TSTP Solution File: SWW474+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWW474+1 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n011.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 : Fri Sep 1 00:50:20 EDT 2023
% Result : Theorem 33.96s 5.29s
% Output : Proof 91.80s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SWW474+1 : TPTP v8.1.2. Released v5.3.0.
% 0.10/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n011.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Aug 27 22:18:40 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.59 ________ _____
% 0.19/0.59 ___ __ \_________(_)________________________________
% 0.19/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.59
% 0.19/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.59 (2023-06-19)
% 0.19/0.59
% 0.19/0.59 (c) Philipp Rümmer, 2009-2023
% 0.19/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.59 Amanda Stjerna.
% 0.19/0.59 Free software under BSD-3-Clause.
% 0.19/0.59
% 0.19/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.59
% 0.19/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.61 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
% 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 8.88/2.03 Prover 4: Preprocessing ...
% 9.45/2.06 Prover 1: Preprocessing ...
% 9.45/2.10 Prover 6: Preprocessing ...
% 9.45/2.10 Prover 3: Preprocessing ...
% 9.45/2.10 Prover 0: Preprocessing ...
% 9.45/2.10 Prover 5: Preprocessing ...
% 10.11/2.11 Prover 2: Preprocessing ...
% 26.79/4.31 Prover 1: Warning: ignoring some quantifiers
% 26.94/4.34 Prover 3: Warning: ignoring some quantifiers
% 26.94/4.41 Prover 1: Constructing countermodel ...
% 27.59/4.42 Prover 3: Constructing countermodel ...
% 27.59/4.44 Prover 6: Proving ...
% 30.87/4.85 Prover 5: Proving ...
% 30.87/4.88 Prover 4: Warning: ignoring some quantifiers
% 32.22/5.03 Prover 4: Constructing countermodel ...
% 32.58/5.11 Prover 0: Proving ...
% 33.96/5.28 Prover 3: proved (4656ms)
% 33.96/5.29
% 33.96/5.29 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 33.96/5.29
% 33.96/5.30 Prover 6: stopped
% 33.96/5.30 Prover 5: stopped
% 34.37/5.32 Prover 0: stopped
% 34.69/5.36 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 34.69/5.36 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 34.69/5.36 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 34.69/5.36 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 37.72/5.86 Prover 2: Proving ...
% 37.72/5.86 Prover 2: stopped
% 38.43/5.87 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 39.15/6.00 Prover 8: Preprocessing ...
% 39.71/6.05 Prover 10: Preprocessing ...
% 40.22/6.11 Prover 7: Preprocessing ...
% 40.89/6.17 Prover 11: Preprocessing ...
% 42.00/6.31 Prover 13: Preprocessing ...
% 46.15/6.86 Prover 10: Warning: ignoring some quantifiers
% 46.91/7.00 Prover 10: Constructing countermodel ...
% 46.91/7.03 Prover 8: Warning: ignoring some quantifiers
% 47.79/7.09 Prover 8: Constructing countermodel ...
% 47.79/7.10 Prover 7: Warning: ignoring some quantifiers
% 49.05/7.23 Prover 7: Constructing countermodel ...
% 49.48/7.33 Prover 13: Warning: ignoring some quantifiers
% 50.18/7.41 Prover 11: Warning: ignoring some quantifiers
% 50.78/7.49 Prover 13: Constructing countermodel ...
% 51.42/7.53 Prover 11: Constructing countermodel ...
% 76.35/10.84 Prover 13: stopped
% 76.35/10.86 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 78.56/11.13 Prover 16: Preprocessing ...
% 85.44/12.02 Prover 16: Warning: ignoring some quantifiers
% 86.72/12.12 Prover 16: Constructing countermodel ...
% 91.04/12.68 Prover 10: Found proof (size 202)
% 91.04/12.68 Prover 10: proved (7357ms)
% 91.04/12.68 Prover 7: stopped
% 91.04/12.68 Prover 16: stopped
% 91.04/12.68 Prover 1: stopped
% 91.04/12.68 Prover 11: stopped
% 91.04/12.68 Prover 8: stopped
% 91.22/12.71 Prover 4: stopped
% 91.22/12.71
% 91.22/12.71 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 91.22/12.71
% 91.35/12.75 % SZS output start Proof for theBenchmark
% 91.35/12.76 Assumptions after simplification:
% 91.35/12.76 ---------------------------------
% 91.35/12.76
% 91.35/12.76 (conj_0)
% 91.35/12.77 $i(hoare_165779456gleton) & hBOOL(hoare_165779456gleton)
% 91.35/12.77
% 91.35/12.77 (conj_1)
% 91.35/12.77 $i(wT_bodies) & hBOOL(wT_bodies)
% 91.35/12.77
% 91.35/12.77 (conj_2)
% 91.35/12.79 $i(fa) & $i(finite364844667_state) & ? [v0: $i] :
% 91.35/12.79 (hAPP_f971112728l_bool(finite364844667_state, fa) = v0 & $i(v0) & hBOOL(v0))
% 91.35/12.79
% 91.35/12.79 (conj_3)
% 91.35/12.79 $i(y) & $i(fa) & $i(member1338687867_state) & $i(hoare_Mirabelle_MGT) & ?
% 91.35/12.79 [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 91.35/12.79 (hAPP_H30606679l_bool(member1338687867_state, v0) = v1 &
% 91.35/12.79 hAPP_c1126217667_state(hoare_Mirabelle_MGT, y) = v0 &
% 91.35/12.79 hAPP_f971112728l_bool(v1, fa) = v2 & $i(v2) & $i(v1) & $i(v0) & ~
% 91.35/12.79 hBOOL(v2))
% 91.35/12.79
% 91.35/12.79 (conj_4)
% 91.35/12.79 $i(fa) & $i(body) & $i(the_com) & $i(hoare_Mirabelle_MGT) &
% 91.35/12.79 $i(ord_le1285840794e_bool) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3:
% 91.35/12.79 $i] : ? [v4: $i] : ? [v5: $i] :
% 91.35/12.79 (cOMBB_699532858_pname(hoare_Mirabelle_MGT, v1) = v2 &
% 91.35/12.79 cOMBB_923936821_pname(the_com, body) = v1 & image_2003357581_state(v2, v3) =
% 91.35/12.79 v4 & hAPP_f72706945l_bool(ord_le1285840794e_bool, fa) = v0 &
% 91.35/12.79 hAPP_f971112728l_bool(v0, v4) = v5 & dom_pname_com(body) = v3 & $i(v5) &
% 91.35/12.79 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & hBOOL(v5))
% 91.35/12.79
% 91.35/12.79 (conj_5)
% 91.35/12.80 $i(y) & $i(body) & $i(pn) & ? [v0: $i] : (some_com(y) = v0 &
% 91.35/12.80 hAPP_p799580910on_com(body, pn) = v0 & $i(v0))
% 91.35/12.80
% 91.35/12.80 (conj_6)
% 91.35/12.80 $i(fa) & $i(body) & $i(body_1) & $i(hoare_Mirabelle_MGT) & ? [v0: $i] : ?
% 91.35/12.80 [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 91.35/12.80 (cOMBB_699532858_pname(hoare_Mirabelle_MGT, body_1) = v0 &
% 91.35/12.80 image_2003357581_state(v0, v1) = v2 & hoare_1598289066_state(v2) = v3 &
% 91.35/12.80 hAPP_f971112728l_bool(v3, fa) = v4 & dom_pname_com(body) = v1 & $i(v4) &
% 91.35/12.80 $i(v3) & $i(v2) & $i(v1) & $i(v0) & hBOOL(v4))
% 91.35/12.80
% 91.35/12.80 (conj_7)
% 91.35/12.80 $i(y) & $i(body) & $i(body_1) & $i(hoare_Mirabelle_MGT) &
% 91.35/12.80 $i(bot_bo620288102e_bool) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3:
% 91.35/12.80 $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] :
% 91.35/12.80 (cOMBB_699532858_pname(hoare_Mirabelle_MGT, body_1) = v0 &
% 91.35/12.80 image_2003357581_state(v0, v1) = v2 &
% 91.35/12.80 hAPP_c1126217667_state(hoare_Mirabelle_MGT, y) = v4 &
% 91.35/12.80 insert1415133716_state(v4, bot_bo620288102e_bool) = v5 &
% 91.35/12.80 hoare_1598289066_state(v2) = v3 & hAPP_f971112728l_bool(v3, v5) = v6 &
% 91.35/12.80 dom_pname_com(body) = v1 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) &
% 91.35/12.80 $i(v1) & $i(v0) & ~ hBOOL(v6))
% 91.35/12.80
% 91.35/12.80 (fact_0_empty)
% 91.35/12.80 $i(bot_bo620288102e_bool) & ! [v0: $i] : ! [v1: $i] : ( ~
% 91.35/12.80 (hoare_1598289066_state(v0) = v1) | ~ $i(v0) | ? [v2: $i] :
% 91.35/12.80 (hAPP_f971112728l_bool(v1, bot_bo620288102e_bool) = v2 & $i(v2) &
% 91.35/12.80 hBOOL(v2)))
% 91.35/12.80
% 91.35/12.80 (fact_103_MGF)
% 91.35/12.80 $i(hoare_Mirabelle_MGT) & $i(bot_bo620288102e_bool) &
% 91.35/12.80 $i(hoare_165779456gleton) & $i(wT_bodies) & ? [v0: $i] :
% 91.35/12.80 (hoare_1598289066_state(bot_bo620288102e_bool) = v0 & $i(v0) & ! [v1: $i] :
% 91.35/12.80 ! [v2: $i] : ( ~ (hAPP_c1126217667_state(hoare_Mirabelle_MGT, v1) = v2) | ~
% 91.35/12.80 $i(v1) | ~ hBOOL(hoare_165779456gleton) | ~ hBOOL(wT_bodies) | ? [v3:
% 91.35/12.80 $i] : ? [v4: $i] : ? [v5: $i] : ((insert1415133716_state(v2,
% 91.35/12.80 bot_bo620288102e_bool) = v4 & hAPP_f971112728l_bool(v0, v4) = v5 &
% 91.35/12.80 $i(v5) & $i(v4) & hBOOL(v5)) | (wt(v1) = v3 & $i(v3) & ~
% 91.35/12.80 hBOOL(v3)))))
% 91.35/12.80
% 91.35/12.80 (fact_14_finite__imageI)
% 91.35/12.80 $i(finite364844667_state) & $i(finite_finite_pname) & ! [v0: $i] : ! [v1:
% 91.35/12.80 $i] : ! [v2: $i] : ( ~ (image_2003357581_state(v0, v1) = v2) | ~ $i(v1) |
% 91.35/12.80 ~ $i(v0) | ? [v3: $i] : ? [v4: $i] :
% 91.35/12.80 ((hAPP_f971112728l_bool(finite364844667_state, v2) = v4 & $i(v4) &
% 91.35/12.80 hBOOL(v4)) | (hAPP_f1664156314l_bool(finite_finite_pname, v1) = v3 &
% 91.35/12.80 $i(v3) & ~ hBOOL(v3))))
% 91.35/12.80
% 91.35/12.80 (fact_166_empty__def)
% 91.35/12.81 $i(bot_bo620288102e_bool) & $i(fFalse) & ? [v0: $i] :
% 91.35/12.81 (cOMBK_659609255_state(fFalse) = v0 & collec307967673_state(v0) =
% 91.35/12.81 bot_bo620288102e_bool & $i(v0))
% 91.35/12.81
% 91.35/12.81 (fact_173_insert__ident)
% 91.35/12.81 $i(member1338687867_state) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 91.35/12.81 $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 91.35/12.81 (hAPP_H30606679l_bool(member1338687867_state, v1) = v3) | ~
% 91.35/12.81 (hAPP_f971112728l_bool(v3, v2) = v4) | ~ (hAPP_f971112728l_bool(v3, v0) =
% 91.35/12.81 v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | hBOOL(v5) | hBOOL(v4) | ? [v6:
% 91.35/12.81 $i] : ? [v7: $i] : (( ~ (v2 = v0) | (v7 = v6 & insert1415133716_state(v1,
% 91.35/12.81 v0) = v6 & $i(v6))) & (v2 = v0 | ( ~ (v7 = v6) &
% 91.35/12.81 insert1415133716_state(v1, v2) = v6 & insert1415133716_state(v1, v0) =
% 91.35/12.81 v7 & $i(v7) & $i(v6)))))
% 91.35/12.81
% 91.35/12.81 (fact_181_insert__absorb2)
% 91.35/12.81 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~
% 91.35/12.81 (insert1415133716_state(v0, v2) = v3) | ~ (insert1415133716_state(v0, v1) =
% 91.35/12.81 v2) | ~ $i(v1) | ~ $i(v0))
% 91.35/12.81
% 91.35/12.81 (fact_234_finite__insert)
% 91.35/12.81 $i(finite364844667_state) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 91.35/12.81 (insert1415133716_state(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i]
% 91.35/12.81 : ? [v4: $i] : ((hAPP_f971112728l_bool(finite364844667_state, v2) = v4 &
% 91.35/12.81 $i(v4) & hBOOL(v4)) | (hAPP_f971112728l_bool(finite364844667_state, v1)
% 91.35/12.81 = v3 & $i(v3) & ~ hBOOL(v3)))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 91.35/12.81 $i] : ( ~ (insert1415133716_state(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ?
% 91.35/12.81 [v3: $i] : ? [v4: $i] : ((hAPP_f971112728l_bool(finite364844667_state, v2)
% 91.35/12.81 = v3 & $i(v3) & ~ hBOOL(v3)) |
% 91.35/12.81 (hAPP_f971112728l_bool(finite364844667_state, v1) = v4 & $i(v4) &
% 91.35/12.81 hBOOL(v4))))
% 91.35/12.81
% 91.35/12.81 (fact_244_finite__subset)
% 91.35/12.81 $i(ord_le313189616e_bool) & $i(finite_finite_pname) & ! [v0: $i] : ! [v1:
% 91.35/12.81 $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 91.35/12.81 (hAPP_f434788991l_bool(ord_le313189616e_bool, v0) = v2) | ~
% 91.35/12.81 (hAPP_f1664156314l_bool(v2, v1) = v3) | ~ $i(v1) | ~ $i(v0) | ~ hBOOL(v3)
% 91.35/12.81 | ? [v4: $i] : ? [v5: $i] : ((hAPP_f1664156314l_bool(finite_finite_pname,
% 91.35/12.81 v1) = v4 & $i(v4) & ~ hBOOL(v4)) |
% 91.35/12.81 (hAPP_f1664156314l_bool(finite_finite_pname, v0) = v5 & $i(v5) &
% 91.35/12.81 hBOOL(v5))))
% 91.35/12.81
% 91.35/12.81 (fact_245_finite__subset)
% 91.35/12.81 $i(finite364844667_state) & $i(ord_le1285840794e_bool) & ! [v0: $i] : ! [v1:
% 91.35/12.81 $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 91.35/12.81 (hAPP_f72706945l_bool(ord_le1285840794e_bool, v0) = v2) | ~
% 91.35/12.81 (hAPP_f971112728l_bool(v2, v1) = v3) | ~ $i(v1) | ~ $i(v0) | ~ hBOOL(v3)
% 91.35/12.81 | ? [v4: $i] : ? [v5: $i] : ((hAPP_f971112728l_bool(finite364844667_state,
% 91.35/12.81 v1) = v4 & $i(v4) & ~ hBOOL(v4)) |
% 91.35/12.81 (hAPP_f971112728l_bool(finite364844667_state, v0) = v5 & $i(v5) &
% 91.35/12.81 hBOOL(v5))))
% 91.35/12.81
% 91.35/12.81 (fact_248_rev__finite__subset)
% 91.35/12.81 $i(ord_le313189616e_bool) & $i(finite_finite_pname) & ! [v0: $i] : ! [v1:
% 91.35/12.81 $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 91.35/12.81 (hAPP_f434788991l_bool(ord_le313189616e_bool, v0) = v2) | ~
% 91.35/12.81 (hAPP_f1664156314l_bool(v2, v1) = v3) | ~ $i(v1) | ~ $i(v0) | ~ hBOOL(v3)
% 91.35/12.81 | ? [v4: $i] : ? [v5: $i] : ((hAPP_f1664156314l_bool(finite_finite_pname,
% 91.35/12.81 v1) = v4 & $i(v4) & ~ hBOOL(v4)) |
% 91.35/12.81 (hAPP_f1664156314l_bool(finite_finite_pname, v0) = v5 & $i(v5) &
% 91.35/12.81 hBOOL(v5))))
% 91.35/12.81
% 91.35/12.81 (fact_249_rev__finite__subset)
% 91.35/12.82 $i(finite364844667_state) & $i(ord_le1285840794e_bool) & ! [v0: $i] : ! [v1:
% 91.35/12.82 $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 91.35/12.82 (hAPP_f72706945l_bool(ord_le1285840794e_bool, v0) = v2) | ~
% 91.35/12.82 (hAPP_f971112728l_bool(v2, v1) = v3) | ~ $i(v1) | ~ $i(v0) | ~ hBOOL(v3)
% 91.35/12.82 | ? [v4: $i] : ? [v5: $i] : ((hAPP_f971112728l_bool(finite364844667_state,
% 91.35/12.82 v1) = v4 & $i(v4) & ~ hBOOL(v4)) |
% 91.35/12.82 (hAPP_f971112728l_bool(finite364844667_state, v0) = v5 & $i(v5) &
% 91.35/12.82 hBOOL(v5))))
% 91.35/12.82
% 91.35/12.82 (fact_255_Collect__def)
% 91.35/12.82 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (collec307967673_state(v0) = v1) |
% 91.35/12.82 ~ $i(v0))
% 91.35/12.82
% 91.35/12.82 (fact_269_subset__image__iff)
% 91.35/12.82 $i(ord_le313189616e_bool) & $i(ord_le1285840794e_bool) & ! [v0: $i] : ! [v1:
% 91.35/12.82 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] :
% 91.35/12.82 ! [v7: $i] : ! [v8: $i] : ( ~ (image_2003357581_state(v1, v2) = v4) | ~
% 91.35/12.82 (hAPP_f72706945l_bool(ord_le1285840794e_bool, v0) = v3) | ~
% 91.35/12.82 (hAPP_f971112728l_bool(v3, v4) = v5) | ~
% 91.35/12.82 (hAPP_f434788991l_bool(ord_le313189616e_bool, v6) = v7) | ~
% 91.35/12.82 (hAPP_f1664156314l_bool(v7, v2) = v8) | ~ $i(v6) | ~ $i(v2) | ~ $i(v1) |
% 91.35/12.82 ~ $i(v0) | ~ hBOOL(v8) | ~ is_fun_pname_bool(v6) | hBOOL(v5) | ? [v9: $i]
% 91.35/12.82 : ( ~ (v9 = v0) & image_2003357581_state(v1, v6) = v9 & $i(v9))) & ! [v0:
% 91.35/12.82 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] :
% 91.35/12.82 ( ~ (image_2003357581_state(v1, v2) = v4) | ~
% 91.35/12.82 (hAPP_f72706945l_bool(ord_le1285840794e_bool, v0) = v3) | ~
% 91.35/12.82 (hAPP_f971112728l_bool(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 91.35/12.82 ~ hBOOL(v5) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] :
% 91.35/12.82 (image_2003357581_state(v1, v6) = v0 &
% 91.35/12.82 hAPP_f434788991l_bool(ord_le313189616e_bool, v6) = v7 &
% 91.35/12.82 hAPP_f1664156314l_bool(v7, v2) = v8 & $i(v8) & $i(v7) & $i(v6) & hBOOL(v8)
% 91.35/12.82 & is_fun_pname_bool(v6)))
% 91.35/12.82
% 91.35/12.82 (fact_287_MGF__lemma1)
% 91.35/12.82 $i(member_pname) & $i(body) & $i(body_1) & $i(hoare_Mirabelle_MGT) &
% 91.35/12.82 $i(bot_bo620288102e_bool) & $i(hoare_165779456gleton) & ? [v0: $i] :
% 91.35/12.82 (dom_pname_com(body) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 91.35/12.82 ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 91.35/12.82 (hAPP_c1126217667_state(hoare_Mirabelle_MGT, v1) = v4) | ~
% 91.35/12.82 (insert1415133716_state(v4, bot_bo620288102e_bool) = v5) | ~
% 91.35/12.82 (hoare_1598289066_state(v2) = v3) | ~ (hAPP_f971112728l_bool(v3, v5) =
% 91.35/12.82 v6) | ~ $i(v2) | ~ $i(v1) | ~ hBOOL(hoare_165779456gleton) |
% 91.35/12.82 hBOOL(v6) | ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ?
% 91.35/12.82 [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : ($i(v8) &
% 91.35/12.82 ((hAPP_pname_com(body_1, v8) = v11 &
% 91.35/12.82 hAPP_c1126217667_state(hoare_Mirabelle_MGT, v11) = v12 &
% 91.35/12.82 insert1415133716_state(v12, bot_bo620288102e_bool) = v13 &
% 91.35/12.82 hAPP_f971112728l_bool(v3, v13) = v14 & hAPP_f1664156314l_bool(v9,
% 91.35/12.82 v0) = v10 & hAPP_p338031245l_bool(member_pname, v8) = v9 & $i(v14)
% 91.35/12.82 & $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & hBOOL(v10) &
% 91.35/12.82 is_pname(v8) & ~ hBOOL(v14)) | (wt(v1) = v7 & $i(v7) & ~
% 91.35/12.82 hBOOL(v7))))))
% 91.35/12.82
% 91.35/12.82 (fact_288_WT__bodiesD)
% 91.35/12.82 $i(body) & $i(wT_bodies) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 91.35/12.82 $i] : ( ~ (hAPP_p799580910on_com(body, v0) = v2) | ~ (wt(v1) = v3) | ~
% 91.35/12.82 $i(v1) | ~ $i(v0) | ~ hBOOL(wT_bodies) | hBOOL(v3) | ? [v4: $i] : ( ~ (v4
% 91.35/12.82 = v2) & some_com(v1) = v4 & $i(v4)))
% 91.35/12.82
% 91.35/12.82 (fact_298_finite__dom__body)
% 91.35/12.82 $i(body) & $i(finite_finite_pname) & ? [v0: $i] : ? [v1: $i] :
% 91.35/12.82 (hAPP_f1664156314l_bool(finite_finite_pname, v0) = v1 & dom_pname_com(body) =
% 91.35/12.82 v0 & $i(v1) & $i(v0) & hBOOL(v1))
% 91.35/12.82
% 91.35/12.82 (fact_4_cut)
% 91.35/12.82 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 91.35/12.82 $i] : ( ~ (hoare_1598289066_state(v0) = v3) | ~ (hAPP_f971112728l_bool(v3,
% 91.35/12.82 v2) = v5) | ~ (hAPP_f971112728l_bool(v3, v1) = v4) | ~ $i(v2) | ~
% 91.35/12.82 $i(v1) | ~ $i(v0) | ~ hBOOL(v4) | hBOOL(v5) | ? [v6: $i] : ? [v7: $i] :
% 91.35/12.83 (hoare_1598289066_state(v1) = v6 & hAPP_f971112728l_bool(v6, v2) = v7 &
% 91.35/12.83 $i(v7) & $i(v6) & ~ hBOOL(v7)))
% 91.35/12.83
% 91.35/12.83 (fact_6_derivs__insertD)
% 91.80/12.83 $i(bot_bo620288102e_bool) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 91.80/12.83 $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 91.80/12.83 (insert1415133716_state(v1, bot_bo620288102e_bool) = v4) | ~
% 91.80/12.83 (hoare_1598289066_state(v0) = v3) | ~ (hAPP_f971112728l_bool(v3, v4) = v5)
% 91.80/12.83 | ~ (hAPP_f971112728l_bool(v3, v2) = v6) | ~ $i(v2) | ~ $i(v1) | ~
% 91.80/12.83 $i(v0) | hBOOL(v6) | ? [v7: $i] : ? [v8: $i] : (insert1415133716_state(v1,
% 91.80/12.83 v2) = v7 & hAPP_f971112728l_bool(v3, v7) = v8 & $i(v8) & $i(v7) & ~
% 91.80/12.83 hBOOL(v8))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : !
% 91.80/12.83 [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (insert1415133716_state(v1,
% 91.80/12.83 bot_bo620288102e_bool) = v4) | ~ (hoare_1598289066_state(v0) = v3) | ~
% 91.80/12.83 (hAPP_f971112728l_bool(v3, v4) = v5) | ~ (hAPP_f971112728l_bool(v3, v2) =
% 91.80/12.83 v6) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | hBOOL(v5) | ? [v7: $i] : ?
% 91.80/12.83 [v8: $i] : (insert1415133716_state(v1, v2) = v7 & hAPP_f971112728l_bool(v3,
% 91.80/12.83 v7) = v8 & $i(v8) & $i(v7) & ~ hBOOL(v8)))
% 91.80/12.83
% 91.80/12.83 (gsy_c_Com_OWT__bodies)
% 91.80/12.83 $i(wT_bodies) & is_bool(wT_bodies)
% 91.80/12.83
% 91.80/12.83 (gsy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com__O_004)
% 91.80/12.83 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (hAPP_f971112728l_bool(v0, v1) =
% 91.80/12.83 v2) | ~ $i(v1) | ~ $i(v0) | is_bool(v2))
% 91.80/12.83
% 91.80/12.83 (help_fFalse_1_1_T)
% 91.80/12.83 $i(fTrue) & $i(fFalse) & ! [v0: $i] : (v0 = fTrue | v0 = fFalse | ~ $i(v0) |
% 91.80/12.83 ~ is_bool(v0))
% 91.80/12.83
% 91.80/12.83 (help_fFalse_1_1_U)
% 91.80/12.83 $i(fFalse) & ~ hBOOL(fFalse)
% 91.80/12.83
% 91.80/12.83 (function-axioms)
% 91.80/12.86 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 91.80/12.86 (hAPP_f2143399574l_bool(v3, v2) = v1) | ~ (hAPP_f2143399574l_bool(v3, v2) =
% 91.80/12.86 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 91.80/12.86 ~ (hAPP_f637090980l_bool(v3, v2) = v1) | ~ (hAPP_f637090980l_bool(v3, v2) =
% 91.80/12.86 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 91.80/12.86 ~ (hAPP_f32027384l_bool(v3, v2) = v1) | ~ (hAPP_f32027384l_bool(v3, v2) =
% 91.80/12.86 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 91.80/12.86 ~ (hAPP_H1187982158l_bool(v3, v2) = v1) | ~ (hAPP_H1187982158l_bool(v3, v2)
% 91.80/12.86 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0
% 91.80/12.86 | ~ (cOMBB_699532858_pname(v3, v2) = v1) | ~ (cOMBB_699532858_pname(v3,
% 91.80/12.86 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 91.80/12.86 = v0 | ~ (hAPP_f1476298914l_bool(v3, v2) = v1) | ~
% 91.80/12.86 (hAPP_f1476298914l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 91.80/12.86 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBB_923936821_pname(v3, v2) = v1) | ~
% 91.80/12.86 (cOMBB_923936821_pname(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 91.80/12.86 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_p393069232l_bool(v3, v2) = v1) | ~
% 91.80/12.86 (hAPP_p393069232l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 91.80/12.86 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_b589554111l_bool(v3, v2) = v1) | ~
% 91.80/12.86 (hAPP_b589554111l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 91.80/12.86 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f1201187855l_bool(v3, v2) = v1) | ~
% 91.80/12.86 (hAPP_f1201187855l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 91.80/12.86 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f98417237e_bool(v3, v2) = v1) | ~
% 91.80/12.86 (hAPP_f98417237e_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 91.80/12.86 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBB_1522210668e_bool(v3, v2) = v1) | ~
% 91.80/12.86 (cOMBB_1522210668e_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 91.80/12.86 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBB_2144135922_state(v3, v2) = v1) | ~
% 91.80/12.86 (cOMBB_2144135922_state(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 91.80/12.86 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_p1422361149_state(v3, v2) = v1) | ~
% 91.80/12.86 (hAPP_p1422361149_state(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 91.80/12.86 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f1387463497_state(v3, v2) = v1) | ~
% 91.80/12.86 (hAPP_f1387463497_state(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 91.80/12.86 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f888949707_state(v3, v2) = v1) | ~
% 91.80/12.86 (hAPP_f888949707_state(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 91.80/12.86 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_p442853985e_bool(v3, v2) = v1) | ~
% 91.80/12.86 (hAPP_p442853985e_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 91.80/12.86 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_H1049623551e_bool(v3, v2) = v1) | ~
% 91.80/12.86 (hAPP_H1049623551e_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 91.80/12.86 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f2134636538on_com(v3, v2) = v1) | ~
% 91.80/12.86 (hAPP_f2134636538on_com(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 91.80/12.86 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f2138803836on_com(v3, v2) = v1) | ~
% 91.80/12.86 (hAPP_f2138803836on_com(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 91.80/12.86 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f210337421l_bool(v3, v2) = v1) | ~
% 91.80/12.86 (hAPP_f210337421l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 91.80/12.86 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f556039215l_bool(v3, v2) = v1) | ~
% 91.80/12.86 (hAPP_f556039215l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 91.80/12.86 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_H30606679l_bool(v3, v2) = v1) | ~
% 91.80/12.86 (hAPP_H30606679l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 91.80/12.86 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBB_2095475776e_bool(v3, v2) = v1) | ~
% 91.80/12.86 (cOMBB_2095475776e_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 91.80/12.86 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBB_1585081418e_bool(v3, v2) = v1) | ~
% 91.80/12.86 (cOMBB_1585081418e_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 91.80/12.86 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBS_2066081387l_bool(v3, v2) = v1) | ~
% 91.80/12.86 (cOMBS_2066081387l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 91.80/12.86 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBB_404111180l_bool(v3, v2) = v1) | ~
% 91.80/12.86 (cOMBB_404111180l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 91.80/12.86 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBS_1358309691l_bool(v3, v2) = v1) | ~
% 91.80/12.86 (cOMBS_1358309691l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 91.80/12.86 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBB_689948150l_bool(v3, v2) = v1) | ~
% 91.80/12.86 (cOMBB_689948150l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 91.80/12.86 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBS_811933079l_bool(v3, v2) = v1) | ~
% 91.80/12.86 (cOMBS_811933079l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 91.80/12.86 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBB_962198420_state(v3, v2) = v1) | ~
% 91.80/12.86 (cOMBB_962198420_state(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 91.80/12.86 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBS_458705923l_bool(v3, v2) = v1) | ~
% 91.80/12.86 (cOMBS_458705923l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 91.80/12.86 $i] : ! [v3: $i] : (v1 = v0 | ~ (cOMBB_675860798_pname(v3, v2) = v1) | ~
% 91.80/12.86 (cOMBB_675860798_pname(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 91.80/12.86 $i] : ! [v3: $i] : (v1 = v0 | ~ (insert1556680138e_bool(v3, v2) = v1) | ~
% 91.80/12.86 (insert1556680138e_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 91.80/12.86 $i] : ! [v3: $i] : (v1 = v0 | ~ (insert203537868l_bool(v3, v2) = v1) | ~
% 91.80/12.86 (insert203537868l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 91.80/12.86 $i] : ! [v3: $i] : (v1 = v0 | ~ (insert1117693814l_bool(v3, v2) = v1) | ~
% 91.80/12.86 (insert1117693814l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 91.80/12.86 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_1828608335e_bool(v3, v2) = v1) | ~
% 91.80/12.86 (image_1828608335e_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 91.80/12.86 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_1761575943l_bool(v3, v2) = v1) | ~
% 91.80/12.86 (image_1761575943l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 91.80/12.86 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_1210605179l_bool(v3, v2) = v1) | ~
% 91.80/12.86 (image_1210605179l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 91.80/12.86 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_70449425e_bool(v3, v2) = v1) | ~
% 91.80/12.86 (image_70449425e_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 91.80/12.86 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_288317893l_bool(v3, v2) = v1) | ~
% 91.80/12.86 (image_288317893l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 91.80/12.86 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_1642285373l_bool(v3, v2) = v1) | ~
% 91.80/12.86 (image_1642285373l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 91.80/12.86 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_516545147_state(v3, v2) = v1) | ~
% 91.80/12.86 (image_516545147_state(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 91.80/12.86 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_18964633_state(v3, v2) = v1) | ~
% 91.80/12.86 (image_18964633_state(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 91.80/12.86 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_892968839_state(v3, v2) = v1) | ~
% 91.80/12.86 (image_892968839_state(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 91.80/12.86 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_677922117_state(v3, v2) = v1) | ~
% 91.80/12.86 (image_677922117_state(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 91.80/12.86 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_2003357581_state(v3, v2) = v1) | ~
% 91.80/12.86 (image_2003357581_state(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 91.80/12.86 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f510955609l_bool(v3, v2) = v1) | ~
% 91.80/12.86 (hAPP_f510955609l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 91.80/12.86 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f585161855l_bool(v3, v2) = v1) | ~
% 91.80/12.86 (hAPP_f585161855l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 91.80/12.86 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f667366769l_bool(v3, v2) = v1) | ~
% 91.80/12.86 (hAPP_f667366769l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 91.80/12.86 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f1759205631l_bool(v3, v2) = v1) | ~
% 91.80/12.86 (hAPP_f1759205631l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 91.80/12.86 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_pname_com(v3, v2) = v1) | ~
% 91.80/12.86 (hAPP_pname_com(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 91.80/12.86 ! [v3: $i] : (v1 = v0 | ~ (hAPP_p799580910on_com(v3, v2) = v1) | ~
% 91.80/12.86 (hAPP_p799580910on_com(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 91.80/12.86 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_option_com_com(v3, v2) = v1) | ~
% 91.80/12.86 (hAPP_option_com_com(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 91.80/12.86 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_c1126217667_state(v3, v2) = v1) | ~
% 91.80/12.86 (hAPP_c1126217667_state(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 91.80/12.86 $i] : ! [v3: $i] : (v1 = v0 | ~ (insert1415133716_state(v3, v2) = v1) | ~
% 91.80/12.86 (insert1415133716_state(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 91.80/12.86 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f72706945l_bool(v3, v2) = v1) | ~
% 91.80/12.86 (hAPP_f72706945l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 91.80/12.86 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f1022807134l_bool(v3, v2) = v1) | ~
% 91.80/12.86 (hAPP_f1022807134l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 91.80/12.86 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f595608956l_bool(v3, v2) = v1) | ~
% 91.80/12.86 (hAPP_f595608956l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 91.80/12.86 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f468958928l_bool(v3, v2) = v1) | ~
% 91.80/12.86 (hAPP_f468958928l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 91.80/12.86 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f389811538l_bool(v3, v2) = v1) | ~
% 91.80/12.86 (hAPP_f389811538l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 91.80/12.86 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f166538662l_bool(v3, v2) = v1) | ~
% 91.80/12.86 (hAPP_f166538662l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 91.80/12.86 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f559147733l_bool(v3, v2) = v1) | ~
% 91.80/12.86 (hAPP_f559147733l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 91.80/12.86 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f1935102916l_bool(v3, v2) = v1) | ~
% 91.80/12.86 (hAPP_f1935102916l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 91.80/12.86 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f971112728l_bool(v3, v2) = v1) | ~
% 91.80/12.86 (hAPP_f971112728l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 91.80/12.86 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f560369737_pname(v3, v2) = v1) | ~
% 91.80/12.86 (hAPP_f560369737_pname(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 91.80/12.86 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f434788991l_bool(v3, v2) = v1) | ~
% 91.80/12.86 (hAPP_f434788991l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 91.80/12.86 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f759274231e_bool(v3, v2) = v1) | ~
% 91.80/12.86 (hAPP_f759274231e_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 91.80/12.86 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f1664156314l_bool(v3, v2) = v1) | ~
% 91.80/12.86 (hAPP_f1664156314l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 91.80/12.86 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_f1297739591_pname(v3, v2) = v1) | ~
% 91.80/12.86 (hAPP_f1297739591_pname(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 91.80/12.86 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_H356885323e_bool(v3, v2) = v1) | ~
% 91.80/12.86 (hAPP_H356885323e_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 91.80/12.86 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_H78829294e_bool(v3, v2) = v1) | ~
% 91.80/12.86 (hAPP_H78829294e_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 91.80/12.86 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_H1621176307_pname(v3, v2) = v1) | ~
% 91.80/12.86 (hAPP_H1621176307_pname(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 91.80/12.86 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_bool_bool(v3, v2) = v1) | ~
% 91.80/12.86 (hAPP_bool_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 91.80/12.86 ! [v3: $i] : (v1 = v0 | ~ (hAPP_p338031245l_bool(v3, v2) = v1) | ~
% 91.80/12.86 (hAPP_p338031245l_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 91.80/12.86 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_p61793385e_bool(v3, v2) = v1) | ~
% 91.80/12.86 (hAPP_p61793385e_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 91.80/12.86 $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP_pname_bool(v3, v2) = v1) | ~
% 91.80/12.86 (hAPP_pname_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 91.80/12.86 ! [v3: $i] : (v1 = v0 | ~ (hAPP_pname_pname(v3, v2) = v1) | ~
% 91.80/12.86 (hAPP_pname_pname(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 91.80/12.86 ! [v3: $i] : (v1 = v0 | ~ (insert1325755072e_bool(v3, v2) = v1) | ~
% 91.80/12.86 (insert1325755072e_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 91.80/12.86 $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_pname(v3, v2) = v1) | ~
% 91.80/12.86 (insert_pname(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 91.80/12.86 [v3: $i] : (v1 = v0 | ~ (image_1619336331_pname(v3, v2) = v1) | ~
% 91.80/12.86 (image_1619336331_pname(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 91.80/12.86 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_1705983821_pname(v3, v2) = v1) | ~
% 91.80/12.86 (image_1705983821_pname(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 91.80/12.86 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_187965177_pname(v3, v2) = v1) | ~
% 91.80/12.86 (image_187965177_pname(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 91.80/12.86 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_1283814551_pname(v3, v2) = v1) | ~
% 91.80/12.86 (image_1283814551_pname(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 91.80/12.86 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_2131964411e_bool(v3, v2) = v1) | ~
% 91.80/12.86 (image_2131964411e_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 91.80/12.86 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_54689091_pname(v3, v2) = v1) | ~
% 91.80/12.86 (image_54689091_pname(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 91.80/12.86 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_47868345e_bool(v3, v2) = v1) | ~
% 91.80/12.86 (image_47868345e_bool(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 91.80/12.86 $i] : ! [v3: $i] : (v1 = v0 | ~ (image_pname_pname(v3, v2) = v1) | ~
% 91.80/12.86 (image_pname_pname(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 91.80/12.86 : ! [v3: $i] : (v1 = v0 | ~ (fun(v3, v2) = v1) | ~ (fun(v3, v2) = v0)) & !
% 91.80/12.86 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 91.80/12.86 (cOMBS_350070575l_bool(v3, v2) = v1) | ~ (cOMBS_350070575l_bool(v3, v2) =
% 91.80/12.86 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 91.80/12.86 ~ (cOMBS_568398431l_bool(v3, v2) = v1) | ~ (cOMBS_568398431l_bool(v3, v2) =
% 91.80/12.86 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 91.80/12.86 ~ (cOMBB_307249310e_bool(v3, v2) = v1) | ~ (cOMBB_307249310e_bool(v3, v2) =
% 91.80/12.86 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 91.80/12.86 ~ (cOMBB_647938656_pname(v3, v2) = v1) | ~ (cOMBB_647938656_pname(v3, v2) =
% 91.80/12.86 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 91.80/12.86 (cOMBC_1114453604l_bool(v2) = v1) | ~ (cOMBC_1114453604l_bool(v2) = v0)) &
% 91.80/12.86 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 91.80/12.86 (cOMBC_1988546018l_bool(v2) = v1) | ~ (cOMBC_1988546018l_bool(v2) = v0)) &
% 91.80/12.86 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 91.80/12.86 (cOMBC_1734175330l_bool(v2) = v1) | ~ (cOMBC_1734175330l_bool(v2) = v0)) &
% 91.80/12.86 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 91.80/12.86 (cOMBC_1058051404l_bool(v2) = v1) | ~ (cOMBC_1058051404l_bool(v2) = v0)) &
% 91.80/12.86 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 91.80/12.86 (cOMBC_654211620e_bool(v2) = v1) | ~ (cOMBC_654211620e_bool(v2) = v0)) & !
% 91.80/12.86 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 91.80/12.86 (cOMBC_1149511130e_bool(v2) = v1) | ~ (cOMBC_1149511130e_bool(v2) = v0)) &
% 91.80/12.86 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 91.80/12.86 (cOMBK_659609255_state(v2) = v1) | ~ (cOMBK_659609255_state(v2) = v0)) & !
% 91.80/12.86 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 91.80/12.87 (cOMBK_129401207e_bool(v2) = v1) | ~ (cOMBK_129401207e_bool(v2) = v0)) & !
% 91.80/12.87 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 91.80/12.87 (cOMBK_482404831l_bool(v2) = v1) | ~ (cOMBK_482404831l_bool(v2) = v0)) & !
% 91.80/12.87 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 91.80/12.87 (dom_fu1342267980ol_com(v2) = v1) | ~ (dom_fu1342267980ol_com(v2) = v0)) &
% 91.80/12.87 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (some_com(v2) = v1) |
% 91.80/12.87 ~ (some_com(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0
% 91.80/12.87 | ~ (cOMBK_1589414042e_bool(v2) = v1) | ~ (cOMBK_1589414042e_bool(v2) =
% 91.80/12.87 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 91.80/12.87 (cOMBK_948730864e_bool(v2) = v1) | ~ (cOMBK_948730864e_bool(v2) = v0)) & !
% 91.80/12.87 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 91.80/12.87 (cOMBK_701929478e_bool(v2) = v1) | ~ (cOMBK_701929478e_bool(v2) = v0)) & !
% 91.80/12.87 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 91.80/12.87 (cOMBK_1503445380e_bool(v2) = v1) | ~ (cOMBK_1503445380e_bool(v2) = v0)) &
% 91.80/12.87 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (cOMBK_pname_pname(v2)
% 91.80/12.87 = v1) | ~ (cOMBK_pname_pname(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 91.80/12.87 [v2: $i] : (v1 = v0 | ~ (cOMBK_1706929794_pname(v2) = v1) | ~
% 91.80/12.87 (cOMBK_1706929794_pname(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 91.80/12.87 : (v1 = v0 | ~ (cOMBK_37193422_pname(v2) = v1) | ~ (cOMBK_37193422_pname(v2)
% 91.80/12.87 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 91.80/12.87 (cOMBK_1039769424_state(v2) = v1) | ~ (cOMBK_1039769424_state(v2) = v0)) &
% 91.80/12.87 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 91.80/12.87 (cOMBK_2035509764_state(v2) = v1) | ~ (cOMBK_2035509764_state(v2) = v0)) &
% 91.80/12.87 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 91.80/12.87 (cOMBK_168215364_state(v2) = v1) | ~ (cOMBK_168215364_state(v2) = v0)) & !
% 91.80/12.87 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 91.80/12.87 (cOMBK_367030522_pname(v2) = v1) | ~ (cOMBK_367030522_pname(v2) = v0)) & !
% 91.80/12.87 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 91.80/12.87 (collec307967673_state(v2) = v1) | ~ (collec307967673_state(v2) = v0)) & !
% 91.80/12.87 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (cOMBC_7971162l_bool(v2)
% 91.80/12.87 = v1) | ~ (cOMBC_7971162l_bool(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 91.80/12.87 ! [v2: $i] : (v1 = v0 | ~ (collec1613912337l_bool(v2) = v1) | ~
% 91.80/12.87 (collec1613912337l_bool(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 91.80/12.87 : (v1 = v0 | ~ (cOMBC_1691491604l_bool(v2) = v1) | ~
% 91.80/12.87 (cOMBC_1691491604l_bool(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 91.80/12.87 : (v1 = v0 | ~ (collec488126193l_bool(v2) = v1) | ~
% 91.80/12.87 (collec488126193l_bool(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 91.80/12.87 : (v1 = v0 | ~ (cOMBC_747715418l_bool(v2) = v1) | ~
% 91.80/12.87 (cOMBC_747715418l_bool(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 91.80/12.87 : (v1 = v0 | ~ (collec256567069l_bool(v2) = v1) | ~
% 91.80/12.87 (collec256567069l_bool(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 91.80/12.87 : (v1 = v0 | ~ (cOMBC_336095980l_bool(v2) = v1) | ~
% 91.80/12.87 (cOMBC_336095980l_bool(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 91.80/12.87 : (v1 = v0 | ~ (collec792590109l_bool(v2) = v1) | ~
% 91.80/12.87 (collec792590109l_bool(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 91.80/12.87 : (v1 = v0 | ~ (cOMBC_449066458l_bool(v2) = v1) | ~
% 91.80/12.87 (cOMBC_449066458l_bool(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 91.80/12.87 : (v1 = v0 | ~ (collec1823980261e_bool(v2) = v1) | ~
% 91.80/12.87 (collec1823980261e_bool(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 91.80/12.87 : (v1 = v0 | ~ (cOMBC_1284144636l_bool(v2) = v1) | ~
% 91.80/12.87 (cOMBC_1284144636l_bool(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 91.80/12.87 : (v1 = v0 | ~ (hoare_1598289066_state(v2) = v1) | ~
% 91.80/12.87 (hoare_1598289066_state(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 91.80/12.87 : (v1 = v0 | ~ (collec1974731493e_bool(v2) = v1) | ~
% 91.80/12.87 (collec1974731493e_bool(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 91.80/12.87 : (v1 = v0 | ~ (collect_pname(v2) = v1) | ~ (collect_pname(v2) = v0)) & !
% 91.80/12.87 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 91.80/12.87 (dom_fu2081503504ol_com(v2) = v1) | ~ (dom_fu2081503504ol_com(v2) = v0)) &
% 91.80/12.87 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (dom_pname_com(v2) =
% 91.80/12.87 v1) | ~ (dom_pname_com(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 91.80/12.87 $i] : (v1 = v0 | ~ (undefi64961550l_bool(v2) = v1) | ~
% 91.80/12.87 (undefi64961550l_bool(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 91.80/12.87 (v1 = v0 | ~ (undefi17486888e_bool(v2) = v1) | ~ (undefi17486888e_bool(v2) =
% 91.80/12.87 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 91.80/12.87 (undefined_pname(v2) = v1) | ~ (undefined_pname(v2) = v0)) & ! [v0: $i] :
% 91.80/12.87 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (wt(v2) = v1) | ~ (wt(v2) = v0)) &
% 91.80/12.87 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 91.80/12.87 (cOMBK_1857069011e_bool(v2) = v1) | ~ (cOMBK_1857069011e_bool(v2) = v0)) &
% 91.80/12.87 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (cOMBK_bool_pname(v2) =
% 91.80/12.87 v1) | ~ (cOMBK_bool_pname(v2) = v0))
% 91.80/12.87
% 91.80/12.87 Further assumptions not needed in the proof:
% 91.80/12.87 --------------------------------------------
% 91.80/12.87 fact_100_subset__singletonD, fact_101_subset__singletonD,
% 91.80/12.87 fact_102_subset__singletonD, fact_104_emptyE, fact_105_emptyE, fact_106_emptyE,
% 91.80/12.87 fact_107_emptyE, fact_108_insertCI, fact_109_insertCI,
% 91.80/12.87 fact_10_finite__Collect__subsets, fact_110_insertCI, fact_111_insertCI,
% 91.80/12.87 fact_112_insertE, fact_113_insertE, fact_114_insertE, fact_115_insertE,
% 91.80/12.87 fact_116_equalityI, fact_117_equalityI, fact_118_equalityI, fact_119_equalityI,
% 91.80/12.87 fact_11_finite__Collect__subsets, fact_120_subsetD, fact_121_subsetD,
% 91.80/12.87 fact_122_subsetD, fact_123_subsetD, fact_124_image__eqI, fact_125_image__eqI,
% 91.80/12.87 fact_126_image__eqI, fact_127_image__eqI, fact_128_image__eqI,
% 91.80/12.87 fact_129_image__eqI, fact_12_finite__Collect__subsets, fact_130_image__eqI,
% 91.80/12.87 fact_131_image__eqI, fact_132_image__eqI, fact_133_image__eqI,
% 91.80/12.87 fact_134_image__eqI, fact_135_equals0D, fact_136_equals0D, fact_137_equals0D,
% 91.80/12.87 fact_138_equals0D, fact_139_Collect__empty__eq,
% 91.80/12.87 fact_13_finite__Collect__subsets, fact_140_Collect__empty__eq,
% 91.80/12.87 fact_141_Collect__empty__eq, fact_142_Collect__empty__eq,
% 91.80/12.87 fact_143_Collect__empty__eq, fact_144_Collect__empty__eq, fact_145_empty__iff,
% 91.80/12.87 fact_146_empty__iff, fact_147_empty__iff, fact_148_empty__iff,
% 91.80/12.87 fact_149_empty__Collect__eq, fact_150_empty__Collect__eq,
% 91.80/12.87 fact_151_empty__Collect__eq, fact_152_empty__Collect__eq,
% 91.80/12.87 fact_153_empty__Collect__eq, fact_154_empty__Collect__eq, fact_155_ex__in__conv,
% 91.80/12.87 fact_156_ex__in__conv, fact_157_ex__in__conv, fact_158_ex__in__conv,
% 91.80/12.87 fact_159_all__not__in__conv, fact_15_finite__imageI,
% 91.80/12.87 fact_160_all__not__in__conv, fact_161_all__not__in__conv,
% 91.80/12.87 fact_162_all__not__in__conv, fact_163_empty__def, fact_164_empty__def,
% 91.80/12.87 fact_165_empty__def, fact_167_empty__def, fact_168_insert__absorb,
% 91.80/12.87 fact_169_insert__absorb, fact_16_finite__imageI, fact_170_insertI2,
% 91.80/12.87 fact_171_insertI2, fact_172_insert__ident, fact_174_insert__code,
% 91.80/12.87 fact_175_insert__code, fact_176_insert__iff, fact_177_insert__iff,
% 91.80/12.87 fact_178_insert__commute, fact_179_insert__commute, fact_17_finite__imageI,
% 91.80/12.87 fact_180_insert__absorb2, fact_182_insert__Collect, fact_183_insert__Collect,
% 91.80/12.87 fact_184_insert__Collect, fact_185_insert__Collect, fact_186_insert__compr,
% 91.80/12.87 fact_187_insert__compr, fact_188_insert__compr, fact_189_insert__compr,
% 91.80/12.87 fact_18_finite__imageI, fact_190_insertI1, fact_191_insertI1,
% 91.80/12.87 fact_192_equalityE, fact_193_equalityE, fact_194_subset__trans,
% 91.80/12.87 fact_195_subset__trans, fact_196_set__mp, fact_197_set__mp,
% 91.80/12.87 fact_198_set__rev__mp, fact_199_set__rev__mp, fact_19_finite__imageI,
% 91.80/12.87 fact_1_asm, fact_200_in__mono, fact_201_in__mono, fact_202_equalityD2,
% 91.80/12.87 fact_203_equalityD2, fact_204_equalityD1, fact_205_equalityD1,
% 91.80/12.87 fact_206_set__eq__subset, fact_207_set__eq__subset, fact_208_subset__refl,
% 91.80/12.87 fact_209_subset__refl, fact_20_finite__imageI, fact_210_rev__image__eqI,
% 91.80/12.87 fact_211_imageI, fact_212_image__iff, fact_213_finite__Collect__disjI,
% 91.80/12.87 fact_214_finite__Collect__disjI, fact_215_finite__Collect__disjI,
% 91.80/12.87 fact_216_finite__Collect__disjI, fact_217_insert__compr__raw,
% 91.80/12.87 fact_218_insert__compr__raw, fact_219_insert__compr__raw,
% 91.80/12.87 fact_21_finite__imageI, fact_220_insert__compr__raw, fact_221_singleton__inject,
% 91.80/12.87 fact_222_singleton__inject, fact_223_singletonE, fact_224_singletonE,
% 91.80/12.87 fact_225_doubleton__eq__iff, fact_226_doubleton__eq__iff,
% 91.80/12.87 fact_227_singleton__iff, fact_228_singleton__iff, fact_229_insert__not__empty,
% 91.80/12.87 fact_22_finite__imageI, fact_230_insert__not__empty,
% 91.80/12.87 fact_231_empty__not__insert, fact_232_empty__not__insert,
% 91.80/12.87 fact_233_finite__insert, fact_235_finite__insert, fact_236_finite__insert,
% 91.80/12.87 fact_237_subset__empty, fact_238_subset__empty, fact_239_image__is__empty,
% 91.80/12.87 fact_23_finite__imageI, fact_240_image__empty, fact_241_empty__is__image,
% 91.80/12.87 fact_242_finite__subset, fact_243_finite__subset, fact_246_rev__finite__subset,
% 91.80/12.87 fact_247_rev__finite__subset, fact_24_finite__imageI, fact_250_insert__mono,
% 91.80/12.87 fact_251_insert__mono, fact_252_mem__def, fact_253_mem__def,
% 91.80/12.87 fact_254_Collect__def, fact_256_Collect__def, fact_257_Collect__def,
% 91.80/12.87 fact_258_subset__insertI2, fact_259_subset__insertI2, fact_25_finite__imageI,
% 91.80/12.87 fact_260_subset__insert, fact_261_subset__insert, fact_262_insert__subset,
% 91.80/12.87 fact_263_insert__subset, fact_264_subset__insertI, fact_265_subset__insertI,
% 91.80/12.87 fact_266_insert__image, fact_267_image__insert, fact_268_image__mono,
% 91.80/12.87 fact_26_finite__imageI, fact_270_domI, fact_271_Collect__conv__if,
% 91.80/12.87 fact_272_Collect__conv__if, fact_273_Collect__conv__if,
% 91.80/12.87 fact_274_Collect__conv__if, fact_275_Collect__conv__if2,
% 91.80/12.87 fact_276_Collect__conv__if2, fact_277_Collect__conv__if2,
% 91.80/12.87 fact_278_Collect__conv__if2, fact_279_singleton__conv, fact_27_finite__imageI,
% 91.80/12.87 fact_280_singleton__conv, fact_281_singleton__conv, fact_282_singleton__conv,
% 91.80/12.87 fact_283_singleton__conv2, fact_284_singleton__conv2, fact_285_singleton__conv2,
% 91.80/12.87 fact_286_singleton__conv2, fact_289_imageE, fact_28_finite__imageI,
% 91.80/12.87 fact_290_finite__subset__induct, fact_291_finite__subset__induct,
% 91.80/12.87 fact_292_finite__subset__induct, fact_293_finite__subset__induct,
% 91.80/12.87 fact_294_WTs__elim__cases_I7_J, fact_295_subsetI, fact_296_subsetI,
% 91.80/12.87 fact_297_finite__subset__image, fact_299_com_Osimps_I6_J,
% 91.80/12.87 fact_29_finite__imageI, fact_2_weaken, fact_30_finite__imageI,
% 91.80/12.87 fact_31_finite__imageI, fact_32_finite__imageI, fact_33_empty__subsetI,
% 91.80/12.87 fact_34_empty__subsetI, fact_35_empty__subsetI, fact_36_empty__subsetI,
% 91.80/12.87 fact_37_finite_OinsertI, fact_38_finite_OinsertI, fact_39_finite_OinsertI,
% 91.80/12.87 fact_3_thin, fact_40_finite_OinsertI, fact_41_finite_OinsertI,
% 91.80/12.87 fact_42_finite_OinsertI, fact_43_finite_OemptyI, fact_44_finite_OemptyI,
% 91.80/12.87 fact_45_finite_OemptyI, fact_46_finite_OemptyI, fact_47_finite_OemptyI,
% 91.80/12.87 fact_48_finite_OemptyI, fact_49_finite__Collect__conjI,
% 91.80/12.87 fact_50_finite__Collect__conjI, fact_51_finite__Collect__conjI,
% 91.80/12.87 fact_52_finite__Collect__conjI, fact_53_finite__Collect__conjI,
% 91.80/12.87 fact_54_finite__Collect__conjI, fact_55_image__constant__conv,
% 91.80/12.87 fact_56_image__constant__conv, fact_57_image__constant__conv,
% 91.80/12.87 fact_58_image__constant__conv, fact_59_image__constant__conv,
% 91.80/12.87 fact_5_hoare__derivs_Oinsert, fact_60_image__constant__conv,
% 91.80/12.87 fact_61_image__constant__conv, fact_62_image__constant__conv,
% 91.80/12.87 fact_63_image__constant__conv, fact_64_image__constant__conv,
% 91.80/12.87 fact_65_image__constant__conv, fact_66_image__constant, fact_67_image__constant,
% 91.80/12.87 fact_68_image__constant, fact_69_image__constant, fact_70_image__constant,
% 91.80/12.87 fact_71_image__constant, fact_72_image__constant, fact_73_image__constant,
% 91.80/12.87 fact_74_image__constant, fact_75_image__constant, fact_76_image__constant,
% 91.80/12.87 fact_77_insert__dom, fact_78_insert__dom, fact_79_insert__dom,
% 91.80/12.87 fact_7_MGT__BodyN, fact_80_finite__surj, fact_81_finite__surj,
% 91.80/12.87 fact_82_finite__surj, fact_83_finite__surj, fact_84_finite__surj,
% 91.80/12.87 fact_85_finite__surj, fact_86_finite__surj, fact_87_finite__surj,
% 91.80/12.87 fact_88_finite__surj, fact_89_finite__surj, fact_8_finite__Collect__subsets,
% 91.80/12.87 fact_90_finite__surj, fact_91_finite__surj, fact_92_finite__surj,
% 91.80/12.87 fact_93_finite__surj, fact_94_finite__surj, fact_95_finite__surj,
% 91.80/12.87 fact_96_finite__surj, fact_97_finite__surj, fact_98_finite__surj,
% 91.80/12.87 fact_99_subset__singletonD, fact_9_finite__Collect__subsets,
% 91.80/12.87 gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Opname,
% 91.80/12.87 gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Com__Opname_Mtc_,
% 91.80/12.87 gsy_c_COMBK_000tc__HOL__Obool_000tc__Com__Opname,
% 91.80/12.87 gsy_c_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,
% 91.80/12.87 gsy_c_COMBS_000tc__Com__Opname_000tc__HOL__Obool_000tc__HOL__Obool,
% 91.80/12.87 gsy_c_COMBS_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__Obool_000t,
% 91.80/12.87 gsy_c_Com_OWT, gsy_c_Finite__Set_Ofinite_000tc__Com__Opname,
% 91.80/12.87 gsy_c_HOL_Oundefined_000tc__Com__Opname,
% 91.80/12.87 gsy_c_HOL_Oundefined_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,
% 91.80/12.87 gsy_c_HOL_Oundefined_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc_,
% 91.80/12.87 gsy_c_Hoare__Mirabelle__jfehddehev_Ostate__not__singleton,
% 91.80/12.87 gsy_c_Map_Odom_000tc__Com__Opname_000tc__Com__Ocom,
% 91.80/12.87 gsy_c_Map_Odom_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Com__Ocom,
% 91.80/12.87 gsy_c_Orderings_Obot__class_Obot_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,
% 91.80/12.87 gsy_c_Orderings_Obot__class_Obot_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__,
% 91.80/12.87 gsy_c_Set_OCollect_000tc__Com__Opname,
% 91.80/12.87 gsy_c_Set_OCollect_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,
% 91.80/12.87 gsy_c_Set_Oimage_000tc__Com__Opname_000tc__Com__Opname,
% 91.80/12.87 gsy_c_Set_Oimage_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_,
% 91.80/12.87 gsy_c_Set_Oimage_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com__Osta,
% 91.80/12.87 gsy_c_Set_Oimage_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com__Osta_001,
% 91.80/12.87 gsy_c_Set_Oimage_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Com__Opnam,
% 91.80/12.87 gsy_c_Set_Oimage_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__,
% 91.80/12.87 gsy_c_Set_Oimage_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL,
% 91.80/12.87 gsy_c_Set_Oimage_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otri,
% 91.80/12.87 gsy_c_Set_Oinsert_000tc__Com__Opname,
% 91.80/12.87 gsy_c_Set_Oinsert_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J, gsy_c_fFalse,
% 91.80/12.87 gsy_c_fTrue, gsy_c_hAPP_000tc__Com__Opname_000tc__Com__Opname,
% 91.80/12.87 gsy_c_hAPP_000tc__Com__Opname_000tc__HOL__Obool,
% 91.80/12.87 gsy_c_hAPP_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,
% 91.80/12.87 gsy_c_hAPP_000tc__Com__Opname_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obo,
% 91.80/12.87 gsy_c_hAPP_000tc__HOL__Obool_000tc__HOL__Obool,
% 91.80/12.87 gsy_c_hAPP_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com__Ostate_J_0,
% 91.80/12.87 gsy_c_hAPP_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com__Ostate_J_0_002,
% 91.80/12.87 gsy_c_hAPP_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com__Ostate_J_0_003,
% 91.80/12.87 gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Com__Opname,
% 91.80/12.87 gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__Obool,
% 91.80/12.87 gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_Itc__Com__Op,
% 91.80/12.87 gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_Itc,
% 91.80/12.87 gsy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com__O,
% 91.80/12.87 gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL__Oboo,
% 91.80/12.87 gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL__Oboo_005,
% 91.80/12.87 gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple_It,
% 91.80/12.87 gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__,
% 91.80/12.87 gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Hoare____Mirabelle____jfehddehev__O,
% 91.80/12.87 gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Oboo,
% 91.80/12.87 gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Hoare____Mirabelle____jfeh,
% 91.80/12.87 gsy_v_pn,
% 91.80/12.87 help_COMBB_1_1_COMBB_000tc__Com__Ocom_000tc__Hoare____Mirabelle____jfehddehev__O,
% 91.80/12.87 help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Opname_U,
% 91.80/12.87 help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Hoare____Mirabel,
% 91.80/12.87 help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Com__Op,
% 91.80/12.87 help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Hoare__,
% 91.80/12.87 help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo,
% 91.80/12.87 help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_006,
% 91.80/12.87 help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_008,
% 91.80/12.87 help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_009,
% 91.80/12.87 help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_011,
% 91.80/12.87 help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_015,
% 91.80/12.87 help_COMBB_1_1_COMBB_000tc__Option__Ooption_Itc__Com__Ocom_J_000tc__Com__Ocom_00,
% 91.80/12.87 help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__Com__Opname_000tc__HOL__Obool_U,
% 91.80/12.87 help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob,
% 91.80/12.87 help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com__,
% 91.80/12.87 help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com___014,
% 91.80/12.87 help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It,
% 91.80/12.87 help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_010,
% 91.80/12.87 help_COMBC_1_1_COMBC_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple_I,
% 91.80/12.87 help_COMBC_1_1_COMBC_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple_I_016,
% 91.80/12.87 help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc_,
% 91.80/12.87 help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____jfehddehev__,
% 91.80/12.87 help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obo,
% 91.80/12.87 help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__fun_Itc__Hoare____Mirabelle____jfe,
% 91.80/12.87 help_COMBK_1_1_COMBK_000tc__Com__Opname_000tc__Com__Opname_U,
% 91.80/12.87 help_COMBK_1_1_COMBK_000tc__Com__Opname_000tc__Hoare____Mirabelle____jfehddehev_,
% 91.80/12.87 help_COMBK_1_1_COMBK_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob,
% 91.80/12.87 help_COMBK_1_1_COMBK_000tc__Com__Opname_000tc__fun_Itc__Hoare____Mirabelle____jf,
% 91.80/12.87 help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Com__Opname_U,
% 91.80/12.87 help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Hoare____Mirabelle____jfehddehev__,
% 91.80/12.87 help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obo,
% 91.80/12.87 help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Hoare____Mirabelle____jfe,
% 91.80/12.87 help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__Hoare____Mirabel,
% 91.80/12.87 help_COMBK_1_1_COMBK_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com__,
% 91.80/12.87 help_COMBK_1_1_COMBK_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com___007,
% 91.80/12.87 help_COMBK_1_1_COMBK_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com___012,
% 91.80/12.87 help_COMBK_1_1_COMBK_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Com__O,
% 91.80/12.87 help_COMBK_1_1_COMBK_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Hoare_,
% 91.80/12.87 help_COMBK_1_1_COMBK_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple_I,
% 91.80/12.87 help_COMBK_1_1_COMBK_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple_I_013,
% 91.80/12.87 help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__HOL__Obool_000tc__HOL__Obool_U,
% 91.80/12.87 help_COMBS_1_1_COMBS_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com__,
% 91.80/12.87 help_COMBS_1_1_COMBS_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__O,
% 91.80/12.87 help_COMBS_1_1_COMBS_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple_I,
% 91.80/12.87 help_COMBS_1_1_COMBS_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc_,
% 91.80/12.87 help_COMBS_1_1_COMBS_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____jfehddehev__,
% 91.80/12.87 help_fNot_1_1_U, help_fNot_2_1_U, help_fconj_1_1_U, help_fconj_2_1_U,
% 91.80/12.87 help_fconj_3_1_U, help_fdisj_1_1_U, help_fdisj_2_1_U, help_fdisj_3_1_U,
% 91.80/12.87 help_fequal_1_1_fequal_000tc__Com__Opname_T,
% 91.80/12.87 help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com,
% 91.80/12.87 help_fequal_1_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T,
% 91.80/12.87 help_fequal_1_1_fequal_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple,
% 91.80/12.87 help_fequal_2_1_fequal_000tc__Com__Opname_T,
% 91.80/12.87 help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com,
% 91.80/12.87 help_fequal_2_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T,
% 91.80/12.87 help_fequal_2_1_fequal_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple,
% 91.80/12.87 help_fimplies_1_1_U, help_fimplies_2_1_U, help_fimplies_3_1_U
% 91.80/12.87
% 91.80/12.87 Those formulas are unsatisfiable:
% 91.80/12.87 ---------------------------------
% 91.80/12.87
% 91.80/12.87 Begin of proof
% 91.80/12.87 |
% 91.80/12.87 | ALPHA: (gsy_c_Com_OWT__bodies) implies:
% 91.80/12.87 | (1) is_bool(wT_bodies)
% 91.80/12.87 |
% 91.80/12.87 | ALPHA: (fact_0_empty) implies:
% 91.80/12.88 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (hoare_1598289066_state(v0) = v1) | ~
% 91.80/12.88 | $i(v0) | ? [v2: $i] : (hAPP_f971112728l_bool(v1,
% 91.80/12.88 | bot_bo620288102e_bool) = v2 & $i(v2) & hBOOL(v2)))
% 91.80/12.88 |
% 91.80/12.88 | ALPHA: (fact_6_derivs__insertD) implies:
% 91.80/12.88 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 91.80/12.88 | ! [v5: $i] : ! [v6: $i] : ( ~ (insert1415133716_state(v1,
% 91.80/12.88 | bot_bo620288102e_bool) = v4) | ~ (hoare_1598289066_state(v0) =
% 91.80/12.88 | v3) | ~ (hAPP_f971112728l_bool(v3, v4) = v5) | ~
% 91.80/12.88 | (hAPP_f971112728l_bool(v3, v2) = v6) | ~ $i(v2) | ~ $i(v1) | ~
% 91.80/12.88 | $i(v0) | hBOOL(v5) | ? [v7: $i] : ? [v8: $i] :
% 91.80/12.88 | (insert1415133716_state(v1, v2) = v7 & hAPP_f971112728l_bool(v3, v7)
% 91.80/12.88 | = v8 & $i(v8) & $i(v7) & ~ hBOOL(v8)))
% 91.80/12.88 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 91.80/12.88 | ! [v5: $i] : ! [v6: $i] : ( ~ (insert1415133716_state(v1,
% 91.80/12.88 | bot_bo620288102e_bool) = v4) | ~ (hoare_1598289066_state(v0) =
% 91.80/12.88 | v3) | ~ (hAPP_f971112728l_bool(v3, v4) = v5) | ~
% 91.80/12.88 | (hAPP_f971112728l_bool(v3, v2) = v6) | ~ $i(v2) | ~ $i(v1) | ~
% 91.80/12.88 | $i(v0) | hBOOL(v6) | ? [v7: $i] : ? [v8: $i] :
% 91.80/12.88 | (insert1415133716_state(v1, v2) = v7 & hAPP_f971112728l_bool(v3, v7)
% 91.80/12.88 | = v8 & $i(v8) & $i(v7) & ~ hBOOL(v8)))
% 91.80/12.88 |
% 91.80/12.88 | ALPHA: (fact_14_finite__imageI) implies:
% 91.80/12.88 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 91.80/12.88 | (image_2003357581_state(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ?
% 91.80/12.88 | [v3: $i] : ? [v4: $i] :
% 91.80/12.88 | ((hAPP_f971112728l_bool(finite364844667_state, v2) = v4 & $i(v4) &
% 91.80/12.88 | hBOOL(v4)) | (hAPP_f1664156314l_bool(finite_finite_pname, v1) =
% 91.80/12.88 | v3 & $i(v3) & ~ hBOOL(v3))))
% 91.80/12.88 |
% 91.80/12.88 | ALPHA: (fact_103_MGF) implies:
% 91.80/12.88 | (6) ? [v0: $i] : (hoare_1598289066_state(bot_bo620288102e_bool) = v0 &
% 91.80/12.88 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~
% 91.80/12.88 | (hAPP_c1126217667_state(hoare_Mirabelle_MGT, v1) = v2) | ~ $i(v1)
% 91.80/12.88 | | ~ hBOOL(hoare_165779456gleton) | ~ hBOOL(wT_bodies) | ? [v3:
% 91.80/12.88 | $i] : ? [v4: $i] : ? [v5: $i] : ((insert1415133716_state(v2,
% 91.80/12.88 | bot_bo620288102e_bool) = v4 & hAPP_f971112728l_bool(v0, v4) =
% 91.80/12.88 | v5 & $i(v5) & $i(v4) & hBOOL(v5)) | (wt(v1) = v3 & $i(v3) & ~
% 91.80/12.88 | hBOOL(v3)))))
% 91.80/12.88 |
% 91.80/12.88 | ALPHA: (fact_166_empty__def) implies:
% 91.80/12.88 | (7) ? [v0: $i] : (cOMBK_659609255_state(fFalse) = v0 &
% 91.80/12.88 | collec307967673_state(v0) = bot_bo620288102e_bool & $i(v0))
% 91.80/12.88 |
% 91.80/12.88 | ALPHA: (fact_173_insert__ident) implies:
% 91.80/12.88 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 91.80/12.88 | ! [v5: $i] : ( ~ (hAPP_H30606679l_bool(member1338687867_state, v1) =
% 91.80/12.88 | v3) | ~ (hAPP_f971112728l_bool(v3, v2) = v4) | ~
% 91.80/12.88 | (hAPP_f971112728l_bool(v3, v0) = v5) | ~ $i(v2) | ~ $i(v1) | ~
% 91.80/12.88 | $i(v0) | hBOOL(v5) | hBOOL(v4) | ? [v6: $i] : ? [v7: $i] : (( ~ (v2
% 91.80/12.88 | = v0) | (v7 = v6 & insert1415133716_state(v1, v0) = v6 &
% 91.80/12.88 | $i(v6))) & (v2 = v0 | ( ~ (v7 = v6) &
% 91.80/12.88 | insert1415133716_state(v1, v2) = v6 &
% 91.80/12.88 | insert1415133716_state(v1, v0) = v7 & $i(v7) & $i(v6)))))
% 91.80/12.88 |
% 91.80/12.88 | ALPHA: (fact_234_finite__insert) implies:
% 91.80/12.88 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 91.80/12.88 | (insert1415133716_state(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ?
% 91.80/12.88 | [v3: $i] : ? [v4: $i] :
% 91.80/12.88 | ((hAPP_f971112728l_bool(finite364844667_state, v2) = v4 & $i(v4) &
% 91.80/12.88 | hBOOL(v4)) | (hAPP_f971112728l_bool(finite364844667_state, v1) =
% 91.80/12.88 | v3 & $i(v3) & ~ hBOOL(v3))))
% 91.80/12.88 |
% 91.80/12.88 | ALPHA: (fact_248_rev__finite__subset) implies:
% 91.80/12.88 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 91.80/12.88 | (hAPP_f434788991l_bool(ord_le313189616e_bool, v0) = v2) | ~
% 91.80/12.88 | (hAPP_f1664156314l_bool(v2, v1) = v3) | ~ $i(v1) | ~ $i(v0) | ~
% 91.80/12.88 | hBOOL(v3) | ? [v4: $i] : ? [v5: $i] :
% 91.80/12.88 | ((hAPP_f1664156314l_bool(finite_finite_pname, v1) = v4 & $i(v4) & ~
% 91.80/12.88 | hBOOL(v4)) | (hAPP_f1664156314l_bool(finite_finite_pname, v0) =
% 91.80/12.88 | v5 & $i(v5) & hBOOL(v5))))
% 91.80/12.88 |
% 91.80/12.88 | ALPHA: (fact_249_rev__finite__subset) implies:
% 91.80/12.88 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 91.80/12.88 | (hAPP_f72706945l_bool(ord_le1285840794e_bool, v0) = v2) | ~
% 91.80/12.88 | (hAPP_f971112728l_bool(v2, v1) = v3) | ~ $i(v1) | ~ $i(v0) | ~
% 91.80/12.88 | hBOOL(v3) | ? [v4: $i] : ? [v5: $i] :
% 91.80/12.88 | ((hAPP_f971112728l_bool(finite364844667_state, v1) = v4 & $i(v4) &
% 91.80/12.88 | ~ hBOOL(v4)) | (hAPP_f971112728l_bool(finite364844667_state, v0)
% 91.80/12.88 | = v5 & $i(v5) & hBOOL(v5))))
% 91.80/12.88 |
% 91.80/12.88 | ALPHA: (fact_269_subset__image__iff) implies:
% 91.80/12.89 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 91.80/12.89 | ! [v5: $i] : ( ~ (image_2003357581_state(v1, v2) = v4) | ~
% 91.80/12.89 | (hAPP_f72706945l_bool(ord_le1285840794e_bool, v0) = v3) | ~
% 91.80/12.89 | (hAPP_f971112728l_bool(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~
% 91.80/12.89 | $i(v0) | ~ hBOOL(v5) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] :
% 91.80/12.89 | (image_2003357581_state(v1, v6) = v0 &
% 91.80/12.89 | hAPP_f434788991l_bool(ord_le313189616e_bool, v6) = v7 &
% 91.80/12.89 | hAPP_f1664156314l_bool(v7, v2) = v8 & $i(v8) & $i(v7) & $i(v6) &
% 91.80/12.89 | hBOOL(v8) & is_fun_pname_bool(v6)))
% 91.80/12.89 |
% 91.80/12.89 | ALPHA: (fact_287_MGF__lemma1) implies:
% 91.80/12.89 | (13) ? [v0: $i] : (dom_pname_com(body) = v0 & $i(v0) & ! [v1: $i] : !
% 91.80/12.89 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (
% 91.80/12.89 | ~ (hAPP_c1126217667_state(hoare_Mirabelle_MGT, v1) = v4) | ~
% 91.80/12.89 | (insert1415133716_state(v4, bot_bo620288102e_bool) = v5) | ~
% 91.80/12.89 | (hoare_1598289066_state(v2) = v3) | ~ (hAPP_f971112728l_bool(v3,
% 91.80/12.89 | v5) = v6) | ~ $i(v2) | ~ $i(v1) | ~
% 91.80/12.89 | hBOOL(hoare_165779456gleton) | hBOOL(v6) | ? [v7: $i] : ? [v8:
% 91.80/12.89 | $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] :
% 91.80/12.89 | ? [v13: $i] : ? [v14: $i] : ($i(v8) & ((hAPP_pname_com(body_1,
% 91.80/12.89 | v8) = v11 & hAPP_c1126217667_state(hoare_Mirabelle_MGT,
% 91.80/12.89 | v11) = v12 & insert1415133716_state(v12,
% 91.80/12.89 | bot_bo620288102e_bool) = v13 & hAPP_f971112728l_bool(v3,
% 91.80/12.89 | v13) = v14 & hAPP_f1664156314l_bool(v9, v0) = v10 &
% 91.80/12.89 | hAPP_p338031245l_bool(member_pname, v8) = v9 & $i(v14) &
% 91.80/12.89 | $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & hBOOL(v10)
% 91.80/12.89 | & is_pname(v8) & ~ hBOOL(v14)) | (wt(v1) = v7 & $i(v7) & ~
% 91.80/12.89 | hBOOL(v7))))))
% 91.80/12.89 |
% 91.80/12.89 | ALPHA: (fact_288_WT__bodiesD) implies:
% 91.80/12.89 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 91.80/12.89 | (hAPP_p799580910on_com(body, v0) = v2) | ~ (wt(v1) = v3) | ~
% 91.80/12.89 | $i(v1) | ~ $i(v0) | ~ hBOOL(wT_bodies) | hBOOL(v3) | ? [v4: $i] :
% 91.80/12.89 | ( ~ (v4 = v2) & some_com(v1) = v4 & $i(v4)))
% 91.80/12.89 |
% 91.80/12.89 | ALPHA: (fact_298_finite__dom__body) implies:
% 91.80/12.89 | (15) ? [v0: $i] : ? [v1: $i] :
% 91.80/12.89 | (hAPP_f1664156314l_bool(finite_finite_pname, v0) = v1 &
% 91.80/12.89 | dom_pname_com(body) = v0 & $i(v1) & $i(v0) & hBOOL(v1))
% 91.80/12.89 |
% 91.80/12.89 | ALPHA: (help_fFalse_1_1_U) implies:
% 91.80/12.89 | (16) ~ hBOOL(fFalse)
% 91.80/12.89 |
% 91.80/12.89 | ALPHA: (help_fFalse_1_1_T) implies:
% 91.80/12.89 | (17) ! [v0: $i] : (v0 = fTrue | v0 = fFalse | ~ $i(v0) | ~ is_bool(v0))
% 91.80/12.89 |
% 91.80/12.89 | ALPHA: (conj_0) implies:
% 91.80/12.89 | (18) hBOOL(hoare_165779456gleton)
% 91.80/12.89 |
% 91.80/12.89 | ALPHA: (conj_1) implies:
% 91.80/12.89 | (19) hBOOL(wT_bodies)
% 91.80/12.89 | (20) $i(wT_bodies)
% 91.80/12.89 |
% 91.80/12.89 | ALPHA: (conj_2) implies:
% 91.80/12.89 | (21) ? [v0: $i] : (hAPP_f971112728l_bool(finite364844667_state, fa) = v0 &
% 91.80/12.89 | $i(v0) & hBOOL(v0))
% 91.80/12.89 |
% 91.80/12.89 | ALPHA: (conj_3) implies:
% 91.80/12.89 | (22) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 91.80/12.89 | (hAPP_H30606679l_bool(member1338687867_state, v0) = v1 &
% 91.80/12.89 | hAPP_c1126217667_state(hoare_Mirabelle_MGT, y) = v0 &
% 91.80/12.89 | hAPP_f971112728l_bool(v1, fa) = v2 & $i(v2) & $i(v1) & $i(v0) & ~
% 91.80/12.89 | hBOOL(v2))
% 91.80/12.89 |
% 91.80/12.89 | ALPHA: (conj_4) implies:
% 91.80/12.89 | (23) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 91.80/12.89 | ? [v5: $i] : (cOMBB_699532858_pname(hoare_Mirabelle_MGT, v1) = v2 &
% 91.80/12.89 | cOMBB_923936821_pname(the_com, body) = v1 &
% 91.80/12.89 | image_2003357581_state(v2, v3) = v4 &
% 91.80/12.89 | hAPP_f72706945l_bool(ord_le1285840794e_bool, fa) = v0 &
% 91.80/12.89 | hAPP_f971112728l_bool(v0, v4) = v5 & dom_pname_com(body) = v3 &
% 91.80/12.89 | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & hBOOL(v5))
% 91.80/12.89 |
% 91.80/12.89 | ALPHA: (conj_5) implies:
% 91.80/12.89 | (24) $i(pn)
% 91.80/12.89 | (25) ? [v0: $i] : (some_com(y) = v0 & hAPP_p799580910on_com(body, pn) = v0
% 91.80/12.89 | & $i(v0))
% 91.80/12.89 |
% 91.80/12.89 | ALPHA: (conj_6) implies:
% 91.80/12.89 | (26) $i(fa)
% 91.80/12.89 | (27) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 91.80/12.89 | (cOMBB_699532858_pname(hoare_Mirabelle_MGT, body_1) = v0 &
% 91.80/12.89 | image_2003357581_state(v0, v1) = v2 & hoare_1598289066_state(v2) =
% 91.80/12.89 | v3 & hAPP_f971112728l_bool(v3, fa) = v4 & dom_pname_com(body) = v1 &
% 91.80/12.89 | $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & hBOOL(v4))
% 91.80/12.89 |
% 91.80/12.89 | ALPHA: (conj_7) implies:
% 91.80/12.89 | (28) $i(y)
% 91.80/12.89 | (29) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 91.80/12.89 | ? [v5: $i] : ? [v6: $i] : (cOMBB_699532858_pname(hoare_Mirabelle_MGT,
% 91.80/12.89 | body_1) = v0 & image_2003357581_state(v0, v1) = v2 &
% 91.80/12.89 | hAPP_c1126217667_state(hoare_Mirabelle_MGT, y) = v4 &
% 91.80/12.89 | insert1415133716_state(v4, bot_bo620288102e_bool) = v5 &
% 91.80/12.89 | hoare_1598289066_state(v2) = v3 & hAPP_f971112728l_bool(v3, v5) = v6
% 91.80/12.89 | & dom_pname_com(body) = v1 & $i(v6) & $i(v5) & $i(v4) & $i(v3) &
% 91.80/12.89 | $i(v2) & $i(v1) & $i(v0) & ~ hBOOL(v6))
% 91.80/12.89 |
% 91.80/12.89 | ALPHA: (function-axioms) implies:
% 91.80/12.89 | (30) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 91.80/12.89 | (dom_pname_com(v2) = v1) | ~ (dom_pname_com(v2) = v0))
% 91.80/12.89 | (31) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 91.80/12.89 | (hoare_1598289066_state(v2) = v1) | ~ (hoare_1598289066_state(v2) =
% 91.80/12.89 | v0))
% 91.80/12.89 | (32) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (some_com(v2)
% 91.80/12.89 | = v1) | ~ (some_com(v2) = v0))
% 91.80/12.89 | (33) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 91.80/12.89 | (hAPP_f1664156314l_bool(v3, v2) = v1) | ~
% 91.80/12.89 | (hAPP_f1664156314l_bool(v3, v2) = v0))
% 91.80/12.89 | (34) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 91.80/12.89 | (hAPP_f971112728l_bool(v3, v2) = v1) | ~ (hAPP_f971112728l_bool(v3,
% 91.80/12.89 | v2) = v0))
% 91.80/12.90 | (35) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 91.80/12.90 | (insert1415133716_state(v3, v2) = v1) | ~
% 91.80/12.90 | (insert1415133716_state(v3, v2) = v0))
% 91.80/12.90 | (36) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 91.80/12.90 | (hAPP_c1126217667_state(v3, v2) = v1) | ~
% 91.80/12.90 | (hAPP_c1126217667_state(v3, v2) = v0))
% 91.80/12.90 | (37) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 91.80/12.90 | (image_2003357581_state(v3, v2) = v1) | ~
% 91.80/12.90 | (image_2003357581_state(v3, v2) = v0))
% 91.80/12.90 | (38) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 91.80/12.90 | (cOMBB_699532858_pname(v3, v2) = v1) | ~ (cOMBB_699532858_pname(v3,
% 91.80/12.90 | v2) = v0))
% 91.80/12.90 |
% 91.80/12.90 | DELTA: instantiating (7) with fresh symbol all_374_0 gives:
% 91.80/12.90 | (39) cOMBK_659609255_state(fFalse) = all_374_0 &
% 91.80/12.90 | collec307967673_state(all_374_0) = bot_bo620288102e_bool &
% 91.80/12.90 | $i(all_374_0)
% 91.80/12.90 |
% 91.80/12.90 | ALPHA: (39) implies:
% 91.80/12.90 | (40) $i(all_374_0)
% 91.80/12.90 | (41) collec307967673_state(all_374_0) = bot_bo620288102e_bool
% 91.80/12.90 |
% 91.80/12.90 | DELTA: instantiating (25) with fresh symbol all_380_0 gives:
% 91.80/12.90 | (42) some_com(y) = all_380_0 & hAPP_p799580910on_com(body, pn) = all_380_0
% 91.80/12.90 | & $i(all_380_0)
% 91.80/12.90 |
% 91.80/12.90 | ALPHA: (42) implies:
% 91.80/12.90 | (43) hAPP_p799580910on_com(body, pn) = all_380_0
% 91.80/12.90 | (44) some_com(y) = all_380_0
% 91.80/12.90 |
% 91.80/12.90 | DELTA: instantiating (21) with fresh symbol all_392_0 gives:
% 91.80/12.90 | (45) hAPP_f971112728l_bool(finite364844667_state, fa) = all_392_0 &
% 91.80/12.90 | $i(all_392_0) & hBOOL(all_392_0)
% 91.80/12.90 |
% 91.80/12.90 | ALPHA: (45) implies:
% 91.80/12.90 | (46) hAPP_f971112728l_bool(finite364844667_state, fa) = all_392_0
% 91.80/12.90 |
% 91.80/12.90 | DELTA: instantiating (15) with fresh symbols all_405_0, all_405_1 gives:
% 91.80/12.90 | (47) hAPP_f1664156314l_bool(finite_finite_pname, all_405_1) = all_405_0 &
% 91.80/12.90 | dom_pname_com(body) = all_405_1 & $i(all_405_0) & $i(all_405_1) &
% 91.80/12.90 | hBOOL(all_405_0)
% 91.80/12.90 |
% 91.80/12.90 | ALPHA: (47) implies:
% 91.80/12.90 | (48) hBOOL(all_405_0)
% 91.80/12.90 | (49) dom_pname_com(body) = all_405_1
% 91.80/12.90 | (50) hAPP_f1664156314l_bool(finite_finite_pname, all_405_1) = all_405_0
% 91.80/12.90 |
% 91.80/12.90 | DELTA: instantiating (22) with fresh symbols all_418_0, all_418_1, all_418_2
% 91.80/12.90 | gives:
% 91.80/12.90 | (51) hAPP_H30606679l_bool(member1338687867_state, all_418_2) = all_418_1 &
% 91.80/12.90 | hAPP_c1126217667_state(hoare_Mirabelle_MGT, y) = all_418_2 &
% 91.80/12.90 | hAPP_f971112728l_bool(all_418_1, fa) = all_418_0 & $i(all_418_0) &
% 91.80/12.90 | $i(all_418_1) & $i(all_418_2) & ~ hBOOL(all_418_0)
% 91.80/12.90 |
% 91.80/12.90 | ALPHA: (51) implies:
% 91.80/12.90 | (52) ~ hBOOL(all_418_0)
% 91.80/12.90 | (53) hAPP_f971112728l_bool(all_418_1, fa) = all_418_0
% 91.80/12.90 | (54) hAPP_c1126217667_state(hoare_Mirabelle_MGT, y) = all_418_2
% 91.80/12.90 | (55) hAPP_H30606679l_bool(member1338687867_state, all_418_2) = all_418_1
% 91.80/12.90 |
% 91.80/12.90 | DELTA: instantiating (27) with fresh symbols all_432_0, all_432_1, all_432_2,
% 91.80/12.90 | all_432_3, all_432_4 gives:
% 91.80/12.90 | (56) cOMBB_699532858_pname(hoare_Mirabelle_MGT, body_1) = all_432_4 &
% 91.80/12.90 | image_2003357581_state(all_432_4, all_432_3) = all_432_2 &
% 91.80/12.90 | hoare_1598289066_state(all_432_2) = all_432_1 &
% 91.80/12.90 | hAPP_f971112728l_bool(all_432_1, fa) = all_432_0 & dom_pname_com(body)
% 91.80/12.90 | = all_432_3 & $i(all_432_0) & $i(all_432_1) & $i(all_432_2) &
% 91.80/12.90 | $i(all_432_3) & $i(all_432_4) & hBOOL(all_432_0)
% 91.80/12.90 |
% 91.80/12.90 | ALPHA: (56) implies:
% 91.80/12.90 | (57) hBOOL(all_432_0)
% 91.80/12.90 | (58) $i(all_432_3)
% 91.80/12.90 | (59) $i(all_432_0)
% 91.80/12.90 | (60) dom_pname_com(body) = all_432_3
% 91.80/12.90 | (61) hAPP_f971112728l_bool(all_432_1, fa) = all_432_0
% 91.80/12.90 | (62) hoare_1598289066_state(all_432_2) = all_432_1
% 91.80/12.90 | (63) image_2003357581_state(all_432_4, all_432_3) = all_432_2
% 91.80/12.90 | (64) cOMBB_699532858_pname(hoare_Mirabelle_MGT, body_1) = all_432_4
% 91.80/12.90 |
% 91.80/12.90 | DELTA: instantiating (23) with fresh symbols all_488_0, all_488_1, all_488_2,
% 91.80/12.90 | all_488_3, all_488_4, all_488_5 gives:
% 91.80/12.90 | (65) cOMBB_699532858_pname(hoare_Mirabelle_MGT, all_488_4) = all_488_3 &
% 91.80/12.90 | cOMBB_923936821_pname(the_com, body) = all_488_4 &
% 91.80/12.90 | image_2003357581_state(all_488_3, all_488_2) = all_488_1 &
% 91.80/12.90 | hAPP_f72706945l_bool(ord_le1285840794e_bool, fa) = all_488_5 &
% 91.80/12.90 | hAPP_f971112728l_bool(all_488_5, all_488_1) = all_488_0 &
% 91.80/12.90 | dom_pname_com(body) = all_488_2 & $i(all_488_0) & $i(all_488_1) &
% 91.80/12.90 | $i(all_488_2) & $i(all_488_3) & $i(all_488_4) & $i(all_488_5) &
% 91.80/12.90 | hBOOL(all_488_0)
% 91.80/12.90 |
% 91.80/12.90 | ALPHA: (65) implies:
% 91.80/12.90 | (66) hBOOL(all_488_0)
% 91.80/12.90 | (67) $i(all_488_3)
% 91.80/12.90 | (68) $i(all_488_1)
% 91.80/12.90 | (69) dom_pname_com(body) = all_488_2
% 91.80/12.90 | (70) hAPP_f971112728l_bool(all_488_5, all_488_1) = all_488_0
% 91.80/12.90 | (71) hAPP_f72706945l_bool(ord_le1285840794e_bool, fa) = all_488_5
% 91.80/12.90 | (72) image_2003357581_state(all_488_3, all_488_2) = all_488_1
% 91.80/12.90 |
% 91.80/12.90 | DELTA: instantiating (6) with fresh symbol all_490_0 gives:
% 91.80/12.90 | (73) hoare_1598289066_state(bot_bo620288102e_bool) = all_490_0 &
% 91.80/12.90 | $i(all_490_0) & ! [v0: $i] : ! [v1: $i] : ( ~
% 91.80/12.90 | (hAPP_c1126217667_state(hoare_Mirabelle_MGT, v0) = v1) | ~ $i(v0) |
% 91.80/12.90 | ~ hBOOL(hoare_165779456gleton) | ~ hBOOL(wT_bodies) | ? [v2: $i]
% 91.80/12.90 | : ? [v3: $i] : ? [v4: $i] : ((insert1415133716_state(v1,
% 91.80/12.90 | bot_bo620288102e_bool) = v3 & hAPP_f971112728l_bool(all_490_0,
% 91.80/12.90 | v3) = v4 & $i(v4) & $i(v3) & hBOOL(v4)) | (wt(v0) = v2 &
% 91.80/12.90 | $i(v2) & ~ hBOOL(v2))))
% 91.80/12.90 |
% 91.80/12.90 | ALPHA: (73) implies:
% 91.80/12.90 | (74) hoare_1598289066_state(bot_bo620288102e_bool) = all_490_0
% 91.80/12.91 | (75) ! [v0: $i] : ! [v1: $i] : ( ~
% 91.80/12.91 | (hAPP_c1126217667_state(hoare_Mirabelle_MGT, v0) = v1) | ~ $i(v0) |
% 91.80/12.91 | ~ hBOOL(hoare_165779456gleton) | ~ hBOOL(wT_bodies) | ? [v2: $i]
% 91.80/12.91 | : ? [v3: $i] : ? [v4: $i] : ((insert1415133716_state(v1,
% 91.80/12.91 | bot_bo620288102e_bool) = v3 & hAPP_f971112728l_bool(all_490_0,
% 91.80/12.91 | v3) = v4 & $i(v4) & $i(v3) & hBOOL(v4)) | (wt(v0) = v2 &
% 91.80/12.91 | $i(v2) & ~ hBOOL(v2))))
% 91.80/12.91 |
% 91.80/12.91 | DELTA: instantiating (29) with fresh symbols all_493_0, all_493_1, all_493_2,
% 91.80/12.91 | all_493_3, all_493_4, all_493_5, all_493_6 gives:
% 91.80/12.91 | (76) cOMBB_699532858_pname(hoare_Mirabelle_MGT, body_1) = all_493_6 &
% 91.80/12.91 | image_2003357581_state(all_493_6, all_493_5) = all_493_4 &
% 91.80/12.91 | hAPP_c1126217667_state(hoare_Mirabelle_MGT, y) = all_493_2 &
% 91.80/12.91 | insert1415133716_state(all_493_2, bot_bo620288102e_bool) = all_493_1 &
% 91.80/12.91 | hoare_1598289066_state(all_493_4) = all_493_3 &
% 91.80/12.91 | hAPP_f971112728l_bool(all_493_3, all_493_1) = all_493_0 &
% 91.80/12.91 | dom_pname_com(body) = all_493_5 & $i(all_493_0) & $i(all_493_1) &
% 91.80/12.91 | $i(all_493_2) & $i(all_493_3) & $i(all_493_4) & $i(all_493_5) &
% 91.80/12.91 | $i(all_493_6) & ~ hBOOL(all_493_0)
% 91.80/12.91 |
% 91.80/12.91 | ALPHA: (76) implies:
% 91.80/12.91 | (77) ~ hBOOL(all_493_0)
% 91.80/12.91 | (78) $i(all_493_4)
% 91.80/12.91 | (79) $i(all_493_3)
% 91.80/12.91 | (80) $i(all_493_2)
% 91.80/12.91 | (81) $i(all_493_1)
% 91.80/12.91 | (82) dom_pname_com(body) = all_493_5
% 91.80/12.91 | (83) hAPP_f971112728l_bool(all_493_3, all_493_1) = all_493_0
% 91.80/12.91 | (84) hoare_1598289066_state(all_493_4) = all_493_3
% 91.80/12.91 | (85) insert1415133716_state(all_493_2, bot_bo620288102e_bool) = all_493_1
% 91.80/12.91 | (86) hAPP_c1126217667_state(hoare_Mirabelle_MGT, y) = all_493_2
% 91.80/12.91 | (87) image_2003357581_state(all_493_6, all_493_5) = all_493_4
% 91.80/12.91 | (88) cOMBB_699532858_pname(hoare_Mirabelle_MGT, body_1) = all_493_6
% 91.80/12.91 |
% 91.80/12.91 | DELTA: instantiating (13) with fresh symbol all_507_0 gives:
% 91.80/12.91 | (89) dom_pname_com(body) = all_507_0 & $i(all_507_0) & ! [v0: $i] : !
% 91.80/12.91 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 91.80/12.91 | (hAPP_c1126217667_state(hoare_Mirabelle_MGT, v0) = v3) | ~
% 91.80/12.91 | (insert1415133716_state(v3, bot_bo620288102e_bool) = v4) | ~
% 91.80/12.91 | (hoare_1598289066_state(v1) = v2) | ~ (hAPP_f971112728l_bool(v2,
% 91.80/12.91 | v4) = v5) | ~ $i(v1) | ~ $i(v0) | ~
% 91.80/12.91 | hBOOL(hoare_165779456gleton) | hBOOL(v5) | ? [v6: $i] : ? [v7: $i]
% 91.80/12.91 | : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12:
% 91.80/12.91 | $i] : ? [v13: $i] : ($i(v7) & ((hAPP_pname_com(body_1, v7) = v10
% 91.80/12.91 | & hAPP_c1126217667_state(hoare_Mirabelle_MGT, v10) = v11 &
% 91.80/12.91 | insert1415133716_state(v11, bot_bo620288102e_bool) = v12 &
% 91.80/12.91 | hAPP_f971112728l_bool(v2, v12) = v13 &
% 91.80/12.91 | hAPP_f1664156314l_bool(v8, all_507_0) = v9 &
% 91.80/12.91 | hAPP_p338031245l_bool(member_pname, v7) = v8 & $i(v13) &
% 91.80/12.91 | $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & hBOOL(v9) &
% 91.80/12.91 | is_pname(v7) & ~ hBOOL(v13)) | (wt(v0) = v6 & $i(v6) & ~
% 91.80/12.91 | hBOOL(v6)))))
% 91.80/12.91 |
% 91.80/12.91 | ALPHA: (89) implies:
% 91.80/12.91 | (90) dom_pname_com(body) = all_507_0
% 91.80/12.91 |
% 91.80/12.91 | GROUND_INST: instantiating (30) with all_432_3, all_488_2, body, simplifying
% 91.80/12.91 | with (60), (69) gives:
% 91.80/12.91 | (91) all_488_2 = all_432_3
% 91.80/12.91 |
% 91.80/12.91 | GROUND_INST: instantiating (30) with all_493_5, all_507_0, body, simplifying
% 91.80/12.91 | with (82), (90) gives:
% 91.80/12.91 | (92) all_507_0 = all_493_5
% 91.80/12.91 |
% 91.80/12.91 | GROUND_INST: instantiating (30) with all_488_2, all_507_0, body, simplifying
% 91.80/12.91 | with (69), (90) gives:
% 91.80/12.91 | (93) all_507_0 = all_488_2
% 91.80/12.91 |
% 91.80/12.91 | GROUND_INST: instantiating (30) with all_405_1, all_507_0, body, simplifying
% 91.80/12.91 | with (49), (90) gives:
% 91.80/12.91 | (94) all_507_0 = all_405_1
% 91.80/12.91 |
% 91.80/12.91 | GROUND_INST: instantiating (36) with all_418_2, all_493_2, y,
% 91.80/12.91 | hoare_Mirabelle_MGT, simplifying with (54), (86) gives:
% 91.80/12.91 | (95) all_493_2 = all_418_2
% 91.80/12.91 |
% 91.80/12.91 | GROUND_INST: instantiating (38) with all_432_4, all_493_6, body_1,
% 91.80/12.91 | hoare_Mirabelle_MGT, simplifying with (64), (88) gives:
% 91.80/12.91 | (96) all_493_6 = all_432_4
% 91.80/12.91 |
% 91.80/12.91 | COMBINE_EQS: (92), (93) imply:
% 91.80/12.91 | (97) all_493_5 = all_488_2
% 91.80/12.91 |
% 91.80/12.91 | COMBINE_EQS: (92), (94) imply:
% 91.80/12.91 | (98) all_493_5 = all_405_1
% 91.80/12.91 |
% 91.80/12.91 | COMBINE_EQS: (97), (98) imply:
% 91.80/12.91 | (99) all_488_2 = all_405_1
% 91.80/12.91 |
% 91.80/12.91 | SIMP: (99) implies:
% 91.80/12.91 | (100) all_488_2 = all_405_1
% 91.80/12.91 |
% 91.80/12.91 | COMBINE_EQS: (91), (100) imply:
% 91.80/12.91 | (101) all_432_3 = all_405_1
% 91.80/12.91 |
% 91.80/12.91 | REDUCE: (87), (96), (98) imply:
% 91.80/12.91 | (102) image_2003357581_state(all_432_4, all_405_1) = all_493_4
% 91.80/12.91 |
% 91.80/12.91 | REDUCE: (72), (100) imply:
% 91.80/12.91 | (103) image_2003357581_state(all_488_3, all_405_1) = all_488_1
% 91.80/12.91 |
% 91.80/12.91 | REDUCE: (63), (101) imply:
% 91.80/12.91 | (104) image_2003357581_state(all_432_4, all_405_1) = all_432_2
% 91.80/12.91 |
% 91.80/12.91 | REDUCE: (85), (95) imply:
% 91.80/12.91 | (105) insert1415133716_state(all_418_2, bot_bo620288102e_bool) = all_493_1
% 91.80/12.91 |
% 91.80/12.91 | REDUCE: (80), (95) imply:
% 91.80/12.91 | (106) $i(all_418_2)
% 91.80/12.91 |
% 91.80/12.91 | REDUCE: (58), (101) imply:
% 91.80/12.91 | (107) $i(all_405_1)
% 91.80/12.91 |
% 91.80/12.91 | GROUND_INST: instantiating (37) with all_432_2, all_493_4, all_405_1,
% 91.80/12.91 | all_432_4, simplifying with (102), (104) gives:
% 91.80/12.91 | (108) all_493_4 = all_432_2
% 91.80/12.91 |
% 91.80/12.91 | REDUCE: (84), (108) imply:
% 91.80/12.91 | (109) hoare_1598289066_state(all_432_2) = all_493_3
% 91.80/12.91 |
% 91.80/12.91 | REDUCE: (78), (108) imply:
% 91.80/12.91 | (110) $i(all_432_2)
% 91.80/12.91 |
% 91.80/12.91 | GROUND_INST: instantiating (31) with all_432_1, all_493_3, all_432_2,
% 91.80/12.91 | simplifying with (62), (109) gives:
% 91.80/12.91 | (111) all_493_3 = all_432_1
% 91.80/12.91 |
% 91.80/12.91 | REDUCE: (83), (111) imply:
% 91.80/12.91 | (112) hAPP_f971112728l_bool(all_432_1, all_493_1) = all_493_0
% 91.80/12.92 |
% 91.80/12.92 | REDUCE: (79), (111) imply:
% 91.80/12.92 | (113) $i(all_432_1)
% 91.80/12.92 |
% 91.80/12.92 | GROUND_INST: instantiating (17) with wT_bodies, simplifying with (1), (20)
% 91.80/12.92 | gives:
% 91.80/12.92 | (114) fTrue = wT_bodies | fFalse = wT_bodies
% 91.80/12.92 |
% 91.80/12.92 | GROUND_INST: instantiating
% 91.80/12.92 | (gsy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com__O_004)
% 91.80/12.92 | with all_432_1, fa, all_432_0, simplifying with (26), (61), (113)
% 91.80/12.92 | gives:
% 91.80/12.92 | (115) is_bool(all_432_0)
% 91.80/12.92 |
% 91.80/12.92 | GROUND_INST: instantiating (2) with all_432_2, all_432_1, simplifying with
% 91.80/12.92 | (62), (110) gives:
% 91.80/12.92 | (116) ? [v0: $i] : (hAPP_f971112728l_bool(all_432_1,
% 91.80/12.92 | bot_bo620288102e_bool) = v0 & $i(v0) & hBOOL(v0))
% 91.80/12.92 |
% 91.80/12.92 | GROUND_INST: instantiating (11) with fa, all_488_1, all_488_5, all_488_0,
% 91.80/12.92 | simplifying with (26), (66), (68), (70), (71) gives:
% 91.80/12.92 | (117) ? [v0: $i] : ? [v1: $i] :
% 91.80/12.92 | ((hAPP_f971112728l_bool(finite364844667_state, all_488_1) = v0 &
% 91.80/12.92 | $i(v0) & ~ hBOOL(v0)) |
% 91.80/12.92 | (hAPP_f971112728l_bool(finite364844667_state, fa) = v1 & $i(v1) &
% 91.80/12.92 | hBOOL(v1)))
% 91.80/12.92 |
% 91.80/12.92 | GROUND_INST: instantiating (4) with all_432_2, all_418_2, all_493_1,
% 91.80/12.92 | all_432_1, all_493_1, all_493_0, all_493_0, simplifying with
% 91.80/12.92 | (62), (77), (81), (105), (106), (110), (112) gives:
% 91.80/12.92 | (118) ? [v0: $i] : ? [v1: $i] : (insert1415133716_state(all_418_2,
% 91.80/12.92 | all_493_1) = v0 & hAPP_f971112728l_bool(all_432_1, v0) = v1 &
% 91.80/12.92 | $i(v1) & $i(v0) & ~ hBOOL(v1))
% 91.80/12.92 |
% 91.80/12.92 | GROUND_INST: instantiating (3) with all_432_2, all_418_2, fa, all_432_1,
% 91.80/12.92 | all_493_1, all_493_0, all_432_0, simplifying with (26), (61),
% 91.80/12.92 | (62), (77), (105), (106), (110), (112) gives:
% 91.80/12.92 | (119) ? [v0: $i] : ? [v1: $i] : (insert1415133716_state(all_418_2, fa) =
% 91.80/12.92 | v0 & hAPP_f971112728l_bool(all_432_1, v0) = v1 & $i(v1) & $i(v0) &
% 91.80/12.92 | ~ hBOOL(v1))
% 91.80/12.92 |
% 91.80/12.92 | GROUND_INST: instantiating (75) with y, all_418_2, simplifying with (18),
% 91.80/12.92 | (19), (28), (54) gives:
% 91.80/12.92 | (120) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 91.80/12.92 | ((insert1415133716_state(all_418_2, bot_bo620288102e_bool) = v1 &
% 91.80/12.92 | hAPP_f971112728l_bool(all_490_0, v1) = v2 & $i(v2) & $i(v1) &
% 91.80/12.92 | hBOOL(v2)) | (wt(y) = v0 & $i(v0) & ~ hBOOL(v0)))
% 91.80/12.92 |
% 91.80/12.92 | GROUND_INST: instantiating (12) with fa, all_488_3, all_405_1, all_488_5,
% 91.80/12.92 | all_488_1, all_488_0, simplifying with (26), (66), (67), (70),
% 91.80/12.92 | (71), (103), (107) gives:
% 91.80/12.92 | (121) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 91.80/12.92 | (image_2003357581_state(all_488_3, v0) = fa &
% 91.80/12.92 | hAPP_f434788991l_bool(ord_le313189616e_bool, v0) = v1 &
% 91.80/12.92 | hAPP_f1664156314l_bool(v1, all_405_1) = v2 & $i(v2) & $i(v1) &
% 91.80/12.92 | $i(v0) & hBOOL(v2) & is_fun_pname_bool(v0))
% 91.80/12.92 |
% 91.80/12.92 | GROUND_INST: instantiating (5) with all_488_3, all_405_1, all_488_1,
% 91.80/12.92 | simplifying with (67), (103), (107) gives:
% 91.80/12.92 | (122) ? [v0: $i] : ? [v1: $i] :
% 91.80/12.92 | ((hAPP_f971112728l_bool(finite364844667_state, all_488_1) = v1 &
% 91.80/12.92 | $i(v1) & hBOOL(v1)) |
% 91.80/12.92 | (hAPP_f1664156314l_bool(finite_finite_pname, all_405_1) = v0 &
% 91.80/12.92 | $i(v0) & ~ hBOOL(v0)))
% 91.80/12.92 |
% 91.80/12.92 | GROUND_INST: instantiating (fact_255_Collect__def) with all_374_0,
% 91.80/12.92 | bot_bo620288102e_bool, simplifying with (40), (41) gives:
% 91.80/12.92 | (123) all_374_0 = bot_bo620288102e_bool
% 91.80/12.92 |
% 91.80/12.92 | GROUND_INST: instantiating (8) with fa, all_418_2, fa, all_418_1, all_418_0,
% 91.80/12.92 | all_418_0, simplifying with (26), (52), (53), (55), (106) gives:
% 91.80/12.92 | (124) ? [v0: $i] : (insert1415133716_state(all_418_2, fa) = v0 & $i(v0))
% 91.80/12.92 |
% 91.80/12.92 | DELTA: instantiating (124) with fresh symbol all_528_0 gives:
% 91.80/12.92 | (125) insert1415133716_state(all_418_2, fa) = all_528_0 & $i(all_528_0)
% 91.80/12.92 |
% 91.80/12.92 | ALPHA: (125) implies:
% 91.80/12.92 | (126) insert1415133716_state(all_418_2, fa) = all_528_0
% 91.80/12.92 |
% 91.80/12.92 | DELTA: instantiating (116) with fresh symbol all_538_0 gives:
% 91.80/12.92 | (127) hAPP_f971112728l_bool(all_432_1, bot_bo620288102e_bool) = all_538_0 &
% 91.80/12.92 | $i(all_538_0) & hBOOL(all_538_0)
% 91.80/12.92 |
% 91.80/12.92 | ALPHA: (127) implies:
% 91.80/12.92 | (128) hBOOL(all_538_0)
% 91.80/12.92 | (129) hAPP_f971112728l_bool(all_432_1, bot_bo620288102e_bool) = all_538_0
% 91.80/12.92 |
% 91.80/12.92 | DELTA: instantiating (119) with fresh symbols all_544_0, all_544_1 gives:
% 91.80/12.92 | (130) insert1415133716_state(all_418_2, fa) = all_544_1 &
% 91.80/12.92 | hAPP_f971112728l_bool(all_432_1, all_544_1) = all_544_0 &
% 91.80/12.92 | $i(all_544_0) & $i(all_544_1) & ~ hBOOL(all_544_0)
% 91.80/12.92 |
% 91.80/12.92 | ALPHA: (130) implies:
% 91.80/12.92 | (131) ~ hBOOL(all_544_0)
% 91.80/12.92 | (132) $i(all_544_1)
% 91.80/12.92 | (133) hAPP_f971112728l_bool(all_432_1, all_544_1) = all_544_0
% 91.80/12.92 | (134) insert1415133716_state(all_418_2, fa) = all_544_1
% 91.80/12.92 |
% 91.80/12.92 | DELTA: instantiating (118) with fresh symbols all_548_0, all_548_1 gives:
% 91.80/12.92 | (135) insert1415133716_state(all_418_2, all_493_1) = all_548_1 &
% 91.80/12.92 | hAPP_f971112728l_bool(all_432_1, all_548_1) = all_548_0 &
% 91.80/12.92 | $i(all_548_0) & $i(all_548_1) & ~ hBOOL(all_548_0)
% 91.80/12.92 |
% 91.80/12.92 | ALPHA: (135) implies:
% 91.80/12.92 | (136) ~ hBOOL(all_548_0)
% 91.80/12.92 | (137) $i(all_548_1)
% 91.80/12.92 | (138) hAPP_f971112728l_bool(all_432_1, all_548_1) = all_548_0
% 91.80/12.92 | (139) insert1415133716_state(all_418_2, all_493_1) = all_548_1
% 91.80/12.92 |
% 91.80/12.92 | DELTA: instantiating (122) with fresh symbols all_553_0, all_553_1 gives:
% 91.80/12.92 | (140) (hAPP_f971112728l_bool(finite364844667_state, all_488_1) = all_553_0
% 91.80/12.92 | & $i(all_553_0) & hBOOL(all_553_0)) |
% 91.80/12.92 | (hAPP_f1664156314l_bool(finite_finite_pname, all_405_1) = all_553_1 &
% 91.80/12.92 | $i(all_553_1) & ~ hBOOL(all_553_1))
% 91.80/12.92 |
% 91.80/12.92 | DELTA: instantiating (117) with fresh symbols all_554_0, all_554_1 gives:
% 91.80/12.93 | (141) (hAPP_f971112728l_bool(finite364844667_state, all_488_1) = all_554_1
% 91.80/12.93 | & $i(all_554_1) & ~ hBOOL(all_554_1)) |
% 91.80/12.93 | (hAPP_f971112728l_bool(finite364844667_state, fa) = all_554_0 &
% 91.80/12.93 | $i(all_554_0) & hBOOL(all_554_0))
% 91.80/12.93 |
% 91.80/12.93 | DELTA: instantiating (121) with fresh symbols all_555_0, all_555_1, all_555_2
% 91.80/12.93 | gives:
% 91.80/12.93 | (142) image_2003357581_state(all_488_3, all_555_2) = fa &
% 91.80/12.93 | hAPP_f434788991l_bool(ord_le313189616e_bool, all_555_2) = all_555_1 &
% 91.80/12.93 | hAPP_f1664156314l_bool(all_555_1, all_405_1) = all_555_0 &
% 91.80/12.93 | $i(all_555_0) & $i(all_555_1) & $i(all_555_2) & hBOOL(all_555_0) &
% 91.80/12.93 | is_fun_pname_bool(all_555_2)
% 91.80/12.93 |
% 91.80/12.93 | ALPHA: (142) implies:
% 91.80/12.93 | (143) hBOOL(all_555_0)
% 91.80/12.93 | (144) $i(all_555_2)
% 91.80/12.93 | (145) hAPP_f1664156314l_bool(all_555_1, all_405_1) = all_555_0
% 91.80/12.93 | (146) hAPP_f434788991l_bool(ord_le313189616e_bool, all_555_2) = all_555_1
% 91.80/12.93 | (147) image_2003357581_state(all_488_3, all_555_2) = fa
% 91.80/12.93 |
% 91.80/12.93 | DELTA: instantiating (120) with fresh symbols all_557_0, all_557_1, all_557_2
% 91.80/12.93 | gives:
% 91.80/12.93 | (148) (insert1415133716_state(all_418_2, bot_bo620288102e_bool) = all_557_1
% 91.80/12.93 | & hAPP_f971112728l_bool(all_490_0, all_557_1) = all_557_0 &
% 91.80/12.93 | $i(all_557_0) & $i(all_557_1) & hBOOL(all_557_0)) | (wt(y) =
% 91.80/12.93 | all_557_2 & $i(all_557_2) & ~ hBOOL(all_557_2))
% 91.80/12.93 |
% 91.80/12.93 | REDUCE: (40), (123) imply:
% 91.80/12.93 | (149) $i(bot_bo620288102e_bool)
% 91.80/12.93 |
% 91.80/12.93 | BETA: splitting (140) gives:
% 91.80/12.93 |
% 91.80/12.93 | Case 1:
% 91.80/12.93 | |
% 91.80/12.93 | | (150) hAPP_f971112728l_bool(finite364844667_state, all_488_1) = all_553_0
% 91.80/12.93 | | & $i(all_553_0) & hBOOL(all_553_0)
% 91.80/12.93 | |
% 91.80/12.93 | | ALPHA: (150) implies:
% 91.80/12.93 | | (151) hBOOL(all_553_0)
% 91.80/12.93 | | (152) hAPP_f971112728l_bool(finite364844667_state, all_488_1) = all_553_0
% 91.80/12.93 | |
% 91.80/12.93 | | BETA: splitting (141) gives:
% 91.80/12.93 | |
% 91.80/12.93 | | Case 1:
% 91.80/12.93 | | |
% 91.80/12.93 | | | (153) hAPP_f971112728l_bool(finite364844667_state, all_488_1) =
% 91.80/12.93 | | | all_554_1 & $i(all_554_1) & ~ hBOOL(all_554_1)
% 91.80/12.93 | | |
% 91.80/12.93 | | | ALPHA: (153) implies:
% 91.80/12.93 | | | (154) ~ hBOOL(all_554_1)
% 91.80/12.93 | | | (155) hAPP_f971112728l_bool(finite364844667_state, all_488_1) =
% 91.80/12.93 | | | all_554_1
% 91.80/12.93 | | |
% 91.80/12.93 | | | GROUND_INST: instantiating (34) with all_553_0, all_554_1, all_488_1,
% 91.80/12.93 | | | finite364844667_state, simplifying with (152), (155) gives:
% 91.80/12.93 | | | (156) all_554_1 = all_553_0
% 91.80/12.93 | | |
% 91.80/12.93 | | | REDUCE: (154), (156) imply:
% 91.80/12.93 | | | (157) ~ hBOOL(all_553_0)
% 91.80/12.93 | | |
% 91.80/12.93 | | | PRED_UNIFY: (151), (157) imply:
% 91.80/12.93 | | | (158) $false
% 91.80/12.93 | | |
% 91.80/12.93 | | | CLOSE: (158) is inconsistent.
% 91.80/12.93 | | |
% 91.80/12.93 | | Case 2:
% 91.80/12.93 | | |
% 91.80/12.93 | | | (159) hAPP_f971112728l_bool(finite364844667_state, fa) = all_554_0 &
% 91.80/12.93 | | | $i(all_554_0) & hBOOL(all_554_0)
% 91.80/12.93 | | |
% 91.80/12.93 | | | ALPHA: (159) implies:
% 91.80/12.93 | | | (160) hAPP_f971112728l_bool(finite364844667_state, fa) = all_554_0
% 91.80/12.93 | | |
% 91.80/12.93 | | | GROUND_INST: instantiating (34) with all_392_0, all_554_0, fa,
% 91.80/12.93 | | | finite364844667_state, simplifying with (46), (160) gives:
% 91.80/12.93 | | | (161) all_554_0 = all_392_0
% 91.80/12.93 | | |
% 91.80/12.93 | | | GROUND_INST: instantiating (35) with all_528_0, all_544_1, fa, all_418_2,
% 91.80/12.93 | | | simplifying with (126), (134) gives:
% 91.80/12.93 | | | (162) all_544_1 = all_528_0
% 91.80/12.93 | | |
% 91.80/12.93 | | | REDUCE: (133), (162) imply:
% 91.80/12.93 | | | (163) hAPP_f971112728l_bool(all_432_1, all_528_0) = all_544_0
% 91.80/12.93 | | |
% 91.80/12.93 | | | REDUCE: (132), (162) imply:
% 91.80/12.93 | | | (164) $i(all_528_0)
% 91.80/12.93 | | |
% 91.80/12.93 | | | GROUND_INST: instantiating (17) with all_432_0, simplifying with (59),
% 91.80/12.93 | | | (115) gives:
% 91.80/12.93 | | | (165) all_432_0 = fTrue | all_432_0 = fFalse
% 91.80/12.93 | | |
% 91.80/12.93 | | | GROUND_INST: instantiating (10) with all_555_2, all_405_1, all_555_1,
% 91.80/12.93 | | | all_555_0, simplifying with (107), (143), (144), (145), (146)
% 91.80/12.93 | | | gives:
% 91.80/12.93 | | | (166) ? [v0: $i] : ? [v1: $i] :
% 91.80/12.93 | | | ((hAPP_f1664156314l_bool(finite_finite_pname, all_555_2) = v1 &
% 91.80/12.93 | | | $i(v1) & hBOOL(v1)) |
% 91.80/12.93 | | | (hAPP_f1664156314l_bool(finite_finite_pname, all_405_1) = v0 &
% 91.80/12.93 | | | $i(v0) & ~ hBOOL(v0)))
% 91.80/12.93 | | |
% 91.80/12.93 | | | GROUND_INST: instantiating (fact_4_cut) with all_432_2,
% 91.80/12.93 | | | bot_bo620288102e_bool, all_493_1, all_432_1, all_538_0,
% 91.80/12.93 | | | all_493_0, simplifying with (62), (77), (81), (110), (112),
% 91.80/12.93 | | | (128), (129), (149) gives:
% 91.80/12.93 | | | (167) ? [v0: $i] : ? [v1: $i] :
% 91.80/12.93 | | | (hoare_1598289066_state(bot_bo620288102e_bool) = v0 &
% 91.80/12.93 | | | hAPP_f971112728l_bool(v0, all_493_1) = v1 & $i(v1) & $i(v0) &
% 91.80/12.93 | | | ~ hBOOL(v1))
% 91.80/12.93 | | |
% 91.80/12.93 | | | GROUND_INST: instantiating (fact_4_cut) with all_432_2,
% 91.80/12.93 | | | bot_bo620288102e_bool, all_528_0, all_432_1, all_538_0,
% 91.80/12.93 | | | all_544_0, simplifying with (62), (110), (128), (129), (131),
% 91.80/12.93 | | | (149), (163), (164) gives:
% 91.80/12.93 | | | (168) ? [v0: $i] : ? [v1: $i] :
% 91.80/12.93 | | | (hoare_1598289066_state(bot_bo620288102e_bool) = v0 &
% 91.80/12.93 | | | hAPP_f971112728l_bool(v0, all_528_0) = v1 & $i(v1) & $i(v0) &
% 91.80/12.93 | | | ~ hBOOL(v1))
% 91.80/12.93 | | |
% 91.80/12.94 | | | GROUND_INST: instantiating (fact_4_cut) with all_432_2,
% 91.80/12.94 | | | bot_bo620288102e_bool, all_548_1, all_432_1, all_538_0,
% 91.80/12.94 | | | all_548_0, simplifying with (62), (110), (128), (129), (136),
% 91.80/12.94 | | | (137), (138), (149) gives:
% 91.80/12.94 | | | (169) ? [v0: $i] : ? [v1: $i] :
% 91.80/12.94 | | | (hoare_1598289066_state(bot_bo620288102e_bool) = v0 &
% 91.80/12.94 | | | hAPP_f971112728l_bool(v0, all_548_1) = v1 & $i(v1) & $i(v0) &
% 91.80/12.94 | | | ~ hBOOL(v1))
% 91.80/12.94 | | |
% 91.80/12.94 | | | GROUND_INST: instantiating (9) with all_418_2, fa, all_528_0, simplifying
% 91.80/12.94 | | | with (26), (106), (126) gives:
% 91.80/12.94 | | | (170) ? [v0: $i] : ? [v1: $i] :
% 91.80/12.94 | | | ((hAPP_f971112728l_bool(finite364844667_state, all_528_0) = v1 &
% 91.80/12.94 | | | $i(v1) & hBOOL(v1)) |
% 91.80/12.94 | | | (hAPP_f971112728l_bool(finite364844667_state, fa) = v0 & $i(v0)
% 91.80/12.94 | | | & ~ hBOOL(v0)))
% 91.80/12.94 | | |
% 91.80/12.94 | | | GROUND_INST: instantiating (fact_181_insert__absorb2) with all_418_2,
% 91.80/12.94 | | | bot_bo620288102e_bool, all_493_1, all_548_1, simplifying with
% 91.80/12.94 | | | (105), (106), (139), (149) gives:
% 91.80/12.94 | | | (171) all_548_1 = all_493_1
% 91.80/12.94 | | |
% 91.80/12.94 | | | GROUND_INST: instantiating (5) with all_488_3, all_555_2, fa, simplifying
% 91.80/12.94 | | | with (67), (144), (147) gives:
% 91.80/12.94 | | | (172) ? [v0: $i] : ? [v1: $i] :
% 91.80/12.94 | | | ((hAPP_f971112728l_bool(finite364844667_state, fa) = v1 & $i(v1)
% 91.80/12.94 | | | & hBOOL(v1)) | (hAPP_f1664156314l_bool(finite_finite_pname,
% 91.80/12.94 | | | all_555_2) = v0 & $i(v0) & ~ hBOOL(v0)))
% 91.80/12.94 | | |
% 91.80/12.94 | | | DELTA: instantiating (169) with fresh symbols all_602_0, all_602_1 gives:
% 91.80/12.94 | | | (173) hoare_1598289066_state(bot_bo620288102e_bool) = all_602_1 &
% 91.80/12.94 | | | hAPP_f971112728l_bool(all_602_1, all_548_1) = all_602_0 &
% 91.80/12.94 | | | $i(all_602_0) & $i(all_602_1) & ~ hBOOL(all_602_0)
% 91.80/12.94 | | |
% 91.80/12.94 | | | ALPHA: (173) implies:
% 91.80/12.94 | | | (174) ~ hBOOL(all_602_0)
% 91.80/12.94 | | | (175) hAPP_f971112728l_bool(all_602_1, all_548_1) = all_602_0
% 91.80/12.94 | | | (176) hoare_1598289066_state(bot_bo620288102e_bool) = all_602_1
% 91.80/12.94 | | |
% 91.80/12.94 | | | DELTA: instantiating (168) with fresh symbols all_608_0, all_608_1 gives:
% 91.80/12.94 | | | (177) hoare_1598289066_state(bot_bo620288102e_bool) = all_608_1 &
% 91.80/12.94 | | | hAPP_f971112728l_bool(all_608_1, all_528_0) = all_608_0 &
% 91.80/12.94 | | | $i(all_608_0) & $i(all_608_1) & ~ hBOOL(all_608_0)
% 91.80/12.94 | | |
% 91.80/12.94 | | | ALPHA: (177) implies:
% 91.80/12.94 | | | (178) hoare_1598289066_state(bot_bo620288102e_bool) = all_608_1
% 91.80/12.94 | | |
% 91.80/12.94 | | | DELTA: instantiating (167) with fresh symbols all_616_0, all_616_1 gives:
% 91.80/12.94 | | | (179) hoare_1598289066_state(bot_bo620288102e_bool) = all_616_1 &
% 91.80/12.94 | | | hAPP_f971112728l_bool(all_616_1, all_493_1) = all_616_0 &
% 91.80/12.94 | | | $i(all_616_0) & $i(all_616_1) & ~ hBOOL(all_616_0)
% 91.80/12.94 | | |
% 91.80/12.94 | | | ALPHA: (179) implies:
% 91.80/12.94 | | | (180) hoare_1598289066_state(bot_bo620288102e_bool) = all_616_1
% 91.80/12.94 | | |
% 91.80/12.94 | | | DELTA: instantiating (166) with fresh symbols all_618_0, all_618_1 gives:
% 91.80/12.94 | | | (181) (hAPP_f1664156314l_bool(finite_finite_pname, all_555_2) =
% 91.80/12.94 | | | all_618_0 & $i(all_618_0) & hBOOL(all_618_0)) |
% 91.80/12.94 | | | (hAPP_f1664156314l_bool(finite_finite_pname, all_405_1) =
% 91.80/12.94 | | | all_618_1 & $i(all_618_1) & ~ hBOOL(all_618_1))
% 91.80/12.94 | | |
% 91.80/12.94 | | | DELTA: instantiating (172) with fresh symbols all_619_0, all_619_1 gives:
% 91.80/12.94 | | | (182) (hAPP_f971112728l_bool(finite364844667_state, fa) = all_619_0 &
% 91.80/12.94 | | | $i(all_619_0) & hBOOL(all_619_0)) |
% 91.80/12.94 | | | (hAPP_f1664156314l_bool(finite_finite_pname, all_555_2) =
% 91.80/12.94 | | | all_619_1 & $i(all_619_1) & ~ hBOOL(all_619_1))
% 91.80/12.94 | | |
% 91.80/12.94 | | | DELTA: instantiating (170) with fresh symbols all_623_0, all_623_1 gives:
% 91.80/12.94 | | | (183) (hAPP_f971112728l_bool(finite364844667_state, all_528_0) =
% 91.80/12.94 | | | all_623_0 & $i(all_623_0) & hBOOL(all_623_0)) |
% 91.80/12.94 | | | (hAPP_f971112728l_bool(finite364844667_state, fa) = all_623_1 &
% 91.80/12.94 | | | $i(all_623_1) & ~ hBOOL(all_623_1))
% 91.80/12.94 | | |
% 91.80/12.94 | | | REDUCE: (171), (175) imply:
% 91.80/12.94 | | | (184) hAPP_f971112728l_bool(all_602_1, all_493_1) = all_602_0
% 91.80/12.94 | | |
% 91.80/12.94 | | | BETA: splitting (181) gives:
% 91.80/12.94 | | |
% 91.80/12.94 | | | Case 1:
% 91.80/12.94 | | | |
% 91.80/12.94 | | | | (185) hAPP_f1664156314l_bool(finite_finite_pname, all_555_2) =
% 91.80/12.94 | | | | all_618_0 & $i(all_618_0) & hBOOL(all_618_0)
% 91.80/12.94 | | | |
% 91.80/12.94 | | | | ALPHA: (185) implies:
% 91.80/12.94 | | | | (186) hBOOL(all_618_0)
% 91.80/12.94 | | | | (187) hAPP_f1664156314l_bool(finite_finite_pname, all_555_2) =
% 91.80/12.94 | | | | all_618_0
% 91.80/12.94 | | | |
% 91.80/12.94 | | | | BETA: splitting (182) gives:
% 91.80/12.94 | | | |
% 91.80/12.94 | | | | Case 1:
% 91.80/12.94 | | | | |
% 91.80/12.94 | | | | | (188) hAPP_f971112728l_bool(finite364844667_state, fa) = all_619_0
% 91.80/12.94 | | | | | & $i(all_619_0) & hBOOL(all_619_0)
% 91.80/12.94 | | | | |
% 91.80/12.94 | | | | | ALPHA: (188) implies:
% 91.80/12.94 | | | | | (189) hBOOL(all_619_0)
% 91.80/12.94 | | | | | (190) hAPP_f971112728l_bool(finite364844667_state, fa) = all_619_0
% 91.80/12.94 | | | | |
% 91.80/12.94 | | | | | BETA: splitting (183) gives:
% 91.80/12.94 | | | | |
% 91.80/12.94 | | | | | Case 1:
% 91.80/12.94 | | | | | |
% 91.80/12.94 | | | | | |
% 91.80/12.94 | | | | | | GROUND_INST: instantiating (31) with all_490_0, all_616_1,
% 91.80/12.94 | | | | | | bot_bo620288102e_bool, simplifying with (74), (180)
% 91.80/12.94 | | | | | | gives:
% 91.80/12.94 | | | | | | (191) all_616_1 = all_490_0
% 91.80/12.94 | | | | | |
% 91.80/12.94 | | | | | | GROUND_INST: instantiating (31) with all_608_1, all_616_1,
% 91.80/12.94 | | | | | | bot_bo620288102e_bool, simplifying with (178), (180)
% 91.80/12.94 | | | | | | gives:
% 91.80/12.94 | | | | | | (192) all_616_1 = all_608_1
% 91.80/12.94 | | | | | |
% 91.80/12.94 | | | | | | GROUND_INST: instantiating (31) with all_602_1, all_616_1,
% 91.80/12.94 | | | | | | bot_bo620288102e_bool, simplifying with (176), (180)
% 91.80/12.94 | | | | | | gives:
% 91.80/12.94 | | | | | | (193) all_616_1 = all_602_1
% 91.80/12.94 | | | | | |
% 91.80/12.94 | | | | | | COMBINE_EQS: (191), (192) imply:
% 91.80/12.94 | | | | | | (194) all_608_1 = all_490_0
% 91.80/12.94 | | | | | |
% 91.80/12.94 | | | | | | COMBINE_EQS: (192), (193) imply:
% 91.80/12.94 | | | | | | (195) all_608_1 = all_602_1
% 91.80/12.94 | | | | | |
% 91.80/12.94 | | | | | | COMBINE_EQS: (194), (195) imply:
% 91.80/12.94 | | | | | | (196) all_602_1 = all_490_0
% 91.80/12.94 | | | | | |
% 91.80/12.94 | | | | | | SIMP: (196) implies:
% 91.80/12.94 | | | | | | (197) all_602_1 = all_490_0
% 91.80/12.94 | | | | | |
% 91.80/12.94 | | | | | | REDUCE: (184), (197) imply:
% 91.80/12.94 | | | | | | (198) hAPP_f971112728l_bool(all_490_0, all_493_1) = all_602_0
% 91.80/12.94 | | | | | |
% 91.80/12.94 | | | | | | BETA: splitting (148) gives:
% 91.80/12.94 | | | | | |
% 91.80/12.94 | | | | | | Case 1:
% 91.80/12.94 | | | | | | |
% 91.80/12.94 | | | | | | | (199) insert1415133716_state(all_418_2, bot_bo620288102e_bool)
% 91.80/12.94 | | | | | | | = all_557_1 & hAPP_f971112728l_bool(all_490_0, all_557_1)
% 91.80/12.94 | | | | | | | = all_557_0 & $i(all_557_0) & $i(all_557_1) &
% 91.80/12.94 | | | | | | | hBOOL(all_557_0)
% 91.80/12.94 | | | | | | |
% 91.80/12.94 | | | | | | | ALPHA: (199) implies:
% 91.80/12.94 | | | | | | | (200) hBOOL(all_557_0)
% 91.80/12.94 | | | | | | | (201) hAPP_f971112728l_bool(all_490_0, all_557_1) = all_557_0
% 91.80/12.94 | | | | | | | (202) insert1415133716_state(all_418_2, bot_bo620288102e_bool)
% 91.80/12.94 | | | | | | | = all_557_1
% 91.80/12.94 | | | | | | |
% 91.80/12.94 | | | | | | | GROUND_INST: instantiating (35) with all_493_1, all_557_1,
% 91.80/12.94 | | | | | | | bot_bo620288102e_bool, all_418_2, simplifying with
% 91.80/12.94 | | | | | | | (105), (202) gives:
% 91.80/12.94 | | | | | | | (203) all_557_1 = all_493_1
% 91.80/12.94 | | | | | | |
% 91.80/12.94 | | | | | | | REDUCE: (201), (203) imply:
% 91.80/12.94 | | | | | | | (204) hAPP_f971112728l_bool(all_490_0, all_493_1) = all_557_0
% 91.80/12.94 | | | | | | |
% 91.80/12.94 | | | | | | | GROUND_INST: instantiating (34) with all_602_0, all_557_0,
% 91.80/12.94 | | | | | | | all_493_1, all_490_0, simplifying with (198), (204)
% 91.80/12.94 | | | | | | | gives:
% 91.80/12.94 | | | | | | | (205) all_602_0 = all_557_0
% 91.80/12.94 | | | | | | |
% 91.80/12.94 | | | | | | | REDUCE: (174), (205) imply:
% 91.80/12.94 | | | | | | | (206) ~ hBOOL(all_557_0)
% 91.80/12.94 | | | | | | |
% 91.80/12.94 | | | | | | | PRED_UNIFY: (200), (206) imply:
% 91.80/12.95 | | | | | | | (207) $false
% 91.80/12.95 | | | | | | |
% 91.80/12.95 | | | | | | | CLOSE: (207) is inconsistent.
% 91.80/12.95 | | | | | | |
% 91.80/12.95 | | | | | | Case 2:
% 91.80/12.95 | | | | | | |
% 91.80/12.95 | | | | | | | (208) wt(y) = all_557_2 & $i(all_557_2) & ~ hBOOL(all_557_2)
% 91.80/12.95 | | | | | | |
% 91.80/12.95 | | | | | | | ALPHA: (208) implies:
% 91.80/12.95 | | | | | | | (209) ~ hBOOL(all_557_2)
% 91.80/12.95 | | | | | | | (210) wt(y) = all_557_2
% 91.80/12.95 | | | | | | |
% 91.80/12.95 | | | | | | | BETA: splitting (114) gives:
% 91.80/12.95 | | | | | | |
% 91.80/12.95 | | | | | | | Case 1:
% 91.80/12.95 | | | | | | | |
% 91.80/12.95 | | | | | | | | (211) fFalse = wT_bodies
% 91.80/12.95 | | | | | | | |
% 91.80/12.95 | | | | | | | | REDUCE: (16), (211) imply:
% 91.80/12.95 | | | | | | | | (212) ~ hBOOL(wT_bodies)
% 91.80/12.95 | | | | | | | |
% 91.80/12.95 | | | | | | | | PRED_UNIFY: (19), (212) imply:
% 91.80/12.95 | | | | | | | | (213) $false
% 91.80/12.95 | | | | | | | |
% 91.80/12.95 | | | | | | | | CLOSE: (213) is inconsistent.
% 91.80/12.95 | | | | | | | |
% 91.80/12.95 | | | | | | | Case 2:
% 91.80/12.95 | | | | | | | |
% 91.80/12.95 | | | | | | | | (214) fTrue = wT_bodies
% 91.80/12.95 | | | | | | | |
% 91.80/12.95 | | | | | | | | BETA: splitting (165) gives:
% 91.80/12.95 | | | | | | | |
% 91.80/12.95 | | | | | | | | Case 1:
% 91.80/12.95 | | | | | | | | |
% 91.80/12.95 | | | | | | | | | (215) all_432_0 = fTrue
% 91.80/12.95 | | | | | | | | |
% 91.80/12.95 | | | | | | | | | COMBINE_EQS: (214), (215) imply:
% 91.80/12.95 | | | | | | | | | (216) all_432_0 = wT_bodies
% 91.80/12.95 | | | | | | | | |
% 91.80/12.95 | | | | | | | | | GROUND_INST: instantiating (14) with pn, y, all_380_0,
% 91.80/12.95 | | | | | | | | | all_557_2, simplifying with (19), (24), (28),
% 91.80/12.95 | | | | | | | | | (43), (209), (210) gives:
% 91.80/12.95 | | | | | | | | | (217) ? [v0: any] : ( ~ (v0 = all_380_0) & some_com(y) =
% 91.80/12.95 | | | | | | | | | v0 & $i(v0))
% 91.80/12.95 | | | | | | | | |
% 91.80/12.95 | | | | | | | | | DELTA: instantiating (217) with fresh symbol all_1001_0 gives:
% 91.80/12.95 | | | | | | | | | (218) ~ (all_1001_0 = all_380_0) & some_com(y) =
% 91.80/12.95 | | | | | | | | | all_1001_0 & $i(all_1001_0)
% 91.80/12.95 | | | | | | | | |
% 91.80/12.95 | | | | | | | | | ALPHA: (218) implies:
% 91.80/12.95 | | | | | | | | | (219) ~ (all_1001_0 = all_380_0)
% 91.80/12.95 | | | | | | | | | (220) some_com(y) = all_1001_0
% 91.80/12.95 | | | | | | | | |
% 91.80/12.95 | | | | | | | | | GROUND_INST: instantiating (32) with all_380_0, all_1001_0, y,
% 91.80/12.95 | | | | | | | | | simplifying with (44), (220) gives:
% 91.80/12.95 | | | | | | | | | (221) all_1001_0 = all_380_0
% 91.80/12.95 | | | | | | | | |
% 91.80/12.95 | | | | | | | | | REDUCE: (219), (221) imply:
% 91.80/12.95 | | | | | | | | | (222) $false
% 91.80/12.95 | | | | | | | | |
% 91.80/12.95 | | | | | | | | | CLOSE: (222) is inconsistent.
% 91.80/12.95 | | | | | | | | |
% 91.80/12.95 | | | | | | | | Case 2:
% 91.80/12.95 | | | | | | | | |
% 91.80/12.95 | | | | | | | | | (223) all_432_0 = fFalse
% 91.80/12.95 | | | | | | | | |
% 91.80/12.95 | | | | | | | | | REDUCE: (57), (223) imply:
% 91.80/12.95 | | | | | | | | | (224) hBOOL(fFalse)
% 91.80/12.95 | | | | | | | | |
% 91.80/12.95 | | | | | | | | | PRED_UNIFY: (16), (224) imply:
% 91.80/12.95 | | | | | | | | | (225) $false
% 91.80/12.95 | | | | | | | | |
% 91.80/12.95 | | | | | | | | | CLOSE: (225) is inconsistent.
% 91.80/12.95 | | | | | | | | |
% 91.80/12.95 | | | | | | | | End of split
% 91.80/12.95 | | | | | | | |
% 91.80/12.95 | | | | | | | End of split
% 91.80/12.95 | | | | | | |
% 91.80/12.95 | | | | | | End of split
% 91.80/12.95 | | | | | |
% 91.80/12.95 | | | | | Case 2:
% 91.80/12.95 | | | | | |
% 91.80/12.95 | | | | | | (226) hAPP_f971112728l_bool(finite364844667_state, fa) =
% 91.80/12.95 | | | | | | all_623_1 & $i(all_623_1) & ~ hBOOL(all_623_1)
% 91.80/12.95 | | | | | |
% 91.80/12.95 | | | | | | ALPHA: (226) implies:
% 91.80/12.95 | | | | | | (227) ~ hBOOL(all_623_1)
% 91.80/12.95 | | | | | | (228) hAPP_f971112728l_bool(finite364844667_state, fa) =
% 91.80/12.95 | | | | | | all_623_1
% 91.80/12.95 | | | | | |
% 91.80/12.95 | | | | | | GROUND_INST: instantiating (34) with all_392_0, all_623_1, fa,
% 91.80/12.95 | | | | | | finite364844667_state, simplifying with (46), (228)
% 91.80/12.95 | | | | | | gives:
% 91.80/12.95 | | | | | | (229) all_623_1 = all_392_0
% 91.80/12.95 | | | | | |
% 91.80/12.95 | | | | | | GROUND_INST: instantiating (34) with all_619_0, all_623_1, fa,
% 91.80/12.95 | | | | | | finite364844667_state, simplifying with (190), (228)
% 91.80/12.95 | | | | | | gives:
% 91.80/12.95 | | | | | | (230) all_623_1 = all_619_0
% 91.80/12.95 | | | | | |
% 91.80/12.95 | | | | | | COMBINE_EQS: (229), (230) imply:
% 91.80/12.95 | | | | | | (231) all_619_0 = all_392_0
% 91.80/12.95 | | | | | |
% 91.80/12.95 | | | | | | SIMP: (231) implies:
% 91.80/12.95 | | | | | | (232) all_619_0 = all_392_0
% 91.80/12.95 | | | | | |
% 91.80/12.95 | | | | | | REDUCE: (189), (232) imply:
% 91.80/12.95 | | | | | | (233) hBOOL(all_392_0)
% 91.80/12.95 | | | | | |
% 91.80/12.95 | | | | | | REDUCE: (227), (229) imply:
% 91.80/12.95 | | | | | | (234) ~ hBOOL(all_392_0)
% 91.80/12.95 | | | | | |
% 91.80/12.95 | | | | | | PRED_UNIFY: (233), (234) imply:
% 91.80/12.95 | | | | | | (235) $false
% 91.80/12.95 | | | | | |
% 91.80/12.95 | | | | | | CLOSE: (235) is inconsistent.
% 91.80/12.95 | | | | | |
% 91.80/12.95 | | | | | End of split
% 91.80/12.95 | | | | |
% 91.80/12.95 | | | | Case 2:
% 91.80/12.95 | | | | |
% 91.80/12.95 | | | | | (236) hAPP_f1664156314l_bool(finite_finite_pname, all_555_2) =
% 91.80/12.95 | | | | | all_619_1 & $i(all_619_1) & ~ hBOOL(all_619_1)
% 91.80/12.95 | | | | |
% 91.80/12.95 | | | | | ALPHA: (236) implies:
% 91.80/12.95 | | | | | (237) ~ hBOOL(all_619_1)
% 91.80/12.95 | | | | | (238) hAPP_f1664156314l_bool(finite_finite_pname, all_555_2) =
% 91.80/12.95 | | | | | all_619_1
% 91.80/12.95 | | | | |
% 91.80/12.95 | | | | | GROUND_INST: instantiating (33) with all_618_0, all_619_1, all_555_2,
% 91.80/12.95 | | | | | finite_finite_pname, simplifying with (187), (238) gives:
% 91.80/12.95 | | | | | (239) all_619_1 = all_618_0
% 91.80/12.95 | | | | |
% 91.80/12.95 | | | | | REDUCE: (237), (239) imply:
% 91.80/12.95 | | | | | (240) ~ hBOOL(all_618_0)
% 91.80/12.95 | | | | |
% 91.80/12.95 | | | | | PRED_UNIFY: (186), (240) imply:
% 91.80/12.95 | | | | | (241) $false
% 91.80/12.95 | | | | |
% 91.80/12.95 | | | | | CLOSE: (241) is inconsistent.
% 91.80/12.95 | | | | |
% 91.80/12.95 | | | | End of split
% 91.80/12.95 | | | |
% 91.80/12.95 | | | Case 2:
% 91.80/12.95 | | | |
% 91.80/12.95 | | | | (242) hAPP_f1664156314l_bool(finite_finite_pname, all_405_1) =
% 91.80/12.95 | | | | all_618_1 & $i(all_618_1) & ~ hBOOL(all_618_1)
% 91.80/12.95 | | | |
% 91.80/12.95 | | | | ALPHA: (242) implies:
% 91.80/12.95 | | | | (243) ~ hBOOL(all_618_1)
% 91.80/12.95 | | | | (244) hAPP_f1664156314l_bool(finite_finite_pname, all_405_1) =
% 91.80/12.95 | | | | all_618_1
% 91.80/12.95 | | | |
% 91.80/12.95 | | | | GROUND_INST: instantiating (33) with all_405_0, all_618_1, all_405_1,
% 91.80/12.95 | | | | finite_finite_pname, simplifying with (50), (244) gives:
% 91.80/12.95 | | | | (245) all_618_1 = all_405_0
% 91.80/12.95 | | | |
% 91.80/12.95 | | | | REDUCE: (243), (245) imply:
% 91.80/12.95 | | | | (246) ~ hBOOL(all_405_0)
% 91.80/12.95 | | | |
% 91.80/12.95 | | | | PRED_UNIFY: (48), (246) imply:
% 91.80/12.95 | | | | (247) $false
% 91.80/12.95 | | | |
% 91.80/12.95 | | | | CLOSE: (247) is inconsistent.
% 91.80/12.95 | | | |
% 91.80/12.95 | | | End of split
% 91.80/12.95 | | |
% 91.80/12.95 | | End of split
% 91.80/12.95 | |
% 91.80/12.95 | Case 2:
% 91.80/12.95 | |
% 91.80/12.95 | | (248) hAPP_f1664156314l_bool(finite_finite_pname, all_405_1) = all_553_1
% 91.80/12.95 | | & $i(all_553_1) & ~ hBOOL(all_553_1)
% 91.80/12.95 | |
% 91.80/12.95 | | ALPHA: (248) implies:
% 91.80/12.95 | | (249) ~ hBOOL(all_553_1)
% 91.80/12.95 | | (250) hAPP_f1664156314l_bool(finite_finite_pname, all_405_1) = all_553_1
% 91.80/12.95 | |
% 91.80/12.96 | | GROUND_INST: instantiating (33) with all_405_0, all_553_1, all_405_1,
% 91.80/12.96 | | finite_finite_pname, simplifying with (50), (250) gives:
% 91.80/12.96 | | (251) all_553_1 = all_405_0
% 91.80/12.96 | |
% 91.80/12.96 | | REDUCE: (249), (251) imply:
% 91.80/12.96 | | (252) ~ hBOOL(all_405_0)
% 91.80/12.96 | |
% 91.80/12.96 | | PRED_UNIFY: (48), (252) imply:
% 91.80/12.96 | | (253) $false
% 91.80/12.96 | |
% 91.80/12.96 | | CLOSE: (253) is inconsistent.
% 91.80/12.96 | |
% 91.80/12.96 | End of split
% 91.80/12.96 |
% 91.80/12.96 End of proof
% 91.80/12.96 % SZS output end Proof for theBenchmark
% 91.80/12.96
% 91.80/12.96 12362ms
%------------------------------------------------------------------------------