TSTP Solution File: SCT115+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SCT115+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 : n021.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 14:20:41 EDT 2023
% Result : Theorem 219.41s 30.35s
% Output : Proof 222.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SCT115+1 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n021.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Aug 24 15:39:55 EDT 2023
% 0.12/0.34 % 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
% 0.19/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.62 Running up to 7 provers in parallel.
% 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 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 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 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
% 12.93/2.53 Prover 4: Preprocessing ...
% 13.93/2.59 Prover 1: Preprocessing ...
% 13.93/2.59 Prover 3: Preprocessing ...
% 13.93/2.59 Prover 2: Preprocessing ...
% 13.93/2.62 Prover 0: Preprocessing ...
% 13.93/2.62 Prover 6: Preprocessing ...
% 13.93/2.63 Prover 5: Preprocessing ...
% 35.92/5.60 Prover 1: Warning: ignoring some quantifiers
% 37.13/5.73 Prover 3: Warning: ignoring some quantifiers
% 37.72/5.79 Prover 6: Proving ...
% 38.02/5.82 Prover 3: Constructing countermodel ...
% 38.22/5.87 Prover 1: Constructing countermodel ...
% 39.96/6.06 Prover 5: Proving ...
% 39.96/6.08 Prover 4: Warning: ignoring some quantifiers
% 41.81/6.34 Prover 4: Constructing countermodel ...
% 42.52/6.47 Prover 0: Proving ...
% 43.69/6.60 Prover 2: Proving ...
% 88.92/12.60 Prover 2: stopped
% 88.92/12.60 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 92.30/13.04 Prover 7: Preprocessing ...
% 99.76/13.97 Prover 5: stopped
% 99.76/13.99 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 100.57/14.09 Prover 7: Warning: ignoring some quantifiers
% 102.03/14.24 Prover 7: Constructing countermodel ...
% 104.23/14.59 Prover 8: Preprocessing ...
% 110.42/15.37 Prover 8: Warning: ignoring some quantifiers
% 111.07/15.47 Prover 8: Constructing countermodel ...
% 114.80/15.97 Prover 1: stopped
% 114.80/15.98 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 118.30/16.41 Prover 9: Preprocessing ...
% 128.83/17.88 Prover 6: stopped
% 128.83/17.88 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 131.34/18.11 Prover 9: Warning: ignoring some quantifiers
% 131.66/18.20 Prover 9: Constructing countermodel ...
% 133.68/18.50 Prover 10: Preprocessing ...
% 138.16/19.03 Prover 10: Warning: ignoring some quantifiers
% 138.58/19.13 Prover 10: Constructing countermodel ...
% 218.80/30.25 Prover 8: Found proof (size 3162)
% 218.80/30.25 Prover 8: proved (16166ms)
% 218.80/30.25 Prover 9: stopped
% 218.80/30.25 Prover 3: stopped
% 219.25/30.26 Prover 7: stopped
% 219.25/30.26 Prover 4: stopped
% 219.28/30.28 Prover 0: stopped
% 219.41/30.35 Prover 10: stopped
% 219.41/30.35
% 219.41/30.35 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 219.41/30.35
% 219.55/30.43 % SZS output start Proof for theBenchmark
% 219.55/30.45 Assumptions after simplification:
% 219.55/30.45 ---------------------------------
% 219.55/30.45
% 219.55/30.45 (conj_0)
% 219.55/30.46 ~ (v_x = v_y) & $i(v_x) & $i(v_y)
% 219.55/30.46
% 219.55/30.46 (conj_1)
% 219.74/30.49 $i(v_L) & $i(tc_Arrow__Order__Mirabelle_Oalt) & ? [v0: $i] :
% 219.74/30.49 (tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt) =
% 219.74/30.49 v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = v1 | ~
% 219.74/30.49 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 219.74/30.49 tc_Arrow__Order__Mirabelle_Oalt, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1)
% 219.74/30.49 | ? [v4: any] : ? [v5: $i] : ? [v6: any] :
% 219.74/30.49 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 219.74/30.49 tc_Arrow__Order__Mirabelle_Oalt, v2, v1) = v5 & c_member(v0, v5, v_L)
% 219.74/30.49 = v6 & c_member(v0, v3, v_L) = v4 & $i(v5) & (v6 = 0 | v4 = 0))) & !
% 219.74/30.49 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 219.74/30.49 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 219.74/30.49 tc_Arrow__Order__Mirabelle_Oalt, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1)
% 219.74/30.49 | ? [v4: int] : ( ~ (v4 = 0) & c_member(v0, v3, v_L) = v4) | ! [v4: $i]
% 219.74/30.49 : ! [v5: $i] : ( ~
% 219.74/30.49 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 219.74/30.49 tc_Arrow__Order__Mirabelle_Oalt, v1, v4) = v5) | ~ $i(v4) | ? [v6:
% 219.74/30.49 $i] : ? [v7: any] : ? [v8: any] :
% 219.74/30.49 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 219.74/30.49 tc_Arrow__Order__Mirabelle_Oalt, v2, v4) = v6 & c_member(v0, v6,
% 219.74/30.49 v_L) = v7 & c_member(v0, v5, v_L) = v8 & $i(v6) & ( ~ (v7 = 0) | v8
% 219.74/30.49 = 0)))) & ! [v1: $i] : ! [v2: $i] : ( ~
% 219.74/30.49 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 219.74/30.49 tc_Arrow__Order__Mirabelle_Oalt, v1, v1) = v2) | ~ $i(v1) | ? [v3:
% 219.74/30.49 int] : ( ~ (v3 = 0) & c_member(v0, v2, v_L) = v3)))
% 219.74/30.49
% 219.74/30.49 (conj_2)
% 219.74/30.50 $i(v_L) & $i(v_x) & $i(v_y) & $i(tc_Arrow__Order__Mirabelle_Oalt) & ? [v0:
% 219.74/30.50 $i] : (tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 219.74/30.50 tc_Arrow__Order__Mirabelle_Oalt) = v0 & $i(v0) & ( ? [v1: $i] : ? [v2:
% 219.74/30.50 $i] : ? [v3: $i] : ? [v4: any] : ? [v5: $i] : ? [v6: any] : ? [v7:
% 219.74/30.50 $i] : ? [v8: any] : ? [v9: $i] : ? [v10: any] : ? [v11: $i] : ?
% 219.74/30.50 [v12: any] : ? [v13: $i] : ? [v14: any] : ( ~ (v2 = v1) &
% 219.74/30.50 c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 219.74/30.50 tc_Arrow__Order__Mirabelle_Oalt, v2, v1) = v9 &
% 219.74/30.50 c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 219.74/30.50 tc_Arrow__Order__Mirabelle_Oalt, v2, v_y) = v11 &
% 219.74/30.50 c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 219.74/30.50 tc_Arrow__Order__Mirabelle_Oalt, v1, v2) = v3 &
% 219.74/30.50 c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 219.74/30.50 tc_Arrow__Order__Mirabelle_Oalt, v1, v_y) = v5 &
% 219.74/30.50 c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 219.74/30.50 tc_Arrow__Order__Mirabelle_Oalt, v_y, v2) = v7 &
% 219.74/30.50 c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 219.74/30.50 tc_Arrow__Order__Mirabelle_Oalt, v_y, v1) = v13 & c_member(v0, v13,
% 219.74/30.50 v_L) = v14 & c_member(v0, v11, v_L) = v12 & c_member(v0, v9, v_L) =
% 219.74/30.50 v10 & c_member(v0, v7, v_L) = v8 & c_member(v0, v5, v_L) = v6 &
% 219.74/30.50 c_member(v0, v3, v_L) = v4 & $i(v13) & $i(v11) & $i(v9) & $i(v7) &
% 219.74/30.50 $i(v5) & $i(v3) & $i(v2) & $i(v1) & ( ~ (v14 = 0) | ~ (v2 = v_x) | v1 =
% 219.74/30.50 v_x) & ( ~ (v12 = 0) | ~ (v1 = v_x) | v2 = v_x) & ( ~ (v10 = 0) | v2
% 219.74/30.50 = v_x | v1 = v_x) & ( ~ (v8 = 0) | ~ (v1 = v_x) | v2 = v_x) & ( ~ (v6
% 219.74/30.50 = 0) | ~ (v2 = v_x) | v1 = v_x) & ( ~ (v4 = 0) | v2 = v_x | v1 =
% 219.74/30.50 v_x) & ( ~ (v2 = v_x) | ~ (v1 = v_y)) & ( ~ (v2 = v_y) | ~ (v1 =
% 219.74/30.50 v_x))) | ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: any] : ?
% 219.74/30.50 [v5: $i] : ? [v6: any] : ? [v7: $i] : ? [v8: any] : ? [v9: $i] : ?
% 219.74/30.50 [v10: any] : (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 219.74/30.50 tc_Arrow__Order__Mirabelle_Oalt, v2, v_y) = v5 &
% 219.74/30.50 c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 219.74/30.50 tc_Arrow__Order__Mirabelle_Oalt, v1, v2) = v3 &
% 219.74/30.50 c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 219.74/30.50 tc_Arrow__Order__Mirabelle_Oalt, v1, v_y) = v7 &
% 219.74/30.50 c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 219.74/30.50 tc_Arrow__Order__Mirabelle_Oalt, v_y, v2) = v9 & c_member(v0, v9, v_L)
% 219.74/30.50 = v10 & c_member(v0, v7, v_L) = v8 & c_member(v0, v5, v_L) = v6 &
% 219.74/30.50 c_member(v0, v3, v_L) = v4 & $i(v9) & $i(v7) & $i(v5) & $i(v3) & $i(v2)
% 219.74/30.50 & $i(v1) & ((v10 = 0 & v1 = v_x & ~ (v2 = v_x) & ? [v11: $i] : ?
% 219.74/30.50 [v12: $i] : ? [v13: any] : ? [v14: $i] : ? [v15: any] :
% 219.74/30.50 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 219.74/30.50 tc_Arrow__Order__Mirabelle_Oalt, v2, v11) = v12 &
% 219.74/30.50 c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 219.74/30.50 tc_Arrow__Order__Mirabelle_Oalt, v_y, v11) = v14 & c_member(v0,
% 219.74/30.50 v14, v_L) = v15 & c_member(v0, v12, v_L) = v13 & $i(v14) &
% 219.74/30.50 $i(v12) & $i(v11) & ((v13 = 0 & ~ (v15 = 0) & ~ (v11 = v_x) & ~
% 219.74/30.50 (v11 = v_y)) | (v11 = v_x & v6 = 0)))) | ( ~ (v1 = v_x) & ((v8
% 219.74/30.50 = 0 & v2 = v_x & ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ?
% 219.74/30.50 [v14: int] : ( ~ (v14 = 0) & ~ (v11 = v_x) &
% 219.74/30.50 c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 219.74/30.50 tc_Arrow__Order__Mirabelle_Oalt, v1, v11) = v13 &
% 219.74/30.50 c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 219.74/30.50 tc_Arrow__Order__Mirabelle_Oalt, v_y, v11) = v12 &
% 219.74/30.50 c_member(v0, v13, v_L) = v14 & c_member(v0, v12, v_L) = 0 &
% 219.74/30.50 $i(v13) & $i(v12) & $i(v11))) | (v4 = 0 & ~ (v2 = v_x) & ?
% 219.74/30.50 [v11: $i] : ? [v12: $i] : ? [v13: any] : ? [v14: $i] : ?
% 219.74/30.50 [v15: any] :
% 219.74/30.50 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 219.74/30.50 tc_Arrow__Order__Mirabelle_Oalt, v2, v11) = v12 &
% 219.74/30.50 c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 219.74/30.50 tc_Arrow__Order__Mirabelle_Oalt, v1, v11) = v14 &
% 219.74/30.50 c_member(v0, v14, v_L) = v15 & c_member(v0, v12, v_L) = v13 &
% 219.74/30.50 $i(v14) & $i(v12) & $i(v11) & ((v13 = 0 & ~ (v15 = 0) & ~
% 219.74/30.50 (v11 = v_x)) | (v11 = v_x & v6 = 0 & ~ (v8 = 0)))))))))))
% 219.74/30.50
% 219.74/30.50 (fact_Lin__irrefl)
% 219.74/30.51 $i(c_Arrow__Order__Mirabelle_OLin) & $i(tc_HOL_Obool) &
% 219.74/30.51 $i(tc_Arrow__Order__Mirabelle_Oalt) & ? [v0: $i] : ? [v1: $i] : (tc_fun(v0,
% 219.74/30.51 tc_HOL_Obool) = v1 & tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 219.74/30.51 tc_Arrow__Order__Mirabelle_Oalt) = v0 & $i(v1) & $i(v0) & ! [v2: $i] : !
% 219.74/30.51 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 219.74/30.51 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 219.74/30.51 tc_Arrow__Order__Mirabelle_Oalt, v2, v3) = v5) | ~ (c_member(v0, v5,
% 219.74/30.51 v4) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v6: any] : ? [v7:
% 219.74/30.51 $i] : ? [v8: any] :
% 219.74/30.51 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 219.74/30.51 tc_Arrow__Order__Mirabelle_Oalt, v3, v2) = v7 & c_member(v1, v4,
% 219.74/30.51 c_Arrow__Order__Mirabelle_OLin) = v6 & c_member(v0, v7, v4) = v8 &
% 219.74/30.51 $i(v7) & ( ~ (v8 = 0) | ~ (v6 = 0)))))
% 219.74/30.51
% 219.74/30.51 (fact_antisymD)
% 219.74/30.51 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 219.74/30.51 $i] : (v1 = v0 | ~ (tc_prod(v3, v3) = v4) | ~ (c_Product__Type_OPair(v3,
% 219.74/30.51 v3, v0, v1) = v5) | ~ (c_member(v4, v5, v2) = 0) | ~ $i(v3) | ~
% 219.74/30.51 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: $i] : ? [v8: any] :
% 219.74/30.51 (c_Relation_Oantisym(v3, v2) = v6 & c_Product__Type_OPair(v3, v3, v1, v0) =
% 219.74/30.51 v7 & c_member(v4, v7, v2) = v8 & $i(v7) & ( ~ (v8 = 0) | ~ (v6 = 0))))
% 219.74/30.51
% 219.74/30.51 (fact_converse__in__Lin)
% 219.74/30.51 $i(c_Arrow__Order__Mirabelle_OLin) & $i(tc_HOL_Obool) &
% 219.74/30.51 $i(tc_Arrow__Order__Mirabelle_Oalt) & ? [v0: $i] : ? [v1: $i] : (tc_fun(v0,
% 219.74/30.51 tc_HOL_Obool) = v1 & tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 219.74/30.51 tc_Arrow__Order__Mirabelle_Oalt) = v0 & $i(v1) & $i(v0) & ! [v2: $i] : !
% 219.74/30.51 [v3: int] : (v3 = 0 | ~ (c_member(v1, v2, c_Arrow__Order__Mirabelle_OLin) =
% 219.74/30.51 v3) | ~ $i(v2) | ? [v4: $i] : ? [v5: int] : ( ~ (v5 = 0) &
% 219.74/30.51 c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,
% 219.74/30.51 tc_Arrow__Order__Mirabelle_Oalt, v2) = v4 & c_member(v1, v4,
% 219.74/30.51 c_Arrow__Order__Mirabelle_OLin) = v5 & $i(v4))) & ! [v2: $i] : ( ~
% 219.74/30.51 (c_member(v1, v2, c_Arrow__Order__Mirabelle_OLin) = 0) | ~ $i(v2) | ?
% 219.74/30.51 [v3: $i] : (c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,
% 219.74/30.51 tc_Arrow__Order__Mirabelle_Oalt, v2) = v3 & c_member(v1, v3,
% 219.74/30.51 c_Arrow__Order__Mirabelle_OLin) = 0 & $i(v3))))
% 219.74/30.51
% 219.74/30.51 (fact_in__above)
% 219.74/30.51 $i(c_Arrow__Order__Mirabelle_OLin) & $i(tc_HOL_Obool) &
% 219.74/30.51 $i(tc_Arrow__Order__Mirabelle_Oalt) & ? [v0: $i] : ? [v1: $i] : (tc_fun(v0,
% 219.74/30.51 tc_HOL_Obool) = v1 & tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 219.74/30.51 tc_Arrow__Order__Mirabelle_Oalt) = v0 & $i(v1) & $i(v0) & ! [v2: $i] : !
% 219.74/30.51 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8:
% 219.74/30.51 $i] : ! [v9: any] : (v6 = v5 | ~ (c_Arrow__Order__Mirabelle_Oabove(v4,
% 219.74/30.51 v6, v5) = v8) | ~
% 219.74/30.51 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 219.74/30.51 tc_Arrow__Order__Mirabelle_Oalt, v3, v2) = v7) | ~ (c_member(v0, v7,
% 219.74/30.51 v8) = v9) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2)
% 219.74/30.51 | ? [v10: any] : ? [v11: $i] : ? [v12: any] : ? [v13: $i] : ? [v14:
% 219.74/30.51 any] : ? [v15: any] :
% 219.74/30.51 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 219.74/30.51 tc_Arrow__Order__Mirabelle_Oalt, v6, v2) = v11 &
% 219.74/30.51 c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 219.74/30.51 tc_Arrow__Order__Mirabelle_Oalt, v3, v6) = v13 & c_member(v1, v4,
% 219.74/30.51 c_Arrow__Order__Mirabelle_OLin) = v10 & c_member(v0, v13, v4) = v14 &
% 219.74/30.51 c_member(v0, v11, v4) = v12 & c_member(v0, v7, v4) = v15 & $i(v13) &
% 219.74/30.51 $i(v11) & ( ~ (v10 = 0) | (( ~ (v9 = 0) | ( ~ (v3 = v2) & ( ~ (v5 = v3)
% 219.74/30.51 | v12 = 0) & (v5 = v3 | (( ~ (v5 = v2) | v14 = 0 | v6 = v3) &
% 219.74/30.51 (v15 = 0 | v5 = v2))))) & (v9 = 0 | v3 = v2 | (v5 = v3 & ~
% 219.74/30.51 (v12 = 0)) | ( ~ (v5 = v3) & ((v5 = v2 & ~ (v14 = 0) & ~ (v6 =
% 219.74/30.51 v3)) | ( ~ (v15 = 0) & ~ (v5 = v2))))))))))
% 219.74/30.51
% 219.74/30.51 (fact_in__below)
% 219.74/30.52 $i(c_Arrow__Order__Mirabelle_OLin) & $i(tc_HOL_Obool) &
% 219.74/30.52 $i(tc_Arrow__Order__Mirabelle_Oalt) & ? [v0: $i] : ? [v1: $i] : (tc_fun(v0,
% 219.74/30.52 tc_HOL_Obool) = v1 & tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 219.74/30.52 tc_Arrow__Order__Mirabelle_Oalt) = v0 & $i(v1) & $i(v0) & ! [v2: $i] : !
% 219.74/30.52 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8:
% 219.74/30.52 $i] : ! [v9: any] : (v6 = v5 | ~ (c_Arrow__Order__Mirabelle_Obelow(v4,
% 219.74/30.52 v6, v5) = v8) | ~
% 219.74/30.52 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 219.74/30.52 tc_Arrow__Order__Mirabelle_Oalt, v3, v2) = v7) | ~ (c_member(v0, v7,
% 219.74/30.52 v8) = v9) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2)
% 219.74/30.52 | ? [v10: any] : ? [v11: $i] : ? [v12: any] : ? [v13: $i] : ? [v14:
% 219.74/30.52 any] : ? [v15: any] :
% 219.74/30.52 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 219.74/30.52 tc_Arrow__Order__Mirabelle_Oalt, v5, v2) = v13 &
% 219.74/30.52 c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 219.74/30.52 tc_Arrow__Order__Mirabelle_Oalt, v3, v5) = v11 & c_member(v1, v4,
% 219.74/30.52 c_Arrow__Order__Mirabelle_OLin) = v10 & c_member(v0, v13, v4) = v14 &
% 219.74/30.52 c_member(v0, v11, v4) = v12 & c_member(v0, v7, v4) = v15 & $i(v13) &
% 219.74/30.52 $i(v11) & ( ~ (v10 = 0) | (( ~ (v9 = 0) | ( ~ (v3 = v2) & ( ~ (v6 = v2)
% 219.74/30.52 | v12 = 0) & (v6 = v2 | (( ~ (v6 = v3) | v14 = 0 | v5 = v2) &
% 219.74/30.52 (v15 = 0 | v6 = v3))))) & (v9 = 0 | v3 = v2 | (v6 = v2 & ~
% 219.74/30.52 (v12 = 0)) | ( ~ (v6 = v2) & ((v6 = v3 & ~ (v14 = 0) & ~ (v5 =
% 219.74/30.52 v2)) | ( ~ (v15 = 0) & ~ (v6 = v3))))))))))
% 219.74/30.52
% 219.74/30.52 (fact_in__mkbot)
% 219.74/30.52 $i(tc_Arrow__Order__Mirabelle_Oalt) & ? [v0: $i] :
% 219.74/30.52 (tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt) =
% 219.74/30.52 v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 219.74/30.52 [v5: $i] : ! [v6: $i] : ! [v7: int] : (v7 = 0 | v3 = v1 | ~
% 219.74/30.52 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 219.74/30.52 tc_Arrow__Order__Mirabelle_Oalt, v4, v3) = v5) | ~
% 219.74/30.52 (c_Arrow__Order__Mirabelle_Omkbot(v2, v1) = v6) | ~ (c_member(v0, v5, v6)
% 219.74/30.52 = v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ( ~ (v4 = v1) &
% 219.74/30.52 ? [v8: int] : ( ~ (v8 = 0) & c_member(v0, v5, v2) = v8))) & ! [v1: $i]
% 219.74/30.52 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 219.74/30.52 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 219.74/30.52 tc_Arrow__Order__Mirabelle_Oalt, v4, v3) = v5) | ~
% 219.74/30.52 (c_Arrow__Order__Mirabelle_Omkbot(v2, v1) = v6) | ~ (c_member(v0, v5, v6)
% 219.74/30.52 = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ( ~ (v3 = v1) &
% 219.74/30.52 (v4 = v1 | c_member(v0, v5, v2) = 0))))
% 219.74/30.52
% 219.74/30.52 (fact_in__mktop)
% 219.74/30.52 $i(tc_Arrow__Order__Mirabelle_Oalt) & ? [v0: $i] :
% 219.74/30.52 (tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt) =
% 219.74/30.52 v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 219.74/30.52 [v5: $i] : ! [v6: $i] : ! [v7: int] : (v7 = 0 | v4 = v1 | ~
% 219.74/30.52 (c_Arrow__Order__Mirabelle_Omktop(v2, v1) = v6) | ~
% 219.74/30.52 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 219.74/30.52 tc_Arrow__Order__Mirabelle_Oalt, v4, v3) = v5) | ~ (c_member(v0, v5,
% 219.74/30.52 v6) = v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ( ~ (v3 =
% 219.74/30.52 v1) & ? [v8: int] : ( ~ (v8 = 0) & c_member(v0, v5, v2) = v8))) & !
% 219.74/30.52 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6:
% 219.74/30.52 $i] : ( ~ (c_Arrow__Order__Mirabelle_Omktop(v2, v1) = v6) | ~
% 219.74/30.52 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 219.74/30.52 tc_Arrow__Order__Mirabelle_Oalt, v4, v3) = v5) | ~ (c_member(v0, v5,
% 219.74/30.52 v6) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ( ~ (v4 =
% 219.74/30.52 v1) & (v3 = v1 | c_member(v0, v5, v2) = 0))))
% 219.74/30.52
% 219.74/30.52 (fact_linear__alt)
% 219.74/30.52 $i(c_Arrow__Order__Mirabelle_OLin) & $i(tc_HOL_Obool) &
% 219.74/30.52 $i(tc_Arrow__Order__Mirabelle_Oalt) & ? [v0: $i] : ? [v1: $i] : (tc_fun(v0,
% 219.74/30.52 tc_HOL_Obool) = v1 & tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 219.74/30.52 tc_Arrow__Order__Mirabelle_Oalt) = v0 & $i(v1) & $i(v0) & ? [v2: $i] :
% 219.74/30.52 (c_member(v1, v2, c_Arrow__Order__Mirabelle_OLin) = 0 & $i(v2)))
% 219.74/30.52
% 219.74/30.52 (fact_mem__def)
% 219.74/30.53 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 219.74/30.53 (c_member(v2, v1, v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 219.74/30.53 $i] : ? [v5: int] : ( ~ (v5 = 0) & hBOOL(v4) = v5 & hAPP(v0, v1) = v4 &
% 219.74/30.53 $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (c_member(v2, v1,
% 219.74/30.53 v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (hBOOL(v3)
% 219.74/30.53 = 0 & hAPP(v0, v1) = v3 & $i(v3)))
% 219.74/30.53
% 219.74/30.53 (fact_mkbot__Lin)
% 219.74/30.53 $i(c_Arrow__Order__Mirabelle_OLin) & $i(tc_HOL_Obool) &
% 219.74/30.53 $i(tc_Arrow__Order__Mirabelle_Oalt) & ? [v0: $i] : ? [v1: $i] : (tc_fun(v0,
% 219.74/30.53 tc_HOL_Obool) = v1 & tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 219.74/30.53 tc_Arrow__Order__Mirabelle_Oalt) = v0 & $i(v1) & $i(v0) & ! [v2: $i] : !
% 219.74/30.53 [v3: $i] : ! [v4: $i] : ( ~ (c_Arrow__Order__Mirabelle_Omkbot(v3, v2) = v4)
% 219.74/30.53 | ~ $i(v3) | ~ $i(v2) | ? [v5: any] : ? [v6: any] : (c_member(v1, v4,
% 219.74/30.53 c_Arrow__Order__Mirabelle_OLin) = v6 & c_member(v1, v3,
% 219.74/30.53 c_Arrow__Order__Mirabelle_OLin) = v5 & ( ~ (v5 = 0) | v6 = 0))))
% 219.74/30.53
% 219.74/30.53 (fact_mktop__Lin)
% 219.74/30.53 $i(c_Arrow__Order__Mirabelle_OLin) & $i(tc_HOL_Obool) &
% 219.74/30.53 $i(tc_Arrow__Order__Mirabelle_Oalt) & ? [v0: $i] : ? [v1: $i] : (tc_fun(v0,
% 219.74/30.53 tc_HOL_Obool) = v1 & tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 219.74/30.53 tc_Arrow__Order__Mirabelle_Oalt) = v0 & $i(v1) & $i(v0) & ! [v2: $i] : !
% 219.74/30.53 [v3: $i] : ! [v4: $i] : ( ~ (c_Arrow__Order__Mirabelle_Omktop(v3, v2) = v4)
% 219.74/30.53 | ~ $i(v3) | ~ $i(v2) | ? [v5: any] : ? [v6: any] : (c_member(v1, v4,
% 219.74/30.53 c_Arrow__Order__Mirabelle_OLin) = v6 & c_member(v1, v3,
% 219.74/30.53 c_Arrow__Order__Mirabelle_OLin) = v5 & ( ~ (v5 = 0) | v6 = 0))))
% 219.74/30.53
% 219.74/30.53 (fact_notin__Lin__iff)
% 219.74/30.53 $i(c_Arrow__Order__Mirabelle_OLin) & $i(tc_HOL_Obool) &
% 219.74/30.53 $i(tc_Arrow__Order__Mirabelle_Oalt) & ? [v0: $i] : ? [v1: $i] : (tc_fun(v0,
% 219.74/30.53 tc_HOL_Obool) = v1 & tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 219.74/30.53 tc_Arrow__Order__Mirabelle_Oalt) = v0 & $i(v1) & $i(v0) & ! [v2: $i] : !
% 219.74/30.53 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: any] : (v3 = v2 | ~
% 219.74/30.53 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 219.74/30.53 tc_Arrow__Order__Mirabelle_Oalt, v2, v3) = v5) | ~ (c_member(v0, v5,
% 219.74/30.53 v4) = v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v7: any] : ? [v8:
% 219.74/30.53 $i] : ? [v9: any] :
% 219.74/30.53 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 219.74/30.53 tc_Arrow__Order__Mirabelle_Oalt, v3, v2) = v8 & c_member(v1, v4,
% 219.74/30.53 c_Arrow__Order__Mirabelle_OLin) = v7 & c_member(v0, v8, v4) = v9 &
% 219.74/30.53 $i(v8) & ( ~ (v7 = 0) | (( ~ (v9 = 0) | ~ (v6 = 0)) & (v9 = 0 | v6 =
% 219.74/30.53 0))))))
% 219.74/30.53
% 219.74/30.53 (fact_single__valuedD)
% 219.74/30.53 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 219.74/30.53 $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : (v1 = v0 | ~ (tc_prod(v5,
% 219.74/30.53 v4) = v6) | ~ (c_Product__Type_OPair(v5, v4, v2, v1) = v7) | ~
% 219.74/30.53 (c_Product__Type_OPair(v5, v4, v2, v0) = v8) | ~ (c_member(v6, v8, v3) = 0)
% 219.74/30.53 | ~ (c_member(v6, v7, v3) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~
% 219.74/30.53 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v9: int] : ( ~ (v9 = 0) &
% 219.74/30.53 c_Relation_Osingle__valued(v5, v4, v3) = v9))
% 219.74/30.53
% 219.74/30.53 (fact_transD)
% 219.74/30.53 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 219.74/30.53 $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: int] : (v8 = 0 | ~ (tc_prod(v4,
% 219.74/30.53 v4) = v5) | ~ (c_Product__Type_OPair(v4, v4, v2, v0) = v7) | ~
% 219.74/30.53 (c_Product__Type_OPair(v4, v4, v1, v0) = v6) | ~ (c_member(v5, v7, v3) =
% 219.74/30.53 v8) | ~ (c_member(v5, v6, v3) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) |
% 219.74/30.53 ~ $i(v1) | ~ $i(v0) | ? [v9: any] : ? [v10: $i] : ? [v11: any] :
% 219.74/30.53 (c_Relation_Otrans(v4, v3) = v9 & c_Product__Type_OPair(v4, v4, v2, v1) =
% 219.74/30.53 v10 & c_member(v5, v10, v3) = v11 & $i(v10) & ( ~ (v11 = 0) | ~ (v9 =
% 219.74/30.54 0))))
% 219.74/30.54
% 219.74/30.54 (fact_wf__asym)
% 219.74/30.54 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 219.74/30.54 $i] : ( ~ (tc_prod(v3, v3) = v4) | ~ (c_Product__Type_OPair(v3, v3, v0, v1)
% 219.74/30.54 = v5) | ~ (c_member(v4, v5, v2) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1)
% 219.74/30.54 | ~ $i(v0) | ? [v6: any] : ? [v7: $i] : ? [v8: any] :
% 219.74/30.54 (c_Wellfounded_Owf(v3, v2) = v6 & c_Product__Type_OPair(v3, v3, v1, v0) = v7
% 219.74/30.54 & c_member(v4, v7, v2) = v8 & $i(v7) & ( ~ (v8 = 0) | ~ (v6 = 0))))
% 219.74/30.54
% 219.74/30.54 (fact_wf__not__sym)
% 219.74/30.54 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 219.74/30.54 $i] : ( ~ (tc_prod(v3, v3) = v4) | ~ (c_Product__Type_OPair(v3, v3, v0, v1)
% 219.74/30.54 = v5) | ~ (c_member(v4, v5, v2) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1)
% 219.74/30.54 | ~ $i(v0) | ? [v6: any] : ? [v7: $i] : ? [v8: any] :
% 219.74/30.54 (c_Wellfounded_Owf(v3, v2) = v6 & c_Product__Type_OPair(v3, v3, v1, v0) = v7
% 219.74/30.54 & c_member(v4, v7, v2) = v8 & $i(v7) & ( ~ (v8 = 0) | ~ (v6 = 0))))
% 219.74/30.54
% 219.74/30.54 (function-axioms)
% 220.15/30.58 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 220.15/30.58 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v1 = v0 |
% 220.15/30.58 ~ (c_Nitpick_Ofold__graph_H(v7, v6, v5, v4, v3, v2) = v1) | ~
% 220.15/30.58 (c_Nitpick_Ofold__graph_H(v7, v6, v5, v4, v3, v2) = v0)) & ! [v0: $i] : !
% 220.15/30.58 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i]
% 220.15/30.58 : ! [v7: $i] : (v1 = v0 | ~ (c_Product__Type_Ocurry(v7, v6, v5, v4, v3, v2)
% 220.15/30.58 = v1) | ~ (c_Product__Type_Ocurry(v7, v6, v5, v4, v3, v2) = v0)) & !
% 220.15/30.59 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 220.15/30.59 $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v1 = v0 | ~
% 220.15/30.59 (c_Recdef_Owfrec__rel(v7, v6, v5, v4, v3, v2) = v1) | ~
% 220.15/30.59 (c_Recdef_Owfrec__rel(v7, v6, v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 220.15/30.59 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] :
% 220.15/30.59 (v1 = v0 | ~ (c_Nitpick_Owf__wfrec_H(v6, v5, v4, v3, v2) = v1) | ~
% 220.15/30.59 (c_Nitpick_Owf__wfrec_H(v6, v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 220.15/30.59 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] :
% 220.15/30.59 (v1 = v0 | ~ (c_Recdef_Ocut(v6, v5, v4, v3, v2) = v1) | ~ (c_Recdef_Ocut(v6,
% 220.15/30.59 v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 220.15/30.59 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~
% 220.15/30.59 (c_Product__Type_Ointernal__split(v6, v5, v4, v3, v2) = v1) | ~
% 220.15/30.59 (c_Product__Type_Ointernal__split(v6, v5, v4, v3, v2) = v0)) & ! [v0: $i] :
% 220.15/30.59 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6:
% 220.15/30.59 $i] : (v1 = v0 | ~ (c_Product__Type_Oprod_Oprod__rec(v6, v5, v4, v3, v2) =
% 220.15/30.59 v1) | ~ (c_Product__Type_Oprod_Oprod__rec(v6, v5, v4, v3, v2) = v0)) & !
% 220.15/30.59 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i]
% 220.15/30.59 : (v1 = v0 | ~ (c_Relation_OImage(v5, v4, v3, v2) = v1) | ~
% 220.15/30.59 (c_Relation_OImage(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 220.15/30.59 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~
% 220.15/30.59 (c_Recdef_Owfrec(v5, v4, v3, v2) = v1) | ~ (c_Recdef_Owfrec(v5, v4, v3, v2)
% 220.15/30.59 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 220.15/30.59 $i] : ! [v5: $i] : (v1 = v0 | ~ (c_Product__Type_OSigma(v5, v4, v3, v2) =
% 220.15/30.59 v1) | ~ (c_Product__Type_OSigma(v5, v4, v3, v2) = v0)) & ! [v0: $i] : !
% 220.15/30.59 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 |
% 220.15/30.59 ~ (c_Nitpick_Owf__wfrec(v5, v4, v3, v2) = v1) | ~ (c_Nitpick_Owf__wfrec(v5,
% 220.15/30.59 v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 220.15/30.59 $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~
% 220.15/30.59 (c_Wellfounded_Olex__prod(v5, v4, v3, v2) = v1) | ~
% 220.15/30.59 (c_Wellfounded_Olex__prod(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 220.15/30.59 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~
% 220.15/30.59 (c_Recdef_Osame__fst(v5, v4, v3, v2) = v1) | ~ (c_Recdef_Osame__fst(v5, v4,
% 220.15/30.59 v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 220.15/30.59 ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (c_Product__Type_OPair(v5, v4, v3,
% 220.15/30.59 v2) = v1) | ~ (c_Product__Type_OPair(v5, v4, v3, v2) = v0)) & ! [v0:
% 220.15/30.59 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 220.15/30.59 : ! [v4: $i] : (v1 = v0 | ~ (c_Equiv__Relations_Oequiv(v4, v3, v2) = v1) |
% 220.15/30.59 ~ (c_Equiv__Relations_Oequiv(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 220.15/30.59 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 220.15/30.59 (c_Lattices_Osemilattice__inf__class_Oinf(v4, v3, v2) = v1) | ~
% 220.15/30.59 (c_Lattices_Osemilattice__inf__class_Oinf(v4, v3, v2) = v0)) & ! [v0:
% 220.15/30.59 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 220.15/30.59 : ! [v4: $i] : (v1 = v0 | ~ (c_Orderings_Oord__class_Oless__eq(v4, v3, v2) =
% 220.15/30.59 v1) | ~ (c_Orderings_Oord__class_Oless__eq(v4, v3, v2) = v0)) & ! [v0:
% 220.15/30.59 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 220.15/30.59 (c_Wellfounded_Omlex__prod(v4, v3, v2) = v1) | ~
% 220.15/30.59 (c_Wellfounded_Omlex__prod(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] :
% 220.15/30.59 ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 =
% 220.15/30.59 v0 | ~ (c_Orderings_Oord__class_Oless(v4, v3, v2) = v1) | ~
% 220.15/30.59 (c_Orderings_Oord__class_Oless(v4, v3, v2) = v0)) & ! [v0:
% 220.15/30.59 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 220.15/30.59 : ! [v4: $i] : (v1 = v0 | ~ (c_Order__Relation_Opartial__order__on(v4, v3,
% 220.15/30.59 v2) = v1) | ~ (c_Order__Relation_Opartial__order__on(v4, v3, v2) = v0))
% 220.15/30.59 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 220.15/30.59 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (c_Order__Relation_Owell__order__on(v4,
% 220.15/30.59 v3, v2) = v1) | ~ (c_Order__Relation_Owell__order__on(v4, v3, v2) =
% 220.15/30.59 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 220.15/30.59 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 220.15/30.59 (c_Order__Relation_Opreorder__on(v4, v3, v2) = v1) | ~
% 220.15/30.59 (c_Order__Relation_Opreorder__on(v4, v3, v2) = v0)) & ! [v0:
% 220.15/30.59 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 220.15/30.59 : ! [v4: $i] : (v1 = v0 | ~ (c_Order__Relation_Olinear__order__on(v4, v3,
% 220.15/30.59 v2) = v1) | ~ (c_Order__Relation_Olinear__order__on(v4, v3, v2) = v0))
% 220.15/30.59 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 220.15/30.59 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 220.15/30.59 (c_Order__Relation_Ostrict__linear__order__on(v4, v3, v2) = v1) | ~
% 220.15/30.59 (c_Order__Relation_Ostrict__linear__order__on(v4, v3, v2) = v0)) & ! [v0:
% 220.15/30.59 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 220.15/30.59 (c_Groups_Ominus__class_Ominus(v4, v3, v2) = v1) | ~
% 220.15/30.59 (c_Groups_Ominus__class_Ominus(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 220.15/30.59 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 220.15/30.59 (c_Lattices_Osemilattice__sup__class_Osup(v4, v3, v2) = v1) | ~
% 220.15/30.59 (c_Lattices_Osemilattice__sup__class_Osup(v4, v3, v2) = v0)) & ! [v0: $i] :
% 220.15/30.59 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 220.15/30.59 (c_Set_Oinsert(v4, v3, v2) = v1) | ~ (c_Set_Oinsert(v4, v3, v2) = v0)) & !
% 220.15/30.59 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 220.15/30.59 $i] : ! [v4: $i] : (v1 = v0 | ~ (c_Relation_Orefl__on(v4, v3, v2) = v1) |
% 220.15/30.59 ~ (c_Relation_Orefl__on(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 220.15/30.59 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 220.15/30.59 (c_Relation_Oinv__image(v4, v3, v2) = v1) | ~ (c_Relation_Oinv__image(v4,
% 220.15/30.59 v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool]
% 220.15/30.59 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 220.15/30.59 (c_Relation_Ototal__on(v4, v3, v2) = v1) | ~ (c_Relation_Ototal__on(v4, v3,
% 220.15/30.59 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : !
% 220.15/30.59 [v4: $i] : (v1 = v0 | ~ (c_Relation_ODomain(v4, v3, v2) = v1) | ~
% 220.15/30.59 (c_Relation_ODomain(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 220.15/30.59 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 |
% 220.15/30.59 ~ (c_Relation_Osingle__valued(v4, v3, v2) = v1) | ~
% 220.15/30.59 (c_Relation_Osingle__valued(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 220.15/30.59 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (c_Relation_ORange(v4,
% 220.15/30.59 v3, v2) = v1) | ~ (c_Relation_ORange(v4, v3, v2) = v0)) & ! [v0: $i] :
% 220.15/30.59 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 220.15/30.59 (c_Relation_Oconverse(v4, v3, v2) = v1) | ~ (c_Relation_Oconverse(v4, v3,
% 220.15/30.59 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : !
% 220.15/30.59 [v4: $i] : (v1 = v0 | ~ (c_Arrow__Order__Mirabelle_Obelow(v4, v3, v2) = v1) |
% 220.15/30.59 ~ (c_Arrow__Order__Mirabelle_Obelow(v4, v3, v2) = v0)) & ! [v0: $i] : !
% 220.15/30.59 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 220.15/30.59 (c_Arrow__Order__Mirabelle_Oabove(v4, v3, v2) = v1) | ~
% 220.15/30.59 (c_Arrow__Order__Mirabelle_Oabove(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 220.15/30.59 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 220.15/30.59 (c_FunDef_Oin__rel(v4, v3, v2) = v1) | ~ (c_FunDef_Oin__rel(v4, v3, v2) =
% 220.15/30.59 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 220.15/30.59 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (c_member(v4, v3, v2) = v1)
% 220.15/30.59 | ~ (c_member(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 220.15/30.59 : ! [v3: $i] : (v1 = v0 | ~ (c_Set_Othe__elem(v3, v2) = v1) | ~
% 220.15/30.59 (c_Set_Othe__elem(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 220.15/30.59 ! [v3: $i] : (v1 = v0 | ~ (c_Relation_OField(v3, v2) = v1) | ~
% 220.15/30.59 (c_Relation_OField(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 220.15/30.59 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 220.15/30.59 (c_Wellfounded_OwfP(v3, v2) = v1) | ~ (c_Wellfounded_OwfP(v3, v2) = v0)) &
% 220.15/30.59 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 220.15/30.59 $i] : (v1 = v0 | ~ (c_Wellfounded_Owf(v3, v2) = v1) | ~
% 220.15/30.59 (c_Wellfounded_Owf(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 220.15/30.59 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 220.15/30.59 (c_Relation_Otrans(v3, v2) = v1) | ~ (c_Relation_Otrans(v3, v2) = v0)) & !
% 220.15/30.59 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 220.15/30.59 $i] : (v1 = v0 | ~ (c_Wellfounded_Oacyclic(v3, v2) = v1) | ~
% 220.15/30.59 (c_Wellfounded_Oacyclic(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 220.15/30.59 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 220.15/30.59 (c_Relation_Oantisym(v3, v2) = v1) | ~ (c_Relation_Oantisym(v3, v2) = v0))
% 220.15/30.59 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 220.15/30.59 (c_Transitive__Closure_Otrancl(v3, v2) = v1) | ~
% 220.15/30.59 (c_Transitive__Closure_Otrancl(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 220.15/30.59 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (c_Relation_OId__on(v3, v2) = v1) |
% 220.15/30.59 ~ (c_Relation_OId__on(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 220.15/30.59 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 220.15/30.59 (c_Relation_Oirrefl(v3, v2) = v1) | ~ (c_Relation_Oirrefl(v3, v2) = v0)) &
% 220.15/30.59 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 220.15/30.59 (c_Transitive__Closure_Ortrancl(v3, v2) = v1) | ~
% 220.15/30.59 (c_Transitive__Closure_Ortrancl(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 220.15/30.59 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (c_Wellfounded_Oacc(v3, v2) = v1) |
% 220.15/30.59 ~ (c_Wellfounded_Oacc(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 220.15/30.59 $i] : ! [v3: $i] : (v1 = v0 | ~ (tc_fun(v3, v2) = v1) | ~ (tc_fun(v3, v2)
% 220.15/30.59 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 220.15/30.59 $i] : ! [v3: $i] : (v1 = v0 | ~ (c_Nitpick_Orefl_H(v3, v2) = v1) | ~
% 220.15/30.59 (c_Nitpick_Orefl_H(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 220.15/30.59 : ! [v3: $i] : (v1 = v0 | ~ (c_Arrow__Order__Mirabelle_Omktop(v3, v2) = v1)
% 220.15/30.59 | ~ (c_Arrow__Order__Mirabelle_Omktop(v3, v2) = v0)) & ! [v0: $i] : !
% 220.15/30.59 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tc_prod(v3, v2) = v1) |
% 220.15/30.59 ~ (tc_prod(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 220.15/30.59 [v3: $i] : (v1 = v0 | ~ (c_Arrow__Order__Mirabelle_Omkbot(v3, v2) = v1) | ~
% 220.15/30.59 (c_Arrow__Order__Mirabelle_Omkbot(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 220.15/30.59 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP(v3, v2) = v1) | ~ (hAPP(v3,
% 220.15/30.59 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 220.15/30.59 ! [v2: $i] : (v1 = v0 | ~ (class_Lattices_Obounded__lattice(v2) = v1) | ~
% 220.15/30.59 (class_Lattices_Obounded__lattice(v2) = v0)) & ! [v0: MultipleValueBool] :
% 220.15/30.59 ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~
% 220.15/30.59 (class_Lattices_Osemilattice__inf(v2) = v1) | ~
% 220.15/30.59 (class_Lattices_Osemilattice__inf(v2) = v0)) & ! [v0: MultipleValueBool] :
% 220.15/30.59 ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~
% 220.15/30.59 (class_Orderings_Oord(v2) = v1) | ~ (class_Orderings_Oord(v2) = v0)) & !
% 220.15/30.59 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0
% 220.15/30.59 | ~ (class_Orderings_Oorder(v2) = v1) | ~ (class_Orderings_Oorder(v2) =
% 220.15/30.59 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 220.15/30.59 $i] : (v1 = v0 | ~ (class_Orderings_Olinorder(v2) = v1) | ~
% 220.15/30.59 (class_Orderings_Olinorder(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 220.15/30.59 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~
% 220.15/30.59 (class_Orderings_Opreorder(v2) = v1) | ~ (class_Orderings_Opreorder(v2) =
% 220.15/30.59 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 220.15/30.59 $i] : (v1 = v0 | ~ (class_Orderings_Obot(v2) = v1) | ~
% 220.15/30.59 (class_Orderings_Obot(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 220.15/30.59 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~
% 220.15/30.59 (class_Groups_Oab__group__add(v2) = v1) | ~
% 220.15/30.59 (class_Groups_Oab__group__add(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 220.15/30.59 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~
% 220.15/30.59 (class_Lattices_Obounded__lattice__bot(v2) = v1) | ~
% 220.15/30.59 (class_Lattices_Obounded__lattice__bot(v2) = v0)) & ! [v0: $i] : ! [v1:
% 220.15/30.59 $i] : ! [v2: $i] : (v1 = v0 | ~ (c_Orderings_Obot__class_Obot(v2) = v1) |
% 220.15/30.59 ~ (c_Orderings_Obot__class_Obot(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 220.15/30.59 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~
% 220.15/30.59 (class_Groups_Oordered__ab__group__add(v2) = v1) | ~
% 220.15/30.59 (class_Groups_Oordered__ab__group__add(v2) = v0)) & ! [v0: $i] : ! [v1:
% 220.15/30.59 $i] : ! [v2: $i] : (v1 = v0 | ~ (c_Wellfounded_Omeasure(v2) = v1) | ~
% 220.15/30.59 (c_Wellfounded_Omeasure(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 220.15/30.59 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~
% 220.15/30.59 (class_Lattices_Osemilattice__sup(v2) = v1) | ~
% 220.15/30.59 (class_Lattices_Osemilattice__sup(v2) = v0)) & ! [v0: MultipleValueBool] :
% 220.15/30.59 ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~
% 220.15/30.59 (class_Lattices_Olattice(v2) = v1) | ~ (class_Lattices_Olattice(v2) = v0))
% 220.15/30.59 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1
% 220.15/30.59 = v0 | ~ (class_Groups_Ominus(v2) = v1) | ~ (class_Groups_Ominus(v2) =
% 220.15/30.59 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 220.15/30.59 (c_Relation_OId(v2) = v1) | ~ (c_Relation_OId(v2) = v0)) & ! [v0: $i] : !
% 220.15/30.59 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (c_fequal(v2) = v1) | ~ (c_fequal(v2)
% 220.15/30.59 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 220.15/30.59 $i] : (v1 = v0 | ~ (hBOOL(v2) = v1) | ~ (hBOOL(v2) = v0)) & ? [v0: $i] :
% 220.15/30.59 ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6:
% 220.15/30.59 MultipleValueBool] : (c_Nitpick_Ofold__graph_H(v5, v4, v3, v2, v1, v0) = v6)
% 220.15/30.59 & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ?
% 220.15/30.59 [v5: $i] : ? [v6: MultipleValueBool] : (c_Recdef_Owfrec__rel(v5, v4, v3, v2,
% 220.15/30.59 v1, v0) = v6) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ?
% 220.15/30.59 [v4: $i] : ? [v5: $i] : ? [v6: $i] : (c_Product__Type_Ocurry(v5, v4, v3, v2,
% 220.15/30.59 v1, v0) = v6 & $i(v6)) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3:
% 220.15/30.59 $i] : ? [v4: $i] : ? [v5: $i] : (c_Nitpick_Owf__wfrec_H(v4, v3, v2, v1,
% 220.15/30.59 v0) = v5 & $i(v5)) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i]
% 220.15/30.59 : ? [v4: $i] : ? [v5: $i] : (c_Recdef_Ocut(v4, v3, v2, v1, v0) = v5 &
% 220.15/30.59 $i(v5)) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4:
% 220.15/30.59 $i] : ? [v5: $i] : (c_Product__Type_Ointernal__split(v4, v3, v2, v1, v0) =
% 220.15/30.59 v5 & $i(v5)) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ?
% 220.15/30.59 [v4: $i] : ? [v5: $i] : (c_Product__Type_Oprod_Oprod__rec(v4, v3, v2, v1, v0)
% 220.15/30.59 = v5 & $i(v5)) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ?
% 220.15/30.59 [v4: $i] : (c_Relation_OImage(v3, v2, v1, v0) = v4 & $i(v4)) & ? [v0: $i] :
% 220.15/30.59 ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : (c_Recdef_Owfrec(v3,
% 220.15/30.59 v2, v1, v0) = v4 & $i(v4)) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ?
% 220.15/30.59 [v3: $i] : ? [v4: $i] : (c_Product__Type_OSigma(v3, v2, v1, v0) = v4 &
% 220.15/30.59 $i(v4)) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4:
% 220.15/30.59 $i] : (c_Nitpick_Owf__wfrec(v3, v2, v1, v0) = v4 & $i(v4)) & ? [v0: $i] :
% 220.15/30.59 ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 220.15/30.59 (c_Wellfounded_Olex__prod(v3, v2, v1, v0) = v4 & $i(v4)) & ? [v0: $i] : ?
% 220.15/30.59 [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : (c_Recdef_Osame__fst(v3,
% 220.15/30.59 v2, v1, v0) = v4 & $i(v4)) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ?
% 220.15/30.59 [v3: $i] : ? [v4: $i] : (c_Product__Type_OPair(v3, v2, v1, v0) = v4 & $i(v4))
% 220.15/30.59 & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: MultipleValueBool] :
% 220.15/30.59 (c_Equiv__Relations_Oequiv(v2, v1, v0) = v3) & ? [v0: $i] : ? [v1: $i] : ?
% 220.15/30.59 [v2: $i] : ? [v3: MultipleValueBool] : (c_Orderings_Oord__class_Oless__eq(v2,
% 220.15/30.59 v1, v0) = v3) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3:
% 220.15/30.59 MultipleValueBool] : (c_Orderings_Oord__class_Oless(v2, v1, v0) = v3) & ?
% 220.15/30.59 [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: MultipleValueBool] :
% 220.15/30.59 (c_Order__Relation_Opartial__order__on(v2, v1, v0) = v3) & ? [v0: $i] : ?
% 220.15/30.59 [v1: $i] : ? [v2: $i] : ? [v3: MultipleValueBool] :
% 220.15/30.59 (c_Order__Relation_Owell__order__on(v2, v1, v0) = v3) & ? [v0: $i] : ? [v1:
% 220.15/30.59 $i] : ? [v2: $i] : ? [v3: MultipleValueBool] :
% 220.15/30.59 (c_Order__Relation_Opreorder__on(v2, v1, v0) = v3) & ? [v0: $i] : ? [v1: $i]
% 220.15/30.59 : ? [v2: $i] : ? [v3: MultipleValueBool] :
% 220.15/30.59 (c_Order__Relation_Olinear__order__on(v2, v1, v0) = v3) & ? [v0: $i] : ?
% 220.15/30.59 [v1: $i] : ? [v2: $i] : ? [v3: MultipleValueBool] :
% 220.15/30.59 (c_Order__Relation_Ostrict__linear__order__on(v2, v1, v0) = v3) & ? [v0: $i]
% 220.15/30.59 : ? [v1: $i] : ? [v2: $i] : ? [v3: MultipleValueBool] :
% 220.15/30.59 (c_Relation_Orefl__on(v2, v1, v0) = v3) & ? [v0: $i] : ? [v1: $i] : ? [v2:
% 220.15/30.59 $i] : ? [v3: MultipleValueBool] : (c_Relation_Ototal__on(v2, v1, v0) = v3)
% 220.15/30.59 & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: MultipleValueBool] :
% 220.15/30.59 (c_Relation_Osingle__valued(v2, v1, v0) = v3) & ? [v0: $i] : ? [v1: $i] : ?
% 220.15/30.59 [v2: $i] : ? [v3: MultipleValueBool] : (c_member(v2, v1, v0) = v3) & ? [v0:
% 220.15/30.59 $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 220.15/30.59 (c_Lattices_Osemilattice__inf__class_Oinf(v2, v1, v0) = v3 & $i(v3)) & ? [v0:
% 220.15/30.59 $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 220.15/30.59 (c_Wellfounded_Omlex__prod(v2, v1, v0) = v3 & $i(v3)) & ? [v0: $i] : ? [v1:
% 220.15/30.59 $i] : ? [v2: $i] : ? [v3: $i] : (c_Groups_Ominus__class_Ominus(v2, v1, v0)
% 220.15/30.59 = v3 & $i(v3)) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 220.15/30.59 (c_Lattices_Osemilattice__sup__class_Osup(v2, v1, v0) = v3 & $i(v3)) & ? [v0:
% 220.15/30.59 $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (c_Set_Oinsert(v2, v1, v0) =
% 220.15/30.59 v3 & $i(v3)) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 220.15/30.59 (c_Relation_Oinv__image(v2, v1, v0) = v3 & $i(v3)) & ? [v0: $i] : ? [v1: $i]
% 220.15/30.59 : ? [v2: $i] : ? [v3: $i] : (c_Relation_ODomain(v2, v1, v0) = v3 & $i(v3)) &
% 220.15/30.59 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (c_Relation_ORange(v2,
% 220.15/30.59 v1, v0) = v3 & $i(v3)) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3:
% 220.15/30.59 $i] : (c_Relation_Oconverse(v2, v1, v0) = v3 & $i(v3)) & ? [v0: $i] : ?
% 220.15/30.59 [v1: $i] : ? [v2: $i] : ? [v3: $i] : (c_Arrow__Order__Mirabelle_Obelow(v2,
% 220.15/30.59 v1, v0) = v3 & $i(v3)) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3:
% 220.15/30.59 $i] : (c_Arrow__Order__Mirabelle_Oabove(v2, v1, v0) = v3 & $i(v3)) & ? [v0:
% 220.15/30.59 $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (c_FunDef_Oin__rel(v2, v1,
% 220.15/30.59 v0) = v3 & $i(v3)) & ? [v0: $i] : ? [v1: $i] : ? [v2:
% 220.15/30.59 MultipleValueBool] : (c_Wellfounded_OwfP(v1, v0) = v2) & ? [v0: $i] : ?
% 220.15/30.59 [v1: $i] : ? [v2: MultipleValueBool] : (c_Wellfounded_Owf(v1, v0) = v2) & ?
% 220.15/30.59 [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : (c_Relation_Otrans(v1,
% 220.15/30.59 v0) = v2) & ? [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] :
% 220.15/30.59 (c_Wellfounded_Oacyclic(v1, v0) = v2) & ? [v0: $i] : ? [v1: $i] : ? [v2:
% 220.15/30.59 MultipleValueBool] : (c_Relation_Oantisym(v1, v0) = v2) & ? [v0: $i] : ?
% 220.15/30.59 [v1: $i] : ? [v2: MultipleValueBool] : (c_Relation_Oirrefl(v1, v0) = v2) & ?
% 220.15/30.59 [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : (c_Nitpick_Orefl_H(v1,
% 220.15/30.59 v0) = v2) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 220.15/30.59 (c_Set_Othe__elem(v1, v0) = v2 & $i(v2)) & ? [v0: $i] : ? [v1: $i] : ? [v2:
% 220.15/30.59 $i] : (c_Relation_OField(v1, v0) = v2 & $i(v2)) & ? [v0: $i] : ? [v1: $i]
% 220.15/30.59 : ? [v2: $i] : (c_Transitive__Closure_Otrancl(v1, v0) = v2 & $i(v2)) & ?
% 220.15/30.59 [v0: $i] : ? [v1: $i] : ? [v2: $i] : (c_Relation_OId__on(v1, v0) = v2 &
% 220.15/30.59 $i(v2)) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 220.15/30.59 (c_Transitive__Closure_Ortrancl(v1, v0) = v2 & $i(v2)) & ? [v0: $i] : ? [v1:
% 220.15/30.59 $i] : ? [v2: $i] : (c_Wellfounded_Oacc(v1, v0) = v2 & $i(v2)) & ? [v0: $i]
% 220.15/30.59 : ? [v1: $i] : ? [v2: $i] : (tc_fun(v1, v0) = v2 & $i(v2)) & ? [v0: $i] :
% 220.15/30.59 ? [v1: $i] : ? [v2: $i] : (c_Arrow__Order__Mirabelle_Omktop(v1, v0) = v2 &
% 220.15/30.59 $i(v2)) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (tc_prod(v1, v0) = v2 &
% 220.15/30.59 $i(v2)) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 220.15/30.59 (c_Arrow__Order__Mirabelle_Omkbot(v1, v0) = v2 & $i(v2)) & ? [v0: $i] : ?
% 220.15/30.59 [v1: $i] : ? [v2: $i] : (hAPP(v1, v0) = v2 & $i(v2)) & ? [v0: $i] : ? [v1:
% 220.15/30.59 MultipleValueBool] : (class_Lattices_Obounded__lattice(v0) = v1) & ? [v0:
% 220.15/30.59 $i] : ? [v1: MultipleValueBool] : (class_Lattices_Osemilattice__inf(v0) =
% 220.15/30.59 v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : (class_Orderings_Oord(v0) =
% 220.15/30.59 v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : (class_Orderings_Oorder(v0)
% 220.15/30.59 = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] :
% 220.15/30.59 (class_Orderings_Olinorder(v0) = v1) & ? [v0: $i] : ? [v1:
% 220.15/30.59 MultipleValueBool] : (class_Orderings_Opreorder(v0) = v1) & ? [v0: $i] : ?
% 220.15/30.59 [v1: MultipleValueBool] : (class_Orderings_Obot(v0) = v1) & ? [v0: $i] : ?
% 220.15/30.59 [v1: MultipleValueBool] : (class_Groups_Oab__group__add(v0) = v1) & ? [v0:
% 220.15/30.59 $i] : ? [v1: MultipleValueBool] :
% 220.15/30.59 (class_Lattices_Obounded__lattice__bot(v0) = v1) & ? [v0: $i] : ? [v1:
% 220.15/30.59 MultipleValueBool] : (class_Groups_Oordered__ab__group__add(v0) = v1) & ?
% 220.15/30.59 [v0: $i] : ? [v1: MultipleValueBool] : (class_Lattices_Osemilattice__sup(v0)
% 220.15/30.59 = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] :
% 220.15/30.59 (class_Lattices_Olattice(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool]
% 220.15/30.59 : (class_Groups_Ominus(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] :
% 220.15/30.59 (hBOOL(v0) = v1) & ? [v0: $i] : ? [v1: $i] :
% 220.15/30.59 (c_Orderings_Obot__class_Obot(v0) = v1 & $i(v1)) & ? [v0: $i] : ? [v1: $i] :
% 220.15/30.59 (c_Wellfounded_Omeasure(v0) = v1 & $i(v1)) & ? [v0: $i] : ? [v1: $i] :
% 220.15/30.59 (c_Relation_OId(v0) = v1 & $i(v1)) & ? [v0: $i] : ? [v1: $i] : (c_fequal(v0)
% 220.15/30.59 = v1 & $i(v1))
% 220.15/30.59
% 220.15/30.59 Further assumptions not needed in the proof:
% 220.15/30.59 --------------------------------------------
% 220.15/30.60 arity_HOL__Obool__Groups_Ominus, arity_HOL__Obool__Lattices_Obounded__lattice,
% 220.15/30.60 arity_HOL__Obool__Lattices_Obounded__lattice__bot,
% 220.15/30.60 arity_HOL__Obool__Lattices_Olattice,
% 220.15/30.60 arity_HOL__Obool__Lattices_Osemilattice__inf,
% 220.15/30.60 arity_HOL__Obool__Lattices_Osemilattice__sup, arity_HOL__Obool__Orderings_Obot,
% 220.15/30.60 arity_HOL__Obool__Orderings_Oord, arity_HOL__Obool__Orderings_Oorder,
% 220.15/30.60 arity_HOL__Obool__Orderings_Opreorder, arity_Nat__Onat__Groups_Ominus,
% 220.15/30.60 arity_Nat__Onat__Lattices_Olattice, arity_Nat__Onat__Lattices_Osemilattice__inf,
% 220.15/30.60 arity_Nat__Onat__Lattices_Osemilattice__sup, arity_Nat__Onat__Orderings_Obot,
% 220.15/30.60 arity_Nat__Onat__Orderings_Olinorder, arity_Nat__Onat__Orderings_Oord,
% 220.15/30.60 arity_Nat__Onat__Orderings_Oorder, arity_Nat__Onat__Orderings_Opreorder,
% 220.15/30.60 arity_fun__Groups_Ominus, arity_fun__Lattices_Obounded__lattice,
% 220.15/30.60 arity_fun__Lattices_Obounded__lattice__bot, arity_fun__Lattices_Olattice,
% 220.15/30.60 arity_fun__Lattices_Osemilattice__inf, arity_fun__Lattices_Osemilattice__sup,
% 220.15/30.60 arity_fun__Orderings_Obot, arity_fun__Orderings_Oord,
% 220.15/30.60 arity_fun__Orderings_Oorder, arity_fun__Orderings_Opreorder, fact_DiffD1,
% 220.15/30.60 fact_DiffD2, fact_DiffE, fact_DiffI, fact_Diff__cancel, fact_Diff__empty,
% 220.15/30.60 fact_Diff__idemp, fact_Diff__iff, fact_Diff__insert, fact_Diff__insert2,
% 220.15/30.60 fact_Diff__insert__absorb, fact_Diff__mono, fact_Diff__partition,
% 220.15/30.60 fact_Diff__subset, fact_Diff__subset__conv, fact_DomainE, fact_DomainI,
% 220.15/30.60 fact_Domain__Diff__subset, fact_Domain__Id__on, fact_Domain__Un__eq,
% 220.15/30.60 fact_Domain__converse, fact_Domain__empty, fact_Domain__empty__iff,
% 220.15/30.60 fact_Domain__iff, fact_Domain__insert, fact_Domain__mono, fact_Field__Un,
% 220.15/30.60 fact_Field__converse, fact_Field__def, fact_Field__empty, fact_Field__insert,
% 220.15/30.60 fact_IdE, fact_IdI, fact_Id__onE, fact_Id__on__empty, fact_Id__on__eqI,
% 220.15/30.60 fact_Id__on__iff, fact_ImageE, fact_Image__Id, fact_Image__Int__subset,
% 220.15/30.60 fact_Image__Un, fact_Image__closed__trancl, fact_Image__empty, fact_Image__iff,
% 220.15/30.60 fact_Image__mono, fact_Image__singleton__iff, fact_IntE, fact_IntI,
% 220.15/30.60 fact_Nitpick_Orefl_H__def, fact_Nitpick_Owf__wfrec_H__def,
% 220.15/30.60 fact_Not__Domain__rtrancl, fact_Pair__eq, fact_Pair__inject,
% 220.15/30.60 fact_Partial__order__eq__Image1__Image1__iff, fact_RangeE, fact_RangeI,
% 220.15/30.60 fact_Range__Diff__subset, fact_Range__Id__on, fact_Range__Un__eq,
% 220.15/30.60 fact_Range__converse, fact_Range__def, fact_Range__empty,
% 220.15/30.60 fact_Range__empty__iff, fact_Range__iff, fact_Range__insert,
% 220.15/30.60 fact_Refl__antisym__eq__Image1__Image1__iff, fact_SigmaD1, fact_SigmaD2,
% 220.15/30.60 fact_SigmaE, fact_SigmaE2, fact_SigmaI, fact_Sigma__empty1,
% 220.15/30.60 fact_Transitive__Closure_Otrancl__into__trancl, fact_UnCI, fact_UnE, fact_UnI1,
% 220.15/30.60 fact_UnI2, fact_Un__Diff, fact_Un__Diff__cancel, fact_Un__Diff__cancel2,
% 220.15/30.60 fact_Un__Image, fact_Un__Int__assoc__eq, fact_Un__absorb, fact_Un__absorb1,
% 220.15/30.60 fact_Un__absorb2, fact_Un__assoc, fact_Un__commute, fact_Un__empty,
% 220.15/30.60 fact_Un__empty__left, fact_Un__empty__right, fact_Un__iff,
% 220.15/30.60 fact_Un__insert__left, fact_Un__insert__right, fact_Un__least,
% 220.15/30.60 fact_Un__left__absorb, fact_Un__left__commute, fact_Un__mono, fact_Un__upper1,
% 220.15/30.60 fact_Un__upper2, fact_acc_OaccI, fact_acc_Osimps, fact_acc__downward,
% 220.15/30.60 fact_acc__downwards, fact_acc__downwards__aux, fact_acc__subset, fact_acc__wfD,
% 220.15/30.60 fact_acc__wfI, fact_acyclicI, fact_acyclic__converse, fact_acyclic__def,
% 220.15/30.60 fact_acyclic__impl__antisym__rtrancl, fact_acyclic__insert,
% 220.15/30.60 fact_acyclic__subset, fact_all__not__in__conv, fact_antisymI, fact_antisym__Id,
% 220.15/30.60 fact_antisym__Id__on, fact_antisym__converse, fact_antisym__def,
% 220.15/30.60 fact_antisym__empty, fact_antisym__reflcl, fact_antisym__subset, fact_ball__Un,
% 220.15/30.60 fact_bex__Un, fact_bot__apply, fact_bot__least, fact_converseD, fact_converseE,
% 220.15/30.60 fact_converseI, fact_converse__Id, fact_converse__Id__on, fact_converse__Un,
% 220.15/30.60 fact_converse__converse, fact_converse__iff, fact_converse__inv__image,
% 220.15/30.60 fact_converse__rtranclE, fact_converse__rtranclE2,
% 220.15/30.60 fact_converse__rtrancl__induct, fact_converse__rtrancl__induct2,
% 220.15/30.60 fact_converse__rtrancl__into__rtrancl, fact_converse__tranclE, fact_curryD,
% 220.15/30.60 fact_curryE, fact_curryI, fact_curry__conv, fact_cut__apply, fact_cuts__eq,
% 220.15/30.60 fact_def__wfrec, fact_diff__eq__diff__eq, fact_diff__eq__diff__less,
% 220.15/30.60 fact_diff__eq__diff__less__eq, fact_diff__single__insert, fact_distrib__inf__le,
% 220.15/30.60 fact_distrib__sup__le, fact_double__diff, fact_doubleton__eq__iff, fact_emptyE,
% 220.15/30.60 fact_empty__Diff, fact_empty__iff, fact_empty__not__insert, fact_empty__subsetI,
% 220.15/30.60 fact_eq__mem, fact_eq__mem__trans, fact_eqelem__imp__iff, fact_eqset__imp__iff,
% 220.15/30.60 fact_equalityCE, fact_equalityD1, fact_equalityD2, fact_equalityE,
% 220.15/30.60 fact_equalityI, fact_equals0D, fact_ex__in__conv, fact_ext,
% 220.15/30.60 fact_fold__graph_H_Oequations_I1_J, fact_fold__graph_H_Oequations_I2_J,
% 220.15/30.60 fact_fold__graph_H_Ointros_I1_J, fact_fold__graph_H_Ointros_I2_J,
% 220.15/30.60 fact_in__inv__image, fact_in__lex__prod, fact_in__measure, fact_in__mono,
% 220.15/30.60 fact_in__rel__def, fact_in__rtrancl__UnI, fact_inf1E, fact_inf1I, fact_inf__le1,
% 220.15/30.60 fact_inf__le2, fact_inf__sup__aci_I5_J, fact_inf__sup__aci_I6_J,
% 220.15/30.60 fact_inf__sup__aci_I7_J, fact_inf__sup__aci_I8_J, fact_inf__sup__ord_I1_J,
% 220.15/30.60 fact_inf__sup__ord_I2_J, fact_inf__sup__ord_I3_J, fact_inf__sup__ord_I4_J,
% 220.15/30.60 fact_insertCI, fact_insertE, fact_insertI1, fact_insertI2, fact_insert__Diff,
% 220.15/30.60 fact_insert__Diff1, fact_insert__Diff__if, fact_insert__Diff__single,
% 220.15/30.60 fact_insert__absorb, fact_insert__absorb2, fact_insert__code,
% 220.15/30.60 fact_insert__commute, fact_insert__ident, fact_insert__iff, fact_insert__is__Un,
% 220.15/30.60 fact_insert__mono, fact_insert__not__empty, fact_insert__subset,
% 220.15/30.60 fact_internal__split__conv, fact_irrefl__def, fact_irrefl__diff__Id,
% 220.15/30.60 fact_irrefl__tranclI, fact_irrefl__trancl__rD, fact_leD, fact_leI,
% 220.15/30.60 fact_le__funD, fact_le__funE, fact_le__fun__def, fact_le__iff__inf,
% 220.15/30.60 fact_le__iff__sup, fact_le__inf__iff, fact_le__supE, fact_le__supI,
% 220.15/30.60 fact_le__supI1, fact_le__supI2, fact_le__sup__iff, fact_less__by__empty,
% 220.15/30.60 fact_less__eq, fact_less__fun__def, fact_less__imp__neq, fact_less__le__not__le,
% 220.15/30.60 fact_less__supI1, fact_less__supI2, fact_less__than__def, fact_less__than__iff,
% 220.15/30.60 fact_linear__order__on__converse, fact_linear__order__on__def,
% 220.15/30.60 fact_linorder__antisym__conv1, fact_linorder__antisym__conv2,
% 220.15/30.60 fact_linorder__antisym__conv3, fact_linorder__cases, fact_linorder__le__cases,
% 220.15/30.60 fact_linorder__le__less__linear, fact_linorder__less__linear,
% 220.15/30.60 fact_linorder__linear, fact_linorder__neqE, fact_linorder__neq__iff,
% 220.15/30.60 fact_linorder__not__le, fact_linorder__not__less, fact_lnear__order__on__empty,
% 220.15/30.60 fact_measure__def, fact_mem__Sigma__iff, fact_minus__apply, fact_mlex__leq,
% 220.15/30.60 fact_mlex__less, fact_mono__Field, fact_not__acc__down, fact_not__leE,
% 220.15/30.60 fact_not__less__iff__gr__or__eq, fact_not__psubset__empty,
% 220.15/30.60 fact_ord__eq__le__trans, fact_ord__eq__less__trans, fact_ord__le__eq__trans,
% 220.15/30.60 fact_ord__less__eq__trans, fact_order__antisym, fact_order__antisym__conv,
% 220.15/30.60 fact_order__eq__iff, fact_order__eq__refl, fact_order__le__imp__less__or__eq,
% 220.15/30.60 fact_order__le__less, fact_order__le__less__trans, fact_order__le__neq__trans,
% 220.15/30.60 fact_order__less__asym, fact_order__less__asym_H, fact_order__less__imp__le,
% 220.15/30.60 fact_order__less__imp__not__eq, fact_order__less__imp__not__eq2,
% 220.15/30.60 fact_order__less__imp__not__less, fact_order__less__irrefl,
% 220.15/30.60 fact_order__less__le, fact_order__less__le__trans, fact_order__less__not__sym,
% 220.15/30.60 fact_order__less__trans, fact_order__neq__le__trans, fact_order__refl,
% 220.15/30.60 fact_order__trans, fact_pair__in__Id__conv, fact_partial__order__on__converse,
% 220.15/30.60 fact_partial__order__on__def, fact_partial__order__on__empty,
% 220.15/30.60 fact_pred__nat__trancl__eq__le, fact_predicate1D, fact_preorder__on__converse,
% 220.15/30.60 fact_preorder__on__def, fact_preorder__on__empty, fact_prod_Orecs,
% 220.15/30.60 fact_psubsetD, fact_psubset__eq, fact_psubset__imp__subset,
% 220.15/30.60 fact_psubset__insert__iff, fact_psubset__subset__trans, fact_psubset__trans,
% 220.15/30.60 fact_r__into__rtrancl, fact_r__into__trancl_H, fact_r__r__into__trancl,
% 220.15/30.60 fact_refl__onD, fact_refl__onD1, fact_refl__onD2, fact_refl__on__Id__on,
% 220.15/30.60 fact_refl__on__Un, fact_refl__on__converse, fact_refl__on__empty,
% 220.15/30.60 fact_reflcl__trancl, fact_rev__ImageI, fact_rev__predicate1D, fact_rtranclD,
% 220.15/30.60 fact_rtranclE, fact_rtrancl_Ortrancl__into__rtrancl,
% 220.15/30.60 fact_rtrancl_Ortrancl__refl, fact_rtrancl__Un__rtrancl,
% 220.15/30.60 fact_rtrancl__Un__separatorE, fact_rtrancl__Un__separator__converseE,
% 220.15/30.60 fact_rtrancl__Un__subset, fact_rtrancl__converse, fact_rtrancl__converseD,
% 220.15/30.60 fact_rtrancl__converseI, fact_rtrancl__empty, fact_rtrancl__eq__or__trancl,
% 220.15/30.60 fact_rtrancl__idemp, fact_rtrancl__induct, fact_rtrancl__induct2,
% 220.15/30.60 fact_rtrancl__into__trancl1, fact_rtrancl__into__trancl2, fact_rtrancl__mono,
% 220.15/30.60 fact_rtrancl__r__diff__Id, fact_rtrancl__reflcl, fact_rtrancl__reflcl__absorb,
% 220.15/30.60 fact_rtrancl__subset, fact_rtrancl__subset__rtrancl,
% 220.15/30.60 fact_rtrancl__trancl__absorb, fact_rtrancl__trancl__trancl, fact_rtrancl__trans,
% 220.15/30.60 fact_same__fstI, fact_set__eq__subset, fact_set__mp, fact_set__rev__mp,
% 220.15/30.60 fact_single__valuedI, fact_single__valued__Id, fact_single__valued__Id__on,
% 220.15/30.60 fact_single__valued__confluent, fact_single__valued__def,
% 220.15/30.60 fact_single__valued__subset, fact_singletonE, fact_singleton__iff,
% 220.15/30.60 fact_singleton__inject, fact_split__paired__All,
% 220.15/30.60 fact_strict__linear__order__on__def, fact_strict__linear__order__on__diff__Id,
% 220.15/30.60 fact_subsetD, fact_subset__Image1__Image1__iff, fact_subset__Image__Image__iff,
% 220.15/30.60 fact_subset__Un__eq, fact_subset__empty, fact_subset__equiv__class,
% 220.15/30.60 fact_subset__iff__psubset__eq, fact_subset__insert, fact_subset__insertI,
% 220.15/30.60 fact_subset__insertI2, fact_subset__insert__iff, fact_subset__psubset__trans,
% 220.15/30.60 fact_subset__refl, fact_subset__singletonD, fact_subset__trans, fact_sup1CI,
% 220.15/30.60 fact_sup1E, fact_sup1I1, fact_sup1I2, fact_sup_Oassoc, fact_sup_Ocommute,
% 220.15/30.60 fact_sup_Oidem, fact_sup_Oleft__commute, fact_sup_Oleft__idem,
% 220.15/30.60 fact_sup__absorb1, fact_sup__absorb2, fact_sup__apply, fact_sup__assoc,
% 220.15/30.60 fact_sup__bot__left, fact_sup__bot__right, fact_sup__commute,
% 220.15/30.60 fact_sup__eq__bot__iff, fact_sup__ge1, fact_sup__ge2, fact_sup__idem,
% 220.15/30.60 fact_sup__least, fact_sup__left__commute, fact_sup__left__idem, fact_sup__mono,
% 220.15/30.60 fact_termination__basic__simps_I5_J, fact_tfl__cut__apply, fact_tfl__wfrec,
% 220.15/30.60 fact_the__elem__eq, fact_total__on__converse, fact_total__on__def,
% 220.15/30.60 fact_total__on__diff__Id, fact_total__on__empty, fact_tranclD, fact_tranclD2,
% 220.15/30.60 fact_tranclE, fact_trancl_Or__into__trancl, fact_trancl__converse,
% 220.15/30.60 fact_trancl__converseD, fact_trancl__converseI, fact_trancl__domain,
% 220.15/30.60 fact_trancl__empty, fact_trancl__id, fact_trancl__into__rtrancl,
% 220.15/30.60 fact_trancl__into__trancl2, fact_trancl__mono, fact_trancl__range,
% 220.15/30.60 fact_trancl__reflcl, fact_trancl__rtrancl__absorb, fact_trancl__rtrancl__trancl,
% 220.15/30.60 fact_trancl__trans, fact_transI, fact_trans__Id, fact_trans__Id__on,
% 220.15/30.60 fact_trans__converse, fact_trans__def, fact_trans__diff__Id,
% 220.15/30.60 fact_trans__inv__image, fact_trans__less__than, fact_trans__lex__prod,
% 220.15/30.60 fact_trans__reflclI, fact_trans__rtrancl, fact_trans__trancl,
% 220.15/30.60 fact_well__order__on__def, fact_well__order__on__empty, fact_wfE__pf,
% 220.15/30.60 fact_wfP__subset, fact_wf__acc__iff, fact_wf__acyclic,
% 220.15/30.60 fact_wf__converse__trancl, fact_wf__empty, fact_wf__eq__minimal,
% 220.15/30.60 fact_wf__in__rel, fact_wf__insert, fact_wf__inv__image, fact_wf__irrefl,
% 220.15/30.60 fact_wf__less__than, fact_wf__lex__prod, fact_wf__measure, fact_wf__mlex,
% 220.15/30.60 fact_wf__not__refl, fact_wf__pred__nat, fact_wf__same__fst, fact_wf__subset,
% 220.15/30.60 fact_wf__trancl, fact_wfrec, fact_wfrec__rel_Oequations,
% 220.15/30.60 fact_wfrec__rel_Ointros, fact_wfrec__rel_Osimps, fact_xt1_I10_J, fact_xt1_I11_J,
% 220.15/30.60 fact_xt1_I12_J, fact_xt1_I1_J, fact_xt1_I2_J, fact_xt1_I3_J, fact_xt1_I4_J,
% 220.15/30.60 fact_xt1_I5_J, fact_xt1_I6_J, fact_xt1_I7_J, fact_xt1_I8_J, fact_xt1_I9_J,
% 220.15/30.60 help_c__fequal__1, help_c__fequal__2
% 220.15/30.60
% 220.15/30.60 Those formulas are unsatisfiable:
% 220.15/30.60 ---------------------------------
% 220.15/30.60
% 220.15/30.60 Begin of proof
% 220.15/30.60 |
% 220.15/30.60 | ALPHA: (fact_in__mkbot) implies:
% 220.15/30.61 | (1) ? [v0: $i] : (tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 220.15/30.61 | tc_Arrow__Order__Mirabelle_Oalt) = v0 & $i(v0) & ! [v1: $i] : !
% 220.15/30.61 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : !
% 220.15/30.61 | [v7: int] : (v7 = 0 | v3 = v1 | ~
% 220.15/30.61 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.15/30.61 | tc_Arrow__Order__Mirabelle_Oalt, v4, v3) = v5) | ~
% 220.15/30.61 | (c_Arrow__Order__Mirabelle_Omkbot(v2, v1) = v6) | ~ (c_member(v0,
% 220.15/30.61 | v5, v6) = v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) |
% 220.15/30.61 | ( ~ (v4 = v1) & ? [v8: int] : ( ~ (v8 = 0) & c_member(v0, v5, v2)
% 220.15/30.61 | = v8))) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i]
% 220.15/30.61 | : ! [v5: $i] : ! [v6: $i] : ( ~
% 220.15/30.61 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.15/30.61 | tc_Arrow__Order__Mirabelle_Oalt, v4, v3) = v5) | ~
% 220.15/30.61 | (c_Arrow__Order__Mirabelle_Omkbot(v2, v1) = v6) | ~ (c_member(v0,
% 220.15/30.61 | v5, v6) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) |
% 220.15/30.61 | ( ~ (v3 = v1) & (v4 = v1 | c_member(v0, v5, v2) = 0))))
% 220.15/30.61 |
% 220.15/30.61 | ALPHA: (fact_in__mktop) implies:
% 220.34/30.61 | (2) ? [v0: $i] : (tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.61 | tc_Arrow__Order__Mirabelle_Oalt) = v0 & $i(v0) & ! [v1: $i] : !
% 220.34/30.61 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : !
% 220.34/30.61 | [v7: int] : (v7 = 0 | v4 = v1 | ~
% 220.34/30.61 | (c_Arrow__Order__Mirabelle_Omktop(v2, v1) = v6) | ~
% 220.34/30.61 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.61 | tc_Arrow__Order__Mirabelle_Oalt, v4, v3) = v5) | ~
% 220.34/30.61 | (c_member(v0, v5, v6) = v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) |
% 220.34/30.61 | ~ $i(v1) | ( ~ (v3 = v1) & ? [v8: int] : ( ~ (v8 = 0) &
% 220.34/30.61 | c_member(v0, v5, v2) = v8))) & ! [v1: $i] : ! [v2: $i] : !
% 220.34/30.61 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 220.34/30.61 | (c_Arrow__Order__Mirabelle_Omktop(v2, v1) = v6) | ~
% 220.34/30.61 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.61 | tc_Arrow__Order__Mirabelle_Oalt, v4, v3) = v5) | ~
% 220.34/30.61 | (c_member(v0, v5, v6) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 220.34/30.61 | $i(v1) | ( ~ (v4 = v1) & (v3 = v1 | c_member(v0, v5, v2) = 0))))
% 220.34/30.61 |
% 220.34/30.61 | ALPHA: (fact_mem__def) implies:
% 220.34/30.61 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 220.34/30.61 | (c_member(v2, v1, v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 220.34/30.61 | [v4: $i] : ? [v5: int] : ( ~ (v5 = 0) & hBOOL(v4) = v5 & hAPP(v0,
% 220.34/30.61 | v1) = v4 & $i(v4)))
% 220.34/30.61 |
% 220.34/30.61 | ALPHA: (fact_Lin__irrefl) implies:
% 220.34/30.61 | (4) ? [v0: $i] : ? [v1: $i] : (tc_fun(v0, tc_HOL_Obool) = v1 &
% 220.34/30.61 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.61 | tc_Arrow__Order__Mirabelle_Oalt) = v0 & $i(v1) & $i(v0) & ! [v2:
% 220.34/30.61 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 220.34/30.61 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.61 | tc_Arrow__Order__Mirabelle_Oalt, v2, v3) = v5) | ~
% 220.34/30.61 | (c_member(v0, v5, v4) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ?
% 220.34/30.61 | [v6: any] : ? [v7: $i] : ? [v8: any] :
% 220.34/30.61 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.61 | tc_Arrow__Order__Mirabelle_Oalt, v3, v2) = v7 & c_member(v1,
% 220.34/30.61 | v4, c_Arrow__Order__Mirabelle_OLin) = v6 & c_member(v0, v7, v4)
% 220.34/30.61 | = v8 & $i(v7) & ( ~ (v8 = 0) | ~ (v6 = 0)))))
% 220.34/30.61 |
% 220.34/30.61 | ALPHA: (fact_notin__Lin__iff) implies:
% 220.34/30.62 | (5) ? [v0: $i] : ? [v1: $i] : (tc_fun(v0, tc_HOL_Obool) = v1 &
% 220.34/30.62 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.62 | tc_Arrow__Order__Mirabelle_Oalt) = v0 & $i(v1) & $i(v0) & ! [v2:
% 220.34/30.62 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: any] : (v3
% 220.34/30.62 | = v2 | ~ (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.62 | tc_Arrow__Order__Mirabelle_Oalt, v2, v3) = v5) | ~
% 220.34/30.62 | (c_member(v0, v5, v4) = v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) |
% 220.34/30.62 | ? [v7: any] : ? [v8: $i] : ? [v9: any] :
% 220.34/30.62 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.62 | tc_Arrow__Order__Mirabelle_Oalt, v3, v2) = v8 & c_member(v1,
% 220.34/30.62 | v4, c_Arrow__Order__Mirabelle_OLin) = v7 & c_member(v0, v8, v4)
% 220.34/30.62 | = v9 & $i(v8) & ( ~ (v7 = 0) | (( ~ (v9 = 0) | ~ (v6 = 0)) & (v9
% 220.34/30.62 | = 0 | v6 = 0))))))
% 220.34/30.62 |
% 220.34/30.62 | ALPHA: (fact_mkbot__Lin) implies:
% 220.34/30.62 | (6) ? [v0: $i] : ? [v1: $i] : (tc_fun(v0, tc_HOL_Obool) = v1 &
% 220.34/30.62 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.62 | tc_Arrow__Order__Mirabelle_Oalt) = v0 & $i(v1) & $i(v0) & ! [v2:
% 220.34/30.62 | $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 220.34/30.62 | (c_Arrow__Order__Mirabelle_Omkbot(v3, v2) = v4) | ~ $i(v3) | ~
% 220.34/30.62 | $i(v2) | ? [v5: any] : ? [v6: any] : (c_member(v1, v4,
% 220.34/30.62 | c_Arrow__Order__Mirabelle_OLin) = v6 & c_member(v1, v3,
% 220.34/30.62 | c_Arrow__Order__Mirabelle_OLin) = v5 & ( ~ (v5 = 0) | v6 =
% 220.34/30.62 | 0))))
% 220.34/30.62 |
% 220.34/30.62 | ALPHA: (fact_mktop__Lin) implies:
% 220.34/30.62 | (7) ? [v0: $i] : ? [v1: $i] : (tc_fun(v0, tc_HOL_Obool) = v1 &
% 220.34/30.62 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.62 | tc_Arrow__Order__Mirabelle_Oalt) = v0 & $i(v1) & $i(v0) & ! [v2:
% 220.34/30.62 | $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 220.34/30.62 | (c_Arrow__Order__Mirabelle_Omktop(v3, v2) = v4) | ~ $i(v3) | ~
% 220.34/30.62 | $i(v2) | ? [v5: any] : ? [v6: any] : (c_member(v1, v4,
% 220.34/30.62 | c_Arrow__Order__Mirabelle_OLin) = v6 & c_member(v1, v3,
% 220.34/30.62 | c_Arrow__Order__Mirabelle_OLin) = v5 & ( ~ (v5 = 0) | v6 =
% 220.34/30.62 | 0))))
% 220.34/30.62 |
% 220.34/30.62 | ALPHA: (fact_in__above) implies:
% 220.34/30.62 | (8) ? [v0: $i] : ? [v1: $i] : (tc_fun(v0, tc_HOL_Obool) = v1 &
% 220.34/30.62 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.62 | tc_Arrow__Order__Mirabelle_Oalt) = v0 & $i(v1) & $i(v0) & ! [v2:
% 220.34/30.62 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : !
% 220.34/30.62 | [v7: $i] : ! [v8: $i] : ! [v9: any] : (v6 = v5 | ~
% 220.34/30.62 | (c_Arrow__Order__Mirabelle_Oabove(v4, v6, v5) = v8) | ~
% 220.34/30.62 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.62 | tc_Arrow__Order__Mirabelle_Oalt, v3, v2) = v7) | ~
% 220.34/30.62 | (c_member(v0, v7, v8) = v9) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) |
% 220.34/30.62 | ~ $i(v3) | ~ $i(v2) | ? [v10: any] : ? [v11: $i] : ? [v12: any]
% 220.34/30.62 | : ? [v13: $i] : ? [v14: any] : ? [v15: any] :
% 220.34/30.62 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.62 | tc_Arrow__Order__Mirabelle_Oalt, v6, v2) = v11 &
% 220.34/30.62 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.62 | tc_Arrow__Order__Mirabelle_Oalt, v3, v6) = v13 & c_member(v1,
% 220.34/30.62 | v4, c_Arrow__Order__Mirabelle_OLin) = v10 & c_member(v0, v13,
% 220.34/30.62 | v4) = v14 & c_member(v0, v11, v4) = v12 & c_member(v0, v7, v4)
% 220.34/30.62 | = v15 & $i(v13) & $i(v11) & ( ~ (v10 = 0) | (( ~ (v9 = 0) | ( ~
% 220.34/30.62 | (v3 = v2) & ( ~ (v5 = v3) | v12 = 0) & (v5 = v3 | (( ~
% 220.34/30.62 | (v5 = v2) | v14 = 0 | v6 = v3) & (v15 = 0 | v5 =
% 220.34/30.62 | v2))))) & (v9 = 0 | v3 = v2 | (v5 = v3 & ~ (v12 =
% 220.34/30.62 | 0)) | ( ~ (v5 = v3) & ((v5 = v2 & ~ (v14 = 0) & ~ (v6
% 220.34/30.62 | = v3)) | ( ~ (v15 = 0) & ~ (v5 = v2))))))))))
% 220.34/30.62 |
% 220.34/30.62 | ALPHA: (fact_in__below) implies:
% 220.34/30.62 | (9) ? [v0: $i] : ? [v1: $i] : (tc_fun(v0, tc_HOL_Obool) = v1 &
% 220.34/30.62 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.62 | tc_Arrow__Order__Mirabelle_Oalt) = v0 & $i(v1) & $i(v0) & ! [v2:
% 220.34/30.62 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : !
% 220.34/30.62 | [v7: $i] : ! [v8: $i] : ! [v9: any] : (v6 = v5 | ~
% 220.34/30.62 | (c_Arrow__Order__Mirabelle_Obelow(v4, v6, v5) = v8) | ~
% 220.34/30.62 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.62 | tc_Arrow__Order__Mirabelle_Oalt, v3, v2) = v7) | ~
% 220.34/30.62 | (c_member(v0, v7, v8) = v9) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) |
% 220.34/30.62 | ~ $i(v3) | ~ $i(v2) | ? [v10: any] : ? [v11: $i] : ? [v12: any]
% 220.34/30.62 | : ? [v13: $i] : ? [v14: any] : ? [v15: any] :
% 220.34/30.62 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.62 | tc_Arrow__Order__Mirabelle_Oalt, v5, v2) = v13 &
% 220.34/30.62 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.62 | tc_Arrow__Order__Mirabelle_Oalt, v3, v5) = v11 & c_member(v1,
% 220.34/30.62 | v4, c_Arrow__Order__Mirabelle_OLin) = v10 & c_member(v0, v13,
% 220.34/30.62 | v4) = v14 & c_member(v0, v11, v4) = v12 & c_member(v0, v7, v4)
% 220.34/30.62 | = v15 & $i(v13) & $i(v11) & ( ~ (v10 = 0) | (( ~ (v9 = 0) | ( ~
% 220.34/30.62 | (v3 = v2) & ( ~ (v6 = v2) | v12 = 0) & (v6 = v2 | (( ~
% 220.34/30.62 | (v6 = v3) | v14 = 0 | v5 = v2) & (v15 = 0 | v6 =
% 220.34/30.62 | v3))))) & (v9 = 0 | v3 = v2 | (v6 = v2 & ~ (v12 =
% 220.34/30.62 | 0)) | ( ~ (v6 = v2) & ((v6 = v3 & ~ (v14 = 0) & ~ (v5
% 220.34/30.62 | = v2)) | ( ~ (v15 = 0) & ~ (v6 = v3))))))))))
% 220.34/30.62 |
% 220.34/30.62 | ALPHA: (fact_linear__alt) implies:
% 220.34/30.62 | (10) ? [v0: $i] : ? [v1: $i] : (tc_fun(v0, tc_HOL_Obool) = v1 &
% 220.34/30.62 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.62 | tc_Arrow__Order__Mirabelle_Oalt) = v0 & $i(v1) & $i(v0) & ? [v2:
% 220.34/30.62 | $i] : (c_member(v1, v2, c_Arrow__Order__Mirabelle_OLin) = 0 &
% 220.34/30.62 | $i(v2)))
% 220.34/30.62 |
% 220.34/30.62 | ALPHA: (fact_converse__in__Lin) implies:
% 220.34/30.62 | (11) ? [v0: $i] : ? [v1: $i] : (tc_fun(v0, tc_HOL_Obool) = v1 &
% 220.34/30.62 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.62 | tc_Arrow__Order__Mirabelle_Oalt) = v0 & $i(v1) & $i(v0) & ! [v2:
% 220.34/30.62 | $i] : ! [v3: int] : (v3 = 0 | ~ (c_member(v1, v2,
% 220.34/30.62 | c_Arrow__Order__Mirabelle_OLin) = v3) | ~ $i(v2) | ? [v4:
% 220.34/30.62 | $i] : ? [v5: int] : ( ~ (v5 = 0) &
% 220.34/30.62 | c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.62 | tc_Arrow__Order__Mirabelle_Oalt, v2) = v4 & c_member(v1, v4,
% 220.34/30.62 | c_Arrow__Order__Mirabelle_OLin) = v5 & $i(v4))) & ! [v2: $i]
% 220.34/30.62 | : ( ~ (c_member(v1, v2, c_Arrow__Order__Mirabelle_OLin) = 0) | ~
% 220.34/30.62 | $i(v2) | ? [v3: $i] :
% 220.34/30.62 | (c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.62 | tc_Arrow__Order__Mirabelle_Oalt, v2) = v3 & c_member(v1, v3,
% 220.34/30.62 | c_Arrow__Order__Mirabelle_OLin) = 0 & $i(v3))))
% 220.34/30.62 |
% 220.34/30.62 | ALPHA: (conj_0) implies:
% 220.34/30.62 | (12) ~ (v_x = v_y)
% 220.34/30.63 |
% 220.34/30.63 | ALPHA: (conj_1) implies:
% 220.34/30.63 | (13) ? [v0: $i] : (tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.63 | tc_Arrow__Order__Mirabelle_Oalt) = v0 & $i(v0) & ! [v1: $i] : !
% 220.34/30.63 | [v2: $i] : ! [v3: $i] : (v2 = v1 | ~
% 220.34/30.63 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.63 | tc_Arrow__Order__Mirabelle_Oalt, v1, v2) = v3) | ~ $i(v2) |
% 220.34/30.63 | ~ $i(v1) | ? [v4: any] : ? [v5: $i] : ? [v6: any] :
% 220.34/30.63 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.63 | tc_Arrow__Order__Mirabelle_Oalt, v2, v1) = v5 & c_member(v0,
% 220.34/30.63 | v5, v_L) = v6 & c_member(v0, v3, v_L) = v4 & $i(v5) & (v6 = 0
% 220.34/30.63 | | v4 = 0))) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 220.34/30.63 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.63 | tc_Arrow__Order__Mirabelle_Oalt, v1, v2) = v3) | ~ $i(v2) |
% 220.34/30.63 | ~ $i(v1) | ? [v4: int] : ( ~ (v4 = 0) & c_member(v0, v3, v_L) =
% 220.34/30.63 | v4) | ! [v4: $i] : ! [v5: $i] : ( ~
% 220.34/30.63 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.63 | tc_Arrow__Order__Mirabelle_Oalt, v1, v4) = v5) | ~ $i(v4) |
% 220.34/30.63 | ? [v6: $i] : ? [v7: any] : ? [v8: any] :
% 220.34/30.63 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.63 | tc_Arrow__Order__Mirabelle_Oalt, v2, v4) = v6 & c_member(v0,
% 220.34/30.63 | v6, v_L) = v7 & c_member(v0, v5, v_L) = v8 & $i(v6) & ( ~
% 220.34/30.63 | (v7 = 0) | v8 = 0)))) & ! [v1: $i] : ! [v2: $i] : ( ~
% 220.34/30.63 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.63 | tc_Arrow__Order__Mirabelle_Oalt, v1, v1) = v2) | ~ $i(v1) |
% 220.34/30.63 | ? [v3: int] : ( ~ (v3 = 0) & c_member(v0, v2, v_L) = v3)))
% 220.34/30.63 |
% 220.34/30.63 | ALPHA: (conj_2) implies:
% 220.34/30.63 | (14) $i(tc_Arrow__Order__Mirabelle_Oalt)
% 220.34/30.63 | (15) $i(v_y)
% 220.34/30.63 | (16) $i(v_L)
% 220.34/30.63 | (17) ? [v0: $i] : (tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.63 | tc_Arrow__Order__Mirabelle_Oalt) = v0 & $i(v0) & ( ? [v1: $i] : ?
% 220.34/30.63 | [v2: $i] : ? [v3: $i] : ? [v4: any] : ? [v5: $i] : ? [v6: any]
% 220.34/30.63 | : ? [v7: $i] : ? [v8: any] : ? [v9: $i] : ? [v10: any] : ?
% 220.34/30.63 | [v11: $i] : ? [v12: any] : ? [v13: $i] : ? [v14: any] : ( ~ (v2
% 220.34/30.63 | = v1) & c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.63 | tc_Arrow__Order__Mirabelle_Oalt, v2, v1) = v9 &
% 220.34/30.63 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.63 | tc_Arrow__Order__Mirabelle_Oalt, v2, v_y) = v11 &
% 220.34/30.63 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.63 | tc_Arrow__Order__Mirabelle_Oalt, v1, v2) = v3 &
% 220.34/30.63 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.63 | tc_Arrow__Order__Mirabelle_Oalt, v1, v_y) = v5 &
% 220.34/30.63 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.63 | tc_Arrow__Order__Mirabelle_Oalt, v_y, v2) = v7 &
% 220.34/30.63 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.63 | tc_Arrow__Order__Mirabelle_Oalt, v_y, v1) = v13 & c_member(v0,
% 220.34/30.63 | v13, v_L) = v14 & c_member(v0, v11, v_L) = v12 & c_member(v0,
% 220.34/30.63 | v9, v_L) = v10 & c_member(v0, v7, v_L) = v8 & c_member(v0, v5,
% 220.34/30.63 | v_L) = v6 & c_member(v0, v3, v_L) = v4 & $i(v13) & $i(v11) &
% 220.34/30.63 | $i(v9) & $i(v7) & $i(v5) & $i(v3) & $i(v2) & $i(v1) & ( ~ (v14 =
% 220.34/30.63 | 0) | ~ (v2 = v_x) | v1 = v_x) & ( ~ (v12 = 0) | ~ (v1 =
% 220.34/30.63 | v_x) | v2 = v_x) & ( ~ (v10 = 0) | v2 = v_x | v1 = v_x) & (
% 220.34/30.63 | ~ (v8 = 0) | ~ (v1 = v_x) | v2 = v_x) & ( ~ (v6 = 0) | ~ (v2
% 220.34/30.63 | = v_x) | v1 = v_x) & ( ~ (v4 = 0) | v2 = v_x | v1 = v_x) & (
% 220.34/30.63 | ~ (v2 = v_x) | ~ (v1 = v_y)) & ( ~ (v2 = v_y) | ~ (v1 =
% 220.34/30.63 | v_x))) | ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4:
% 220.34/30.63 | any] : ? [v5: $i] : ? [v6: any] : ? [v7: $i] : ? [v8: any] :
% 220.34/30.63 | ? [v9: $i] : ? [v10: any] :
% 220.34/30.63 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.63 | tc_Arrow__Order__Mirabelle_Oalt, v2, v_y) = v5 &
% 220.34/30.63 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.63 | tc_Arrow__Order__Mirabelle_Oalt, v1, v2) = v3 &
% 220.34/30.63 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.63 | tc_Arrow__Order__Mirabelle_Oalt, v1, v_y) = v7 &
% 220.34/30.63 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.63 | tc_Arrow__Order__Mirabelle_Oalt, v_y, v2) = v9 & c_member(v0,
% 220.34/30.63 | v9, v_L) = v10 & c_member(v0, v7, v_L) = v8 & c_member(v0, v5,
% 220.34/30.63 | v_L) = v6 & c_member(v0, v3, v_L) = v4 & $i(v9) & $i(v7) &
% 220.34/30.63 | $i(v5) & $i(v3) & $i(v2) & $i(v1) & ((v10 = 0 & v1 = v_x & ~
% 220.34/30.63 | (v2 = v_x) & ? [v11: $i] : ? [v12: $i] : ? [v13: any] :
% 220.34/30.63 | ? [v14: $i] : ? [v15: any] :
% 220.34/30.63 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.63 | tc_Arrow__Order__Mirabelle_Oalt, v2, v11) = v12 &
% 220.34/30.63 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.63 | tc_Arrow__Order__Mirabelle_Oalt, v_y, v11) = v14 &
% 220.34/30.63 | c_member(v0, v14, v_L) = v15 & c_member(v0, v12, v_L) =
% 220.34/30.63 | v13 & $i(v14) & $i(v12) & $i(v11) & ((v13 = 0 & ~ (v15 =
% 220.34/30.63 | 0) & ~ (v11 = v_x) & ~ (v11 = v_y)) | (v11 = v_x &
% 220.34/30.63 | v6 = 0)))) | ( ~ (v1 = v_x) & ((v8 = 0 & v2 = v_x & ?
% 220.34/30.63 | [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: int]
% 220.34/30.63 | : ( ~ (v14 = 0) & ~ (v11 = v_x) &
% 220.34/30.63 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.63 | tc_Arrow__Order__Mirabelle_Oalt, v1, v11) = v13 &
% 220.34/30.63 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.63 | tc_Arrow__Order__Mirabelle_Oalt, v_y, v11) = v12 &
% 220.34/30.63 | c_member(v0, v13, v_L) = v14 & c_member(v0, v12, v_L)
% 220.34/30.63 | = 0 & $i(v13) & $i(v12) & $i(v11))) | (v4 = 0 & ~ (v2
% 220.34/30.63 | = v_x) & ? [v11: $i] : ? [v12: $i] : ? [v13: any] :
% 220.34/30.63 | ? [v14: $i] : ? [v15: any] :
% 220.34/30.63 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.63 | tc_Arrow__Order__Mirabelle_Oalt, v2, v11) = v12 &
% 220.34/30.63 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.63 | tc_Arrow__Order__Mirabelle_Oalt, v1, v11) = v14 &
% 220.34/30.63 | c_member(v0, v14, v_L) = v15 & c_member(v0, v12, v_L)
% 220.34/30.63 | = v13 & $i(v14) & $i(v12) & $i(v11) & ((v13 = 0 & ~
% 220.34/30.63 | (v15 = 0) & ~ (v11 = v_x)) | (v11 = v_x & v6 = 0
% 220.34/30.63 | & ~ (v8 = 0)))))))))))
% 220.34/30.63 |
% 220.34/30.63 | ALPHA: (function-axioms) implies:
% 220.34/30.64 | (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 220.34/30.64 | (tc_prod(v3, v2) = v1) | ~ (tc_prod(v3, v2) = v0))
% 220.34/30.64 | (19) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 220.34/30.64 | : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (c_member(v4, v3, v2) =
% 220.34/30.64 | v1) | ~ (c_member(v4, v3, v2) = v0))
% 220.34/30.64 | (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 220.34/30.64 | ! [v5: $i] : (v1 = v0 | ~ (c_Product__Type_OPair(v5, v4, v3, v2) =
% 220.34/30.64 | v1) | ~ (c_Product__Type_OPair(v5, v4, v3, v2) = v0))
% 220.34/30.64 |
% 220.34/30.64 | DELTA: instantiating (10) with fresh symbols all_625_0, all_625_1 gives:
% 220.34/30.64 | (21) tc_fun(all_625_1, tc_HOL_Obool) = all_625_0 &
% 220.34/30.64 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.64 | tc_Arrow__Order__Mirabelle_Oalt) = all_625_1 & $i(all_625_0) &
% 220.34/30.64 | $i(all_625_1) & ? [v0: $i] : (c_member(all_625_0, v0,
% 220.34/30.64 | c_Arrow__Order__Mirabelle_OLin) = 0 & $i(v0))
% 220.34/30.64 |
% 220.34/30.64 | ALPHA: (21) implies:
% 220.34/30.64 | (22) tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.64 | tc_Arrow__Order__Mirabelle_Oalt) = all_625_1
% 220.34/30.64 |
% 220.34/30.64 | DELTA: instantiating (7) with fresh symbols all_634_0, all_634_1 gives:
% 220.34/30.64 | (23) tc_fun(all_634_1, tc_HOL_Obool) = all_634_0 &
% 220.34/30.64 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.64 | tc_Arrow__Order__Mirabelle_Oalt) = all_634_1 & $i(all_634_0) &
% 220.34/30.64 | $i(all_634_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 220.34/30.64 | (c_Arrow__Order__Mirabelle_Omktop(v1, v0) = v2) | ~ $i(v1) | ~
% 220.34/30.64 | $i(v0) | ? [v3: any] : ? [v4: any] : (c_member(all_634_0, v2,
% 220.34/30.64 | c_Arrow__Order__Mirabelle_OLin) = v4 & c_member(all_634_0, v1,
% 220.34/30.64 | c_Arrow__Order__Mirabelle_OLin) = v3 & ( ~ (v3 = 0) | v4 = 0)))
% 220.34/30.64 |
% 220.34/30.64 | ALPHA: (23) implies:
% 220.34/30.64 | (24) $i(all_634_1)
% 220.34/30.64 | (25) tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.64 | tc_Arrow__Order__Mirabelle_Oalt) = all_634_1
% 220.34/30.64 |
% 220.34/30.64 | DELTA: instantiating (6) with fresh symbols all_637_0, all_637_1 gives:
% 220.34/30.64 | (26) tc_fun(all_637_1, tc_HOL_Obool) = all_637_0 &
% 220.34/30.64 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.64 | tc_Arrow__Order__Mirabelle_Oalt) = all_637_1 & $i(all_637_0) &
% 220.34/30.64 | $i(all_637_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 220.34/30.64 | (c_Arrow__Order__Mirabelle_Omkbot(v1, v0) = v2) | ~ $i(v1) | ~
% 220.34/30.64 | $i(v0) | ? [v3: any] : ? [v4: any] : (c_member(all_637_0, v2,
% 220.34/30.64 | c_Arrow__Order__Mirabelle_OLin) = v4 & c_member(all_637_0, v1,
% 220.34/30.64 | c_Arrow__Order__Mirabelle_OLin) = v3 & ( ~ (v3 = 0) | v4 = 0)))
% 220.34/30.64 |
% 220.34/30.64 | ALPHA: (26) implies:
% 220.34/30.64 | (27) tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.64 | tc_Arrow__Order__Mirabelle_Oalt) = all_637_1
% 220.34/30.64 |
% 220.34/30.64 | DELTA: instantiating (4) with fresh symbols all_642_0, all_642_1 gives:
% 220.34/30.64 | (28) tc_fun(all_642_1, tc_HOL_Obool) = all_642_0 &
% 220.34/30.64 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.64 | tc_Arrow__Order__Mirabelle_Oalt) = all_642_1 & $i(all_642_0) &
% 220.34/30.64 | $i(all_642_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 220.34/30.64 | : ( ~ (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.64 | tc_Arrow__Order__Mirabelle_Oalt, v0, v1) = v3) | ~
% 220.34/30.64 | (c_member(all_642_1, v3, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~
% 220.34/30.64 | $i(v0) | ? [v4: any] : ? [v5: $i] : ? [v6: any] :
% 220.34/30.64 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.64 | tc_Arrow__Order__Mirabelle_Oalt, v1, v0) = v5 &
% 220.34/30.64 | c_member(all_642_0, v2, c_Arrow__Order__Mirabelle_OLin) = v4 &
% 220.34/30.64 | c_member(all_642_1, v5, v2) = v6 & $i(v5) & ( ~ (v6 = 0) | ~ (v4
% 220.34/30.64 | = 0))))
% 220.34/30.64 |
% 220.34/30.64 | ALPHA: (28) implies:
% 220.34/30.64 | (29) tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.64 | tc_Arrow__Order__Mirabelle_Oalt) = all_642_1
% 220.34/30.64 |
% 220.34/30.64 | DELTA: instantiating (11) with fresh symbols all_648_0, all_648_1 gives:
% 220.34/30.64 | (30) tc_fun(all_648_1, tc_HOL_Obool) = all_648_0 &
% 220.34/30.64 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.64 | tc_Arrow__Order__Mirabelle_Oalt) = all_648_1 & $i(all_648_0) &
% 220.34/30.64 | $i(all_648_1) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~
% 220.34/30.64 | (c_member(all_648_0, v0, c_Arrow__Order__Mirabelle_OLin) = v1) | ~
% 220.34/30.64 | $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) &
% 220.34/30.64 | c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.64 | tc_Arrow__Order__Mirabelle_Oalt, v0) = v2 & c_member(all_648_0,
% 220.34/30.64 | v2, c_Arrow__Order__Mirabelle_OLin) = v3 & $i(v2))) & ! [v0:
% 220.34/30.64 | $i] : ( ~ (c_member(all_648_0, v0, c_Arrow__Order__Mirabelle_OLin) =
% 220.34/30.64 | 0) | ~ $i(v0) | ? [v1: $i] :
% 220.34/30.64 | (c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.64 | tc_Arrow__Order__Mirabelle_Oalt, v0) = v1 & c_member(all_648_0,
% 220.34/30.64 | v1, c_Arrow__Order__Mirabelle_OLin) = 0 & $i(v1)))
% 220.34/30.64 |
% 220.34/30.64 | ALPHA: (30) implies:
% 220.34/30.64 | (31) tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.64 | tc_Arrow__Order__Mirabelle_Oalt) = all_648_1
% 220.34/30.64 |
% 220.34/30.64 | DELTA: instantiating (5) with fresh symbols all_657_0, all_657_1 gives:
% 220.34/30.64 | (32) tc_fun(all_657_1, tc_HOL_Obool) = all_657_0 &
% 220.34/30.64 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.64 | tc_Arrow__Order__Mirabelle_Oalt) = all_657_1 & $i(all_657_0) &
% 220.34/30.64 | $i(all_657_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 220.34/30.64 | : ! [v4: any] : (v1 = v0 | ~
% 220.34/30.64 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.64 | tc_Arrow__Order__Mirabelle_Oalt, v0, v1) = v3) | ~
% 220.34/30.64 | (c_member(all_657_1, v3, v2) = v4) | ~ $i(v2) | ~ $i(v1) | ~
% 220.34/30.64 | $i(v0) | ? [v5: any] : ? [v6: $i] : ? [v7: any] :
% 220.34/30.64 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.64 | tc_Arrow__Order__Mirabelle_Oalt, v1, v0) = v6 &
% 220.34/30.64 | c_member(all_657_0, v2, c_Arrow__Order__Mirabelle_OLin) = v5 &
% 220.34/30.64 | c_member(all_657_1, v6, v2) = v7 & $i(v6) & ( ~ (v5 = 0) | (( ~
% 220.34/30.64 | (v7 = 0) | ~ (v4 = 0)) & (v7 = 0 | v4 = 0)))))
% 220.34/30.64 |
% 220.34/30.64 | ALPHA: (32) implies:
% 220.34/30.64 | (33) tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.64 | tc_Arrow__Order__Mirabelle_Oalt) = all_657_1
% 220.34/30.64 |
% 220.34/30.64 | DELTA: instantiating (2) with fresh symbol all_666_0 gives:
% 220.34/30.65 | (34) tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.65 | tc_Arrow__Order__Mirabelle_Oalt) = all_666_0 & $i(all_666_0) & !
% 220.34/30.65 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 220.34/30.65 | [v5: $i] : ! [v6: int] : (v6 = 0 | v3 = v0 | ~
% 220.34/30.65 | (c_Arrow__Order__Mirabelle_Omktop(v1, v0) = v5) | ~
% 220.34/30.65 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.65 | tc_Arrow__Order__Mirabelle_Oalt, v3, v2) = v4) | ~
% 220.34/30.65 | (c_member(all_666_0, v4, v5) = v6) | ~ $i(v3) | ~ $i(v2) | ~
% 220.34/30.65 | $i(v1) | ~ $i(v0) | ( ~ (v2 = v0) & ? [v7: int] : ( ~ (v7 = 0) &
% 220.34/30.65 | c_member(all_666_0, v4, v1) = v7))) & ! [v0: $i] : ! [v1: $i]
% 220.34/30.65 | : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 220.34/30.65 | (c_Arrow__Order__Mirabelle_Omktop(v1, v0) = v5) | ~
% 220.34/30.65 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.65 | tc_Arrow__Order__Mirabelle_Oalt, v3, v2) = v4) | ~
% 220.34/30.65 | (c_member(all_666_0, v4, v5) = 0) | ~ $i(v3) | ~ $i(v2) | ~
% 220.34/30.65 | $i(v1) | ~ $i(v0) | ( ~ (v3 = v0) & (v2 = v0 | c_member(all_666_0,
% 220.34/30.65 | v4, v1) = 0)))
% 220.34/30.65 |
% 220.34/30.65 | ALPHA: (34) implies:
% 220.34/30.65 | (35) tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.65 | tc_Arrow__Order__Mirabelle_Oalt) = all_666_0
% 220.34/30.65 |
% 220.34/30.65 | DELTA: instantiating (1) with fresh symbol all_669_0 gives:
% 220.34/30.65 | (36) tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.65 | tc_Arrow__Order__Mirabelle_Oalt) = all_669_0 & $i(all_669_0) & !
% 220.34/30.65 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 220.34/30.65 | [v5: $i] : ! [v6: int] : (v6 = 0 | v2 = v0 | ~
% 220.34/30.65 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.65 | tc_Arrow__Order__Mirabelle_Oalt, v3, v2) = v4) | ~
% 220.34/30.65 | (c_Arrow__Order__Mirabelle_Omkbot(v1, v0) = v5) | ~
% 220.34/30.65 | (c_member(all_669_0, v4, v5) = v6) | ~ $i(v3) | ~ $i(v2) | ~
% 220.34/30.65 | $i(v1) | ~ $i(v0) | ( ~ (v3 = v0) & ? [v7: int] : ( ~ (v7 = 0) &
% 220.34/30.65 | c_member(all_669_0, v4, v1) = v7))) & ! [v0: $i] : ! [v1: $i]
% 220.34/30.65 | : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 220.34/30.65 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.65 | tc_Arrow__Order__Mirabelle_Oalt, v3, v2) = v4) | ~
% 220.34/30.65 | (c_Arrow__Order__Mirabelle_Omkbot(v1, v0) = v5) | ~
% 220.34/30.65 | (c_member(all_669_0, v4, v5) = 0) | ~ $i(v3) | ~ $i(v2) | ~
% 220.34/30.65 | $i(v1) | ~ $i(v0) | ( ~ (v2 = v0) & (v3 = v0 | c_member(all_669_0,
% 220.34/30.65 | v4, v1) = 0)))
% 220.34/30.65 |
% 220.34/30.65 | ALPHA: (36) implies:
% 220.34/30.65 | (37) tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.65 | tc_Arrow__Order__Mirabelle_Oalt) = all_669_0
% 220.34/30.65 |
% 220.34/30.65 | DELTA: instantiating (13) with fresh symbol all_674_0 gives:
% 220.34/30.65 | (38) tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.65 | tc_Arrow__Order__Mirabelle_Oalt) = all_674_0 & $i(all_674_0) & !
% 220.34/30.65 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 220.34/30.65 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.65 | tc_Arrow__Order__Mirabelle_Oalt, v0, v1) = v2) | ~ $i(v1) | ~
% 220.34/30.65 | $i(v0) | ? [v3: any] : ? [v4: $i] : ? [v5: any] :
% 220.34/30.65 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.65 | tc_Arrow__Order__Mirabelle_Oalt, v1, v0) = v4 &
% 220.34/30.65 | c_member(all_674_0, v4, v_L) = v5 & c_member(all_674_0, v2, v_L) =
% 220.34/30.65 | v3 & $i(v4) & (v5 = 0 | v3 = 0))) & ! [v0: $i] : ! [v1: $i] : !
% 220.34/30.65 | [v2: $i] : ( ~ (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.65 | tc_Arrow__Order__Mirabelle_Oalt, v0, v1) = v2) | ~ $i(v1) | ~
% 220.34/30.65 | $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & c_member(all_674_0, v2, v_L)
% 220.34/30.65 | = v3) | ! [v3: $i] : ! [v4: $i] : ( ~
% 220.34/30.65 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.65 | tc_Arrow__Order__Mirabelle_Oalt, v0, v3) = v4) | ~ $i(v3) |
% 220.34/30.65 | ? [v5: $i] : ? [v6: any] : ? [v7: any] :
% 220.34/30.65 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.65 | tc_Arrow__Order__Mirabelle_Oalt, v1, v3) = v5 &
% 220.34/30.65 | c_member(all_674_0, v5, v_L) = v6 & c_member(all_674_0, v4, v_L)
% 220.34/30.65 | = v7 & $i(v5) & ( ~ (v6 = 0) | v7 = 0)))) & ! [v0: $i] : !
% 220.34/30.65 | [v1: $i] : ( ~ (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.65 | tc_Arrow__Order__Mirabelle_Oalt, v0, v0) = v1) | ~ $i(v0) | ?
% 220.34/30.65 | [v2: int] : ( ~ (v2 = 0) & c_member(all_674_0, v1, v_L) = v2))
% 220.34/30.65 |
% 220.34/30.65 | ALPHA: (38) implies:
% 220.34/30.65 | (39) tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.65 | tc_Arrow__Order__Mirabelle_Oalt) = all_674_0
% 220.34/30.65 | (40) ! [v0: $i] : ! [v1: $i] : ( ~
% 220.34/30.65 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.65 | tc_Arrow__Order__Mirabelle_Oalt, v0, v0) = v1) | ~ $i(v0) | ?
% 220.34/30.65 | [v2: int] : ( ~ (v2 = 0) & c_member(all_674_0, v1, v_L) = v2))
% 220.34/30.65 | (41) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 220.34/30.65 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.65 | tc_Arrow__Order__Mirabelle_Oalt, v0, v1) = v2) | ~ $i(v1) | ~
% 220.34/30.65 | $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & c_member(all_674_0, v2, v_L)
% 220.34/30.65 | = v3) | ! [v3: $i] : ! [v4: $i] : ( ~
% 220.34/30.65 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.65 | tc_Arrow__Order__Mirabelle_Oalt, v0, v3) = v4) | ~ $i(v3) |
% 220.34/30.65 | ? [v5: $i] : ? [v6: any] : ? [v7: any] :
% 220.34/30.65 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.65 | tc_Arrow__Order__Mirabelle_Oalt, v1, v3) = v5 &
% 220.34/30.65 | c_member(all_674_0, v5, v_L) = v6 & c_member(all_674_0, v4, v_L)
% 220.34/30.65 | = v7 & $i(v5) & ( ~ (v6 = 0) | v7 = 0))))
% 220.34/30.65 | (42) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 220.34/30.65 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.65 | tc_Arrow__Order__Mirabelle_Oalt, v0, v1) = v2) | ~ $i(v1) | ~
% 220.34/30.65 | $i(v0) | ? [v3: any] : ? [v4: $i] : ? [v5: any] :
% 220.34/30.65 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.65 | tc_Arrow__Order__Mirabelle_Oalt, v1, v0) = v4 &
% 220.34/30.65 | c_member(all_674_0, v4, v_L) = v5 & c_member(all_674_0, v2, v_L) =
% 220.34/30.65 | v3 & $i(v4) & (v5 = 0 | v3 = 0)))
% 220.34/30.65 |
% 220.34/30.65 | DELTA: instantiating (9) with fresh symbols all_677_0, all_677_1 gives:
% 220.34/30.66 | (43) tc_fun(all_677_1, tc_HOL_Obool) = all_677_0 &
% 220.34/30.66 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.66 | tc_Arrow__Order__Mirabelle_Oalt) = all_677_1 & $i(all_677_0) &
% 220.34/30.66 | $i(all_677_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 220.34/30.66 | : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: any] : (v4 = v3 |
% 220.34/30.66 | ~ (c_Arrow__Order__Mirabelle_Obelow(v2, v4, v3) = v6) | ~
% 220.34/30.66 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.66 | tc_Arrow__Order__Mirabelle_Oalt, v1, v0) = v5) | ~
% 220.34/30.66 | (c_member(all_677_1, v5, v6) = v7) | ~ $i(v4) | ~ $i(v3) | ~
% 220.34/30.66 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v8: any] : ? [v9: $i] : ?
% 220.34/30.66 | [v10: any] : ? [v11: $i] : ? [v12: any] : ? [v13: any] :
% 220.34/30.66 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.66 | tc_Arrow__Order__Mirabelle_Oalt, v3, v0) = v11 &
% 220.34/30.66 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.66 | tc_Arrow__Order__Mirabelle_Oalt, v1, v3) = v9 &
% 220.34/30.66 | c_member(all_677_0, v2, c_Arrow__Order__Mirabelle_OLin) = v8 &
% 220.34/30.66 | c_member(all_677_1, v11, v2) = v12 & c_member(all_677_1, v9, v2) =
% 220.34/30.66 | v10 & c_member(all_677_1, v5, v2) = v13 & $i(v11) & $i(v9) & ( ~
% 220.34/30.66 | (v8 = 0) | (( ~ (v7 = 0) | ( ~ (v1 = v0) & ( ~ (v4 = v0) | v10 =
% 220.34/30.66 | 0) & (v4 = v0 | (( ~ (v4 = v1) | v12 = 0 | v3 = v0) &
% 220.34/30.66 | (v13 = 0 | v4 = v1))))) & (v7 = 0 | v1 = v0 | (v4 = v0
% 220.34/30.66 | & ~ (v10 = 0)) | ( ~ (v4 = v0) & ((v4 = v1 & ~ (v12 = 0)
% 220.34/30.66 | & ~ (v3 = v0)) | ( ~ (v13 = 0) & ~ (v4 = v1)))))))))
% 220.34/30.66 |
% 220.34/30.66 | ALPHA: (43) implies:
% 220.34/30.66 | (44) tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.66 | tc_Arrow__Order__Mirabelle_Oalt) = all_677_1
% 220.34/30.66 |
% 220.34/30.66 | DELTA: instantiating (8) with fresh symbols all_680_0, all_680_1 gives:
% 220.34/30.66 | (45) tc_fun(all_680_1, tc_HOL_Obool) = all_680_0 &
% 220.34/30.66 | tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.66 | tc_Arrow__Order__Mirabelle_Oalt) = all_680_1 & $i(all_680_0) &
% 220.34/30.66 | $i(all_680_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 220.34/30.66 | : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: any] : (v4 = v3 |
% 220.34/30.66 | ~ (c_Arrow__Order__Mirabelle_Oabove(v2, v4, v3) = v6) | ~
% 220.34/30.66 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.66 | tc_Arrow__Order__Mirabelle_Oalt, v1, v0) = v5) | ~
% 220.34/30.66 | (c_member(all_680_1, v5, v6) = v7) | ~ $i(v4) | ~ $i(v3) | ~
% 220.34/30.66 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v8: any] : ? [v9: $i] : ?
% 220.34/30.66 | [v10: any] : ? [v11: $i] : ? [v12: any] : ? [v13: any] :
% 220.34/30.66 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.66 | tc_Arrow__Order__Mirabelle_Oalt, v4, v0) = v9 &
% 220.34/30.66 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.66 | tc_Arrow__Order__Mirabelle_Oalt, v1, v4) = v11 &
% 220.34/30.66 | c_member(all_680_0, v2, c_Arrow__Order__Mirabelle_OLin) = v8 &
% 220.34/30.66 | c_member(all_680_1, v11, v2) = v12 & c_member(all_680_1, v9, v2) =
% 220.34/30.66 | v10 & c_member(all_680_1, v5, v2) = v13 & $i(v11) & $i(v9) & ( ~
% 220.34/30.66 | (v8 = 0) | (( ~ (v7 = 0) | ( ~ (v1 = v0) & ( ~ (v3 = v1) | v10 =
% 220.34/30.66 | 0) & (v3 = v1 | (( ~ (v3 = v0) | v12 = 0 | v4 = v1) &
% 220.34/30.66 | (v13 = 0 | v3 = v0))))) & (v7 = 0 | v1 = v0 | (v3 = v1
% 220.34/30.66 | & ~ (v10 = 0)) | ( ~ (v3 = v1) & ((v3 = v0 & ~ (v12 = 0)
% 220.34/30.66 | & ~ (v4 = v1)) | ( ~ (v13 = 0) & ~ (v3 = v0)))))))))
% 220.34/30.66 |
% 220.34/30.66 | ALPHA: (45) implies:
% 220.34/30.66 | (46) tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.66 | tc_Arrow__Order__Mirabelle_Oalt) = all_680_1
% 220.34/30.66 |
% 220.34/30.66 | DELTA: instantiating (17) with fresh symbol all_683_0 gives:
% 220.34/30.66 | (47) tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.66 | tc_Arrow__Order__Mirabelle_Oalt) = all_683_0 & $i(all_683_0) & ( ?
% 220.34/30.66 | [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] : ? [v4: $i] :
% 220.34/30.66 | ? [v5: any] : ? [v6: $i] : ? [v7: any] : ? [v8: $i] : ? [v9:
% 220.34/30.66 | any] : ? [v10: $i] : ? [v11: any] : ? [v12: $i] : ? [v13: any]
% 220.34/30.66 | : ( ~ (v1 = v0) &
% 220.34/30.66 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.66 | tc_Arrow__Order__Mirabelle_Oalt, v1, v0) = v8 &
% 220.34/30.66 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.66 | tc_Arrow__Order__Mirabelle_Oalt, v1, v_y) = v10 &
% 220.34/30.66 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.66 | tc_Arrow__Order__Mirabelle_Oalt, v0, v1) = v2 &
% 220.34/30.66 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.66 | tc_Arrow__Order__Mirabelle_Oalt, v0, v_y) = v4 &
% 220.34/30.66 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.66 | tc_Arrow__Order__Mirabelle_Oalt, v_y, v1) = v6 &
% 220.34/30.66 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.66 | tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = v12 &
% 220.34/30.66 | c_member(all_683_0, v12, v_L) = v13 & c_member(all_683_0, v10,
% 220.34/30.66 | v_L) = v11 & c_member(all_683_0, v8, v_L) = v9 &
% 220.34/30.66 | c_member(all_683_0, v6, v_L) = v7 & c_member(all_683_0, v4, v_L) =
% 220.34/30.66 | v5 & c_member(all_683_0, v2, v_L) = v3 & $i(v12) & $i(v10) &
% 220.34/30.66 | $i(v8) & $i(v6) & $i(v4) & $i(v2) & $i(v1) & $i(v0) & ( ~ (v13 =
% 220.34/30.66 | 0) | ~ (v1 = v_x) | v0 = v_x) & ( ~ (v11 = 0) | ~ (v0 = v_x)
% 220.34/30.66 | | v1 = v_x) & ( ~ (v9 = 0) | v1 = v_x | v0 = v_x) & ( ~ (v7 = 0)
% 220.34/30.66 | | ~ (v0 = v_x) | v1 = v_x) & ( ~ (v5 = 0) | ~ (v1 = v_x) | v0
% 220.34/30.66 | = v_x) & ( ~ (v3 = 0) | v1 = v_x | v0 = v_x) & ( ~ (v1 = v_x) |
% 220.34/30.66 | ~ (v0 = v_y)) & ( ~ (v1 = v_y) | ~ (v0 = v_x))) | ? [v0: $i] :
% 220.34/30.66 | ? [v1: $i] : ? [v2: $i] : ? [v3: any] : ? [v4: $i] : ? [v5:
% 220.34/30.66 | any] : ? [v6: $i] : ? [v7: any] : ? [v8: $i] : ? [v9: any] :
% 220.34/30.66 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.66 | tc_Arrow__Order__Mirabelle_Oalt, v1, v_y) = v4 &
% 220.34/30.66 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.66 | tc_Arrow__Order__Mirabelle_Oalt, v0, v1) = v2 &
% 220.34/30.66 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.66 | tc_Arrow__Order__Mirabelle_Oalt, v0, v_y) = v6 &
% 220.34/30.66 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.66 | tc_Arrow__Order__Mirabelle_Oalt, v_y, v1) = v8 &
% 220.34/30.66 | c_member(all_683_0, v8, v_L) = v9 & c_member(all_683_0, v6, v_L) =
% 220.34/30.66 | v7 & c_member(all_683_0, v4, v_L) = v5 & c_member(all_683_0, v2,
% 220.34/30.66 | v_L) = v3 & $i(v8) & $i(v6) & $i(v4) & $i(v2) & $i(v1) & $i(v0)
% 220.34/30.66 | & ((v9 = 0 & v0 = v_x & ~ (v1 = v_x) & ? [v10: $i] : ? [v11:
% 220.34/30.66 | $i] : ? [v12: any] : ? [v13: $i] : ? [v14: any] :
% 220.34/30.66 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.66 | tc_Arrow__Order__Mirabelle_Oalt, v1, v10) = v11 &
% 220.34/30.66 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.66 | tc_Arrow__Order__Mirabelle_Oalt, v_y, v10) = v13 &
% 220.34/30.66 | c_member(all_683_0, v13, v_L) = v14 & c_member(all_683_0,
% 220.34/30.66 | v11, v_L) = v12 & $i(v13) & $i(v11) & $i(v10) & ((v12 = 0
% 220.34/30.66 | & ~ (v14 = 0) & ~ (v10 = v_x) & ~ (v10 = v_y)) | (v10
% 220.34/30.66 | = v_x & v5 = 0)))) | ( ~ (v0 = v_x) & ((v7 = 0 & v1 =
% 220.34/30.66 | v_x & ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ?
% 220.34/30.66 | [v13: int] : ( ~ (v13 = 0) & ~ (v10 = v_x) &
% 220.34/30.66 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.66 | tc_Arrow__Order__Mirabelle_Oalt, v0, v10) = v12 &
% 220.34/30.66 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.66 | tc_Arrow__Order__Mirabelle_Oalt, v_y, v10) = v11 &
% 220.34/30.66 | c_member(all_683_0, v12, v_L) = v13 &
% 220.34/30.66 | c_member(all_683_0, v11, v_L) = 0 & $i(v12) & $i(v11) &
% 220.34/30.66 | $i(v10))) | (v3 = 0 & ~ (v1 = v_x) & ? [v10: $i] : ?
% 220.34/30.66 | [v11: $i] : ? [v12: any] : ? [v13: $i] : ? [v14: any] :
% 220.34/30.66 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.66 | tc_Arrow__Order__Mirabelle_Oalt, v1, v10) = v11 &
% 220.34/30.66 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.66 | tc_Arrow__Order__Mirabelle_Oalt, v0, v10) = v13 &
% 220.34/30.66 | c_member(all_683_0, v13, v_L) = v14 &
% 220.34/30.66 | c_member(all_683_0, v11, v_L) = v12 & $i(v13) & $i(v11)
% 220.34/30.66 | & $i(v10) & ((v12 = 0 & ~ (v14 = 0) & ~ (v10 = v_x)) |
% 220.34/30.66 | (v10 = v_x & v5 = 0 & ~ (v7 = 0))))))))))
% 220.34/30.66 |
% 220.34/30.66 | ALPHA: (47) implies:
% 220.34/30.66 | (48) tc_prod(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.66 | tc_Arrow__Order__Mirabelle_Oalt) = all_683_0
% 220.34/30.67 | (49) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] : ? [v4: $i] :
% 220.34/30.67 | ? [v5: any] : ? [v6: $i] : ? [v7: any] : ? [v8: $i] : ? [v9: any]
% 220.34/30.67 | : ? [v10: $i] : ? [v11: any] : ? [v12: $i] : ? [v13: any] : ( ~
% 220.34/30.67 | (v1 = v0) & c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.67 | tc_Arrow__Order__Mirabelle_Oalt, v1, v0) = v8 &
% 220.34/30.67 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.67 | tc_Arrow__Order__Mirabelle_Oalt, v1, v_y) = v10 &
% 220.34/30.67 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.67 | tc_Arrow__Order__Mirabelle_Oalt, v0, v1) = v2 &
% 220.34/30.67 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.67 | tc_Arrow__Order__Mirabelle_Oalt, v0, v_y) = v4 &
% 220.34/30.67 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.67 | tc_Arrow__Order__Mirabelle_Oalt, v_y, v1) = v6 &
% 220.34/30.67 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.67 | tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = v12 &
% 220.34/30.67 | c_member(all_683_0, v12, v_L) = v13 & c_member(all_683_0, v10, v_L)
% 220.34/30.67 | = v11 & c_member(all_683_0, v8, v_L) = v9 & c_member(all_683_0, v6,
% 220.34/30.67 | v_L) = v7 & c_member(all_683_0, v4, v_L) = v5 &
% 220.34/30.67 | c_member(all_683_0, v2, v_L) = v3 & $i(v12) & $i(v10) & $i(v8) &
% 220.34/30.67 | $i(v6) & $i(v4) & $i(v2) & $i(v1) & $i(v0) & ( ~ (v13 = 0) | ~ (v1
% 220.34/30.67 | = v_x) | v0 = v_x) & ( ~ (v11 = 0) | ~ (v0 = v_x) | v1 = v_x) &
% 220.34/30.67 | ( ~ (v9 = 0) | v1 = v_x | v0 = v_x) & ( ~ (v7 = 0) | ~ (v0 = v_x) |
% 220.34/30.67 | v1 = v_x) & ( ~ (v5 = 0) | ~ (v1 = v_x) | v0 = v_x) & ( ~ (v3 =
% 220.34/30.67 | 0) | v1 = v_x | v0 = v_x) & ( ~ (v1 = v_x) | ~ (v0 = v_y)) & (
% 220.34/30.67 | ~ (v1 = v_y) | ~ (v0 = v_x))) | ? [v0: $i] : ? [v1: $i] : ?
% 220.34/30.67 | [v2: $i] : ? [v3: any] : ? [v4: $i] : ? [v5: any] : ? [v6: $i] :
% 220.34/30.67 | ? [v7: any] : ? [v8: $i] : ? [v9: any] :
% 220.34/30.67 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.67 | tc_Arrow__Order__Mirabelle_Oalt, v1, v_y) = v4 &
% 220.34/30.67 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.67 | tc_Arrow__Order__Mirabelle_Oalt, v0, v1) = v2 &
% 220.34/30.67 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.67 | tc_Arrow__Order__Mirabelle_Oalt, v0, v_y) = v6 &
% 220.34/30.67 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.67 | tc_Arrow__Order__Mirabelle_Oalt, v_y, v1) = v8 &
% 220.34/30.67 | c_member(all_683_0, v8, v_L) = v9 & c_member(all_683_0, v6, v_L) =
% 220.34/30.67 | v7 & c_member(all_683_0, v4, v_L) = v5 & c_member(all_683_0, v2,
% 220.34/30.67 | v_L) = v3 & $i(v8) & $i(v6) & $i(v4) & $i(v2) & $i(v1) & $i(v0) &
% 220.34/30.67 | ((v9 = 0 & v0 = v_x & ~ (v1 = v_x) & ? [v10: $i] : ? [v11: $i] :
% 220.34/30.67 | ? [v12: any] : ? [v13: $i] : ? [v14: any] :
% 220.34/30.67 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.67 | tc_Arrow__Order__Mirabelle_Oalt, v1, v10) = v11 &
% 220.34/30.67 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.67 | tc_Arrow__Order__Mirabelle_Oalt, v_y, v10) = v13 &
% 220.34/30.67 | c_member(all_683_0, v13, v_L) = v14 & c_member(all_683_0, v11,
% 220.34/30.67 | v_L) = v12 & $i(v13) & $i(v11) & $i(v10) & ((v12 = 0 & ~
% 220.34/30.67 | (v14 = 0) & ~ (v10 = v_x) & ~ (v10 = v_y)) | (v10 = v_x
% 220.34/30.67 | & v5 = 0)))) | ( ~ (v0 = v_x) & ((v7 = 0 & v1 = v_x & ?
% 220.34/30.67 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: int] : (
% 220.34/30.67 | ~ (v13 = 0) & ~ (v10 = v_x) &
% 220.34/30.67 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.67 | tc_Arrow__Order__Mirabelle_Oalt, v0, v10) = v12 &
% 220.34/30.67 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.67 | tc_Arrow__Order__Mirabelle_Oalt, v_y, v10) = v11 &
% 220.34/30.67 | c_member(all_683_0, v12, v_L) = v13 & c_member(all_683_0,
% 220.34/30.67 | v11, v_L) = 0 & $i(v12) & $i(v11) & $i(v10))) | (v3 = 0
% 220.34/30.67 | & ~ (v1 = v_x) & ? [v10: $i] : ? [v11: $i] : ? [v12:
% 220.34/30.67 | any] : ? [v13: $i] : ? [v14: any] :
% 220.34/30.67 | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.67 | tc_Arrow__Order__Mirabelle_Oalt, v1, v10) = v11 &
% 220.34/30.67 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.67 | tc_Arrow__Order__Mirabelle_Oalt, v0, v10) = v13 &
% 220.34/30.67 | c_member(all_683_0, v13, v_L) = v14 & c_member(all_683_0,
% 220.34/30.67 | v11, v_L) = v12 & $i(v13) & $i(v11) & $i(v10) & ((v12 =
% 220.34/30.67 | 0 & ~ (v14 = 0) & ~ (v10 = v_x)) | (v10 = v_x & v5 =
% 220.34/30.67 | 0 & ~ (v7 = 0)))))))))
% 220.34/30.67 |
% 220.34/30.67 | GROUND_INST: instantiating (18) with all_637_1, all_657_1,
% 220.34/30.67 | tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.67 | simplifying with (27), (33) gives:
% 220.34/30.67 | (50) all_657_1 = all_637_1
% 220.34/30.67 |
% 220.34/30.67 | GROUND_INST: instantiating (18) with all_625_1, all_657_1,
% 220.34/30.67 | tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.67 | simplifying with (22), (33) gives:
% 220.34/30.67 | (51) all_657_1 = all_625_1
% 220.34/30.67 |
% 220.34/30.67 | GROUND_INST: instantiating (18) with all_666_0, all_669_0,
% 220.34/30.67 | tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.67 | simplifying with (35), (37) gives:
% 220.34/30.67 | (52) all_669_0 = all_666_0
% 220.34/30.67 |
% 220.34/30.67 | GROUND_INST: instantiating (18) with all_657_1, all_669_0,
% 220.34/30.67 | tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.67 | simplifying with (33), (37) gives:
% 220.34/30.67 | (53) all_669_0 = all_657_1
% 220.34/30.67 |
% 220.34/30.67 | GROUND_INST: instantiating (18) with all_648_1, all_669_0,
% 220.34/30.67 | tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.67 | simplifying with (31), (37) gives:
% 220.34/30.67 | (54) all_669_0 = all_648_1
% 220.34/30.67 |
% 220.34/30.67 | GROUND_INST: instantiating (18) with all_666_0, all_674_0,
% 220.34/30.67 | tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.67 | simplifying with (35), (39) gives:
% 220.34/30.67 | (55) all_674_0 = all_666_0
% 220.34/30.67 |
% 220.34/30.67 | GROUND_INST: instantiating (18) with all_657_1, all_677_1,
% 220.34/30.67 | tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.67 | simplifying with (33), (44) gives:
% 220.34/30.67 | (56) all_677_1 = all_657_1
% 220.34/30.67 |
% 220.34/30.67 | GROUND_INST: instantiating (18) with all_642_1, all_677_1,
% 220.34/30.67 | tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.67 | simplifying with (29), (44) gives:
% 220.34/30.67 | (57) all_677_1 = all_642_1
% 220.34/30.67 |
% 220.34/30.67 | GROUND_INST: instantiating (18) with all_680_1, all_683_0,
% 220.34/30.67 | tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.67 | simplifying with (46), (48) gives:
% 220.34/30.67 | (58) all_683_0 = all_680_1
% 220.34/30.67 |
% 220.34/30.67 | GROUND_INST: instantiating (18) with all_674_0, all_683_0,
% 220.34/30.67 | tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.67 | simplifying with (39), (48) gives:
% 220.34/30.67 | (59) all_683_0 = all_674_0
% 220.34/30.67 |
% 220.34/30.67 | GROUND_INST: instantiating (18) with all_634_1, all_683_0,
% 220.34/30.67 | tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.67 | simplifying with (25), (48) gives:
% 220.34/30.67 | (60) all_683_0 = all_634_1
% 220.34/30.67 |
% 220.34/30.67 | COMBINE_EQS: (58), (59) imply:
% 220.34/30.67 | (61) all_680_1 = all_674_0
% 220.34/30.67 |
% 220.34/30.67 | COMBINE_EQS: (58), (60) imply:
% 220.34/30.67 | (62) all_680_1 = all_634_1
% 220.34/30.67 |
% 220.34/30.67 | COMBINE_EQS: (61), (62) imply:
% 220.34/30.67 | (63) all_674_0 = all_634_1
% 220.34/30.67 |
% 220.34/30.67 | SIMP: (63) implies:
% 220.34/30.67 | (64) all_674_0 = all_634_1
% 220.34/30.67 |
% 220.34/30.67 | COMBINE_EQS: (56), (57) imply:
% 220.34/30.67 | (65) all_657_1 = all_642_1
% 220.34/30.67 |
% 220.34/30.67 | SIMP: (65) implies:
% 220.34/30.67 | (66) all_657_1 = all_642_1
% 220.34/30.67 |
% 220.34/30.67 | COMBINE_EQS: (55), (64) imply:
% 220.34/30.67 | (67) all_666_0 = all_634_1
% 220.34/30.67 |
% 220.34/30.67 | SIMP: (67) implies:
% 220.34/30.67 | (68) all_666_0 = all_634_1
% 220.34/30.67 |
% 220.34/30.67 | COMBINE_EQS: (53), (54) imply:
% 220.34/30.67 | (69) all_657_1 = all_648_1
% 220.34/30.67 |
% 220.34/30.67 | SIMP: (69) implies:
% 220.34/30.67 | (70) all_657_1 = all_648_1
% 220.34/30.67 |
% 220.34/30.67 | COMBINE_EQS: (52), (54) imply:
% 220.34/30.67 | (71) all_666_0 = all_648_1
% 220.34/30.67 |
% 220.34/30.67 | SIMP: (71) implies:
% 220.34/30.67 | (72) all_666_0 = all_648_1
% 220.34/30.68 |
% 220.34/30.68 | COMBINE_EQS: (68), (72) imply:
% 220.34/30.68 | (73) all_648_1 = all_634_1
% 220.34/30.68 |
% 220.34/30.68 | SIMP: (73) implies:
% 220.34/30.68 | (74) all_648_1 = all_634_1
% 220.34/30.68 |
% 220.34/30.68 | COMBINE_EQS: (51), (66) imply:
% 220.34/30.68 | (75) all_642_1 = all_625_1
% 220.34/30.68 |
% 220.34/30.68 | COMBINE_EQS: (50), (66) imply:
% 220.34/30.68 | (76) all_642_1 = all_637_1
% 220.34/30.68 |
% 220.34/30.68 | COMBINE_EQS: (66), (70) imply:
% 220.34/30.68 | (77) all_648_1 = all_642_1
% 220.34/30.68 |
% 220.34/30.68 | SIMP: (77) implies:
% 220.34/30.68 | (78) all_648_1 = all_642_1
% 220.34/30.68 |
% 220.34/30.68 | COMBINE_EQS: (74), (78) imply:
% 220.34/30.68 | (79) all_642_1 = all_634_1
% 220.34/30.68 |
% 220.34/30.68 | SIMP: (79) implies:
% 220.34/30.68 | (80) all_642_1 = all_634_1
% 220.34/30.68 |
% 220.34/30.68 | COMBINE_EQS: (75), (76) imply:
% 220.34/30.68 | (81) all_637_1 = all_625_1
% 220.34/30.68 |
% 220.34/30.68 | COMBINE_EQS: (76), (80) imply:
% 220.34/30.68 | (82) all_637_1 = all_634_1
% 220.34/30.68 |
% 220.34/30.68 | COMBINE_EQS: (81), (82) imply:
% 220.34/30.68 | (83) all_634_1 = all_625_1
% 220.34/30.68 |
% 220.34/30.68 | COMBINE_EQS: (64), (83) imply:
% 220.34/30.68 | (84) all_674_0 = all_625_1
% 220.34/30.68 |
% 220.34/30.68 | COMBINE_EQS: (62), (83) imply:
% 220.34/30.68 | (85) all_680_1 = all_625_1
% 220.34/30.68 |
% 220.34/30.68 | COMBINE_EQS: (58), (85) imply:
% 220.34/30.68 | (86) all_683_0 = all_625_1
% 220.34/30.68 |
% 220.34/30.68 | REDUCE: (24), (83) imply:
% 220.34/30.68 | (87) $i(all_625_1)
% 220.34/30.68 |
% 220.34/30.68 | BETA: splitting (49) gives:
% 220.34/30.68 |
% 220.34/30.68 | Case 1:
% 220.34/30.68 | |
% 220.34/30.68 | | (88) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] : ? [v4: $i]
% 220.34/30.68 | | : ? [v5: any] : ? [v6: $i] : ? [v7: any] : ? [v8: $i] : ? [v9:
% 220.34/30.68 | | any] : ? [v10: $i] : ? [v11: any] : ? [v12: $i] : ? [v13: any]
% 220.34/30.68 | | : ( ~ (v1 = v0) &
% 220.34/30.68 | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.68 | | tc_Arrow__Order__Mirabelle_Oalt, v1, v0) = v8 &
% 220.34/30.68 | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.68 | | tc_Arrow__Order__Mirabelle_Oalt, v1, v_y) = v10 &
% 220.34/30.68 | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.68 | | tc_Arrow__Order__Mirabelle_Oalt, v0, v1) = v2 &
% 220.34/30.68 | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.68 | | tc_Arrow__Order__Mirabelle_Oalt, v0, v_y) = v4 &
% 220.34/30.68 | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.68 | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v1) = v6 &
% 220.34/30.68 | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.68 | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = v12 &
% 220.34/30.68 | | c_member(all_683_0, v12, v_L) = v13 & c_member(all_683_0, v10,
% 220.34/30.68 | | v_L) = v11 & c_member(all_683_0, v8, v_L) = v9 &
% 220.34/30.68 | | c_member(all_683_0, v6, v_L) = v7 & c_member(all_683_0, v4, v_L) =
% 220.34/30.68 | | v5 & c_member(all_683_0, v2, v_L) = v3 & $i(v12) & $i(v10) &
% 220.34/30.68 | | $i(v8) & $i(v6) & $i(v4) & $i(v2) & $i(v1) & $i(v0) & ( ~ (v13 =
% 220.34/30.68 | | 0) | ~ (v1 = v_x) | v0 = v_x) & ( ~ (v11 = 0) | ~ (v0 = v_x)
% 220.34/30.68 | | | v1 = v_x) & ( ~ (v9 = 0) | v1 = v_x | v0 = v_x) & ( ~ (v7 = 0)
% 220.34/30.68 | | | ~ (v0 = v_x) | v1 = v_x) & ( ~ (v5 = 0) | ~ (v1 = v_x) | v0
% 220.34/30.68 | | = v_x) & ( ~ (v3 = 0) | v1 = v_x | v0 = v_x) & ( ~ (v1 = v_x) |
% 220.34/30.68 | | ~ (v0 = v_y)) & ( ~ (v1 = v_y) | ~ (v0 = v_x)))
% 220.34/30.68 | |
% 220.34/30.68 | | DELTA: instantiating (88) with fresh symbols all_870_0, all_870_1,
% 220.34/30.68 | | all_870_2, all_870_3, all_870_4, all_870_5, all_870_6, all_870_7,
% 220.34/30.68 | | all_870_8, all_870_9, all_870_10, all_870_11, all_870_12, all_870_13
% 220.34/30.68 | | gives:
% 220.34/30.68 | | (89) ~ (all_870_12 = all_870_13) &
% 220.34/30.68 | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.68 | | tc_Arrow__Order__Mirabelle_Oalt, all_870_12, all_870_13) =
% 220.34/30.68 | | all_870_5 & c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.68 | | tc_Arrow__Order__Mirabelle_Oalt, all_870_12, v_y) = all_870_3 &
% 220.34/30.68 | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.68 | | tc_Arrow__Order__Mirabelle_Oalt, all_870_13, all_870_12) =
% 220.34/30.68 | | all_870_11 & c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.68 | | tc_Arrow__Order__Mirabelle_Oalt, all_870_13, v_y) = all_870_9 &
% 220.34/30.68 | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.68 | | tc_Arrow__Order__Mirabelle_Oalt, v_y, all_870_12) = all_870_7 &
% 220.34/30.68 | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.68 | | tc_Arrow__Order__Mirabelle_Oalt, v_y, all_870_13) = all_870_1 &
% 220.34/30.68 | | c_member(all_683_0, all_870_1, v_L) = all_870_0 &
% 220.34/30.68 | | c_member(all_683_0, all_870_3, v_L) = all_870_2 &
% 220.34/30.68 | | c_member(all_683_0, all_870_5, v_L) = all_870_4 &
% 220.34/30.68 | | c_member(all_683_0, all_870_7, v_L) = all_870_6 &
% 220.34/30.68 | | c_member(all_683_0, all_870_9, v_L) = all_870_8 &
% 220.34/30.68 | | c_member(all_683_0, all_870_11, v_L) = all_870_10 & $i(all_870_1) &
% 220.34/30.68 | | $i(all_870_3) & $i(all_870_5) & $i(all_870_7) & $i(all_870_9) &
% 220.34/30.68 | | $i(all_870_11) & $i(all_870_12) & $i(all_870_13) & ( ~ (all_870_0 =
% 220.34/30.68 | | 0) | ~ (all_870_12 = v_x) | all_870_13 = v_x) & ( ~ (all_870_2
% 220.34/30.68 | | = 0) | ~ (all_870_13 = v_x) | all_870_12 = v_x) & ( ~
% 220.34/30.68 | | (all_870_4 = 0) | all_870_12 = v_x | all_870_13 = v_x) & ( ~
% 220.34/30.68 | | (all_870_6 = 0) | ~ (all_870_13 = v_x) | all_870_12 = v_x) & ( ~
% 220.34/30.68 | | (all_870_8 = 0) | ~ (all_870_12 = v_x) | all_870_13 = v_x) & ( ~
% 220.34/30.68 | | (all_870_10 = 0) | all_870_12 = v_x | all_870_13 = v_x) & ( ~
% 220.34/30.68 | | (all_870_12 = v_x) | ~ (all_870_13 = v_y)) & ( ~ (all_870_12 =
% 220.34/30.68 | | v_y) | ~ (all_870_13 = v_x))
% 220.34/30.68 | |
% 220.34/30.68 | | ALPHA: (89) implies:
% 220.34/30.68 | | (90) ~ (all_870_12 = all_870_13)
% 220.34/30.68 | | (91) $i(all_870_13)
% 220.34/30.68 | | (92) $i(all_870_12)
% 220.34/30.68 | | (93) $i(all_870_9)
% 220.34/30.68 | | (94) c_member(all_683_0, all_870_11, v_L) = all_870_10
% 220.34/30.68 | | (95) c_member(all_683_0, all_870_9, v_L) = all_870_8
% 220.34/30.68 | | (96) c_member(all_683_0, all_870_7, v_L) = all_870_6
% 220.34/30.68 | | (97) c_member(all_683_0, all_870_5, v_L) = all_870_4
% 220.34/30.68 | | (98) c_member(all_683_0, all_870_3, v_L) = all_870_2
% 220.34/30.68 | | (99) c_member(all_683_0, all_870_1, v_L) = all_870_0
% 220.34/30.68 | | (100) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.68 | | tc_Arrow__Order__Mirabelle_Oalt, v_y, all_870_13) = all_870_1
% 220.34/30.68 | | (101) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.68 | | tc_Arrow__Order__Mirabelle_Oalt, v_y, all_870_12) = all_870_7
% 220.34/30.68 | | (102) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.68 | | tc_Arrow__Order__Mirabelle_Oalt, all_870_13, v_y) = all_870_9
% 220.34/30.68 | | (103) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.68 | | tc_Arrow__Order__Mirabelle_Oalt, all_870_13, all_870_12) =
% 220.34/30.68 | | all_870_11
% 220.34/30.68 | | (104) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.68 | | tc_Arrow__Order__Mirabelle_Oalt, all_870_12, v_y) = all_870_3
% 220.34/30.68 | | (105) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.68 | | tc_Arrow__Order__Mirabelle_Oalt, all_870_12, all_870_13) =
% 220.34/30.68 | | all_870_5
% 220.34/30.68 | | (106) ~ (all_870_12 = v_y) | ~ (all_870_13 = v_x)
% 220.34/30.68 | | (107) ~ (all_870_12 = v_x) | ~ (all_870_13 = v_y)
% 220.34/30.68 | | (108) ~ (all_870_10 = 0) | all_870_12 = v_x | all_870_13 = v_x
% 220.34/30.68 | | (109) ~ (all_870_8 = 0) | ~ (all_870_12 = v_x) | all_870_13 = v_x
% 220.34/30.68 | | (110) ~ (all_870_6 = 0) | ~ (all_870_13 = v_x) | all_870_12 = v_x
% 220.34/30.68 | | (111) ~ (all_870_4 = 0) | all_870_12 = v_x | all_870_13 = v_x
% 220.34/30.68 | | (112) ~ (all_870_2 = 0) | ~ (all_870_13 = v_x) | all_870_12 = v_x
% 220.34/30.69 | | (113) ~ (all_870_0 = 0) | ~ (all_870_12 = v_x) | all_870_13 = v_x
% 220.34/30.69 | |
% 220.34/30.69 | | REDUCE: (86), (99) imply:
% 220.34/30.69 | | (114) c_member(all_625_1, all_870_1, v_L) = all_870_0
% 220.34/30.69 | |
% 220.34/30.69 | | REDUCE: (86), (98) imply:
% 220.34/30.69 | | (115) c_member(all_625_1, all_870_3, v_L) = all_870_2
% 220.34/30.69 | |
% 220.34/30.69 | | REDUCE: (86), (97) imply:
% 220.34/30.69 | | (116) c_member(all_625_1, all_870_5, v_L) = all_870_4
% 220.34/30.69 | |
% 220.34/30.69 | | REDUCE: (86), (96) imply:
% 220.34/30.69 | | (117) c_member(all_625_1, all_870_7, v_L) = all_870_6
% 220.34/30.69 | |
% 220.34/30.69 | | REDUCE: (86), (95) imply:
% 220.34/30.69 | | (118) c_member(all_625_1, all_870_9, v_L) = all_870_8
% 220.34/30.69 | |
% 220.34/30.69 | | REDUCE: (86), (94) imply:
% 220.34/30.69 | | (119) c_member(all_625_1, all_870_11, v_L) = all_870_10
% 220.34/30.69 | |
% 220.34/30.69 | | GROUND_INST: instantiating (3) with v_L, all_870_9, all_625_1, all_870_8,
% 220.34/30.69 | | simplifying with (16), (87), (93), (118) gives:
% 220.34/30.69 | | (120) all_870_8 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 220.34/30.69 | | hBOOL(v0) = v1 & hAPP(v_L, all_870_9) = v0 & $i(v0))
% 220.34/30.69 | |
% 220.34/30.69 | | GROUND_INST: instantiating (42) with v_y, all_870_13, all_870_1, simplifying
% 220.34/30.69 | | with (15), (91), (100) gives:
% 220.34/30.69 | | (121) all_870_13 = v_y | ? [v0: any] : ? [v1: $i] : ? [v2: any] :
% 220.34/30.69 | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.69 | | tc_Arrow__Order__Mirabelle_Oalt, all_870_13, v_y) = v1 &
% 220.34/30.69 | | c_member(all_674_0, v1, v_L) = v2 & c_member(all_674_0,
% 220.34/30.69 | | all_870_1, v_L) = v0 & $i(v1) & (v2 = 0 | v0 = 0))
% 220.34/30.69 | |
% 220.34/30.69 | | GROUND_INST: instantiating (41) with v_y, all_870_13, all_870_1, simplifying
% 220.34/30.69 | | with (15), (91), (100) gives:
% 220.34/30.69 | | (122) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_674_0, all_870_1, v_L) =
% 220.34/30.69 | | v0) | ! [v0: $i] : ! [v1: $i] : ( ~
% 220.34/30.69 | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.69 | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = v1) | ~ $i(v0) |
% 220.34/30.69 | | ? [v2: $i] : ? [v3: any] : ? [v4: any] :
% 220.34/30.69 | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.69 | | tc_Arrow__Order__Mirabelle_Oalt, all_870_13, v0) = v2 &
% 220.34/30.69 | | c_member(all_674_0, v2, v_L) = v3 & c_member(all_674_0, v1,
% 220.34/30.69 | | v_L) = v4 & $i(v2) & ( ~ (v3 = 0) | v4 = 0)))
% 220.34/30.69 | |
% 220.34/30.69 | | GROUND_INST: instantiating (42) with v_y, all_870_12, all_870_7, simplifying
% 220.34/30.69 | | with (15), (92), (101) gives:
% 220.34/30.69 | | (123) all_870_12 = v_y | ? [v0: any] : ? [v1: $i] : ? [v2: any] :
% 220.34/30.69 | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.69 | | tc_Arrow__Order__Mirabelle_Oalt, all_870_12, v_y) = v1 &
% 220.34/30.69 | | c_member(all_674_0, v1, v_L) = v2 & c_member(all_674_0,
% 220.34/30.69 | | all_870_7, v_L) = v0 & $i(v1) & (v2 = 0 | v0 = 0))
% 220.34/30.69 | |
% 220.34/30.69 | | GROUND_INST: instantiating (42) with all_870_13, v_y, all_870_9, simplifying
% 220.34/30.69 | | with (15), (91), (102) gives:
% 220.34/30.69 | | (124) all_870_13 = v_y | ? [v0: any] : ? [v1: $i] : ? [v2: any] :
% 220.34/30.69 | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.69 | | tc_Arrow__Order__Mirabelle_Oalt, v_y, all_870_13) = v1 &
% 220.34/30.69 | | c_member(all_674_0, v1, v_L) = v2 & c_member(all_674_0,
% 220.34/30.69 | | all_870_9, v_L) = v0 & $i(v1) & (v2 = 0 | v0 = 0))
% 220.34/30.69 | |
% 220.34/30.69 | | GROUND_INST: instantiating (42) with all_870_13, all_870_12, all_870_11,
% 220.34/30.69 | | simplifying with (91), (92), (103) gives:
% 220.34/30.69 | | (125) all_870_12 = all_870_13 | ? [v0: any] : ? [v1: $i] : ? [v2: any]
% 220.34/30.69 | | : (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.69 | | tc_Arrow__Order__Mirabelle_Oalt, all_870_12, all_870_13) = v1 &
% 220.34/30.69 | | c_member(all_674_0, v1, v_L) = v2 & c_member(all_674_0,
% 220.34/30.69 | | all_870_11, v_L) = v0 & $i(v1) & (v2 = 0 | v0 = 0))
% 220.34/30.69 | |
% 220.34/30.69 | | GROUND_INST: instantiating (41) with all_870_13, all_870_12, all_870_11,
% 220.34/30.69 | | simplifying with (91), (92), (103) gives:
% 220.34/30.69 | | (126) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_674_0, all_870_11, v_L)
% 220.34/30.69 | | = v0) | ! [v0: $i] : ! [v1: $i] : ( ~
% 220.34/30.69 | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.69 | | tc_Arrow__Order__Mirabelle_Oalt, all_870_13, v0) = v1) | ~
% 220.34/30.69 | | $i(v0) | ? [v2: $i] : ? [v3: any] : ? [v4: any] :
% 220.34/30.69 | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.69 | | tc_Arrow__Order__Mirabelle_Oalt, all_870_12, v0) = v2 &
% 220.34/30.69 | | c_member(all_674_0, v2, v_L) = v3 & c_member(all_674_0, v1,
% 220.34/30.69 | | v_L) = v4 & $i(v2) & ( ~ (v3 = 0) | v4 = 0)))
% 220.34/30.69 | |
% 220.34/30.69 | | GROUND_INST: instantiating (42) with all_870_12, v_y, all_870_3, simplifying
% 220.34/30.69 | | with (15), (92), (104) gives:
% 220.34/30.69 | | (127) all_870_12 = v_y | ? [v0: any] : ? [v1: $i] : ? [v2: any] :
% 220.34/30.69 | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.69 | | tc_Arrow__Order__Mirabelle_Oalt, v_y, all_870_12) = v1 &
% 220.34/30.69 | | c_member(all_674_0, v1, v_L) = v2 & c_member(all_674_0,
% 220.34/30.69 | | all_870_3, v_L) = v0 & $i(v1) & (v2 = 0 | v0 = 0))
% 220.34/30.69 | |
% 220.34/30.69 | | GROUND_INST: instantiating (42) with all_870_12, all_870_13, all_870_5,
% 220.34/30.69 | | simplifying with (91), (92), (105) gives:
% 220.34/30.69 | | (128) all_870_12 = all_870_13 | ? [v0: any] : ? [v1: $i] : ? [v2: any]
% 220.34/30.69 | | : (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.69 | | tc_Arrow__Order__Mirabelle_Oalt, all_870_13, all_870_12) = v1 &
% 220.34/30.69 | | c_member(all_674_0, v1, v_L) = v2 & c_member(all_674_0,
% 220.34/30.69 | | all_870_5, v_L) = v0 & $i(v1) & (v2 = 0 | v0 = 0))
% 220.34/30.69 | |
% 220.34/30.69 | | GROUND_INST: instantiating (41) with all_870_12, all_870_13, all_870_5,
% 220.34/30.69 | | simplifying with (91), (92), (105) gives:
% 220.34/30.69 | | (129) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_674_0, all_870_5, v_L) =
% 220.34/30.69 | | v0) | ! [v0: $i] : ! [v1: $i] : ( ~
% 220.34/30.69 | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.69 | | tc_Arrow__Order__Mirabelle_Oalt, all_870_12, v0) = v1) | ~
% 220.34/30.69 | | $i(v0) | ? [v2: $i] : ? [v3: any] : ? [v4: any] :
% 220.34/30.69 | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.69 | | tc_Arrow__Order__Mirabelle_Oalt, all_870_13, v0) = v2 &
% 220.34/30.69 | | c_member(all_674_0, v2, v_L) = v3 & c_member(all_674_0, v1,
% 220.34/30.69 | | v_L) = v4 & $i(v2) & ( ~ (v3 = 0) | v4 = 0)))
% 220.34/30.69 | |
% 220.34/30.69 | | BETA: splitting (106) gives:
% 220.34/30.69 | |
% 220.34/30.69 | | Case 1:
% 220.34/30.69 | | |
% 220.34/30.69 | | | (130) ~ (all_870_12 = v_y)
% 220.34/30.69 | | |
% 220.34/30.69 | | | BETA: splitting (107) gives:
% 220.34/30.69 | | |
% 220.34/30.69 | | | Case 1:
% 220.34/30.69 | | | |
% 220.34/30.70 | | | | (131) ~ (all_870_12 = v_x)
% 220.34/30.70 | | | |
% 220.34/30.70 | | | | BETA: splitting (129) gives:
% 220.34/30.70 | | | |
% 220.34/30.70 | | | | Case 1:
% 220.34/30.70 | | | | |
% 220.34/30.70 | | | | | (132) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_674_0, all_870_5,
% 220.34/30.70 | | | | | v_L) = v0)
% 220.34/30.70 | | | | |
% 220.34/30.70 | | | | | DELTA: instantiating (132) with fresh symbol all_1183_0 gives:
% 220.34/30.70 | | | | | (133) ~ (all_1183_0 = 0) & c_member(all_674_0, all_870_5, v_L) =
% 220.34/30.70 | | | | | all_1183_0
% 220.34/30.70 | | | | |
% 220.34/30.70 | | | | | ALPHA: (133) implies:
% 220.34/30.70 | | | | | (134) c_member(all_674_0, all_870_5, v_L) = all_1183_0
% 220.34/30.70 | | | | |
% 220.34/30.70 | | | | | REDUCE: (84), (134) imply:
% 220.34/30.70 | | | | | (135) c_member(all_625_1, all_870_5, v_L) = all_1183_0
% 220.34/30.70 | | | | |
% 220.34/30.70 | | | | | GROUND_INST: instantiating (19) with all_870_4, all_1183_0, v_L,
% 220.34/30.70 | | | | | all_870_5, all_625_1, simplifying with (116), (135)
% 220.34/30.70 | | | | | gives:
% 220.34/30.70 | | | | | (136) all_1183_0 = all_870_4
% 220.34/30.70 | | | | |
% 220.34/30.70 | | | | | BETA: splitting (128) gives:
% 220.34/30.70 | | | | |
% 220.34/30.70 | | | | | Case 1:
% 220.34/30.70 | | | | | |
% 220.34/30.70 | | | | | | (137) all_870_12 = all_870_13
% 220.34/30.70 | | | | | |
% 220.34/30.70 | | | | | | REDUCE: (90), (137) imply:
% 220.34/30.70 | | | | | | (138) $false
% 220.34/30.70 | | | | | |
% 220.34/30.70 | | | | | | CLOSE: (138) is inconsistent.
% 220.34/30.70 | | | | | |
% 220.34/30.70 | | | | | Case 2:
% 220.34/30.70 | | | | | |
% 220.34/30.70 | | | | | | (139) ? [v0: any] : ? [v1: $i] : ? [v2: any] :
% 220.34/30.70 | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.70 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_13,
% 220.34/30.70 | | | | | | all_870_12) = v1 & c_member(all_674_0, v1, v_L) = v2 &
% 220.34/30.70 | | | | | | c_member(all_674_0, all_870_5, v_L) = v0 & $i(v1) & (v2 =
% 220.34/30.70 | | | | | | 0 | v0 = 0))
% 220.34/30.70 | | | | | |
% 220.34/30.70 | | | | | | DELTA: instantiating (139) with fresh symbols all_1193_0,
% 220.34/30.70 | | | | | | all_1193_1, all_1193_2 gives:
% 220.34/30.70 | | | | | | (140) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.70 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_13, all_870_12)
% 220.34/30.70 | | | | | | = all_1193_1 & c_member(all_674_0, all_1193_1, v_L) =
% 220.34/30.70 | | | | | | all_1193_0 & c_member(all_674_0, all_870_5, v_L) =
% 220.34/30.70 | | | | | | all_1193_2 & $i(all_1193_1) & (all_1193_0 = 0 | all_1193_2
% 220.34/30.70 | | | | | | = 0)
% 220.34/30.70 | | | | | |
% 220.34/30.70 | | | | | | ALPHA: (140) implies:
% 220.34/30.70 | | | | | | (141) c_member(all_674_0, all_870_5, v_L) = all_1193_2
% 220.34/30.70 | | | | | |
% 220.34/30.70 | | | | | | REDUCE: (84), (141) imply:
% 220.34/30.70 | | | | | | (142) c_member(all_625_1, all_870_5, v_L) = all_1193_2
% 220.34/30.70 | | | | | |
% 220.34/30.70 | | | | | | BETA: splitting (125) gives:
% 220.34/30.70 | | | | | |
% 220.34/30.70 | | | | | | Case 1:
% 220.34/30.70 | | | | | | |
% 220.34/30.70 | | | | | | | (143) all_870_12 = all_870_13
% 220.34/30.70 | | | | | | |
% 220.34/30.70 | | | | | | | REDUCE: (90), (143) imply:
% 220.34/30.70 | | | | | | | (144) $false
% 220.34/30.70 | | | | | | |
% 220.34/30.70 | | | | | | | CLOSE: (144) is inconsistent.
% 220.34/30.70 | | | | | | |
% 220.34/30.70 | | | | | | Case 2:
% 220.34/30.70 | | | | | | |
% 220.34/30.70 | | | | | | | (145) ? [v0: any] : ? [v1: $i] : ? [v2: any] :
% 220.34/30.70 | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.70 | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_12,
% 220.34/30.70 | | | | | | | all_870_13) = v1 & c_member(all_674_0, v1, v_L) = v2
% 220.34/30.70 | | | | | | | & c_member(all_674_0, all_870_11, v_L) = v0 & $i(v1) &
% 220.34/30.70 | | | | | | | (v2 = 0 | v0 = 0))
% 220.34/30.70 | | | | | | |
% 220.34/30.70 | | | | | | | DELTA: instantiating (145) with fresh symbols all_1204_0,
% 220.34/30.70 | | | | | | | all_1204_1, all_1204_2 gives:
% 220.34/30.70 | | | | | | | (146) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.70 | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_12,
% 220.34/30.70 | | | | | | | all_870_13) = all_1204_1 & c_member(all_674_0,
% 220.34/30.70 | | | | | | | all_1204_1, v_L) = all_1204_0 & c_member(all_674_0,
% 220.34/30.70 | | | | | | | all_870_11, v_L) = all_1204_2 & $i(all_1204_1) &
% 220.34/30.70 | | | | | | | (all_1204_0 = 0 | all_1204_2 = 0)
% 220.34/30.70 | | | | | | |
% 220.34/30.70 | | | | | | | ALPHA: (146) implies:
% 220.34/30.70 | | | | | | | (147) c_member(all_674_0, all_870_11, v_L) = all_1204_2
% 220.34/30.70 | | | | | | | (148) c_member(all_674_0, all_1204_1, v_L) = all_1204_0
% 220.34/30.70 | | | | | | | (149) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.70 | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_12,
% 220.34/30.70 | | | | | | | all_870_13) = all_1204_1
% 220.34/30.70 | | | | | | |
% 220.34/30.70 | | | | | | | REDUCE: (84), (148) imply:
% 220.34/30.70 | | | | | | | (150) c_member(all_625_1, all_1204_1, v_L) = all_1204_0
% 220.34/30.70 | | | | | | |
% 220.34/30.70 | | | | | | | REDUCE: (84), (147) imply:
% 220.34/30.70 | | | | | | | (151) c_member(all_625_1, all_870_11, v_L) = all_1204_2
% 220.34/30.70 | | | | | | |
% 220.34/30.70 | | | | | | | GROUND_INST: instantiating (19) with all_870_10, all_1204_2, v_L,
% 220.34/30.70 | | | | | | | all_870_11, all_625_1, simplifying with (119), (151)
% 220.34/30.70 | | | | | | | gives:
% 220.34/30.70 | | | | | | | (152) all_1204_2 = all_870_10
% 220.34/30.70 | | | | | | |
% 220.34/30.70 | | | | | | | GROUND_INST: instantiating (19) with all_870_4, all_1193_2, v_L,
% 220.34/30.70 | | | | | | | all_870_5, all_625_1, simplifying with (116), (142)
% 220.34/30.70 | | | | | | | gives:
% 220.34/30.70 | | | | | | | (153) all_1193_2 = all_870_4
% 220.34/30.70 | | | | | | |
% 220.34/30.70 | | | | | | | GROUND_INST: instantiating (20) with all_870_5, all_1204_1,
% 220.34/30.70 | | | | | | | all_870_13, all_870_12,
% 220.34/30.70 | | | | | | | tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.70 | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with
% 220.34/30.70 | | | | | | | (105), (149) gives:
% 220.34/30.70 | | | | | | | (154) all_1204_1 = all_870_5
% 220.34/30.70 | | | | | | |
% 220.34/30.70 | | | | | | | REDUCE: (150), (154) imply:
% 220.34/30.70 | | | | | | | (155) c_member(all_625_1, all_870_5, v_L) = all_1204_0
% 220.34/30.70 | | | | | | |
% 220.34/30.70 | | | | | | | GROUND_INST: instantiating (19) with all_870_4, all_1204_0, v_L,
% 220.34/30.70 | | | | | | | all_870_5, all_625_1, simplifying with (116), (155)
% 220.34/30.70 | | | | | | | gives:
% 220.34/30.70 | | | | | | | (156) all_1204_0 = all_870_4
% 220.34/30.70 | | | | | | |
% 220.34/30.70 | | | | | | | BETA: splitting (108) gives:
% 220.34/30.70 | | | | | | |
% 220.34/30.70 | | | | | | | Case 1:
% 220.34/30.70 | | | | | | | |
% 220.34/30.70 | | | | | | | | (157) ~ (all_870_10 = 0)
% 220.34/30.70 | | | | | | | |
% 220.34/30.70 | | | | | | | | DELTA: instantiating (139) with fresh symbols all_1211_0,
% 220.34/30.70 | | | | | | | | all_1211_1, all_1211_2 gives:
% 220.34/30.70 | | | | | | | | (158) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.70 | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_13,
% 220.34/30.70 | | | | | | | | all_870_12) = all_1211_1 & c_member(all_674_0,
% 220.34/30.70 | | | | | | | | all_1211_1, v_L) = all_1211_0 & c_member(all_674_0,
% 220.34/30.70 | | | | | | | | all_870_5, v_L) = all_1211_2 & $i(all_1211_1) &
% 220.34/30.70 | | | | | | | | (all_1211_0 = 0 | all_1211_2 = 0)
% 220.34/30.70 | | | | | | | |
% 220.34/30.70 | | | | | | | | REF_CLOSE: (19), (20), (84), (90), (101), (105), (110), (111),
% 220.34/30.70 | | | | | | | | (112), (115), (116), (117), (119), (123), (125),
% 220.34/30.70 | | | | | | | | (127), (130), (131), (157), (158) are inconsistent by
% 220.34/30.70 | | | | | | | | sub-proof #18.
% 220.34/30.70 | | | | | | | |
% 220.34/30.70 | | | | | | | Case 2:
% 220.34/30.70 | | | | | | | |
% 220.34/30.70 | | | | | | | | (159) all_870_12 = v_x | all_870_13 = v_x
% 220.34/30.70 | | | | | | | |
% 220.34/30.70 | | | | | | | | REF_CLOSE: (19), (20), (84), (90), (101), (110), (112), (115),
% 220.34/30.70 | | | | | | | | (117), (123), (127), (130), (131), (159) are
% 220.34/30.70 | | | | | | | | inconsistent by sub-proof #19.
% 220.34/30.70 | | | | | | | |
% 220.34/30.70 | | | | | | | End of split
% 220.34/30.70 | | | | | | |
% 220.34/30.71 | | | | | | End of split
% 220.34/30.71 | | | | | |
% 220.34/30.71 | | | | | End of split
% 220.34/30.71 | | | | |
% 220.34/30.71 | | | | Case 2:
% 220.34/30.71 | | | | |
% 220.34/30.71 | | | | | (160) ! [v0: $i] : ! [v1: $i] : ( ~
% 220.34/30.71 | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.71 | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_12, v0) = v1)
% 220.34/30.71 | | | | | | ~ $i(v0) | ? [v2: $i] : ? [v3: any] : ? [v4: any] :
% 220.34/30.71 | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.71 | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_13, v0) = v2 &
% 220.34/30.71 | | | | | c_member(all_674_0, v2, v_L) = v3 & c_member(all_674_0,
% 220.34/30.71 | | | | | v1, v_L) = v4 & $i(v2) & ( ~ (v3 = 0) | v4 = 0)))
% 220.34/30.71 | | | | |
% 220.34/30.71 | | | | | GROUND_INST: instantiating (160) with v_y, all_870_3, simplifying with
% 220.34/30.71 | | | | | (15), (104) gives:
% 220.34/30.71 | | | | | (161) ? [v0: $i] : ? [v1: any] : ? [v2: any] :
% 220.34/30.71 | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.71 | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_13, v_y) = v0 &
% 220.34/30.71 | | | | | c_member(all_674_0, v0, v_L) = v1 & c_member(all_674_0,
% 220.34/30.71 | | | | | all_870_3, v_L) = v2 & $i(v0) & ( ~ (v1 = 0) | v2 = 0))
% 220.34/30.71 | | | | |
% 220.34/30.71 | | | | | GROUND_INST: instantiating (160) with all_870_13, all_870_5,
% 220.34/30.71 | | | | | simplifying with (91), (105) gives:
% 220.34/30.71 | | | | | (162) ? [v0: $i] : ? [v1: any] : ? [v2: any] :
% 220.34/30.71 | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.71 | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_13, all_870_13)
% 220.34/30.71 | | | | | = v0 & c_member(all_674_0, v0, v_L) = v1 &
% 220.34/30.71 | | | | | c_member(all_674_0, all_870_5, v_L) = v2 & $i(v0) & ( ~ (v1
% 220.34/30.71 | | | | | = 0) | v2 = 0))
% 220.34/30.71 | | | | |
% 220.34/30.71 | | | | | DELTA: instantiating (162) with fresh symbols all_1184_0, all_1184_1,
% 220.34/30.71 | | | | | all_1184_2 gives:
% 220.34/30.71 | | | | | (163) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.71 | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_13, all_870_13) =
% 220.34/30.71 | | | | | all_1184_2 & c_member(all_674_0, all_1184_2, v_L) =
% 220.34/30.71 | | | | | all_1184_1 & c_member(all_674_0, all_870_5, v_L) = all_1184_0
% 220.34/30.71 | | | | | & $i(all_1184_2) & ( ~ (all_1184_1 = 0) | all_1184_0 = 0)
% 220.34/30.71 | | | | |
% 220.34/30.71 | | | | | ALPHA: (163) implies:
% 220.34/30.71 | | | | | (164) c_member(all_674_0, all_870_5, v_L) = all_1184_0
% 220.34/30.71 | | | | |
% 220.34/30.71 | | | | | DELTA: instantiating (161) with fresh symbols all_1186_0, all_1186_1,
% 220.34/30.71 | | | | | all_1186_2 gives:
% 220.34/30.71 | | | | | (165) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.71 | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_13, v_y) =
% 220.34/30.71 | | | | | all_1186_2 & c_member(all_674_0, all_1186_2, v_L) =
% 220.34/30.71 | | | | | all_1186_1 & c_member(all_674_0, all_870_3, v_L) = all_1186_0
% 220.34/30.71 | | | | | & $i(all_1186_2) & ( ~ (all_1186_1 = 0) | all_1186_0 = 0)
% 220.34/30.71 | | | | |
% 220.34/30.71 | | | | | ALPHA: (165) implies:
% 220.34/30.71 | | | | | (166) c_member(all_674_0, all_870_3, v_L) = all_1186_0
% 220.34/30.71 | | | | | (167) c_member(all_674_0, all_1186_2, v_L) = all_1186_1
% 220.34/30.71 | | | | | (168) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.71 | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_13, v_y) =
% 220.34/30.71 | | | | | all_1186_2
% 220.34/30.71 | | | | | (169) ~ (all_1186_1 = 0) | all_1186_0 = 0
% 220.34/30.71 | | | | |
% 220.34/30.71 | | | | | REDUCE: (84), (167) imply:
% 220.34/30.71 | | | | | (170) c_member(all_625_1, all_1186_2, v_L) = all_1186_1
% 220.34/30.71 | | | | |
% 220.34/30.71 | | | | | REDUCE: (84), (166) imply:
% 220.34/30.71 | | | | | (171) c_member(all_625_1, all_870_3, v_L) = all_1186_0
% 220.34/30.71 | | | | |
% 220.34/30.71 | | | | | REDUCE: (84), (164) imply:
% 220.34/30.71 | | | | | (172) c_member(all_625_1, all_870_5, v_L) = all_1184_0
% 220.34/30.71 | | | | |
% 220.34/30.71 | | | | | GROUND_INST: instantiating (19) with all_870_4, all_1184_0, v_L,
% 220.34/30.71 | | | | | all_870_5, all_625_1, simplifying with (116), (172)
% 220.34/30.71 | | | | | gives:
% 220.34/30.71 | | | | | (173) all_1184_0 = all_870_4
% 220.34/30.71 | | | | |
% 220.34/30.71 | | | | | GROUND_INST: instantiating (19) with all_870_2, all_1186_0, v_L,
% 220.34/30.71 | | | | | all_870_3, all_625_1, simplifying with (115), (171)
% 220.34/30.71 | | | | | gives:
% 220.34/30.71 | | | | | (174) all_1186_0 = all_870_2
% 220.34/30.71 | | | | |
% 220.34/30.71 | | | | | GROUND_INST: instantiating (20) with all_870_9, all_1186_2, v_y,
% 220.34/30.71 | | | | | all_870_13, tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.71 | | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with (102),
% 220.34/30.71 | | | | | (168) gives:
% 220.34/30.71 | | | | | (175) all_1186_2 = all_870_9
% 220.34/30.71 | | | | |
% 220.34/30.71 | | | | | REDUCE: (170), (175) imply:
% 220.34/30.71 | | | | | (176) c_member(all_625_1, all_870_9, v_L) = all_1186_1
% 220.34/30.71 | | | | |
% 220.34/30.71 | | | | | GROUND_INST: instantiating (19) with all_870_8, all_1186_1, v_L,
% 220.34/30.71 | | | | | all_870_9, all_625_1, simplifying with (118), (176)
% 220.34/30.71 | | | | | gives:
% 220.34/30.71 | | | | | (177) all_1186_1 = all_870_8
% 220.34/30.71 | | | | |
% 220.34/30.71 | | | | | BETA: splitting (126) gives:
% 220.34/30.71 | | | | |
% 220.34/30.71 | | | | | Case 1:
% 220.34/30.71 | | | | | |
% 220.34/30.71 | | | | | | (178) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_674_0,
% 220.34/30.71 | | | | | | all_870_11, v_L) = v0)
% 220.34/30.71 | | | | | |
% 220.34/30.71 | | | | | | DELTA: instantiating (178) with fresh symbol all_1201_0 gives:
% 220.34/30.71 | | | | | | (179) ~ (all_1201_0 = 0) & c_member(all_674_0, all_870_11, v_L)
% 220.34/30.71 | | | | | | = all_1201_0
% 220.34/30.71 | | | | | |
% 220.34/30.71 | | | | | | ALPHA: (179) implies:
% 220.34/30.71 | | | | | | (180) ~ (all_1201_0 = 0)
% 220.34/30.71 | | | | | | (181) c_member(all_674_0, all_870_11, v_L) = all_1201_0
% 220.34/30.71 | | | | | |
% 220.34/30.71 | | | | | | REDUCE: (84), (181) imply:
% 220.34/30.71 | | | | | | (182) c_member(all_625_1, all_870_11, v_L) = all_1201_0
% 220.34/30.71 | | | | | |
% 220.34/30.71 | | | | | | GROUND_INST: instantiating (19) with all_870_10, all_1201_0, v_L,
% 220.34/30.71 | | | | | | all_870_11, all_625_1, simplifying with (119), (182)
% 220.34/30.71 | | | | | | gives:
% 220.34/30.71 | | | | | | (183) all_1201_0 = all_870_10
% 220.34/30.71 | | | | | |
% 220.34/30.71 | | | | | | REDUCE: (180), (183) imply:
% 220.34/30.71 | | | | | | (184) ~ (all_870_10 = 0)
% 220.34/30.71 | | | | | |
% 220.34/30.71 | | | | | | BETA: splitting (128) gives:
% 220.34/30.71 | | | | | |
% 220.34/30.71 | | | | | | Case 1:
% 220.34/30.71 | | | | | | |
% 220.34/30.71 | | | | | | | (185) all_870_12 = all_870_13
% 220.34/30.71 | | | | | | |
% 220.34/30.71 | | | | | | | REDUCE: (90), (185) imply:
% 220.34/30.71 | | | | | | | (186) $false
% 220.34/30.71 | | | | | | |
% 220.34/30.71 | | | | | | | CLOSE: (186) is inconsistent.
% 220.34/30.71 | | | | | | |
% 220.34/30.71 | | | | | | Case 2:
% 220.34/30.71 | | | | | | |
% 220.34/30.71 | | | | | | | (187) ? [v0: any] : ? [v1: $i] : ? [v2: any] :
% 220.34/30.71 | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.71 | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_13,
% 220.34/30.71 | | | | | | | all_870_12) = v1 & c_member(all_674_0, v1, v_L) = v2
% 220.34/30.71 | | | | | | | & c_member(all_674_0, all_870_5, v_L) = v0 & $i(v1) &
% 220.34/30.71 | | | | | | | (v2 = 0 | v0 = 0))
% 220.34/30.71 | | | | | | |
% 220.34/30.71 | | | | | | | DELTA: instantiating (187) with fresh symbols all_1211_0,
% 220.34/30.71 | | | | | | | all_1211_1, all_1211_2 gives:
% 220.34/30.71 | | | | | | | (188) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.71 | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_13,
% 220.34/30.71 | | | | | | | all_870_12) = all_1211_1 & c_member(all_674_0,
% 220.34/30.71 | | | | | | | all_1211_1, v_L) = all_1211_0 & c_member(all_674_0,
% 220.34/30.71 | | | | | | | all_870_5, v_L) = all_1211_2 & $i(all_1211_1) &
% 220.34/30.71 | | | | | | | (all_1211_0 = 0 | all_1211_2 = 0)
% 220.34/30.71 | | | | | | |
% 220.34/30.71 | | | | | | | REF_CLOSE: (19), (20), (84), (90), (101), (105), (110), (111),
% 220.34/30.71 | | | | | | | (112), (115), (116), (117), (119), (123), (125), (127),
% 220.34/30.71 | | | | | | | (130), (131), (184), (188) are inconsistent by
% 220.34/30.71 | | | | | | | sub-proof #18.
% 220.34/30.71 | | | | | | |
% 220.34/30.71 | | | | | | End of split
% 220.34/30.71 | | | | | |
% 220.34/30.71 | | | | | Case 2:
% 220.34/30.71 | | | | | |
% 220.34/30.71 | | | | | | (189) ! [v0: $i] : ! [v1: $i] : ( ~
% 220.34/30.71 | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.71 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_13, v0) =
% 220.34/30.71 | | | | | | v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: any] : ? [v4:
% 220.34/30.71 | | | | | | any] :
% 220.34/30.71 | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.71 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_12, v0) = v2
% 220.34/30.71 | | | | | | & c_member(all_674_0, v2, v_L) = v3 &
% 220.34/30.71 | | | | | | c_member(all_674_0, v1, v_L) = v4 & $i(v2) & ( ~ (v3 =
% 220.34/30.71 | | | | | | 0) | v4 = 0)))
% 220.34/30.71 | | | | | |
% 220.34/30.71 | | | | | | GROUND_INST: instantiating (189) with v_y, all_870_9, simplifying
% 220.34/30.71 | | | | | | with (15), (102) gives:
% 220.34/30.72 | | | | | | (190) ? [v0: $i] : ? [v1: any] : ? [v2: any] :
% 220.34/30.72 | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.72 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_12, v_y) = v0
% 220.34/30.72 | | | | | | & c_member(all_674_0, v0, v_L) = v1 & c_member(all_674_0,
% 220.34/30.72 | | | | | | all_870_9, v_L) = v2 & $i(v0) & ( ~ (v1 = 0) | v2 = 0))
% 220.34/30.72 | | | | | |
% 220.34/30.72 | | | | | | GROUND_INST: instantiating (189) with all_870_12, all_870_11,
% 220.34/30.72 | | | | | | simplifying with (92), (103) gives:
% 220.34/30.72 | | | | | | (191) ? [v0: $i] : ? [v1: any] : ? [v2: any] :
% 220.34/30.72 | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.72 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_12,
% 220.34/30.72 | | | | | | all_870_12) = v0 & c_member(all_674_0, v0, v_L) = v1 &
% 220.34/30.72 | | | | | | c_member(all_674_0, all_870_11, v_L) = v2 & $i(v0) & ( ~
% 220.34/30.72 | | | | | | (v1 = 0) | v2 = 0))
% 220.34/30.72 | | | | | |
% 220.34/30.72 | | | | | | DELTA: instantiating (191) with fresh symbols all_1202_0,
% 220.34/30.72 | | | | | | all_1202_1, all_1202_2 gives:
% 220.34/30.72 | | | | | | (192) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.72 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_12, all_870_12)
% 220.34/30.72 | | | | | | = all_1202_2 & c_member(all_674_0, all_1202_2, v_L) =
% 220.34/30.72 | | | | | | all_1202_1 & c_member(all_674_0, all_870_11, v_L) =
% 220.34/30.72 | | | | | | all_1202_0 & $i(all_1202_2) & ( ~ (all_1202_1 = 0) |
% 220.34/30.72 | | | | | | all_1202_0 = 0)
% 220.34/30.72 | | | | | |
% 220.34/30.72 | | | | | | ALPHA: (192) implies:
% 220.34/30.72 | | | | | | (193) c_member(all_674_0, all_870_11, v_L) = all_1202_0
% 220.34/30.72 | | | | | | (194) ~ (all_1202_1 = 0) | all_1202_0 = 0
% 220.34/30.72 | | | | | |
% 220.34/30.72 | | | | | | DELTA: instantiating (190) with fresh symbols all_1204_0,
% 220.34/30.72 | | | | | | all_1204_1, all_1204_2 gives:
% 220.34/30.72 | | | | | | (195) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.72 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_12, v_y) =
% 220.34/30.72 | | | | | | all_1204_2 & c_member(all_674_0, all_1204_2, v_L) =
% 220.34/30.72 | | | | | | all_1204_1 & c_member(all_674_0, all_870_9, v_L) =
% 220.34/30.72 | | | | | | all_1204_0 & $i(all_1204_2) & ( ~ (all_1204_1 = 0) |
% 220.34/30.72 | | | | | | all_1204_0 = 0)
% 220.34/30.72 | | | | | |
% 220.34/30.72 | | | | | | ALPHA: (195) implies:
% 220.34/30.72 | | | | | | (196) c_member(all_674_0, all_870_9, v_L) = all_1204_0
% 220.34/30.72 | | | | | | (197) c_member(all_674_0, all_1204_2, v_L) = all_1204_1
% 220.34/30.72 | | | | | | (198) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.72 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_12, v_y) =
% 220.34/30.72 | | | | | | all_1204_2
% 220.34/30.72 | | | | | |
% 220.34/30.72 | | | | | | REDUCE: (84), (197) imply:
% 220.34/30.72 | | | | | | (199) c_member(all_625_1, all_1204_2, v_L) = all_1204_1
% 220.34/30.72 | | | | | |
% 220.34/30.72 | | | | | | REDUCE: (84), (196) imply:
% 220.34/30.72 | | | | | | (200) c_member(all_625_1, all_870_9, v_L) = all_1204_0
% 220.34/30.72 | | | | | |
% 220.34/30.72 | | | | | | REDUCE: (84), (193) imply:
% 220.34/30.72 | | | | | | (201) c_member(all_625_1, all_870_11, v_L) = all_1202_0
% 220.34/30.72 | | | | | |
% 220.34/30.72 | | | | | | GROUND_INST: instantiating (19) with all_870_10, all_1202_0, v_L,
% 220.34/30.72 | | | | | | all_870_11, all_625_1, simplifying with (119), (201)
% 220.34/30.72 | | | | | | gives:
% 220.34/30.72 | | | | | | (202) all_1202_0 = all_870_10
% 220.34/30.72 | | | | | |
% 220.34/30.72 | | | | | | GROUND_INST: instantiating (19) with all_870_8, all_1204_0, v_L,
% 220.34/30.72 | | | | | | all_870_9, all_625_1, simplifying with (118), (200)
% 220.34/30.72 | | | | | | gives:
% 220.34/30.72 | | | | | | (203) all_1204_0 = all_870_8
% 220.34/30.72 | | | | | |
% 220.34/30.72 | | | | | | GROUND_INST: instantiating (20) with all_870_3, all_1204_2, v_y,
% 220.34/30.72 | | | | | | all_870_12, tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.72 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with
% 220.34/30.72 | | | | | | (104), (198) gives:
% 220.34/30.72 | | | | | | (204) all_1204_2 = all_870_3
% 220.34/30.72 | | | | | |
% 220.34/30.72 | | | | | | REDUCE: (199), (204) imply:
% 220.34/30.72 | | | | | | (205) c_member(all_625_1, all_870_3, v_L) = all_1204_1
% 220.34/30.72 | | | | | |
% 220.34/30.72 | | | | | | GROUND_INST: instantiating (19) with all_870_2, all_1204_1, v_L,
% 220.34/30.72 | | | | | | all_870_3, all_625_1, simplifying with (115), (205)
% 220.34/30.72 | | | | | | gives:
% 220.34/30.72 | | | | | | (206) all_1204_1 = all_870_2
% 220.34/30.72 | | | | | |
% 220.34/30.72 | | | | | | BETA: splitting (122) gives:
% 220.34/30.72 | | | | | |
% 220.34/30.72 | | | | | | Case 1:
% 220.34/30.72 | | | | | | |
% 220.34/30.72 | | | | | | | (207) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_674_0,
% 220.34/30.72 | | | | | | | all_870_1, v_L) = v0)
% 220.34/30.72 | | | | | | |
% 220.34/30.72 | | | | | | | DELTA: instantiating (207) with fresh symbol all_1219_0 gives:
% 220.34/30.72 | | | | | | | (208) ~ (all_1219_0 = 0) & c_member(all_674_0, all_870_1, v_L)
% 220.34/30.72 | | | | | | | = all_1219_0
% 220.34/30.72 | | | | | | |
% 220.34/30.72 | | | | | | | ALPHA: (208) implies:
% 220.34/30.72 | | | | | | | (209) ~ (all_1219_0 = 0)
% 220.34/30.72 | | | | | | | (210) c_member(all_674_0, all_870_1, v_L) = all_1219_0
% 220.34/30.72 | | | | | | |
% 220.34/30.72 | | | | | | | REDUCE: (84), (210) imply:
% 220.34/30.72 | | | | | | | (211) c_member(all_625_1, all_870_1, v_L) = all_1219_0
% 220.34/30.72 | | | | | | |
% 220.34/30.72 | | | | | | | GROUND_INST: instantiating (19) with all_870_0, all_1219_0, v_L,
% 220.34/30.72 | | | | | | | all_870_1, all_625_1, simplifying with (114), (211)
% 220.34/30.72 | | | | | | | gives:
% 220.34/30.72 | | | | | | | (212) all_1219_0 = all_870_0
% 220.34/30.72 | | | | | | |
% 220.34/30.72 | | | | | | | REDUCE: (209), (212) imply:
% 220.34/30.72 | | | | | | | (213) ~ (all_870_0 = 0)
% 220.34/30.72 | | | | | | |
% 220.34/30.72 | | | | | | | BETA: splitting (128) gives:
% 220.34/30.72 | | | | | | |
% 220.34/30.72 | | | | | | | Case 1:
% 220.34/30.72 | | | | | | | |
% 220.34/30.72 | | | | | | | | (214) all_870_12 = all_870_13
% 220.34/30.72 | | | | | | | |
% 220.34/30.72 | | | | | | | | REDUCE: (90), (214) imply:
% 220.34/30.72 | | | | | | | | (215) $false
% 220.34/30.72 | | | | | | | |
% 220.34/30.72 | | | | | | | | CLOSE: (215) is inconsistent.
% 220.34/30.72 | | | | | | | |
% 220.34/30.72 | | | | | | | Case 2:
% 220.34/30.72 | | | | | | | |
% 220.34/30.72 | | | | | | | | (216) ? [v0: any] : ? [v1: $i] : ? [v2: any] :
% 220.34/30.72 | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.72 | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_13,
% 220.34/30.72 | | | | | | | | all_870_12) = v1 & c_member(all_674_0, v1, v_L) =
% 220.34/30.72 | | | | | | | | v2 & c_member(all_674_0, all_870_5, v_L) = v0 &
% 220.34/30.72 | | | | | | | | $i(v1) & (v2 = 0 | v0 = 0))
% 220.34/30.72 | | | | | | | |
% 220.34/30.72 | | | | | | | | DELTA: instantiating (216) with fresh symbols all_1243_0,
% 220.34/30.72 | | | | | | | | all_1243_1, all_1243_2 gives:
% 220.34/30.72 | | | | | | | | (217) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.72 | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_13,
% 220.34/30.72 | | | | | | | | all_870_12) = all_1243_1 & c_member(all_674_0,
% 220.34/30.72 | | | | | | | | all_1243_1, v_L) = all_1243_0 & c_member(all_674_0,
% 220.34/30.72 | | | | | | | | all_870_5, v_L) = all_1243_2 & $i(all_1243_1) &
% 220.34/30.72 | | | | | | | | (all_1243_0 = 0 | all_1243_2 = 0)
% 220.34/30.72 | | | | | | | |
% 220.34/30.72 | | | | | | | | ALPHA: (217) implies:
% 220.34/30.72 | | | | | | | | (218) c_member(all_674_0, all_870_5, v_L) = all_1243_2
% 220.34/30.72 | | | | | | | |
% 220.34/30.72 | | | | | | | | REDUCE: (84), (218) imply:
% 220.34/30.72 | | | | | | | | (219) c_member(all_625_1, all_870_5, v_L) = all_1243_2
% 220.34/30.72 | | | | | | | |
% 220.34/30.72 | | | | | | | | BETA: splitting (125) gives:
% 220.34/30.72 | | | | | | | |
% 220.34/30.72 | | | | | | | | Case 1:
% 220.34/30.72 | | | | | | | | |
% 220.34/30.72 | | | | | | | | | (220) all_870_12 = all_870_13
% 220.34/30.72 | | | | | | | | |
% 220.34/30.72 | | | | | | | | | REDUCE: (90), (220) imply:
% 220.34/30.72 | | | | | | | | | (221) $false
% 220.34/30.72 | | | | | | | | |
% 220.34/30.72 | | | | | | | | | CLOSE: (221) is inconsistent.
% 220.34/30.72 | | | | | | | | |
% 220.34/30.72 | | | | | | | | Case 2:
% 220.34/30.72 | | | | | | | | |
% 220.34/30.72 | | | | | | | | | (222) ? [v0: any] : ? [v1: $i] : ? [v2: any] :
% 220.34/30.72 | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.72 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_12,
% 220.34/30.72 | | | | | | | | | all_870_13) = v1 & c_member(all_674_0, v1, v_L) =
% 220.34/30.72 | | | | | | | | | v2 & c_member(all_674_0, all_870_11, v_L) = v0 &
% 220.34/30.72 | | | | | | | | | $i(v1) & (v2 = 0 | v0 = 0))
% 220.34/30.72 | | | | | | | | |
% 220.34/30.72 | | | | | | | | | DELTA: instantiating (222) with fresh symbols all_1249_0,
% 220.34/30.72 | | | | | | | | | all_1249_1, all_1249_2 gives:
% 220.34/30.72 | | | | | | | | | (223) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.72 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_12,
% 220.34/30.72 | | | | | | | | | all_870_13) = all_1249_1 & c_member(all_674_0,
% 220.34/30.72 | | | | | | | | | all_1249_1, v_L) = all_1249_0 & c_member(all_674_0,
% 220.34/30.72 | | | | | | | | | all_870_11, v_L) = all_1249_2 & $i(all_1249_1) &
% 220.34/30.72 | | | | | | | | | (all_1249_0 = 0 | all_1249_2 = 0)
% 220.34/30.72 | | | | | | | | |
% 220.34/30.72 | | | | | | | | | ALPHA: (223) implies:
% 220.34/30.72 | | | | | | | | | (224) c_member(all_674_0, all_870_11, v_L) = all_1249_2
% 220.34/30.72 | | | | | | | | | (225) c_member(all_674_0, all_1249_1, v_L) = all_1249_0
% 220.34/30.72 | | | | | | | | | (226) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.72 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_12,
% 220.34/30.72 | | | | | | | | | all_870_13) = all_1249_1
% 220.34/30.72 | | | | | | | | | (227) all_1249_0 = 0 | all_1249_2 = 0
% 220.34/30.72 | | | | | | | | |
% 220.34/30.72 | | | | | | | | | REDUCE: (84), (225) imply:
% 220.34/30.72 | | | | | | | | | (228) c_member(all_625_1, all_1249_1, v_L) = all_1249_0
% 220.34/30.72 | | | | | | | | |
% 220.34/30.72 | | | | | | | | | REDUCE: (84), (224) imply:
% 220.34/30.72 | | | | | | | | | (229) c_member(all_625_1, all_870_11, v_L) = all_1249_2
% 220.34/30.72 | | | | | | | | |
% 220.34/30.72 | | | | | | | | | GROUND_INST: instantiating (19) with all_870_10, all_1249_2,
% 220.34/30.72 | | | | | | | | | v_L, all_870_11, all_625_1, simplifying with
% 220.34/30.72 | | | | | | | | | (119), (229) gives:
% 220.34/30.72 | | | | | | | | | (230) all_1249_2 = all_870_10
% 220.34/30.72 | | | | | | | | |
% 220.34/30.72 | | | | | | | | | GROUND_INST: instantiating (19) with all_870_4, all_1243_2,
% 220.34/30.72 | | | | | | | | | v_L, all_870_5, all_625_1, simplifying with (116),
% 220.34/30.72 | | | | | | | | | (219) gives:
% 220.34/30.72 | | | | | | | | | (231) all_1243_2 = all_870_4
% 220.34/30.72 | | | | | | | | |
% 220.34/30.73 | | | | | | | | | GROUND_INST: instantiating (20) with all_870_5, all_1249_1,
% 220.34/30.73 | | | | | | | | | all_870_13, all_870_12,
% 220.34/30.73 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.73 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with
% 220.34/30.73 | | | | | | | | | (105), (226) gives:
% 220.34/30.73 | | | | | | | | | (232) all_1249_1 = all_870_5
% 220.34/30.73 | | | | | | | | |
% 220.34/30.73 | | | | | | | | | REDUCE: (228), (232) imply:
% 220.34/30.73 | | | | | | | | | (233) c_member(all_625_1, all_870_5, v_L) = all_1249_0
% 220.34/30.73 | | | | | | | | |
% 220.34/30.73 | | | | | | | | | BETA: splitting (227) gives:
% 220.34/30.73 | | | | | | | | |
% 220.34/30.73 | | | | | | | | | Case 1:
% 220.34/30.73 | | | | | | | | | |
% 220.34/30.73 | | | | | | | | | | (234) all_1249_0 = 0
% 220.34/30.73 | | | | | | | | | |
% 220.34/30.73 | | | | | | | | | | REDUCE: (233), (234) imply:
% 220.34/30.73 | | | | | | | | | | (235) c_member(all_625_1, all_870_5, v_L) = 0
% 220.34/30.73 | | | | | | | | | |
% 220.34/30.73 | | | | | | | | | | GROUND_INST: instantiating (19) with all_870_4, 0, v_L,
% 220.34/30.73 | | | | | | | | | | all_870_5, all_625_1, simplifying with (116),
% 220.34/30.73 | | | | | | | | | | (235) gives:
% 220.34/30.73 | | | | | | | | | | (236) all_870_4 = 0
% 220.34/30.73 | | | | | | | | | |
% 220.34/30.73 | | | | | | | | | | BETA: splitting (111) gives:
% 220.34/30.73 | | | | | | | | | |
% 220.34/30.73 | | | | | | | | | | Case 1:
% 220.34/30.73 | | | | | | | | | | |
% 220.34/30.73 | | | | | | | | | | | (237) ~ (all_870_4 = 0)
% 220.34/30.73 | | | | | | | | | | |
% 220.34/30.73 | | | | | | | | | | | REDUCE: (236), (237) imply:
% 220.34/30.73 | | | | | | | | | | | (238) $false
% 220.34/30.73 | | | | | | | | | | |
% 220.34/30.73 | | | | | | | | | | | CLOSE: (238) is inconsistent.
% 220.34/30.73 | | | | | | | | | | |
% 220.34/30.73 | | | | | | | | | | Case 2:
% 220.34/30.73 | | | | | | | | | | |
% 220.34/30.73 | | | | | | | | | | | (239) all_870_12 = v_x | all_870_13 = v_x
% 220.34/30.73 | | | | | | | | | | |
% 220.34/30.73 | | | | | | | | | | | REF_CLOSE: (12), (19), (20), (84), (90), (102), (112), (114),
% 220.34/30.73 | | | | | | | | | | | (118), (120), (121), (124), (131), (169), (174),
% 220.34/30.73 | | | | | | | | | | | (177), (213), (239) are inconsistent by sub-proof
% 220.34/30.73 | | | | | | | | | | | #17.
% 220.34/30.73 | | | | | | | | | | |
% 220.34/30.73 | | | | | | | | | | End of split
% 220.34/30.73 | | | | | | | | | |
% 220.34/30.73 | | | | | | | | | Case 2:
% 220.34/30.73 | | | | | | | | | |
% 220.34/30.73 | | | | | | | | | | (240) all_1249_2 = 0
% 220.34/30.73 | | | | | | | | | |
% 220.34/30.73 | | | | | | | | | | COMBINE_EQS: (230), (240) imply:
% 220.34/30.73 | | | | | | | | | | (241) all_870_10 = 0
% 220.34/30.73 | | | | | | | | | |
% 220.34/30.73 | | | | | | | | | | BETA: splitting (108) gives:
% 220.34/30.73 | | | | | | | | | |
% 220.34/30.73 | | | | | | | | | | Case 1:
% 220.34/30.73 | | | | | | | | | | |
% 220.34/30.73 | | | | | | | | | | | (242) ~ (all_870_10 = 0)
% 220.34/30.73 | | | | | | | | | | |
% 220.34/30.73 | | | | | | | | | | | REDUCE: (241), (242) imply:
% 220.34/30.73 | | | | | | | | | | | (243) $false
% 220.34/30.73 | | | | | | | | | | |
% 220.34/30.73 | | | | | | | | | | | CLOSE: (243) is inconsistent.
% 220.34/30.73 | | | | | | | | | | |
% 220.34/30.73 | | | | | | | | | | Case 2:
% 220.34/30.73 | | | | | | | | | | |
% 220.34/30.73 | | | | | | | | | | | (244) all_870_12 = v_x | all_870_13 = v_x
% 220.34/30.73 | | | | | | | | | | |
% 220.34/30.73 | | | | | | | | | | | REF_CLOSE: (12), (19), (20), (84), (90), (102), (112), (114),
% 220.34/30.73 | | | | | | | | | | | (118), (120), (121), (124), (131), (169), (174),
% 220.34/30.73 | | | | | | | | | | | (177), (213), (244) are inconsistent by sub-proof
% 220.34/30.73 | | | | | | | | | | | #17.
% 220.34/30.73 | | | | | | | | | | |
% 220.34/30.73 | | | | | | | | | | End of split
% 220.34/30.73 | | | | | | | | | |
% 220.34/30.73 | | | | | | | | | End of split
% 220.34/30.73 | | | | | | | | |
% 220.34/30.73 | | | | | | | | End of split
% 220.34/30.73 | | | | | | | |
% 220.34/30.73 | | | | | | | End of split
% 220.34/30.73 | | | | | | |
% 220.34/30.73 | | | | | | Case 2:
% 220.34/30.73 | | | | | | |
% 220.34/30.73 | | | | | | | (245) ! [v0: $i] : ! [v1: $i] : ( ~
% 220.34/30.73 | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.73 | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = v1) |
% 220.34/30.73 | | | | | | | ~ $i(v0) | ? [v2: $i] : ? [v3: any] : ? [v4: any] :
% 220.34/30.73 | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.73 | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_13, v0) =
% 220.34/30.73 | | | | | | | v2 & c_member(all_674_0, v2, v_L) = v3 &
% 220.34/30.73 | | | | | | | c_member(all_674_0, v1, v_L) = v4 & $i(v2) & ( ~ (v3
% 220.34/30.73 | | | | | | | = 0) | v4 = 0)))
% 220.34/30.73 | | | | | | |
% 220.34/30.73 | | | | | | | GROUND_INST: instantiating (245) with all_870_12, all_870_7,
% 220.34/30.73 | | | | | | | simplifying with (92), (101) gives:
% 220.34/30.73 | | | | | | | (246) ? [v0: $i] : ? [v1: any] : ? [v2: any] :
% 220.34/30.73 | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.73 | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_13,
% 220.34/30.73 | | | | | | | all_870_12) = v0 & c_member(all_674_0, v0, v_L) = v1
% 220.34/30.73 | | | | | | | & c_member(all_674_0, all_870_7, v_L) = v2 & $i(v0) & (
% 220.34/30.73 | | | | | | | ~ (v1 = 0) | v2 = 0))
% 220.34/30.73 | | | | | | |
% 220.34/30.73 | | | | | | | DELTA: instantiating (246) with fresh symbols all_1220_0,
% 220.34/30.73 | | | | | | | all_1220_1, all_1220_2 gives:
% 220.34/30.73 | | | | | | | (247) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.73 | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_13,
% 220.34/30.73 | | | | | | | all_870_12) = all_1220_2 & c_member(all_674_0,
% 220.34/30.73 | | | | | | | all_1220_2, v_L) = all_1220_1 & c_member(all_674_0,
% 220.34/30.73 | | | | | | | all_870_7, v_L) = all_1220_0 & $i(all_1220_2) & ( ~
% 220.34/30.73 | | | | | | | (all_1220_1 = 0) | all_1220_0 = 0)
% 220.34/30.73 | | | | | | |
% 220.34/30.73 | | | | | | | ALPHA: (247) implies:
% 220.34/30.73 | | | | | | | (248) c_member(all_674_0, all_870_7, v_L) = all_1220_0
% 220.34/30.73 | | | | | | | (249) c_member(all_674_0, all_1220_2, v_L) = all_1220_1
% 220.34/30.73 | | | | | | | (250) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.73 | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_13,
% 220.34/30.73 | | | | | | | all_870_12) = all_1220_2
% 220.34/30.73 | | | | | | | (251) ~ (all_1220_1 = 0) | all_1220_0 = 0
% 220.34/30.73 | | | | | | |
% 220.34/30.73 | | | | | | | REDUCE: (84), (249) imply:
% 220.34/30.73 | | | | | | | (252) c_member(all_625_1, all_1220_2, v_L) = all_1220_1
% 220.34/30.73 | | | | | | |
% 220.34/30.73 | | | | | | | REDUCE: (84), (248) imply:
% 220.34/30.73 | | | | | | | (253) c_member(all_625_1, all_870_7, v_L) = all_1220_0
% 220.34/30.73 | | | | | | |
% 220.34/30.73 | | | | | | | GROUND_INST: instantiating (19) with all_870_6, all_1220_0, v_L,
% 220.34/30.73 | | | | | | | all_870_7, all_625_1, simplifying with (117), (253)
% 220.34/30.73 | | | | | | | gives:
% 220.34/30.73 | | | | | | | (254) all_1220_0 = all_870_6
% 220.34/30.73 | | | | | | |
% 220.34/30.73 | | | | | | | GROUND_INST: instantiating (20) with all_870_11, all_1220_2,
% 220.34/30.73 | | | | | | | all_870_12, all_870_13,
% 220.34/30.73 | | | | | | | tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.73 | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with
% 220.34/30.73 | | | | | | | (103), (250) gives:
% 220.34/30.73 | | | | | | | (255) all_1220_2 = all_870_11
% 220.34/30.73 | | | | | | |
% 220.34/30.73 | | | | | | | REDUCE: (252), (255) imply:
% 220.34/30.73 | | | | | | | (256) c_member(all_625_1, all_870_11, v_L) = all_1220_1
% 220.34/30.73 | | | | | | |
% 220.34/30.73 | | | | | | | GROUND_INST: instantiating (19) with all_870_10, all_1220_1, v_L,
% 220.34/30.73 | | | | | | | all_870_11, all_625_1, simplifying with (119), (256)
% 220.34/30.73 | | | | | | | gives:
% 220.34/30.73 | | | | | | | (257) all_1220_1 = all_870_10
% 220.34/30.73 | | | | | | |
% 220.34/30.73 | | | | | | | BETA: splitting (125) gives:
% 220.34/30.73 | | | | | | |
% 220.34/30.73 | | | | | | | Case 1:
% 220.34/30.73 | | | | | | | |
% 220.34/30.73 | | | | | | | | (258) all_870_12 = all_870_13
% 220.34/30.73 | | | | | | | |
% 220.34/30.73 | | | | | | | | REDUCE: (90), (258) imply:
% 220.34/30.73 | | | | | | | | (259) $false
% 220.34/30.73 | | | | | | | |
% 220.34/30.73 | | | | | | | | CLOSE: (259) is inconsistent.
% 220.34/30.73 | | | | | | | |
% 220.34/30.73 | | | | | | | Case 2:
% 220.34/30.73 | | | | | | | |
% 220.34/30.73 | | | | | | | | (260) ? [v0: any] : ? [v1: $i] : ? [v2: any] :
% 220.34/30.73 | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.73 | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_12,
% 220.34/30.73 | | | | | | | | all_870_13) = v1 & c_member(all_674_0, v1, v_L) =
% 220.34/30.73 | | | | | | | | v2 & c_member(all_674_0, all_870_11, v_L) = v0 &
% 220.34/30.73 | | | | | | | | $i(v1) & (v2 = 0 | v0 = 0))
% 220.34/30.73 | | | | | | | |
% 220.34/30.73 | | | | | | | | DELTA: instantiating (260) with fresh symbols all_1262_0,
% 220.34/30.73 | | | | | | | | all_1262_1, all_1262_2 gives:
% 220.34/30.73 | | | | | | | | (261) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.73 | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_12,
% 220.34/30.73 | | | | | | | | all_870_13) = all_1262_1 & c_member(all_674_0,
% 220.34/30.73 | | | | | | | | all_1262_1, v_L) = all_1262_0 & c_member(all_674_0,
% 220.34/30.73 | | | | | | | | all_870_11, v_L) = all_1262_2 & $i(all_1262_1) &
% 220.34/30.73 | | | | | | | | (all_1262_0 = 0 | all_1262_2 = 0)
% 220.34/30.73 | | | | | | | |
% 220.34/30.73 | | | | | | | | ALPHA: (261) implies:
% 220.34/30.73 | | | | | | | | (262) c_member(all_674_0, all_870_11, v_L) = all_1262_2
% 220.34/30.73 | | | | | | | |
% 220.34/30.73 | | | | | | | | REDUCE: (84), (262) imply:
% 220.34/30.73 | | | | | | | | (263) c_member(all_625_1, all_870_11, v_L) = all_1262_2
% 220.34/30.73 | | | | | | | |
% 220.34/30.73 | | | | | | | | BETA: splitting (128) gives:
% 220.34/30.73 | | | | | | | |
% 220.34/30.73 | | | | | | | | Case 1:
% 220.34/30.73 | | | | | | | | |
% 220.34/30.73 | | | | | | | | | (264) all_870_12 = all_870_13
% 220.34/30.73 | | | | | | | | |
% 220.34/30.73 | | | | | | | | | REDUCE: (90), (264) imply:
% 220.34/30.73 | | | | | | | | | (265) $false
% 220.34/30.73 | | | | | | | | |
% 220.34/30.73 | | | | | | | | | CLOSE: (265) is inconsistent.
% 220.34/30.73 | | | | | | | | |
% 220.34/30.73 | | | | | | | | Case 2:
% 220.34/30.73 | | | | | | | | |
% 220.34/30.73 | | | | | | | | | (266) ? [v0: any] : ? [v1: $i] : ? [v2: any] :
% 220.34/30.73 | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.73 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_13,
% 220.34/30.73 | | | | | | | | | all_870_12) = v1 & c_member(all_674_0, v1, v_L) =
% 220.34/30.73 | | | | | | | | | v2 & c_member(all_674_0, all_870_5, v_L) = v0 &
% 220.34/30.73 | | | | | | | | | $i(v1) & (v2 = 0 | v0 = 0))
% 220.34/30.73 | | | | | | | | |
% 220.34/30.73 | | | | | | | | | DELTA: instantiating (266) with fresh symbols all_1268_0,
% 220.34/30.73 | | | | | | | | | all_1268_1, all_1268_2 gives:
% 220.34/30.73 | | | | | | | | | (267) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.73 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_13,
% 220.34/30.73 | | | | | | | | | all_870_12) = all_1268_1 & c_member(all_674_0,
% 220.34/30.73 | | | | | | | | | all_1268_1, v_L) = all_1268_0 & c_member(all_674_0,
% 220.34/30.73 | | | | | | | | | all_870_5, v_L) = all_1268_2 & $i(all_1268_1) &
% 220.34/30.73 | | | | | | | | | (all_1268_0 = 0 | all_1268_2 = 0)
% 220.34/30.73 | | | | | | | | |
% 220.34/30.73 | | | | | | | | | ALPHA: (267) implies:
% 220.34/30.73 | | | | | | | | | (268) c_member(all_674_0, all_870_5, v_L) = all_1268_2
% 220.34/30.73 | | | | | | | | | (269) c_member(all_674_0, all_1268_1, v_L) = all_1268_0
% 220.34/30.73 | | | | | | | | | (270) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.73 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_13,
% 220.34/30.73 | | | | | | | | | all_870_12) = all_1268_1
% 220.34/30.74 | | | | | | | | | (271) all_1268_0 = 0 | all_1268_2 = 0
% 220.34/30.74 | | | | | | | | |
% 220.34/30.74 | | | | | | | | | REDUCE: (84), (269) imply:
% 220.34/30.74 | | | | | | | | | (272) c_member(all_625_1, all_1268_1, v_L) = all_1268_0
% 220.34/30.74 | | | | | | | | |
% 220.34/30.74 | | | | | | | | | REDUCE: (84), (268) imply:
% 220.34/30.74 | | | | | | | | | (273) c_member(all_625_1, all_870_5, v_L) = all_1268_2
% 220.34/30.74 | | | | | | | | |
% 220.34/30.74 | | | | | | | | | GROUND_INST: instantiating (19) with all_870_10, all_1262_2,
% 220.34/30.74 | | | | | | | | | v_L, all_870_11, all_625_1, simplifying with
% 220.34/30.74 | | | | | | | | | (119), (263) gives:
% 220.34/30.74 | | | | | | | | | (274) all_1262_2 = all_870_10
% 220.34/30.74 | | | | | | | | |
% 220.34/30.74 | | | | | | | | | GROUND_INST: instantiating (19) with all_870_4, all_1268_2,
% 220.34/30.74 | | | | | | | | | v_L, all_870_5, all_625_1, simplifying with (116),
% 220.34/30.74 | | | | | | | | | (273) gives:
% 220.34/30.74 | | | | | | | | | (275) all_1268_2 = all_870_4
% 220.34/30.74 | | | | | | | | |
% 220.34/30.74 | | | | | | | | | GROUND_INST: instantiating (20) with all_870_11, all_1268_1,
% 220.34/30.74 | | | | | | | | | all_870_12, all_870_13,
% 220.34/30.74 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.74 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with
% 220.34/30.74 | | | | | | | | | (103), (270) gives:
% 220.34/30.74 | | | | | | | | | (276) all_1268_1 = all_870_11
% 220.34/30.74 | | | | | | | | |
% 220.34/30.74 | | | | | | | | | REDUCE: (272), (276) imply:
% 220.34/30.74 | | | | | | | | | (277) c_member(all_625_1, all_870_11, v_L) = all_1268_0
% 220.34/30.74 | | | | | | | | |
% 220.34/30.74 | | | | | | | | | BETA: splitting (271) gives:
% 220.34/30.74 | | | | | | | | |
% 220.34/30.74 | | | | | | | | | Case 1:
% 220.34/30.74 | | | | | | | | | |
% 220.34/30.74 | | | | | | | | | | (278) all_1268_0 = 0
% 220.34/30.74 | | | | | | | | | |
% 220.34/30.74 | | | | | | | | | | REDUCE: (277), (278) imply:
% 220.34/30.74 | | | | | | | | | | (279) c_member(all_625_1, all_870_11, v_L) = 0
% 220.34/30.74 | | | | | | | | | |
% 220.34/30.74 | | | | | | | | | | GROUND_INST: instantiating (19) with all_870_10, 0, v_L,
% 220.34/30.74 | | | | | | | | | | all_870_11, all_625_1, simplifying with (119),
% 220.34/30.74 | | | | | | | | | | (279) gives:
% 220.34/30.74 | | | | | | | | | | (280) all_870_10 = 0
% 220.34/30.74 | | | | | | | | | |
% 220.34/30.74 | | | | | | | | | | BETA: splitting (108) gives:
% 220.34/30.74 | | | | | | | | | |
% 220.34/30.74 | | | | | | | | | | Case 1:
% 220.34/30.74 | | | | | | | | | | |
% 220.34/30.74 | | | | | | | | | | | (281) ~ (all_870_10 = 0)
% 220.34/30.74 | | | | | | | | | | |
% 220.34/30.74 | | | | | | | | | | | REDUCE: (280), (281) imply:
% 220.34/30.74 | | | | | | | | | | | (282) $false
% 220.34/30.74 | | | | | | | | | | |
% 220.34/30.74 | | | | | | | | | | | CLOSE: (282) is inconsistent.
% 220.34/30.74 | | | | | | | | | | |
% 220.34/30.74 | | | | | | | | | | Case 2:
% 220.34/30.74 | | | | | | | | | | |
% 220.34/30.74 | | | | | | | | | | | (283) all_870_12 = v_x | all_870_13 = v_x
% 220.34/30.74 | | | | | | | | | | |
% 220.34/30.74 | | | | | | | | | | | REF_CLOSE: (19), (20), (84), (90), (101), (110), (112),
% 220.34/30.74 | | | | | | | | | | | (115), (117), (123), (127), (130), (131), (194),
% 220.34/30.74 | | | | | | | | | | | (202), (251), (254), (257), (283) are inconsistent
% 220.34/30.74 | | | | | | | | | | | by sub-proof #16.
% 220.34/30.74 | | | | | | | | | | |
% 220.34/30.74 | | | | | | | | | | End of split
% 220.34/30.74 | | | | | | | | | |
% 220.34/30.74 | | | | | | | | | Case 2:
% 220.34/30.74 | | | | | | | | | |
% 220.34/30.74 | | | | | | | | | | (284) all_1268_2 = 0
% 220.34/30.74 | | | | | | | | | |
% 220.34/30.74 | | | | | | | | | | COMBINE_EQS: (275), (284) imply:
% 220.34/30.74 | | | | | | | | | | (285) all_870_4 = 0
% 220.34/30.74 | | | | | | | | | |
% 220.34/30.74 | | | | | | | | | | BETA: splitting (111) gives:
% 220.34/30.74 | | | | | | | | | |
% 220.34/30.74 | | | | | | | | | | Case 1:
% 220.34/30.74 | | | | | | | | | | |
% 220.34/30.74 | | | | | | | | | | | (286) ~ (all_870_4 = 0)
% 220.34/30.74 | | | | | | | | | | |
% 220.34/30.74 | | | | | | | | | | | REDUCE: (285), (286) imply:
% 220.34/30.74 | | | | | | | | | | | (287) $false
% 220.34/30.74 | | | | | | | | | | |
% 220.34/30.74 | | | | | | | | | | | CLOSE: (287) is inconsistent.
% 220.34/30.74 | | | | | | | | | | |
% 220.34/30.74 | | | | | | | | | | Case 2:
% 220.34/30.74 | | | | | | | | | | |
% 220.34/30.74 | | | | | | | | | | | (288) all_870_12 = v_x | all_870_13 = v_x
% 220.34/30.74 | | | | | | | | | | |
% 220.34/30.74 | | | | | | | | | | | REF_CLOSE: (19), (20), (84), (90), (101), (110), (112),
% 220.34/30.74 | | | | | | | | | | | (115), (117), (123), (127), (130), (131), (194),
% 220.34/30.74 | | | | | | | | | | | (202), (251), (254), (257), (288) are inconsistent
% 220.34/30.74 | | | | | | | | | | | by sub-proof #16.
% 220.34/30.74 | | | | | | | | | | |
% 220.34/30.74 | | | | | | | | | | End of split
% 220.34/30.74 | | | | | | | | | |
% 220.34/30.74 | | | | | | | | | End of split
% 220.34/30.74 | | | | | | | | |
% 220.34/30.74 | | | | | | | | End of split
% 220.34/30.74 | | | | | | | |
% 220.34/30.74 | | | | | | | End of split
% 220.34/30.74 | | | | | | |
% 220.34/30.74 | | | | | | End of split
% 220.34/30.74 | | | | | |
% 220.34/30.74 | | | | | End of split
% 220.34/30.74 | | | | |
% 220.34/30.74 | | | | End of split
% 220.34/30.74 | | | |
% 220.34/30.74 | | | Case 2:
% 220.34/30.74 | | | |
% 220.34/30.74 | | | | (289) all_870_12 = v_x
% 220.34/30.74 | | | | (290) ~ (all_870_13 = v_y)
% 220.34/30.74 | | | |
% 220.34/30.74 | | | | REDUCE: (90), (289) imply:
% 220.34/30.74 | | | | (291) ~ (all_870_13 = v_x)
% 220.34/30.74 | | | |
% 220.34/30.74 | | | | SIMP: (291) implies:
% 220.34/30.74 | | | | (292) ~ (all_870_13 = v_x)
% 220.34/30.74 | | | |
% 220.34/30.74 | | | | REF_CLOSE: (19), (20), (84), (102), (109), (113), (114), (118), (121),
% 220.34/30.74 | | | | (124), (289), (290), (292) are inconsistent by sub-proof #14.
% 220.34/30.74 | | | |
% 220.34/30.74 | | | End of split
% 220.34/30.74 | | |
% 220.34/30.74 | | Case 2:
% 220.34/30.74 | | |
% 220.34/30.74 | | | (293) all_870_12 = v_y
% 220.34/30.74 | | | (294) ~ (all_870_13 = v_x)
% 220.34/30.74 | | |
% 220.34/30.74 | | | REDUCE: (90), (293) imply:
% 220.34/30.74 | | | (295) ~ (all_870_13 = v_y)
% 220.34/30.74 | | |
% 220.34/30.74 | | | SIMP: (295) implies:
% 220.34/30.74 | | | (296) ~ (all_870_13 = v_y)
% 220.34/30.74 | | |
% 220.34/30.74 | | | REDUCE: (103), (293) imply:
% 220.34/30.74 | | | (297) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.74 | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_13, v_y) = all_870_11
% 220.34/30.74 | | |
% 220.34/30.74 | | | BETA: splitting (111) gives:
% 220.34/30.74 | | |
% 220.34/30.74 | | | Case 1:
% 220.34/30.74 | | | |
% 220.34/30.74 | | | | (298) ~ (all_870_4 = 0)
% 220.34/30.74 | | | |
% 220.34/30.74 | | | | BETA: splitting (125) gives:
% 220.34/30.74 | | | |
% 220.34/30.74 | | | | Case 1:
% 220.34/30.74 | | | | |
% 220.34/30.74 | | | | | (299) all_870_12 = all_870_13
% 220.34/30.74 | | | | |
% 220.34/30.74 | | | | | COMBINE_EQS: (293), (299) imply:
% 220.34/30.74 | | | | | (300) all_870_13 = v_y
% 220.34/30.74 | | | | |
% 220.34/30.74 | | | | | SIMP: (300) implies:
% 220.34/30.74 | | | | | (301) all_870_13 = v_y
% 220.34/30.74 | | | | |
% 220.34/30.74 | | | | | REDUCE: (296), (301) imply:
% 220.34/30.74 | | | | | (302) $false
% 220.34/30.74 | | | | |
% 220.34/30.74 | | | | | CLOSE: (302) is inconsistent.
% 220.34/30.74 | | | | |
% 220.34/30.74 | | | | Case 2:
% 220.34/30.74 | | | | |
% 220.34/30.74 | | | | | (303) ? [v0: any] : ? [v1: $i] : ? [v2: any] :
% 220.34/30.74 | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.74 | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_12, all_870_13)
% 220.34/30.74 | | | | | = v1 & c_member(all_674_0, v1, v_L) = v2 &
% 220.34/30.74 | | | | | c_member(all_674_0, all_870_11, v_L) = v0 & $i(v1) & (v2 =
% 220.34/30.74 | | | | | 0 | v0 = 0))
% 220.34/30.74 | | | | |
% 220.34/30.74 | | | | | DELTA: instantiating (303) with fresh symbols all_1180_0, all_1180_1,
% 220.34/30.74 | | | | | all_1180_2 gives:
% 220.34/30.74 | | | | | (304) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.74 | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_12, all_870_13) =
% 220.34/30.74 | | | | | all_1180_1 & c_member(all_674_0, all_1180_1, v_L) =
% 220.34/30.74 | | | | | all_1180_0 & c_member(all_674_0, all_870_11, v_L) =
% 220.34/30.74 | | | | | all_1180_2 & $i(all_1180_1) & (all_1180_0 = 0 | all_1180_2 =
% 220.34/30.74 | | | | | 0)
% 220.34/30.74 | | | | |
% 220.34/30.74 | | | | | ALPHA: (304) implies:
% 220.34/30.74 | | | | | (305) c_member(all_674_0, all_870_11, v_L) = all_1180_2
% 220.34/30.74 | | | | |
% 220.34/30.74 | | | | | REDUCE: (84), (305) imply:
% 220.34/30.74 | | | | | (306) c_member(all_625_1, all_870_11, v_L) = all_1180_2
% 220.34/30.74 | | | | |
% 220.34/30.74 | | | | | BETA: splitting (128) gives:
% 220.34/30.74 | | | | |
% 220.34/30.74 | | | | | Case 1:
% 220.34/30.74 | | | | | |
% 220.34/30.74 | | | | | | (307) all_870_12 = all_870_13
% 220.34/30.74 | | | | | |
% 220.34/30.74 | | | | | | COMBINE_EQS: (293), (307) imply:
% 220.34/30.74 | | | | | | (308) all_870_13 = v_y
% 220.34/30.74 | | | | | |
% 220.34/30.74 | | | | | | SIMP: (308) implies:
% 220.34/30.74 | | | | | | (309) all_870_13 = v_y
% 220.34/30.74 | | | | | |
% 220.34/30.74 | | | | | | REDUCE: (296), (309) imply:
% 220.34/30.74 | | | | | | (310) $false
% 220.34/30.74 | | | | | |
% 220.34/30.74 | | | | | | CLOSE: (310) is inconsistent.
% 220.34/30.74 | | | | | |
% 220.34/30.74 | | | | | Case 2:
% 220.34/30.74 | | | | | |
% 220.34/30.74 | | | | | | (311) ? [v0: any] : ? [v1: $i] : ? [v2: any] :
% 220.34/30.74 | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.74 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_13,
% 220.34/30.74 | | | | | | all_870_12) = v1 & c_member(all_674_0, v1, v_L) = v2 &
% 220.34/30.74 | | | | | | c_member(all_674_0, all_870_5, v_L) = v0 & $i(v1) & (v2 =
% 220.34/30.74 | | | | | | 0 | v0 = 0))
% 220.34/30.74 | | | | | |
% 220.34/30.74 | | | | | | DELTA: instantiating (311) with fresh symbols all_1191_0,
% 220.34/30.74 | | | | | | all_1191_1, all_1191_2 gives:
% 220.34/30.74 | | | | | | (312) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.74 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_13, all_870_12)
% 220.34/30.74 | | | | | | = all_1191_1 & c_member(all_674_0, all_1191_1, v_L) =
% 220.34/30.74 | | | | | | all_1191_0 & c_member(all_674_0, all_870_5, v_L) =
% 220.34/30.74 | | | | | | all_1191_2 & $i(all_1191_1) & (all_1191_0 = 0 | all_1191_2
% 220.34/30.74 | | | | | | = 0)
% 220.34/30.74 | | | | | |
% 220.34/30.74 | | | | | | ALPHA: (312) implies:
% 220.34/30.74 | | | | | | (313) c_member(all_674_0, all_870_5, v_L) = all_1191_2
% 220.34/30.74 | | | | | | (314) c_member(all_674_0, all_1191_1, v_L) = all_1191_0
% 220.34/30.74 | | | | | | (315) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.74 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_13, all_870_12)
% 220.34/30.74 | | | | | | = all_1191_1
% 220.34/30.74 | | | | | | (316) all_1191_0 = 0 | all_1191_2 = 0
% 220.34/30.74 | | | | | |
% 220.34/30.74 | | | | | | REDUCE: (293), (315) imply:
% 220.34/30.74 | | | | | | (317) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.74 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_13, v_y) =
% 220.34/30.74 | | | | | | all_1191_1
% 220.34/30.74 | | | | | |
% 220.34/30.74 | | | | | | REDUCE: (84), (314) imply:
% 220.34/30.74 | | | | | | (318) c_member(all_625_1, all_1191_1, v_L) = all_1191_0
% 220.34/30.74 | | | | | |
% 220.34/30.74 | | | | | | REDUCE: (84), (313) imply:
% 220.34/30.74 | | | | | | (319) c_member(all_625_1, all_870_5, v_L) = all_1191_2
% 220.34/30.74 | | | | | |
% 220.34/30.74 | | | | | | BETA: splitting (108) gives:
% 220.34/30.74 | | | | | |
% 220.34/30.74 | | | | | | Case 1:
% 220.34/30.74 | | | | | | |
% 220.34/30.74 | | | | | | | (320) ~ (all_870_10 = 0)
% 220.34/30.74 | | | | | | |
% 220.34/30.75 | | | | | | | GROUND_INST: instantiating (19) with all_870_10, all_1180_2, v_L,
% 220.34/30.75 | | | | | | | all_870_11, all_625_1, simplifying with (119), (306)
% 220.34/30.75 | | | | | | | gives:
% 220.34/30.75 | | | | | | | (321) all_1180_2 = all_870_10
% 220.34/30.75 | | | | | | |
% 220.34/30.75 | | | | | | | GROUND_INST: instantiating (19) with all_870_4, all_1191_2, v_L,
% 220.34/30.75 | | | | | | | all_870_5, all_625_1, simplifying with (116), (319)
% 220.34/30.75 | | | | | | | gives:
% 220.34/30.75 | | | | | | | (322) all_1191_2 = all_870_4
% 220.34/30.75 | | | | | | |
% 220.34/30.75 | | | | | | | GROUND_INST: instantiating (20) with all_870_9, all_1191_1, v_y,
% 220.34/30.75 | | | | | | | all_870_13, tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.75 | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with
% 220.34/30.75 | | | | | | | (102), (317) gives:
% 220.34/30.75 | | | | | | | (323) all_1191_1 = all_870_9
% 220.34/30.75 | | | | | | |
% 220.34/30.75 | | | | | | | GROUND_INST: instantiating (20) with all_870_11, all_1191_1, v_y,
% 220.34/30.75 | | | | | | | all_870_13, tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.75 | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with
% 220.34/30.75 | | | | | | | (297), (317) gives:
% 220.34/30.75 | | | | | | | (324) all_1191_1 = all_870_11
% 220.34/30.75 | | | | | | |
% 220.34/30.75 | | | | | | | COMBINE_EQS: (323), (324) imply:
% 220.34/30.75 | | | | | | | (325) all_870_9 = all_870_11
% 220.34/30.75 | | | | | | |
% 220.34/30.75 | | | | | | | SIMP: (325) implies:
% 220.34/30.75 | | | | | | | (326) all_870_9 = all_870_11
% 220.34/30.75 | | | | | | |
% 220.34/30.75 | | | | | | | REDUCE: (318), (324) imply:
% 220.34/30.75 | | | | | | | (327) c_member(all_625_1, all_870_11, v_L) = all_1191_0
% 220.34/30.75 | | | | | | |
% 220.34/30.75 | | | | | | | REDUCE: (118), (326) imply:
% 220.34/30.75 | | | | | | | (328) c_member(all_625_1, all_870_11, v_L) = all_870_8
% 220.34/30.75 | | | | | | |
% 220.34/30.75 | | | | | | | BETA: splitting (316) gives:
% 220.34/30.75 | | | | | | |
% 220.34/30.75 | | | | | | | Case 1:
% 220.34/30.75 | | | | | | | |
% 220.34/30.75 | | | | | | | | (329) all_1191_0 = 0
% 220.34/30.75 | | | | | | | |
% 220.34/30.75 | | | | | | | | REDUCE: (327), (329) imply:
% 220.34/30.75 | | | | | | | | (330) c_member(all_625_1, all_870_11, v_L) = 0
% 220.34/30.75 | | | | | | | |
% 220.34/30.75 | | | | | | | | GROUND_INST: instantiating (19) with all_870_10, all_870_8, v_L,
% 220.34/30.75 | | | | | | | | all_870_11, all_625_1, simplifying with (119),
% 220.34/30.75 | | | | | | | | (328) gives:
% 220.34/30.75 | | | | | | | | (331) all_870_8 = all_870_10
% 220.34/30.75 | | | | | | | |
% 220.34/30.75 | | | | | | | | GROUND_INST: instantiating (19) with 0, all_870_8, v_L,
% 220.34/30.75 | | | | | | | | all_870_11, all_625_1, simplifying with (328),
% 220.34/30.75 | | | | | | | | (330) gives:
% 220.34/30.75 | | | | | | | | (332) all_870_8 = 0
% 220.34/30.75 | | | | | | | |
% 220.34/30.75 | | | | | | | | COMBINE_EQS: (331), (332) imply:
% 220.34/30.75 | | | | | | | | (333) all_870_10 = 0
% 220.34/30.75 | | | | | | | |
% 220.34/30.75 | | | | | | | | REDUCE: (320), (333) imply:
% 220.34/30.75 | | | | | | | | (334) $false
% 220.34/30.75 | | | | | | | |
% 220.34/30.75 | | | | | | | | CLOSE: (334) is inconsistent.
% 220.34/30.75 | | | | | | | |
% 220.34/30.75 | | | | | | | Case 2:
% 220.34/30.75 | | | | | | | |
% 220.34/30.75 | | | | | | | | (335) all_1191_2 = 0
% 220.34/30.75 | | | | | | | |
% 220.34/30.75 | | | | | | | | COMBINE_EQS: (322), (335) imply:
% 220.34/30.75 | | | | | | | | (336) all_870_4 = 0
% 220.34/30.75 | | | | | | | |
% 220.34/30.75 | | | | | | | | REDUCE: (298), (336) imply:
% 220.34/30.75 | | | | | | | | (337) $false
% 220.34/30.75 | | | | | | | |
% 220.34/30.75 | | | | | | | | CLOSE: (337) is inconsistent.
% 220.34/30.75 | | | | | | | |
% 220.34/30.75 | | | | | | | End of split
% 220.34/30.75 | | | | | | |
% 220.34/30.75 | | | | | | Case 2:
% 220.34/30.75 | | | | | | |
% 220.34/30.75 | | | | | | | (338) all_870_12 = v_x | all_870_13 = v_x
% 220.34/30.75 | | | | | | |
% 220.34/30.75 | | | | | | | REF_CLOSE: (19), (20), (84), (102), (109), (113), (114), (118),
% 220.34/30.75 | | | | | | | (121), (124), (294), (296), (338) are inconsistent by
% 220.34/30.75 | | | | | | | sub-proof #13.
% 220.34/30.75 | | | | | | |
% 220.34/30.75 | | | | | | End of split
% 220.34/30.75 | | | | | |
% 220.34/30.75 | | | | | End of split
% 220.34/30.75 | | | | |
% 220.34/30.75 | | | | End of split
% 220.34/30.75 | | | |
% 220.34/30.75 | | | Case 2:
% 220.34/30.75 | | | |
% 220.34/30.75 | | | | (339) all_870_12 = v_x | all_870_13 = v_x
% 220.34/30.75 | | | |
% 220.34/30.75 | | | | REF_CLOSE: (19), (20), (84), (102), (109), (113), (114), (118), (121),
% 220.34/30.75 | | | | (124), (294), (296), (339) are inconsistent by sub-proof #13.
% 220.34/30.75 | | | |
% 220.34/30.75 | | | End of split
% 220.34/30.75 | | |
% 220.34/30.75 | | End of split
% 220.34/30.75 | |
% 220.34/30.75 | Case 2:
% 220.34/30.75 | |
% 220.34/30.75 | | (340) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] : ? [v4:
% 220.34/30.75 | | $i] : ? [v5: any] : ? [v6: $i] : ? [v7: any] : ? [v8: $i] :
% 220.34/30.75 | | ? [v9: any] :
% 220.34/30.75 | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.75 | | tc_Arrow__Order__Mirabelle_Oalt, v1, v_y) = v4 &
% 220.34/30.75 | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.75 | | tc_Arrow__Order__Mirabelle_Oalt, v0, v1) = v2 &
% 220.34/30.75 | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.75 | | tc_Arrow__Order__Mirabelle_Oalt, v0, v_y) = v6 &
% 220.34/30.75 | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.75 | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v1) = v8 &
% 220.34/30.75 | | c_member(all_683_0, v8, v_L) = v9 & c_member(all_683_0, v6, v_L)
% 220.34/30.75 | | = v7 & c_member(all_683_0, v4, v_L) = v5 & c_member(all_683_0,
% 220.34/30.75 | | v2, v_L) = v3 & $i(v8) & $i(v6) & $i(v4) & $i(v2) & $i(v1) &
% 220.34/30.75 | | $i(v0) & ((v9 = 0 & v0 = v_x & ~ (v1 = v_x) & ? [v10: $i] : ?
% 220.34/30.75 | | [v11: $i] : ? [v12: any] : ? [v13: $i] : ? [v14: any] :
% 220.34/30.75 | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.75 | | tc_Arrow__Order__Mirabelle_Oalt, v1, v10) = v11 &
% 220.34/30.75 | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.75 | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v10) = v13 &
% 220.34/30.75 | | c_member(all_683_0, v13, v_L) = v14 & c_member(all_683_0,
% 220.34/30.75 | | v11, v_L) = v12 & $i(v13) & $i(v11) & $i(v10) & ((v12 = 0
% 220.34/30.75 | | & ~ (v14 = 0) & ~ (v10 = v_x) & ~ (v10 = v_y)) |
% 220.34/30.75 | | (v10 = v_x & v5 = 0)))) | ( ~ (v0 = v_x) & ((v7 = 0 & v1
% 220.34/30.75 | | = v_x & ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ?
% 220.34/30.75 | | [v13: int] : ( ~ (v13 = 0) & ~ (v10 = v_x) &
% 220.34/30.75 | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.75 | | tc_Arrow__Order__Mirabelle_Oalt, v0, v10) = v12 &
% 220.34/30.75 | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.75 | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v10) = v11 &
% 220.34/30.75 | | c_member(all_683_0, v12, v_L) = v13 &
% 220.34/30.75 | | c_member(all_683_0, v11, v_L) = 0 & $i(v12) & $i(v11) &
% 220.34/30.75 | | $i(v10))) | (v3 = 0 & ~ (v1 = v_x) & ? [v10: $i] : ?
% 220.34/30.75 | | [v11: $i] : ? [v12: any] : ? [v13: $i] : ? [v14: any]
% 220.34/30.75 | | : (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.75 | | tc_Arrow__Order__Mirabelle_Oalt, v1, v10) = v11 &
% 220.34/30.75 | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.75 | | tc_Arrow__Order__Mirabelle_Oalt, v0, v10) = v13 &
% 220.34/30.75 | | c_member(all_683_0, v13, v_L) = v14 &
% 220.34/30.75 | | c_member(all_683_0, v11, v_L) = v12 & $i(v13) & $i(v11)
% 220.34/30.75 | | & $i(v10) & ((v12 = 0 & ~ (v14 = 0) & ~ (v10 = v_x))
% 220.34/30.75 | | | (v10 = v_x & v5 = 0 & ~ (v7 = 0)))))))))
% 220.34/30.75 | |
% 220.34/30.75 | | DELTA: instantiating (340) with fresh symbols all_870_0, all_870_1,
% 220.34/30.75 | | all_870_2, all_870_3, all_870_4, all_870_5, all_870_6, all_870_7,
% 220.34/30.75 | | all_870_8, all_870_9 gives:
% 220.34/30.75 | | (341) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.75 | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v_y) = all_870_5 &
% 220.34/30.75 | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.75 | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9, all_870_8) =
% 220.34/30.75 | | all_870_7 & c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.75 | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v_y) = all_870_3 &
% 220.34/30.75 | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.75 | | tc_Arrow__Order__Mirabelle_Oalt, v_y, all_870_8) = all_870_1 &
% 220.34/30.75 | | c_member(all_683_0, all_870_1, v_L) = all_870_0 &
% 220.34/30.75 | | c_member(all_683_0, all_870_3, v_L) = all_870_2 &
% 220.34/30.75 | | c_member(all_683_0, all_870_5, v_L) = all_870_4 &
% 220.34/30.75 | | c_member(all_683_0, all_870_7, v_L) = all_870_6 & $i(all_870_1) &
% 220.34/30.75 | | $i(all_870_3) & $i(all_870_5) & $i(all_870_7) & $i(all_870_8) &
% 220.34/30.75 | | $i(all_870_9) & ((all_870_0 = 0 & all_870_9 = v_x & ~ (all_870_8 =
% 220.34/30.75 | | v_x) & ? [v0: $i] : ? [v1: $i] : ? [v2: any] : ? [v3: $i]
% 220.34/30.75 | | : ? [v4: any] :
% 220.34/30.75 | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.75 | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v0) = v1 &
% 220.34/30.75 | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.75 | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = v3 &
% 220.34/30.75 | | c_member(all_683_0, v3, v_L) = v4 & c_member(all_683_0, v1,
% 220.34/30.75 | | v_L) = v2 & $i(v3) & $i(v1) & $i(v0) & ((v2 = 0 & ~ (v4 =
% 220.34/30.75 | | 0) & ~ (v0 = v_x) & ~ (v0 = v_y)) | (v0 = v_x &
% 220.34/30.75 | | all_870_4 = 0)))) | ( ~ (all_870_9 = v_x) & ((all_870_2 =
% 220.34/30.75 | | 0 & all_870_8 = v_x & ? [v0: $i] : ? [v1: $i] : ? [v2:
% 220.34/30.75 | | $i] : ? [v3: int] : ( ~ (v3 = 0) & ~ (v0 = v_x) &
% 220.34/30.75 | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.75 | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v0) = v2 &
% 220.34/30.75 | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.75 | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = v1 &
% 220.34/30.75 | | c_member(all_683_0, v2, v_L) = v3 & c_member(all_683_0,
% 220.34/30.75 | | v1, v_L) = 0 & $i(v2) & $i(v1) & $i(v0))) | (all_870_6
% 220.34/30.75 | | = 0 & ~ (all_870_8 = v_x) & ? [v0: $i] : ? [v1: $i] : ?
% 220.34/30.75 | | [v2: any] : ? [v3: $i] : ? [v4: any] :
% 220.34/30.75 | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.75 | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v0) = v1 &
% 220.34/30.75 | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.75 | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v0) = v3 &
% 220.34/30.75 | | c_member(all_683_0, v3, v_L) = v4 & c_member(all_683_0,
% 220.34/30.75 | | v1, v_L) = v2 & $i(v3) & $i(v1) & $i(v0) & ((v2 = 0 &
% 220.34/30.75 | | ~ (v4 = 0) & ~ (v0 = v_x)) | (v0 = v_x & all_870_4 =
% 220.34/30.75 | | 0 & ~ (all_870_2 = 0))))))))
% 220.34/30.75 | |
% 220.34/30.75 | | ALPHA: (341) implies:
% 220.34/30.75 | | (342) $i(all_870_9)
% 220.34/30.75 | | (343) $i(all_870_8)
% 220.34/30.75 | | (344) $i(all_870_7)
% 220.34/30.75 | | (345) $i(all_870_5)
% 220.34/30.75 | | (346) $i(all_870_3)
% 220.34/30.75 | | (347) $i(all_870_1)
% 220.34/30.75 | | (348) c_member(all_683_0, all_870_7, v_L) = all_870_6
% 220.34/30.75 | | (349) c_member(all_683_0, all_870_5, v_L) = all_870_4
% 220.34/30.75 | | (350) c_member(all_683_0, all_870_3, v_L) = all_870_2
% 220.34/30.76 | | (351) c_member(all_683_0, all_870_1, v_L) = all_870_0
% 220.34/30.76 | | (352) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.76 | | tc_Arrow__Order__Mirabelle_Oalt, v_y, all_870_8) = all_870_1
% 220.34/30.76 | | (353) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.76 | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v_y) = all_870_3
% 220.34/30.76 | | (354) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.76 | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9, all_870_8) =
% 220.34/30.76 | | all_870_7
% 220.34/30.76 | | (355) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.76 | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v_y) = all_870_5
% 220.34/30.76 | | (356) (all_870_0 = 0 & all_870_9 = v_x & ~ (all_870_8 = v_x) & ? [v0:
% 220.34/30.76 | | $i] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ? [v4: any] :
% 220.34/30.76 | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.76 | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v0) = v1 &
% 220.34/30.76 | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.76 | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = v3 &
% 220.34/30.76 | | c_member(all_683_0, v3, v_L) = v4 & c_member(all_683_0, v1,
% 220.34/30.76 | | v_L) = v2 & $i(v3) & $i(v1) & $i(v0) & ((v2 = 0 & ~ (v4 = 0)
% 220.34/30.76 | | & ~ (v0 = v_x) & ~ (v0 = v_y)) | (v0 = v_x & all_870_4 =
% 220.34/30.76 | | 0)))) | ( ~ (all_870_9 = v_x) & ((all_870_2 = 0 & all_870_8
% 220.34/30.76 | | = v_x & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3:
% 220.34/30.76 | | int] : ( ~ (v3 = 0) & ~ (v0 = v_x) &
% 220.34/30.76 | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.76 | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v0) = v2 &
% 220.34/30.76 | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.76 | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = v1 &
% 220.34/30.76 | | c_member(all_683_0, v2, v_L) = v3 & c_member(all_683_0, v1,
% 220.34/30.76 | | v_L) = 0 & $i(v2) & $i(v1) & $i(v0))) | (all_870_6 = 0 &
% 220.34/30.76 | | ~ (all_870_8 = v_x) & ? [v0: $i] : ? [v1: $i] : ? [v2:
% 220.34/30.76 | | any] : ? [v3: $i] : ? [v4: any] :
% 220.34/30.76 | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.76 | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v0) = v1 &
% 220.34/30.76 | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.34/30.76 | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v0) = v3 &
% 220.34/30.76 | | c_member(all_683_0, v3, v_L) = v4 & c_member(all_683_0, v1,
% 220.34/30.76 | | v_L) = v2 & $i(v3) & $i(v1) & $i(v0) & ((v2 = 0 & ~ (v4
% 220.34/30.76 | | = 0) & ~ (v0 = v_x)) | (v0 = v_x & all_870_4 = 0 &
% 220.34/30.76 | | ~ (all_870_2 = 0)))))))
% 220.34/30.76 | |
% 220.34/30.76 | | REDUCE: (86), (351) imply:
% 220.34/30.76 | | (357) c_member(all_625_1, all_870_1, v_L) = all_870_0
% 220.34/30.76 | |
% 220.34/30.76 | | REDUCE: (86), (350) imply:
% 220.34/30.76 | | (358) c_member(all_625_1, all_870_3, v_L) = all_870_2
% 220.34/30.76 | |
% 220.34/30.76 | | REDUCE: (86), (349) imply:
% 220.34/30.76 | | (359) c_member(all_625_1, all_870_5, v_L) = all_870_4
% 220.34/30.76 | |
% 220.34/30.76 | | REDUCE: (86), (348) imply:
% 220.34/30.76 | | (360) c_member(all_625_1, all_870_7, v_L) = all_870_6
% 220.34/30.76 | |
% 220.34/30.76 | | GROUND_INST: instantiating (3) with v_L, all_870_7, all_625_1, all_870_6,
% 220.34/30.76 | | simplifying with (16), (87), (344), (360) gives:
% 220.85/30.76 | | (361) all_870_6 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 220.85/30.76 | | hBOOL(v0) = v1 & hAPP(v_L, all_870_7) = v0 & $i(v0))
% 220.85/30.76 | |
% 220.85/30.76 | | GROUND_INST: instantiating (3) with v_L, all_870_5, all_625_1, all_870_4,
% 220.85/30.76 | | simplifying with (16), (87), (345), (359) gives:
% 220.85/30.76 | | (362) all_870_4 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 220.85/30.76 | | hBOOL(v0) = v1 & hAPP(v_L, all_870_5) = v0 & $i(v0))
% 220.85/30.76 | |
% 220.85/30.76 | | GROUND_INST: instantiating (3) with v_L, all_870_3, all_625_1, all_870_2,
% 220.85/30.76 | | simplifying with (16), (87), (346), (358) gives:
% 220.85/30.76 | | (363) all_870_2 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 220.85/30.76 | | hBOOL(v0) = v1 & hAPP(v_L, all_870_3) = v0 & $i(v0))
% 220.85/30.76 | |
% 220.85/30.76 | | GROUND_INST: instantiating (3) with v_L, all_870_1, all_625_1, all_870_0,
% 220.85/30.76 | | simplifying with (16), (87), (347), (357) gives:
% 220.85/30.76 | | (364) all_870_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 220.85/30.76 | | hBOOL(v0) = v1 & hAPP(v_L, all_870_1) = v0 & $i(v0))
% 220.85/30.76 | |
% 220.85/30.76 | | GROUND_INST: instantiating (42) with v_y, all_870_8, all_870_1, simplifying
% 220.85/30.76 | | with (15), (343), (352) gives:
% 220.85/30.76 | | (365) all_870_8 = v_y | ? [v0: any] : ? [v1: $i] : ? [v2: any] :
% 220.85/30.76 | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.76 | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v_y) = v1 &
% 220.85/30.76 | | c_member(all_674_0, v1, v_L) = v2 & c_member(all_674_0,
% 220.85/30.76 | | all_870_1, v_L) = v0 & $i(v1) & (v2 = 0 | v0 = 0))
% 220.85/30.76 | |
% 220.85/30.76 | | GROUND_INST: instantiating (41) with v_y, all_870_8, all_870_1, simplifying
% 220.85/30.76 | | with (15), (343), (352) gives:
% 220.85/30.76 | | (366) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_674_0, all_870_1, v_L) =
% 220.85/30.76 | | v0) | ! [v0: $i] : ! [v1: $i] : ( ~
% 220.85/30.76 | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.76 | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = v1) | ~ $i(v0) |
% 220.85/30.76 | | ? [v2: $i] : ? [v3: any] : ? [v4: any] :
% 220.85/30.76 | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.76 | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v0) = v2 &
% 220.85/30.76 | | c_member(all_674_0, v2, v_L) = v3 & c_member(all_674_0, v1,
% 220.85/30.76 | | v_L) = v4 & $i(v2) & ( ~ (v3 = 0) | v4 = 0)))
% 220.85/30.76 | |
% 220.85/30.76 | | GROUND_INST: instantiating (42) with all_870_9, v_y, all_870_3, simplifying
% 220.85/30.76 | | with (15), (342), (353) gives:
% 220.85/30.76 | | (367) all_870_9 = v_y | ? [v0: any] : ? [v1: $i] : ? [v2: any] :
% 220.85/30.76 | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.76 | | tc_Arrow__Order__Mirabelle_Oalt, v_y, all_870_9) = v1 &
% 220.85/30.76 | | c_member(all_674_0, v1, v_L) = v2 & c_member(all_674_0,
% 220.85/30.76 | | all_870_3, v_L) = v0 & $i(v1) & (v2 = 0 | v0 = 0))
% 220.85/30.76 | |
% 220.85/30.76 | | GROUND_INST: instantiating (41) with all_870_9, v_y, all_870_3, simplifying
% 220.85/30.76 | | with (15), (342), (353) gives:
% 220.85/30.76 | | (368) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_674_0, all_870_3, v_L) =
% 220.85/30.76 | | v0) | ! [v0: $i] : ! [v1: $i] : ( ~
% 220.85/30.76 | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.76 | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v0) = v1) | ~
% 220.85/30.76 | | $i(v0) | ? [v2: $i] : ? [v3: any] : ? [v4: any] :
% 220.85/30.76 | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.76 | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = v2 &
% 220.85/30.76 | | c_member(all_674_0, v2, v_L) = v3 & c_member(all_674_0, v1,
% 220.85/30.76 | | v_L) = v4 & $i(v2) & ( ~ (v3 = 0) | v4 = 0)))
% 220.85/30.76 | |
% 220.85/30.76 | | GROUND_INST: instantiating (42) with all_870_9, all_870_8, all_870_7,
% 220.85/30.76 | | simplifying with (342), (343), (354) gives:
% 220.85/30.76 | | (369) all_870_8 = all_870_9 | ? [v0: any] : ? [v1: $i] : ? [v2: any] :
% 220.85/30.76 | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.76 | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, all_870_9) = v1 &
% 220.85/30.76 | | c_member(all_674_0, v1, v_L) = v2 & c_member(all_674_0,
% 220.85/30.76 | | all_870_7, v_L) = v0 & $i(v1) & (v2 = 0 | v0 = 0))
% 220.85/30.76 | |
% 220.85/30.76 | | GROUND_INST: instantiating (41) with all_870_9, all_870_8, all_870_7,
% 220.85/30.76 | | simplifying with (342), (343), (354) gives:
% 220.85/30.76 | | (370) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_674_0, all_870_7, v_L) =
% 220.85/30.76 | | v0) | ! [v0: $i] : ! [v1: $i] : ( ~
% 220.85/30.76 | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.76 | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v0) = v1) | ~
% 220.85/30.76 | | $i(v0) | ? [v2: $i] : ? [v3: any] : ? [v4: any] :
% 220.85/30.76 | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.76 | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v0) = v2 &
% 220.85/30.76 | | c_member(all_674_0, v2, v_L) = v3 & c_member(all_674_0, v1,
% 220.85/30.76 | | v_L) = v4 & $i(v2) & ( ~ (v3 = 0) | v4 = 0)))
% 220.85/30.76 | |
% 220.85/30.76 | | GROUND_INST: instantiating (42) with all_870_8, v_y, all_870_5, simplifying
% 220.85/30.76 | | with (15), (343), (355) gives:
% 220.85/30.76 | | (371) all_870_8 = v_y | ? [v0: any] : ? [v1: $i] : ? [v2: any] :
% 220.85/30.76 | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.76 | | tc_Arrow__Order__Mirabelle_Oalt, v_y, all_870_8) = v1 &
% 220.85/30.76 | | c_member(all_674_0, v1, v_L) = v2 & c_member(all_674_0,
% 220.85/30.76 | | all_870_5, v_L) = v0 & $i(v1) & (v2 = 0 | v0 = 0))
% 220.85/30.76 | |
% 220.85/30.77 | | GROUND_INST: instantiating (41) with all_870_8, v_y, all_870_5, simplifying
% 220.85/30.77 | | with (15), (343), (355) gives:
% 220.85/30.77 | | (372) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_674_0, all_870_5, v_L) =
% 220.85/30.77 | | v0) | ! [v0: $i] : ! [v1: $i] : ( ~
% 220.85/30.77 | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.77 | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v0) = v1) | ~
% 220.85/30.77 | | $i(v0) | ? [v2: $i] : ? [v3: any] : ? [v4: any] :
% 220.85/30.77 | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.77 | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = v2 &
% 220.85/30.77 | | c_member(all_674_0, v2, v_L) = v3 & c_member(all_674_0, v1,
% 220.85/30.77 | | v_L) = v4 & $i(v2) & ( ~ (v3 = 0) | v4 = 0)))
% 220.85/30.77 | |
% 220.85/30.77 | | BETA: splitting (356) gives:
% 220.85/30.77 | |
% 220.85/30.77 | | Case 1:
% 220.85/30.77 | | |
% 220.85/30.77 | | | (373) all_870_0 = 0 & all_870_9 = v_x & ~ (all_870_8 = v_x) & ? [v0:
% 220.85/30.77 | | | $i] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ? [v4: any] :
% 220.85/30.77 | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.77 | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v0) = v1 &
% 220.85/30.77 | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.77 | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = v3 &
% 220.85/30.77 | | | c_member(all_683_0, v3, v_L) = v4 & c_member(all_683_0, v1,
% 220.85/30.77 | | | v_L) = v2 & $i(v3) & $i(v1) & $i(v0) & ((v2 = 0 & ~ (v4 = 0)
% 220.85/30.77 | | | & ~ (v0 = v_x) & ~ (v0 = v_y)) | (v0 = v_x & all_870_4 =
% 220.85/30.77 | | | 0)))
% 220.85/30.77 | | |
% 220.85/30.77 | | | ALPHA: (373) implies:
% 220.85/30.77 | | | (374) all_870_9 = v_x
% 220.85/30.77 | | | (375) all_870_0 = 0
% 220.85/30.77 | | | (376) ~ (all_870_8 = v_x)
% 220.85/30.77 | | | (377) ? [v0: $i] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ? [v4:
% 220.85/30.77 | | | any] : (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.77 | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v0) = v1 &
% 220.85/30.77 | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.77 | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = v3 &
% 220.85/30.77 | | | c_member(all_683_0, v3, v_L) = v4 & c_member(all_683_0, v1,
% 220.85/30.77 | | | v_L) = v2 & $i(v3) & $i(v1) & $i(v0) & ((v2 = 0 & ~ (v4 = 0)
% 220.85/30.77 | | | & ~ (v0 = v_x) & ~ (v0 = v_y)) | (v0 = v_x & all_870_4 =
% 220.85/30.77 | | | 0)))
% 220.85/30.77 | | |
% 220.85/30.77 | | | DELTA: instantiating (377) with fresh symbols all_1072_0, all_1072_1,
% 220.85/30.77 | | | all_1072_2, all_1072_3, all_1072_4 gives:
% 220.85/30.77 | | | (378) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.77 | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, all_1072_4) =
% 220.85/30.77 | | | all_1072_3 &
% 220.85/30.77 | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.77 | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, all_1072_4) = all_1072_1
% 220.85/30.77 | | | & c_member(all_683_0, all_1072_1, v_L) = all_1072_0 &
% 220.85/30.77 | | | c_member(all_683_0, all_1072_3, v_L) = all_1072_2 &
% 220.85/30.77 | | | $i(all_1072_1) & $i(all_1072_3) & $i(all_1072_4) & ((all_1072_2 =
% 220.85/30.77 | | | 0 & ~ (all_1072_0 = 0) & ~ (all_1072_4 = v_x) & ~
% 220.85/30.77 | | | (all_1072_4 = v_y)) | (all_1072_4 = v_x & all_870_4 = 0))
% 220.85/30.77 | | |
% 220.85/30.77 | | | ALPHA: (378) implies:
% 220.85/30.77 | | | (379) $i(all_1072_4)
% 220.85/30.77 | | | (380) c_member(all_683_0, all_1072_3, v_L) = all_1072_2
% 220.85/30.77 | | | (381) c_member(all_683_0, all_1072_1, v_L) = all_1072_0
% 220.85/30.77 | | | (382) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.77 | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, all_1072_4) = all_1072_1
% 220.85/30.77 | | | (383) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.77 | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, all_1072_4) =
% 220.85/30.77 | | | all_1072_3
% 220.85/30.77 | | | (384) (all_1072_2 = 0 & ~ (all_1072_0 = 0) & ~ (all_1072_4 = v_x) &
% 220.85/30.77 | | | ~ (all_1072_4 = v_y)) | (all_1072_4 = v_x & all_870_4 = 0)
% 220.85/30.77 | | |
% 220.85/30.77 | | | REDUCE: (353), (374) imply:
% 220.85/30.77 | | | (385) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.77 | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v_y) = all_870_3
% 220.85/30.77 | | |
% 220.85/30.77 | | | REDUCE: (86), (381) imply:
% 220.85/30.77 | | | (386) c_member(all_625_1, all_1072_1, v_L) = all_1072_0
% 220.85/30.77 | | |
% 220.85/30.77 | | | REDUCE: (86), (380) imply:
% 220.85/30.77 | | | (387) c_member(all_625_1, all_1072_3, v_L) = all_1072_2
% 220.85/30.77 | | |
% 220.85/30.77 | | | REDUCE: (357), (375) imply:
% 220.85/30.77 | | | (388) c_member(all_625_1, all_870_1, v_L) = 0
% 220.85/30.77 | | |
% 220.85/30.77 | | | REDUCE: (342), (374) imply:
% 220.85/30.77 | | | (389) $i(v_x)
% 220.85/30.77 | | |
% 220.85/30.77 | | | BETA: splitting (366) gives:
% 220.85/30.77 | | |
% 220.85/30.77 | | | Case 1:
% 220.85/30.77 | | | |
% 220.85/30.77 | | | | (390) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_674_0, all_870_1,
% 220.85/30.77 | | | | v_L) = v0)
% 220.85/30.77 | | | |
% 220.85/30.77 | | | | REF_CLOSE: (19), (84), (388), (390) are inconsistent by sub-proof #12.
% 220.85/30.77 | | | |
% 220.85/30.77 | | | Case 2:
% 220.85/30.77 | | | |
% 220.85/30.77 | | | | (391) ! [v0: $i] : ! [v1: $i] : ( ~
% 220.85/30.77 | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.77 | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = v1) | ~
% 220.85/30.77 | | | | $i(v0) | ? [v2: $i] : ? [v3: any] : ? [v4: any] :
% 220.85/30.77 | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.77 | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v0) = v2 &
% 220.85/30.77 | | | | c_member(all_674_0, v2, v_L) = v3 & c_member(all_674_0, v1,
% 220.85/30.77 | | | | v_L) = v4 & $i(v2) & ( ~ (v3 = 0) | v4 = 0)))
% 220.85/30.77 | | | |
% 220.85/30.77 | | | | GROUND_INST: instantiating (391) with all_870_8, all_870_1, simplifying
% 220.85/30.77 | | | | with (343), (352) gives:
% 220.85/30.77 | | | | (392) ? [v0: $i] : ? [v1: any] : ? [v2: any] :
% 220.85/30.77 | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.77 | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, all_870_8) = v0
% 220.85/30.77 | | | | & c_member(all_674_0, v0, v_L) = v1 & c_member(all_674_0,
% 220.85/30.77 | | | | all_870_1, v_L) = v2 & $i(v0) & ( ~ (v1 = 0) | v2 = 0))
% 220.85/30.77 | | | |
% 220.85/30.77 | | | | DELTA: instantiating (392) with fresh symbols all_1078_0, all_1078_1,
% 220.85/30.77 | | | | all_1078_2 gives:
% 220.85/30.77 | | | | (393) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.77 | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, all_870_8) =
% 220.85/30.77 | | | | all_1078_2 & c_member(all_674_0, all_1078_2, v_L) = all_1078_1
% 220.85/30.77 | | | | & c_member(all_674_0, all_870_1, v_L) = all_1078_0 &
% 220.85/30.77 | | | | $i(all_1078_2) & ( ~ (all_1078_1 = 0) | all_1078_0 = 0)
% 220.85/30.77 | | | |
% 220.85/30.77 | | | | ALPHA: (393) implies:
% 220.85/30.77 | | | | (394) c_member(all_674_0, all_870_1, v_L) = all_1078_0
% 220.85/30.77 | | | |
% 220.85/30.77 | | | | REDUCE: (84), (394) imply:
% 220.85/30.77 | | | | (395) c_member(all_625_1, all_870_1, v_L) = all_1078_0
% 220.85/30.77 | | | |
% 220.85/30.77 | | | | BETA: splitting (369) gives:
% 220.85/30.77 | | | |
% 220.85/30.77 | | | | Case 1:
% 220.85/30.77 | | | | |
% 220.85/30.77 | | | | | (396) all_870_8 = all_870_9
% 220.85/30.77 | | | | |
% 220.85/30.77 | | | | | COMBINE_EQS: (374), (396) imply:
% 220.85/30.77 | | | | | (397) all_870_8 = v_x
% 220.85/30.77 | | | | |
% 220.85/30.77 | | | | | REDUCE: (376), (397) imply:
% 220.85/30.77 | | | | | (398) $false
% 220.85/30.77 | | | | |
% 220.85/30.77 | | | | | CLOSE: (398) is inconsistent.
% 220.85/30.77 | | | | |
% 220.85/30.77 | | | | Case 2:
% 220.85/30.77 | | | | |
% 220.85/30.77 | | | | | (399) ? [v0: any] : ? [v1: $i] : ? [v2: any] :
% 220.85/30.77 | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.77 | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, all_870_9) =
% 220.85/30.77 | | | | | v1 & c_member(all_674_0, v1, v_L) = v2 &
% 220.85/30.77 | | | | | c_member(all_674_0, all_870_7, v_L) = v0 & $i(v1) & (v2 = 0
% 220.85/30.77 | | | | | | v0 = 0))
% 220.85/30.77 | | | | |
% 220.85/30.77 | | | | | DELTA: instantiating (399) with fresh symbols all_1083_0, all_1083_1,
% 220.85/30.77 | | | | | all_1083_2 gives:
% 220.85/30.77 | | | | | (400) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.77 | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, all_870_9) =
% 220.85/30.77 | | | | | all_1083_1 & c_member(all_674_0, all_1083_1, v_L) =
% 220.85/30.77 | | | | | all_1083_0 & c_member(all_674_0, all_870_7, v_L) = all_1083_2
% 220.85/30.77 | | | | | & $i(all_1083_1) & (all_1083_0 = 0 | all_1083_2 = 0)
% 220.85/30.77 | | | | |
% 220.85/30.77 | | | | | ALPHA: (400) implies:
% 220.85/30.77 | | | | | (401) c_member(all_674_0, all_870_7, v_L) = all_1083_2
% 220.85/30.77 | | | | | (402) c_member(all_674_0, all_1083_1, v_L) = all_1083_0
% 220.85/30.77 | | | | | (403) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.77 | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, all_870_9) =
% 220.85/30.77 | | | | | all_1083_1
% 220.85/30.77 | | | | | (404) all_1083_0 = 0 | all_1083_2 = 0
% 220.85/30.77 | | | | |
% 220.85/30.77 | | | | | REDUCE: (374), (403) imply:
% 220.85/30.77 | | | | | (405) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.77 | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v_x) =
% 220.85/30.77 | | | | | all_1083_1
% 220.85/30.77 | | | | |
% 220.85/30.77 | | | | | REDUCE: (84), (402) imply:
% 220.85/30.77 | | | | | (406) c_member(all_625_1, all_1083_1, v_L) = all_1083_0
% 220.85/30.77 | | | | |
% 220.85/30.77 | | | | | REDUCE: (84), (401) imply:
% 220.85/30.77 | | | | | (407) c_member(all_625_1, all_870_7, v_L) = all_1083_2
% 220.85/30.77 | | | | |
% 220.85/30.77 | | | | | BETA: splitting (367) gives:
% 220.85/30.77 | | | | |
% 220.85/30.77 | | | | | Case 1:
% 220.85/30.77 | | | | | |
% 220.85/30.77 | | | | | | (408) all_870_9 = v_y
% 220.85/30.77 | | | | | |
% 220.85/30.77 | | | | | | COMBINE_EQS: (374), (408) imply:
% 220.85/30.77 | | | | | | (409) v_x = v_y
% 220.85/30.77 | | | | | |
% 220.85/30.77 | | | | | | REDUCE: (12), (409) imply:
% 220.85/30.77 | | | | | | (410) $false
% 220.85/30.77 | | | | | |
% 220.85/30.77 | | | | | | CLOSE: (410) is inconsistent.
% 220.85/30.77 | | | | | |
% 220.85/30.77 | | | | | Case 2:
% 220.85/30.77 | | | | | |
% 220.85/30.77 | | | | | | (411) ~ (all_870_9 = v_y)
% 220.85/30.77 | | | | | | (412) ? [v0: any] : ? [v1: $i] : ? [v2: any] :
% 220.85/30.77 | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.77 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, all_870_9) = v1 &
% 220.85/30.77 | | | | | | c_member(all_674_0, v1, v_L) = v2 & c_member(all_674_0,
% 220.85/30.77 | | | | | | all_870_3, v_L) = v0 & $i(v1) & (v2 = 0 | v0 = 0))
% 220.85/30.77 | | | | | |
% 220.85/30.77 | | | | | | DELTA: instantiating (412) with fresh symbols all_1088_0,
% 220.85/30.77 | | | | | | all_1088_1, all_1088_2 gives:
% 220.85/30.77 | | | | | | (413) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.77 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, all_870_9) =
% 220.85/30.77 | | | | | | all_1088_1 & c_member(all_674_0, all_1088_1, v_L) =
% 220.85/30.77 | | | | | | all_1088_0 & c_member(all_674_0, all_870_3, v_L) =
% 220.85/30.77 | | | | | | all_1088_2 & $i(all_1088_1) & (all_1088_0 = 0 | all_1088_2
% 220.85/30.77 | | | | | | = 0)
% 220.85/30.77 | | | | | |
% 220.85/30.77 | | | | | | ALPHA: (413) implies:
% 220.85/30.78 | | | | | | (414) c_member(all_674_0, all_870_3, v_L) = all_1088_2
% 220.85/30.78 | | | | | |
% 220.85/30.78 | | | | | | REDUCE: (84), (414) imply:
% 220.85/30.78 | | | | | | (415) c_member(all_625_1, all_870_3, v_L) = all_1088_2
% 220.85/30.78 | | | | | |
% 220.85/30.78 | | | | | | GROUND_INST: instantiating (19) with all_870_6, all_1083_2, v_L,
% 220.85/30.78 | | | | | | all_870_7, all_625_1, simplifying with (360), (407)
% 220.85/30.78 | | | | | | gives:
% 220.85/30.78 | | | | | | (416) all_1083_2 = all_870_6
% 220.85/30.78 | | | | | |
% 220.85/30.78 | | | | | | GROUND_INST: instantiating (19) with all_870_2, all_1088_2, v_L,
% 220.85/30.78 | | | | | | all_870_3, all_625_1, simplifying with (358), (415)
% 220.85/30.78 | | | | | | gives:
% 220.85/30.78 | | | | | | (417) all_1088_2 = all_870_2
% 220.85/30.78 | | | | | |
% 220.85/30.78 | | | | | | GROUND_INST: instantiating (19) with 0, all_1078_0, v_L, all_870_1,
% 220.85/30.78 | | | | | | all_625_1, simplifying with (388), (395) gives:
% 220.85/30.78 | | | | | | (418) all_1078_0 = 0
% 220.85/30.78 | | | | | |
% 220.85/30.78 | | | | | | BETA: splitting (362) gives:
% 220.85/30.78 | | | | | |
% 220.85/30.78 | | | | | | Case 1:
% 220.85/30.78 | | | | | | |
% 220.85/30.78 | | | | | | | (419) all_870_4 = 0
% 220.85/30.78 | | | | | | |
% 220.85/30.78 | | | | | | | REDUCE: (359), (419) imply:
% 220.85/30.78 | | | | | | | (420) c_member(all_625_1, all_870_5, v_L) = 0
% 220.85/30.78 | | | | | | |
% 220.85/30.78 | | | | | | | BETA: splitting (372) gives:
% 220.85/30.78 | | | | | | |
% 220.85/30.78 | | | | | | | Case 1:
% 220.85/30.78 | | | | | | | |
% 220.85/30.78 | | | | | | | | (421) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_674_0,
% 220.85/30.78 | | | | | | | | all_870_5, v_L) = v0)
% 220.85/30.78 | | | | | | | |
% 220.85/30.78 | | | | | | | | REF_CLOSE: (19), (84), (420), (421) are inconsistent by
% 220.85/30.78 | | | | | | | | sub-proof #11.
% 220.85/30.78 | | | | | | | |
% 220.85/30.78 | | | | | | | Case 2:
% 220.85/30.78 | | | | | | | |
% 220.85/30.78 | | | | | | | | (422) ! [v0: $i] : ! [v1: $i] : ( ~
% 220.85/30.78 | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.78 | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v0) =
% 220.85/30.78 | | | | | | | | v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: any] : ?
% 220.85/30.78 | | | | | | | | [v4: any] :
% 220.85/30.78 | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.78 | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = v2 &
% 220.85/30.78 | | | | | | | | c_member(all_674_0, v2, v_L) = v3 &
% 220.85/30.78 | | | | | | | | c_member(all_674_0, v1, v_L) = v4 & $i(v2) & ( ~
% 220.85/30.78 | | | | | | | | (v3 = 0) | v4 = 0)))
% 220.85/30.78 | | | | | | | |
% 220.85/30.78 | | | | | | | | GROUND_INST: instantiating (422) with v_y, all_870_5,
% 220.85/30.78 | | | | | | | | simplifying with (15), (355) gives:
% 220.85/30.78 | | | | | | | | (423) ? [v0: $i] : ? [v1: any] : ? [v2: any] :
% 220.85/30.78 | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.78 | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v_y) = v0 &
% 220.85/30.78 | | | | | | | | c_member(all_674_0, v0, v_L) = v1 &
% 220.85/30.78 | | | | | | | | c_member(all_674_0, all_870_5, v_L) = v2 & $i(v0) & (
% 220.85/30.78 | | | | | | | | ~ (v1 = 0) | v2 = 0))
% 220.85/30.78 | | | | | | | |
% 220.85/30.78 | | | | | | | | DELTA: instantiating (423) with fresh symbols all_1114_0,
% 220.85/30.78 | | | | | | | | all_1114_1, all_1114_2 gives:
% 220.85/30.78 | | | | | | | | (424) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.78 | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v_y) =
% 220.85/30.78 | | | | | | | | all_1114_2 & c_member(all_674_0, all_1114_2, v_L) =
% 220.85/30.78 | | | | | | | | all_1114_1 & c_member(all_674_0, all_870_5, v_L) =
% 220.85/30.78 | | | | | | | | all_1114_0 & $i(all_1114_2) & ( ~ (all_1114_1 = 0) |
% 220.85/30.78 | | | | | | | | all_1114_0 = 0)
% 220.85/30.78 | | | | | | | |
% 220.85/30.78 | | | | | | | | ALPHA: (424) implies:
% 220.85/30.78 | | | | | | | | (425) c_member(all_674_0, all_870_5, v_L) = all_1114_0
% 220.85/30.78 | | | | | | | | (426) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.78 | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v_y) =
% 220.85/30.78 | | | | | | | | all_1114_2
% 220.85/30.78 | | | | | | | |
% 220.85/30.78 | | | | | | | | REDUCE: (84), (425) imply:
% 220.85/30.78 | | | | | | | | (427) c_member(all_625_1, all_870_5, v_L) = all_1114_0
% 220.85/30.78 | | | | | | | |
% 220.85/30.78 | | | | | | | | GROUND_INST: instantiating (19) with 0, all_1114_0, v_L,
% 220.85/30.78 | | | | | | | | all_870_5, all_625_1, simplifying with (420), (427)
% 220.85/30.78 | | | | | | | | gives:
% 220.85/30.78 | | | | | | | | (428) all_1114_0 = 0
% 220.85/30.78 | | | | | | | |
% 220.85/30.78 | | | | | | | | BETA: splitting (370) gives:
% 220.85/30.78 | | | | | | | |
% 220.85/30.78 | | | | | | | | Case 1:
% 220.85/30.78 | | | | | | | | |
% 220.85/30.78 | | | | | | | | | (429) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_674_0,
% 220.85/30.78 | | | | | | | | | all_870_7, v_L) = v0)
% 220.85/30.78 | | | | | | | | |
% 220.85/30.78 | | | | | | | | | DELTA: instantiating (429) with fresh symbol all_1125_0 gives:
% 220.85/30.78 | | | | | | | | | (430) ~ (all_1125_0 = 0) & c_member(all_674_0, all_870_7,
% 220.85/30.78 | | | | | | | | | v_L) = all_1125_0
% 220.85/30.78 | | | | | | | | |
% 220.85/30.78 | | | | | | | | | ALPHA: (430) implies:
% 220.85/30.78 | | | | | | | | | (431) ~ (all_1125_0 = 0)
% 220.85/30.78 | | | | | | | | | (432) c_member(all_674_0, all_870_7, v_L) = all_1125_0
% 220.85/30.78 | | | | | | | | |
% 220.85/30.78 | | | | | | | | | REDUCE: (84), (432) imply:
% 220.85/30.78 | | | | | | | | | (433) c_member(all_625_1, all_870_7, v_L) = all_1125_0
% 220.85/30.78 | | | | | | | | |
% 220.85/30.78 | | | | | | | | | GROUND_INST: instantiating (19) with all_870_6, all_1125_0,
% 220.85/30.78 | | | | | | | | | v_L, all_870_7, all_625_1, simplifying with (360),
% 220.85/30.78 | | | | | | | | | (433) gives:
% 220.85/30.78 | | | | | | | | | (434) all_1125_0 = all_870_6
% 220.85/30.78 | | | | | | | | |
% 220.85/30.78 | | | | | | | | | REDUCE: (431), (434) imply:
% 220.85/30.78 | | | | | | | | | (435) ~ (all_870_6 = 0)
% 220.85/30.78 | | | | | | | | |
% 220.85/30.78 | | | | | | | | | BETA: splitting (404) gives:
% 220.85/30.78 | | | | | | | | |
% 220.85/30.78 | | | | | | | | | Case 1:
% 220.85/30.78 | | | | | | | | | |
% 220.85/30.78 | | | | | | | | | | (436) all_1083_0 = 0
% 220.85/30.78 | | | | | | | | | |
% 220.85/30.78 | | | | | | | | | | REDUCE: (406), (436) imply:
% 220.85/30.78 | | | | | | | | | | (437) c_member(all_625_1, all_1083_1, v_L) = 0
% 220.85/30.78 | | | | | | | | | |
% 220.85/30.78 | | | | | | | | | | GROUND_INST: instantiating (fact_wf__not__sym) with v_y,
% 220.85/30.78 | | | | | | | | | | all_870_8, v_L, tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.78 | | | | | | | | | | all_625_1, all_870_1, simplifying with (14), (15),
% 220.85/30.78 | | | | | | | | | | (16), (22), (343), (352), (388) gives:
% 220.85/30.78 | | | | | | | | | | (438) ? [v0: any] : ? [v1: $i] : ? [v2: any] :
% 220.85/30.78 | | | | | | | | | | (c_Wellfounded_Owf(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.78 | | | | | | | | | | v_L) = v0 &
% 220.85/30.78 | | | | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.78 | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8,
% 220.85/30.78 | | | | | | | | | | v_y) = v1 & c_member(all_625_1, v1, v_L) = v2 &
% 220.85/30.78 | | | | | | | | | | $i(v1) & ( ~ (v2 = 0) | ~ (v0 = 0)))
% 220.85/30.78 | | | | | | | | | |
% 220.85/30.78 | | | | | | | | | | GROUND_INST: instantiating (40) with v_y, all_1114_2,
% 220.85/30.78 | | | | | | | | | | simplifying with (15), (426) gives:
% 220.85/30.78 | | | | | | | | | | (439) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_674_0,
% 220.85/30.78 | | | | | | | | | | all_1114_2, v_L) = v0)
% 220.85/30.78 | | | | | | | | | |
% 220.85/30.78 | | | | | | | | | | GROUND_INST: instantiating (391) with v_y, all_1114_2,
% 220.85/30.78 | | | | | | | | | | simplifying with (15), (426) gives:
% 220.85/30.78 | | | | | | | | | | (440) ? [v0: $i] : ? [v1: any] : ? [v2: any] :
% 220.85/30.78 | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.78 | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8,
% 220.85/30.78 | | | | | | | | | | v_y) = v0 & c_member(all_674_0, v0, v_L) = v1 &
% 220.85/30.78 | | | | | | | | | | c_member(all_674_0, all_1114_2, v_L) = v2 &
% 220.85/30.78 | | | | | | | | | | $i(v0) & ( ~ (v1 = 0) | v2 = 0))
% 220.85/30.78 | | | | | | | | | |
% 220.85/30.78 | | | | | | | | | | GROUND_INST: instantiating (fact_single__valuedD) with v_x,
% 220.85/30.78 | | | | | | | | | | v_y, all_870_8, v_L,
% 220.85/30.78 | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.78 | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_625_1,
% 220.85/30.78 | | | | | | | | | | all_870_5, all_1083_1, simplifying with (14),
% 220.85/30.78 | | | | | | | | | | (15), (16), (22), (343), (355), (389), (405),
% 220.85/30.78 | | | | | | | | | | (420), (437) gives:
% 220.85/30.78 | | | | | | | | | | (441) v_x = v_y | ? [v0: int] : ( ~ (v0 = 0) &
% 220.85/30.78 | | | | | | | | | | c_Relation_Osingle__valued(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.78 | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_L) = v0)
% 220.85/30.78 | | | | | | | | | |
% 220.85/30.78 | | | | | | | | | | DELTA: instantiating (439) with fresh symbol all_1161_0
% 220.85/30.78 | | | | | | | | | | gives:
% 220.85/30.78 | | | | | | | | | | (442) ~ (all_1161_0 = 0) & c_member(all_674_0,
% 220.85/30.78 | | | | | | | | | | all_1114_2, v_L) = all_1161_0
% 220.85/30.78 | | | | | | | | | |
% 220.85/30.78 | | | | | | | | | | ALPHA: (442) implies:
% 220.85/30.78 | | | | | | | | | | (443) ~ (all_1161_0 = 0)
% 220.85/30.78 | | | | | | | | | | (444) c_member(all_674_0, all_1114_2, v_L) = all_1161_0
% 220.85/30.78 | | | | | | | | | |
% 220.85/30.78 | | | | | | | | | | DELTA: instantiating (438) with fresh symbols all_1193_0,
% 220.85/30.78 | | | | | | | | | | all_1193_1, all_1193_2 gives:
% 220.85/30.78 | | | | | | | | | | (445) c_Wellfounded_Owf(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.78 | | | | | | | | | | v_L) = all_1193_2 &
% 220.85/30.78 | | | | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.78 | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v_y)
% 220.85/30.78 | | | | | | | | | | = all_1193_1 & c_member(all_625_1, all_1193_1, v_L)
% 220.85/30.78 | | | | | | | | | | = all_1193_0 & $i(all_1193_1) & ( ~ (all_1193_0 =
% 220.85/30.78 | | | | | | | | | | 0) | ~ (all_1193_2 = 0))
% 220.85/30.78 | | | | | | | | | |
% 220.85/30.78 | | | | | | | | | | ALPHA: (445) implies:
% 220.85/30.78 | | | | | | | | | | (446) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.78 | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v_y)
% 220.85/30.78 | | | | | | | | | | = all_1193_1
% 220.85/30.78 | | | | | | | | | |
% 220.85/30.78 | | | | | | | | | | DELTA: instantiating (440) with fresh symbols all_1199_0,
% 220.85/30.78 | | | | | | | | | | all_1199_1, all_1199_2 gives:
% 220.85/30.78 | | | | | | | | | | (447) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.78 | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v_y)
% 220.85/30.78 | | | | | | | | | | = all_1199_2 & c_member(all_674_0, all_1199_2, v_L)
% 220.85/30.78 | | | | | | | | | | = all_1199_1 & c_member(all_674_0, all_1114_2, v_L)
% 220.85/30.78 | | | | | | | | | | = all_1199_0 & $i(all_1199_2) & ( ~ (all_1199_1 =
% 220.85/30.78 | | | | | | | | | | 0) | all_1199_0 = 0)
% 220.85/30.78 | | | | | | | | | |
% 220.85/30.78 | | | | | | | | | | ALPHA: (447) implies:
% 220.85/30.78 | | | | | | | | | | (448) c_member(all_674_0, all_1114_2, v_L) = all_1199_0
% 220.85/30.78 | | | | | | | | | | (449) c_member(all_674_0, all_1199_2, v_L) = all_1199_1
% 220.85/30.78 | | | | | | | | | | (450) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.78 | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v_y)
% 220.85/30.78 | | | | | | | | | | = all_1199_2
% 220.85/30.78 | | | | | | | | | | (451) ~ (all_1199_1 = 0) | all_1199_0 = 0
% 220.85/30.78 | | | | | | | | | |
% 220.85/30.78 | | | | | | | | | | REDUCE: (84), (449) imply:
% 220.85/30.78 | | | | | | | | | | (452) c_member(all_625_1, all_1199_2, v_L) = all_1199_1
% 220.85/30.78 | | | | | | | | | |
% 220.85/30.78 | | | | | | | | | | REDUCE: (84), (448) imply:
% 220.85/30.78 | | | | | | | | | | (453) c_member(all_625_1, all_1114_2, v_L) = all_1199_0
% 220.85/30.78 | | | | | | | | | |
% 220.85/30.78 | | | | | | | | | | REDUCE: (84), (444) imply:
% 220.85/30.78 | | | | | | | | | | (454) c_member(all_625_1, all_1114_2, v_L) = all_1161_0
% 220.85/30.78 | | | | | | | | | |
% 220.85/30.78 | | | | | | | | | | BETA: splitting (441) gives:
% 220.85/30.78 | | | | | | | | | |
% 220.85/30.78 | | | | | | | | | | Case 1:
% 220.85/30.78 | | | | | | | | | | |
% 220.85/30.78 | | | | | | | | | | | (455) v_x = v_y
% 220.85/30.78 | | | | | | | | | | |
% 220.85/30.78 | | | | | | | | | | | REDUCE: (12), (455) imply:
% 220.85/30.78 | | | | | | | | | | | (456) $false
% 220.85/30.78 | | | | | | | | | | |
% 220.85/30.78 | | | | | | | | | | | CLOSE: (456) is inconsistent.
% 220.85/30.78 | | | | | | | | | | |
% 220.85/30.78 | | | | | | | | | | Case 2:
% 220.85/30.78 | | | | | | | | | | |
% 220.85/30.78 | | | | | | | | | | |
% 220.85/30.78 | | | | | | | | | | | GROUND_INST: instantiating (19) with all_1161_0, all_1199_0,
% 220.85/30.78 | | | | | | | | | | | v_L, all_1114_2, all_625_1, simplifying with
% 220.85/30.78 | | | | | | | | | | | (453), (454) gives:
% 220.85/30.78 | | | | | | | | | | | (457) all_1199_0 = all_1161_0
% 220.85/30.78 | | | | | | | | | | |
% 220.85/30.78 | | | | | | | | | | | GROUND_INST: instantiating (20) with all_870_5, all_1199_2,
% 220.85/30.78 | | | | | | | | | | | v_y, all_870_8, tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.78 | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with
% 220.85/30.78 | | | | | | | | | | | (355), (450) gives:
% 220.85/30.78 | | | | | | | | | | | (458) all_1199_2 = all_870_5
% 220.85/30.78 | | | | | | | | | | |
% 220.85/30.78 | | | | | | | | | | | GROUND_INST: instantiating (20) with all_1193_1, all_1199_2,
% 220.85/30.78 | | | | | | | | | | | v_y, all_870_8, tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.78 | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with
% 220.85/30.78 | | | | | | | | | | | (446), (450) gives:
% 220.85/30.78 | | | | | | | | | | | (459) all_1199_2 = all_1193_1
% 220.85/30.78 | | | | | | | | | | |
% 220.85/30.78 | | | | | | | | | | | COMBINE_EQS: (458), (459) imply:
% 220.85/30.78 | | | | | | | | | | | (460) all_1193_1 = all_870_5
% 220.85/30.78 | | | | | | | | | | |
% 220.85/30.78 | | | | | | | | | | | REDUCE: (452), (458) imply:
% 220.85/30.78 | | | | | | | | | | | (461) c_member(all_625_1, all_870_5, v_L) = all_1199_1
% 220.85/30.78 | | | | | | | | | | |
% 220.85/30.78 | | | | | | | | | | | BETA: splitting (451) gives:
% 220.85/30.78 | | | | | | | | | | |
% 220.85/30.78 | | | | | | | | | | | Case 1:
% 220.85/30.78 | | | | | | | | | | | |
% 220.85/30.78 | | | | | | | | | | | | (462) ~ (all_1199_1 = 0)
% 220.85/30.78 | | | | | | | | | | | |
% 220.85/30.78 | | | | | | | | | | | | GROUND_INST: instantiating (19) with 0, all_1199_1, v_L,
% 220.85/30.78 | | | | | | | | | | | | all_870_5, all_625_1, simplifying with (420),
% 220.85/30.78 | | | | | | | | | | | | (461) gives:
% 220.85/30.78 | | | | | | | | | | | | (463) all_1199_1 = 0
% 220.85/30.78 | | | | | | | | | | | |
% 220.85/30.78 | | | | | | | | | | | | REDUCE: (462), (463) imply:
% 220.85/30.78 | | | | | | | | | | | | (464) $false
% 220.85/30.78 | | | | | | | | | | | |
% 220.85/30.78 | | | | | | | | | | | | CLOSE: (464) is inconsistent.
% 220.85/30.78 | | | | | | | | | | | |
% 220.85/30.78 | | | | | | | | | | | Case 2:
% 220.85/30.78 | | | | | | | | | | | |
% 220.85/30.78 | | | | | | | | | | | | (465) all_1199_0 = 0
% 220.85/30.78 | | | | | | | | | | | |
% 220.85/30.78 | | | | | | | | | | | | COMBINE_EQS: (457), (465) imply:
% 220.85/30.78 | | | | | | | | | | | | (466) all_1161_0 = 0
% 220.85/30.78 | | | | | | | | | | | |
% 220.85/30.78 | | | | | | | | | | | | REDUCE: (443), (466) imply:
% 220.85/30.78 | | | | | | | | | | | | (467) $false
% 220.85/30.78 | | | | | | | | | | | |
% 220.85/30.78 | | | | | | | | | | | | CLOSE: (467) is inconsistent.
% 220.85/30.78 | | | | | | | | | | | |
% 220.85/30.78 | | | | | | | | | | | End of split
% 220.85/30.78 | | | | | | | | | | |
% 220.85/30.78 | | | | | | | | | | End of split
% 220.85/30.79 | | | | | | | | | |
% 220.85/30.79 | | | | | | | | | Case 2:
% 220.85/30.79 | | | | | | | | | |
% 220.85/30.79 | | | | | | | | | | (468) all_1083_2 = 0
% 220.85/30.79 | | | | | | | | | |
% 220.85/30.79 | | | | | | | | | | COMBINE_EQS: (416), (468) imply:
% 220.85/30.79 | | | | | | | | | | (469) all_870_6 = 0
% 220.85/30.79 | | | | | | | | | |
% 220.85/30.79 | | | | | | | | | | REDUCE: (435), (469) imply:
% 220.85/30.79 | | | | | | | | | | (470) $false
% 220.85/30.79 | | | | | | | | | |
% 220.85/30.79 | | | | | | | | | | CLOSE: (470) is inconsistent.
% 220.85/30.79 | | | | | | | | | |
% 220.85/30.79 | | | | | | | | | End of split
% 220.85/30.79 | | | | | | | | |
% 220.85/30.79 | | | | | | | | Case 2:
% 220.85/30.79 | | | | | | | | |
% 220.85/30.79 | | | | | | | | | (471) ! [v0: $i] : ! [v1: $i] : ( ~
% 220.85/30.79 | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.79 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v0)
% 220.85/30.79 | | | | | | | | | = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: any] :
% 220.85/30.79 | | | | | | | | | ? [v4: any] :
% 220.85/30.79 | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.79 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v0)
% 220.85/30.79 | | | | | | | | | = v2 & c_member(all_674_0, v2, v_L) = v3 &
% 220.85/30.79 | | | | | | | | | c_member(all_674_0, v1, v_L) = v4 & $i(v2) & ( ~
% 220.85/30.79 | | | | | | | | | (v3 = 0) | v4 = 0)))
% 220.85/30.79 | | | | | | | | |
% 220.85/30.79 | | | | | | | | | BETA: splitting (363) gives:
% 220.85/30.79 | | | | | | | | |
% 220.85/30.79 | | | | | | | | | Case 1:
% 220.85/30.79 | | | | | | | | | |
% 220.85/30.79 | | | | | | | | | | (472) all_870_2 = 0
% 220.85/30.79 | | | | | | | | | |
% 220.85/30.79 | | | | | | | | | | REDUCE: (358), (472) imply:
% 220.85/30.79 | | | | | | | | | | (473) c_member(all_625_1, all_870_3, v_L) = 0
% 220.85/30.79 | | | | | | | | | |
% 220.85/30.79 | | | | | | | | | | GROUND_INST: instantiating (fact_wf__not__sym) with v_y,
% 220.85/30.79 | | | | | | | | | | all_870_8, v_L, tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.79 | | | | | | | | | | all_625_1, all_870_1, simplifying with (14), (15),
% 220.85/30.79 | | | | | | | | | | (16), (22), (343), (352), (388) gives:
% 220.85/30.79 | | | | | | | | | | (474) ? [v0: any] : ? [v1: $i] : ? [v2: any] :
% 220.85/30.79 | | | | | | | | | | (c_Wellfounded_Owf(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.79 | | | | | | | | | | v_L) = v0 &
% 220.85/30.79 | | | | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.79 | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8,
% 220.85/30.79 | | | | | | | | | | v_y) = v1 & c_member(all_625_1, v1, v_L) = v2 &
% 220.85/30.79 | | | | | | | | | | $i(v1) & ( ~ (v2 = 0) | ~ (v0 = 0)))
% 220.85/30.79 | | | | | | | | | |
% 220.85/30.79 | | | | | | | | | | GROUND_INST: instantiating (40) with v_y, all_1114_2,
% 220.85/30.79 | | | | | | | | | | simplifying with (15), (426) gives:
% 220.85/30.79 | | | | | | | | | | (475) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_674_0,
% 220.85/30.79 | | | | | | | | | | all_1114_2, v_L) = v0)
% 220.85/30.79 | | | | | | | | | |
% 220.85/30.79 | | | | | | | | | | GROUND_INST: instantiating (391) with v_y, all_1114_2,
% 220.85/30.79 | | | | | | | | | | simplifying with (15), (426) gives:
% 220.85/30.79 | | | | | | | | | | (476) ? [v0: $i] : ? [v1: any] : ? [v2: any] :
% 220.85/30.79 | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.79 | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8,
% 220.85/30.79 | | | | | | | | | | v_y) = v0 & c_member(all_674_0, v0, v_L) = v1 &
% 220.85/30.79 | | | | | | | | | | c_member(all_674_0, all_1114_2, v_L) = v2 &
% 220.85/30.79 | | | | | | | | | | $i(v0) & ( ~ (v1 = 0) | v2 = 0))
% 220.85/30.79 | | | | | | | | | |
% 220.85/30.79 | | | | | | | | | | GROUND_INST: instantiating (fact_antisymD) with v_x, v_y, v_L,
% 220.85/30.79 | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_625_1,
% 220.85/30.79 | | | | | | | | | | all_870_3, simplifying with (14), (15), (16),
% 220.85/30.79 | | | | | | | | | | (22), (385), (389), (473) gives:
% 220.85/30.79 | | | | | | | | | | (477) v_x = v_y | ? [v0: any] : ? [v1: $i] : ? [v2:
% 220.85/30.79 | | | | | | | | | | any] :
% 220.85/30.79 | | | | | | | | | | (c_Relation_Oantisym(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.79 | | | | | | | | | | v_L) = v0 &
% 220.85/30.79 | | | | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.79 | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v_x) = v1
% 220.85/30.79 | | | | | | | | | | & c_member(all_625_1, v1, v_L) = v2 & $i(v1) & (
% 220.85/30.79 | | | | | | | | | | ~ (v2 = 0) | ~ (v0 = 0)))
% 220.85/30.79 | | | | | | | | | |
% 220.85/30.79 | | | | | | | | | | DELTA: instantiating (475) with fresh symbol all_1157_0
% 220.85/30.79 | | | | | | | | | | gives:
% 220.85/30.79 | | | | | | | | | | (478) ~ (all_1157_0 = 0) & c_member(all_674_0,
% 220.85/30.79 | | | | | | | | | | all_1114_2, v_L) = all_1157_0
% 220.85/30.79 | | | | | | | | | |
% 220.85/30.79 | | | | | | | | | | ALPHA: (478) implies:
% 220.85/30.79 | | | | | | | | | | (479) ~ (all_1157_0 = 0)
% 220.85/30.79 | | | | | | | | | | (480) c_member(all_674_0, all_1114_2, v_L) = all_1157_0
% 220.85/30.79 | | | | | | | | | |
% 220.85/30.79 | | | | | | | | | | DELTA: instantiating (474) with fresh symbols all_1189_0,
% 220.85/30.79 | | | | | | | | | | all_1189_1, all_1189_2 gives:
% 220.85/30.79 | | | | | | | | | | (481) c_Wellfounded_Owf(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.79 | | | | | | | | | | v_L) = all_1189_2 &
% 220.85/30.79 | | | | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.79 | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v_y)
% 220.85/30.79 | | | | | | | | | | = all_1189_1 & c_member(all_625_1, all_1189_1, v_L)
% 220.85/30.79 | | | | | | | | | | = all_1189_0 & $i(all_1189_1) & ( ~ (all_1189_0 =
% 220.85/30.79 | | | | | | | | | | 0) | ~ (all_1189_2 = 0))
% 220.85/30.79 | | | | | | | | | |
% 220.85/30.79 | | | | | | | | | | ALPHA: (481) implies:
% 220.85/30.79 | | | | | | | | | | (482) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.79 | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v_y)
% 220.85/30.79 | | | | | | | | | | = all_1189_1
% 220.85/30.79 | | | | | | | | | |
% 220.85/30.79 | | | | | | | | | | DELTA: instantiating (476) with fresh symbols all_1195_0,
% 220.85/30.79 | | | | | | | | | | all_1195_1, all_1195_2 gives:
% 220.85/30.79 | | | | | | | | | | (483) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.79 | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v_y)
% 220.85/30.79 | | | | | | | | | | = all_1195_2 & c_member(all_674_0, all_1195_2, v_L)
% 220.85/30.79 | | | | | | | | | | = all_1195_1 & c_member(all_674_0, all_1114_2, v_L)
% 220.85/30.79 | | | | | | | | | | = all_1195_0 & $i(all_1195_2) & ( ~ (all_1195_1 =
% 220.85/30.79 | | | | | | | | | | 0) | all_1195_0 = 0)
% 220.85/30.79 | | | | | | | | | |
% 220.85/30.79 | | | | | | | | | | ALPHA: (483) implies:
% 220.85/30.79 | | | | | | | | | | (484) c_member(all_674_0, all_1114_2, v_L) = all_1195_0
% 220.85/30.79 | | | | | | | | | | (485) c_member(all_674_0, all_1195_2, v_L) = all_1195_1
% 220.85/30.79 | | | | | | | | | | (486) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.79 | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v_y)
% 220.85/30.79 | | | | | | | | | | = all_1195_2
% 220.85/30.79 | | | | | | | | | | (487) ~ (all_1195_1 = 0) | all_1195_0 = 0
% 220.85/30.79 | | | | | | | | | |
% 220.85/30.79 | | | | | | | | | | REDUCE: (84), (485) imply:
% 220.85/30.79 | | | | | | | | | | (488) c_member(all_625_1, all_1195_2, v_L) = all_1195_1
% 220.85/30.79 | | | | | | | | | |
% 220.85/30.79 | | | | | | | | | | REDUCE: (84), (484) imply:
% 220.85/30.79 | | | | | | | | | | (489) c_member(all_625_1, all_1114_2, v_L) = all_1195_0
% 220.85/30.79 | | | | | | | | | |
% 220.85/30.79 | | | | | | | | | | REDUCE: (84), (480) imply:
% 220.85/30.79 | | | | | | | | | | (490) c_member(all_625_1, all_1114_2, v_L) = all_1157_0
% 220.85/30.79 | | | | | | | | | |
% 220.85/30.79 | | | | | | | | | | BETA: splitting (477) gives:
% 220.85/30.79 | | | | | | | | | |
% 220.85/30.79 | | | | | | | | | | Case 1:
% 220.85/30.79 | | | | | | | | | | |
% 220.85/30.79 | | | | | | | | | | | (491) v_x = v_y
% 220.85/30.79 | | | | | | | | | | |
% 220.85/30.79 | | | | | | | | | | | REDUCE: (12), (491) imply:
% 220.85/30.79 | | | | | | | | | | | (492) $false
% 220.85/30.79 | | | | | | | | | | |
% 220.85/30.79 | | | | | | | | | | | CLOSE: (492) is inconsistent.
% 220.85/30.79 | | | | | | | | | | |
% 220.85/30.79 | | | | | | | | | | Case 2:
% 220.85/30.79 | | | | | | | | | | |
% 220.85/30.79 | | | | | | | | | | |
% 220.85/30.79 | | | | | | | | | | | GROUND_INST: instantiating (19) with all_1157_0, all_1195_0,
% 220.85/30.79 | | | | | | | | | | | v_L, all_1114_2, all_625_1, simplifying with
% 220.85/30.79 | | | | | | | | | | | (489), (490) gives:
% 220.85/30.79 | | | | | | | | | | | (493) all_1195_0 = all_1157_0
% 220.85/30.79 | | | | | | | | | | |
% 220.85/30.79 | | | | | | | | | | | GROUND_INST: instantiating (20) with all_870_5, all_1195_2,
% 220.85/30.79 | | | | | | | | | | | v_y, all_870_8, tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.79 | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with
% 220.85/30.79 | | | | | | | | | | | (355), (486) gives:
% 220.85/30.79 | | | | | | | | | | | (494) all_1195_2 = all_870_5
% 220.85/30.79 | | | | | | | | | | |
% 220.85/30.79 | | | | | | | | | | | GROUND_INST: instantiating (20) with all_1189_1, all_1195_2,
% 220.85/30.79 | | | | | | | | | | | v_y, all_870_8, tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.79 | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with
% 220.85/30.79 | | | | | | | | | | | (482), (486) gives:
% 220.85/30.79 | | | | | | | | | | | (495) all_1195_2 = all_1189_1
% 220.85/30.79 | | | | | | | | | | |
% 220.85/30.79 | | | | | | | | | | | COMBINE_EQS: (494), (495) imply:
% 220.85/30.79 | | | | | | | | | | | (496) all_1189_1 = all_870_5
% 220.85/30.79 | | | | | | | | | | |
% 220.85/30.79 | | | | | | | | | | | REDUCE: (488), (494) imply:
% 220.85/30.79 | | | | | | | | | | | (497) c_member(all_625_1, all_870_5, v_L) = all_1195_1
% 220.85/30.79 | | | | | | | | | | |
% 220.85/30.79 | | | | | | | | | | | BETA: splitting (487) gives:
% 220.85/30.79 | | | | | | | | | | |
% 220.85/30.79 | | | | | | | | | | | Case 1:
% 220.85/30.79 | | | | | | | | | | | |
% 220.85/30.79 | | | | | | | | | | | | (498) ~ (all_1195_1 = 0)
% 220.85/30.79 | | | | | | | | | | | |
% 220.85/30.79 | | | | | | | | | | | | GROUND_INST: instantiating (19) with 0, all_1195_1, v_L,
% 220.85/30.79 | | | | | | | | | | | | all_870_5, all_625_1, simplifying with (420),
% 220.85/30.79 | | | | | | | | | | | | (497) gives:
% 220.85/30.79 | | | | | | | | | | | | (499) all_1195_1 = 0
% 220.85/30.79 | | | | | | | | | | | |
% 220.85/30.79 | | | | | | | | | | | | REDUCE: (498), (499) imply:
% 220.85/30.79 | | | | | | | | | | | | (500) $false
% 220.85/30.79 | | | | | | | | | | | |
% 220.85/30.79 | | | | | | | | | | | | CLOSE: (500) is inconsistent.
% 220.85/30.79 | | | | | | | | | | | |
% 220.85/30.79 | | | | | | | | | | | Case 2:
% 220.85/30.79 | | | | | | | | | | | |
% 220.85/30.79 | | | | | | | | | | | | (501) all_1195_0 = 0
% 220.85/30.79 | | | | | | | | | | | |
% 220.85/30.79 | | | | | | | | | | | | COMBINE_EQS: (493), (501) imply:
% 220.85/30.79 | | | | | | | | | | | | (502) all_1157_0 = 0
% 220.85/30.79 | | | | | | | | | | | |
% 220.85/30.79 | | | | | | | | | | | | REDUCE: (479), (502) imply:
% 220.85/30.79 | | | | | | | | | | | | (503) $false
% 220.85/30.79 | | | | | | | | | | | |
% 220.85/30.79 | | | | | | | | | | | | CLOSE: (503) is inconsistent.
% 220.85/30.79 | | | | | | | | | | | |
% 220.85/30.79 | | | | | | | | | | | End of split
% 220.85/30.79 | | | | | | | | | | |
% 220.85/30.79 | | | | | | | | | | End of split
% 220.85/30.79 | | | | | | | | | |
% 220.85/30.79 | | | | | | | | | Case 2:
% 220.85/30.79 | | | | | | | | | |
% 220.85/30.79 | | | | | | | | | | (504) ~ (all_870_2 = 0)
% 220.85/30.79 | | | | | | | | | |
% 220.85/30.79 | | | | | | | | | | GROUND_INST: instantiating (471) with v_y, all_870_3,
% 220.85/30.79 | | | | | | | | | | simplifying with (15), (353) gives:
% 220.85/30.79 | | | | | | | | | | (505) ? [v0: $i] : ? [v1: any] : ? [v2: any] :
% 220.85/30.79 | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.79 | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8,
% 220.85/30.79 | | | | | | | | | | v_y) = v0 & c_member(all_674_0, v0, v_L) = v1 &
% 220.85/30.79 | | | | | | | | | | c_member(all_674_0, all_870_3, v_L) = v2 & $i(v0)
% 220.85/30.79 | | | | | | | | | | & ( ~ (v1 = 0) | v2 = 0))
% 220.85/30.79 | | | | | | | | | |
% 220.85/30.79 | | | | | | | | | | REF_CLOSE: (19), (20), (84), (355), (358), (420), (504),
% 220.85/30.79 | | | | | | | | | | (505) are inconsistent by sub-proof #10.
% 220.85/30.79 | | | | | | | | | |
% 220.85/30.79 | | | | | | | | | End of split
% 220.85/30.79 | | | | | | | | |
% 220.85/30.79 | | | | | | | | End of split
% 220.85/30.79 | | | | | | | |
% 220.85/30.79 | | | | | | | End of split
% 220.85/30.79 | | | | | | |
% 220.85/30.79 | | | | | | Case 2:
% 220.85/30.79 | | | | | | |
% 220.85/30.79 | | | | | | | (506) ~ (all_870_4 = 0)
% 220.85/30.79 | | | | | | |
% 220.85/30.79 | | | | | | | BETA: splitting (384) gives:
% 220.85/30.79 | | | | | | |
% 220.85/30.79 | | | | | | | Case 1:
% 220.85/30.79 | | | | | | | |
% 220.85/30.79 | | | | | | | | (507) all_1072_2 = 0 & ~ (all_1072_0 = 0) & ~ (all_1072_4 =
% 220.85/30.79 | | | | | | | | v_x) & ~ (all_1072_4 = v_y)
% 220.85/30.79 | | | | | | | |
% 220.85/30.79 | | | | | | | | ALPHA: (507) implies:
% 220.85/30.79 | | | | | | | | (508) all_1072_2 = 0
% 220.85/30.79 | | | | | | | | (509) ~ (all_1072_4 = v_y)
% 220.85/30.79 | | | | | | | | (510) ~ (all_1072_0 = 0)
% 220.85/30.79 | | | | | | | |
% 220.85/30.79 | | | | | | | | REDUCE: (387), (508) imply:
% 220.85/30.79 | | | | | | | | (511) c_member(all_625_1, all_1072_3, v_L) = 0
% 220.85/30.79 | | | | | | | |
% 220.85/30.79 | | | | | | | | GROUND_INST: instantiating (391) with all_1072_4, all_1072_1,
% 220.85/30.79 | | | | | | | | simplifying with (379), (382) gives:
% 220.85/30.79 | | | | | | | | (512) ? [v0: $i] : ? [v1: any] : ? [v2: any] :
% 220.85/30.79 | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.79 | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8,
% 220.85/30.79 | | | | | | | | all_1072_4) = v0 & c_member(all_674_0, v0, v_L) =
% 220.85/30.79 | | | | | | | | v1 & c_member(all_674_0, all_1072_1, v_L) = v2 &
% 220.85/30.79 | | | | | | | | $i(v0) & ( ~ (v1 = 0) | v2 = 0))
% 220.85/30.79 | | | | | | | |
% 220.85/30.79 | | | | | | | | GROUND_INST: instantiating (42) with v_y, all_1072_4,
% 220.85/30.79 | | | | | | | | all_1072_1, simplifying with (15), (379), (382)
% 220.85/30.79 | | | | | | | | gives:
% 220.85/30.79 | | | | | | | | (513) all_1072_4 = v_y | ? [v0: any] : ? [v1: $i] : ? [v2:
% 220.85/30.79 | | | | | | | | any] :
% 220.85/30.79 | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.79 | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_1072_4, v_y) =
% 220.85/30.79 | | | | | | | | v1 & c_member(all_674_0, v1, v_L) = v2 &
% 220.85/30.79 | | | | | | | | c_member(all_674_0, all_1072_1, v_L) = v0 & $i(v1) &
% 220.85/30.79 | | | | | | | | (v2 = 0 | v0 = 0))
% 220.85/30.79 | | | | | | | |
% 220.85/30.79 | | | | | | | | GROUND_INST: instantiating (41) with all_870_8, all_1072_4,
% 220.85/30.79 | | | | | | | | all_1072_3, simplifying with (343), (379), (383)
% 220.85/30.79 | | | | | | | | gives:
% 220.85/30.80 | | | | | | | | (514) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_674_0,
% 220.85/30.80 | | | | | | | | all_1072_3, v_L) = v0) | ! [v0: $i] : ! [v1: $i]
% 220.85/30.80 | | | | | | | | : ( ~
% 220.85/30.80 | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.80 | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v0) =
% 220.85/30.80 | | | | | | | | v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: any] : ?
% 220.85/30.80 | | | | | | | | [v4: any] :
% 220.85/30.80 | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.80 | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_1072_4, v0)
% 220.85/30.80 | | | | | | | | = v2 & c_member(all_674_0, v2, v_L) = v3 &
% 220.85/30.80 | | | | | | | | c_member(all_674_0, v1, v_L) = v4 & $i(v2) & ( ~
% 220.85/30.80 | | | | | | | | (v3 = 0) | v4 = 0)))
% 220.85/30.80 | | | | | | | |
% 220.85/30.80 | | | | | | | | DELTA: instantiating (512) with fresh symbols all_1203_0,
% 220.85/30.80 | | | | | | | | all_1203_1, all_1203_2 gives:
% 220.85/30.80 | | | | | | | | (515) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.80 | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8,
% 220.85/30.80 | | | | | | | | all_1072_4) = all_1203_2 & c_member(all_674_0,
% 220.85/30.80 | | | | | | | | all_1203_2, v_L) = all_1203_1 & c_member(all_674_0,
% 220.85/30.80 | | | | | | | | all_1072_1, v_L) = all_1203_0 & $i(all_1203_2) & ( ~
% 220.85/30.80 | | | | | | | | (all_1203_1 = 0) | all_1203_0 = 0)
% 220.85/30.80 | | | | | | | |
% 220.85/30.80 | | | | | | | | ALPHA: (515) implies:
% 220.85/30.80 | | | | | | | | (516) c_member(all_674_0, all_1072_1, v_L) = all_1203_0
% 220.85/30.80 | | | | | | | | (517) c_member(all_674_0, all_1203_2, v_L) = all_1203_1
% 220.85/30.80 | | | | | | | | (518) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.80 | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8,
% 220.85/30.80 | | | | | | | | all_1072_4) = all_1203_2
% 220.85/30.80 | | | | | | | | (519) ~ (all_1203_1 = 0) | all_1203_0 = 0
% 220.85/30.80 | | | | | | | |
% 220.85/30.80 | | | | | | | | REDUCE: (84), (517) imply:
% 220.85/30.80 | | | | | | | | (520) c_member(all_625_1, all_1203_2, v_L) = all_1203_1
% 220.85/30.80 | | | | | | | |
% 220.85/30.80 | | | | | | | | REDUCE: (84), (516) imply:
% 220.85/30.80 | | | | | | | | (521) c_member(all_625_1, all_1072_1, v_L) = all_1203_0
% 220.85/30.80 | | | | | | | |
% 220.85/30.80 | | | | | | | | BETA: splitting (514) gives:
% 220.85/30.80 | | | | | | | |
% 220.85/30.80 | | | | | | | | Case 1:
% 220.85/30.80 | | | | | | | | |
% 220.85/30.80 | | | | | | | | | (522) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_674_0,
% 220.85/30.80 | | | | | | | | | all_1072_3, v_L) = v0)
% 220.85/30.80 | | | | | | | | |
% 220.85/30.80 | | | | | | | | | DELTA: instantiating (522) with fresh symbol all_1228_0 gives:
% 220.85/30.80 | | | | | | | | | (523) ~ (all_1228_0 = 0) & c_member(all_674_0, all_1072_3,
% 220.85/30.80 | | | | | | | | | v_L) = all_1228_0
% 220.85/30.80 | | | | | | | | |
% 220.85/30.80 | | | | | | | | | ALPHA: (523) implies:
% 220.85/30.80 | | | | | | | | | (524) ~ (all_1228_0 = 0)
% 220.85/30.80 | | | | | | | | | (525) c_member(all_674_0, all_1072_3, v_L) = all_1228_0
% 220.85/30.80 | | | | | | | | |
% 220.85/30.80 | | | | | | | | | REDUCE: (84), (525) imply:
% 220.85/30.80 | | | | | | | | | (526) c_member(all_625_1, all_1072_3, v_L) = all_1228_0
% 220.85/30.80 | | | | | | | | |
% 220.85/30.80 | | | | | | | | | GROUND_INST: instantiating (19) with 0, all_1228_0, v_L,
% 220.85/30.80 | | | | | | | | | all_1072_3, all_625_1, simplifying with (511),
% 220.85/30.80 | | | | | | | | | (526) gives:
% 220.85/30.80 | | | | | | | | | (527) all_1228_0 = 0
% 220.85/30.80 | | | | | | | | |
% 220.85/30.80 | | | | | | | | | REDUCE: (524), (527) imply:
% 220.85/30.80 | | | | | | | | | (528) $false
% 220.85/30.80 | | | | | | | | |
% 220.85/30.80 | | | | | | | | | CLOSE: (528) is inconsistent.
% 220.85/30.80 | | | | | | | | |
% 220.85/30.80 | | | | | | | | Case 2:
% 220.85/30.80 | | | | | | | | |
% 220.85/30.80 | | | | | | | | | (529) ! [v0: $i] : ! [v1: $i] : ( ~
% 220.85/30.80 | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.80 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v0)
% 220.85/30.80 | | | | | | | | | = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: any] :
% 220.85/30.80 | | | | | | | | | ? [v4: any] :
% 220.85/30.80 | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.80 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_1072_4,
% 220.85/30.80 | | | | | | | | | v0) = v2 & c_member(all_674_0, v2, v_L) = v3 &
% 220.85/30.80 | | | | | | | | | c_member(all_674_0, v1, v_L) = v4 & $i(v2) & ( ~
% 220.85/30.80 | | | | | | | | | (v3 = 0) | v4 = 0)))
% 220.85/30.80 | | | | | | | | |
% 220.85/30.80 | | | | | | | | | GROUND_INST: instantiating (529) with all_1072_4, all_1072_3,
% 220.85/30.80 | | | | | | | | | simplifying with (379), (383) gives:
% 220.85/30.80 | | | | | | | | | (530) ? [v0: $i] : ? [v1: any] : ? [v2: any] :
% 220.85/30.80 | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.80 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_1072_4,
% 220.85/30.80 | | | | | | | | | all_1072_4) = v0 & c_member(all_674_0, v0, v_L) =
% 220.85/30.80 | | | | | | | | | v1 & c_member(all_674_0, all_1072_3, v_L) = v2 &
% 220.85/30.80 | | | | | | | | | $i(v0) & ( ~ (v1 = 0) | v2 = 0))
% 220.85/30.80 | | | | | | | | |
% 220.85/30.80 | | | | | | | | | DELTA: instantiating (530) with fresh symbols all_1231_0,
% 220.85/30.80 | | | | | | | | | all_1231_1, all_1231_2 gives:
% 220.85/30.80 | | | | | | | | | (531) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.80 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_1072_4,
% 220.85/30.80 | | | | | | | | | all_1072_4) = all_1231_2 & c_member(all_674_0,
% 220.85/30.80 | | | | | | | | | all_1231_2, v_L) = all_1231_1 & c_member(all_674_0,
% 220.85/30.80 | | | | | | | | | all_1072_3, v_L) = all_1231_0 & $i(all_1231_2) & (
% 220.85/30.80 | | | | | | | | | ~ (all_1231_1 = 0) | all_1231_0 = 0)
% 220.85/30.80 | | | | | | | | |
% 220.85/30.80 | | | | | | | | | ALPHA: (531) implies:
% 220.85/30.80 | | | | | | | | | (532) c_member(all_674_0, all_1072_3, v_L) = all_1231_0
% 220.85/30.80 | | | | | | | | |
% 220.85/30.80 | | | | | | | | | REDUCE: (84), (532) imply:
% 220.85/30.80 | | | | | | | | | (533) c_member(all_625_1, all_1072_3, v_L) = all_1231_0
% 220.85/30.80 | | | | | | | | |
% 220.85/30.80 | | | | | | | | | BETA: splitting (513) gives:
% 220.85/30.80 | | | | | | | | |
% 220.85/30.80 | | | | | | | | | Case 1:
% 220.85/30.80 | | | | | | | | | |
% 220.85/30.80 | | | | | | | | | | (534) all_1072_4 = v_y
% 220.85/30.80 | | | | | | | | | |
% 220.85/30.80 | | | | | | | | | | REDUCE: (509), (534) imply:
% 220.85/30.80 | | | | | | | | | | (535) $false
% 220.85/30.80 | | | | | | | | | |
% 220.85/30.80 | | | | | | | | | | CLOSE: (535) is inconsistent.
% 220.85/30.80 | | | | | | | | | |
% 220.85/30.80 | | | | | | | | | Case 2:
% 220.85/30.80 | | | | | | | | | |
% 220.85/30.80 | | | | | | | | | | (536) ? [v0: any] : ? [v1: $i] : ? [v2: any] :
% 220.85/30.80 | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.80 | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_1072_4,
% 220.85/30.80 | | | | | | | | | | v_y) = v1 & c_member(all_674_0, v1, v_L) = v2 &
% 220.85/30.80 | | | | | | | | | | c_member(all_674_0, all_1072_1, v_L) = v0 &
% 220.85/30.80 | | | | | | | | | | $i(v1) & (v2 = 0 | v0 = 0))
% 220.85/30.80 | | | | | | | | | |
% 220.85/30.80 | | | | | | | | | | DELTA: instantiating (536) with fresh symbols all_1267_0,
% 220.85/30.80 | | | | | | | | | | all_1267_1, all_1267_2 gives:
% 220.85/30.80 | | | | | | | | | | (537) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.80 | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_1072_4, v_y)
% 220.85/30.80 | | | | | | | | | | = all_1267_1 & c_member(all_674_0, all_1267_1, v_L)
% 220.85/30.80 | | | | | | | | | | = all_1267_0 & c_member(all_674_0, all_1072_1, v_L)
% 220.85/30.80 | | | | | | | | | | = all_1267_2 & $i(all_1267_1) & (all_1267_0 = 0 |
% 220.85/30.80 | | | | | | | | | | all_1267_2 = 0)
% 220.85/30.80 | | | | | | | | | |
% 220.85/30.80 | | | | | | | | | | ALPHA: (537) implies:
% 220.85/30.80 | | | | | | | | | | (538) c_member(all_674_0, all_1072_1, v_L) = all_1267_2
% 220.85/30.80 | | | | | | | | | |
% 220.85/30.80 | | | | | | | | | | REDUCE: (84), (538) imply:
% 220.85/30.80 | | | | | | | | | | (539) c_member(all_625_1, all_1072_1, v_L) = all_1267_2
% 220.85/30.80 | | | | | | | | | |
% 220.85/30.80 | | | | | | | | | | GROUND_INST: instantiating (19) with 0, all_1231_0, v_L,
% 220.85/30.80 | | | | | | | | | | all_1072_3, all_625_1, simplifying with (511),
% 220.85/30.80 | | | | | | | | | | (533) gives:
% 220.85/30.80 | | | | | | | | | | (540) all_1231_0 = 0
% 220.85/30.80 | | | | | | | | | |
% 220.85/30.80 | | | | | | | | | | GROUND_INST: instantiating (19) with all_1072_0, all_1267_2,
% 220.85/30.80 | | | | | | | | | | v_L, all_1072_1, all_625_1, simplifying with
% 220.85/30.80 | | | | | | | | | | (386), (539) gives:
% 220.85/30.80 | | | | | | | | | | (541) all_1267_2 = all_1072_0
% 220.85/30.80 | | | | | | | | | |
% 220.85/30.80 | | | | | | | | | | GROUND_INST: instantiating (19) with all_1203_0, all_1267_2,
% 220.85/30.80 | | | | | | | | | | v_L, all_1072_1, all_625_1, simplifying with
% 220.85/30.80 | | | | | | | | | | (521), (539) gives:
% 220.85/30.80 | | | | | | | | | | (542) all_1267_2 = all_1203_0
% 220.85/30.80 | | | | | | | | | |
% 220.85/30.80 | | | | | | | | | | GROUND_INST: instantiating (20) with all_1072_3, all_1203_2,
% 220.85/30.80 | | | | | | | | | | all_1072_4, all_870_8,
% 220.85/30.80 | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.80 | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with
% 220.85/30.80 | | | | | | | | | | (383), (518) gives:
% 220.85/30.80 | | | | | | | | | | (543) all_1203_2 = all_1072_3
% 220.85/30.80 | | | | | | | | | |
% 220.85/30.80 | | | | | | | | | | COMBINE_EQS: (541), (542) imply:
% 220.85/30.80 | | | | | | | | | | (544) all_1203_0 = all_1072_0
% 220.85/30.80 | | | | | | | | | |
% 220.85/30.80 | | | | | | | | | | REDUCE: (520), (543) imply:
% 220.85/30.80 | | | | | | | | | | (545) c_member(all_625_1, all_1072_3, v_L) = all_1203_1
% 220.85/30.80 | | | | | | | | | |
% 220.85/30.80 | | | | | | | | | | BETA: splitting (519) gives:
% 220.85/30.80 | | | | | | | | | |
% 220.85/30.80 | | | | | | | | | | Case 1:
% 220.85/30.80 | | | | | | | | | | |
% 220.85/30.80 | | | | | | | | | | | (546) ~ (all_1203_1 = 0)
% 220.85/30.80 | | | | | | | | | | |
% 220.85/30.80 | | | | | | | | | | | GROUND_INST: instantiating (19) with 0, all_1203_1, v_L,
% 220.85/30.80 | | | | | | | | | | | all_1072_3, all_625_1, simplifying with (511),
% 220.85/30.80 | | | | | | | | | | | (545) gives:
% 220.85/30.80 | | | | | | | | | | | (547) all_1203_1 = 0
% 220.85/30.80 | | | | | | | | | | |
% 220.85/30.80 | | | | | | | | | | | REDUCE: (546), (547) imply:
% 220.85/30.80 | | | | | | | | | | | (548) $false
% 220.85/30.80 | | | | | | | | | | |
% 220.85/30.80 | | | | | | | | | | | CLOSE: (548) is inconsistent.
% 220.85/30.80 | | | | | | | | | | |
% 220.85/30.80 | | | | | | | | | | Case 2:
% 220.85/30.80 | | | | | | | | | | |
% 220.85/30.80 | | | | | | | | | | | (549) all_1203_0 = 0
% 220.85/30.80 | | | | | | | | | | |
% 220.85/30.80 | | | | | | | | | | | COMBINE_EQS: (544), (549) imply:
% 220.85/30.80 | | | | | | | | | | | (550) all_1072_0 = 0
% 220.85/30.80 | | | | | | | | | | |
% 220.85/30.80 | | | | | | | | | | | REDUCE: (510), (550) imply:
% 220.85/30.80 | | | | | | | | | | | (551) $false
% 220.85/30.80 | | | | | | | | | | |
% 220.85/30.80 | | | | | | | | | | | CLOSE: (551) is inconsistent.
% 220.85/30.80 | | | | | | | | | | |
% 220.85/30.80 | | | | | | | | | | End of split
% 220.85/30.80 | | | | | | | | | |
% 220.85/30.80 | | | | | | | | | End of split
% 220.85/30.80 | | | | | | | | |
% 220.85/30.80 | | | | | | | | End of split
% 220.85/30.80 | | | | | | | |
% 220.85/30.80 | | | | | | | Case 2:
% 220.85/30.80 | | | | | | | |
% 220.85/30.80 | | | | | | | | (552) all_1072_4 = v_x & all_870_4 = 0
% 220.85/30.80 | | | | | | | |
% 220.85/30.80 | | | | | | | | ALPHA: (552) implies:
% 220.85/30.80 | | | | | | | | (553) all_870_4 = 0
% 220.85/30.80 | | | | | | | |
% 220.85/30.80 | | | | | | | | REDUCE: (506), (553) imply:
% 220.85/30.80 | | | | | | | | (554) $false
% 220.85/30.80 | | | | | | | |
% 220.85/30.80 | | | | | | | | CLOSE: (554) is inconsistent.
% 220.85/30.80 | | | | | | | |
% 220.85/30.80 | | | | | | | End of split
% 220.85/30.80 | | | | | | |
% 220.85/30.80 | | | | | | End of split
% 220.85/30.80 | | | | | |
% 220.85/30.80 | | | | | End of split
% 220.85/30.80 | | | | |
% 220.85/30.80 | | | | End of split
% 220.85/30.80 | | | |
% 220.85/30.80 | | | End of split
% 220.85/30.80 | | |
% 220.85/30.80 | | Case 2:
% 220.85/30.80 | | |
% 220.85/30.80 | | | (555) ~ (all_870_9 = v_x) & ((all_870_2 = 0 & all_870_8 = v_x & ?
% 220.85/30.80 | | | [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3
% 220.85/30.80 | | | = 0) & ~ (v0 = v_x) &
% 220.85/30.80 | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.80 | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v0) = v2 &
% 220.85/30.80 | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.80 | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = v1 &
% 220.85/30.80 | | | c_member(all_683_0, v2, v_L) = v3 & c_member(all_683_0, v1,
% 220.85/30.80 | | | v_L) = 0 & $i(v2) & $i(v1) & $i(v0))) | (all_870_6 = 0 &
% 220.85/30.80 | | | ~ (all_870_8 = v_x) & ? [v0: $i] : ? [v1: $i] : ? [v2:
% 220.85/30.80 | | | any] : ? [v3: $i] : ? [v4: any] :
% 220.85/30.80 | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.80 | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v0) = v1 &
% 220.85/30.80 | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.80 | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v0) = v3 &
% 220.85/30.80 | | | c_member(all_683_0, v3, v_L) = v4 & c_member(all_683_0, v1,
% 220.85/30.80 | | | v_L) = v2 & $i(v3) & $i(v1) & $i(v0) & ((v2 = 0 & ~ (v4
% 220.85/30.80 | | | = 0) & ~ (v0 = v_x)) | (v0 = v_x & all_870_4 = 0 &
% 220.85/30.80 | | | ~ (all_870_2 = 0))))))
% 220.85/30.80 | | |
% 220.85/30.80 | | | ALPHA: (555) implies:
% 220.85/30.80 | | | (556) ~ (all_870_9 = v_x)
% 220.85/30.81 | | | (557) (all_870_2 = 0 & all_870_8 = v_x & ? [v0: $i] : ? [v1: $i] : ?
% 220.85/30.81 | | | [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & ~ (v0 = v_x) &
% 220.85/30.81 | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.81 | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v0) = v2 &
% 220.85/30.81 | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.81 | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = v1 &
% 220.85/30.81 | | | c_member(all_683_0, v2, v_L) = v3 & c_member(all_683_0, v1,
% 220.85/30.81 | | | v_L) = 0 & $i(v2) & $i(v1) & $i(v0))) | (all_870_6 = 0 & ~
% 220.85/30.81 | | | (all_870_8 = v_x) & ? [v0: $i] : ? [v1: $i] : ? [v2: any] :
% 220.85/30.81 | | | ? [v3: $i] : ? [v4: any] :
% 220.85/30.81 | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.81 | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v0) = v1 &
% 220.85/30.81 | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.81 | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v0) = v3 &
% 220.85/30.81 | | | c_member(all_683_0, v3, v_L) = v4 & c_member(all_683_0, v1,
% 220.85/30.81 | | | v_L) = v2 & $i(v3) & $i(v1) & $i(v0) & ((v2 = 0 & ~ (v4 =
% 220.85/30.81 | | | 0) & ~ (v0 = v_x)) | (v0 = v_x & all_870_4 = 0 & ~
% 220.85/30.81 | | | (all_870_2 = 0)))))
% 220.85/30.81 | | |
% 220.85/30.81 | | | BETA: splitting (368) gives:
% 220.85/30.81 | | |
% 220.85/30.81 | | | Case 1:
% 220.85/30.81 | | | |
% 220.85/30.81 | | | | (558) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_674_0, all_870_3,
% 220.85/30.81 | | | | v_L) = v0)
% 220.85/30.81 | | | |
% 220.85/30.81 | | | | DELTA: instantiating (558) with fresh symbol all_1135_0 gives:
% 220.85/30.81 | | | | (559) ~ (all_1135_0 = 0) & c_member(all_674_0, all_870_3, v_L) =
% 220.85/30.81 | | | | all_1135_0
% 220.85/30.81 | | | |
% 220.85/30.81 | | | | ALPHA: (559) implies:
% 220.85/30.81 | | | | (560) ~ (all_1135_0 = 0)
% 220.85/30.81 | | | | (561) c_member(all_674_0, all_870_3, v_L) = all_1135_0
% 220.85/30.81 | | | |
% 220.85/30.81 | | | | REDUCE: (84), (561) imply:
% 220.85/30.81 | | | | (562) c_member(all_625_1, all_870_3, v_L) = all_1135_0
% 220.85/30.81 | | | |
% 220.85/30.81 | | | | GROUND_INST: instantiating (19) with all_870_2, all_1135_0, v_L,
% 220.85/30.81 | | | | all_870_3, all_625_1, simplifying with (358), (562) gives:
% 220.85/30.81 | | | | (563) all_1135_0 = all_870_2
% 220.85/30.81 | | | |
% 220.85/30.81 | | | | REDUCE: (560), (563) imply:
% 220.85/30.81 | | | | (564) ~ (all_870_2 = 0)
% 220.85/30.81 | | | |
% 220.85/30.81 | | | | BETA: splitting (557) gives:
% 220.85/30.81 | | | |
% 220.85/30.81 | | | | Case 1:
% 220.85/30.81 | | | | |
% 220.85/30.81 | | | | | (565) all_870_2 = 0 & all_870_8 = v_x & ? [v0: $i] : ? [v1: $i] :
% 220.85/30.81 | | | | | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & ~ (v0 = v_x) &
% 220.85/30.81 | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.81 | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v0) = v2 &
% 220.85/30.81 | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.81 | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = v1 &
% 220.85/30.81 | | | | | c_member(all_683_0, v2, v_L) = v3 & c_member(all_683_0, v1,
% 220.85/30.81 | | | | | v_L) = 0 & $i(v2) & $i(v1) & $i(v0))
% 220.85/30.81 | | | | |
% 220.85/30.81 | | | | | ALPHA: (565) implies:
% 220.85/30.81 | | | | | (566) all_870_2 = 0
% 220.85/30.81 | | | | |
% 220.85/30.81 | | | | | REDUCE: (564), (566) imply:
% 220.85/30.81 | | | | | (567) $false
% 220.85/30.81 | | | | |
% 220.85/30.81 | | | | | CLOSE: (567) is inconsistent.
% 220.85/30.81 | | | | |
% 220.85/30.81 | | | | Case 2:
% 220.85/30.81 | | | | |
% 220.85/30.81 | | | | | (568) all_870_6 = 0 & ~ (all_870_8 = v_x) & ? [v0: $i] : ? [v1:
% 220.85/30.81 | | | | | $i] : ? [v2: any] : ? [v3: $i] : ? [v4: any] :
% 220.85/30.81 | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.81 | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v0) = v1 &
% 220.85/30.81 | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.81 | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v0) = v3 &
% 220.85/30.81 | | | | | c_member(all_683_0, v3, v_L) = v4 & c_member(all_683_0, v1,
% 220.85/30.81 | | | | | v_L) = v2 & $i(v3) & $i(v1) & $i(v0) & ((v2 = 0 & ~ (v4
% 220.85/30.81 | | | | | = 0) & ~ (v0 = v_x)) | (v0 = v_x & all_870_4 = 0 &
% 220.85/30.81 | | | | | ~ (all_870_2 = 0))))
% 220.85/30.81 | | | | |
% 220.85/30.81 | | | | | ALPHA: (568) implies:
% 220.85/30.81 | | | | | (569) all_870_6 = 0
% 220.85/30.81 | | | | |
% 220.85/30.81 | | | | | REDUCE: (360), (569) imply:
% 220.85/30.81 | | | | | (570) c_member(all_625_1, all_870_7, v_L) = 0
% 220.85/30.81 | | | | |
% 220.85/30.81 | | | | | BETA: splitting (370) gives:
% 220.85/30.81 | | | | |
% 220.85/30.81 | | | | | Case 1:
% 220.85/30.81 | | | | | |
% 220.85/30.81 | | | | | | (571) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_674_0,
% 220.85/30.81 | | | | | | all_870_7, v_L) = v0)
% 220.85/30.81 | | | | | |
% 220.85/30.81 | | | | | | REF_CLOSE: (19), (84), (570), (571) are inconsistent by sub-proof
% 220.85/30.81 | | | | | | #9.
% 220.85/30.81 | | | | | |
% 220.85/30.81 | | | | | Case 2:
% 220.85/30.81 | | | | | |
% 220.85/30.81 | | | | | | (572) ! [v0: $i] : ! [v1: $i] : ( ~
% 220.85/30.81 | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.81 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v0) = v1)
% 220.85/30.81 | | | | | | | ~ $i(v0) | ? [v2: $i] : ? [v3: any] : ? [v4: any] :
% 220.85/30.81 | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.81 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v0) = v2
% 220.85/30.81 | | | | | | & c_member(all_674_0, v2, v_L) = v3 &
% 220.85/30.81 | | | | | | c_member(all_674_0, v1, v_L) = v4 & $i(v2) & ( ~ (v3 =
% 220.85/30.81 | | | | | | 0) | v4 = 0)))
% 220.85/30.81 | | | | | |
% 220.85/30.81 | | | | | | GROUND_INST: instantiating (572) with v_y, all_870_3, simplifying
% 220.85/30.81 | | | | | | with (15), (353) gives:
% 220.85/30.81 | | | | | | (573) ? [v0: $i] : ? [v1: any] : ? [v2: any] :
% 220.85/30.81 | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.81 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v_y) = v0 &
% 220.85/30.81 | | | | | | c_member(all_674_0, v0, v_L) = v1 & c_member(all_674_0,
% 220.85/30.81 | | | | | | all_870_3, v_L) = v2 & $i(v0) & ( ~ (v1 = 0) | v2 = 0))
% 220.85/30.81 | | | | | |
% 220.85/30.81 | | | | | | DELTA: instantiating (573) with fresh symbols all_1158_0,
% 220.85/30.81 | | | | | | all_1158_1, all_1158_2 gives:
% 220.85/30.81 | | | | | | (574) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.81 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v_y) =
% 220.85/30.81 | | | | | | all_1158_2 & c_member(all_674_0, all_1158_2, v_L) =
% 220.85/30.81 | | | | | | all_1158_1 & c_member(all_674_0, all_870_3, v_L) =
% 220.85/30.81 | | | | | | all_1158_0 & $i(all_1158_2) & ( ~ (all_1158_1 = 0) |
% 220.85/30.81 | | | | | | all_1158_0 = 0)
% 220.85/30.81 | | | | | |
% 220.85/30.81 | | | | | | ALPHA: (574) implies:
% 220.85/30.81 | | | | | | (575) c_member(all_674_0, all_870_3, v_L) = all_1158_0
% 220.85/30.81 | | | | | | (576) c_member(all_674_0, all_1158_2, v_L) = all_1158_1
% 220.85/30.81 | | | | | | (577) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.81 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v_y) =
% 220.85/30.81 | | | | | | all_1158_2
% 220.85/30.81 | | | | | | (578) ~ (all_1158_1 = 0) | all_1158_0 = 0
% 220.85/30.81 | | | | | |
% 220.85/30.81 | | | | | | REDUCE: (84), (576) imply:
% 220.85/30.81 | | | | | | (579) c_member(all_625_1, all_1158_2, v_L) = all_1158_1
% 220.85/30.81 | | | | | |
% 220.85/30.81 | | | | | | REDUCE: (84), (575) imply:
% 220.85/30.81 | | | | | | (580) c_member(all_625_1, all_870_3, v_L) = all_1158_0
% 220.85/30.81 | | | | | |
% 220.85/30.81 | | | | | | GROUND_INST: instantiating (19) with all_870_2, all_1158_0, v_L,
% 220.85/30.81 | | | | | | all_870_3, all_625_1, simplifying with (358), (580)
% 220.85/30.81 | | | | | | gives:
% 220.85/30.81 | | | | | | (581) all_1158_0 = all_870_2
% 220.85/30.81 | | | | | |
% 220.85/30.81 | | | | | | GROUND_INST: instantiating (20) with all_870_5, all_1158_2, v_y,
% 220.85/30.81 | | | | | | all_870_8, tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.81 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with
% 220.85/30.81 | | | | | | (355), (577) gives:
% 220.85/30.81 | | | | | | (582) all_1158_2 = all_870_5
% 220.85/30.81 | | | | | |
% 220.85/30.81 | | | | | | REDUCE: (579), (582) imply:
% 220.85/30.81 | | | | | | (583) c_member(all_625_1, all_870_5, v_L) = all_1158_1
% 220.85/30.81 | | | | | |
% 220.85/30.81 | | | | | | BETA: splitting (578) gives:
% 220.85/30.81 | | | | | |
% 220.85/30.81 | | | | | | Case 1:
% 220.85/30.81 | | | | | | |
% 220.85/30.81 | | | | | | | (584) ~ (all_1158_1 = 0)
% 220.85/30.81 | | | | | | |
% 220.85/30.81 | | | | | | | GROUND_INST: instantiating (19) with all_870_4, all_1158_1, v_L,
% 220.85/30.81 | | | | | | | all_870_5, all_625_1, simplifying with (359), (583)
% 220.85/30.81 | | | | | | | gives:
% 220.85/30.81 | | | | | | | (585) all_1158_1 = all_870_4
% 220.85/30.81 | | | | | | |
% 220.85/30.81 | | | | | | | REDUCE: (584), (585) imply:
% 220.85/30.81 | | | | | | | (586) ~ (all_870_4 = 0)
% 220.85/30.81 | | | | | | |
% 220.85/30.81 | | | | | | | BETA: splitting (367) gives:
% 220.85/30.81 | | | | | | |
% 220.85/30.81 | | | | | | | Case 1:
% 220.85/30.81 | | | | | | | |
% 220.85/30.81 | | | | | | | | (587) all_870_9 = v_y
% 220.85/30.81 | | | | | | | |
% 220.85/30.81 | | | | | | | | REDUCE: (354), (587) imply:
% 220.85/30.81 | | | | | | | | (588) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.81 | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, all_870_8) =
% 220.85/30.81 | | | | | | | | all_870_7
% 220.85/30.81 | | | | | | | |
% 220.85/30.81 | | | | | | | | BETA: splitting (557) gives:
% 220.85/30.81 | | | | | | | |
% 220.85/30.81 | | | | | | | | Case 1:
% 220.85/30.81 | | | | | | | | |
% 220.85/30.81 | | | | | | | | | (589) all_870_2 = 0 & all_870_8 = v_x & ? [v0: $i] : ?
% 220.85/30.81 | | | | | | | | | [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0)
% 220.85/30.81 | | | | | | | | | & ~ (v0 = v_x) &
% 220.85/30.81 | | | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.81 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v0) =
% 220.85/30.81 | | | | | | | | | v2 &
% 220.85/30.81 | | | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.81 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = v1 &
% 220.85/30.81 | | | | | | | | | c_member(all_683_0, v2, v_L) = v3 &
% 220.85/30.81 | | | | | | | | | c_member(all_683_0, v1, v_L) = 0 & $i(v2) & $i(v1)
% 220.85/30.81 | | | | | | | | | & $i(v0))
% 220.85/30.81 | | | | | | | | |
% 220.85/30.81 | | | | | | | | | ALPHA: (589) implies:
% 220.85/30.81 | | | | | | | | | (590) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3:
% 220.85/30.81 | | | | | | | | | int] : ( ~ (v3 = 0) & ~ (v0 = v_x) &
% 220.85/30.81 | | | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.81 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v0) =
% 220.85/30.81 | | | | | | | | | v2 &
% 220.85/30.81 | | | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.81 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = v1 &
% 220.85/30.81 | | | | | | | | | c_member(all_683_0, v2, v_L) = v3 &
% 220.85/30.81 | | | | | | | | | c_member(all_683_0, v1, v_L) = 0 & $i(v2) & $i(v1)
% 220.85/30.81 | | | | | | | | | & $i(v0))
% 220.85/30.81 | | | | | | | | |
% 220.85/30.81 | | | | | | | | | REF_CLOSE: (19), (20), (86), (587), (590) are inconsistent by
% 220.85/30.81 | | | | | | | | | sub-proof #8.
% 220.85/30.81 | | | | | | | | |
% 220.85/30.81 | | | | | | | | Case 2:
% 220.85/30.81 | | | | | | | | |
% 220.85/30.81 | | | | | | | | |
% 220.85/30.81 | | | | | | | | | ALPHA: (568) implies:
% 220.85/30.81 | | | | | | | | | (591) ? [v0: $i] : ? [v1: $i] : ? [v2: any] : ? [v3:
% 220.85/30.81 | | | | | | | | | $i] : ? [v4: any] :
% 220.85/30.81 | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.81 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v0) =
% 220.85/30.81 | | | | | | | | | v1 &
% 220.85/30.81 | | | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.81 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v0) =
% 220.85/30.81 | | | | | | | | | v3 & c_member(all_683_0, v3, v_L) = v4 &
% 220.85/30.81 | | | | | | | | | c_member(all_683_0, v1, v_L) = v2 & $i(v3) & $i(v1)
% 220.85/30.81 | | | | | | | | | & $i(v0) & ((v2 = 0 & ~ (v4 = 0) & ~ (v0 = v_x))
% 220.85/30.81 | | | | | | | | | | (v0 = v_x & all_870_4 = 0 & ~ (all_870_2 =
% 220.85/30.81 | | | | | | | | | 0))))
% 220.85/30.81 | | | | | | | | |
% 220.85/30.81 | | | | | | | | | REF_CLOSE: (19), (20), (41), (84), (86), (343), (352), (357),
% 220.85/30.81 | | | | | | | | | (360), (366), (569), (586), (587), (588), (591) are
% 220.85/30.81 | | | | | | | | | inconsistent by sub-proof #7.
% 220.85/30.81 | | | | | | | | |
% 220.85/30.81 | | | | | | | | End of split
% 220.85/30.81 | | | | | | | |
% 220.85/30.81 | | | | | | | Case 2:
% 220.85/30.81 | | | | | | | |
% 220.85/30.81 | | | | | | | | (592) ~ (all_870_9 = v_y)
% 220.85/30.82 | | | | | | | | (593) ? [v0: any] : ? [v1: $i] : ? [v2: any] :
% 220.85/30.82 | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.82 | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, all_870_9) =
% 220.85/30.82 | | | | | | | | v1 & c_member(all_674_0, v1, v_L) = v2 &
% 220.85/30.82 | | | | | | | | c_member(all_674_0, all_870_3, v_L) = v0 & $i(v1) &
% 220.85/30.82 | | | | | | | | (v2 = 0 | v0 = 0))
% 220.85/30.82 | | | | | | | |
% 220.85/30.82 | | | | | | | | DELTA: instantiating (593) with fresh symbols all_1137_0,
% 220.85/30.82 | | | | | | | | all_1137_1, all_1137_2 gives:
% 220.85/30.82 | | | | | | | | (594) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.82 | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, all_870_9) =
% 220.85/30.82 | | | | | | | | all_1137_1 & c_member(all_674_0, all_1137_1, v_L) =
% 220.85/30.82 | | | | | | | | all_1137_0 & c_member(all_674_0, all_870_3, v_L) =
% 220.85/30.82 | | | | | | | | all_1137_2 & $i(all_1137_1) & (all_1137_0 = 0 |
% 220.85/30.82 | | | | | | | | all_1137_2 = 0)
% 220.85/30.82 | | | | | | | |
% 220.85/30.82 | | | | | | | | ALPHA: (594) implies:
% 220.85/30.82 | | | | | | | | (595) c_member(all_674_0, all_870_3, v_L) = all_1137_2
% 220.85/30.82 | | | | | | | | (596) c_member(all_674_0, all_1137_1, v_L) = all_1137_0
% 220.85/30.82 | | | | | | | | (597) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.82 | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, all_870_9) =
% 220.85/30.82 | | | | | | | | all_1137_1
% 220.85/30.82 | | | | | | | | (598) all_1137_0 = 0 | all_1137_2 = 0
% 220.85/30.82 | | | | | | | |
% 220.85/30.82 | | | | | | | | REDUCE: (84), (596) imply:
% 220.85/30.82 | | | | | | | | (599) c_member(all_625_1, all_1137_1, v_L) = all_1137_0
% 220.85/30.82 | | | | | | | |
% 220.85/30.82 | | | | | | | | REDUCE: (84), (595) imply:
% 220.85/30.82 | | | | | | | | (600) c_member(all_625_1, all_870_3, v_L) = all_1137_2
% 220.85/30.82 | | | | | | | |
% 220.85/30.82 | | | | | | | | GROUND_INST: instantiating (19) with all_870_2, all_1137_2, v_L,
% 220.85/30.82 | | | | | | | | all_870_3, all_625_1, simplifying with (358), (600)
% 220.85/30.82 | | | | | | | | gives:
% 220.85/30.82 | | | | | | | | (601) all_1137_2 = all_870_2
% 220.85/30.82 | | | | | | | |
% 220.85/30.82 | | | | | | | | BETA: splitting (364) gives:
% 220.85/30.82 | | | | | | | |
% 220.85/30.82 | | | | | | | | Case 1:
% 220.85/30.82 | | | | | | | | |
% 220.85/30.82 | | | | | | | | | (602) all_870_0 = 0
% 220.85/30.82 | | | | | | | | |
% 220.85/30.82 | | | | | | | | | REDUCE: (357), (602) imply:
% 220.85/30.82 | | | | | | | | | (603) c_member(all_625_1, all_870_1, v_L) = 0
% 220.85/30.82 | | | | | | | | |
% 220.85/30.82 | | | | | | | | | BETA: splitting (366) gives:
% 220.85/30.82 | | | | | | | | |
% 220.85/30.82 | | | | | | | | | Case 1:
% 220.85/30.82 | | | | | | | | | |
% 220.85/30.82 | | | | | | | | | | (604) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_674_0,
% 220.85/30.82 | | | | | | | | | | all_870_1, v_L) = v0)
% 220.85/30.82 | | | | | | | | | |
% 220.85/30.82 | | | | | | | | | | REF_CLOSE: (19), (84), (603), (604) are inconsistent by
% 220.85/30.82 | | | | | | | | | | sub-proof #12.
% 220.85/30.82 | | | | | | | | | |
% 220.85/30.82 | | | | | | | | | Case 2:
% 220.85/30.82 | | | | | | | | | |
% 220.85/30.82 | | | | | | | | | | (605) ! [v0: $i] : ! [v1: $i] : ( ~
% 220.85/30.82 | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.82 | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) =
% 220.85/30.82 | | | | | | | | | | v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: any] :
% 220.85/30.82 | | | | | | | | | | ? [v4: any] :
% 220.85/30.82 | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.82 | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8,
% 220.85/30.82 | | | | | | | | | | v0) = v2 & c_member(all_674_0, v2, v_L) = v3
% 220.85/30.82 | | | | | | | | | | & c_member(all_674_0, v1, v_L) = v4 & $i(v2) &
% 220.85/30.82 | | | | | | | | | | ( ~ (v3 = 0) | v4 = 0)))
% 220.85/30.82 | | | | | | | | | |
% 220.85/30.82 | | | | | | | | | | GROUND_INST: instantiating (605) with all_870_8, all_870_1,
% 220.85/30.82 | | | | | | | | | | simplifying with (343), (352) gives:
% 220.85/30.82 | | | | | | | | | | (606) ? [v0: $i] : ? [v1: any] : ? [v2: any] :
% 220.85/30.82 | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.82 | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8,
% 220.85/30.82 | | | | | | | | | | all_870_8) = v0 & c_member(all_674_0, v0, v_L)
% 220.85/30.82 | | | | | | | | | | = v1 & c_member(all_674_0, all_870_1, v_L) = v2 &
% 220.85/30.82 | | | | | | | | | | $i(v0) & ( ~ (v1 = 0) | v2 = 0))
% 220.85/30.82 | | | | | | | | | |
% 220.85/30.82 | | | | | | | | | | DELTA: instantiating (606) with fresh symbols all_1153_0,
% 220.85/30.82 | | | | | | | | | | all_1153_1, all_1153_2 gives:
% 220.85/30.82 | | | | | | | | | | (607) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.82 | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8,
% 220.85/30.82 | | | | | | | | | | all_870_8) = all_1153_2 & c_member(all_674_0,
% 220.85/30.82 | | | | | | | | | | all_1153_2, v_L) = all_1153_1 &
% 220.85/30.82 | | | | | | | | | | c_member(all_674_0, all_870_1, v_L) = all_1153_0 &
% 220.85/30.82 | | | | | | | | | | $i(all_1153_2) & ( ~ (all_1153_1 = 0) | all_1153_0
% 220.85/30.82 | | | | | | | | | | = 0)
% 220.85/30.82 | | | | | | | | | |
% 220.85/30.82 | | | | | | | | | | ALPHA: (607) implies:
% 220.85/30.82 | | | | | | | | | | (608) c_member(all_674_0, all_870_1, v_L) = all_1153_0
% 220.85/30.82 | | | | | | | | | |
% 220.85/30.82 | | | | | | | | | | REDUCE: (84), (608) imply:
% 220.85/30.82 | | | | | | | | | | (609) c_member(all_625_1, all_870_1, v_L) = all_1153_0
% 220.85/30.82 | | | | | | | | | |
% 220.85/30.82 | | | | | | | | | | GROUND_INST: instantiating (19) with 0, all_1153_0, v_L,
% 220.85/30.82 | | | | | | | | | | all_870_1, all_625_1, simplifying with (603),
% 220.85/30.82 | | | | | | | | | | (609) gives:
% 220.85/30.82 | | | | | | | | | | (610) all_1153_0 = 0
% 220.85/30.82 | | | | | | | | | |
% 220.85/30.82 | | | | | | | | | | BETA: splitting (370) gives:
% 220.85/30.82 | | | | | | | | | |
% 220.85/30.82 | | | | | | | | | | Case 1:
% 220.85/30.82 | | | | | | | | | | |
% 220.85/30.82 | | | | | | | | | | | (611) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_674_0,
% 220.85/30.82 | | | | | | | | | | | all_870_7, v_L) = v0)
% 220.85/30.82 | | | | | | | | | | |
% 220.85/30.82 | | | | | | | | | | | DELTA: instantiating (611) with fresh symbol all_1164_0
% 220.85/30.82 | | | | | | | | | | | gives:
% 220.85/30.82 | | | | | | | | | | | (612) ~ (all_1164_0 = 0) & c_member(all_674_0,
% 220.85/30.82 | | | | | | | | | | | all_870_7, v_L) = all_1164_0
% 220.85/30.82 | | | | | | | | | | |
% 220.85/30.82 | | | | | | | | | | | ALPHA: (612) implies:
% 220.85/30.82 | | | | | | | | | | | (613) ~ (all_1164_0 = 0)
% 220.85/30.82 | | | | | | | | | | | (614) c_member(all_674_0, all_870_7, v_L) = all_1164_0
% 220.85/30.82 | | | | | | | | | | |
% 220.85/30.82 | | | | | | | | | | | REDUCE: (84), (614) imply:
% 220.85/30.82 | | | | | | | | | | | (615) c_member(all_625_1, all_870_7, v_L) = all_1164_0
% 220.85/30.82 | | | | | | | | | | |
% 220.85/30.82 | | | | | | | | | | | GROUND_INST: instantiating (19) with all_870_6, all_1164_0,
% 220.85/30.82 | | | | | | | | | | | v_L, all_870_7, all_625_1, simplifying with (360),
% 220.85/30.82 | | | | | | | | | | | (615) gives:
% 220.85/30.82 | | | | | | | | | | | (616) all_1164_0 = all_870_6
% 220.85/30.82 | | | | | | | | | | |
% 220.85/30.82 | | | | | | | | | | | REDUCE: (613), (616) imply:
% 220.85/30.82 | | | | | | | | | | | (617) ~ (all_870_6 = 0)
% 220.85/30.82 | | | | | | | | | | |
% 220.85/30.82 | | | | | | | | | | | BETA: splitting (557) gives:
% 220.85/30.82 | | | | | | | | | | |
% 220.85/30.82 | | | | | | | | | | | Case 1:
% 220.85/30.82 | | | | | | | | | | | |
% 220.85/30.82 | | | | | | | | | | | | (618) all_870_2 = 0 & all_870_8 = v_x & ? [v0: $i] : ?
% 220.85/30.82 | | | | | | | | | | | | [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 =
% 220.85/30.82 | | | | | | | | | | | | 0) & ~ (v0 = v_x) &
% 220.85/30.82 | | | | | | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.82 | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9,
% 220.85/30.82 | | | | | | | | | | | | v0) = v2 &
% 220.85/30.82 | | | | | | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.82 | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = v1
% 220.85/30.82 | | | | | | | | | | | | & c_member(all_683_0, v2, v_L) = v3 &
% 220.85/30.82 | | | | | | | | | | | | c_member(all_683_0, v1, v_L) = 0 & $i(v2) &
% 220.85/30.82 | | | | | | | | | | | | $i(v1) & $i(v0))
% 220.85/30.82 | | | | | | | | | | | |
% 220.85/30.82 | | | | | | | | | | | | ALPHA: (618) implies:
% 220.85/30.82 | | | | | | | | | | | | (619) all_870_2 = 0
% 220.85/30.82 | | | | | | | | | | | |
% 220.85/30.82 | | | | | | | | | | | | REDUCE: (358), (619) imply:
% 220.85/30.82 | | | | | | | | | | | | (620) c_member(all_625_1, all_870_3, v_L) = 0
% 220.85/30.82 | | | | | | | | | | | |
% 220.85/30.82 | | | | | | | | | | | | BETA: splitting (368) gives:
% 220.85/30.82 | | | | | | | | | | | |
% 220.85/30.82 | | | | | | | | | | | | Case 1:
% 220.85/30.82 | | | | | | | | | | | | |
% 220.85/30.82 | | | | | | | | | | | | |
% 220.85/30.82 | | | | | | | | | | | | | DELTA: instantiating (558) with fresh symbol all_1184_0
% 220.85/30.82 | | | | | | | | | | | | | gives:
% 220.85/30.82 | | | | | | | | | | | | | (621) ~ (all_1184_0 = 0) & c_member(all_674_0,
% 220.85/30.82 | | | | | | | | | | | | | all_870_3, v_L) = all_1184_0
% 220.85/30.82 | | | | | | | | | | | | |
% 220.85/30.82 | | | | | | | | | | | | | ALPHA: (621) implies:
% 220.85/30.82 | | | | | | | | | | | | | (622) ~ (all_1184_0 = 0)
% 220.85/30.82 | | | | | | | | | | | | | (623) c_member(all_674_0, all_870_3, v_L) = all_1184_0
% 220.85/30.82 | | | | | | | | | | | | |
% 220.85/30.82 | | | | | | | | | | | | | REDUCE: (84), (623) imply:
% 220.85/30.82 | | | | | | | | | | | | | (624) c_member(all_625_1, all_870_3, v_L) = all_1184_0
% 220.85/30.82 | | | | | | | | | | | | |
% 220.85/30.82 | | | | | | | | | | | | | GROUND_INST: instantiating (19) with 0, all_1184_0, v_L,
% 220.85/30.82 | | | | | | | | | | | | | all_870_3, all_625_1, simplifying with (620),
% 220.85/30.82 | | | | | | | | | | | | | (624) gives:
% 220.85/30.82 | | | | | | | | | | | | | (625) all_1184_0 = 0
% 220.85/30.82 | | | | | | | | | | | | |
% 220.85/30.82 | | | | | | | | | | | | | REDUCE: (622), (625) imply:
% 220.85/30.82 | | | | | | | | | | | | | (626) $false
% 220.85/30.82 | | | | | | | | | | | | |
% 220.85/30.82 | | | | | | | | | | | | | CLOSE: (626) is inconsistent.
% 220.85/30.82 | | | | | | | | | | | | |
% 220.85/30.82 | | | | | | | | | | | | Case 2:
% 220.85/30.82 | | | | | | | | | | | | |
% 220.85/30.82 | | | | | | | | | | | | | (627) ! [v0: $i] : ! [v1: $i] : ( ~
% 220.85/30.82 | | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.82 | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9,
% 220.85/30.82 | | | | | | | | | | | | | v0) = v1) | ~ $i(v0) | ? [v2: $i] : ?
% 220.85/30.82 | | | | | | | | | | | | | [v3: any] : ? [v4: any] :
% 220.85/30.82 | | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.82 | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) =
% 220.85/30.82 | | | | | | | | | | | | | v2 & c_member(all_674_0, v2, v_L) = v3 &
% 220.85/30.82 | | | | | | | | | | | | | c_member(all_674_0, v1, v_L) = v4 & $i(v2) & (
% 220.85/30.82 | | | | | | | | | | | | | ~ (v3 = 0) | v4 = 0)))
% 220.85/30.82 | | | | | | | | | | | | |
% 220.85/30.82 | | | | | | | | | | | | | DELTA: instantiating (611) with fresh symbol all_1197_0
% 220.85/30.82 | | | | | | | | | | | | | gives:
% 220.85/30.82 | | | | | | | | | | | | | (628) ~ (all_1197_0 = 0) & c_member(all_674_0,
% 220.85/30.82 | | | | | | | | | | | | | all_870_7, v_L) = all_1197_0
% 220.85/30.82 | | | | | | | | | | | | |
% 220.85/30.82 | | | | | | | | | | | | | ALPHA: (628) implies:
% 220.85/30.82 | | | | | | | | | | | | | (629) ~ (all_1197_0 = 0)
% 220.85/30.82 | | | | | | | | | | | | | (630) c_member(all_674_0, all_870_7, v_L) = all_1197_0
% 220.85/30.82 | | | | | | | | | | | | |
% 220.85/30.82 | | | | | | | | | | | | | REDUCE: (84), (630) imply:
% 220.85/30.82 | | | | | | | | | | | | | (631) c_member(all_625_1, all_870_7, v_L) = all_1197_0
% 220.85/30.82 | | | | | | | | | | | | |
% 220.85/30.82 | | | | | | | | | | | | | GROUND_INST: instantiating (19) with all_870_6, all_1197_0,
% 220.85/30.82 | | | | | | | | | | | | | v_L, all_870_7, all_625_1, simplifying with (360),
% 220.85/30.82 | | | | | | | | | | | | | (631) gives:
% 220.85/30.82 | | | | | | | | | | | | | (632) all_1197_0 = all_870_6
% 220.85/30.82 | | | | | | | | | | | | |
% 220.85/30.82 | | | | | | | | | | | | | BETA: splitting (557) gives:
% 220.85/30.82 | | | | | | | | | | | | |
% 220.85/30.82 | | | | | | | | | | | | | Case 1:
% 220.85/30.82 | | | | | | | | | | | | | |
% 220.85/30.82 | | | | | | | | | | | | | |
% 220.85/30.82 | | | | | | | | | | | | | | ALPHA: (618) implies:
% 220.85/30.82 | | | | | | | | | | | | | | (633) all_870_8 = v_x
% 220.85/30.82 | | | | | | | | | | | | | | (634) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3:
% 220.85/30.82 | | | | | | | | | | | | | | int] : ( ~ (v3 = 0) & ~ (v0 = v_x) &
% 220.85/30.82 | | | | | | | | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.82 | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9,
% 220.85/30.82 | | | | | | | | | | | | | | v0) = v2 &
% 220.85/30.82 | | | | | | | | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.82 | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = v1
% 220.85/30.82 | | | | | | | | | | | | | | & c_member(all_683_0, v2, v_L) = v3 &
% 220.85/30.82 | | | | | | | | | | | | | | c_member(all_683_0, v1, v_L) = 0 & $i(v2) &
% 220.85/30.82 | | | | | | | | | | | | | | $i(v1) & $i(v0))
% 220.85/30.82 | | | | | | | | | | | | | |
% 220.85/30.82 | | | | | | | | | | | | | | DELTA: instantiating (634) with fresh symbols all_1207_0,
% 220.85/30.82 | | | | | | | | | | | | | | all_1207_1, all_1207_2, all_1207_3 gives:
% 220.85/30.82 | | | | | | | | | | | | | | (635) ~ (all_1207_0 = 0) & ~ (all_1207_3 = v_x) &
% 220.85/30.82 | | | | | | | | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.82 | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9,
% 220.85/30.82 | | | | | | | | | | | | | | all_1207_3) = all_1207_1 &
% 220.85/30.82 | | | | | | | | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.82 | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y,
% 220.85/30.82 | | | | | | | | | | | | | | all_1207_3) = all_1207_2 & c_member(all_683_0,
% 220.85/30.82 | | | | | | | | | | | | | | all_1207_1, v_L) = all_1207_0 &
% 220.85/30.82 | | | | | | | | | | | | | | c_member(all_683_0, all_1207_2, v_L) = 0 &
% 220.85/30.82 | | | | | | | | | | | | | | $i(all_1207_1) & $i(all_1207_2) & $i(all_1207_3)
% 220.85/30.82 | | | | | | | | | | | | | |
% 220.85/30.82 | | | | | | | | | | | | | | ALPHA: (635) implies:
% 220.85/30.82 | | | | | | | | | | | | | | (636) ~ (all_1207_0 = 0)
% 220.85/30.82 | | | | | | | | | | | | | | (637) $i(all_1207_3)
% 220.85/30.82 | | | | | | | | | | | | | | (638) c_member(all_683_0, all_1207_2, v_L) = 0
% 220.85/30.82 | | | | | | | | | | | | | | (639) c_member(all_683_0, all_1207_1, v_L) = all_1207_0
% 220.85/30.82 | | | | | | | | | | | | | | (640) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.82 | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y,
% 220.85/30.82 | | | | | | | | | | | | | | all_1207_3) = all_1207_2
% 220.85/30.82 | | | | | | | | | | | | | | (641) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.82 | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9,
% 220.85/30.82 | | | | | | | | | | | | | | all_1207_3) = all_1207_1
% 220.85/30.82 | | | | | | | | | | | | | |
% 220.85/30.82 | | | | | | | | | | | | | | REDUCE: (86), (639) imply:
% 220.85/30.82 | | | | | | | | | | | | | | (642) c_member(all_625_1, all_1207_1, v_L) = all_1207_0
% 220.85/30.82 | | | | | | | | | | | | | |
% 220.85/30.82 | | | | | | | | | | | | | | REDUCE: (86), (638) imply:
% 220.85/30.82 | | | | | | | | | | | | | | (643) c_member(all_625_1, all_1207_2, v_L) = 0
% 220.85/30.82 | | | | | | | | | | | | | |
% 220.85/30.82 | | | | | | | | | | | | | | REDUCE: (343), (633) imply:
% 220.85/30.82 | | | | | | | | | | | | | | (644) $i(v_x)
% 220.85/30.82 | | | | | | | | | | | | | |
% 220.85/30.82 | | | | | | | | | | | | | | BETA: splitting (369) gives:
% 220.85/30.82 | | | | | | | | | | | | | |
% 220.85/30.82 | | | | | | | | | | | | | | Case 1:
% 220.85/30.82 | | | | | | | | | | | | | | |
% 220.85/30.82 | | | | | | | | | | | | | | | (645) all_870_8 = all_870_9
% 220.85/30.82 | | | | | | | | | | | | | | |
% 220.85/30.82 | | | | | | | | | | | | | | | COMBINE_EQS: (633), (645) imply:
% 220.85/30.82 | | | | | | | | | | | | | | | (646) all_870_9 = v_x
% 220.85/30.82 | | | | | | | | | | | | | | |
% 220.85/30.82 | | | | | | | | | | | | | | | SIMP: (646) implies:
% 220.85/30.82 | | | | | | | | | | | | | | | (647) all_870_9 = v_x
% 220.85/30.82 | | | | | | | | | | | | | | |
% 220.85/30.82 | | | | | | | | | | | | | | | REDUCE: (556), (647) imply:
% 220.85/30.82 | | | | | | | | | | | | | | | (648) $false
% 220.85/30.82 | | | | | | | | | | | | | | |
% 220.85/30.82 | | | | | | | | | | | | | | | CLOSE: (648) is inconsistent.
% 220.85/30.82 | | | | | | | | | | | | | | |
% 220.85/30.82 | | | | | | | | | | | | | | Case 2:
% 220.85/30.82 | | | | | | | | | | | | | | |
% 220.85/30.82 | | | | | | | | | | | | | | | (649) ~ (all_870_8 = all_870_9)
% 220.85/30.82 | | | | | | | | | | | | | | | (650) ? [v0: any] : ? [v1: $i] : ? [v2: any] :
% 220.85/30.82 | | | | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.82 | | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8,
% 220.85/30.82 | | | | | | | | | | | | | | | all_870_9) = v1 & c_member(all_674_0, v1, v_L)
% 220.85/30.82 | | | | | | | | | | | | | | | = v2 & c_member(all_674_0, all_870_7, v_L) = v0
% 220.85/30.82 | | | | | | | | | | | | | | | & $i(v1) & (v2 = 0 | v0 = 0))
% 220.85/30.83 | | | | | | | | | | | | | | |
% 220.85/30.83 | | | | | | | | | | | | | | | DELTA: instantiating (650) with fresh symbols all_1218_0,
% 220.85/30.83 | | | | | | | | | | | | | | | all_1218_1, all_1218_2 gives:
% 220.85/30.83 | | | | | | | | | | | | | | | (651) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.83 | | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8,
% 220.85/30.83 | | | | | | | | | | | | | | | all_870_9) = all_1218_1 & c_member(all_674_0,
% 220.85/30.83 | | | | | | | | | | | | | | | all_1218_1, v_L) = all_1218_0 &
% 220.85/30.83 | | | | | | | | | | | | | | | c_member(all_674_0, all_870_7, v_L) = all_1218_2 &
% 220.85/30.83 | | | | | | | | | | | | | | | $i(all_1218_1) & (all_1218_0 = 0 | all_1218_2 = 0)
% 220.85/30.83 | | | | | | | | | | | | | | |
% 220.85/30.83 | | | | | | | | | | | | | | | ALPHA: (651) implies:
% 220.85/30.83 | | | | | | | | | | | | | | | (652) c_member(all_674_0, all_870_7, v_L) = all_1218_2
% 220.85/30.83 | | | | | | | | | | | | | | | (653) c_member(all_674_0, all_1218_1, v_L) = all_1218_0
% 220.85/30.83 | | | | | | | | | | | | | | | (654) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.83 | | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8,
% 220.85/30.83 | | | | | | | | | | | | | | | all_870_9) = all_1218_1
% 220.85/30.83 | | | | | | | | | | | | | | | (655) all_1218_0 = 0 | all_1218_2 = 0
% 220.85/30.83 | | | | | | | | | | | | | | |
% 220.85/30.83 | | | | | | | | | | | | | | | REDUCE: (633), (649) imply:
% 220.85/30.83 | | | | | | | | | | | | | | | (656) ~ (all_870_9 = v_x)
% 220.85/30.83 | | | | | | | | | | | | | | |
% 220.85/30.83 | | | | | | | | | | | | | | | REDUCE: (633), (654) imply:
% 220.85/30.83 | | | | | | | | | | | | | | | (657) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.83 | | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, all_870_9)
% 220.85/30.83 | | | | | | | | | | | | | | | = all_1218_1
% 220.85/30.83 | | | | | | | | | | | | | | |
% 220.85/30.83 | | | | | | | | | | | | | | | REDUCE: (84), (653) imply:
% 220.85/30.83 | | | | | | | | | | | | | | | (658) c_member(all_625_1, all_1218_1, v_L) = all_1218_0
% 220.85/30.83 | | | | | | | | | | | | | | |
% 220.85/30.83 | | | | | | | | | | | | | | | REDUCE: (84), (652) imply:
% 220.85/30.83 | | | | | | | | | | | | | | | (659) c_member(all_625_1, all_870_7, v_L) = all_1218_2
% 220.85/30.83 | | | | | | | | | | | | | | |
% 220.85/30.83 | | | | | | | | | | | | | | | GROUND_INST: instantiating (19) with all_870_6, all_1218_2,
% 220.85/30.83 | | | | | | | | | | | | | | | v_L, all_870_7, all_625_1, simplifying with (360),
% 220.85/30.83 | | | | | | | | | | | | | | | (659) gives:
% 220.85/30.83 | | | | | | | | | | | | | | | (660) all_1218_2 = all_870_6
% 220.85/30.83 | | | | | | | | | | | | | | |
% 220.85/30.83 | | | | | | | | | | | | | | | BETA: splitting (655) gives:
% 220.85/30.83 | | | | | | | | | | | | | | |
% 220.85/30.83 | | | | | | | | | | | | | | | Case 1:
% 220.85/30.83 | | | | | | | | | | | | | | | |
% 220.85/30.83 | | | | | | | | | | | | | | | | (661) all_1218_0 = 0
% 220.85/30.83 | | | | | | | | | | | | | | | |
% 220.85/30.83 | | | | | | | | | | | | | | | | REDUCE: (658), (661) imply:
% 220.85/30.83 | | | | | | | | | | | | | | | | (662) c_member(all_625_1, all_1218_1, v_L) = 0
% 220.85/30.83 | | | | | | | | | | | | | | | |
% 220.85/30.83 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (605) with all_1207_3, all_1207_2,
% 220.85/30.83 | | | | | | | | | | | | | | | | simplifying with (637), (640) gives:
% 220.85/30.83 | | | | | | | | | | | | | | | | (663) ? [v0: $i] : ? [v1: any] : ? [v2: any] :
% 220.85/30.83 | | | | | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.83 | | | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8,
% 220.85/30.83 | | | | | | | | | | | | | | | | all_1207_3) = v0 & c_member(all_674_0, v0,
% 220.85/30.83 | | | | | | | | | | | | | | | | v_L) = v1 & c_member(all_674_0, all_1207_2,
% 220.85/30.83 | | | | | | | | | | | | | | | | v_L) = v2 & $i(v0) & ( ~ (v1 = 0) | v2 = 0))
% 220.85/30.83 | | | | | | | | | | | | | | | |
% 220.85/30.83 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (41) with v_y, all_1207_3,
% 220.85/30.83 | | | | | | | | | | | | | | | | all_1207_2, simplifying with (15), (637), (640)
% 220.85/30.83 | | | | | | | | | | | | | | | | gives:
% 220.85/30.83 | | | | | | | | | | | | | | | | (664) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_674_0,
% 220.85/30.83 | | | | | | | | | | | | | | | | all_1207_2, v_L) = v0) | ! [v0: $i] : ! [v1:
% 220.85/30.83 | | | | | | | | | | | | | | | | $i] : ( ~
% 220.85/30.83 | | | | | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.83 | | | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) =
% 220.85/30.83 | | | | | | | | | | | | | | | | v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: any] :
% 220.85/30.83 | | | | | | | | | | | | | | | | ? [v4: any] :
% 220.85/30.83 | | | | | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.83 | | | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_1207_3,
% 220.85/30.83 | | | | | | | | | | | | | | | | v0) = v2 & c_member(all_674_0, v2, v_L) = v3
% 220.85/30.83 | | | | | | | | | | | | | | | | & c_member(all_674_0, v1, v_L) = v4 & $i(v2) &
% 220.85/30.83 | | | | | | | | | | | | | | | | ( ~ (v3 = 0) | v4 = 0)))
% 220.85/30.83 | | | | | | | | | | | | | | | |
% 220.85/30.83 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (fact_antisymD) with v_x, all_870_9,
% 220.85/30.83 | | | | | | | | | | | | | | | | v_L, tc_Arrow__Order__Mirabelle_Oalt, all_625_1,
% 220.85/30.83 | | | | | | | | | | | | | | | | all_1218_1, simplifying with (14), (16), (22),
% 220.85/30.83 | | | | | | | | | | | | | | | | (342), (644), (657), (662) gives:
% 220.85/30.83 | | | | | | | | | | | | | | | | (665) all_870_9 = v_x | ? [v0: any] : ? [v1: $i] : ?
% 220.85/30.83 | | | | | | | | | | | | | | | | [v2: any] :
% 220.85/30.83 | | | | | | | | | | | | | | | | (c_Relation_Oantisym(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.83 | | | | | | | | | | | | | | | | v_L) = v0 &
% 220.85/30.83 | | | | | | | | | | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.83 | | | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9,
% 220.85/30.83 | | | | | | | | | | | | | | | | v_x) = v1 & c_member(all_625_1, v1, v_L) = v2
% 220.85/30.83 | | | | | | | | | | | | | | | | & $i(v1) & ( ~ (v2 = 0) | ~ (v0 = 0)))
% 220.85/30.83 | | | | | | | | | | | | | | | |
% 220.85/30.83 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (627) with all_1207_3, all_1207_1,
% 220.85/30.83 | | | | | | | | | | | | | | | | simplifying with (637), (641) gives:
% 220.85/30.83 | | | | | | | | | | | | | | | | (666) ? [v0: $i] : ? [v1: any] : ? [v2: any] :
% 220.85/30.83 | | | | | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.83 | | | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y,
% 220.85/30.83 | | | | | | | | | | | | | | | | all_1207_3) = v0 & c_member(all_674_0, v0,
% 220.85/30.83 | | | | | | | | | | | | | | | | v_L) = v1 & c_member(all_674_0, all_1207_1,
% 220.85/30.83 | | | | | | | | | | | | | | | | v_L) = v2 & $i(v0) & ( ~ (v1 = 0) | v2 = 0))
% 220.85/30.83 | | | | | | | | | | | | | | | |
% 220.85/30.83 | | | | | | | | | | | | | | | | DELTA: instantiating (663) with fresh symbols all_1277_0,
% 220.85/30.83 | | | | | | | | | | | | | | | | all_1277_1, all_1277_2 gives:
% 220.85/30.83 | | | | | | | | | | | | | | | | (667) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.83 | | | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8,
% 220.85/30.83 | | | | | | | | | | | | | | | | all_1207_3) = all_1277_2 & c_member(all_674_0,
% 220.85/30.83 | | | | | | | | | | | | | | | | all_1277_2, v_L) = all_1277_1 &
% 220.85/30.83 | | | | | | | | | | | | | | | | c_member(all_674_0, all_1207_2, v_L) = all_1277_0
% 220.85/30.83 | | | | | | | | | | | | | | | | & $i(all_1277_2) & ( ~ (all_1277_1 = 0) |
% 220.85/30.83 | | | | | | | | | | | | | | | | all_1277_0 = 0)
% 220.85/30.83 | | | | | | | | | | | | | | | |
% 220.85/30.83 | | | | | | | | | | | | | | | | ALPHA: (667) implies:
% 220.85/30.83 | | | | | | | | | | | | | | | | (668) c_member(all_674_0, all_1207_2, v_L) = all_1277_0
% 220.85/30.83 | | | | | | | | | | | | | | | |
% 220.85/30.83 | | | | | | | | | | | | | | | | DELTA: instantiating (666) with fresh symbols all_1283_0,
% 220.85/30.83 | | | | | | | | | | | | | | | | all_1283_1, all_1283_2 gives:
% 220.85/30.83 | | | | | | | | | | | | | | | | (669) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.83 | | | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y,
% 220.85/30.83 | | | | | | | | | | | | | | | | all_1207_3) = all_1283_2 & c_member(all_674_0,
% 220.85/30.83 | | | | | | | | | | | | | | | | all_1283_2, v_L) = all_1283_1 &
% 220.85/30.83 | | | | | | | | | | | | | | | | c_member(all_674_0, all_1207_1, v_L) = all_1283_0
% 220.85/30.83 | | | | | | | | | | | | | | | | & $i(all_1283_2) & ( ~ (all_1283_1 = 0) |
% 220.85/30.83 | | | | | | | | | | | | | | | | all_1283_0 = 0)
% 220.85/30.83 | | | | | | | | | | | | | | | |
% 220.85/30.83 | | | | | | | | | | | | | | | | ALPHA: (669) implies:
% 220.85/30.83 | | | | | | | | | | | | | | | | (670) c_member(all_674_0, all_1207_1, v_L) = all_1283_0
% 220.85/30.83 | | | | | | | | | | | | | | | | (671) c_member(all_674_0, all_1283_2, v_L) = all_1283_1
% 220.85/30.83 | | | | | | | | | | | | | | | | (672) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.83 | | | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y,
% 220.85/30.83 | | | | | | | | | | | | | | | | all_1207_3) = all_1283_2
% 220.85/30.83 | | | | | | | | | | | | | | | | (673) ~ (all_1283_1 = 0) | all_1283_0 = 0
% 220.85/30.83 | | | | | | | | | | | | | | | |
% 220.85/30.83 | | | | | | | | | | | | | | | | REDUCE: (84), (671) imply:
% 220.85/30.83 | | | | | | | | | | | | | | | | (674) c_member(all_625_1, all_1283_2, v_L) = all_1283_1
% 220.85/30.83 | | | | | | | | | | | | | | | |
% 220.85/30.83 | | | | | | | | | | | | | | | | REDUCE: (84), (670) imply:
% 220.85/30.83 | | | | | | | | | | | | | | | | (675) c_member(all_625_1, all_1207_1, v_L) = all_1283_0
% 220.85/30.83 | | | | | | | | | | | | | | | |
% 220.85/30.83 | | | | | | | | | | | | | | | | REDUCE: (84), (668) imply:
% 220.85/30.83 | | | | | | | | | | | | | | | | (676) c_member(all_625_1, all_1207_2, v_L) = all_1277_0
% 220.85/30.83 | | | | | | | | | | | | | | | |
% 220.85/30.83 | | | | | | | | | | | | | | | | BETA: splitting (665) gives:
% 220.85/30.83 | | | | | | | | | | | | | | | |
% 220.85/30.83 | | | | | | | | | | | | | | | | Case 1:
% 220.85/30.83 | | | | | | | | | | | | | | | | |
% 220.85/30.83 | | | | | | | | | | | | | | | | | (677) all_870_9 = v_x
% 220.85/30.83 | | | | | | | | | | | | | | | | |
% 220.85/30.83 | | | | | | | | | | | | | | | | | REDUCE: (556), (677) imply:
% 220.85/30.83 | | | | | | | | | | | | | | | | | (678) $false
% 220.85/30.83 | | | | | | | | | | | | | | | | |
% 220.85/30.83 | | | | | | | | | | | | | | | | | CLOSE: (678) is inconsistent.
% 220.85/30.83 | | | | | | | | | | | | | | | | |
% 220.85/30.83 | | | | | | | | | | | | | | | | Case 2:
% 220.85/30.83 | | | | | | | | | | | | | | | | |
% 220.85/30.83 | | | | | | | | | | | | | | | | |
% 220.85/30.83 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (19) with 0, all_1277_0, v_L,
% 220.85/30.83 | | | | | | | | | | | | | | | | | all_1207_2, all_625_1, simplifying with (643),
% 220.85/30.83 | | | | | | | | | | | | | | | | | (676) gives:
% 220.85/30.83 | | | | | | | | | | | | | | | | | (679) all_1277_0 = 0
% 220.85/30.83 | | | | | | | | | | | | | | | | |
% 220.85/30.83 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (19) with all_1207_0, all_1283_0,
% 220.85/30.83 | | | | | | | | | | | | | | | | | v_L, all_1207_1, all_625_1, simplifying with
% 220.85/30.83 | | | | | | | | | | | | | | | | | (642), (675) gives:
% 220.85/30.83 | | | | | | | | | | | | | | | | | (680) all_1283_0 = all_1207_0
% 220.85/30.83 | | | | | | | | | | | | | | | | |
% 220.85/30.83 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with all_1207_2, all_1283_2,
% 220.85/30.83 | | | | | | | | | | | | | | | | | all_1207_3, v_y, tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.83 | | | | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with
% 220.85/30.83 | | | | | | | | | | | | | | | | | (640), (672) gives:
% 220.85/30.83 | | | | | | | | | | | | | | | | | (681) all_1283_2 = all_1207_2
% 220.85/30.83 | | | | | | | | | | | | | | | | |
% 220.85/30.83 | | | | | | | | | | | | | | | | | REDUCE: (674), (681) imply:
% 220.85/30.83 | | | | | | | | | | | | | | | | | (682) c_member(all_625_1, all_1207_2, v_L) = all_1283_1
% 220.85/30.83 | | | | | | | | | | | | | | | | |
% 220.85/30.83 | | | | | | | | | | | | | | | | | BETA: splitting (673) gives:
% 220.85/30.83 | | | | | | | | | | | | | | | | |
% 220.85/30.83 | | | | | | | | | | | | | | | | | Case 1:
% 220.85/30.83 | | | | | | | | | | | | | | | | | |
% 220.85/30.83 | | | | | | | | | | | | | | | | | | (683) ~ (all_1283_1 = 0)
% 220.85/30.83 | | | | | | | | | | | | | | | | | |
% 220.85/30.83 | | | | | | | | | | | | | | | | | | BETA: splitting (664) gives:
% 220.85/30.83 | | | | | | | | | | | | | | | | | |
% 220.85/30.83 | | | | | | | | | | | | | | | | | | Case 1:
% 220.85/30.83 | | | | | | | | | | | | | | | | | | |
% 220.85/30.83 | | | | | | | | | | | | | | | | | | | (684) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_674_0,
% 220.85/30.83 | | | | | | | | | | | | | | | | | | | all_1207_2, v_L) = v0)
% 220.85/30.83 | | | | | | | | | | | | | | | | | | |
% 220.85/30.83 | | | | | | | | | | | | | | | | | | | DELTA: instantiating (684) with fresh symbol all_1360_0
% 220.85/30.83 | | | | | | | | | | | | | | | | | | | gives:
% 220.85/30.83 | | | | | | | | | | | | | | | | | | | (685) ~ (all_1360_0 = 0) & c_member(all_674_0,
% 220.85/30.83 | | | | | | | | | | | | | | | | | | | all_1207_2, v_L) = all_1360_0
% 220.85/30.83 | | | | | | | | | | | | | | | | | | |
% 220.85/30.83 | | | | | | | | | | | | | | | | | | | ALPHA: (685) implies:
% 220.85/30.83 | | | | | | | | | | | | | | | | | | | (686) c_member(all_674_0, all_1207_2, v_L) = all_1360_0
% 220.85/30.83 | | | | | | | | | | | | | | | | | | |
% 220.85/30.83 | | | | | | | | | | | | | | | | | | | REDUCE: (84), (686) imply:
% 220.85/30.83 | | | | | | | | | | | | | | | | | | | (687) c_member(all_625_1, all_1207_2, v_L) = all_1360_0
% 220.85/30.83 | | | | | | | | | | | | | | | | | | |
% 220.85/30.83 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (19) with 0, all_1360_0, v_L,
% 220.85/30.83 | | | | | | | | | | | | | | | | | | | all_1207_2, all_625_1, simplifying with (643),
% 220.85/30.83 | | | | | | | | | | | | | | | | | | | (687) gives:
% 220.85/30.83 | | | | | | | | | | | | | | | | | | | (688) all_1360_0 = 0
% 220.85/30.83 | | | | | | | | | | | | | | | | | | |
% 220.85/30.83 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (19) with all_1283_1, all_1360_0,
% 220.85/30.83 | | | | | | | | | | | | | | | | | | | v_L, all_1207_2, all_625_1, simplifying with
% 220.85/30.83 | | | | | | | | | | | | | | | | | | | (682), (687) gives:
% 220.85/30.83 | | | | | | | | | | | | | | | | | | | (689) all_1360_0 = all_1283_1
% 220.85/30.83 | | | | | | | | | | | | | | | | | | |
% 220.85/30.83 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (688), (689) imply:
% 220.85/30.83 | | | | | | | | | | | | | | | | | | | (690) all_1283_1 = 0
% 220.85/30.83 | | | | | | | | | | | | | | | | | | |
% 220.85/30.83 | | | | | | | | | | | | | | | | | | | SIMP: (690) implies:
% 220.85/30.83 | | | | | | | | | | | | | | | | | | | (691) all_1283_1 = 0
% 220.85/30.83 | | | | | | | | | | | | | | | | | | |
% 220.85/30.83 | | | | | | | | | | | | | | | | | | | REDUCE: (683), (691) imply:
% 220.85/30.83 | | | | | | | | | | | | | | | | | | | (692) $false
% 220.85/30.83 | | | | | | | | | | | | | | | | | | |
% 220.85/30.83 | | | | | | | | | | | | | | | | | | | CLOSE: (692) is inconsistent.
% 220.85/30.83 | | | | | | | | | | | | | | | | | | |
% 220.85/30.83 | | | | | | | | | | | | | | | | | | Case 2:
% 220.85/30.83 | | | | | | | | | | | | | | | | | | |
% 220.85/30.83 | | | | | | | | | | | | | | | | | | | (693) ! [v0: $i] : ! [v1: $i] : ( ~
% 220.85/30.83 | | | | | | | | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.83 | | | | | | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) =
% 220.85/30.83 | | | | | | | | | | | | | | | | | | | v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: any] :
% 220.85/30.83 | | | | | | | | | | | | | | | | | | | ? [v4: any] :
% 220.85/30.83 | | | | | | | | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.83 | | | | | | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_1207_3,
% 220.85/30.83 | | | | | | | | | | | | | | | | | | | v0) = v2 & c_member(all_674_0, v2, v_L) = v3
% 220.85/30.83 | | | | | | | | | | | | | | | | | | | & c_member(all_674_0, v1, v_L) = v4 & $i(v2) &
% 220.85/30.83 | | | | | | | | | | | | | | | | | | | ( ~ (v3 = 0) | v4 = 0)))
% 220.85/30.83 | | | | | | | | | | | | | | | | | | |
% 220.85/30.83 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (693) with all_1207_3, all_1207_2,
% 220.85/30.83 | | | | | | | | | | | | | | | | | | | simplifying with (637), (640) gives:
% 220.85/30.83 | | | | | | | | | | | | | | | | | | | (694) ? [v0: $i] : ? [v1: any] : ? [v2: any] :
% 220.85/30.83 | | | | | | | | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.83 | | | | | | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_1207_3,
% 220.85/30.83 | | | | | | | | | | | | | | | | | | | all_1207_3) = v0 & c_member(all_674_0, v0,
% 220.85/30.83 | | | | | | | | | | | | | | | | | | | v_L) = v1 & c_member(all_674_0, all_1207_2,
% 220.85/30.83 | | | | | | | | | | | | | | | | | | | v_L) = v2 & $i(v0) & ( ~ (v1 = 0) | v2 = 0))
% 220.85/30.83 | | | | | | | | | | | | | | | | | | |
% 220.85/30.83 | | | | | | | | | | | | | | | | | | | DELTA: instantiating (694) with fresh symbols all_1361_0,
% 220.85/30.83 | | | | | | | | | | | | | | | | | | | all_1361_1, all_1361_2 gives:
% 220.85/30.83 | | | | | | | | | | | | | | | | | | | (695) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.83 | | | | | | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_1207_3,
% 220.85/30.83 | | | | | | | | | | | | | | | | | | | all_1207_3) = all_1361_2 & c_member(all_674_0,
% 220.85/30.83 | | | | | | | | | | | | | | | | | | | all_1361_2, v_L) = all_1361_1 &
% 220.85/30.83 | | | | | | | | | | | | | | | | | | | c_member(all_674_0, all_1207_2, v_L) = all_1361_0
% 220.85/30.83 | | | | | | | | | | | | | | | | | | | & $i(all_1361_2) & ( ~ (all_1361_1 = 0) |
% 220.85/30.83 | | | | | | | | | | | | | | | | | | | all_1361_0 = 0)
% 220.85/30.83 | | | | | | | | | | | | | | | | | | |
% 220.85/30.83 | | | | | | | | | | | | | | | | | | | ALPHA: (695) implies:
% 220.85/30.83 | | | | | | | | | | | | | | | | | | | (696) c_member(all_674_0, all_1207_2, v_L) = all_1361_0
% 220.85/30.83 | | | | | | | | | | | | | | | | | | |
% 220.85/30.83 | | | | | | | | | | | | | | | | | | | REDUCE: (84), (696) imply:
% 220.85/30.83 | | | | | | | | | | | | | | | | | | | (697) c_member(all_625_1, all_1207_2, v_L) = all_1361_0
% 220.85/30.83 | | | | | | | | | | | | | | | | | | |
% 220.85/30.83 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (19) with 0, all_1361_0, v_L,
% 220.85/30.83 | | | | | | | | | | | | | | | | | | | all_1207_2, all_625_1, simplifying with (643),
% 220.85/30.83 | | | | | | | | | | | | | | | | | | | (697) gives:
% 220.85/30.83 | | | | | | | | | | | | | | | | | | | (698) all_1361_0 = 0
% 220.85/30.83 | | | | | | | | | | | | | | | | | | |
% 220.85/30.83 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (19) with all_1283_1, all_1361_0,
% 220.85/30.83 | | | | | | | | | | | | | | | | | | | v_L, all_1207_2, all_625_1, simplifying with
% 220.85/30.83 | | | | | | | | | | | | | | | | | | | (682), (697) gives:
% 220.85/30.83 | | | | | | | | | | | | | | | | | | | (699) all_1361_0 = all_1283_1
% 220.85/30.83 | | | | | | | | | | | | | | | | | | |
% 220.85/30.83 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (698), (699) imply:
% 220.85/30.83 | | | | | | | | | | | | | | | | | | | (700) all_1283_1 = 0
% 220.85/30.83 | | | | | | | | | | | | | | | | | | |
% 220.85/30.83 | | | | | | | | | | | | | | | | | | | REDUCE: (683), (700) imply:
% 220.85/30.83 | | | | | | | | | | | | | | | | | | | (701) $false
% 220.85/30.83 | | | | | | | | | | | | | | | | | | |
% 220.85/30.83 | | | | | | | | | | | | | | | | | | | CLOSE: (701) is inconsistent.
% 220.85/30.83 | | | | | | | | | | | | | | | | | | |
% 220.85/30.83 | | | | | | | | | | | | | | | | | | End of split
% 220.85/30.83 | | | | | | | | | | | | | | | | | |
% 220.85/30.83 | | | | | | | | | | | | | | | | | Case 2:
% 220.85/30.83 | | | | | | | | | | | | | | | | | |
% 220.85/30.83 | | | | | | | | | | | | | | | | | | (702) all_1283_0 = 0
% 220.85/30.83 | | | | | | | | | | | | | | | | | |
% 220.85/30.83 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (680), (702) imply:
% 220.85/30.83 | | | | | | | | | | | | | | | | | | (703) all_1207_0 = 0
% 220.85/30.83 | | | | | | | | | | | | | | | | | |
% 220.85/30.83 | | | | | | | | | | | | | | | | | | REDUCE: (636), (703) imply:
% 220.85/30.84 | | | | | | | | | | | | | | | | | | (704) $false
% 220.85/30.84 | | | | | | | | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | | | | | | | | | CLOSE: (704) is inconsistent.
% 220.85/30.84 | | | | | | | | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | | | | | | | | End of split
% 220.85/30.84 | | | | | | | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | | | | | | | End of split
% 220.85/30.84 | | | | | | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | | | | | | Case 2:
% 220.85/30.84 | | | | | | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | | | | | | | (705) all_1218_2 = 0
% 220.85/30.84 | | | | | | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | | | | | | | REDUCE: (569), (617) imply:
% 220.85/30.84 | | | | | | | | | | | | | | | | (706) $false
% 220.85/30.84 | | | | | | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | | | | | | | CLOSE: (706) is inconsistent.
% 220.85/30.84 | | | | | | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | | | | | | End of split
% 220.85/30.84 | | | | | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | | | | | End of split
% 220.85/30.84 | | | | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | | | | Case 2:
% 220.85/30.84 | | | | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | | | | | REDUCE: (569), (617) imply:
% 220.85/30.84 | | | | | | | | | | | | | | (707) $false
% 220.85/30.84 | | | | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | | | | | CLOSE: (707) is inconsistent.
% 220.85/30.84 | | | | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | | | | End of split
% 220.85/30.84 | | | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | | | End of split
% 220.85/30.84 | | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | | Case 2:
% 220.85/30.84 | | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | | | REDUCE: (569), (617) imply:
% 220.85/30.84 | | | | | | | | | | | | (708) $false
% 220.85/30.84 | | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | | | CLOSE: (708) is inconsistent.
% 220.85/30.84 | | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | | End of split
% 220.85/30.84 | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | Case 2:
% 220.85/30.84 | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | | GROUND_INST: instantiating (572) with all_870_8, all_870_7,
% 220.85/30.84 | | | | | | | | | | | simplifying with (343), (354) gives:
% 220.85/30.84 | | | | | | | | | | | (709) ? [v0: $i] : ? [v1: any] : ? [v2: any] :
% 220.85/30.84 | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.84 | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8,
% 220.85/30.84 | | | | | | | | | | | all_870_8) = v0 & c_member(all_674_0, v0, v_L)
% 220.85/30.84 | | | | | | | | | | | = v1 & c_member(all_674_0, all_870_7, v_L) = v2
% 220.85/30.84 | | | | | | | | | | | & $i(v0) & ( ~ (v1 = 0) | v2 = 0))
% 220.85/30.84 | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | | DELTA: instantiating (709) with fresh symbols all_1165_0,
% 220.85/30.84 | | | | | | | | | | | all_1165_1, all_1165_2 gives:
% 220.85/30.84 | | | | | | | | | | | (710) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.84 | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8,
% 220.85/30.84 | | | | | | | | | | | all_870_8) = all_1165_2 & c_member(all_674_0,
% 220.85/30.84 | | | | | | | | | | | all_1165_2, v_L) = all_1165_1 &
% 220.85/30.84 | | | | | | | | | | | c_member(all_674_0, all_870_7, v_L) = all_1165_0 &
% 220.85/30.84 | | | | | | | | | | | $i(all_1165_2) & ( ~ (all_1165_1 = 0) | all_1165_0
% 220.85/30.84 | | | | | | | | | | | = 0)
% 220.85/30.84 | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | | ALPHA: (710) implies:
% 220.85/30.84 | | | | | | | | | | | (711) c_member(all_674_0, all_870_7, v_L) = all_1165_0
% 220.85/30.84 | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | | REDUCE: (84), (711) imply:
% 220.85/30.84 | | | | | | | | | | | (712) c_member(all_625_1, all_870_7, v_L) = all_1165_0
% 220.85/30.84 | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | | GROUND_INST: instantiating (19) with all_870_6, all_1165_0,
% 220.85/30.84 | | | | | | | | | | | v_L, all_870_7, all_625_1, simplifying with (360),
% 220.85/30.84 | | | | | | | | | | | (712) gives:
% 220.85/30.84 | | | | | | | | | | | (713) all_1165_0 = all_870_6
% 220.85/30.84 | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | | BETA: splitting (369) gives:
% 220.85/30.84 | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | | Case 1:
% 220.85/30.84 | | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | | | (714) all_870_8 = all_870_9
% 220.85/30.84 | | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | | | REDUCE: (355), (714) imply:
% 220.85/30.84 | | | | | | | | | | | | (715) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.84 | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v_y)
% 220.85/30.84 | | | | | | | | | | | | = all_870_5
% 220.85/30.84 | | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | | | BETA: splitting (557) gives:
% 220.85/30.84 | | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | | | Case 1:
% 220.85/30.84 | | | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | | | | (716) all_870_2 = 0 & all_870_8 = v_x & ? [v0: $i] : ?
% 220.85/30.84 | | | | | | | | | | | | | [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 =
% 220.85/30.84 | | | | | | | | | | | | | 0) & ~ (v0 = v_x) &
% 220.85/30.84 | | | | | | | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.84 | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9,
% 220.85/30.84 | | | | | | | | | | | | | v0) = v2 &
% 220.85/30.84 | | | | | | | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.84 | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = v1
% 220.85/30.84 | | | | | | | | | | | | | & c_member(all_683_0, v2, v_L) = v3 &
% 220.85/30.84 | | | | | | | | | | | | | c_member(all_683_0, v1, v_L) = 0 & $i(v2) &
% 220.85/30.84 | | | | | | | | | | | | | $i(v1) & $i(v0))
% 220.85/30.84 | | | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | | | | ALPHA: (716) implies:
% 220.85/30.84 | | | | | | | | | | | | | (717) all_870_8 = v_x
% 220.85/30.84 | | | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | | | | COMBINE_EQS: (714), (717) imply:
% 220.85/30.84 | | | | | | | | | | | | | (718) all_870_9 = v_x
% 220.85/30.84 | | | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | | | | REDUCE: (556), (718) imply:
% 220.85/30.84 | | | | | | | | | | | | | (719) $false
% 220.85/30.84 | | | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | | | | CLOSE: (719) is inconsistent.
% 220.85/30.84 | | | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | | | Case 2:
% 220.85/30.84 | | | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | | | | ALPHA: (568) implies:
% 220.85/30.84 | | | | | | | | | | | | | (720) ? [v0: $i] : ? [v1: $i] : ? [v2: any] : ? [v3:
% 220.85/30.84 | | | | | | | | | | | | | $i] : ? [v4: any] :
% 220.85/30.84 | | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.84 | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8,
% 220.85/30.84 | | | | | | | | | | | | | v0) = v1 &
% 220.85/30.84 | | | | | | | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.84 | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9,
% 220.85/30.84 | | | | | | | | | | | | | v0) = v3 & c_member(all_683_0, v3, v_L) = v4 &
% 220.85/30.84 | | | | | | | | | | | | | c_member(all_683_0, v1, v_L) = v2 & $i(v3) &
% 220.85/30.84 | | | | | | | | | | | | | $i(v1) & $i(v0) & ((v2 = 0 & ~ (v4 = 0) & ~
% 220.85/30.84 | | | | | | | | | | | | | (v0 = v_x)) | (v0 = v_x & all_870_4 = 0 & ~
% 220.85/30.84 | | | | | | | | | | | | | (all_870_2 = 0))))
% 220.85/30.84 | | | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | | | | DELTA: instantiating (720) with fresh symbols all_1202_0,
% 220.85/30.84 | | | | | | | | | | | | | all_1202_1, all_1202_2, all_1202_3, all_1202_4
% 220.85/30.84 | | | | | | | | | | | | | gives:
% 220.85/30.84 | | | | | | | | | | | | | (721) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.84 | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8,
% 220.85/30.84 | | | | | | | | | | | | | all_1202_4) = all_1202_3 &
% 220.85/30.84 | | | | | | | | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.84 | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9,
% 220.85/30.84 | | | | | | | | | | | | | all_1202_4) = all_1202_1 & c_member(all_683_0,
% 220.85/30.84 | | | | | | | | | | | | | all_1202_1, v_L) = all_1202_0 &
% 220.85/30.84 | | | | | | | | | | | | | c_member(all_683_0, all_1202_3, v_L) = all_1202_2
% 220.85/30.84 | | | | | | | | | | | | | & $i(all_1202_1) & $i(all_1202_3) & $i(all_1202_4)
% 220.85/30.84 | | | | | | | | | | | | | & ((all_1202_2 = 0 & ~ (all_1202_0 = 0) & ~
% 220.85/30.84 | | | | | | | | | | | | | (all_1202_4 = v_x)) | (all_1202_4 = v_x &
% 220.85/30.84 | | | | | | | | | | | | | all_870_4 = 0 & ~ (all_870_2 = 0)))
% 220.85/30.84 | | | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | | | | ALPHA: (721) implies:
% 220.85/30.84 | | | | | | | | | | | | | (722) c_member(all_683_0, all_1202_3, v_L) = all_1202_2
% 220.85/30.84 | | | | | | | | | | | | | (723) c_member(all_683_0, all_1202_1, v_L) = all_1202_0
% 220.85/30.84 | | | | | | | | | | | | | (724) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.84 | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9,
% 220.85/30.84 | | | | | | | | | | | | | all_1202_4) = all_1202_1
% 220.85/30.84 | | | | | | | | | | | | | (725) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.84 | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8,
% 220.85/30.84 | | | | | | | | | | | | | all_1202_4) = all_1202_3
% 220.85/30.84 | | | | | | | | | | | | | (726) (all_1202_2 = 0 & ~ (all_1202_0 = 0) & ~
% 220.85/30.84 | | | | | | | | | | | | | (all_1202_4 = v_x)) | (all_1202_4 = v_x &
% 220.85/30.84 | | | | | | | | | | | | | all_870_4 = 0 & ~ (all_870_2 = 0))
% 220.85/30.84 | | | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | | | | REDUCE: (714), (725) imply:
% 220.85/30.84 | | | | | | | | | | | | | (727) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.84 | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9,
% 220.85/30.84 | | | | | | | | | | | | | all_1202_4) = all_1202_3
% 220.85/30.84 | | | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | | | | REDUCE: (86), (723) imply:
% 220.85/30.84 | | | | | | | | | | | | | (728) c_member(all_625_1, all_1202_1, v_L) = all_1202_0
% 220.85/30.84 | | | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | | | | REDUCE: (86), (722) imply:
% 220.85/30.84 | | | | | | | | | | | | | (729) c_member(all_625_1, all_1202_3, v_L) = all_1202_2
% 220.85/30.84 | | | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | | | | GROUND_INST: instantiating (20) with all_870_3, all_870_5, v_y,
% 220.85/30.84 | | | | | | | | | | | | | all_870_9, tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.84 | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with
% 220.85/30.84 | | | | | | | | | | | | | (353), (715) gives:
% 220.85/30.84 | | | | | | | | | | | | | (730) all_870_3 = all_870_5
% 220.85/30.84 | | | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | | | | GROUND_INST: instantiating (20) with all_1202_3, all_1202_1,
% 220.85/30.84 | | | | | | | | | | | | | all_1202_4, all_870_9,
% 220.85/30.84 | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.84 | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with
% 220.85/30.84 | | | | | | | | | | | | | (724), (727) gives:
% 220.85/30.84 | | | | | | | | | | | | | (731) all_1202_1 = all_1202_3
% 220.85/30.84 | | | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | | | | REDUCE: (728), (731) imply:
% 220.85/30.84 | | | | | | | | | | | | | (732) c_member(all_625_1, all_1202_3, v_L) = all_1202_0
% 220.85/30.84 | | | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | | | | REDUCE: (358), (730) imply:
% 220.85/30.84 | | | | | | | | | | | | | (733) c_member(all_625_1, all_870_5, v_L) = all_870_2
% 220.85/30.84 | | | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | | | | GROUND_INST: instantiating (19) with all_870_4, all_870_2, v_L,
% 220.85/30.84 | | | | | | | | | | | | | all_870_5, all_625_1, simplifying with (359),
% 220.85/30.84 | | | | | | | | | | | | | (733) gives:
% 220.85/30.84 | | | | | | | | | | | | | (734) all_870_2 = all_870_4
% 220.85/30.84 | | | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | | | | GROUND_INST: instantiating (19) with all_1202_2, all_1202_0,
% 220.85/30.84 | | | | | | | | | | | | | v_L, all_1202_3, all_625_1, simplifying with
% 220.85/30.84 | | | | | | | | | | | | | (729), (732) gives:
% 220.85/30.84 | | | | | | | | | | | | | (735) all_1202_0 = all_1202_2
% 220.85/30.84 | | | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | | | | BETA: splitting (726) gives:
% 220.85/30.84 | | | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | | | | Case 1:
% 220.85/30.84 | | | | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | | | | | (736) all_1202_2 = 0 & ~ (all_1202_0 = 0) & ~
% 220.85/30.84 | | | | | | | | | | | | | | (all_1202_4 = v_x)
% 220.85/30.84 | | | | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | | | | | ALPHA: (736) implies:
% 220.85/30.84 | | | | | | | | | | | | | | (737) all_1202_2 = 0
% 220.85/30.84 | | | | | | | | | | | | | | (738) ~ (all_1202_0 = 0)
% 220.85/30.84 | | | | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | | | | | COMBINE_EQS: (735), (737) imply:
% 220.85/30.84 | | | | | | | | | | | | | | (739) all_1202_0 = 0
% 220.85/30.84 | | | | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | | | | | REDUCE: (738), (739) imply:
% 220.85/30.84 | | | | | | | | | | | | | | (740) $false
% 220.85/30.84 | | | | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | | | | | CLOSE: (740) is inconsistent.
% 220.85/30.84 | | | | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | | | | Case 2:
% 220.85/30.84 | | | | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | | | | | (741) all_1202_4 = v_x & all_870_4 = 0 & ~ (all_870_2 =
% 220.85/30.84 | | | | | | | | | | | | | | 0)
% 220.85/30.84 | | | | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | | | | | ALPHA: (741) implies:
% 220.85/30.84 | | | | | | | | | | | | | | (742) all_870_4 = 0
% 220.85/30.84 | | | | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | | | | | COMBINE_EQS: (734), (742) imply:
% 220.85/30.84 | | | | | | | | | | | | | | (743) all_870_2 = 0
% 220.85/30.84 | | | | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | | | | | REDUCE: (564), (743) imply:
% 220.85/30.84 | | | | | | | | | | | | | | (744) $false
% 220.85/30.84 | | | | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | | | | | CLOSE: (744) is inconsistent.
% 220.85/30.84 | | | | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | | | | End of split
% 220.85/30.84 | | | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | | | End of split
% 220.85/30.84 | | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | | Case 2:
% 220.85/30.84 | | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | | | (745) ~ (all_870_8 = all_870_9)
% 220.85/30.84 | | | | | | | | | | | | (746) ? [v0: any] : ? [v1: $i] : ? [v2: any] :
% 220.85/30.84 | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.84 | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8,
% 220.85/30.84 | | | | | | | | | | | | all_870_9) = v1 & c_member(all_674_0, v1, v_L)
% 220.85/30.84 | | | | | | | | | | | | = v2 & c_member(all_674_0, all_870_7, v_L) = v0
% 220.85/30.84 | | | | | | | | | | | | & $i(v1) & (v2 = 0 | v0 = 0))
% 220.85/30.84 | | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | | | DELTA: instantiating (746) with fresh symbols all_1177_0,
% 220.85/30.84 | | | | | | | | | | | | all_1177_1, all_1177_2 gives:
% 220.85/30.84 | | | | | | | | | | | | (747) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.84 | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8,
% 220.85/30.84 | | | | | | | | | | | | all_870_9) = all_1177_1 & c_member(all_674_0,
% 220.85/30.84 | | | | | | | | | | | | all_1177_1, v_L) = all_1177_0 &
% 220.85/30.84 | | | | | | | | | | | | c_member(all_674_0, all_870_7, v_L) = all_1177_2 &
% 220.85/30.84 | | | | | | | | | | | | $i(all_1177_1) & (all_1177_0 = 0 | all_1177_2 = 0)
% 220.85/30.84 | | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | | | ALPHA: (747) implies:
% 220.85/30.84 | | | | | | | | | | | | (748) c_member(all_674_0, all_870_7, v_L) = all_1177_2
% 220.85/30.84 | | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | | | REDUCE: (84), (748) imply:
% 220.85/30.84 | | | | | | | | | | | | (749) c_member(all_625_1, all_870_7, v_L) = all_1177_2
% 220.85/30.84 | | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | | | GROUND_INST: instantiating (19) with all_870_6, all_1177_2,
% 220.85/30.84 | | | | | | | | | | | | v_L, all_870_7, all_625_1, simplifying with (360),
% 220.85/30.84 | | | | | | | | | | | | (749) gives:
% 220.85/30.84 | | | | | | | | | | | | (750) all_1177_2 = all_870_6
% 220.85/30.84 | | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | | | BETA: splitting (361) gives:
% 220.85/30.84 | | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | | | Case 1:
% 220.85/30.84 | | | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | | | | BETA: splitting (368) gives:
% 220.85/30.84 | | | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | | | | Case 1:
% 220.85/30.84 | | | | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | | | | | DELTA: instantiating (558) with fresh symbol all_1194_0
% 220.85/30.84 | | | | | | | | | | | | | | gives:
% 220.85/30.84 | | | | | | | | | | | | | | (751) ~ (all_1194_0 = 0) & c_member(all_674_0,
% 220.85/30.84 | | | | | | | | | | | | | | all_870_3, v_L) = all_1194_0
% 220.85/30.84 | | | | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | | | | | REF_CLOSE: (14), (15), (16), (19), (20), (22), (41), (84),
% 220.85/30.84 | | | | | | | | | | | | | | (86), (342), (343), (352), (358), (557), (572),
% 220.85/30.84 | | | | | | | | | | | | | | (586), (597), (598), (599), (601), (603), (745),
% 220.85/30.84 | | | | | | | | | | | | | | (751), (fact_single__valuedD) are inconsistent by
% 220.85/30.84 | | | | | | | | | | | | | | sub-proof #6.
% 220.85/30.84 | | | | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | | | | Case 2:
% 220.85/30.84 | | | | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | | | | | (752) ! [v0: $i] : ! [v1: $i] : ( ~
% 220.85/30.84 | | | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.84 | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9,
% 220.85/30.84 | | | | | | | | | | | | | | v0) = v1) | ~ $i(v0) | ? [v2: $i] : ?
% 220.85/30.84 | | | | | | | | | | | | | | [v3: any] : ? [v4: any] :
% 220.85/30.84 | | | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.84 | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) =
% 220.85/30.84 | | | | | | | | | | | | | | v2 & c_member(all_674_0, v2, v_L) = v3 &
% 220.85/30.84 | | | | | | | | | | | | | | c_member(all_674_0, v1, v_L) = v4 & $i(v2) & (
% 220.85/30.84 | | | | | | | | | | | | | | ~ (v3 = 0) | v4 = 0)))
% 220.85/30.84 | | | | | | | | | | | | | |
% 220.85/30.84 | | | | | | | | | | | | | | GROUND_INST: instantiating (752) with v_y, all_870_3,
% 220.85/30.84 | | | | | | | | | | | | | | simplifying with (15), (353) gives:
% 220.85/30.84 | | | | | | | | | | | | | | (753) ? [v0: $i] : ? [v1: any] : ? [v2: any] :
% 220.85/30.84 | | | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.84 | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v_y) =
% 220.85/30.84 | | | | | | | | | | | | | | v0 & c_member(all_674_0, v0, v_L) = v1 &
% 220.85/30.84 | | | | | | | | | | | | | | c_member(all_674_0, all_870_3, v_L) = v2 &
% 220.85/30.85 | | | | | | | | | | | | | | $i(v0) & ( ~ (v1 = 0) | v2 = 0))
% 220.85/30.85 | | | | | | | | | | | | | |
% 220.85/30.85 | | | | | | | | | | | | | | REF_CLOSE: (3), (12), (14), (15), (16), (19), (20), (22),
% 220.85/30.85 | | | | | | | | | | | | | | (41), (84), (86), (87), (342), (343), (352),
% 220.85/30.85 | | | | | | | | | | | | | | (353), (354), (358), (363), (557), (570), (572),
% 220.85/30.85 | | | | | | | | | | | | | | (586), (603), (605), (752), (753),
% 220.85/30.85 | | | | | | | | | | | | | | (fact_single__valuedD) are inconsistent by
% 220.85/30.85 | | | | | | | | | | | | | | sub-proof #4.
% 220.85/30.85 | | | | | | | | | | | | | |
% 220.85/30.85 | | | | | | | | | | | | | End of split
% 220.85/30.85 | | | | | | | | | | | | |
% 220.85/30.85 | | | | | | | | | | | | Case 2:
% 220.85/30.85 | | | | | | | | | | | | |
% 220.85/30.85 | | | | | | | | | | | | | (754) ~ (all_870_6 = 0)
% 220.85/30.85 | | | | | | | | | | | | |
% 220.85/30.85 | | | | | | | | | | | | | BETA: splitting (368) gives:
% 220.85/30.85 | | | | | | | | | | | | |
% 220.85/30.85 | | | | | | | | | | | | | Case 1:
% 220.85/30.85 | | | | | | | | | | | | | |
% 220.85/30.85 | | | | | | | | | | | | | |
% 220.85/30.85 | | | | | | | | | | | | | | DELTA: instantiating (558) with fresh symbol all_1194_0
% 220.85/30.85 | | | | | | | | | | | | | | gives:
% 220.85/30.85 | | | | | | | | | | | | | | (755) ~ (all_1194_0 = 0) & c_member(all_674_0,
% 220.85/30.85 | | | | | | | | | | | | | | all_870_3, v_L) = all_1194_0
% 220.85/30.85 | | | | | | | | | | | | | |
% 220.85/30.85 | | | | | | | | | | | | | | REF_CLOSE: (14), (15), (16), (19), (20), (22), (41), (84),
% 220.85/30.85 | | | | | | | | | | | | | | (86), (342), (343), (352), (358), (557), (572),
% 220.85/30.85 | | | | | | | | | | | | | | (586), (597), (598), (599), (601), (603), (745),
% 220.85/30.85 | | | | | | | | | | | | | | (755), (fact_single__valuedD) are inconsistent by
% 220.85/30.85 | | | | | | | | | | | | | | sub-proof #6.
% 220.85/30.85 | | | | | | | | | | | | | |
% 220.85/30.85 | | | | | | | | | | | | | Case 2:
% 220.85/30.85 | | | | | | | | | | | | | |
% 220.85/30.85 | | | | | | | | | | | | | | (756) ! [v0: $i] : ! [v1: $i] : ( ~
% 220.85/30.85 | | | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.85 | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9,
% 220.85/30.85 | | | | | | | | | | | | | | v0) = v1) | ~ $i(v0) | ? [v2: $i] : ?
% 220.85/30.85 | | | | | | | | | | | | | | [v3: any] : ? [v4: any] :
% 220.85/30.85 | | | | | | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 220.85/30.85 | | | | | | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) =
% 220.85/30.85 | | | | | | | | | | | | | | v2 & c_member(all_674_0, v2, v_L) = v3 &
% 220.85/30.85 | | | | | | | | | | | | | | c_member(all_674_0, v1, v_L) = v4 & $i(v2) & (
% 220.85/30.85 | | | | | | | | | | | | | | ~ (v3 = 0) | v4 = 0)))
% 220.85/30.85 | | | | | | | | | | | | | |
% 220.85/30.85 | | | | | | | | | | | | | | REF_CLOSE: (15), (19), (20), (41), (84), (86), (360), (369),
% 220.85/30.85 | | | | | | | | | | | | | | (556), (557), (754), (756) are inconsistent by
% 220.85/30.85 | | | | | | | | | | | | | | sub-proof #3.
% 220.85/30.85 | | | | | | | | | | | | | |
% 220.85/30.85 | | | | | | | | | | | | | End of split
% 220.85/30.85 | | | | | | | | | | | | |
% 220.85/30.85 | | | | | | | | | | | | End of split
% 220.85/30.85 | | | | | | | | | | | |
% 220.85/30.85 | | | | | | | | | | | End of split
% 220.85/30.85 | | | | | | | | | | |
% 220.85/30.85 | | | | | | | | | | End of split
% 220.85/30.85 | | | | | | | | | |
% 220.85/30.85 | | | | | | | | | End of split
% 220.85/30.85 | | | | | | | | |
% 220.85/30.85 | | | | | | | | Case 2:
% 220.85/30.85 | | | | | | | | |
% 221.40/30.85 | | | | | | | | | (757) ~ (all_870_0 = 0)
% 221.40/30.85 | | | | | | | | |
% 221.40/30.85 | | | | | | | | | REF_CLOSE: (12), (14), (16), (19), (20), (22), (41), (84),
% 221.40/30.85 | | | | | | | | | (86), (342), (343), (353), (354), (355), (357),
% 221.40/30.85 | | | | | | | | | (358), (359), (360), (365), (367), (368), (370),
% 221.40/30.85 | | | | | | | | | (371), (557), (586), (592), (757), (fact_transD)
% 221.40/30.85 | | | | | | | | | are inconsistent by sub-proof #2.
% 221.40/30.85 | | | | | | | | |
% 221.40/30.85 | | | | | | | | End of split
% 221.40/30.85 | | | | | | | |
% 221.40/30.85 | | | | | | | End of split
% 221.40/30.85 | | | | | | |
% 221.40/30.85 | | | | | | Case 2:
% 221.40/30.85 | | | | | | |
% 221.40/30.85 | | | | | | | (758) all_1158_0 = 0
% 221.40/30.85 | | | | | | |
% 221.40/30.85 | | | | | | | COMBINE_EQS: (581), (758) imply:
% 221.40/30.85 | | | | | | | (759) all_870_2 = 0
% 221.40/30.85 | | | | | | |
% 221.40/30.85 | | | | | | | REDUCE: (564), (759) imply:
% 221.40/30.85 | | | | | | | (760) $false
% 221.40/30.85 | | | | | | |
% 221.40/30.85 | | | | | | | CLOSE: (760) is inconsistent.
% 221.40/30.85 | | | | | | |
% 221.40/30.85 | | | | | | End of split
% 221.40/30.85 | | | | | |
% 221.40/30.85 | | | | | End of split
% 221.40/30.85 | | | | |
% 221.40/30.85 | | | | End of split
% 221.40/30.85 | | | |
% 221.40/30.85 | | | Case 2:
% 221.40/30.85 | | | |
% 221.40/30.85 | | | | (761) ! [v0: $i] : ! [v1: $i] : ( ~
% 221.40/30.85 | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.85 | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v0) = v1) |
% 221.40/30.85 | | | | ~ $i(v0) | ? [v2: $i] : ? [v3: any] : ? [v4: any] :
% 221.40/30.85 | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.85 | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = v2 &
% 221.40/30.85 | | | | c_member(all_674_0, v2, v_L) = v3 & c_member(all_674_0, v1,
% 221.40/30.85 | | | | v_L) = v4 & $i(v2) & ( ~ (v3 = 0) | v4 = 0)))
% 221.40/30.85 | | | |
% 221.40/30.85 | | | | GROUND_INST: instantiating (761) with v_y, all_870_3, simplifying with
% 221.40/30.85 | | | | (15), (353) gives:
% 221.40/30.85 | | | | (762) ? [v0: $i] : ? [v1: any] : ? [v2: any] :
% 221.40/30.85 | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.85 | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v_y) = v0 &
% 221.40/30.85 | | | | c_member(all_674_0, v0, v_L) = v1 & c_member(all_674_0,
% 221.40/30.85 | | | | all_870_3, v_L) = v2 & $i(v0) & ( ~ (v1 = 0) | v2 = 0))
% 221.40/30.85 | | | |
% 221.40/30.85 | | | | GROUND_INST: instantiating (761) with all_870_8, all_870_7, simplifying
% 221.40/30.85 | | | | with (343), (354) gives:
% 221.40/30.85 | | | | (763) ? [v0: $i] : ? [v1: any] : ? [v2: any] :
% 221.40/30.85 | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.85 | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, all_870_8) = v0 &
% 221.40/30.85 | | | | c_member(all_674_0, v0, v_L) = v1 & c_member(all_674_0,
% 221.40/30.85 | | | | all_870_7, v_L) = v2 & $i(v0) & ( ~ (v1 = 0) | v2 = 0))
% 221.40/30.85 | | | |
% 221.40/30.85 | | | | DELTA: instantiating (763) with fresh symbols all_1136_0, all_1136_1,
% 221.40/30.85 | | | | all_1136_2 gives:
% 221.40/30.85 | | | | (764) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.85 | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, all_870_8) = all_1136_2
% 221.40/30.85 | | | | & c_member(all_674_0, all_1136_2, v_L) = all_1136_1 &
% 221.40/30.85 | | | | c_member(all_674_0, all_870_7, v_L) = all_1136_0 &
% 221.40/30.85 | | | | $i(all_1136_2) & ( ~ (all_1136_1 = 0) | all_1136_0 = 0)
% 221.40/30.85 | | | |
% 221.40/30.85 | | | | ALPHA: (764) implies:
% 221.40/30.85 | | | | (765) c_member(all_674_0, all_870_7, v_L) = all_1136_0
% 221.40/30.85 | | | | (766) c_member(all_674_0, all_1136_2, v_L) = all_1136_1
% 221.40/30.85 | | | | (767) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.85 | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, all_870_8) = all_1136_2
% 221.40/30.85 | | | | (768) ~ (all_1136_1 = 0) | all_1136_0 = 0
% 221.40/30.85 | | | |
% 221.40/30.85 | | | | DELTA: instantiating (762) with fresh symbols all_1138_0, all_1138_1,
% 221.40/30.85 | | | | all_1138_2 gives:
% 221.40/30.85 | | | | (769) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.85 | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v_y) = all_1138_2 &
% 221.40/30.85 | | | | c_member(all_674_0, all_1138_2, v_L) = all_1138_1 &
% 221.40/30.85 | | | | c_member(all_674_0, all_870_3, v_L) = all_1138_0 &
% 221.40/30.85 | | | | $i(all_1138_2) & ( ~ (all_1138_1 = 0) | all_1138_0 = 0)
% 221.40/30.85 | | | |
% 221.40/30.85 | | | | ALPHA: (769) implies:
% 221.40/30.85 | | | | (770) c_member(all_674_0, all_870_3, v_L) = all_1138_0
% 221.40/30.85 | | | |
% 221.40/30.85 | | | | REDUCE: (84), (766) imply:
% 221.40/30.85 | | | | (771) c_member(all_625_1, all_1136_2, v_L) = all_1136_1
% 221.40/30.85 | | | |
% 221.40/30.85 | | | | REDUCE: (84), (770) imply:
% 221.40/30.85 | | | | (772) c_member(all_625_1, all_870_3, v_L) = all_1138_0
% 221.40/30.85 | | | |
% 221.40/30.85 | | | | REDUCE: (84), (765) imply:
% 221.40/30.85 | | | | (773) c_member(all_625_1, all_870_7, v_L) = all_1136_0
% 221.40/30.85 | | | |
% 221.40/30.85 | | | | GROUND_INST: instantiating (19) with all_870_6, all_1136_0, v_L,
% 221.40/30.85 | | | | all_870_7, all_625_1, simplifying with (360), (773) gives:
% 221.40/30.85 | | | | (774) all_1136_0 = all_870_6
% 221.40/30.85 | | | |
% 221.40/30.85 | | | | GROUND_INST: instantiating (19) with all_870_2, all_1138_0, v_L,
% 221.40/30.85 | | | | all_870_3, all_625_1, simplifying with (358), (772) gives:
% 221.40/30.85 | | | | (775) all_1138_0 = all_870_2
% 221.40/30.85 | | | |
% 221.40/30.85 | | | | GROUND_INST: instantiating (20) with all_870_1, all_1136_2, all_870_8,
% 221.40/30.85 | | | | v_y, tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.85 | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with (352),
% 221.40/30.85 | | | | (767) gives:
% 221.40/30.85 | | | | (776) all_1136_2 = all_870_1
% 221.40/30.85 | | | |
% 221.40/30.85 | | | | REDUCE: (771), (776) imply:
% 221.40/30.85 | | | | (777) c_member(all_625_1, all_870_1, v_L) = all_1136_1
% 221.40/30.85 | | | |
% 221.40/30.85 | | | | GROUND_INST: instantiating (19) with all_870_0, all_1136_1, v_L,
% 221.40/30.85 | | | | all_870_1, all_625_1, simplifying with (357), (777) gives:
% 221.40/30.85 | | | | (778) all_1136_1 = all_870_0
% 221.40/30.85 | | | |
% 221.40/30.85 | | | | BETA: splitting (367) gives:
% 221.40/30.85 | | | |
% 221.40/30.85 | | | | Case 1:
% 221.40/30.85 | | | | |
% 221.40/30.85 | | | | | (779) all_870_9 = v_y
% 221.40/30.85 | | | | |
% 221.40/30.85 | | | | | REDUCE: (354), (779) imply:
% 221.40/30.85 | | | | | (780) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.85 | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, all_870_8) =
% 221.40/30.85 | | | | | all_870_7
% 221.40/30.85 | | | | |
% 221.40/30.85 | | | | | BETA: splitting (557) gives:
% 221.40/30.85 | | | | |
% 221.40/30.85 | | | | | Case 1:
% 221.40/30.85 | | | | | |
% 221.40/30.85 | | | | | | (781) all_870_2 = 0 & all_870_8 = v_x & ? [v0: $i] : ? [v1: $i]
% 221.40/30.85 | | | | | | : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & ~ (v0 = v_x)
% 221.40/30.85 | | | | | | & c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.85 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v0) = v2 &
% 221.40/30.85 | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.85 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = v1 &
% 221.40/30.85 | | | | | | c_member(all_683_0, v2, v_L) = v3 & c_member(all_683_0,
% 221.40/30.85 | | | | | | v1, v_L) = 0 & $i(v2) & $i(v1) & $i(v0))
% 221.40/30.85 | | | | | |
% 221.40/30.85 | | | | | | ALPHA: (781) implies:
% 221.40/30.85 | | | | | | (782) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : (
% 221.40/30.85 | | | | | | ~ (v3 = 0) & ~ (v0 = v_x) &
% 221.40/30.85 | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.85 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v0) = v2 &
% 221.40/30.85 | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.85 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = v1 &
% 221.40/30.85 | | | | | | c_member(all_683_0, v2, v_L) = v3 & c_member(all_683_0,
% 221.40/30.85 | | | | | | v1, v_L) = 0 & $i(v2) & $i(v1) & $i(v0))
% 221.40/30.85 | | | | | |
% 221.40/30.85 | | | | | | REF_CLOSE: (19), (20), (86), (779), (782) are inconsistent by
% 221.40/30.85 | | | | | | sub-proof #8.
% 221.40/30.85 | | | | | |
% 221.40/30.85 | | | | | Case 2:
% 221.40/30.85 | | | | | |
% 221.40/30.85 | | | | | | (783) all_870_6 = 0 & ~ (all_870_8 = v_x) & ? [v0: $i] : ?
% 221.40/30.85 | | | | | | [v1: $i] : ? [v2: any] : ? [v3: $i] : ? [v4: any] :
% 221.40/30.85 | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.85 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v0) = v1 &
% 221.40/30.85 | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.85 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v0) = v3 &
% 221.40/30.85 | | | | | | c_member(all_683_0, v3, v_L) = v4 & c_member(all_683_0,
% 221.40/30.85 | | | | | | v1, v_L) = v2 & $i(v3) & $i(v1) & $i(v0) & ((v2 = 0 &
% 221.40/30.85 | | | | | | ~ (v4 = 0) & ~ (v0 = v_x)) | (v0 = v_x & all_870_4 =
% 221.40/30.85 | | | | | | 0 & ~ (all_870_2 = 0))))
% 221.40/30.85 | | | | | |
% 221.40/30.85 | | | | | | ALPHA: (783) implies:
% 221.40/30.85 | | | | | | (784) all_870_6 = 0
% 221.40/30.86 | | | | | | (785) ? [v0: $i] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ?
% 221.40/30.86 | | | | | | [v4: any] :
% 221.40/30.86 | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.86 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v0) = v1 &
% 221.40/30.86 | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.86 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v0) = v3 &
% 221.40/30.86 | | | | | | c_member(all_683_0, v3, v_L) = v4 & c_member(all_683_0,
% 221.40/30.86 | | | | | | v1, v_L) = v2 & $i(v3) & $i(v1) & $i(v0) & ((v2 = 0 &
% 221.40/30.86 | | | | | | ~ (v4 = 0) & ~ (v0 = v_x)) | (v0 = v_x & all_870_4 =
% 221.40/30.86 | | | | | | 0 & ~ (all_870_2 = 0))))
% 221.40/30.86 | | | | | |
% 221.40/30.86 | | | | | | BETA: splitting (362) gives:
% 221.40/30.86 | | | | | |
% 221.40/30.86 | | | | | | Case 1:
% 221.40/30.86 | | | | | | |
% 221.40/30.86 | | | | | | | (786) all_870_4 = 0
% 221.40/30.86 | | | | | | |
% 221.40/30.86 | | | | | | | REDUCE: (359), (786) imply:
% 221.40/30.86 | | | | | | | (787) c_member(all_625_1, all_870_5, v_L) = 0
% 221.40/30.86 | | | | | | |
% 221.40/30.86 | | | | | | | REF_CLOSE: (3), (15), (16), (19), (20), (41), (84), (86), (87),
% 221.40/30.86 | | | | | | | (342), (343), (353), (354), (355), (358), (360), (361),
% 221.40/30.86 | | | | | | | (369), (370), (372), (556), (557), (761), (787) are
% 221.40/30.86 | | | | | | | inconsistent by sub-proof #1.
% 221.40/30.86 | | | | | | |
% 221.40/30.86 | | | | | | Case 2:
% 221.40/30.86 | | | | | | |
% 221.40/30.86 | | | | | | | (788) ~ (all_870_4 = 0)
% 221.40/30.86 | | | | | | |
% 221.40/30.86 | | | | | | | REF_CLOSE: (19), (20), (41), (84), (86), (343), (352), (357),
% 221.40/30.86 | | | | | | | (360), (366), (779), (780), (784), (785), (788) are
% 221.40/30.86 | | | | | | | inconsistent by sub-proof #7.
% 221.40/30.86 | | | | | | |
% 221.40/30.86 | | | | | | End of split
% 221.40/30.86 | | | | | |
% 221.40/30.86 | | | | | End of split
% 221.40/30.86 | | | | |
% 221.40/30.86 | | | | Case 2:
% 221.40/30.86 | | | | |
% 221.40/30.86 | | | | | (789) ~ (all_870_9 = v_y)
% 221.40/30.86 | | | | | (790) ? [v0: any] : ? [v1: $i] : ? [v2: any] :
% 221.40/30.86 | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.86 | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, all_870_9) = v1 &
% 221.40/30.86 | | | | | c_member(all_674_0, v1, v_L) = v2 & c_member(all_674_0,
% 221.40/30.86 | | | | | all_870_3, v_L) = v0 & $i(v1) & (v2 = 0 | v0 = 0))
% 221.40/30.86 | | | | |
% 221.40/30.86 | | | | | DELTA: instantiating (790) with fresh symbols all_1154_0, all_1154_1,
% 221.40/30.86 | | | | | all_1154_2 gives:
% 221.40/30.86 | | | | | (791) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.86 | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, all_870_9) =
% 221.40/30.86 | | | | | all_1154_1 & c_member(all_674_0, all_1154_1, v_L) =
% 221.40/30.86 | | | | | all_1154_0 & c_member(all_674_0, all_870_3, v_L) = all_1154_2
% 221.40/30.86 | | | | | & $i(all_1154_1) & (all_1154_0 = 0 | all_1154_2 = 0)
% 221.40/30.86 | | | | |
% 221.40/30.86 | | | | | ALPHA: (791) implies:
% 221.40/30.86 | | | | | (792) c_member(all_674_0, all_870_3, v_L) = all_1154_2
% 221.40/30.86 | | | | |
% 221.40/30.86 | | | | | REDUCE: (84), (792) imply:
% 221.40/30.86 | | | | | (793) c_member(all_625_1, all_870_3, v_L) = all_1154_2
% 221.40/30.86 | | | | |
% 221.40/30.86 | | | | | GROUND_INST: instantiating (19) with all_870_2, all_1154_2, v_L,
% 221.40/30.86 | | | | | all_870_3, all_625_1, simplifying with (358), (793)
% 221.40/30.86 | | | | | gives:
% 221.40/30.86 | | | | | (794) all_1154_2 = all_870_2
% 221.40/30.86 | | | | |
% 221.40/30.86 | | | | | BETA: splitting (364) gives:
% 221.40/30.86 | | | | |
% 221.40/30.86 | | | | | Case 1:
% 221.40/30.86 | | | | | |
% 221.40/30.86 | | | | | | (795) all_870_0 = 0
% 221.40/30.86 | | | | | |
% 221.40/30.86 | | | | | | COMBINE_EQS: (778), (795) imply:
% 221.40/30.86 | | | | | | (796) all_1136_1 = 0
% 221.40/30.86 | | | | | |
% 221.40/30.86 | | | | | | REDUCE: (357), (795) imply:
% 221.40/30.86 | | | | | | (797) c_member(all_625_1, all_870_1, v_L) = 0
% 221.40/30.86 | | | | | |
% 221.40/30.86 | | | | | | BETA: splitting (768) gives:
% 221.40/30.86 | | | | | |
% 221.40/30.86 | | | | | | Case 1:
% 221.40/30.86 | | | | | | |
% 221.40/30.86 | | | | | | | (798) ~ (all_1136_1 = 0)
% 221.40/30.86 | | | | | | |
% 221.40/30.86 | | | | | | | REDUCE: (796), (798) imply:
% 221.40/30.86 | | | | | | | (799) $false
% 221.40/30.86 | | | | | | |
% 221.40/30.86 | | | | | | | CLOSE: (799) is inconsistent.
% 221.40/30.86 | | | | | | |
% 221.40/30.86 | | | | | | Case 2:
% 221.40/30.86 | | | | | | |
% 221.40/30.86 | | | | | | | (800) all_1136_0 = 0
% 221.40/30.86 | | | | | | |
% 221.40/30.86 | | | | | | | COMBINE_EQS: (774), (800) imply:
% 221.40/30.86 | | | | | | | (801) all_870_6 = 0
% 221.40/30.86 | | | | | | |
% 221.40/30.86 | | | | | | | REDUCE: (360), (801) imply:
% 221.40/30.86 | | | | | | | (802) c_member(all_625_1, all_870_7, v_L) = 0
% 221.40/30.86 | | | | | | |
% 221.40/30.86 | | | | | | | BETA: splitting (370) gives:
% 221.40/30.86 | | | | | | |
% 221.40/30.86 | | | | | | | Case 1:
% 221.40/30.86 | | | | | | | |
% 221.40/30.86 | | | | | | | | (803) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_674_0,
% 221.40/30.86 | | | | | | | | all_870_7, v_L) = v0)
% 221.40/30.86 | | | | | | | |
% 221.40/30.86 | | | | | | | | REF_CLOSE: (19), (84), (802), (803) are inconsistent by
% 221.40/30.86 | | | | | | | | sub-proof #9.
% 221.40/30.86 | | | | | | | |
% 221.40/30.86 | | | | | | | Case 2:
% 221.40/30.86 | | | | | | | |
% 221.40/30.86 | | | | | | | | (804) ! [v0: $i] : ! [v1: $i] : ( ~
% 221.40/30.86 | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.86 | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v0) =
% 221.40/30.86 | | | | | | | | v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: any] : ?
% 221.40/30.86 | | | | | | | | [v4: any] :
% 221.40/30.86 | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.86 | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v0) =
% 221.40/30.86 | | | | | | | | v2 & c_member(all_674_0, v2, v_L) = v3 &
% 221.40/30.86 | | | | | | | | c_member(all_674_0, v1, v_L) = v4 & $i(v2) & ( ~
% 221.40/30.86 | | | | | | | | (v3 = 0) | v4 = 0)))
% 221.40/30.86 | | | | | | | |
% 221.40/30.86 | | | | | | | | GROUND_INST: instantiating (804) with v_y, all_870_3,
% 221.40/30.86 | | | | | | | | simplifying with (15), (353) gives:
% 221.40/30.86 | | | | | | | | (805) ? [v0: $i] : ? [v1: any] : ? [v2: any] :
% 221.40/30.86 | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.86 | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v_y) =
% 221.40/30.86 | | | | | | | | v0 & c_member(all_674_0, v0, v_L) = v1 &
% 221.40/30.86 | | | | | | | | c_member(all_674_0, all_870_3, v_L) = v2 & $i(v0) & (
% 221.40/30.86 | | | | | | | | ~ (v1 = 0) | v2 = 0))
% 221.40/30.86 | | | | | | | |
% 221.40/30.86 | | | | | | | | GROUND_INST: instantiating (804) with all_870_8, all_870_7,
% 221.40/30.86 | | | | | | | | simplifying with (343), (354) gives:
% 221.40/30.86 | | | | | | | | (806) ? [v0: $i] : ? [v1: any] : ? [v2: any] :
% 221.40/30.86 | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.86 | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8,
% 221.40/30.86 | | | | | | | | all_870_8) = v0 & c_member(all_674_0, v0, v_L) = v1
% 221.40/30.86 | | | | | | | | & c_member(all_674_0, all_870_7, v_L) = v2 & $i(v0) &
% 221.40/30.86 | | | | | | | | ( ~ (v1 = 0) | v2 = 0))
% 221.40/30.86 | | | | | | | |
% 221.40/30.86 | | | | | | | | BETA: splitting (366) gives:
% 221.40/30.86 | | | | | | | |
% 221.40/30.86 | | | | | | | | Case 1:
% 221.40/30.86 | | | | | | | | |
% 221.40/30.86 | | | | | | | | | (807) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_674_0,
% 221.40/30.86 | | | | | | | | | all_870_1, v_L) = v0)
% 221.40/30.86 | | | | | | | | |
% 221.40/30.86 | | | | | | | | | REF_CLOSE: (19), (84), (797), (807) are inconsistent by
% 221.40/30.86 | | | | | | | | | sub-proof #12.
% 221.40/30.86 | | | | | | | | |
% 221.40/30.86 | | | | | | | | Case 2:
% 221.40/30.86 | | | | | | | | |
% 221.40/30.86 | | | | | | | | | (808) ! [v0: $i] : ! [v1: $i] : ( ~
% 221.40/30.86 | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.86 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = v1)
% 221.40/30.86 | | | | | | | | | | ~ $i(v0) | ? [v2: $i] : ? [v3: any] : ? [v4:
% 221.40/30.86 | | | | | | | | | any] :
% 221.40/30.86 | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.86 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v0)
% 221.40/30.86 | | | | | | | | | = v2 & c_member(all_674_0, v2, v_L) = v3 &
% 221.40/30.86 | | | | | | | | | c_member(all_674_0, v1, v_L) = v4 & $i(v2) & ( ~
% 221.40/30.86 | | | | | | | | | (v3 = 0) | v4 = 0)))
% 221.40/30.86 | | | | | | | | |
% 221.40/30.86 | | | | | | | | | GROUND_INST: instantiating (808) with all_870_8, all_870_1,
% 221.40/30.86 | | | | | | | | | simplifying with (343), (352) gives:
% 221.40/30.86 | | | | | | | | | (809) ? [v0: $i] : ? [v1: any] : ? [v2: any] :
% 221.40/30.86 | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.86 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8,
% 221.40/30.86 | | | | | | | | | all_870_8) = v0 & c_member(all_674_0, v0, v_L) =
% 221.40/30.86 | | | | | | | | | v1 & c_member(all_674_0, all_870_1, v_L) = v2 &
% 221.40/30.86 | | | | | | | | | $i(v0) & ( ~ (v1 = 0) | v2 = 0))
% 221.40/30.86 | | | | | | | | |
% 221.40/30.86 | | | | | | | | | DELTA: instantiating (806) with fresh symbols all_1176_0,
% 221.40/30.86 | | | | | | | | | all_1176_1, all_1176_2 gives:
% 221.40/30.86 | | | | | | | | | (810) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.86 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8,
% 221.40/30.86 | | | | | | | | | all_870_8) = all_1176_2 & c_member(all_674_0,
% 221.40/30.86 | | | | | | | | | all_1176_2, v_L) = all_1176_1 & c_member(all_674_0,
% 221.40/30.86 | | | | | | | | | all_870_7, v_L) = all_1176_0 & $i(all_1176_2) & ( ~
% 221.40/30.86 | | | | | | | | | (all_1176_1 = 0) | all_1176_0 = 0)
% 221.40/30.86 | | | | | | | | |
% 221.40/30.86 | | | | | | | | | ALPHA: (810) implies:
% 221.40/30.86 | | | | | | | | | (811) c_member(all_674_0, all_870_7, v_L) = all_1176_0
% 221.40/30.86 | | | | | | | | |
% 221.40/30.86 | | | | | | | | | DELTA: instantiating (805) with fresh symbols all_1178_0,
% 221.40/30.86 | | | | | | | | | all_1178_1, all_1178_2 gives:
% 221.40/30.86 | | | | | | | | | (812) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.86 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v_y) =
% 221.40/30.86 | | | | | | | | | all_1178_2 & c_member(all_674_0, all_1178_2, v_L) =
% 221.40/30.86 | | | | | | | | | all_1178_1 & c_member(all_674_0, all_870_3, v_L) =
% 221.40/30.86 | | | | | | | | | all_1178_0 & $i(all_1178_2) & ( ~ (all_1178_1 = 0) |
% 221.40/30.86 | | | | | | | | | all_1178_0 = 0)
% 221.40/30.86 | | | | | | | | |
% 221.40/30.86 | | | | | | | | | ALPHA: (812) implies:
% 221.40/30.86 | | | | | | | | | (813) c_member(all_674_0, all_870_3, v_L) = all_1178_0
% 221.40/30.86 | | | | | | | | | (814) c_member(all_674_0, all_1178_2, v_L) = all_1178_1
% 221.40/30.86 | | | | | | | | | (815) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.86 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v_y) =
% 221.40/30.86 | | | | | | | | | all_1178_2
% 221.40/30.86 | | | | | | | | |
% 221.40/30.86 | | | | | | | | | DELTA: instantiating (809) with fresh symbols all_1180_0,
% 221.40/30.86 | | | | | | | | | all_1180_1, all_1180_2 gives:
% 221.40/30.86 | | | | | | | | | (816) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.86 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8,
% 221.40/30.86 | | | | | | | | | all_870_8) = all_1180_2 & c_member(all_674_0,
% 221.40/30.86 | | | | | | | | | all_1180_2, v_L) = all_1180_1 & c_member(all_674_0,
% 221.40/30.86 | | | | | | | | | all_870_1, v_L) = all_1180_0 & $i(all_1180_2) & ( ~
% 221.40/30.86 | | | | | | | | | (all_1180_1 = 0) | all_1180_0 = 0)
% 221.40/30.86 | | | | | | | | |
% 221.40/30.86 | | | | | | | | | ALPHA: (816) implies:
% 221.40/30.86 | | | | | | | | | (817) c_member(all_674_0, all_870_1, v_L) = all_1180_0
% 221.40/30.86 | | | | | | | | |
% 221.40/30.86 | | | | | | | | | REDUCE: (84), (814) imply:
% 221.40/30.86 | | | | | | | | | (818) c_member(all_625_1, all_1178_2, v_L) = all_1178_1
% 221.40/30.86 | | | | | | | | |
% 221.40/30.86 | | | | | | | | | REDUCE: (84), (817) imply:
% 221.40/30.86 | | | | | | | | | (819) c_member(all_625_1, all_870_1, v_L) = all_1180_0
% 221.40/30.86 | | | | | | | | |
% 221.40/30.86 | | | | | | | | | REDUCE: (84), (813) imply:
% 221.40/30.86 | | | | | | | | | (820) c_member(all_625_1, all_870_3, v_L) = all_1178_0
% 221.40/30.86 | | | | | | | | |
% 221.40/30.86 | | | | | | | | | REDUCE: (84), (811) imply:
% 221.40/30.86 | | | | | | | | | (821) c_member(all_625_1, all_870_7, v_L) = all_1176_0
% 221.40/30.86 | | | | | | | | |
% 221.40/30.86 | | | | | | | | | GROUND_INST: instantiating (19) with 0, all_1176_0, v_L,
% 221.40/30.86 | | | | | | | | | all_870_7, all_625_1, simplifying with (802),
% 221.40/30.86 | | | | | | | | | (821) gives:
% 221.40/30.86 | | | | | | | | | (822) all_1176_0 = 0
% 221.40/30.86 | | | | | | | | |
% 221.40/30.86 | | | | | | | | | GROUND_INST: instantiating (19) with all_870_2, all_1178_0,
% 221.40/30.86 | | | | | | | | | v_L, all_870_3, all_625_1, simplifying with (358),
% 221.40/30.86 | | | | | | | | | (820) gives:
% 221.40/30.86 | | | | | | | | | (823) all_1178_0 = all_870_2
% 221.40/30.86 | | | | | | | | |
% 221.40/30.86 | | | | | | | | | GROUND_INST: instantiating (19) with 0, all_1180_0, v_L,
% 221.40/30.86 | | | | | | | | | all_870_1, all_625_1, simplifying with (797),
% 221.40/30.86 | | | | | | | | | (819) gives:
% 221.40/30.86 | | | | | | | | | (824) all_1180_0 = 0
% 221.40/30.86 | | | | | | | | |
% 221.40/30.86 | | | | | | | | | GROUND_INST: instantiating (20) with all_870_5, all_1178_2,
% 221.40/30.86 | | | | | | | | | v_y, all_870_8, tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.86 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with
% 221.40/30.86 | | | | | | | | | (355), (815) gives:
% 221.40/30.86 | | | | | | | | | (825) all_1178_2 = all_870_5
% 221.40/30.86 | | | | | | | | |
% 221.40/30.86 | | | | | | | | | REDUCE: (818), (825) imply:
% 221.40/30.86 | | | | | | | | | (826) c_member(all_625_1, all_870_5, v_L) = all_1178_1
% 221.40/30.86 | | | | | | | | |
% 221.40/30.86 | | | | | | | | | GROUND_INST: instantiating (19) with all_870_4, all_1178_1,
% 221.40/30.86 | | | | | | | | | v_L, all_870_5, all_625_1, simplifying with (359),
% 221.40/30.86 | | | | | | | | | (826) gives:
% 221.40/30.86 | | | | | | | | | (827) all_1178_1 = all_870_4
% 221.40/30.86 | | | | | | | | |
% 221.40/30.86 | | | | | | | | | BETA: splitting (362) gives:
% 221.40/30.86 | | | | | | | | |
% 221.40/30.86 | | | | | | | | | Case 1:
% 221.40/30.86 | | | | | | | | | |
% 221.40/30.86 | | | | | | | | | | (828) all_870_4 = 0
% 221.40/30.86 | | | | | | | | | |
% 221.40/30.86 | | | | | | | | | | REDUCE: (359), (828) imply:
% 221.40/30.86 | | | | | | | | | | (829) c_member(all_625_1, all_870_5, v_L) = 0
% 221.40/30.86 | | | | | | | | | |
% 221.40/30.86 | | | | | | | | | | REF_CLOSE: (3), (15), (16), (19), (20), (41), (84), (86),
% 221.40/30.86 | | | | | | | | | | (87), (342), (343), (353), (354), (355), (358),
% 221.40/30.86 | | | | | | | | | | (360), (361), (369), (370), (372), (556), (557),
% 221.40/30.86 | | | | | | | | | | (761), (829) are inconsistent by sub-proof #1.
% 221.40/30.86 | | | | | | | | | |
% 221.40/30.86 | | | | | | | | | Case 2:
% 221.40/30.86 | | | | | | | | | |
% 221.40/30.86 | | | | | | | | | | (830) ~ (all_870_4 = 0)
% 221.40/30.86 | | | | | | | | | |
% 221.40/30.87 | | | | | | | | | | REF_CLOSE: (3), (12), (14), (15), (16), (19), (20), (22),
% 221.40/30.87 | | | | | | | | | | (41), (84), (86), (87), (342), (343), (352),
% 221.40/30.87 | | | | | | | | | | (353), (354), (358), (363), (557), (761), (762),
% 221.40/30.87 | | | | | | | | | | (797), (802), (804), (808), (830),
% 221.40/30.87 | | | | | | | | | | (fact_single__valuedD) are inconsistent by
% 221.40/30.87 | | | | | | | | | | sub-proof #4.
% 221.40/30.87 | | | | | | | | | |
% 221.40/30.87 | | | | | | | | | End of split
% 221.40/30.87 | | | | | | | | |
% 221.40/30.87 | | | | | | | | End of split
% 221.40/30.87 | | | | | | | |
% 221.40/30.87 | | | | | | | End of split
% 221.40/30.87 | | | | | | |
% 221.40/30.87 | | | | | | End of split
% 221.40/30.87 | | | | | |
% 221.40/30.87 | | | | | Case 2:
% 221.40/30.87 | | | | | |
% 221.40/30.87 | | | | | | (831) ~ (all_870_0 = 0)
% 221.40/30.87 | | | | | |
% 221.40/30.87 | | | | | | BETA: splitting (370) gives:
% 221.40/30.87 | | | | | |
% 221.40/30.87 | | | | | | Case 1:
% 221.40/30.87 | | | | | | |
% 221.40/30.87 | | | | | | | (832) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_674_0,
% 221.40/30.87 | | | | | | | all_870_7, v_L) = v0)
% 221.40/30.87 | | | | | | |
% 221.40/30.87 | | | | | | | DELTA: instantiating (832) with fresh symbol all_1179_0 gives:
% 221.40/30.87 | | | | | | | (833) ~ (all_1179_0 = 0) & c_member(all_674_0, all_870_7, v_L)
% 221.40/30.87 | | | | | | | = all_1179_0
% 221.40/30.87 | | | | | | |
% 221.40/30.87 | | | | | | | ALPHA: (833) implies:
% 221.40/30.87 | | | | | | | (834) ~ (all_1179_0 = 0)
% 221.40/30.87 | | | | | | | (835) c_member(all_674_0, all_870_7, v_L) = all_1179_0
% 221.40/30.87 | | | | | | |
% 221.40/30.87 | | | | | | | REDUCE: (84), (835) imply:
% 221.40/30.87 | | | | | | | (836) c_member(all_625_1, all_870_7, v_L) = all_1179_0
% 221.40/30.87 | | | | | | |
% 221.40/30.87 | | | | | | | GROUND_INST: instantiating (19) with all_870_6, all_1179_0, v_L,
% 221.40/30.87 | | | | | | | all_870_7, all_625_1, simplifying with (360), (836)
% 221.40/30.87 | | | | | | | gives:
% 221.40/30.87 | | | | | | | (837) all_1179_0 = all_870_6
% 221.40/30.87 | | | | | | |
% 221.40/30.87 | | | | | | | REDUCE: (834), (837) imply:
% 221.40/30.87 | | | | | | | (838) ~ (all_870_6 = 0)
% 221.40/30.87 | | | | | | |
% 221.40/30.87 | | | | | | | REF_CLOSE: (15), (19), (20), (41), (84), (86), (360), (369),
% 221.40/30.87 | | | | | | | (556), (557), (761), (838) are inconsistent by
% 221.40/30.87 | | | | | | | sub-proof #3.
% 221.40/30.87 | | | | | | |
% 221.40/30.87 | | | | | | Case 2:
% 221.40/30.87 | | | | | | |
% 221.40/30.87 | | | | | | | (839) ! [v0: $i] : ! [v1: $i] : ( ~
% 221.40/30.87 | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.87 | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v0) =
% 221.40/30.87 | | | | | | | v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: any] : ?
% 221.40/30.87 | | | | | | | [v4: any] :
% 221.40/30.87 | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.87 | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v0) =
% 221.40/30.87 | | | | | | | v2 & c_member(all_674_0, v2, v_L) = v3 &
% 221.40/30.87 | | | | | | | c_member(all_674_0, v1, v_L) = v4 & $i(v2) & ( ~ (v3
% 221.40/30.87 | | | | | | | = 0) | v4 = 0)))
% 221.40/30.87 | | | | | | |
% 221.40/30.87 | | | | | | | GROUND_INST: instantiating (839) with all_870_8, all_870_7,
% 221.40/30.87 | | | | | | | simplifying with (343), (354) gives:
% 221.40/30.87 | | | | | | | (840) ? [v0: $i] : ? [v1: any] : ? [v2: any] :
% 221.40/30.87 | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.87 | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8,
% 221.40/30.87 | | | | | | | all_870_8) = v0 & c_member(all_674_0, v0, v_L) = v1 &
% 221.40/30.87 | | | | | | | c_member(all_674_0, all_870_7, v_L) = v2 & $i(v0) & ( ~
% 221.40/30.87 | | | | | | | (v1 = 0) | v2 = 0))
% 221.40/30.87 | | | | | | |
% 221.40/30.87 | | | | | | | DELTA: instantiating (840) with fresh symbols all_1180_0,
% 221.40/30.87 | | | | | | | all_1180_1, all_1180_2 gives:
% 221.40/30.87 | | | | | | | (841) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.87 | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, all_870_8)
% 221.40/30.87 | | | | | | | = all_1180_2 & c_member(all_674_0, all_1180_2, v_L) =
% 221.40/30.87 | | | | | | | all_1180_1 & c_member(all_674_0, all_870_7, v_L) =
% 221.40/30.87 | | | | | | | all_1180_0 & $i(all_1180_2) & ( ~ (all_1180_1 = 0) |
% 221.40/30.87 | | | | | | | all_1180_0 = 0)
% 221.40/30.87 | | | | | | |
% 221.40/30.87 | | | | | | | ALPHA: (841) implies:
% 221.40/30.87 | | | | | | | (842) c_member(all_674_0, all_870_7, v_L) = all_1180_0
% 221.40/30.87 | | | | | | |
% 221.40/30.87 | | | | | | | REDUCE: (84), (842) imply:
% 221.40/30.87 | | | | | | | (843) c_member(all_625_1, all_870_7, v_L) = all_1180_0
% 221.40/30.87 | | | | | | |
% 221.40/30.87 | | | | | | | GROUND_INST: instantiating (19) with all_870_6, all_1180_0, v_L,
% 221.40/30.87 | | | | | | | all_870_7, all_625_1, simplifying with (360), (843)
% 221.40/30.87 | | | | | | | gives:
% 221.40/30.87 | | | | | | | (844) all_1180_0 = all_870_6
% 221.40/30.87 | | | | | | |
% 221.40/30.87 | | | | | | | BETA: splitting (362) gives:
% 221.40/30.87 | | | | | | |
% 221.40/30.87 | | | | | | | Case 1:
% 221.40/30.87 | | | | | | | |
% 221.40/30.87 | | | | | | | | (845) all_870_4 = 0
% 221.40/30.87 | | | | | | | |
% 221.40/30.87 | | | | | | | | REDUCE: (359), (845) imply:
% 221.40/30.87 | | | | | | | | (846) c_member(all_625_1, all_870_5, v_L) = 0
% 221.40/30.87 | | | | | | | |
% 221.40/30.87 | | | | | | | | REF_CLOSE: (3), (15), (16), (19), (20), (41), (84), (86), (87),
% 221.40/30.87 | | | | | | | | (342), (343), (353), (354), (355), (358), (360),
% 221.40/30.87 | | | | | | | | (361), (369), (370), (372), (556), (557), (761),
% 221.40/30.87 | | | | | | | | (846) are inconsistent by sub-proof #1.
% 221.40/30.87 | | | | | | | |
% 221.40/30.87 | | | | | | | Case 2:
% 221.40/30.87 | | | | | | | |
% 221.40/30.87 | | | | | | | | (847) ~ (all_870_4 = 0)
% 221.40/30.87 | | | | | | | |
% 221.40/30.87 | | | | | | | | REF_CLOSE: (12), (14), (16), (19), (20), (22), (41), (84), (86),
% 221.40/30.87 | | | | | | | | (342), (343), (353), (354), (355), (357), (358),
% 221.40/30.87 | | | | | | | | (359), (360), (365), (367), (368), (370), (371),
% 221.40/30.87 | | | | | | | | (557), (789), (831), (847), (fact_transD) are
% 221.40/30.87 | | | | | | | | inconsistent by sub-proof #2.
% 221.40/30.87 | | | | | | | |
% 221.40/30.87 | | | | | | | End of split
% 221.40/30.87 | | | | | | |
% 221.40/30.87 | | | | | | End of split
% 221.40/30.87 | | | | | |
% 221.40/30.87 | | | | | End of split
% 221.40/30.87 | | | | |
% 221.40/30.87 | | | | End of split
% 221.40/30.87 | | | |
% 221.40/30.87 | | | End of split
% 221.40/30.87 | | |
% 221.40/30.87 | | End of split
% 221.40/30.87 | |
% 221.40/30.87 | End of split
% 221.40/30.87 |
% 221.40/30.87 End of proof
% 221.40/30.87
% 221.40/30.87 Sub-proof #1 shows that the following formulas are inconsistent:
% 221.40/30.87 ----------------------------------------------------------------
% 221.40/30.87 (1) $i(v_L)
% 221.40/30.87 (2) $i(all_870_9)
% 221.40/30.87 (3) all_870_8 = all_870_9 | ? [v0: any] : ? [v1: $i] : ? [v2: any] :
% 221.40/30.87 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.87 tc_Arrow__Order__Mirabelle_Oalt, all_870_8, all_870_9) = v1 &
% 221.40/30.87 c_member(all_674_0, v1, v_L) = v2 & c_member(all_674_0, all_870_7, v_L)
% 221.40/30.87 = v0 & $i(v1) & (v2 = 0 | v0 = 0))
% 221.40/30.87 (4) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_674_0, all_870_7, v_L) = v0) |
% 221.40/30.87 ! [v0: $i] : ! [v1: $i] : ( ~
% 221.40/30.87 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.87 tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v0) = v1) | ~ $i(v0) |
% 221.40/30.87 ? [v2: $i] : ? [v3: any] : ? [v4: any] :
% 221.40/30.87 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.87 tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v0) = v2 &
% 221.40/30.87 c_member(all_674_0, v2, v_L) = v3 & c_member(all_674_0, v1, v_L) = v4
% 221.40/30.87 & $i(v2) & ( ~ (v3 = 0) | v4 = 0)))
% 221.40/30.87 (5) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.87 tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v_y) = all_870_5
% 221.40/30.87 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 221.40/30.87 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.87 tc_Arrow__Order__Mirabelle_Oalt, v0, v1) = v2) | ~ $i(v1) | ~
% 221.40/30.87 $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & c_member(all_674_0, v2, v_L) =
% 221.40/30.87 v3) | ! [v3: $i] : ! [v4: $i] : ( ~
% 221.40/30.87 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.87 tc_Arrow__Order__Mirabelle_Oalt, v0, v3) = v4) | ~ $i(v3) | ?
% 221.40/30.87 [v5: $i] : ? [v6: any] : ? [v7: any] :
% 221.40/30.87 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.87 tc_Arrow__Order__Mirabelle_Oalt, v1, v3) = v5 &
% 221.40/30.87 c_member(all_674_0, v5, v_L) = v6 & c_member(all_674_0, v4, v_L) =
% 221.40/30.87 v7 & $i(v5) & ( ~ (v6 = 0) | v7 = 0))))
% 221.40/30.87 (7) c_member(all_625_1, all_870_7, v_L) = all_870_6
% 221.40/30.87 (8) $i(all_625_1)
% 221.40/30.87 (9) $i(all_870_8)
% 221.40/30.87 (10) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.87 tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v_y) = all_870_3
% 221.40/30.87 (11) $i(v_y)
% 221.40/30.87 (12) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.87 tc_Arrow__Order__Mirabelle_Oalt, all_870_9, all_870_8) = all_870_7
% 221.40/30.87 (13) ~ (all_870_9 = v_x)
% 221.40/30.87 (14) all_674_0 = all_625_1
% 221.40/30.87 (15) all_870_6 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & hBOOL(v0) =
% 221.40/30.87 v1 & hAPP(v_L, all_870_7) = v0 & $i(v0))
% 221.40/30.87 (16) (all_870_2 = 0 & all_870_8 = v_x & ? [v0: $i] : ? [v1: $i] : ? [v2:
% 221.40/30.87 $i] : ? [v3: int] : ( ~ (v3 = 0) & ~ (v0 = v_x) &
% 221.40/30.87 c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.87 tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v0) = v2 &
% 221.40/30.87 c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.87 tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = v1 &
% 221.40/30.87 c_member(all_683_0, v2, v_L) = v3 & c_member(all_683_0, v1, v_L) = 0
% 221.40/30.87 & $i(v2) & $i(v1) & $i(v0))) | (all_870_6 = 0 & ~ (all_870_8 = v_x)
% 221.40/30.87 & ? [v0: $i] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ? [v4:
% 221.40/30.87 any] : (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.87 tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v0) = v1 &
% 221.40/30.87 c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.87 tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v0) = v3 &
% 221.40/30.87 c_member(all_683_0, v3, v_L) = v4 & c_member(all_683_0, v1, v_L) =
% 221.40/30.87 v2 & $i(v3) & $i(v1) & $i(v0) & ((v2 = 0 & ~ (v4 = 0) & ~ (v0 =
% 221.40/30.87 v_x)) | (v0 = v_x & all_870_4 = 0 & ~ (all_870_2 = 0)))))
% 221.40/30.87 (17) c_member(all_625_1, all_870_3, v_L) = all_870_2
% 221.40/30.87 (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 221.40/30.87 (c_member(v2, v1, v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 221.40/30.87 [v4: $i] : ? [v5: int] : ( ~ (v5 = 0) & hBOOL(v4) = v5 & hAPP(v0, v1)
% 221.40/30.87 = v4 & $i(v4)))
% 221.40/30.87 (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 221.40/30.87 [v5: $i] : (v1 = v0 | ~ (c_Product__Type_OPair(v5, v4, v3, v2) = v1) |
% 221.40/30.87 ~ (c_Product__Type_OPair(v5, v4, v3, v2) = v0))
% 221.40/30.87 (20) c_member(all_625_1, all_870_5, v_L) = 0
% 221.40/30.88 (21) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 221.40/30.88 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (c_member(v4, v3, v2) = v1) |
% 221.40/30.88 ~ (c_member(v4, v3, v2) = v0))
% 221.40/30.88 (22) all_683_0 = all_625_1
% 221.40/30.88 (23) ! [v0: $i] : ! [v1: $i] : ( ~
% 221.40/30.88 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.88 tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v0) = v1) | ~ $i(v0)
% 221.40/30.88 | ? [v2: $i] : ? [v3: any] : ? [v4: any] :
% 221.40/30.88 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.88 tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = v2 &
% 221.40/30.88 c_member(all_674_0, v2, v_L) = v3 & c_member(all_674_0, v1, v_L) =
% 221.40/30.88 v4 & $i(v2) & ( ~ (v3 = 0) | v4 = 0)))
% 221.40/30.88 (24) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_674_0, all_870_5, v_L) = v0)
% 221.40/30.88 | ! [v0: $i] : ! [v1: $i] : ( ~
% 221.40/30.88 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.88 tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v0) = v1) | ~ $i(v0)
% 221.40/30.88 | ? [v2: $i] : ? [v3: any] : ? [v4: any] :
% 221.40/30.88 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.88 tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = v2 &
% 221.40/30.88 c_member(all_674_0, v2, v_L) = v3 & c_member(all_674_0, v1, v_L) =
% 221.40/30.88 v4 & $i(v2) & ( ~ (v3 = 0) | v4 = 0)))
% 221.40/30.88
% 221.40/30.88 Begin of proof
% 221.40/30.88 |
% 221.40/30.88 | BETA: splitting (24) gives:
% 221.40/30.88 |
% 221.40/30.88 | Case 1:
% 221.40/30.88 | |
% 221.40/30.88 | | (25) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_674_0, all_870_5, v_L) =
% 221.40/30.88 | | v0)
% 221.40/30.88 | |
% 221.40/30.88 | | REF_CLOSE: (14), (20), (21), (25) are inconsistent by sub-proof #11.
% 221.40/30.88 | |
% 221.40/30.88 | Case 2:
% 221.40/30.88 | |
% 221.40/30.88 | | (26) ! [v0: $i] : ! [v1: $i] : ( ~
% 221.40/30.88 | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.88 | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v0) = v1) | ~
% 221.40/30.88 | | $i(v0) | ? [v2: $i] : ? [v3: any] : ? [v4: any] :
% 221.40/30.88 | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.88 | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = v2 &
% 221.40/30.88 | | c_member(all_674_0, v2, v_L) = v3 & c_member(all_674_0, v1, v_L)
% 221.40/30.88 | | = v4 & $i(v2) & ( ~ (v3 = 0) | v4 = 0)))
% 221.40/30.88 | |
% 221.40/30.88 | | BETA: splitting (15) gives:
% 221.40/30.88 | |
% 221.40/30.88 | | Case 1:
% 221.40/30.88 | | |
% 221.40/30.88 | | | (27) all_870_6 = 0
% 221.40/30.88 | | |
% 221.40/30.88 | | | REDUCE: (7), (27) imply:
% 221.40/30.88 | | | (28) c_member(all_625_1, all_870_7, v_L) = 0
% 221.40/30.88 | | |
% 221.40/30.88 | | | BETA: splitting (4) gives:
% 221.40/30.88 | | |
% 221.40/30.88 | | | Case 1:
% 221.40/30.88 | | | |
% 221.40/30.88 | | | | (29) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_674_0, all_870_7,
% 221.40/30.88 | | | | v_L) = v0)
% 221.40/30.88 | | | |
% 221.40/30.88 | | | | REF_CLOSE: (14), (21), (28), (29) are inconsistent by sub-proof #9.
% 221.40/30.88 | | | |
% 221.40/30.88 | | | Case 2:
% 221.40/30.88 | | | |
% 221.40/30.88 | | | | (30) ! [v0: $i] : ! [v1: $i] : ( ~
% 221.40/30.88 | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.88 | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v0) = v1) | ~
% 221.40/30.88 | | | | $i(v0) | ? [v2: $i] : ? [v3: any] : ? [v4: any] :
% 221.40/30.88 | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.88 | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v0) = v2 &
% 221.40/30.88 | | | | c_member(all_674_0, v2, v_L) = v3 & c_member(all_674_0, v1,
% 221.40/30.88 | | | | v_L) = v4 & $i(v2) & ( ~ (v3 = 0) | v4 = 0)))
% 221.40/30.88 | | | |
% 221.40/30.88 | | | | GROUND_INST: instantiating (30) with all_870_8, all_870_7, simplifying
% 221.40/30.88 | | | | with (9), (12) gives:
% 221.40/30.88 | | | | (31) ? [v0: $i] : ? [v1: any] : ? [v2: any] :
% 221.40/30.88 | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.88 | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, all_870_8) = v0
% 221.40/30.88 | | | | & c_member(all_674_0, v0, v_L) = v1 & c_member(all_674_0,
% 221.40/30.88 | | | | all_870_7, v_L) = v2 & $i(v0) & ( ~ (v1 = 0) | v2 = 0))
% 221.40/30.88 | | | |
% 221.40/30.88 | | | | DELTA: instantiating (31) with fresh symbols all_1195_0, all_1195_1,
% 221.40/30.88 | | | | all_1195_2 gives:
% 221.40/30.88 | | | | (32) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.88 | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, all_870_8) =
% 221.40/30.88 | | | | all_1195_2 & c_member(all_674_0, all_1195_2, v_L) = all_1195_1 &
% 221.40/30.88 | | | | c_member(all_674_0, all_870_7, v_L) = all_1195_0 &
% 221.40/30.88 | | | | $i(all_1195_2) & ( ~ (all_1195_1 = 0) | all_1195_0 = 0)
% 221.40/30.88 | | | |
% 221.40/30.88 | | | | ALPHA: (32) implies:
% 221.40/30.88 | | | | (33) c_member(all_674_0, all_870_7, v_L) = all_1195_0
% 221.40/30.88 | | | |
% 221.40/30.88 | | | | REDUCE: (14), (33) imply:
% 221.40/30.88 | | | | (34) c_member(all_625_1, all_870_7, v_L) = all_1195_0
% 221.40/30.88 | | | |
% 221.40/30.88 | | | | GROUND_INST: instantiating (21) with 0, all_1195_0, v_L, all_870_7,
% 221.40/30.88 | | | | all_625_1, simplifying with (28), (34) gives:
% 221.40/30.88 | | | | (35) all_1195_0 = 0
% 221.40/30.88 | | | |
% 221.40/30.88 | | | | BETA: splitting (16) gives:
% 221.40/30.88 | | | |
% 221.40/30.88 | | | | Case 1:
% 221.40/30.88 | | | | |
% 221.40/30.88 | | | | | (36) all_870_2 = 0 & all_870_8 = v_x & ? [v0: $i] : ? [v1: $i] :
% 221.40/30.88 | | | | | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & ~ (v0 = v_x) &
% 221.40/30.88 | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.88 | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v0) = v2 &
% 221.40/30.88 | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.88 | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = v1 &
% 221.40/30.88 | | | | | c_member(all_683_0, v2, v_L) = v3 & c_member(all_683_0, v1,
% 221.40/30.88 | | | | | v_L) = 0 & $i(v2) & $i(v1) & $i(v0))
% 221.40/30.88 | | | | |
% 221.40/30.88 | | | | | ALPHA: (36) implies:
% 221.40/30.88 | | | | | (37) all_870_8 = v_x
% 221.40/30.88 | | | | | (38) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~
% 221.40/30.88 | | | | | (v3 = 0) & ~ (v0 = v_x) &
% 221.40/30.88 | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.88 | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v0) = v2 &
% 221.40/30.88 | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.88 | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = v1 &
% 221.40/30.88 | | | | | c_member(all_683_0, v2, v_L) = v3 & c_member(all_683_0, v1,
% 221.40/30.88 | | | | | v_L) = 0 & $i(v2) & $i(v1) & $i(v0))
% 221.40/30.88 | | | | |
% 221.40/30.88 | | | | | DELTA: instantiating (38) with fresh symbols all_1394_0, all_1394_1,
% 221.40/30.88 | | | | | all_1394_2, all_1394_3 gives:
% 221.40/30.88 | | | | | (39) ~ (all_1394_0 = 0) & ~ (all_1394_3 = v_x) &
% 221.40/30.88 | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.88 | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9, all_1394_3) =
% 221.40/30.88 | | | | | all_1394_1 &
% 221.40/30.88 | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.88 | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, all_1394_3) =
% 221.40/30.88 | | | | | all_1394_2 & c_member(all_683_0, all_1394_1, v_L) = all_1394_0
% 221.40/30.88 | | | | | & c_member(all_683_0, all_1394_2, v_L) = 0 & $i(all_1394_1) &
% 221.40/30.88 | | | | | $i(all_1394_2) & $i(all_1394_3)
% 221.40/30.88 | | | | |
% 221.40/30.88 | | | | | ALPHA: (39) implies:
% 221.40/30.88 | | | | | (40) ~ (all_1394_0 = 0)
% 221.40/30.88 | | | | | (41) $i(all_1394_3)
% 221.40/30.88 | | | | | (42) $i(all_1394_1)
% 221.40/30.88 | | | | | (43) c_member(all_683_0, all_1394_2, v_L) = 0
% 221.40/30.88 | | | | | (44) c_member(all_683_0, all_1394_1, v_L) = all_1394_0
% 221.40/30.88 | | | | | (45) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.88 | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, all_1394_3) =
% 221.40/30.88 | | | | | all_1394_2
% 221.40/30.88 | | | | | (46) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.88 | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9, all_1394_3) =
% 221.40/30.88 | | | | | all_1394_1
% 221.40/30.88 | | | | |
% 221.40/30.88 | | | | | REDUCE: (12), (37) imply:
% 221.40/30.88 | | | | | (47) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.88 | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v_x) = all_870_7
% 221.40/30.88 | | | | |
% 221.40/30.88 | | | | | REDUCE: (22), (44) imply:
% 221.40/30.88 | | | | | (48) c_member(all_625_1, all_1394_1, v_L) = all_1394_0
% 221.40/30.88 | | | | |
% 221.40/30.88 | | | | | REDUCE: (22), (43) imply:
% 221.40/30.88 | | | | | (49) c_member(all_625_1, all_1394_2, v_L) = 0
% 221.40/30.88 | | | | |
% 221.40/30.88 | | | | | REDUCE: (9), (37) imply:
% 221.40/30.88 | | | | | (50) $i(v_x)
% 221.40/30.88 | | | | |
% 221.40/30.88 | | | | | GROUND_INST: instantiating (18) with v_L, all_1394_1, all_625_1,
% 221.40/30.88 | | | | | all_1394_0, simplifying with (1), (8), (42), (48) gives:
% 221.40/30.88 | | | | | (51) all_1394_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 221.40/30.88 | | | | | hBOOL(v0) = v1 & hAPP(v_L, all_1394_1) = v0 & $i(v0))
% 221.40/30.88 | | | | |
% 221.40/30.88 | | | | | GROUND_INST: instantiating (6) with v_y, all_1394_3, all_1394_2,
% 221.40/30.88 | | | | | simplifying with (11), (41), (45) gives:
% 221.40/30.88 | | | | | (52) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_674_0, all_1394_2,
% 221.40/30.88 | | | | | v_L) = v0) | ! [v0: $i] : ! [v1: $i] : ( ~
% 221.40/30.88 | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.88 | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = v1) | ~
% 221.40/30.88 | | | | | $i(v0) | ? [v2: $i] : ? [v3: any] : ? [v4: any] :
% 221.40/30.88 | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.88 | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_1394_3, v0) = v2 &
% 221.40/30.88 | | | | | c_member(all_674_0, v2, v_L) = v3 & c_member(all_674_0,
% 221.40/30.88 | | | | | v1, v_L) = v4 & $i(v2) & ( ~ (v3 = 0) | v4 = 0)))
% 221.40/30.88 | | | | |
% 221.40/30.88 | | | | | GROUND_INST: instantiating (6) with all_870_9, v_x, all_870_7,
% 221.40/30.88 | | | | | simplifying with (2), (47), (50) gives:
% 221.40/30.88 | | | | | (53) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_674_0, all_870_7,
% 221.40/30.88 | | | | | v_L) = v0) | ! [v0: $i] : ! [v1: $i] : ( ~
% 221.40/30.88 | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.88 | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v0) = v1) |
% 221.40/30.88 | | | | | ~ $i(v0) | ? [v2: $i] : ? [v3: any] : ? [v4: any] :
% 221.40/30.88 | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.88 | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v0) = v2 &
% 221.40/30.88 | | | | | c_member(all_674_0, v2, v_L) = v3 & c_member(all_674_0,
% 221.40/30.88 | | | | | v1, v_L) = v4 & $i(v2) & ( ~ (v3 = 0) | v4 = 0)))
% 221.40/30.88 | | | | |
% 221.40/30.88 | | | | | GROUND_INST: instantiating (30) with all_1394_3, all_1394_1,
% 221.40/30.88 | | | | | simplifying with (41), (46) gives:
% 221.40/30.88 | | | | | (54) ? [v0: $i] : ? [v1: any] : ? [v2: any] :
% 221.40/30.88 | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.88 | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, all_1394_3) =
% 221.40/30.88 | | | | | v0 & c_member(all_674_0, v0, v_L) = v1 & c_member(all_674_0,
% 221.40/30.88 | | | | | all_1394_1, v_L) = v2 & $i(v0) & ( ~ (v1 = 0) | v2 = 0))
% 221.40/30.88 | | | | |
% 221.40/30.88 | | | | | GROUND_INST: instantiating (23) with all_1394_3, all_1394_1,
% 221.40/30.88 | | | | | simplifying with (41), (46) gives:
% 221.40/30.89 | | | | | (55) ? [v0: $i] : ? [v1: any] : ? [v2: any] :
% 221.40/30.89 | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.89 | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, all_1394_3) = v0 &
% 221.40/30.89 | | | | | c_member(all_674_0, v0, v_L) = v1 & c_member(all_674_0,
% 221.40/30.89 | | | | | all_1394_1, v_L) = v2 & $i(v0) & ( ~ (v1 = 0) | v2 = 0))
% 221.40/30.89 | | | | |
% 221.40/30.89 | | | | | DELTA: instantiating (55) with fresh symbols all_1429_0, all_1429_1,
% 221.40/30.89 | | | | | all_1429_2 gives:
% 221.40/30.89 | | | | | (56) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.89 | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, all_1394_3) =
% 221.40/30.89 | | | | | all_1429_2 & c_member(all_674_0, all_1429_2, v_L) = all_1429_1
% 221.40/30.89 | | | | | & c_member(all_674_0, all_1394_1, v_L) = all_1429_0 &
% 221.40/30.89 | | | | | $i(all_1429_2) & ( ~ (all_1429_1 = 0) | all_1429_0 = 0)
% 221.40/30.89 | | | | |
% 221.40/30.89 | | | | | ALPHA: (56) implies:
% 221.40/30.89 | | | | | (57) c_member(all_674_0, all_1394_1, v_L) = all_1429_0
% 221.40/30.89 | | | | | (58) c_member(all_674_0, all_1429_2, v_L) = all_1429_1
% 221.40/30.89 | | | | | (59) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.89 | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, all_1394_3) =
% 221.40/30.89 | | | | | all_1429_2
% 221.40/30.89 | | | | | (60) ~ (all_1429_1 = 0) | all_1429_0 = 0
% 221.40/30.89 | | | | |
% 221.40/30.89 | | | | | DELTA: instantiating (54) with fresh symbols all_1441_0, all_1441_1,
% 221.40/30.89 | | | | | all_1441_2 gives:
% 221.40/30.89 | | | | | (61) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.89 | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, all_1394_3) =
% 221.40/30.89 | | | | | all_1441_2 & c_member(all_674_0, all_1441_2, v_L) = all_1441_1
% 221.40/30.89 | | | | | & c_member(all_674_0, all_1394_1, v_L) = all_1441_0 &
% 221.40/30.89 | | | | | $i(all_1441_2) & ( ~ (all_1441_1 = 0) | all_1441_0 = 0)
% 221.40/30.89 | | | | |
% 221.40/30.89 | | | | | ALPHA: (61) implies:
% 221.40/30.89 | | | | | (62) c_member(all_674_0, all_1394_1, v_L) = all_1441_0
% 221.40/30.89 | | | | |
% 221.40/30.89 | | | | | REDUCE: (14), (58) imply:
% 221.40/30.89 | | | | | (63) c_member(all_625_1, all_1429_2, v_L) = all_1429_1
% 221.40/30.89 | | | | |
% 221.40/30.89 | | | | | REDUCE: (14), (62) imply:
% 221.40/30.89 | | | | | (64) c_member(all_625_1, all_1394_1, v_L) = all_1441_0
% 221.40/30.89 | | | | |
% 221.40/30.89 | | | | | REDUCE: (14), (57) imply:
% 221.40/30.89 | | | | | (65) c_member(all_625_1, all_1394_1, v_L) = all_1429_0
% 221.40/30.89 | | | | |
% 221.40/30.89 | | | | | BETA: splitting (52) gives:
% 221.40/30.89 | | | | |
% 221.40/30.89 | | | | | Case 1:
% 221.40/30.89 | | | | | |
% 221.40/30.89 | | | | | | (66) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_674_0,
% 221.40/30.89 | | | | | | all_1394_2, v_L) = v0)
% 221.40/30.89 | | | | | |
% 221.40/30.89 | | | | | | DELTA: instantiating (66) with fresh symbol all_1471_0 gives:
% 221.40/30.89 | | | | | | (67) ~ (all_1471_0 = 0) & c_member(all_674_0, all_1394_2, v_L) =
% 221.40/30.89 | | | | | | all_1471_0
% 221.40/30.89 | | | | | |
% 221.40/30.89 | | | | | | ALPHA: (67) implies:
% 221.40/30.89 | | | | | | (68) ~ (all_1471_0 = 0)
% 221.40/30.89 | | | | | | (69) c_member(all_674_0, all_1394_2, v_L) = all_1471_0
% 221.40/30.89 | | | | | |
% 221.40/30.89 | | | | | | REDUCE: (14), (69) imply:
% 221.40/30.89 | | | | | | (70) c_member(all_625_1, all_1394_2, v_L) = all_1471_0
% 221.40/30.89 | | | | | |
% 221.40/30.89 | | | | | | GROUND_INST: instantiating (21) with 0, all_1471_0, v_L, all_1394_2,
% 221.40/30.89 | | | | | | all_625_1, simplifying with (49), (70) gives:
% 221.40/30.89 | | | | | | (71) all_1471_0 = 0
% 221.40/30.89 | | | | | |
% 221.40/30.89 | | | | | | REDUCE: (68), (71) imply:
% 221.40/30.89 | | | | | | (72) $false
% 221.40/30.89 | | | | | |
% 221.40/30.89 | | | | | | CLOSE: (72) is inconsistent.
% 221.40/30.89 | | | | | |
% 221.40/30.89 | | | | | Case 2:
% 221.40/30.89 | | | | | |
% 221.40/30.89 | | | | | | (73) ! [v0: $i] : ! [v1: $i] : ( ~
% 221.40/30.89 | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.89 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = v1) | ~
% 221.40/30.89 | | | | | | $i(v0) | ? [v2: $i] : ? [v3: any] : ? [v4: any] :
% 221.40/30.89 | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.89 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_1394_3, v0) = v2
% 221.40/30.89 | | | | | | & c_member(all_674_0, v2, v_L) = v3 &
% 221.40/30.89 | | | | | | c_member(all_674_0, v1, v_L) = v4 & $i(v2) & ( ~ (v3 =
% 221.40/30.89 | | | | | | 0) | v4 = 0)))
% 221.40/30.89 | | | | | |
% 221.40/30.89 | | | | | | GROUND_INST: instantiating (73) with all_1394_3, all_1394_2,
% 221.40/30.89 | | | | | | simplifying with (41), (45) gives:
% 221.40/30.89 | | | | | | (74) ? [v0: $i] : ? [v1: any] : ? [v2: any] :
% 221.40/30.89 | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.89 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_1394_3, all_1394_3)
% 221.40/30.89 | | | | | | = v0 & c_member(all_674_0, v0, v_L) = v1 &
% 221.40/30.89 | | | | | | c_member(all_674_0, all_1394_2, v_L) = v2 & $i(v0) & ( ~
% 221.40/30.89 | | | | | | (v1 = 0) | v2 = 0))
% 221.40/30.89 | | | | | |
% 221.40/30.89 | | | | | | DELTA: instantiating (74) with fresh symbols all_1474_0, all_1474_1,
% 221.40/30.89 | | | | | | all_1474_2 gives:
% 221.40/30.89 | | | | | | (75) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.89 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_1394_3, all_1394_3) =
% 221.40/30.89 | | | | | | all_1474_2 & c_member(all_674_0, all_1474_2, v_L) =
% 221.40/30.89 | | | | | | all_1474_1 & c_member(all_674_0, all_1394_2, v_L) =
% 221.40/30.89 | | | | | | all_1474_0 & $i(all_1474_2) & ( ~ (all_1474_1 = 0) |
% 221.40/30.89 | | | | | | all_1474_0 = 0)
% 221.40/30.89 | | | | | |
% 221.40/30.89 | | | | | | ALPHA: (75) implies:
% 221.40/30.89 | | | | | | (76) c_member(all_674_0, all_1394_2, v_L) = all_1474_0
% 221.40/30.89 | | | | | |
% 221.40/30.89 | | | | | | REDUCE: (14), (76) imply:
% 221.40/30.89 | | | | | | (77) c_member(all_625_1, all_1394_2, v_L) = all_1474_0
% 221.40/30.89 | | | | | |
% 221.40/30.89 | | | | | | BETA: splitting (53) gives:
% 221.40/30.89 | | | | | |
% 221.40/30.89 | | | | | | Case 1:
% 221.40/30.89 | | | | | | |
% 221.40/30.89 | | | | | | | (78) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_674_0,
% 221.40/30.89 | | | | | | | all_870_7, v_L) = v0)
% 221.40/30.89 | | | | | | |
% 221.40/30.89 | | | | | | | REF_CLOSE: (14), (21), (28), (78) are inconsistent by sub-proof
% 221.40/30.89 | | | | | | | #9.
% 221.40/30.89 | | | | | | |
% 221.40/30.89 | | | | | | Case 2:
% 221.40/30.89 | | | | | | |
% 221.40/30.89 | | | | | | | (79) ! [v0: $i] : ! [v1: $i] : ( ~
% 221.40/30.89 | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.89 | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v0) =
% 221.40/30.89 | | | | | | | v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: any] : ? [v4:
% 221.40/30.89 | | | | | | | any] :
% 221.40/30.89 | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.89 | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v0) = v2 &
% 221.40/30.89 | | | | | | | c_member(all_674_0, v2, v_L) = v3 &
% 221.40/30.89 | | | | | | | c_member(all_674_0, v1, v_L) = v4 & $i(v2) & ( ~ (v3 =
% 221.40/30.89 | | | | | | | 0) | v4 = 0)))
% 221.40/30.89 | | | | | | |
% 221.40/30.89 | | | | | | | GROUND_INST: instantiating (79) with all_1394_3, all_1394_1,
% 221.40/30.89 | | | | | | | simplifying with (41), (46) gives:
% 221.40/30.89 | | | | | | | (80) ? [v0: $i] : ? [v1: any] : ? [v2: any] :
% 221.40/30.89 | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.89 | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, all_1394_3) = v0
% 221.40/30.89 | | | | | | | & c_member(all_674_0, v0, v_L) = v1 &
% 221.40/30.89 | | | | | | | c_member(all_674_0, all_1394_1, v_L) = v2 & $i(v0) & ( ~
% 221.40/30.89 | | | | | | | (v1 = 0) | v2 = 0))
% 221.40/30.89 | | | | | | |
% 221.40/30.89 | | | | | | | DELTA: instantiating (80) with fresh symbols all_1495_0,
% 221.40/30.89 | | | | | | | all_1495_1, all_1495_2 gives:
% 221.40/30.89 | | | | | | | (81) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.89 | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, all_1394_3) =
% 221.40/30.89 | | | | | | | all_1495_2 & c_member(all_674_0, all_1495_2, v_L) =
% 221.40/30.89 | | | | | | | all_1495_1 & c_member(all_674_0, all_1394_1, v_L) =
% 221.40/30.89 | | | | | | | all_1495_0 & $i(all_1495_2) & ( ~ (all_1495_1 = 0) |
% 221.40/30.89 | | | | | | | all_1495_0 = 0)
% 221.40/30.89 | | | | | | |
% 221.40/30.89 | | | | | | | ALPHA: (81) implies:
% 221.40/30.89 | | | | | | | (82) c_member(all_674_0, all_1394_1, v_L) = all_1495_0
% 221.40/30.89 | | | | | | |
% 221.40/30.89 | | | | | | | REDUCE: (14), (82) imply:
% 221.40/30.89 | | | | | | | (83) c_member(all_625_1, all_1394_1, v_L) = all_1495_0
% 221.40/30.89 | | | | | | |
% 221.40/30.89 | | | | | | | BETA: splitting (51) gives:
% 221.40/30.89 | | | | | | |
% 221.40/30.89 | | | | | | | Case 1:
% 221.40/30.89 | | | | | | | |
% 221.40/30.89 | | | | | | | | (84) all_1394_0 = 0
% 221.40/30.89 | | | | | | | |
% 221.40/30.89 | | | | | | | | REDUCE: (40), (84) imply:
% 221.40/30.89 | | | | | | | | (85) $false
% 221.40/30.89 | | | | | | | |
% 221.40/30.89 | | | | | | | | CLOSE: (85) is inconsistent.
% 221.40/30.89 | | | | | | | |
% 221.40/30.89 | | | | | | | Case 2:
% 221.40/30.89 | | | | | | | |
% 221.40/30.89 | | | | | | | |
% 221.40/30.89 | | | | | | | | GROUND_INST: instantiating (21) with 0, all_1474_0, v_L,
% 221.40/30.89 | | | | | | | | all_1394_2, all_625_1, simplifying with (49), (77)
% 221.40/30.89 | | | | | | | | gives:
% 221.40/30.89 | | | | | | | | (86) all_1474_0 = 0
% 221.40/30.89 | | | | | | | |
% 221.40/30.89 | | | | | | | | GROUND_INST: instantiating (21) with all_1394_0, all_1495_0,
% 221.40/30.89 | | | | | | | | v_L, all_1394_1, all_625_1, simplifying with (48),
% 221.40/30.89 | | | | | | | | (83) gives:
% 221.40/30.89 | | | | | | | | (87) all_1495_0 = all_1394_0
% 221.40/30.89 | | | | | | | |
% 221.40/30.89 | | | | | | | | GROUND_INST: instantiating (21) with all_1441_0, all_1495_0,
% 221.40/30.89 | | | | | | | | v_L, all_1394_1, all_625_1, simplifying with (64),
% 221.40/30.89 | | | | | | | | (83) gives:
% 221.40/30.89 | | | | | | | | (88) all_1495_0 = all_1441_0
% 221.40/30.89 | | | | | | | |
% 221.40/30.89 | | | | | | | | GROUND_INST: instantiating (21) with all_1429_0, all_1495_0,
% 221.40/30.89 | | | | | | | | v_L, all_1394_1, all_625_1, simplifying with (65),
% 221.40/30.89 | | | | | | | | (83) gives:
% 221.40/30.89 | | | | | | | | (89) all_1495_0 = all_1429_0
% 221.40/30.89 | | | | | | | |
% 221.40/30.89 | | | | | | | | GROUND_INST: instantiating (19) with all_1394_2, all_1429_2,
% 221.40/30.89 | | | | | | | | all_1394_3, v_y, tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.89 | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with
% 221.40/30.89 | | | | | | | | (45), (59) gives:
% 221.40/30.89 | | | | | | | | (90) all_1429_2 = all_1394_2
% 221.40/30.89 | | | | | | | |
% 221.40/30.89 | | | | | | | | COMBINE_EQS: (87), (88) imply:
% 221.40/30.89 | | | | | | | | (91) all_1441_0 = all_1394_0
% 221.40/30.89 | | | | | | | |
% 221.40/30.89 | | | | | | | | COMBINE_EQS: (88), (89) imply:
% 221.40/30.89 | | | | | | | | (92) all_1441_0 = all_1429_0
% 221.40/30.89 | | | | | | | |
% 221.40/30.89 | | | | | | | | COMBINE_EQS: (91), (92) imply:
% 221.40/30.89 | | | | | | | | (93) all_1429_0 = all_1394_0
% 221.40/30.89 | | | | | | | |
% 221.40/30.89 | | | | | | | | SIMP: (93) implies:
% 221.40/30.89 | | | | | | | | (94) all_1429_0 = all_1394_0
% 221.40/30.89 | | | | | | | |
% 221.40/30.89 | | | | | | | | REDUCE: (63), (90) imply:
% 221.40/30.89 | | | | | | | | (95) c_member(all_625_1, all_1394_2, v_L) = all_1429_1
% 221.40/30.89 | | | | | | | |
% 221.40/30.89 | | | | | | | | BETA: splitting (60) gives:
% 221.40/30.89 | | | | | | | |
% 221.40/30.89 | | | | | | | | Case 1:
% 221.40/30.89 | | | | | | | | |
% 221.40/30.89 | | | | | | | | | (96) ~ (all_1429_1 = 0)
% 221.40/30.89 | | | | | | | | |
% 221.40/30.89 | | | | | | | | | GROUND_INST: instantiating (21) with 0, all_1429_1, v_L,
% 221.40/30.89 | | | | | | | | | all_1394_2, all_625_1, simplifying with (49), (95)
% 221.40/30.89 | | | | | | | | | gives:
% 221.40/30.89 | | | | | | | | | (97) all_1429_1 = 0
% 221.40/30.89 | | | | | | | | |
% 221.40/30.89 | | | | | | | | | REDUCE: (96), (97) imply:
% 221.40/30.89 | | | | | | | | | (98) $false
% 221.40/30.89 | | | | | | | | |
% 221.40/30.89 | | | | | | | | | CLOSE: (98) is inconsistent.
% 221.40/30.89 | | | | | | | | |
% 221.40/30.89 | | | | | | | | Case 2:
% 221.40/30.89 | | | | | | | | |
% 221.40/30.89 | | | | | | | | | (99) all_1429_0 = 0
% 221.40/30.89 | | | | | | | | |
% 221.40/30.89 | | | | | | | | | COMBINE_EQS: (94), (99) imply:
% 221.40/30.89 | | | | | | | | | (100) all_1394_0 = 0
% 221.40/30.89 | | | | | | | | |
% 221.40/30.89 | | | | | | | | | SIMP: (100) implies:
% 221.40/30.89 | | | | | | | | | (101) all_1394_0 = 0
% 221.40/30.89 | | | | | | | | |
% 221.40/30.89 | | | | | | | | | REDUCE: (40), (101) imply:
% 221.40/30.89 | | | | | | | | | (102) $false
% 221.40/30.89 | | | | | | | | |
% 221.40/30.89 | | | | | | | | | CLOSE: (102) is inconsistent.
% 221.40/30.89 | | | | | | | | |
% 221.40/30.89 | | | | | | | | End of split
% 221.40/30.89 | | | | | | | |
% 221.40/30.89 | | | | | | | End of split
% 221.40/30.89 | | | | | | |
% 221.40/30.89 | | | | | | End of split
% 221.40/30.89 | | | | | |
% 221.40/30.89 | | | | | End of split
% 221.40/30.89 | | | | |
% 221.40/30.89 | | | | Case 2:
% 221.40/30.89 | | | | |
% 221.40/30.89 | | | | | (103) all_870_6 = 0 & ~ (all_870_8 = v_x) & ? [v0: $i] : ? [v1:
% 221.40/30.89 | | | | | $i] : ? [v2: any] : ? [v3: $i] : ? [v4: any] :
% 221.40/30.89 | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.89 | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v0) = v1 &
% 221.40/30.89 | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.89 | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v0) = v3 &
% 221.40/30.89 | | | | | c_member(all_683_0, v3, v_L) = v4 & c_member(all_683_0, v1,
% 221.40/30.89 | | | | | v_L) = v2 & $i(v3) & $i(v1) & $i(v0) & ((v2 = 0 & ~ (v4
% 221.40/30.89 | | | | | = 0) & ~ (v0 = v_x)) | (v0 = v_x & all_870_4 = 0 &
% 221.40/30.89 | | | | | ~ (all_870_2 = 0))))
% 221.40/30.89 | | | | |
% 221.40/30.89 | | | | | ALPHA: (103) implies:
% 221.40/30.89 | | | | | (104) ? [v0: $i] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ?
% 221.40/30.89 | | | | | [v4: any] :
% 221.40/30.89 | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.89 | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v0) = v1 &
% 221.40/30.89 | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.89 | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v0) = v3 &
% 221.40/30.89 | | | | | c_member(all_683_0, v3, v_L) = v4 & c_member(all_683_0, v1,
% 221.40/30.89 | | | | | v_L) = v2 & $i(v3) & $i(v1) & $i(v0) & ((v2 = 0 & ~ (v4
% 221.40/30.89 | | | | | = 0) & ~ (v0 = v_x)) | (v0 = v_x & all_870_4 = 0 &
% 221.40/30.89 | | | | | ~ (all_870_2 = 0))))
% 221.40/30.89 | | | | |
% 221.40/30.89 | | | | | DELTA: instantiating (104) with fresh symbols all_1394_0, all_1394_1,
% 221.40/30.89 | | | | | all_1394_2, all_1394_3, all_1394_4 gives:
% 221.40/30.89 | | | | | (105) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.89 | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, all_1394_4) =
% 221.40/30.89 | | | | | all_1394_3 &
% 221.40/30.89 | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.89 | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9, all_1394_4) =
% 221.40/30.89 | | | | | all_1394_1 & c_member(all_683_0, all_1394_1, v_L) =
% 221.40/30.89 | | | | | all_1394_0 & c_member(all_683_0, all_1394_3, v_L) =
% 221.40/30.89 | | | | | all_1394_2 & $i(all_1394_1) & $i(all_1394_3) & $i(all_1394_4)
% 221.40/30.89 | | | | | & ((all_1394_2 = 0 & ~ (all_1394_0 = 0) & ~ (all_1394_4 =
% 221.40/30.89 | | | | | v_x)) | (all_1394_4 = v_x & all_870_4 = 0 & ~
% 221.40/30.89 | | | | | (all_870_2 = 0)))
% 221.40/30.89 | | | | |
% 221.40/30.89 | | | | | ALPHA: (105) implies:
% 221.40/30.90 | | | | | (106) $i(all_1394_4)
% 221.40/30.90 | | | | | (107) c_member(all_683_0, all_1394_3, v_L) = all_1394_2
% 221.40/30.90 | | | | | (108) c_member(all_683_0, all_1394_1, v_L) = all_1394_0
% 221.40/30.90 | | | | | (109) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.90 | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9, all_1394_4) =
% 221.40/30.90 | | | | | all_1394_1
% 221.40/30.90 | | | | | (110) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.90 | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, all_1394_4) =
% 221.40/30.90 | | | | | all_1394_3
% 221.40/30.90 | | | | | (111) (all_1394_2 = 0 & ~ (all_1394_0 = 0) & ~ (all_1394_4 =
% 221.40/30.90 | | | | | v_x)) | (all_1394_4 = v_x & all_870_4 = 0 & ~ (all_870_2
% 221.40/30.90 | | | | | = 0))
% 221.40/30.90 | | | | |
% 221.40/30.90 | | | | | REDUCE: (22), (108) imply:
% 221.40/30.90 | | | | | (112) c_member(all_625_1, all_1394_1, v_L) = all_1394_0
% 221.40/30.90 | | | | |
% 221.40/30.90 | | | | | REDUCE: (22), (107) imply:
% 221.40/30.90 | | | | | (113) c_member(all_625_1, all_1394_3, v_L) = all_1394_2
% 221.40/30.90 | | | | |
% 221.40/30.90 | | | | | BETA: splitting (111) gives:
% 221.40/30.90 | | | | |
% 221.40/30.90 | | | | | Case 1:
% 221.40/30.90 | | | | | |
% 221.40/30.90 | | | | | | (114) all_1394_2 = 0 & ~ (all_1394_0 = 0) & ~ (all_1394_4 =
% 221.40/30.90 | | | | | | v_x)
% 221.40/30.90 | | | | | |
% 221.40/30.90 | | | | | | ALPHA: (114) implies:
% 221.40/30.90 | | | | | | (115) all_1394_2 = 0
% 221.40/30.90 | | | | | | (116) ~ (all_1394_0 = 0)
% 221.40/30.90 | | | | | |
% 221.40/30.90 | | | | | | REDUCE: (113), (115) imply:
% 221.40/30.90 | | | | | | (117) c_member(all_625_1, all_1394_3, v_L) = 0
% 221.40/30.90 | | | | | |
% 221.40/30.90 | | | | | | GROUND_INST: instantiating (30) with all_1394_4, all_1394_1,
% 221.40/30.90 | | | | | | simplifying with (106), (109) gives:
% 221.40/30.90 | | | | | | (118) ? [v0: $i] : ? [v1: any] : ? [v2: any] :
% 221.40/30.90 | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.90 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, all_1394_4)
% 221.40/30.90 | | | | | | = v0 & c_member(all_674_0, v0, v_L) = v1 &
% 221.40/30.90 | | | | | | c_member(all_674_0, all_1394_1, v_L) = v2 & $i(v0) & ( ~
% 221.40/30.90 | | | | | | (v1 = 0) | v2 = 0))
% 221.40/30.90 | | | | | |
% 221.40/30.90 | | | | | | GROUND_INST: instantiating (23) with all_1394_4, all_1394_1,
% 221.40/30.90 | | | | | | simplifying with (106), (109) gives:
% 221.40/30.90 | | | | | | (119) ? [v0: $i] : ? [v1: any] : ? [v2: any] :
% 221.40/30.90 | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.90 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, all_1394_4) = v0
% 221.40/30.90 | | | | | | & c_member(all_674_0, v0, v_L) = v1 & c_member(all_674_0,
% 221.40/30.90 | | | | | | all_1394_1, v_L) = v2 & $i(v0) & ( ~ (v1 = 0) | v2 =
% 221.40/30.90 | | | | | | 0))
% 221.40/30.90 | | | | | |
% 221.40/30.90 | | | | | | GROUND_INST: instantiating (26) with all_1394_4, all_1394_3,
% 221.40/30.90 | | | | | | simplifying with (106), (110) gives:
% 221.40/30.90 | | | | | | (120) ? [v0: $i] : ? [v1: any] : ? [v2: any] :
% 221.40/30.90 | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.90 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, all_1394_4) = v0
% 221.40/30.90 | | | | | | & c_member(all_674_0, v0, v_L) = v1 & c_member(all_674_0,
% 221.40/30.90 | | | | | | all_1394_3, v_L) = v2 & $i(v0) & ( ~ (v1 = 0) | v2 =
% 221.40/30.90 | | | | | | 0))
% 221.40/30.90 | | | | | |
% 221.40/30.90 | | | | | | GROUND_INST: instantiating (6) with all_870_8, all_1394_4,
% 221.40/30.90 | | | | | | all_1394_3, simplifying with (9), (106), (110) gives:
% 221.40/30.90 | | | | | | (121) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_674_0,
% 221.40/30.90 | | | | | | all_1394_3, v_L) = v0) | ! [v0: $i] : ! [v1: $i] : (
% 221.40/30.90 | | | | | | ~ (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.90 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v0) = v1)
% 221.40/30.90 | | | | | | | ~ $i(v0) | ? [v2: $i] : ? [v3: any] : ? [v4: any] :
% 221.40/30.90 | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.90 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_1394_4, v0) = v2
% 221.40/30.90 | | | | | | & c_member(all_674_0, v2, v_L) = v3 &
% 221.40/30.90 | | | | | | c_member(all_674_0, v1, v_L) = v4 & $i(v2) & ( ~ (v3 =
% 221.40/30.90 | | | | | | 0) | v4 = 0)))
% 221.40/30.90 | | | | | |
% 221.40/30.90 | | | | | | DELTA: instantiating (120) with fresh symbols all_1431_0,
% 221.40/30.90 | | | | | | all_1431_1, all_1431_2 gives:
% 221.40/30.90 | | | | | | (122) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.90 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, all_1394_4) =
% 221.40/30.90 | | | | | | all_1431_2 & c_member(all_674_0, all_1431_2, v_L) =
% 221.40/30.90 | | | | | | all_1431_1 & c_member(all_674_0, all_1394_3, v_L) =
% 221.40/30.90 | | | | | | all_1431_0 & $i(all_1431_2) & ( ~ (all_1431_1 = 0) |
% 221.40/30.90 | | | | | | all_1431_0 = 0)
% 221.40/30.90 | | | | | |
% 221.40/30.90 | | | | | | ALPHA: (122) implies:
% 221.40/30.90 | | | | | | (123) c_member(all_674_0, all_1394_3, v_L) = all_1431_0
% 221.40/30.90 | | | | | |
% 221.40/30.90 | | | | | | DELTA: instantiating (118) with fresh symbols all_1439_0,
% 221.40/30.90 | | | | | | all_1439_1, all_1439_2 gives:
% 221.40/30.90 | | | | | | (124) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.90 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, all_1394_4) =
% 221.40/30.90 | | | | | | all_1439_2 & c_member(all_674_0, all_1439_2, v_L) =
% 221.40/30.90 | | | | | | all_1439_1 & c_member(all_674_0, all_1394_1, v_L) =
% 221.40/30.90 | | | | | | all_1439_0 & $i(all_1439_2) & ( ~ (all_1439_1 = 0) |
% 221.40/30.90 | | | | | | all_1439_0 = 0)
% 221.40/30.90 | | | | | |
% 221.40/30.90 | | | | | | ALPHA: (124) implies:
% 221.40/30.90 | | | | | | (125) c_member(all_674_0, all_1394_1, v_L) = all_1439_0
% 221.40/30.90 | | | | | | (126) c_member(all_674_0, all_1439_2, v_L) = all_1439_1
% 221.40/30.90 | | | | | | (127) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.90 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, all_1394_4) =
% 221.40/30.90 | | | | | | all_1439_2
% 221.40/30.90 | | | | | | (128) ~ (all_1439_1 = 0) | all_1439_0 = 0
% 221.40/30.90 | | | | | |
% 221.40/30.90 | | | | | | DELTA: instantiating (119) with fresh symbols all_1441_0,
% 221.40/30.90 | | | | | | all_1441_1, all_1441_2 gives:
% 221.40/30.90 | | | | | | (129) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.90 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, all_1394_4) =
% 221.40/30.90 | | | | | | all_1441_2 & c_member(all_674_0, all_1441_2, v_L) =
% 221.40/30.90 | | | | | | all_1441_1 & c_member(all_674_0, all_1394_1, v_L) =
% 221.40/30.90 | | | | | | all_1441_0 & $i(all_1441_2) & ( ~ (all_1441_1 = 0) |
% 221.40/30.90 | | | | | | all_1441_0 = 0)
% 221.40/30.90 | | | | | |
% 221.40/30.90 | | | | | | ALPHA: (129) implies:
% 221.40/30.90 | | | | | | (130) c_member(all_674_0, all_1394_1, v_L) = all_1441_0
% 221.40/30.90 | | | | | |
% 221.40/30.90 | | | | | | REDUCE: (14), (126) imply:
% 221.40/30.90 | | | | | | (131) c_member(all_625_1, all_1439_2, v_L) = all_1439_1
% 221.40/30.90 | | | | | |
% 221.40/30.90 | | | | | | REDUCE: (14), (130) imply:
% 221.40/30.90 | | | | | | (132) c_member(all_625_1, all_1394_1, v_L) = all_1441_0
% 221.40/30.90 | | | | | |
% 221.40/30.90 | | | | | | REDUCE: (14), (125) imply:
% 221.40/30.90 | | | | | | (133) c_member(all_625_1, all_1394_1, v_L) = all_1439_0
% 221.40/30.90 | | | | | |
% 221.40/30.90 | | | | | | REDUCE: (14), (123) imply:
% 221.40/30.90 | | | | | | (134) c_member(all_625_1, all_1394_3, v_L) = all_1431_0
% 221.40/30.90 | | | | | |
% 221.40/30.90 | | | | | | GROUND_INST: instantiating (21) with 0, all_1431_0, v_L, all_1394_3,
% 221.40/30.90 | | | | | | all_625_1, simplifying with (117), (134) gives:
% 221.40/30.90 | | | | | | (135) all_1431_0 = 0
% 221.40/30.90 | | | | | |
% 221.40/30.90 | | | | | | GROUND_INST: instantiating (21) with all_1394_0, all_1441_0, v_L,
% 221.40/30.90 | | | | | | all_1394_1, all_625_1, simplifying with (112), (132)
% 221.40/30.90 | | | | | | gives:
% 221.40/30.90 | | | | | | (136) all_1441_0 = all_1394_0
% 221.40/30.90 | | | | | |
% 221.40/30.90 | | | | | | GROUND_INST: instantiating (21) with all_1439_0, all_1441_0, v_L,
% 221.40/30.90 | | | | | | all_1394_1, all_625_1, simplifying with (132), (133)
% 221.40/30.90 | | | | | | gives:
% 221.40/30.90 | | | | | | (137) all_1441_0 = all_1439_0
% 221.40/30.90 | | | | | |
% 221.40/30.90 | | | | | | GROUND_INST: instantiating (19) with all_1394_3, all_1439_2,
% 221.40/30.90 | | | | | | all_1394_4, all_870_8, tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.90 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with
% 221.40/30.90 | | | | | | (110), (127) gives:
% 221.40/30.90 | | | | | | (138) all_1439_2 = all_1394_3
% 221.40/30.90 | | | | | |
% 221.40/30.90 | | | | | | COMBINE_EQS: (136), (137) imply:
% 221.40/30.90 | | | | | | (139) all_1439_0 = all_1394_0
% 221.40/30.90 | | | | | |
% 221.40/30.90 | | | | | | REDUCE: (131), (138) imply:
% 221.40/30.90 | | | | | | (140) c_member(all_625_1, all_1394_3, v_L) = all_1439_1
% 221.40/30.90 | | | | | |
% 221.40/30.90 | | | | | | BETA: splitting (128) gives:
% 221.40/30.90 | | | | | |
% 221.40/30.90 | | | | | | Case 1:
% 221.40/30.90 | | | | | | |
% 221.40/30.90 | | | | | | | (141) ~ (all_1439_1 = 0)
% 221.40/30.90 | | | | | | |
% 221.40/30.90 | | | | | | | BETA: splitting (121) gives:
% 221.40/30.90 | | | | | | |
% 221.40/30.90 | | | | | | | Case 1:
% 221.40/30.90 | | | | | | | |
% 221.40/30.90 | | | | | | | | (142) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_674_0,
% 221.40/30.90 | | | | | | | | all_1394_3, v_L) = v0)
% 221.40/30.90 | | | | | | | |
% 221.40/30.90 | | | | | | | | DELTA: instantiating (142) with fresh symbol all_1495_0 gives:
% 221.40/30.90 | | | | | | | | (143) ~ (all_1495_0 = 0) & c_member(all_674_0, all_1394_3,
% 221.40/30.90 | | | | | | | | v_L) = all_1495_0
% 221.40/30.90 | | | | | | | |
% 221.40/30.90 | | | | | | | | ALPHA: (143) implies:
% 221.40/30.90 | | | | | | | | (144) c_member(all_674_0, all_1394_3, v_L) = all_1495_0
% 221.40/30.90 | | | | | | | |
% 221.40/30.90 | | | | | | | | REDUCE: (14), (144) imply:
% 221.40/30.90 | | | | | | | | (145) c_member(all_625_1, all_1394_3, v_L) = all_1495_0
% 221.40/30.90 | | | | | | | |
% 221.40/30.90 | | | | | | | | GROUND_INST: instantiating (21) with 0, all_1495_0, v_L,
% 221.40/30.90 | | | | | | | | all_1394_3, all_625_1, simplifying with (117),
% 221.40/30.90 | | | | | | | | (145) gives:
% 221.40/30.90 | | | | | | | | (146) all_1495_0 = 0
% 221.40/30.90 | | | | | | | |
% 221.40/30.90 | | | | | | | | GROUND_INST: instantiating (21) with all_1439_1, all_1495_0,
% 221.40/30.90 | | | | | | | | v_L, all_1394_3, all_625_1, simplifying with (140),
% 221.40/30.90 | | | | | | | | (145) gives:
% 221.40/30.90 | | | | | | | | (147) all_1495_0 = all_1439_1
% 221.40/30.90 | | | | | | | |
% 221.40/30.90 | | | | | | | | COMBINE_EQS: (146), (147) imply:
% 221.40/30.90 | | | | | | | | (148) all_1439_1 = 0
% 221.40/30.90 | | | | | | | |
% 221.40/30.90 | | | | | | | | REDUCE: (141), (148) imply:
% 221.40/30.90 | | | | | | | | (149) $false
% 221.40/30.90 | | | | | | | |
% 221.40/30.90 | | | | | | | | CLOSE: (149) is inconsistent.
% 221.40/30.90 | | | | | | | |
% 221.40/30.90 | | | | | | | Case 2:
% 221.40/30.90 | | | | | | | |
% 221.40/30.90 | | | | | | | | (150) ! [v0: $i] : ! [v1: $i] : ( ~
% 221.40/30.90 | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.90 | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v0) =
% 221.40/30.90 | | | | | | | | v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: any] : ?
% 221.40/30.90 | | | | | | | | [v4: any] :
% 221.40/30.90 | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.40/30.90 | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_1394_4, v0)
% 221.40/30.90 | | | | | | | | = v2 & c_member(all_674_0, v2, v_L) = v3 &
% 221.40/30.90 | | | | | | | | c_member(all_674_0, v1, v_L) = v4 & $i(v2) & ( ~
% 221.40/30.90 | | | | | | | | (v3 = 0) | v4 = 0)))
% 221.40/30.90 | | | | | | | |
% 221.40/30.90 | | | | | | | | GROUND_INST: instantiating (150) with all_1394_4, all_1394_3,
% 221.40/30.90 | | | | | | | | simplifying with (106), (110) gives:
% 221.64/30.90 | | | | | | | | (151) ? [v0: $i] : ? [v1: any] : ? [v2: any] :
% 221.64/30.90 | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.90 | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_1394_4,
% 221.64/30.90 | | | | | | | | all_1394_4) = v0 & c_member(all_674_0, v0, v_L) =
% 221.64/30.90 | | | | | | | | v1 & c_member(all_674_0, all_1394_3, v_L) = v2 &
% 221.64/30.90 | | | | | | | | $i(v0) & ( ~ (v1 = 0) | v2 = 0))
% 221.64/30.90 | | | | | | | |
% 221.64/30.90 | | | | | | | | DELTA: instantiating (151) with fresh symbols all_1496_0,
% 221.64/30.90 | | | | | | | | all_1496_1, all_1496_2 gives:
% 221.64/30.90 | | | | | | | | (152) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.90 | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_1394_4,
% 221.64/30.90 | | | | | | | | all_1394_4) = all_1496_2 & c_member(all_674_0,
% 221.64/30.90 | | | | | | | | all_1496_2, v_L) = all_1496_1 & c_member(all_674_0,
% 221.64/30.90 | | | | | | | | all_1394_3, v_L) = all_1496_0 & $i(all_1496_2) & ( ~
% 221.64/30.90 | | | | | | | | (all_1496_1 = 0) | all_1496_0 = 0)
% 221.64/30.90 | | | | | | | |
% 221.64/30.90 | | | | | | | | ALPHA: (152) implies:
% 221.64/30.90 | | | | | | | | (153) c_member(all_674_0, all_1394_3, v_L) = all_1496_0
% 221.64/30.90 | | | | | | | |
% 221.64/30.90 | | | | | | | | REDUCE: (14), (153) imply:
% 221.64/30.90 | | | | | | | | (154) c_member(all_625_1, all_1394_3, v_L) = all_1496_0
% 221.64/30.90 | | | | | | | |
% 221.64/30.90 | | | | | | | | GROUND_INST: instantiating (21) with 0, all_1496_0, v_L,
% 221.64/30.90 | | | | | | | | all_1394_3, all_625_1, simplifying with (117),
% 221.64/30.90 | | | | | | | | (154) gives:
% 221.64/30.90 | | | | | | | | (155) all_1496_0 = 0
% 221.64/30.90 | | | | | | | |
% 221.64/30.90 | | | | | | | | GROUND_INST: instantiating (21) with all_1439_1, all_1496_0,
% 221.64/30.90 | | | | | | | | v_L, all_1394_3, all_625_1, simplifying with (140),
% 221.64/30.90 | | | | | | | | (154) gives:
% 221.64/30.90 | | | | | | | | (156) all_1496_0 = all_1439_1
% 221.64/30.90 | | | | | | | |
% 221.64/30.90 | | | | | | | | COMBINE_EQS: (155), (156) imply:
% 221.64/30.90 | | | | | | | | (157) all_1439_1 = 0
% 221.64/30.90 | | | | | | | |
% 221.64/30.90 | | | | | | | | REDUCE: (141), (157) imply:
% 221.64/30.90 | | | | | | | | (158) $false
% 221.64/30.90 | | | | | | | |
% 221.64/30.90 | | | | | | | | CLOSE: (158) is inconsistent.
% 221.64/30.90 | | | | | | | |
% 221.64/30.90 | | | | | | | End of split
% 221.64/30.90 | | | | | | |
% 221.64/30.90 | | | | | | Case 2:
% 221.64/30.90 | | | | | | |
% 221.64/30.90 | | | | | | | (159) all_1439_0 = 0
% 221.64/30.90 | | | | | | |
% 221.64/30.90 | | | | | | | COMBINE_EQS: (139), (159) imply:
% 221.64/30.90 | | | | | | | (160) all_1394_0 = 0
% 221.64/30.90 | | | | | | |
% 221.64/30.90 | | | | | | | REDUCE: (116), (160) imply:
% 221.64/30.90 | | | | | | | (161) $false
% 221.64/30.90 | | | | | | |
% 221.64/30.90 | | | | | | | CLOSE: (161) is inconsistent.
% 221.64/30.90 | | | | | | |
% 221.64/30.90 | | | | | | End of split
% 221.64/30.90 | | | | | |
% 221.64/30.90 | | | | | Case 2:
% 221.64/30.90 | | | | | |
% 221.64/30.90 | | | | | | (162) all_1394_4 = v_x & all_870_4 = 0 & ~ (all_870_2 = 0)
% 221.64/30.90 | | | | | |
% 221.64/30.90 | | | | | | ALPHA: (162) implies:
% 221.64/30.90 | | | | | | (163) ~ (all_870_2 = 0)
% 221.64/30.90 | | | | | |
% 221.64/30.90 | | | | | | BETA: splitting (4) gives:
% 221.64/30.90 | | | | | |
% 221.64/30.90 | | | | | | Case 1:
% 221.64/30.90 | | | | | | |
% 221.64/30.90 | | | | | | | (164) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_674_0,
% 221.64/30.90 | | | | | | | all_870_7, v_L) = v0)
% 221.64/30.90 | | | | | | |
% 221.64/30.91 | | | | | | | REF_CLOSE: (14), (21), (28), (164) are inconsistent by sub-proof
% 221.64/30.91 | | | | | | | #9.
% 221.64/30.91 | | | | | | |
% 221.64/30.91 | | | | | | Case 2:
% 221.64/30.91 | | | | | | |
% 221.64/30.91 | | | | | | |
% 221.64/30.91 | | | | | | | GROUND_INST: instantiating (30) with v_y, all_870_3, simplifying
% 221.64/30.91 | | | | | | | with (10), (11) gives:
% 221.64/30.91 | | | | | | | (165) ? [v0: $i] : ? [v1: any] : ? [v2: any] :
% 221.64/30.91 | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.91 | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v_y) = v0
% 221.64/30.91 | | | | | | | & c_member(all_674_0, v0, v_L) = v1 &
% 221.64/30.91 | | | | | | | c_member(all_674_0, all_870_3, v_L) = v2 & $i(v0) & ( ~
% 221.64/30.91 | | | | | | | (v1 = 0) | v2 = 0))
% 221.64/30.91 | | | | | | |
% 221.64/30.91 | | | | | | | REF_CLOSE: (5), (14), (17), (19), (20), (21), (163), (165) are
% 221.64/30.91 | | | | | | | inconsistent by sub-proof #10.
% 221.64/30.91 | | | | | | |
% 221.64/30.91 | | | | | | End of split
% 221.64/30.91 | | | | | |
% 221.64/30.91 | | | | | End of split
% 221.64/30.91 | | | | |
% 221.64/30.91 | | | | End of split
% 221.64/30.91 | | | |
% 221.64/30.91 | | | End of split
% 221.64/30.91 | | |
% 221.64/30.91 | | Case 2:
% 221.64/30.91 | | |
% 221.64/30.91 | | | (166) ~ (all_870_6 = 0)
% 221.64/30.91 | | |
% 221.64/30.91 | | | REF_CLOSE: (3), (6), (7), (11), (13), (14), (16), (19), (21), (22), (23),
% 221.64/30.91 | | | (166) are inconsistent by sub-proof #3.
% 221.64/30.91 | | |
% 221.64/30.91 | | End of split
% 221.64/30.91 | |
% 221.64/30.91 | End of split
% 221.64/30.91 |
% 221.64/30.91 End of proof
% 221.64/30.91
% 221.64/30.91 Sub-proof #2 shows that the following formulas are inconsistent:
% 221.64/30.91 ----------------------------------------------------------------
% 221.64/30.91 (1) $i(v_L)
% 221.64/30.91 (2) $i(all_870_9)
% 221.64/30.91 (3) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_674_0, all_870_7, v_L) = v0) |
% 221.64/30.91 ! [v0: $i] : ! [v1: $i] : ( ~
% 221.64/30.91 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.91 tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v0) = v1) | ~ $i(v0) |
% 221.64/30.91 ? [v2: $i] : ? [v3: any] : ? [v4: any] :
% 221.64/30.91 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.91 tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v0) = v2 &
% 221.64/30.91 c_member(all_674_0, v2, v_L) = v3 & c_member(all_674_0, v1, v_L) = v4
% 221.64/30.91 & $i(v2) & ( ~ (v3 = 0) | v4 = 0)))
% 221.64/30.91 (4) all_870_9 = v_y | ? [v0: any] : ? [v1: $i] : ? [v2: any] :
% 221.64/30.91 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.91 tc_Arrow__Order__Mirabelle_Oalt, v_y, all_870_9) = v1 &
% 221.64/30.91 c_member(all_674_0, v1, v_L) = v2 & c_member(all_674_0, all_870_3, v_L)
% 221.64/30.91 = v0 & $i(v1) & (v2 = 0 | v0 = 0))
% 221.64/30.91 (5) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.91 tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v_y) = all_870_5
% 221.64/30.91 (6) tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)
% 221.64/30.91 = all_625_1
% 221.64/30.91 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 221.64/30.91 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.91 tc_Arrow__Order__Mirabelle_Oalt, v0, v1) = v2) | ~ $i(v1) | ~
% 221.64/30.91 $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & c_member(all_674_0, v2, v_L) =
% 221.64/30.91 v3) | ! [v3: $i] : ! [v4: $i] : ( ~
% 221.64/30.91 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.91 tc_Arrow__Order__Mirabelle_Oalt, v0, v3) = v4) | ~ $i(v3) | ?
% 221.64/30.91 [v5: $i] : ? [v6: any] : ? [v7: any] :
% 221.64/30.91 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.91 tc_Arrow__Order__Mirabelle_Oalt, v1, v3) = v5 &
% 221.64/30.91 c_member(all_674_0, v5, v_L) = v6 & c_member(all_674_0, v4, v_L) =
% 221.64/30.91 v7 & $i(v5) & ( ~ (v6 = 0) | v7 = 0))))
% 221.64/30.91 (8) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_674_0, all_870_3, v_L) = v0) |
% 221.64/30.91 ! [v0: $i] : ! [v1: $i] : ( ~
% 221.64/30.91 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.91 tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v0) = v1) | ~ $i(v0) |
% 221.64/30.91 ? [v2: $i] : ? [v3: any] : ? [v4: any] :
% 221.64/30.91 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.91 tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = v2 &
% 221.64/30.91 c_member(all_674_0, v2, v_L) = v3 & c_member(all_674_0, v1, v_L) = v4
% 221.64/30.91 & $i(v2) & ( ~ (v3 = 0) | v4 = 0)))
% 221.64/30.91 (9) c_member(all_625_1, all_870_7, v_L) = all_870_6
% 221.64/30.91 (10) $i(all_870_8)
% 221.64/30.91 (11) all_870_8 = v_y | ? [v0: any] : ? [v1: $i] : ? [v2: any] :
% 221.64/30.91 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.91 tc_Arrow__Order__Mirabelle_Oalt, v_y, all_870_8) = v1 &
% 221.64/30.91 c_member(all_674_0, v1, v_L) = v2 & c_member(all_674_0, all_870_5,
% 221.64/30.91 v_L) = v0 & $i(v1) & (v2 = 0 | v0 = 0))
% 221.64/30.91 (12) c_member(all_625_1, all_870_5, v_L) = all_870_4
% 221.64/30.91 (13) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.91 tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v_y) = all_870_3
% 221.64/30.91 (14) all_870_8 = v_y | ? [v0: any] : ? [v1: $i] : ? [v2: any] :
% 221.64/30.91 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.91 tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v_y) = v1 &
% 221.64/30.91 c_member(all_674_0, v1, v_L) = v2 & c_member(all_674_0, all_870_1,
% 221.64/30.91 v_L) = v0 & $i(v1) & (v2 = 0 | v0 = 0))
% 221.64/30.91 (15) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.91 tc_Arrow__Order__Mirabelle_Oalt, all_870_9, all_870_8) = all_870_7
% 221.64/30.91 (16) ~ (v_x = v_y)
% 221.64/30.91 (17) c_member(all_625_1, all_870_1, v_L) = all_870_0
% 221.64/30.91 (18) all_674_0 = all_625_1
% 221.64/30.91 (19) (all_870_2 = 0 & all_870_8 = v_x & ? [v0: $i] : ? [v1: $i] : ? [v2:
% 221.64/30.91 $i] : ? [v3: int] : ( ~ (v3 = 0) & ~ (v0 = v_x) &
% 221.64/30.91 c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.91 tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v0) = v2 &
% 221.64/30.91 c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.91 tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = v1 &
% 221.64/30.91 c_member(all_683_0, v2, v_L) = v3 & c_member(all_683_0, v1, v_L) = 0
% 221.64/30.91 & $i(v2) & $i(v1) & $i(v0))) | (all_870_6 = 0 & ~ (all_870_8 = v_x)
% 221.64/30.91 & ? [v0: $i] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ? [v4:
% 221.64/30.91 any] : (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.91 tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v0) = v1 &
% 221.64/30.91 c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.91 tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v0) = v3 &
% 221.64/30.91 c_member(all_683_0, v3, v_L) = v4 & c_member(all_683_0, v1, v_L) =
% 221.64/30.91 v2 & $i(v3) & $i(v1) & $i(v0) & ((v2 = 0 & ~ (v4 = 0) & ~ (v0 =
% 221.64/30.91 v_x)) | (v0 = v_x & all_870_4 = 0 & ~ (all_870_2 = 0)))))
% 221.64/30.91 (20) c_member(all_625_1, all_870_3, v_L) = all_870_2
% 221.64/30.91 (21) $i(tc_Arrow__Order__Mirabelle_Oalt)
% 221.64/30.91 (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 221.64/30.91 [v5: $i] : (v1 = v0 | ~ (c_Product__Type_OPair(v5, v4, v3, v2) = v1) |
% 221.64/30.91 ~ (c_Product__Type_OPair(v5, v4, v3, v2) = v0))
% 221.64/30.91 (23) ~ (all_870_9 = v_y)
% 221.64/30.91 (24) ~ (all_870_4 = 0)
% 221.64/30.91 (25) ~ (all_870_0 = 0)
% 221.64/30.91 (26) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 221.64/30.91 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (c_member(v4, v3, v2) = v1) |
% 221.64/30.91 ~ (c_member(v4, v3, v2) = v0))
% 221.64/30.91 (27) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 221.64/30.91 [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: int] : (v8 = 0 | ~
% 221.64/30.91 (tc_prod(v4, v4) = v5) | ~ (c_Product__Type_OPair(v4, v4, v2, v0) =
% 221.64/30.91 v7) | ~ (c_Product__Type_OPair(v4, v4, v1, v0) = v6) | ~
% 221.64/30.91 (c_member(v5, v7, v3) = v8) | ~ (c_member(v5, v6, v3) = 0) | ~
% 221.64/30.91 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v9: any]
% 221.64/30.91 : ? [v10: $i] : ? [v11: any] : (c_Relation_Otrans(v4, v3) = v9 &
% 221.64/30.91 c_Product__Type_OPair(v4, v4, v2, v1) = v10 & c_member(v5, v10, v3)
% 221.64/30.91 = v11 & $i(v10) & ( ~ (v11 = 0) | ~ (v9 = 0))))
% 221.64/30.91 (28) all_683_0 = all_625_1
% 221.64/30.91
% 221.64/30.91 Begin of proof
% 221.64/30.91 |
% 221.64/30.91 | BETA: splitting (11) gives:
% 221.64/30.91 |
% 221.64/30.91 | Case 1:
% 221.64/30.91 | |
% 221.64/30.91 | | (29) all_870_8 = v_y
% 221.64/30.91 | |
% 221.64/30.91 | | REDUCE: (15), (29) imply:
% 221.64/30.91 | | (30) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.91 | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v_y) = all_870_7
% 221.64/30.91 | |
% 221.64/30.91 | | REDUCE: (10), (29) imply:
% 221.64/30.91 | | (31) $i(v_y)
% 221.64/30.91 | |
% 221.64/30.91 | | BETA: splitting (19) gives:
% 221.64/30.91 | |
% 221.64/30.91 | | Case 1:
% 221.64/30.91 | | |
% 221.64/30.91 | | | (32) all_870_2 = 0 & all_870_8 = v_x & ? [v0: $i] : ? [v1: $i] : ?
% 221.64/30.91 | | | [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & ~ (v0 = v_x) &
% 221.64/30.91 | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.91 | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v0) = v2 &
% 221.64/30.91 | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.91 | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = v1 &
% 221.64/30.91 | | | c_member(all_683_0, v2, v_L) = v3 & c_member(all_683_0, v1, v_L)
% 221.64/30.91 | | | = 0 & $i(v2) & $i(v1) & $i(v0))
% 221.64/30.91 | | |
% 221.64/30.91 | | | ALPHA: (32) implies:
% 221.64/30.91 | | | (33) all_870_8 = v_x
% 221.64/30.91 | | |
% 221.64/30.91 | | | COMBINE_EQS: (29), (33) imply:
% 221.64/30.91 | | | (34) v_x = v_y
% 221.64/30.91 | | |
% 221.64/30.91 | | | SIMP: (34) implies:
% 221.64/30.91 | | | (35) v_x = v_y
% 221.64/30.91 | | |
% 221.64/30.91 | | | REDUCE: (16), (35) imply:
% 221.64/30.91 | | | (36) $false
% 221.64/30.91 | | |
% 221.64/30.91 | | | CLOSE: (36) is inconsistent.
% 221.64/30.91 | | |
% 221.64/30.91 | | Case 2:
% 221.64/30.91 | | |
% 221.64/30.92 | | | (37) all_870_6 = 0 & ~ (all_870_8 = v_x) & ? [v0: $i] : ? [v1: $i] :
% 221.64/30.92 | | | ? [v2: any] : ? [v3: $i] : ? [v4: any] :
% 221.64/30.92 | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.92 | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v0) = v1 &
% 221.64/30.92 | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.92 | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v0) = v3 &
% 221.64/30.92 | | | c_member(all_683_0, v3, v_L) = v4 & c_member(all_683_0, v1, v_L)
% 221.64/30.92 | | | = v2 & $i(v3) & $i(v1) & $i(v0) & ((v2 = 0 & ~ (v4 = 0) & ~
% 221.64/30.92 | | | (v0 = v_x)) | (v0 = v_x & all_870_4 = 0 & ~ (all_870_2 =
% 221.64/30.92 | | | 0))))
% 221.64/30.92 | | |
% 221.64/30.92 | | | ALPHA: (37) implies:
% 221.64/30.92 | | | (38) all_870_6 = 0
% 221.64/30.92 | | | (39) ? [v0: $i] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ? [v4:
% 221.64/30.92 | | | any] : (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.92 | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v0) = v1 &
% 221.64/30.92 | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.92 | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v0) = v3 &
% 221.64/30.92 | | | c_member(all_683_0, v3, v_L) = v4 & c_member(all_683_0, v1, v_L)
% 221.64/30.92 | | | = v2 & $i(v3) & $i(v1) & $i(v0) & ((v2 = 0 & ~ (v4 = 0) & ~
% 221.64/30.92 | | | (v0 = v_x)) | (v0 = v_x & all_870_4 = 0 & ~ (all_870_2 =
% 221.64/30.92 | | | 0))))
% 221.64/30.92 | | |
% 221.64/30.92 | | | REDUCE: (9), (38) imply:
% 221.64/30.92 | | | (40) c_member(all_625_1, all_870_7, v_L) = 0
% 221.64/30.92 | | |
% 221.64/30.92 | | | GROUND_INST: instantiating (22) with all_870_3, all_870_7, v_y, all_870_9,
% 221.64/30.92 | | | tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.92 | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with (13), (30)
% 221.64/30.92 | | | gives:
% 221.64/30.92 | | | (41) all_870_3 = all_870_7
% 221.64/30.92 | | |
% 221.64/30.92 | | | REDUCE: (20), (41) imply:
% 221.64/30.92 | | | (42) c_member(all_625_1, all_870_7, v_L) = all_870_2
% 221.64/30.92 | | |
% 221.64/30.92 | | | GROUND_INST: instantiating (26) with 0, all_870_2, v_L, all_870_7,
% 221.64/30.92 | | | all_625_1, simplifying with (40), (42) gives:
% 221.64/30.92 | | | (43) all_870_2 = 0
% 221.64/30.92 | | |
% 221.64/30.92 | | | BETA: splitting (8) gives:
% 221.64/30.92 | | |
% 221.64/30.92 | | | Case 1:
% 221.64/30.92 | | | |
% 221.64/30.92 | | | | (44) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_674_0, all_870_3,
% 221.64/30.92 | | | | v_L) = v0)
% 221.64/30.92 | | | |
% 221.64/30.92 | | | | DELTA: instantiating (44) with fresh symbol all_1178_0 gives:
% 221.64/30.92 | | | | (45) ~ (all_1178_0 = 0) & c_member(all_674_0, all_870_3, v_L) =
% 221.64/30.92 | | | | all_1178_0
% 221.64/30.92 | | | |
% 221.64/30.92 | | | | ALPHA: (45) implies:
% 221.64/30.92 | | | | (46) ~ (all_1178_0 = 0)
% 221.64/30.92 | | | | (47) c_member(all_674_0, all_870_3, v_L) = all_1178_0
% 221.64/30.92 | | | |
% 221.64/30.92 | | | | REDUCE: (18), (41), (47) imply:
% 221.64/30.92 | | | | (48) c_member(all_625_1, all_870_7, v_L) = all_1178_0
% 221.64/30.92 | | | |
% 221.64/30.92 | | | | GROUND_INST: instantiating (26) with 0, all_1178_0, v_L, all_870_7,
% 221.64/30.92 | | | | all_625_1, simplifying with (40), (48) gives:
% 221.64/30.92 | | | | (49) all_1178_0 = 0
% 221.64/30.92 | | | |
% 221.64/30.92 | | | | REDUCE: (46), (49) imply:
% 221.64/30.92 | | | | (50) $false
% 221.64/30.92 | | | |
% 221.64/30.92 | | | | CLOSE: (50) is inconsistent.
% 221.64/30.92 | | | |
% 221.64/30.92 | | | Case 2:
% 221.64/30.92 | | | |
% 221.64/30.92 | | | | (51) ! [v0: $i] : ! [v1: $i] : ( ~
% 221.64/30.92 | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.92 | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v0) = v1) | ~
% 221.64/30.92 | | | | $i(v0) | ? [v2: $i] : ? [v3: any] : ? [v4: any] :
% 221.64/30.92 | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.92 | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = v2 &
% 221.64/30.92 | | | | c_member(all_674_0, v2, v_L) = v3 & c_member(all_674_0, v1,
% 221.64/30.92 | | | | v_L) = v4 & $i(v2) & ( ~ (v3 = 0) | v4 = 0)))
% 221.64/30.92 | | | |
% 221.64/30.92 | | | | DELTA: instantiating (39) with fresh symbols all_1200_0, all_1200_1,
% 221.64/30.92 | | | | all_1200_2, all_1200_3, all_1200_4 gives:
% 221.64/30.92 | | | | (52) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.92 | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, all_1200_4) =
% 221.64/30.92 | | | | all_1200_3 &
% 221.64/30.92 | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.92 | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9, all_1200_4) =
% 221.64/30.92 | | | | all_1200_1 & c_member(all_683_0, all_1200_1, v_L) = all_1200_0 &
% 221.64/30.92 | | | | c_member(all_683_0, all_1200_3, v_L) = all_1200_2 &
% 221.64/30.92 | | | | $i(all_1200_1) & $i(all_1200_3) & $i(all_1200_4) & ((all_1200_2
% 221.64/30.92 | | | | = 0 & ~ (all_1200_0 = 0) & ~ (all_1200_4 = v_x)) |
% 221.64/30.92 | | | | (all_1200_4 = v_x & all_870_4 = 0 & ~ (all_870_2 = 0)))
% 221.64/30.92 | | | |
% 221.64/30.92 | | | | ALPHA: (52) implies:
% 221.64/30.92 | | | | (53) $i(all_1200_4)
% 221.64/30.92 | | | | (54) c_member(all_683_0, all_1200_3, v_L) = all_1200_2
% 221.64/30.92 | | | | (55) c_member(all_683_0, all_1200_1, v_L) = all_1200_0
% 221.64/30.92 | | | | (56) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.92 | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9, all_1200_4) =
% 221.64/30.92 | | | | all_1200_1
% 221.64/30.92 | | | | (57) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.92 | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, all_1200_4) =
% 221.64/30.92 | | | | all_1200_3
% 221.64/30.92 | | | | (58) (all_1200_2 = 0 & ~ (all_1200_0 = 0) & ~ (all_1200_4 = v_x)) |
% 221.64/30.92 | | | | (all_1200_4 = v_x & all_870_4 = 0 & ~ (all_870_2 = 0))
% 221.64/30.92 | | | |
% 221.64/30.92 | | | | REDUCE: (29), (57) imply:
% 221.64/30.92 | | | | (59) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.92 | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, all_1200_4) = all_1200_3
% 221.64/30.92 | | | |
% 221.64/30.92 | | | | REDUCE: (28), (55) imply:
% 221.64/30.92 | | | | (60) c_member(all_625_1, all_1200_1, v_L) = all_1200_0
% 221.64/30.92 | | | |
% 221.64/30.92 | | | | REDUCE: (28), (54) imply:
% 221.64/30.92 | | | | (61) c_member(all_625_1, all_1200_3, v_L) = all_1200_2
% 221.64/30.92 | | | |
% 221.64/30.92 | | | | BETA: splitting (58) gives:
% 221.64/30.92 | | | |
% 221.64/30.92 | | | | Case 1:
% 221.64/30.92 | | | | |
% 221.64/30.92 | | | | | (62) all_1200_2 = 0 & ~ (all_1200_0 = 0) & ~ (all_1200_4 = v_x)
% 221.64/30.92 | | | | |
% 221.64/30.92 | | | | | ALPHA: (62) implies:
% 221.64/30.92 | | | | | (63) all_1200_2 = 0
% 221.64/30.92 | | | | | (64) ~ (all_1200_0 = 0)
% 221.64/30.92 | | | | |
% 221.64/30.92 | | | | | REDUCE: (61), (63) imply:
% 221.64/30.92 | | | | | (65) c_member(all_625_1, all_1200_3, v_L) = 0
% 221.64/30.92 | | | | |
% 221.64/30.92 | | | | | BETA: splitting (3) gives:
% 221.64/30.92 | | | | |
% 221.64/30.92 | | | | | Case 1:
% 221.64/30.92 | | | | | |
% 221.64/30.92 | | | | | | (66) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_674_0, all_870_7,
% 221.64/30.92 | | | | | | v_L) = v0)
% 221.64/30.92 | | | | | |
% 221.64/30.92 | | | | | | REF_CLOSE: (18), (26), (40), (66) are inconsistent by sub-proof #9.
% 221.64/30.92 | | | | | |
% 221.64/30.92 | | | | | Case 2:
% 221.64/30.92 | | | | | |
% 221.64/30.92 | | | | | | (67) ! [v0: $i] : ! [v1: $i] : ( ~
% 221.64/30.92 | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.92 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v0) = v1)
% 221.64/30.92 | | | | | | | ~ $i(v0) | ? [v2: $i] : ? [v3: any] : ? [v4: any] :
% 221.64/30.92 | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.92 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v0) = v2 &
% 221.64/30.92 | | | | | | c_member(all_674_0, v2, v_L) = v3 & c_member(all_674_0,
% 221.64/30.92 | | | | | | v1, v_L) = v4 & $i(v2) & ( ~ (v3 = 0) | v4 = 0)))
% 221.64/30.92 | | | | | |
% 221.64/30.92 | | | | | | GROUND_INST: instantiating (7) with v_y, all_1200_4, all_1200_3,
% 221.64/30.92 | | | | | | simplifying with (31), (53), (59) gives:
% 221.64/30.92 | | | | | | (68) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_674_0,
% 221.64/30.92 | | | | | | all_1200_3, v_L) = v0) | ! [v0: $i] : ! [v1: $i] : ( ~
% 221.64/30.92 | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.92 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = v1) | ~
% 221.64/30.92 | | | | | | $i(v0) | ? [v2: $i] : ? [v3: any] : ? [v4: any] :
% 221.64/30.92 | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.92 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_1200_4, v0) = v2
% 221.64/30.92 | | | | | | & c_member(all_674_0, v2, v_L) = v3 &
% 221.64/30.92 | | | | | | c_member(all_674_0, v1, v_L) = v4 & $i(v2) & ( ~ (v3 =
% 221.64/30.92 | | | | | | 0) | v4 = 0)))
% 221.64/30.92 | | | | | |
% 221.64/30.92 | | | | | | GROUND_INST: instantiating (27) with all_1200_4, v_y, all_870_9,
% 221.64/30.92 | | | | | | v_L, tc_Arrow__Order__Mirabelle_Oalt, all_625_1,
% 221.64/30.92 | | | | | | all_1200_3, all_1200_1, all_1200_0, simplifying with
% 221.64/30.92 | | | | | | (1), (2), (6), (21), (31), (53), (56), (59), (60), (65)
% 221.64/30.92 | | | | | | gives:
% 221.64/30.92 | | | | | | (69) all_1200_0 = 0 | ? [v0: any] : ? [v1: $i] : ? [v2: any] :
% 221.64/30.92 | | | | | | (c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt, v_L) =
% 221.64/30.92 | | | | | | v0 &
% 221.64/30.92 | | | | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.92 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v_y) = v1 &
% 221.64/30.92 | | | | | | c_member(all_625_1, v1, v_L) = v2 & $i(v1) & ( ~ (v2 = 0)
% 221.64/30.92 | | | | | | | ~ (v0 = 0)))
% 221.64/30.92 | | | | | |
% 221.64/30.92 | | | | | | GROUND_INST: instantiating (67) with all_1200_4, all_1200_1,
% 221.64/30.92 | | | | | | simplifying with (53), (56) gives:
% 221.64/30.92 | | | | | | (70) ? [v0: $i] : ? [v1: any] : ? [v2: any] :
% 221.64/30.92 | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.92 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, all_1200_4)
% 221.64/30.92 | | | | | | = v0 & c_member(all_674_0, v0, v_L) = v1 &
% 221.64/30.92 | | | | | | c_member(all_674_0, all_1200_1, v_L) = v2 & $i(v0) & ( ~
% 221.64/30.92 | | | | | | (v1 = 0) | v2 = 0))
% 221.64/30.92 | | | | | |
% 221.64/30.92 | | | | | | GROUND_INST: instantiating (51) with all_1200_4, all_1200_1,
% 221.64/30.92 | | | | | | simplifying with (53), (56) gives:
% 221.64/30.92 | | | | | | (71) ? [v0: $i] : ? [v1: any] : ? [v2: any] :
% 221.64/30.92 | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.92 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, all_1200_4) = v0 &
% 221.64/30.92 | | | | | | c_member(all_674_0, v0, v_L) = v1 & c_member(all_674_0,
% 221.64/30.92 | | | | | | all_1200_1, v_L) = v2 & $i(v0) & ( ~ (v1 = 0) | v2 = 0))
% 221.64/30.92 | | | | | |
% 221.64/30.92 | | | | | | DELTA: instantiating (71) with fresh symbols all_1262_0, all_1262_1,
% 221.64/30.92 | | | | | | all_1262_2 gives:
% 221.64/30.92 | | | | | | (72) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.92 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, all_1200_4) =
% 221.64/30.92 | | | | | | all_1262_2 & c_member(all_674_0, all_1262_2, v_L) =
% 221.64/30.92 | | | | | | all_1262_1 & c_member(all_674_0, all_1200_1, v_L) =
% 221.64/30.92 | | | | | | all_1262_0 & $i(all_1262_2) & ( ~ (all_1262_1 = 0) |
% 221.64/30.92 | | | | | | all_1262_0 = 0)
% 221.64/30.92 | | | | | |
% 221.64/30.92 | | | | | | ALPHA: (72) implies:
% 221.64/30.92 | | | | | | (73) c_member(all_674_0, all_1200_1, v_L) = all_1262_0
% 221.64/30.92 | | | | | | (74) c_member(all_674_0, all_1262_2, v_L) = all_1262_1
% 221.64/30.92 | | | | | | (75) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.92 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, all_1200_4) =
% 221.64/30.92 | | | | | | all_1262_2
% 221.64/30.92 | | | | | | (76) ~ (all_1262_1 = 0) | all_1262_0 = 0
% 221.64/30.92 | | | | | |
% 221.64/30.92 | | | | | | DELTA: instantiating (70) with fresh symbols all_1264_0, all_1264_1,
% 221.64/30.92 | | | | | | all_1264_2 gives:
% 221.64/30.92 | | | | | | (77) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.92 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, all_1200_4) =
% 221.64/30.92 | | | | | | all_1264_2 & c_member(all_674_0, all_1264_2, v_L) =
% 221.64/30.92 | | | | | | all_1264_1 & c_member(all_674_0, all_1200_1, v_L) =
% 221.64/30.92 | | | | | | all_1264_0 & $i(all_1264_2) & ( ~ (all_1264_1 = 0) |
% 221.64/30.92 | | | | | | all_1264_0 = 0)
% 221.64/30.92 | | | | | |
% 221.64/30.92 | | | | | | ALPHA: (77) implies:
% 221.64/30.92 | | | | | | (78) c_member(all_674_0, all_1200_1, v_L) = all_1264_0
% 221.64/30.92 | | | | | | (79) c_member(all_674_0, all_1264_2, v_L) = all_1264_1
% 221.64/30.92 | | | | | | (80) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.92 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, all_1200_4) =
% 221.64/30.92 | | | | | | all_1264_2
% 221.64/30.92 | | | | | |
% 221.64/30.92 | | | | | | REDUCE: (29), (80) imply:
% 221.64/30.92 | | | | | | (81) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.92 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, all_1200_4) =
% 221.64/30.92 | | | | | | all_1264_2
% 221.64/30.92 | | | | | |
% 221.64/30.92 | | | | | | REDUCE: (18), (79) imply:
% 221.64/30.92 | | | | | | (82) c_member(all_625_1, all_1264_2, v_L) = all_1264_1
% 221.64/30.92 | | | | | |
% 221.64/30.92 | | | | | | REDUCE: (18), (74) imply:
% 221.64/30.92 | | | | | | (83) c_member(all_625_1, all_1262_2, v_L) = all_1262_1
% 221.64/30.92 | | | | | |
% 221.64/30.93 | | | | | | REDUCE: (18), (78) imply:
% 221.64/30.93 | | | | | | (84) c_member(all_625_1, all_1200_1, v_L) = all_1264_0
% 221.64/30.93 | | | | | |
% 221.64/30.93 | | | | | | REDUCE: (18), (73) imply:
% 221.64/30.93 | | | | | | (85) c_member(all_625_1, all_1200_1, v_L) = all_1262_0
% 221.64/30.93 | | | | | |
% 221.64/30.93 | | | | | | BETA: splitting (68) gives:
% 221.64/30.93 | | | | | |
% 221.64/30.93 | | | | | | Case 1:
% 221.64/30.93 | | | | | | |
% 221.64/30.93 | | | | | | | (86) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_674_0,
% 221.64/30.93 | | | | | | | all_1200_3, v_L) = v0)
% 221.64/30.93 | | | | | | |
% 221.64/30.93 | | | | | | | DELTA: instantiating (86) with fresh symbol all_1277_0 gives:
% 221.64/30.93 | | | | | | | (87) ~ (all_1277_0 = 0) & c_member(all_674_0, all_1200_3, v_L)
% 221.64/30.93 | | | | | | | = all_1277_0
% 221.64/30.93 | | | | | | |
% 221.64/30.93 | | | | | | | ALPHA: (87) implies:
% 221.64/30.93 | | | | | | | (88) ~ (all_1277_0 = 0)
% 221.64/30.93 | | | | | | | (89) c_member(all_674_0, all_1200_3, v_L) = all_1277_0
% 221.64/30.93 | | | | | | |
% 221.64/30.93 | | | | | | | REDUCE: (18), (89) imply:
% 221.64/30.93 | | | | | | | (90) c_member(all_625_1, all_1200_3, v_L) = all_1277_0
% 221.64/30.93 | | | | | | |
% 221.64/30.93 | | | | | | | GROUND_INST: instantiating (26) with 0, all_1277_0, v_L,
% 221.64/30.93 | | | | | | | all_1200_3, all_625_1, simplifying with (65), (90)
% 221.64/30.93 | | | | | | | gives:
% 221.64/30.93 | | | | | | | (91) all_1277_0 = 0
% 221.64/30.93 | | | | | | |
% 221.64/30.93 | | | | | | | REDUCE: (88), (91) imply:
% 221.64/30.93 | | | | | | | (92) $false
% 221.64/30.93 | | | | | | |
% 221.64/30.93 | | | | | | | CLOSE: (92) is inconsistent.
% 221.64/30.93 | | | | | | |
% 221.64/30.93 | | | | | | Case 2:
% 221.64/30.93 | | | | | | |
% 221.64/30.93 | | | | | | | (93) ! [v0: $i] : ! [v1: $i] : ( ~
% 221.64/30.93 | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.93 | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = v1) | ~
% 221.64/30.93 | | | | | | | $i(v0) | ? [v2: $i] : ? [v3: any] : ? [v4: any] :
% 221.64/30.93 | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.93 | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_1200_4, v0) =
% 221.64/30.93 | | | | | | | v2 & c_member(all_674_0, v2, v_L) = v3 &
% 221.64/30.93 | | | | | | | c_member(all_674_0, v1, v_L) = v4 & $i(v2) & ( ~ (v3 =
% 221.64/30.93 | | | | | | | 0) | v4 = 0)))
% 221.64/30.93 | | | | | | |
% 221.64/30.93 | | | | | | | GROUND_INST: instantiating (93) with all_1200_4, all_1200_3,
% 221.64/30.93 | | | | | | | simplifying with (53), (59) gives:
% 221.64/30.93 | | | | | | | (94) ? [v0: $i] : ? [v1: any] : ? [v2: any] :
% 221.64/30.93 | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.93 | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_1200_4,
% 221.64/30.93 | | | | | | | all_1200_4) = v0 & c_member(all_674_0, v0, v_L) = v1 &
% 221.64/30.93 | | | | | | | c_member(all_674_0, all_1200_3, v_L) = v2 & $i(v0) & ( ~
% 221.64/30.93 | | | | | | | (v1 = 0) | v2 = 0))
% 221.64/30.93 | | | | | | |
% 221.64/30.93 | | | | | | | DELTA: instantiating (94) with fresh symbols all_1278_0,
% 221.64/30.93 | | | | | | | all_1278_1, all_1278_2 gives:
% 221.64/30.93 | | | | | | | (95) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.93 | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_1200_4, all_1200_4)
% 221.64/30.93 | | | | | | | = all_1278_2 & c_member(all_674_0, all_1278_2, v_L) =
% 221.64/30.93 | | | | | | | all_1278_1 & c_member(all_674_0, all_1200_3, v_L) =
% 221.64/30.93 | | | | | | | all_1278_0 & $i(all_1278_2) & ( ~ (all_1278_1 = 0) |
% 221.64/30.93 | | | | | | | all_1278_0 = 0)
% 221.64/30.93 | | | | | | |
% 221.64/30.93 | | | | | | | ALPHA: (95) implies:
% 221.64/30.93 | | | | | | | (96) c_member(all_674_0, all_1200_3, v_L) = all_1278_0
% 221.64/30.93 | | | | | | |
% 221.64/30.93 | | | | | | | REDUCE: (18), (96) imply:
% 221.64/30.93 | | | | | | | (97) c_member(all_625_1, all_1200_3, v_L) = all_1278_0
% 221.64/30.93 | | | | | | |
% 221.64/30.93 | | | | | | | BETA: splitting (69) gives:
% 221.64/30.93 | | | | | | |
% 221.64/30.93 | | | | | | | Case 1:
% 221.64/30.93 | | | | | | | |
% 221.64/30.93 | | | | | | | | (98) all_1200_0 = 0
% 221.64/30.93 | | | | | | | |
% 221.64/30.93 | | | | | | | | REDUCE: (64), (98) imply:
% 221.64/30.93 | | | | | | | | (99) $false
% 221.64/30.93 | | | | | | | |
% 221.64/30.93 | | | | | | | | CLOSE: (99) is inconsistent.
% 221.64/30.93 | | | | | | | |
% 221.64/30.93 | | | | | | | Case 2:
% 221.64/30.93 | | | | | | | |
% 221.64/30.93 | | | | | | | |
% 221.64/30.93 | | | | | | | | GROUND_INST: instantiating (26) with 0, all_1278_0, v_L,
% 221.64/30.93 | | | | | | | | all_1200_3, all_625_1, simplifying with (65), (97)
% 221.64/30.93 | | | | | | | | gives:
% 221.64/30.93 | | | | | | | | (100) all_1278_0 = 0
% 221.64/30.93 | | | | | | | |
% 221.64/30.93 | | | | | | | | GROUND_INST: instantiating (26) with all_1200_0, all_1264_0,
% 221.64/30.93 | | | | | | | | v_L, all_1200_1, all_625_1, simplifying with (60),
% 221.64/30.93 | | | | | | | | (84) gives:
% 221.64/30.93 | | | | | | | | (101) all_1264_0 = all_1200_0
% 221.64/30.93 | | | | | | | |
% 221.64/30.93 | | | | | | | | GROUND_INST: instantiating (26) with all_1262_0, all_1264_0,
% 221.64/30.93 | | | | | | | | v_L, all_1200_1, all_625_1, simplifying with (84),
% 221.64/30.93 | | | | | | | | (85) gives:
% 221.64/30.93 | | | | | | | | (102) all_1264_0 = all_1262_0
% 221.64/30.93 | | | | | | | |
% 221.64/30.93 | | | | | | | | GROUND_INST: instantiating (22) with all_1200_3, all_1264_2,
% 221.64/30.93 | | | | | | | | all_1200_4, v_y, tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.93 | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with
% 221.64/30.93 | | | | | | | | (59), (81) gives:
% 221.64/30.93 | | | | | | | | (103) all_1264_2 = all_1200_3
% 221.64/30.93 | | | | | | | |
% 221.64/30.93 | | | | | | | | GROUND_INST: instantiating (22) with all_1262_2, all_1264_2,
% 221.64/30.93 | | | | | | | | all_1200_4, v_y, tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.93 | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with
% 221.64/30.93 | | | | | | | | (75), (81) gives:
% 221.64/30.93 | | | | | | | | (104) all_1264_2 = all_1262_2
% 221.64/30.93 | | | | | | | |
% 221.64/30.93 | | | | | | | | COMBINE_EQS: (101), (102) imply:
% 221.64/30.93 | | | | | | | | (105) all_1262_0 = all_1200_0
% 221.64/30.93 | | | | | | | |
% 221.64/30.93 | | | | | | | | COMBINE_EQS: (103), (104) imply:
% 221.64/30.93 | | | | | | | | (106) all_1262_2 = all_1200_3
% 221.64/30.93 | | | | | | | |
% 221.64/30.93 | | | | | | | | SIMP: (106) implies:
% 221.64/30.93 | | | | | | | | (107) all_1262_2 = all_1200_3
% 221.64/30.93 | | | | | | | |
% 221.64/30.93 | | | | | | | | REDUCE: (82), (103) imply:
% 221.64/30.93 | | | | | | | | (108) c_member(all_625_1, all_1200_3, v_L) = all_1264_1
% 221.64/30.93 | | | | | | | |
% 221.64/30.93 | | | | | | | | REDUCE: (83), (107) imply:
% 221.64/30.93 | | | | | | | | (109) c_member(all_625_1, all_1200_3, v_L) = all_1262_1
% 221.64/30.93 | | | | | | | |
% 221.64/30.93 | | | | | | | | BETA: splitting (76) gives:
% 221.64/30.93 | | | | | | | |
% 221.64/30.93 | | | | | | | | Case 1:
% 221.64/30.93 | | | | | | | | |
% 221.64/30.93 | | | | | | | | | (110) ~ (all_1262_1 = 0)
% 221.64/30.93 | | | | | | | | |
% 221.64/30.93 | | | | | | | | | GROUND_INST: instantiating (26) with 0, all_1264_1, v_L,
% 221.64/30.93 | | | | | | | | | all_1200_3, all_625_1, simplifying with (65),
% 221.64/30.93 | | | | | | | | | (108) gives:
% 221.64/30.93 | | | | | | | | | (111) all_1264_1 = 0
% 221.64/30.93 | | | | | | | | |
% 221.64/30.93 | | | | | | | | | GROUND_INST: instantiating (26) with all_1262_1, all_1264_1,
% 221.64/30.93 | | | | | | | | | v_L, all_1200_3, all_625_1, simplifying with
% 221.64/30.93 | | | | | | | | | (108), (109) gives:
% 221.64/30.93 | | | | | | | | | (112) all_1264_1 = all_1262_1
% 221.64/30.93 | | | | | | | | |
% 221.64/30.93 | | | | | | | | | COMBINE_EQS: (111), (112) imply:
% 221.64/30.93 | | | | | | | | | (113) all_1262_1 = 0
% 221.64/30.93 | | | | | | | | |
% 221.64/30.93 | | | | | | | | | REDUCE: (110), (113) imply:
% 221.64/30.93 | | | | | | | | | (114) $false
% 221.64/30.93 | | | | | | | | |
% 221.64/30.93 | | | | | | | | | CLOSE: (114) is inconsistent.
% 221.64/30.93 | | | | | | | | |
% 221.64/30.93 | | | | | | | | Case 2:
% 221.64/30.93 | | | | | | | | |
% 221.64/30.93 | | | | | | | | | (115) all_1262_0 = 0
% 221.64/30.93 | | | | | | | | |
% 221.64/30.93 | | | | | | | | | COMBINE_EQS: (105), (115) imply:
% 221.64/30.93 | | | | | | | | | (116) all_1200_0 = 0
% 221.64/30.93 | | | | | | | | |
% 221.64/30.93 | | | | | | | | | SIMP: (116) implies:
% 221.64/30.93 | | | | | | | | | (117) all_1200_0 = 0
% 221.64/30.93 | | | | | | | | |
% 221.64/30.93 | | | | | | | | | REDUCE: (64), (117) imply:
% 221.64/30.93 | | | | | | | | | (118) $false
% 221.64/30.93 | | | | | | | | |
% 221.64/30.93 | | | | | | | | | CLOSE: (118) is inconsistent.
% 221.64/30.93 | | | | | | | | |
% 221.64/30.93 | | | | | | | | End of split
% 221.64/30.93 | | | | | | | |
% 221.64/30.93 | | | | | | | End of split
% 221.64/30.93 | | | | | | |
% 221.64/30.93 | | | | | | End of split
% 221.64/30.93 | | | | | |
% 221.64/30.93 | | | | | End of split
% 221.64/30.93 | | | | |
% 221.64/30.93 | | | | Case 2:
% 221.64/30.93 | | | | |
% 221.64/30.93 | | | | | (119) all_1200_4 = v_x & all_870_4 = 0 & ~ (all_870_2 = 0)
% 221.64/30.93 | | | | |
% 221.64/30.93 | | | | | ALPHA: (119) implies:
% 221.64/30.93 | | | | | (120) ~ (all_870_2 = 0)
% 221.64/30.93 | | | | |
% 221.64/30.93 | | | | | BETA: splitting (4) gives:
% 221.64/30.93 | | | | |
% 221.64/30.93 | | | | | Case 1:
% 221.64/30.93 | | | | | |
% 221.64/30.93 | | | | | | (121) all_870_9 = v_y
% 221.64/30.93 | | | | | |
% 221.64/30.93 | | | | | | REDUCE: (23), (121) imply:
% 221.64/30.93 | | | | | | (122) $false
% 221.64/30.93 | | | | | |
% 221.64/30.93 | | | | | | CLOSE: (122) is inconsistent.
% 221.64/30.93 | | | | | |
% 221.64/30.93 | | | | | Case 2:
% 221.64/30.93 | | | | | |
% 221.64/30.93 | | | | | |
% 221.64/30.93 | | | | | | REDUCE: (43), (120) imply:
% 221.64/30.93 | | | | | | (123) $false
% 221.64/30.93 | | | | | |
% 221.64/30.93 | | | | | | CLOSE: (123) is inconsistent.
% 221.64/30.93 | | | | | |
% 221.64/30.93 | | | | | End of split
% 221.64/30.93 | | | | |
% 221.64/30.93 | | | | End of split
% 221.64/30.93 | | | |
% 221.64/30.93 | | | End of split
% 221.64/30.93 | | |
% 221.64/30.93 | | End of split
% 221.64/30.93 | |
% 221.64/30.93 | Case 2:
% 221.64/30.93 | |
% 221.64/30.93 | | (124) ~ (all_870_8 = v_y)
% 221.64/30.93 | | (125) ? [v0: any] : ? [v1: $i] : ? [v2: any] :
% 221.64/30.93 | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.93 | | tc_Arrow__Order__Mirabelle_Oalt, v_y, all_870_8) = v1 &
% 221.64/30.93 | | c_member(all_674_0, v1, v_L) = v2 & c_member(all_674_0,
% 221.64/30.93 | | all_870_5, v_L) = v0 & $i(v1) & (v2 = 0 | v0 = 0))
% 221.64/30.93 | |
% 221.64/30.93 | | DELTA: instantiating (125) with fresh symbols all_1206_0, all_1206_1,
% 221.64/30.93 | | all_1206_2 gives:
% 221.64/30.93 | | (126) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.93 | | tc_Arrow__Order__Mirabelle_Oalt, v_y, all_870_8) = all_1206_1 &
% 221.64/30.93 | | c_member(all_674_0, all_1206_1, v_L) = all_1206_0 &
% 221.64/30.93 | | c_member(all_674_0, all_870_5, v_L) = all_1206_2 & $i(all_1206_1) &
% 221.64/30.93 | | (all_1206_0 = 0 | all_1206_2 = 0)
% 221.64/30.93 | |
% 221.64/30.93 | | ALPHA: (126) implies:
% 221.64/30.93 | | (127) c_member(all_674_0, all_870_5, v_L) = all_1206_2
% 221.64/30.93 | |
% 221.64/30.93 | | REDUCE: (18), (127) imply:
% 221.64/30.93 | | (128) c_member(all_625_1, all_870_5, v_L) = all_1206_2
% 221.64/30.93 | |
% 221.64/30.93 | | BETA: splitting (14) gives:
% 221.64/30.93 | |
% 221.64/30.93 | | Case 1:
% 221.64/30.93 | | |
% 221.64/30.93 | | | (129) all_870_8 = v_y
% 221.64/30.93 | | |
% 221.64/30.93 | | | REDUCE: (124), (129) imply:
% 221.64/30.93 | | | (130) $false
% 221.64/30.93 | | |
% 221.64/30.93 | | | CLOSE: (130) is inconsistent.
% 221.64/30.93 | | |
% 221.64/30.93 | | Case 2:
% 221.64/30.93 | | |
% 221.64/30.93 | | | (131) ? [v0: any] : ? [v1: $i] : ? [v2: any] :
% 221.64/30.93 | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.93 | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v_y) = v1 &
% 221.64/30.93 | | | c_member(all_674_0, v1, v_L) = v2 & c_member(all_674_0,
% 221.64/30.93 | | | all_870_1, v_L) = v0 & $i(v1) & (v2 = 0 | v0 = 0))
% 221.64/30.93 | | |
% 221.64/30.93 | | | DELTA: instantiating (131) with fresh symbols all_1212_0, all_1212_1,
% 221.64/30.93 | | | all_1212_2 gives:
% 221.64/30.93 | | | (132) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.93 | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v_y) = all_1212_1 &
% 221.64/30.93 | | | c_member(all_674_0, all_1212_1, v_L) = all_1212_0 &
% 221.64/30.93 | | | c_member(all_674_0, all_870_1, v_L) = all_1212_2 & $i(all_1212_1)
% 221.64/30.93 | | | & (all_1212_0 = 0 | all_1212_2 = 0)
% 221.64/30.93 | | |
% 221.64/30.93 | | | ALPHA: (132) implies:
% 221.64/30.93 | | | (133) c_member(all_674_0, all_870_1, v_L) = all_1212_2
% 221.64/30.93 | | | (134) c_member(all_674_0, all_1212_1, v_L) = all_1212_0
% 221.64/30.93 | | | (135) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.93 | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v_y) = all_1212_1
% 221.64/30.93 | | | (136) all_1212_0 = 0 | all_1212_2 = 0
% 221.64/30.93 | | |
% 221.64/30.93 | | | REDUCE: (18), (134) imply:
% 221.64/30.93 | | | (137) c_member(all_625_1, all_1212_1, v_L) = all_1212_0
% 221.64/30.93 | | |
% 221.64/30.93 | | | REDUCE: (18), (133) imply:
% 221.64/30.93 | | | (138) c_member(all_625_1, all_870_1, v_L) = all_1212_2
% 221.64/30.93 | | |
% 221.64/30.93 | | | GROUND_INST: instantiating (26) with all_870_4, all_1206_2, v_L,
% 221.64/30.93 | | | all_870_5, all_625_1, simplifying with (12), (128) gives:
% 221.64/30.93 | | | (139) all_1206_2 = all_870_4
% 221.64/30.93 | | |
% 221.64/30.93 | | | GROUND_INST: instantiating (26) with all_870_0, all_1212_2, v_L,
% 221.64/30.93 | | | all_870_1, all_625_1, simplifying with (17), (138) gives:
% 221.64/30.93 | | | (140) all_1212_2 = all_870_0
% 221.64/30.93 | | |
% 221.64/30.93 | | | GROUND_INST: instantiating (22) with all_870_5, all_1212_1, v_y,
% 221.64/30.93 | | | all_870_8, tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.93 | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with (5), (135)
% 221.64/30.93 | | | gives:
% 221.64/30.93 | | | (141) all_1212_1 = all_870_5
% 221.64/30.93 | | |
% 221.64/30.93 | | | REDUCE: (137), (141) imply:
% 221.64/30.93 | | | (142) c_member(all_625_1, all_870_5, v_L) = all_1212_0
% 221.64/30.93 | | |
% 221.64/30.93 | | | BETA: splitting (136) gives:
% 221.64/30.93 | | |
% 221.64/30.93 | | | Case 1:
% 221.64/30.93 | | | |
% 221.64/30.93 | | | | (143) all_1212_0 = 0
% 221.64/30.93 | | | |
% 221.64/30.93 | | | | REDUCE: (142), (143) imply:
% 221.64/30.93 | | | | (144) c_member(all_625_1, all_870_5, v_L) = 0
% 221.64/30.93 | | | |
% 221.64/30.93 | | | | GROUND_INST: instantiating (26) with all_870_4, 0, v_L, all_870_5,
% 221.64/30.93 | | | | all_625_1, simplifying with (12), (144) gives:
% 221.64/30.93 | | | | (145) all_870_4 = 0
% 221.64/30.93 | | | |
% 221.64/30.93 | | | | REDUCE: (24), (145) imply:
% 221.64/30.93 | | | | (146) $false
% 221.64/30.93 | | | |
% 221.64/30.93 | | | | CLOSE: (146) is inconsistent.
% 221.64/30.93 | | | |
% 221.64/30.93 | | | Case 2:
% 221.64/30.93 | | | |
% 221.64/30.93 | | | | (147) all_1212_2 = 0
% 221.64/30.93 | | | |
% 221.64/30.93 | | | | COMBINE_EQS: (140), (147) imply:
% 221.64/30.93 | | | | (148) all_870_0 = 0
% 221.64/30.93 | | | |
% 221.64/30.93 | | | | REDUCE: (25), (148) imply:
% 221.64/30.93 | | | | (149) $false
% 221.64/30.93 | | | |
% 221.64/30.93 | | | | CLOSE: (149) is inconsistent.
% 221.64/30.93 | | | |
% 221.64/30.93 | | | End of split
% 221.64/30.93 | | |
% 221.64/30.93 | | End of split
% 221.64/30.93 | |
% 221.64/30.93 | End of split
% 221.64/30.93 |
% 221.64/30.93 End of proof
% 221.64/30.93
% 221.64/30.93 Sub-proof #3 shows that the following formulas are inconsistent:
% 221.64/30.93 ----------------------------------------------------------------
% 221.64/30.93 (1) all_870_8 = all_870_9 | ? [v0: any] : ? [v1: $i] : ? [v2: any] :
% 221.64/30.93 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.93 tc_Arrow__Order__Mirabelle_Oalt, all_870_8, all_870_9) = v1 &
% 221.64/30.93 c_member(all_674_0, v1, v_L) = v2 & c_member(all_674_0, all_870_7, v_L)
% 221.64/30.93 = v0 & $i(v1) & (v2 = 0 | v0 = 0))
% 221.64/30.94 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 221.64/30.94 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.94 tc_Arrow__Order__Mirabelle_Oalt, v0, v1) = v2) | ~ $i(v1) | ~
% 221.64/30.94 $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & c_member(all_674_0, v2, v_L) =
% 221.64/30.94 v3) | ! [v3: $i] : ! [v4: $i] : ( ~
% 221.64/30.94 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.94 tc_Arrow__Order__Mirabelle_Oalt, v0, v3) = v4) | ~ $i(v3) | ?
% 221.64/30.94 [v5: $i] : ? [v6: any] : ? [v7: any] :
% 221.64/30.94 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.94 tc_Arrow__Order__Mirabelle_Oalt, v1, v3) = v5 &
% 221.64/30.94 c_member(all_674_0, v5, v_L) = v6 & c_member(all_674_0, v4, v_L) =
% 221.64/30.94 v7 & $i(v5) & ( ~ (v6 = 0) | v7 = 0))))
% 221.64/30.94 (3) c_member(all_625_1, all_870_7, v_L) = all_870_6
% 221.64/30.94 (4) $i(v_y)
% 221.64/30.94 (5) ~ (all_870_9 = v_x)
% 221.64/30.94 (6) all_674_0 = all_625_1
% 221.64/30.94 (7) (all_870_2 = 0 & all_870_8 = v_x & ? [v0: $i] : ? [v1: $i] : ? [v2:
% 221.64/30.94 $i] : ? [v3: int] : ( ~ (v3 = 0) & ~ (v0 = v_x) &
% 221.64/30.94 c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.94 tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v0) = v2 &
% 221.64/30.94 c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.94 tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = v1 &
% 221.64/30.94 c_member(all_683_0, v2, v_L) = v3 & c_member(all_683_0, v1, v_L) = 0
% 221.64/30.94 & $i(v2) & $i(v1) & $i(v0))) | (all_870_6 = 0 & ~ (all_870_8 = v_x)
% 221.64/30.94 & ? [v0: $i] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ? [v4: any]
% 221.64/30.94 : (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.94 tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v0) = v1 &
% 221.64/30.94 c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.94 tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v0) = v3 &
% 221.64/30.94 c_member(all_683_0, v3, v_L) = v4 & c_member(all_683_0, v1, v_L) = v2
% 221.64/30.94 & $i(v3) & $i(v1) & $i(v0) & ((v2 = 0 & ~ (v4 = 0) & ~ (v0 = v_x))
% 221.64/30.94 | (v0 = v_x & all_870_4 = 0 & ~ (all_870_2 = 0)))))
% 221.64/30.94 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 221.64/30.94 [v5: $i] : (v1 = v0 | ~ (c_Product__Type_OPair(v5, v4, v3, v2) = v1) |
% 221.64/30.94 ~ (c_Product__Type_OPair(v5, v4, v3, v2) = v0))
% 221.64/30.94 (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 221.64/30.94 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (c_member(v4, v3, v2) = v1) | ~
% 221.64/30.94 (c_member(v4, v3, v2) = v0))
% 221.64/30.94 (10) all_683_0 = all_625_1
% 221.64/30.94 (11) ~ (all_870_6 = 0)
% 221.64/30.94 (12) ! [v0: $i] : ! [v1: $i] : ( ~
% 221.64/30.94 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.94 tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v0) = v1) | ~ $i(v0)
% 221.64/30.94 | ? [v2: $i] : ? [v3: any] : ? [v4: any] :
% 221.64/30.94 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.94 tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = v2 &
% 221.64/30.94 c_member(all_674_0, v2, v_L) = v3 & c_member(all_674_0, v1, v_L) =
% 221.64/30.94 v4 & $i(v2) & ( ~ (v3 = 0) | v4 = 0)))
% 221.64/30.94
% 221.64/30.94 Begin of proof
% 221.64/30.94 |
% 221.64/30.94 | BETA: splitting (7) gives:
% 221.64/30.94 |
% 221.64/30.94 | Case 1:
% 221.64/30.94 | |
% 221.64/30.94 | | (13) all_870_2 = 0 & all_870_8 = v_x & ? [v0: $i] : ? [v1: $i] : ?
% 221.64/30.94 | | [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & ~ (v0 = v_x) &
% 221.64/30.94 | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.94 | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v0) = v2 &
% 221.64/30.94 | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.94 | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = v1 &
% 221.64/30.94 | | c_member(all_683_0, v2, v_L) = v3 & c_member(all_683_0, v1, v_L) =
% 221.64/30.94 | | 0 & $i(v2) & $i(v1) & $i(v0))
% 221.64/30.94 | |
% 221.64/30.94 | | ALPHA: (13) implies:
% 221.64/30.94 | | (14) all_870_8 = v_x
% 221.64/30.94 | | (15) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 =
% 221.64/30.94 | | 0) & ~ (v0 = v_x) &
% 221.64/30.94 | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.94 | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v0) = v2 &
% 221.64/30.94 | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.94 | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = v1 &
% 221.64/30.94 | | c_member(all_683_0, v2, v_L) = v3 & c_member(all_683_0, v1, v_L) =
% 221.64/30.94 | | 0 & $i(v2) & $i(v1) & $i(v0))
% 221.64/30.94 | |
% 221.64/30.94 | | DELTA: instantiating (15) with fresh symbols all_1197_0, all_1197_1,
% 221.64/30.94 | | all_1197_2, all_1197_3 gives:
% 221.64/30.94 | | (16) ~ (all_1197_0 = 0) & ~ (all_1197_3 = v_x) &
% 221.64/30.94 | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.94 | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9, all_1197_3) =
% 221.64/30.94 | | all_1197_1 & c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.94 | | tc_Arrow__Order__Mirabelle_Oalt, v_y, all_1197_3) = all_1197_2 &
% 221.64/30.94 | | c_member(all_683_0, all_1197_1, v_L) = all_1197_0 &
% 221.64/30.94 | | c_member(all_683_0, all_1197_2, v_L) = 0 & $i(all_1197_1) &
% 221.64/30.94 | | $i(all_1197_2) & $i(all_1197_3)
% 221.64/30.94 | |
% 221.64/30.94 | | ALPHA: (16) implies:
% 221.64/30.94 | | (17) ~ (all_1197_0 = 0)
% 221.64/30.94 | | (18) $i(all_1197_3)
% 221.64/30.94 | | (19) c_member(all_683_0, all_1197_2, v_L) = 0
% 221.64/30.94 | | (20) c_member(all_683_0, all_1197_1, v_L) = all_1197_0
% 221.64/30.94 | | (21) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.94 | | tc_Arrow__Order__Mirabelle_Oalt, v_y, all_1197_3) = all_1197_2
% 221.64/30.94 | | (22) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.94 | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9, all_1197_3) =
% 221.64/30.94 | | all_1197_1
% 221.64/30.94 | |
% 221.64/30.94 | | REDUCE: (10), (20) imply:
% 221.64/30.94 | | (23) c_member(all_625_1, all_1197_1, v_L) = all_1197_0
% 221.64/30.94 | |
% 221.64/30.94 | | REDUCE: (10), (19) imply:
% 221.64/30.94 | | (24) c_member(all_625_1, all_1197_2, v_L) = 0
% 221.64/30.94 | |
% 221.64/30.94 | | BETA: splitting (1) gives:
% 221.64/30.94 | |
% 221.64/30.94 | | Case 1:
% 221.64/30.94 | | |
% 221.64/30.94 | | | (25) all_870_8 = all_870_9
% 221.64/30.94 | | |
% 221.64/30.94 | | | COMBINE_EQS: (14), (25) imply:
% 221.64/30.94 | | | (26) all_870_9 = v_x
% 221.64/30.94 | | |
% 221.64/30.94 | | | SIMP: (26) implies:
% 221.64/30.94 | | | (27) all_870_9 = v_x
% 221.64/30.94 | | |
% 221.64/30.94 | | | REDUCE: (5), (27) imply:
% 221.64/30.94 | | | (28) $false
% 221.64/30.94 | | |
% 221.64/30.94 | | | CLOSE: (28) is inconsistent.
% 221.64/30.94 | | |
% 221.64/30.94 | | Case 2:
% 221.64/30.94 | | |
% 221.64/30.94 | | | (29) ? [v0: any] : ? [v1: $i] : ? [v2: any] :
% 221.64/30.94 | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.94 | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, all_870_9) = v1 &
% 221.64/30.94 | | | c_member(all_674_0, v1, v_L) = v2 & c_member(all_674_0,
% 221.64/30.94 | | | all_870_7, v_L) = v0 & $i(v1) & (v2 = 0 | v0 = 0))
% 221.64/30.94 | | |
% 221.64/30.94 | | | DELTA: instantiating (29) with fresh symbols all_1203_0, all_1203_1,
% 221.64/30.94 | | | all_1203_2 gives:
% 221.64/30.94 | | | (30) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.94 | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, all_870_9) =
% 221.64/30.94 | | | all_1203_1 & c_member(all_674_0, all_1203_1, v_L) = all_1203_0 &
% 221.64/30.94 | | | c_member(all_674_0, all_870_7, v_L) = all_1203_2 & $i(all_1203_1)
% 221.64/30.94 | | | & (all_1203_0 = 0 | all_1203_2 = 0)
% 221.64/30.94 | | |
% 221.64/30.94 | | | ALPHA: (30) implies:
% 221.64/30.94 | | | (31) c_member(all_674_0, all_870_7, v_L) = all_1203_2
% 221.64/30.94 | | | (32) all_1203_0 = 0 | all_1203_2 = 0
% 221.64/30.94 | | |
% 221.64/30.94 | | | REDUCE: (6), (31) imply:
% 221.64/30.94 | | | (33) c_member(all_625_1, all_870_7, v_L) = all_1203_2
% 221.64/30.94 | | |
% 221.64/30.94 | | | GROUND_INST: instantiating (9) with all_870_6, all_1203_2, v_L, all_870_7,
% 221.64/30.94 | | | all_625_1, simplifying with (3), (33) gives:
% 221.64/30.94 | | | (34) all_1203_2 = all_870_6
% 221.64/30.94 | | |
% 221.64/30.94 | | | BETA: splitting (32) gives:
% 221.64/30.94 | | |
% 221.64/30.94 | | | Case 1:
% 221.64/30.94 | | | |
% 221.64/30.94 | | | |
% 221.64/30.94 | | | | GROUND_INST: instantiating (2) with v_y, all_1197_3, all_1197_2,
% 221.64/30.94 | | | | simplifying with (4), (18), (21) gives:
% 221.64/30.94 | | | | (35) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_674_0, all_1197_2,
% 221.64/30.94 | | | | v_L) = v0) | ! [v0: $i] : ! [v1: $i] : ( ~
% 221.64/30.94 | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.94 | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = v1) | ~
% 221.64/30.94 | | | | $i(v0) | ? [v2: $i] : ? [v3: any] : ? [v4: any] :
% 221.64/30.94 | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.94 | | | | tc_Arrow__Order__Mirabelle_Oalt, all_1197_3, v0) = v2 &
% 221.64/30.94 | | | | c_member(all_674_0, v2, v_L) = v3 & c_member(all_674_0, v1,
% 221.64/30.94 | | | | v_L) = v4 & $i(v2) & ( ~ (v3 = 0) | v4 = 0)))
% 221.64/30.94 | | | |
% 221.64/30.94 | | | | GROUND_INST: instantiating (12) with all_1197_3, all_1197_1, simplifying
% 221.64/30.94 | | | | with (18), (22) gives:
% 221.64/30.94 | | | | (36) ? [v0: $i] : ? [v1: any] : ? [v2: any] :
% 221.64/30.94 | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.94 | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, all_1197_3) = v0 &
% 221.64/30.94 | | | | c_member(all_674_0, v0, v_L) = v1 & c_member(all_674_0,
% 221.64/30.94 | | | | all_1197_1, v_L) = v2 & $i(v0) & ( ~ (v1 = 0) | v2 = 0))
% 221.64/30.94 | | | |
% 221.64/30.94 | | | | DELTA: instantiating (36) with fresh symbols all_1260_0, all_1260_1,
% 221.64/30.94 | | | | all_1260_2 gives:
% 221.64/30.94 | | | | (37) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.94 | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, all_1197_3) = all_1260_2
% 221.64/30.94 | | | | & c_member(all_674_0, all_1260_2, v_L) = all_1260_1 &
% 221.64/30.94 | | | | c_member(all_674_0, all_1197_1, v_L) = all_1260_0 &
% 221.64/30.94 | | | | $i(all_1260_2) & ( ~ (all_1260_1 = 0) | all_1260_0 = 0)
% 221.64/30.94 | | | |
% 221.64/30.94 | | | | ALPHA: (37) implies:
% 221.64/30.94 | | | | (38) c_member(all_674_0, all_1197_1, v_L) = all_1260_0
% 221.64/30.94 | | | | (39) c_member(all_674_0, all_1260_2, v_L) = all_1260_1
% 221.64/30.94 | | | | (40) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.94 | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, all_1197_3) = all_1260_2
% 221.64/30.94 | | | | (41) ~ (all_1260_1 = 0) | all_1260_0 = 0
% 221.64/30.94 | | | |
% 221.64/30.94 | | | | REDUCE: (6), (39) imply:
% 221.64/30.94 | | | | (42) c_member(all_625_1, all_1260_2, v_L) = all_1260_1
% 221.64/30.94 | | | |
% 221.64/30.94 | | | | REDUCE: (6), (38) imply:
% 221.64/30.94 | | | | (43) c_member(all_625_1, all_1197_1, v_L) = all_1260_0
% 221.64/30.94 | | | |
% 221.64/30.94 | | | | BETA: splitting (35) gives:
% 221.64/30.94 | | | |
% 221.64/30.94 | | | | Case 1:
% 221.64/30.94 | | | | |
% 221.64/30.94 | | | | | (44) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_674_0, all_1197_2,
% 221.64/30.94 | | | | | v_L) = v0)
% 221.64/30.94 | | | | |
% 221.64/30.94 | | | | | DELTA: instantiating (44) with fresh symbol all_1285_0 gives:
% 221.64/30.94 | | | | | (45) ~ (all_1285_0 = 0) & c_member(all_674_0, all_1197_2, v_L) =
% 221.64/30.94 | | | | | all_1285_0
% 221.64/30.94 | | | | |
% 221.64/30.94 | | | | | ALPHA: (45) implies:
% 221.64/30.94 | | | | | (46) ~ (all_1285_0 = 0)
% 221.64/30.95 | | | | | (47) c_member(all_674_0, all_1197_2, v_L) = all_1285_0
% 221.64/30.95 | | | | |
% 221.64/30.95 | | | | | REDUCE: (6), (47) imply:
% 221.64/30.95 | | | | | (48) c_member(all_625_1, all_1197_2, v_L) = all_1285_0
% 221.64/30.95 | | | | |
% 221.64/30.95 | | | | | GROUND_INST: instantiating (9) with 0, all_1285_0, v_L, all_1197_2,
% 221.64/30.95 | | | | | all_625_1, simplifying with (24), (48) gives:
% 221.64/30.95 | | | | | (49) all_1285_0 = 0
% 221.64/30.95 | | | | |
% 221.64/30.95 | | | | | REDUCE: (46), (49) imply:
% 221.64/30.95 | | | | | (50) $false
% 221.64/30.95 | | | | |
% 221.64/30.95 | | | | | CLOSE: (50) is inconsistent.
% 221.64/30.95 | | | | |
% 221.64/30.95 | | | | Case 2:
% 221.64/30.95 | | | | |
% 221.64/30.95 | | | | | (51) ! [v0: $i] : ! [v1: $i] : ( ~
% 221.64/30.95 | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.95 | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = v1) | ~
% 221.64/30.95 | | | | | $i(v0) | ? [v2: $i] : ? [v3: any] : ? [v4: any] :
% 221.64/30.95 | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.95 | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_1197_3, v0) = v2 &
% 221.64/30.95 | | | | | c_member(all_674_0, v2, v_L) = v3 & c_member(all_674_0,
% 221.64/30.95 | | | | | v1, v_L) = v4 & $i(v2) & ( ~ (v3 = 0) | v4 = 0)))
% 221.64/30.95 | | | | |
% 221.64/30.95 | | | | | GROUND_INST: instantiating (51) with all_1197_3, all_1197_2,
% 221.64/30.95 | | | | | simplifying with (18), (21) gives:
% 221.64/30.95 | | | | | (52) ? [v0: $i] : ? [v1: any] : ? [v2: any] :
% 221.64/30.95 | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.95 | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_1197_3, all_1197_3) =
% 221.64/30.95 | | | | | v0 & c_member(all_674_0, v0, v_L) = v1 & c_member(all_674_0,
% 221.64/30.95 | | | | | all_1197_2, v_L) = v2 & $i(v0) & ( ~ (v1 = 0) | v2 = 0))
% 221.64/30.95 | | | | |
% 221.64/30.95 | | | | | DELTA: instantiating (52) with fresh symbols all_1288_0, all_1288_1,
% 221.64/30.95 | | | | | all_1288_2 gives:
% 221.64/30.95 | | | | | (53) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.95 | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_1197_3, all_1197_3) =
% 221.64/30.95 | | | | | all_1288_2 & c_member(all_674_0, all_1288_2, v_L) = all_1288_1
% 221.64/30.95 | | | | | & c_member(all_674_0, all_1197_2, v_L) = all_1288_0 &
% 221.64/30.95 | | | | | $i(all_1288_2) & ( ~ (all_1288_1 = 0) | all_1288_0 = 0)
% 221.64/30.95 | | | | |
% 221.64/30.95 | | | | | ALPHA: (53) implies:
% 221.64/30.95 | | | | | (54) c_member(all_674_0, all_1197_2, v_L) = all_1288_0
% 221.64/30.95 | | | | |
% 221.64/30.95 | | | | | REDUCE: (6), (54) imply:
% 221.64/30.95 | | | | | (55) c_member(all_625_1, all_1197_2, v_L) = all_1288_0
% 221.64/30.95 | | | | |
% 221.64/30.95 | | | | | GROUND_INST: instantiating (9) with 0, all_1288_0, v_L, all_1197_2,
% 221.64/30.95 | | | | | all_625_1, simplifying with (24), (55) gives:
% 221.64/30.95 | | | | | (56) all_1288_0 = 0
% 221.64/30.95 | | | | |
% 221.64/30.95 | | | | | GROUND_INST: instantiating (9) with all_1197_0, all_1260_0, v_L,
% 221.64/30.95 | | | | | all_1197_1, all_625_1, simplifying with (23), (43) gives:
% 221.64/30.95 | | | | | (57) all_1260_0 = all_1197_0
% 221.64/30.95 | | | | |
% 221.64/30.95 | | | | | GROUND_INST: instantiating (8) with all_1197_2, all_1260_2,
% 221.64/30.95 | | | | | all_1197_3, v_y, tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.95 | | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with (21),
% 221.64/30.95 | | | | | (40) gives:
% 221.64/30.95 | | | | | (58) all_1260_2 = all_1197_2
% 221.64/30.95 | | | | |
% 221.64/30.95 | | | | | REDUCE: (42), (58) imply:
% 221.64/30.95 | | | | | (59) c_member(all_625_1, all_1197_2, v_L) = all_1260_1
% 221.64/30.95 | | | | |
% 221.64/30.95 | | | | | BETA: splitting (41) gives:
% 221.64/30.95 | | | | |
% 221.64/30.95 | | | | | Case 1:
% 221.64/30.95 | | | | | |
% 221.64/30.95 | | | | | | (60) ~ (all_1260_1 = 0)
% 221.64/30.95 | | | | | |
% 221.64/30.95 | | | | | | GROUND_INST: instantiating (9) with 0, all_1260_1, v_L, all_1197_2,
% 221.64/30.95 | | | | | | all_625_1, simplifying with (24), (59) gives:
% 221.64/30.95 | | | | | | (61) all_1260_1 = 0
% 221.64/30.95 | | | | | |
% 221.64/30.95 | | | | | | REDUCE: (60), (61) imply:
% 221.64/30.95 | | | | | | (62) $false
% 221.64/30.95 | | | | | |
% 221.64/30.95 | | | | | | CLOSE: (62) is inconsistent.
% 221.64/30.95 | | | | | |
% 221.64/30.95 | | | | | Case 2:
% 221.64/30.95 | | | | | |
% 221.64/30.95 | | | | | | (63) all_1260_0 = 0
% 221.64/30.95 | | | | | |
% 221.64/30.95 | | | | | | COMBINE_EQS: (57), (63) imply:
% 221.64/30.95 | | | | | | (64) all_1197_0 = 0
% 221.64/30.95 | | | | | |
% 221.64/30.95 | | | | | | REDUCE: (17), (64) imply:
% 221.64/30.95 | | | | | | (65) $false
% 221.64/30.95 | | | | | |
% 221.64/30.95 | | | | | | CLOSE: (65) is inconsistent.
% 221.64/30.95 | | | | | |
% 221.64/30.95 | | | | | End of split
% 221.64/30.95 | | | | |
% 221.64/30.95 | | | | End of split
% 221.64/30.95 | | | |
% 221.64/30.95 | | | Case 2:
% 221.64/30.95 | | | |
% 221.64/30.95 | | | | (66) all_1203_2 = 0
% 221.64/30.95 | | | |
% 221.64/30.95 | | | | COMBINE_EQS: (34), (66) imply:
% 221.64/30.95 | | | | (67) all_870_6 = 0
% 221.64/30.95 | | | |
% 221.64/30.95 | | | | REDUCE: (11), (67) imply:
% 221.64/30.95 | | | | (68) $false
% 221.64/30.95 | | | |
% 221.64/30.95 | | | | CLOSE: (68) is inconsistent.
% 221.64/30.95 | | | |
% 221.64/30.95 | | | End of split
% 221.64/30.95 | | |
% 221.64/30.95 | | End of split
% 221.64/30.95 | |
% 221.64/30.95 | Case 2:
% 221.64/30.95 | |
% 221.64/30.95 | | (69) all_870_6 = 0 & ~ (all_870_8 = v_x) & ? [v0: $i] : ? [v1: $i] :
% 221.64/30.95 | | ? [v2: any] : ? [v3: $i] : ? [v4: any] :
% 221.64/30.95 | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.95 | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v0) = v1 &
% 221.64/30.95 | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.95 | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v0) = v3 &
% 221.64/30.95 | | c_member(all_683_0, v3, v_L) = v4 & c_member(all_683_0, v1, v_L) =
% 221.64/30.95 | | v2 & $i(v3) & $i(v1) & $i(v0) & ((v2 = 0 & ~ (v4 = 0) & ~ (v0 =
% 221.64/30.95 | | v_x)) | (v0 = v_x & all_870_4 = 0 & ~ (all_870_2 = 0))))
% 221.64/30.95 | |
% 221.64/30.95 | | ALPHA: (69) implies:
% 221.64/30.95 | | (70) all_870_6 = 0
% 221.64/30.95 | |
% 221.64/30.95 | | REDUCE: (11), (70) imply:
% 221.64/30.95 | | (71) $false
% 221.64/30.95 | |
% 221.64/30.95 | | CLOSE: (71) is inconsistent.
% 221.64/30.95 | |
% 221.64/30.95 | End of split
% 221.64/30.95 |
% 221.64/30.95 End of proof
% 221.64/30.95
% 221.64/30.95 Sub-proof #4 shows that the following formulas are inconsistent:
% 221.64/30.95 ----------------------------------------------------------------
% 221.64/30.95 (1) $i(v_L)
% 221.64/30.95 (2) $i(all_870_9)
% 221.64/30.95 (3) ? [v0: $i] : ? [v1: any] : ? [v2: any] :
% 221.64/30.95 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.95 tc_Arrow__Order__Mirabelle_Oalt, v_y, v_y) = v0 & c_member(all_674_0,
% 221.64/30.95 v0, v_L) = v1 & c_member(all_674_0, all_870_3, v_L) = v2 & $i(v0) & (
% 221.64/30.95 ~ (v1 = 0) | v2 = 0))
% 221.64/30.95 (4) tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)
% 221.64/30.95 = all_625_1
% 221.64/30.95 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 221.64/30.95 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.95 tc_Arrow__Order__Mirabelle_Oalt, v0, v1) = v2) | ~ $i(v1) | ~
% 221.64/30.95 $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & c_member(all_674_0, v2, v_L) =
% 221.64/30.95 v3) | ! [v3: $i] : ! [v4: $i] : ( ~
% 221.64/30.95 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.95 tc_Arrow__Order__Mirabelle_Oalt, v0, v3) = v4) | ~ $i(v3) | ?
% 221.64/30.95 [v5: $i] : ? [v6: any] : ? [v7: any] :
% 221.64/30.95 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.95 tc_Arrow__Order__Mirabelle_Oalt, v1, v3) = v5 &
% 221.64/30.95 c_member(all_674_0, v5, v_L) = v6 & c_member(all_674_0, v4, v_L) =
% 221.64/30.95 v7 & $i(v5) & ( ~ (v6 = 0) | v7 = 0))))
% 221.64/30.95 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 221.64/30.95 [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : (v1 = v0 | ~
% 221.64/30.95 (tc_prod(v5, v4) = v6) | ~ (c_Product__Type_OPair(v5, v4, v2, v1) =
% 221.64/30.95 v7) | ~ (c_Product__Type_OPair(v5, v4, v2, v0) = v8) | ~
% 221.64/30.95 (c_member(v6, v8, v3) = 0) | ~ (c_member(v6, v7, v3) = 0) | ~ $i(v5)
% 221.64/30.95 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v9:
% 221.64/30.95 int] : ( ~ (v9 = 0) & c_Relation_Osingle__valued(v5, v4, v3) = v9))
% 221.64/30.95 (7) ! [v0: $i] : ! [v1: $i] : ( ~
% 221.64/30.95 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.95 tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v0) = v1) | ~ $i(v0) |
% 221.64/30.95 ? [v2: $i] : ? [v3: any] : ? [v4: any] :
% 221.64/30.95 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.95 tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v0) = v2 &
% 221.64/30.95 c_member(all_674_0, v2, v_L) = v3 & c_member(all_674_0, v1, v_L) = v4
% 221.64/30.95 & $i(v2) & ( ~ (v3 = 0) | v4 = 0)))
% 221.64/30.95 (8) $i(all_625_1)
% 221.64/30.95 (9) c_member(all_625_1, all_870_7, v_L) = 0
% 221.64/30.95 (10) $i(all_870_8)
% 221.64/30.95 (11) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.95 tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v_y) = all_870_3
% 221.64/30.95 (12) $i(v_y)
% 221.64/30.95 (13) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.95 tc_Arrow__Order__Mirabelle_Oalt, all_870_9, all_870_8) = all_870_7
% 221.64/30.95 (14) ~ (v_x = v_y)
% 221.64/30.95 (15) all_870_2 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & hBOOL(v0) =
% 221.64/30.95 v1 & hAPP(v_L, all_870_3) = v0 & $i(v0))
% 221.64/30.95 (16) all_674_0 = all_625_1
% 221.64/30.95 (17) c_member(all_625_1, all_870_1, v_L) = 0
% 221.64/30.95 (18) (all_870_2 = 0 & all_870_8 = v_x & ? [v0: $i] : ? [v1: $i] : ? [v2:
% 221.64/30.95 $i] : ? [v3: int] : ( ~ (v3 = 0) & ~ (v0 = v_x) &
% 221.64/30.95 c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.95 tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v0) = v2 &
% 221.64/30.95 c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.64/30.95 tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = v1 &
% 221.64/30.95 c_member(all_683_0, v2, v_L) = v3 & c_member(all_683_0, v1, v_L) = 0
% 221.64/30.95 & $i(v2) & $i(v1) & $i(v0))) | (all_870_6 = 0 & ~ (all_870_8 = v_x)
% 221.64/30.95 & ? [v0: $i] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ? [v4:
% 221.85/30.95 any] : (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.95 tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v0) = v1 &
% 221.85/30.95 c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.95 tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v0) = v3 &
% 221.85/30.95 c_member(all_683_0, v3, v_L) = v4 & c_member(all_683_0, v1, v_L) =
% 221.85/30.95 v2 & $i(v3) & $i(v1) & $i(v0) & ((v2 = 0 & ~ (v4 = 0) & ~ (v0 =
% 221.85/30.95 v_x)) | (v0 = v_x & all_870_4 = 0 & ~ (all_870_2 = 0)))))
% 221.85/30.95 (19) c_member(all_625_1, all_870_3, v_L) = all_870_2
% 221.85/30.95 (20) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.95 tc_Arrow__Order__Mirabelle_Oalt, v_y, all_870_8) = all_870_1
% 221.85/30.95 (21) ! [v0: $i] : ! [v1: $i] : ( ~
% 221.85/30.95 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.95 tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = v1) | ~ $i(v0) | ?
% 221.85/30.95 [v2: $i] : ? [v3: any] : ? [v4: any] :
% 221.85/30.95 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.95 tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v0) = v2 &
% 221.85/30.95 c_member(all_674_0, v2, v_L) = v3 & c_member(all_674_0, v1, v_L) =
% 221.85/30.95 v4 & $i(v2) & ( ~ (v3 = 0) | v4 = 0)))
% 221.85/30.96 (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 221.85/30.96 (c_member(v2, v1, v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 221.85/30.96 [v4: $i] : ? [v5: int] : ( ~ (v5 = 0) & hBOOL(v4) = v5 & hAPP(v0, v1)
% 221.85/30.96 = v4 & $i(v4)))
% 221.85/30.96 (23) $i(tc_Arrow__Order__Mirabelle_Oalt)
% 221.85/30.96 (24) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 221.85/30.96 [v5: $i] : (v1 = v0 | ~ (c_Product__Type_OPair(v5, v4, v3, v2) = v1) |
% 221.85/30.96 ~ (c_Product__Type_OPair(v5, v4, v3, v2) = v0))
% 221.85/30.96 (25) ~ (all_870_4 = 0)
% 221.85/30.96 (26) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 221.85/30.96 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (c_member(v4, v3, v2) = v1) |
% 221.85/30.96 ~ (c_member(v4, v3, v2) = v0))
% 221.85/30.96 (27) all_683_0 = all_625_1
% 221.85/30.96 (28) ! [v0: $i] : ! [v1: $i] : ( ~
% 221.85/30.96 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.96 tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v0) = v1) | ~ $i(v0)
% 221.85/30.96 | ? [v2: $i] : ? [v3: any] : ? [v4: any] :
% 221.85/30.96 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.96 tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = v2 &
% 221.85/30.96 c_member(all_674_0, v2, v_L) = v3 & c_member(all_674_0, v1, v_L) =
% 221.85/30.96 v4 & $i(v2) & ( ~ (v3 = 0) | v4 = 0)))
% 221.85/30.96
% 221.85/30.96 Begin of proof
% 221.85/30.96 |
% 221.85/30.96 | DELTA: instantiating (3) with fresh symbols all_1195_0, all_1195_1, all_1195_2
% 221.85/30.96 | gives:
% 221.85/30.96 | (29) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.96 | tc_Arrow__Order__Mirabelle_Oalt, v_y, v_y) = all_1195_2 &
% 221.85/30.96 | c_member(all_674_0, all_1195_2, v_L) = all_1195_1 &
% 221.85/30.96 | c_member(all_674_0, all_870_3, v_L) = all_1195_0 & $i(all_1195_2) & (
% 221.85/30.96 | ~ (all_1195_1 = 0) | all_1195_0 = 0)
% 221.85/30.96 |
% 221.85/30.96 | ALPHA: (29) implies:
% 221.85/30.96 | (30) c_member(all_674_0, all_870_3, v_L) = all_1195_0
% 221.85/30.96 |
% 221.85/30.96 | REDUCE: (16), (30) imply:
% 221.85/30.96 | (31) c_member(all_625_1, all_870_3, v_L) = all_1195_0
% 221.85/30.96 |
% 221.85/30.96 | GROUND_INST: instantiating (26) with all_870_2, all_1195_0, v_L, all_870_3,
% 221.85/30.96 | all_625_1, simplifying with (19), (31) gives:
% 221.85/30.96 | (32) all_1195_0 = all_870_2
% 221.85/30.96 |
% 221.85/30.96 | BETA: splitting (15) gives:
% 221.85/30.96 |
% 221.85/30.96 | Case 1:
% 221.85/30.96 | |
% 221.85/30.96 | | (33) all_870_2 = 0
% 221.85/30.96 | |
% 221.85/30.96 | | REDUCE: (19), (33) imply:
% 221.85/30.96 | | (34) c_member(all_625_1, all_870_3, v_L) = 0
% 221.85/30.96 | |
% 221.85/30.96 | | GROUND_INST: instantiating (6) with v_y, all_870_8, all_870_9, v_L,
% 221.85/30.96 | | tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.96 | | tc_Arrow__Order__Mirabelle_Oalt, all_625_1, all_870_7,
% 221.85/30.96 | | all_870_3, simplifying with (1), (2), (4), (9), (10), (11),
% 221.85/30.96 | | (12), (13), (23), (34) gives:
% 221.85/30.96 | | (35) all_870_8 = v_y | ? [v0: int] : ( ~ (v0 = 0) &
% 221.85/30.96 | | c_Relation_Osingle__valued(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.96 | | tc_Arrow__Order__Mirabelle_Oalt, v_L) = v0)
% 221.85/30.96 | |
% 221.85/30.96 | | BETA: splitting (18) gives:
% 221.85/30.96 | |
% 221.85/30.96 | | Case 1:
% 221.85/30.96 | | |
% 221.85/30.96 | | | (36) all_870_2 = 0 & all_870_8 = v_x & ? [v0: $i] : ? [v1: $i] : ?
% 221.85/30.96 | | | [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & ~ (v0 = v_x) &
% 221.85/30.96 | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.96 | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v0) = v2 &
% 221.85/30.96 | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.96 | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = v1 &
% 221.85/30.96 | | | c_member(all_683_0, v2, v_L) = v3 & c_member(all_683_0, v1, v_L)
% 221.85/30.96 | | | = 0 & $i(v2) & $i(v1) & $i(v0))
% 221.85/30.96 | | |
% 221.85/30.96 | | | ALPHA: (36) implies:
% 221.85/30.96 | | | (37) all_870_8 = v_x
% 221.85/30.96 | | | (38) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 =
% 221.85/30.96 | | | 0) & ~ (v0 = v_x) &
% 221.85/30.96 | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.96 | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v0) = v2 &
% 221.85/30.96 | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.96 | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = v1 &
% 221.85/30.96 | | | c_member(all_683_0, v2, v_L) = v3 & c_member(all_683_0, v1, v_L)
% 221.85/30.96 | | | = 0 & $i(v2) & $i(v1) & $i(v0))
% 221.85/30.96 | | |
% 221.85/30.96 | | | DELTA: instantiating (38) with fresh symbols all_1391_0, all_1391_1,
% 221.85/30.96 | | | all_1391_2, all_1391_3 gives:
% 221.85/30.96 | | | (39) ~ (all_1391_0 = 0) & ~ (all_1391_3 = v_x) &
% 221.85/30.96 | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.96 | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9, all_1391_3) =
% 221.85/30.96 | | | all_1391_1 &
% 221.85/30.96 | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.96 | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, all_1391_3) = all_1391_2 &
% 221.85/30.96 | | | c_member(all_683_0, all_1391_1, v_L) = all_1391_0 &
% 221.85/30.96 | | | c_member(all_683_0, all_1391_2, v_L) = 0 & $i(all_1391_1) &
% 221.85/30.96 | | | $i(all_1391_2) & $i(all_1391_3)
% 221.85/30.96 | | |
% 221.85/30.96 | | | ALPHA: (39) implies:
% 221.85/30.96 | | | (40) ~ (all_1391_0 = 0)
% 221.85/30.96 | | | (41) $i(all_1391_3)
% 221.85/30.96 | | | (42) $i(all_1391_1)
% 221.85/30.96 | | | (43) c_member(all_683_0, all_1391_2, v_L) = 0
% 221.85/30.96 | | | (44) c_member(all_683_0, all_1391_1, v_L) = all_1391_0
% 221.85/30.96 | | | (45) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.96 | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, all_1391_3) = all_1391_2
% 221.85/30.96 | | | (46) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.96 | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9, all_1391_3) =
% 221.85/30.96 | | | all_1391_1
% 221.85/30.96 | | |
% 221.85/30.96 | | | REDUCE: (13), (37) imply:
% 221.85/30.96 | | | (47) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.96 | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v_x) = all_870_7
% 221.85/30.96 | | |
% 221.85/30.96 | | | REDUCE: (20), (37) imply:
% 221.85/30.96 | | | (48) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.96 | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v_x) = all_870_1
% 221.85/30.96 | | |
% 221.85/30.96 | | | REDUCE: (27), (44) imply:
% 221.85/30.96 | | | (49) c_member(all_625_1, all_1391_1, v_L) = all_1391_0
% 221.85/30.96 | | |
% 221.85/30.96 | | | REDUCE: (27), (43) imply:
% 221.85/30.96 | | | (50) c_member(all_625_1, all_1391_2, v_L) = 0
% 221.85/30.96 | | |
% 221.85/30.96 | | | REDUCE: (10), (37) imply:
% 221.85/30.96 | | | (51) $i(v_x)
% 221.85/30.96 | | |
% 221.85/30.96 | | | BETA: splitting (35) gives:
% 221.85/30.96 | | |
% 221.85/30.96 | | | Case 1:
% 221.85/30.96 | | | |
% 221.85/30.96 | | | | (52) all_870_8 = v_y
% 221.85/30.96 | | | |
% 221.85/30.96 | | | | COMBINE_EQS: (37), (52) imply:
% 221.85/30.96 | | | | (53) v_x = v_y
% 221.85/30.96 | | | |
% 221.85/30.96 | | | | SIMP: (53) implies:
% 221.85/30.96 | | | | (54) v_x = v_y
% 221.85/30.96 | | | |
% 221.85/30.96 | | | | REDUCE: (14), (54) imply:
% 221.85/30.96 | | | | (55) $false
% 221.85/30.96 | | | |
% 221.85/30.96 | | | | CLOSE: (55) is inconsistent.
% 221.85/30.96 | | | |
% 221.85/30.96 | | | Case 2:
% 221.85/30.96 | | | |
% 221.85/30.96 | | | |
% 221.85/30.96 | | | | GROUND_INST: instantiating (22) with v_L, all_1391_1, all_625_1,
% 221.85/30.96 | | | | all_1391_0, simplifying with (1), (8), (42), (49) gives:
% 221.85/30.96 | | | | (56) all_1391_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 221.85/30.96 | | | | hBOOL(v0) = v1 & hAPP(v_L, all_1391_1) = v0 & $i(v0))
% 221.85/30.96 | | | |
% 221.85/30.96 | | | | GROUND_INST: instantiating (5) with v_y, v_x, all_870_1, simplifying
% 221.85/30.96 | | | | with (12), (48), (51) gives:
% 221.85/30.96 | | | | (57) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_674_0, all_870_1,
% 221.85/30.96 | | | | v_L) = v0) | ! [v0: $i] : ! [v1: $i] : ( ~
% 221.85/30.96 | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.96 | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = v1) | ~
% 221.85/30.96 | | | | $i(v0) | ? [v2: $i] : ? [v3: any] : ? [v4: any] :
% 221.85/30.96 | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.96 | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v0) = v2 &
% 221.85/30.96 | | | | c_member(all_674_0, v2, v_L) = v3 & c_member(all_674_0, v1,
% 221.85/30.96 | | | | v_L) = v4 & $i(v2) & ( ~ (v3 = 0) | v4 = 0)))
% 221.85/30.96 | | | |
% 221.85/30.96 | | | | GROUND_INST: instantiating (21) with all_1391_3, all_1391_2, simplifying
% 221.85/30.96 | | | | with (41), (45) gives:
% 221.85/30.96 | | | | (58) ? [v0: $i] : ? [v1: any] : ? [v2: any] :
% 221.85/30.96 | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.96 | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, all_1391_3) = v0
% 221.85/30.96 | | | | & c_member(all_674_0, v0, v_L) = v1 & c_member(all_674_0,
% 221.85/30.96 | | | | all_1391_2, v_L) = v2 & $i(v0) & ( ~ (v1 = 0) | v2 = 0))
% 221.85/30.96 | | | |
% 221.85/30.96 | | | | GROUND_INST: instantiating (5) with v_y, all_1391_3, all_1391_2,
% 221.85/30.96 | | | | simplifying with (12), (41), (45) gives:
% 221.85/30.96 | | | | (59) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_674_0, all_1391_2,
% 221.85/30.96 | | | | v_L) = v0) | ! [v0: $i] : ! [v1: $i] : ( ~
% 221.85/30.96 | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.96 | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = v1) | ~
% 221.85/30.96 | | | | $i(v0) | ? [v2: $i] : ? [v3: any] : ? [v4: any] :
% 221.85/30.96 | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.96 | | | | tc_Arrow__Order__Mirabelle_Oalt, all_1391_3, v0) = v2 &
% 221.85/30.96 | | | | c_member(all_674_0, v2, v_L) = v3 & c_member(all_674_0, v1,
% 221.85/30.96 | | | | v_L) = v4 & $i(v2) & ( ~ (v3 = 0) | v4 = 0)))
% 221.85/30.96 | | | |
% 221.85/30.96 | | | | GROUND_INST: instantiating (5) with all_870_9, v_x, all_870_7,
% 221.85/30.96 | | | | simplifying with (2), (47), (51) gives:
% 221.85/30.96 | | | | (60) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_674_0, all_870_7,
% 221.85/30.96 | | | | v_L) = v0) | ! [v0: $i] : ! [v1: $i] : ( ~
% 221.85/30.96 | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.96 | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v0) = v1) | ~
% 221.85/30.96 | | | | $i(v0) | ? [v2: $i] : ? [v3: any] : ? [v4: any] :
% 221.85/30.96 | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.96 | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v0) = v2 &
% 221.85/30.96 | | | | c_member(all_674_0, v2, v_L) = v3 & c_member(all_674_0, v1,
% 221.85/30.96 | | | | v_L) = v4 & $i(v2) & ( ~ (v3 = 0) | v4 = 0)))
% 221.85/30.96 | | | |
% 221.85/30.96 | | | | GROUND_INST: instantiating (7) with all_1391_3, all_1391_1, simplifying
% 221.85/30.96 | | | | with (41), (46) gives:
% 221.85/30.96 | | | | (61) ? [v0: $i] : ? [v1: any] : ? [v2: any] :
% 221.85/30.96 | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.96 | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, all_1391_3) = v0
% 221.85/30.96 | | | | & c_member(all_674_0, v0, v_L) = v1 & c_member(all_674_0,
% 221.85/30.96 | | | | all_1391_1, v_L) = v2 & $i(v0) & ( ~ (v1 = 0) | v2 = 0))
% 221.85/30.96 | | | |
% 221.85/30.96 | | | | GROUND_INST: instantiating (28) with all_1391_3, all_1391_1, simplifying
% 221.85/30.96 | | | | with (41), (46) gives:
% 221.85/30.97 | | | | (62) ? [v0: $i] : ? [v1: any] : ? [v2: any] :
% 221.85/30.97 | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.97 | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, all_1391_3) = v0 &
% 221.85/30.97 | | | | c_member(all_674_0, v0, v_L) = v1 & c_member(all_674_0,
% 221.85/30.97 | | | | all_1391_1, v_L) = v2 & $i(v0) & ( ~ (v1 = 0) | v2 = 0))
% 221.85/30.97 | | | |
% 221.85/30.97 | | | | DELTA: instantiating (58) with fresh symbols all_1426_0, all_1426_1,
% 221.85/30.97 | | | | all_1426_2 gives:
% 221.85/30.97 | | | | (63) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.97 | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, all_1391_3) =
% 221.85/30.97 | | | | all_1426_2 & c_member(all_674_0, all_1426_2, v_L) = all_1426_1 &
% 221.85/30.97 | | | | c_member(all_674_0, all_1391_2, v_L) = all_1426_0 &
% 221.85/30.97 | | | | $i(all_1426_2) & ( ~ (all_1426_1 = 0) | all_1426_0 = 0)
% 221.85/30.97 | | | |
% 221.85/30.97 | | | | ALPHA: (63) implies:
% 221.85/30.97 | | | | (64) c_member(all_674_0, all_1391_2, v_L) = all_1426_0
% 221.85/30.97 | | | |
% 221.85/30.97 | | | | DELTA: instantiating (62) with fresh symbols all_1432_0, all_1432_1,
% 221.85/30.97 | | | | all_1432_2 gives:
% 221.85/30.97 | | | | (65) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.97 | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, all_1391_3) = all_1432_2
% 221.85/30.97 | | | | & c_member(all_674_0, all_1432_2, v_L) = all_1432_1 &
% 221.85/30.97 | | | | c_member(all_674_0, all_1391_1, v_L) = all_1432_0 &
% 221.85/30.97 | | | | $i(all_1432_2) & ( ~ (all_1432_1 = 0) | all_1432_0 = 0)
% 221.85/30.97 | | | |
% 221.85/30.97 | | | | ALPHA: (65) implies:
% 221.85/30.97 | | | | (66) c_member(all_674_0, all_1391_1, v_L) = all_1432_0
% 221.85/30.97 | | | | (67) c_member(all_674_0, all_1432_2, v_L) = all_1432_1
% 221.85/30.97 | | | | (68) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.97 | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, all_1391_3) = all_1432_2
% 221.85/30.97 | | | | (69) ~ (all_1432_1 = 0) | all_1432_0 = 0
% 221.85/30.97 | | | |
% 221.85/30.97 | | | | DELTA: instantiating (61) with fresh symbols all_1434_0, all_1434_1,
% 221.85/30.97 | | | | all_1434_2 gives:
% 221.85/30.97 | | | | (70) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.97 | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, all_1391_3) =
% 221.85/30.97 | | | | all_1434_2 & c_member(all_674_0, all_1434_2, v_L) = all_1434_1 &
% 221.85/30.97 | | | | c_member(all_674_0, all_1391_1, v_L) = all_1434_0 &
% 221.85/30.97 | | | | $i(all_1434_2) & ( ~ (all_1434_1 = 0) | all_1434_0 = 0)
% 221.85/30.97 | | | |
% 221.85/30.97 | | | | ALPHA: (70) implies:
% 221.85/30.97 | | | | (71) c_member(all_674_0, all_1391_1, v_L) = all_1434_0
% 221.85/30.97 | | | |
% 221.85/30.97 | | | | REDUCE: (16), (67) imply:
% 221.85/30.97 | | | | (72) c_member(all_625_1, all_1432_2, v_L) = all_1432_1
% 221.85/30.97 | | | |
% 221.85/30.97 | | | | REDUCE: (16), (71) imply:
% 221.85/30.97 | | | | (73) c_member(all_625_1, all_1391_1, v_L) = all_1434_0
% 221.85/30.97 | | | |
% 221.85/30.97 | | | | REDUCE: (16), (66) imply:
% 221.85/30.97 | | | | (74) c_member(all_625_1, all_1391_1, v_L) = all_1432_0
% 221.85/30.97 | | | |
% 221.85/30.97 | | | | REDUCE: (16), (64) imply:
% 221.85/30.97 | | | | (75) c_member(all_625_1, all_1391_2, v_L) = all_1426_0
% 221.85/30.97 | | | |
% 221.85/30.97 | | | | BETA: splitting (57) gives:
% 221.85/30.97 | | | |
% 221.85/30.97 | | | | Case 1:
% 221.85/30.97 | | | | |
% 221.85/30.97 | | | | | (76) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_674_0, all_870_1,
% 221.85/30.97 | | | | | v_L) = v0)
% 221.85/30.97 | | | | |
% 221.85/30.97 | | | | | REF_CLOSE: (16), (17), (26), (76) are inconsistent by sub-proof #12.
% 221.85/30.97 | | | | |
% 221.85/30.97 | | | | Case 2:
% 221.85/30.97 | | | | |
% 221.85/30.97 | | | | | (77) ! [v0: $i] : ! [v1: $i] : ( ~
% 221.85/30.97 | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.97 | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = v1) | ~
% 221.85/30.97 | | | | | $i(v0) | ? [v2: $i] : ? [v3: any] : ? [v4: any] :
% 221.85/30.97 | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.97 | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v0) = v2 &
% 221.85/30.97 | | | | | c_member(all_674_0, v2, v_L) = v3 & c_member(all_674_0,
% 221.85/30.97 | | | | | v1, v_L) = v4 & $i(v2) & ( ~ (v3 = 0) | v4 = 0)))
% 221.85/30.97 | | | | |
% 221.85/30.97 | | | | | GROUND_INST: instantiating (77) with all_1391_3, all_1391_2,
% 221.85/30.97 | | | | | simplifying with (41), (45) gives:
% 221.85/30.97 | | | | | (78) ? [v0: $i] : ? [v1: any] : ? [v2: any] :
% 221.85/30.97 | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.97 | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, all_1391_3) = v0 &
% 221.85/30.97 | | | | | c_member(all_674_0, v0, v_L) = v1 & c_member(all_674_0,
% 221.85/30.97 | | | | | all_1391_2, v_L) = v2 & $i(v0) & ( ~ (v1 = 0) | v2 = 0))
% 221.85/30.97 | | | | |
% 221.85/30.97 | | | | | BETA: splitting (60) gives:
% 221.85/30.97 | | | | |
% 221.85/30.97 | | | | | Case 1:
% 221.85/30.97 | | | | | |
% 221.85/30.97 | | | | | | (79) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_674_0, all_870_7,
% 221.85/30.97 | | | | | | v_L) = v0)
% 221.85/30.97 | | | | | |
% 221.85/30.97 | | | | | | REF_CLOSE: (9), (16), (26), (79) are inconsistent by sub-proof #9.
% 221.85/30.97 | | | | | |
% 221.85/30.97 | | | | | Case 2:
% 221.85/30.97 | | | | | |
% 221.85/30.97 | | | | | | (80) ! [v0: $i] : ! [v1: $i] : ( ~
% 221.85/30.97 | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.97 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v0) = v1)
% 221.85/30.97 | | | | | | | ~ $i(v0) | ? [v2: $i] : ? [v3: any] : ? [v4: any] :
% 221.85/30.97 | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.97 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v0) = v2 &
% 221.85/30.97 | | | | | | c_member(all_674_0, v2, v_L) = v3 & c_member(all_674_0,
% 221.85/30.97 | | | | | | v1, v_L) = v4 & $i(v2) & ( ~ (v3 = 0) | v4 = 0)))
% 221.85/30.97 | | | | | |
% 221.85/30.97 | | | | | | GROUND_INST: instantiating (80) with all_1391_3, all_1391_1,
% 221.85/30.97 | | | | | | simplifying with (41), (46) gives:
% 221.85/30.97 | | | | | | (81) ? [v0: $i] : ? [v1: any] : ? [v2: any] :
% 221.85/30.97 | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.97 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, all_1391_3) = v0 &
% 221.85/30.97 | | | | | | c_member(all_674_0, v0, v_L) = v1 & c_member(all_674_0,
% 221.85/30.97 | | | | | | all_1391_1, v_L) = v2 & $i(v0) & ( ~ (v1 = 0) | v2 = 0))
% 221.85/30.97 | | | | | |
% 221.85/30.97 | | | | | | DELTA: instantiating (78) with fresh symbols all_1472_0, all_1472_1,
% 221.85/30.97 | | | | | | all_1472_2 gives:
% 221.85/30.97 | | | | | | (82) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.97 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, all_1391_3) =
% 221.85/30.97 | | | | | | all_1472_2 & c_member(all_674_0, all_1472_2, v_L) =
% 221.85/30.97 | | | | | | all_1472_1 & c_member(all_674_0, all_1391_2, v_L) =
% 221.85/30.97 | | | | | | all_1472_0 & $i(all_1472_2) & ( ~ (all_1472_1 = 0) |
% 221.85/30.97 | | | | | | all_1472_0 = 0)
% 221.85/30.97 | | | | | |
% 221.85/30.97 | | | | | | ALPHA: (82) implies:
% 221.85/30.97 | | | | | | (83) c_member(all_674_0, all_1391_2, v_L) = all_1472_0
% 221.85/30.97 | | | | | |
% 221.85/30.97 | | | | | | DELTA: instantiating (81) with fresh symbols all_1476_0, all_1476_1,
% 221.85/30.97 | | | | | | all_1476_2 gives:
% 221.85/30.97 | | | | | | (84) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.97 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, all_1391_3) =
% 221.85/30.97 | | | | | | all_1476_2 & c_member(all_674_0, all_1476_2, v_L) =
% 221.85/30.97 | | | | | | all_1476_1 & c_member(all_674_0, all_1391_1, v_L) =
% 221.85/30.97 | | | | | | all_1476_0 & $i(all_1476_2) & ( ~ (all_1476_1 = 0) |
% 221.85/30.97 | | | | | | all_1476_0 = 0)
% 221.85/30.97 | | | | | |
% 221.85/30.97 | | | | | | ALPHA: (84) implies:
% 221.85/30.97 | | | | | | (85) c_member(all_674_0, all_1391_1, v_L) = all_1476_0
% 221.85/30.97 | | | | | |
% 221.85/30.97 | | | | | | REDUCE: (16), (85) imply:
% 221.85/30.97 | | | | | | (86) c_member(all_625_1, all_1391_1, v_L) = all_1476_0
% 221.85/30.97 | | | | | |
% 221.85/30.97 | | | | | | REDUCE: (16), (83) imply:
% 221.85/30.97 | | | | | | (87) c_member(all_625_1, all_1391_2, v_L) = all_1472_0
% 221.85/30.97 | | | | | |
% 221.85/30.97 | | | | | | BETA: splitting (56) gives:
% 221.85/30.97 | | | | | |
% 221.85/30.97 | | | | | | Case 1:
% 221.85/30.97 | | | | | | |
% 221.85/30.97 | | | | | | | (88) all_1391_0 = 0
% 221.85/30.97 | | | | | | |
% 221.85/30.97 | | | | | | | REDUCE: (40), (88) imply:
% 221.85/30.97 | | | | | | | (89) $false
% 221.85/30.97 | | | | | | |
% 221.85/30.97 | | | | | | | CLOSE: (89) is inconsistent.
% 221.85/30.97 | | | | | | |
% 221.85/30.97 | | | | | | Case 2:
% 221.85/30.97 | | | | | | |
% 221.85/30.97 | | | | | | |
% 221.85/30.97 | | | | | | | GROUND_INST: instantiating (26) with 0, all_1472_0, v_L,
% 221.85/30.97 | | | | | | | all_1391_2, all_625_1, simplifying with (50), (87)
% 221.85/30.97 | | | | | | | gives:
% 221.85/30.97 | | | | | | | (90) all_1472_0 = 0
% 221.85/30.97 | | | | | | |
% 221.85/30.97 | | | | | | | GROUND_INST: instantiating (26) with all_1426_0, all_1472_0, v_L,
% 221.85/30.97 | | | | | | | all_1391_2, all_625_1, simplifying with (75), (87)
% 221.85/30.97 | | | | | | | gives:
% 221.85/30.97 | | | | | | | (91) all_1472_0 = all_1426_0
% 221.85/30.97 | | | | | | |
% 221.85/30.97 | | | | | | | GROUND_INST: instantiating (26) with all_1391_0, all_1434_0, v_L,
% 221.85/30.97 | | | | | | | all_1391_1, all_625_1, simplifying with (49), (73)
% 221.85/30.97 | | | | | | | gives:
% 221.85/30.97 | | | | | | | (92) all_1434_0 = all_1391_0
% 221.85/30.97 | | | | | | |
% 221.85/30.97 | | | | | | | GROUND_INST: instantiating (26) with all_1434_0, all_1476_0, v_L,
% 221.85/30.97 | | | | | | | all_1391_1, all_625_1, simplifying with (73), (86)
% 221.85/30.97 | | | | | | | gives:
% 221.85/30.97 | | | | | | | (93) all_1476_0 = all_1434_0
% 221.85/30.97 | | | | | | |
% 221.85/30.97 | | | | | | | GROUND_INST: instantiating (26) with all_1432_0, all_1476_0, v_L,
% 221.85/30.97 | | | | | | | all_1391_1, all_625_1, simplifying with (74), (86)
% 221.85/30.97 | | | | | | | gives:
% 221.85/30.97 | | | | | | | (94) all_1476_0 = all_1432_0
% 221.85/30.97 | | | | | | |
% 221.85/30.97 | | | | | | | GROUND_INST: instantiating (24) with all_1391_2, all_1432_2,
% 221.85/30.97 | | | | | | | all_1391_3, v_y, tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.97 | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with
% 221.85/30.97 | | | | | | | (45), (68) gives:
% 221.85/30.97 | | | | | | | (95) all_1432_2 = all_1391_2
% 221.85/30.97 | | | | | | |
% 221.85/30.97 | | | | | | | COMBINE_EQS: (93), (94) imply:
% 221.85/30.97 | | | | | | | (96) all_1434_0 = all_1432_0
% 221.85/30.97 | | | | | | |
% 221.85/30.97 | | | | | | | SIMP: (96) implies:
% 221.85/30.97 | | | | | | | (97) all_1434_0 = all_1432_0
% 221.85/30.97 | | | | | | |
% 221.85/30.97 | | | | | | | COMBINE_EQS: (90), (91) imply:
% 221.85/30.97 | | | | | | | (98) all_1426_0 = 0
% 221.85/30.97 | | | | | | |
% 221.85/30.97 | | | | | | | COMBINE_EQS: (92), (97) imply:
% 221.85/30.97 | | | | | | | (99) all_1432_0 = all_1391_0
% 221.85/30.97 | | | | | | |
% 221.85/30.97 | | | | | | | REDUCE: (72), (95) imply:
% 221.85/30.97 | | | | | | | (100) c_member(all_625_1, all_1391_2, v_L) = all_1432_1
% 221.85/30.97 | | | | | | |
% 221.85/30.97 | | | | | | | BETA: splitting (69) gives:
% 221.85/30.97 | | | | | | |
% 221.85/30.97 | | | | | | | Case 1:
% 221.85/30.97 | | | | | | | |
% 221.85/30.97 | | | | | | | | (101) ~ (all_1432_1 = 0)
% 221.85/30.97 | | | | | | | |
% 221.85/30.97 | | | | | | | | BETA: splitting (59) gives:
% 221.85/30.97 | | | | | | | |
% 221.85/30.97 | | | | | | | | Case 1:
% 221.85/30.97 | | | | | | | | |
% 221.85/30.97 | | | | | | | | | (102) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_674_0,
% 221.85/30.97 | | | | | | | | | all_1391_2, v_L) = v0)
% 221.85/30.97 | | | | | | | | |
% 221.85/30.97 | | | | | | | | | DELTA: instantiating (102) with fresh symbol all_1524_0 gives:
% 221.85/30.97 | | | | | | | | | (103) ~ (all_1524_0 = 0) & c_member(all_674_0, all_1391_2,
% 221.85/30.97 | | | | | | | | | v_L) = all_1524_0
% 221.85/30.97 | | | | | | | | |
% 221.85/30.97 | | | | | | | | | ALPHA: (103) implies:
% 221.85/30.97 | | | | | | | | | (104) c_member(all_674_0, all_1391_2, v_L) = all_1524_0
% 221.85/30.97 | | | | | | | | |
% 221.85/30.97 | | | | | | | | | REDUCE: (16), (104) imply:
% 221.85/30.97 | | | | | | | | | (105) c_member(all_625_1, all_1391_2, v_L) = all_1524_0
% 221.85/30.97 | | | | | | | | |
% 221.85/30.97 | | | | | | | | | GROUND_INST: instantiating (26) with 0, all_1524_0, v_L,
% 221.85/30.97 | | | | | | | | | all_1391_2, all_625_1, simplifying with (50),
% 221.85/30.97 | | | | | | | | | (105) gives:
% 221.85/30.97 | | | | | | | | | (106) all_1524_0 = 0
% 221.85/30.97 | | | | | | | | |
% 221.85/30.97 | | | | | | | | | GROUND_INST: instantiating (26) with all_1432_1, all_1524_0,
% 221.85/30.97 | | | | | | | | | v_L, all_1391_2, all_625_1, simplifying with
% 221.85/30.97 | | | | | | | | | (100), (105) gives:
% 221.85/30.97 | | | | | | | | | (107) all_1524_0 = all_1432_1
% 221.85/30.97 | | | | | | | | |
% 221.85/30.97 | | | | | | | | | COMBINE_EQS: (106), (107) imply:
% 221.85/30.97 | | | | | | | | | (108) all_1432_1 = 0
% 221.85/30.97 | | | | | | | | |
% 221.85/30.97 | | | | | | | | | REDUCE: (101), (108) imply:
% 221.85/30.97 | | | | | | | | | (109) $false
% 221.85/30.97 | | | | | | | | |
% 221.85/30.97 | | | | | | | | | CLOSE: (109) is inconsistent.
% 221.85/30.97 | | | | | | | | |
% 221.85/30.97 | | | | | | | | Case 2:
% 221.85/30.97 | | | | | | | | |
% 221.85/30.97 | | | | | | | | | (110) ! [v0: $i] : ! [v1: $i] : ( ~
% 221.85/30.97 | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.97 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = v1)
% 221.85/30.97 | | | | | | | | | | ~ $i(v0) | ? [v2: $i] : ? [v3: any] : ? [v4:
% 221.85/30.97 | | | | | | | | | any] :
% 221.85/30.97 | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.97 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_1391_3,
% 221.85/30.97 | | | | | | | | | v0) = v2 & c_member(all_674_0, v2, v_L) = v3 &
% 221.85/30.97 | | | | | | | | | c_member(all_674_0, v1, v_L) = v4 & $i(v2) & ( ~
% 221.85/30.97 | | | | | | | | | (v3 = 0) | v4 = 0)))
% 221.85/30.97 | | | | | | | | |
% 221.85/30.97 | | | | | | | | | GROUND_INST: instantiating (110) with all_1391_3, all_1391_2,
% 221.85/30.97 | | | | | | | | | simplifying with (41), (45) gives:
% 221.85/30.97 | | | | | | | | | (111) ? [v0: $i] : ? [v1: any] : ? [v2: any] :
% 221.85/30.97 | | | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.97 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_1391_3,
% 221.85/30.97 | | | | | | | | | all_1391_3) = v0 & c_member(all_674_0, v0, v_L) =
% 221.85/30.97 | | | | | | | | | v1 & c_member(all_674_0, all_1391_2, v_L) = v2 &
% 221.85/30.97 | | | | | | | | | $i(v0) & ( ~ (v1 = 0) | v2 = 0))
% 221.85/30.97 | | | | | | | | |
% 221.85/30.97 | | | | | | | | | DELTA: instantiating (111) with fresh symbols all_1525_0,
% 221.85/30.97 | | | | | | | | | all_1525_1, all_1525_2 gives:
% 221.85/30.97 | | | | | | | | | (112) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.97 | | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_1391_3,
% 221.85/30.97 | | | | | | | | | all_1391_3) = all_1525_2 & c_member(all_674_0,
% 221.85/30.97 | | | | | | | | | all_1525_2, v_L) = all_1525_1 & c_member(all_674_0,
% 221.85/30.97 | | | | | | | | | all_1391_2, v_L) = all_1525_0 & $i(all_1525_2) & (
% 221.85/30.97 | | | | | | | | | ~ (all_1525_1 = 0) | all_1525_0 = 0)
% 221.85/30.97 | | | | | | | | |
% 221.85/30.97 | | | | | | | | | ALPHA: (112) implies:
% 221.85/30.97 | | | | | | | | | (113) c_member(all_674_0, all_1391_2, v_L) = all_1525_0
% 221.85/30.97 | | | | | | | | |
% 221.85/30.97 | | | | | | | | | REDUCE: (16), (113) imply:
% 221.85/30.97 | | | | | | | | | (114) c_member(all_625_1, all_1391_2, v_L) = all_1525_0
% 221.85/30.97 | | | | | | | | |
% 221.85/30.97 | | | | | | | | | GROUND_INST: instantiating (26) with 0, all_1525_0, v_L,
% 221.85/30.97 | | | | | | | | | all_1391_2, all_625_1, simplifying with (50),
% 221.85/30.97 | | | | | | | | | (114) gives:
% 221.85/30.97 | | | | | | | | | (115) all_1525_0 = 0
% 221.85/30.97 | | | | | | | | |
% 221.85/30.97 | | | | | | | | | GROUND_INST: instantiating (26) with all_1432_1, all_1525_0,
% 221.85/30.97 | | | | | | | | | v_L, all_1391_2, all_625_1, simplifying with
% 221.85/30.97 | | | | | | | | | (100), (114) gives:
% 221.85/30.97 | | | | | | | | | (116) all_1525_0 = all_1432_1
% 221.85/30.97 | | | | | | | | |
% 221.85/30.97 | | | | | | | | | COMBINE_EQS: (115), (116) imply:
% 221.85/30.97 | | | | | | | | | (117) all_1432_1 = 0
% 221.85/30.97 | | | | | | | | |
% 221.85/30.97 | | | | | | | | | REDUCE: (101), (117) imply:
% 221.85/30.97 | | | | | | | | | (118) $false
% 221.85/30.97 | | | | | | | | |
% 221.85/30.97 | | | | | | | | | CLOSE: (118) is inconsistent.
% 221.85/30.97 | | | | | | | | |
% 221.85/30.97 | | | | | | | | End of split
% 221.85/30.97 | | | | | | | |
% 221.85/30.97 | | | | | | | Case 2:
% 221.85/30.97 | | | | | | | |
% 221.85/30.98 | | | | | | | | (119) all_1432_0 = 0
% 221.85/30.98 | | | | | | | |
% 221.85/30.98 | | | | | | | | COMBINE_EQS: (99), (119) imply:
% 221.85/30.98 | | | | | | | | (120) all_1391_0 = 0
% 221.85/30.98 | | | | | | | |
% 221.85/30.98 | | | | | | | | SIMP: (120) implies:
% 221.85/30.98 | | | | | | | | (121) all_1391_0 = 0
% 221.85/30.98 | | | | | | | |
% 221.85/30.98 | | | | | | | | REDUCE: (40), (121) imply:
% 221.85/30.98 | | | | | | | | (122) $false
% 221.85/30.98 | | | | | | | |
% 221.85/30.98 | | | | | | | | CLOSE: (122) is inconsistent.
% 221.85/30.98 | | | | | | | |
% 221.85/30.98 | | | | | | | End of split
% 221.85/30.98 | | | | | | |
% 221.85/30.98 | | | | | | End of split
% 221.85/30.98 | | | | | |
% 221.85/30.98 | | | | | End of split
% 221.85/30.98 | | | | |
% 221.85/30.98 | | | | End of split
% 221.85/30.98 | | | |
% 221.85/30.98 | | | End of split
% 221.85/30.98 | | |
% 221.85/30.98 | | Case 2:
% 221.85/30.98 | | |
% 221.85/30.98 | | | (123) all_870_6 = 0 & ~ (all_870_8 = v_x) & ? [v0: $i] : ? [v1: $i]
% 221.85/30.98 | | | : ? [v2: any] : ? [v3: $i] : ? [v4: any] :
% 221.85/30.98 | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.98 | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v0) = v1 &
% 221.85/30.98 | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.98 | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v0) = v3 &
% 221.85/30.98 | | | c_member(all_683_0, v3, v_L) = v4 & c_member(all_683_0, v1,
% 221.85/30.98 | | | v_L) = v2 & $i(v3) & $i(v1) & $i(v0) & ((v2 = 0 & ~ (v4 = 0)
% 221.85/30.98 | | | & ~ (v0 = v_x)) | (v0 = v_x & all_870_4 = 0 & ~
% 221.85/30.98 | | | (all_870_2 = 0))))
% 221.85/30.98 | | |
% 221.85/30.98 | | | ALPHA: (123) implies:
% 221.85/30.98 | | | (124) ? [v0: $i] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ? [v4:
% 221.85/30.98 | | | any] : (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.98 | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v0) = v1 &
% 221.85/30.98 | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.98 | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v0) = v3 &
% 221.85/30.98 | | | c_member(all_683_0, v3, v_L) = v4 & c_member(all_683_0, v1,
% 221.85/30.98 | | | v_L) = v2 & $i(v3) & $i(v1) & $i(v0) & ((v2 = 0 & ~ (v4 = 0)
% 221.85/30.98 | | | & ~ (v0 = v_x)) | (v0 = v_x & all_870_4 = 0 & ~
% 221.85/30.98 | | | (all_870_2 = 0))))
% 221.85/30.98 | | |
% 221.85/30.98 | | | REF_CLOSE: (5), (7), (10), (16), (24), (25), (26), (27), (28), (124) are
% 221.85/30.98 | | | inconsistent by sub-proof #5.
% 221.85/30.98 | | |
% 221.85/30.98 | | End of split
% 221.85/30.98 | |
% 221.85/30.98 | Case 2:
% 221.85/30.98 | |
% 221.85/30.98 | | (125) ~ (all_870_2 = 0)
% 221.85/30.98 | |
% 221.85/30.98 | | BETA: splitting (18) gives:
% 221.85/30.98 | |
% 221.85/30.98 | | Case 1:
% 221.85/30.98 | | |
% 221.85/30.98 | | | (126) all_870_2 = 0 & all_870_8 = v_x & ? [v0: $i] : ? [v1: $i] : ?
% 221.85/30.98 | | | [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & ~ (v0 = v_x) &
% 221.85/30.98 | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.98 | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v0) = v2 &
% 221.85/30.98 | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.98 | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = v1 &
% 221.85/30.98 | | | c_member(all_683_0, v2, v_L) = v3 & c_member(all_683_0, v1,
% 221.85/30.98 | | | v_L) = 0 & $i(v2) & $i(v1) & $i(v0))
% 221.85/30.98 | | |
% 221.85/30.98 | | | ALPHA: (126) implies:
% 221.85/30.98 | | | (127) all_870_2 = 0
% 221.85/30.98 | | |
% 221.85/30.98 | | | REDUCE: (125), (127) imply:
% 221.85/30.98 | | | (128) $false
% 221.85/30.98 | | |
% 221.85/30.98 | | | CLOSE: (128) is inconsistent.
% 221.85/30.98 | | |
% 221.85/30.98 | | Case 2:
% 221.85/30.98 | | |
% 221.85/30.98 | | | (129) all_870_6 = 0 & ~ (all_870_8 = v_x) & ? [v0: $i] : ? [v1: $i]
% 221.85/30.98 | | | : ? [v2: any] : ? [v3: $i] : ? [v4: any] :
% 221.85/30.98 | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.98 | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v0) = v1 &
% 221.85/30.98 | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.98 | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v0) = v3 &
% 221.85/30.98 | | | c_member(all_683_0, v3, v_L) = v4 & c_member(all_683_0, v1,
% 221.85/30.98 | | | v_L) = v2 & $i(v3) & $i(v1) & $i(v0) & ((v2 = 0 & ~ (v4 = 0)
% 221.85/30.98 | | | & ~ (v0 = v_x)) | (v0 = v_x & all_870_4 = 0 & ~
% 221.85/30.98 | | | (all_870_2 = 0))))
% 221.85/30.98 | | |
% 221.85/30.98 | | | ALPHA: (129) implies:
% 221.85/30.98 | | | (130) ? [v0: $i] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ? [v4:
% 221.85/30.98 | | | any] : (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.98 | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v0) = v1 &
% 221.85/30.98 | | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.98 | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v0) = v3 &
% 221.85/30.98 | | | c_member(all_683_0, v3, v_L) = v4 & c_member(all_683_0, v1,
% 221.85/30.98 | | | v_L) = v2 & $i(v3) & $i(v1) & $i(v0) & ((v2 = 0 & ~ (v4 = 0)
% 221.85/30.98 | | | & ~ (v0 = v_x)) | (v0 = v_x & all_870_4 = 0 & ~
% 221.85/30.98 | | | (all_870_2 = 0))))
% 221.85/30.98 | | |
% 221.85/30.98 | | | REF_CLOSE: (5), (7), (10), (16), (24), (25), (26), (27), (28), (130) are
% 221.85/30.98 | | | inconsistent by sub-proof #5.
% 221.85/30.98 | | |
% 221.85/30.98 | | End of split
% 221.85/30.98 | |
% 221.85/30.98 | End of split
% 221.85/30.98 |
% 221.85/30.98 End of proof
% 221.85/30.98
% 221.85/30.98 Sub-proof #5 shows that the following formulas are inconsistent:
% 221.85/30.98 ----------------------------------------------------------------
% 221.85/30.98 (1) ? [v0: $i] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ? [v4: any] :
% 221.85/30.98 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.98 tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v0) = v1 &
% 221.85/30.98 c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.98 tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v0) = v3 &
% 221.85/30.98 c_member(all_683_0, v3, v_L) = v4 & c_member(all_683_0, v1, v_L) = v2 &
% 221.85/30.98 $i(v3) & $i(v1) & $i(v0) & ((v2 = 0 & ~ (v4 = 0) & ~ (v0 = v_x)) |
% 221.85/30.98 (v0 = v_x & all_870_4 = 0 & ~ (all_870_2 = 0))))
% 221.85/30.98 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 221.85/30.98 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.98 tc_Arrow__Order__Mirabelle_Oalt, v0, v1) = v2) | ~ $i(v1) | ~
% 221.85/30.98 $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & c_member(all_674_0, v2, v_L) =
% 221.85/30.98 v3) | ! [v3: $i] : ! [v4: $i] : ( ~
% 221.85/30.98 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.98 tc_Arrow__Order__Mirabelle_Oalt, v0, v3) = v4) | ~ $i(v3) | ?
% 221.85/30.98 [v5: $i] : ? [v6: any] : ? [v7: any] :
% 221.85/30.98 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.98 tc_Arrow__Order__Mirabelle_Oalt, v1, v3) = v5 &
% 221.85/30.98 c_member(all_674_0, v5, v_L) = v6 & c_member(all_674_0, v4, v_L) =
% 221.85/30.98 v7 & $i(v5) & ( ~ (v6 = 0) | v7 = 0))))
% 221.85/30.98 (3) ! [v0: $i] : ! [v1: $i] : ( ~
% 221.85/30.98 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.98 tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v0) = v1) | ~ $i(v0) |
% 221.85/30.98 ? [v2: $i] : ? [v3: any] : ? [v4: any] :
% 221.85/30.98 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.98 tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v0) = v2 &
% 221.85/30.98 c_member(all_674_0, v2, v_L) = v3 & c_member(all_674_0, v1, v_L) = v4
% 221.85/30.98 & $i(v2) & ( ~ (v3 = 0) | v4 = 0)))
% 221.85/30.98 (4) $i(all_870_8)
% 221.85/30.98 (5) all_674_0 = all_625_1
% 221.85/30.98 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 221.85/30.98 [v5: $i] : (v1 = v0 | ~ (c_Product__Type_OPair(v5, v4, v3, v2) = v1) |
% 221.85/30.98 ~ (c_Product__Type_OPair(v5, v4, v3, v2) = v0))
% 221.85/30.98 (7) ~ (all_870_4 = 0)
% 221.85/30.98 (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 221.85/30.98 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (c_member(v4, v3, v2) = v1) | ~
% 221.85/30.98 (c_member(v4, v3, v2) = v0))
% 221.85/30.98 (9) all_683_0 = all_625_1
% 221.85/30.98 (10) ! [v0: $i] : ! [v1: $i] : ( ~
% 221.85/30.98 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.98 tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v0) = v1) | ~ $i(v0)
% 221.85/30.98 | ? [v2: $i] : ? [v3: any] : ? [v4: any] :
% 221.85/30.98 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.98 tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = v2 &
% 221.85/30.98 c_member(all_674_0, v2, v_L) = v3 & c_member(all_674_0, v1, v_L) =
% 221.85/30.98 v4 & $i(v2) & ( ~ (v3 = 0) | v4 = 0)))
% 221.85/30.98
% 221.85/30.98 Begin of proof
% 221.85/30.98 |
% 221.85/30.98 | DELTA: instantiating (1) with fresh symbols all_1391_0, all_1391_1,
% 221.85/30.98 | all_1391_2, all_1391_3, all_1391_4 gives:
% 221.85/30.98 | (11) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.98 | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, all_1391_4) = all_1391_3
% 221.85/30.98 | & c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.98 | tc_Arrow__Order__Mirabelle_Oalt, all_870_9, all_1391_4) = all_1391_1
% 221.85/30.98 | & c_member(all_683_0, all_1391_1, v_L) = all_1391_0 &
% 221.85/30.98 | c_member(all_683_0, all_1391_3, v_L) = all_1391_2 & $i(all_1391_1) &
% 221.85/30.98 | $i(all_1391_3) & $i(all_1391_4) & ((all_1391_2 = 0 & ~ (all_1391_0 =
% 221.85/30.98 | 0) & ~ (all_1391_4 = v_x)) | (all_1391_4 = v_x & all_870_4 = 0
% 221.85/30.98 | & ~ (all_870_2 = 0)))
% 221.85/30.98 |
% 221.85/30.98 | ALPHA: (11) implies:
% 221.85/30.98 | (12) $i(all_1391_4)
% 221.85/30.98 | (13) c_member(all_683_0, all_1391_3, v_L) = all_1391_2
% 221.85/30.98 | (14) c_member(all_683_0, all_1391_1, v_L) = all_1391_0
% 221.85/30.98 | (15) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.98 | tc_Arrow__Order__Mirabelle_Oalt, all_870_9, all_1391_4) = all_1391_1
% 221.85/30.98 | (16) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.98 | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, all_1391_4) = all_1391_3
% 221.85/30.98 | (17) (all_1391_2 = 0 & ~ (all_1391_0 = 0) & ~ (all_1391_4 = v_x)) |
% 221.85/30.98 | (all_1391_4 = v_x & all_870_4 = 0 & ~ (all_870_2 = 0))
% 221.85/30.98 |
% 221.85/30.98 | REDUCE: (9), (14) imply:
% 221.85/30.98 | (18) c_member(all_625_1, all_1391_1, v_L) = all_1391_0
% 221.85/30.98 |
% 221.85/30.98 | REDUCE: (9), (13) imply:
% 221.85/30.98 | (19) c_member(all_625_1, all_1391_3, v_L) = all_1391_2
% 221.85/30.98 |
% 221.85/30.98 | BETA: splitting (17) gives:
% 221.85/30.98 |
% 221.85/30.98 | Case 1:
% 221.85/30.98 | |
% 221.85/30.98 | | (20) all_1391_2 = 0 & ~ (all_1391_0 = 0) & ~ (all_1391_4 = v_x)
% 221.85/30.98 | |
% 221.85/30.98 | | ALPHA: (20) implies:
% 221.85/30.98 | | (21) all_1391_2 = 0
% 221.85/30.98 | | (22) ~ (all_1391_0 = 0)
% 221.85/30.98 | |
% 221.85/30.98 | | REDUCE: (19), (21) imply:
% 221.85/30.98 | | (23) c_member(all_625_1, all_1391_3, v_L) = 0
% 221.85/30.98 | |
% 221.85/30.98 | | GROUND_INST: instantiating (3) with all_1391_4, all_1391_1, simplifying with
% 221.85/30.98 | | (12), (15) gives:
% 221.85/30.98 | | (24) ? [v0: $i] : ? [v1: any] : ? [v2: any] :
% 221.85/30.98 | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.98 | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, all_1391_4) = v0 &
% 221.85/30.98 | | c_member(all_674_0, v0, v_L) = v1 & c_member(all_674_0,
% 221.85/30.98 | | all_1391_1, v_L) = v2 & $i(v0) & ( ~ (v1 = 0) | v2 = 0))
% 221.85/30.98 | |
% 221.85/30.98 | | GROUND_INST: instantiating (10) with all_1391_4, all_1391_1, simplifying
% 221.85/30.98 | | with (12), (15) gives:
% 221.85/30.99 | | (25) ? [v0: $i] : ? [v1: any] : ? [v2: any] :
% 221.85/30.99 | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.99 | | tc_Arrow__Order__Mirabelle_Oalt, v_y, all_1391_4) = v0 &
% 221.85/30.99 | | c_member(all_674_0, v0, v_L) = v1 & c_member(all_674_0,
% 221.85/30.99 | | all_1391_1, v_L) = v2 & $i(v0) & ( ~ (v1 = 0) | v2 = 0))
% 221.85/30.99 | |
% 221.85/30.99 | | GROUND_INST: instantiating (2) with all_870_8, all_1391_4, all_1391_3,
% 221.85/30.99 | | simplifying with (4), (12), (16) gives:
% 221.85/30.99 | | (26) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_674_0, all_1391_3, v_L) =
% 221.85/30.99 | | v0) | ! [v0: $i] : ! [v1: $i] : ( ~
% 221.85/30.99 | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.99 | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v0) = v1) | ~
% 221.85/30.99 | | $i(v0) | ? [v2: $i] : ? [v3: any] : ? [v4: any] :
% 221.85/30.99 | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.99 | | tc_Arrow__Order__Mirabelle_Oalt, all_1391_4, v0) = v2 &
% 221.85/30.99 | | c_member(all_674_0, v2, v_L) = v3 & c_member(all_674_0, v1, v_L)
% 221.85/30.99 | | = v4 & $i(v2) & ( ~ (v3 = 0) | v4 = 0)))
% 221.85/30.99 | |
% 221.85/30.99 | | DELTA: instantiating (24) with fresh symbols all_1426_0, all_1426_1,
% 221.85/30.99 | | all_1426_2 gives:
% 221.85/30.99 | | (27) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.99 | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, all_1391_4) =
% 221.85/30.99 | | all_1426_2 & c_member(all_674_0, all_1426_2, v_L) = all_1426_1 &
% 221.85/30.99 | | c_member(all_674_0, all_1391_1, v_L) = all_1426_0 & $i(all_1426_2) &
% 221.85/30.99 | | ( ~ (all_1426_1 = 0) | all_1426_0 = 0)
% 221.85/30.99 | |
% 221.85/30.99 | | ALPHA: (27) implies:
% 221.85/30.99 | | (28) c_member(all_674_0, all_1391_1, v_L) = all_1426_0
% 221.85/30.99 | | (29) c_member(all_674_0, all_1426_2, v_L) = all_1426_1
% 221.85/30.99 | | (30) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.99 | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, all_1391_4) =
% 221.85/30.99 | | all_1426_2
% 221.85/30.99 | | (31) ~ (all_1426_1 = 0) | all_1426_0 = 0
% 221.85/30.99 | |
% 221.85/30.99 | | DELTA: instantiating (25) with fresh symbols all_1440_0, all_1440_1,
% 221.85/30.99 | | all_1440_2 gives:
% 221.85/30.99 | | (32) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.99 | | tc_Arrow__Order__Mirabelle_Oalt, v_y, all_1391_4) = all_1440_2 &
% 221.85/30.99 | | c_member(all_674_0, all_1440_2, v_L) = all_1440_1 &
% 221.85/30.99 | | c_member(all_674_0, all_1391_1, v_L) = all_1440_0 & $i(all_1440_2) &
% 221.85/30.99 | | ( ~ (all_1440_1 = 0) | all_1440_0 = 0)
% 221.85/30.99 | |
% 221.85/30.99 | | ALPHA: (32) implies:
% 221.85/30.99 | | (33) c_member(all_674_0, all_1391_1, v_L) = all_1440_0
% 221.85/30.99 | |
% 221.85/30.99 | | REDUCE: (5), (29) imply:
% 221.85/30.99 | | (34) c_member(all_625_1, all_1426_2, v_L) = all_1426_1
% 221.85/30.99 | |
% 221.85/30.99 | | REDUCE: (5), (33) imply:
% 221.85/30.99 | | (35) c_member(all_625_1, all_1391_1, v_L) = all_1440_0
% 221.85/30.99 | |
% 221.85/30.99 | | REDUCE: (5), (28) imply:
% 221.85/30.99 | | (36) c_member(all_625_1, all_1391_1, v_L) = all_1426_0
% 221.85/30.99 | |
% 221.85/30.99 | | BETA: splitting (26) gives:
% 221.85/30.99 | |
% 221.85/30.99 | | Case 1:
% 221.85/30.99 | | |
% 221.85/30.99 | | | (37) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_674_0, all_1391_3, v_L)
% 221.85/30.99 | | | = v0)
% 221.85/30.99 | | |
% 221.85/30.99 | | | DELTA: instantiating (37) with fresh symbol all_1464_0 gives:
% 221.85/30.99 | | | (38) ~ (all_1464_0 = 0) & c_member(all_674_0, all_1391_3, v_L) =
% 221.85/30.99 | | | all_1464_0
% 221.85/30.99 | | |
% 221.85/30.99 | | | ALPHA: (38) implies:
% 221.85/30.99 | | | (39) ~ (all_1464_0 = 0)
% 221.85/30.99 | | | (40) c_member(all_674_0, all_1391_3, v_L) = all_1464_0
% 221.85/30.99 | | |
% 221.85/30.99 | | | REDUCE: (5), (40) imply:
% 221.85/30.99 | | | (41) c_member(all_625_1, all_1391_3, v_L) = all_1464_0
% 221.85/30.99 | | |
% 221.85/30.99 | | | GROUND_INST: instantiating (8) with 0, all_1464_0, v_L, all_1391_3,
% 221.85/30.99 | | | all_625_1, simplifying with (23), (41) gives:
% 221.85/30.99 | | | (42) all_1464_0 = 0
% 221.85/30.99 | | |
% 221.85/30.99 | | | REDUCE: (39), (42) imply:
% 221.85/30.99 | | | (43) $false
% 221.85/30.99 | | |
% 221.85/30.99 | | | CLOSE: (43) is inconsistent.
% 221.85/30.99 | | |
% 221.85/30.99 | | Case 2:
% 221.85/30.99 | | |
% 221.85/30.99 | | | (44) ! [v0: $i] : ! [v1: $i] : ( ~
% 221.85/30.99 | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.99 | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v0) = v1) | ~
% 221.85/30.99 | | | $i(v0) | ? [v2: $i] : ? [v3: any] : ? [v4: any] :
% 221.85/30.99 | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.99 | | | tc_Arrow__Order__Mirabelle_Oalt, all_1391_4, v0) = v2 &
% 221.85/30.99 | | | c_member(all_674_0, v2, v_L) = v3 & c_member(all_674_0, v1,
% 221.85/30.99 | | | v_L) = v4 & $i(v2) & ( ~ (v3 = 0) | v4 = 0)))
% 221.85/30.99 | | |
% 221.85/30.99 | | | GROUND_INST: instantiating (44) with all_1391_4, all_1391_3, simplifying
% 221.85/30.99 | | | with (12), (16) gives:
% 221.85/30.99 | | | (45) ? [v0: $i] : ? [v1: any] : ? [v2: any] :
% 221.85/30.99 | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.99 | | | tc_Arrow__Order__Mirabelle_Oalt, all_1391_4, all_1391_4) = v0
% 221.85/30.99 | | | & c_member(all_674_0, v0, v_L) = v1 & c_member(all_674_0,
% 221.85/30.99 | | | all_1391_3, v_L) = v2 & $i(v0) & ( ~ (v1 = 0) | v2 = 0))
% 221.85/30.99 | | |
% 221.85/30.99 | | | DELTA: instantiating (45) with fresh symbols all_1467_0, all_1467_1,
% 221.85/30.99 | | | all_1467_2 gives:
% 221.85/30.99 | | | (46) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.99 | | | tc_Arrow__Order__Mirabelle_Oalt, all_1391_4, all_1391_4) =
% 221.85/30.99 | | | all_1467_2 & c_member(all_674_0, all_1467_2, v_L) = all_1467_1 &
% 221.85/30.99 | | | c_member(all_674_0, all_1391_3, v_L) = all_1467_0 & $i(all_1467_2)
% 221.85/30.99 | | | & ( ~ (all_1467_1 = 0) | all_1467_0 = 0)
% 221.85/30.99 | | |
% 221.85/30.99 | | | ALPHA: (46) implies:
% 221.85/30.99 | | | (47) c_member(all_674_0, all_1391_3, v_L) = all_1467_0
% 221.85/30.99 | | |
% 221.85/30.99 | | | REDUCE: (5), (47) imply:
% 221.85/30.99 | | | (48) c_member(all_625_1, all_1391_3, v_L) = all_1467_0
% 221.85/30.99 | | |
% 221.85/30.99 | | | GROUND_INST: instantiating (8) with 0, all_1467_0, v_L, all_1391_3,
% 221.85/30.99 | | | all_625_1, simplifying with (23), (48) gives:
% 221.85/30.99 | | | (49) all_1467_0 = 0
% 221.85/30.99 | | |
% 221.85/30.99 | | | GROUND_INST: instantiating (8) with all_1391_0, all_1440_0, v_L,
% 221.85/30.99 | | | all_1391_1, all_625_1, simplifying with (18), (35) gives:
% 221.85/30.99 | | | (50) all_1440_0 = all_1391_0
% 221.85/30.99 | | |
% 221.85/30.99 | | | GROUND_INST: instantiating (8) with all_1426_0, all_1440_0, v_L,
% 221.85/30.99 | | | all_1391_1, all_625_1, simplifying with (35), (36) gives:
% 221.85/30.99 | | | (51) all_1440_0 = all_1426_0
% 221.85/30.99 | | |
% 221.85/30.99 | | | GROUND_INST: instantiating (6) with all_1391_3, all_1426_2, all_1391_4,
% 221.85/30.99 | | | all_870_8, tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.99 | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with (16), (30)
% 221.85/30.99 | | | gives:
% 221.85/30.99 | | | (52) all_1426_2 = all_1391_3
% 221.85/30.99 | | |
% 221.85/30.99 | | | COMBINE_EQS: (50), (51) imply:
% 221.85/30.99 | | | (53) all_1426_0 = all_1391_0
% 221.85/30.99 | | |
% 221.85/30.99 | | | REDUCE: (34), (52) imply:
% 221.85/30.99 | | | (54) c_member(all_625_1, all_1391_3, v_L) = all_1426_1
% 221.85/30.99 | | |
% 221.85/30.99 | | | BETA: splitting (31) gives:
% 221.85/30.99 | | |
% 221.85/30.99 | | | Case 1:
% 221.85/30.99 | | | |
% 221.85/30.99 | | | | (55) ~ (all_1426_1 = 0)
% 221.85/30.99 | | | |
% 221.85/30.99 | | | | GROUND_INST: instantiating (8) with 0, all_1426_1, v_L, all_1391_3,
% 221.85/30.99 | | | | all_625_1, simplifying with (23), (54) gives:
% 221.85/30.99 | | | | (56) all_1426_1 = 0
% 221.85/30.99 | | | |
% 221.85/30.99 | | | | REDUCE: (55), (56) imply:
% 221.85/30.99 | | | | (57) $false
% 221.85/30.99 | | | |
% 221.85/30.99 | | | | CLOSE: (57) is inconsistent.
% 221.85/30.99 | | | |
% 221.85/30.99 | | | Case 2:
% 221.85/30.99 | | | |
% 221.85/30.99 | | | | (58) all_1426_0 = 0
% 221.85/30.99 | | | |
% 221.85/30.99 | | | | COMBINE_EQS: (53), (58) imply:
% 221.85/30.99 | | | | (59) all_1391_0 = 0
% 221.85/30.99 | | | |
% 221.85/30.99 | | | | REDUCE: (22), (59) imply:
% 221.85/30.99 | | | | (60) $false
% 221.85/30.99 | | | |
% 221.85/30.99 | | | | CLOSE: (60) is inconsistent.
% 221.85/30.99 | | | |
% 221.85/30.99 | | | End of split
% 221.85/30.99 | | |
% 221.85/30.99 | | End of split
% 221.85/30.99 | |
% 221.85/30.99 | Case 2:
% 221.85/30.99 | |
% 221.85/30.99 | | (61) all_1391_4 = v_x & all_870_4 = 0 & ~ (all_870_2 = 0)
% 221.85/30.99 | |
% 221.85/30.99 | | ALPHA: (61) implies:
% 221.85/30.99 | | (62) all_870_4 = 0
% 221.85/30.99 | |
% 221.85/30.99 | | REDUCE: (7), (62) imply:
% 221.85/30.99 | | (63) $false
% 221.85/30.99 | |
% 221.85/30.99 | | CLOSE: (63) is inconsistent.
% 221.85/30.99 | |
% 221.85/30.99 | End of split
% 221.85/30.99 |
% 221.85/30.99 End of proof
% 221.85/30.99
% 221.85/30.99 Sub-proof #6 shows that the following formulas are inconsistent:
% 221.85/30.99 ----------------------------------------------------------------
% 221.85/30.99 (1) $i(v_L)
% 221.85/30.99 (2) $i(all_870_9)
% 221.85/30.99 (3) tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)
% 221.85/30.99 = all_625_1
% 221.85/30.99 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 221.85/30.99 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.99 tc_Arrow__Order__Mirabelle_Oalt, v0, v1) = v2) | ~ $i(v1) | ~
% 221.85/30.99 $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & c_member(all_674_0, v2, v_L) =
% 221.85/30.99 v3) | ! [v3: $i] : ! [v4: $i] : ( ~
% 221.85/30.99 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.99 tc_Arrow__Order__Mirabelle_Oalt, v0, v3) = v4) | ~ $i(v3) | ?
% 221.85/30.99 [v5: $i] : ? [v6: any] : ? [v7: any] :
% 221.85/30.99 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.99 tc_Arrow__Order__Mirabelle_Oalt, v1, v3) = v5 &
% 221.85/30.99 c_member(all_674_0, v5, v_L) = v6 & c_member(all_674_0, v4, v_L) =
% 221.85/30.99 v7 & $i(v5) & ( ~ (v6 = 0) | v7 = 0))))
% 221.85/30.99 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 221.85/30.99 [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : (v1 = v0 | ~
% 221.85/30.99 (tc_prod(v5, v4) = v6) | ~ (c_Product__Type_OPair(v5, v4, v2, v1) =
% 221.85/30.99 v7) | ~ (c_Product__Type_OPair(v5, v4, v2, v0) = v8) | ~
% 221.85/30.99 (c_member(v6, v8, v3) = 0) | ~ (c_member(v6, v7, v3) = 0) | ~ $i(v5)
% 221.85/30.99 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v9:
% 221.85/30.99 int] : ( ~ (v9 = 0) & c_Relation_Osingle__valued(v5, v4, v3) = v9))
% 221.85/30.99 (6) ! [v0: $i] : ! [v1: $i] : ( ~
% 221.85/30.99 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.99 tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v0) = v1) | ~ $i(v0) |
% 221.85/30.99 ? [v2: $i] : ? [v3: any] : ? [v4: any] :
% 221.85/30.99 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.99 tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v0) = v2 &
% 221.85/30.99 c_member(all_674_0, v2, v_L) = v3 & c_member(all_674_0, v1, v_L) = v4
% 221.85/30.99 & $i(v2) & ( ~ (v3 = 0) | v4 = 0)))
% 221.85/30.99 (7) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.99 tc_Arrow__Order__Mirabelle_Oalt, v_y, all_870_9) = all_1137_1
% 221.85/30.99 (8) $i(all_870_8)
% 221.85/30.99 (9) $i(v_y)
% 221.85/30.99 (10) all_674_0 = all_625_1
% 221.85/30.99 (11) c_member(all_625_1, all_870_1, v_L) = 0
% 221.85/30.99 (12) all_1137_0 = 0 | all_1137_2 = 0
% 221.85/30.99 (13) (all_870_2 = 0 & all_870_8 = v_x & ? [v0: $i] : ? [v1: $i] : ? [v2:
% 221.85/30.99 $i] : ? [v3: int] : ( ~ (v3 = 0) & ~ (v0 = v_x) &
% 221.85/30.99 c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.99 tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v0) = v2 &
% 221.85/30.99 c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.99 tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = v1 &
% 221.85/30.99 c_member(all_683_0, v2, v_L) = v3 & c_member(all_683_0, v1, v_L) = 0
% 221.85/30.99 & $i(v2) & $i(v1) & $i(v0))) | (all_870_6 = 0 & ~ (all_870_8 = v_x)
% 221.85/30.99 & ? [v0: $i] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ? [v4:
% 221.85/30.99 any] : (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.99 tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v0) = v1 &
% 221.85/30.99 c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.99 tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v0) = v3 &
% 221.85/30.99 c_member(all_683_0, v3, v_L) = v4 & c_member(all_683_0, v1, v_L) =
% 221.85/30.99 v2 & $i(v3) & $i(v1) & $i(v0) & ((v2 = 0 & ~ (v4 = 0) & ~ (v0 =
% 221.85/30.99 v_x)) | (v0 = v_x & all_870_4 = 0 & ~ (all_870_2 = 0)))))
% 221.85/30.99 (14) c_member(all_625_1, all_870_3, v_L) = all_870_2
% 221.85/30.99 (15) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/30.99 tc_Arrow__Order__Mirabelle_Oalt, v_y, all_870_8) = all_870_1
% 221.85/30.99 (16) all_1137_2 = all_870_2
% 221.85/30.99 (17) $i(tc_Arrow__Order__Mirabelle_Oalt)
% 221.85/31.00 (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 221.85/31.00 [v5: $i] : (v1 = v0 | ~ (c_Product__Type_OPair(v5, v4, v3, v2) = v1) |
% 221.85/31.00 ~ (c_Product__Type_OPair(v5, v4, v3, v2) = v0))
% 221.85/31.00 (19) c_member(all_625_1, all_1137_1, v_L) = all_1137_0
% 221.85/31.00 (20) ~ (all_870_4 = 0)
% 221.85/31.00 (21) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 221.85/31.00 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (c_member(v4, v3, v2) = v1) |
% 221.85/31.00 ~ (c_member(v4, v3, v2) = v0))
% 221.85/31.00 (22) all_683_0 = all_625_1
% 221.85/31.00 (23) ~ (all_870_8 = all_870_9)
% 221.85/31.00 (24) ~ (all_1194_0 = 0) & c_member(all_674_0, all_870_3, v_L) = all_1194_0
% 221.85/31.00
% 221.85/31.00 Begin of proof
% 221.85/31.00 |
% 221.85/31.00 | ALPHA: (24) implies:
% 221.85/31.00 | (25) ~ (all_1194_0 = 0)
% 221.85/31.00 | (26) c_member(all_674_0, all_870_3, v_L) = all_1194_0
% 221.85/31.00 |
% 221.85/31.00 | REDUCE: (10), (26) imply:
% 221.85/31.00 | (27) c_member(all_625_1, all_870_3, v_L) = all_1194_0
% 221.85/31.00 |
% 221.85/31.00 | GROUND_INST: instantiating (21) with all_870_2, all_1194_0, v_L, all_870_3,
% 221.85/31.00 | all_625_1, simplifying with (14), (27) gives:
% 221.85/31.00 | (28) all_1194_0 = all_870_2
% 221.85/31.00 |
% 221.85/31.00 | REDUCE: (25), (28) imply:
% 221.85/31.00 | (29) ~ (all_870_2 = 0)
% 221.85/31.00 |
% 221.85/31.00 | BETA: splitting (13) gives:
% 221.85/31.00 |
% 221.85/31.00 | Case 1:
% 221.85/31.00 | |
% 221.85/31.00 | | (30) all_870_2 = 0 & all_870_8 = v_x & ? [v0: $i] : ? [v1: $i] : ?
% 221.85/31.00 | | [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & ~ (v0 = v_x) &
% 221.85/31.00 | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.00 | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v0) = v2 &
% 221.85/31.00 | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.00 | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = v1 &
% 221.85/31.00 | | c_member(all_683_0, v2, v_L) = v3 & c_member(all_683_0, v1, v_L) =
% 221.85/31.00 | | 0 & $i(v2) & $i(v1) & $i(v0))
% 221.85/31.00 | |
% 221.85/31.00 | | ALPHA: (30) implies:
% 221.85/31.00 | | (31) all_870_2 = 0
% 221.85/31.00 | |
% 221.85/31.00 | | REDUCE: (29), (31) imply:
% 221.85/31.00 | | (32) $false
% 221.85/31.00 | |
% 221.85/31.00 | | CLOSE: (32) is inconsistent.
% 221.85/31.00 | |
% 221.85/31.00 | Case 2:
% 221.85/31.00 | |
% 221.85/31.00 | | (33) all_870_6 = 0 & ~ (all_870_8 = v_x) & ? [v0: $i] : ? [v1: $i] :
% 221.85/31.00 | | ? [v2: any] : ? [v3: $i] : ? [v4: any] :
% 221.85/31.00 | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.00 | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v0) = v1 &
% 221.85/31.00 | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.00 | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v0) = v3 &
% 221.85/31.00 | | c_member(all_683_0, v3, v_L) = v4 & c_member(all_683_0, v1, v_L) =
% 221.85/31.00 | | v2 & $i(v3) & $i(v1) & $i(v0) & ((v2 = 0 & ~ (v4 = 0) & ~ (v0 =
% 221.85/31.00 | | v_x)) | (v0 = v_x & all_870_4 = 0 & ~ (all_870_2 = 0))))
% 221.85/31.00 | |
% 221.85/31.00 | | ALPHA: (33) implies:
% 221.85/31.00 | | (34) ? [v0: $i] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ? [v4:
% 221.85/31.00 | | any] : (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.00 | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v0) = v1 &
% 221.85/31.00 | | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.00 | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v0) = v3 &
% 221.85/31.00 | | c_member(all_683_0, v3, v_L) = v4 & c_member(all_683_0, v1, v_L) =
% 221.85/31.00 | | v2 & $i(v3) & $i(v1) & $i(v0) & ((v2 = 0 & ~ (v4 = 0) & ~ (v0 =
% 221.85/31.00 | | v_x)) | (v0 = v_x & all_870_4 = 0 & ~ (all_870_2 = 0))))
% 221.85/31.00 | |
% 221.85/31.00 | | DELTA: instantiating (34) with fresh symbols all_1204_0, all_1204_1,
% 221.85/31.00 | | all_1204_2, all_1204_3, all_1204_4 gives:
% 221.85/31.00 | | (35) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.00 | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, all_1204_4) =
% 221.85/31.00 | | all_1204_3 & c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.00 | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9, all_1204_4) =
% 221.85/31.00 | | all_1204_1 & c_member(all_683_0, all_1204_1, v_L) = all_1204_0 &
% 221.85/31.00 | | c_member(all_683_0, all_1204_3, v_L) = all_1204_2 & $i(all_1204_1) &
% 221.85/31.00 | | $i(all_1204_3) & $i(all_1204_4) & ((all_1204_2 = 0 & ~ (all_1204_0
% 221.85/31.00 | | = 0) & ~ (all_1204_4 = v_x)) | (all_1204_4 = v_x & all_870_4
% 221.85/31.00 | | = 0 & ~ (all_870_2 = 0)))
% 221.85/31.00 | |
% 221.85/31.00 | | ALPHA: (35) implies:
% 221.85/31.00 | | (36) $i(all_1204_4)
% 221.85/31.00 | | (37) c_member(all_683_0, all_1204_3, v_L) = all_1204_2
% 221.85/31.00 | | (38) c_member(all_683_0, all_1204_1, v_L) = all_1204_0
% 221.85/31.00 | | (39) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.00 | | tc_Arrow__Order__Mirabelle_Oalt, all_870_9, all_1204_4) =
% 221.85/31.00 | | all_1204_1
% 221.85/31.00 | | (40) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.00 | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, all_1204_4) =
% 221.85/31.00 | | all_1204_3
% 221.85/31.00 | | (41) (all_1204_2 = 0 & ~ (all_1204_0 = 0) & ~ (all_1204_4 = v_x)) |
% 221.85/31.00 | | (all_1204_4 = v_x & all_870_4 = 0 & ~ (all_870_2 = 0))
% 221.85/31.00 | |
% 221.85/31.00 | | REDUCE: (22), (38) imply:
% 221.85/31.00 | | (42) c_member(all_625_1, all_1204_1, v_L) = all_1204_0
% 221.85/31.00 | |
% 221.85/31.00 | | REDUCE: (22), (37) imply:
% 221.85/31.00 | | (43) c_member(all_625_1, all_1204_3, v_L) = all_1204_2
% 221.85/31.00 | |
% 221.85/31.00 | | BETA: splitting (12) gives:
% 221.85/31.00 | |
% 221.85/31.00 | | Case 1:
% 221.85/31.00 | | |
% 221.85/31.00 | | | (44) all_1137_0 = 0
% 221.85/31.00 | | |
% 221.85/31.00 | | | REDUCE: (19), (44) imply:
% 221.85/31.00 | | | (45) c_member(all_625_1, all_1137_1, v_L) = 0
% 221.85/31.00 | | |
% 221.85/31.00 | | | BETA: splitting (41) gives:
% 221.85/31.00 | | |
% 221.85/31.00 | | | Case 1:
% 221.85/31.00 | | | |
% 221.85/31.00 | | | | (46) all_1204_2 = 0 & ~ (all_1204_0 = 0) & ~ (all_1204_4 = v_x)
% 221.85/31.00 | | | |
% 221.85/31.00 | | | | ALPHA: (46) implies:
% 221.85/31.00 | | | | (47) all_1204_2 = 0
% 221.85/31.00 | | | | (48) ~ (all_1204_0 = 0)
% 221.85/31.00 | | | |
% 221.85/31.00 | | | | REDUCE: (43), (47) imply:
% 221.85/31.00 | | | | (49) c_member(all_625_1, all_1204_3, v_L) = 0
% 221.85/31.00 | | | |
% 221.85/31.00 | | | | GROUND_INST: instantiating (5) with all_870_9, all_870_8, v_y, v_L,
% 221.85/31.00 | | | | tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.00 | | | | tc_Arrow__Order__Mirabelle_Oalt, all_625_1, all_870_1,
% 221.85/31.00 | | | | all_1137_1, simplifying with (1), (2), (3), (7), (8), (9),
% 221.85/31.00 | | | | (11), (15), (17), (45) gives:
% 221.85/31.00 | | | | (50) all_870_8 = all_870_9 | ? [v0: int] : ( ~ (v0 = 0) &
% 221.85/31.00 | | | | c_Relation_Osingle__valued(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.00 | | | | tc_Arrow__Order__Mirabelle_Oalt, v_L) = v0)
% 221.85/31.00 | | | |
% 221.85/31.00 | | | | GROUND_INST: instantiating (6) with all_1204_4, all_1204_1, simplifying
% 221.85/31.00 | | | | with (36), (39) gives:
% 221.85/31.00 | | | | (51) ? [v0: $i] : ? [v1: any] : ? [v2: any] :
% 221.85/31.00 | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.00 | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, all_1204_4) = v0
% 221.85/31.00 | | | | & c_member(all_674_0, v0, v_L) = v1 & c_member(all_674_0,
% 221.85/31.00 | | | | all_1204_1, v_L) = v2 & $i(v0) & ( ~ (v1 = 0) | v2 = 0))
% 221.85/31.00 | | | |
% 221.85/31.00 | | | | GROUND_INST: instantiating (4) with all_870_8, all_1204_4, all_1204_3,
% 221.85/31.00 | | | | simplifying with (8), (36), (40) gives:
% 221.85/31.00 | | | | (52) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_674_0, all_1204_3,
% 221.85/31.00 | | | | v_L) = v0) | ! [v0: $i] : ! [v1: $i] : ( ~
% 221.85/31.00 | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.00 | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v0) = v1) | ~
% 221.85/31.00 | | | | $i(v0) | ? [v2: $i] : ? [v3: any] : ? [v4: any] :
% 221.85/31.00 | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.00 | | | | tc_Arrow__Order__Mirabelle_Oalt, all_1204_4, v0) = v2 &
% 221.85/31.00 | | | | c_member(all_674_0, v2, v_L) = v3 & c_member(all_674_0, v1,
% 221.85/31.00 | | | | v_L) = v4 & $i(v2) & ( ~ (v3 = 0) | v4 = 0)))
% 221.85/31.00 | | | |
% 221.85/31.00 | | | | DELTA: instantiating (51) with fresh symbols all_1278_0, all_1278_1,
% 221.85/31.00 | | | | all_1278_2 gives:
% 221.85/31.00 | | | | (53) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.00 | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, all_1204_4) =
% 221.85/31.00 | | | | all_1278_2 & c_member(all_674_0, all_1278_2, v_L) = all_1278_1 &
% 221.85/31.00 | | | | c_member(all_674_0, all_1204_1, v_L) = all_1278_0 &
% 221.85/31.00 | | | | $i(all_1278_2) & ( ~ (all_1278_1 = 0) | all_1278_0 = 0)
% 221.85/31.00 | | | |
% 221.85/31.00 | | | | ALPHA: (53) implies:
% 221.85/31.00 | | | | (54) c_member(all_674_0, all_1204_1, v_L) = all_1278_0
% 221.85/31.00 | | | | (55) c_member(all_674_0, all_1278_2, v_L) = all_1278_1
% 221.85/31.00 | | | | (56) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.00 | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, all_1204_4) =
% 221.85/31.00 | | | | all_1278_2
% 221.85/31.00 | | | | (57) ~ (all_1278_1 = 0) | all_1278_0 = 0
% 221.85/31.00 | | | |
% 221.85/31.00 | | | | REDUCE: (10), (55) imply:
% 221.85/31.00 | | | | (58) c_member(all_625_1, all_1278_2, v_L) = all_1278_1
% 221.85/31.00 | | | |
% 221.85/31.00 | | | | REDUCE: (10), (54) imply:
% 221.85/31.00 | | | | (59) c_member(all_625_1, all_1204_1, v_L) = all_1278_0
% 221.85/31.00 | | | |
% 221.85/31.00 | | | | BETA: splitting (52) gives:
% 221.85/31.00 | | | |
% 221.85/31.00 | | | | Case 1:
% 221.85/31.00 | | | | |
% 221.85/31.00 | | | | | (60) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_674_0, all_1204_3,
% 221.85/31.00 | | | | | v_L) = v0)
% 221.85/31.00 | | | | |
% 221.85/31.00 | | | | | DELTA: instantiating (60) with fresh symbol all_1295_0 gives:
% 221.85/31.00 | | | | | (61) ~ (all_1295_0 = 0) & c_member(all_674_0, all_1204_3, v_L) =
% 221.85/31.00 | | | | | all_1295_0
% 221.85/31.00 | | | | |
% 221.85/31.00 | | | | | ALPHA: (61) implies:
% 221.85/31.00 | | | | | (62) ~ (all_1295_0 = 0)
% 221.85/31.00 | | | | | (63) c_member(all_674_0, all_1204_3, v_L) = all_1295_0
% 221.85/31.00 | | | | |
% 221.85/31.00 | | | | | REDUCE: (10), (63) imply:
% 221.85/31.00 | | | | | (64) c_member(all_625_1, all_1204_3, v_L) = all_1295_0
% 221.85/31.00 | | | | |
% 221.85/31.00 | | | | | GROUND_INST: instantiating (21) with 0, all_1295_0, v_L, all_1204_3,
% 221.85/31.00 | | | | | all_625_1, simplifying with (49), (64) gives:
% 221.85/31.00 | | | | | (65) all_1295_0 = 0
% 221.85/31.00 | | | | |
% 221.85/31.00 | | | | | REDUCE: (62), (65) imply:
% 221.85/31.00 | | | | | (66) $false
% 221.85/31.00 | | | | |
% 221.85/31.00 | | | | | CLOSE: (66) is inconsistent.
% 221.85/31.00 | | | | |
% 221.85/31.00 | | | | Case 2:
% 221.85/31.00 | | | | |
% 221.85/31.00 | | | | | (67) ! [v0: $i] : ! [v1: $i] : ( ~
% 221.85/31.00 | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.00 | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v0) = v1) |
% 221.85/31.00 | | | | | ~ $i(v0) | ? [v2: $i] : ? [v3: any] : ? [v4: any] :
% 221.85/31.00 | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.00 | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_1204_4, v0) = v2 &
% 221.85/31.00 | | | | | c_member(all_674_0, v2, v_L) = v3 & c_member(all_674_0,
% 221.85/31.00 | | | | | v1, v_L) = v4 & $i(v2) & ( ~ (v3 = 0) | v4 = 0)))
% 221.85/31.00 | | | | |
% 221.85/31.00 | | | | | GROUND_INST: instantiating (67) with all_1204_4, all_1204_3,
% 221.85/31.00 | | | | | simplifying with (36), (40) gives:
% 221.85/31.00 | | | | | (68) ? [v0: $i] : ? [v1: any] : ? [v2: any] :
% 221.85/31.00 | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.00 | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_1204_4, all_1204_4) =
% 221.85/31.00 | | | | | v0 & c_member(all_674_0, v0, v_L) = v1 & c_member(all_674_0,
% 221.85/31.00 | | | | | all_1204_3, v_L) = v2 & $i(v0) & ( ~ (v1 = 0) | v2 = 0))
% 221.85/31.00 | | | | |
% 221.85/31.00 | | | | | DELTA: instantiating (68) with fresh symbols all_1296_0, all_1296_1,
% 221.85/31.00 | | | | | all_1296_2 gives:
% 221.85/31.00 | | | | | (69) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.00 | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_1204_4, all_1204_4) =
% 221.85/31.00 | | | | | all_1296_2 & c_member(all_674_0, all_1296_2, v_L) = all_1296_1
% 221.85/31.00 | | | | | & c_member(all_674_0, all_1204_3, v_L) = all_1296_0 &
% 221.85/31.00 | | | | | $i(all_1296_2) & ( ~ (all_1296_1 = 0) | all_1296_0 = 0)
% 221.85/31.00 | | | | |
% 221.85/31.00 | | | | | ALPHA: (69) implies:
% 221.85/31.01 | | | | | (70) c_member(all_674_0, all_1204_3, v_L) = all_1296_0
% 221.85/31.01 | | | | |
% 221.85/31.01 | | | | | REDUCE: (10), (70) imply:
% 221.85/31.01 | | | | | (71) c_member(all_625_1, all_1204_3, v_L) = all_1296_0
% 221.85/31.01 | | | | |
% 221.85/31.01 | | | | | BETA: splitting (50) gives:
% 221.85/31.01 | | | | |
% 221.85/31.01 | | | | | Case 1:
% 221.85/31.01 | | | | | |
% 221.85/31.01 | | | | | | (72) all_870_8 = all_870_9
% 221.85/31.01 | | | | | |
% 221.85/31.01 | | | | | | REDUCE: (23), (72) imply:
% 221.85/31.01 | | | | | | (73) $false
% 221.85/31.01 | | | | | |
% 221.85/31.01 | | | | | | CLOSE: (73) is inconsistent.
% 221.85/31.01 | | | | | |
% 221.85/31.01 | | | | | Case 2:
% 221.85/31.01 | | | | | |
% 221.85/31.01 | | | | | |
% 221.85/31.01 | | | | | | GROUND_INST: instantiating (21) with 0, all_1296_0, v_L, all_1204_3,
% 221.85/31.01 | | | | | | all_625_1, simplifying with (49), (71) gives:
% 221.85/31.01 | | | | | | (74) all_1296_0 = 0
% 221.85/31.01 | | | | | |
% 221.85/31.01 | | | | | | GROUND_INST: instantiating (21) with all_1204_0, all_1278_0, v_L,
% 221.85/31.01 | | | | | | all_1204_1, all_625_1, simplifying with (42), (59)
% 221.85/31.01 | | | | | | gives:
% 221.85/31.01 | | | | | | (75) all_1278_0 = all_1204_0
% 221.85/31.01 | | | | | |
% 221.85/31.01 | | | | | | GROUND_INST: instantiating (18) with all_1204_3, all_1278_2,
% 221.85/31.01 | | | | | | all_1204_4, all_870_8, tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.01 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with (40),
% 221.85/31.01 | | | | | | (56) gives:
% 221.85/31.01 | | | | | | (76) all_1278_2 = all_1204_3
% 221.85/31.01 | | | | | |
% 221.85/31.01 | | | | | | REDUCE: (58), (76) imply:
% 221.85/31.01 | | | | | | (77) c_member(all_625_1, all_1204_3, v_L) = all_1278_1
% 221.85/31.01 | | | | | |
% 221.85/31.01 | | | | | | BETA: splitting (57) gives:
% 221.85/31.01 | | | | | |
% 221.85/31.01 | | | | | | Case 1:
% 221.85/31.01 | | | | | | |
% 221.85/31.01 | | | | | | | (78) ~ (all_1278_1 = 0)
% 221.85/31.01 | | | | | | |
% 221.85/31.01 | | | | | | | GROUND_INST: instantiating (21) with 0, all_1278_1, v_L,
% 221.85/31.01 | | | | | | | all_1204_3, all_625_1, simplifying with (49), (77)
% 221.85/31.01 | | | | | | | gives:
% 221.85/31.01 | | | | | | | (79) all_1278_1 = 0
% 221.85/31.01 | | | | | | |
% 221.85/31.01 | | | | | | | REDUCE: (78), (79) imply:
% 221.85/31.01 | | | | | | | (80) $false
% 221.85/31.01 | | | | | | |
% 221.85/31.01 | | | | | | | CLOSE: (80) is inconsistent.
% 221.85/31.01 | | | | | | |
% 221.85/31.01 | | | | | | Case 2:
% 221.85/31.01 | | | | | | |
% 221.85/31.01 | | | | | | | (81) all_1278_0 = 0
% 221.85/31.01 | | | | | | |
% 221.85/31.01 | | | | | | | COMBINE_EQS: (75), (81) imply:
% 221.85/31.01 | | | | | | | (82) all_1204_0 = 0
% 221.85/31.01 | | | | | | |
% 221.85/31.01 | | | | | | | REDUCE: (48), (82) imply:
% 221.85/31.01 | | | | | | | (83) $false
% 221.85/31.01 | | | | | | |
% 221.85/31.01 | | | | | | | CLOSE: (83) is inconsistent.
% 221.85/31.01 | | | | | | |
% 221.85/31.01 | | | | | | End of split
% 221.85/31.01 | | | | | |
% 221.85/31.01 | | | | | End of split
% 221.85/31.01 | | | | |
% 221.85/31.01 | | | | End of split
% 221.85/31.01 | | | |
% 221.85/31.01 | | | Case 2:
% 221.85/31.01 | | | |
% 221.85/31.01 | | | | (84) all_1204_4 = v_x & all_870_4 = 0 & ~ (all_870_2 = 0)
% 221.85/31.01 | | | |
% 221.85/31.01 | | | | ALPHA: (84) implies:
% 221.85/31.01 | | | | (85) all_870_4 = 0
% 221.85/31.01 | | | |
% 221.85/31.01 | | | | REDUCE: (20), (85) imply:
% 221.85/31.01 | | | | (86) $false
% 221.85/31.01 | | | |
% 221.85/31.01 | | | | CLOSE: (86) is inconsistent.
% 221.85/31.01 | | | |
% 221.85/31.01 | | | End of split
% 221.85/31.01 | | |
% 221.85/31.01 | | Case 2:
% 221.85/31.01 | | |
% 221.85/31.01 | | | (87) all_1137_2 = 0
% 221.85/31.01 | | |
% 221.85/31.01 | | | COMBINE_EQS: (16), (87) imply:
% 221.85/31.01 | | | (88) all_870_2 = 0
% 221.85/31.01 | | |
% 221.85/31.01 | | | REDUCE: (29), (88) imply:
% 221.85/31.01 | | | (89) $false
% 221.85/31.01 | | |
% 221.85/31.01 | | | CLOSE: (89) is inconsistent.
% 221.85/31.01 | | |
% 221.85/31.01 | | End of split
% 221.85/31.01 | |
% 221.85/31.01 | End of split
% 221.85/31.01 |
% 221.85/31.01 End of proof
% 221.85/31.01
% 221.85/31.01 Sub-proof #7 shows that the following formulas are inconsistent:
% 221.85/31.01 ----------------------------------------------------------------
% 221.85/31.01 (1) ? [v0: $i] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ? [v4: any] :
% 221.85/31.01 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.01 tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v0) = v1 &
% 221.85/31.01 c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.01 tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v0) = v3 &
% 221.85/31.01 c_member(all_683_0, v3, v_L) = v4 & c_member(all_683_0, v1, v_L) = v2 &
% 221.85/31.01 $i(v3) & $i(v1) & $i(v0) & ((v2 = 0 & ~ (v4 = 0) & ~ (v0 = v_x)) |
% 221.85/31.01 (v0 = v_x & all_870_4 = 0 & ~ (all_870_2 = 0))))
% 221.85/31.01 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 221.85/31.01 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.01 tc_Arrow__Order__Mirabelle_Oalt, v0, v1) = v2) | ~ $i(v1) | ~
% 221.85/31.01 $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & c_member(all_674_0, v2, v_L) =
% 221.85/31.01 v3) | ! [v3: $i] : ! [v4: $i] : ( ~
% 221.85/31.01 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.01 tc_Arrow__Order__Mirabelle_Oalt, v0, v3) = v4) | ~ $i(v3) | ?
% 221.85/31.01 [v5: $i] : ? [v6: any] : ? [v7: any] :
% 221.85/31.01 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.01 tc_Arrow__Order__Mirabelle_Oalt, v1, v3) = v5 &
% 221.85/31.01 c_member(all_674_0, v5, v_L) = v6 & c_member(all_674_0, v4, v_L) =
% 221.85/31.01 v7 & $i(v5) & ( ~ (v6 = 0) | v7 = 0))))
% 221.85/31.01 (3) c_member(all_625_1, all_870_7, v_L) = all_870_6
% 221.85/31.01 (4) $i(all_870_8)
% 221.85/31.01 (5) c_member(all_625_1, all_870_1, v_L) = all_870_0
% 221.85/31.01 (6) all_674_0 = all_625_1
% 221.85/31.01 (7) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.01 tc_Arrow__Order__Mirabelle_Oalt, v_y, all_870_8) = all_870_7
% 221.85/31.01 (8) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.01 tc_Arrow__Order__Mirabelle_Oalt, v_y, all_870_8) = all_870_1
% 221.85/31.01 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 221.85/31.01 [v5: $i] : (v1 = v0 | ~ (c_Product__Type_OPair(v5, v4, v3, v2) = v1) |
% 221.85/31.01 ~ (c_Product__Type_OPair(v5, v4, v3, v2) = v0))
% 221.85/31.01 (10) all_870_9 = v_y
% 221.85/31.01 (11) ~ (all_870_4 = 0)
% 221.85/31.01 (12) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 221.85/31.01 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (c_member(v4, v3, v2) = v1) |
% 221.85/31.01 ~ (c_member(v4, v3, v2) = v0))
% 221.85/31.01 (13) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_674_0, all_870_1, v_L) = v0)
% 221.85/31.01 | ! [v0: $i] : ! [v1: $i] : ( ~
% 221.85/31.01 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.01 tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = v1) | ~ $i(v0) | ?
% 221.85/31.01 [v2: $i] : ? [v3: any] : ? [v4: any] :
% 221.85/31.01 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.01 tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v0) = v2 &
% 221.85/31.01 c_member(all_674_0, v2, v_L) = v3 & c_member(all_674_0, v1, v_L) =
% 221.85/31.01 v4 & $i(v2) & ( ~ (v3 = 0) | v4 = 0)))
% 221.85/31.01 (14) all_683_0 = all_625_1
% 221.85/31.01 (15) all_870_6 = 0
% 221.85/31.01
% 221.85/31.01 Begin of proof
% 221.85/31.01 |
% 221.85/31.01 | DELTA: instantiating (1) with fresh symbols all_1141_0, all_1141_1,
% 221.85/31.01 | all_1141_2, all_1141_3, all_1141_4 gives:
% 221.85/31.01 | (16) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.01 | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, all_1141_4) = all_1141_3
% 221.85/31.01 | & c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.01 | tc_Arrow__Order__Mirabelle_Oalt, all_870_9, all_1141_4) = all_1141_1
% 221.85/31.01 | & c_member(all_683_0, all_1141_1, v_L) = all_1141_0 &
% 221.85/31.01 | c_member(all_683_0, all_1141_3, v_L) = all_1141_2 & $i(all_1141_1) &
% 221.85/31.01 | $i(all_1141_3) & $i(all_1141_4) & ((all_1141_2 = 0 & ~ (all_1141_0 =
% 221.85/31.01 | 0) & ~ (all_1141_4 = v_x)) | (all_1141_4 = v_x & all_870_4 = 0
% 221.85/31.01 | & ~ (all_870_2 = 0)))
% 221.85/31.01 |
% 221.85/31.01 | ALPHA: (16) implies:
% 221.85/31.01 | (17) $i(all_1141_4)
% 221.85/31.01 | (18) c_member(all_683_0, all_1141_3, v_L) = all_1141_2
% 221.85/31.01 | (19) c_member(all_683_0, all_1141_1, v_L) = all_1141_0
% 221.85/31.01 | (20) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.01 | tc_Arrow__Order__Mirabelle_Oalt, all_870_9, all_1141_4) = all_1141_1
% 221.85/31.01 | (21) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.01 | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, all_1141_4) = all_1141_3
% 221.85/31.01 | (22) (all_1141_2 = 0 & ~ (all_1141_0 = 0) & ~ (all_1141_4 = v_x)) |
% 221.85/31.01 | (all_1141_4 = v_x & all_870_4 = 0 & ~ (all_870_2 = 0))
% 221.85/31.01 |
% 221.85/31.01 | REDUCE: (10), (20) imply:
% 221.85/31.01 | (23) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.01 | tc_Arrow__Order__Mirabelle_Oalt, v_y, all_1141_4) = all_1141_1
% 221.85/31.01 |
% 221.85/31.01 | REDUCE: (14), (19) imply:
% 221.85/31.01 | (24) c_member(all_625_1, all_1141_1, v_L) = all_1141_0
% 221.85/31.01 |
% 221.85/31.01 | REDUCE: (14), (18) imply:
% 221.85/31.01 | (25) c_member(all_625_1, all_1141_3, v_L) = all_1141_2
% 221.85/31.01 |
% 221.85/31.01 | REDUCE: (3), (15) imply:
% 221.85/31.01 | (26) c_member(all_625_1, all_870_7, v_L) = 0
% 221.85/31.01 |
% 221.85/31.01 | BETA: splitting (22) gives:
% 221.85/31.01 |
% 221.85/31.01 | Case 1:
% 221.85/31.01 | |
% 221.85/31.01 | | (27) all_1141_2 = 0 & ~ (all_1141_0 = 0) & ~ (all_1141_4 = v_x)
% 221.85/31.01 | |
% 221.85/31.01 | | ALPHA: (27) implies:
% 221.85/31.01 | | (28) all_1141_2 = 0
% 221.85/31.01 | | (29) ~ (all_1141_0 = 0)
% 221.85/31.01 | |
% 221.85/31.01 | | REDUCE: (25), (28) imply:
% 221.85/31.01 | | (30) c_member(all_625_1, all_1141_3, v_L) = 0
% 221.85/31.01 | |
% 221.85/31.01 | | GROUND_INST: instantiating (9) with all_870_1, all_870_7, all_870_8, v_y,
% 221.85/31.01 | | tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.01 | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with (7), (8)
% 221.85/31.01 | | gives:
% 221.85/31.01 | | (31) all_870_1 = all_870_7
% 221.85/31.01 | |
% 221.85/31.01 | | REDUCE: (5), (31) imply:
% 221.85/31.01 | | (32) c_member(all_625_1, all_870_7, v_L) = all_870_0
% 221.85/31.01 | |
% 221.85/31.01 | | GROUND_INST: instantiating (12) with 0, all_870_0, v_L, all_870_7,
% 221.85/31.01 | | all_625_1, simplifying with (26), (32) gives:
% 221.85/31.01 | | (33) all_870_0 = 0
% 221.85/31.01 | |
% 221.85/31.01 | | BETA: splitting (13) gives:
% 221.85/31.01 | |
% 221.85/31.01 | | Case 1:
% 221.85/31.01 | | |
% 221.85/31.01 | | | (34) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_674_0, all_870_1, v_L)
% 221.85/31.01 | | | = v0)
% 221.85/31.01 | | |
% 221.85/31.01 | | | DELTA: instantiating (34) with fresh symbol all_1170_0 gives:
% 221.85/31.01 | | | (35) ~ (all_1170_0 = 0) & c_member(all_674_0, all_870_1, v_L) =
% 221.85/31.01 | | | all_1170_0
% 221.85/31.01 | | |
% 221.85/31.01 | | | ALPHA: (35) implies:
% 221.85/31.01 | | | (36) ~ (all_1170_0 = 0)
% 221.85/31.01 | | | (37) c_member(all_674_0, all_870_1, v_L) = all_1170_0
% 221.85/31.01 | | |
% 221.85/31.01 | | | REDUCE: (6), (31), (37) imply:
% 221.85/31.01 | | | (38) c_member(all_625_1, all_870_7, v_L) = all_1170_0
% 221.85/31.01 | | |
% 221.85/31.01 | | | GROUND_INST: instantiating (12) with 0, all_1170_0, v_L, all_870_7,
% 221.85/31.01 | | | all_625_1, simplifying with (26), (38) gives:
% 221.85/31.01 | | | (39) all_1170_0 = 0
% 221.85/31.01 | | |
% 221.85/31.01 | | | REDUCE: (36), (39) imply:
% 221.85/31.01 | | | (40) $false
% 221.85/31.01 | | |
% 221.85/31.01 | | | CLOSE: (40) is inconsistent.
% 221.85/31.01 | | |
% 221.85/31.01 | | Case 2:
% 221.85/31.01 | | |
% 221.85/31.01 | | | (41) ! [v0: $i] : ! [v1: $i] : ( ~
% 221.85/31.01 | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.01 | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = v1) | ~ $i(v0)
% 221.85/31.01 | | | | ? [v2: $i] : ? [v3: any] : ? [v4: any] :
% 221.85/31.01 | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.01 | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v0) = v2 &
% 221.85/31.01 | | | c_member(all_674_0, v2, v_L) = v3 & c_member(all_674_0, v1,
% 221.85/31.01 | | | v_L) = v4 & $i(v2) & ( ~ (v3 = 0) | v4 = 0)))
% 221.85/31.01 | | |
% 221.85/31.01 | | | GROUND_INST: instantiating (41) with all_1141_4, all_1141_1, simplifying
% 221.85/31.01 | | | with (17), (23) gives:
% 221.85/31.01 | | | (42) ? [v0: $i] : ? [v1: any] : ? [v2: any] :
% 221.85/31.01 | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.01 | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, all_1141_4) = v0 &
% 221.85/31.01 | | | c_member(all_674_0, v0, v_L) = v1 & c_member(all_674_0,
% 221.85/31.01 | | | all_1141_1, v_L) = v2 & $i(v0) & ( ~ (v1 = 0) | v2 = 0))
% 221.85/31.01 | | |
% 221.85/31.01 | | | GROUND_INST: instantiating (2) with all_870_8, all_1141_4, all_1141_3,
% 221.85/31.01 | | | simplifying with (4), (17), (21) gives:
% 221.85/31.02 | | | (43) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_674_0, all_1141_3, v_L)
% 221.85/31.02 | | | = v0) | ! [v0: $i] : ! [v1: $i] : ( ~
% 221.85/31.02 | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.02 | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v0) = v1) | ~
% 221.85/31.02 | | | $i(v0) | ? [v2: $i] : ? [v3: any] : ? [v4: any] :
% 221.85/31.02 | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.02 | | | tc_Arrow__Order__Mirabelle_Oalt, all_1141_4, v0) = v2 &
% 221.85/31.02 | | | c_member(all_674_0, v2, v_L) = v3 & c_member(all_674_0, v1,
% 221.85/31.02 | | | v_L) = v4 & $i(v2) & ( ~ (v3 = 0) | v4 = 0)))
% 221.85/31.02 | | |
% 221.85/31.02 | | | DELTA: instantiating (42) with fresh symbols all_1219_0, all_1219_1,
% 221.85/31.02 | | | all_1219_2 gives:
% 221.85/31.02 | | | (44) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.02 | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, all_1141_4) =
% 221.85/31.02 | | | all_1219_2 & c_member(all_674_0, all_1219_2, v_L) = all_1219_1 &
% 221.85/31.02 | | | c_member(all_674_0, all_1141_1, v_L) = all_1219_0 & $i(all_1219_2)
% 221.85/31.02 | | | & ( ~ (all_1219_1 = 0) | all_1219_0 = 0)
% 221.85/31.02 | | |
% 221.85/31.02 | | | ALPHA: (44) implies:
% 221.85/31.02 | | | (45) c_member(all_674_0, all_1141_1, v_L) = all_1219_0
% 221.85/31.02 | | | (46) c_member(all_674_0, all_1219_2, v_L) = all_1219_1
% 221.85/31.02 | | | (47) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.02 | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, all_1141_4) =
% 221.85/31.02 | | | all_1219_2
% 221.85/31.02 | | | (48) ~ (all_1219_1 = 0) | all_1219_0 = 0
% 221.85/31.02 | | |
% 221.85/31.02 | | | REDUCE: (6), (46) imply:
% 221.85/31.02 | | | (49) c_member(all_625_1, all_1219_2, v_L) = all_1219_1
% 221.85/31.02 | | |
% 221.85/31.02 | | | REDUCE: (6), (45) imply:
% 221.85/31.02 | | | (50) c_member(all_625_1, all_1141_1, v_L) = all_1219_0
% 221.85/31.02 | | |
% 221.85/31.02 | | | BETA: splitting (43) gives:
% 221.85/31.02 | | |
% 221.85/31.02 | | | Case 1:
% 221.85/31.02 | | | |
% 221.85/31.02 | | | | (51) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_674_0, all_1141_3,
% 221.85/31.02 | | | | v_L) = v0)
% 221.85/31.02 | | | |
% 221.85/31.02 | | | | DELTA: instantiating (51) with fresh symbol all_1230_0 gives:
% 221.85/31.02 | | | | (52) ~ (all_1230_0 = 0) & c_member(all_674_0, all_1141_3, v_L) =
% 221.85/31.02 | | | | all_1230_0
% 221.85/31.02 | | | |
% 221.85/31.02 | | | | ALPHA: (52) implies:
% 221.85/31.02 | | | | (53) ~ (all_1230_0 = 0)
% 221.85/31.02 | | | | (54) c_member(all_674_0, all_1141_3, v_L) = all_1230_0
% 221.85/31.02 | | | |
% 221.85/31.02 | | | | REDUCE: (6), (54) imply:
% 221.85/31.02 | | | | (55) c_member(all_625_1, all_1141_3, v_L) = all_1230_0
% 221.85/31.02 | | | |
% 221.85/31.02 | | | | GROUND_INST: instantiating (12) with 0, all_1230_0, v_L, all_1141_3,
% 221.85/31.02 | | | | all_625_1, simplifying with (30), (55) gives:
% 221.85/31.02 | | | | (56) all_1230_0 = 0
% 221.85/31.02 | | | |
% 221.85/31.02 | | | | REDUCE: (53), (56) imply:
% 221.85/31.02 | | | | (57) $false
% 221.85/31.02 | | | |
% 221.85/31.02 | | | | CLOSE: (57) is inconsistent.
% 221.85/31.02 | | | |
% 221.85/31.02 | | | Case 2:
% 221.85/31.02 | | | |
% 221.85/31.02 | | | | (58) ! [v0: $i] : ! [v1: $i] : ( ~
% 221.85/31.02 | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.02 | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v0) = v1) | ~
% 221.85/31.02 | | | | $i(v0) | ? [v2: $i] : ? [v3: any] : ? [v4: any] :
% 221.85/31.02 | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.02 | | | | tc_Arrow__Order__Mirabelle_Oalt, all_1141_4, v0) = v2 &
% 221.85/31.02 | | | | c_member(all_674_0, v2, v_L) = v3 & c_member(all_674_0, v1,
% 221.85/31.02 | | | | v_L) = v4 & $i(v2) & ( ~ (v3 = 0) | v4 = 0)))
% 221.85/31.02 | | | |
% 221.85/31.02 | | | | GROUND_INST: instantiating (58) with all_1141_4, all_1141_3, simplifying
% 221.85/31.02 | | | | with (17), (21) gives:
% 221.85/31.02 | | | | (59) ? [v0: $i] : ? [v1: any] : ? [v2: any] :
% 221.85/31.02 | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.02 | | | | tc_Arrow__Order__Mirabelle_Oalt, all_1141_4, all_1141_4) =
% 221.85/31.02 | | | | v0 & c_member(all_674_0, v0, v_L) = v1 & c_member(all_674_0,
% 221.85/31.02 | | | | all_1141_3, v_L) = v2 & $i(v0) & ( ~ (v1 = 0) | v2 = 0))
% 221.85/31.02 | | | |
% 221.85/31.02 | | | | DELTA: instantiating (59) with fresh symbols all_1231_0, all_1231_1,
% 221.85/31.02 | | | | all_1231_2 gives:
% 221.85/31.02 | | | | (60) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.02 | | | | tc_Arrow__Order__Mirabelle_Oalt, all_1141_4, all_1141_4) =
% 221.85/31.02 | | | | all_1231_2 & c_member(all_674_0, all_1231_2, v_L) = all_1231_1 &
% 221.85/31.02 | | | | c_member(all_674_0, all_1141_3, v_L) = all_1231_0 &
% 221.85/31.02 | | | | $i(all_1231_2) & ( ~ (all_1231_1 = 0) | all_1231_0 = 0)
% 221.85/31.02 | | | |
% 221.85/31.02 | | | | ALPHA: (60) implies:
% 221.85/31.02 | | | | (61) c_member(all_674_0, all_1141_3, v_L) = all_1231_0
% 221.85/31.02 | | | |
% 221.85/31.02 | | | | REDUCE: (6), (61) imply:
% 221.85/31.02 | | | | (62) c_member(all_625_1, all_1141_3, v_L) = all_1231_0
% 221.85/31.02 | | | |
% 221.85/31.02 | | | | GROUND_INST: instantiating (12) with 0, all_1231_0, v_L, all_1141_3,
% 221.85/31.02 | | | | all_625_1, simplifying with (30), (62) gives:
% 221.85/31.02 | | | | (63) all_1231_0 = 0
% 221.85/31.02 | | | |
% 221.85/31.02 | | | | GROUND_INST: instantiating (12) with all_1141_0, all_1219_0, v_L,
% 221.85/31.02 | | | | all_1141_1, all_625_1, simplifying with (24), (50) gives:
% 221.85/31.02 | | | | (64) all_1219_0 = all_1141_0
% 221.85/31.02 | | | |
% 221.85/31.02 | | | | GROUND_INST: instantiating (9) with all_1141_3, all_1219_2, all_1141_4,
% 221.85/31.02 | | | | all_870_8, tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.02 | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with (21),
% 221.85/31.02 | | | | (47) gives:
% 221.85/31.02 | | | | (65) all_1219_2 = all_1141_3
% 221.85/31.02 | | | |
% 221.85/31.02 | | | | REDUCE: (49), (65) imply:
% 221.85/31.02 | | | | (66) c_member(all_625_1, all_1141_3, v_L) = all_1219_1
% 221.85/31.02 | | | |
% 221.85/31.02 | | | | BETA: splitting (48) gives:
% 221.85/31.02 | | | |
% 221.85/31.02 | | | | Case 1:
% 221.85/31.02 | | | | |
% 221.85/31.02 | | | | | (67) ~ (all_1219_1 = 0)
% 221.85/31.02 | | | | |
% 221.85/31.02 | | | | | GROUND_INST: instantiating (12) with 0, all_1219_1, v_L, all_1141_3,
% 221.85/31.02 | | | | | all_625_1, simplifying with (30), (66) gives:
% 221.85/31.02 | | | | | (68) all_1219_1 = 0
% 221.85/31.02 | | | | |
% 221.85/31.02 | | | | | REDUCE: (67), (68) imply:
% 221.85/31.02 | | | | | (69) $false
% 221.85/31.02 | | | | |
% 221.85/31.02 | | | | | CLOSE: (69) is inconsistent.
% 221.85/31.02 | | | | |
% 221.85/31.02 | | | | Case 2:
% 221.85/31.02 | | | | |
% 221.85/31.02 | | | | | (70) all_1219_0 = 0
% 221.85/31.02 | | | | |
% 221.85/31.02 | | | | | COMBINE_EQS: (64), (70) imply:
% 221.85/31.02 | | | | | (71) all_1141_0 = 0
% 221.85/31.02 | | | | |
% 221.85/31.02 | | | | | REDUCE: (29), (71) imply:
% 221.85/31.02 | | | | | (72) $false
% 221.85/31.02 | | | | |
% 221.85/31.02 | | | | | CLOSE: (72) is inconsistent.
% 221.85/31.02 | | | | |
% 221.85/31.02 | | | | End of split
% 221.85/31.02 | | | |
% 221.85/31.02 | | | End of split
% 221.85/31.02 | | |
% 221.85/31.02 | | End of split
% 221.85/31.02 | |
% 221.85/31.02 | Case 2:
% 221.85/31.02 | |
% 221.85/31.02 | | (73) all_1141_4 = v_x & all_870_4 = 0 & ~ (all_870_2 = 0)
% 221.85/31.02 | |
% 221.85/31.02 | | ALPHA: (73) implies:
% 221.85/31.02 | | (74) all_870_4 = 0
% 221.85/31.02 | |
% 221.85/31.02 | | REDUCE: (11), (74) imply:
% 221.85/31.02 | | (75) $false
% 221.85/31.02 | |
% 221.85/31.02 | | CLOSE: (75) is inconsistent.
% 221.85/31.02 | |
% 221.85/31.02 | End of split
% 221.85/31.02 |
% 221.85/31.02 End of proof
% 221.85/31.02
% 221.85/31.02 Sub-proof #8 shows that the following formulas are inconsistent:
% 221.85/31.02 ----------------------------------------------------------------
% 221.85/31.02 (1) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) &
% 221.85/31.02 ~ (v0 = v_x) & c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.02 tc_Arrow__Order__Mirabelle_Oalt, all_870_9, v0) = v2 &
% 221.85/31.02 c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.02 tc_Arrow__Order__Mirabelle_Oalt, v_y, v0) = v1 & c_member(all_683_0,
% 221.85/31.02 v2, v_L) = v3 & c_member(all_683_0, v1, v_L) = 0 & $i(v2) & $i(v1) &
% 221.85/31.02 $i(v0))
% 221.85/31.02 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 221.85/31.02 [v5: $i] : (v1 = v0 | ~ (c_Product__Type_OPair(v5, v4, v3, v2) = v1) |
% 221.85/31.02 ~ (c_Product__Type_OPair(v5, v4, v3, v2) = v0))
% 221.85/31.02 (3) all_870_9 = v_y
% 221.85/31.02 (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 221.85/31.02 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (c_member(v4, v3, v2) = v1) | ~
% 221.85/31.02 (c_member(v4, v3, v2) = v0))
% 221.85/31.02 (5) all_683_0 = all_625_1
% 221.85/31.02
% 221.85/31.02 Begin of proof
% 221.85/31.02 |
% 221.85/31.02 | DELTA: instantiating (1) with fresh symbols all_1154_0, all_1154_1,
% 221.85/31.02 | all_1154_2, all_1154_3 gives:
% 221.85/31.02 | (6) ~ (all_1154_0 = 0) & ~ (all_1154_3 = v_x) &
% 221.85/31.02 | c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.02 | tc_Arrow__Order__Mirabelle_Oalt, all_870_9, all_1154_3) = all_1154_1
% 221.85/31.02 | & c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.02 | tc_Arrow__Order__Mirabelle_Oalt, v_y, all_1154_3) = all_1154_2 &
% 221.85/31.02 | c_member(all_683_0, all_1154_1, v_L) = all_1154_0 & c_member(all_683_0,
% 221.85/31.02 | all_1154_2, v_L) = 0 & $i(all_1154_1) & $i(all_1154_2) &
% 221.85/31.02 | $i(all_1154_3)
% 221.85/31.02 |
% 221.85/31.02 | ALPHA: (6) implies:
% 221.85/31.02 | (7) ~ (all_1154_0 = 0)
% 221.85/31.02 | (8) c_member(all_683_0, all_1154_2, v_L) = 0
% 221.85/31.02 | (9) c_member(all_683_0, all_1154_1, v_L) = all_1154_0
% 221.85/31.02 | (10) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.02 | tc_Arrow__Order__Mirabelle_Oalt, v_y, all_1154_3) = all_1154_2
% 221.85/31.02 | (11) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.02 | tc_Arrow__Order__Mirabelle_Oalt, all_870_9, all_1154_3) = all_1154_1
% 221.85/31.02 |
% 221.85/31.02 | REDUCE: (3), (11) imply:
% 221.85/31.02 | (12) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.02 | tc_Arrow__Order__Mirabelle_Oalt, v_y, all_1154_3) = all_1154_1
% 221.85/31.02 |
% 221.85/31.02 | REDUCE: (5), (9) imply:
% 221.85/31.02 | (13) c_member(all_625_1, all_1154_1, v_L) = all_1154_0
% 221.85/31.02 |
% 221.85/31.02 | REDUCE: (5), (8) imply:
% 221.85/31.02 | (14) c_member(all_625_1, all_1154_2, v_L) = 0
% 221.85/31.02 |
% 221.85/31.02 | GROUND_INST: instantiating (2) with all_1154_2, all_1154_1, all_1154_3, v_y,
% 221.85/31.02 | tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.02 | simplifying with (10), (12) gives:
% 221.85/31.02 | (15) all_1154_1 = all_1154_2
% 221.85/31.02 |
% 221.85/31.02 | REDUCE: (13), (15) imply:
% 221.85/31.02 | (16) c_member(all_625_1, all_1154_2, v_L) = all_1154_0
% 221.85/31.02 |
% 221.85/31.02 | GROUND_INST: instantiating (4) with 0, all_1154_0, v_L, all_1154_2, all_625_1,
% 221.85/31.02 | simplifying with (14), (16) gives:
% 221.85/31.02 | (17) all_1154_0 = 0
% 221.85/31.02 |
% 221.85/31.02 | REDUCE: (7), (17) imply:
% 221.85/31.02 | (18) $false
% 221.85/31.02 |
% 221.85/31.02 | CLOSE: (18) is inconsistent.
% 221.85/31.02 |
% 221.85/31.02 End of proof
% 221.85/31.02
% 221.85/31.02 Sub-proof #9 shows that the following formulas are inconsistent:
% 221.85/31.02 ----------------------------------------------------------------
% 221.85/31.02 (1) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_674_0, all_870_7, v_L) = v0)
% 221.85/31.02 (2) all_674_0 = all_625_1
% 221.85/31.02 (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 221.85/31.02 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (c_member(v4, v3, v2) = v1) | ~
% 221.85/31.02 (c_member(v4, v3, v2) = v0))
% 221.85/31.02 (4) c_member(all_625_1, all_870_7, v_L) = 0
% 221.85/31.02
% 221.85/31.02 Begin of proof
% 221.85/31.02 |
% 221.85/31.02 | DELTA: instantiating (1) with fresh symbol all_1151_0 gives:
% 221.85/31.02 | (5) ~ (all_1151_0 = 0) & c_member(all_674_0, all_870_7, v_L) = all_1151_0
% 221.85/31.02 |
% 221.85/31.02 | ALPHA: (5) implies:
% 221.85/31.02 | (6) ~ (all_1151_0 = 0)
% 221.85/31.02 | (7) c_member(all_674_0, all_870_7, v_L) = all_1151_0
% 221.85/31.02 |
% 221.85/31.02 | REDUCE: (2), (7) imply:
% 221.85/31.02 | (8) c_member(all_625_1, all_870_7, v_L) = all_1151_0
% 221.85/31.02 |
% 221.85/31.02 | GROUND_INST: instantiating (3) with 0, all_1151_0, v_L, all_870_7, all_625_1,
% 221.85/31.02 | simplifying with (4), (8) gives:
% 221.85/31.02 | (9) all_1151_0 = 0
% 221.85/31.02 |
% 221.85/31.02 | REDUCE: (6), (9) imply:
% 221.85/31.02 | (10) $false
% 221.85/31.02 |
% 221.85/31.02 | CLOSE: (10) is inconsistent.
% 221.85/31.02 |
% 221.85/31.02 End of proof
% 221.85/31.02
% 221.85/31.02 Sub-proof #10 shows that the following formulas are inconsistent:
% 221.85/31.02 ----------------------------------------------------------------
% 221.85/31.02 (1) ? [v0: $i] : ? [v1: any] : ? [v2: any] :
% 221.85/31.02 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.02 tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v_y) = v0 &
% 221.85/31.02 c_member(all_674_0, v0, v_L) = v1 & c_member(all_674_0, all_870_3, v_L)
% 221.85/31.02 = v2 & $i(v0) & ( ~ (v1 = 0) | v2 = 0))
% 221.85/31.02 (2) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.02 tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v_y) = all_870_5
% 221.85/31.02 (3) all_674_0 = all_625_1
% 221.85/31.02 (4) ~ (all_870_2 = 0)
% 221.85/31.02 (5) c_member(all_625_1, all_870_3, v_L) = all_870_2
% 221.85/31.03 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 221.85/31.03 [v5: $i] : (v1 = v0 | ~ (c_Product__Type_OPair(v5, v4, v3, v2) = v1) |
% 221.85/31.03 ~ (c_Product__Type_OPair(v5, v4, v3, v2) = v0))
% 221.85/31.03 (7) c_member(all_625_1, all_870_5, v_L) = 0
% 221.85/31.03 (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 221.85/31.03 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (c_member(v4, v3, v2) = v1) | ~
% 221.85/31.03 (c_member(v4, v3, v2) = v0))
% 221.85/31.03
% 221.85/31.03 Begin of proof
% 221.85/31.03 |
% 221.85/31.03 | DELTA: instantiating (1) with fresh symbols all_1211_0, all_1211_1, all_1211_2
% 221.85/31.03 | gives:
% 221.85/31.03 | (9) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.03 | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v_y) = all_1211_2 &
% 221.85/31.03 | c_member(all_674_0, all_1211_2, v_L) = all_1211_1 & c_member(all_674_0,
% 221.85/31.03 | all_870_3, v_L) = all_1211_0 & $i(all_1211_2) & ( ~ (all_1211_1 = 0)
% 221.85/31.03 | | all_1211_0 = 0)
% 221.85/31.03 |
% 221.85/31.03 | ALPHA: (9) implies:
% 221.85/31.03 | (10) c_member(all_674_0, all_870_3, v_L) = all_1211_0
% 221.85/31.03 | (11) c_member(all_674_0, all_1211_2, v_L) = all_1211_1
% 221.85/31.03 | (12) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.03 | tc_Arrow__Order__Mirabelle_Oalt, all_870_8, v_y) = all_1211_2
% 221.85/31.03 | (13) ~ (all_1211_1 = 0) | all_1211_0 = 0
% 221.85/31.03 |
% 221.85/31.03 | REDUCE: (3), (11) imply:
% 221.85/31.03 | (14) c_member(all_625_1, all_1211_2, v_L) = all_1211_1
% 221.85/31.03 |
% 221.85/31.03 | REDUCE: (3), (10) imply:
% 221.85/31.03 | (15) c_member(all_625_1, all_870_3, v_L) = all_1211_0
% 221.85/31.03 |
% 221.85/31.03 | GROUND_INST: instantiating (8) with all_870_2, all_1211_0, v_L, all_870_3,
% 221.85/31.03 | all_625_1, simplifying with (5), (15) gives:
% 221.85/31.03 | (16) all_1211_0 = all_870_2
% 221.85/31.03 |
% 221.85/31.03 | GROUND_INST: instantiating (6) with all_870_5, all_1211_2, v_y, all_870_8,
% 221.85/31.03 | tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.03 | simplifying with (2), (12) gives:
% 221.85/31.03 | (17) all_1211_2 = all_870_5
% 221.85/31.03 |
% 221.85/31.03 | REDUCE: (14), (17) imply:
% 221.85/31.03 | (18) c_member(all_625_1, all_870_5, v_L) = all_1211_1
% 221.85/31.03 |
% 221.85/31.03 | BETA: splitting (13) gives:
% 221.85/31.03 |
% 221.85/31.03 | Case 1:
% 221.85/31.03 | |
% 221.85/31.03 | | (19) ~ (all_1211_1 = 0)
% 221.85/31.03 | |
% 221.85/31.03 | | GROUND_INST: instantiating (8) with 0, all_1211_1, v_L, all_870_5,
% 221.85/31.03 | | all_625_1, simplifying with (7), (18) gives:
% 221.85/31.03 | | (20) all_1211_1 = 0
% 221.85/31.03 | |
% 221.85/31.03 | | REDUCE: (19), (20) imply:
% 221.85/31.03 | | (21) $false
% 221.85/31.03 | |
% 221.85/31.03 | | CLOSE: (21) is inconsistent.
% 221.85/31.03 | |
% 221.85/31.03 | Case 2:
% 221.85/31.03 | |
% 221.85/31.03 | | (22) all_1211_0 = 0
% 221.85/31.03 | |
% 221.85/31.03 | | COMBINE_EQS: (16), (22) imply:
% 221.85/31.03 | | (23) all_870_2 = 0
% 221.85/31.03 | |
% 221.85/31.03 | | REDUCE: (4), (23) imply:
% 221.85/31.03 | | (24) $false
% 221.85/31.03 | |
% 221.85/31.03 | | CLOSE: (24) is inconsistent.
% 221.85/31.03 | |
% 221.85/31.03 | End of split
% 221.85/31.03 |
% 221.85/31.03 End of proof
% 221.85/31.03
% 221.85/31.03 Sub-proof #11 shows that the following formulas are inconsistent:
% 221.85/31.03 ----------------------------------------------------------------
% 221.85/31.03 (1) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_674_0, all_870_5, v_L) = v0)
% 221.85/31.03 (2) all_674_0 = all_625_1
% 221.85/31.03 (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 221.85/31.03 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (c_member(v4, v3, v2) = v1) | ~
% 221.85/31.03 (c_member(v4, v3, v2) = v0))
% 221.85/31.03 (4) c_member(all_625_1, all_870_5, v_L) = 0
% 221.85/31.03
% 221.85/31.03 Begin of proof
% 221.85/31.03 |
% 221.85/31.03 | DELTA: instantiating (1) with fresh symbol all_1218_0 gives:
% 221.85/31.03 | (5) ~ (all_1218_0 = 0) & c_member(all_674_0, all_870_5, v_L) = all_1218_0
% 221.85/31.03 |
% 221.85/31.03 | ALPHA: (5) implies:
% 221.85/31.03 | (6) ~ (all_1218_0 = 0)
% 221.85/31.03 | (7) c_member(all_674_0, all_870_5, v_L) = all_1218_0
% 221.85/31.03 |
% 221.85/31.03 | REDUCE: (2), (7) imply:
% 221.85/31.03 | (8) c_member(all_625_1, all_870_5, v_L) = all_1218_0
% 221.85/31.03 |
% 221.85/31.03 | GROUND_INST: instantiating (3) with 0, all_1218_0, v_L, all_870_5, all_625_1,
% 221.85/31.03 | simplifying with (4), (8) gives:
% 221.85/31.03 | (9) all_1218_0 = 0
% 221.85/31.03 |
% 221.85/31.03 | REDUCE: (6), (9) imply:
% 221.85/31.03 | (10) $false
% 221.85/31.03 |
% 221.85/31.03 | CLOSE: (10) is inconsistent.
% 221.85/31.03 |
% 221.85/31.03 End of proof
% 221.85/31.03
% 221.85/31.03 Sub-proof #12 shows that the following formulas are inconsistent:
% 221.85/31.03 ----------------------------------------------------------------
% 221.85/31.03 (1) ? [v0: int] : ( ~ (v0 = 0) & c_member(all_674_0, all_870_1, v_L) = v0)
% 221.85/31.03 (2) all_674_0 = all_625_1
% 221.85/31.03 (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 221.85/31.03 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (c_member(v4, v3, v2) = v1) | ~
% 221.85/31.03 (c_member(v4, v3, v2) = v0))
% 221.85/31.03 (4) c_member(all_625_1, all_870_1, v_L) = 0
% 221.85/31.03
% 221.85/31.03 Begin of proof
% 221.85/31.03 |
% 221.85/31.03 | DELTA: instantiating (1) with fresh symbol all_1203_0 gives:
% 221.85/31.03 | (5) ~ (all_1203_0 = 0) & c_member(all_674_0, all_870_1, v_L) = all_1203_0
% 221.85/31.03 |
% 221.85/31.03 | ALPHA: (5) implies:
% 221.85/31.03 | (6) ~ (all_1203_0 = 0)
% 221.85/31.03 | (7) c_member(all_674_0, all_870_1, v_L) = all_1203_0
% 221.85/31.03 |
% 221.85/31.03 | REDUCE: (2), (7) imply:
% 221.85/31.03 | (8) c_member(all_625_1, all_870_1, v_L) = all_1203_0
% 221.85/31.03 |
% 221.85/31.03 | GROUND_INST: instantiating (3) with 0, all_1203_0, v_L, all_870_1, all_625_1,
% 221.85/31.03 | simplifying with (4), (8) gives:
% 221.85/31.03 | (9) all_1203_0 = 0
% 221.85/31.03 |
% 221.85/31.03 | REDUCE: (6), (9) imply:
% 221.85/31.03 | (10) $false
% 221.85/31.03 |
% 221.85/31.03 | CLOSE: (10) is inconsistent.
% 221.85/31.03 |
% 221.85/31.03 End of proof
% 221.85/31.03
% 221.85/31.03 Sub-proof #13 shows that the following formulas are inconsistent:
% 221.85/31.03 ----------------------------------------------------------------
% 221.85/31.03 (1) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.03 tc_Arrow__Order__Mirabelle_Oalt, all_870_13, v_y) = all_870_9
% 221.85/31.03 (2) all_870_13 = v_y | ? [v0: any] : ? [v1: $i] : ? [v2: any] :
% 221.85/31.03 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.03 tc_Arrow__Order__Mirabelle_Oalt, all_870_13, v_y) = v1 &
% 221.85/31.03 c_member(all_674_0, v1, v_L) = v2 & c_member(all_674_0, all_870_1, v_L)
% 221.85/31.03 = v0 & $i(v1) & (v2 = 0 | v0 = 0))
% 221.85/31.03 (3) all_870_12 = v_x | all_870_13 = v_x
% 221.85/31.03 (4) c_member(all_625_1, all_870_1, v_L) = all_870_0
% 221.85/31.03 (5) c_member(all_625_1, all_870_9, v_L) = all_870_8
% 221.85/31.03 (6) ~ (all_870_8 = 0) | ~ (all_870_12 = v_x) | all_870_13 = v_x
% 221.85/31.03 (7) all_870_13 = v_y | ? [v0: any] : ? [v1: $i] : ? [v2: any] :
% 221.85/31.03 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.03 tc_Arrow__Order__Mirabelle_Oalt, v_y, all_870_13) = v1 &
% 221.85/31.03 c_member(all_674_0, v1, v_L) = v2 & c_member(all_674_0, all_870_9, v_L)
% 221.85/31.03 = v0 & $i(v1) & (v2 = 0 | v0 = 0))
% 221.85/31.03 (8) all_674_0 = all_625_1
% 221.85/31.03 (9) ~ (all_870_13 = v_x)
% 221.85/31.03 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 221.85/31.03 [v5: $i] : (v1 = v0 | ~ (c_Product__Type_OPair(v5, v4, v3, v2) = v1) |
% 221.85/31.03 ~ (c_Product__Type_OPair(v5, v4, v3, v2) = v0))
% 221.85/31.03 (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 221.85/31.03 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (c_member(v4, v3, v2) = v1) |
% 221.85/31.03 ~ (c_member(v4, v3, v2) = v0))
% 221.85/31.03 (12) ~ (all_870_0 = 0) | ~ (all_870_12 = v_x) | all_870_13 = v_x
% 221.85/31.03 (13) ~ (all_870_13 = v_y)
% 221.85/31.03
% 221.85/31.03 Begin of proof
% 221.85/31.03 |
% 221.85/31.03 | BETA: splitting (3) gives:
% 221.85/31.03 |
% 221.85/31.03 | Case 1:
% 221.85/31.03 | |
% 221.85/31.03 | | (14) all_870_12 = v_x
% 221.85/31.03 | |
% 221.85/31.03 | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 221.85/31.03 | | (14) are inconsistent by sub-proof #14.
% 221.85/31.03 | |
% 221.85/31.03 | Case 2:
% 221.85/31.03 | |
% 221.85/31.03 | | (15) all_870_13 = v_x
% 221.85/31.03 | |
% 221.85/31.03 | | REDUCE: (9), (15) imply:
% 221.85/31.03 | | (16) $false
% 221.85/31.03 | |
% 221.85/31.03 | | CLOSE: (16) is inconsistent.
% 221.85/31.03 | |
% 221.85/31.03 | End of split
% 221.85/31.03 |
% 221.85/31.03 End of proof
% 221.85/31.03
% 221.85/31.03 Sub-proof #14 shows that the following formulas are inconsistent:
% 221.85/31.03 ----------------------------------------------------------------
% 221.85/31.03 (1) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.03 tc_Arrow__Order__Mirabelle_Oalt, all_870_13, v_y) = all_870_9
% 221.85/31.03 (2) all_870_13 = v_y | ? [v0: any] : ? [v1: $i] : ? [v2: any] :
% 221.85/31.03 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.03 tc_Arrow__Order__Mirabelle_Oalt, all_870_13, v_y) = v1 &
% 221.85/31.03 c_member(all_674_0, v1, v_L) = v2 & c_member(all_674_0, all_870_1, v_L)
% 221.85/31.03 = v0 & $i(v1) & (v2 = 0 | v0 = 0))
% 221.85/31.03 (3) all_870_12 = v_x
% 221.85/31.03 (4) c_member(all_625_1, all_870_1, v_L) = all_870_0
% 221.85/31.03 (5) c_member(all_625_1, all_870_9, v_L) = all_870_8
% 221.85/31.03 (6) ~ (all_870_8 = 0) | ~ (all_870_12 = v_x) | all_870_13 = v_x
% 221.85/31.03 (7) all_870_13 = v_y | ? [v0: any] : ? [v1: $i] : ? [v2: any] :
% 221.85/31.03 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.03 tc_Arrow__Order__Mirabelle_Oalt, v_y, all_870_13) = v1 &
% 221.85/31.03 c_member(all_674_0, v1, v_L) = v2 & c_member(all_674_0, all_870_9, v_L)
% 221.85/31.03 = v0 & $i(v1) & (v2 = 0 | v0 = 0))
% 221.85/31.03 (8) all_674_0 = all_625_1
% 221.85/31.03 (9) ~ (all_870_13 = v_x)
% 221.85/31.03 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 221.85/31.03 [v5: $i] : (v1 = v0 | ~ (c_Product__Type_OPair(v5, v4, v3, v2) = v1) |
% 221.85/31.03 ~ (c_Product__Type_OPair(v5, v4, v3, v2) = v0))
% 221.85/31.03 (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 221.85/31.03 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (c_member(v4, v3, v2) = v1) |
% 221.85/31.03 ~ (c_member(v4, v3, v2) = v0))
% 221.85/31.03 (12) ~ (all_870_0 = 0) | ~ (all_870_12 = v_x) | all_870_13 = v_x
% 221.85/31.03 (13) ~ (all_870_13 = v_y)
% 221.85/31.03
% 221.85/31.03 Begin of proof
% 221.85/31.03 |
% 221.85/31.03 | BETA: splitting (12) gives:
% 221.85/31.03 |
% 221.85/31.03 | Case 1:
% 221.85/31.03 | |
% 221.85/31.03 | | (14) ~ (all_870_0 = 0)
% 221.85/31.03 | |
% 221.85/31.03 | | BETA: splitting (7) gives:
% 221.85/31.03 | |
% 221.85/31.03 | | Case 1:
% 221.85/31.03 | | |
% 221.85/31.03 | | | (15) all_870_13 = v_y
% 221.85/31.03 | | |
% 221.85/31.03 | | | REDUCE: (13), (15) imply:
% 221.85/31.03 | | | (16) $false
% 221.85/31.03 | | |
% 221.85/31.03 | | | CLOSE: (16) is inconsistent.
% 221.85/31.03 | | |
% 221.85/31.03 | | Case 2:
% 221.85/31.03 | | |
% 221.85/31.03 | | | (17) ? [v0: any] : ? [v1: $i] : ? [v2: any] :
% 221.85/31.03 | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.03 | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, all_870_13) = v1 &
% 221.85/31.03 | | | c_member(all_674_0, v1, v_L) = v2 & c_member(all_674_0,
% 221.85/31.03 | | | all_870_9, v_L) = v0 & $i(v1) & (v2 = 0 | v0 = 0))
% 221.85/31.03 | | |
% 221.85/31.03 | | | DELTA: instantiating (17) with fresh symbols all_1186_0, all_1186_1,
% 221.85/31.03 | | | all_1186_2 gives:
% 221.85/31.04 | | | (18) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.04 | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, all_870_13) = all_1186_1 &
% 221.85/31.04 | | | c_member(all_674_0, all_1186_1, v_L) = all_1186_0 &
% 221.85/31.04 | | | c_member(all_674_0, all_870_9, v_L) = all_1186_2 & $i(all_1186_1)
% 221.85/31.04 | | | & (all_1186_0 = 0 | all_1186_2 = 0)
% 221.85/31.04 | | |
% 221.85/31.04 | | | ALPHA: (18) implies:
% 221.85/31.04 | | | (19) c_member(all_674_0, all_870_9, v_L) = all_1186_2
% 221.85/31.04 | | |
% 221.85/31.04 | | | REDUCE: (8), (19) imply:
% 221.85/31.04 | | | (20) c_member(all_625_1, all_870_9, v_L) = all_1186_2
% 221.85/31.04 | | |
% 221.85/31.04 | | | BETA: splitting (2) gives:
% 221.85/31.04 | | |
% 221.85/31.04 | | | Case 1:
% 221.85/31.04 | | | |
% 221.85/31.04 | | | | (21) all_870_13 = v_y
% 221.85/31.04 | | | |
% 221.85/31.04 | | | | REDUCE: (13), (21) imply:
% 221.85/31.04 | | | | (22) $false
% 221.85/31.04 | | | |
% 221.85/31.04 | | | | CLOSE: (22) is inconsistent.
% 221.85/31.04 | | | |
% 221.85/31.04 | | | Case 2:
% 221.85/31.04 | | | |
% 221.85/31.04 | | | | (23) ? [v0: any] : ? [v1: $i] : ? [v2: any] :
% 221.85/31.04 | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.04 | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_13, v_y) = v1 &
% 221.85/31.04 | | | | c_member(all_674_0, v1, v_L) = v2 & c_member(all_674_0,
% 221.85/31.04 | | | | all_870_1, v_L) = v0 & $i(v1) & (v2 = 0 | v0 = 0))
% 221.85/31.04 | | | |
% 221.85/31.04 | | | | DELTA: instantiating (23) with fresh symbols all_1192_0, all_1192_1,
% 221.85/31.04 | | | | all_1192_2 gives:
% 221.85/31.04 | | | | (24) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.04 | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_13, v_y) = all_1192_1
% 221.85/31.04 | | | | & c_member(all_674_0, all_1192_1, v_L) = all_1192_0 &
% 221.85/31.04 | | | | c_member(all_674_0, all_870_1, v_L) = all_1192_2 &
% 221.85/31.04 | | | | $i(all_1192_1) & (all_1192_0 = 0 | all_1192_2 = 0)
% 221.85/31.04 | | | |
% 221.85/31.04 | | | | ALPHA: (24) implies:
% 221.85/31.04 | | | | (25) c_member(all_674_0, all_870_1, v_L) = all_1192_2
% 221.85/31.04 | | | | (26) c_member(all_674_0, all_1192_1, v_L) = all_1192_0
% 221.85/31.04 | | | | (27) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.04 | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_13, v_y) = all_1192_1
% 221.85/31.04 | | | | (28) all_1192_0 = 0 | all_1192_2 = 0
% 221.85/31.04 | | | |
% 221.85/31.04 | | | | REDUCE: (8), (26) imply:
% 221.85/31.04 | | | | (29) c_member(all_625_1, all_1192_1, v_L) = all_1192_0
% 221.85/31.04 | | | |
% 221.85/31.04 | | | | REDUCE: (8), (25) imply:
% 221.85/31.04 | | | | (30) c_member(all_625_1, all_870_1, v_L) = all_1192_2
% 221.85/31.04 | | | |
% 221.85/31.04 | | | | BETA: splitting (6) gives:
% 221.85/31.04 | | | |
% 221.85/31.04 | | | | Case 1:
% 221.85/31.04 | | | | |
% 221.85/31.04 | | | | | (31) ~ (all_870_8 = 0)
% 221.85/31.04 | | | | |
% 221.85/31.04 | | | | | GROUND_INST: instantiating (11) with all_870_8, all_1186_2, v_L,
% 221.85/31.04 | | | | | all_870_9, all_625_1, simplifying with (5), (20) gives:
% 221.85/31.04 | | | | | (32) all_1186_2 = all_870_8
% 221.85/31.04 | | | | |
% 221.85/31.04 | | | | | GROUND_INST: instantiating (11) with all_870_0, all_1192_2, v_L,
% 221.85/31.04 | | | | | all_870_1, all_625_1, simplifying with (4), (30) gives:
% 221.85/31.04 | | | | | (33) all_1192_2 = all_870_0
% 221.85/31.04 | | | | |
% 221.85/31.04 | | | | | GROUND_INST: instantiating (10) with all_870_9, all_1192_1, v_y,
% 221.85/31.04 | | | | | all_870_13, tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.04 | | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with (1),
% 221.85/31.04 | | | | | (27) gives:
% 221.85/31.04 | | | | | (34) all_1192_1 = all_870_9
% 221.85/31.04 | | | | |
% 221.85/31.04 | | | | | REDUCE: (29), (34) imply:
% 221.85/31.04 | | | | | (35) c_member(all_625_1, all_870_9, v_L) = all_1192_0
% 221.85/31.04 | | | | |
% 221.85/31.04 | | | | | BETA: splitting (28) gives:
% 221.85/31.04 | | | | |
% 221.85/31.04 | | | | | Case 1:
% 221.85/31.04 | | | | | |
% 221.85/31.04 | | | | | | (36) all_1192_0 = 0
% 221.85/31.04 | | | | | |
% 221.85/31.04 | | | | | | REDUCE: (35), (36) imply:
% 221.85/31.04 | | | | | | (37) c_member(all_625_1, all_870_9, v_L) = 0
% 221.85/31.04 | | | | | |
% 221.85/31.04 | | | | | | GROUND_INST: instantiating (11) with all_870_8, 0, v_L, all_870_9,
% 221.85/31.04 | | | | | | all_625_1, simplifying with (5), (37) gives:
% 221.85/31.04 | | | | | | (38) all_870_8 = 0
% 221.85/31.04 | | | | | |
% 221.85/31.04 | | | | | | REDUCE: (31), (38) imply:
% 221.85/31.04 | | | | | | (39) $false
% 221.85/31.04 | | | | | |
% 221.85/31.04 | | | | | | CLOSE: (39) is inconsistent.
% 221.85/31.04 | | | | | |
% 221.85/31.04 | | | | | Case 2:
% 221.85/31.04 | | | | | |
% 221.85/31.04 | | | | | | (40) all_1192_2 = 0
% 221.85/31.04 | | | | | |
% 221.85/31.04 | | | | | | COMBINE_EQS: (33), (40) imply:
% 221.85/31.04 | | | | | | (41) all_870_0 = 0
% 221.85/31.04 | | | | | |
% 221.85/31.04 | | | | | | REDUCE: (14), (41) imply:
% 221.85/31.04 | | | | | | (42) $false
% 221.85/31.04 | | | | | |
% 221.85/31.04 | | | | | | CLOSE: (42) is inconsistent.
% 221.85/31.04 | | | | | |
% 221.85/31.04 | | | | | End of split
% 221.85/31.04 | | | | |
% 221.85/31.04 | | | | Case 2:
% 221.85/31.04 | | | | |
% 221.85/31.04 | | | | | (43) ~ (all_870_12 = v_x) | all_870_13 = v_x
% 221.85/31.04 | | | | |
% 221.85/31.04 | | | | | REF_CLOSE: (3), (9), (43) are inconsistent by sub-proof #15.
% 221.85/31.04 | | | | |
% 221.85/31.04 | | | | End of split
% 221.85/31.04 | | | |
% 221.85/31.04 | | | End of split
% 221.85/31.04 | | |
% 221.85/31.04 | | End of split
% 221.85/31.04 | |
% 221.85/31.04 | Case 2:
% 221.85/31.04 | |
% 221.85/31.04 | | (44) ~ (all_870_12 = v_x) | all_870_13 = v_x
% 221.85/31.04 | |
% 221.85/31.04 | | REF_CLOSE: (3), (9), (44) are inconsistent by sub-proof #15.
% 221.85/31.04 | |
% 221.85/31.04 | End of split
% 221.85/31.04 |
% 221.85/31.04 End of proof
% 221.85/31.04
% 221.85/31.04 Sub-proof #15 shows that the following formulas are inconsistent:
% 221.85/31.04 ----------------------------------------------------------------
% 221.85/31.04 (1) ~ (all_870_12 = v_x) | all_870_13 = v_x
% 221.85/31.04 (2) all_870_12 = v_x
% 221.85/31.04 (3) ~ (all_870_13 = v_x)
% 221.85/31.04
% 221.85/31.04 Begin of proof
% 221.85/31.04 |
% 221.85/31.04 | BETA: splitting (1) gives:
% 221.85/31.04 |
% 221.85/31.04 | Case 1:
% 221.85/31.04 | |
% 221.85/31.04 | | (4) ~ (all_870_12 = v_x)
% 221.85/31.04 | |
% 221.85/31.04 | | REDUCE: (2), (4) imply:
% 221.85/31.04 | | (5) $false
% 221.85/31.04 | |
% 221.85/31.04 | | CLOSE: (5) is inconsistent.
% 221.85/31.04 | |
% 221.85/31.04 | Case 2:
% 221.85/31.04 | |
% 221.85/31.04 | | (6) all_870_13 = v_x
% 221.85/31.04 | |
% 221.85/31.04 | | REDUCE: (3), (6) imply:
% 221.85/31.04 | | (7) $false
% 221.85/31.04 | |
% 221.85/31.04 | | CLOSE: (7) is inconsistent.
% 221.85/31.04 | |
% 221.85/31.04 | End of split
% 221.85/31.04 |
% 221.85/31.04 End of proof
% 221.85/31.04
% 221.85/31.04 Sub-proof #16 shows that the following formulas are inconsistent:
% 221.85/31.04 ----------------------------------------------------------------
% 221.85/31.04 (1) ~ (all_870_12 = all_870_13)
% 221.85/31.04 (2) all_1220_1 = all_870_10
% 221.85/31.04 (3) c_member(all_625_1, all_870_7, v_L) = all_870_6
% 221.85/31.04 (4) ~ (all_1220_1 = 0) | all_1220_0 = 0
% 221.85/31.04 (5) all_1202_0 = all_870_10
% 221.85/31.04 (6) all_870_12 = v_x | all_870_13 = v_x
% 221.85/31.04 (7) ~ (all_870_2 = 0) | ~ (all_870_13 = v_x) | all_870_12 = v_x
% 221.85/31.04 (8) all_870_12 = v_y | ? [v0: any] : ? [v1: $i] : ? [v2: any] :
% 221.85/31.04 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.04 tc_Arrow__Order__Mirabelle_Oalt, all_870_12, v_y) = v1 &
% 221.85/31.04 c_member(all_674_0, v1, v_L) = v2 & c_member(all_674_0, all_870_7, v_L)
% 221.85/31.04 = v0 & $i(v1) & (v2 = 0 | v0 = 0))
% 221.85/31.04 (9) ~ (all_1202_1 = 0) | all_1202_0 = 0
% 221.85/31.04 (10) ~ (all_870_12 = v_x)
% 221.85/31.04 (11) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.04 tc_Arrow__Order__Mirabelle_Oalt, v_y, all_870_12) = all_870_7
% 221.85/31.04 (12) all_870_12 = v_y | ? [v0: any] : ? [v1: $i] : ? [v2: any] :
% 221.85/31.04 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.04 tc_Arrow__Order__Mirabelle_Oalt, v_y, all_870_12) = v1 &
% 221.85/31.04 c_member(all_674_0, v1, v_L) = v2 & c_member(all_674_0, all_870_3,
% 221.85/31.04 v_L) = v0 & $i(v1) & (v2 = 0 | v0 = 0))
% 221.85/31.04 (13) all_1220_0 = all_870_6
% 221.85/31.04 (14) ~ (all_870_12 = v_y)
% 221.85/31.04 (15) all_674_0 = all_625_1
% 221.85/31.04 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 221.85/31.04 [v5: $i] : (v1 = v0 | ~ (c_Product__Type_OPair(v5, v4, v3, v2) = v1) |
% 221.85/31.04 ~ (c_Product__Type_OPair(v5, v4, v3, v2) = v0))
% 221.85/31.04 (17) c_member(all_625_1, all_870_3, v_L) = all_870_2
% 221.85/31.04 (18) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 221.85/31.04 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (c_member(v4, v3, v2) = v1) |
% 221.85/31.04 ~ (c_member(v4, v3, v2) = v0))
% 221.85/31.04 (19) ~ (all_870_6 = 0) | ~ (all_870_13 = v_x) | all_870_12 = v_x
% 221.85/31.04
% 221.85/31.04 Begin of proof
% 221.85/31.04 |
% 221.85/31.04 | BETA: splitting (6) gives:
% 221.85/31.04 |
% 221.85/31.04 | Case 1:
% 221.85/31.04 | |
% 221.85/31.04 | | (20) all_870_12 = v_x
% 221.85/31.04 | |
% 221.85/31.04 | | REDUCE: (10), (20) imply:
% 221.85/31.04 | | (21) $false
% 221.85/31.04 | |
% 221.85/31.04 | | CLOSE: (21) is inconsistent.
% 221.85/31.04 | |
% 221.85/31.04 | Case 2:
% 221.85/31.04 | |
% 221.85/31.04 | | (22) all_870_13 = v_x
% 221.85/31.04 | |
% 221.85/31.04 | | BETA: splitting (19) gives:
% 221.85/31.04 | |
% 221.85/31.04 | | Case 1:
% 221.85/31.04 | | |
% 221.85/31.04 | | | (23) ~ (all_870_6 = 0)
% 221.85/31.04 | | |
% 221.85/31.04 | | | BETA: splitting (7) gives:
% 221.85/31.04 | | |
% 221.85/31.04 | | | Case 1:
% 221.85/31.04 | | | |
% 221.85/31.04 | | | | (24) ~ (all_870_2 = 0)
% 221.85/31.04 | | | |
% 221.85/31.04 | | | | BETA: splitting (4) gives:
% 221.85/31.04 | | | |
% 221.85/31.04 | | | | Case 1:
% 221.85/31.04 | | | | |
% 221.85/31.04 | | | | | (25) ~ (all_1220_1 = 0)
% 221.85/31.04 | | | | |
% 221.85/31.04 | | | | | REDUCE: (2), (25) imply:
% 221.85/31.04 | | | | | (26) ~ (all_870_10 = 0)
% 221.85/31.04 | | | | |
% 221.85/31.04 | | | | | BETA: splitting (8) gives:
% 221.85/31.04 | | | | |
% 221.85/31.04 | | | | | Case 1:
% 221.85/31.04 | | | | | |
% 221.85/31.04 | | | | | | (27) all_870_12 = v_y
% 221.85/31.04 | | | | | |
% 221.85/31.04 | | | | | | REDUCE: (14), (27) imply:
% 221.85/31.04 | | | | | | (28) $false
% 221.85/31.04 | | | | | |
% 221.85/31.04 | | | | | | CLOSE: (28) is inconsistent.
% 221.85/31.04 | | | | | |
% 221.85/31.04 | | | | | Case 2:
% 221.85/31.04 | | | | | |
% 221.85/31.04 | | | | | | (29) ? [v0: any] : ? [v1: $i] : ? [v2: any] :
% 221.85/31.04 | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.04 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_12, v_y) = v1 &
% 221.85/31.04 | | | | | | c_member(all_674_0, v1, v_L) = v2 & c_member(all_674_0,
% 221.85/31.04 | | | | | | all_870_7, v_L) = v0 & $i(v1) & (v2 = 0 | v0 = 0))
% 221.85/31.04 | | | | | |
% 221.85/31.04 | | | | | | DELTA: instantiating (29) with fresh symbols all_1285_0, all_1285_1,
% 221.85/31.04 | | | | | | all_1285_2 gives:
% 221.85/31.04 | | | | | | (30) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.04 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_12, v_y) =
% 221.85/31.04 | | | | | | all_1285_1 & c_member(all_674_0, all_1285_1, v_L) =
% 221.85/31.04 | | | | | | all_1285_0 & c_member(all_674_0, all_870_7, v_L) =
% 221.85/31.04 | | | | | | all_1285_2 & $i(all_1285_1) & (all_1285_0 = 0 | all_1285_2 =
% 221.85/31.04 | | | | | | 0)
% 221.85/31.04 | | | | | |
% 221.85/31.04 | | | | | | ALPHA: (30) implies:
% 221.85/31.04 | | | | | | (31) c_member(all_674_0, all_870_7, v_L) = all_1285_2
% 221.85/31.04 | | | | | |
% 221.85/31.04 | | | | | | REDUCE: (15), (31) imply:
% 221.85/31.04 | | | | | | (32) c_member(all_625_1, all_870_7, v_L) = all_1285_2
% 221.85/31.04 | | | | | |
% 221.85/31.04 | | | | | | BETA: splitting (12) gives:
% 221.85/31.04 | | | | | |
% 221.85/31.04 | | | | | | Case 1:
% 221.85/31.04 | | | | | | |
% 221.85/31.04 | | | | | | | (33) all_870_12 = v_y
% 221.85/31.04 | | | | | | |
% 221.85/31.04 | | | | | | | REDUCE: (14), (33) imply:
% 221.85/31.04 | | | | | | | (34) $false
% 221.85/31.04 | | | | | | |
% 221.85/31.04 | | | | | | | CLOSE: (34) is inconsistent.
% 221.85/31.04 | | | | | | |
% 221.85/31.04 | | | | | | Case 2:
% 221.85/31.04 | | | | | | |
% 221.85/31.04 | | | | | | | (35) ? [v0: any] : ? [v1: $i] : ? [v2: any] :
% 221.85/31.04 | | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.04 | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, all_870_12) = v1
% 221.85/31.04 | | | | | | | & c_member(all_674_0, v1, v_L) = v2 &
% 221.85/31.04 | | | | | | | c_member(all_674_0, all_870_3, v_L) = v0 & $i(v1) & (v2
% 221.85/31.04 | | | | | | | = 0 | v0 = 0))
% 221.85/31.04 | | | | | | |
% 221.85/31.04 | | | | | | | DELTA: instantiating (35) with fresh symbols all_1326_0,
% 221.85/31.04 | | | | | | | all_1326_1, all_1326_2 gives:
% 221.85/31.04 | | | | | | | (36) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.04 | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, all_870_12) =
% 221.85/31.04 | | | | | | | all_1326_1 & c_member(all_674_0, all_1326_1, v_L) =
% 221.85/31.04 | | | | | | | all_1326_0 & c_member(all_674_0, all_870_3, v_L) =
% 221.85/31.04 | | | | | | | all_1326_2 & $i(all_1326_1) & (all_1326_0 = 0 | all_1326_2
% 221.85/31.04 | | | | | | | = 0)
% 221.85/31.04 | | | | | | |
% 221.85/31.04 | | | | | | | ALPHA: (36) implies:
% 221.85/31.04 | | | | | | | (37) c_member(all_674_0, all_870_3, v_L) = all_1326_2
% 221.85/31.04 | | | | | | | (38) c_member(all_674_0, all_1326_1, v_L) = all_1326_0
% 221.85/31.04 | | | | | | | (39) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.04 | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, all_870_12) =
% 221.85/31.04 | | | | | | | all_1326_1
% 221.85/31.04 | | | | | | | (40) all_1326_0 = 0 | all_1326_2 = 0
% 221.85/31.04 | | | | | | |
% 221.85/31.04 | | | | | | | REDUCE: (15), (38) imply:
% 221.85/31.04 | | | | | | | (41) c_member(all_625_1, all_1326_1, v_L) = all_1326_0
% 221.85/31.04 | | | | | | |
% 221.85/31.04 | | | | | | | REDUCE: (15), (37) imply:
% 221.85/31.04 | | | | | | | (42) c_member(all_625_1, all_870_3, v_L) = all_1326_2
% 221.85/31.04 | | | | | | |
% 221.85/31.04 | | | | | | | BETA: splitting (9) gives:
% 221.85/31.04 | | | | | | |
% 221.85/31.04 | | | | | | | Case 1:
% 221.85/31.04 | | | | | | | |
% 221.85/31.04 | | | | | | | |
% 221.85/31.04 | | | | | | | | GROUND_INST: instantiating (18) with all_870_6, all_1285_2, v_L,
% 221.85/31.04 | | | | | | | | all_870_7, all_625_1, simplifying with (3), (32)
% 221.85/31.04 | | | | | | | | gives:
% 221.85/31.04 | | | | | | | | (43) all_1285_2 = all_870_6
% 221.85/31.04 | | | | | | | |
% 221.85/31.04 | | | | | | | | GROUND_INST: instantiating (18) with all_870_2, all_1326_2, v_L,
% 221.85/31.04 | | | | | | | | all_870_3, all_625_1, simplifying with (17), (42)
% 221.85/31.04 | | | | | | | | gives:
% 221.85/31.04 | | | | | | | | (44) all_1326_2 = all_870_2
% 221.85/31.04 | | | | | | | |
% 221.85/31.04 | | | | | | | | GROUND_INST: instantiating (16) with all_870_7, all_1326_1,
% 221.85/31.04 | | | | | | | | all_870_12, v_y, tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.04 | | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with
% 221.85/31.04 | | | | | | | | (11), (39) gives:
% 221.85/31.04 | | | | | | | | (45) all_1326_1 = all_870_7
% 221.85/31.04 | | | | | | | |
% 221.85/31.05 | | | | | | | | REDUCE: (41), (45) imply:
% 221.85/31.05 | | | | | | | | (46) c_member(all_625_1, all_870_7, v_L) = all_1326_0
% 221.85/31.05 | | | | | | | |
% 221.85/31.05 | | | | | | | | BETA: splitting (40) gives:
% 221.85/31.05 | | | | | | | |
% 221.85/31.05 | | | | | | | | Case 1:
% 221.85/31.05 | | | | | | | | |
% 221.85/31.05 | | | | | | | | | (47) all_1326_0 = 0
% 221.85/31.05 | | | | | | | | |
% 221.85/31.05 | | | | | | | | | REDUCE: (46), (47) imply:
% 221.85/31.05 | | | | | | | | | (48) c_member(all_625_1, all_870_7, v_L) = 0
% 221.85/31.05 | | | | | | | | |
% 221.85/31.05 | | | | | | | | | REF_CLOSE: (3), (18), (23), (48) are inconsistent by sub-proof
% 221.85/31.05 | | | | | | | | | #21.
% 221.85/31.05 | | | | | | | | |
% 221.85/31.05 | | | | | | | | Case 2:
% 221.85/31.05 | | | | | | | | |
% 221.85/31.05 | | | | | | | | | (49) all_1326_2 = 0
% 221.85/31.05 | | | | | | | | |
% 221.85/31.05 | | | | | | | | | COMBINE_EQS: (44), (49) imply:
% 221.85/31.05 | | | | | | | | | (50) all_870_2 = 0
% 221.85/31.05 | | | | | | | | |
% 221.85/31.05 | | | | | | | | | REDUCE: (24), (50) imply:
% 221.85/31.05 | | | | | | | | | (51) $false
% 221.85/31.05 | | | | | | | | |
% 221.85/31.05 | | | | | | | | | CLOSE: (51) is inconsistent.
% 221.85/31.05 | | | | | | | | |
% 221.85/31.05 | | | | | | | | End of split
% 221.85/31.05 | | | | | | | |
% 221.85/31.05 | | | | | | | Case 2:
% 221.85/31.05 | | | | | | | |
% 221.85/31.05 | | | | | | | | (52) all_1202_0 = 0
% 221.85/31.05 | | | | | | | |
% 221.85/31.05 | | | | | | | | COMBINE_EQS: (5), (52) imply:
% 221.85/31.05 | | | | | | | | (53) all_870_10 = 0
% 221.85/31.05 | | | | | | | |
% 221.85/31.05 | | | | | | | | SIMP: (53) implies:
% 221.85/31.05 | | | | | | | | (54) all_870_10 = 0
% 221.85/31.05 | | | | | | | |
% 221.85/31.05 | | | | | | | | REDUCE: (26), (54) imply:
% 221.85/31.05 | | | | | | | | (55) $false
% 221.85/31.05 | | | | | | | |
% 221.85/31.05 | | | | | | | | CLOSE: (55) is inconsistent.
% 221.85/31.05 | | | | | | | |
% 221.85/31.05 | | | | | | | End of split
% 221.85/31.05 | | | | | | |
% 221.85/31.05 | | | | | | End of split
% 221.85/31.05 | | | | | |
% 221.85/31.05 | | | | | End of split
% 221.85/31.05 | | | | |
% 221.85/31.05 | | | | Case 2:
% 221.85/31.05 | | | | |
% 221.85/31.05 | | | | | (56) all_1220_0 = 0
% 221.85/31.05 | | | | |
% 221.85/31.05 | | | | | COMBINE_EQS: (13), (56) imply:
% 221.85/31.05 | | | | | (57) all_870_6 = 0
% 221.85/31.05 | | | | |
% 221.85/31.05 | | | | | SIMP: (57) implies:
% 221.85/31.05 | | | | | (58) all_870_6 = 0
% 221.85/31.05 | | | | |
% 221.85/31.05 | | | | | REDUCE: (23), (58) imply:
% 221.85/31.05 | | | | | (59) $false
% 221.85/31.05 | | | | |
% 221.85/31.05 | | | | | CLOSE: (59) is inconsistent.
% 221.85/31.05 | | | | |
% 221.85/31.05 | | | | End of split
% 221.85/31.05 | | | |
% 221.85/31.05 | | | Case 2:
% 221.85/31.05 | | | |
% 221.85/31.05 | | | | (60) ~ (all_870_13 = v_x) | all_870_12 = v_x
% 221.85/31.05 | | | |
% 221.85/31.05 | | | | REF_CLOSE: (10), (22), (60) are inconsistent by sub-proof #20.
% 221.85/31.05 | | | |
% 221.85/31.05 | | | End of split
% 221.85/31.05 | | |
% 221.85/31.05 | | Case 2:
% 221.85/31.05 | | |
% 221.85/31.05 | | | (61) ~ (all_870_13 = v_x) | all_870_12 = v_x
% 221.85/31.05 | | |
% 221.85/31.05 | | | REF_CLOSE: (10), (22), (61) are inconsistent by sub-proof #20.
% 221.85/31.05 | | |
% 221.85/31.05 | | End of split
% 221.85/31.05 | |
% 221.85/31.05 | End of split
% 221.85/31.05 |
% 221.85/31.05 End of proof
% 221.85/31.05
% 221.85/31.05 Sub-proof #17 shows that the following formulas are inconsistent:
% 221.85/31.05 ----------------------------------------------------------------
% 221.85/31.05 (1) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.05 tc_Arrow__Order__Mirabelle_Oalt, all_870_13, v_y) = all_870_9
% 221.85/31.05 (2) ~ (all_870_12 = all_870_13)
% 221.85/31.05 (3) all_870_13 = v_y | ? [v0: any] : ? [v1: $i] : ? [v2: any] :
% 221.85/31.05 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 221.85/31.05 tc_Arrow__Order__Mirabelle_Oalt, all_870_13, v_y) = v1 &
% 221.85/31.05 c_member(all_674_0, v1, v_L) = v2 & c_member(all_674_0, all_870_1, v_L)
% 221.85/31.05 = v0 & $i(v1) & (v2 = 0 | v0 = 0))
% 221.85/31.05 (4) all_1186_1 = all_870_8
% 221.85/31.05 (5) all_870_12 = v_x | all_870_13 = v_x
% 221.85/31.05 (6) ~ (all_870_2 = 0) | ~ (all_870_13 = v_x) | all_870_12 = v_x
% 221.85/31.05 (7) ~ (all_870_12 = v_x)
% 221.85/31.05 (8) all_1186_0 = all_870_2
% 221.85/31.05 (9) ~ (all_1186_1 = 0) | all_1186_0 = 0
% 221.85/31.05 (10) c_member(all_625_1, all_870_1, v_L) = all_870_0
% 221.85/31.05 (11) c_member(all_625_1, all_870_9, v_L) = all_870_8
% 222.24/31.05 (12) all_870_13 = v_y | ? [v0: any] : ? [v1: $i] : ? [v2: any] :
% 222.24/31.05 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 222.24/31.05 tc_Arrow__Order__Mirabelle_Oalt, v_y, all_870_13) = v1 &
% 222.24/31.05 c_member(all_674_0, v1, v_L) = v2 & c_member(all_674_0, all_870_9,
% 222.24/31.05 v_L) = v0 & $i(v1) & (v2 = 0 | v0 = 0))
% 222.24/31.05 (13) ~ (v_x = v_y)
% 222.24/31.05 (14) ~ (all_870_0 = 0)
% 222.24/31.05 (15) all_674_0 = all_625_1
% 222.24/31.05 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 222.24/31.05 [v5: $i] : (v1 = v0 | ~ (c_Product__Type_OPair(v5, v4, v3, v2) = v1) |
% 222.24/31.05 ~ (c_Product__Type_OPair(v5, v4, v3, v2) = v0))
% 222.24/31.05 (17) all_870_8 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & hBOOL(v0) =
% 222.24/31.05 v1 & hAPP(v_L, all_870_9) = v0 & $i(v0))
% 222.24/31.05 (18) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 222.24/31.05 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (c_member(v4, v3, v2) = v1) |
% 222.24/31.05 ~ (c_member(v4, v3, v2) = v0))
% 222.24/31.05
% 222.24/31.05 Begin of proof
% 222.24/31.05 |
% 222.24/31.05 | BETA: splitting (5) gives:
% 222.24/31.05 |
% 222.24/31.05 | Case 1:
% 222.24/31.05 | |
% 222.24/31.05 | | (19) all_870_12 = v_x
% 222.24/31.05 | |
% 222.24/31.05 | | REDUCE: (7), (19) imply:
% 222.24/31.05 | | (20) $false
% 222.24/31.05 | |
% 222.24/31.05 | | CLOSE: (20) is inconsistent.
% 222.24/31.05 | |
% 222.24/31.05 | Case 2:
% 222.24/31.05 | |
% 222.24/31.05 | | (21) all_870_13 = v_x
% 222.24/31.05 | |
% 222.24/31.05 | | REDUCE: (1), (21) imply:
% 222.24/31.05 | | (22) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 222.24/31.05 | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v_y) = all_870_9
% 222.24/31.05 | |
% 222.24/31.05 | | BETA: splitting (3) gives:
% 222.24/31.05 | |
% 222.24/31.05 | | Case 1:
% 222.24/31.05 | | |
% 222.24/31.05 | | | (23) all_870_13 = v_y
% 222.24/31.05 | | |
% 222.24/31.05 | | | COMBINE_EQS: (21), (23) imply:
% 222.24/31.05 | | | (24) v_x = v_y
% 222.24/31.05 | | |
% 222.24/31.05 | | | REDUCE: (13), (24) imply:
% 222.24/31.05 | | | (25) $false
% 222.24/31.05 | | |
% 222.24/31.05 | | | CLOSE: (25) is inconsistent.
% 222.24/31.05 | | |
% 222.24/31.05 | | Case 2:
% 222.24/31.05 | | |
% 222.24/31.05 | | | (26) ~ (all_870_13 = v_y)
% 222.24/31.05 | | | (27) ? [v0: any] : ? [v1: $i] : ? [v2: any] :
% 222.24/31.05 | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 222.24/31.05 | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_13, v_y) = v1 &
% 222.24/31.05 | | | c_member(all_674_0, v1, v_L) = v2 & c_member(all_674_0,
% 222.24/31.05 | | | all_870_1, v_L) = v0 & $i(v1) & (v2 = 0 | v0 = 0))
% 222.24/31.05 | | |
% 222.24/31.05 | | | DELTA: instantiating (27) with fresh symbols all_1253_0, all_1253_1,
% 222.24/31.05 | | | all_1253_2 gives:
% 222.24/31.05 | | | (28) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 222.24/31.05 | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_13, v_y) = all_1253_1 &
% 222.24/31.05 | | | c_member(all_674_0, all_1253_1, v_L) = all_1253_0 &
% 222.24/31.05 | | | c_member(all_674_0, all_870_1, v_L) = all_1253_2 & $i(all_1253_1)
% 222.24/31.05 | | | & (all_1253_0 = 0 | all_1253_2 = 0)
% 222.24/31.05 | | |
% 222.24/31.05 | | | ALPHA: (28) implies:
% 222.24/31.05 | | | (29) c_member(all_674_0, all_870_1, v_L) = all_1253_2
% 222.24/31.05 | | | (30) c_member(all_674_0, all_1253_1, v_L) = all_1253_0
% 222.24/31.05 | | | (31) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 222.24/31.05 | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_13, v_y) = all_1253_1
% 222.24/31.05 | | | (32) all_1253_0 = 0 | all_1253_2 = 0
% 222.24/31.05 | | |
% 222.24/31.05 | | | REDUCE: (21), (31) imply:
% 222.24/31.05 | | | (33) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 222.24/31.05 | | | tc_Arrow__Order__Mirabelle_Oalt, v_x, v_y) = all_1253_1
% 222.24/31.05 | | |
% 222.24/31.05 | | | REDUCE: (15), (30) imply:
% 222.24/31.05 | | | (34) c_member(all_625_1, all_1253_1, v_L) = all_1253_0
% 222.24/31.05 | | |
% 222.24/31.05 | | | REDUCE: (15), (29) imply:
% 222.24/31.05 | | | (35) c_member(all_625_1, all_870_1, v_L) = all_1253_2
% 222.24/31.05 | | |
% 222.24/31.05 | | | BETA: splitting (6) gives:
% 222.24/31.05 | | |
% 222.24/31.05 | | | Case 1:
% 222.24/31.05 | | | |
% 222.24/31.05 | | | | (36) ~ (all_870_2 = 0)
% 222.24/31.05 | | | |
% 222.24/31.05 | | | | BETA: splitting (12) gives:
% 222.24/31.05 | | | |
% 222.24/31.05 | | | | Case 1:
% 222.24/31.05 | | | | |
% 222.24/31.05 | | | | | (37) all_870_13 = v_y
% 222.24/31.05 | | | | |
% 222.24/31.05 | | | | | COMBINE_EQS: (21), (37) imply:
% 222.24/31.05 | | | | | (38) v_x = v_y
% 222.24/31.05 | | | | |
% 222.24/31.05 | | | | | REDUCE: (13), (38) imply:
% 222.24/31.05 | | | | | (39) $false
% 222.24/31.05 | | | | |
% 222.24/31.05 | | | | | CLOSE: (39) is inconsistent.
% 222.24/31.05 | | | | |
% 222.24/31.05 | | | | Case 2:
% 222.24/31.05 | | | | |
% 222.24/31.05 | | | | | (40) ? [v0: any] : ? [v1: $i] : ? [v2: any] :
% 222.24/31.05 | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 222.24/31.05 | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, all_870_13) = v1 &
% 222.24/31.05 | | | | | c_member(all_674_0, v1, v_L) = v2 & c_member(all_674_0,
% 222.24/31.05 | | | | | all_870_9, v_L) = v0 & $i(v1) & (v2 = 0 | v0 = 0))
% 222.24/31.05 | | | | |
% 222.24/31.05 | | | | | DELTA: instantiating (40) with fresh symbols all_1285_0, all_1285_1,
% 222.24/31.05 | | | | | all_1285_2 gives:
% 222.24/31.05 | | | | | (41) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 222.24/31.05 | | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, all_870_13) =
% 222.24/31.05 | | | | | all_1285_1 & c_member(all_674_0, all_1285_1, v_L) = all_1285_0
% 222.24/31.05 | | | | | & c_member(all_674_0, all_870_9, v_L) = all_1285_2 &
% 222.24/31.05 | | | | | $i(all_1285_1) & (all_1285_0 = 0 | all_1285_2 = 0)
% 222.24/31.05 | | | | |
% 222.24/31.05 | | | | | ALPHA: (41) implies:
% 222.24/31.05 | | | | | (42) c_member(all_674_0, all_870_9, v_L) = all_1285_2
% 222.24/31.05 | | | | |
% 222.24/31.05 | | | | | REDUCE: (15), (42) imply:
% 222.24/31.05 | | | | | (43) c_member(all_625_1, all_870_9, v_L) = all_1285_2
% 222.24/31.05 | | | | |
% 222.24/31.05 | | | | | BETA: splitting (9) gives:
% 222.24/31.05 | | | | |
% 222.24/31.05 | | | | | Case 1:
% 222.24/31.05 | | | | | |
% 222.24/31.05 | | | | | | (44) ~ (all_1186_1 = 0)
% 222.24/31.05 | | | | | |
% 222.24/31.05 | | | | | | REDUCE: (4), (44) imply:
% 222.24/31.05 | | | | | | (45) ~ (all_870_8 = 0)
% 222.24/31.05 | | | | | |
% 222.24/31.05 | | | | | | BETA: splitting (17) gives:
% 222.24/31.05 | | | | | |
% 222.24/31.05 | | | | | | Case 1:
% 222.24/31.05 | | | | | | |
% 222.24/31.05 | | | | | | | (46) all_870_8 = 0
% 222.24/31.05 | | | | | | |
% 222.24/31.05 | | | | | | | REDUCE: (45), (46) imply:
% 222.24/31.05 | | | | | | | (47) $false
% 222.24/31.05 | | | | | | |
% 222.24/31.05 | | | | | | | CLOSE: (47) is inconsistent.
% 222.24/31.05 | | | | | | |
% 222.24/31.05 | | | | | | Case 2:
% 222.24/31.05 | | | | | | |
% 222.24/31.05 | | | | | | |
% 222.24/31.05 | | | | | | | GROUND_INST: instantiating (18) with all_870_8, all_1285_2, v_L,
% 222.24/31.05 | | | | | | | all_870_9, all_625_1, simplifying with (11), (43)
% 222.24/31.05 | | | | | | | gives:
% 222.24/31.05 | | | | | | | (48) all_1285_2 = all_870_8
% 222.24/31.05 | | | | | | |
% 222.24/31.05 | | | | | | | GROUND_INST: instantiating (18) with all_870_0, all_1253_2, v_L,
% 222.24/31.05 | | | | | | | all_870_1, all_625_1, simplifying with (10), (35)
% 222.24/31.05 | | | | | | | gives:
% 222.24/31.05 | | | | | | | (49) all_1253_2 = all_870_0
% 222.24/31.05 | | | | | | |
% 222.24/31.05 | | | | | | | GROUND_INST: instantiating (16) with all_870_9, all_1253_1, v_y,
% 222.24/31.05 | | | | | | | v_x, tc_Arrow__Order__Mirabelle_Oalt,
% 222.24/31.05 | | | | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with
% 222.24/31.05 | | | | | | | (22), (33) gives:
% 222.24/31.05 | | | | | | | (50) all_1253_1 = all_870_9
% 222.24/31.05 | | | | | | |
% 222.24/31.05 | | | | | | | REDUCE: (34), (50) imply:
% 222.24/31.05 | | | | | | | (51) c_member(all_625_1, all_870_9, v_L) = all_1253_0
% 222.24/31.05 | | | | | | |
% 222.24/31.05 | | | | | | | BETA: splitting (32) gives:
% 222.24/31.05 | | | | | | |
% 222.24/31.05 | | | | | | | Case 1:
% 222.24/31.05 | | | | | | | |
% 222.24/31.05 | | | | | | | | (52) all_1253_0 = 0
% 222.24/31.05 | | | | | | | |
% 222.24/31.05 | | | | | | | | REDUCE: (51), (52) imply:
% 222.24/31.05 | | | | | | | | (53) c_member(all_625_1, all_870_9, v_L) = 0
% 222.24/31.05 | | | | | | | |
% 222.24/31.05 | | | | | | | | GROUND_INST: instantiating (18) with all_870_8, 0, v_L,
% 222.24/31.05 | | | | | | | | all_870_9, all_625_1, simplifying with (11), (53)
% 222.24/31.05 | | | | | | | | gives:
% 222.24/31.05 | | | | | | | | (54) all_870_8 = 0
% 222.24/31.05 | | | | | | | |
% 222.24/31.05 | | | | | | | | REDUCE: (45), (54) imply:
% 222.24/31.05 | | | | | | | | (55) $false
% 222.24/31.05 | | | | | | | |
% 222.24/31.05 | | | | | | | | CLOSE: (55) is inconsistent.
% 222.24/31.05 | | | | | | | |
% 222.24/31.05 | | | | | | | Case 2:
% 222.24/31.05 | | | | | | | |
% 222.24/31.05 | | | | | | | | (56) all_1253_2 = 0
% 222.24/31.05 | | | | | | | |
% 222.24/31.05 | | | | | | | | COMBINE_EQS: (49), (56) imply:
% 222.24/31.05 | | | | | | | | (57) all_870_0 = 0
% 222.24/31.05 | | | | | | | |
% 222.24/31.05 | | | | | | | | REDUCE: (14), (57) imply:
% 222.24/31.05 | | | | | | | | (58) $false
% 222.24/31.05 | | | | | | | |
% 222.24/31.05 | | | | | | | | CLOSE: (58) is inconsistent.
% 222.24/31.05 | | | | | | | |
% 222.24/31.05 | | | | | | | End of split
% 222.24/31.05 | | | | | | |
% 222.24/31.05 | | | | | | End of split
% 222.24/31.05 | | | | | |
% 222.24/31.05 | | | | | Case 2:
% 222.24/31.05 | | | | | |
% 222.24/31.05 | | | | | | (59) all_1186_0 = 0
% 222.24/31.05 | | | | | |
% 222.24/31.05 | | | | | | COMBINE_EQS: (8), (59) imply:
% 222.24/31.05 | | | | | | (60) all_870_2 = 0
% 222.24/31.05 | | | | | |
% 222.24/31.05 | | | | | | REDUCE: (36), (60) imply:
% 222.24/31.05 | | | | | | (61) $false
% 222.24/31.05 | | | | | |
% 222.24/31.05 | | | | | | CLOSE: (61) is inconsistent.
% 222.24/31.05 | | | | | |
% 222.24/31.05 | | | | | End of split
% 222.24/31.05 | | | | |
% 222.24/31.05 | | | | End of split
% 222.24/31.05 | | | |
% 222.24/31.05 | | | Case 2:
% 222.24/31.05 | | | |
% 222.24/31.05 | | | | (62) ~ (all_870_13 = v_x) | all_870_12 = v_x
% 222.24/31.05 | | | |
% 222.24/31.05 | | | | REF_CLOSE: (7), (21), (62) are inconsistent by sub-proof #20.
% 222.24/31.05 | | | |
% 222.24/31.05 | | | End of split
% 222.24/31.05 | | |
% 222.24/31.05 | | End of split
% 222.24/31.05 | |
% 222.24/31.05 | End of split
% 222.24/31.05 |
% 222.24/31.05 End of proof
% 222.24/31.05
% 222.24/31.05 Sub-proof #18 shows that the following formulas are inconsistent:
% 222.24/31.05 ----------------------------------------------------------------
% 222.24/31.05 (1) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 222.24/31.05 tc_Arrow__Order__Mirabelle_Oalt, all_870_13, all_870_12) = all_1211_1 &
% 222.24/31.05 c_member(all_674_0, all_1211_1, v_L) = all_1211_0 & c_member(all_674_0,
% 222.24/31.05 all_870_5, v_L) = all_1211_2 & $i(all_1211_1) & (all_1211_0 = 0 |
% 222.24/31.05 all_1211_2 = 0)
% 222.24/31.05 (2) ~ (all_870_12 = all_870_13)
% 222.24/31.05 (3) ~ (all_870_10 = 0)
% 222.24/31.05 (4) c_member(all_625_1, all_870_7, v_L) = all_870_6
% 222.24/31.05 (5) ~ (all_870_2 = 0) | ~ (all_870_13 = v_x) | all_870_12 = v_x
% 222.24/31.06 (6) all_870_12 = v_y | ? [v0: any] : ? [v1: $i] : ? [v2: any] :
% 222.24/31.06 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 222.24/31.06 tc_Arrow__Order__Mirabelle_Oalt, all_870_12, v_y) = v1 &
% 222.24/31.06 c_member(all_674_0, v1, v_L) = v2 & c_member(all_674_0, all_870_7, v_L)
% 222.24/31.06 = v0 & $i(v1) & (v2 = 0 | v0 = 0))
% 222.24/31.06 (7) ~ (all_870_12 = v_x)
% 222.24/31.06 (8) ~ (all_870_4 = 0) | all_870_12 = v_x | all_870_13 = v_x
% 222.24/31.06 (9) c_member(all_625_1, all_870_5, v_L) = all_870_4
% 222.24/31.06 (10) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 222.24/31.06 tc_Arrow__Order__Mirabelle_Oalt, v_y, all_870_12) = all_870_7
% 222.24/31.06 (11) all_870_12 = v_y | ? [v0: any] : ? [v1: $i] : ? [v2: any] :
% 222.24/31.06 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 222.24/31.06 tc_Arrow__Order__Mirabelle_Oalt, v_y, all_870_12) = v1 &
% 222.24/31.06 c_member(all_674_0, v1, v_L) = v2 & c_member(all_674_0, all_870_3,
% 222.24/31.06 v_L) = v0 & $i(v1) & (v2 = 0 | v0 = 0))
% 222.24/31.06 (12) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 222.24/31.06 tc_Arrow__Order__Mirabelle_Oalt, all_870_12, all_870_13) = all_870_5
% 222.24/31.06 (13) ~ (all_870_12 = v_y)
% 222.24/31.06 (14) all_870_12 = all_870_13 | ? [v0: any] : ? [v1: $i] : ? [v2: any] :
% 222.24/31.06 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 222.24/31.06 tc_Arrow__Order__Mirabelle_Oalt, all_870_12, all_870_13) = v1 &
% 222.24/31.06 c_member(all_674_0, v1, v_L) = v2 & c_member(all_674_0, all_870_11,
% 222.24/31.06 v_L) = v0 & $i(v1) & (v2 = 0 | v0 = 0))
% 222.24/31.06 (15) all_674_0 = all_625_1
% 222.24/31.06 (16) c_member(all_625_1, all_870_11, v_L) = all_870_10
% 222.24/31.06 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 222.24/31.06 [v5: $i] : (v1 = v0 | ~ (c_Product__Type_OPair(v5, v4, v3, v2) = v1) |
% 222.24/31.06 ~ (c_Product__Type_OPair(v5, v4, v3, v2) = v0))
% 222.24/31.06 (18) c_member(all_625_1, all_870_3, v_L) = all_870_2
% 222.24/31.06 (19) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 222.24/31.06 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (c_member(v4, v3, v2) = v1) |
% 222.24/31.06 ~ (c_member(v4, v3, v2) = v0))
% 222.24/31.06 (20) ~ (all_870_6 = 0) | ~ (all_870_13 = v_x) | all_870_12 = v_x
% 222.24/31.06
% 222.24/31.06 Begin of proof
% 222.24/31.06 |
% 222.24/31.06 | ALPHA: (1) implies:
% 222.24/31.06 | (21) c_member(all_674_0, all_870_5, v_L) = all_1211_2
% 222.24/31.06 |
% 222.24/31.06 | REDUCE: (15), (21) imply:
% 222.24/31.06 | (22) c_member(all_625_1, all_870_5, v_L) = all_1211_2
% 222.24/31.06 |
% 222.24/31.06 | BETA: splitting (14) gives:
% 222.24/31.06 |
% 222.24/31.06 | Case 1:
% 222.24/31.06 | |
% 222.24/31.06 | | (23) all_870_12 = all_870_13
% 222.24/31.06 | |
% 222.24/31.06 | | REDUCE: (2), (23) imply:
% 222.24/31.06 | | (24) $false
% 222.24/31.06 | |
% 222.24/31.06 | | CLOSE: (24) is inconsistent.
% 222.24/31.06 | |
% 222.24/31.06 | Case 2:
% 222.24/31.06 | |
% 222.24/31.06 | | (25) ? [v0: any] : ? [v1: $i] : ? [v2: any] :
% 222.24/31.06 | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 222.24/31.06 | | tc_Arrow__Order__Mirabelle_Oalt, all_870_12, all_870_13) = v1 &
% 222.24/31.06 | | c_member(all_674_0, v1, v_L) = v2 & c_member(all_674_0,
% 222.24/31.06 | | all_870_11, v_L) = v0 & $i(v1) & (v2 = 0 | v0 = 0))
% 222.24/31.06 | |
% 222.24/31.06 | | DELTA: instantiating (25) with fresh symbols all_1217_0, all_1217_1,
% 222.24/31.06 | | all_1217_2 gives:
% 222.24/31.06 | | (26) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 222.24/31.06 | | tc_Arrow__Order__Mirabelle_Oalt, all_870_12, all_870_13) =
% 222.24/31.06 | | all_1217_1 & c_member(all_674_0, all_1217_1, v_L) = all_1217_0 &
% 222.24/31.06 | | c_member(all_674_0, all_870_11, v_L) = all_1217_2 & $i(all_1217_1) &
% 222.24/31.06 | | (all_1217_0 = 0 | all_1217_2 = 0)
% 222.24/31.06 | |
% 222.24/31.06 | | ALPHA: (26) implies:
% 222.24/31.06 | | (27) c_member(all_674_0, all_870_11, v_L) = all_1217_2
% 222.24/31.06 | | (28) c_member(all_674_0, all_1217_1, v_L) = all_1217_0
% 222.24/31.06 | | (29) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 222.24/31.06 | | tc_Arrow__Order__Mirabelle_Oalt, all_870_12, all_870_13) =
% 222.24/31.06 | | all_1217_1
% 222.24/31.06 | | (30) all_1217_0 = 0 | all_1217_2 = 0
% 222.24/31.06 | |
% 222.24/31.06 | | REDUCE: (15), (28) imply:
% 222.24/31.06 | | (31) c_member(all_625_1, all_1217_1, v_L) = all_1217_0
% 222.24/31.06 | |
% 222.24/31.06 | | REDUCE: (15), (27) imply:
% 222.24/31.06 | | (32) c_member(all_625_1, all_870_11, v_L) = all_1217_2
% 222.24/31.06 | |
% 222.24/31.06 | | GROUND_INST: instantiating (19) with all_870_10, all_1217_2, v_L,
% 222.24/31.06 | | all_870_11, all_625_1, simplifying with (16), (32) gives:
% 222.24/31.06 | | (33) all_1217_2 = all_870_10
% 222.24/31.06 | |
% 222.24/31.06 | | GROUND_INST: instantiating (19) with all_870_4, all_1211_2, v_L, all_870_5,
% 222.24/31.06 | | all_625_1, simplifying with (9), (22) gives:
% 222.24/31.06 | | (34) all_1211_2 = all_870_4
% 222.24/31.06 | |
% 222.24/31.06 | | GROUND_INST: instantiating (17) with all_870_5, all_1217_1, all_870_13,
% 222.24/31.06 | | all_870_12, tc_Arrow__Order__Mirabelle_Oalt,
% 222.24/31.06 | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with (12), (29)
% 222.24/31.06 | | gives:
% 222.24/31.06 | | (35) all_1217_1 = all_870_5
% 222.24/31.06 | |
% 222.24/31.06 | | REDUCE: (31), (35) imply:
% 222.24/31.06 | | (36) c_member(all_625_1, all_870_5, v_L) = all_1217_0
% 222.24/31.06 | |
% 222.24/31.06 | | BETA: splitting (30) gives:
% 222.24/31.06 | |
% 222.24/31.06 | | Case 1:
% 222.24/31.06 | | |
% 222.24/31.06 | | | (37) all_1217_0 = 0
% 222.24/31.06 | | |
% 222.24/31.06 | | | REDUCE: (36), (37) imply:
% 222.24/31.06 | | | (38) c_member(all_625_1, all_870_5, v_L) = 0
% 222.24/31.06 | | |
% 222.24/31.06 | | | GROUND_INST: instantiating (19) with all_870_4, 0, v_L, all_870_5,
% 222.24/31.06 | | | all_625_1, simplifying with (9), (38) gives:
% 222.24/31.06 | | | (39) all_870_4 = 0
% 222.24/31.06 | | |
% 222.24/31.06 | | | BETA: splitting (8) gives:
% 222.24/31.06 | | |
% 222.24/31.06 | | | Case 1:
% 222.24/31.06 | | | |
% 222.24/31.06 | | | | (40) ~ (all_870_4 = 0)
% 222.24/31.06 | | | |
% 222.24/31.06 | | | | REDUCE: (39), (40) imply:
% 222.24/31.06 | | | | (41) $false
% 222.24/31.06 | | | |
% 222.24/31.06 | | | | CLOSE: (41) is inconsistent.
% 222.24/31.06 | | | |
% 222.24/31.06 | | | Case 2:
% 222.24/31.06 | | | |
% 222.24/31.06 | | | | (42) all_870_12 = v_x | all_870_13 = v_x
% 222.24/31.06 | | | |
% 222.24/31.06 | | | | REF_CLOSE: (2), (4), (5), (6), (7), (10), (11), (13), (15), (17), (18),
% 222.24/31.06 | | | | (19), (20), (42) are inconsistent by sub-proof #19.
% 222.24/31.06 | | | |
% 222.24/31.06 | | | End of split
% 222.24/31.06 | | |
% 222.24/31.06 | | Case 2:
% 222.24/31.06 | | |
% 222.24/31.06 | | | (43) all_1217_2 = 0
% 222.24/31.06 | | |
% 222.24/31.06 | | | COMBINE_EQS: (33), (43) imply:
% 222.24/31.06 | | | (44) all_870_10 = 0
% 222.24/31.06 | | |
% 222.24/31.06 | | | REDUCE: (3), (44) imply:
% 222.24/31.06 | | | (45) $false
% 222.24/31.06 | | |
% 222.24/31.06 | | | CLOSE: (45) is inconsistent.
% 222.24/31.06 | | |
% 222.24/31.06 | | End of split
% 222.24/31.06 | |
% 222.24/31.06 | End of split
% 222.24/31.06 |
% 222.24/31.06 End of proof
% 222.24/31.06
% 222.24/31.06 Sub-proof #19 shows that the following formulas are inconsistent:
% 222.24/31.06 ----------------------------------------------------------------
% 222.24/31.06 (1) ~ (all_870_12 = all_870_13)
% 222.24/31.06 (2) c_member(all_625_1, all_870_7, v_L) = all_870_6
% 222.24/31.06 (3) all_870_12 = v_x | all_870_13 = v_x
% 222.24/31.06 (4) ~ (all_870_2 = 0) | ~ (all_870_13 = v_x) | all_870_12 = v_x
% 222.24/31.06 (5) all_870_12 = v_y | ? [v0: any] : ? [v1: $i] : ? [v2: any] :
% 222.24/31.06 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 222.24/31.06 tc_Arrow__Order__Mirabelle_Oalt, all_870_12, v_y) = v1 &
% 222.24/31.06 c_member(all_674_0, v1, v_L) = v2 & c_member(all_674_0, all_870_7, v_L)
% 222.24/31.06 = v0 & $i(v1) & (v2 = 0 | v0 = 0))
% 222.24/31.06 (6) ~ (all_870_12 = v_x)
% 222.24/31.06 (7) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 222.24/31.06 tc_Arrow__Order__Mirabelle_Oalt, v_y, all_870_12) = all_870_7
% 222.24/31.06 (8) all_870_12 = v_y | ? [v0: any] : ? [v1: $i] : ? [v2: any] :
% 222.24/31.06 (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 222.24/31.06 tc_Arrow__Order__Mirabelle_Oalt, v_y, all_870_12) = v1 &
% 222.24/31.06 c_member(all_674_0, v1, v_L) = v2 & c_member(all_674_0, all_870_3, v_L)
% 222.24/31.06 = v0 & $i(v1) & (v2 = 0 | v0 = 0))
% 222.24/31.06 (9) ~ (all_870_12 = v_y)
% 222.24/31.06 (10) all_674_0 = all_625_1
% 222.24/31.06 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 222.24/31.06 [v5: $i] : (v1 = v0 | ~ (c_Product__Type_OPair(v5, v4, v3, v2) = v1) |
% 222.24/31.06 ~ (c_Product__Type_OPair(v5, v4, v3, v2) = v0))
% 222.24/31.06 (12) c_member(all_625_1, all_870_3, v_L) = all_870_2
% 222.24/31.06 (13) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 222.24/31.06 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (c_member(v4, v3, v2) = v1) |
% 222.24/31.06 ~ (c_member(v4, v3, v2) = v0))
% 222.24/31.06 (14) ~ (all_870_6 = 0) | ~ (all_870_13 = v_x) | all_870_12 = v_x
% 222.24/31.06
% 222.24/31.06 Begin of proof
% 222.24/31.06 |
% 222.24/31.06 | BETA: splitting (3) gives:
% 222.24/31.06 |
% 222.24/31.06 | Case 1:
% 222.24/31.06 | |
% 222.24/31.06 | | (15) all_870_12 = v_x
% 222.24/31.06 | |
% 222.24/31.06 | | REDUCE: (6), (15) imply:
% 222.24/31.06 | | (16) $false
% 222.24/31.06 | |
% 222.24/31.06 | | CLOSE: (16) is inconsistent.
% 222.24/31.06 | |
% 222.24/31.06 | Case 2:
% 222.24/31.06 | |
% 222.24/31.06 | | (17) all_870_13 = v_x
% 222.24/31.06 | |
% 222.24/31.06 | | BETA: splitting (4) gives:
% 222.24/31.06 | |
% 222.24/31.06 | | Case 1:
% 222.24/31.06 | | |
% 222.24/31.06 | | | (18) ~ (all_870_2 = 0)
% 222.24/31.06 | | |
% 222.24/31.06 | | | BETA: splitting (8) gives:
% 222.24/31.06 | | |
% 222.24/31.06 | | | Case 1:
% 222.24/31.06 | | | |
% 222.24/31.06 | | | | (19) all_870_12 = v_y
% 222.24/31.06 | | | |
% 222.24/31.06 | | | | REDUCE: (9), (19) imply:
% 222.24/31.06 | | | | (20) $false
% 222.24/31.06 | | | |
% 222.24/31.06 | | | | CLOSE: (20) is inconsistent.
% 222.24/31.06 | | | |
% 222.24/31.06 | | | Case 2:
% 222.24/31.06 | | | |
% 222.24/31.06 | | | | (21) ? [v0: any] : ? [v1: $i] : ? [v2: any] :
% 222.24/31.06 | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 222.24/31.06 | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, all_870_12) = v1 &
% 222.24/31.06 | | | | c_member(all_674_0, v1, v_L) = v2 & c_member(all_674_0,
% 222.24/31.06 | | | | all_870_3, v_L) = v0 & $i(v1) & (v2 = 0 | v0 = 0))
% 222.24/31.06 | | | |
% 222.24/31.06 | | | | DELTA: instantiating (21) with fresh symbols all_1253_0, all_1253_1,
% 222.24/31.06 | | | | all_1253_2 gives:
% 222.24/31.06 | | | | (22) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 222.24/31.06 | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, all_870_12) = all_1253_1
% 222.24/31.06 | | | | & c_member(all_674_0, all_1253_1, v_L) = all_1253_0 &
% 222.24/31.06 | | | | c_member(all_674_0, all_870_3, v_L) = all_1253_2 &
% 222.24/31.06 | | | | $i(all_1253_1) & (all_1253_0 = 0 | all_1253_2 = 0)
% 222.24/31.06 | | | |
% 222.24/31.06 | | | | ALPHA: (22) implies:
% 222.24/31.06 | | | | (23) c_member(all_674_0, all_870_3, v_L) = all_1253_2
% 222.24/31.06 | | | | (24) c_member(all_674_0, all_1253_1, v_L) = all_1253_0
% 222.24/31.06 | | | | (25) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 222.24/31.06 | | | | tc_Arrow__Order__Mirabelle_Oalt, v_y, all_870_12) = all_1253_1
% 222.24/31.06 | | | | (26) all_1253_0 = 0 | all_1253_2 = 0
% 222.24/31.06 | | | |
% 222.24/31.06 | | | | REDUCE: (10), (24) imply:
% 222.24/31.06 | | | | (27) c_member(all_625_1, all_1253_1, v_L) = all_1253_0
% 222.24/31.06 | | | |
% 222.24/31.06 | | | | REDUCE: (10), (23) imply:
% 222.24/31.06 | | | | (28) c_member(all_625_1, all_870_3, v_L) = all_1253_2
% 222.24/31.06 | | | |
% 222.24/31.06 | | | | BETA: splitting (14) gives:
% 222.24/31.06 | | | |
% 222.24/31.06 | | | | Case 1:
% 222.24/31.06 | | | | |
% 222.24/31.06 | | | | | (29) ~ (all_870_6 = 0)
% 222.24/31.06 | | | | |
% 222.24/31.06 | | | | | BETA: splitting (5) gives:
% 222.24/31.06 | | | | |
% 222.24/31.06 | | | | | Case 1:
% 222.24/31.06 | | | | | |
% 222.24/31.06 | | | | | | (30) all_870_12 = v_y
% 222.24/31.06 | | | | | |
% 222.24/31.06 | | | | | | REDUCE: (9), (30) imply:
% 222.24/31.06 | | | | | | (31) $false
% 222.24/31.06 | | | | | |
% 222.24/31.06 | | | | | | CLOSE: (31) is inconsistent.
% 222.24/31.06 | | | | | |
% 222.24/31.06 | | | | | Case 2:
% 222.24/31.06 | | | | | |
% 222.24/31.07 | | | | | | (32) ? [v0: any] : ? [v1: $i] : ? [v2: any] :
% 222.24/31.07 | | | | | | (c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 222.24/31.07 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_12, v_y) = v1 &
% 222.24/31.07 | | | | | | c_member(all_674_0, v1, v_L) = v2 & c_member(all_674_0,
% 222.24/31.07 | | | | | | all_870_7, v_L) = v0 & $i(v1) & (v2 = 0 | v0 = 0))
% 222.24/31.07 | | | | | |
% 222.24/31.07 | | | | | | DELTA: instantiating (32) with fresh symbols all_1268_0, all_1268_1,
% 222.24/31.07 | | | | | | all_1268_2 gives:
% 222.24/31.07 | | | | | | (33) c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,
% 222.24/31.07 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, all_870_12, v_y) =
% 222.24/31.07 | | | | | | all_1268_1 & c_member(all_674_0, all_1268_1, v_L) =
% 222.24/31.07 | | | | | | all_1268_0 & c_member(all_674_0, all_870_7, v_L) =
% 222.24/31.07 | | | | | | all_1268_2 & $i(all_1268_1) & (all_1268_0 = 0 | all_1268_2 =
% 222.24/31.07 | | | | | | 0)
% 222.24/31.07 | | | | | |
% 222.24/31.07 | | | | | | ALPHA: (33) implies:
% 222.24/31.07 | | | | | | (34) c_member(all_674_0, all_870_7, v_L) = all_1268_2
% 222.24/31.07 | | | | | |
% 222.24/31.07 | | | | | | REDUCE: (10), (34) imply:
% 222.24/31.07 | | | | | | (35) c_member(all_625_1, all_870_7, v_L) = all_1268_2
% 222.24/31.07 | | | | | |
% 222.24/31.07 | | | | | | GROUND_INST: instantiating (13) with all_870_6, all_1268_2, v_L,
% 222.24/31.07 | | | | | | all_870_7, all_625_1, simplifying with (2), (35) gives:
% 222.24/31.07 | | | | | | (36) all_1268_2 = all_870_6
% 222.24/31.07 | | | | | |
% 222.24/31.07 | | | | | | GROUND_INST: instantiating (13) with all_870_2, all_1253_2, v_L,
% 222.24/31.07 | | | | | | all_870_3, all_625_1, simplifying with (12), (28)
% 222.24/31.07 | | | | | | gives:
% 222.24/31.07 | | | | | | (37) all_1253_2 = all_870_2
% 222.24/31.07 | | | | | |
% 222.24/31.07 | | | | | | GROUND_INST: instantiating (11) with all_870_7, all_1253_1,
% 222.24/31.07 | | | | | | all_870_12, v_y, tc_Arrow__Order__Mirabelle_Oalt,
% 222.24/31.07 | | | | | | tc_Arrow__Order__Mirabelle_Oalt, simplifying with (7),
% 222.24/31.07 | | | | | | (25) gives:
% 222.24/31.07 | | | | | | (38) all_1253_1 = all_870_7
% 222.24/31.07 | | | | | |
% 222.24/31.07 | | | | | | REDUCE: (27), (38) imply:
% 222.24/31.07 | | | | | | (39) c_member(all_625_1, all_870_7, v_L) = all_1253_0
% 222.24/31.07 | | | | | |
% 222.24/31.07 | | | | | | BETA: splitting (26) gives:
% 222.24/31.07 | | | | | |
% 222.24/31.07 | | | | | | Case 1:
% 222.24/31.07 | | | | | | |
% 222.24/31.07 | | | | | | | (40) all_1253_0 = 0
% 222.24/31.07 | | | | | | |
% 222.24/31.07 | | | | | | | REDUCE: (39), (40) imply:
% 222.24/31.07 | | | | | | | (41) c_member(all_625_1, all_870_7, v_L) = 0
% 222.24/31.07 | | | | | | |
% 222.24/31.07 | | | | | | | REF_CLOSE: (2), (13), (29), (41) are inconsistent by sub-proof
% 222.24/31.07 | | | | | | | #21.
% 222.24/31.07 | | | | | | |
% 222.24/31.07 | | | | | | Case 2:
% 222.24/31.07 | | | | | | |
% 222.24/31.07 | | | | | | | (42) all_1253_2 = 0
% 222.24/31.07 | | | | | | |
% 222.24/31.07 | | | | | | | COMBINE_EQS: (37), (42) imply:
% 222.24/31.07 | | | | | | | (43) all_870_2 = 0
% 222.24/31.07 | | | | | | |
% 222.24/31.07 | | | | | | | REDUCE: (18), (43) imply:
% 222.24/31.07 | | | | | | | (44) $false
% 222.24/31.07 | | | | | | |
% 222.24/31.07 | | | | | | | CLOSE: (44) is inconsistent.
% 222.24/31.07 | | | | | | |
% 222.24/31.07 | | | | | | End of split
% 222.24/31.07 | | | | | |
% 222.24/31.07 | | | | | End of split
% 222.24/31.07 | | | | |
% 222.24/31.07 | | | | Case 2:
% 222.24/31.07 | | | | |
% 222.24/31.07 | | | | | (45) ~ (all_870_13 = v_x) | all_870_12 = v_x
% 222.24/31.07 | | | | |
% 222.24/31.07 | | | | | REF_CLOSE: (6), (17), (45) are inconsistent by sub-proof #20.
% 222.24/31.07 | | | | |
% 222.24/31.07 | | | | End of split
% 222.24/31.07 | | | |
% 222.24/31.07 | | | End of split
% 222.24/31.07 | | |
% 222.24/31.07 | | Case 2:
% 222.24/31.07 | | |
% 222.24/31.07 | | | (46) ~ (all_870_13 = v_x) | all_870_12 = v_x
% 222.24/31.07 | | |
% 222.24/31.07 | | | REF_CLOSE: (6), (17), (46) are inconsistent by sub-proof #20.
% 222.24/31.07 | | |
% 222.24/31.07 | | End of split
% 222.24/31.07 | |
% 222.24/31.07 | End of split
% 222.24/31.07 |
% 222.24/31.07 End of proof
% 222.24/31.07
% 222.24/31.07 Sub-proof #20 shows that the following formulas are inconsistent:
% 222.24/31.07 ----------------------------------------------------------------
% 222.24/31.07 (1) ~ (all_870_13 = v_x) | all_870_12 = v_x
% 222.24/31.07 (2) all_870_13 = v_x
% 222.24/31.07 (3) ~ (all_870_12 = v_x)
% 222.24/31.07
% 222.24/31.07 Begin of proof
% 222.24/31.07 |
% 222.24/31.07 | BETA: splitting (1) gives:
% 222.24/31.07 |
% 222.24/31.07 | Case 1:
% 222.24/31.07 | |
% 222.24/31.07 | | (4) ~ (all_870_13 = v_x)
% 222.24/31.07 | |
% 222.24/31.07 | | REDUCE: (2), (4) imply:
% 222.24/31.07 | | (5) $false
% 222.24/31.07 | |
% 222.24/31.07 | | CLOSE: (5) is inconsistent.
% 222.24/31.07 | |
% 222.24/31.07 | Case 2:
% 222.24/31.07 | |
% 222.24/31.07 | | (6) all_870_12 = v_x
% 222.24/31.07 | |
% 222.24/31.07 | | REDUCE: (3), (6) imply:
% 222.24/31.07 | | (7) $false
% 222.24/31.07 | |
% 222.24/31.07 | | CLOSE: (7) is inconsistent.
% 222.24/31.07 | |
% 222.24/31.07 | End of split
% 222.24/31.07 |
% 222.24/31.07 End of proof
% 222.24/31.07
% 222.24/31.07 Sub-proof #21 shows that the following formulas are inconsistent:
% 222.24/31.07 ----------------------------------------------------------------
% 222.24/31.07 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 222.24/31.07 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (c_member(v4, v3, v2) = v1) | ~
% 222.24/31.07 (c_member(v4, v3, v2) = v0))
% 222.24/31.07 (2) c_member(all_625_1, all_870_7, v_L) = all_870_6
% 222.24/31.07 (3) c_member(all_625_1, all_870_7, v_L) = 0
% 222.24/31.07 (4) ~ (all_870_6 = 0)
% 222.24/31.07
% 222.24/31.07 Begin of proof
% 222.24/31.07 |
% 222.24/31.07 | GROUND_INST: instantiating (1) with all_870_6, 0, v_L, all_870_7, all_625_1,
% 222.24/31.07 | simplifying with (2), (3) gives:
% 222.24/31.07 | (5) all_870_6 = 0
% 222.24/31.07 |
% 222.24/31.07 | REDUCE: (4), (5) imply:
% 222.24/31.07 | (6) $false
% 222.24/31.07 |
% 222.24/31.07 | CLOSE: (6) is inconsistent.
% 222.24/31.07 |
% 222.24/31.07 End of proof
% 222.24/31.07 % SZS output end Proof for theBenchmark
% 222.24/31.07
% 222.24/31.07 30462ms
%------------------------------------------------------------------------------