/27.16 | | | | | | | | | | | | | v_L) = v1 & c_member(all_676_0, all_1197_1, % 194.05/27.16 | | | | | | | | | | | | | v_L) = v2 & $i(v0) & ( ~ (v1 = 0) | v2 = 0)) % 194.05/27.16 | | | | | | | | | | | | | % 194.05/27.16 | | | | | | | | | | | | | DELTA: instantiating (1351) with fresh symbols % 194.05/27.16 | | | | | | | | | | | | | all_1268_0, all_1268_1, all_1268_2 gives: % 194.05/27.16 | | | | | | | | | | | | | (1352) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.16 | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, % 194.05/27.16 | | | | | | | | | | | | | all_1197_3) = all_1268_2 & c_member(all_676_0, % 194.05/27.16 | | | | | | | | | | | | | all_1268_2, v_L) = all_1268_1 & % 194.05/27.16 | | | | | | | | | | | | | c_member(all_676_0, all_1197_1, v_L) = all_1268_0 % 194.05/27.16 | | | | | | | | | | | | | & $i(all_1268_2) & ( ~ (all_1268_1 = 0) | % 194.05/27.16 | | | | | | | | | | | | | all_1268_0 = 0) % 194.05/27.16 | | | | | | | | | | | | | % 194.05/27.16 | | | | | | | | | | | | | ALPHA: (1352) implies: % 194.05/27.16 | | | | | | | | | | | | | (1353) c_member(all_676_0, all_1197_1, v_L) = all_1268_0 % 194.05/27.16 | | | | | | | | | | | | | (1354) c_member(all_676_0, all_1268_2, v_L) = all_1268_1 % 194.05/27.16 | | | | | | | | | | | | | (1355) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.16 | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, % 194.05/27.16 | | | | | | | | | | | | | all_1197_3) = all_1268_2 % 194.05/27.16 | | | | | | | | | | | | | (1356) ~ (all_1268_1 = 0) | all_1268_0 = 0 % 194.05/27.16 | | | | | | | | | | | | | % 194.05/27.16 | | | | | | | | | | | | | DELTA: instantiating (1350) with fresh symbols % 194.05/27.16 | | | | | | | | | | | | | all_1270_0, all_1270_1, all_1270_2 gives: % 194.05/27.16 | | | | | | | | | | | | | (1357) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.16 | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, % 194.05/27.16 | | | | | | | | | | | | | all_1197_3) = all_1270_2 & c_member(all_676_0, % 194.05/27.16 | | | | | | | | | | | | | all_1270_2, v_L) = all_1270_1 & % 194.05/27.16 | | | | | | | | | | | | | c_member(all_676_0, all_1197_1, v_L) = all_1270_0 % 194.05/27.16 | | | | | | | | | | | | | & $i(all_1270_2) & ( ~ (all_1270_1 = 0) | % 194.05/27.16 | | | | | | | | | | | | | all_1270_0 = 0) % 194.05/27.16 | | | | | | | | | | | | | % 194.05/27.16 | | | | | | | | | | | | | ALPHA: (1357) implies: % 194.05/27.16 | | | | | | | | | | | | | (1358) c_member(all_676_0, all_1197_1, v_L) = all_1270_0 % 194.05/27.16 | | | | | | | | | | | | | % 194.05/27.16 | | | | | | | | | | | | | REDUCE: (89), (1354) imply: % 194.05/27.16 | | | | | | | | | | | | | (1359) c_member(all_622_1, all_1268_2, v_L) = all_1268_1 % 194.05/27.16 | | | | | | | | | | | | | % 194.05/27.16 | | | | | | | | | | | | | REDUCE: (89), (1358) imply: % 194.05/27.16 | | | | | | | | | | | | | (1360) c_member(all_622_1, all_1197_1, v_L) = all_1270_0 % 194.05/27.16 | | | | | | | | | | | | | % 194.05/27.16 | | | | | | | | | | | | | REDUCE: (89), (1353) imply: % 194.05/27.16 | | | | | | | | | | | | | (1361) c_member(all_622_1, all_1197_1, v_L) = all_1268_0 % 194.05/27.16 | | | | | | | | | | | | | % 194.05/27.16 | | | | | | | | | | | | | BETA: splitting (1349) gives: % 194.05/27.16 | | | | | | | | | | | | | % 194.05/27.16 | | | | | | | | | | | | | Case 1: % 194.05/27.16 | | | | | | | | | | | | | | % 194.05/27.16 | | | | | | | | | | | | | | (1362) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_676_0, % 194.05/27.16 | | | | | | | | | | | | | | all_1197_2, v_L) = v0) % 194.05/27.16 | | | | | | | | | | | | | | % 194.05/27.16 | | | | | | | | | | | | | | DELTA: instantiating (1362) with fresh symbol all_1282_0 % 194.05/27.16 | | | | | | | | | | | | | | gives: % 194.05/27.16 | | | | | | | | | | | | | | (1363) ~ (all_1282_0 = 0) & c_member(all_676_0, % 194.05/27.16 | | | | | | | | | | | | | | all_1197_2, v_L) = all_1282_0 % 194.05/27.16 | | | | | | | | | | | | | | % 194.05/27.16 | | | | | | | | | | | | | | ALPHA: (1363) implies: % 194.05/27.16 | | | | | | | | | | | | | | (1364) ~ (all_1282_0 = 0) % 194.05/27.16 | | | | | | | | | | | | | | (1365) c_member(all_676_0, all_1197_2, v_L) = all_1282_0 % 194.05/27.16 | | | | | | | | | | | | | | % 194.05/27.16 | | | | | | | | | | | | | | REDUCE: (89), (1365) imply: % 194.05/27.16 | | | | | | | | | | | | | | (1366) c_member(all_622_1, all_1197_2, v_L) = all_1282_0 % 194.05/27.16 | | | | | | | | | | | | | | % 194.05/27.16 | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with 0, all_1282_0, v_L, % 194.05/27.16 | | | | | | | | | | | | | | all_1197_2, all_622_1, simplifying with (1343), % 194.05/27.16 | | | | | | | | | | | | | | (1366) gives: % 194.05/27.16 | | | | | | | | | | | | | | (1367) all_1282_0 = 0 % 194.05/27.16 | | | | | | | | | | | | | | % 194.05/27.16 | | | | | | | | | | | | | | REDUCE: (1364), (1367) imply: % 194.05/27.16 | | | | | | | | | | | | | | (1368) $false % 194.05/27.16 | | | | | | | | | | | | | | % 194.05/27.16 | | | | | | | | | | | | | | CLOSE: (1368) is inconsistent. % 194.05/27.16 | | | | | | | | | | | | | | % 194.05/27.16 | | | | | | | | | | | | | Case 2: % 194.05/27.16 | | | | | | | | | | | | | | % 194.05/27.16 | | | | | | | | | | | | | | (1369) ! [v0: $i] : ! [v1: $i] : ( ~ % 194.05/27.16 | | | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.16 | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v0) = % 194.05/27.16 | | | | | | | | | | | | | | v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: any] : % 194.05/27.16 | | | | | | | | | | | | | | ? [v4: any] : % 194.05/27.16 | | | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.16 | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_1197_3, % 194.05/27.16 | | | | | | | | | | | | | | v0) = v2 & c_member(all_676_0, v2, v_L) = v3 % 194.05/27.16 | | | | | | | | | | | | | | & c_member(all_676_0, v1, v_L) = v4 & $i(v2) & % 194.05/27.16 | | | | | | | | | | | | | | ( ~ (v3 = 0) | v4 = 0))) % 194.05/27.16 | | | | | | | | | | | | | | % 194.05/27.16 | | | | | | | | | | | | | | GROUND_INST: instantiating (1369) with all_1197_3, all_1197_2, % 194.05/27.16 | | | | | | | | | | | | | | simplifying with (1335), (1338) gives: % 194.05/27.16 | | | | | | | | | | | | | | (1370) ? [v0: $i] : ? [v1: any] : ? [v2: any] : % 194.05/27.16 | | | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.16 | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_1197_3, % 194.05/27.16 | | | | | | | | | | | | | | all_1197_3) = v0 & c_member(all_676_0, v0, % 194.05/27.16 | | | | | | | | | | | | | | v_L) = v1 & c_member(all_676_0, all_1197_2, % 194.05/27.16 | | | | | | | | | | | | | | v_L) = v2 & $i(v0) & ( ~ (v1 = 0) | v2 = 0)) % 194.05/27.16 | | | | | | | | | | | | | | % 194.05/27.16 | | | | | | | | | | | | | | BETA: splitting (1347) gives: % 194.05/27.16 | | | | | | | | | | | | | | % 194.05/27.16 | | | | | | | | | | | | | | Case 1: % 194.05/27.16 | | | | | | | | | | | | | | | % 194.05/27.16 | | | | | | | | | | | | | | | (1371) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_676_0, % 194.05/27.16 | | | | | | | | | | | | | | | all_872_3, v_L) = v0) % 194.05/27.16 | | | | | | | | | | | | | | | % 194.05/27.16 | | | | | | | | | | | | | | | DELTA: instantiating (1371) with fresh symbol all_1283_0 % 194.05/27.16 | | | | | | | | | | | | | | | gives: % 194.05/27.16 | | | | | | | | | | | | | | | (1372) ~ (all_1283_0 = 0) & c_member(all_676_0, % 194.05/27.16 | | | | | | | | | | | | | | | all_872_3, v_L) = all_1283_0 % 194.05/27.16 | | | | | | | | | | | | | | | % 194.05/27.16 | | | | | | | | | | | | | | | ALPHA: (1372) implies: % 194.05/27.16 | | | | | | | | | | | | | | | (1373) ~ (all_1283_0 = 0) % 194.05/27.16 | | | | | | | | | | | | | | | (1374) c_member(all_676_0, all_872_3, v_L) = all_1283_0 % 194.05/27.16 | | | | | | | | | | | | | | | % 194.05/27.16 | | | | | | | | | | | | | | | REDUCE: (89), (1374) imply: % 194.05/27.16 | | | | | | | | | | | | | | | (1375) c_member(all_622_1, all_872_3, v_L) = all_1283_0 % 194.05/27.16 | | | | | | | | | | | | | | | % 194.05/27.16 | | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with 0, all_1283_0, v_L, % 194.05/27.16 | | | | | | | | | | | | | | | all_872_3, all_622_1, simplifying with (1197), % 194.05/27.16 | | | | | | | | | | | | | | | (1375) gives: % 194.05/27.16 | | | | | | | | | | | | | | | (1376) all_1283_0 = 0 % 194.05/27.16 | | | | | | | | | | | | | | | % 194.05/27.16 | | | | | | | | | | | | | | | REDUCE: (1373), (1376) imply: % 194.05/27.16 | | | | | | | | | | | | | | | (1377) $false % 194.05/27.16 | | | | | | | | | | | | | | | % 194.05/27.16 | | | | | | | | | | | | | | | CLOSE: (1377) is inconsistent. % 194.05/27.16 | | | | | | | | | | | | | | | % 194.05/27.16 | | | | | | | | | | | | | | Case 2: % 194.05/27.16 | | | | | | | | | | | | | | | % 194.05/27.16 | | | | | | | | | | | | | | | % 194.05/27.16 | | | | | | | | | | | | | | | DELTA: instantiating (1370) with fresh symbols % 194.05/27.16 | | | | | | | | | | | | | | | all_1284_0, all_1284_1, all_1284_2 gives: % 194.05/27.16 | | | | | | | | | | | | | | | (1378) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.16 | | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_1197_3, % 194.05/27.16 | | | | | | | | | | | | | | | all_1197_3) = all_1284_2 & c_member(all_676_0, % 194.05/27.16 | | | | | | | | | | | | | | | all_1284_2, v_L) = all_1284_1 & % 194.05/27.16 | | | | | | | | | | | | | | | c_member(all_676_0, all_1197_2, v_L) = all_1284_0 % 194.05/27.16 | | | | | | | | | | | | | | | & $i(all_1284_2) & ( ~ (all_1284_1 = 0) | % 194.05/27.16 | | | | | | | | | | | | | | | all_1284_0 = 0) % 194.05/27.16 | | | | | | | | | | | | | | | % 194.05/27.16 | | | | | | | | | | | | | | | ALPHA: (1378) implies: % 194.05/27.16 | | | | | | | | | | | | | | | (1379) c_member(all_676_0, all_1197_2, v_L) = all_1284_0 % 194.05/27.16 | | | | | | | | | | | | | | | % 194.05/27.16 | | | | | | | | | | | | | | | REDUCE: (89), (1379) imply: % 194.05/27.16 | | | | | | | | | | | | | | | (1380) c_member(all_622_1, all_1197_2, v_L) = all_1284_0 % 194.05/27.16 | | | | | | | | | | | | | | | % 194.05/27.16 | | | | | | | | | | | | | | | BETA: splitting (1348) gives: % 194.05/27.16 | | | | | | | | | | | | | | | % 194.05/27.16 | | | | | | | | | | | | | | | Case 1: % 194.05/27.16 | | | | | | | | | | | | | | | | % 194.05/27.16 | | | | | | | | | | | | | | | | (1381) all_872_9 = v_x % 194.05/27.16 | | | | | | | | | | | | | | | | % 194.05/27.16 | | | | | | | | | | | | | | | | REDUCE: (1045), (1381) imply: % 194.05/27.16 | | | | | | | | | | | | | | | | (1382) $false % 194.05/27.16 | | | | | | | | | | | | | | | | % 194.05/27.16 | | | | | | | | | | | | | | | | CLOSE: (1382) is inconsistent. % 194.05/27.16 | | | | | | | | | | | | | | | | % 194.05/27.16 | | | | | | | | | | | | | | | Case 2: % 194.05/27.16 | | | | | | | | | | | | | | | | % 194.05/27.16 | | | | | | | | | | | | | | | | % 194.05/27.16 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with 0, all_1284_0, v_L, % 194.05/27.16 | | | | | | | | | | | | | | | | all_1197_2, all_622_1, simplifying with (1343), % 194.05/27.16 | | | | | | | | | | | | | | | | (1380) gives: % 194.05/27.16 | | | | | | | | | | | | | | | | (1383) all_1284_0 = 0 % 194.05/27.16 | | | | | | | | | | | | | | | | % 194.05/27.16 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with all_1197_0, all_1270_0, % 194.05/27.16 | | | | | | | | | | | | | | | | v_L, all_1197_1, all_622_1, simplifying with % 194.05/27.16 | | | | | | | | | | | | | | | | (1342), (1360) gives: % 194.05/27.16 | | | | | | | | | | | | | | | | (1384) all_1270_0 = all_1197_0 % 194.05/27.16 | | | | | | | | | | | | | | | | % 194.05/27.16 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with all_1268_0, all_1270_0, % 194.05/27.16 | | | | | | | | | | | | | | | | v_L, all_1197_1, all_622_1, simplifying with % 194.05/27.16 | | | | | | | | | | | | | | | | (1360), (1361) gives: % 194.05/27.16 | | | | | | | | | | | | | | | | (1385) all_1270_0 = all_1268_0 % 194.05/27.16 | | | | | | | | | | | | | | | | % 194.05/27.16 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (21) with all_1197_2, all_1268_2, % 194.05/27.16 | | | | | | | | | | | | | | | | all_1197_3, v_x, tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.16 | | | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with % 194.05/27.16 | | | | | | | | | | | | | | | | (1338), (1355) gives: % 194.05/27.16 | | | | | | | | | | | | | | | | (1386) all_1268_2 = all_1197_2 % 194.05/27.16 | | | | | | | | | | | | | | | | % 194.05/27.16 | | | | | | | | | | | | | | | | COMBINE_EQS: (1384), (1385) imply: % 194.05/27.16 | | | | | | | | | | | | | | | | (1387) all_1268_0 = all_1197_0 % 194.05/27.16 | | | | | | | | | | | | | | | | % 194.05/27.16 | | | | | | | | | | | | | | | | SIMP: (1387) implies: % 194.05/27.16 | | | | | | | | | | | | | | | | (1388) all_1268_0 = all_1197_0 % 194.05/27.16 | | | | | | | | | | | | | | | | % 194.05/27.16 | | | | | | | | | | | | | | | | REDUCE: (1359), (1386) imply: % 194.05/27.16 | | | | | | | | | | | | | | | | (1389) c_member(all_622_1, all_1197_2, v_L) = all_1268_1 % 194.05/27.16 | | | | | | | | | | | | | | | | % 194.05/27.16 | | | | | | | | | | | | | | | | BETA: splitting (1356) gives: % 194.05/27.16 | | | | | | | | | | | | | | | | % 194.05/27.16 | | | | | | | | | | | | | | | | Case 1: % 194.05/27.16 | | | | | | | | | | | | | | | | | % 194.05/27.16 | | | | | | | | | | | | | | | | | (1390) ~ (all_1268_1 = 0) % 194.05/27.16 | | | | | | | | | | | | | | | | | % 194.05/27.16 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with 0, all_1268_1, v_L, % 194.05/27.16 | | | | | | | | | | | | | | | | | all_1197_2, all_622_1, simplifying with (1343), % 194.05/27.16 | | | | | | | | | | | | | | | | | (1389) gives: % 194.05/27.16 | | | | | | | | | | | | | | | | | (1391) all_1268_1 = 0 % 194.05/27.16 | | | | | | | | | | | | | | | | | % 194.05/27.16 | | | | | | | | | | | | | | | | | REDUCE: (1390), (1391) imply: % 194.05/27.16 | | | | | | | | | | | | | | | | | (1392) $false % 194.05/27.16 | | | | | | | | | | | | | | | | | % 194.05/27.16 | | | | | | | | | | | | | | | | | CLOSE: (1392) is inconsistent. % 194.05/27.16 | | | | | | | | | | | | | | | | | % 194.05/27.16 | | | | | | | | | | | | | | | | Case 2: % 194.05/27.16 | | | | | | | | | | | | | | | | | % 194.05/27.16 | | | | | | | | | | | | | | | | | (1393) all_1268_0 = 0 % 194.05/27.16 | | | | | | | | | | | | | | | | | % 194.05/27.16 | | | | | | | | | | | | | | | | | COMBINE_EQS: (1388), (1393) imply: % 194.05/27.16 | | | | | | | | | | | | | | | | | (1394) all_1197_0 = 0 % 194.05/27.16 | | | | | | | | | | | | | | | | | % 194.05/27.16 | | | | | | | | | | | | | | | | | REDUCE: (1334), (1394) imply: % 194.05/27.16 | | | | | | | | | | | | | | | | | (1395) $false % 194.05/27.16 | | | | | | | | | | | | | | | | | % 194.05/27.16 | | | | | | | | | | | | | | | | | CLOSE: (1395) is inconsistent. % 194.05/27.16 | | | | | | | | | | | | | | | | | % 194.05/27.16 | | | | | | | | | | | | | | | | End of split % 194.05/27.16 | | | | | | | | | | | | | | | | % 194.05/27.16 | | | | | | | | | | | | | | | End of split % 194.05/27.16 | | | | | | | | | | | | | | | % 194.05/27.16 | | | | | | | | | | | | | | End of split % 194.05/27.16 | | | | | | | | | | | | | | % 194.05/27.16 | | | | | | | | | | | | | End of split % 194.05/27.16 | | | | | | | | | | | | | % 194.05/27.16 | | | | | | | | | | | | Case 2: % 194.05/27.16 | | | | | | | | | | | | | % 194.05/27.16 | | | | | | | | | | | | | (1396) all_1152_2 = 0 % 194.05/27.16 | | | | | | | | | | | | | % 194.05/27.16 | | | | | | | | | | | | | COMBINE_EQS: (1188), (1396) imply: % 194.05/27.16 | | | | | | | | | | | | | (1397) all_872_6 = 0 % 194.05/27.17 | | | | | | | | | | | | | % 194.05/27.17 | | | | | | | | | | | | | REDUCE: (1329), (1397) imply: % 194.05/27.17 | | | | | | | | | | | | | (1398) $false % 194.05/27.17 | | | | | | | | | | | | | % 194.05/27.17 | | | | | | | | | | | | | CLOSE: (1398) is inconsistent. % 194.05/27.17 | | | | | | | | | | | | | % 194.05/27.17 | | | | | | | | | | | | End of split % 194.05/27.17 | | | | | | | | | | | | % 194.05/27.17 | | | | | | | | | | | Case 2: % 194.05/27.17 | | | | | | | | | | | | % 194.05/27.17 | | | | | | | | | | | | (1399) all_872_6 = 0 & ~ (all_872_8 = v_y) & ? [v0: $i] % 194.05/27.17 | | | | | | | | | | | | : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ? % 194.05/27.17 | | | | | | | | | | | | [v4: any] : % 194.05/27.17 | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.17 | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, % 194.05/27.17 | | | | | | | | | | | | v0) = v1 & % 194.05/27.17 | | | | | | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.17 | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, % 194.05/27.17 | | | | | | | | | | | | v0) = v3 & c_member(all_685_0, v3, v_L) = v4 & % 194.05/27.17 | | | | | | | | | | | | c_member(all_685_0, v1, v_L) = v2 & $i(v3) & % 194.05/27.17 | | | | | | | | | | | | $i(v1) & $i(v0) & ((v2 = 0 & ~ (v4 = 0) & ~ % 194.05/27.17 | | | | | | | | | | | | (v0 = v_y)) | (v0 = v_y & all_872_2 = 0 & ~ % 194.05/27.17 | | | | | | | | | | | | (all_872_4 = 0) & ~ (all_872_9 = v_x)) | % 194.05/27.17 | | | | | | | | | | | | (v0 = v_y & all_872_8 = v_x & ~ (all_872_4 = % 194.05/27.17 | | | | | | | | | | | | 0) & ~ (all_872_9 = v_x)))) % 194.05/27.17 | | | | | | | | | | | | % 194.05/27.17 | | | | | | | | | | | | ALPHA: (1399) implies: % 194.05/27.17 | | | | | | | | | | | | (1400) all_872_6 = 0 % 194.05/27.17 | | | | | | | | | | | | % 194.05/27.17 | | | | | | | | | | | | REDUCE: (1329), (1400) imply: % 194.05/27.17 | | | | | | | | | | | | (1401) $false % 194.05/27.17 | | | | | | | | | | | | % 194.05/27.17 | | | | | | | | | | | | CLOSE: (1401) is inconsistent. % 194.05/27.17 | | | | | | | | | | | | % 194.05/27.17 | | | | | | | | | | | End of split % 194.05/27.17 | | | | | | | | | | | % 194.05/27.17 | | | | | | | | | | End of split % 194.05/27.17 | | | | | | | | | | % 194.05/27.17 | | | | | | | | | Case 2: % 194.05/27.17 | | | | | | | | | | % 194.05/27.17 | | | | | | | | | | (1402) ~ (all_872_2 = 0) % 194.05/27.17 | | | | | | | | | | % 194.05/27.17 | | | | | | | | | | REF_CLOSE: (3), (13), (17), (20), (21), (44), (89), (90), % 194.05/27.17 | | | | | | | | | | (91), (170), (180), (181), (182), (184), (185), % 194.05/27.17 | | | | | | | | | | (186), (187), (192), (198), (657), (1023), (1156), % 194.05/27.17 | | | | | | | | | | (1195), (1402) are inconsistent by sub-proof #2. % 194.05/27.17 | | | | | | | | | | % 194.05/27.17 | | | | | | | | | End of split % 194.05/27.17 | | | | | | | | | % 194.05/27.17 | | | | | | | | Case 2: % 194.05/27.17 | | | | | | | | | % 194.05/27.17 | | | | | | | | | (1403) ! [v0: $i] : ! [v1: $i] : ( ~ % 194.05/27.17 | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.17 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v0) = % 194.05/27.17 | | | | | | | | | v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: any] : % 194.05/27.17 | | | | | | | | | ? [v4: any] : % 194.05/27.17 | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.17 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, % 194.05/27.17 | | | | | | | | | v0) = v2 & c_member(all_676_0, v2, v_L) = v3 & % 194.05/27.17 | | | | | | | | | c_member(all_676_0, v1, v_L) = v4 & $i(v2) & ( ~ % 194.05/27.17 | | | | | | | | | (v3 = 0) | v4 = 0))) % 194.05/27.17 | | | | | | | | | % 194.05/27.17 | | | | | | | | | GROUND_INST: instantiating (1403) with all_872_8, all_872_1, % 194.05/27.17 | | | | | | | | | simplifying with (170), (179) gives: % 194.05/27.17 | | | | | | | | | (1404) ? [v0: $i] : ? [v1: any] : ? [v2: any] : % 194.05/27.17 | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.17 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, % 194.05/27.17 | | | | | | | | | all_872_8) = v0 & c_member(all_676_0, v0, v_L) = % 194.05/27.17 | | | | | | | | | v1 & c_member(all_676_0, all_872_1, v_L) = v2 & % 194.05/27.17 | | | | | | | | | $i(v0) & ( ~ (v1 = 0) | v2 = 0)) % 194.05/27.17 | | | | | | | | | % 194.05/27.17 | | | | | | | | | DELTA: instantiating (1404) with fresh symbols all_1164_0, % 194.05/27.17 | | | | | | | | | all_1164_1, all_1164_2 gives: % 194.05/27.17 | | | | | | | | | (1405) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.17 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, % 194.05/27.17 | | | | | | | | | all_872_8) = all_1164_2 & c_member(all_676_0, % 194.05/27.17 | | | | | | | | | all_1164_2, v_L) = all_1164_1 & % 194.05/27.17 | | | | | | | | | c_member(all_676_0, all_872_1, v_L) = all_1164_0 & % 194.05/27.17 | | | | | | | | | $i(all_1164_2) & ( ~ (all_1164_1 = 0) | all_1164_0 = % 194.05/27.17 | | | | | | | | | 0) % 194.05/27.17 | | | | | | | | | % 194.05/27.17 | | | | | | | | | ALPHA: (1405) implies: % 194.05/27.17 | | | | | | | | | (1406) $i(all_1164_2) % 194.05/27.17 | | | | | | | | | (1407) c_member(all_676_0, all_872_1, v_L) = all_1164_0 % 194.05/27.17 | | | | | | | | | (1408) c_member(all_676_0, all_1164_2, v_L) = all_1164_1 % 194.05/27.17 | | | | | | | | | (1409) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.17 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, % 194.05/27.17 | | | | | | | | | all_872_8) = all_1164_2 % 194.05/27.17 | | | | | | | | | (1410) ~ (all_1164_1 = 0) | all_1164_0 = 0 % 194.05/27.17 | | | | | | | | | % 194.05/27.17 | | | | | | | | | REDUCE: (89), (1408) imply: % 194.05/27.17 | | | | | | | | | (1411) c_member(all_622_1, all_1164_2, v_L) = all_1164_1 % 194.05/27.17 | | | | | | | | | % 194.05/27.17 | | | | | | | | | REDUCE: (89), (1407) imply: % 194.05/27.17 | | | | | | | | | (1412) c_member(all_622_1, all_872_1, v_L) = all_1164_0 % 194.05/27.17 | | | | | | | | | % 194.05/27.17 | | | | | | | | | GROUND_INST: instantiating (20) with all_872_0, all_1164_0, % 194.05/27.17 | | | | | | | | | v_L, all_872_1, all_622_1, simplifying with (184), % 194.05/27.17 | | | | | | | | | (1412) gives: % 194.05/27.17 | | | | | | | | | (1413) all_1164_0 = all_872_0 % 194.05/27.17 | | | | | | | | | % 194.05/27.17 | | | | | | | | | GROUND_INST: instantiating (21) with all_1134_2, all_1164_2, % 194.05/27.17 | | | | | | | | | all_872_8, all_872_8, % 194.05/27.17 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.17 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with % 194.05/27.17 | | | | | | | | | (1163), (1409) gives: % 194.05/27.17 | | | | | | | | | (1414) all_1164_2 = all_1134_2 % 194.05/27.17 | | | | | | | | | % 194.05/27.17 | | | | | | | | | REDUCE: (1411), (1414) imply: % 194.05/27.17 | | | | | | | | | (1415) c_member(all_622_1, all_1134_2, v_L) = all_1164_1 % 194.05/27.17 | | | | | | | | | % 194.05/27.17 | | | | | | | | | GROUND_INST: instantiating (20) with all_1134_1, all_1164_1, % 194.05/27.17 | | | | | | | | | v_L, all_1134_2, all_622_1, simplifying with % 194.05/27.17 | | | | | | | | | (1170), (1415) gives: % 194.05/27.17 | | | | | | | | | (1416) all_1164_1 = all_1134_1 % 194.05/27.17 | | | | | | | | | % 194.05/27.17 | | | | | | | | | BETA: splitting (191) gives: % 194.05/27.17 | | | | | | | | | % 194.05/27.17 | | | | | | | | | Case 1: % 194.05/27.17 | | | | | | | | | | % 194.05/27.17 | | | | | | | | | | (1417) all_872_0 = 0 % 194.05/27.17 | | | | | | | | | | % 194.05/27.17 | | | | | | | | | | REDUCE: (184), (1417) imply: % 194.05/27.17 | | | | | | | | | | (1418) c_member(all_622_1, all_872_1, v_L) = 0 % 194.05/27.17 | | | | | | | | | | % 194.05/27.17 | | | | | | | | | | BETA: splitting (190) gives: % 194.05/27.17 | | | | | | | | | | % 194.05/27.17 | | | | | | | | | | Case 1: % 194.05/27.17 | | | | | | | | | | | % 194.05/27.17 | | | | | | | | | | | (1419) all_872_2 = 0 % 194.05/27.17 | | | | | | | | | | | % 194.05/27.17 | | | | | | | | | | | REDUCE: (185), (1419) imply: % 194.05/27.17 | | | | | | | | | | | (1420) c_member(all_622_1, all_872_3, v_L) = 0 % 194.05/27.17 | | | | | | | | | | | % 194.05/27.17 | | | | | | | | | | | GROUND_INST: instantiating (fact_wf__not__sym) with v_x, % 194.05/27.17 | | | | | | | | | | | all_872_8, v_L, tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.17 | | | | | | | | | | | all_622_1, all_872_1, simplifying with (15), (16), % 194.05/27.17 | | | | | | | | | | | (17), (23), (170), (179), (1418) gives: % 194.05/27.17 | | | | | | | | | | | (1421) ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 194.05/27.17 | | | | | | | | | | | (c_Wellfounded_Owf(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.17 | | | | | | | | | | | v_L) = v0 & % 194.05/27.17 | | | | | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.17 | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, % 194.05/27.17 | | | | | | | | | | | v_x) = v1 & c_member(all_622_1, v1, v_L) = v2 % 194.05/27.17 | | | | | | | | | | | & $i(v1) & ( ~ (v2 = 0) | ~ (v0 = 0))) % 194.05/27.17 | | | | | | | | | | | % 194.05/27.17 | | | | | | | | | | | GROUND_INST: instantiating (43) with v_x, all_1092_2, % 194.05/27.17 | | | | | | | | | | | simplifying with (16), (922) gives: % 194.05/27.17 | | | | | | | | | | | (1422) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_676_0, % 194.05/27.17 | | | | | | | | | | | all_1092_2, v_L) = v0) % 194.05/27.17 | | | | | | | | | | | % 194.05/27.17 | | | | | | | | | | | GROUND_INST: instantiating (1403) with v_x, all_1092_2, % 194.05/27.17 | | | | | | | | | | | simplifying with (16), (922) gives: % 194.05/27.17 | | | | | | | | | | | (1423) ? [v0: $i] : ? [v1: any] : ? [v2: any] : % 194.05/27.17 | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.17 | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, % 194.05/27.17 | | | | | | | | | | | v_x) = v0 & c_member(all_676_0, v0, v_L) = v1 % 194.05/27.17 | | | | | | | | | | | & c_member(all_676_0, all_1092_2, v_L) = v2 & % 194.05/27.17 | | | | | | | | | | | $i(v0) & ( ~ (v1 = 0) | v2 = 0)) % 194.05/27.17 | | | | | | | | | | | % 194.05/27.17 | | | | | | | | | | | DELTA: instantiating (1422) with fresh symbol all_1223_0 % 194.05/27.17 | | | | | | | | | | | gives: % 194.05/27.17 | | | | | | | | | | | (1424) ~ (all_1223_0 = 0) & c_member(all_676_0, % 194.05/27.17 | | | | | | | | | | | all_1092_2, v_L) = all_1223_0 % 194.05/27.17 | | | | | | | | | | | % 194.05/27.17 | | | | | | | | | | | ALPHA: (1424) implies: % 194.05/27.17 | | | | | | | | | | | (1425) ~ (all_1223_0 = 0) % 194.05/27.17 | | | | | | | | | | | (1426) c_member(all_676_0, all_1092_2, v_L) = all_1223_0 % 194.05/27.17 | | | | | | | | | | | % 194.05/27.17 | | | | | | | | | | | DELTA: instantiating (1423) with fresh symbols all_1253_0, % 194.05/27.17 | | | | | | | | | | | all_1253_1, all_1253_2 gives: % 194.05/27.17 | | | | | | | | | | | (1427) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.17 | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v_x) % 194.05/27.17 | | | | | | | | | | | = all_1253_2 & c_member(all_676_0, all_1253_2, % 194.05/27.17 | | | | | | | | | | | v_L) = all_1253_1 & c_member(all_676_0, % 194.05/27.17 | | | | | | | | | | | all_1092_2, v_L) = all_1253_0 & $i(all_1253_2) & % 194.05/27.17 | | | | | | | | | | | ( ~ (all_1253_1 = 0) | all_1253_0 = 0) % 194.05/27.17 | | | | | | | | | | | % 194.05/27.17 | | | | | | | | | | | ALPHA: (1427) implies: % 194.05/27.17 | | | | | | | | | | | (1428) c_member(all_676_0, all_1092_2, v_L) = all_1253_0 % 194.05/27.17 | | | | | | | | | | | (1429) c_member(all_676_0, all_1253_2, v_L) = all_1253_1 % 194.05/27.17 | | | | | | | | | | | (1430) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.17 | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v_x) % 194.05/27.17 | | | | | | | | | | | = all_1253_2 % 194.05/27.17 | | | | | | | | | | | (1431) ~ (all_1253_1 = 0) | all_1253_0 = 0 % 194.05/27.17 | | | | | | | | | | | % 194.05/27.17 | | | | | | | | | | | DELTA: instantiating (1421) with fresh symbols all_1257_0, % 194.05/27.17 | | | | | | | | | | | all_1257_1, all_1257_2 gives: % 194.05/27.17 | | | | | | | | | | | (1432) c_Wellfounded_Owf(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.17 | | | | | | | | | | | v_L) = all_1257_2 & % 194.05/27.17 | | | | | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.17 | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v_x) % 194.05/27.17 | | | | | | | | | | | = all_1257_1 & c_member(all_622_1, all_1257_1, % 194.05/27.17 | | | | | | | | | | | v_L) = all_1257_0 & $i(all_1257_1) & ( ~ % 194.05/27.17 | | | | | | | | | | | (all_1257_0 = 0) | ~ (all_1257_2 = 0)) % 194.05/27.17 | | | | | | | | | | | % 194.05/27.17 | | | | | | | | | | | ALPHA: (1432) implies: % 194.05/27.17 | | | | | | | | | | | (1433) c_member(all_622_1, all_1257_1, v_L) = all_1257_0 % 194.05/27.17 | | | | | | | | | | | (1434) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.17 | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v_x) % 194.05/27.17 | | | | | | | | | | | = all_1257_1 % 194.05/27.17 | | | | | | | | | | | % 194.05/27.17 | | | | | | | | | | | REDUCE: (89), (1429) imply: % 194.05/27.17 | | | | | | | | | | | (1435) c_member(all_622_1, all_1253_2, v_L) = all_1253_1 % 194.05/27.17 | | | | | | | | | | | % 194.05/27.17 | | | | | | | | | | | REDUCE: (89), (1428) imply: % 194.05/27.17 | | | | | | | | | | | (1436) c_member(all_622_1, all_1092_2, v_L) = all_1253_0 % 194.05/27.17 | | | | | | | | | | | % 194.05/27.17 | | | | | | | | | | | REDUCE: (89), (1426) imply: % 194.05/27.17 | | | | | | | | | | | (1437) c_member(all_622_1, all_1092_2, v_L) = all_1223_0 % 194.05/27.17 | | | | | | | | | | | % 194.05/27.17 | | | | | | | | | | | GROUND_INST: instantiating (20) with all_1223_0, all_1253_0, % 194.05/27.17 | | | | | | | | | | | v_L, all_1092_2, all_622_1, simplifying with % 194.05/27.17 | | | | | | | | | | | (1436), (1437) gives: % 194.05/27.17 | | | | | | | | | | | (1438) all_1253_0 = all_1223_0 % 194.05/27.17 | | | | | | | | | | | % 194.05/27.17 | | | | | | | | | | | GROUND_INST: instantiating (21) with all_872_3, all_1257_1, % 194.05/27.17 | | | | | | | | | | | v_x, all_872_8, tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.17 | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with % 194.05/27.17 | | | | | | | | | | | (182), (1434) gives: % 194.05/27.17 | | | | | | | | | | | (1439) all_1257_1 = all_872_3 % 194.05/27.17 | | | | | | | | | | | % 194.05/27.17 | | | | | | | | | | | GROUND_INST: instantiating (21) with all_1253_2, all_1257_1, % 194.05/27.17 | | | | | | | | | | | v_x, all_872_8, tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.17 | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with % 194.05/27.17 | | | | | | | | | | | (1430), (1434) gives: % 194.05/27.17 | | | | | | | | | | | (1440) all_1257_1 = all_1253_2 % 194.05/27.17 | | | | | | | | | | | % 194.05/27.17 | | | | | | | | | | | COMBINE_EQS: (1439), (1440) imply: % 194.05/27.17 | | | | | | | | | | | (1441) all_1253_2 = all_872_3 % 194.05/27.17 | | | | | | | | | | | % 194.05/27.17 | | | | | | | | | | | REDUCE: (1433), (1439) imply: % 194.05/27.17 | | | | | | | | | | | (1442) c_member(all_622_1, all_872_3, v_L) = all_1257_0 % 194.05/27.17 | | | | | | | | | | | % 194.05/27.17 | | | | | | | | | | | REDUCE: (1435), (1441) imply: % 194.05/27.17 | | | | | | | | | | | (1443) c_member(all_622_1, all_872_3, v_L) = all_1253_1 % 194.05/27.17 | | | | | | | | | | | % 194.05/27.17 | | | | | | | | | | | BETA: splitting (1431) gives: % 194.05/27.17 | | | | | | | | | | | % 194.05/27.17 | | | | | | | | | | | Case 1: % 194.05/27.17 | | | | | | | | | | | | % 194.05/27.17 | | | | | | | | | | | | (1444) ~ (all_1253_1 = 0) % 194.05/27.17 | | | | | | | | | | | | % 194.05/27.17 | | | | | | | | | | | | GROUND_INST: instantiating (20) with 0, all_1257_0, v_L, % 194.05/27.17 | | | | | | | | | | | | all_872_3, all_622_1, simplifying with (1420), % 194.05/27.17 | | | | | | | | | | | | (1442) gives: % 194.05/27.17 | | | | | | | | | | | | (1445) all_1257_0 = 0 % 194.05/27.17 | | | | | | | | | | | | % 194.05/27.17 | | | | | | | | | | | | GROUND_INST: instantiating (20) with all_1253_1, all_1257_0, % 194.05/27.17 | | | | | | | | | | | | v_L, all_872_3, all_622_1, simplifying with % 194.05/27.17 | | | | | | | | | | | | (1442), (1443) gives: % 194.05/27.17 | | | | | | | | | | | | (1446) all_1257_0 = all_1253_1 % 194.05/27.17 | | | | | | | | | | | | % 194.05/27.17 | | | | | | | | | | | | COMBINE_EQS: (1445), (1446) imply: % 194.05/27.17 | | | | | | | | | | | | (1447) all_1253_1 = 0 % 194.05/27.17 | | | | | | | | | | | | % 194.05/27.17 | | | | | | | | | | | | SIMP: (1447) implies: % 194.05/27.17 | | | | | | | | | | | | (1448) all_1253_1 = 0 % 194.05/27.17 | | | | | | | | | | | | % 194.05/27.17 | | | | | | | | | | | | REDUCE: (1444), (1448) imply: % 194.05/27.17 | | | | | | | | | | | | (1449) $false % 194.05/27.17 | | | | | | | | | | | | % 194.05/27.17 | | | | | | | | | | | | CLOSE: (1449) is inconsistent. % 194.05/27.17 | | | | | | | | | | | | % 194.05/27.17 | | | | | | | | | | | Case 2: % 194.05/27.17 | | | | | | | | | | | | % 194.05/27.17 | | | | | | | | | | | | (1450) all_1253_0 = 0 % 194.05/27.17 | | | | | | | | | | | | % 194.05/27.17 | | | | | | | | | | | | COMBINE_EQS: (1438), (1450) imply: % 194.05/27.17 | | | | | | | | | | | | (1451) all_1223_0 = 0 % 194.05/27.17 | | | | | | | | | | | | % 194.05/27.17 | | | | | | | | | | | | SIMP: (1451) implies: % 194.05/27.17 | | | | | | | | | | | | (1452) all_1223_0 = 0 % 194.05/27.17 | | | | | | | | | | | | % 194.05/27.17 | | | | | | | | | | | | REDUCE: (1425), (1452) imply: % 194.05/27.17 | | | | | | | | | | | | (1453) $false % 194.05/27.17 | | | | | | | | | | | | % 194.05/27.17 | | | | | | | | | | | | CLOSE: (1453) is inconsistent. % 194.05/27.17 | | | | | | | | | | | | % 194.05/27.17 | | | | | | | | | | | End of split % 194.05/27.17 | | | | | | | | | | | % 194.05/27.17 | | | | | | | | | | Case 2: % 194.05/27.17 | | | | | | | | | | | % 194.05/27.17 | | | | | | | | | | | (1454) ~ (all_872_2 = 0) % 194.05/27.17 | | | | | | | | | | | % 194.05/27.17 | | | | | | | | | | | BETA: splitting (923) gives: % 194.05/27.17 | | | | | | | | | | | % 194.05/27.17 | | | | | | | | | | | Case 1: % 194.05/27.17 | | | | | | | | | | | | % 194.05/27.17 | | | | | | | | | | | | % 194.05/27.17 | | | | | | | | | | | | GROUND_INST: instantiating (43) with all_872_8, all_1134_2, % 194.05/27.17 | | | | | | | | | | | | simplifying with (170), (1163) gives: % 194.05/27.17 | | | | | | | | | | | | (1455) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_676_0, % 194.05/27.17 | | | | | | | | | | | | all_1134_2, v_L) = v0) % 194.05/27.17 | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | GROUND_INST: instantiating (918) with all_872_8, all_1134_2, % 194.05/27.18 | | | | | | | | | | | | simplifying with (170), (1163) gives: % 194.05/27.18 | | | | | | | | | | | | (1456) ? [v0: $i] : ? [v1: any] : ? [v2: any] : % 194.05/27.18 | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.18 | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, % 194.05/27.18 | | | | | | | | | | | | all_872_8) = v0 & c_member(all_676_0, v0, v_L) % 194.05/27.18 | | | | | | | | | | | | = v1 & c_member(all_676_0, all_1134_2, v_L) = v2 % 194.05/27.18 | | | | | | | | | | | | & $i(v0) & ( ~ (v1 = 0) | v2 = 0)) % 194.05/27.18 | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | DELTA: instantiating (1455) with fresh symbol all_1225_0 % 194.05/27.18 | | | | | | | | | | | | gives: % 194.05/27.18 | | | | | | | | | | | | (1457) ~ (all_1225_0 = 0) & c_member(all_676_0, % 194.05/27.18 | | | | | | | | | | | | all_1134_2, v_L) = all_1225_0 % 194.05/27.18 | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | ALPHA: (1457) implies: % 194.05/27.18 | | | | | | | | | | | | (1458) ~ (all_1225_0 = 0) % 194.05/27.18 | | | | | | | | | | | | (1459) c_member(all_676_0, all_1134_2, v_L) = all_1225_0 % 194.05/27.18 | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | DELTA: instantiating (1456) with fresh symbols % 194.05/27.18 | | | | | | | | | | | | all_1253_0, all_1253_1, all_1253_2 gives: % 194.05/27.18 | | | | | | | | | | | | (1460) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.18 | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, all_872_8) % 194.05/27.18 | | | | | | | | | | | | = all_1253_2 & c_member(all_676_0, all_1253_2, % 194.05/27.18 | | | | | | | | | | | | v_L) = all_1253_1 & c_member(all_676_0, % 194.05/27.18 | | | | | | | | | | | | all_1134_2, v_L) = all_1253_0 & $i(all_1253_2) & % 194.05/27.18 | | | | | | | | | | | | ( ~ (all_1253_1 = 0) | all_1253_0 = 0) % 194.05/27.18 | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | ALPHA: (1460) implies: % 194.05/27.18 | | | | | | | | | | | | (1461) c_member(all_676_0, all_1134_2, v_L) = all_1253_0 % 194.05/27.18 | | | | | | | | | | | | (1462) c_member(all_676_0, all_1253_2, v_L) = all_1253_1 % 194.05/27.18 | | | | | | | | | | | | (1463) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.18 | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, all_872_8) % 194.05/27.18 | | | | | | | | | | | | = all_1253_2 % 194.05/27.18 | | | | | | | | | | | | (1464) ~ (all_1253_1 = 0) | all_1253_0 = 0 % 194.05/27.18 | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | REDUCE: (89), (1462) imply: % 194.05/27.18 | | | | | | | | | | | | (1465) c_member(all_622_1, all_1253_2, v_L) = all_1253_1 % 194.05/27.18 | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | REDUCE: (89), (1461) imply: % 194.05/27.18 | | | | | | | | | | | | (1466) c_member(all_622_1, all_1134_2, v_L) = all_1253_0 % 194.05/27.18 | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | REDUCE: (89), (1459) imply: % 194.05/27.18 | | | | | | | | | | | | (1467) c_member(all_622_1, all_1134_2, v_L) = all_1225_0 % 194.05/27.18 | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | GROUND_INST: instantiating (20) with all_1225_0, all_1253_0, % 194.05/27.18 | | | | | | | | | | | | v_L, all_1134_2, all_622_1, simplifying with % 194.05/27.18 | | | | | | | | | | | | (1466), (1467) gives: % 194.05/27.18 | | | | | | | | | | | | (1468) all_1253_0 = all_1225_0 % 194.05/27.18 | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | GROUND_INST: instantiating (21) with all_872_1, all_1253_2, % 194.05/27.18 | | | | | | | | | | | | all_872_8, v_x, tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.18 | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with % 194.05/27.18 | | | | | | | | | | | | (179), (1463) gives: % 194.05/27.18 | | | | | | | | | | | | (1469) all_1253_2 = all_872_1 % 194.05/27.18 | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | REDUCE: (1465), (1469) imply: % 194.05/27.18 | | | | | | | | | | | | (1470) c_member(all_622_1, all_872_1, v_L) = all_1253_1 % 194.05/27.18 | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | BETA: splitting (1464) gives: % 194.05/27.18 | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | Case 1: % 194.05/27.18 | | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | | (1471) ~ (all_1253_1 = 0) % 194.05/27.18 | | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | | GROUND_INST: instantiating (20) with 0, all_1253_1, v_L, % 194.05/27.18 | | | | | | | | | | | | | all_872_1, all_622_1, simplifying with (1418), % 194.05/27.18 | | | | | | | | | | | | | (1470) gives: % 194.05/27.18 | | | | | | | | | | | | | (1472) all_1253_1 = 0 % 194.05/27.18 | | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | | REDUCE: (1471), (1472) imply: % 194.05/27.18 | | | | | | | | | | | | | (1473) $false % 194.05/27.18 | | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | | CLOSE: (1473) is inconsistent. % 194.05/27.18 | | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | Case 2: % 194.05/27.18 | | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | | (1474) all_1253_0 = 0 % 194.05/27.18 | | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | | COMBINE_EQS: (1468), (1474) imply: % 194.05/27.18 | | | | | | | | | | | | | (1475) all_1225_0 = 0 % 194.05/27.18 | | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | | REDUCE: (1458), (1475) imply: % 194.05/27.18 | | | | | | | | | | | | | (1476) $false % 194.05/27.18 | | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | | CLOSE: (1476) is inconsistent. % 194.05/27.18 | | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | End of split % 194.05/27.18 | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | Case 2: % 194.05/27.18 | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | (1477) all_1092_0 = 0 % 194.05/27.18 | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | COMBINE_EQS: (925), (1477) imply: % 194.05/27.18 | | | | | | | | | | | | (1478) all_872_2 = 0 % 194.05/27.18 | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | REDUCE: (1454), (1478) imply: % 194.05/27.18 | | | | | | | | | | | | (1479) $false % 194.05/27.18 | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | CLOSE: (1479) is inconsistent. % 194.05/27.18 | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | End of split % 194.05/27.18 | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | End of split % 194.05/27.18 | | | | | | | | | | % 194.05/27.18 | | | | | | | | | Case 2: % 194.05/27.18 | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | (1480) ~ (all_872_0 = 0) % 194.05/27.18 | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | BETA: splitting (1410) gives: % 194.05/27.18 | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | Case 1: % 194.05/27.18 | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | (1481) ~ (all_1164_1 = 0) % 194.05/27.18 | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | REDUCE: (1416), (1481) imply: % 194.05/27.18 | | | | | | | | | | | (1482) ~ (all_1134_1 = 0) % 194.05/27.18 | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | BETA: splitting (188) gives: % 194.05/27.18 | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | Case 1: % 194.05/27.18 | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | (1483) all_872_6 = 0 % 194.05/27.18 | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | REDUCE: (187), (1483) imply: % 194.05/27.18 | | | | | | | | | | | | (1484) c_member(all_622_1, all_872_7, v_L) = 0 % 194.05/27.18 | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | BETA: splitting (190) gives: % 194.05/27.18 | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | Case 1: % 194.05/27.18 | | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | | (1485) all_872_2 = 0 % 194.05/27.18 | | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | | REDUCE: (185), (1485) imply: % 194.05/27.18 | | | | | | | | | | | | | (1486) c_member(all_622_1, all_872_3, v_L) = 0 % 194.05/27.18 | | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | | GROUND_INST: instantiating (43) with v_x, all_1092_2, % 194.05/27.18 | | | | | | | | | | | | | simplifying with (16), (922) gives: % 194.05/27.18 | | | | | | | | | | | | | (1487) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_676_0, % 194.05/27.18 | | | | | | | | | | | | | all_1092_2, v_L) = v0) % 194.05/27.18 | | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | | GROUND_INST: instantiating (1403) with v_x, all_1092_2, % 194.05/27.18 | | | | | | | | | | | | | simplifying with (16), (922) gives: % 194.05/27.18 | | | | | | | | | | | | | (1488) ? [v0: $i] : ? [v1: any] : ? [v2: any] : % 194.05/27.18 | | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.18 | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, % 194.05/27.18 | | | | | | | | | | | | | v_x) = v0 & c_member(all_676_0, v0, v_L) = v1 % 194.05/27.18 | | | | | | | | | | | | | & c_member(all_676_0, all_1092_2, v_L) = v2 & % 194.05/27.18 | | | | | | | | | | | | | $i(v0) & ( ~ (v1 = 0) | v2 = 0)) % 194.05/27.18 | | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | | DELTA: instantiating (1487) with fresh symbol all_1229_0 % 194.05/27.18 | | | | | | | | | | | | | gives: % 194.05/27.18 | | | | | | | | | | | | | (1489) ~ (all_1229_0 = 0) & c_member(all_676_0, % 194.05/27.18 | | | | | | | | | | | | | all_1092_2, v_L) = all_1229_0 % 194.05/27.18 | | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | | ALPHA: (1489) implies: % 194.05/27.18 | | | | | | | | | | | | | (1490) ~ (all_1229_0 = 0) % 194.05/27.18 | | | | | | | | | | | | | (1491) c_member(all_676_0, all_1092_2, v_L) = all_1229_0 % 194.05/27.18 | | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | | DELTA: instantiating (1488) with fresh symbols % 194.05/27.18 | | | | | | | | | | | | | all_1263_0, all_1263_1, all_1263_2 gives: % 194.05/27.18 | | | | | | | | | | | | | (1492) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.18 | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v_x) % 194.05/27.18 | | | | | | | | | | | | | = all_1263_2 & c_member(all_676_0, all_1263_2, % 194.05/27.18 | | | | | | | | | | | | | v_L) = all_1263_1 & c_member(all_676_0, % 194.05/27.18 | | | | | | | | | | | | | all_1092_2, v_L) = all_1263_0 & $i(all_1263_2) & % 194.05/27.18 | | | | | | | | | | | | | ( ~ (all_1263_1 = 0) | all_1263_0 = 0) % 194.05/27.18 | | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | | ALPHA: (1492) implies: % 194.05/27.18 | | | | | | | | | | | | | (1493) c_member(all_676_0, all_1092_2, v_L) = all_1263_0 % 194.05/27.18 | | | | | | | | | | | | | (1494) c_member(all_676_0, all_1263_2, v_L) = all_1263_1 % 194.05/27.18 | | | | | | | | | | | | | (1495) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.18 | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v_x) % 194.05/27.18 | | | | | | | | | | | | | = all_1263_2 % 194.05/27.18 | | | | | | | | | | | | | (1496) ~ (all_1263_1 = 0) | all_1263_0 = 0 % 194.05/27.18 | | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | | REDUCE: (89), (1494) imply: % 194.05/27.18 | | | | | | | | | | | | | (1497) c_member(all_622_1, all_1263_2, v_L) = all_1263_1 % 194.05/27.18 | | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | | REDUCE: (89), (1493) imply: % 194.05/27.18 | | | | | | | | | | | | | (1498) c_member(all_622_1, all_1092_2, v_L) = all_1263_0 % 194.05/27.18 | | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | | REDUCE: (89), (1491) imply: % 194.05/27.18 | | | | | | | | | | | | | (1499) c_member(all_622_1, all_1092_2, v_L) = all_1229_0 % 194.05/27.18 | | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | | GROUND_INST: instantiating (20) with all_1229_0, all_1263_0, % 194.05/27.18 | | | | | | | | | | | | | v_L, all_1092_2, all_622_1, simplifying with % 194.05/27.18 | | | | | | | | | | | | | (1498), (1499) gives: % 194.05/27.18 | | | | | | | | | | | | | (1500) all_1263_0 = all_1229_0 % 194.05/27.18 | | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | | GROUND_INST: instantiating (21) with all_872_3, all_1263_2, % 194.05/27.18 | | | | | | | | | | | | | v_x, all_872_8, tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.18 | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with % 194.05/27.18 | | | | | | | | | | | | | (182), (1495) gives: % 194.05/27.18 | | | | | | | | | | | | | (1501) all_1263_2 = all_872_3 % 194.05/27.18 | | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | | REDUCE: (1497), (1501) imply: % 194.05/27.18 | | | | | | | | | | | | | (1502) c_member(all_622_1, all_872_3, v_L) = all_1263_1 % 194.05/27.18 | | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | | BETA: splitting (1496) gives: % 194.05/27.18 | | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | | Case 1: % 194.05/27.18 | | | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | | | (1503) ~ (all_1263_1 = 0) % 194.05/27.18 | | | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with 0, all_1263_1, v_L, % 194.05/27.18 | | | | | | | | | | | | | | all_872_3, all_622_1, simplifying with (1486), % 194.05/27.18 | | | | | | | | | | | | | | (1502) gives: % 194.05/27.18 | | | | | | | | | | | | | | (1504) all_1263_1 = 0 % 194.05/27.18 | | | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | | | REDUCE: (1503), (1504) imply: % 194.05/27.18 | | | | | | | | | | | | | | (1505) $false % 194.05/27.18 | | | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | | | CLOSE: (1505) is inconsistent. % 194.05/27.18 | | | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | | Case 2: % 194.05/27.18 | | | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | | | (1506) all_1263_0 = 0 % 194.05/27.18 | | | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | | | COMBINE_EQS: (1500), (1506) imply: % 194.05/27.18 | | | | | | | | | | | | | | (1507) all_1229_0 = 0 % 194.05/27.18 | | | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | | | SIMP: (1507) implies: % 194.05/27.18 | | | | | | | | | | | | | | (1508) all_1229_0 = 0 % 194.05/27.18 | | | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | | | REDUCE: (1490), (1508) imply: % 194.05/27.18 | | | | | | | | | | | | | | (1509) $false % 194.05/27.18 | | | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | | | CLOSE: (1509) is inconsistent. % 194.05/27.18 | | | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | | End of split % 194.05/27.18 | | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | Case 2: % 194.05/27.18 | | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | | (1510) ~ (all_872_2 = 0) % 194.05/27.18 | | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | | REF_CLOSE: (3), (13), (17), (20), (21), (44), (89), (90), % 194.05/27.18 | | | | | | | | | | | | | (91), (170), (180), (181), (182), (184), (185), % 194.05/27.18 | | | | | | | | | | | | | (186), (192), (198), (657), (1023), (1156), % 194.05/27.18 | | | | | | | | | | | | | (1480), (1484), (1510) are inconsistent by % 194.05/27.18 | | | | | | | | | | | | | sub-proof #7. % 194.05/27.18 | | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | End of split % 194.05/27.18 | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | Case 2: % 194.05/27.18 | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | (1511) ~ (all_872_6 = 0) % 194.05/27.18 | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | BETA: splitting (657) gives: % 194.05/27.18 | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | Case 1: % 194.05/27.18 | | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | | (1512) all_872_4 = 0 & all_872_8 = v_y & ? [v0: $i] : ? % 194.05/27.18 | | | | | | | | | | | | | [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = % 194.05/27.18 | | | | | | | | | | | | | 0) & ~ (v0 = v_y) & % 194.05/27.18 | | | | | | | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.18 | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, % 194.05/27.18 | | | | | | | | | | | | | v0) = v2 & % 194.05/27.18 | | | | | | | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.18 | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v0) = v1 % 194.05/27.18 | | | | | | | | | | | | | & c_member(all_685_0, v2, v_L) = v3 & % 194.05/27.18 | | | | | | | | | | | | | c_member(all_685_0, v1, v_L) = 0 & $i(v2) & % 194.05/27.18 | | | | | | | | | | | | | $i(v1) & $i(v0)) % 194.05/27.18 | | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | | ALPHA: (1512) implies: % 194.05/27.18 | | | | | | | | | | | | | (1513) all_872_8 = v_y % 194.05/27.18 | | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | | REDUCE: (182), (1513) imply: % 194.05/27.18 | | | | | | | | | | | | | (1514) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.18 | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v_x) = % 194.05/27.18 | | | | | | | | | | | | | all_872_3 % 194.05/27.18 | | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | | BETA: splitting (198) gives: % 194.05/27.18 | | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | | Case 1: % 194.05/27.18 | | | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | | | (1515) all_872_8 = v_x % 194.05/27.18 | | | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | | | COMBINE_EQS: (1513), (1515) imply: % 194.05/27.18 | | | | | | | | | | | | | | (1516) v_x = v_y % 194.05/27.18 | | | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | | | REDUCE: (13), (1516) imply: % 194.05/27.18 | | | | | | | | | | | | | | (1517) $false % 194.05/27.18 | | | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | | | CLOSE: (1517) is inconsistent. % 194.05/27.18 | | | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | | Case 2: % 194.05/27.18 | | | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | | | (1518) ~ (all_872_8 = v_x) % 194.05/27.18 | | | | | | | | | | | | | | (1519) ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 194.05/27.18 | | | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.18 | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, % 194.05/27.18 | | | | | | | | | | | | | | all_872_8) = v1 & c_member(all_676_0, v1, v_L) % 194.05/27.18 | | | | | | | | | | | | | | = v2 & c_member(all_676_0, all_872_3, v_L) = v0 % 194.05/27.18 | | | | | | | | | | | | | | & $i(v1) & (v2 = 0 | v0 = 0)) % 194.05/27.18 | | | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | | | DELTA: instantiating (1519) with fresh symbols % 194.05/27.18 | | | | | | | | | | | | | | all_1204_0, all_1204_1, all_1204_2 gives: % 194.05/27.18 | | | | | | | | | | | | | | (1520) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.18 | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, all_872_8) % 194.05/27.18 | | | | | | | | | | | | | | = all_1204_1 & c_member(all_676_0, all_1204_1, % 194.05/27.18 | | | | | | | | | | | | | | v_L) = all_1204_0 & c_member(all_676_0, % 194.05/27.18 | | | | | | | | | | | | | | all_872_3, v_L) = all_1204_2 & $i(all_1204_1) & % 194.05/27.18 | | | | | | | | | | | | | | (all_1204_0 = 0 | all_1204_2 = 0) % 194.05/27.18 | | | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | | | ALPHA: (1520) implies: % 194.05/27.18 | | | | | | | | | | | | | | (1521) c_member(all_676_0, all_872_3, v_L) = all_1204_2 % 194.05/27.18 | | | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | | | REDUCE: (1513), (1518) imply: % 194.05/27.18 | | | | | | | | | | | | | | (1522) ~ (v_x = v_y) % 194.05/27.18 | | | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | | | REDUCE: (89), (1521) imply: % 194.05/27.18 | | | | | | | | | | | | | | (1523) c_member(all_622_1, all_872_3, v_L) = all_1204_2 % 194.05/27.18 | | | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | | | BETA: splitting (192) gives: % 194.05/27.18 | | | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | | | Case 1: % 194.05/27.18 | | | | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | | | | (1524) all_872_8 = v_x % 194.05/27.18 | | | | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | | | | COMBINE_EQS: (1513), (1524) imply: % 194.05/27.18 | | | | | | | | | | | | | | | (1525) v_x = v_y % 194.05/27.18 | | | | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | | | | REDUCE: (13), (1525) imply: % 194.05/27.18 | | | | | | | | | | | | | | | (1526) $false % 194.05/27.18 | | | | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | | | | CLOSE: (1526) is inconsistent. % 194.05/27.18 | | | | | | | | | | | | | | | % 194.05/27.18 | | | | | | | | | | | | | | Case 2: % 194.05/27.18 | | | | | | | | | | | | | | | % 194.05/27.19 | | | | | | | | | | | | | | | (1527) ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 194.05/27.19 | | | | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.19 | | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, % 194.05/27.19 | | | | | | | | | | | | | | | v_x) = v1 & c_member(all_676_0, v1, v_L) = v2 % 194.05/27.19 | | | | | | | | | | | | | | | & c_member(all_676_0, all_872_1, v_L) = v0 & % 194.05/27.19 | | | | | | | | | | | | | | | $i(v1) & (v2 = 0 | v0 = 0)) % 194.05/27.19 | | | | | | | | | | | | | | | % 194.05/27.19 | | | | | | | | | | | | | | | DELTA: instantiating (1527) with fresh symbols % 194.05/27.19 | | | | | | | | | | | | | | | all_1210_0, all_1210_1, all_1210_2 gives: % 194.05/27.19 | | | | | | | | | | | | | | | (1528) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.19 | | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v_x) % 194.05/27.19 | | | | | | | | | | | | | | | = all_1210_1 & c_member(all_676_0, all_1210_1, % 194.05/27.19 | | | | | | | | | | | | | | | v_L) = all_1210_0 & c_member(all_676_0, % 194.05/27.19 | | | | | | | | | | | | | | | all_872_1, v_L) = all_1210_2 & $i(all_1210_1) & % 194.05/27.19 | | | | | | | | | | | | | | | (all_1210_0 = 0 | all_1210_2 = 0) % 194.05/27.19 | | | | | | | | | | | | | | | % 194.05/27.19 | | | | | | | | | | | | | | | ALPHA: (1528) implies: % 194.05/27.19 | | | | | | | | | | | | | | | (1529) c_member(all_676_0, all_872_1, v_L) = all_1210_2 % 194.05/27.19 | | | | | | | | | | | | | | | (1530) c_member(all_676_0, all_1210_1, v_L) = all_1210_0 % 194.05/27.19 | | | | | | | | | | | | | | | (1531) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.19 | | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v_x) % 194.05/27.19 | | | | | | | | | | | | | | | = all_1210_1 % 194.05/27.19 | | | | | | | | | | | | | | | (1532) all_1210_0 = 0 | all_1210_2 = 0 % 194.05/27.19 | | | | | | | | | | | | | | | % 194.05/27.19 | | | | | | | | | | | | | | | REDUCE: (1513), (1531) imply: % 194.05/27.19 | | | | | | | | | | | | | | | (1533) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.19 | | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v_x) = % 194.05/27.19 | | | | | | | | | | | | | | | all_1210_1 % 194.05/27.19 | | | | | | | | | | | | | | | % 194.05/27.19 | | | | | | | | | | | | | | | REDUCE: (89), (1530) imply: % 194.05/27.19 | | | | | | | | | | | | | | | (1534) c_member(all_622_1, all_1210_1, v_L) = all_1210_0 % 194.05/27.19 | | | | | | | | | | | | | | | % 194.05/27.19 | | | | | | | | | | | | | | | REDUCE: (89), (1529) imply: % 194.05/27.19 | | | | | | | | | | | | | | | (1535) c_member(all_622_1, all_872_1, v_L) = all_1210_2 % 194.05/27.19 | | | | | | | | | | | | | | | % 194.05/27.19 | | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with all_872_2, all_1204_2, % 194.05/27.19 | | | | | | | | | | | | | | | v_L, all_872_3, all_622_1, simplifying with (185), % 194.05/27.19 | | | | | | | | | | | | | | | (1523) gives: % 194.05/27.19 | | | | | | | | | | | | | | | (1536) all_1204_2 = all_872_2 % 194.05/27.19 | | | | | | | | | | | | | | | % 194.05/27.19 | | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with all_872_0, all_1210_2, % 194.05/27.19 | | | | | | | | | | | | | | | v_L, all_872_1, all_622_1, simplifying with (184), % 194.05/27.19 | | | | | | | | | | | | | | | (1535) gives: % 194.05/27.19 | | | | | | | | | | | | | | | (1537) all_1210_2 = all_872_0 % 194.05/27.19 | | | | | | | | | | | | | | | % 194.05/27.19 | | | | | | | | | | | | | | | GROUND_INST: instantiating (21) with all_872_3, all_1210_1, % 194.05/27.19 | | | | | | | | | | | | | | | v_x, v_y, tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.19 | | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with % 194.05/27.19 | | | | | | | | | | | | | | | (1514), (1533) gives: % 194.05/27.19 | | | | | | | | | | | | | | | (1538) all_1210_1 = all_872_3 % 194.05/27.19 | | | | | | | | | | | | | | | % 194.05/27.19 | | | | | | | | | | | | | | | REDUCE: (1534), (1538) imply: % 194.05/27.19 | | | | | | | | | | | | | | | (1539) c_member(all_622_1, all_872_3, v_L) = all_1210_0 % 194.05/27.19 | | | | | | | | | | | | | | | % 194.05/27.19 | | | | | | | | | | | | | | | BETA: splitting (1532) gives: % 194.05/27.19 | | | | | | | | | | | | | | | % 194.05/27.19 | | | | | | | | | | | | | | | Case 1: % 194.05/27.19 | | | | | | | | | | | | | | | | % 194.05/27.19 | | | | | | | | | | | | | | | | (1540) all_1210_0 = 0 % 194.05/27.19 | | | | | | | | | | | | | | | | % 194.05/27.19 | | | | | | | | | | | | | | | | REDUCE: (1539), (1540) imply: % 194.05/27.19 | | | | | | | | | | | | | | | | (1541) c_member(all_622_1, all_872_3, v_L) = 0 % 194.05/27.19 | | | | | | | | | | | | | | | | % 194.05/27.19 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with all_872_2, 0, v_L, % 194.05/27.19 | | | | | | | | | | | | | | | | all_872_3, all_622_1, simplifying with (185), % 194.05/27.19 | | | | | | | | | | | | | | | | (1541) gives: % 194.05/27.19 | | | | | | | | | | | | | | | | (1542) all_872_2 = 0 % 194.05/27.19 | | | | | | | | | | | | | | | | % 194.05/27.19 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with v_L, all_1134_2, all_622_1, % 194.05/27.19 | | | | | | | | | | | | | | | | all_1134_1, simplifying with (17), (91), (1160), % 194.05/27.19 | | | | | | | | | | | | | | | | (1170) gives: % 194.05/27.19 | | | | | | | | | | | | | | | | (1543) all_1134_1 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ % 194.05/27.19 | | | | | | | | | | | | | | | | (v1 = 0) & hBOOL(v0) = v1 & hAPP(v_L, % 194.05/27.19 | | | | | | | | | | | | | | | | all_1134_2) = v0 & $i(v0)) % 194.05/27.19 | | | | | | | | | | | | | | | | % 194.05/27.19 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (43) with v_x, all_1092_2, % 194.05/27.19 | | | | | | | | | | | | | | | | simplifying with (16), (922) gives: % 194.05/27.19 | | | | | | | | | | | | | | | | (1544) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_676_0, % 194.05/27.19 | | | | | | | | | | | | | | | | all_1092_2, v_L) = v0) % 194.05/27.19 | | | | | | | | | | | | | | | | % 194.05/27.19 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1403) with v_x, all_1092_2, % 194.05/27.19 | | | | | | | | | | | | | | | | simplifying with (16), (922) gives: % 194.05/27.19 | | | | | | | | | | | | | | | | (1545) ? [v0: $i] : ? [v1: any] : ? [v2: any] : % 194.05/27.19 | | | | | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.19 | | | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, % 194.05/27.19 | | | | | | | | | | | | | | | | v_x) = v0 & c_member(all_676_0, v0, v_L) = v1 % 194.05/27.19 | | | | | | | | | | | | | | | | & c_member(all_676_0, all_1092_2, v_L) = v2 & % 194.05/27.19 | | | | | | | | | | | | | | | | $i(v0) & ( ~ (v1 = 0) | v2 = 0)) % 194.05/27.19 | | | | | | | | | | | | | | | | % 194.05/27.19 | | | | | | | | | | | | | | | | DELTA: instantiating (1544) with fresh symbol all_1253_0 % 194.05/27.19 | | | | | | | | | | | | | | | | gives: % 194.05/27.19 | | | | | | | | | | | | | | | | (1546) ~ (all_1253_0 = 0) & c_member(all_676_0, % 194.05/27.19 | | | | | | | | | | | | | | | | all_1092_2, v_L) = all_1253_0 % 194.05/27.19 | | | | | | | | | | | | | | | | % 194.05/27.19 | | | | | | | | | | | | | | | | ALPHA: (1546) implies: % 194.05/27.19 | | | | | | | | | | | | | | | | (1547) ~ (all_1253_0 = 0) % 194.05/27.19 | | | | | | | | | | | | | | | | (1548) c_member(all_676_0, all_1092_2, v_L) = all_1253_0 % 194.05/27.19 | | | | | | | | | | | | | | | | % 194.05/27.19 | | | | | | | | | | | | | | | | DELTA: instantiating (1545) with fresh symbols % 194.05/27.19 | | | | | | | | | | | | | | | | all_1289_0, all_1289_1, all_1289_2 gives: % 194.05/27.19 | | | | | | | | | | | | | | | | (1549) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.19 | | | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v_x) % 194.05/27.19 | | | | | | | | | | | | | | | | = all_1289_2 & c_member(all_676_0, all_1289_2, % 194.05/27.19 | | | | | | | | | | | | | | | | v_L) = all_1289_1 & c_member(all_676_0, % 194.05/27.19 | | | | | | | | | | | | | | | | all_1092_2, v_L) = all_1289_0 & $i(all_1289_2) & % 194.05/27.19 | | | | | | | | | | | | | | | | ( ~ (all_1289_1 = 0) | all_1289_0 = 0) % 194.05/27.19 | | | | | | | | | | | | | | | | % 194.05/27.19 | | | | | | | | | | | | | | | | ALPHA: (1549) implies: % 194.05/27.19 | | | | | | | | | | | | | | | | (1550) c_member(all_676_0, all_1092_2, v_L) = all_1289_0 % 194.05/27.19 | | | | | | | | | | | | | | | | (1551) c_member(all_676_0, all_1289_2, v_L) = all_1289_1 % 194.05/27.19 | | | | | | | | | | | | | | | | (1552) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.19 | | | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v_x) % 194.05/27.19 | | | | | | | | | | | | | | | | = all_1289_2 % 194.05/27.19 | | | | | | | | | | | | | | | | (1553) ~ (all_1289_1 = 0) | all_1289_0 = 0 % 194.05/27.19 | | | | | | | | | | | | | | | | % 194.05/27.19 | | | | | | | | | | | | | | | | REDUCE: (1513), (1552) imply: % 194.05/27.19 | | | | | | | | | | | | | | | | (1554) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.19 | | | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v_x) = % 194.05/27.19 | | | | | | | | | | | | | | | | all_1289_2 % 194.05/27.19 | | | | | | | | | | | | | | | | % 194.05/27.19 | | | | | | | | | | | | | | | | REDUCE: (89), (1551) imply: % 194.05/27.19 | | | | | | | | | | | | | | | | (1555) c_member(all_622_1, all_1289_2, v_L) = all_1289_1 % 194.05/27.19 | | | | | | | | | | | | | | | | % 194.05/27.19 | | | | | | | | | | | | | | | | REDUCE: (89), (1550) imply: % 194.05/27.19 | | | | | | | | | | | | | | | | (1556) c_member(all_622_1, all_1092_2, v_L) = all_1289_0 % 194.05/27.19 | | | | | | | | | | | | | | | | % 194.05/27.19 | | | | | | | | | | | | | | | | REDUCE: (89), (1548) imply: % 194.05/27.19 | | | | | | | | | | | | | | | | (1557) c_member(all_622_1, all_1092_2, v_L) = all_1253_0 % 194.05/27.19 | | | | | | | | | | | | | | | | % 194.05/27.19 | | | | | | | | | | | | | | | | BETA: splitting (1543) gives: % 194.05/27.19 | | | | | | | | | | | | | | | | % 194.05/27.19 | | | | | | | | | | | | | | | | Case 1: % 194.05/27.19 | | | | | | | | | | | | | | | | | % 194.05/27.19 | | | | | | | | | | | | | | | | | (1558) all_1134_1 = 0 % 194.05/27.19 | | | | | | | | | | | | | | | | | % 194.05/27.19 | | | | | | | | | | | | | | | | | REDUCE: (1482), (1558) imply: % 194.05/27.19 | | | | | | | | | | | | | | | | | (1559) $false % 194.05/27.19 | | | | | | | | | | | | | | | | | % 194.05/27.19 | | | | | | | | | | | | | | | | | CLOSE: (1559) is inconsistent. % 194.05/27.19 | | | | | | | | | | | | | | | | | % 194.05/27.19 | | | | | | | | | | | | | | | | Case 2: % 194.05/27.19 | | | | | | | | | | | | | | | | | % 194.05/27.19 | | | | | | | | | | | | | | | | | % 194.05/27.19 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with all_1253_0, all_1289_0, % 194.05/27.19 | | | | | | | | | | | | | | | | | v_L, all_1092_2, all_622_1, simplifying with % 194.05/27.19 | | | | | | | | | | | | | | | | | (1556), (1557) gives: % 194.05/27.19 | | | | | | | | | | | | | | | | | (1560) all_1289_0 = all_1253_0 % 194.05/27.19 | | | | | | | | | | | | | | | | | % 194.05/27.19 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (21) with all_872_3, all_1289_2, % 194.05/27.19 | | | | | | | | | | | | | | | | | v_x, v_y, tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.19 | | | | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with % 194.05/27.19 | | | | | | | | | | | | | | | | | (1514), (1554) gives: % 194.05/27.19 | | | | | | | | | | | | | | | | | (1561) all_1289_2 = all_872_3 % 194.05/27.19 | | | | | | | | | | | | | | | | | % 194.05/27.19 | | | | | | | | | | | | | | | | | REDUCE: (1555), (1561) imply: % 194.05/27.19 | | | | | | | | | | | | | | | | | (1562) c_member(all_622_1, all_872_3, v_L) = all_1289_1 % 194.05/27.19 | | | | | | | | | | | | | | | | | % 194.05/27.19 | | | | | | | | | | | | | | | | | BETA: splitting (1553) gives: % 194.05/27.19 | | | | | | | | | | | | | | | | | % 194.05/27.19 | | | | | | | | | | | | | | | | | Case 1: % 194.05/27.19 | | | | | | | | | | | | | | | | | | % 194.05/27.19 | | | | | | | | | | | | | | | | | | (1563) ~ (all_1289_1 = 0) % 194.05/27.19 | | | | | | | | | | | | | | | | | | % 194.05/27.19 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with 0, all_1289_1, v_L, % 194.05/27.19 | | | | | | | | | | | | | | | | | | all_872_3, all_622_1, simplifying with (1541), % 194.05/27.19 | | | | | | | | | | | | | | | | | | (1562) gives: % 194.05/27.19 | | | | | | | | | | | | | | | | | | (1564) all_1289_1 = 0 % 194.05/27.19 | | | | | | | | | | | | | | | | | | % 194.05/27.19 | | | | | | | | | | | | | | | | | | REDUCE: (1563), (1564) imply: % 194.05/27.19 | | | | | | | | | | | | | | | | | | (1565) $false % 194.05/27.19 | | | | | | | | | | | | | | | | | | % 194.05/27.19 | | | | | | | | | | | | | | | | | | CLOSE: (1565) is inconsistent. % 194.05/27.19 | | | | | | | | | | | | | | | | | | % 194.05/27.19 | | | | | | | | | | | | | | | | | Case 2: % 194.05/27.19 | | | | | | | | | | | | | | | | | | % 194.05/27.19 | | | | | | | | | | | | | | | | | | (1566) all_1289_0 = 0 % 194.05/27.19 | | | | | | | | | | | | | | | | | | % 194.05/27.19 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1560), (1566) imply: % 194.05/27.19 | | | | | | | | | | | | | | | | | | (1567) all_1253_0 = 0 % 194.05/27.19 | | | | | | | | | | | | | | | | | | % 194.05/27.19 | | | | | | | | | | | | | | | | | | REDUCE: (1547), (1567) imply: % 194.05/27.19 | | | | | | | | | | | | | | | | | | (1568) $false % 194.05/27.19 | | | | | | | | | | | | | | | | | | % 194.05/27.19 | | | | | | | | | | | | | | | | | | CLOSE: (1568) is inconsistent. % 194.05/27.19 | | | | | | | | | | | | | | | | | | % 194.05/27.19 | | | | | | | | | | | | | | | | | End of split % 194.05/27.19 | | | | | | | | | | | | | | | | | % 194.05/27.19 | | | | | | | | | | | | | | | | End of split % 194.05/27.19 | | | | | | | | | | | | | | | | % 194.05/27.19 | | | | | | | | | | | | | | | Case 2: % 194.05/27.19 | | | | | | | | | | | | | | | | % 194.05/27.19 | | | | | | | | | | | | | | | | (1569) all_1210_2 = 0 % 194.05/27.19 | | | | | | | | | | | | | | | | % 194.05/27.19 | | | | | | | | | | | | | | | | COMBINE_EQS: (1537), (1569) imply: % 194.05/27.19 | | | | | | | | | | | | | | | | (1570) all_872_0 = 0 % 194.05/27.19 | | | | | | | | | | | | | | | | % 194.05/27.19 | | | | | | | | | | | | | | | | REDUCE: (1480), (1570) imply: % 194.05/27.19 | | | | | | | | | | | | | | | | (1571) $false % 194.05/27.19 | | | | | | | | | | | | | | | | % 194.05/27.19 | | | | | | | | | | | | | | | | CLOSE: (1571) is inconsistent. % 194.05/27.19 | | | | | | | | | | | | | | | | % 194.05/27.19 | | | | | | | | | | | | | | | End of split % 194.05/27.19 | | | | | | | | | | | | | | | % 194.05/27.19 | | | | | | | | | | | | | | End of split % 194.05/27.19 | | | | | | | | | | | | | | % 194.05/27.19 | | | | | | | | | | | | | End of split % 194.05/27.19 | | | | | | | | | | | | | % 194.05/27.19 | | | | | | | | | | | | Case 2: % 194.05/27.19 | | | | | | | | | | | | | % 194.05/27.19 | | | | | | | | | | | | | (1572) all_872_6 = 0 & ~ (all_872_8 = v_y) & ? [v0: $i] % 194.05/27.19 | | | | | | | | | | | | | : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ? % 194.05/27.19 | | | | | | | | | | | | | [v4: any] : % 194.05/27.19 | | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.19 | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, % 194.05/27.19 | | | | | | | | | | | | | v0) = v1 & % 194.05/27.19 | | | | | | | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.19 | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, % 194.05/27.19 | | | | | | | | | | | | | v0) = v3 & c_member(all_685_0, v3, v_L) = v4 & % 194.05/27.19 | | | | | | | | | | | | | c_member(all_685_0, v1, v_L) = v2 & $i(v3) & % 194.05/27.19 | | | | | | | | | | | | | $i(v1) & $i(v0) & ((v2 = 0 & ~ (v4 = 0) & ~ % 194.05/27.19 | | | | | | | | | | | | | (v0 = v_y)) | (v0 = v_y & all_872_2 = 0 & ~ % 194.05/27.19 | | | | | | | | | | | | | (all_872_4 = 0) & ~ (all_872_9 = v_x)) | % 194.05/27.19 | | | | | | | | | | | | | (v0 = v_y & all_872_8 = v_x & ~ (all_872_4 = % 194.05/27.19 | | | | | | | | | | | | | 0) & ~ (all_872_9 = v_x)))) % 194.05/27.19 | | | | | | | | | | | | | % 194.05/27.19 | | | | | | | | | | | | | ALPHA: (1572) implies: % 194.05/27.19 | | | | | | | | | | | | | (1573) all_872_6 = 0 % 194.05/27.19 | | | | | | | | | | | | | % 194.05/27.19 | | | | | | | | | | | | | REDUCE: (1511), (1573) imply: % 194.05/27.19 | | | | | | | | | | | | | (1574) $false % 194.05/27.19 | | | | | | | | | | | | | % 194.05/27.19 | | | | | | | | | | | | | CLOSE: (1574) is inconsistent. % 194.05/27.19 | | | | | | | | | | | | | % 194.05/27.19 | | | | | | | | | | | | End of split % 194.05/27.19 | | | | | | | | | | | | % 194.05/27.19 | | | | | | | | | | | End of split % 194.05/27.19 | | | | | | | | | | | % 194.05/27.19 | | | | | | | | | | Case 2: % 194.05/27.19 | | | | | | | | | | | % 194.05/27.19 | | | | | | | | | | | (1575) all_1164_0 = 0 % 194.05/27.19 | | | | | | | | | | | % 194.05/27.19 | | | | | | | | | | | COMBINE_EQS: (1413), (1575) imply: % 194.05/27.19 | | | | | | | | | | | (1576) all_872_0 = 0 % 194.05/27.19 | | | | | | | | | | | % 194.05/27.19 | | | | | | | | | | | REDUCE: (1480), (1576) imply: % 194.05/27.19 | | | | | | | | | | | (1577) $false % 194.05/27.19 | | | | | | | | | | | % 194.05/27.19 | | | | | | | | | | | CLOSE: (1577) is inconsistent. % 194.05/27.19 | | | | | | | | | | | % 194.05/27.19 | | | | | | | | | | End of split % 194.05/27.19 | | | | | | | | | | % 194.05/27.19 | | | | | | | | | End of split % 194.05/27.19 | | | | | | | | | % 194.05/27.19 | | | | | | | | End of split % 194.05/27.19 | | | | | | | | % 194.05/27.19 | | | | | | | End of split % 194.05/27.19 | | | | | | | % 194.05/27.19 | | | | | | End of split % 194.05/27.19 | | | | | | % 194.05/27.19 | | | | | End of split % 194.05/27.19 | | | | | % 194.05/27.19 | | | | End of split % 194.05/27.19 | | | | % 194.05/27.19 | | | End of split % 194.05/27.19 | | | % 194.05/27.19 | | End of split % 194.05/27.19 | | % 194.05/27.19 | End of split % 194.05/27.19 | % 194.05/27.19 End of proof % 194.05/27.19 % 194.05/27.19 Sub-proof #1 shows that the following formulas are inconsistent: % 194.05/27.19 ---------------------------------------------------------------- % 194.05/27.19 (1) c_member(all_622_1, all_872_3, v_L) = all_872_2 % 194.05/27.19 (2) all_1136_0 = all_872_4 % 194.05/27.19 (3) ~ (all_1136_1 = 0) | all_1136_0 = 0 % 194.05/27.19 (4) ~ (all_872_4 = 0) % 194.05/27.19 (5) all_676_0 = all_622_1 % 194.05/27.19 (6) c_member(all_622_1, all_872_7, v_L) = 0 % 194.05/27.19 (7) all_872_8 = v_x | ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 194.05/27.19 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.19 tc_Arrow__Order__Mirabelle_Oalt, v_x, all_872_8) = v1 & % 194.05/27.19 c_member(all_676_0, v1, v_L) = v2 & c_member(all_676_0, all_872_3, v_L) % 194.05/27.19 = v0 & $i(v1) & (v2 = 0 | v0 = 0)) % 194.05/27.19 (8) all_1136_1 = all_872_2 % 194.05/27.19 (9) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.19 tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v_x) = all_872_5 % 194.05/27.19 (10) ~ (all_872_0 = 0) % 194.05/27.19 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 194.05/27.19 [v5: $i] : (v1 = v0 | ~ (c_Product__Type_OPair(v5, v4, v3, v2) = v1) | % 194.05/27.19 ~ (c_Product__Type_OPair(v5, v4, v3, v2) = v0)) % 194.05/27.20 (12) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.20 tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v_x) = all_872_3 % 194.05/27.20 (13) all_872_8 = v_x | ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 194.05/27.20 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.20 tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v_x) = v1 & % 194.05/27.20 c_member(all_676_0, v1, v_L) = v2 & c_member(all_676_0, all_872_1, % 194.05/27.20 v_L) = v0 & $i(v1) & (v2 = 0 | v0 = 0)) % 194.05/27.20 (14) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.20 tc_Arrow__Order__Mirabelle_Oalt, all_872_9, all_872_8) = all_872_7 % 194.05/27.20 (15) c_member(all_622_1, all_872_1, v_L) = all_872_0 % 194.05/27.20 (16) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 194.05/27.20 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (c_member(v4, v3, v2) = v1) | % 194.05/27.20 ~ (c_member(v4, v3, v2) = v0)) % 194.05/27.20 (17) c_member(all_622_1, all_872_5, v_L) = all_872_4 % 194.05/27.20 % 194.05/27.20 Begin of proof % 194.05/27.20 | % 194.05/27.20 | BETA: splitting (3) gives: % 194.05/27.20 | % 194.05/27.20 | Case 1: % 194.05/27.20 | | % 194.05/27.20 | | (18) ~ (all_1136_1 = 0) % 194.05/27.20 | | % 194.05/27.20 | | REDUCE: (8), (18) imply: % 194.05/27.20 | | (19) ~ (all_872_2 = 0) % 194.05/27.20 | | % 194.05/27.20 | | REF_CLOSE: (1), (4), (5), (6), (7), (9), (10), (11), (12), (13), (14), (15), % 194.05/27.20 | | (16), (17), (19) are inconsistent by sub-proof #4. % 194.05/27.20 | | % 194.05/27.20 | Case 2: % 194.05/27.20 | | % 194.05/27.20 | | (20) all_1136_0 = 0 % 194.05/27.20 | | % 194.05/27.20 | | COMBINE_EQS: (2), (20) imply: % 194.05/27.20 | | (21) all_872_4 = 0 % 194.05/27.20 | | % 194.05/27.20 | | REDUCE: (4), (21) imply: % 194.05/27.20 | | (22) $false % 194.05/27.20 | | % 194.05/27.20 | | CLOSE: (22) is inconsistent. % 194.05/27.20 | | % 194.05/27.20 | End of split % 194.05/27.20 | % 194.05/27.20 End of proof % 194.05/27.20 % 194.05/27.20 Sub-proof #2 shows that the following formulas are inconsistent: % 194.05/27.20 ---------------------------------------------------------------- % 194.05/27.20 (1) c_member(all_622_1, all_872_3, v_L) = all_872_2 % 194.05/27.20 (2) $i(all_872_8) % 194.05/27.20 (3) $i(v_L) % 194.05/27.20 (4) (all_872_4 = 0 & all_872_8 = v_y & ? [v0: $i] : ? [v1: $i] : ? [v2: % 194.05/27.20 $i] : ? [v3: int] : ( ~ (v3 = 0) & ~ (v0 = v_y) & % 194.05/27.20 c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.20 tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v0) = v2 & % 194.05/27.20 c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.20 tc_Arrow__Order__Mirabelle_Oalt, v_x, v0) = v1 & % 194.05/27.20 c_member(all_685_0, v2, v_L) = v3 & c_member(all_685_0, v1, v_L) = 0 % 194.05/27.20 & $i(v2) & $i(v1) & $i(v0))) | (all_872_6 = 0 & ~ (all_872_8 = v_y) % 194.05/27.20 & ? [v0: $i] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ? [v4: any] % 194.05/27.20 : (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.20 tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v0) = v1 & % 194.05/27.20 c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.20 tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v0) = v3 & % 194.05/27.20 c_member(all_685_0, v3, v_L) = v4 & c_member(all_685_0, v1, v_L) = v2 % 194.05/27.20 & $i(v3) & $i(v1) & $i(v0) & ((v2 = 0 & ~ (v4 = 0) & ~ (v0 = v_y)) % 194.05/27.20 | (v0 = v_y & all_872_2 = 0 & ~ (all_872_4 = 0) & ~ (all_872_9 = % 194.05/27.20 v_x)) | (v0 = v_y & all_872_8 = v_x & ~ (all_872_4 = 0) & ~ % 194.05/27.20 (all_872_9 = v_x))))) % 194.05/27.20 (5) $i(all_622_1) % 194.05/27.20 (6) ~ (all_872_2 = 0) % 194.05/27.20 (7) all_685_0 = all_622_1 % 194.05/27.20 (8) ! [v0: $i] : ! [v1: $i] : ( ~ % 194.05/27.20 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.20 tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v0) = v1) | ~ $i(v0) | % 194.05/27.20 ? [v2: $i] : ? [v3: any] : ? [v4: any] : % 194.05/27.20 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.20 tc_Arrow__Order__Mirabelle_Oalt, v_x, v0) = v2 & % 194.05/27.20 c_member(all_676_0, v2, v_L) = v3 & c_member(all_676_0, v1, v_L) = v4 % 194.05/27.20 & $i(v2) & ( ~ (v3 = 0) | v4 = 0))) % 194.05/27.20 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 194.05/27.20 (c_member(v2, v1, v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 194.05/27.20 [v4: $i] : ? [v5: int] : ( ~ (v5 = 0) & hBOOL(v4) = v5 & hAPP(v0, v1) % 194.05/27.20 = v4 & $i(v4))) % 194.05/27.20 (10) all_676_0 = all_622_1 % 194.05/27.20 (11) all_872_8 = v_x | ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 194.05/27.20 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.20 tc_Arrow__Order__Mirabelle_Oalt, v_x, all_872_8) = v1 & % 194.05/27.20 c_member(all_676_0, v1, v_L) = v2 & c_member(all_676_0, all_872_3, % 194.05/27.20 v_L) = v0 & $i(v1) & (v2 = 0 | v0 = 0)) % 194.05/27.20 (12) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.20 tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v_x) = all_872_5 % 194.05/27.20 (13) ~ (all_872_0 = 0) % 194.05/27.20 (14) ! [v0: $i] : ! [v1: $i] : ( ~ % 194.05/27.20 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.20 tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v0) = v1) | ~ $i(v0) % 194.05/27.20 | ? [v2: $i] : ? [v3: any] : ? [v4: any] : % 194.05/27.20 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.20 tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v0) = v2 & % 194.05/27.20 c_member(all_676_0, v2, v_L) = v3 & c_member(all_676_0, v1, v_L) = % 194.05/27.20 v4 & $i(v2) & ( ~ (v3 = 0) | v4 = 0))) % 194.05/27.20 (15) ~ (v_x = v_y) % 194.05/27.20 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 194.05/27.20 [v5: $i] : (v1 = v0 | ~ (c_Product__Type_OPair(v5, v4, v3, v2) = v1) | % 194.05/27.20 ~ (c_Product__Type_OPair(v5, v4, v3, v2) = v0)) % 194.05/27.20 (17) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.20 tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v_x) = all_872_3 % 194.05/27.20 (18) c_member(all_622_1, all_872_7, v_L) = all_872_6 % 194.05/27.20 (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 194.05/27.20 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.20 tc_Arrow__Order__Mirabelle_Oalt, v0, v1) = v2) | ~ $i(v1) | ~ % 194.05/27.20 $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & c_member(all_676_0, v2, v_L) = % 194.05/27.20 v3) | ! [v3: $i] : ! [v4: $i] : ( ~ % 194.05/27.20 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.20 tc_Arrow__Order__Mirabelle_Oalt, v0, v3) = v4) | ~ $i(v3) | ? % 194.05/27.20 [v5: $i] : ? [v6: any] : ? [v7: any] : % 194.05/27.20 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.20 tc_Arrow__Order__Mirabelle_Oalt, v1, v3) = v5 & % 194.05/27.20 c_member(all_676_0, v5, v_L) = v6 & c_member(all_676_0, v4, v_L) = % 194.05/27.20 v7 & $i(v5) & ( ~ (v6 = 0) | v7 = 0)))) % 194.05/27.20 (20) all_872_8 = v_x | ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 194.05/27.20 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.20 tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v_x) = v1 & % 194.05/27.20 c_member(all_676_0, v1, v_L) = v2 & c_member(all_676_0, all_872_1, % 194.05/27.20 v_L) = v0 & $i(v1) & (v2 = 0 | v0 = 0)) % 194.05/27.20 (21) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.05/27.20 tc_Arrow__Order__Mirabelle_Oalt, all_872_9, all_872_8) = all_872_7 % 194.05/27.20 (22) c_member(all_622_1, all_872_1, v_L) = all_872_0 % 194.05/27.20 (23) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 194.05/27.20 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (c_member(v4, v3, v2) = v1) | % 194.05/27.20 ~ (c_member(v4, v3, v2) = v0)) % 194.49/27.20 (24) c_member(all_622_1, all_872_5, v_L) = all_872_4 % 194.49/27.20 % 194.49/27.20 Begin of proof % 194.49/27.20 | % 194.49/27.20 | BETA: splitting (11) gives: % 194.49/27.20 | % 194.49/27.20 | Case 1: % 194.49/27.20 | | % 194.49/27.20 | | (25) all_872_8 = v_x % 194.49/27.20 | | % 194.49/27.20 | | REDUCE: (21), (25) imply: % 194.49/27.20 | | (26) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.20 | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v_x) = all_872_7 % 194.49/27.20 | | % 194.49/27.20 | | REDUCE: (2), (25) imply: % 194.49/27.20 | | (27) $i(v_x) % 194.49/27.20 | | % 194.49/27.20 | | BETA: splitting (4) gives: % 194.49/27.20 | | % 194.49/27.20 | | Case 1: % 194.49/27.20 | | | % 194.49/27.20 | | | (28) all_872_4 = 0 & all_872_8 = v_y & ? [v0: $i] : ? [v1: $i] : ? % 194.49/27.20 | | | [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & ~ (v0 = v_y) & % 194.49/27.20 | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.20 | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v0) = v2 & % 194.49/27.20 | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.20 | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v0) = v1 & % 194.49/27.20 | | | c_member(all_685_0, v2, v_L) = v3 & c_member(all_685_0, v1, v_L) % 194.49/27.20 | | | = 0 & $i(v2) & $i(v1) & $i(v0)) % 194.49/27.20 | | | % 194.49/27.20 | | | ALPHA: (28) implies: % 194.49/27.20 | | | (29) all_872_8 = v_y % 194.49/27.20 | | | % 194.49/27.20 | | | COMBINE_EQS: (25), (29) imply: % 194.49/27.20 | | | (30) v_x = v_y % 194.49/27.20 | | | % 194.49/27.20 | | | SIMP: (30) implies: % 194.49/27.20 | | | (31) v_x = v_y % 194.49/27.20 | | | % 194.49/27.20 | | | REDUCE: (15), (31) imply: % 194.49/27.20 | | | (32) $false % 194.49/27.20 | | | % 194.49/27.20 | | | CLOSE: (32) is inconsistent. % 194.49/27.20 | | | % 194.49/27.20 | | Case 2: % 194.49/27.20 | | | % 194.49/27.21 | | | (33) all_872_6 = 0 & ~ (all_872_8 = v_y) & ? [v0: $i] : ? [v1: $i] : % 194.49/27.21 | | | ? [v2: any] : ? [v3: $i] : ? [v4: any] : % 194.49/27.21 | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.21 | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v0) = v1 & % 194.49/27.21 | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.21 | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v0) = v3 & % 194.49/27.21 | | | c_member(all_685_0, v3, v_L) = v4 & c_member(all_685_0, v1, v_L) % 194.49/27.21 | | | = v2 & $i(v3) & $i(v1) & $i(v0) & ((v2 = 0 & ~ (v4 = 0) & ~ % 194.49/27.21 | | | (v0 = v_y)) | (v0 = v_y & all_872_2 = 0 & ~ (all_872_4 = 0) % 194.49/27.21 | | | & ~ (all_872_9 = v_x)) | (v0 = v_y & all_872_8 = v_x & ~ % 194.49/27.21 | | | (all_872_4 = 0) & ~ (all_872_9 = v_x)))) % 194.49/27.21 | | | % 194.49/27.21 | | | ALPHA: (33) implies: % 194.49/27.21 | | | (34) all_872_6 = 0 % 194.49/27.21 | | | (35) ? [v0: $i] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ? [v4: % 194.49/27.21 | | | any] : (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.21 | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v0) = v1 & % 194.49/27.21 | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.21 | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v0) = v3 & % 194.49/27.21 | | | c_member(all_685_0, v3, v_L) = v4 & c_member(all_685_0, v1, v_L) % 194.49/27.21 | | | = v2 & $i(v3) & $i(v1) & $i(v0) & ((v2 = 0 & ~ (v4 = 0) & ~ % 194.49/27.21 | | | (v0 = v_y)) | (v0 = v_y & all_872_2 = 0 & ~ (all_872_4 = 0) % 194.49/27.21 | | | & ~ (all_872_9 = v_x)) | (v0 = v_y & all_872_8 = v_x & ~ % 194.49/27.21 | | | (all_872_4 = 0) & ~ (all_872_9 = v_x)))) % 194.49/27.21 | | | % 194.49/27.21 | | | REDUCE: (18), (34) imply: % 194.49/27.21 | | | (36) c_member(all_622_1, all_872_7, v_L) = 0 % 194.49/27.21 | | | % 194.49/27.21 | | | REF_CLOSE: (3), (5), (7), (8), (9), (10), (12), (14), (16), (19), (23), % 194.49/27.21 | | | (24), (25), (26), (27), (35), (36) are inconsistent by % 194.49/27.21 | | | sub-proof #10. % 194.49/27.21 | | | % 194.49/27.21 | | End of split % 194.49/27.21 | | % 194.49/27.21 | Case 2: % 194.49/27.21 | | % 194.49/27.21 | | (37) ~ (all_872_8 = v_x) % 194.49/27.21 | | % 194.49/27.21 | | REF_CLOSE: (1), (6), (10), (11), (13), (16), (17), (20), (22), (23), (37) % 194.49/27.21 | | are inconsistent by sub-proof #8. % 194.49/27.21 | | % 194.49/27.21 | End of split % 194.49/27.21 | % 194.49/27.21 End of proof % 194.49/27.21 % 194.49/27.21 Sub-proof #3 shows that the following formulas are inconsistent: % 194.49/27.21 ---------------------------------------------------------------- % 194.49/27.21 (1) all_872_8 = all_872_9 | ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 194.49/27.21 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.21 tc_Arrow__Order__Mirabelle_Oalt, all_872_8, all_872_9) = v1 & % 194.49/27.21 c_member(all_676_0, v1, v_L) = v2 & c_member(all_676_0, all_872_7, v_L) % 194.49/27.21 = v0 & $i(v1) & (v2 = 0 | v0 = 0)) % 194.49/27.21 (2) c_member(all_622_1, all_872_3, v_L) = all_872_2 % 194.49/27.21 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 194.49/27.21 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.21 tc_Arrow__Order__Mirabelle_Oalt, v0, v1) = v2) | ~ $i(v1) | ~ % 194.49/27.21 $i(v0) | ? [v3: any] : ? [v4: $i] : ? [v5: any] : % 194.49/27.21 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.21 tc_Arrow__Order__Mirabelle_Oalt, v1, v0) = v4 & c_member(all_676_0, % 194.49/27.21 v4, v_L) = v5 & c_member(all_676_0, v2, v_L) = v3 & $i(v4) & (v5 = % 194.49/27.21 0 | v3 = 0))) % 194.49/27.21 (4) $i(all_872_8) % 194.49/27.21 (5) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_676_0, all_872_7, v_L) = v0) | % 194.49/27.21 ! [v0: $i] : ! [v1: $i] : ( ~ % 194.49/27.21 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.21 tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v0) = v1) | ~ $i(v0) | % 194.49/27.21 ? [v2: $i] : ? [v3: any] : ? [v4: any] : % 194.49/27.21 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.21 tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v0) = v2 & % 194.49/27.21 c_member(all_676_0, v2, v_L) = v3 & c_member(all_676_0, v1, v_L) = v4 % 194.49/27.21 & $i(v2) & ( ~ (v3 = 0) | v4 = 0))) % 194.49/27.21 (6) $i(v_L) % 194.49/27.21 (7) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.21 tc_Arrow__Order__Mirabelle_Oalt, v_x, all_872_9) = all_1109_1 % 194.49/27.21 (8) $i(tc_Arrow__Order__Mirabelle_Oalt) % 194.49/27.21 (9) all_872_6 = 0 % 194.49/27.21 (10) tc_prod(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.21 tc_Arrow__Order__Mirabelle_Oalt) = all_622_1 % 194.49/27.21 (11) ~ (all_872_2 = 0) % 194.49/27.21 (12) all_685_0 = all_622_1 % 194.49/27.21 (13) ~ (all_872_9 = v_x) % 194.49/27.21 (14) c_member(all_622_1, all_1109_1, v_L) = all_1109_0 % 194.49/27.21 (15) all_1109_2 = all_872_4 % 194.49/27.21 (16) ~ (all_872_4 = 0) % 194.49/27.21 (17) all_676_0 = all_622_1 % 194.49/27.21 (18) all_872_8 = v_x | ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 194.49/27.21 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.21 tc_Arrow__Order__Mirabelle_Oalt, v_x, all_872_8) = v1 & % 194.49/27.21 c_member(all_676_0, v1, v_L) = v2 & c_member(all_676_0, all_872_3, % 194.49/27.21 v_L) = v0 & $i(v1) & (v2 = 0 | v0 = 0)) % 194.49/27.21 (19) ? [v0: $i] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ? [v4: any] : % 194.49/27.21 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.21 tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v0) = v1 & % 194.49/27.21 c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.21 tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v0) = v3 & % 194.49/27.21 c_member(all_685_0, v3, v_L) = v4 & c_member(all_685_0, v1, v_L) = v2 % 194.49/27.21 & $i(v3) & $i(v1) & $i(v0) & ((v2 = 0 & ~ (v4 = 0) & ~ (v0 = v_y)) | % 194.49/27.21 (v0 = v_y & all_872_2 = 0 & ~ (all_872_4 = 0) & ~ (all_872_9 = % 194.49/27.21 v_x)) | (v0 = v_y & all_872_8 = v_x & ~ (all_872_4 = 0) & ~ % 194.49/27.21 (all_872_9 = v_x)))) % 194.49/27.21 (20) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.21 tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v_x) = all_872_5 % 194.49/27.21 (21) $i(all_872_9) % 194.49/27.21 (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 194.49/27.21 [v5: $i] : ( ~ (tc_prod(v3, v3) = v4) | ~ (c_Product__Type_OPair(v3, % 194.49/27.21 v3, v0, v1) = v5) | ~ (c_member(v4, v5, v2) = 0) | ~ $i(v3) | ~ % 194.49/27.21 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: $i] : ? [v8: % 194.49/27.21 any] : (c_Wellfounded_Owf(v3, v2) = v6 & c_Product__Type_OPair(v3, % 194.49/27.21 v3, v1, v0) = v7 & c_member(v4, v7, v2) = v8 & $i(v7) & ( ~ (v8 = % 194.49/27.21 0) | ~ (v6 = 0)))) % 194.49/27.21 (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 194.49/27.21 [v5: $i] : (v1 = v0 | ~ (c_Product__Type_OPair(v5, v4, v3, v2) = v1) | % 194.49/27.21 ~ (c_Product__Type_OPair(v5, v4, v3, v2) = v0)) % 194.49/27.21 (24) all_872_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & hBOOL(v0) = % 194.49/27.21 v1 & hAPP(v_L, all_872_1) = v0 & $i(v0)) % 194.49/27.21 (25) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.21 tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v_x) = all_872_3 % 194.49/27.21 (26) c_member(all_622_1, all_872_7, v_L) = all_872_6 % 194.49/27.21 (27) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 194.49/27.21 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.21 tc_Arrow__Order__Mirabelle_Oalt, v0, v1) = v2) | ~ $i(v1) | ~ % 194.49/27.21 $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & c_member(all_676_0, v2, v_L) = % 194.49/27.21 v3) | ! [v3: $i] : ! [v4: $i] : ( ~ % 194.49/27.21 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.21 tc_Arrow__Order__Mirabelle_Oalt, v0, v3) = v4) | ~ $i(v3) | ? % 194.49/27.21 [v5: $i] : ? [v6: any] : ? [v7: any] : % 194.49/27.21 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.21 tc_Arrow__Order__Mirabelle_Oalt, v1, v3) = v5 & % 194.49/27.21 c_member(all_676_0, v5, v_L) = v6 & c_member(all_676_0, v4, v_L) = % 194.49/27.21 v7 & $i(v5) & ( ~ (v6 = 0) | v7 = 0)))) % 194.49/27.21 (28) all_872_8 = v_x | ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 194.49/27.21 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.21 tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v_x) = v1 & % 194.49/27.21 c_member(all_676_0, v1, v_L) = v2 & c_member(all_676_0, all_872_1, % 194.49/27.21 v_L) = v0 & $i(v1) & (v2 = 0 | v0 = 0)) % 194.49/27.21 (29) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.21 tc_Arrow__Order__Mirabelle_Oalt, all_872_9, all_872_8) = all_872_7 % 194.49/27.21 (30) c_member(all_622_1, all_872_1, v_L) = all_872_0 % 194.49/27.21 (31) $i(v_x) % 194.49/27.22 (32) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 194.49/27.22 [v5: $i] : (v1 = v0 | ~ (tc_prod(v3, v3) = v4) | ~ % 194.49/27.22 (c_Product__Type_OPair(v3, v3, v0, v1) = v5) | ~ (c_member(v4, v5, % 194.49/27.22 v2) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: % 194.49/27.22 any] : ? [v7: $i] : ? [v8: any] : (c_Relation_Oantisym(v3, v2) = % 194.49/27.22 v6 & c_Product__Type_OPair(v3, v3, v1, v0) = v7 & c_member(v4, v7, % 194.49/27.22 v2) = v8 & $i(v7) & ( ~ (v8 = 0) | ~ (v6 = 0)))) % 194.49/27.22 (33) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_676_0, all_872_1, v_L) = v0) % 194.49/27.22 | ! [v0: $i] : ! [v1: $i] : ( ~ % 194.49/27.22 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.22 tc_Arrow__Order__Mirabelle_Oalt, v_x, v0) = v1) | ~ $i(v0) | ? % 194.49/27.22 [v2: $i] : ? [v3: any] : ? [v4: any] : % 194.49/27.22 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.22 tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v0) = v2 & % 194.49/27.22 c_member(all_676_0, v2, v_L) = v3 & c_member(all_676_0, v1, v_L) = % 194.49/27.22 v4 & $i(v2) & ( ~ (v3 = 0) | v4 = 0))) % 194.49/27.22 (34) all_1109_0 = 0 | all_1109_2 = 0 % 194.49/27.22 (35) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 194.49/27.22 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (c_member(v4, v3, v2) = v1) | % 194.49/27.22 ~ (c_member(v4, v3, v2) = v0)) % 194.49/27.22 (36) c_member(all_622_1, all_872_5, v_L) = all_872_4 % 194.49/27.22 % 194.49/27.22 Begin of proof % 194.49/27.22 | % 194.49/27.22 | DELTA: instantiating (19) with fresh symbols all_1127_0, all_1127_1, % 194.49/27.22 | all_1127_2, all_1127_3, all_1127_4 gives: % 194.49/27.22 | (37) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.22 | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, all_1127_4) = all_1127_3 % 194.49/27.22 | & c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.22 | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, all_1127_4) = all_1127_1 % 194.49/27.22 | & c_member(all_685_0, all_1127_1, v_L) = all_1127_0 & % 194.49/27.22 | c_member(all_685_0, all_1127_3, v_L) = all_1127_2 & $i(all_1127_1) & % 194.49/27.22 | $i(all_1127_3) & $i(all_1127_4) & ((all_1127_2 = 0 & ~ (all_1127_0 = % 194.49/27.22 | 0) & ~ (all_1127_4 = v_y)) | (all_1127_4 = v_y & all_872_2 = 0 % 194.49/27.22 | & ~ (all_872_4 = 0) & ~ (all_872_9 = v_x)) | (all_1127_4 = v_y & % 194.49/27.22 | all_872_8 = v_x & ~ (all_872_4 = 0) & ~ (all_872_9 = v_x))) % 194.49/27.22 | % 194.49/27.22 | ALPHA: (37) implies: % 194.49/27.22 | (38) $i(all_1127_4) % 194.49/27.22 | (39) c_member(all_685_0, all_1127_3, v_L) = all_1127_2 % 194.49/27.22 | (40) c_member(all_685_0, all_1127_1, v_L) = all_1127_0 % 194.49/27.22 | (41) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.22 | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, all_1127_4) = all_1127_1 % 194.49/27.22 | (42) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.22 | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, all_1127_4) = all_1127_3 % 194.49/27.22 | (43) (all_1127_2 = 0 & ~ (all_1127_0 = 0) & ~ (all_1127_4 = v_y)) | % 194.49/27.22 | (all_1127_4 = v_y & all_872_2 = 0 & ~ (all_872_4 = 0) & ~ (all_872_9 % 194.49/27.22 | = v_x)) | (all_1127_4 = v_y & all_872_8 = v_x & ~ (all_872_4 = 0) % 194.49/27.22 | & ~ (all_872_9 = v_x)) % 194.49/27.22 | % 194.49/27.22 | REDUCE: (12), (40) imply: % 194.49/27.22 | (44) c_member(all_622_1, all_1127_1, v_L) = all_1127_0 % 194.49/27.22 | % 194.49/27.22 | REDUCE: (12), (39) imply: % 194.49/27.22 | (45) c_member(all_622_1, all_1127_3, v_L) = all_1127_2 % 194.49/27.22 | % 194.49/27.22 | REDUCE: (9), (26) imply: % 194.49/27.22 | (46) c_member(all_622_1, all_872_7, v_L) = 0 % 194.49/27.22 | % 194.49/27.22 | BETA: splitting (34) gives: % 194.49/27.22 | % 194.49/27.22 | Case 1: % 194.49/27.22 | | % 194.49/27.22 | | (47) all_1109_0 = 0 % 194.49/27.22 | | % 194.49/27.22 | | REDUCE: (14), (47) imply: % 194.49/27.22 | | (48) c_member(all_622_1, all_1109_1, v_L) = 0 % 194.49/27.22 | | % 194.49/27.22 | | BETA: splitting (5) gives: % 194.49/27.22 | | % 194.49/27.22 | | Case 1: % 194.49/27.22 | | | % 194.49/27.22 | | | (49) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_676_0, all_872_7, v_L) % 194.49/27.22 | | | = v0) % 194.49/27.22 | | | % 194.49/27.22 | | | DELTA: instantiating (49) with fresh symbol all_1123_0 gives: % 194.49/27.22 | | | (50) ~ (all_1123_0 = 0) & c_member(all_676_0, all_872_7, v_L) = % 194.49/27.22 | | | all_1123_0 % 194.49/27.22 | | | % 194.49/27.22 | | | REF_CLOSE: (17), (35), (46), (50) are inconsistent by sub-proof #14. % 194.49/27.22 | | | % 194.49/27.22 | | Case 2: % 194.49/27.22 | | | % 194.49/27.22 | | | (51) ! [v0: $i] : ! [v1: $i] : ( ~ % 194.49/27.22 | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.22 | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v0) = v1) | ~ % 194.49/27.22 | | | $i(v0) | ? [v2: $i] : ? [v3: any] : ? [v4: any] : % 194.49/27.22 | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.22 | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v0) = v2 & % 194.49/27.22 | | | c_member(all_676_0, v2, v_L) = v3 & c_member(all_676_0, v1, % 194.49/27.22 | | | v_L) = v4 & $i(v2) & ( ~ (v3 = 0) | v4 = 0))) % 194.49/27.22 | | | % 194.49/27.22 | | | GROUND_INST: instantiating (51) with all_872_8, all_872_7, simplifying % 194.49/27.22 | | | with (4), (29) gives: % 194.49/27.22 | | | (52) ? [v0: $i] : ? [v1: any] : ? [v2: any] : % 194.49/27.22 | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.22 | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, all_872_8) = v0 & % 194.49/27.22 | | | c_member(all_676_0, v0, v_L) = v1 & c_member(all_676_0, % 194.49/27.22 | | | all_872_7, v_L) = v2 & $i(v0) & ( ~ (v1 = 0) | v2 = 0)) % 194.49/27.22 | | | % 194.49/27.22 | | | DELTA: instantiating (52) with fresh symbols all_1136_0, all_1136_1, % 194.49/27.22 | | | all_1136_2 gives: % 194.49/27.22 | | | (53) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.22 | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, all_872_8) = % 194.49/27.22 | | | all_1136_2 & c_member(all_676_0, all_1136_2, v_L) = all_1136_1 & % 194.49/27.22 | | | c_member(all_676_0, all_872_7, v_L) = all_1136_0 & $i(all_1136_2) % 194.49/27.22 | | | & ( ~ (all_1136_1 = 0) | all_1136_0 = 0) % 194.49/27.22 | | | % 194.49/27.22 | | | ALPHA: (53) implies: % 194.49/27.22 | | | (54) c_member(all_676_0, all_872_7, v_L) = all_1136_0 % 194.49/27.22 | | | % 194.49/27.22 | | | REDUCE: (17), (54) imply: % 194.49/27.22 | | | (55) c_member(all_622_1, all_872_7, v_L) = all_1136_0 % 194.49/27.22 | | | % 194.49/27.22 | | | GROUND_INST: instantiating (35) with 0, all_1136_0, v_L, all_872_7, % 194.49/27.22 | | | all_622_1, simplifying with (46), (55) gives: % 194.49/27.22 | | | (56) all_1136_0 = 0 % 194.49/27.22 | | | % 194.49/27.22 | | | BETA: splitting (24) gives: % 194.49/27.22 | | | % 194.49/27.22 | | | Case 1: % 194.49/27.22 | | | | % 194.49/27.22 | | | | (57) all_872_0 = 0 % 194.49/27.22 | | | | % 194.49/27.22 | | | | REDUCE: (30), (57) imply: % 194.49/27.22 | | | | (58) c_member(all_622_1, all_872_1, v_L) = 0 % 194.49/27.22 | | | | % 194.49/27.22 | | | | BETA: splitting (33) gives: % 194.49/27.22 | | | | % 194.49/27.22 | | | | Case 1: % 194.49/27.22 | | | | | % 194.49/27.22 | | | | | (59) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_676_0, all_872_1, % 194.49/27.22 | | | | | v_L) = v0) % 194.49/27.22 | | | | | % 194.49/27.22 | | | | | DELTA: instantiating (59) with fresh symbol all_1151_0 gives: % 194.49/27.22 | | | | | (60) ~ (all_1151_0 = 0) & c_member(all_676_0, all_872_1, v_L) = % 194.49/27.22 | | | | | all_1151_0 % 194.49/27.22 | | | | | % 194.49/27.22 | | | | | REF_CLOSE: (17), (35), (58), (60) are inconsistent by sub-proof #17. % 194.49/27.22 | | | | | % 194.49/27.22 | | | | Case 2: % 194.49/27.22 | | | | | % 194.49/27.22 | | | | | (61) ! [v0: $i] : ! [v1: $i] : ( ~ % 194.49/27.22 | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.22 | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v0) = v1) | ~ % 194.49/27.22 | | | | | $i(v0) | ? [v2: $i] : ? [v3: any] : ? [v4: any] : % 194.49/27.22 | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.22 | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v0) = v2 & % 194.49/27.22 | | | | | c_member(all_676_0, v2, v_L) = v3 & c_member(all_676_0, % 194.49/27.22 | | | | | v1, v_L) = v4 & $i(v2) & ( ~ (v3 = 0) | v4 = 0))) % 194.49/27.22 | | | | | % 194.49/27.22 | | | | | BETA: splitting (1) gives: % 194.49/27.22 | | | | | % 194.49/27.22 | | | | | Case 1: % 194.49/27.22 | | | | | | % 194.49/27.22 | | | | | | (62) all_872_8 = all_872_9 % 194.49/27.22 | | | | | | % 194.49/27.22 | | | | | | REDUCE: (25), (62) imply: % 194.49/27.22 | | | | | | (63) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.22 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v_x) = % 194.49/27.22 | | | | | | all_872_3 % 194.49/27.22 | | | | | | % 194.49/27.22 | | | | | | REF_CLOSE: (2), (12), (19), (20), (23), (35), (36), (62), (63) are % 194.49/27.22 | | | | | | inconsistent by sub-proof #6. % 194.49/27.22 | | | | | | % 194.49/27.22 | | | | | Case 2: % 194.49/27.22 | | | | | | % 194.49/27.22 | | | | | | (64) ~ (all_872_8 = all_872_9) % 194.49/27.22 | | | | | | (65) ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 194.49/27.22 | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.22 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, all_872_9) = % 194.49/27.22 | | | | | | v1 & c_member(all_676_0, v1, v_L) = v2 & % 194.49/27.22 | | | | | | c_member(all_676_0, all_872_7, v_L) = v0 & $i(v1) & (v2 = % 194.49/27.22 | | | | | | 0 | v0 = 0)) % 194.49/27.22 | | | | | | % 194.49/27.22 | | | | | | DELTA: instantiating (65) with fresh symbols all_1164_0, all_1164_1, % 194.49/27.22 | | | | | | all_1164_2 gives: % 194.49/27.22 | | | | | | (66) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.22 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, all_872_9) = % 194.49/27.22 | | | | | | all_1164_1 & c_member(all_676_0, all_1164_1, v_L) = % 194.49/27.22 | | | | | | all_1164_0 & c_member(all_676_0, all_872_7, v_L) = % 194.49/27.22 | | | | | | all_1164_2 & $i(all_1164_1) & (all_1164_0 = 0 | all_1164_2 = % 194.49/27.22 | | | | | | 0) % 194.49/27.22 | | | | | | % 194.49/27.22 | | | | | | ALPHA: (66) implies: % 194.49/27.22 | | | | | | (67) c_member(all_676_0, all_872_7, v_L) = all_1164_2 % 194.49/27.22 | | | | | | (68) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.22 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, all_872_9) = % 194.49/27.22 | | | | | | all_1164_1 % 194.49/27.22 | | | | | | % 194.49/27.22 | | | | | | REDUCE: (17), (67) imply: % 194.49/27.22 | | | | | | (69) c_member(all_622_1, all_872_7, v_L) = all_1164_2 % 194.49/27.22 | | | | | | % 194.49/27.22 | | | | | | GROUND_INST: instantiating (35) with 0, all_1164_2, v_L, all_872_7, % 194.49/27.22 | | | | | | all_622_1, simplifying with (46), (69) gives: % 194.49/27.22 | | | | | | (70) all_1164_2 = 0 % 194.49/27.22 | | | | | | % 194.49/27.22 | | | | | | GROUND_INST: instantiating (32) with v_x, all_872_9, v_L, % 194.49/27.22 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_622_1, all_1109_1, % 194.49/27.22 | | | | | | simplifying with (6), (7), (8), (10), (21), (31), (48) % 194.49/27.22 | | | | | | gives: % 194.49/27.22 | | | | | | (71) all_872_9 = v_x | ? [v0: any] : ? [v1: $i] : ? [v2: any] % 194.49/27.22 | | | | | | : (c_Relation_Oantisym(tc_Arrow__Order__Mirabelle_Oalt, v_L) % 194.49/27.22 | | | | | | = v0 & % 194.49/27.22 | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.22 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v_x) = v1 & % 194.49/27.22 | | | | | | c_member(all_622_1, v1, v_L) = v2 & $i(v1) & ( ~ (v2 = 0) % 194.49/27.22 | | | | | | | ~ (v0 = 0))) % 194.49/27.22 | | | | | | % 194.49/27.22 | | | | | | GROUND_INST: instantiating (22) with v_x, all_872_9, v_L, % 194.49/27.22 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_622_1, all_1109_1, % 194.49/27.22 | | | | | | simplifying with (6), (7), (8), (10), (21), (31), (48) % 194.49/27.22 | | | | | | gives: % 194.49/27.22 | | | | | | (72) ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 194.49/27.22 | | | | | | (c_Wellfounded_Owf(tc_Arrow__Order__Mirabelle_Oalt, v_L) = % 194.49/27.22 | | | | | | v0 & % 194.49/27.22 | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.22 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v_x) = v1 & % 194.49/27.22 | | | | | | c_member(all_622_1, v1, v_L) = v2 & $i(v1) & ( ~ (v2 = 0) % 194.49/27.22 | | | | | | | ~ (v0 = 0))) % 194.49/27.22 | | | | | | % 194.49/27.22 | | | | | | GROUND_INST: instantiating (61) with all_872_9, all_1109_1, % 194.49/27.22 | | | | | | simplifying with (7), (21) gives: % 194.49/27.23 | | | | | | (73) ? [v0: $i] : ? [v1: any] : ? [v2: any] : % 194.49/27.23 | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.23 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, all_872_9) = % 194.49/27.23 | | | | | | v0 & c_member(all_676_0, v0, v_L) = v1 & % 194.49/27.23 | | | | | | c_member(all_676_0, all_1109_1, v_L) = v2 & $i(v0) & ( ~ % 194.49/27.23 | | | | | | (v1 = 0) | v2 = 0)) % 194.49/27.23 | | | | | | % 194.49/27.23 | | | | | | GROUND_INST: instantiating (27) with v_x, all_872_9, all_1109_1, % 194.49/27.23 | | | | | | simplifying with (7), (21), (31) gives: % 194.49/27.23 | | | | | | (74) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_676_0, % 194.49/27.23 | | | | | | all_1109_1, v_L) = v0) | ! [v0: $i] : ! [v1: $i] : ( ~ % 194.49/27.23 | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.23 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v0) = v1) | ~ % 194.49/27.23 | | | | | | $i(v0) | ? [v2: $i] : ? [v3: any] : ? [v4: any] : % 194.49/27.23 | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.23 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v0) = v2 & % 194.49/27.23 | | | | | | c_member(all_676_0, v2, v_L) = v3 & c_member(all_676_0, % 194.49/27.23 | | | | | | v1, v_L) = v4 & $i(v2) & ( ~ (v3 = 0) | v4 = 0))) % 194.49/27.23 | | | | | | % 194.49/27.23 | | | | | | GROUND_INST: instantiating (51) with all_1127_4, all_1127_1, % 194.49/27.23 | | | | | | simplifying with (38), (41) gives: % 194.49/27.23 | | | | | | (75) ? [v0: $i] : ? [v1: any] : ? [v2: any] : % 194.49/27.23 | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.23 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, all_1127_4) % 194.49/27.23 | | | | | | = v0 & c_member(all_676_0, v0, v_L) = v1 & % 194.49/27.23 | | | | | | c_member(all_676_0, all_1127_1, v_L) = v2 & $i(v0) & ( ~ % 194.49/27.23 | | | | | | (v1 = 0) | v2 = 0)) % 194.49/27.23 | | | | | | % 194.49/27.23 | | | | | | GROUND_INST: instantiating (3) with all_872_8, all_872_9, % 194.49/27.23 | | | | | | all_1164_1, simplifying with (4), (21), (68) gives: % 194.49/27.23 | | | | | | (76) all_872_8 = all_872_9 | ? [v0: any] : ? [v1: $i] : ? [v2: % 194.49/27.23 | | | | | | any] : % 194.49/27.23 | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.23 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, all_872_8) = % 194.49/27.23 | | | | | | v1 & c_member(all_676_0, v1, v_L) = v2 & % 194.49/27.23 | | | | | | c_member(all_676_0, all_1164_1, v_L) = v0 & $i(v1) & (v2 = % 194.49/27.23 | | | | | | 0 | v0 = 0)) % 194.49/27.23 | | | | | | % 194.49/27.23 | | | | | | DELTA: instantiating (72) with fresh symbols all_1217_0, all_1217_1, % 194.49/27.23 | | | | | | all_1217_2 gives: % 194.49/27.23 | | | | | | (77) c_Wellfounded_Owf(tc_Arrow__Order__Mirabelle_Oalt, v_L) = % 194.49/27.23 | | | | | | all_1217_2 & % 194.49/27.23 | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.23 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v_x) = % 194.49/27.23 | | | | | | all_1217_1 & c_member(all_622_1, all_1217_1, v_L) = % 194.49/27.23 | | | | | | all_1217_0 & $i(all_1217_1) & ( ~ (all_1217_0 = 0) | ~ % 194.49/27.23 | | | | | | (all_1217_2 = 0)) % 194.49/27.23 | | | | | | % 194.49/27.23 | | | | | | ALPHA: (77) implies: % 194.49/27.23 | | | | | | (78) c_member(all_622_1, all_1217_1, v_L) = all_1217_0 % 194.49/27.23 | | | | | | (79) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.23 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v_x) = % 194.49/27.23 | | | | | | all_1217_1 % 194.49/27.23 | | | | | | % 194.49/27.23 | | | | | | DELTA: instantiating (75) with fresh symbols all_1223_0, all_1223_1, % 194.49/27.23 | | | | | | all_1223_2 gives: % 194.49/27.23 | | | | | | (80) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.23 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, all_1127_4) = % 194.49/27.23 | | | | | | all_1223_2 & c_member(all_676_0, all_1223_2, v_L) = % 194.49/27.23 | | | | | | all_1223_1 & c_member(all_676_0, all_1127_1, v_L) = % 194.49/27.23 | | | | | | all_1223_0 & $i(all_1223_2) & ( ~ (all_1223_1 = 0) | % 194.49/27.23 | | | | | | all_1223_0 = 0) % 194.49/27.23 | | | | | | % 194.49/27.23 | | | | | | ALPHA: (80) implies: % 194.49/27.23 | | | | | | (81) c_member(all_676_0, all_1127_1, v_L) = all_1223_0 % 194.49/27.23 | | | | | | (82) c_member(all_676_0, all_1223_2, v_L) = all_1223_1 % 194.49/27.23 | | | | | | (83) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.23 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, all_1127_4) = % 194.49/27.23 | | | | | | all_1223_2 % 194.49/27.23 | | | | | | (84) ~ (all_1223_1 = 0) | all_1223_0 = 0 % 194.49/27.23 | | | | | | % 194.49/27.23 | | | | | | DELTA: instantiating (73) with fresh symbols all_1225_0, all_1225_1, % 194.49/27.23 | | | | | | all_1225_2 gives: % 194.49/27.23 | | | | | | (85) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.23 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, all_872_9) = % 194.49/27.23 | | | | | | all_1225_2 & c_member(all_676_0, all_1225_2, v_L) = % 194.49/27.23 | | | | | | all_1225_1 & c_member(all_676_0, all_1109_1, v_L) = % 194.49/27.23 | | | | | | all_1225_0 & $i(all_1225_2) & ( ~ (all_1225_1 = 0) | % 194.49/27.23 | | | | | | all_1225_0 = 0) % 194.49/27.23 | | | | | | % 194.49/27.23 | | | | | | ALPHA: (85) implies: % 194.49/27.23 | | | | | | (86) c_member(all_676_0, all_1109_1, v_L) = all_1225_0 % 194.49/27.23 | | | | | | % 194.49/27.23 | | | | | | REDUCE: (17), (82) imply: % 194.49/27.23 | | | | | | (87) c_member(all_622_1, all_1223_2, v_L) = all_1223_1 % 194.49/27.23 | | | | | | % 194.49/27.23 | | | | | | REDUCE: (17), (81) imply: % 194.49/27.23 | | | | | | (88) c_member(all_622_1, all_1127_1, v_L) = all_1223_0 % 194.49/27.23 | | | | | | % 194.49/27.23 | | | | | | REDUCE: (17), (86) imply: % 194.49/27.23 | | | | | | (89) c_member(all_622_1, all_1109_1, v_L) = all_1225_0 % 194.49/27.23 | | | | | | % 194.49/27.23 | | | | | | BETA: splitting (76) gives: % 194.49/27.23 | | | | | | % 194.49/27.23 | | | | | | Case 1: % 194.49/27.23 | | | | | | | % 194.49/27.23 | | | | | | | (90) all_872_8 = all_872_9 % 194.49/27.23 | | | | | | | % 194.49/27.23 | | | | | | | REDUCE: (64), (90) imply: % 194.49/27.23 | | | | | | | (91) $false % 194.49/27.23 | | | | | | | % 194.49/27.23 | | | | | | | CLOSE: (91) is inconsistent. % 194.49/27.23 | | | | | | | % 194.49/27.23 | | | | | | Case 2: % 194.49/27.23 | | | | | | | % 194.49/27.23 | | | | | | | (92) ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 194.49/27.23 | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.23 | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, all_872_8) % 194.49/27.23 | | | | | | | = v1 & c_member(all_676_0, v1, v_L) = v2 & % 194.49/27.23 | | | | | | | c_member(all_676_0, all_1164_1, v_L) = v0 & $i(v1) & (v2 % 194.49/27.23 | | | | | | | = 0 | v0 = 0)) % 194.49/27.23 | | | | | | | % 194.49/27.23 | | | | | | | DELTA: instantiating (92) with fresh symbols all_1231_0, % 194.49/27.23 | | | | | | | all_1231_1, all_1231_2 gives: % 194.49/27.23 | | | | | | | (93) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.23 | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, all_872_8) = % 194.49/27.23 | | | | | | | all_1231_1 & c_member(all_676_0, all_1231_1, v_L) = % 194.49/27.23 | | | | | | | all_1231_0 & c_member(all_676_0, all_1164_1, v_L) = % 194.49/27.23 | | | | | | | all_1231_2 & $i(all_1231_1) & (all_1231_0 = 0 | all_1231_2 % 194.49/27.23 | | | | | | | = 0) % 194.49/27.23 | | | | | | | % 194.49/27.23 | | | | | | | ALPHA: (93) implies: % 194.49/27.23 | | | | | | | (94) c_member(all_676_0, all_1231_1, v_L) = all_1231_0 % 194.49/27.23 | | | | | | | (95) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.23 | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, all_872_8) = % 194.49/27.23 | | | | | | | all_1231_1 % 194.49/27.23 | | | | | | | % 194.49/27.23 | | | | | | | REDUCE: (17), (94) imply: % 194.49/27.23 | | | | | | | (96) c_member(all_622_1, all_1231_1, v_L) = all_1231_0 % 194.49/27.23 | | | | | | | % 194.49/27.23 | | | | | | | BETA: splitting (71) gives: % 194.49/27.23 | | | | | | | % 194.49/27.23 | | | | | | | Case 1: % 194.49/27.23 | | | | | | | | % 194.49/27.23 | | | | | | | | (97) all_872_9 = v_x % 194.49/27.23 | | | | | | | | % 194.49/27.23 | | | | | | | | REDUCE: (13), (97) imply: % 194.49/27.23 | | | | | | | | (98) $false % 194.49/27.23 | | | | | | | | % 194.49/27.23 | | | | | | | | CLOSE: (98) is inconsistent. % 194.49/27.23 | | | | | | | | % 194.49/27.23 | | | | | | | Case 2: % 194.49/27.23 | | | | | | | | % 194.49/27.23 | | | | | | | | (99) ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 194.49/27.23 | | | | | | | | (c_Relation_Oantisym(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.23 | | | | | | | | v_L) = v0 & % 194.49/27.23 | | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.23 | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v_x) = % 194.49/27.23 | | | | | | | | v1 & c_member(all_622_1, v1, v_L) = v2 & $i(v1) & ( ~ % 194.49/27.23 | | | | | | | | (v2 = 0) | ~ (v0 = 0))) % 194.49/27.23 | | | | | | | | % 194.49/27.23 | | | | | | | | DELTA: instantiating (99) with fresh symbols all_1241_0, % 194.49/27.23 | | | | | | | | all_1241_1, all_1241_2 gives: % 194.49/27.23 | | | | | | | | (100) c_Relation_Oantisym(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.23 | | | | | | | | v_L) = all_1241_2 & % 194.49/27.23 | | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.23 | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v_x) = % 194.49/27.23 | | | | | | | | all_1241_1 & c_member(all_622_1, all_1241_1, v_L) = % 194.49/27.23 | | | | | | | | all_1241_0 & $i(all_1241_1) & ( ~ (all_1241_0 = 0) | ~ % 194.49/27.23 | | | | | | | | (all_1241_2 = 0)) % 194.49/27.23 | | | | | | | | % 194.49/27.23 | | | | | | | | ALPHA: (100) implies: % 194.49/27.23 | | | | | | | | (101) c_member(all_622_1, all_1241_1, v_L) = all_1241_0 % 194.49/27.23 | | | | | | | | (102) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.23 | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v_x) = % 194.49/27.23 | | | | | | | | all_1241_1 % 194.49/27.23 | | | | | | | | % 194.49/27.23 | | | | | | | | GROUND_INST: instantiating (35) with 0, all_1225_0, v_L, % 194.49/27.23 | | | | | | | | all_1109_1, all_622_1, simplifying with (48), (89) % 194.49/27.23 | | | | | | | | gives: % 194.49/27.23 | | | | | | | | (103) all_1225_0 = 0 % 194.49/27.23 | | | | | | | | % 194.49/27.23 | | | | | | | | GROUND_INST: instantiating (35) with all_1127_0, all_1223_0, % 194.49/27.23 | | | | | | | | v_L, all_1127_1, all_622_1, simplifying with (44), % 194.49/27.23 | | | | | | | | (88) gives: % 194.49/27.23 | | | | | | | | (104) all_1223_0 = all_1127_0 % 194.49/27.23 | | | | | | | | % 194.49/27.23 | | | | | | | | GROUND_INST: instantiating (23) with all_872_5, all_1241_1, v_x, % 194.49/27.23 | | | | | | | | all_872_9, tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.23 | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with % 194.49/27.23 | | | | | | | | (20), (102) gives: % 194.49/27.23 | | | | | | | | (105) all_1241_1 = all_872_5 % 194.49/27.23 | | | | | | | | % 194.49/27.23 | | | | | | | | GROUND_INST: instantiating (23) with all_1217_1, all_1241_1, % 194.49/27.23 | | | | | | | | v_x, all_872_9, tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.23 | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with % 194.49/27.23 | | | | | | | | (79), (102) gives: % 194.49/27.23 | | | | | | | | (106) all_1241_1 = all_1217_1 % 194.49/27.23 | | | | | | | | % 194.49/27.23 | | | | | | | | GROUND_INST: instantiating (23) with all_872_7, all_1231_1, % 194.49/27.23 | | | | | | | | all_872_8, all_872_9, % 194.49/27.23 | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.23 | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with % 194.49/27.23 | | | | | | | | (29), (95) gives: % 194.49/27.23 | | | | | | | | (107) all_1231_1 = all_872_7 % 194.49/27.23 | | | | | | | | % 194.49/27.23 | | | | | | | | GROUND_INST: instantiating (23) with all_1127_3, all_1223_2, % 194.49/27.23 | | | | | | | | all_1127_4, all_872_8, % 194.49/27.23 | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.23 | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with % 194.49/27.23 | | | | | | | | (42), (83) gives: % 194.49/27.23 | | | | | | | | (108) all_1223_2 = all_1127_3 % 194.49/27.23 | | | | | | | | % 194.49/27.23 | | | | | | | | COMBINE_EQS: (105), (106) imply: % 194.49/27.23 | | | | | | | | (109) all_1217_1 = all_872_5 % 194.49/27.23 | | | | | | | | % 194.49/27.23 | | | | | | | | SIMP: (109) implies: % 194.49/27.23 | | | | | | | | (110) all_1217_1 = all_872_5 % 194.49/27.23 | | | | | | | | % 194.49/27.23 | | | | | | | | REDUCE: (101), (105) imply: % 194.49/27.23 | | | | | | | | (111) c_member(all_622_1, all_872_5, v_L) = all_1241_0 % 194.49/27.23 | | | | | | | | % 194.49/27.23 | | | | | | | | REDUCE: (96), (107) imply: % 194.49/27.23 | | | | | | | | (112) c_member(all_622_1, all_872_7, v_L) = all_1231_0 % 194.49/27.23 | | | | | | | | % 194.49/27.23 | | | | | | | | REDUCE: (87), (108) imply: % 194.49/27.23 | | | | | | | | (113) c_member(all_622_1, all_1127_3, v_L) = all_1223_1 % 194.49/27.23 | | | | | | | | % 194.49/27.23 | | | | | | | | REDUCE: (78), (110) imply: % 194.49/27.23 | | | | | | | | (114) c_member(all_622_1, all_872_5, v_L) = all_1217_0 % 194.49/27.23 | | | | | | | | % 194.49/27.23 | | | | | | | | BETA: splitting (74) gives: % 194.49/27.23 | | | | | | | | % 194.49/27.23 | | | | | | | | Case 1: % 194.49/27.23 | | | | | | | | | % 194.49/27.23 | | | | | | | | | (115) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_676_0, % 194.49/27.23 | | | | | | | | | all_1109_1, v_L) = v0) % 194.49/27.23 | | | | | | | | | % 194.49/27.23 | | | | | | | | | DELTA: instantiating (115) with fresh symbol all_1255_0 gives: % 194.49/27.23 | | | | | | | | | (116) ~ (all_1255_0 = 0) & c_member(all_676_0, all_1109_1, % 194.49/27.23 | | | | | | | | | v_L) = all_1255_0 % 194.49/27.23 | | | | | | | | | % 194.49/27.23 | | | | | | | | | ALPHA: (116) implies: % 194.49/27.23 | | | | | | | | | (117) ~ (all_1255_0 = 0) % 194.49/27.23 | | | | | | | | | (118) c_member(all_676_0, all_1109_1, v_L) = all_1255_0 % 194.49/27.23 | | | | | | | | | % 194.49/27.23 | | | | | | | | | REDUCE: (17), (118) imply: % 194.49/27.23 | | | | | | | | | (119) c_member(all_622_1, all_1109_1, v_L) = all_1255_0 % 194.49/27.23 | | | | | | | | | % 194.49/27.23 | | | | | | | | | GROUND_INST: instantiating (35) with 0, all_1255_0, v_L, % 194.49/27.23 | | | | | | | | | all_1109_1, all_622_1, simplifying with (48), % 194.49/27.23 | | | | | | | | | (119) gives: % 194.49/27.23 | | | | | | | | | (120) all_1255_0 = 0 % 194.49/27.23 | | | | | | | | | % 194.49/27.23 | | | | | | | | | REDUCE: (117), (120) imply: % 194.49/27.23 | | | | | | | | | (121) $false % 194.49/27.23 | | | | | | | | | % 194.49/27.23 | | | | | | | | | CLOSE: (121) is inconsistent. % 194.49/27.23 | | | | | | | | | % 194.49/27.23 | | | | | | | | Case 2: % 194.49/27.23 | | | | | | | | | % 194.49/27.23 | | | | | | | | | % 194.49/27.23 | | | | | | | | | GROUND_INST: instantiating (35) with 0, all_1231_0, v_L, % 194.49/27.23 | | | | | | | | | all_872_7, all_622_1, simplifying with (46), (112) % 194.49/27.23 | | | | | | | | | gives: % 194.49/27.23 | | | | | | | | | (122) all_1231_0 = 0 % 194.49/27.23 | | | | | | | | | % 194.49/27.23 | | | | | | | | | GROUND_INST: instantiating (35) with all_872_4, all_1241_0, % 194.49/27.23 | | | | | | | | | v_L, all_872_5, all_622_1, simplifying with (36), % 194.49/27.23 | | | | | | | | | (111) gives: % 194.49/27.23 | | | | | | | | | (123) all_1241_0 = all_872_4 % 194.49/27.23 | | | | | | | | | % 194.49/27.23 | | | | | | | | | GROUND_INST: instantiating (35) with all_1217_0, all_1241_0, % 194.49/27.23 | | | | | | | | | v_L, all_872_5, all_622_1, simplifying with (111), % 194.49/27.23 | | | | | | | | | (114) gives: % 194.49/27.23 | | | | | | | | | (124) all_1241_0 = all_1217_0 % 194.49/27.23 | | | | | | | | | % 194.49/27.23 | | | | | | | | | GROUND_INST: instantiating (35) with all_1127_2, all_1223_1, % 194.49/27.23 | | | | | | | | | v_L, all_1127_3, all_622_1, simplifying with (45), % 194.49/27.23 | | | | | | | | | (113) gives: % 194.49/27.23 | | | | | | | | | (125) all_1223_1 = all_1127_2 % 194.49/27.23 | | | | | | | | | % 194.49/27.23 | | | | | | | | | COMBINE_EQS: (123), (124) imply: % 194.49/27.23 | | | | | | | | | (126) all_1217_0 = all_872_4 % 194.49/27.23 | | | | | | | | | % 194.49/27.23 | | | | | | | | | SIMP: (126) implies: % 194.49/27.23 | | | | | | | | | (127) all_1217_0 = all_872_4 % 194.49/27.23 | | | | | | | | | % 194.49/27.23 | | | | | | | | | BETA: splitting (43) gives: % 194.49/27.23 | | | | | | | | | % 194.49/27.23 | | | | | | | | | Case 1: % 194.49/27.23 | | | | | | | | | | % 194.49/27.23 | | | | | | | | | | (128) all_1127_2 = 0 & ~ (all_1127_0 = 0) & ~ % 194.49/27.23 | | | | | | | | | | (all_1127_4 = v_y) % 194.49/27.23 | | | | | | | | | | % 194.49/27.23 | | | | | | | | | | ALPHA: (128) implies: % 194.49/27.23 | | | | | | | | | | (129) all_1127_2 = 0 % 194.49/27.23 | | | | | | | | | | (130) ~ (all_1127_0 = 0) % 194.49/27.23 | | | | | | | | | | % 194.49/27.23 | | | | | | | | | | COMBINE_EQS: (125), (129) imply: % 194.49/27.23 | | | | | | | | | | (131) all_1223_1 = 0 % 194.49/27.23 | | | | | | | | | | % 194.49/27.23 | | | | | | | | | | BETA: splitting (84) gives: % 194.49/27.23 | | | | | | | | | | % 194.49/27.23 | | | | | | | | | | Case 1: % 194.49/27.23 | | | | | | | | | | | % 194.49/27.23 | | | | | | | | | | | (132) ~ (all_1223_1 = 0) % 194.49/27.23 | | | | | | | | | | | % 194.49/27.23 | | | | | | | | | | | REDUCE: (131), (132) imply: % 194.49/27.23 | | | | | | | | | | | (133) $false % 194.49/27.23 | | | | | | | | | | | % 194.49/27.23 | | | | | | | | | | | CLOSE: (133) is inconsistent. % 194.49/27.23 | | | | | | | | | | | % 194.49/27.23 | | | | | | | | | | Case 2: % 194.49/27.23 | | | | | | | | | | | % 194.49/27.23 | | | | | | | | | | | (134) all_1223_0 = 0 % 194.49/27.23 | | | | | | | | | | | % 194.49/27.24 | | | | | | | | | | | COMBINE_EQS: (104), (134) imply: % 194.49/27.24 | | | | | | | | | | | (135) all_1127_0 = 0 % 194.49/27.24 | | | | | | | | | | | % 194.49/27.24 | | | | | | | | | | | REDUCE: (130), (135) imply: % 194.49/27.24 | | | | | | | | | | | (136) $false % 194.49/27.24 | | | | | | | | | | | % 194.49/27.24 | | | | | | | | | | | CLOSE: (136) is inconsistent. % 194.49/27.24 | | | | | | | | | | | % 194.49/27.24 | | | | | | | | | | End of split % 194.49/27.24 | | | | | | | | | | % 194.49/27.24 | | | | | | | | | Case 2: % 194.49/27.24 | | | | | | | | | | % 194.49/27.24 | | | | | | | | | | (137) (all_1127_4 = v_y & all_872_2 = 0 & ~ (all_872_4 = % 194.49/27.24 | | | | | | | | | | 0) & ~ (all_872_9 = v_x)) | (all_1127_4 = v_y % 194.49/27.24 | | | | | | | | | | & all_872_8 = v_x & ~ (all_872_4 = 0) & ~ % 194.49/27.24 | | | | | | | | | | (all_872_9 = v_x)) % 194.49/27.24 | | | | | | | | | | % 194.49/27.24 | | | | | | | | | | BETA: splitting (137) gives: % 194.49/27.24 | | | | | | | | | | % 194.49/27.24 | | | | | | | | | | Case 1: % 194.49/27.24 | | | | | | | | | | | % 194.49/27.24 | | | | | | | | | | | (138) all_1127_4 = v_y & all_872_2 = 0 & ~ (all_872_4 = % 194.49/27.24 | | | | | | | | | | | 0) & ~ (all_872_9 = v_x) % 194.49/27.24 | | | | | | | | | | | % 194.49/27.24 | | | | | | | | | | | ALPHA: (138) implies: % 194.49/27.24 | | | | | | | | | | | (139) all_872_2 = 0 % 194.49/27.24 | | | | | | | | | | | % 194.49/27.24 | | | | | | | | | | | REDUCE: (11), (139) imply: % 194.49/27.24 | | | | | | | | | | | (140) $false % 194.49/27.24 | | | | | | | | | | | % 194.49/27.24 | | | | | | | | | | | CLOSE: (140) is inconsistent. % 194.49/27.24 | | | | | | | | | | | % 194.49/27.24 | | | | | | | | | | Case 2: % 194.49/27.24 | | | | | | | | | | | % 194.49/27.24 | | | | | | | | | | | (141) all_1127_4 = v_y & all_872_8 = v_x & ~ (all_872_4 % 194.49/27.24 | | | | | | | | | | | = 0) & ~ (all_872_9 = v_x) % 194.49/27.24 | | | | | | | | | | | % 194.49/27.24 | | | | | | | | | | | ALPHA: (141) implies: % 194.49/27.24 | | | | | | | | | | | (142) all_872_8 = v_x % 194.49/27.24 | | | | | | | | | | | % 194.49/27.24 | | | | | | | | | | | REDUCE: (29), (142) imply: % 194.49/27.24 | | | | | | | | | | | (143) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.24 | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v_x) % 194.49/27.24 | | | | | | | | | | | = all_872_7 % 194.49/27.24 | | | | | | | | | | | % 194.49/27.24 | | | | | | | | | | | REF_CLOSE: (16), (20), (23), (35), (36), (46), (143) are % 194.49/27.24 | | | | | | | | | | | inconsistent by sub-proof #11. % 194.49/27.24 | | | | | | | | | | | % 194.49/27.24 | | | | | | | | | | End of split % 194.49/27.24 | | | | | | | | | | % 194.49/27.24 | | | | | | | | | End of split % 194.49/27.24 | | | | | | | | | % 194.49/27.24 | | | | | | | | End of split % 194.49/27.24 | | | | | | | | % 194.49/27.24 | | | | | | | End of split % 194.49/27.24 | | | | | | | % 194.49/27.24 | | | | | | End of split % 194.49/27.24 | | | | | | % 194.49/27.24 | | | | | End of split % 194.49/27.24 | | | | | % 194.49/27.24 | | | | End of split % 194.49/27.24 | | | | % 194.49/27.24 | | | Case 2: % 194.49/27.24 | | | | % 194.49/27.24 | | | | (144) ~ (all_872_0 = 0) % 194.49/27.24 | | | | % 194.49/27.24 | | | | REF_CLOSE: (2), (11), (16), (17), (18), (20), (23), (25), (28), (29), % 194.49/27.24 | | | | (30), (35), (36), (46), (144) are inconsistent by sub-proof % 194.49/27.24 | | | | #4. % 194.49/27.24 | | | | % 194.49/27.24 | | | End of split % 194.49/27.24 | | | % 194.49/27.24 | | End of split % 194.49/27.24 | | % 194.49/27.24 | Case 2: % 194.49/27.24 | | % 194.49/27.24 | | (145) all_1109_2 = 0 % 194.49/27.24 | | % 194.49/27.24 | | COMBINE_EQS: (15), (145) imply: % 194.49/27.24 | | (146) all_872_4 = 0 % 194.49/27.24 | | % 194.49/27.24 | | REDUCE: (16), (146) imply: % 194.49/27.24 | | (147) $false % 194.49/27.24 | | % 194.49/27.24 | | CLOSE: (147) is inconsistent. % 194.49/27.24 | | % 194.49/27.24 | End of split % 194.49/27.24 | % 194.49/27.24 End of proof % 194.49/27.24 % 194.49/27.24 Sub-proof #4 shows that the following formulas are inconsistent: % 194.49/27.24 ---------------------------------------------------------------- % 194.49/27.24 (1) c_member(all_622_1, all_872_3, v_L) = all_872_2 % 194.49/27.24 (2) ~ (all_872_2 = 0) % 194.49/27.24 (3) ~ (all_872_4 = 0) % 194.49/27.24 (4) all_676_0 = all_622_1 % 194.49/27.24 (5) c_member(all_622_1, all_872_7, v_L) = 0 % 194.49/27.24 (6) all_872_8 = v_x | ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 194.49/27.24 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.24 tc_Arrow__Order__Mirabelle_Oalt, v_x, all_872_8) = v1 & % 194.49/27.24 c_member(all_676_0, v1, v_L) = v2 & c_member(all_676_0, all_872_3, v_L) % 194.49/27.24 = v0 & $i(v1) & (v2 = 0 | v0 = 0)) % 194.49/27.24 (7) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.24 tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v_x) = all_872_5 % 194.49/27.24 (8) ~ (all_872_0 = 0) % 194.49/27.24 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 194.49/27.24 [v5: $i] : (v1 = v0 | ~ (c_Product__Type_OPair(v5, v4, v3, v2) = v1) | % 194.49/27.24 ~ (c_Product__Type_OPair(v5, v4, v3, v2) = v0)) % 194.49/27.24 (10) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.24 tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v_x) = all_872_3 % 194.49/27.24 (11) all_872_8 = v_x | ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 194.49/27.24 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.24 tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v_x) = v1 & % 194.49/27.24 c_member(all_676_0, v1, v_L) = v2 & c_member(all_676_0, all_872_1, % 194.49/27.24 v_L) = v0 & $i(v1) & (v2 = 0 | v0 = 0)) % 194.49/27.24 (12) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.24 tc_Arrow__Order__Mirabelle_Oalt, all_872_9, all_872_8) = all_872_7 % 194.49/27.24 (13) c_member(all_622_1, all_872_1, v_L) = all_872_0 % 194.49/27.24 (14) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 194.49/27.24 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (c_member(v4, v3, v2) = v1) | % 194.49/27.24 ~ (c_member(v4, v3, v2) = v0)) % 194.49/27.24 (15) c_member(all_622_1, all_872_5, v_L) = all_872_4 % 194.49/27.24 % 194.49/27.24 Begin of proof % 194.49/27.24 | % 194.49/27.24 | BETA: splitting (11) gives: % 194.49/27.24 | % 194.49/27.24 | Case 1: % 194.49/27.24 | | % 194.49/27.24 | | (16) all_872_8 = v_x % 194.49/27.24 | | % 194.49/27.24 | | REDUCE: (12), (16) imply: % 194.49/27.24 | | (17) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.24 | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v_x) = all_872_7 % 194.49/27.24 | | % 194.49/27.24 | | REF_CLOSE: (3), (5), (7), (9), (14), (15), (17) are inconsistent by % 194.49/27.24 | | sub-proof #11. % 194.49/27.24 | | % 194.49/27.24 | Case 2: % 194.49/27.24 | | % 194.49/27.24 | | (18) ~ (all_872_8 = v_x) % 194.49/27.24 | | (19) ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 194.49/27.24 | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.24 | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v_x) = v1 & % 194.49/27.24 | | c_member(all_676_0, v1, v_L) = v2 & c_member(all_676_0, all_872_1, % 194.49/27.24 | | v_L) = v0 & $i(v1) & (v2 = 0 | v0 = 0)) % 194.49/27.24 | | % 194.49/27.24 | | DELTA: instantiating (19) with fresh symbols all_1201_0, all_1201_1, % 194.49/27.24 | | all_1201_2 gives: % 194.49/27.24 | | (20) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.24 | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v_x) = all_1201_1 & % 194.49/27.24 | | c_member(all_676_0, all_1201_1, v_L) = all_1201_0 & % 194.49/27.24 | | c_member(all_676_0, all_872_1, v_L) = all_1201_2 & $i(all_1201_1) & % 194.49/27.24 | | (all_1201_0 = 0 | all_1201_2 = 0) % 194.49/27.24 | | % 194.49/27.24 | | REF_CLOSE: (1), (2), (4), (6), (8), (9), (10), (13), (14), (18), (20) are % 194.49/27.24 | | inconsistent by sub-proof #9. % 194.49/27.24 | | % 194.49/27.24 | End of split % 194.49/27.24 | % 194.49/27.24 End of proof % 194.49/27.24 % 194.49/27.24 Sub-proof #5 shows that the following formulas are inconsistent: % 194.49/27.24 ---------------------------------------------------------------- % 194.49/27.24 (1) c_member(all_622_1, all_872_3, v_L) = all_872_2 % 194.49/27.24 (2) (all_872_4 = 0 & all_872_8 = v_y & ? [v0: $i] : ? [v1: $i] : ? [v2: % 194.49/27.24 $i] : ? [v3: int] : ( ~ (v3 = 0) & ~ (v0 = v_y) & % 194.49/27.24 c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.24 tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v0) = v2 & % 194.49/27.24 c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.24 tc_Arrow__Order__Mirabelle_Oalt, v_x, v0) = v1 & % 194.49/27.24 c_member(all_685_0, v2, v_L) = v3 & c_member(all_685_0, v1, v_L) = 0 % 194.49/27.24 & $i(v2) & $i(v1) & $i(v0))) | (all_872_6 = 0 & ~ (all_872_8 = v_y) % 194.49/27.24 & ? [v0: $i] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ? [v4: any] % 194.49/27.24 : (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.24 tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v0) = v1 & % 194.49/27.24 c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.24 tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v0) = v3 & % 194.49/27.24 c_member(all_685_0, v3, v_L) = v4 & c_member(all_685_0, v1, v_L) = v2 % 194.49/27.24 & $i(v3) & $i(v1) & $i(v0) & ((v2 = 0 & ~ (v4 = 0) & ~ (v0 = v_y)) % 194.49/27.24 | (v0 = v_y & all_872_2 = 0 & ~ (all_872_4 = 0) & ~ (all_872_9 = % 194.49/27.24 v_x)) | (v0 = v_y & all_872_8 = v_x & ~ (all_872_4 = 0) & ~ % 194.49/27.24 (all_872_9 = v_x))))) % 194.49/27.24 (3) all_685_0 = all_622_1 % 194.49/27.24 (4) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.24 tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v_x) = all_872_5 % 194.49/27.24 (5) all_872_8 = all_872_9 % 194.49/27.24 (6) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.24 tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v_x) = all_872_3 % 194.49/27.24 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 194.49/27.24 [v5: $i] : (v1 = v0 | ~ (c_Product__Type_OPair(v5, v4, v3, v2) = v1) | % 194.49/27.24 ~ (c_Product__Type_OPair(v5, v4, v3, v2) = v0)) % 194.49/27.24 (8) ~ (all_872_9 = v_y) % 194.49/27.24 (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 194.49/27.24 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (c_member(v4, v3, v2) = v1) | ~ % 194.49/27.24 (c_member(v4, v3, v2) = v0)) % 194.49/27.24 (10) c_member(all_622_1, all_872_5, v_L) = all_872_4 % 194.49/27.24 % 194.49/27.24 Begin of proof % 194.49/27.24 | % 194.49/27.24 | BETA: splitting (2) gives: % 194.49/27.24 | % 194.49/27.24 | Case 1: % 194.49/27.24 | | % 194.49/27.24 | | (11) all_872_4 = 0 & all_872_8 = v_y & ? [v0: $i] : ? [v1: $i] : ? % 194.49/27.24 | | [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & ~ (v0 = v_y) & % 194.49/27.24 | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.24 | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v0) = v2 & % 194.49/27.24 | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.24 | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v0) = v1 & % 194.49/27.24 | | c_member(all_685_0, v2, v_L) = v3 & c_member(all_685_0, v1, v_L) = % 194.49/27.24 | | 0 & $i(v2) & $i(v1) & $i(v0)) % 194.49/27.24 | | % 194.49/27.24 | | ALPHA: (11) implies: % 194.49/27.24 | | (12) all_872_8 = v_y % 194.49/27.24 | | % 194.49/27.24 | | COMBINE_EQS: (5), (12) imply: % 194.49/27.24 | | (13) all_872_9 = v_y % 194.49/27.24 | | % 194.49/27.24 | | SIMP: (13) implies: % 194.49/27.24 | | (14) all_872_9 = v_y % 194.49/27.24 | | % 194.49/27.24 | | REDUCE: (8), (14) imply: % 194.49/27.24 | | (15) $false % 194.49/27.24 | | % 194.49/27.24 | | CLOSE: (15) is inconsistent. % 194.49/27.24 | | % 194.49/27.24 | Case 2: % 194.49/27.24 | | % 194.49/27.25 | | (16) all_872_6 = 0 & ~ (all_872_8 = v_y) & ? [v0: $i] : ? [v1: $i] : % 194.49/27.25 | | ? [v2: any] : ? [v3: $i] : ? [v4: any] : % 194.49/27.25 | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.25 | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v0) = v1 & % 194.49/27.25 | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.25 | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v0) = v3 & % 194.49/27.25 | | c_member(all_685_0, v3, v_L) = v4 & c_member(all_685_0, v1, v_L) = % 194.49/27.25 | | v2 & $i(v3) & $i(v1) & $i(v0) & ((v2 = 0 & ~ (v4 = 0) & ~ (v0 = % 194.49/27.25 | | v_y)) | (v0 = v_y & all_872_2 = 0 & ~ (all_872_4 = 0) & ~ % 194.49/27.25 | | (all_872_9 = v_x)) | (v0 = v_y & all_872_8 = v_x & ~ % 194.49/27.25 | | (all_872_4 = 0) & ~ (all_872_9 = v_x)))) % 194.49/27.25 | | % 194.49/27.25 | | ALPHA: (16) implies: % 194.49/27.25 | | (17) ? [v0: $i] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ? [v4: % 194.49/27.25 | | any] : (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.25 | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v0) = v1 & % 194.49/27.25 | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.25 | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v0) = v3 & % 194.49/27.25 | | c_member(all_685_0, v3, v_L) = v4 & c_member(all_685_0, v1, v_L) = % 194.49/27.25 | | v2 & $i(v3) & $i(v1) & $i(v0) & ((v2 = 0 & ~ (v4 = 0) & ~ (v0 = % 194.49/27.25 | | v_y)) | (v0 = v_y & all_872_2 = 0 & ~ (all_872_4 = 0) & ~ % 194.49/27.25 | | (all_872_9 = v_x)) | (v0 = v_y & all_872_8 = v_x & ~ % 194.49/27.25 | | (all_872_4 = 0) & ~ (all_872_9 = v_x)))) % 194.49/27.25 | | % 194.49/27.25 | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (9), (10), (17) are inconsistent by % 194.49/27.25 | | sub-proof #6. % 194.49/27.25 | | % 194.49/27.25 | End of split % 194.49/27.25 | % 194.49/27.25 End of proof % 194.49/27.25 % 194.49/27.25 Sub-proof #6 shows that the following formulas are inconsistent: % 194.49/27.25 ---------------------------------------------------------------- % 194.49/27.25 (1) c_member(all_622_1, all_872_3, v_L) = all_872_2 % 194.49/27.25 (2) all_685_0 = all_622_1 % 194.49/27.25 (3) ? [v0: $i] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ? [v4: any] : % 194.49/27.25 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.25 tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v0) = v1 & % 194.49/27.25 c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.25 tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v0) = v3 & % 194.49/27.25 c_member(all_685_0, v3, v_L) = v4 & c_member(all_685_0, v1, v_L) = v2 & % 194.49/27.25 $i(v3) & $i(v1) & $i(v0) & ((v2 = 0 & ~ (v4 = 0) & ~ (v0 = v_y)) | % 194.49/27.25 (v0 = v_y & all_872_2 = 0 & ~ (all_872_4 = 0) & ~ (all_872_9 = % 194.49/27.25 v_x)) | (v0 = v_y & all_872_8 = v_x & ~ (all_872_4 = 0) & ~ % 194.49/27.25 (all_872_9 = v_x)))) % 194.49/27.25 (4) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.25 tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v_x) = all_872_5 % 194.49/27.25 (5) all_872_8 = all_872_9 % 194.49/27.25 (6) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.25 tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v_x) = all_872_3 % 194.49/27.25 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 194.49/27.25 [v5: $i] : (v1 = v0 | ~ (c_Product__Type_OPair(v5, v4, v3, v2) = v1) | % 194.49/27.25 ~ (c_Product__Type_OPair(v5, v4, v3, v2) = v0)) % 194.49/27.25 (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 194.49/27.25 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (c_member(v4, v3, v2) = v1) | ~ % 194.49/27.25 (c_member(v4, v3, v2) = v0)) % 194.49/27.25 (9) c_member(all_622_1, all_872_5, v_L) = all_872_4 % 194.49/27.25 % 194.49/27.25 Begin of proof % 194.49/27.25 | % 194.49/27.25 | DELTA: instantiating (3) with fresh symbols all_1156_0, all_1156_1, % 194.49/27.25 | all_1156_2, all_1156_3, all_1156_4 gives: % 194.49/27.25 | (10) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.25 | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, all_1156_4) = all_1156_3 % 194.49/27.25 | & c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.25 | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, all_1156_4) = all_1156_1 % 194.49/27.25 | & c_member(all_685_0, all_1156_1, v_L) = all_1156_0 & % 194.49/27.25 | c_member(all_685_0, all_1156_3, v_L) = all_1156_2 & $i(all_1156_1) & % 194.49/27.25 | $i(all_1156_3) & $i(all_1156_4) & ((all_1156_2 = 0 & ~ (all_1156_0 = % 194.49/27.25 | 0) & ~ (all_1156_4 = v_y)) | (all_1156_4 = v_y & all_872_2 = 0 % 194.49/27.25 | & ~ (all_872_4 = 0) & ~ (all_872_9 = v_x)) | (all_1156_4 = v_y & % 194.49/27.25 | all_872_8 = v_x & ~ (all_872_4 = 0) & ~ (all_872_9 = v_x))) % 194.49/27.25 | % 194.49/27.25 | ALPHA: (10) implies: % 194.49/27.25 | (11) c_member(all_685_0, all_1156_3, v_L) = all_1156_2 % 194.49/27.25 | (12) c_member(all_685_0, all_1156_1, v_L) = all_1156_0 % 194.49/27.25 | (13) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.25 | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, all_1156_4) = all_1156_1 % 194.49/27.25 | (14) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.25 | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, all_1156_4) = all_1156_3 % 194.49/27.25 | (15) (all_1156_2 = 0 & ~ (all_1156_0 = 0) & ~ (all_1156_4 = v_y)) | % 194.49/27.25 | (all_1156_4 = v_y & all_872_2 = 0 & ~ (all_872_4 = 0) & ~ (all_872_9 % 194.49/27.25 | = v_x)) | (all_1156_4 = v_y & all_872_8 = v_x & ~ (all_872_4 = 0) % 194.49/27.25 | & ~ (all_872_9 = v_x)) % 194.49/27.25 | % 194.49/27.25 | REDUCE: (5), (14) imply: % 194.49/27.25 | (16) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.25 | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, all_1156_4) = all_1156_3 % 194.49/27.25 | % 194.49/27.25 | REDUCE: (2), (12) imply: % 194.49/27.25 | (17) c_member(all_622_1, all_1156_1, v_L) = all_1156_0 % 194.49/27.25 | % 194.49/27.25 | REDUCE: (2), (11) imply: % 194.49/27.25 | (18) c_member(all_622_1, all_1156_3, v_L) = all_1156_2 % 194.49/27.25 | % 194.49/27.25 | GROUND_INST: instantiating (7) with all_872_5, all_872_3, v_x, all_872_9, % 194.49/27.25 | tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.25 | simplifying with (4), (6) gives: % 194.49/27.25 | (19) all_872_3 = all_872_5 % 194.49/27.25 | % 194.49/27.25 | GROUND_INST: instantiating (7) with all_1156_3, all_1156_1, all_1156_4, % 194.49/27.25 | all_872_9, tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.25 | tc_Arrow__Order__Mirabelle_Oalt, simplifying with (13), (16) % 194.49/27.25 | gives: % 194.49/27.25 | (20) all_1156_1 = all_1156_3 % 194.49/27.25 | % 194.49/27.25 | REDUCE: (17), (20) imply: % 194.49/27.25 | (21) c_member(all_622_1, all_1156_3, v_L) = all_1156_0 % 194.49/27.25 | % 194.49/27.25 | REDUCE: (1), (19) imply: % 194.49/27.25 | (22) c_member(all_622_1, all_872_5, v_L) = all_872_2 % 194.49/27.25 | % 194.49/27.25 | GROUND_INST: instantiating (8) with all_872_4, all_872_2, v_L, all_872_5, % 194.49/27.25 | all_622_1, simplifying with (9), (22) gives: % 194.49/27.25 | (23) all_872_2 = all_872_4 % 194.49/27.25 | % 194.49/27.25 | GROUND_INST: instantiating (8) with all_1156_2, all_1156_0, v_L, all_1156_3, % 194.49/27.25 | all_622_1, simplifying with (18), (21) gives: % 194.49/27.25 | (24) all_1156_0 = all_1156_2 % 194.49/27.25 | % 194.49/27.25 | BETA: splitting (15) gives: % 194.49/27.25 | % 194.49/27.25 | Case 1: % 194.49/27.25 | | % 194.49/27.25 | | (25) all_1156_2 = 0 & ~ (all_1156_0 = 0) & ~ (all_1156_4 = v_y) % 194.49/27.25 | | % 194.49/27.25 | | ALPHA: (25) implies: % 194.49/27.25 | | (26) all_1156_2 = 0 % 194.49/27.25 | | (27) ~ (all_1156_0 = 0) % 194.49/27.25 | | % 194.49/27.25 | | COMBINE_EQS: (24), (26) imply: % 194.49/27.25 | | (28) all_1156_0 = 0 % 194.49/27.25 | | % 194.49/27.25 | | REDUCE: (27), (28) imply: % 194.49/27.25 | | (29) $false % 194.49/27.25 | | % 194.49/27.25 | | CLOSE: (29) is inconsistent. % 194.49/27.25 | | % 194.49/27.25 | Case 2: % 194.49/27.25 | | % 194.49/27.25 | | (30) (all_1156_4 = v_y & all_872_2 = 0 & ~ (all_872_4 = 0) & ~ % 194.49/27.25 | | (all_872_9 = v_x)) | (all_1156_4 = v_y & all_872_8 = v_x & ~ % 194.49/27.25 | | (all_872_4 = 0) & ~ (all_872_9 = v_x)) % 194.49/27.25 | | % 194.49/27.25 | | BETA: splitting (30) gives: % 194.49/27.25 | | % 194.49/27.25 | | Case 1: % 194.49/27.25 | | | % 194.49/27.25 | | | (31) all_1156_4 = v_y & all_872_2 = 0 & ~ (all_872_4 = 0) & ~ % 194.49/27.25 | | | (all_872_9 = v_x) % 194.49/27.25 | | | % 194.49/27.25 | | | ALPHA: (31) implies: % 194.49/27.25 | | | (32) all_872_2 = 0 % 194.49/27.25 | | | (33) ~ (all_872_4 = 0) % 194.49/27.25 | | | % 194.49/27.25 | | | COMBINE_EQS: (23), (32) imply: % 194.49/27.25 | | | (34) all_872_4 = 0 % 194.49/27.25 | | | % 194.49/27.25 | | | REDUCE: (33), (34) imply: % 194.49/27.25 | | | (35) $false % 194.49/27.25 | | | % 194.49/27.25 | | | CLOSE: (35) is inconsistent. % 194.49/27.25 | | | % 194.49/27.25 | | Case 2: % 194.49/27.25 | | | % 194.49/27.25 | | | (36) all_1156_4 = v_y & all_872_8 = v_x & ~ (all_872_4 = 0) & ~ % 194.49/27.25 | | | (all_872_9 = v_x) % 194.49/27.25 | | | % 194.49/27.25 | | | ALPHA: (36) implies: % 194.49/27.25 | | | (37) all_872_8 = v_x % 194.49/27.25 | | | (38) ~ (all_872_9 = v_x) % 194.49/27.25 | | | % 194.49/27.25 | | | COMBINE_EQS: (5), (37) imply: % 194.49/27.25 | | | (39) all_872_9 = v_x % 194.49/27.25 | | | % 194.49/27.25 | | | REDUCE: (38), (39) imply: % 194.49/27.25 | | | (40) $false % 194.49/27.25 | | | % 194.49/27.25 | | | CLOSE: (40) is inconsistent. % 194.49/27.25 | | | % 194.49/27.25 | | End of split % 194.49/27.25 | | % 194.49/27.25 | End of split % 194.49/27.25 | % 194.49/27.25 End of proof % 194.49/27.25 % 194.49/27.25 Sub-proof #7 shows that the following formulas are inconsistent: % 194.49/27.25 ---------------------------------------------------------------- % 194.49/27.25 (1) c_member(all_622_1, all_872_3, v_L) = all_872_2 % 194.49/27.25 (2) $i(all_872_8) % 194.49/27.25 (3) $i(v_L) % 194.49/27.25 (4) (all_872_4 = 0 & all_872_8 = v_y & ? [v0: $i] : ? [v1: $i] : ? [v2: % 194.49/27.25 $i] : ? [v3: int] : ( ~ (v3 = 0) & ~ (v0 = v_y) & % 194.49/27.25 c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.25 tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v0) = v2 & % 194.49/27.25 c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.25 tc_Arrow__Order__Mirabelle_Oalt, v_x, v0) = v1 & % 194.49/27.25 c_member(all_685_0, v2, v_L) = v3 & c_member(all_685_0, v1, v_L) = 0 % 194.49/27.25 & $i(v2) & $i(v1) & $i(v0))) | (all_872_6 = 0 & ~ (all_872_8 = v_y) % 194.49/27.25 & ? [v0: $i] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ? [v4: any] % 194.49/27.25 : (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.25 tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v0) = v1 & % 194.49/27.25 c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.25 tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v0) = v3 & % 194.49/27.25 c_member(all_685_0, v3, v_L) = v4 & c_member(all_685_0, v1, v_L) = v2 % 194.49/27.25 & $i(v3) & $i(v1) & $i(v0) & ((v2 = 0 & ~ (v4 = 0) & ~ (v0 = v_y)) % 194.49/27.25 | (v0 = v_y & all_872_2 = 0 & ~ (all_872_4 = 0) & ~ (all_872_9 = % 194.49/27.25 v_x)) | (v0 = v_y & all_872_8 = v_x & ~ (all_872_4 = 0) & ~ % 194.49/27.25 (all_872_9 = v_x))))) % 194.49/27.25 (5) $i(all_622_1) % 194.49/27.25 (6) ~ (all_872_2 = 0) % 194.49/27.25 (7) all_685_0 = all_622_1 % 194.49/27.25 (8) ! [v0: $i] : ! [v1: $i] : ( ~ % 194.49/27.25 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.25 tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v0) = v1) | ~ $i(v0) | % 194.49/27.25 ? [v2: $i] : ? [v3: any] : ? [v4: any] : % 194.49/27.25 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.25 tc_Arrow__Order__Mirabelle_Oalt, v_x, v0) = v2 & % 194.49/27.25 c_member(all_676_0, v2, v_L) = v3 & c_member(all_676_0, v1, v_L) = v4 % 194.49/27.25 & $i(v2) & ( ~ (v3 = 0) | v4 = 0))) % 194.49/27.25 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 194.49/27.25 (c_member(v2, v1, v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 194.49/27.25 [v4: $i] : ? [v5: int] : ( ~ (v5 = 0) & hBOOL(v4) = v5 & hAPP(v0, v1) % 194.49/27.26 = v4 & $i(v4))) % 194.49/27.26 (10) all_676_0 = all_622_1 % 194.49/27.26 (11) c_member(all_622_1, all_872_7, v_L) = 0 % 194.49/27.26 (12) all_872_8 = v_x | ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 194.49/27.26 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.26 tc_Arrow__Order__Mirabelle_Oalt, v_x, all_872_8) = v1 & % 194.49/27.26 c_member(all_676_0, v1, v_L) = v2 & c_member(all_676_0, all_872_3, % 194.49/27.26 v_L) = v0 & $i(v1) & (v2 = 0 | v0 = 0)) % 194.49/27.26 (13) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.26 tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v_x) = all_872_5 % 194.49/27.26 (14) ~ (all_872_0 = 0) % 194.49/27.26 (15) ! [v0: $i] : ! [v1: $i] : ( ~ % 194.49/27.26 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.26 tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v0) = v1) | ~ $i(v0) % 194.49/27.26 | ? [v2: $i] : ? [v3: any] : ? [v4: any] : % 194.49/27.26 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.26 tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v0) = v2 & % 194.49/27.26 c_member(all_676_0, v2, v_L) = v3 & c_member(all_676_0, v1, v_L) = % 194.49/27.26 v4 & $i(v2) & ( ~ (v3 = 0) | v4 = 0))) % 194.49/27.26 (16) ~ (v_x = v_y) % 194.49/27.26 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 194.49/27.26 [v5: $i] : (v1 = v0 | ~ (c_Product__Type_OPair(v5, v4, v3, v2) = v1) | % 194.49/27.26 ~ (c_Product__Type_OPair(v5, v4, v3, v2) = v0)) % 194.49/27.26 (18) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.26 tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v_x) = all_872_3 % 194.49/27.26 (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 194.49/27.26 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.26 tc_Arrow__Order__Mirabelle_Oalt, v0, v1) = v2) | ~ $i(v1) | ~ % 194.49/27.26 $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & c_member(all_676_0, v2, v_L) = % 194.49/27.26 v3) | ! [v3: $i] : ! [v4: $i] : ( ~ % 194.49/27.26 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.26 tc_Arrow__Order__Mirabelle_Oalt, v0, v3) = v4) | ~ $i(v3) | ? % 194.49/27.26 [v5: $i] : ? [v6: any] : ? [v7: any] : % 194.49/27.26 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.26 tc_Arrow__Order__Mirabelle_Oalt, v1, v3) = v5 & % 194.49/27.26 c_member(all_676_0, v5, v_L) = v6 & c_member(all_676_0, v4, v_L) = % 194.49/27.26 v7 & $i(v5) & ( ~ (v6 = 0) | v7 = 0)))) % 194.49/27.26 (20) all_872_8 = v_x | ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 194.49/27.26 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.26 tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v_x) = v1 & % 194.49/27.26 c_member(all_676_0, v1, v_L) = v2 & c_member(all_676_0, all_872_1, % 194.49/27.26 v_L) = v0 & $i(v1) & (v2 = 0 | v0 = 0)) % 194.49/27.26 (21) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.26 tc_Arrow__Order__Mirabelle_Oalt, all_872_9, all_872_8) = all_872_7 % 194.49/27.26 (22) c_member(all_622_1, all_872_1, v_L) = all_872_0 % 194.49/27.26 (23) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 194.49/27.26 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (c_member(v4, v3, v2) = v1) | % 194.49/27.26 ~ (c_member(v4, v3, v2) = v0)) % 194.49/27.26 (24) c_member(all_622_1, all_872_5, v_L) = all_872_4 % 194.49/27.26 % 194.49/27.26 Begin of proof % 194.49/27.26 | % 194.49/27.26 | BETA: splitting (12) gives: % 194.49/27.26 | % 194.49/27.26 | Case 1: % 194.49/27.26 | | % 194.49/27.26 | | (25) all_872_8 = v_x % 194.49/27.26 | | % 194.49/27.26 | | REDUCE: (21), (25) imply: % 194.49/27.26 | | (26) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.26 | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v_x) = all_872_7 % 194.49/27.26 | | % 194.49/27.26 | | REDUCE: (2), (25) imply: % 194.49/27.26 | | (27) $i(v_x) % 194.49/27.26 | | % 194.49/27.26 | | BETA: splitting (4) gives: % 194.49/27.26 | | % 194.49/27.26 | | Case 1: % 194.49/27.26 | | | % 194.49/27.26 | | | (28) all_872_4 = 0 & all_872_8 = v_y & ? [v0: $i] : ? [v1: $i] : ? % 194.49/27.26 | | | [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & ~ (v0 = v_y) & % 194.49/27.26 | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.26 | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v0) = v2 & % 194.49/27.26 | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.26 | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v0) = v1 & % 194.49/27.26 | | | c_member(all_685_0, v2, v_L) = v3 & c_member(all_685_0, v1, v_L) % 194.49/27.26 | | | = 0 & $i(v2) & $i(v1) & $i(v0)) % 194.49/27.26 | | | % 194.49/27.26 | | | ALPHA: (28) implies: % 194.49/27.26 | | | (29) all_872_8 = v_y % 194.49/27.26 | | | % 194.49/27.26 | | | COMBINE_EQS: (25), (29) imply: % 194.49/27.26 | | | (30) v_x = v_y % 194.49/27.26 | | | % 194.49/27.26 | | | REDUCE: (16), (30) imply: % 194.49/27.26 | | | (31) $false % 194.49/27.26 | | | % 194.49/27.26 | | | CLOSE: (31) is inconsistent. % 194.49/27.26 | | | % 194.49/27.26 | | Case 2: % 194.49/27.26 | | | % 194.49/27.26 | | | (32) all_872_6 = 0 & ~ (all_872_8 = v_y) & ? [v0: $i] : ? [v1: $i] : % 194.49/27.26 | | | ? [v2: any] : ? [v3: $i] : ? [v4: any] : % 194.49/27.26 | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.26 | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v0) = v1 & % 194.49/27.26 | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.26 | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v0) = v3 & % 194.49/27.26 | | | c_member(all_685_0, v3, v_L) = v4 & c_member(all_685_0, v1, v_L) % 194.49/27.26 | | | = v2 & $i(v3) & $i(v1) & $i(v0) & ((v2 = 0 & ~ (v4 = 0) & ~ % 194.49/27.26 | | | (v0 = v_y)) | (v0 = v_y & all_872_2 = 0 & ~ (all_872_4 = 0) % 194.49/27.26 | | | & ~ (all_872_9 = v_x)) | (v0 = v_y & all_872_8 = v_x & ~ % 194.49/27.26 | | | (all_872_4 = 0) & ~ (all_872_9 = v_x)))) % 194.49/27.26 | | | % 194.49/27.26 | | | ALPHA: (32) implies: % 194.49/27.26 | | | (33) ? [v0: $i] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ? [v4: % 194.49/27.26 | | | any] : (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.26 | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v0) = v1 & % 194.49/27.26 | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.26 | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v0) = v3 & % 194.49/27.26 | | | c_member(all_685_0, v3, v_L) = v4 & c_member(all_685_0, v1, v_L) % 194.49/27.26 | | | = v2 & $i(v3) & $i(v1) & $i(v0) & ((v2 = 0 & ~ (v4 = 0) & ~ % 194.49/27.26 | | | (v0 = v_y)) | (v0 = v_y & all_872_2 = 0 & ~ (all_872_4 = 0) % 194.49/27.26 | | | & ~ (all_872_9 = v_x)) | (v0 = v_y & all_872_8 = v_x & ~ % 194.49/27.26 | | | (all_872_4 = 0) & ~ (all_872_9 = v_x)))) % 194.49/27.26 | | | % 194.49/27.26 | | | REF_CLOSE: (3), (5), (7), (8), (9), (10), (11), (13), (15), (17), (19), % 194.49/27.26 | | | (23), (24), (25), (26), (27), (33) are inconsistent by % 194.49/27.26 | | | sub-proof #10. % 194.49/27.26 | | | % 194.49/27.26 | | End of split % 194.49/27.26 | | % 194.49/27.26 | Case 2: % 194.49/27.26 | | % 194.49/27.26 | | (34) ~ (all_872_8 = v_x) % 194.49/27.26 | | % 194.49/27.26 | | REF_CLOSE: (1), (6), (10), (12), (14), (17), (18), (20), (22), (23), (34) % 194.49/27.26 | | are inconsistent by sub-proof #8. % 194.49/27.26 | | % 194.49/27.26 | End of split % 194.49/27.26 | % 194.49/27.26 End of proof % 194.49/27.26 % 194.49/27.26 Sub-proof #8 shows that the following formulas are inconsistent: % 194.49/27.26 ---------------------------------------------------------------- % 194.49/27.26 (1) c_member(all_622_1, all_872_3, v_L) = all_872_2 % 194.49/27.26 (2) ~ (all_872_2 = 0) % 194.49/27.26 (3) all_676_0 = all_622_1 % 194.49/27.26 (4) all_872_8 = v_x | ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 194.49/27.26 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.26 tc_Arrow__Order__Mirabelle_Oalt, v_x, all_872_8) = v1 & % 194.49/27.26 c_member(all_676_0, v1, v_L) = v2 & c_member(all_676_0, all_872_3, v_L) % 194.49/27.26 = v0 & $i(v1) & (v2 = 0 | v0 = 0)) % 194.49/27.26 (5) ~ (all_872_0 = 0) % 194.49/27.26 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 194.49/27.26 [v5: $i] : (v1 = v0 | ~ (c_Product__Type_OPair(v5, v4, v3, v2) = v1) | % 194.49/27.26 ~ (c_Product__Type_OPair(v5, v4, v3, v2) = v0)) % 194.49/27.26 (7) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.26 tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v_x) = all_872_3 % 194.49/27.26 (8) all_872_8 = v_x | ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 194.49/27.26 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.26 tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v_x) = v1 & % 194.49/27.26 c_member(all_676_0, v1, v_L) = v2 & c_member(all_676_0, all_872_1, v_L) % 194.49/27.26 = v0 & $i(v1) & (v2 = 0 | v0 = 0)) % 194.49/27.26 (9) c_member(all_622_1, all_872_1, v_L) = all_872_0 % 194.49/27.26 (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 194.49/27.26 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (c_member(v4, v3, v2) = v1) | % 194.49/27.26 ~ (c_member(v4, v3, v2) = v0)) % 194.49/27.26 (11) ~ (all_872_8 = v_x) % 194.49/27.26 % 194.49/27.26 Begin of proof % 194.49/27.26 | % 194.49/27.26 | BETA: splitting (8) gives: % 194.49/27.26 | % 194.49/27.26 | Case 1: % 194.49/27.26 | | % 194.49/27.26 | | (12) all_872_8 = v_x % 194.49/27.26 | | % 194.49/27.26 | | REDUCE: (11), (12) imply: % 194.49/27.26 | | (13) $false % 194.49/27.26 | | % 194.49/27.26 | | CLOSE: (13) is inconsistent. % 194.49/27.26 | | % 194.49/27.26 | Case 2: % 194.49/27.26 | | % 194.49/27.26 | | (14) ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 194.49/27.26 | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.26 | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v_x) = v1 & % 194.49/27.26 | | c_member(all_676_0, v1, v_L) = v2 & c_member(all_676_0, all_872_1, % 194.49/27.26 | | v_L) = v0 & $i(v1) & (v2 = 0 | v0 = 0)) % 194.49/27.26 | | % 194.49/27.26 | | DELTA: instantiating (14) with fresh symbols all_1201_0, all_1201_1, % 194.49/27.26 | | all_1201_2 gives: % 194.49/27.27 | | (15) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.27 | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v_x) = all_1201_1 & % 194.49/27.27 | | c_member(all_676_0, all_1201_1, v_L) = all_1201_0 & % 194.49/27.27 | | c_member(all_676_0, all_872_1, v_L) = all_1201_2 & $i(all_1201_1) & % 194.49/27.27 | | (all_1201_0 = 0 | all_1201_2 = 0) % 194.49/27.27 | | % 194.49/27.27 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (15) are % 194.49/27.27 | | inconsistent by sub-proof #9. % 194.49/27.27 | | % 194.49/27.27 | End of split % 194.49/27.27 | % 194.49/27.27 End of proof % 194.49/27.27 % 194.49/27.27 Sub-proof #9 shows that the following formulas are inconsistent: % 194.49/27.27 ---------------------------------------------------------------- % 194.49/27.27 (1) c_member(all_622_1, all_872_3, v_L) = all_872_2 % 194.49/27.27 (2) ~ (all_872_2 = 0) % 194.49/27.27 (3) all_676_0 = all_622_1 % 194.49/27.27 (4) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.27 tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v_x) = all_1201_1 & % 194.49/27.27 c_member(all_676_0, all_1201_1, v_L) = all_1201_0 & c_member(all_676_0, % 194.49/27.27 all_872_1, v_L) = all_1201_2 & $i(all_1201_1) & (all_1201_0 = 0 | % 194.49/27.27 all_1201_2 = 0) % 194.49/27.27 (5) all_872_8 = v_x | ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 194.49/27.27 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.27 tc_Arrow__Order__Mirabelle_Oalt, v_x, all_872_8) = v1 & % 194.49/27.27 c_member(all_676_0, v1, v_L) = v2 & c_member(all_676_0, all_872_3, v_L) % 194.49/27.27 = v0 & $i(v1) & (v2 = 0 | v0 = 0)) % 194.49/27.27 (6) ~ (all_872_0 = 0) % 194.49/27.27 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 194.49/27.27 [v5: $i] : (v1 = v0 | ~ (c_Product__Type_OPair(v5, v4, v3, v2) = v1) | % 194.49/27.27 ~ (c_Product__Type_OPair(v5, v4, v3, v2) = v0)) % 194.49/27.27 (8) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.27 tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v_x) = all_872_3 % 194.49/27.27 (9) c_member(all_622_1, all_872_1, v_L) = all_872_0 % 194.49/27.27 (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 194.49/27.27 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (c_member(v4, v3, v2) = v1) | % 194.49/27.27 ~ (c_member(v4, v3, v2) = v0)) % 194.49/27.27 (11) ~ (all_872_8 = v_x) % 194.49/27.27 % 194.49/27.27 Begin of proof % 194.49/27.27 | % 194.49/27.27 | ALPHA: (4) implies: % 194.49/27.27 | (12) c_member(all_676_0, all_872_1, v_L) = all_1201_2 % 194.49/27.27 | (13) c_member(all_676_0, all_1201_1, v_L) = all_1201_0 % 194.49/27.27 | (14) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.27 | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v_x) = all_1201_1 % 194.49/27.27 | (15) all_1201_0 = 0 | all_1201_2 = 0 % 194.49/27.27 | % 194.49/27.27 | REDUCE: (3), (13) imply: % 194.49/27.27 | (16) c_member(all_622_1, all_1201_1, v_L) = all_1201_0 % 194.49/27.27 | % 194.49/27.27 | REDUCE: (3), (12) imply: % 194.49/27.27 | (17) c_member(all_622_1, all_872_1, v_L) = all_1201_2 % 194.49/27.27 | % 194.49/27.27 | BETA: splitting (5) gives: % 194.49/27.27 | % 194.49/27.27 | Case 1: % 194.49/27.27 | | % 194.49/27.27 | | (18) all_872_8 = v_x % 194.49/27.27 | | % 194.49/27.27 | | REDUCE: (11), (18) imply: % 194.49/27.27 | | (19) $false % 194.49/27.27 | | % 194.49/27.27 | | CLOSE: (19) is inconsistent. % 194.49/27.27 | | % 194.49/27.27 | Case 2: % 194.49/27.27 | | % 194.49/27.27 | | (20) ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 194.49/27.27 | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.27 | | tc_Arrow__Order__Mirabelle_Oalt, v_x, all_872_8) = v1 & % 194.49/27.27 | | c_member(all_676_0, v1, v_L) = v2 & c_member(all_676_0, all_872_3, % 194.49/27.27 | | v_L) = v0 & $i(v1) & (v2 = 0 | v0 = 0)) % 194.49/27.27 | | % 194.49/27.27 | | DELTA: instantiating (20) with fresh symbols all_1207_0, all_1207_1, % 194.49/27.27 | | all_1207_2 gives: % 194.49/27.27 | | (21) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.27 | | tc_Arrow__Order__Mirabelle_Oalt, v_x, all_872_8) = all_1207_1 & % 194.49/27.27 | | c_member(all_676_0, all_1207_1, v_L) = all_1207_0 & % 194.49/27.27 | | c_member(all_676_0, all_872_3, v_L) = all_1207_2 & $i(all_1207_1) & % 194.49/27.27 | | (all_1207_0 = 0 | all_1207_2 = 0) % 194.49/27.27 | | % 194.49/27.27 | | ALPHA: (21) implies: % 194.49/27.27 | | (22) c_member(all_676_0, all_872_3, v_L) = all_1207_2 % 194.49/27.27 | | % 194.49/27.27 | | REDUCE: (3), (22) imply: % 194.49/27.27 | | (23) c_member(all_622_1, all_872_3, v_L) = all_1207_2 % 194.49/27.27 | | % 194.49/27.27 | | GROUND_INST: instantiating (10) with all_872_2, all_1207_2, v_L, all_872_3, % 194.49/27.27 | | all_622_1, simplifying with (1), (23) gives: % 194.49/27.27 | | (24) all_1207_2 = all_872_2 % 194.49/27.27 | | % 194.49/27.27 | | GROUND_INST: instantiating (10) with all_872_0, all_1201_2, v_L, all_872_1, % 194.49/27.27 | | all_622_1, simplifying with (9), (17) gives: % 194.49/27.27 | | (25) all_1201_2 = all_872_0 % 194.49/27.27 | | % 194.49/27.27 | | GROUND_INST: instantiating (7) with all_872_3, all_1201_1, v_x, all_872_8, % 194.49/27.27 | | tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.27 | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with (8), (14) % 194.49/27.27 | | gives: % 194.49/27.27 | | (26) all_1201_1 = all_872_3 % 194.49/27.27 | | % 194.49/27.27 | | REDUCE: (16), (26) imply: % 194.49/27.27 | | (27) c_member(all_622_1, all_872_3, v_L) = all_1201_0 % 194.49/27.27 | | % 194.49/27.27 | | BETA: splitting (15) gives: % 194.49/27.27 | | % 194.49/27.27 | | Case 1: % 194.49/27.27 | | | % 194.49/27.27 | | | (28) all_1201_0 = 0 % 194.49/27.27 | | | % 194.49/27.27 | | | REDUCE: (27), (28) imply: % 194.49/27.27 | | | (29) c_member(all_622_1, all_872_3, v_L) = 0 % 194.49/27.27 | | | % 194.49/27.27 | | | REF_CLOSE: (1), (2), (10), (29) are inconsistent by sub-proof #13. % 194.49/27.27 | | | % 194.49/27.27 | | Case 2: % 194.49/27.27 | | | % 194.49/27.27 | | | (30) all_1201_2 = 0 % 194.49/27.27 | | | % 194.49/27.27 | | | COMBINE_EQS: (25), (30) imply: % 194.49/27.27 | | | (31) all_872_0 = 0 % 194.49/27.27 | | | % 194.49/27.27 | | | REDUCE: (6), (31) imply: % 194.49/27.27 | | | (32) $false % 194.49/27.27 | | | % 194.49/27.27 | | | CLOSE: (32) is inconsistent. % 194.49/27.27 | | | % 194.49/27.27 | | End of split % 194.49/27.27 | | % 194.49/27.27 | End of split % 194.49/27.27 | % 194.49/27.27 End of proof % 194.49/27.27 % 194.49/27.27 Sub-proof #10 shows that the following formulas are inconsistent: % 194.49/27.27 ---------------------------------------------------------------- % 194.49/27.27 (1) $i(v_L) % 194.49/27.27 (2) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.27 tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v_x) = all_872_7 % 194.49/27.27 (3) $i(all_622_1) % 194.49/27.27 (4) all_685_0 = all_622_1 % 194.49/27.27 (5) ! [v0: $i] : ! [v1: $i] : ( ~ % 194.49/27.27 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.27 tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v0) = v1) | ~ $i(v0) | % 194.49/27.27 ? [v2: $i] : ? [v3: any] : ? [v4: any] : % 194.49/27.27 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.27 tc_Arrow__Order__Mirabelle_Oalt, v_x, v0) = v2 & % 194.49/27.27 c_member(all_676_0, v2, v_L) = v3 & c_member(all_676_0, v1, v_L) = v4 % 194.49/27.27 & $i(v2) & ( ~ (v3 = 0) | v4 = 0))) % 194.49/27.27 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 194.49/27.27 (c_member(v2, v1, v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 194.49/27.27 [v4: $i] : ? [v5: int] : ( ~ (v5 = 0) & hBOOL(v4) = v5 & hAPP(v0, v1) % 194.49/27.27 = v4 & $i(v4))) % 194.49/27.27 (7) all_676_0 = all_622_1 % 194.49/27.27 (8) c_member(all_622_1, all_872_7, v_L) = 0 % 194.49/27.27 (9) ? [v0: $i] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ? [v4: any] : % 194.49/27.27 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.27 tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v0) = v1 & % 194.49/27.27 c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.27 tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v0) = v3 & % 194.49/27.27 c_member(all_685_0, v3, v_L) = v4 & c_member(all_685_0, v1, v_L) = v2 & % 194.49/27.27 $i(v3) & $i(v1) & $i(v0) & ((v2 = 0 & ~ (v4 = 0) & ~ (v0 = v_y)) | % 194.49/27.27 (v0 = v_y & all_872_2 = 0 & ~ (all_872_4 = 0) & ~ (all_872_9 = % 194.49/27.27 v_x)) | (v0 = v_y & all_872_8 = v_x & ~ (all_872_4 = 0) & ~ % 194.49/27.27 (all_872_9 = v_x)))) % 194.49/27.27 (10) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.27 tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v_x) = all_872_5 % 194.49/27.27 (11) ! [v0: $i] : ! [v1: $i] : ( ~ % 194.49/27.27 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.27 tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v0) = v1) | ~ $i(v0) % 194.49/27.27 | ? [v2: $i] : ? [v3: any] : ? [v4: any] : % 194.49/27.27 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.27 tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v0) = v2 & % 194.49/27.27 c_member(all_676_0, v2, v_L) = v3 & c_member(all_676_0, v1, v_L) = % 194.49/27.27 v4 & $i(v2) & ( ~ (v3 = 0) | v4 = 0))) % 194.49/27.27 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 194.49/27.27 [v5: $i] : (v1 = v0 | ~ (c_Product__Type_OPair(v5, v4, v3, v2) = v1) | % 194.49/27.27 ~ (c_Product__Type_OPair(v5, v4, v3, v2) = v0)) % 194.49/27.27 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 194.49/27.27 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.27 tc_Arrow__Order__Mirabelle_Oalt, v0, v1) = v2) | ~ $i(v1) | ~ % 194.49/27.27 $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & c_member(all_676_0, v2, v_L) = % 194.49/27.27 v3) | ! [v3: $i] : ! [v4: $i] : ( ~ % 194.49/27.27 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.27 tc_Arrow__Order__Mirabelle_Oalt, v0, v3) = v4) | ~ $i(v3) | ? % 194.49/27.27 [v5: $i] : ? [v6: any] : ? [v7: any] : % 194.49/27.27 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.27 tc_Arrow__Order__Mirabelle_Oalt, v1, v3) = v5 & % 194.49/27.27 c_member(all_676_0, v5, v_L) = v6 & c_member(all_676_0, v4, v_L) = % 194.49/27.27 v7 & $i(v5) & ( ~ (v6 = 0) | v7 = 0)))) % 194.49/27.27 (14) $i(v_x) % 194.49/27.27 (15) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 194.49/27.27 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (c_member(v4, v3, v2) = v1) | % 194.49/27.27 ~ (c_member(v4, v3, v2) = v0)) % 194.49/27.27 (16) c_member(all_622_1, all_872_5, v_L) = all_872_4 % 194.49/27.27 (17) all_872_8 = v_x % 194.49/27.27 % 194.49/27.27 Begin of proof % 194.49/27.27 | % 194.49/27.27 | DELTA: instantiating (9) with fresh symbols all_1217_0, all_1217_1, % 194.49/27.27 | all_1217_2, all_1217_3, all_1217_4 gives: % 194.49/27.27 | (18) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.27 | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, all_1217_4) = all_1217_3 % 194.49/27.27 | & c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.27 | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, all_1217_4) = all_1217_1 % 194.49/27.27 | & c_member(all_685_0, all_1217_1, v_L) = all_1217_0 & % 194.49/27.27 | c_member(all_685_0, all_1217_3, v_L) = all_1217_2 & $i(all_1217_1) & % 194.49/27.27 | $i(all_1217_3) & $i(all_1217_4) & ((all_1217_2 = 0 & ~ (all_1217_0 = % 194.49/27.27 | 0) & ~ (all_1217_4 = v_y)) | (all_1217_4 = v_y & all_872_2 = 0 % 194.49/27.27 | & ~ (all_872_4 = 0) & ~ (all_872_9 = v_x)) | (all_1217_4 = v_y & % 194.49/27.27 | all_872_8 = v_x & ~ (all_872_4 = 0) & ~ (all_872_9 = v_x))) % 194.49/27.27 | % 194.49/27.27 | ALPHA: (18) implies: % 194.49/27.27 | (19) $i(all_1217_4) % 194.49/27.27 | (20) $i(all_1217_1) % 194.49/27.27 | (21) c_member(all_685_0, all_1217_3, v_L) = all_1217_2 % 194.49/27.27 | (22) c_member(all_685_0, all_1217_1, v_L) = all_1217_0 % 194.49/27.27 | (23) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.27 | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, all_1217_4) = all_1217_1 % 194.49/27.28 | (24) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.28 | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, all_1217_4) = all_1217_3 % 194.49/27.28 | (25) (all_1217_2 = 0 & ~ (all_1217_0 = 0) & ~ (all_1217_4 = v_y)) | % 194.49/27.28 | (all_1217_4 = v_y & all_872_2 = 0 & ~ (all_872_4 = 0) & ~ (all_872_9 % 194.49/27.28 | = v_x)) | (all_1217_4 = v_y & all_872_8 = v_x & ~ (all_872_4 = 0) % 194.49/27.28 | & ~ (all_872_9 = v_x)) % 194.49/27.28 | % 194.49/27.28 | REDUCE: (17), (24) imply: % 194.49/27.28 | (26) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.28 | tc_Arrow__Order__Mirabelle_Oalt, v_x, all_1217_4) = all_1217_3 % 194.49/27.28 | % 194.49/27.28 | REDUCE: (4), (22) imply: % 194.49/27.28 | (27) c_member(all_622_1, all_1217_1, v_L) = all_1217_0 % 194.49/27.28 | % 194.49/27.28 | REDUCE: (4), (21) imply: % 194.49/27.28 | (28) c_member(all_622_1, all_1217_3, v_L) = all_1217_2 % 194.49/27.28 | % 194.49/27.28 | BETA: splitting (25) gives: % 194.49/27.28 | % 194.49/27.28 | Case 1: % 194.49/27.28 | | % 194.49/27.28 | | (29) all_1217_2 = 0 & ~ (all_1217_0 = 0) & ~ (all_1217_4 = v_y) % 194.49/27.28 | | % 194.49/27.28 | | ALPHA: (29) implies: % 194.49/27.28 | | (30) all_1217_2 = 0 % 194.49/27.28 | | (31) ~ (all_1217_0 = 0) % 194.49/27.28 | | % 194.49/27.28 | | REDUCE: (28), (30) imply: % 194.49/27.28 | | (32) c_member(all_622_1, all_1217_3, v_L) = 0 % 194.49/27.28 | | % 194.49/27.28 | | GROUND_INST: instantiating (6) with v_L, all_1217_1, all_622_1, all_1217_0, % 194.49/27.28 | | simplifying with (1), (3), (20), (27) gives: % 194.49/27.28 | | (33) all_1217_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 194.49/27.28 | | hBOOL(v0) = v1 & hAPP(v_L, all_1217_1) = v0 & $i(v0)) % 194.49/27.28 | | % 194.49/27.28 | | GROUND_INST: instantiating (13) with v_x, all_1217_4, all_1217_3, % 194.49/27.28 | | simplifying with (14), (19), (26) gives: % 194.49/27.28 | | (34) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_676_0, all_1217_3, v_L) = % 194.49/27.28 | | v0) | ! [v0: $i] : ! [v1: $i] : ( ~ % 194.49/27.28 | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.28 | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v0) = v1) | ~ $i(v0) | % 194.49/27.28 | | ? [v2: $i] : ? [v3: any] : ? [v4: any] : % 194.49/27.28 | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.28 | | tc_Arrow__Order__Mirabelle_Oalt, all_1217_4, v0) = v2 & % 194.49/27.28 | | c_member(all_676_0, v2, v_L) = v3 & c_member(all_676_0, v1, v_L) % 194.49/27.28 | | = v4 & $i(v2) & ( ~ (v3 = 0) | v4 = 0))) % 194.49/27.28 | | % 194.49/27.28 | | GROUND_INST: instantiating (11) with all_1217_4, all_1217_1, simplifying % 194.49/27.28 | | with (19), (23) gives: % 194.49/27.28 | | (35) ? [v0: $i] : ? [v1: any] : ? [v2: any] : % 194.49/27.28 | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.28 | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, all_1217_4) = v0 & % 194.49/27.28 | | c_member(all_676_0, v0, v_L) = v1 & c_member(all_676_0, % 194.49/27.28 | | all_1217_1, v_L) = v2 & $i(v0) & ( ~ (v1 = 0) | v2 = 0)) % 194.49/27.28 | | % 194.49/27.28 | | GROUND_INST: instantiating (5) with all_1217_4, all_1217_1, simplifying with % 194.49/27.28 | | (19), (23) gives: % 194.49/27.28 | | (36) ? [v0: $i] : ? [v1: any] : ? [v2: any] : % 194.49/27.28 | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.28 | | tc_Arrow__Order__Mirabelle_Oalt, v_x, all_1217_4) = v0 & % 194.49/27.28 | | c_member(all_676_0, v0, v_L) = v1 & c_member(all_676_0, % 194.49/27.28 | | all_1217_1, v_L) = v2 & $i(v0) & ( ~ (v1 = 0) | v2 = 0)) % 194.49/27.28 | | % 194.49/27.28 | | DELTA: instantiating (36) with fresh symbols all_1284_0, all_1284_1, % 194.49/27.28 | | all_1284_2 gives: % 194.49/27.28 | | (37) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.28 | | tc_Arrow__Order__Mirabelle_Oalt, v_x, all_1217_4) = all_1284_2 & % 194.49/27.28 | | c_member(all_676_0, all_1284_2, v_L) = all_1284_1 & % 194.49/27.28 | | c_member(all_676_0, all_1217_1, v_L) = all_1284_0 & $i(all_1284_2) & % 194.49/27.28 | | ( ~ (all_1284_1 = 0) | all_1284_0 = 0) % 194.49/27.28 | | % 194.49/27.28 | | ALPHA: (37) implies: % 194.49/27.28 | | (38) c_member(all_676_0, all_1217_1, v_L) = all_1284_0 % 194.49/27.28 | | (39) c_member(all_676_0, all_1284_2, v_L) = all_1284_1 % 194.49/27.28 | | (40) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.28 | | tc_Arrow__Order__Mirabelle_Oalt, v_x, all_1217_4) = all_1284_2 % 194.49/27.28 | | (41) ~ (all_1284_1 = 0) | all_1284_0 = 0 % 194.49/27.28 | | % 194.49/27.28 | | DELTA: instantiating (35) with fresh symbols all_1286_0, all_1286_1, % 194.49/27.28 | | all_1286_2 gives: % 194.49/27.28 | | (42) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.28 | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, all_1217_4) = % 194.49/27.28 | | all_1286_2 & c_member(all_676_0, all_1286_2, v_L) = all_1286_1 & % 194.49/27.28 | | c_member(all_676_0, all_1217_1, v_L) = all_1286_0 & $i(all_1286_2) & % 194.49/27.28 | | ( ~ (all_1286_1 = 0) | all_1286_0 = 0) % 194.49/27.28 | | % 194.49/27.28 | | ALPHA: (42) implies: % 194.49/27.28 | | (43) c_member(all_676_0, all_1217_1, v_L) = all_1286_0 % 194.49/27.28 | | (44) c_member(all_676_0, all_1286_2, v_L) = all_1286_1 % 194.49/27.28 | | (45) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.28 | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, all_1217_4) = % 194.49/27.28 | | all_1286_2 % 194.49/27.28 | | % 194.49/27.28 | | REDUCE: (17), (45) imply: % 194.49/27.28 | | (46) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.28 | | tc_Arrow__Order__Mirabelle_Oalt, v_x, all_1217_4) = all_1286_2 % 194.49/27.28 | | % 194.49/27.28 | | REDUCE: (7), (44) imply: % 194.49/27.28 | | (47) c_member(all_622_1, all_1286_2, v_L) = all_1286_1 % 194.49/27.28 | | % 194.49/27.28 | | REDUCE: (7), (39) imply: % 194.49/27.28 | | (48) c_member(all_622_1, all_1284_2, v_L) = all_1284_1 % 194.49/27.28 | | % 194.49/27.28 | | REDUCE: (7), (43) imply: % 194.49/27.28 | | (49) c_member(all_622_1, all_1217_1, v_L) = all_1286_0 % 194.49/27.28 | | % 194.49/27.28 | | REDUCE: (7), (38) imply: % 194.49/27.28 | | (50) c_member(all_622_1, all_1217_1, v_L) = all_1284_0 % 194.49/27.28 | | % 194.49/27.28 | | BETA: splitting (34) gives: % 194.49/27.28 | | % 194.49/27.28 | | Case 1: % 194.49/27.28 | | | % 194.49/27.28 | | | (51) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_676_0, all_1217_3, v_L) % 194.49/27.28 | | | = v0) % 194.49/27.28 | | | % 194.49/27.28 | | | DELTA: instantiating (51) with fresh symbol all_1293_0 gives: % 194.49/27.28 | | | (52) ~ (all_1293_0 = 0) & c_member(all_676_0, all_1217_3, v_L) = % 194.49/27.28 | | | all_1293_0 % 194.49/27.28 | | | % 194.49/27.28 | | | ALPHA: (52) implies: % 194.49/27.28 | | | (53) ~ (all_1293_0 = 0) % 194.49/27.28 | | | (54) c_member(all_676_0, all_1217_3, v_L) = all_1293_0 % 194.49/27.28 | | | % 194.49/27.28 | | | REDUCE: (7), (54) imply: % 194.49/27.28 | | | (55) c_member(all_622_1, all_1217_3, v_L) = all_1293_0 % 194.49/27.28 | | | % 194.49/27.28 | | | GROUND_INST: instantiating (15) with 0, all_1293_0, v_L, all_1217_3, % 194.49/27.28 | | | all_622_1, simplifying with (32), (55) gives: % 194.49/27.28 | | | (56) all_1293_0 = 0 % 194.49/27.28 | | | % 194.49/27.28 | | | REDUCE: (53), (56) imply: % 194.49/27.28 | | | (57) $false % 194.49/27.28 | | | % 194.49/27.28 | | | CLOSE: (57) is inconsistent. % 194.49/27.28 | | | % 194.49/27.28 | | Case 2: % 194.49/27.28 | | | % 194.49/27.28 | | | (58) ! [v0: $i] : ! [v1: $i] : ( ~ % 194.49/27.28 | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.28 | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v0) = v1) | ~ $i(v0) % 194.49/27.28 | | | | ? [v2: $i] : ? [v3: any] : ? [v4: any] : % 194.49/27.28 | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.28 | | | tc_Arrow__Order__Mirabelle_Oalt, all_1217_4, v0) = v2 & % 194.49/27.28 | | | c_member(all_676_0, v2, v_L) = v3 & c_member(all_676_0, v1, % 194.49/27.28 | | | v_L) = v4 & $i(v2) & ( ~ (v3 = 0) | v4 = 0))) % 194.49/27.28 | | | % 194.49/27.28 | | | GROUND_INST: instantiating (58) with all_1217_4, all_1217_3, simplifying % 194.49/27.28 | | | with (19), (26) gives: % 194.49/27.28 | | | (59) ? [v0: $i] : ? [v1: any] : ? [v2: any] : % 194.49/27.28 | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.28 | | | tc_Arrow__Order__Mirabelle_Oalt, all_1217_4, all_1217_4) = v0 % 194.49/27.28 | | | & c_member(all_676_0, v0, v_L) = v1 & c_member(all_676_0, % 194.49/27.28 | | | all_1217_3, v_L) = v2 & $i(v0) & ( ~ (v1 = 0) | v2 = 0)) % 194.49/27.28 | | | % 194.49/27.28 | | | DELTA: instantiating (59) with fresh symbols all_1294_0, all_1294_1, % 194.49/27.28 | | | all_1294_2 gives: % 194.49/27.28 | | | (60) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.28 | | | tc_Arrow__Order__Mirabelle_Oalt, all_1217_4, all_1217_4) = % 194.49/27.28 | | | all_1294_2 & c_member(all_676_0, all_1294_2, v_L) = all_1294_1 & % 194.49/27.28 | | | c_member(all_676_0, all_1217_3, v_L) = all_1294_0 & $i(all_1294_2) % 194.49/27.28 | | | & ( ~ (all_1294_1 = 0) | all_1294_0 = 0) % 194.49/27.28 | | | % 194.49/27.28 | | | ALPHA: (60) implies: % 194.49/27.28 | | | (61) c_member(all_676_0, all_1217_3, v_L) = all_1294_0 % 194.49/27.28 | | | % 194.49/27.28 | | | REDUCE: (7), (61) imply: % 194.49/27.28 | | | (62) c_member(all_622_1, all_1217_3, v_L) = all_1294_0 % 194.49/27.28 | | | % 194.49/27.28 | | | BETA: splitting (33) gives: % 194.49/27.28 | | | % 194.49/27.28 | | | Case 1: % 194.49/27.28 | | | | % 194.49/27.28 | | | | (63) all_1217_0 = 0 % 194.49/27.28 | | | | % 194.49/27.28 | | | | REDUCE: (31), (63) imply: % 194.49/27.28 | | | | (64) $false % 194.49/27.28 | | | | % 194.49/27.28 | | | | CLOSE: (64) is inconsistent. % 194.49/27.28 | | | | % 194.49/27.28 | | | Case 2: % 194.49/27.28 | | | | % 194.49/27.28 | | | | % 194.49/27.28 | | | | GROUND_INST: instantiating (15) with 0, all_1294_0, v_L, all_1217_3, % 194.49/27.28 | | | | all_622_1, simplifying with (32), (62) gives: % 194.49/27.28 | | | | (65) all_1294_0 = 0 % 194.49/27.28 | | | | % 194.49/27.28 | | | | GROUND_INST: instantiating (15) with all_1217_0, all_1286_0, v_L, % 194.49/27.28 | | | | all_1217_1, all_622_1, simplifying with (27), (49) gives: % 194.49/27.28 | | | | (66) all_1286_0 = all_1217_0 % 194.49/27.28 | | | | % 194.49/27.28 | | | | GROUND_INST: instantiating (15) with all_1284_0, all_1286_0, v_L, % 194.49/27.28 | | | | all_1217_1, all_622_1, simplifying with (49), (50) gives: % 194.49/27.28 | | | | (67) all_1286_0 = all_1284_0 % 194.49/27.28 | | | | % 194.49/27.28 | | | | GROUND_INST: instantiating (12) with all_1217_3, all_1286_2, all_1217_4, % 194.49/27.28 | | | | v_x, tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.28 | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with (26), % 194.49/27.28 | | | | (46) gives: % 194.49/27.28 | | | | (68) all_1286_2 = all_1217_3 % 194.49/27.28 | | | | % 194.49/27.28 | | | | GROUND_INST: instantiating (12) with all_1284_2, all_1286_2, all_1217_4, % 194.49/27.28 | | | | v_x, tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.28 | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with (40), % 194.49/27.28 | | | | (46) gives: % 194.49/27.28 | | | | (69) all_1286_2 = all_1284_2 % 194.49/27.28 | | | | % 194.49/27.28 | | | | COMBINE_EQS: (66), (67) imply: % 194.49/27.28 | | | | (70) all_1284_0 = all_1217_0 % 194.49/27.28 | | | | % 194.49/27.28 | | | | COMBINE_EQS: (68), (69) imply: % 194.49/27.28 | | | | (71) all_1284_2 = all_1217_3 % 194.49/27.28 | | | | % 194.49/27.28 | | | | REDUCE: (47), (68) imply: % 194.49/27.28 | | | | (72) c_member(all_622_1, all_1217_3, v_L) = all_1286_1 % 194.49/27.28 | | | | % 194.49/27.28 | | | | REDUCE: (48), (71) imply: % 194.49/27.28 | | | | (73) c_member(all_622_1, all_1217_3, v_L) = all_1284_1 % 194.49/27.28 | | | | % 194.49/27.28 | | | | BETA: splitting (41) gives: % 194.49/27.28 | | | | % 194.49/27.28 | | | | Case 1: % 194.49/27.28 | | | | | % 194.49/27.28 | | | | | (74) ~ (all_1284_1 = 0) % 194.49/27.28 | | | | | % 194.49/27.28 | | | | | GROUND_INST: instantiating (15) with 0, all_1286_1, v_L, all_1217_3, % 194.49/27.28 | | | | | all_622_1, simplifying with (32), (72) gives: % 194.49/27.28 | | | | | (75) all_1286_1 = 0 % 194.49/27.28 | | | | | % 194.49/27.28 | | | | | GROUND_INST: instantiating (15) with all_1284_1, all_1286_1, v_L, % 194.49/27.28 | | | | | all_1217_3, all_622_1, simplifying with (72), (73) gives: % 194.49/27.28 | | | | | (76) all_1286_1 = all_1284_1 % 194.49/27.28 | | | | | % 194.49/27.28 | | | | | COMBINE_EQS: (75), (76) imply: % 194.49/27.28 | | | | | (77) all_1284_1 = 0 % 194.49/27.28 | | | | | % 194.49/27.28 | | | | | REDUCE: (74), (77) imply: % 194.49/27.28 | | | | | (78) $false % 194.49/27.28 | | | | | % 194.49/27.28 | | | | | CLOSE: (78) is inconsistent. % 194.49/27.28 | | | | | % 194.49/27.28 | | | | Case 2: % 194.49/27.28 | | | | | % 194.49/27.28 | | | | | (79) all_1284_0 = 0 % 194.49/27.28 | | | | | % 194.49/27.28 | | | | | COMBINE_EQS: (70), (79) imply: % 194.49/27.28 | | | | | (80) all_1217_0 = 0 % 194.49/27.28 | | | | | % 194.49/27.28 | | | | | SIMP: (80) implies: % 194.49/27.28 | | | | | (81) all_1217_0 = 0 % 194.49/27.28 | | | | | % 194.49/27.28 | | | | | REDUCE: (31), (81) imply: % 194.49/27.28 | | | | | (82) $false % 194.49/27.28 | | | | | % 194.49/27.28 | | | | | CLOSE: (82) is inconsistent. % 194.49/27.28 | | | | | % 194.49/27.28 | | | | End of split % 194.49/27.28 | | | | % 194.49/27.28 | | | End of split % 194.49/27.28 | | | % 194.49/27.28 | | End of split % 194.49/27.28 | | % 194.49/27.28 | Case 2: % 194.49/27.28 | | % 194.49/27.28 | | (83) (all_1217_4 = v_y & all_872_2 = 0 & ~ (all_872_4 = 0) & ~ % 194.49/27.28 | | (all_872_9 = v_x)) | (all_1217_4 = v_y & all_872_8 = v_x & ~ % 194.49/27.28 | | (all_872_4 = 0) & ~ (all_872_9 = v_x)) % 194.49/27.28 | | % 194.49/27.28 | | BETA: splitting (83) gives: % 194.49/27.28 | | % 194.49/27.28 | | Case 1: % 194.49/27.28 | | | % 194.49/27.28 | | | (84) all_1217_4 = v_y & all_872_2 = 0 & ~ (all_872_4 = 0) & ~ % 194.49/27.28 | | | (all_872_9 = v_x) % 194.49/27.28 | | | % 194.49/27.28 | | | ALPHA: (84) implies: % 194.49/27.28 | | | (85) ~ (all_872_4 = 0) % 194.49/27.28 | | | % 194.49/27.29 | | | REF_CLOSE: (2), (8), (10), (12), (15), (16), (85) are inconsistent by % 194.49/27.29 | | | sub-proof #11. % 194.49/27.29 | | | % 194.49/27.29 | | Case 2: % 194.49/27.29 | | | % 194.49/27.29 | | | (86) all_1217_4 = v_y & all_872_8 = v_x & ~ (all_872_4 = 0) & ~ % 194.49/27.29 | | | (all_872_9 = v_x) % 194.49/27.29 | | | % 194.49/27.29 | | | ALPHA: (86) implies: % 194.49/27.29 | | | (87) ~ (all_872_4 = 0) % 194.49/27.29 | | | % 194.49/27.29 | | | REF_CLOSE: (2), (8), (10), (12), (15), (16), (87) are inconsistent by % 194.49/27.29 | | | sub-proof #11. % 194.49/27.29 | | | % 194.49/27.29 | | End of split % 194.49/27.29 | | % 194.49/27.29 | End of split % 194.49/27.29 | % 194.49/27.29 End of proof % 194.49/27.29 % 194.49/27.29 Sub-proof #11 shows that the following formulas are inconsistent: % 194.49/27.29 ---------------------------------------------------------------- % 194.49/27.29 (1) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.29 tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v_x) = all_872_7 % 194.49/27.29 (2) ~ (all_872_4 = 0) % 194.49/27.29 (3) c_member(all_622_1, all_872_7, v_L) = 0 % 194.49/27.29 (4) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.29 tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v_x) = all_872_5 % 194.49/27.29 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 194.49/27.29 [v5: $i] : (v1 = v0 | ~ (c_Product__Type_OPair(v5, v4, v3, v2) = v1) | % 194.49/27.29 ~ (c_Product__Type_OPair(v5, v4, v3, v2) = v0)) % 194.49/27.29 (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 194.49/27.29 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (c_member(v4, v3, v2) = v1) | ~ % 194.49/27.29 (c_member(v4, v3, v2) = v0)) % 194.49/27.29 (7) c_member(all_622_1, all_872_5, v_L) = all_872_4 % 194.49/27.29 % 194.49/27.29 Begin of proof % 194.49/27.29 | % 194.49/27.29 | GROUND_INST: instantiating (5) with all_872_5, all_872_7, v_x, all_872_9, % 194.49/27.29 | tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.29 | simplifying with (1), (4) gives: % 194.49/27.29 | (8) all_872_5 = all_872_7 % 194.49/27.29 | % 194.49/27.29 | REDUCE: (7), (8) imply: % 194.49/27.29 | (9) c_member(all_622_1, all_872_7, v_L) = all_872_4 % 194.49/27.29 | % 194.49/27.29 | GROUND_INST: instantiating (6) with 0, all_872_4, v_L, all_872_7, all_622_1, % 194.49/27.29 | simplifying with (3), (9) gives: % 194.49/27.29 | (10) all_872_4 = 0 % 194.49/27.29 | % 194.49/27.29 | REDUCE: (2), (10) imply: % 194.49/27.29 | (11) $false % 194.49/27.29 | % 194.49/27.29 | CLOSE: (11) is inconsistent. % 194.49/27.29 | % 194.49/27.29 End of proof % 194.49/27.29 % 194.49/27.29 Sub-proof #12 shows that the following formulas are inconsistent: % 194.49/27.29 ---------------------------------------------------------------- % 194.49/27.29 (1) $i(all_872_8) % 194.49/27.29 (2) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.29 tc_Arrow__Order__Mirabelle_Oalt, v_x, all_872_8) = all_872_7 % 194.49/27.29 (3) (all_872_4 = 0 & all_872_8 = v_y & ? [v0: $i] : ? [v1: $i] : ? [v2: % 194.49/27.29 $i] : ? [v3: int] : ( ~ (v3 = 0) & ~ (v0 = v_y) & % 194.49/27.29 c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.29 tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v0) = v2 & % 194.49/27.29 c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.29 tc_Arrow__Order__Mirabelle_Oalt, v_x, v0) = v1 & % 194.49/27.29 c_member(all_685_0, v2, v_L) = v3 & c_member(all_685_0, v1, v_L) = 0 % 194.49/27.29 & $i(v2) & $i(v1) & $i(v0))) | (all_872_6 = 0 & ~ (all_872_8 = v_y) % 194.49/27.29 & ? [v0: $i] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ? [v4: any] % 194.49/27.29 : (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.29 tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v0) = v1 & % 194.49/27.29 c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.29 tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v0) = v3 & % 194.49/27.29 c_member(all_685_0, v3, v_L) = v4 & c_member(all_685_0, v1, v_L) = v2 % 194.49/27.29 & $i(v3) & $i(v1) & $i(v0) & ((v2 = 0 & ~ (v4 = 0) & ~ (v0 = v_y)) % 194.49/27.29 | (v0 = v_y & all_872_2 = 0 & ~ (all_872_4 = 0) & ~ (all_872_9 = % 194.49/27.29 v_x)) | (v0 = v_y & all_872_8 = v_x & ~ (all_872_4 = 0) & ~ % 194.49/27.29 (all_872_9 = v_x))))) % 194.49/27.29 (4) all_685_0 = all_622_1 % 194.49/27.29 (5) all_872_9 = v_x % 194.49/27.29 (6) all_676_0 = all_622_1 % 194.49/27.29 (7) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.29 tc_Arrow__Order__Mirabelle_Oalt, v_x, all_872_8) = all_872_1 % 194.49/27.29 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 194.49/27.29 [v5: $i] : (v1 = v0 | ~ (c_Product__Type_OPair(v5, v4, v3, v2) = v1) | % 194.49/27.29 ~ (c_Product__Type_OPair(v5, v4, v3, v2) = v0)) % 194.49/27.29 (9) c_member(all_622_1, all_872_7, v_L) = all_872_6 % 194.49/27.29 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 194.49/27.29 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.29 tc_Arrow__Order__Mirabelle_Oalt, v0, v1) = v2) | ~ $i(v1) | ~ % 194.49/27.29 $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & c_member(all_676_0, v2, v_L) = % 194.49/27.29 v3) | ! [v3: $i] : ! [v4: $i] : ( ~ % 194.49/27.29 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.29 tc_Arrow__Order__Mirabelle_Oalt, v0, v3) = v4) | ~ $i(v3) | ? % 194.49/27.29 [v5: $i] : ? [v6: any] : ? [v7: any] : % 194.49/27.29 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.49/27.29 tc_Arrow__Order__Mirabelle_Oalt, v1, v3) = v5 & % 194.49/27.29 c_member(all_676_0, v5, v_L) = v6 & c_member(all_676_0, v4, v_L) = % 194.49/27.29 v7 & $i(v5) & ( ~ (v6 = 0) | v7 = 0)))) % 194.49/27.29 (11) c_member(all_622_1, all_872_1, v_L) = all_872_0 % 194.86/27.29 (12) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_676_0, all_872_1, v_L) = v0) % 194.86/27.29 | ! [v0: $i] : ! [v1: $i] : ( ~ % 194.86/27.29 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.86/27.29 tc_Arrow__Order__Mirabelle_Oalt, v_x, v0) = v1) | ~ $i(v0) | ? % 194.86/27.29 [v2: $i] : ? [v3: any] : ? [v4: any] : % 194.86/27.29 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.86/27.29 tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v0) = v2 & % 194.86/27.29 c_member(all_676_0, v2, v_L) = v3 & c_member(all_676_0, v1, v_L) = % 194.86/27.29 v4 & $i(v2) & ( ~ (v3 = 0) | v4 = 0))) % 194.86/27.29 (13) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 194.86/27.29 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (c_member(v4, v3, v2) = v1) | % 194.86/27.29 ~ (c_member(v4, v3, v2) = v0)) % 194.86/27.29 % 194.86/27.29 Begin of proof % 194.86/27.29 | % 194.86/27.29 | BETA: splitting (3) gives: % 194.86/27.29 | % 194.86/27.29 | Case 1: % 194.86/27.29 | | % 194.86/27.29 | | (14) all_872_4 = 0 & all_872_8 = v_y & ? [v0: $i] : ? [v1: $i] : ? % 194.86/27.29 | | [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & ~ (v0 = v_y) & % 194.86/27.29 | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.86/27.29 | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v0) = v2 & % 194.86/27.29 | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.86/27.29 | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v0) = v1 & % 194.86/27.29 | | c_member(all_685_0, v2, v_L) = v3 & c_member(all_685_0, v1, v_L) = % 194.86/27.29 | | 0 & $i(v2) & $i(v1) & $i(v0)) % 194.86/27.29 | | % 194.86/27.29 | | ALPHA: (14) implies: % 194.86/27.29 | | (15) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = % 194.86/27.29 | | 0) & ~ (v0 = v_y) & % 194.86/27.29 | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.86/27.29 | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v0) = v2 & % 194.86/27.29 | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.86/27.29 | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v0) = v1 & % 194.86/27.29 | | c_member(all_685_0, v2, v_L) = v3 & c_member(all_685_0, v1, v_L) = % 194.86/27.29 | | 0 & $i(v2) & $i(v1) & $i(v0)) % 194.86/27.29 | | % 194.86/27.29 | | DELTA: instantiating (15) with fresh symbols all_1126_0, all_1126_1, % 194.86/27.29 | | all_1126_2, all_1126_3 gives: % 194.86/27.29 | | (16) ~ (all_1126_0 = 0) & ~ (all_1126_3 = v_y) & % 194.86/27.29 | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.86/27.29 | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, all_1126_3) = % 194.86/27.29 | | all_1126_1 & c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.86/27.29 | | tc_Arrow__Order__Mirabelle_Oalt, v_x, all_1126_3) = all_1126_2 & % 194.86/27.29 | | c_member(all_685_0, all_1126_1, v_L) = all_1126_0 & % 194.86/27.29 | | c_member(all_685_0, all_1126_2, v_L) = 0 & $i(all_1126_1) & % 194.86/27.29 | | $i(all_1126_2) & $i(all_1126_3) % 194.86/27.29 | | % 194.86/27.29 | | ALPHA: (16) implies: % 194.86/27.29 | | (17) ~ (all_1126_0 = 0) % 194.86/27.29 | | (18) c_member(all_685_0, all_1126_2, v_L) = 0 % 194.86/27.29 | | (19) c_member(all_685_0, all_1126_1, v_L) = all_1126_0 % 194.86/27.29 | | (20) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.86/27.29 | | tc_Arrow__Order__Mirabelle_Oalt, v_x, all_1126_3) = all_1126_2 % 194.86/27.29 | | (21) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.86/27.29 | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, all_1126_3) = % 194.86/27.29 | | all_1126_1 % 194.86/27.29 | | % 194.86/27.29 | | REDUCE: (5), (21) imply: % 194.86/27.29 | | (22) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.86/27.29 | | tc_Arrow__Order__Mirabelle_Oalt, v_x, all_1126_3) = all_1126_1 % 194.86/27.29 | | % 194.86/27.29 | | REDUCE: (4), (19) imply: % 194.86/27.29 | | (23) c_member(all_622_1, all_1126_1, v_L) = all_1126_0 % 194.86/27.29 | | % 194.86/27.29 | | REDUCE: (4), (18) imply: % 194.86/27.29 | | (24) c_member(all_622_1, all_1126_2, v_L) = 0 % 194.86/27.29 | | % 194.86/27.29 | | GROUND_INST: instantiating (8) with all_1126_2, all_1126_1, all_1126_3, v_x, % 194.86/27.29 | | tc_Arrow__Order__Mirabelle_Oalt, % 194.86/27.29 | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with (20), (22) % 194.86/27.29 | | gives: % 194.86/27.29 | | (25) all_1126_1 = all_1126_2 % 194.86/27.29 | | % 194.86/27.29 | | REDUCE: (23), (25) imply: % 194.86/27.29 | | (26) c_member(all_622_1, all_1126_2, v_L) = all_1126_0 % 194.86/27.29 | | % 194.86/27.29 | | GROUND_INST: instantiating (13) with 0, all_1126_0, v_L, all_1126_2, % 194.86/27.29 | | all_622_1, simplifying with (24), (26) gives: % 194.86/27.29 | | (27) all_1126_0 = 0 % 194.86/27.29 | | % 194.86/27.29 | | REDUCE: (17), (27) imply: % 194.86/27.29 | | (28) $false % 194.86/27.29 | | % 194.86/27.29 | | CLOSE: (28) is inconsistent. % 194.86/27.29 | | % 194.86/27.29 | Case 2: % 194.86/27.29 | | % 194.86/27.29 | | (29) all_872_6 = 0 & ~ (all_872_8 = v_y) & ? [v0: $i] : ? [v1: $i] : % 194.86/27.29 | | ? [v2: any] : ? [v3: $i] : ? [v4: any] : % 194.86/27.29 | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.86/27.29 | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v0) = v1 & % 194.86/27.29 | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.86/27.29 | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v0) = v3 & % 194.86/27.29 | | c_member(all_685_0, v3, v_L) = v4 & c_member(all_685_0, v1, v_L) = % 194.86/27.29 | | v2 & $i(v3) & $i(v1) & $i(v0) & ((v2 = 0 & ~ (v4 = 0) & ~ (v0 = % 194.86/27.29 | | v_y)) | (v0 = v_y & all_872_2 = 0 & ~ (all_872_4 = 0) & ~ % 194.86/27.29 | | (all_872_9 = v_x)) | (v0 = v_y & all_872_8 = v_x & ~ % 194.86/27.29 | | (all_872_4 = 0) & ~ (all_872_9 = v_x)))) % 194.86/27.29 | | % 194.86/27.29 | | ALPHA: (29) implies: % 194.86/27.29 | | (30) all_872_6 = 0 % 194.86/27.30 | | (31) ? [v0: $i] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ? [v4: % 194.86/27.30 | | any] : (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.86/27.30 | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v0) = v1 & % 194.86/27.30 | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.86/27.30 | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, v0) = v3 & % 194.86/27.30 | | c_member(all_685_0, v3, v_L) = v4 & c_member(all_685_0, v1, v_L) = % 194.86/27.30 | | v2 & $i(v3) & $i(v1) & $i(v0) & ((v2 = 0 & ~ (v4 = 0) & ~ (v0 = % 194.86/27.30 | | v_y)) | (v0 = v_y & all_872_2 = 0 & ~ (all_872_4 = 0) & ~ % 194.86/27.30 | | (all_872_9 = v_x)) | (v0 = v_y & all_872_8 = v_x & ~ % 194.86/27.30 | | (all_872_4 = 0) & ~ (all_872_9 = v_x)))) % 194.86/27.30 | | % 194.86/27.30 | | DELTA: instantiating (31) with fresh symbols all_1126_0, all_1126_1, % 194.86/27.30 | | all_1126_2, all_1126_3, all_1126_4 gives: % 194.86/27.30 | | (32) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.86/27.30 | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, all_1126_4) = % 194.86/27.30 | | all_1126_3 & c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.86/27.30 | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, all_1126_4) = % 194.86/27.30 | | all_1126_1 & c_member(all_685_0, all_1126_1, v_L) = all_1126_0 & % 194.86/27.30 | | c_member(all_685_0, all_1126_3, v_L) = all_1126_2 & $i(all_1126_1) & % 194.86/27.30 | | $i(all_1126_3) & $i(all_1126_4) & ((all_1126_2 = 0 & ~ (all_1126_0 % 194.86/27.30 | | = 0) & ~ (all_1126_4 = v_y)) | (all_1126_4 = v_y & all_872_2 % 194.86/27.30 | | = 0 & ~ (all_872_4 = 0) & ~ (all_872_9 = v_x)) | (all_1126_4 = % 194.86/27.30 | | v_y & all_872_8 = v_x & ~ (all_872_4 = 0) & ~ (all_872_9 = % 194.86/27.30 | | v_x))) % 194.86/27.30 | | % 194.86/27.30 | | ALPHA: (32) implies: % 194.86/27.30 | | (33) $i(all_1126_4) % 194.86/27.30 | | (34) c_member(all_685_0, all_1126_3, v_L) = all_1126_2 % 194.86/27.30 | | (35) c_member(all_685_0, all_1126_1, v_L) = all_1126_0 % 194.86/27.30 | | (36) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.86/27.30 | | tc_Arrow__Order__Mirabelle_Oalt, all_872_9, all_1126_4) = % 194.86/27.30 | | all_1126_1 % 194.86/27.30 | | (37) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.86/27.30 | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, all_1126_4) = % 194.86/27.30 | | all_1126_3 % 194.86/27.30 | | (38) (all_1126_2 = 0 & ~ (all_1126_0 = 0) & ~ (all_1126_4 = v_y)) | % 194.86/27.30 | | (all_1126_4 = v_y & all_872_2 = 0 & ~ (all_872_4 = 0) & ~ % 194.86/27.30 | | (all_872_9 = v_x)) | (all_1126_4 = v_y & all_872_8 = v_x & ~ % 194.86/27.30 | | (all_872_4 = 0) & ~ (all_872_9 = v_x)) % 194.86/27.30 | | % 194.86/27.30 | | REDUCE: (5), (36) imply: % 194.86/27.30 | | (39) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.86/27.30 | | tc_Arrow__Order__Mirabelle_Oalt, v_x, all_1126_4) = all_1126_1 % 194.86/27.30 | | % 194.86/27.30 | | REDUCE: (4), (35) imply: % 194.86/27.30 | | (40) c_member(all_622_1, all_1126_1, v_L) = all_1126_0 % 194.86/27.30 | | % 194.86/27.30 | | REDUCE: (4), (34) imply: % 194.86/27.30 | | (41) c_member(all_622_1, all_1126_3, v_L) = all_1126_2 % 194.86/27.30 | | % 194.86/27.30 | | REDUCE: (9), (30) imply: % 194.86/27.30 | | (42) c_member(all_622_1, all_872_7, v_L) = 0 % 194.86/27.30 | | % 194.86/27.30 | | BETA: splitting (38) gives: % 194.86/27.30 | | % 194.86/27.30 | | Case 1: % 194.86/27.30 | | | % 194.86/27.30 | | | (43) all_1126_2 = 0 & ~ (all_1126_0 = 0) & ~ (all_1126_4 = v_y) % 194.86/27.30 | | | % 194.86/27.30 | | | ALPHA: (43) implies: % 194.86/27.30 | | | (44) all_1126_2 = 0 % 194.86/27.30 | | | (45) ~ (all_1126_0 = 0) % 194.86/27.30 | | | % 194.86/27.30 | | | REDUCE: (41), (44) imply: % 194.86/27.30 | | | (46) c_member(all_622_1, all_1126_3, v_L) = 0 % 194.86/27.30 | | | % 194.86/27.30 | | | GROUND_INST: instantiating (8) with all_872_1, all_872_7, all_872_8, v_x, % 194.86/27.30 | | | tc_Arrow__Order__Mirabelle_Oalt, % 194.86/27.30 | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with (2), (7) % 194.86/27.30 | | | gives: % 194.86/27.30 | | | (47) all_872_1 = all_872_7 % 194.86/27.30 | | | % 194.86/27.30 | | | REDUCE: (11), (47) imply: % 194.86/27.30 | | | (48) c_member(all_622_1, all_872_7, v_L) = all_872_0 % 194.86/27.30 | | | % 194.86/27.30 | | | GROUND_INST: instantiating (13) with 0, all_872_0, v_L, all_872_7, % 194.86/27.30 | | | all_622_1, simplifying with (42), (48) gives: % 194.86/27.30 | | | (49) all_872_0 = 0 % 194.86/27.30 | | | % 194.86/27.30 | | | BETA: splitting (12) gives: % 194.86/27.30 | | | % 194.86/27.30 | | | Case 1: % 194.86/27.30 | | | | % 194.86/27.30 | | | | (50) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_676_0, all_872_1, % 194.86/27.30 | | | | v_L) = v0) % 194.86/27.30 | | | | % 194.86/27.30 | | | | DELTA: instantiating (50) with fresh symbol all_1146_0 gives: % 194.86/27.30 | | | | (51) ~ (all_1146_0 = 0) & c_member(all_676_0, all_872_1, v_L) = % 194.86/27.30 | | | | all_1146_0 % 194.86/27.30 | | | | % 194.86/27.30 | | | | ALPHA: (51) implies: % 194.86/27.30 | | | | (52) ~ (all_1146_0 = 0) % 194.86/27.30 | | | | (53) c_member(all_676_0, all_872_1, v_L) = all_1146_0 % 194.86/27.30 | | | | % 194.86/27.30 | | | | REDUCE: (6), (47), (53) imply: % 194.86/27.30 | | | | (54) c_member(all_622_1, all_872_7, v_L) = all_1146_0 % 194.86/27.30 | | | | % 194.86/27.30 | | | | GROUND_INST: instantiating (13) with 0, all_1146_0, v_L, all_872_7, % 194.86/27.30 | | | | all_622_1, simplifying with (42), (54) gives: % 194.86/27.30 | | | | (55) all_1146_0 = 0 % 194.86/27.30 | | | | % 194.86/27.30 | | | | REDUCE: (52), (55) imply: % 194.86/27.30 | | | | (56) $false % 194.86/27.30 | | | | % 194.86/27.30 | | | | CLOSE: (56) is inconsistent. % 194.86/27.30 | | | | % 194.86/27.30 | | | Case 2: % 194.86/27.30 | | | | % 194.86/27.30 | | | | (57) ! [v0: $i] : ! [v1: $i] : ( ~ % 194.86/27.30 | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.86/27.30 | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v0) = v1) | ~ % 194.86/27.30 | | | | $i(v0) | ? [v2: $i] : ? [v3: any] : ? [v4: any] : % 194.86/27.30 | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.86/27.30 | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v0) = v2 & % 194.86/27.30 | | | | c_member(all_676_0, v2, v_L) = v3 & c_member(all_676_0, v1, % 194.86/27.30 | | | | v_L) = v4 & $i(v2) & ( ~ (v3 = 0) | v4 = 0))) % 194.86/27.30 | | | | % 194.86/27.30 | | | | GROUND_INST: instantiating (57) with all_1126_4, all_1126_1, simplifying % 194.86/27.30 | | | | with (33), (39) gives: % 194.86/27.30 | | | | (58) ? [v0: $i] : ? [v1: any] : ? [v2: any] : % 194.86/27.30 | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.86/27.30 | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, all_1126_4) = v0 % 194.86/27.30 | | | | & c_member(all_676_0, v0, v_L) = v1 & c_member(all_676_0, % 194.86/27.30 | | | | all_1126_1, v_L) = v2 & $i(v0) & ( ~ (v1 = 0) | v2 = 0)) % 194.86/27.30 | | | | % 194.86/27.30 | | | | GROUND_INST: instantiating (10) with all_872_8, all_1126_4, all_1126_3, % 194.86/27.30 | | | | simplifying with (1), (33), (37) gives: % 194.86/27.30 | | | | (59) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_676_0, all_1126_3, % 194.86/27.30 | | | | v_L) = v0) | ! [v0: $i] : ! [v1: $i] : ( ~ % 194.86/27.30 | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.86/27.30 | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v0) = v1) | ~ % 194.86/27.30 | | | | $i(v0) | ? [v2: $i] : ? [v3: any] : ? [v4: any] : % 194.86/27.30 | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.86/27.30 | | | | tc_Arrow__Order__Mirabelle_Oalt, all_1126_4, v0) = v2 & % 194.86/27.30 | | | | c_member(all_676_0, v2, v_L) = v3 & c_member(all_676_0, v1, % 194.86/27.30 | | | | v_L) = v4 & $i(v2) & ( ~ (v3 = 0) | v4 = 0))) % 194.86/27.30 | | | | % 194.86/27.30 | | | | DELTA: instantiating (58) with fresh symbols all_1211_0, all_1211_1, % 194.86/27.30 | | | | all_1211_2 gives: % 194.86/27.30 | | | | (60) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.86/27.30 | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, all_1126_4) = % 194.86/27.30 | | | | all_1211_2 & c_member(all_676_0, all_1211_2, v_L) = all_1211_1 & % 194.86/27.30 | | | | c_member(all_676_0, all_1126_1, v_L) = all_1211_0 & % 194.86/27.30 | | | | $i(all_1211_2) & ( ~ (all_1211_1 = 0) | all_1211_0 = 0) % 194.86/27.30 | | | | % 194.86/27.30 | | | | ALPHA: (60) implies: % 194.86/27.30 | | | | (61) c_member(all_676_0, all_1126_1, v_L) = all_1211_0 % 194.86/27.30 | | | | (62) c_member(all_676_0, all_1211_2, v_L) = all_1211_1 % 194.86/27.30 | | | | (63) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.86/27.30 | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, all_1126_4) = % 194.86/27.30 | | | | all_1211_2 % 194.86/27.30 | | | | (64) ~ (all_1211_1 = 0) | all_1211_0 = 0 % 194.86/27.30 | | | | % 194.86/27.30 | | | | REDUCE: (6), (62) imply: % 194.86/27.30 | | | | (65) c_member(all_622_1, all_1211_2, v_L) = all_1211_1 % 194.86/27.30 | | | | % 194.86/27.30 | | | | REDUCE: (6), (61) imply: % 194.86/27.30 | | | | (66) c_member(all_622_1, all_1126_1, v_L) = all_1211_0 % 194.86/27.30 | | | | % 194.86/27.30 | | | | BETA: splitting (59) gives: % 194.86/27.30 | | | | % 194.86/27.30 | | | | Case 1: % 194.86/27.30 | | | | | % 194.86/27.30 | | | | | (67) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_676_0, all_1126_3, % 194.86/27.30 | | | | | v_L) = v0) % 194.86/27.30 | | | | | % 194.86/27.30 | | | | | DELTA: instantiating (67) with fresh symbol all_1222_0 gives: % 194.86/27.30 | | | | | (68) ~ (all_1222_0 = 0) & c_member(all_676_0, all_1126_3, v_L) = % 194.86/27.30 | | | | | all_1222_0 % 194.86/27.30 | | | | | % 194.86/27.30 | | | | | ALPHA: (68) implies: % 194.86/27.30 | | | | | (69) ~ (all_1222_0 = 0) % 194.86/27.30 | | | | | (70) c_member(all_676_0, all_1126_3, v_L) = all_1222_0 % 194.86/27.30 | | | | | % 194.86/27.30 | | | | | REDUCE: (6), (70) imply: % 194.86/27.30 | | | | | (71) c_member(all_622_1, all_1126_3, v_L) = all_1222_0 % 194.86/27.30 | | | | | % 194.86/27.30 | | | | | GROUND_INST: instantiating (13) with 0, all_1222_0, v_L, all_1126_3, % 194.86/27.30 | | | | | all_622_1, simplifying with (46), (71) gives: % 194.86/27.30 | | | | | (72) all_1222_0 = 0 % 194.86/27.30 | | | | | % 194.86/27.30 | | | | | REDUCE: (69), (72) imply: % 194.86/27.30 | | | | | (73) $false % 194.86/27.30 | | | | | % 194.86/27.30 | | | | | CLOSE: (73) is inconsistent. % 194.86/27.30 | | | | | % 194.86/27.30 | | | | Case 2: % 194.86/27.30 | | | | | % 194.86/27.30 | | | | | (74) ! [v0: $i] : ! [v1: $i] : ( ~ % 194.86/27.30 | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.86/27.30 | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_8, v0) = v1) | % 194.86/27.30 | | | | | ~ $i(v0) | ? [v2: $i] : ? [v3: any] : ? [v4: any] : % 194.86/27.30 | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.86/27.30 | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_1126_4, v0) = v2 & % 194.86/27.30 | | | | | c_member(all_676_0, v2, v_L) = v3 & c_member(all_676_0, % 194.86/27.30 | | | | | v1, v_L) = v4 & $i(v2) & ( ~ (v3 = 0) | v4 = 0))) % 194.86/27.30 | | | | | % 194.86/27.30 | | | | | GROUND_INST: instantiating (74) with all_1126_4, all_1126_3, % 194.86/27.30 | | | | | simplifying with (33), (37) gives: % 194.86/27.30 | | | | | (75) ? [v0: $i] : ? [v1: any] : ? [v2: any] : % 194.86/27.30 | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.86/27.30 | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_1126_4, all_1126_4) = % 194.86/27.30 | | | | | v0 & c_member(all_676_0, v0, v_L) = v1 & c_member(all_676_0, % 194.86/27.30 | | | | | all_1126_3, v_L) = v2 & $i(v0) & ( ~ (v1 = 0) | v2 = 0)) % 194.86/27.30 | | | | | % 194.86/27.30 | | | | | DELTA: instantiating (75) with fresh symbols all_1223_0, all_1223_1, % 194.86/27.30 | | | | | all_1223_2 gives: % 194.86/27.30 | | | | | (76) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.86/27.30 | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_1126_4, all_1126_4) = % 194.86/27.30 | | | | | all_1223_2 & c_member(all_676_0, all_1223_2, v_L) = all_1223_1 % 194.86/27.30 | | | | | & c_member(all_676_0, all_1126_3, v_L) = all_1223_0 & % 194.86/27.30 | | | | | $i(all_1223_2) & ( ~ (all_1223_1 = 0) | all_1223_0 = 0) % 194.86/27.30 | | | | | % 194.86/27.30 | | | | | ALPHA: (76) implies: % 194.86/27.30 | | | | | (77) c_member(all_676_0, all_1126_3, v_L) = all_1223_0 % 194.86/27.30 | | | | | % 194.86/27.30 | | | | | REDUCE: (6), (77) imply: % 194.86/27.30 | | | | | (78) c_member(all_622_1, all_1126_3, v_L) = all_1223_0 % 194.86/27.30 | | | | | % 194.86/27.30 | | | | | GROUND_INST: instantiating (13) with 0, all_1223_0, v_L, all_1126_3, % 194.86/27.30 | | | | | all_622_1, simplifying with (46), (78) gives: % 194.86/27.30 | | | | | (79) all_1223_0 = 0 % 194.86/27.30 | | | | | % 194.86/27.30 | | | | | GROUND_INST: instantiating (13) with all_1126_0, all_1211_0, v_L, % 194.86/27.30 | | | | | all_1126_1, all_622_1, simplifying with (40), (66) gives: % 194.86/27.30 | | | | | (80) all_1211_0 = all_1126_0 % 194.86/27.30 | | | | | % 194.86/27.30 | | | | | GROUND_INST: instantiating (8) with all_1126_3, all_1211_2, % 194.86/27.30 | | | | | all_1126_4, all_872_8, tc_Arrow__Order__Mirabelle_Oalt, % 194.86/27.30 | | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with (37), % 194.86/27.30 | | | | | (63) gives: % 194.86/27.30 | | | | | (81) all_1211_2 = all_1126_3 % 194.86/27.30 | | | | | % 194.86/27.30 | | | | | REDUCE: (65), (81) imply: % 194.86/27.30 | | | | | (82) c_member(all_622_1, all_1126_3, v_L) = all_1211_1 % 194.86/27.30 | | | | | % 194.86/27.30 | | | | | BETA: splitting (64) gives: % 194.86/27.30 | | | | | % 194.86/27.30 | | | | | Case 1: % 194.86/27.30 | | | | | | % 194.86/27.30 | | | | | | (83) ~ (all_1211_1 = 0) % 194.86/27.30 | | | | | | % 194.86/27.30 | | | | | | GROUND_INST: instantiating (13) with 0, all_1211_1, v_L, all_1126_3, % 194.86/27.30 | | | | | | all_622_1, simplifying with (46), (82) gives: % 194.86/27.30 | | | | | | (84) all_1211_1 = 0 % 194.86/27.30 | | | | | | % 194.86/27.30 | | | | | | REDUCE: (83), (84) imply: % 194.86/27.31 | | | | | | (85) $false % 194.86/27.31 | | | | | | % 194.86/27.31 | | | | | | CLOSE: (85) is inconsistent. % 194.86/27.31 | | | | | | % 194.86/27.31 | | | | | Case 2: % 194.86/27.31 | | | | | | % 194.86/27.31 | | | | | | (86) all_1211_0 = 0 % 194.86/27.31 | | | | | | % 194.86/27.31 | | | | | | COMBINE_EQS: (80), (86) imply: % 194.86/27.31 | | | | | | (87) all_1126_0 = 0 % 194.86/27.31 | | | | | | % 194.86/27.31 | | | | | | REDUCE: (45), (87) imply: % 194.86/27.31 | | | | | | (88) $false % 194.86/27.31 | | | | | | % 194.86/27.31 | | | | | | CLOSE: (88) is inconsistent. % 194.86/27.31 | | | | | | % 194.86/27.31 | | | | | End of split % 194.86/27.31 | | | | | % 194.86/27.31 | | | | End of split % 194.86/27.31 | | | | % 194.86/27.31 | | | End of split % 194.86/27.31 | | | % 194.86/27.31 | | Case 2: % 194.86/27.31 | | | % 194.86/27.31 | | | (89) (all_1126_4 = v_y & all_872_2 = 0 & ~ (all_872_4 = 0) & ~ % 194.86/27.31 | | | (all_872_9 = v_x)) | (all_1126_4 = v_y & all_872_8 = v_x & ~ % 194.86/27.31 | | | (all_872_4 = 0) & ~ (all_872_9 = v_x)) % 194.86/27.31 | | | % 194.86/27.31 | | | BETA: splitting (89) gives: % 194.86/27.31 | | | % 194.86/27.31 | | | Case 1: % 194.86/27.31 | | | | % 194.86/27.31 | | | | (90) all_1126_4 = v_y & all_872_2 = 0 & ~ (all_872_4 = 0) & ~ % 194.86/27.31 | | | | (all_872_9 = v_x) % 194.86/27.31 | | | | % 194.86/27.31 | | | | ALPHA: (90) implies: % 194.86/27.31 | | | | (91) ~ (all_872_9 = v_x) % 194.86/27.31 | | | | % 194.86/27.31 | | | | REDUCE: (5), (91) imply: % 194.86/27.31 | | | | (92) $false % 194.86/27.31 | | | | % 194.86/27.31 | | | | CLOSE: (92) is inconsistent. % 194.86/27.31 | | | | % 194.86/27.31 | | | Case 2: % 194.86/27.31 | | | | % 194.86/27.31 | | | | (93) all_1126_4 = v_y & all_872_8 = v_x & ~ (all_872_4 = 0) & ~ % 194.86/27.31 | | | | (all_872_9 = v_x) % 194.86/27.31 | | | | % 194.86/27.31 | | | | ALPHA: (93) implies: % 194.86/27.31 | | | | (94) ~ (all_872_9 = v_x) % 194.86/27.31 | | | | % 194.86/27.31 | | | | REDUCE: (5), (94) imply: % 194.86/27.31 | | | | (95) $false % 194.86/27.31 | | | | % 194.86/27.31 | | | | CLOSE: (95) is inconsistent. % 194.86/27.31 | | | | % 194.86/27.31 | | | End of split % 194.86/27.31 | | | % 194.86/27.31 | | End of split % 194.86/27.31 | | % 194.86/27.31 | End of split % 194.86/27.31 | % 194.86/27.31 End of proof % 194.86/27.31 % 194.86/27.31 Sub-proof #13 shows that the following formulas are inconsistent: % 194.86/27.31 ---------------------------------------------------------------- % 194.86/27.31 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 194.86/27.31 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (c_member(v4, v3, v2) = v1) | ~ % 194.86/27.31 (c_member(v4, v3, v2) = v0)) % 194.86/27.31 (2) c_member(all_622_1, all_872_3, v_L) = all_872_2 % 194.86/27.31 (3) c_member(all_622_1, all_872_3, v_L) = 0 % 194.86/27.31 (4) ~ (all_872_2 = 0) % 194.86/27.31 % 194.86/27.31 Begin of proof % 194.86/27.31 | % 194.86/27.31 | GROUND_INST: instantiating (1) with all_872_2, 0, v_L, all_872_3, all_622_1, % 194.86/27.31 | simplifying with (2), (3) gives: % 194.86/27.31 | (5) all_872_2 = 0 % 194.86/27.31 | % 194.86/27.31 | REDUCE: (4), (5) imply: % 194.86/27.31 | (6) $false % 194.86/27.31 | % 194.86/27.31 | CLOSE: (6) is inconsistent. % 194.86/27.31 | % 194.86/27.31 End of proof % 194.86/27.31 % 194.86/27.31 Sub-proof #14 shows that the following formulas are inconsistent: % 194.86/27.31 ---------------------------------------------------------------- % 194.86/27.31 (1) ~ (all_1123_0 = 0) & c_member(all_676_0, all_872_7, v_L) = all_1123_0 % 194.86/27.31 (2) all_676_0 = all_622_1 % 194.86/27.31 (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 194.86/27.31 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (c_member(v4, v3, v2) = v1) | ~ % 194.86/27.31 (c_member(v4, v3, v2) = v0)) % 194.86/27.31 (4) c_member(all_622_1, all_872_7, v_L) = 0 % 194.86/27.31 % 194.86/27.31 Begin of proof % 194.86/27.31 | % 194.86/27.31 | ALPHA: (1) implies: % 194.86/27.31 | (5) ~ (all_1123_0 = 0) % 194.86/27.31 | (6) c_member(all_676_0, all_872_7, v_L) = all_1123_0 % 194.86/27.31 | % 194.86/27.31 | REDUCE: (2), (6) imply: % 194.86/27.31 | (7) c_member(all_622_1, all_872_7, v_L) = all_1123_0 % 194.86/27.31 | % 194.86/27.31 | GROUND_INST: instantiating (3) with 0, all_1123_0, v_L, all_872_7, all_622_1, % 194.86/27.31 | simplifying with (4), (7) gives: % 194.86/27.31 | (8) all_1123_0 = 0 % 194.86/27.31 | % 194.86/27.31 | REDUCE: (5), (8) imply: % 194.86/27.31 | (9) $false % 194.86/27.31 | % 194.86/27.31 | CLOSE: (9) is inconsistent. % 194.86/27.31 | % 194.86/27.31 End of proof % 194.86/27.31 % 194.86/27.31 Sub-proof #15 shows that the following formulas are inconsistent: % 194.86/27.31 ---------------------------------------------------------------- % 194.86/27.31 (1) ~ (all_1124_0 = 0) & c_member(all_676_0, all_872_5, v_L) = all_1124_0 % 194.86/27.31 (2) all_676_0 = all_622_1 % 194.86/27.31 (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 194.86/27.31 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (c_member(v4, v3, v2) = v1) | ~ % 194.86/27.31 (c_member(v4, v3, v2) = v0)) % 194.86/27.31 (4) c_member(all_622_1, all_872_5, v_L) = 0 % 194.86/27.31 % 194.86/27.31 Begin of proof % 194.86/27.31 | % 194.86/27.31 | ALPHA: (1) implies: % 194.86/27.31 | (5) ~ (all_1124_0 = 0) % 194.86/27.31 | (6) c_member(all_676_0, all_872_5, v_L) = all_1124_0 % 194.86/27.31 | % 194.86/27.31 | REDUCE: (2), (6) imply: % 194.86/27.31 | (7) c_member(all_622_1, all_872_5, v_L) = all_1124_0 % 194.86/27.31 | % 194.86/27.31 | GROUND_INST: instantiating (3) with 0, all_1124_0, v_L, all_872_5, all_622_1, % 194.86/27.31 | simplifying with (4), (7) gives: % 194.86/27.31 | (8) all_1124_0 = 0 % 194.86/27.31 | % 194.86/27.31 | REDUCE: (5), (8) imply: % 194.86/27.31 | (9) $false % 194.86/27.31 | % 194.86/27.31 | CLOSE: (9) is inconsistent. % 194.86/27.31 | % 194.86/27.31 End of proof % 194.86/27.31 % 194.86/27.31 Sub-proof #16 shows that the following formulas are inconsistent: % 194.86/27.31 ---------------------------------------------------------------- % 194.86/27.31 (1) ~ (all_1198_0 = 0) & c_member(all_676_0, all_872_3, v_L) = all_1198_0 % 194.86/27.31 (2) all_676_0 = all_622_1 % 194.86/27.31 (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 194.86/27.31 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (c_member(v4, v3, v2) = v1) | ~ % 194.86/27.31 (c_member(v4, v3, v2) = v0)) % 194.86/27.31 (4) c_member(all_622_1, all_872_3, v_L) = 0 % 194.86/27.31 % 194.86/27.31 Begin of proof % 194.86/27.31 | % 194.86/27.31 | ALPHA: (1) implies: % 194.86/27.31 | (5) ~ (all_1198_0 = 0) % 194.86/27.31 | (6) c_member(all_676_0, all_872_3, v_L) = all_1198_0 % 194.86/27.31 | % 194.86/27.31 | REDUCE: (2), (6) imply: % 194.86/27.31 | (7) c_member(all_622_1, all_872_3, v_L) = all_1198_0 % 194.86/27.31 | % 194.86/27.31 | GROUND_INST: instantiating (3) with 0, all_1198_0, v_L, all_872_3, all_622_1, % 194.86/27.31 | simplifying with (4), (7) gives: % 194.86/27.31 | (8) all_1198_0 = 0 % 194.86/27.31 | % 194.86/27.31 | REDUCE: (5), (8) imply: % 194.86/27.31 | (9) $false % 194.86/27.31 | % 194.86/27.31 | CLOSE: (9) is inconsistent. % 194.86/27.31 | % 194.86/27.31 End of proof % 194.86/27.31 % 194.86/27.31 Sub-proof #17 shows that the following formulas are inconsistent: % 194.86/27.31 ---------------------------------------------------------------- % 194.86/27.31 (1) ~ (all_1151_0 = 0) & c_member(all_676_0, all_872_1, v_L) = all_1151_0 % 194.86/27.31 (2) all_676_0 = all_622_1 % 194.86/27.31 (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 194.86/27.31 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (c_member(v4, v3, v2) = v1) | ~ % 194.86/27.31 (c_member(v4, v3, v2) = v0)) % 194.86/27.31 (4) c_member(all_622_1, all_872_1, v_L) = 0 % 194.86/27.31 % 194.86/27.31 Begin of proof % 194.86/27.31 | % 194.86/27.31 | ALPHA: (1) implies: % 194.86/27.31 | (5) ~ (all_1151_0 = 0) % 194.86/27.31 | (6) c_member(all_676_0, all_872_1, v_L) = all_1151_0 % 194.86/27.31 | % 194.86/27.31 | REDUCE: (2), (6) imply: % 194.86/27.31 | (7) c_member(all_622_1, all_872_1, v_L) = all_1151_0 % 194.86/27.31 | % 194.86/27.31 | GROUND_INST: instantiating (3) with 0, all_1151_0, v_L, all_872_1, all_622_1, % 194.86/27.31 | simplifying with (4), (7) gives: % 194.86/27.31 | (8) all_1151_0 = 0 % 194.86/27.31 | % 194.86/27.31 | REDUCE: (5), (8) imply: % 194.86/27.31 | (9) $false % 194.86/27.31 | % 194.86/27.31 | CLOSE: (9) is inconsistent. % 194.86/27.31 | % 194.86/27.31 End of proof % 194.86/27.31 % 194.86/27.31 Sub-proof #18 shows that the following formulas are inconsistent: % 194.86/27.31 ---------------------------------------------------------------- % 194.86/27.31 (1) c_member(all_622_1, all_872_11, v_L) = all_872_10 % 194.86/27.31 (2) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.86/27.31 tc_Arrow__Order__Mirabelle_Oalt, all_872_13, v_x) = all_872_9 % 194.86/27.31 (3) ~ (all_872_4 = 0) | all_872_12 = v_y | all_872_13 = v_y % 194.86/27.31 (4) ~ (all_872_12 = all_872_13) % 194.86/27.31 (5) ~ (all_872_10 = 0) | all_872_12 = v_y | all_872_13 = v_y % 194.86/27.31 (6) all_872_12 = all_872_13 | ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 194.86/27.31 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.86/27.31 tc_Arrow__Order__Mirabelle_Oalt, all_872_13, all_872_12) = v1 & % 194.86/27.31 c_member(all_676_0, v1, v_L) = v2 & c_member(all_676_0, all_872_5, v_L) % 194.86/27.31 = v0 & $i(v1) & (v2 = 0 | v0 = 0)) % 194.86/27.31 (7) ~ (all_872_2 = 0) | ~ (all_872_13 = v_y) | all_872_12 = v_y % 194.86/27.31 (8) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.86/27.31 tc_Arrow__Order__Mirabelle_Oalt, all_872_13, all_872_12) = all_872_11 % 194.86/27.31 (9) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.86/27.31 tc_Arrow__Order__Mirabelle_Oalt, v_x, all_872_12) = all_872_7 % 194.86/27.31 (10) ~ (all_872_12 = v_y) | all_872_13 = v_y % 194.86/27.31 (11) ~ (all_872_12 = v_x) | ~ (all_872_13 = v_y) % 194.86/27.31 (12) all_676_0 = all_622_1 % 194.86/27.31 (13) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.86/27.31 tc_Arrow__Order__Mirabelle_Oalt, all_872_12, all_872_13) = all_872_5 % 194.86/27.31 (14) c_member(all_622_1, all_872_9, v_L) = all_872_8 % 194.86/27.31 (15) ~ (all_872_13 = v_y) % 194.86/27.31 (16) all_872_10 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & hBOOL(v0) = % 194.86/27.31 v1 & hAPP(v_L, all_872_11) = v0 & $i(v0)) % 194.86/27.31 (17) all_872_12 = all_872_13 | ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 194.86/27.31 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.86/27.31 tc_Arrow__Order__Mirabelle_Oalt, all_872_12, all_872_13) = v1 & % 194.86/27.31 c_member(all_676_0, v1, v_L) = v2 & c_member(all_676_0, all_872_11, % 194.86/27.31 v_L) = v0 & $i(v1) & (v2 = 0 | v0 = 0)) % 194.86/27.31 (18) all_872_12 = v_x | ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 194.86/27.31 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.86/27.31 tc_Arrow__Order__Mirabelle_Oalt, all_872_12, v_x) = v1 & % 194.86/27.31 c_member(all_676_0, v1, v_L) = v2 & c_member(all_676_0, all_872_7, % 194.86/27.31 v_L) = v0 & $i(v1) & (v2 = 0 | v0 = 0)) % 194.86/27.31 (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 194.86/27.31 [v5: $i] : (v1 = v0 | ~ (c_Product__Type_OPair(v5, v4, v3, v2) = v1) | % 194.86/27.31 ~ (c_Product__Type_OPair(v5, v4, v3, v2) = v0)) % 194.86/27.31 (20) c_member(all_622_1, all_872_3, v_L) = all_872_2 % 194.86/27.31 (21) all_872_12 = v_x | ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 194.86/27.31 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.86/27.31 tc_Arrow__Order__Mirabelle_Oalt, v_x, all_872_12) = v1 & % 194.86/27.31 c_member(all_676_0, v1, v_L) = v2 & c_member(all_676_0, all_872_3, % 194.86/27.31 v_L) = v0 & $i(v1) & (v2 = 0 | v0 = 0)) % 194.86/27.31 (22) c_member(all_622_1, all_872_5, v_L) = all_872_4 % 194.86/27.31 (23) c_member(all_622_1, all_872_7, v_L) = all_872_6 % 194.86/27.31 (24) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 194.86/27.31 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (c_member(v4, v3, v2) = v1) | % 194.86/27.31 ~ (c_member(v4, v3, v2) = v0)) % 194.86/27.31 (25) ~ (all_872_6 = 0) | ~ (all_872_13 = v_y) | all_872_12 = v_y % 194.86/27.31 % 194.86/27.31 Begin of proof % 194.86/27.31 | % 194.86/27.31 | BETA: splitting (10) gives: % 194.86/27.31 | % 194.86/27.31 | Case 1: % 194.86/27.31 | | % 194.86/27.31 | | (26) ~ (all_872_12 = v_y) % 194.86/27.31 | | % 194.86/27.31 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11), (12), (13), % 194.86/27.31 | | (14), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25), % 194.86/27.31 | | (26) are inconsistent by sub-proof #19. % 194.86/27.31 | | % 194.86/27.31 | Case 2: % 194.86/27.31 | | % 194.86/27.31 | | (27) all_872_13 = v_y % 194.86/27.31 | | % 194.86/27.31 | | REDUCE: (15), (27) imply: % 194.86/27.31 | | (28) $false % 194.86/27.31 | | % 194.86/27.31 | | CLOSE: (28) is inconsistent. % 194.86/27.31 | | % 194.86/27.31 | End of split % 194.86/27.31 | % 194.86/27.31 End of proof % 194.86/27.31 % 194.86/27.31 Sub-proof #19 shows that the following formulas are inconsistent: % 194.86/27.31 ---------------------------------------------------------------- % 194.86/27.31 (1) c_member(all_622_1, all_872_11, v_L) = all_872_10 % 194.86/27.31 (2) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.86/27.31 tc_Arrow__Order__Mirabelle_Oalt, all_872_13, v_x) = all_872_9 % 194.86/27.31 (3) ~ (all_872_4 = 0) | all_872_12 = v_y | all_872_13 = v_y % 194.86/27.31 (4) ~ (all_872_12 = all_872_13) % 194.86/27.32 (5) ~ (all_872_10 = 0) | all_872_12 = v_y | all_872_13 = v_y % 194.86/27.32 (6) all_872_12 = all_872_13 | ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 194.86/27.32 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.86/27.32 tc_Arrow__Order__Mirabelle_Oalt, all_872_13, all_872_12) = v1 & % 194.86/27.32 c_member(all_676_0, v1, v_L) = v2 & c_member(all_676_0, all_872_5, v_L) % 194.86/27.32 = v0 & $i(v1) & (v2 = 0 | v0 = 0)) % 194.86/27.32 (7) ~ (all_872_2 = 0) | ~ (all_872_13 = v_y) | all_872_12 = v_y % 194.86/27.32 (8) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.86/27.32 tc_Arrow__Order__Mirabelle_Oalt, all_872_13, all_872_12) = all_872_11 % 194.86/27.32 (9) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.86/27.32 tc_Arrow__Order__Mirabelle_Oalt, v_x, all_872_12) = all_872_7 % 194.86/27.32 (10) ~ (all_872_12 = v_x) | ~ (all_872_13 = v_y) % 194.86/27.32 (11) all_676_0 = all_622_1 % 194.86/27.32 (12) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.86/27.32 tc_Arrow__Order__Mirabelle_Oalt, all_872_12, all_872_13) = all_872_5 % 194.86/27.32 (13) c_member(all_622_1, all_872_9, v_L) = all_872_8 % 194.86/27.32 (14) ~ (all_872_12 = v_y) % 194.86/27.32 (15) all_872_10 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & hBOOL(v0) = % 194.86/27.32 v1 & hAPP(v_L, all_872_11) = v0 & $i(v0)) % 194.86/27.32 (16) all_872_12 = all_872_13 | ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 194.86/27.32 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.86/27.32 tc_Arrow__Order__Mirabelle_Oalt, all_872_12, all_872_13) = v1 & % 194.86/27.32 c_member(all_676_0, v1, v_L) = v2 & c_member(all_676_0, all_872_11, % 194.86/27.32 v_L) = v0 & $i(v1) & (v2 = 0 | v0 = 0)) % 194.86/27.32 (17) all_872_12 = v_x | ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 194.86/27.32 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.86/27.32 tc_Arrow__Order__Mirabelle_Oalt, all_872_12, v_x) = v1 & % 194.86/27.32 c_member(all_676_0, v1, v_L) = v2 & c_member(all_676_0, all_872_7, % 194.86/27.32 v_L) = v0 & $i(v1) & (v2 = 0 | v0 = 0)) % 194.86/27.32 (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 194.86/27.32 [v5: $i] : (v1 = v0 | ~ (c_Product__Type_OPair(v5, v4, v3, v2) = v1) | % 194.86/27.32 ~ (c_Product__Type_OPair(v5, v4, v3, v2) = v0)) % 194.86/27.32 (19) c_member(all_622_1, all_872_3, v_L) = all_872_2 % 194.86/27.32 (20) all_872_12 = v_x | ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 194.86/27.32 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.86/27.32 tc_Arrow__Order__Mirabelle_Oalt, v_x, all_872_12) = v1 & % 194.86/27.32 c_member(all_676_0, v1, v_L) = v2 & c_member(all_676_0, all_872_3, % 194.86/27.32 v_L) = v0 & $i(v1) & (v2 = 0 | v0 = 0)) % 194.86/27.32 (21) c_member(all_622_1, all_872_5, v_L) = all_872_4 % 194.86/27.32 (22) c_member(all_622_1, all_872_7, v_L) = all_872_6 % 194.86/27.32 (23) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 194.86/27.32 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (c_member(v4, v3, v2) = v1) | % 194.86/27.32 ~ (c_member(v4, v3, v2) = v0)) % 194.86/27.32 (24) ~ (all_872_6 = 0) | ~ (all_872_13 = v_y) | all_872_12 = v_y % 194.86/27.32 % 194.86/27.32 Begin of proof % 194.86/27.32 | % 194.86/27.32 | BETA: splitting (10) gives: % 194.86/27.32 | % 194.86/27.32 | Case 1: % 194.86/27.32 | | % 194.86/27.32 | | (25) ~ (all_872_12 = v_x) % 194.86/27.32 | | % 194.86/27.32 | | BETA: splitting (5) gives: % 194.86/27.32 | | % 194.86/27.32 | | Case 1: % 194.86/27.32 | | | % 194.86/27.32 | | | (26) ~ (all_872_10 = 0) % 194.86/27.32 | | | % 194.86/27.32 | | | BETA: splitting (16) gives: % 194.86/27.32 | | | % 194.86/27.32 | | | Case 1: % 194.86/27.32 | | | | % 194.86/27.32 | | | | (27) all_872_12 = all_872_13 % 194.86/27.32 | | | | % 194.86/27.32 | | | | REDUCE: (4), (27) imply: % 194.86/27.32 | | | | (28) $false % 194.86/27.32 | | | | % 194.86/27.32 | | | | CLOSE: (28) is inconsistent. % 194.86/27.32 | | | | % 194.86/27.32 | | | Case 2: % 194.86/27.32 | | | | % 194.86/27.32 | | | | (29) ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 194.86/27.32 | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.86/27.32 | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_12, all_872_13) = % 194.86/27.32 | | | | v1 & c_member(all_676_0, v1, v_L) = v2 & c_member(all_676_0, % 194.86/27.32 | | | | all_872_11, v_L) = v0 & $i(v1) & (v2 = 0 | v0 = 0)) % 194.86/27.32 | | | | % 194.86/27.32 | | | | DELTA: instantiating (29) with fresh symbols all_1213_0, all_1213_1, % 194.86/27.32 | | | | all_1213_2 gives: % 194.86/27.32 | | | | (30) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.86/27.32 | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_12, all_872_13) = % 194.86/27.32 | | | | all_1213_1 & c_member(all_676_0, all_1213_1, v_L) = all_1213_0 & % 194.86/27.32 | | | | c_member(all_676_0, all_872_11, v_L) = all_1213_2 & % 194.86/27.32 | | | | $i(all_1213_1) & (all_1213_0 = 0 | all_1213_2 = 0) % 194.86/27.32 | | | | % 194.86/27.32 | | | | ALPHA: (30) implies: % 194.86/27.32 | | | | (31) c_member(all_676_0, all_872_11, v_L) = all_1213_2 % 194.86/27.32 | | | | (32) c_member(all_676_0, all_1213_1, v_L) = all_1213_0 % 194.86/27.32 | | | | (33) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.86/27.32 | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_12, all_872_13) = % 194.86/27.32 | | | | all_1213_1 % 194.86/27.32 | | | | (34) all_1213_0 = 0 | all_1213_2 = 0 % 194.86/27.32 | | | | % 194.86/27.32 | | | | REDUCE: (11), (32) imply: % 194.86/27.32 | | | | (35) c_member(all_622_1, all_1213_1, v_L) = all_1213_0 % 194.86/27.32 | | | | % 194.86/27.32 | | | | REDUCE: (11), (31) imply: % 194.86/27.32 | | | | (36) c_member(all_622_1, all_872_11, v_L) = all_1213_2 % 194.86/27.32 | | | | % 194.86/27.32 | | | | BETA: splitting (6) gives: % 194.86/27.32 | | | | % 194.86/27.32 | | | | Case 1: % 194.86/27.32 | | | | | % 194.86/27.32 | | | | | (37) all_872_12 = all_872_13 % 194.86/27.32 | | | | | % 194.86/27.32 | | | | | REDUCE: (4), (37) imply: % 194.86/27.32 | | | | | (38) $false % 194.86/27.32 | | | | | % 194.86/27.32 | | | | | CLOSE: (38) is inconsistent. % 194.86/27.32 | | | | | % 194.86/27.32 | | | | Case 2: % 194.86/27.32 | | | | | % 194.86/27.32 | | | | | (39) ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 194.86/27.32 | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.86/27.32 | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_13, all_872_12) = % 194.86/27.32 | | | | | v1 & c_member(all_676_0, v1, v_L) = v2 & c_member(all_676_0, % 194.86/27.32 | | | | | all_872_5, v_L) = v0 & $i(v1) & (v2 = 0 | v0 = 0)) % 194.86/27.32 | | | | | % 194.86/27.32 | | | | | DELTA: instantiating (39) with fresh symbols all_1219_0, all_1219_1, % 194.86/27.32 | | | | | all_1219_2 gives: % 194.86/27.32 | | | | | (40) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.86/27.32 | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_13, all_872_12) = % 194.86/27.32 | | | | | all_1219_1 & c_member(all_676_0, all_1219_1, v_L) = all_1219_0 % 194.86/27.32 | | | | | & c_member(all_676_0, all_872_5, v_L) = all_1219_2 & % 194.86/27.32 | | | | | $i(all_1219_1) & (all_1219_0 = 0 | all_1219_2 = 0) % 194.86/27.32 | | | | | % 194.86/27.32 | | | | | ALPHA: (40) implies: % 194.86/27.32 | | | | | (41) c_member(all_676_0, all_872_5, v_L) = all_1219_2 % 194.86/27.32 | | | | | % 194.86/27.32 | | | | | REDUCE: (11), (41) imply: % 194.86/27.32 | | | | | (42) c_member(all_622_1, all_872_5, v_L) = all_1219_2 % 194.86/27.32 | | | | | % 194.86/27.32 | | | | | GROUND_INST: instantiating (23) with all_872_10, all_1213_2, v_L, % 194.86/27.32 | | | | | all_872_11, all_622_1, simplifying with (1), (36) gives: % 194.86/27.32 | | | | | (43) all_1213_2 = all_872_10 % 194.86/27.32 | | | | | % 194.86/27.32 | | | | | GROUND_INST: instantiating (23) with all_872_4, all_1219_2, v_L, % 194.86/27.32 | | | | | all_872_5, all_622_1, simplifying with (21), (42) gives: % 194.86/27.32 | | | | | (44) all_1219_2 = all_872_4 % 194.86/27.32 | | | | | % 194.86/27.32 | | | | | GROUND_INST: instantiating (18) with all_872_5, all_1213_1, % 194.86/27.32 | | | | | all_872_13, all_872_12, tc_Arrow__Order__Mirabelle_Oalt, % 194.86/27.32 | | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with (12), % 194.86/27.32 | | | | | (33) gives: % 194.86/27.32 | | | | | (45) all_1213_1 = all_872_5 % 194.86/27.32 | | | | | % 194.86/27.32 | | | | | REDUCE: (35), (45) imply: % 194.86/27.32 | | | | | (46) c_member(all_622_1, all_872_5, v_L) = all_1213_0 % 194.86/27.32 | | | | | % 194.86/27.32 | | | | | BETA: splitting (34) gives: % 194.86/27.32 | | | | | % 194.86/27.32 | | | | | Case 1: % 194.86/27.32 | | | | | | % 194.86/27.32 | | | | | | (47) all_1213_0 = 0 % 194.86/27.32 | | | | | | % 194.86/27.32 | | | | | | REDUCE: (46), (47) imply: % 194.86/27.32 | | | | | | (48) c_member(all_622_1, all_872_5, v_L) = 0 % 194.86/27.32 | | | | | | % 194.86/27.32 | | | | | | GROUND_INST: instantiating (23) with all_872_4, 0, v_L, all_872_5, % 194.86/27.32 | | | | | | all_622_1, simplifying with (21), (48) gives: % 194.86/27.32 | | | | | | (49) all_872_4 = 0 % 194.86/27.32 | | | | | | % 194.86/27.32 | | | | | | BETA: splitting (3) gives: % 194.86/27.32 | | | | | | % 194.86/27.32 | | | | | | Case 1: % 194.86/27.32 | | | | | | | % 194.86/27.32 | | | | | | | (50) ~ (all_872_4 = 0) % 194.86/27.32 | | | | | | | % 194.86/27.32 | | | | | | | REDUCE: (49), (50) imply: % 194.86/27.32 | | | | | | | (51) $false % 194.86/27.32 | | | | | | | % 194.86/27.32 | | | | | | | CLOSE: (51) is inconsistent. % 194.86/27.32 | | | | | | | % 194.86/27.32 | | | | | | Case 2: % 194.86/27.32 | | | | | | | % 194.86/27.32 | | | | | | | (52) all_872_12 = v_y | all_872_13 = v_y % 194.86/27.32 | | | | | | | % 194.86/27.32 | | | | | | | REF_CLOSE: (4), (7), (9), (11), (14), (17), (18), (19), (20), % 194.86/27.32 | | | | | | | (22), (23), (24), (25), (52) are inconsistent by % 194.86/27.32 | | | | | | | sub-proof #21. % 194.86/27.32 | | | | | | | % 194.86/27.32 | | | | | | End of split % 194.86/27.32 | | | | | | % 194.86/27.32 | | | | | Case 2: % 194.86/27.32 | | | | | | % 194.86/27.32 | | | | | | (53) all_1213_2 = 0 % 194.86/27.32 | | | | | | % 194.86/27.32 | | | | | | COMBINE_EQS: (43), (53) imply: % 194.86/27.32 | | | | | | (54) all_872_10 = 0 % 194.86/27.32 | | | | | | % 194.86/27.32 | | | | | | REDUCE: (26), (54) imply: % 194.86/27.32 | | | | | | (55) $false % 194.86/27.32 | | | | | | % 194.86/27.32 | | | | | | CLOSE: (55) is inconsistent. % 194.86/27.32 | | | | | | % 194.86/27.32 | | | | | End of split % 194.86/27.32 | | | | | % 194.86/27.32 | | | | End of split % 194.86/27.32 | | | | % 194.86/27.32 | | | End of split % 194.86/27.32 | | | % 194.86/27.32 | | Case 2: % 194.86/27.32 | | | % 194.86/27.32 | | | (56) all_872_12 = v_y | all_872_13 = v_y % 194.86/27.32 | | | % 194.86/27.32 | | | REF_CLOSE: (4), (7), (9), (11), (14), (17), (18), (19), (20), (22), (23), % 194.86/27.32 | | | (24), (25), (56) are inconsistent by sub-proof #21. % 194.86/27.32 | | | % 194.86/27.32 | | End of split % 194.86/27.32 | | % 194.86/27.32 | Case 2: % 194.86/27.32 | | % 194.86/27.32 | | (57) all_872_12 = v_x % 194.86/27.32 | | (58) ~ (all_872_13 = v_y) % 194.86/27.32 | | % 194.86/27.32 | | REDUCE: (4), (57) imply: % 194.86/27.32 | | (59) ~ (all_872_13 = v_x) % 194.86/27.32 | | % 194.86/27.32 | | SIMP: (59) implies: % 194.86/27.32 | | (60) ~ (all_872_13 = v_x) % 194.86/27.32 | | % 194.86/27.32 | | REDUCE: (14), (57) imply: % 194.86/27.32 | | (61) ~ (v_x = v_y) % 194.86/27.32 | | % 194.86/27.32 | | REDUCE: (8), (57) imply: % 194.86/27.32 | | (62) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.86/27.32 | | tc_Arrow__Order__Mirabelle_Oalt, all_872_13, v_x) = all_872_11 % 194.86/27.32 | | % 194.86/27.32 | | BETA: splitting (3) gives: % 194.86/27.32 | | % 194.86/27.32 | | Case 1: % 194.86/27.32 | | | % 194.86/27.32 | | | (63) ~ (all_872_4 = 0) % 194.86/27.32 | | | % 194.86/27.32 | | | BETA: splitting (5) gives: % 194.86/27.32 | | | % 194.86/27.32 | | | Case 1: % 194.86/27.32 | | | | % 194.86/27.32 | | | | (64) ~ (all_872_10 = 0) % 194.86/27.32 | | | | % 194.86/27.32 | | | | BETA: splitting (16) gives: % 194.86/27.32 | | | | % 194.86/27.32 | | | | Case 1: % 194.86/27.32 | | | | | % 194.86/27.32 | | | | | (65) all_872_12 = all_872_13 % 194.86/27.32 | | | | | % 194.86/27.32 | | | | | COMBINE_EQS: (57), (65) imply: % 194.86/27.32 | | | | | (66) all_872_13 = v_x % 194.86/27.32 | | | | | % 194.86/27.32 | | | | | SIMP: (66) implies: % 194.86/27.32 | | | | | (67) all_872_13 = v_x % 194.86/27.32 | | | | | % 194.86/27.32 | | | | | REDUCE: (60), (67) imply: % 194.86/27.32 | | | | | (68) $false % 194.86/27.32 | | | | | % 194.86/27.32 | | | | | CLOSE: (68) is inconsistent. % 194.86/27.32 | | | | | % 194.86/27.32 | | | | Case 2: % 194.86/27.32 | | | | | % 194.86/27.32 | | | | | (69) ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 194.86/27.32 | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.86/27.32 | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_12, all_872_13) = % 194.86/27.32 | | | | | v1 & c_member(all_676_0, v1, v_L) = v2 & c_member(all_676_0, % 194.86/27.32 | | | | | all_872_11, v_L) = v0 & $i(v1) & (v2 = 0 | v0 = 0)) % 194.86/27.32 | | | | | % 194.86/27.32 | | | | | DELTA: instantiating (69) with fresh symbols all_1174_0, all_1174_1, % 194.86/27.32 | | | | | all_1174_2 gives: % 194.86/27.32 | | | | | (70) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.86/27.32 | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_12, all_872_13) = % 194.86/27.32 | | | | | all_1174_1 & c_member(all_676_0, all_1174_1, v_L) = all_1174_0 % 194.86/27.32 | | | | | & c_member(all_676_0, all_872_11, v_L) = all_1174_2 & % 194.86/27.32 | | | | | $i(all_1174_1) & (all_1174_0 = 0 | all_1174_2 = 0) % 194.86/27.32 | | | | | % 194.86/27.32 | | | | | ALPHA: (70) implies: % 194.86/27.32 | | | | | (71) c_member(all_676_0, all_872_11, v_L) = all_1174_2 % 194.86/27.32 | | | | | % 194.86/27.32 | | | | | REDUCE: (11), (71) imply: % 194.86/27.32 | | | | | (72) c_member(all_622_1, all_872_11, v_L) = all_1174_2 % 194.86/27.32 | | | | | % 194.86/27.32 | | | | | BETA: splitting (6) gives: % 194.86/27.32 | | | | | % 194.86/27.32 | | | | | Case 1: % 194.86/27.32 | | | | | | % 194.86/27.32 | | | | | | (73) all_872_12 = all_872_13 % 194.86/27.32 | | | | | | % 194.86/27.32 | | | | | | COMBINE_EQS: (57), (73) imply: % 194.86/27.32 | | | | | | (74) all_872_13 = v_x % 194.86/27.32 | | | | | | % 194.86/27.32 | | | | | | SIMP: (74) implies: % 194.86/27.32 | | | | | | (75) all_872_13 = v_x % 194.86/27.32 | | | | | | % 194.86/27.32 | | | | | | REDUCE: (60), (75) imply: % 194.86/27.32 | | | | | | (76) $false % 194.86/27.32 | | | | | | % 194.86/27.32 | | | | | | CLOSE: (76) is inconsistent. % 194.86/27.32 | | | | | | % 194.86/27.32 | | | | | Case 2: % 194.86/27.32 | | | | | | % 194.86/27.33 | | | | | | (77) ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 194.86/27.33 | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.86/27.33 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_13, all_872_12) % 194.86/27.33 | | | | | | = v1 & c_member(all_676_0, v1, v_L) = v2 & % 194.86/27.33 | | | | | | c_member(all_676_0, all_872_5, v_L) = v0 & $i(v1) & (v2 = % 194.86/27.33 | | | | | | 0 | v0 = 0)) % 194.86/27.33 | | | | | | % 194.86/27.33 | | | | | | DELTA: instantiating (77) with fresh symbols all_1185_0, all_1185_1, % 194.86/27.33 | | | | | | all_1185_2 gives: % 194.86/27.33 | | | | | | (78) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.86/27.33 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_13, all_872_12) = % 194.86/27.33 | | | | | | all_1185_1 & c_member(all_676_0, all_1185_1, v_L) = % 194.86/27.33 | | | | | | all_1185_0 & c_member(all_676_0, all_872_5, v_L) = % 194.86/27.33 | | | | | | all_1185_2 & $i(all_1185_1) & (all_1185_0 = 0 | all_1185_2 = % 194.86/27.33 | | | | | | 0) % 194.86/27.33 | | | | | | % 194.86/27.33 | | | | | | ALPHA: (78) implies: % 194.86/27.33 | | | | | | (79) c_member(all_676_0, all_872_5, v_L) = all_1185_2 % 194.86/27.33 | | | | | | (80) c_member(all_676_0, all_1185_1, v_L) = all_1185_0 % 194.86/27.33 | | | | | | (81) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.86/27.33 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_13, all_872_12) = % 194.86/27.33 | | | | | | all_1185_1 % 194.86/27.33 | | | | | | (82) all_1185_0 = 0 | all_1185_2 = 0 % 194.86/27.33 | | | | | | % 194.86/27.33 | | | | | | REDUCE: (57), (81) imply: % 194.86/27.33 | | | | | | (83) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.86/27.33 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_13, v_x) = % 194.86/27.33 | | | | | | all_1185_1 % 194.86/27.33 | | | | | | % 194.86/27.33 | | | | | | REDUCE: (11), (80) imply: % 194.86/27.33 | | | | | | (84) c_member(all_622_1, all_1185_1, v_L) = all_1185_0 % 194.86/27.33 | | | | | | % 194.86/27.33 | | | | | | REDUCE: (11), (79) imply: % 194.86/27.33 | | | | | | (85) c_member(all_622_1, all_872_5, v_L) = all_1185_2 % 194.86/27.33 | | | | | | % 194.86/27.33 | | | | | | BETA: splitting (15) gives: % 194.86/27.33 | | | | | | % 194.86/27.33 | | | | | | Case 1: % 194.86/27.33 | | | | | | | % 194.86/27.33 | | | | | | | (86) all_872_10 = 0 % 194.86/27.33 | | | | | | | % 194.86/27.33 | | | | | | | REDUCE: (64), (86) imply: % 194.86/27.33 | | | | | | | (87) $false % 194.86/27.33 | | | | | | | % 194.86/27.33 | | | | | | | CLOSE: (87) is inconsistent. % 194.86/27.33 | | | | | | | % 194.86/27.33 | | | | | | Case 2: % 194.86/27.33 | | | | | | | % 194.86/27.33 | | | | | | | % 194.86/27.33 | | | | | | | GROUND_INST: instantiating (23) with all_872_10, all_1174_2, v_L, % 194.86/27.33 | | | | | | | all_872_11, all_622_1, simplifying with (1), (72) % 194.86/27.33 | | | | | | | gives: % 194.86/27.33 | | | | | | | (88) all_1174_2 = all_872_10 % 194.86/27.33 | | | | | | | % 194.86/27.33 | | | | | | | GROUND_INST: instantiating (23) with all_872_4, all_1185_2, v_L, % 194.86/27.33 | | | | | | | all_872_5, all_622_1, simplifying with (21), (85) % 194.86/27.33 | | | | | | | gives: % 194.86/27.33 | | | | | | | (89) all_1185_2 = all_872_4 % 194.86/27.33 | | | | | | | % 194.86/27.33 | | | | | | | GROUND_INST: instantiating (18) with all_872_9, all_1185_1, v_x, % 194.86/27.33 | | | | | | | all_872_13, tc_Arrow__Order__Mirabelle_Oalt, % 194.86/27.33 | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with % 194.86/27.33 | | | | | | | (2), (83) gives: % 194.86/27.33 | | | | | | | (90) all_1185_1 = all_872_9 % 194.86/27.33 | | | | | | | % 194.86/27.33 | | | | | | | GROUND_INST: instantiating (18) with all_872_11, all_1185_1, v_x, % 194.86/27.33 | | | | | | | all_872_13, tc_Arrow__Order__Mirabelle_Oalt, % 194.86/27.33 | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with % 194.86/27.33 | | | | | | | (62), (83) gives: % 194.86/27.33 | | | | | | | (91) all_1185_1 = all_872_11 % 194.86/27.33 | | | | | | | % 194.86/27.33 | | | | | | | COMBINE_EQS: (90), (91) imply: % 194.86/27.33 | | | | | | | (92) all_872_9 = all_872_11 % 194.86/27.33 | | | | | | | % 194.86/27.33 | | | | | | | SIMP: (92) implies: % 194.86/27.33 | | | | | | | (93) all_872_9 = all_872_11 % 194.86/27.33 | | | | | | | % 194.86/27.33 | | | | | | | REDUCE: (84), (91) imply: % 194.86/27.33 | | | | | | | (94) c_member(all_622_1, all_872_11, v_L) = all_1185_0 % 194.86/27.33 | | | | | | | % 194.86/27.33 | | | | | | | REDUCE: (13), (93) imply: % 194.86/27.33 | | | | | | | (95) c_member(all_622_1, all_872_11, v_L) = all_872_8 % 194.86/27.33 | | | | | | | % 194.86/27.33 | | | | | | | BETA: splitting (82) gives: % 194.86/27.33 | | | | | | | % 194.86/27.33 | | | | | | | Case 1: % 194.86/27.33 | | | | | | | | % 194.86/27.33 | | | | | | | | (96) all_1185_0 = 0 % 194.86/27.33 | | | | | | | | % 194.86/27.33 | | | | | | | | REDUCE: (94), (96) imply: % 194.86/27.33 | | | | | | | | (97) c_member(all_622_1, all_872_11, v_L) = 0 % 194.86/27.33 | | | | | | | | % 194.86/27.33 | | | | | | | | GROUND_INST: instantiating (23) with all_872_10, all_872_8, v_L, % 194.86/27.33 | | | | | | | | all_872_11, all_622_1, simplifying with (1), (95) % 194.86/27.33 | | | | | | | | gives: % 194.86/27.33 | | | | | | | | (98) all_872_8 = all_872_10 % 194.86/27.33 | | | | | | | | % 194.86/27.33 | | | | | | | | GROUND_INST: instantiating (23) with 0, all_872_8, v_L, % 194.86/27.33 | | | | | | | | all_872_11, all_622_1, simplifying with (95), (97) % 194.86/27.33 | | | | | | | | gives: % 194.86/27.33 | | | | | | | | (99) all_872_8 = 0 % 194.86/27.33 | | | | | | | | % 194.86/27.33 | | | | | | | | COMBINE_EQS: (98), (99) imply: % 194.86/27.33 | | | | | | | | (100) all_872_10 = 0 % 194.86/27.33 | | | | | | | | % 194.86/27.33 | | | | | | | | SIMP: (100) implies: % 194.86/27.33 | | | | | | | | (101) all_872_10 = 0 % 194.86/27.33 | | | | | | | | % 194.86/27.33 | | | | | | | | REDUCE: (64), (101) imply: % 194.86/27.33 | | | | | | | | (102) $false % 194.86/27.33 | | | | | | | | % 194.86/27.33 | | | | | | | | CLOSE: (102) is inconsistent. % 194.86/27.33 | | | | | | | | % 194.86/27.33 | | | | | | | Case 2: % 194.86/27.33 | | | | | | | | % 194.86/27.33 | | | | | | | | (103) all_1185_2 = 0 % 194.86/27.33 | | | | | | | | % 194.86/27.33 | | | | | | | | COMBINE_EQS: (89), (103) imply: % 194.86/27.33 | | | | | | | | (104) all_872_4 = 0 % 194.86/27.33 | | | | | | | | % 194.86/27.33 | | | | | | | | REDUCE: (63), (104) imply: % 194.86/27.33 | | | | | | | | (105) $false % 194.86/27.33 | | | | | | | | % 194.86/27.33 | | | | | | | | CLOSE: (105) is inconsistent. % 194.86/27.33 | | | | | | | | % 194.86/27.33 | | | | | | | End of split % 194.86/27.33 | | | | | | | % 194.86/27.33 | | | | | | End of split % 194.86/27.33 | | | | | | % 194.86/27.33 | | | | | End of split % 194.86/27.33 | | | | | % 194.86/27.33 | | | | End of split % 194.86/27.33 | | | | % 194.86/27.33 | | | Case 2: % 194.86/27.33 | | | | % 194.86/27.33 | | | | (106) all_872_12 = v_y | all_872_13 = v_y % 194.86/27.33 | | | | % 194.86/27.33 | | | | REF_CLOSE: (57), (58), (61), (106) are inconsistent by sub-proof #20. % 194.86/27.33 | | | | % 194.86/27.33 | | | End of split % 194.86/27.33 | | | % 194.86/27.33 | | Case 2: % 194.86/27.33 | | | % 194.86/27.33 | | | (107) all_872_12 = v_y | all_872_13 = v_y % 194.86/27.33 | | | % 194.86/27.33 | | | REF_CLOSE: (57), (58), (61), (107) are inconsistent by sub-proof #20. % 194.86/27.33 | | | % 194.86/27.33 | | End of split % 194.86/27.33 | | % 194.86/27.33 | End of split % 194.86/27.33 | % 194.86/27.33 End of proof % 194.86/27.33 % 194.86/27.33 Sub-proof #20 shows that the following formulas are inconsistent: % 194.86/27.33 ---------------------------------------------------------------- % 194.86/27.33 (1) all_872_12 = v_y | all_872_13 = v_y % 194.86/27.33 (2) all_872_12 = v_x % 194.86/27.33 (3) ~ (v_x = v_y) % 194.86/27.33 (4) ~ (all_872_13 = v_y) % 194.86/27.33 % 194.86/27.33 Begin of proof % 194.86/27.33 | % 194.86/27.33 | BETA: splitting (1) gives: % 194.86/27.33 | % 194.86/27.33 | Case 1: % 194.86/27.33 | | % 194.86/27.33 | | (5) all_872_12 = v_y % 194.86/27.33 | | % 194.86/27.33 | | COMBINE_EQS: (2), (5) imply: % 194.86/27.33 | | (6) v_x = v_y % 194.86/27.33 | | % 194.86/27.33 | | REDUCE: (3), (6) imply: % 194.86/27.33 | | (7) $false % 194.86/27.33 | | % 194.86/27.33 | | CLOSE: (7) is inconsistent. % 194.86/27.33 | | % 194.86/27.33 | Case 2: % 194.86/27.33 | | % 194.86/27.33 | | (8) all_872_13 = v_y % 194.86/27.33 | | % 194.86/27.33 | | REDUCE: (4), (8) imply: % 194.86/27.33 | | (9) $false % 194.86/27.33 | | % 194.86/27.33 | | CLOSE: (9) is inconsistent. % 194.86/27.33 | | % 194.86/27.33 | End of split % 194.86/27.33 | % 194.86/27.33 End of proof % 194.86/27.33 % 194.86/27.33 Sub-proof #21 shows that the following formulas are inconsistent: % 194.86/27.33 ---------------------------------------------------------------- % 194.86/27.33 (1) ~ (all_872_12 = all_872_13) % 194.86/27.33 (2) ~ (all_872_2 = 0) | ~ (all_872_13 = v_y) | all_872_12 = v_y % 194.86/27.33 (3) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.86/27.33 tc_Arrow__Order__Mirabelle_Oalt, v_x, all_872_12) = all_872_7 % 194.86/27.33 (4) ~ (all_872_12 = v_x) % 194.86/27.33 (5) all_676_0 = all_622_1 % 194.86/27.33 (6) ~ (all_872_12 = v_y) % 194.86/27.33 (7) all_872_12 = v_x | ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 194.86/27.33 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.86/27.33 tc_Arrow__Order__Mirabelle_Oalt, all_872_12, v_x) = v1 & % 194.86/27.33 c_member(all_676_0, v1, v_L) = v2 & c_member(all_676_0, all_872_7, v_L) % 194.86/27.33 = v0 & $i(v1) & (v2 = 0 | v0 = 0)) % 194.86/27.33 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 194.86/27.33 [v5: $i] : (v1 = v0 | ~ (c_Product__Type_OPair(v5, v4, v3, v2) = v1) | % 194.86/27.33 ~ (c_Product__Type_OPair(v5, v4, v3, v2) = v0)) % 194.86/27.33 (9) c_member(all_622_1, all_872_3, v_L) = all_872_2 % 194.86/27.33 (10) all_872_12 = v_x | ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 194.86/27.33 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.86/27.33 tc_Arrow__Order__Mirabelle_Oalt, v_x, all_872_12) = v1 & % 194.86/27.33 c_member(all_676_0, v1, v_L) = v2 & c_member(all_676_0, all_872_3, % 194.86/27.33 v_L) = v0 & $i(v1) & (v2 = 0 | v0 = 0)) % 194.86/27.33 (11) all_872_12 = v_y | all_872_13 = v_y % 194.86/27.33 (12) c_member(all_622_1, all_872_7, v_L) = all_872_6 % 194.86/27.33 (13) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 194.86/27.33 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (c_member(v4, v3, v2) = v1) | % 194.86/27.33 ~ (c_member(v4, v3, v2) = v0)) % 194.86/27.33 (14) ~ (all_872_6 = 0) | ~ (all_872_13 = v_y) | all_872_12 = v_y % 194.86/27.33 % 194.86/27.33 Begin of proof % 194.86/27.33 | % 194.86/27.33 | BETA: splitting (11) gives: % 194.86/27.33 | % 194.86/27.33 | Case 1: % 194.86/27.33 | | % 194.86/27.33 | | (15) all_872_12 = v_y % 194.86/27.33 | | % 194.86/27.33 | | REDUCE: (6), (15) imply: % 194.86/27.33 | | (16) $false % 194.86/27.33 | | % 194.86/27.33 | | CLOSE: (16) is inconsistent. % 194.86/27.33 | | % 194.86/27.33 | Case 2: % 194.86/27.33 | | % 194.86/27.33 | | (17) all_872_13 = v_y % 194.86/27.33 | | % 194.86/27.33 | | BETA: splitting (2) gives: % 194.86/27.33 | | % 194.86/27.33 | | Case 1: % 194.86/27.33 | | | % 194.86/27.33 | | | (18) ~ (all_872_2 = 0) % 194.86/27.33 | | | % 194.86/27.33 | | | BETA: splitting (14) gives: % 194.86/27.33 | | | % 194.86/27.33 | | | Case 1: % 194.86/27.33 | | | | % 194.86/27.33 | | | | (19) ~ (all_872_6 = 0) % 194.86/27.33 | | | | % 194.86/27.33 | | | | BETA: splitting (7) gives: % 194.86/27.33 | | | | % 194.86/27.33 | | | | Case 1: % 194.86/27.33 | | | | | % 194.86/27.33 | | | | | (20) all_872_12 = v_x % 194.86/27.33 | | | | | % 194.86/27.33 | | | | | REDUCE: (4), (20) imply: % 194.86/27.33 | | | | | (21) $false % 194.86/27.33 | | | | | % 194.86/27.33 | | | | | CLOSE: (21) is inconsistent. % 194.86/27.33 | | | | | % 194.86/27.33 | | | | Case 2: % 194.86/27.33 | | | | | % 194.86/27.33 | | | | | (22) ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 194.86/27.33 | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.86/27.33 | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_12, v_x) = v1 & % 194.86/27.33 | | | | | c_member(all_676_0, v1, v_L) = v2 & c_member(all_676_0, % 194.86/27.33 | | | | | all_872_7, v_L) = v0 & $i(v1) & (v2 = 0 | v0 = 0)) % 194.86/27.33 | | | | | % 194.86/27.33 | | | | | DELTA: instantiating (22) with fresh symbols all_1234_0, all_1234_1, % 194.86/27.33 | | | | | all_1234_2 gives: % 194.86/27.33 | | | | | (23) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.86/27.33 | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_872_12, v_x) = % 194.86/27.33 | | | | | all_1234_1 & c_member(all_676_0, all_1234_1, v_L) = all_1234_0 % 194.86/27.33 | | | | | & c_member(all_676_0, all_872_7, v_L) = all_1234_2 & % 194.86/27.33 | | | | | $i(all_1234_1) & (all_1234_0 = 0 | all_1234_2 = 0) % 194.86/27.33 | | | | | % 194.86/27.33 | | | | | ALPHA: (23) implies: % 194.86/27.33 | | | | | (24) c_member(all_676_0, all_872_7, v_L) = all_1234_2 % 194.86/27.33 | | | | | % 194.86/27.33 | | | | | REDUCE: (5), (24) imply: % 194.86/27.33 | | | | | (25) c_member(all_622_1, all_872_7, v_L) = all_1234_2 % 194.86/27.33 | | | | | % 194.86/27.33 | | | | | BETA: splitting (10) gives: % 194.86/27.33 | | | | | % 194.86/27.33 | | | | | Case 1: % 194.86/27.33 | | | | | | % 194.86/27.33 | | | | | | (26) all_872_12 = v_x % 194.86/27.33 | | | | | | % 194.86/27.33 | | | | | | REDUCE: (4), (26) imply: % 194.86/27.33 | | | | | | (27) $false % 194.86/27.33 | | | | | | % 194.86/27.33 | | | | | | CLOSE: (27) is inconsistent. % 194.86/27.33 | | | | | | % 194.86/27.33 | | | | | Case 2: % 194.86/27.33 | | | | | | % 194.86/27.33 | | | | | | (28) ? [v0: any] : ? [v1: $i] : ? [v2: any] : % 194.86/27.33 | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.86/27.33 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, all_872_12) = v1 & % 194.86/27.33 | | | | | | c_member(all_676_0, v1, v_L) = v2 & c_member(all_676_0, % 194.86/27.33 | | | | | | all_872_3, v_L) = v0 & $i(v1) & (v2 = 0 | v0 = 0)) % 194.86/27.33 | | | | | | % 194.86/27.33 | | | | | | DELTA: instantiating (28) with fresh symbols all_1245_0, all_1245_1, % 194.86/27.33 | | | | | | all_1245_2 gives: % 194.86/27.33 | | | | | | (29) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.86/27.33 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, all_872_12) = % 194.86/27.33 | | | | | | all_1245_1 & c_member(all_676_0, all_1245_1, v_L) = % 194.86/27.33 | | | | | | all_1245_0 & c_member(all_676_0, all_872_3, v_L) = % 194.86/27.33 | | | | | | all_1245_2 & $i(all_1245_1) & (all_1245_0 = 0 | all_1245_2 = % 194.86/27.33 | | | | | | 0) % 194.86/27.33 | | | | | | % 194.86/27.33 | | | | | | ALPHA: (29) implies: % 194.86/27.33 | | | | | | (30) c_member(all_676_0, all_872_3, v_L) = all_1245_2 % 194.86/27.33 | | | | | | (31) c_member(all_676_0, all_1245_1, v_L) = all_1245_0 % 194.86/27.33 | | | | | | (32) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, % 194.86/27.33 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, all_872_12) = % 194.86/27.33 | | | | | | all_1245_1 % 194.86/27.33 | | | | | | (33) all_1245_0 = 0 | all_1245_2 = 0 % 194.86/27.33 | | | | | | % 194.86/27.33 | | | | | | REDUCE: (5), (31) imply: % 194.86/27.33 | | | | | | (34) c_member(all_622_1, all_1245_1, v_L) = all_1245_0 % 194.86/27.33 | | | | | | % 194.86/27.33 | | | | | | REDUCE: (5), (30) imply: % 194.86/27.33 | | | | | | (35) c_member(all_622_1, all_872_3, v_L) = all_1245_2 % 194.86/27.33 | | | | | | % 194.86/27.33 | | | | | | GROUND_INST: instantiating (13) with all_872_6, all_1234_2, v_L, % 194.86/27.33 | | | | | | all_872_7, all_622_1, simplifying with (12), (25) % 194.86/27.33 | | | | | | gives: % 194.86/27.33 | | | | | | (36) all_1234_2 = all_872_6 % 194.86/27.33 | | | | | | % 194.86/27.33 | | | | | | GROUND_INST: instantiating (13) with all_872_2, all_1245_2, v_L, % 194.86/27.33 | | | | | | all_872_3, all_622_1, simplifying with (9), (35) gives: % 194.86/27.33 | | | | | | (37) all_1245_2 = all_872_2 % 194.86/27.33 | | | | | | % 194.86/27.33 | | | | | | GROUND_INST: instantiating (8) with all_872_7, all_1245_1, % 194.86/27.33 | | | | | | all_872_12, v_x, tc_Arrow__Order__Mirabelle_Oalt, % 194.86/27.33 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with (3), % 194.86/27.33 | | | | | | (32) gives: % 194.86/27.33 | | | | | | (38) all_1245_1 = all_872_7 % 194.86/27.33 | | | | | | % 194.86/27.33 | | | | | | REDUCE: (34), (38) imply: % 194.86/27.33 | | | | | | (39) c_member(all_622_1, all_872_7, v_L) = all_1245_0 % 194.86/27.33 | | | | | | % 194.86/27.33 | | | | | | BETA: splitting (33) gives: % 194.86/27.33 | | | | | | % 194.86/27.33 | | | | | | Case 1: % 194.86/27.33 | | | | | | | % 194.86/27.33 | | | | | | | (40) all_1245_0 = 0 % 194.86/27.33 | | | | | | | % 194.86/27.33 | | | | | | | REDUCE: (39), (40) imply: % 194.86/27.33 | | | | | | | (41) c_member(all_622_1, all_872_7, v_L) = 0 % 194.86/27.33 | | | | | | | % 194.86/27.33 | | | | | | | GROUND_INST: instantiating (13) with all_872_6, 0, v_L, all_872_7, % 194.86/27.33 | | | | | | | all_622_1, simplifying with (12), (41) gives: % 194.86/27.33 | | | | | | | (42) all_872_6 = 0 % 194.86/27.33 | | | | | | | % 194.86/27.33 | | | | | | | REDUCE: (19), (42) imply: % 194.86/27.33 | | | | | | | (43) $false % 194.86/27.33 | | | | | | | % 194.86/27.33 | | | | | | | CLOSE: (43) is inconsistent. % 194.86/27.33 | | | | | | | % 194.86/27.33 | | | | | | Case 2: % 194.86/27.33 | | | | | | | % 194.86/27.33 | | | | | | | (44) all_1245_2 = 0 % 194.86/27.33 | | | | | | | % 194.86/27.33 | | | | | | | COMBINE_EQS: (37), (44) imply: % 194.86/27.33 | | | | | | | (45) all_872_2 = 0 % 194.86/27.33 | | | | | | | % 194.86/27.33 | | | | | | | REDUCE: (18), (45) imply: % 194.86/27.33 | | | | | | | (46) $false % 194.86/27.33 | | | | | | | % 194.86/27.33 | | | | | | | CLOSE: (46) is inconsistent. % 194.86/27.33 | | | | | | | % 194.86/27.33 | | | | | | End of split % 194.86/27.33 | | | | | | % 194.86/27.33 | | | | | End of split % 194.86/27.33 | | | | | % 194.86/27.33 | | | | End of split % 194.86/27.33 | | | | % 194.86/27.33 | | | Case 2: % 194.86/27.33 | | | | % 194.86/27.33 | | | | (47) ~ (all_872_13 = v_y) | all_872_12 = v_y % 194.86/27.33 | | | | % 194.86/27.33 | | | | REF_CLOSE: (6), (17), (47) are inconsistent by sub-proof #22. % 194.86/27.33 | | | | % 194.86/27.33 | | | End of split % 194.86/27.33 | | | % 194.86/27.33 | | Case 2: % 194.86/27.33 | | | % 194.86/27.34 | | | (48) ~ (all_872_13 = v_y) | all_872_12 = v_y % 194.86/27.34 | | | % 194.86/27.34 | | | REF_CLOSE: (6), (17), (48) are inconsistent by sub-proof #22. % 194.86/27.34 | | | % 194.86/27.34 | | End of split % 194.86/27.34 | | % 194.86/27.34 | End of split % 194.86/27.34 | % 194.86/27.34 End of proof % 194.86/27.34 % 194.86/27.34 Sub-proof #22 shows that the following formulas are inconsistent: % 194.86/27.34 ---------------------------------------------------------------- % 194.86/27.34 (1) ~ (all_872_13 = v_y) | all_872_12 = v_y % 194.86/27.34 (2) all_872_13 = v_y % 194.86/27.34 (3) ~ (all_872_12 = v_y) % 194.86/27.34 % 194.86/27.34 Begin of proof % 194.86/27.34 | % 194.86/27.34 | BETA: splitting (1) gives: % 194.86/27.34 | % 194.86/27.34 | Case 1: % 194.86/27.34 | | % 194.86/27.34 | | (4) ~ (all_872_13 = v_y) % 194.86/27.34 | | % 194.86/27.34 | | REDUCE: (2), (4) imply: % 194.86/27.34 | | (5) $false % 194.86/27.34 | | % 194.86/27.34 | | CLOSE: (5) is inconsistent. % 194.86/27.34 | | % 194.86/27.34 | Case 2: % 194.86/27.34 | | % 194.86/27.34 | | (6) all_872_12 = v_y % 194.86/27.34 | | % 194.86/27.34 | | REDUCE: (3), (6) imply: % 194.86/27.34 | | (7) $false % 194.86/27.34 | | % 194.86/27.34 | | CLOSE: (7) is inconsistent. % 194.86/27.34 | | % 194.86/27.34 | End of split % 194.86/27.34 | % 194.86/27.34 End of proof % 194.86/27.34 % SZS output end Proof for theBenchmark % 194.86/27.34 % 194.86/27.34 26737ms %------------------------------------------------------------------------------