%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : SWW101+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n017.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  : 600s
% DateTime : Thu Jul 21 00:03:22 EDT 2022

% Result   : Theorem 207.17s 151.52s
% Output   : Proof 211.03s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SWW101+1 : TPTP v8.1.0. Released v5.2.0.
% 0.07/0.13  % Command  : ePrincess-casc -timeout=%d %s
% 0.13/0.34  % Computer : n017.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  : 600
% 0.13/0.34  % DateTime : Sun Jun  5 02:28:00 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.19/0.58          ____       _                          
% 0.19/0.58    ___  / __ \_____(_)___  ________  __________
% 0.19/0.58   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.19/0.58  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.19/0.58  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.19/0.58  
% 0.19/0.58  A Theorem Prover for First-Order Logic
% 0.19/0.58  (ePrincess v.1.0)
% 0.19/0.58  
% 0.19/0.58  (c) Philipp Rümmer, 2009-2015
% 0.19/0.58  (c) Peter Backeman, 2014-2015
% 0.19/0.58  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.19/0.58  Free software under GNU Lesser General Public License (LGPL).
% 0.19/0.58  Bug reports to peter@backeman.se
% 0.19/0.58  
% 0.19/0.58  For more information, visit http://user.uu.se/~petba168/breu/
% 0.19/0.58  
% 0.19/0.58  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.77/0.63  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.77/0.96  Prover 0: Preprocessing ...
% 3.14/1.38  Prover 0: Warning: ignoring some quantifiers
% 3.37/1.41  Prover 0: Constructing countermodel ...
% 5.07/1.78  Prover 0: gave up
% 5.07/1.78  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 5.29/1.83  Prover 1: Preprocessing ...
% 5.70/1.96  Prover 1: Constructing countermodel ...
% 5.93/2.02  Prover 1: gave up
% 5.93/2.02  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 6.29/2.06  Prover 2: Preprocessing ...
% 6.79/2.20  Prover 2: Warning: ignoring some quantifiers
% 6.79/2.21  Prover 2: Constructing countermodel ...
% 15.23/4.21  Prover 3: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 15.45/4.25  Prover 3: Preprocessing ...
% 15.92/4.36  Prover 3: Warning: ignoring some quantifiers
% 15.92/4.37  Prover 3: Constructing countermodel ...
% 16.51/4.49  Prover 3: gave up
% 16.51/4.49  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 16.51/4.51  Prover 4: Preprocessing ...
% 17.26/4.66  Prover 4: Warning: ignoring some quantifiers
% 17.26/4.66  Prover 4: Constructing countermodel ...
% 20.81/5.50  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 21.04/5.54  Prover 5: Preprocessing ...
% 21.60/5.66  Prover 5: Constructing countermodel ...
% 43.40/20.90  Prover 5: stopped
% 43.95/21.10  Prover 6: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 43.95/21.14  Prover 6: Preprocessing ...
% 44.33/21.19  Prover 6: Warning: ignoring some quantifiers
% 44.33/21.19  Prover 6: Constructing countermodel ...
% 123.99/93.09  Prover 2: stopped
% 124.23/93.29  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximalOutermost -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all
% 124.31/93.32  Prover 7: Preprocessing ...
% 124.38/93.36  Prover 7: Proving ...
% 181.74/134.26  Prover 4: stopped
% 181.91/134.46  Prover 8: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all
% 182.13/134.51  Prover 8: Preprocessing ...
% 182.20/134.55  Prover 8: Constructing countermodel ...
% 182.20/134.58  Prover 8: gave up
% 182.20/134.58  Prover 9: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=completeFrugal
% 182.20/134.60  Prover 9: Preprocessing ...
% 182.65/134.67  Prover 9: Proving ...
% 199.61/149.00  Prover 9: stopped
% 199.81/149.20  Prover 10: Options:  -triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 199.94/149.23  Prover 10: Preprocessing ...
% 200.24/149.30  Prover 10: Warning: ignoring some quantifiers
% 200.24/149.31  Prover 10: Constructing countermodel ...
% 200.78/149.42  Prover 10: gave up
% 200.78/149.42  Prover 11: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 200.83/149.43  Prover 11: Preprocessing ...
% 200.83/149.48  Prover 11: Warning: ignoring some quantifiers
% 200.83/149.48  Prover 11: Constructing countermodel ...
% 201.22/149.56  Prover 11: gave up
% 201.22/149.56  Prover 12: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all
% 201.51/149.58  Prover 12: Preprocessing ...
% 201.51/149.62  Prover 12: Constructing countermodel ...
% 201.51/149.64  Prover 12: gave up
% 201.51/149.64  Prover 13: Options:  -triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 201.51/149.66  Prover 13: Preprocessing ...
% 202.01/149.70  Prover 13: Warning: ignoring some quantifiers
% 202.01/149.70  Prover 13: Constructing countermodel ...
% 207.17/151.52  Prover 13: proved (1877ms)
% 207.17/151.52  Prover 6: stopped
% 207.17/151.52  Prover 7: stopped
% 207.17/151.52  
% 207.17/151.52  No countermodel exists, formula is valid
% 207.17/151.52  % SZS status Theorem for theBenchmark
% 207.17/151.52  
% 207.17/151.52  Generating proof ... Warning: ignoring some quantifiers
% 210.23/152.46  found it (size 700)
% 210.23/152.46  
% 210.23/152.46  % SZS output start Proof for theBenchmark
% 210.23/152.46  Assumed formulas after preprocessing and simplification: 
% 210.23/152.46  | (0) false1 = false &  ~ (false2 = false) &  ~ (err = true) &  ~ (err = false) &  ~ (true = false) & not1(true) = false & not1(false) = true & d(err) = 0 & d(true) = 0 & d(false) = 0 &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (impl(v4, v2) = v5) |  ~ (impl(v3, v5) = v6) |  ~ (impl(v1, v2) = v4) |  ~ (impl(v0, v2) = v3) |  ? [v7] :  ? [v8] : (f3(v0, v1, v2) = v7 & lazy_impl(v8, v6) = v7 & prop(v2) = v8)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v1 = v0 |  ~ (f4(v4, v3, v2) = v1) |  ~ (f4(v4, v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v1 = v0 |  ~ (f3(v4, v3, v2) = v1) |  ~ (f3(v4, v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v1 = v0 |  ~ (f2(v4, v3, v2) = v1) |  ~ (f2(v4, v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v1 = v0 |  ~ (f1(v4, v3, v2) = v1) |  ~ (f1(v4, v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (apply(v0, v1) = v3) |  ~ (impl(v3, v2) = v4) | f4(v0, v1, v2) = v4) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (lazy_impl(v0, v3) = v4) |  ~ (impl(v1, v2) = v3) |  ? [v5] :  ? [v6] :  ? [v7] : (f2(v0, v1, v2) = v5 & lazy_impl(v6, v7) = v5 & impl(v4, v2) = v7 & prop(v2) = v6)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (impl(v1, v2) = v3) |  ~ (impl(v0, v3) = v4) |  ? [v5] :  ? [v6] :  ? [v7] : (f1(v0, v1, v2) = v5 & lazy_impl(v6, v7) = v5 & impl(v4, v2) = v7 & prop(v2) = v6)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (f6(v3, v2) = v1) |  ~ (f6(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (f5(v3, v2) = v1) |  ~ (f5(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (apply(v3, v2) = v1) |  ~ (apply(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (or2(v3, v2) = v1) |  ~ (or2(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (or1(v3, v2) = v1) |  ~ (or1(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (lazy_and2(v3, v2) = v1) |  ~ (lazy_and2(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (lazy_and1(v3, v2) = v1) |  ~ (lazy_and1(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (and2(v3, v2) = v1) |  ~ (and2(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (and1(v3, v2) = v1) |  ~ (and1(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (lazy_impl(v3, v2) = v1) |  ~ (lazy_impl(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (impl(v3, v2) = v1) |  ~ (impl(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (existsprefers(v3, v2) = v1) |  ~ (existsprefers(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (forallprefers(v3, v2) = v1) |  ~ (forallprefers(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (f4(v0, v1, v2) = v3) |  ? [v4] : (apply(v0, v1) = v4 & impl(v4, v2) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (f3(v0, v1, v2) = v3) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] : (lazy_impl(v4, v8) = v3 & impl(v6, v2) = v7 & impl(v5, v7) = v8 & impl(v1, v2) = v6 & impl(v0, v2) = v5 & prop(v2) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (f2(v0, v1, v2) = v3) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (lazy_impl(v4, v7) = v3 & lazy_impl(v0, v5) = v6 & impl(v6, v2) = v7 & impl(v1, v2) = v5 & prop(v2) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (f1(v0, v1, v2) = v3) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (lazy_impl(v4, v7) = v3 & impl(v6, v2) = v7 & impl(v1, v2) = v5 & impl(v0, v5) = v6 & prop(v2) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (existsprefers(v0, v1) = v2) | ( ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] : (d(v1) = v4 & d(v0) = v3 & bool(v1) = v6 & bool(v0) = v5 & ( ~ (v4 = 0) | (v3 = 0 & ( ~ (v6 = 0) | v5 = 0)))) & ( ~ (v1 = false) |  ~ (v0 = true)))) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (forallprefers(v0, v1) = v2) | ( ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] : (d(v1) = v4 & d(v0) = v3 & bool(v1) = v6 & bool(v0) = v5 & ( ~ (v4 = 0) | (v3 = 0 & ( ~ (v6 = 0) | v5 = 0)))) & ( ~ (v1 = true) |  ~ (v0 = false)))) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (not2(v2) = v1) |  ~ (not2(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (not1(v2) = v1) |  ~ (not1(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (f7(v2) = v1) |  ~ (f7(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (exists2(v2) = v1) |  ~ (exists2(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (exists1(v2) = v1) |  ~ (exists1(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (prop(v2) = v1) |  ~ (prop(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (phi(v2) = v1) |  ~ (phi(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (d(v2) = v1) |  ~ (d(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (bool(v2) = v1) |  ~ (bool(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (f6(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : (f5(v0, v1) = v4 & lazy_impl(v3, v5) = v2 & impl(v4, v1) = v5 & prop(v1) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (f5(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : (f6(v0, v1) = v3 & lazy_impl(v4, v5) = v3 & impl(v2, v1) = v5 & prop(v1) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (f5(v0, v1) = v2) |  ? [v3] :  ? [v4] : (f4(v0, v3, v1) = v4 & phi(v4) = v2 &  ! [v5] :  ! [v6] : ( ~ (f4(v0, v5, v1) = v6) |  ? [v7] : ( ~ (v7 = 0) & forallprefers(v6, v4) = v7)))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (or2(v0, v1) = v2) |  ? [v3] :  ? [v4] : (f3(v0, v1, v3) = v4 & phi(v4) = v2 &  ! [v5] :  ! [v6] : ( ~ (f3(v0, v1, v5) = v6) |  ? [v7] : ( ~ (v7 = 0) & forallprefers(v6, v4) = v7)))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (or1(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : (phi(v1) = v5 & bool(v1) = v4 & bool(v0) = v3 & ( ~ (v3 = 0) | v5 = v2 | v4 = 0))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (or1(v0, v1) = v2) |  ? [v3] :  ? [v4] : (phi(v0) = v4 & bool(v0) = v3 & (v4 = v2 | v3 = 0))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (lazy_and2(v0, v1) = v2) |  ? [v3] :  ? [v4] : (f2(v0, v1, v3) = v4 & phi(v4) = v2 &  ! [v5] :  ! [v6] : ( ~ (f2(v0, v1, v5) = v6) |  ? [v7] : ( ~ (v7 = 0) & forallprefers(v6, v4) = v7)))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (lazy_and1(v0, v1) = v2) |  ? [v3] :  ? [v4] : (phi(v0) = v4 & bool(v0) = v3 & (v4 = v2 | v3 = 0))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (and2(v0, v1) = v2) |  ? [v3] :  ? [v4] : (f1(v0, v1, v3) = v4 & phi(v4) = v2 &  ! [v5] :  ! [v6] : ( ~ (f1(v0, v1, v5) = v6) |  ? [v7] : ( ~ (v7 = 0) & forallprefers(v6, v4) = v7)))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (and1(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : (phi(v1) = v5 & bool(v1) = v4 & bool(v0) = v3 & ( ~ (v3 = 0) | v5 = v2 | v4 = 0))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (and1(v0, v1) = v2) |  ? [v3] :  ? [v4] : (phi(v0) = v4 & bool(v0) = v3 & (v4 = v2 | v3 = 0))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (lazy_impl(v0, v1) = v2) |  ? [v3] :  ? [v4] : (phi(v0) = v4 & bool(v0) = v3 & (v4 = v2 | v3 = 0))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (impl(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : (phi(v1) = v5 & bool(v1) = v4 & bool(v0) = v3 & ( ~ (v3 = 0) | v5 = v2 | v4 = 0))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (impl(v0, v1) = v2) |  ? [v3] :  ? [v4] : (phi(v0) = v4 & bool(v0) = v3 & (v4 = v2 | v3 = 0))) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (or1(false, v0) = v1) |  ? [v2] : ( ~ (v2 = 0) & bool(v0) = v2)) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (and1(true, v0) = v1) |  ? [v2] : ( ~ (v2 = 0) & bool(v0) = v2)) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (impl(true, v0) = v1) |  ? [v2] : ( ~ (v2 = 0) & bool(v0) = v2)) &  ! [v0] :  ! [v1] : (v1 = true |  ~ (or1(true, v0) = v1) |  ? [v2] : ( ~ (v2 = 0) & bool(v0) = v2)) &  ! [v0] :  ! [v1] : (v1 = true |  ~ (lazy_impl(false, v0) = v1)) &  ! [v0] :  ! [v1] : (v1 = true |  ~ (impl(false, v0) = v1) |  ? [v2] : ( ~ (v2 = 0) & bool(v0) = v2)) &  ! [v0] :  ! [v1] : (v1 = true |  ~ (prop(v0) = v1) |  ? [v2] : ( ~ (v2 = 0) & bool(v0) = v2)) &  ! [v0] :  ! [v1] : (v1 = false |  ~ (lazy_and1(false, v0) = v1)) &  ! [v0] :  ! [v1] : (v1 = false |  ~ (and1(false, v0) = v1) |  ? [v2] : ( ~ (v2 = 0) & bool(v0) = v2)) &  ! [v0] :  ! [v1] : (v1 = false |  ~ (prop(v0) = v1) | bool(v0) = 0) &  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (bool(v0) = v1) | prop(v0) = false) &  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (bool(v0) = v1) |  ? [v2] : ( ~ (v2 = true) & prop(v0) = v2)) &  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (bool(v0) = v1) |  ? [v2] : (not1(v0) = v2 & phi(v0) = v2)) &  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (bool(v0) = v1) | ( ~ (v0 = true) &  ~ (v0 = false))) &  ! [v0] :  ! [v1] : ( ~ (not2(v0) = v1) | impl(v0, false2) = v1) &  ! [v0] :  ! [v1] : ( ~ (not1(v0) = v1) |  ? [v2] :  ? [v3] : (phi(v0) = v3 & bool(v0) = v2 & (v3 = v1 | v2 = 0))) &  ! [v0] :  ! [v1] : ( ~ (f7(v0) = v1) |  ? [v2] : (lazy_impl(v2, v0) = v1 & prop(v0) = v2)) &  ! [v0] :  ! [v1] : ( ~ (exists2(v0) = v1) |  ? [v2] :  ? [v3] : (f6(v0, v2) = v3 & phi(v3) = v1 &  ! [v4] :  ! [v5] : ( ~ (f6(v0, v4) = v5) |  ? [v6] : ( ~ (v6 = 0) & forallprefers(v5, v3) = v6)))) &  ! [v0] :  ! [v1] : ( ~ (exists1(v0) = v1) |  ? [v2] :  ? [v3] : (apply(v0, v2) = v3 & phi(v3) = v1 &  ! [v4] :  ! [v5] : ( ~ (apply(v0, v4) = v5) |  ? [v6] : ( ~ (v6 = 0) & existsprefers(v5, v3) = v6)))) &  ! [v0] :  ! [v1] : ( ~ (lazy_and1(true, v0) = v1) | phi(v0) = v1) &  ! [v0] :  ! [v1] : ( ~ (lazy_impl(true, v0) = v1) | phi(v0) = v1) &  ! [v0] :  ! [v1] : ( ~ (impl(v0, false2) = v1) | not2(v0) = v1) &  ! [v0] :  ! [v1] : ( ~ (prop(v0) = v1) |  ? [v2] : (f7(v0) = v2 & lazy_impl(v1, v0) = v2)) &  ! [v0] :  ! [v1] : ( ~ (phi(v0) = v1) | lazy_and1(true, v0) = v1) &  ! [v0] :  ! [v1] : ( ~ (phi(v0) = v1) | lazy_impl(true, v0) = v1) &  ! [v0] :  ! [v1] : ( ~ (phi(v0) = v1) |  ? [v2] :  ? [v3] : (not1(v0) = v3 & bool(v0) = v2 & (v3 = v1 | v2 = 0))) &  ! [v0] :  ! [v1] : ( ~ (phi(v0) = v1) |  ? [v2] : (d(v0) = v2 & ((v2 = 0 & v1 = v0) | (v1 = err &  ~ (v2 = 0))))) &  ! [v0] :  ! [v1] : ( ~ (existsprefers(v0, v1) = 0) |  ? [v2] :  ? [v3] :  ? [v4] : (d(v1) = 0 & d(v0) = v2 & bool(v1) = v4 & bool(v0) = v3 & ( ~ (v2 = 0) | (v4 = 0 &  ~ (v3 = 0)))) | (v1 = false & v0 = true)) &  ! [v0] :  ! [v1] : ( ~ (forallprefers(v0, v1) = 0) |  ? [v2] :  ? [v3] :  ? [v4] : (d(v1) = 0 & d(v0) = v2 & bool(v1) = v4 & bool(v0) = v3 & ( ~ (v2 = 0) | (v4 = 0 &  ~ (v3 = 0)))) | (v1 = true & v0 = false)) &  ! [v0] :  ! [v1] : ( ~ (d(v0) = v1) |  ? [v2] : (phi(v0) = v2 & ((v2 = v0 & v1 = 0) | (v2 = err &  ~ (v1 = 0))))) &  ! [v0] : (v0 = true | v0 = false |  ~ (bool(v0) = 0)) &  ! [v0] : ( ~ (prop(v0) = true) | bool(v0) = 0) &  ! [v0] : ( ~ (prop(v0) = false) |  ? [v1] : ( ~ (v1 = 0) & bool(v0) = v1)) &  ! [v0] : ( ~ (bool(v0) = 0) | or1(true, v0) = true) &  ! [v0] : ( ~ (bool(v0) = 0) | or1(false, v0) = v0) &  ! [v0] : ( ~ (bool(v0) = 0) | and1(true, v0) = v0) &  ! [v0] : ( ~ (bool(v0) = 0) | and1(false, v0) = false) &  ! [v0] : ( ~ (bool(v0) = 0) | impl(true, v0) = v0) &  ! [v0] : ( ~ (bool(v0) = 0) | impl(false, v0) = true) &  ! [v0] : ( ~ (bool(v0) = 0) | prop(v0) = true) &  ! [v0] : ( ~ (bool(v0) = 0) |  ? [v1] : ( ~ (v1 = false) & prop(v0) = v1)) &  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : f4(v2, v1, v0) = v3 &  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : f3(v2, v1, v0) = v3 &  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : f2(v2, v1, v0) = v3 &  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : f1(v2, v1, v0) = v3 &  ? [v0] :  ? [v1] :  ? [v2] : f6(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : f5(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : apply(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : or2(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : or1(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : lazy_and2(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : lazy_and1(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : and2(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : and1(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : lazy_impl(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : impl(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : existsprefers(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : forallprefers(v1, v0) = v2 &  ? [v0] :  ? [v1] : not2(v0) = v1 &  ? [v0] :  ? [v1] : not1(v0) = v1 &  ? [v0] :  ? [v1] : f7(v0) = v1 &  ? [v0] :  ? [v1] : exists2(v0) = v1 &  ? [v0] :  ? [v1] : exists1(v0) = v1 &  ? [v0] :  ? [v1] : prop(v0) = v1 &  ? [v0] :  ? [v1] : phi(v0) = v1 &  ? [v0] :  ? [v1] : d(v0) = v1 &  ? [v0] :  ? [v1] : bool(v0) = v1 &  ? [v0] :  ? [v1] : (f7(v0) = v1 & phi(v1) = false2 &  ! [v2] :  ! [v3] : ( ~ (f7(v2) = v3) |  ? [v4] : ( ~ (v4 = 0) & forallprefers(v3, v1) = v4)))
% 210.23/152.51  | Applying alpha-rule on (0) yields:
% 210.23/152.51  | (1)  ! [v0] :  ! [v1] : ( ~ (prop(v0) = v1) |  ? [v2] : (f7(v0) = v2 & lazy_impl(v1, v0) = v2))
% 210.23/152.51  | (2)  ? [v0] :  ? [v1] :  ? [v2] : or1(v1, v0) = v2
% 210.23/152.51  | (3)  ! [v0] :  ! [v1] : (v1 = true |  ~ (or1(true, v0) = v1) |  ? [v2] : ( ~ (v2 = 0) & bool(v0) = v2))
% 210.23/152.51  | (4)  ! [v0] : ( ~ (bool(v0) = 0) | or1(false, v0) = v0)
% 210.23/152.51  | (5)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (lazy_and2(v0, v1) = v2) |  ? [v3] :  ? [v4] : (f2(v0, v1, v3) = v4 & phi(v4) = v2 &  ! [v5] :  ! [v6] : ( ~ (f2(v0, v1, v5) = v6) |  ? [v7] : ( ~ (v7 = 0) & forallprefers(v6, v4) = v7))))
% 210.23/152.51  | (6)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (prop(v2) = v1) |  ~ (prop(v2) = v0))
% 210.23/152.51  | (7)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (or1(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : (phi(v1) = v5 & bool(v1) = v4 & bool(v0) = v3 & ( ~ (v3 = 0) | v5 = v2 | v4 = 0)))
% 210.23/152.52  | (8)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (lazy_and1(v3, v2) = v1) |  ~ (lazy_and1(v3, v2) = v0))
% 210.23/152.52  | (9)  ! [v0] : ( ~ (bool(v0) = 0) |  ? [v1] : ( ~ (v1 = false) & prop(v0) = v1))
% 210.23/152.52  | (10)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (impl(v1, v2) = v3) |  ~ (impl(v0, v3) = v4) |  ? [v5] :  ? [v6] :  ? [v7] : (f1(v0, v1, v2) = v5 & lazy_impl(v6, v7) = v5 & impl(v4, v2) = v7 & prop(v2) = v6))
% 210.23/152.52  | (11)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (and1(v0, v1) = v2) |  ? [v3] :  ? [v4] : (phi(v0) = v4 & bool(v0) = v3 & (v4 = v2 | v3 = 0)))
% 210.23/152.52  | (12)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (f4(v0, v1, v2) = v3) |  ? [v4] : (apply(v0, v1) = v4 & impl(v4, v2) = v3))
% 210.23/152.52  | (13)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (bool(v0) = v1) |  ? [v2] : (not1(v0) = v2 & phi(v0) = v2))
% 210.23/152.52  | (14)  ? [v0] :  ? [v1] : (f7(v0) = v1 & phi(v1) = false2 &  ! [v2] :  ! [v3] : ( ~ (f7(v2) = v3) |  ? [v4] : ( ~ (v4 = 0) & forallprefers(v3, v1) = v4)))
% 210.23/152.52  | (15)  ! [v0] :  ! [v1] : ( ~ (phi(v0) = v1) |  ? [v2] :  ? [v3] : (not1(v0) = v3 & bool(v0) = v2 & (v3 = v1 | v2 = 0)))
% 210.23/152.52  | (16)  ? [v0] :  ? [v1] :  ? [v2] : f6(v1, v0) = v2
% 210.23/152.52  | (17)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (exists1(v2) = v1) |  ~ (exists1(v2) = v0))
% 210.23/152.52  | (18)  ? [v0] :  ? [v1] :  ? [v2] : lazy_impl(v1, v0) = v2
% 210.23/152.52  | (19)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (apply(v3, v2) = v1) |  ~ (apply(v3, v2) = v0))
% 210.23/152.52  | (20)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (bool(v0) = v1) | ( ~ (v0 = true) &  ~ (v0 = false)))
% 210.23/152.52  | (21)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v1 = v0 |  ~ (f3(v4, v3, v2) = v1) |  ~ (f3(v4, v3, v2) = v0))
% 210.23/152.52  | (22)  ! [v0] :  ! [v1] : (v1 = true |  ~ (lazy_impl(false, v0) = v1))
% 210.23/152.52  | (23) not1(false) = true
% 210.23/152.52  | (24)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (and1(v3, v2) = v1) |  ~ (and1(v3, v2) = v0))
% 210.23/152.52  | (25)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (f6(v3, v2) = v1) |  ~ (f6(v3, v2) = v0))
% 210.23/152.52  | (26)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (bool(v0) = v1) |  ? [v2] : ( ~ (v2 = true) & prop(v0) = v2))
% 210.23/152.52  | (27)  ! [v0] :  ! [v1] : (v1 = true |  ~ (prop(v0) = v1) |  ? [v2] : ( ~ (v2 = 0) & bool(v0) = v2))
% 210.23/152.52  | (28)  ! [v0] :  ! [v1] : ( ~ (existsprefers(v0, v1) = 0) |  ? [v2] :  ? [v3] :  ? [v4] : (d(v1) = 0 & d(v0) = v2 & bool(v1) = v4 & bool(v0) = v3 & ( ~ (v2 = 0) | (v4 = 0 &  ~ (v3 = 0)))) | (v1 = false & v0 = true))
% 210.23/152.52  | (29) false1 = false
% 210.23/152.52  | (30)  ! [v0] :  ! [v1] : (v1 = true |  ~ (impl(false, v0) = v1) |  ? [v2] : ( ~ (v2 = 0) & bool(v0) = v2))
% 210.23/152.52  | (31)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (f5(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : (f6(v0, v1) = v3 & lazy_impl(v4, v5) = v3 & impl(v2, v1) = v5 & prop(v1) = v4))
% 210.23/152.52  | (32)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (d(v2) = v1) |  ~ (d(v2) = v0))
% 210.23/152.52  | (33)  ! [v0] :  ! [v1] : ( ~ (phi(v0) = v1) | lazy_impl(true, v0) = v1)
% 210.23/152.52  | (34)  ! [v0] :  ! [v1] : ( ~ (lazy_impl(true, v0) = v1) | phi(v0) = v1)
% 210.23/152.52  | (35)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (f5(v3, v2) = v1) |  ~ (f5(v3, v2) = v0))
% 210.67/152.52  | (36)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (or1(v3, v2) = v1) |  ~ (or1(v3, v2) = v0))
% 210.67/152.53  | (37)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (and2(v0, v1) = v2) |  ? [v3] :  ? [v4] : (f1(v0, v1, v3) = v4 & phi(v4) = v2 &  ! [v5] :  ! [v6] : ( ~ (f1(v0, v1, v5) = v6) |  ? [v7] : ( ~ (v7 = 0) & forallprefers(v6, v4) = v7))))
% 210.67/152.53  | (38)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (or2(v3, v2) = v1) |  ~ (or2(v3, v2) = v0))
% 210.67/152.53  | (39)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (and1(true, v0) = v1) |  ? [v2] : ( ~ (v2 = 0) & bool(v0) = v2))
% 210.67/152.53  | (40)  ? [v0] :  ? [v1] : not1(v0) = v1
% 210.67/152.53  | (41)  ~ (false2 = false)
% 210.67/152.53  | (42)  ! [v0] :  ! [v1] : ( ~ (forallprefers(v0, v1) = 0) |  ? [v2] :  ? [v3] :  ? [v4] : (d(v1) = 0 & d(v0) = v2 & bool(v1) = v4 & bool(v0) = v3 & ( ~ (v2 = 0) | (v4 = 0 &  ~ (v3 = 0)))) | (v1 = true & v0 = false))
% 210.67/152.53  | (43)  ! [v0] :  ! [v1] : (v1 = false |  ~ (lazy_and1(false, v0) = v1))
% 210.67/152.53  | (44)  ? [v0] :  ? [v1] :  ? [v2] : apply(v1, v0) = v2
% 210.67/152.53  | (45)  ! [v0] :  ! [v1] : ( ~ (exists1(v0) = v1) |  ? [v2] :  ? [v3] : (apply(v0, v2) = v3 & phi(v3) = v1 &  ! [v4] :  ! [v5] : ( ~ (apply(v0, v4) = v5) |  ? [v6] : ( ~ (v6 = 0) & existsprefers(v5, v3) = v6))))
% 210.67/152.53  | (46) d(true) = 0
% 210.67/152.53  | (47)  ! [v0] : ( ~ (prop(v0) = false) |  ? [v1] : ( ~ (v1 = 0) & bool(v0) = v1))
% 210.67/152.53  | (48)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (apply(v0, v1) = v3) |  ~ (impl(v3, v2) = v4) | f4(v0, v1, v2) = v4)
% 210.67/152.53  | (49)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : f3(v2, v1, v0) = v3
% 210.67/152.53  | (50)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (exists2(v2) = v1) |  ~ (exists2(v2) = v0))
% 210.67/152.53  | (51)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (lazy_impl(v0, v3) = v4) |  ~ (impl(v1, v2) = v3) |  ? [v5] :  ? [v6] :  ? [v7] : (f2(v0, v1, v2) = v5 & lazy_impl(v6, v7) = v5 & impl(v4, v2) = v7 & prop(v2) = v6))
% 210.67/152.53  | (52)  ! [v0] : ( ~ (bool(v0) = 0) | prop(v0) = true)
% 210.67/152.53  | (53)  ! [v0] : ( ~ (prop(v0) = true) | bool(v0) = 0)
% 210.67/152.53  | (54)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (impl(v0, v1) = v2) |  ? [v3] :  ? [v4] : (phi(v0) = v4 & bool(v0) = v3 & (v4 = v2 | v3 = 0)))
% 210.67/152.53  | (55)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (not2(v2) = v1) |  ~ (not2(v2) = v0))
% 210.67/152.53  | (56)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (f2(v0, v1, v2) = v3) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (lazy_impl(v4, v7) = v3 & lazy_impl(v0, v5) = v6 & impl(v6, v2) = v7 & impl(v1, v2) = v5 & prop(v2) = v4))
% 210.67/152.53  | (57)  ! [v0] : ( ~ (bool(v0) = 0) | impl(false, v0) = true)
% 210.67/152.53  | (58)  ! [v0] :  ! [v1] : ( ~ (d(v0) = v1) |  ? [v2] : (phi(v0) = v2 & ((v2 = v0 & v1 = 0) | (v2 = err &  ~ (v1 = 0)))))
% 210.67/152.53  | (59)  ! [v0] : ( ~ (bool(v0) = 0) | or1(true, v0) = true)
% 210.67/152.53  | (60)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (and2(v3, v2) = v1) |  ~ (and2(v3, v2) = v0))
% 210.67/152.53  | (61)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : f2(v2, v1, v0) = v3
% 210.67/152.53  | (62)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (f6(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : (f5(v0, v1) = v4 & lazy_impl(v3, v5) = v2 & impl(v4, v1) = v5 & prop(v1) = v3))
% 210.67/152.53  | (63)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (impl(v3, v2) = v1) |  ~ (impl(v3, v2) = v0))
% 210.67/152.53  | (64)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (not1(v2) = v1) |  ~ (not1(v2) = v0))
% 210.67/152.53  | (65)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (bool(v0) = v1) | prop(v0) = false)
% 210.67/152.53  | (66)  ! [v0] :  ! [v1] : ( ~ (exists2(v0) = v1) |  ? [v2] :  ? [v3] : (f6(v0, v2) = v3 & phi(v3) = v1 &  ! [v4] :  ! [v5] : ( ~ (f6(v0, v4) = v5) |  ? [v6] : ( ~ (v6 = 0) & forallprefers(v5, v3) = v6))))
% 210.67/152.54  | (67)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (phi(v2) = v1) |  ~ (phi(v2) = v0))
% 210.67/152.54  | (68)  ? [v0] :  ? [v1] : f7(v0) = v1
% 210.67/152.54  | (69)  ! [v0] : (v0 = true | v0 = false |  ~ (bool(v0) = 0))
% 210.67/152.54  | (70)  ? [v0] :  ? [v1] : d(v0) = v1
% 210.67/152.54  | (71)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (existsprefers(v3, v2) = v1) |  ~ (existsprefers(v3, v2) = v0))
% 210.67/152.54  | (72)  ? [v0] :  ? [v1] : phi(v0) = v1
% 210.67/152.54  | (73)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v1 = v0 |  ~ (f2(v4, v3, v2) = v1) |  ~ (f2(v4, v3, v2) = v0))
% 210.67/152.54  | (74)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (f1(v0, v1, v2) = v3) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (lazy_impl(v4, v7) = v3 & impl(v6, v2) = v7 & impl(v1, v2) = v5 & impl(v0, v5) = v6 & prop(v2) = v4))
% 210.67/152.54  | (75)  ? [v0] :  ? [v1] : prop(v0) = v1
% 210.67/152.54  | (76)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (or2(v0, v1) = v2) |  ? [v3] :  ? [v4] : (f3(v0, v1, v3) = v4 & phi(v4) = v2 &  ! [v5] :  ! [v6] : ( ~ (f3(v0, v1, v5) = v6) |  ? [v7] : ( ~ (v7 = 0) & forallprefers(v6, v4) = v7))))
% 210.67/152.54  | (77)  ? [v0] :  ? [v1] : exists1(v0) = v1
% 210.67/152.54  | (78)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (lazy_and2(v3, v2) = v1) |  ~ (lazy_and2(v3, v2) = v0))
% 210.67/152.54  | (79)  ! [v0] :  ! [v1] : (v1 = false |  ~ (prop(v0) = v1) | bool(v0) = 0)
% 210.67/152.54  | (80)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (lazy_and1(v0, v1) = v2) |  ? [v3] :  ? [v4] : (phi(v0) = v4 & bool(v0) = v3 & (v4 = v2 | v3 = 0)))
% 210.67/152.54  | (81)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (f3(v0, v1, v2) = v3) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] : (lazy_impl(v4, v8) = v3 & impl(v6, v2) = v7 & impl(v5, v7) = v8 & impl(v1, v2) = v6 & impl(v0, v2) = v5 & prop(v2) = v4))
% 210.67/152.54  | (82)  ! [v0] :  ! [v1] : ( ~ (not1(v0) = v1) |  ? [v2] :  ? [v3] : (phi(v0) = v3 & bool(v0) = v2 & (v3 = v1 | v2 = 0)))
% 210.67/152.54  | (83)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (or1(false, v0) = v1) |  ? [v2] : ( ~ (v2 = 0) & bool(v0) = v2))
% 210.67/152.54  | (84)  ? [v0] :  ? [v1] :  ? [v2] : or2(v1, v0) = v2
% 210.67/152.54  | (85)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : f1(v2, v1, v0) = v3
% 210.67/152.54  | (86)  ? [v0] :  ? [v1] :  ? [v2] : existsprefers(v1, v0) = v2
% 210.67/152.54  | (87)  ? [v0] :  ? [v1] : not2(v0) = v1
% 210.67/152.54  | (88)  ? [v0] :  ? [v1] :  ? [v2] : lazy_and2(v1, v0) = v2
% 210.67/152.54  | (89) d(false) = 0
% 210.67/152.54  | (90) not1(true) = false
% 210.67/152.54  | (91)  ! [v0] :  ! [v1] : ( ~ (f7(v0) = v1) |  ? [v2] : (lazy_impl(v2, v0) = v1 & prop(v0) = v2))
% 210.67/152.54  | (92)  ! [v0] : ( ~ (bool(v0) = 0) | and1(false, v0) = false)
% 210.67/152.54  | (93)  ! [v0] : ( ~ (bool(v0) = 0) | and1(true, v0) = v0)
% 210.67/152.54  | (94)  ? [v0] :  ? [v1] :  ? [v2] : forallprefers(v1, v0) = v2
% 210.67/152.54  | (95)  ! [v0] :  ! [v1] : (v1 = false |  ~ (and1(false, v0) = v1) |  ? [v2] : ( ~ (v2 = 0) & bool(v0) = v2))
% 210.67/152.54  | (96) d(err) = 0
% 210.67/152.54  | (97)  ? [v0] :  ? [v1] :  ? [v2] : lazy_and1(v1, v0) = v2
% 210.67/152.54  | (98)  ! [v0] :  ! [v1] : ( ~ (phi(v0) = v1) |  ? [v2] : (d(v0) = v2 & ((v2 = 0 & v1 = v0) | (v1 = err &  ~ (v2 = 0)))))
% 210.67/152.54  | (99)  ? [v0] :  ? [v1] :  ? [v2] : and2(v1, v0) = v2
% 210.67/152.54  | (100)  ? [v0] :  ? [v1] : bool(v0) = v1
% 210.67/152.54  | (101)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (and1(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : (phi(v1) = v5 & bool(v1) = v4 & bool(v0) = v3 & ( ~ (v3 = 0) | v5 = v2 | v4 = 0)))
% 210.67/152.54  | (102)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (impl(v4, v2) = v5) |  ~ (impl(v3, v5) = v6) |  ~ (impl(v1, v2) = v4) |  ~ (impl(v0, v2) = v3) |  ? [v7] :  ? [v8] : (f3(v0, v1, v2) = v7 & lazy_impl(v8, v6) = v7 & prop(v2) = v8))
% 210.67/152.54  | (103)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (lazy_impl(v3, v2) = v1) |  ~ (lazy_impl(v3, v2) = v0))
% 210.67/152.54  | (104)  ? [v0] :  ? [v1] :  ? [v2] : and1(v1, v0) = v2
% 210.67/152.54  | (105)  ! [v0] : ( ~ (bool(v0) = 0) | impl(true, v0) = v0)
% 210.67/152.54  | (106)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : f4(v2, v1, v0) = v3
% 210.67/152.54  | (107)  ? [v0] :  ? [v1] : exists2(v0) = v1
% 210.67/152.54  | (108)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (existsprefers(v0, v1) = v2) | ( ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] : (d(v1) = v4 & d(v0) = v3 & bool(v1) = v6 & bool(v0) = v5 & ( ~ (v4 = 0) | (v3 = 0 & ( ~ (v6 = 0) | v5 = 0)))) & ( ~ (v1 = false) |  ~ (v0 = true))))
% 210.67/152.54  | (109)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (impl(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : (phi(v1) = v5 & bool(v1) = v4 & bool(v0) = v3 & ( ~ (v3 = 0) | v5 = v2 | v4 = 0)))
% 210.67/152.54  | (110)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (lazy_impl(v0, v1) = v2) |  ? [v3] :  ? [v4] : (phi(v0) = v4 & bool(v0) = v3 & (v4 = v2 | v3 = 0)))
% 210.67/152.54  | (111)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (forallprefers(v3, v2) = v1) |  ~ (forallprefers(v3, v2) = v0))
% 210.67/152.54  | (112)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v1 = v0 |  ~ (f4(v4, v3, v2) = v1) |  ~ (f4(v4, v3, v2) = v0))
% 210.67/152.55  | (113)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (f7(v2) = v1) |  ~ (f7(v2) = v0))
% 210.67/152.55  | (114)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (impl(true, v0) = v1) |  ? [v2] : ( ~ (v2 = 0) & bool(v0) = v2))
% 210.67/152.55  | (115)  ~ (err = false)
% 210.67/152.55  | (116)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (bool(v2) = v1) |  ~ (bool(v2) = v0))
% 210.67/152.55  | (117)  ! [v0] :  ! [v1] : ( ~ (phi(v0) = v1) | lazy_and1(true, v0) = v1)
% 210.67/152.55  | (118)  ! [v0] :  ! [v1] : ( ~ (lazy_and1(true, v0) = v1) | phi(v0) = v1)
% 210.67/152.55  | (119)  ~ (err = true)
% 210.67/152.55  | (120)  ? [v0] :  ? [v1] :  ? [v2] : f5(v1, v0) = v2
% 210.67/152.55  | (121)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (f5(v0, v1) = v2) |  ? [v3] :  ? [v4] : (f4(v0, v3, v1) = v4 & phi(v4) = v2 &  ! [v5] :  ! [v6] : ( ~ (f4(v0, v5, v1) = v6) |  ? [v7] : ( ~ (v7 = 0) & forallprefers(v6, v4) = v7))))
% 210.67/152.55  | (122)  ~ (true = false)
% 210.67/152.55  | (123)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (or1(v0, v1) = v2) |  ? [v3] :  ? [v4] : (phi(v0) = v4 & bool(v0) = v3 & (v4 = v2 | v3 = 0)))
% 210.67/152.55  | (124)  ? [v0] :  ? [v1] :  ? [v2] : impl(v1, v0) = v2
% 210.67/152.55  | (125)  ! [v0] :  ! [v1] : ( ~ (impl(v0, false2) = v1) | not2(v0) = v1)
% 210.67/152.55  | (126)  ! [v0] :  ! [v1] : ( ~ (not2(v0) = v1) | impl(v0, false2) = v1)
% 210.67/152.55  | (127)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (forallprefers(v0, v1) = v2) | ( ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] : (d(v1) = v4 & d(v0) = v3 & bool(v1) = v6 & bool(v0) = v5 & ( ~ (v4 = 0) | (v3 = 0 & ( ~ (v6 = 0) | v5 = 0)))) & ( ~ (v1 = true) |  ~ (v0 = false))))
% 210.67/152.55  | (128)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v1 = v0 |  ~ (f1(v4, v3, v2) = v1) |  ~ (f1(v4, v3, v2) = v0))
% 210.67/152.55  |
% 210.67/152.55  | Instantiating (14) with all_2_0_0, all_2_1_1 yields:
% 210.67/152.55  | (129) f7(all_2_1_1) = all_2_0_0 & phi(all_2_0_0) = false2 &  ! [v0] :  ! [v1] : ( ~ (f7(v0) = v1) |  ? [v2] : ( ~ (v2 = 0) & forallprefers(v1, all_2_0_0) = v2))
% 210.67/152.55  |
% 210.67/152.55  | Applying alpha-rule on (129) yields:
% 210.67/152.55  | (130) f7(all_2_1_1) = all_2_0_0
% 210.67/152.55  | (131) phi(all_2_0_0) = false2
% 210.67/152.55  | (132)  ! [v0] :  ! [v1] : ( ~ (f7(v0) = v1) |  ? [v2] : ( ~ (v2 = 0) & forallprefers(v1, all_2_0_0) = v2))
% 210.67/152.55  |
% 210.67/152.55  | Instantiating formula (82) with false, true and discharging atoms not1(true) = false, yields:
% 210.67/152.55  | (133)  ? [v0] :  ? [v1] : (phi(true) = v1 & bool(true) = v0 & (v1 = false | v0 = 0))
% 210.67/152.55  |
% 210.67/152.55  | Instantiating formula (82) with true, false and discharging atoms not1(false) = true, yields:
% 210.67/152.55  | (134)  ? [v0] :  ? [v1] : (phi(false) = v1 & bool(false) = v0 & (v1 = true | v0 = 0))
% 210.67/152.55  |
% 210.67/152.55  | Instantiating formula (91) with all_2_0_0, all_2_1_1 and discharging atoms f7(all_2_1_1) = all_2_0_0, yields:
% 210.67/152.55  | (135)  ? [v0] : (lazy_impl(v0, all_2_1_1) = all_2_0_0 & prop(all_2_1_1) = v0)
% 210.67/152.55  |
% 210.67/152.55  | Instantiating formula (15) with false2, all_2_0_0 and discharging atoms phi(all_2_0_0) = false2, yields:
% 210.67/152.55  | (136)  ? [v0] :  ? [v1] : (not1(all_2_0_0) = v1 & bool(all_2_0_0) = v0 & (v1 = false2 | v0 = 0))
% 210.67/152.55  |
% 210.67/152.55  | Instantiating formula (98) with false2, all_2_0_0 and discharging atoms phi(all_2_0_0) = false2, yields:
% 210.67/152.55  | (137)  ? [v0] : (d(all_2_0_0) = v0 & ((v0 = 0 & all_2_0_0 = false2) | (false2 = err &  ~ (v0 = 0))))
% 210.67/152.55  |
% 210.67/152.55  | Instantiating formula (58) with 0, err and discharging atoms d(err) = 0, yields:
% 210.67/152.55  | (138) phi(err) = err
% 210.67/152.55  |
% 210.67/152.55  | Instantiating formula (58) with 0, true and discharging atoms d(true) = 0, yields:
% 210.67/152.55  | (139) phi(true) = true
% 210.67/152.55  |
% 210.67/152.55  | Instantiating formula (58) with 0, false and discharging atoms d(false) = 0, yields:
% 210.67/152.55  | (140) phi(false) = false
% 210.67/152.55  |
% 210.67/152.55  | Instantiating (136) with all_63_0_75, all_63_1_76 yields:
% 210.67/152.55  | (141) not1(all_2_0_0) = all_63_0_75 & bool(all_2_0_0) = all_63_1_76 & (all_63_0_75 = false2 | all_63_1_76 = 0)
% 210.67/152.55  |
% 210.67/152.55  | Applying alpha-rule on (141) yields:
% 210.67/152.55  | (142) not1(all_2_0_0) = all_63_0_75
% 210.67/152.55  | (143) bool(all_2_0_0) = all_63_1_76
% 210.67/152.55  | (144) all_63_0_75 = false2 | all_63_1_76 = 0
% 210.67/152.55  |
% 210.67/152.55  | Instantiating (137) with all_65_0_77 yields:
% 210.67/152.55  | (145) d(all_2_0_0) = all_65_0_77 & ((all_65_0_77 = 0 & all_2_0_0 = false2) | (false2 = err &  ~ (all_65_0_77 = 0)))
% 210.67/152.55  |
% 210.67/152.55  | Applying alpha-rule on (145) yields:
% 210.67/152.55  | (146) d(all_2_0_0) = all_65_0_77
% 210.67/152.55  | (147) (all_65_0_77 = 0 & all_2_0_0 = false2) | (false2 = err &  ~ (all_65_0_77 = 0))
% 210.67/152.55  |
% 210.67/152.55  | Instantiating (133) with all_69_0_79, all_69_1_80 yields:
% 210.67/152.55  | (148) phi(true) = all_69_0_79 & bool(true) = all_69_1_80 & (all_69_0_79 = false | all_69_1_80 = 0)
% 210.67/152.55  |
% 210.67/152.55  | Applying alpha-rule on (148) yields:
% 210.67/152.55  | (149) phi(true) = all_69_0_79
% 210.67/152.55  | (150) bool(true) = all_69_1_80
% 210.67/152.55  | (151) all_69_0_79 = false | all_69_1_80 = 0
% 210.67/152.55  |
% 210.67/152.55  | Instantiating (134) with all_71_0_81, all_71_1_82 yields:
% 210.67/152.55  | (152) phi(false) = all_71_0_81 & bool(false) = all_71_1_82 & (all_71_0_81 = true | all_71_1_82 = 0)
% 210.67/152.55  |
% 210.67/152.55  | Applying alpha-rule on (152) yields:
% 210.67/152.55  | (153) phi(false) = all_71_0_81
% 210.67/152.55  | (154) bool(false) = all_71_1_82
% 210.67/152.55  | (155) all_71_0_81 = true | all_71_1_82 = 0
% 210.67/152.55  |
% 210.67/152.55  | Instantiating (135) with all_73_0_83 yields:
% 210.67/152.55  | (156) lazy_impl(all_73_0_83, all_2_1_1) = all_2_0_0 & prop(all_2_1_1) = all_73_0_83
% 210.67/152.55  |
% 210.67/152.55  | Applying alpha-rule on (156) yields:
% 210.67/152.55  | (157) lazy_impl(all_73_0_83, all_2_1_1) = all_2_0_0
% 210.67/152.55  | (158) prop(all_2_1_1) = all_73_0_83
% 210.67/152.55  |
% 210.67/152.55  | Instantiating formula (67) with true, true, all_69_0_79 and discharging atoms phi(true) = all_69_0_79, phi(true) = true, yields:
% 210.67/152.55  | (159) all_69_0_79 = true
% 210.67/152.55  |
% 210.67/152.55  | Instantiating formula (67) with false, false, all_71_0_81 and discharging atoms phi(false) = all_71_0_81, phi(false) = false, yields:
% 210.67/152.55  | (160) all_71_0_81 = false
% 210.67/152.55  |
% 210.67/152.55  | Instantiating formula (20) with all_63_1_76, all_2_0_0 and discharging atoms bool(all_2_0_0) = all_63_1_76, yields:
% 210.67/152.55  | (161) all_63_1_76 = 0 | ( ~ (all_2_0_0 = true) &  ~ (all_2_0_0 = false))
% 210.67/152.55  |
% 210.67/152.55  | Instantiating formula (20) with all_69_1_80, true and discharging atoms bool(true) = all_69_1_80, yields:
% 210.67/152.55  | (162) all_69_1_80 = 0
% 210.67/152.55  |
% 210.67/152.55  | Instantiating formula (20) with all_71_1_82, false and discharging atoms bool(false) = all_71_1_82, yields:
% 210.67/152.55  | (163) all_71_1_82 = 0
% 210.67/152.55  |
% 210.67/152.55  | From (159) and (149) follows:
% 210.67/152.55  | (139) phi(true) = true
% 210.67/152.55  |
% 210.67/152.55  | From (160) and (153) follows:
% 210.67/152.55  | (140) phi(false) = false
% 210.67/152.55  |
% 210.67/152.55  | From (162) and (150) follows:
% 210.67/152.55  | (166) bool(true) = 0
% 210.67/152.55  |
% 210.67/152.55  | From (163) and (154) follows:
% 210.67/152.55  | (167) bool(false) = 0
% 210.67/152.55  |
% 210.67/152.56  | Instantiating formula (82) with all_63_0_75, all_2_0_0 and discharging atoms not1(all_2_0_0) = all_63_0_75, yields:
% 210.67/152.56  | (168)  ? [v0] :  ? [v1] : (phi(all_2_0_0) = v1 & bool(all_2_0_0) = v0 & (v1 = all_63_0_75 | v0 = 0))
% 210.67/152.56  |
% 210.67/152.56  | Instantiating formula (110) with all_2_0_0, all_2_1_1, all_73_0_83 and discharging atoms lazy_impl(all_73_0_83, all_2_1_1) = all_2_0_0, yields:
% 210.67/152.56  | (169)  ? [v0] :  ? [v1] : (phi(all_73_0_83) = v1 & bool(all_73_0_83) = v0 & (v1 = all_2_0_0 | v0 = 0))
% 210.67/152.56  |
% 210.67/152.56  | Instantiating formula (27) with all_73_0_83, all_2_1_1 and discharging atoms prop(all_2_1_1) = all_73_0_83, yields:
% 210.67/152.56  | (170) all_73_0_83 = true |  ? [v0] : ( ~ (v0 = 0) & bool(all_2_1_1) = v0)
% 210.67/152.56  |
% 210.67/152.56  | Instantiating formula (79) with all_73_0_83, all_2_1_1 and discharging atoms prop(all_2_1_1) = all_73_0_83, yields:
% 210.67/152.56  | (171) all_73_0_83 = false | bool(all_2_1_1) = 0
% 210.67/152.56  |
% 210.67/152.56  | Instantiating formula (15) with err, err and discharging atoms phi(err) = err, yields:
% 210.67/152.56  | (172)  ? [v0] :  ? [v1] : (not1(err) = v1 & bool(err) = v0 & (v1 = err | v0 = 0))
% 210.67/152.56  |
% 210.67/152.56  | Instantiating formula (33) with true, true and discharging atoms phi(true) = true, yields:
% 210.67/152.56  | (173) lazy_impl(true, true) = true
% 210.67/152.56  |
% 210.67/152.56  | Instantiating formula (33) with false, false and discharging atoms phi(false) = false, yields:
% 210.67/152.56  | (174) lazy_impl(true, false) = false
% 210.67/152.56  |
% 210.67/152.56  | Instantiating formula (58) with all_65_0_77, all_2_0_0 and discharging atoms d(all_2_0_0) = all_65_0_77, yields:
% 210.67/152.56  | (175)  ? [v0] : (phi(all_2_0_0) = v0 & ((v0 = all_2_0_0 & all_65_0_77 = 0) | (v0 = err &  ~ (all_65_0_77 = 0))))
% 210.67/152.56  |
% 210.67/152.56  | Instantiating formula (105) with true and discharging atoms bool(true) = 0, yields:
% 210.67/152.56  | (176) impl(true, true) = true
% 210.67/152.56  |
% 210.67/152.56  | Instantiating formula (57) with true and discharging atoms bool(true) = 0, yields:
% 210.67/152.56  | (177) impl(false, true) = true
% 210.67/152.56  |
% 210.67/152.56  | Instantiating formula (52) with true and discharging atoms bool(true) = 0, yields:
% 210.67/152.56  | (178) prop(true) = true
% 210.67/152.56  |
% 210.67/152.56  | Instantiating formula (9) with true and discharging atoms bool(true) = 0, yields:
% 210.67/152.56  | (179)  ? [v0] : ( ~ (v0 = false) & prop(true) = v0)
% 210.67/152.56  |
% 210.67/152.56  | Instantiating formula (105) with false and discharging atoms bool(false) = 0, yields:
% 210.67/152.56  | (180) impl(true, false) = false
% 210.67/152.56  |
% 210.67/152.56  | Instantiating formula (57) with false and discharging atoms bool(false) = 0, yields:
% 210.67/152.56  | (181) impl(false, false) = true
% 210.67/152.56  |
% 210.67/152.56  | Instantiating formula (52) with false and discharging atoms bool(false) = 0, yields:
% 210.67/152.56  | (182) prop(false) = true
% 210.67/152.56  |
% 210.67/152.56  | Instantiating formula (9) with false and discharging atoms bool(false) = 0, yields:
% 210.67/152.56  | (183)  ? [v0] : ( ~ (v0 = false) & prop(false) = v0)
% 210.67/152.56  |
% 210.67/152.56  | Instantiating (179) with all_85_0_84 yields:
% 210.67/152.56  | (184)  ~ (all_85_0_84 = false) & prop(true) = all_85_0_84
% 210.67/152.56  |
% 210.67/152.56  | Applying alpha-rule on (184) yields:
% 210.67/152.56  | (185)  ~ (all_85_0_84 = false)
% 210.67/152.56  | (186) prop(true) = all_85_0_84
% 210.67/152.56  |
% 210.67/152.56  | Instantiating (183) with all_87_0_85 yields:
% 210.67/152.56  | (187)  ~ (all_87_0_85 = false) & prop(false) = all_87_0_85
% 210.67/152.56  |
% 210.67/152.56  | Applying alpha-rule on (187) yields:
% 210.67/152.56  | (188)  ~ (all_87_0_85 = false)
% 210.67/152.56  | (189) prop(false) = all_87_0_85
% 210.67/152.56  |
% 210.67/152.56  | Instantiating (172) with all_89_0_86, all_89_1_87 yields:
% 210.67/152.56  | (190) not1(err) = all_89_0_86 & bool(err) = all_89_1_87 & (all_89_0_86 = err | all_89_1_87 = 0)
% 210.67/152.56  |
% 210.67/152.56  | Applying alpha-rule on (190) yields:
% 210.67/152.56  | (191) not1(err) = all_89_0_86
% 210.67/152.56  | (192) bool(err) = all_89_1_87
% 210.67/152.56  | (193) all_89_0_86 = err | all_89_1_87 = 0
% 210.67/152.56  |
% 210.67/152.56  | Instantiating (175) with all_91_0_88 yields:
% 210.67/152.56  | (194) phi(all_2_0_0) = all_91_0_88 & ((all_91_0_88 = all_2_0_0 & all_65_0_77 = 0) | (all_91_0_88 = err &  ~ (all_65_0_77 = 0)))
% 210.67/152.56  |
% 210.67/152.56  | Applying alpha-rule on (194) yields:
% 210.67/152.56  | (195) phi(all_2_0_0) = all_91_0_88
% 210.67/152.56  | (196) (all_91_0_88 = all_2_0_0 & all_65_0_77 = 0) | (all_91_0_88 = err &  ~ (all_65_0_77 = 0))
% 210.67/152.56  |
% 210.67/152.56  | Instantiating (169) with all_93_0_89, all_93_1_90 yields:
% 210.67/152.56  | (197) phi(all_73_0_83) = all_93_0_89 & bool(all_73_0_83) = all_93_1_90 & (all_93_0_89 = all_2_0_0 | all_93_1_90 = 0)
% 210.67/152.56  |
% 210.67/152.56  | Applying alpha-rule on (197) yields:
% 210.67/152.56  | (198) phi(all_73_0_83) = all_93_0_89
% 210.67/152.56  | (199) bool(all_73_0_83) = all_93_1_90
% 210.67/152.56  | (200) all_93_0_89 = all_2_0_0 | all_93_1_90 = 0
% 210.67/152.56  |
% 210.67/152.56  | Instantiating (168) with all_95_0_91, all_95_1_92 yields:
% 210.67/152.56  | (201) phi(all_2_0_0) = all_95_0_91 & bool(all_2_0_0) = all_95_1_92 & (all_95_0_91 = all_63_0_75 | all_95_1_92 = 0)
% 210.67/152.56  |
% 210.67/152.56  | Applying alpha-rule on (201) yields:
% 210.67/152.56  | (202) phi(all_2_0_0) = all_95_0_91
% 210.67/152.56  | (203) bool(all_2_0_0) = all_95_1_92
% 210.67/152.56  | (204) all_95_0_91 = all_63_0_75 | all_95_1_92 = 0
% 210.67/152.56  |
% 210.67/152.56  | Instantiating formula (6) with true, true, all_85_0_84 and discharging atoms prop(true) = all_85_0_84, prop(true) = true, yields:
% 210.67/152.56  | (205) all_85_0_84 = true
% 210.67/152.56  |
% 210.67/152.56  | Instantiating formula (6) with false, true, all_87_0_85 and discharging atoms prop(false) = all_87_0_85, prop(false) = true, yields:
% 210.67/152.56  | (206) all_87_0_85 = true
% 210.67/152.56  |
% 210.67/152.56  | Instantiating formula (67) with all_2_0_0, all_95_0_91, false2 and discharging atoms phi(all_2_0_0) = all_95_0_91, phi(all_2_0_0) = false2, yields:
% 210.67/152.56  | (207) all_95_0_91 = false2
% 210.67/152.56  |
% 210.67/152.56  | Instantiating formula (67) with all_2_0_0, all_91_0_88, all_95_0_91 and discharging atoms phi(all_2_0_0) = all_95_0_91, phi(all_2_0_0) = all_91_0_88, yields:
% 210.67/152.56  | (208) all_95_0_91 = all_91_0_88
% 210.67/152.56  |
% 210.67/152.56  | Instantiating formula (116) with all_2_0_0, all_95_1_92, all_63_1_76 and discharging atoms bool(all_2_0_0) = all_95_1_92, bool(all_2_0_0) = all_63_1_76, yields:
% 210.67/152.56  | (209) all_95_1_92 = all_63_1_76
% 210.67/152.56  |
% 210.67/152.56  | Combining equations (207,208) yields a new equation:
% 210.67/152.56  | (210) all_91_0_88 = false2
% 210.67/152.56  |
% 210.67/152.56  | From (205) and (186) follows:
% 210.67/152.56  | (178) prop(true) = true
% 210.67/152.56  |
% 210.67/152.56  | From (206) and (189) follows:
% 210.67/152.56  | (182) prop(false) = true
% 210.67/152.56  |
% 210.67/152.56  | From (210) and (195) follows:
% 210.67/152.56  | (131) phi(all_2_0_0) = false2
% 210.67/152.56  |
% 210.67/152.56  | From (209) and (203) follows:
% 210.67/152.56  | (143) bool(all_2_0_0) = all_63_1_76
% 210.67/152.56  |
% 210.67/152.56  | Instantiating formula (82) with all_89_0_86, err and discharging atoms not1(err) = all_89_0_86, yields:
% 210.67/152.56  | (215)  ? [v0] :  ? [v1] : (phi(err) = v1 & bool(err) = v0 & (v1 = all_89_0_86 | v0 = 0))
% 210.67/152.56  |
% 210.67/152.56  | Instantiating formula (102) with true, true, true, true, true, true, true and discharging atoms impl(true, true) = true, yields:
% 210.67/152.56  | (216)  ? [v0] :  ? [v1] : (f3(true, true, true) = v0 & lazy_impl(v1, true) = v0 & prop(true) = v1)
% 210.67/152.56  |
% 210.67/152.56  | Instantiating formula (10) with true, true, true, true, true and discharging atoms impl(true, true) = true, yields:
% 210.67/152.56  | (217)  ? [v0] :  ? [v1] :  ? [v2] : (f1(true, true, true) = v0 & lazy_impl(v1, v2) = v0 & impl(true, true) = v2 & prop(true) = v1)
% 210.67/152.56  |
% 210.67/152.56  | Instantiating formula (51) with true, true, true, true, true and discharging atoms lazy_impl(true, true) = true, impl(true, true) = true, yields:
% 210.67/152.56  | (218)  ? [v0] :  ? [v1] :  ? [v2] : (f2(true, true, true) = v0 & lazy_impl(v1, v2) = v0 & impl(true, true) = v2 & prop(true) = v1)
% 210.67/152.56  |
% 210.67/152.56  | Instantiating formula (10) with false, false, false, true, true and discharging atoms impl(true, false) = false, yields:
% 210.67/152.56  | (219)  ? [v0] :  ? [v1] :  ? [v2] : (f1(true, true, false) = v0 & lazy_impl(v1, v2) = v0 & impl(false, false) = v2 & prop(false) = v1)
% 210.67/152.56  |
% 210.67/152.56  | Instantiating formula (51) with false, false, false, true, true and discharging atoms lazy_impl(true, false) = false, impl(true, false) = false, yields:
% 210.67/152.56  | (220)  ? [v0] :  ? [v1] :  ? [v2] : (f2(true, true, false) = v0 & lazy_impl(v1, v2) = v0 & impl(false, false) = v2 & prop(false) = v1)
% 210.67/152.56  |
% 210.67/152.56  | Instantiating formula (10) with true, true, true, false, true and discharging atoms impl(true, true) = true, impl(false, true) = true, yields:
% 210.67/152.56  | (221)  ? [v0] :  ? [v1] :  ? [v2] : (f1(true, false, true) = v0 & lazy_impl(v1, v2) = v0 & impl(true, true) = v2 & prop(true) = v1)
% 210.67/152.56  |
% 210.67/152.56  | Instantiating formula (10) with true, true, true, true, false and discharging atoms impl(true, true) = true, impl(false, true) = true, yields:
% 210.67/152.56  | (222)  ? [v0] :  ? [v1] :  ? [v2] : (f1(false, true, true) = v0 & lazy_impl(v1, v2) = v0 & impl(true, true) = v2 & prop(true) = v1)
% 210.67/152.56  |
% 210.67/152.56  | Instantiating formula (102) with true, true, true, true, true, true, false and discharging atoms impl(true, true) = true, impl(false, true) = true, yields:
% 210.67/152.57  | (223)  ? [v0] :  ? [v1] : (f3(false, true, true) = v0 & lazy_impl(v1, true) = v0 & prop(true) = v1)
% 210.67/152.57  |
% 210.67/152.57  | Instantiating formula (102) with true, true, true, true, true, false, false and discharging atoms impl(true, true) = true, impl(false, true) = true, yields:
% 210.67/152.57  | (224)  ? [v0] :  ? [v1] : (f3(false, false, true) = v0 & lazy_impl(v1, true) = v0 & prop(true) = v1)
% 210.67/152.57  |
% 210.67/152.57  | Instantiating formula (102) with true, true, true, true, true, false, true and discharging atoms impl(true, true) = true, impl(false, true) = true, yields:
% 210.67/152.57  | (225)  ? [v0] :  ? [v1] : (f3(true, false, true) = v0 & lazy_impl(v1, true) = v0 & prop(true) = v1)
% 210.67/152.57  |
% 210.67/152.57  | Instantiating formula (10) with true, true, true, false, false and discharging atoms impl(false, true) = true, yields:
% 210.67/152.57  | (226)  ? [v0] :  ? [v1] :  ? [v2] : (f1(false, false, true) = v0 & lazy_impl(v1, v2) = v0 & impl(true, true) = v2 & prop(true) = v1)
% 210.67/152.57  |
% 210.67/152.57  | Instantiating formula (51) with true, true, true, false, true and discharging atoms lazy_impl(true, true) = true, impl(false, true) = true, yields:
% 210.67/152.57  | (227)  ? [v0] :  ? [v1] :  ? [v2] : (f2(true, false, true) = v0 & lazy_impl(v1, v2) = v0 & impl(true, true) = v2 & prop(true) = v1)
% 210.67/152.57  |
% 210.67/152.57  | Instantiating formula (102) with true, true, false, true, false, true, false and discharging atoms impl(true, true) = true, impl(true, false) = false, impl(false, false) = true, yields:
% 210.67/152.57  | (228)  ? [v0] :  ? [v1] : (f3(false, true, false) = v0 & lazy_impl(v1, true) = v0 & prop(false) = v1)
% 210.67/152.57  |
% 210.67/152.57  | Instantiating formula (10) with true, true, false, false, true and discharging atoms impl(true, true) = true, impl(false, false) = true, yields:
% 210.67/152.57  | (229)  ? [v0] :  ? [v1] :  ? [v2] : (f1(true, false, false) = v0 & lazy_impl(v1, v2) = v0 & impl(true, false) = v2 & prop(false) = v1)
% 210.67/152.57  |
% 210.67/152.57  | Instantiating formula (102) with true, false, true, false, false, false, true and discharging atoms impl(true, false) = false, impl(false, false) = true, yields:
% 210.67/152.57  | (230)  ? [v0] :  ? [v1] : (f3(true, false, false) = v0 & lazy_impl(v1, true) = v0 & prop(false) = v1)
% 210.67/152.57  |
% 210.67/152.57  | Instantiating formula (10) with true, false, false, true, false and discharging atoms impl(true, false) = false, impl(false, false) = true, yields:
% 210.67/152.57  | (231)  ? [v0] :  ? [v1] :  ? [v2] : (f1(false, true, false) = v0 & lazy_impl(v1, v2) = v0 & impl(true, false) = v2 & prop(false) = v1)
% 210.67/152.57  |
% 210.67/152.57  | Instantiating formula (102) with false, false, true, true, false, false, false and discharging atoms impl(true, false) = false, impl(false, false) = true, yields:
% 210.67/152.57  | (232)  ? [v0] :  ? [v1] : (f3(false, false, false) = v0 & lazy_impl(v1, false) = v0 & prop(false) = v1)
% 210.67/152.57  |
% 210.67/152.57  | Instantiating formula (102) with true, true, false, false, false, true, true and discharging atoms impl(true, false) = false, impl(false, true) = true, impl(false, false) = true, yields:
% 210.67/152.57  | (233)  ? [v0] :  ? [v1] : (f3(true, true, false) = v0 & lazy_impl(v1, true) = v0 & prop(false) = v1)
% 210.67/152.57  |
% 210.67/152.57  | Instantiating formula (10) with true, true, false, false, false and discharging atoms impl(false, true) = true, impl(false, false) = true, yields:
% 210.67/152.57  | (234)  ? [v0] :  ? [v1] :  ? [v2] : (f1(false, false, false) = v0 & lazy_impl(v1, v2) = v0 & impl(true, false) = v2 & prop(false) = v1)
% 210.67/152.57  |
% 210.67/152.57  | Instantiating formula (51) with true, true, false, false, true and discharging atoms lazy_impl(true, true) = true, impl(false, false) = true, yields:
% 210.67/152.57  | (235)  ? [v0] :  ? [v1] :  ? [v2] : (f2(true, false, false) = v0 & lazy_impl(v1, v2) = v0 & impl(true, false) = v2 & prop(false) = v1)
% 210.67/152.57  |
% 210.67/152.57  | Instantiating formula (1) with true, true and discharging atoms prop(true) = true, yields:
% 210.67/152.57  | (236)  ? [v0] : (f7(true) = v0 & lazy_impl(true, true) = v0)
% 210.67/152.57  |
% 210.67/152.57  | Instantiating formula (1) with true, false and discharging atoms prop(false) = true, yields:
% 210.67/152.57  | (237)  ? [v0] : (f7(false) = v0 & lazy_impl(true, false) = v0)
% 210.67/152.57  |
% 210.67/152.57  | Instantiating formula (33) with all_93_0_89, all_73_0_83 and discharging atoms phi(all_73_0_83) = all_93_0_89, yields:
% 210.67/152.57  | (238) lazy_impl(true, all_73_0_83) = all_93_0_89
% 210.67/152.57  |
% 210.67/152.57  | Instantiating formula (15) with all_93_0_89, all_73_0_83 and discharging atoms phi(all_73_0_83) = all_93_0_89, yields:
% 210.67/152.57  | (239)  ? [v0] :  ? [v1] : (not1(all_73_0_83) = v1 & bool(all_73_0_83) = v0 & (v1 = all_93_0_89 | v0 = 0))
% 210.67/152.57  |
% 210.67/152.57  | Instantiating formula (98) with all_93_0_89, all_73_0_83 and discharging atoms phi(all_73_0_83) = all_93_0_89, yields:
% 210.67/152.57  | (240)  ? [v0] : (d(all_73_0_83) = v0 & ((v0 = 0 & all_93_0_89 = all_73_0_83) | (all_93_0_89 = err &  ~ (v0 = 0))))
% 210.67/152.57  |
% 210.67/152.57  | Instantiating (239) with all_107_0_93, all_107_1_94 yields:
% 210.67/152.57  | (241) not1(all_73_0_83) = all_107_0_93 & bool(all_73_0_83) = all_107_1_94 & (all_107_0_93 = all_93_0_89 | all_107_1_94 = 0)
% 210.67/152.57  |
% 210.67/152.57  | Applying alpha-rule on (241) yields:
% 210.67/152.57  | (242) not1(all_73_0_83) = all_107_0_93
% 210.67/152.57  | (243) bool(all_73_0_83) = all_107_1_94
% 210.67/152.57  | (244) all_107_0_93 = all_93_0_89 | all_107_1_94 = 0
% 210.67/152.57  |
% 210.67/152.57  | Instantiating (230) with all_109_0_95, all_109_1_96 yields:
% 210.67/152.57  | (245) f3(true, false, false) = all_109_1_96 & lazy_impl(all_109_0_95, true) = all_109_1_96 & prop(false) = all_109_0_95
% 210.67/152.57  |
% 210.67/152.57  | Applying alpha-rule on (245) yields:
% 210.67/152.57  | (246) f3(true, false, false) = all_109_1_96
% 210.67/152.57  | (247) lazy_impl(all_109_0_95, true) = all_109_1_96
% 210.67/152.57  | (248) prop(false) = all_109_0_95
% 210.67/152.57  |
% 210.67/152.57  | Instantiating (229) with all_111_0_97, all_111_1_98, all_111_2_99 yields:
% 210.67/152.57  | (249) f1(true, false, false) = all_111_2_99 & lazy_impl(all_111_1_98, all_111_0_97) = all_111_2_99 & impl(true, false) = all_111_0_97 & prop(false) = all_111_1_98
% 210.67/152.57  |
% 210.67/152.57  | Applying alpha-rule on (249) yields:
% 210.67/152.57  | (250) f1(true, false, false) = all_111_2_99
% 210.67/152.57  | (251) lazy_impl(all_111_1_98, all_111_0_97) = all_111_2_99
% 210.67/152.57  | (252) impl(true, false) = all_111_0_97
% 210.67/152.57  | (253) prop(false) = all_111_1_98
% 210.67/152.57  |
% 210.67/152.57  | Instantiating (240) with all_113_0_100 yields:
% 210.67/152.57  | (254) d(all_73_0_83) = all_113_0_100 & ((all_113_0_100 = 0 & all_93_0_89 = all_73_0_83) | (all_93_0_89 = err &  ~ (all_113_0_100 = 0)))
% 210.67/152.57  |
% 210.67/152.57  | Applying alpha-rule on (254) yields:
% 210.67/152.57  | (255) d(all_73_0_83) = all_113_0_100
% 210.67/152.57  | (256) (all_113_0_100 = 0 & all_93_0_89 = all_73_0_83) | (all_93_0_89 = err &  ~ (all_113_0_100 = 0))
% 210.67/152.57  |
% 210.67/152.57  | Instantiating (228) with all_115_0_101, all_115_1_102 yields:
% 210.67/152.57  | (257) f3(false, true, false) = all_115_1_102 & lazy_impl(all_115_0_101, true) = all_115_1_102 & prop(false) = all_115_0_101
% 210.67/152.57  |
% 210.67/152.57  | Applying alpha-rule on (257) yields:
% 210.67/152.57  | (258) f3(false, true, false) = all_115_1_102
% 210.67/152.57  | (259) lazy_impl(all_115_0_101, true) = all_115_1_102
% 210.67/152.57  | (260) prop(false) = all_115_0_101
% 210.67/152.57  |
% 210.67/152.57  | Instantiating (222) with all_117_0_103, all_117_1_104, all_117_2_105 yields:
% 210.67/152.57  | (261) f1(false, true, true) = all_117_2_105 & lazy_impl(all_117_1_104, all_117_0_103) = all_117_2_105 & impl(true, true) = all_117_0_103 & prop(true) = all_117_1_104
% 210.67/152.57  |
% 210.67/152.57  | Applying alpha-rule on (261) yields:
% 210.67/152.57  | (262) f1(false, true, true) = all_117_2_105
% 210.67/152.57  | (263) lazy_impl(all_117_1_104, all_117_0_103) = all_117_2_105
% 210.67/152.57  | (264) impl(true, true) = all_117_0_103
% 210.67/152.57  | (265) prop(true) = all_117_1_104
% 210.67/152.57  |
% 210.67/152.57  | Instantiating (220) with all_119_0_106, all_119_1_107, all_119_2_108 yields:
% 210.67/152.57  | (266) f2(true, true, false) = all_119_2_108 & lazy_impl(all_119_1_107, all_119_0_106) = all_119_2_108 & impl(false, false) = all_119_0_106 & prop(false) = all_119_1_107
% 210.67/152.57  |
% 210.67/152.57  | Applying alpha-rule on (266) yields:
% 210.67/152.57  | (267) f2(true, true, false) = all_119_2_108
% 210.67/152.57  | (268) lazy_impl(all_119_1_107, all_119_0_106) = all_119_2_108
% 210.67/152.57  | (269) impl(false, false) = all_119_0_106
% 210.67/152.57  | (270) prop(false) = all_119_1_107
% 210.67/152.57  |
% 210.67/152.57  | Instantiating (221) with all_121_0_109, all_121_1_110, all_121_2_111 yields:
% 210.67/152.57  | (271) f1(true, false, true) = all_121_2_111 & lazy_impl(all_121_1_110, all_121_0_109) = all_121_2_111 & impl(true, true) = all_121_0_109 & prop(true) = all_121_1_110
% 210.67/152.57  |
% 210.67/152.57  | Applying alpha-rule on (271) yields:
% 210.67/152.57  | (272) f1(true, false, true) = all_121_2_111
% 210.67/152.57  | (273) lazy_impl(all_121_1_110, all_121_0_109) = all_121_2_111
% 210.67/152.57  | (274) impl(true, true) = all_121_0_109
% 210.67/152.57  | (275) prop(true) = all_121_1_110
% 210.67/152.57  |
% 210.67/152.57  | Instantiating (219) with all_123_0_112, all_123_1_113, all_123_2_114 yields:
% 210.67/152.57  | (276) f1(true, true, false) = all_123_2_114 & lazy_impl(all_123_1_113, all_123_0_112) = all_123_2_114 & impl(false, false) = all_123_0_112 & prop(false) = all_123_1_113
% 210.67/152.57  |
% 210.67/152.57  | Applying alpha-rule on (276) yields:
% 210.67/152.57  | (277) f1(true, true, false) = all_123_2_114
% 210.67/152.57  | (278) lazy_impl(all_123_1_113, all_123_0_112) = all_123_2_114
% 210.67/152.57  | (279) impl(false, false) = all_123_0_112
% 210.67/152.58  | (280) prop(false) = all_123_1_113
% 210.67/152.58  |
% 210.67/152.58  | Instantiating (227) with all_125_0_115, all_125_1_116, all_125_2_117 yields:
% 210.67/152.58  | (281) f2(true, false, true) = all_125_2_117 & lazy_impl(all_125_1_116, all_125_0_115) = all_125_2_117 & impl(true, true) = all_125_0_115 & prop(true) = all_125_1_116
% 210.67/152.58  |
% 210.67/152.58  | Applying alpha-rule on (281) yields:
% 210.67/152.58  | (282) f2(true, false, true) = all_125_2_117
% 210.67/152.58  | (283) lazy_impl(all_125_1_116, all_125_0_115) = all_125_2_117
% 210.67/152.58  | (284) impl(true, true) = all_125_0_115
% 210.67/152.58  | (285) prop(true) = all_125_1_116
% 210.67/152.58  |
% 210.67/152.58  | Instantiating (236) with all_127_0_118 yields:
% 210.67/152.58  | (286) f7(true) = all_127_0_118 & lazy_impl(true, true) = all_127_0_118
% 210.67/152.58  |
% 210.67/152.58  | Applying alpha-rule on (286) yields:
% 210.67/152.58  | (287) f7(true) = all_127_0_118
% 210.67/152.58  | (288) lazy_impl(true, true) = all_127_0_118
% 210.67/152.58  |
% 210.67/152.58  | Instantiating (226) with all_129_0_119, all_129_1_120, all_129_2_121 yields:
% 210.67/152.58  | (289) f1(false, false, true) = all_129_2_121 & lazy_impl(all_129_1_120, all_129_0_119) = all_129_2_121 & impl(true, true) = all_129_0_119 & prop(true) = all_129_1_120
% 210.67/152.58  |
% 210.67/152.58  | Applying alpha-rule on (289) yields:
% 210.67/152.58  | (290) f1(false, false, true) = all_129_2_121
% 210.67/152.58  | (291) lazy_impl(all_129_1_120, all_129_0_119) = all_129_2_121
% 210.67/152.58  | (292) impl(true, true) = all_129_0_119
% 210.67/152.58  | (293) prop(true) = all_129_1_120
% 210.67/152.58  |
% 210.67/152.58  | Instantiating (225) with all_131_0_122, all_131_1_123 yields:
% 210.67/152.58  | (294) f3(true, false, true) = all_131_1_123 & lazy_impl(all_131_0_122, true) = all_131_1_123 & prop(true) = all_131_0_122
% 210.67/152.58  |
% 210.67/152.58  | Applying alpha-rule on (294) yields:
% 210.67/152.58  | (295) f3(true, false, true) = all_131_1_123
% 210.67/152.58  | (296) lazy_impl(all_131_0_122, true) = all_131_1_123
% 210.67/152.58  | (297) prop(true) = all_131_0_122
% 210.67/152.58  |
% 210.67/152.58  | Instantiating (224) with all_133_0_124, all_133_1_125 yields:
% 210.67/152.58  | (298) f3(false, false, true) = all_133_1_125 & lazy_impl(all_133_0_124, true) = all_133_1_125 & prop(true) = all_133_0_124
% 210.67/152.58  |
% 210.67/152.58  | Applying alpha-rule on (298) yields:
% 210.67/152.58  | (299) f3(false, false, true) = all_133_1_125
% 210.67/152.58  | (300) lazy_impl(all_133_0_124, true) = all_133_1_125
% 210.67/152.58  | (301) prop(true) = all_133_0_124
% 210.67/152.58  |
% 210.67/152.58  | Instantiating (237) with all_135_0_126 yields:
% 210.67/152.58  | (302) f7(false) = all_135_0_126 & lazy_impl(true, false) = all_135_0_126
% 210.67/152.58  |
% 210.67/152.58  | Applying alpha-rule on (302) yields:
% 210.67/152.58  | (303) f7(false) = all_135_0_126
% 210.67/152.58  | (304) lazy_impl(true, false) = all_135_0_126
% 210.67/152.58  |
% 210.67/152.58  | Instantiating (234) with all_137_0_127, all_137_1_128, all_137_2_129 yields:
% 210.67/152.58  | (305) f1(false, false, false) = all_137_2_129 & lazy_impl(all_137_1_128, all_137_0_127) = all_137_2_129 & impl(true, false) = all_137_0_127 & prop(false) = all_137_1_128
% 210.67/152.58  |
% 210.67/152.58  | Applying alpha-rule on (305) yields:
% 210.67/152.58  | (306) f1(false, false, false) = all_137_2_129
% 210.67/152.58  | (307) lazy_impl(all_137_1_128, all_137_0_127) = all_137_2_129
% 210.67/152.58  | (308) impl(true, false) = all_137_0_127
% 210.67/152.58  | (309) prop(false) = all_137_1_128
% 210.67/152.58  |
% 210.67/152.58  | Instantiating (233) with all_139_0_130, all_139_1_131 yields:
% 210.67/152.58  | (310) f3(true, true, false) = all_139_1_131 & lazy_impl(all_139_0_130, true) = all_139_1_131 & prop(false) = all_139_0_130
% 210.67/152.58  |
% 210.67/152.58  | Applying alpha-rule on (310) yields:
% 210.67/152.58  | (311) f3(true, true, false) = all_139_1_131
% 210.67/152.58  | (312) lazy_impl(all_139_0_130, true) = all_139_1_131
% 210.67/152.58  | (313) prop(false) = all_139_0_130
% 210.67/152.58  |
% 210.67/152.58  | Instantiating (232) with all_141_0_132, all_141_1_133 yields:
% 210.67/152.58  | (314) f3(false, false, false) = all_141_1_133 & lazy_impl(all_141_0_132, false) = all_141_1_133 & prop(false) = all_141_0_132
% 210.67/152.58  |
% 210.67/152.58  | Applying alpha-rule on (314) yields:
% 210.67/152.58  | (315) f3(false, false, false) = all_141_1_133
% 210.67/152.58  | (316) lazy_impl(all_141_0_132, false) = all_141_1_133
% 210.67/152.58  | (317) prop(false) = all_141_0_132
% 210.67/152.58  |
% 210.67/152.58  | Instantiating (231) with all_143_0_134, all_143_1_135, all_143_2_136 yields:
% 210.67/152.58  | (318) f1(false, true, false) = all_143_2_136 & lazy_impl(all_143_1_135, all_143_0_134) = all_143_2_136 & impl(true, false) = all_143_0_134 & prop(false) = all_143_1_135
% 210.67/152.58  |
% 210.67/152.58  | Applying alpha-rule on (318) yields:
% 210.67/152.58  | (319) f1(false, true, false) = all_143_2_136
% 210.67/152.58  | (320) lazy_impl(all_143_1_135, all_143_0_134) = all_143_2_136
% 210.67/152.58  | (321) impl(true, false) = all_143_0_134
% 210.67/152.58  | (322) prop(false) = all_143_1_135
% 210.67/152.58  |
% 210.67/152.58  | Instantiating (223) with all_145_0_137, all_145_1_138 yields:
% 210.67/152.58  | (323) f3(false, true, true) = all_145_1_138 & lazy_impl(all_145_0_137, true) = all_145_1_138 & prop(true) = all_145_0_137
% 210.67/152.58  |
% 210.67/152.58  | Applying alpha-rule on (323) yields:
% 210.67/152.58  | (324) f3(false, true, true) = all_145_1_138
% 210.67/152.58  | (325) lazy_impl(all_145_0_137, true) = all_145_1_138
% 210.67/152.58  | (326) prop(true) = all_145_0_137
% 210.67/152.58  |
% 210.67/152.58  | Instantiating (235) with all_147_0_139, all_147_1_140, all_147_2_141 yields:
% 210.67/152.58  | (327) f2(true, false, false) = all_147_2_141 & lazy_impl(all_147_1_140, all_147_0_139) = all_147_2_141 & impl(true, false) = all_147_0_139 & prop(false) = all_147_1_140
% 210.67/152.58  |
% 210.67/152.58  | Applying alpha-rule on (327) yields:
% 210.67/152.58  | (328) f2(true, false, false) = all_147_2_141
% 210.67/152.58  | (329) lazy_impl(all_147_1_140, all_147_0_139) = all_147_2_141
% 210.67/152.58  | (330) impl(true, false) = all_147_0_139
% 210.67/152.58  | (331) prop(false) = all_147_1_140
% 210.67/152.58  |
% 210.67/152.58  | Instantiating (218) with all_149_0_142, all_149_1_143, all_149_2_144 yields:
% 210.67/152.58  | (332) f2(true, true, true) = all_149_2_144 & lazy_impl(all_149_1_143, all_149_0_142) = all_149_2_144 & impl(true, true) = all_149_0_142 & prop(true) = all_149_1_143
% 210.67/152.58  |
% 210.67/152.58  | Applying alpha-rule on (332) yields:
% 210.67/152.58  | (333) f2(true, true, true) = all_149_2_144
% 210.67/152.58  | (334) lazy_impl(all_149_1_143, all_149_0_142) = all_149_2_144
% 210.67/152.58  | (335) impl(true, true) = all_149_0_142
% 210.67/152.58  | (336) prop(true) = all_149_1_143
% 210.67/152.58  |
% 210.67/152.58  | Instantiating (216) with all_151_0_145, all_151_1_146 yields:
% 210.67/152.58  | (337) f3(true, true, true) = all_151_1_146 & lazy_impl(all_151_0_145, true) = all_151_1_146 & prop(true) = all_151_0_145
% 210.67/152.58  |
% 210.67/152.58  | Applying alpha-rule on (337) yields:
% 210.67/152.58  | (338) f3(true, true, true) = all_151_1_146
% 210.67/152.58  | (339) lazy_impl(all_151_0_145, true) = all_151_1_146
% 210.67/152.58  | (340) prop(true) = all_151_0_145
% 210.67/152.58  |
% 210.67/152.58  | Instantiating (215) with all_153_0_147, all_153_1_148 yields:
% 210.67/152.58  | (341) phi(err) = all_153_0_147 & bool(err) = all_153_1_148 & (all_153_0_147 = all_89_0_86 | all_153_1_148 = 0)
% 210.67/152.58  |
% 210.67/152.58  | Applying alpha-rule on (341) yields:
% 210.67/152.58  | (342) phi(err) = all_153_0_147
% 210.67/152.58  | (343) bool(err) = all_153_1_148
% 210.67/152.58  | (344) all_153_0_147 = all_89_0_86 | all_153_1_148 = 0
% 210.67/152.58  |
% 210.67/152.58  | Instantiating (217) with all_155_0_149, all_155_1_150, all_155_2_151 yields:
% 210.67/152.58  | (345) f1(true, true, true) = all_155_2_151 & lazy_impl(all_155_1_150, all_155_0_149) = all_155_2_151 & impl(true, true) = all_155_0_149 & prop(true) = all_155_1_150
% 210.67/152.58  |
% 210.67/152.58  | Applying alpha-rule on (345) yields:
% 210.67/152.58  | (346) f1(true, true, true) = all_155_2_151
% 210.67/152.58  | (347) lazy_impl(all_155_1_150, all_155_0_149) = all_155_2_151
% 210.67/152.58  | (348) impl(true, true) = all_155_0_149
% 210.67/152.58  | (349) prop(true) = all_155_1_150
% 210.67/152.58  |
% 210.67/152.58  | Instantiating formula (103) with true, true, all_127_0_118, true and discharging atoms lazy_impl(true, true) = all_127_0_118, lazy_impl(true, true) = true, yields:
% 210.67/152.58  | (350) all_127_0_118 = true
% 210.67/152.58  |
% 210.67/152.58  | Instantiating formula (103) with true, false, all_135_0_126, false and discharging atoms lazy_impl(true, false) = all_135_0_126, lazy_impl(true, false) = false, yields:
% 210.67/152.58  | (351) all_135_0_126 = false
% 210.67/152.58  |
% 210.67/152.58  | Instantiating formula (63) with true, true, all_149_0_142, all_155_0_149 and discharging atoms impl(true, true) = all_155_0_149, impl(true, true) = all_149_0_142, yields:
% 210.67/152.58  | (352) all_155_0_149 = all_149_0_142
% 210.67/152.58  |
% 210.67/152.58  | Instantiating formula (63) with true, true, all_129_0_119, all_149_0_142 and discharging atoms impl(true, true) = all_149_0_142, impl(true, true) = all_129_0_119, yields:
% 210.67/152.58  | (353) all_149_0_142 = all_129_0_119
% 210.67/152.58  |
% 210.67/152.58  | Instantiating formula (63) with true, true, all_125_0_115, all_129_0_119 and discharging atoms impl(true, true) = all_129_0_119, impl(true, true) = all_125_0_115, yields:
% 210.67/152.58  | (354) all_129_0_119 = all_125_0_115
% 210.67/152.58  |
% 210.67/152.58  | Instantiating formula (63) with true, true, all_121_0_109, true and discharging atoms impl(true, true) = all_121_0_109, impl(true, true) = true, yields:
% 210.67/152.58  | (355) all_121_0_109 = true
% 210.67/152.58  |
% 210.67/152.58  | Instantiating formula (63) with true, true, all_121_0_109, all_125_0_115 and discharging atoms impl(true, true) = all_125_0_115, impl(true, true) = all_121_0_109, yields:
% 210.67/152.58  | (356) all_125_0_115 = all_121_0_109
% 210.67/152.58  |
% 210.67/152.58  | Instantiating formula (63) with true, true, all_117_0_103, all_155_0_149 and discharging atoms impl(true, true) = all_155_0_149, impl(true, true) = all_117_0_103, yields:
% 210.67/152.58  | (357) all_155_0_149 = all_117_0_103
% 210.67/152.58  |
% 210.67/152.58  | Instantiating formula (63) with true, false, all_147_0_139, false and discharging atoms impl(true, false) = all_147_0_139, impl(true, false) = false, yields:
% 210.67/152.58  | (358) all_147_0_139 = false
% 210.67/152.58  |
% 210.67/152.58  | Instantiating formula (63) with true, false, all_137_0_127, all_147_0_139 and discharging atoms impl(true, false) = all_147_0_139, impl(true, false) = all_137_0_127, yields:
% 210.67/152.59  | (359) all_147_0_139 = all_137_0_127
% 210.67/152.59  |
% 210.67/152.59  | Instantiating formula (63) with true, false, all_137_0_127, all_143_0_134 and discharging atoms impl(true, false) = all_143_0_134, impl(true, false) = all_137_0_127, yields:
% 210.67/152.59  | (360) all_143_0_134 = all_137_0_127
% 210.67/152.59  |
% 210.67/152.59  | Instantiating formula (63) with true, false, all_111_0_97, all_143_0_134 and discharging atoms impl(true, false) = all_143_0_134, impl(true, false) = all_111_0_97, yields:
% 210.67/152.59  | (361) all_143_0_134 = all_111_0_97
% 210.67/152.59  |
% 210.67/152.59  | Instantiating formula (63) with false, false, all_123_0_112, true and discharging atoms impl(false, false) = all_123_0_112, impl(false, false) = true, yields:
% 210.67/152.59  | (362) all_123_0_112 = true
% 210.67/152.59  |
% 210.67/152.59  | Instantiating formula (63) with false, false, all_119_0_106, all_123_0_112 and discharging atoms impl(false, false) = all_123_0_112, impl(false, false) = all_119_0_106, yields:
% 210.67/152.59  | (363) all_123_0_112 = all_119_0_106
% 210.67/152.59  |
% 210.67/152.59  | Instantiating formula (6) with true, all_151_0_145, all_155_1_150 and discharging atoms prop(true) = all_155_1_150, prop(true) = all_151_0_145, yields:
% 210.67/152.59  | (364) all_155_1_150 = all_151_0_145
% 210.67/152.59  |
% 210.67/152.59  | Instantiating formula (6) with true, all_149_1_143, all_151_0_145 and discharging atoms prop(true) = all_151_0_145, prop(true) = all_149_1_143, yields:
% 210.67/152.59  | (365) all_151_0_145 = all_149_1_143
% 210.67/152.59  |
% 210.67/152.59  | Instantiating formula (6) with true, all_145_0_137, all_155_1_150 and discharging atoms prop(true) = all_155_1_150, prop(true) = all_145_0_137, yields:
% 210.67/152.59  | (366) all_155_1_150 = all_145_0_137
% 210.67/152.59  |
% 210.67/152.59  | Instantiating formula (6) with true, all_133_0_124, all_149_1_143 and discharging atoms prop(true) = all_149_1_143, prop(true) = all_133_0_124, yields:
% 210.67/152.59  | (367) all_149_1_143 = all_133_0_124
% 210.67/152.59  |
% 210.67/152.59  | Instantiating formula (6) with true, all_129_1_120, true and discharging atoms prop(true) = all_129_1_120, prop(true) = true, yields:
% 210.67/152.59  | (368) all_129_1_120 = true
% 210.67/152.59  |
% 210.67/152.59  | Instantiating formula (6) with true, all_129_1_120, all_133_0_124 and discharging atoms prop(true) = all_133_0_124, prop(true) = all_129_1_120, yields:
% 210.67/152.59  | (369) all_133_0_124 = all_129_1_120
% 210.67/152.59  |
% 210.67/152.59  | Instantiating formula (6) with true, all_129_1_120, all_131_0_122 and discharging atoms prop(true) = all_131_0_122, prop(true) = all_129_1_120, yields:
% 210.67/152.59  | (370) all_131_0_122 = all_129_1_120
% 210.67/152.59  |
% 210.67/152.59  | Instantiating formula (6) with true, all_125_1_116, all_149_1_143 and discharging atoms prop(true) = all_149_1_143, prop(true) = all_125_1_116, yields:
% 210.67/152.59  | (371) all_149_1_143 = all_125_1_116
% 210.67/152.59  |
% 210.67/152.59  | Instantiating formula (6) with true, all_121_1_110, all_131_0_122 and discharging atoms prop(true) = all_131_0_122, prop(true) = all_121_1_110, yields:
% 210.67/152.59  | (372) all_131_0_122 = all_121_1_110
% 210.67/152.59  |
% 210.67/152.59  | Instantiating formula (6) with true, all_117_1_104, all_129_1_120 and discharging atoms prop(true) = all_129_1_120, prop(true) = all_117_1_104, yields:
% 210.67/152.59  | (373) all_129_1_120 = all_117_1_104
% 210.67/152.59  |
% 210.67/152.59  | Instantiating formula (6) with false, all_143_1_135, all_147_1_140 and discharging atoms prop(false) = all_147_1_140, prop(false) = all_143_1_135, yields:
% 210.67/152.59  | (374) all_147_1_140 = all_143_1_135
% 210.67/152.59  |
% 210.67/152.59  | Instantiating formula (6) with false, all_139_0_130, all_147_1_140 and discharging atoms prop(false) = all_147_1_140, prop(false) = all_139_0_130, yields:
% 210.67/152.59  | (375) all_147_1_140 = all_139_0_130
% 210.67/152.59  |
% 210.67/152.59  | Instantiating formula (6) with false, all_123_1_113, all_141_0_132 and discharging atoms prop(false) = all_141_0_132, prop(false) = all_123_1_113, yields:
% 210.67/152.59  | (376) all_141_0_132 = all_123_1_113
% 210.67/152.59  |
% 210.67/152.59  | Instantiating formula (6) with false, all_123_1_113, all_139_0_130 and discharging atoms prop(false) = all_139_0_130, prop(false) = all_123_1_113, yields:
% 210.67/152.59  | (377) all_139_0_130 = all_123_1_113
% 210.67/152.59  |
% 210.67/152.59  | Instantiating formula (6) with false, all_123_1_113, all_137_1_128 and discharging atoms prop(false) = all_137_1_128, prop(false) = all_123_1_113, yields:
% 210.67/152.59  | (378) all_137_1_128 = all_123_1_113
% 210.67/152.59  |
% 210.67/152.59  | Instantiating formula (6) with false, all_119_1_107, all_147_1_140 and discharging atoms prop(false) = all_147_1_140, prop(false) = all_119_1_107, yields:
% 210.67/152.59  | (379) all_147_1_140 = all_119_1_107
% 210.67/152.59  |
% 210.67/152.59  | Instantiating formula (6) with false, all_115_0_101, all_137_1_128 and discharging atoms prop(false) = all_137_1_128, prop(false) = all_115_0_101, yields:
% 210.67/152.59  | (380) all_137_1_128 = all_115_0_101
% 210.67/152.59  |
% 210.67/152.59  | Instantiating formula (6) with false, all_111_1_98, true and discharging atoms prop(false) = all_111_1_98, prop(false) = true, yields:
% 210.67/152.59  | (381) all_111_1_98 = true
% 210.67/152.59  |
% 210.67/152.59  | Instantiating formula (6) with false, all_111_1_98, all_137_1_128 and discharging atoms prop(false) = all_137_1_128, prop(false) = all_111_1_98, yields:
% 210.67/152.59  | (382) all_137_1_128 = all_111_1_98
% 210.67/152.59  |
% 210.67/152.59  | Instantiating formula (6) with false, all_109_0_95, all_141_0_132 and discharging atoms prop(false) = all_141_0_132, prop(false) = all_109_0_95, yields:
% 210.67/152.59  | (383) all_141_0_132 = all_109_0_95
% 210.67/152.59  |
% 210.67/152.59  | Instantiating formula (67) with err, all_153_0_147, err and discharging atoms phi(err) = all_153_0_147, phi(err) = err, yields:
% 210.67/152.59  | (384) all_153_0_147 = err
% 210.67/152.59  |
% 210.67/152.59  | Combining equations (352,357) yields a new equation:
% 210.67/152.59  | (385) all_149_0_142 = all_117_0_103
% 210.67/152.59  |
% 210.67/152.59  | Simplifying 385 yields:
% 210.67/152.59  | (386) all_149_0_142 = all_117_0_103
% 210.67/152.59  |
% 210.67/152.59  | Combining equations (364,366) yields a new equation:
% 210.67/152.59  | (387) all_151_0_145 = all_145_0_137
% 210.67/152.59  |
% 210.67/152.59  | Simplifying 387 yields:
% 210.67/152.59  | (388) all_151_0_145 = all_145_0_137
% 210.67/152.59  |
% 210.67/152.59  | Combining equations (365,388) yields a new equation:
% 210.67/152.59  | (389) all_149_1_143 = all_145_0_137
% 210.67/152.59  |
% 210.67/152.59  | Simplifying 389 yields:
% 210.67/152.59  | (390) all_149_1_143 = all_145_0_137
% 210.67/152.59  |
% 210.67/152.59  | Combining equations (353,386) yields a new equation:
% 210.67/152.59  | (391) all_129_0_119 = all_117_0_103
% 210.67/152.59  |
% 210.67/152.59  | Simplifying 391 yields:
% 210.67/152.59  | (392) all_129_0_119 = all_117_0_103
% 210.67/152.59  |
% 210.67/152.59  | Combining equations (367,390) yields a new equation:
% 210.67/152.59  | (393) all_145_0_137 = all_133_0_124
% 210.67/152.59  |
% 210.67/152.59  | Combining equations (371,390) yields a new equation:
% 210.67/152.59  | (394) all_145_0_137 = all_125_1_116
% 210.67/152.59  |
% 210.67/152.59  | Combining equations (359,358) yields a new equation:
% 210.67/152.59  | (395) all_137_0_127 = false
% 210.67/152.59  |
% 210.67/152.59  | Simplifying 395 yields:
% 210.67/152.59  | (396) all_137_0_127 = false
% 210.67/152.59  |
% 210.67/152.59  | Combining equations (379,374) yields a new equation:
% 210.67/152.59  | (397) all_143_1_135 = all_119_1_107
% 210.67/152.59  |
% 210.67/152.59  | Combining equations (375,374) yields a new equation:
% 210.67/152.59  | (398) all_143_1_135 = all_139_0_130
% 210.67/152.59  |
% 210.67/152.59  | Combining equations (393,394) yields a new equation:
% 210.67/152.59  | (399) all_133_0_124 = all_125_1_116
% 210.67/152.59  |
% 210.67/152.59  | Simplifying 399 yields:
% 210.67/152.59  | (400) all_133_0_124 = all_125_1_116
% 210.67/152.59  |
% 210.67/152.59  | Combining equations (360,361) yields a new equation:
% 210.67/152.59  | (401) all_137_0_127 = all_111_0_97
% 210.67/152.59  |
% 210.67/152.59  | Simplifying 401 yields:
% 210.67/152.59  | (402) all_137_0_127 = all_111_0_97
% 210.67/152.59  |
% 210.67/152.59  | Combining equations (398,397) yields a new equation:
% 210.67/152.59  | (403) all_139_0_130 = all_119_1_107
% 210.67/152.59  |
% 210.67/152.59  | Simplifying 403 yields:
% 210.67/152.59  | (404) all_139_0_130 = all_119_1_107
% 210.67/152.59  |
% 210.67/152.59  | Combining equations (376,383) yields a new equation:
% 210.67/152.59  | (405) all_123_1_113 = all_109_0_95
% 210.67/152.59  |
% 210.67/152.59  | Simplifying 405 yields:
% 210.67/152.59  | (406) all_123_1_113 = all_109_0_95
% 210.67/152.59  |
% 210.67/152.59  | Combining equations (377,404) yields a new equation:
% 210.67/152.59  | (407) all_123_1_113 = all_119_1_107
% 210.67/152.59  |
% 210.67/152.59  | Simplifying 407 yields:
% 210.67/152.59  | (408) all_123_1_113 = all_119_1_107
% 210.67/152.59  |
% 210.67/152.59  | Combining equations (396,402) yields a new equation:
% 210.67/152.59  | (409) all_111_0_97 = false
% 210.67/152.59  |
% 210.67/152.59  | Combining equations (382,380) yields a new equation:
% 210.67/152.59  | (410) all_115_0_101 = all_111_1_98
% 210.67/152.59  |
% 210.67/152.59  | Combining equations (378,380) yields a new equation:
% 210.67/152.59  | (411) all_123_1_113 = all_115_0_101
% 210.67/152.59  |
% 210.67/152.59  | Simplifying 411 yields:
% 210.67/152.59  | (412) all_123_1_113 = all_115_0_101
% 210.67/152.59  |
% 210.67/152.59  | Combining equations (369,400) yields a new equation:
% 210.67/152.59  | (413) all_129_1_120 = all_125_1_116
% 210.67/152.59  |
% 210.67/152.59  | Simplifying 413 yields:
% 210.67/152.59  | (414) all_129_1_120 = all_125_1_116
% 210.67/152.59  |
% 210.67/152.59  | Combining equations (370,372) yields a new equation:
% 210.67/152.59  | (415) all_129_1_120 = all_121_1_110
% 210.67/152.59  |
% 210.67/152.59  | Simplifying 415 yields:
% 210.67/152.59  | (416) all_129_1_120 = all_121_1_110
% 210.67/152.59  |
% 210.67/152.59  | Combining equations (354,392) yields a new equation:
% 210.67/152.59  | (417) all_125_0_115 = all_117_0_103
% 210.67/152.59  |
% 210.67/152.59  | Simplifying 417 yields:
% 210.67/152.59  | (418) all_125_0_115 = all_117_0_103
% 210.67/152.59  |
% 210.67/152.59  | Combining equations (368,414) yields a new equation:
% 210.67/152.59  | (419) all_125_1_116 = true
% 210.67/152.59  |
% 210.67/152.59  | Combining equations (373,414) yields a new equation:
% 210.67/152.59  | (420) all_125_1_116 = all_117_1_104
% 210.67/152.59  |
% 210.67/152.59  | Combining equations (416,414) yields a new equation:
% 210.67/152.59  | (421) all_125_1_116 = all_121_1_110
% 210.67/152.59  |
% 210.67/152.59  | Combining equations (356,418) yields a new equation:
% 210.67/152.59  | (422) all_121_0_109 = all_117_0_103
% 210.67/152.59  |
% 210.67/152.59  | Simplifying 422 yields:
% 210.67/152.59  | (423) all_121_0_109 = all_117_0_103
% 210.67/152.59  |
% 210.67/152.59  | Combining equations (420,421) yields a new equation:
% 210.67/152.59  | (424) all_121_1_110 = all_117_1_104
% 210.67/152.59  |
% 210.67/152.59  | Combining equations (419,421) yields a new equation:
% 210.67/152.59  | (425) all_121_1_110 = true
% 210.67/152.59  |
% 210.67/152.59  | Combining equations (362,363) yields a new equation:
% 210.67/152.59  | (426) all_119_0_106 = true
% 210.67/152.59  |
% 210.67/152.59  | Combining equations (406,408) yields a new equation:
% 210.67/152.59  | (427) all_119_1_107 = all_109_0_95
% 210.67/152.59  |
% 210.67/152.59  | Combining equations (412,408) yields a new equation:
% 210.67/152.59  | (428) all_119_1_107 = all_115_0_101
% 210.67/152.59  |
% 210.67/152.59  | Combining equations (355,423) yields a new equation:
% 210.67/152.59  | (429) all_117_0_103 = true
% 210.67/152.59  |
% 210.67/152.59  | Combining equations (425,424) yields a new equation:
% 210.67/152.59  | (430) all_117_1_104 = true
% 210.67/152.59  |
% 210.67/152.59  | Combining equations (428,427) yields a new equation:
% 210.67/152.59  | (431) all_115_0_101 = all_109_0_95
% 210.67/152.59  |
% 210.67/152.59  | Simplifying 431 yields:
% 210.67/152.59  | (432) all_115_0_101 = all_109_0_95
% 210.67/152.59  |
% 210.67/152.59  | Combining equations (410,432) yields a new equation:
% 210.67/152.59  | (433) all_111_1_98 = all_109_0_95
% 210.67/152.59  |
% 210.67/152.59  | Simplifying 433 yields:
% 210.67/152.59  | (434) all_111_1_98 = all_109_0_95
% 210.67/152.59  |
% 210.67/152.59  | Combining equations (381,434) yields a new equation:
% 210.67/152.59  | (435) all_109_0_95 = true
% 210.67/152.59  |
% 210.67/152.59  | Combining equations (435,434) yields a new equation:
% 210.67/152.59  | (381) all_111_1_98 = true
% 210.67/152.59  |
% 210.67/152.59  | Combining equations (435,432) yields a new equation:
% 210.67/152.59  | (437) all_115_0_101 = true
% 210.67/152.59  |
% 210.67/152.59  | Combining equations (435,427) yields a new equation:
% 210.67/152.59  | (438) all_119_1_107 = true
% 210.67/152.59  |
% 210.67/152.59  | Combining equations (430,424) yields a new equation:
% 210.67/152.59  | (425) all_121_1_110 = true
% 210.67/152.59  |
% 210.67/152.59  | Combining equations (429,423) yields a new equation:
% 210.67/152.59  | (355) all_121_0_109 = true
% 210.67/152.59  |
% 210.67/152.59  | Combining equations (438,408) yields a new equation:
% 210.67/152.59  | (441) all_123_1_113 = true
% 210.67/152.59  |
% 210.67/152.59  | Combining equations (426,363) yields a new equation:
% 210.67/152.59  | (362) all_123_0_112 = true
% 210.67/152.59  |
% 210.67/152.59  | Combining equations (425,421) yields a new equation:
% 210.67/152.59  | (419) all_125_1_116 = true
% 210.67/152.59  |
% 210.67/152.59  | Combining equations (429,418) yields a new equation:
% 210.67/152.59  | (444) all_125_0_115 = true
% 210.67/152.59  |
% 210.67/152.59  | Combining equations (419,414) yields a new equation:
% 210.67/152.59  | (368) all_129_1_120 = true
% 210.67/152.59  |
% 210.67/152.59  | Combining equations (429,392) yields a new equation:
% 210.67/152.59  | (446) all_129_0_119 = true
% 210.67/152.59  |
% 210.67/152.59  | Combining equations (425,372) yields a new equation:
% 210.67/152.59  | (447) all_131_0_122 = true
% 210.67/152.59  |
% 210.67/152.59  | Combining equations (419,400) yields a new equation:
% 210.67/152.59  | (448) all_133_0_124 = true
% 210.67/152.59  |
% 210.67/152.59  | Combining equations (437,380) yields a new equation:
% 210.67/152.59  | (449) all_137_1_128 = true
% 210.67/152.59  |
% 210.67/152.59  | Combining equations (409,402) yields a new equation:
% 210.67/152.59  | (396) all_137_0_127 = false
% 210.67/152.59  |
% 210.67/152.59  | Combining equations (438,404) yields a new equation:
% 210.67/152.59  | (451) all_139_0_130 = true
% 210.67/152.59  |
% 210.67/152.59  | Combining equations (435,383) yields a new equation:
% 210.67/152.59  | (452) all_141_0_132 = true
% 210.67/152.59  |
% 210.67/152.59  | Combining equations (438,397) yields a new equation:
% 210.67/152.59  | (453) all_143_1_135 = true
% 210.67/152.59  |
% 210.67/152.59  | Combining equations (409,361) yields a new equation:
% 210.67/152.59  | (454) all_143_0_134 = false
% 210.67/152.59  |
% 210.67/152.59  | Combining equations (419,394) yields a new equation:
% 210.67/152.59  | (455) all_145_0_137 = true
% 210.67/152.59  |
% 210.67/152.59  | Combining equations (453,374) yields a new equation:
% 210.67/152.59  | (456) all_147_1_140 = true
% 210.67/152.59  |
% 210.67/152.59  | Combining equations (455,390) yields a new equation:
% 210.67/152.59  | (457) all_149_1_143 = true
% 210.67/152.59  |
% 210.67/152.59  | Combining equations (429,386) yields a new equation:
% 210.67/152.59  | (458) all_149_0_142 = true
% 210.67/152.59  |
% 210.67/152.59  | Combining equations (455,388) yields a new equation:
% 210.67/152.59  | (459) all_151_0_145 = true
% 210.67/152.59  |
% 210.67/152.59  | Combining equations (455,366) yields a new equation:
% 210.67/152.59  | (460) all_155_1_150 = true
% 210.67/152.59  |
% 210.67/152.59  | Combining equations (429,357) yields a new equation:
% 210.67/152.59  | (461) all_155_0_149 = true
% 210.67/152.59  |
% 210.67/152.59  | From (351) and (303) follows:
% 210.67/152.59  | (462) f7(false) = false
% 210.67/152.59  |
% 210.67/152.59  | From (460)(461) and (347) follows:
% 210.67/152.60  | (463) lazy_impl(true, true) = all_155_2_151
% 210.67/152.60  |
% 210.67/152.60  | From (459) and (339) follows:
% 210.67/152.60  | (464) lazy_impl(true, true) = all_151_1_146
% 210.67/152.60  |
% 210.67/152.60  | From (457)(458) and (334) follows:
% 210.67/152.60  | (465) lazy_impl(true, true) = all_149_2_144
% 210.67/152.60  |
% 210.67/152.60  | From (456)(358) and (329) follows:
% 210.67/152.60  | (466) lazy_impl(true, false) = all_147_2_141
% 210.67/152.60  |
% 210.67/152.60  | From (455) and (325) follows:
% 210.67/152.60  | (467) lazy_impl(true, true) = all_145_1_138
% 210.67/152.60  |
% 210.67/152.60  | From (453)(454) and (320) follows:
% 210.67/152.60  | (468) lazy_impl(true, false) = all_143_2_136
% 210.67/152.60  |
% 210.67/152.60  | From (452) and (316) follows:
% 210.67/152.60  | (469) lazy_impl(true, false) = all_141_1_133
% 210.67/152.60  |
% 210.67/152.60  | From (451) and (312) follows:
% 210.67/152.60  | (470) lazy_impl(true, true) = all_139_1_131
% 210.67/152.60  |
% 210.67/152.60  | From (449)(396) and (307) follows:
% 210.67/152.60  | (471) lazy_impl(true, false) = all_137_2_129
% 210.67/152.60  |
% 210.67/152.60  | From (448) and (300) follows:
% 210.67/152.60  | (472) lazy_impl(true, true) = all_133_1_125
% 210.67/152.60  |
% 210.67/152.60  | From (447) and (296) follows:
% 211.03/152.60  | (473) lazy_impl(true, true) = all_131_1_123
% 211.03/152.60  |
% 211.03/152.60  | From (368)(446) and (291) follows:
% 211.03/152.60  | (474) lazy_impl(true, true) = all_129_2_121
% 211.03/152.60  |
% 211.03/152.60  | From (419)(444) and (283) follows:
% 211.03/152.60  | (475) lazy_impl(true, true) = all_125_2_117
% 211.03/152.60  |
% 211.03/152.60  | From (441)(362) and (278) follows:
% 211.03/152.60  | (476) lazy_impl(true, true) = all_123_2_114
% 211.03/152.60  |
% 211.03/152.60  | From (425)(355) and (273) follows:
% 211.03/152.60  | (477) lazy_impl(true, true) = all_121_2_111
% 211.03/152.60  |
% 211.03/152.60  | From (438)(426) and (268) follows:
% 211.03/152.60  | (478) lazy_impl(true, true) = all_119_2_108
% 211.03/152.60  |
% 211.03/152.60  | From (430)(429) and (263) follows:
% 211.03/152.60  | (479) lazy_impl(true, true) = all_117_2_105
% 211.03/152.60  |
% 211.03/152.60  | From (437) and (259) follows:
% 211.03/152.60  | (480) lazy_impl(true, true) = all_115_1_102
% 211.03/152.60  |
% 211.03/152.60  | From (381)(409) and (251) follows:
% 211.03/152.60  | (481) lazy_impl(true, false) = all_111_2_99
% 211.03/152.60  |
% 211.03/152.60  | From (350) and (288) follows:
% 211.03/152.60  | (173) lazy_impl(true, true) = true
% 211.03/152.60  |
% 211.03/152.60  | From (351) and (304) follows:
% 211.03/152.60  | (174) lazy_impl(true, false) = false
% 211.03/152.60  |
% 211.03/152.60  | From (429) and (264) follows:
% 211.03/152.60  | (176) impl(true, true) = true
% 211.03/152.60  |
% 211.03/152.60  | From (384) and (342) follows:
% 211.03/152.60  | (138) phi(err) = err
% 211.03/152.60  |
% 211.03/152.60  | Instantiating formula (103) with true, true, all_149_2_144, true and discharging atoms lazy_impl(true, true) = all_149_2_144, lazy_impl(true, true) = true, yields:
% 211.03/152.60  | (486) all_149_2_144 = true
% 211.03/152.60  |
% 211.03/152.60  | Instantiating formula (103) with true, true, all_145_1_138, all_151_1_146 and discharging atoms lazy_impl(true, true) = all_151_1_146, lazy_impl(true, true) = all_145_1_138, yields:
% 211.03/152.60  | (487) all_151_1_146 = all_145_1_138
% 211.03/152.60  |
% 211.03/152.60  | Instantiating formula (103) with true, true, all_133_1_125, all_155_2_151 and discharging atoms lazy_impl(true, true) = all_155_2_151, lazy_impl(true, true) = all_133_1_125, yields:
% 211.03/152.60  | (488) all_155_2_151 = all_133_1_125
% 211.03/152.60  |
% 211.03/152.60  | Instantiating formula (103) with true, true, all_133_1_125, all_149_2_144 and discharging atoms lazy_impl(true, true) = all_149_2_144, lazy_impl(true, true) = all_133_1_125, yields:
% 211.03/152.60  | (489) all_149_2_144 = all_133_1_125
% 211.03/152.60  |
% 211.03/152.60  | Instantiating formula (103) with true, true, all_131_1_123, all_139_1_131 and discharging atoms lazy_impl(true, true) = all_139_1_131, lazy_impl(true, true) = all_131_1_123, yields:
% 211.03/152.60  | (490) all_139_1_131 = all_131_1_123
% 211.03/152.60  |
% 211.03/152.60  | Instantiating formula (103) with true, true, all_131_1_123, all_133_1_125 and discharging atoms lazy_impl(true, true) = all_133_1_125, lazy_impl(true, true) = all_131_1_123, yields:
% 211.03/152.60  | (491) all_133_1_125 = all_131_1_123
% 211.03/152.60  |
% 211.03/152.60  | Instantiating formula (103) with true, true, all_129_2_121, all_145_1_138 and discharging atoms lazy_impl(true, true) = all_145_1_138, lazy_impl(true, true) = all_129_2_121, yields:
% 211.03/152.60  | (492) all_145_1_138 = all_129_2_121
% 211.03/152.60  |
% 211.03/152.60  | Instantiating formula (103) with true, true, all_125_2_117, all_133_1_125 and discharging atoms lazy_impl(true, true) = all_133_1_125, lazy_impl(true, true) = all_125_2_117, yields:
% 211.03/152.60  | (493) all_133_1_125 = all_125_2_117
% 211.03/152.60  |
% 211.03/152.60  | Instantiating formula (103) with true, true, all_123_2_114, all_145_1_138 and discharging atoms lazy_impl(true, true) = all_145_1_138, lazy_impl(true, true) = all_123_2_114, yields:
% 211.03/152.60  | (494) all_145_1_138 = all_123_2_114
% 211.03/152.60  |
% 211.03/152.60  | Instantiating formula (103) with true, true, all_121_2_111, all_139_1_131 and discharging atoms lazy_impl(true, true) = all_139_1_131, lazy_impl(true, true) = all_121_2_111, yields:
% 211.03/152.60  | (495) all_139_1_131 = all_121_2_111
% 211.03/152.60  |
% 211.03/152.60  | Instantiating formula (103) with true, true, all_119_2_108, all_155_2_151 and discharging atoms lazy_impl(true, true) = all_155_2_151, lazy_impl(true, true) = all_119_2_108, yields:
% 211.03/152.60  | (496) all_155_2_151 = all_119_2_108
% 211.03/152.60  |
% 211.03/152.60  | Instantiating formula (103) with true, true, all_119_2_108, all_123_2_114 and discharging atoms lazy_impl(true, true) = all_123_2_114, lazy_impl(true, true) = all_119_2_108, yields:
% 211.03/152.60  | (497) all_123_2_114 = all_119_2_108
% 211.03/152.60  |
% 211.03/152.60  | Instantiating formula (103) with true, true, all_117_2_105, all_155_2_151 and discharging atoms lazy_impl(true, true) = all_155_2_151, lazy_impl(true, true) = all_117_2_105, yields:
% 211.03/152.60  | (498) all_155_2_151 = all_117_2_105
% 211.03/152.60  |
% 211.03/152.60  | Instantiating formula (103) with true, true, all_115_1_102, all_151_1_146 and discharging atoms lazy_impl(true, true) = all_151_1_146, lazy_impl(true, true) = all_115_1_102, yields:
% 211.03/152.60  | (499) all_151_1_146 = all_115_1_102
% 211.03/152.60  |
% 211.03/152.60  | Instantiating formula (103) with true, false, all_143_2_136, all_147_2_141 and discharging atoms lazy_impl(true, false) = all_147_2_141, lazy_impl(true, false) = all_143_2_136, yields:
% 211.03/152.60  | (500) all_147_2_141 = all_143_2_136
% 211.03/152.60  |
% 211.03/152.60  | Instantiating formula (103) with true, false, all_141_1_133, false and discharging atoms lazy_impl(true, false) = all_141_1_133, lazy_impl(true, false) = false, yields:
% 211.03/152.60  | (501) all_141_1_133 = false
% 211.03/152.60  |
% 211.03/152.60  | Instantiating formula (103) with true, false, all_141_1_133, all_143_2_136 and discharging atoms lazy_impl(true, false) = all_143_2_136, lazy_impl(true, false) = all_141_1_133, yields:
% 211.03/152.60  | (502) all_143_2_136 = all_141_1_133
% 211.03/152.60  |
% 211.03/152.60  | Instantiating formula (103) with true, false, all_137_2_129, all_141_1_133 and discharging atoms lazy_impl(true, false) = all_141_1_133, lazy_impl(true, false) = all_137_2_129, yields:
% 211.03/152.60  | (503) all_141_1_133 = all_137_2_129
% 211.03/152.60  |
% 211.03/152.60  | Instantiating formula (103) with true, false, all_111_2_99, all_147_2_141 and discharging atoms lazy_impl(true, false) = all_147_2_141, lazy_impl(true, false) = all_111_2_99, yields:
% 211.03/152.60  | (504) all_147_2_141 = all_111_2_99
% 211.03/152.60  |
% 211.03/152.60  | Combining equations (496,498) yields a new equation:
% 211.03/152.60  | (505) all_119_2_108 = all_117_2_105
% 211.03/152.60  |
% 211.03/152.60  | Simplifying 505 yields:
% 211.03/152.60  | (506) all_119_2_108 = all_117_2_105
% 211.03/152.60  |
% 211.03/152.60  | Combining equations (488,498) yields a new equation:
% 211.03/152.60  | (507) all_133_1_125 = all_117_2_105
% 211.03/152.60  |
% 211.03/152.60  | Simplifying 507 yields:
% 211.03/152.60  | (508) all_133_1_125 = all_117_2_105
% 211.03/152.60  |
% 211.03/152.60  | Combining equations (487,499) yields a new equation:
% 211.03/152.60  | (509) all_145_1_138 = all_115_1_102
% 211.03/152.60  |
% 211.03/152.60  | Simplifying 509 yields:
% 211.03/152.60  | (510) all_145_1_138 = all_115_1_102
% 211.03/152.60  |
% 211.03/152.60  | Combining equations (489,486) yields a new equation:
% 211.03/152.60  | (511) all_133_1_125 = true
% 211.03/152.60  |
% 211.03/152.60  | Simplifying 511 yields:
% 211.03/152.60  | (512) all_133_1_125 = true
% 211.03/152.60  |
% 211.03/152.60  | Combining equations (500,504) yields a new equation:
% 211.03/152.60  | (513) all_143_2_136 = all_111_2_99
% 211.03/152.60  |
% 211.03/152.60  | Simplifying 513 yields:
% 211.03/152.60  | (514) all_143_2_136 = all_111_2_99
% 211.03/152.60  |
% 211.03/152.60  | Combining equations (494,492) yields a new equation:
% 211.03/152.60  | (515) all_129_2_121 = all_123_2_114
% 211.03/152.60  |
% 211.03/152.60  | Combining equations (510,492) yields a new equation:
% 211.03/152.60  | (516) all_129_2_121 = all_115_1_102
% 211.03/152.60  |
% 211.03/152.60  | Combining equations (502,514) yields a new equation:
% 211.03/152.60  | (517) all_141_1_133 = all_111_2_99
% 211.03/152.60  |
% 211.03/152.60  | Simplifying 517 yields:
% 211.03/152.60  | (518) all_141_1_133 = all_111_2_99
% 211.03/152.60  |
% 211.03/152.60  | Combining equations (518,503) yields a new equation:
% 211.03/152.60  | (519) all_137_2_129 = all_111_2_99
% 211.03/152.60  |
% 211.03/152.60  | Combining equations (501,503) yields a new equation:
% 211.03/152.60  | (520) all_137_2_129 = false
% 211.03/152.60  |
% 211.03/152.60  | Combining equations (490,495) yields a new equation:
% 211.03/152.60  | (521) all_131_1_123 = all_121_2_111
% 211.03/152.60  |
% 211.03/152.60  | Simplifying 521 yields:
% 211.03/152.60  | (522) all_131_1_123 = all_121_2_111
% 211.03/152.60  |
% 211.03/152.60  | Combining equations (520,519) yields a new equation:
% 211.03/152.60  | (523) all_111_2_99 = false
% 211.03/152.60  |
% 211.03/152.60  | Combining equations (508,493) yields a new equation:
% 211.03/152.60  | (524) all_125_2_117 = all_117_2_105
% 211.03/152.60  |
% 211.03/152.60  | Combining equations (491,493) yields a new equation:
% 211.03/152.60  | (525) all_131_1_123 = all_125_2_117
% 211.03/152.60  |
% 211.03/152.60  | Simplifying 525 yields:
% 211.03/152.60  | (526) all_131_1_123 = all_125_2_117
% 211.03/152.60  |
% 211.03/152.60  | Combining equations (512,493) yields a new equation:
% 211.03/152.60  | (527) all_125_2_117 = true
% 211.03/152.60  |
% 211.03/152.60  | Combining equations (526,522) yields a new equation:
% 211.03/152.60  | (528) all_125_2_117 = all_121_2_111
% 211.03/152.60  |
% 211.03/152.60  | Simplifying 528 yields:
% 211.03/152.60  | (529) all_125_2_117 = all_121_2_111
% 211.03/152.60  |
% 211.03/152.60  | Combining equations (515,516) yields a new equation:
% 211.03/152.60  | (530) all_123_2_114 = all_115_1_102
% 211.03/152.60  |
% 211.03/152.60  | Simplifying 530 yields:
% 211.03/152.60  | (531) all_123_2_114 = all_115_1_102
% 211.03/152.60  |
% 211.03/152.60  | Combining equations (527,529) yields a new equation:
% 211.03/152.60  | (532) all_121_2_111 = true
% 211.03/152.60  |
% 211.03/152.60  | Combining equations (524,529) yields a new equation:
% 211.03/152.60  | (533) all_121_2_111 = all_117_2_105
% 211.03/152.60  |
% 211.03/152.60  | Combining equations (497,531) yields a new equation:
% 211.03/152.60  | (534) all_119_2_108 = all_115_1_102
% 211.03/152.60  |
% 211.03/152.60  | Simplifying 534 yields:
% 211.03/152.60  | (535) all_119_2_108 = all_115_1_102
% 211.03/152.60  |
% 211.03/152.60  | Combining equations (533,532) yields a new equation:
% 211.03/152.60  | (536) all_117_2_105 = true
% 211.03/152.60  |
% 211.03/152.60  | Simplifying 536 yields:
% 211.03/152.60  | (537) all_117_2_105 = true
% 211.03/152.60  |
% 211.03/152.60  | Combining equations (506,535) yields a new equation:
% 211.03/152.60  | (538) all_117_2_105 = all_115_1_102
% 211.03/152.60  |
% 211.03/152.60  | Simplifying 538 yields:
% 211.03/152.60  | (539) all_117_2_105 = all_115_1_102
% 211.03/152.60  |
% 211.03/152.60  | Combining equations (539,537) yields a new equation:
% 211.03/152.60  | (540) all_115_1_102 = true
% 211.03/152.60  |
% 211.03/152.60  | Simplifying 540 yields:
% 211.03/152.60  | (541) all_115_1_102 = true
% 211.03/152.60  |
% 211.03/152.60  | Combining equations (541,535) yields a new equation:
% 211.03/152.60  | (542) all_119_2_108 = true
% 211.03/152.60  |
% 211.03/152.60  | Combining equations (523,504) yields a new equation:
% 211.03/152.60  | (543) all_147_2_141 = false
% 211.03/152.60  |
% 211.03/152.60  | From (486) and (333) follows:
% 211.03/152.60  | (544) f2(true, true, true) = true
% 211.03/152.60  |
% 211.03/152.60  | From (542) and (267) follows:
% 211.03/152.60  | (545) f2(true, true, false) = true
% 211.03/152.60  |
% 211.03/152.60  | From (543) and (328) follows:
% 211.03/152.60  | (546) f2(true, false, false) = false
% 211.03/152.60  |
% 211.03/152.60  | Instantiating formula (82) with all_107_0_93, all_73_0_83 and discharging atoms not1(all_73_0_83) = all_107_0_93, yields:
% 211.03/152.60  | (547)  ? [v0] :  ? [v1] : (phi(all_73_0_83) = v1 & bool(all_73_0_83) = v0 & (v1 = all_107_0_93 | v0 = 0))
% 211.03/152.61  |
% 211.03/152.61  | Instantiating formula (132) with false, false and discharging atoms f7(false) = false, yields:
% 211.03/152.61  | (548)  ? [v0] : ( ~ (v0 = 0) & forallprefers(false, all_2_0_0) = v0)
% 211.03/152.61  |
% 211.03/152.61  | Instantiating formula (58) with all_113_0_100, all_73_0_83 and discharging atoms d(all_73_0_83) = all_113_0_100, yields:
% 211.03/152.61  | (549)  ? [v0] : (phi(all_73_0_83) = v0 & ((v0 = all_73_0_83 & all_113_0_100 = 0) | (v0 = err &  ~ (all_113_0_100 = 0))))
% 211.03/152.61  |
% 211.03/152.61  | Instantiating (549) with all_170_0_152 yields:
% 211.03/152.61  | (550) phi(all_73_0_83) = all_170_0_152 & ((all_170_0_152 = all_73_0_83 & all_113_0_100 = 0) | (all_170_0_152 = err &  ~ (all_113_0_100 = 0)))
% 211.03/152.61  |
% 211.03/152.61  | Applying alpha-rule on (550) yields:
% 211.03/152.61  | (551) phi(all_73_0_83) = all_170_0_152
% 211.03/152.61  | (552) (all_170_0_152 = all_73_0_83 & all_113_0_100 = 0) | (all_170_0_152 = err &  ~ (all_113_0_100 = 0))
% 211.03/152.61  |
% 211.03/152.61  | Instantiating (548) with all_172_0_153 yields:
% 211.03/152.61  | (553)  ~ (all_172_0_153 = 0) & forallprefers(false, all_2_0_0) = all_172_0_153
% 211.03/152.61  |
% 211.03/152.61  | Applying alpha-rule on (553) yields:
% 211.03/152.61  | (554)  ~ (all_172_0_153 = 0)
% 211.03/152.61  | (555) forallprefers(false, all_2_0_0) = all_172_0_153
% 211.03/152.61  |
% 211.03/152.61  | Instantiating (547) with all_176_0_155, all_176_1_156 yields:
% 211.03/152.61  | (556) phi(all_73_0_83) = all_176_0_155 & bool(all_73_0_83) = all_176_1_156 & (all_176_0_155 = all_107_0_93 | all_176_1_156 = 0)
% 211.03/152.61  |
% 211.03/152.61  | Applying alpha-rule on (556) yields:
% 211.03/152.61  | (557) phi(all_73_0_83) = all_176_0_155
% 211.03/152.61  | (558) bool(all_73_0_83) = all_176_1_156
% 211.03/152.61  | (559) all_176_0_155 = all_107_0_93 | all_176_1_156 = 0
% 211.03/152.61  |
% 211.03/152.61  | Instantiating formula (67) with all_73_0_83, all_176_0_155, all_93_0_89 and discharging atoms phi(all_73_0_83) = all_176_0_155, phi(all_73_0_83) = all_93_0_89, yields:
% 211.03/152.61  | (560) all_176_0_155 = all_93_0_89
% 211.03/152.61  |
% 211.03/152.61  | Instantiating formula (67) with all_73_0_83, all_170_0_152, all_176_0_155 and discharging atoms phi(all_73_0_83) = all_176_0_155, phi(all_73_0_83) = all_170_0_152, yields:
% 211.03/152.61  | (561) all_176_0_155 = all_170_0_152
% 211.03/152.61  |
% 211.03/152.61  | Combining equations (561,560) yields a new equation:
% 211.03/152.61  | (562) all_170_0_152 = all_93_0_89
% 211.03/152.61  |
% 211.03/152.61  | Simplifying 562 yields:
% 211.03/152.61  | (563) all_170_0_152 = all_93_0_89
% 211.03/152.61  |
% 211.03/152.61  | From (563) and (551) follows:
% 211.03/152.61  | (198) phi(all_73_0_83) = all_93_0_89
% 211.03/152.61  |
% 211.03/152.61  +-Applying beta-rule and splitting (144), into two cases.
% 211.03/152.61  |-Branch one:
% 211.03/152.61  | (565) all_63_1_76 = 0
% 211.03/152.61  |
% 211.03/152.61  	| From (565) and (143) follows:
% 211.03/152.61  	| (566) bool(all_2_0_0) = 0
% 211.03/152.61  	|
% 211.03/152.61  	| Instantiating formula (69) with all_2_0_0 and discharging atoms bool(all_2_0_0) = 0, yields:
% 211.03/152.61  	| (567) all_2_0_0 = true | all_2_0_0 = false
% 211.03/152.61  	|
% 211.03/152.61  	+-Applying beta-rule and splitting (147), into two cases.
% 211.03/152.61  	|-Branch one:
% 211.03/152.61  	| (568) all_65_0_77 = 0 & all_2_0_0 = false2
% 211.03/152.61  	|
% 211.03/152.61  		| Applying alpha-rule on (568) yields:
% 211.03/152.61  		| (569) all_65_0_77 = 0
% 211.03/152.61  		| (570) all_2_0_0 = false2
% 211.03/152.61  		|
% 211.03/152.61  		| From (570) and (555) follows:
% 211.03/152.61  		| (571) forallprefers(false, false2) = all_172_0_153
% 211.03/152.61  		|
% 211.03/152.61  		+-Applying beta-rule and splitting (567), into two cases.
% 211.03/152.61  		|-Branch one:
% 211.03/152.61  		| (572) all_2_0_0 = true
% 211.03/152.61  		|
% 211.03/152.61  			| Combining equations (572,570) yields a new equation:
% 211.03/152.61  			| (573) false2 = true
% 211.03/152.61  			|
% 211.03/152.61  			| From (573) and (571) follows:
% 211.03/152.61  			| (574) forallprefers(false, true) = all_172_0_153
% 211.03/152.61  			|
% 211.03/152.61  			| Instantiating formula (127) with all_172_0_153, true, false and discharging atoms forallprefers(false, true) = all_172_0_153, yields:
% 211.03/152.61  			| (575) all_172_0_153 = 0
% 211.03/152.61  			|
% 211.03/152.61  			| Equations (575) can reduce 554 to:
% 211.03/152.61  			| (576) $false
% 211.03/152.61  			|
% 211.03/152.61  			|-The branch is then unsatisfiable
% 211.03/152.61  		|-Branch two:
% 211.03/152.61  		| (577)  ~ (all_2_0_0 = true)
% 211.03/152.61  		| (578) all_2_0_0 = false
% 211.03/152.61  		|
% 211.03/152.61  			| Combining equations (578,570) yields a new equation:
% 211.03/152.61  			| (579) false2 = false
% 211.03/152.61  			|
% 211.03/152.61  			| Equations (579) can reduce 41 to:
% 211.03/152.61  			| (576) $false
% 211.03/152.61  			|
% 211.03/152.61  			|-The branch is then unsatisfiable
% 211.03/152.61  	|-Branch two:
% 211.03/152.61  	| (581) false2 = err &  ~ (all_65_0_77 = 0)
% 211.03/152.61  	|
% 211.03/152.61  		| Applying alpha-rule on (581) yields:
% 211.03/152.61  		| (582) false2 = err
% 211.03/152.61  		| (583)  ~ (all_65_0_77 = 0)
% 211.03/152.61  		|
% 211.03/152.61  		| Equations (582) can reduce 41 to:
% 211.03/152.61  		| (115)  ~ (err = false)
% 211.03/152.61  		|
% 211.03/152.61  		| From (582) and (131) follows:
% 211.03/152.61  		| (585) phi(all_2_0_0) = err
% 211.03/152.61  		|
% 211.03/152.61  		| Instantiating formula (127) with all_172_0_153, all_2_0_0, false and discharging atoms forallprefers(false, all_2_0_0) = all_172_0_153, yields:
% 211.03/152.61  		| (586) all_172_0_153 = 0 | ( ~ (all_2_0_0 = true) &  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (d(all_2_0_0) = v1 & d(false) = v0 & bool(all_2_0_0) = v3 & bool(false) = v2 & ( ~ (v1 = 0) | (v0 = 0 & ( ~ (v3 = 0) | v2 = 0)))))
% 211.03/152.61  		|
% 211.03/152.61  		+-Applying beta-rule and splitting (586), into two cases.
% 211.03/152.61  		|-Branch one:
% 211.03/152.61  		| (575) all_172_0_153 = 0
% 211.03/152.61  		|
% 211.03/152.61  			| Equations (575) can reduce 554 to:
% 211.03/152.61  			| (576) $false
% 211.03/152.61  			|
% 211.03/152.61  			|-The branch is then unsatisfiable
% 211.03/152.61  		|-Branch two:
% 211.03/152.61  		| (554)  ~ (all_172_0_153 = 0)
% 211.03/152.61  		| (590)  ~ (all_2_0_0 = true) &  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (d(all_2_0_0) = v1 & d(false) = v0 & bool(all_2_0_0) = v3 & bool(false) = v2 & ( ~ (v1 = 0) | (v0 = 0 & ( ~ (v3 = 0) | v2 = 0))))
% 211.03/152.61  		|
% 211.03/152.61  			| Applying alpha-rule on (590) yields:
% 211.03/152.61  			| (577)  ~ (all_2_0_0 = true)
% 211.03/152.61  			| (592)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (d(all_2_0_0) = v1 & d(false) = v0 & bool(all_2_0_0) = v3 & bool(false) = v2 & ( ~ (v1 = 0) | (v0 = 0 & ( ~ (v3 = 0) | v2 = 0))))
% 211.03/152.61  			|
% 211.03/152.61  			+-Applying beta-rule and splitting (567), into two cases.
% 211.03/152.61  			|-Branch one:
% 211.03/152.61  			| (572) all_2_0_0 = true
% 211.03/152.61  			|
% 211.03/152.61  				| Equations (572) can reduce 577 to:
% 211.03/152.61  				| (576) $false
% 211.03/152.61  				|
% 211.03/152.61  				|-The branch is then unsatisfiable
% 211.03/152.61  			|-Branch two:
% 211.03/152.61  			| (577)  ~ (all_2_0_0 = true)
% 211.03/152.61  			| (578) all_2_0_0 = false
% 211.03/152.61  			|
% 211.03/152.61  				| From (578) and (585) follows:
% 211.03/152.61  				| (597) phi(false) = err
% 211.03/152.61  				|
% 211.03/152.61  				| Instantiating formula (67) with false, err, false and discharging atoms phi(false) = err, phi(false) = false, yields:
% 211.03/152.61  				| (598) err = false
% 211.03/152.61  				|
% 211.03/152.61  				| Equations (598) can reduce 115 to:
% 211.03/152.61  				| (576) $false
% 211.03/152.61  				|
% 211.03/152.61  				|-The branch is then unsatisfiable
% 211.03/152.61  |-Branch two:
% 211.03/152.61  | (600)  ~ (all_63_1_76 = 0)
% 211.03/152.61  | (601) all_63_0_75 = false2
% 211.03/152.61  |
% 211.03/152.61  	+-Applying beta-rule and splitting (161), into two cases.
% 211.03/152.61  	|-Branch one:
% 211.03/152.61  	| (565) all_63_1_76 = 0
% 211.03/152.61  	|
% 211.03/152.61  		| Equations (565) can reduce 600 to:
% 211.03/152.61  		| (576) $false
% 211.03/152.61  		|
% 211.03/152.61  		|-The branch is then unsatisfiable
% 211.03/152.61  	|-Branch two:
% 211.03/152.61  	| (600)  ~ (all_63_1_76 = 0)
% 211.03/152.61  	| (605)  ~ (all_2_0_0 = true) &  ~ (all_2_0_0 = false)
% 211.03/152.61  	|
% 211.03/152.61  		| Applying alpha-rule on (605) yields:
% 211.03/152.61  		| (577)  ~ (all_2_0_0 = true)
% 211.03/152.61  		| (607)  ~ (all_2_0_0 = false)
% 211.03/152.61  		|
% 211.03/152.61  		+-Applying beta-rule and splitting (147), into two cases.
% 211.03/152.61  		|-Branch one:
% 211.03/152.61  		| (568) all_65_0_77 = 0 & all_2_0_0 = false2
% 211.03/152.61  		|
% 211.03/152.61  			| Applying alpha-rule on (568) yields:
% 211.03/152.61  			| (569) all_65_0_77 = 0
% 211.03/152.61  			| (570) all_2_0_0 = false2
% 211.03/152.61  			|
% 211.03/152.61  			| Equations (570) can reduce 577 to:
% 211.03/152.61  			| (611)  ~ (false2 = true)
% 211.03/152.61  			|
% 211.03/152.61  			| Equations (570) can reduce 607 to:
% 211.03/152.61  			| (41)  ~ (false2 = false)
% 211.03/152.61  			|
% 211.03/152.61  			| From (570) and (157) follows:
% 211.03/152.61  			| (613) lazy_impl(all_73_0_83, all_2_1_1) = false2
% 211.03/152.61  			|
% 211.03/152.61  			| From (570) and (131) follows:
% 211.03/152.61  			| (614) phi(false2) = false2
% 211.03/152.61  			|
% 211.03/152.61  			| From (570) and (143) follows:
% 211.03/152.61  			| (615) bool(false2) = all_63_1_76
% 211.03/152.61  			|
% 211.03/152.61  			+-Applying beta-rule and splitting (171), into two cases.
% 211.03/152.61  			|-Branch one:
% 211.03/152.61  			| (616) bool(all_2_1_1) = 0
% 211.03/152.61  			|
% 211.03/152.61  				+-Applying beta-rule and splitting (170), into two cases.
% 211.03/152.61  				|-Branch one:
% 211.03/152.61  				| (617) all_73_0_83 = true
% 211.03/152.61  				|
% 211.03/152.61  					| From (617) and (613) follows:
% 211.03/152.61  					| (618) lazy_impl(true, all_2_1_1) = false2
% 211.03/152.61  					|
% 211.03/152.61  					| From (617) and (238) follows:
% 211.03/152.61  					| (619) lazy_impl(true, true) = all_93_0_89
% 211.03/152.61  					|
% 211.03/152.61  					| From (617) and (158) follows:
% 211.03/152.61  					| (620) prop(all_2_1_1) = true
% 211.03/152.61  					|
% 211.03/152.61  					| From (617) and (198) follows:
% 211.03/152.61  					| (621) phi(true) = all_93_0_89
% 211.03/152.61  					|
% 211.03/152.61  					| Instantiating formula (67) with true, all_93_0_89, true and discharging atoms phi(true) = all_93_0_89, phi(true) = true, yields:
% 211.03/152.61  					| (622) all_93_0_89 = true
% 211.03/152.61  					|
% 211.03/152.61  					| Instantiating formula (69) with all_2_1_1 and discharging atoms bool(all_2_1_1) = 0, yields:
% 211.03/152.61  					| (623) all_2_1_1 = true | all_2_1_1 = false
% 211.03/152.61  					|
% 211.03/152.61  					| From (622) and (619) follows:
% 211.03/152.61  					| (173) lazy_impl(true, true) = true
% 211.03/152.61  					|
% 211.03/152.61  					| Instantiating formula (34) with false2, all_2_1_1 and discharging atoms lazy_impl(true, all_2_1_1) = false2, yields:
% 211.03/152.61  					| (625) phi(all_2_1_1) = false2
% 211.03/152.61  					|
% 211.03/152.61  					| Instantiating formula (105) with all_2_1_1 and discharging atoms bool(all_2_1_1) = 0, yields:
% 211.03/152.61  					| (626) impl(true, all_2_1_1) = all_2_1_1
% 211.03/152.61  					|
% 211.03/152.61  					| Instantiating formula (57) with all_2_1_1 and discharging atoms bool(all_2_1_1) = 0, yields:
% 211.03/152.61  					| (627) impl(false, all_2_1_1) = true
% 211.03/152.61  					|
% 211.03/152.61  					| Instantiating formula (10) with all_2_1_1, all_2_1_1, all_2_1_1, true, true and discharging atoms impl(true, all_2_1_1) = all_2_1_1, yields:
% 211.03/152.61  					| (628)  ? [v0] :  ? [v1] :  ? [v2] : (f1(true, true, all_2_1_1) = v0 & lazy_impl(v1, v2) = v0 & impl(all_2_1_1, all_2_1_1) = v2 & prop(all_2_1_1) = v1)
% 211.03/152.62  					|
% 211.03/152.62  					| Instantiating formula (51) with false2, all_2_1_1, all_2_1_1, true, true and discharging atoms lazy_impl(true, all_2_1_1) = false2, impl(true, all_2_1_1) = all_2_1_1, yields:
% 211.03/152.62  					| (629)  ? [v0] :  ? [v1] :  ? [v2] : (f2(true, true, all_2_1_1) = v0 & lazy_impl(v1, v2) = v0 & impl(false2, all_2_1_1) = v2 & prop(all_2_1_1) = v1)
% 211.03/152.62  					|
% 211.03/152.62  					| Instantiating formula (10) with true, true, all_2_1_1, false, true and discharging atoms impl(true, true) = true, impl(false, all_2_1_1) = true, yields:
% 211.03/152.62  					| (630)  ? [v0] :  ? [v1] :  ? [v2] : (f1(true, false, all_2_1_1) = v0 & lazy_impl(v1, v2) = v0 & impl(true, all_2_1_1) = v2 & prop(all_2_1_1) = v1)
% 211.03/152.62  					|
% 211.03/152.62  					| Instantiating formula (10) with true, true, all_2_1_1, false, false and discharging atoms impl(false, all_2_1_1) = true, impl(false, true) = true, yields:
% 211.03/152.62  					| (631)  ? [v0] :  ? [v1] :  ? [v2] : (f1(false, false, all_2_1_1) = v0 & lazy_impl(v1, v2) = v0 & impl(true, all_2_1_1) = v2 & prop(all_2_1_1) = v1)
% 211.03/152.62  					|
% 211.03/152.62  					| Instantiating formula (10) with true, all_2_1_1, all_2_1_1, true, false and discharging atoms impl(true, all_2_1_1) = all_2_1_1, impl(false, all_2_1_1) = true, yields:
% 211.03/152.62  					| (632)  ? [v0] :  ? [v1] :  ? [v2] : (f1(false, true, all_2_1_1) = v0 & lazy_impl(v1, v2) = v0 & impl(true, all_2_1_1) = v2 & prop(all_2_1_1) = v1)
% 211.03/152.62  					|
% 211.03/152.62  					| Instantiating formula (102) with all_2_1_1, all_2_1_1, true, true, all_2_1_1, false, false and discharging atoms impl(true, all_2_1_1) = all_2_1_1, impl(false, all_2_1_1) = true, yields:
% 211.03/152.62  					| (633)  ? [v0] :  ? [v1] : (f3(false, false, all_2_1_1) = v0 & lazy_impl(v1, all_2_1_1) = v0 & prop(all_2_1_1) = v1)
% 211.03/152.62  					|
% 211.03/152.62  					| Instantiating formula (51) with true, true, all_2_1_1, false, true and discharging atoms lazy_impl(true, true) = true, impl(false, all_2_1_1) = true, yields:
% 211.03/152.62  					| (634)  ? [v0] :  ? [v1] :  ? [v2] : (f2(true, false, all_2_1_1) = v0 & lazy_impl(v1, v2) = v0 & impl(true, all_2_1_1) = v2 & prop(all_2_1_1) = v1)
% 211.03/152.62  					|
% 211.03/152.62  					| Instantiating formula (98) with false2, all_2_1_1 and discharging atoms phi(all_2_1_1) = false2, yields:
% 211.03/152.62  					| (635)  ? [v0] : (d(all_2_1_1) = v0 & ((v0 = 0 & all_2_1_1 = false2) | (false2 = err &  ~ (v0 = 0))))
% 211.03/152.62  					|
% 211.03/152.62  					| Instantiating (633) with all_284_0_190, all_284_1_191 yields:
% 211.03/152.62  					| (636) f3(false, false, all_2_1_1) = all_284_1_191 & lazy_impl(all_284_0_190, all_2_1_1) = all_284_1_191 & prop(all_2_1_1) = all_284_0_190
% 211.03/152.62  					|
% 211.03/152.62  					| Applying alpha-rule on (636) yields:
% 211.03/152.62  					| (637) f3(false, false, all_2_1_1) = all_284_1_191
% 211.03/152.62  					| (638) lazy_impl(all_284_0_190, all_2_1_1) = all_284_1_191
% 211.03/152.62  					| (639) prop(all_2_1_1) = all_284_0_190
% 211.03/152.62  					|
% 211.03/152.62  					| Instantiating (632) with all_286_0_192, all_286_1_193, all_286_2_194 yields:
% 211.03/152.62  					| (640) f1(false, true, all_2_1_1) = all_286_2_194 & lazy_impl(all_286_1_193, all_286_0_192) = all_286_2_194 & impl(true, all_2_1_1) = all_286_0_192 & prop(all_2_1_1) = all_286_1_193
% 211.03/152.62  					|
% 211.03/152.62  					| Applying alpha-rule on (640) yields:
% 211.03/152.62  					| (641) f1(false, true, all_2_1_1) = all_286_2_194
% 211.03/152.62  					| (642) lazy_impl(all_286_1_193, all_286_0_192) = all_286_2_194
% 211.03/152.62  					| (643) impl(true, all_2_1_1) = all_286_0_192
% 211.03/152.62  					| (644) prop(all_2_1_1) = all_286_1_193
% 211.03/152.62  					|
% 211.03/152.62  					| Instantiating (631) with all_288_0_195, all_288_1_196, all_288_2_197 yields:
% 211.03/152.62  					| (645) f1(false, false, all_2_1_1) = all_288_2_197 & lazy_impl(all_288_1_196, all_288_0_195) = all_288_2_197 & impl(true, all_2_1_1) = all_288_0_195 & prop(all_2_1_1) = all_288_1_196
% 211.03/152.62  					|
% 211.03/152.62  					| Applying alpha-rule on (645) yields:
% 211.03/152.62  					| (646) f1(false, false, all_2_1_1) = all_288_2_197
% 211.03/152.62  					| (647) lazy_impl(all_288_1_196, all_288_0_195) = all_288_2_197
% 211.03/152.62  					| (648) impl(true, all_2_1_1) = all_288_0_195
% 211.03/152.62  					| (649) prop(all_2_1_1) = all_288_1_196
% 211.03/152.62  					|
% 211.03/152.62  					| Instantiating (630) with all_290_0_198, all_290_1_199, all_290_2_200 yields:
% 211.03/152.62  					| (650) f1(true, false, all_2_1_1) = all_290_2_200 & lazy_impl(all_290_1_199, all_290_0_198) = all_290_2_200 & impl(true, all_2_1_1) = all_290_0_198 & prop(all_2_1_1) = all_290_1_199
% 211.03/152.62  					|
% 211.03/152.62  					| Applying alpha-rule on (650) yields:
% 211.03/152.62  					| (651) f1(true, false, all_2_1_1) = all_290_2_200
% 211.03/152.62  					| (652) lazy_impl(all_290_1_199, all_290_0_198) = all_290_2_200
% 211.03/152.62  					| (653) impl(true, all_2_1_1) = all_290_0_198
% 211.03/152.62  					| (654) prop(all_2_1_1) = all_290_1_199
% 211.03/152.62  					|
% 211.03/152.62  					| Instantiating (629) with all_292_0_201, all_292_1_202, all_292_2_203 yields:
% 211.03/152.62  					| (655) f2(true, true, all_2_1_1) = all_292_2_203 & lazy_impl(all_292_1_202, all_292_0_201) = all_292_2_203 & impl(false2, all_2_1_1) = all_292_0_201 & prop(all_2_1_1) = all_292_1_202
% 211.03/152.62  					|
% 211.03/152.62  					| Applying alpha-rule on (655) yields:
% 211.03/152.62  					| (656) f2(true, true, all_2_1_1) = all_292_2_203
% 211.03/152.62  					| (657) lazy_impl(all_292_1_202, all_292_0_201) = all_292_2_203
% 211.03/152.62  					| (658) impl(false2, all_2_1_1) = all_292_0_201
% 211.03/152.62  					| (659) prop(all_2_1_1) = all_292_1_202
% 211.03/152.62  					|
% 211.03/152.62  					| Instantiating (635) with all_294_0_204 yields:
% 211.03/152.62  					| (660) d(all_2_1_1) = all_294_0_204 & ((all_294_0_204 = 0 & all_2_1_1 = false2) | (false2 = err &  ~ (all_294_0_204 = 0)))
% 211.03/152.62  					|
% 211.03/152.62  					| Applying alpha-rule on (660) yields:
% 211.03/152.62  					| (661) d(all_2_1_1) = all_294_0_204
% 211.03/152.62  					| (662) (all_294_0_204 = 0 & all_2_1_1 = false2) | (false2 = err &  ~ (all_294_0_204 = 0))
% 211.03/152.62  					|
% 211.03/152.62  					| Instantiating (634) with all_296_0_205, all_296_1_206, all_296_2_207 yields:
% 211.03/152.62  					| (663) f2(true, false, all_2_1_1) = all_296_2_207 & lazy_impl(all_296_1_206, all_296_0_205) = all_296_2_207 & impl(true, all_2_1_1) = all_296_0_205 & prop(all_2_1_1) = all_296_1_206
% 211.03/152.62  					|
% 211.03/152.62  					| Applying alpha-rule on (663) yields:
% 211.03/152.62  					| (664) f2(true, false, all_2_1_1) = all_296_2_207
% 211.03/152.62  					| (665) lazy_impl(all_296_1_206, all_296_0_205) = all_296_2_207
% 211.03/152.62  					| (666) impl(true, all_2_1_1) = all_296_0_205
% 211.03/152.62  					| (667) prop(all_2_1_1) = all_296_1_206
% 211.03/152.62  					|
% 211.03/152.62  					| Instantiating (628) with all_298_0_208, all_298_1_209, all_298_2_210 yields:
% 211.03/152.62  					| (668) f1(true, true, all_2_1_1) = all_298_2_210 & lazy_impl(all_298_1_209, all_298_0_208) = all_298_2_210 & impl(all_2_1_1, all_2_1_1) = all_298_0_208 & prop(all_2_1_1) = all_298_1_209
% 211.03/152.62  					|
% 211.03/152.62  					| Applying alpha-rule on (668) yields:
% 211.03/152.62  					| (669) f1(true, true, all_2_1_1) = all_298_2_210
% 211.03/152.62  					| (670) lazy_impl(all_298_1_209, all_298_0_208) = all_298_2_210
% 211.03/152.62  					| (671) impl(all_2_1_1, all_2_1_1) = all_298_0_208
% 211.03/152.62  					| (672) prop(all_2_1_1) = all_298_1_209
% 211.03/152.62  					|
% 211.03/152.62  					| Instantiating formula (63) with true, all_2_1_1, all_296_0_205, all_2_1_1 and discharging atoms impl(true, all_2_1_1) = all_296_0_205, impl(true, all_2_1_1) = all_2_1_1, yields:
% 211.03/152.62  					| (673) all_296_0_205 = all_2_1_1
% 211.03/152.62  					|
% 211.03/152.62  					| Instantiating formula (63) with true, all_2_1_1, all_290_0_198, all_296_0_205 and discharging atoms impl(true, all_2_1_1) = all_296_0_205, impl(true, all_2_1_1) = all_290_0_198, yields:
% 211.03/152.62  					| (674) all_296_0_205 = all_290_0_198
% 211.03/152.62  					|
% 211.03/152.62  					| Instantiating formula (63) with true, all_2_1_1, all_288_0_195, all_290_0_198 and discharging atoms impl(true, all_2_1_1) = all_290_0_198, impl(true, all_2_1_1) = all_288_0_195, yields:
% 211.03/152.62  					| (675) all_290_0_198 = all_288_0_195
% 211.03/152.62  					|
% 211.03/152.62  					| Instantiating formula (63) with true, all_2_1_1, all_286_0_192, all_288_0_195 and discharging atoms impl(true, all_2_1_1) = all_288_0_195, impl(true, all_2_1_1) = all_286_0_192, yields:
% 211.03/152.62  					| (676) all_288_0_195 = all_286_0_192
% 211.03/152.62  					|
% 211.03/152.62  					| Instantiating formula (6) with all_2_1_1, all_292_1_202, all_296_1_206 and discharging atoms prop(all_2_1_1) = all_296_1_206, prop(all_2_1_1) = all_292_1_202, yields:
% 211.03/152.62  					| (677) all_296_1_206 = all_292_1_202
% 211.03/152.62  					|
% 211.03/152.62  					| Instantiating formula (6) with all_2_1_1, all_290_1_199, all_298_1_209 and discharging atoms prop(all_2_1_1) = all_298_1_209, prop(all_2_1_1) = all_290_1_199, yields:
% 211.03/152.62  					| (678) all_298_1_209 = all_290_1_199
% 211.03/152.62  					|
% 211.03/152.62  					| Instantiating formula (6) with all_2_1_1, all_288_1_196, true and discharging atoms prop(all_2_1_1) = all_288_1_196, prop(all_2_1_1) = true, yields:
% 211.03/152.62  					| (679) all_288_1_196 = true
% 211.03/152.62  					|
% 211.03/152.62  					| Instantiating formula (6) with all_2_1_1, all_288_1_196, all_298_1_209 and discharging atoms prop(all_2_1_1) = all_298_1_209, prop(all_2_1_1) = all_288_1_196, yields:
% 211.03/152.62  					| (680) all_298_1_209 = all_288_1_196
% 211.03/152.62  					|
% 211.03/152.62  					| Instantiating formula (6) with all_2_1_1, all_288_1_196, all_296_1_206 and discharging atoms prop(all_2_1_1) = all_296_1_206, prop(all_2_1_1) = all_288_1_196, yields:
% 211.03/152.62  					| (681) all_296_1_206 = all_288_1_196
% 211.03/152.62  					|
% 211.03/152.62  					| Instantiating formula (6) with all_2_1_1, all_286_1_193, all_296_1_206 and discharging atoms prop(all_2_1_1) = all_296_1_206, prop(all_2_1_1) = all_286_1_193, yields:
% 211.03/152.62  					| (682) all_296_1_206 = all_286_1_193
% 211.03/152.62  					|
% 211.03/152.62  					| Instantiating formula (6) with all_2_1_1, all_284_0_190, all_298_1_209 and discharging atoms prop(all_2_1_1) = all_298_1_209, prop(all_2_1_1) = all_284_0_190, yields:
% 211.03/152.62  					| (683) all_298_1_209 = all_284_0_190
% 211.03/152.62  					|
% 211.03/152.62  					| Combining equations (683,678) yields a new equation:
% 211.03/152.62  					| (684) all_290_1_199 = all_284_0_190
% 211.03/152.62  					|
% 211.03/152.62  					| Combining equations (680,678) yields a new equation:
% 211.03/152.62  					| (685) all_290_1_199 = all_288_1_196
% 211.03/152.62  					|
% 211.03/152.62  					| Combining equations (674,673) yields a new equation:
% 211.03/152.62  					| (686) all_290_0_198 = all_2_1_1
% 211.03/152.62  					|
% 211.03/152.62  					| Simplifying 686 yields:
% 211.03/152.62  					| (687) all_290_0_198 = all_2_1_1
% 211.03/152.62  					|
% 211.03/152.62  					| Combining equations (681,677) yields a new equation:
% 211.03/152.62  					| (688) all_292_1_202 = all_288_1_196
% 211.03/152.62  					|
% 211.03/152.62  					| Combining equations (682,677) yields a new equation:
% 211.03/152.62  					| (689) all_292_1_202 = all_286_1_193
% 211.03/152.62  					|
% 211.03/152.62  					| Combining equations (688,689) yields a new equation:
% 211.03/152.62  					| (690) all_288_1_196 = all_286_1_193
% 211.03/152.62  					|
% 211.03/152.62  					| Simplifying 690 yields:
% 211.03/152.62  					| (691) all_288_1_196 = all_286_1_193
% 211.03/152.62  					|
% 211.03/152.62  					| Combining equations (675,687) yields a new equation:
% 211.03/152.62  					| (692) all_288_0_195 = all_2_1_1
% 211.03/152.62  					|
% 211.03/152.62  					| Simplifying 692 yields:
% 211.03/152.62  					| (693) all_288_0_195 = all_2_1_1
% 211.03/152.62  					|
% 211.03/152.62  					| Combining equations (685,684) yields a new equation:
% 211.03/152.62  					| (694) all_288_1_196 = all_284_0_190
% 211.03/152.62  					|
% 211.03/152.62  					| Simplifying 694 yields:
% 211.03/152.62  					| (695) all_288_1_196 = all_284_0_190
% 211.03/152.62  					|
% 211.03/152.62  					| Combining equations (693,676) yields a new equation:
% 211.03/152.62  					| (696) all_286_0_192 = all_2_1_1
% 211.03/152.62  					|
% 211.03/152.62  					| Combining equations (679,691) yields a new equation:
% 211.03/152.62  					| (697) all_286_1_193 = true
% 211.03/152.62  					|
% 211.03/152.62  					| Combining equations (695,691) yields a new equation:
% 211.03/152.62  					| (698) all_286_1_193 = all_284_0_190
% 211.03/152.62  					|
% 211.03/152.62  					| Combining equations (697,698) yields a new equation:
% 211.03/152.62  					| (699) all_284_0_190 = true
% 211.03/152.62  					|
% 211.03/152.62  					| Combining equations (699,698) yields a new equation:
% 211.03/152.62  					| (697) all_286_1_193 = true
% 211.03/152.62  					|
% 211.03/152.62  					| Combining equations (699,684) yields a new equation:
% 211.03/152.62  					| (701) all_290_1_199 = true
% 211.03/152.62  					|
% 211.03/152.62  					| Combining equations (697,689) yields a new equation:
% 211.03/152.62  					| (702) all_292_1_202 = true
% 211.03/152.62  					|
% 211.03/152.62  					| Combining equations (702,677) yields a new equation:
% 211.03/152.62  					| (703) all_296_1_206 = true
% 211.03/152.62  					|
% 211.03/152.62  					| Combining equations (701,678) yields a new equation:
% 211.03/152.62  					| (704) all_298_1_209 = true
% 211.03/152.62  					|
% 211.03/152.62  					| From (704) and (670) follows:
% 211.03/152.62  					| (705) lazy_impl(true, all_298_0_208) = all_298_2_210
% 211.03/152.62  					|
% 211.03/152.62  					| From (703)(673) and (665) follows:
% 211.03/152.62  					| (706) lazy_impl(true, all_2_1_1) = all_296_2_207
% 211.03/152.62  					|
% 211.03/152.62  					| From (702) and (657) follows:
% 211.03/152.62  					| (707) lazy_impl(true, all_292_0_201) = all_292_2_203
% 211.03/152.62  					|
% 211.03/152.62  					| From (701)(687) and (652) follows:
% 211.03/152.62  					| (708) lazy_impl(true, all_2_1_1) = all_290_2_200
% 211.03/152.62  					|
% 211.03/152.62  					| From (697)(696) and (642) follows:
% 211.03/152.62  					| (709) lazy_impl(true, all_2_1_1) = all_286_2_194
% 211.03/152.62  					|
% 211.03/152.62  					| Instantiating formula (103) with true, all_2_1_1, all_290_2_200, false2 and discharging atoms lazy_impl(true, all_2_1_1) = all_290_2_200, lazy_impl(true, all_2_1_1) = false2, yields:
% 211.03/152.62  					| (710) all_290_2_200 = false2
% 211.03/152.62  					|
% 211.03/152.62  					| Instantiating formula (103) with true, all_2_1_1, all_290_2_200, all_296_2_207 and discharging atoms lazy_impl(true, all_2_1_1) = all_296_2_207, lazy_impl(true, all_2_1_1) = all_290_2_200, yields:
% 211.03/152.62  					| (711) all_296_2_207 = all_290_2_200
% 211.03/152.62  					|
% 211.03/152.62  					| Instantiating formula (103) with true, all_2_1_1, all_286_2_194, all_296_2_207 and discharging atoms lazy_impl(true, all_2_1_1) = all_296_2_207, lazy_impl(true, all_2_1_1) = all_286_2_194, yields:
% 211.03/152.62  					| (712) all_296_2_207 = all_286_2_194
% 211.03/152.62  					|
% 211.03/152.62  					| Combining equations (711,712) yields a new equation:
% 211.03/152.62  					| (713) all_290_2_200 = all_286_2_194
% 211.03/152.62  					|
% 211.03/152.62  					| Simplifying 713 yields:
% 211.03/152.62  					| (714) all_290_2_200 = all_286_2_194
% 211.03/152.62  					|
% 211.03/152.62  					| Combining equations (714,710) yields a new equation:
% 211.03/152.62  					| (715) all_286_2_194 = false2
% 211.03/152.62  					|
% 211.03/152.62  					| Simplifying 715 yields:
% 211.03/152.62  					| (716) all_286_2_194 = false2
% 211.03/152.62  					|
% 211.03/152.62  					| Combining equations (716,712) yields a new equation:
% 211.03/152.62  					| (717) all_296_2_207 = false2
% 211.03/152.62  					|
% 211.03/152.62  					| From (717) and (664) follows:
% 211.03/152.62  					| (718) f2(true, false, all_2_1_1) = false2
% 211.03/152.62  					|
% 211.03/152.62  					| Instantiating formula (34) with all_292_2_203, all_292_0_201 and discharging atoms lazy_impl(true, all_292_0_201) = all_292_2_203, yields:
% 211.03/152.63  					| (719) phi(all_292_0_201) = all_292_2_203
% 211.03/152.63  					|
% 211.03/152.63  					| Instantiating formula (51) with all_298_2_210, all_298_0_208, all_2_1_1, all_2_1_1, true and discharging atoms lazy_impl(true, all_298_0_208) = all_298_2_210, impl(all_2_1_1, all_2_1_1) = all_298_0_208, yields:
% 211.03/152.63  					| (720)  ? [v0] :  ? [v1] :  ? [v2] : (f2(true, all_2_1_1, all_2_1_1) = v0 & lazy_impl(v1, v2) = v0 & impl(all_298_2_210, all_2_1_1) = v2 & prop(all_2_1_1) = v1)
% 211.03/152.63  					|
% 211.03/152.63  					| Instantiating formula (54) with all_292_0_201, all_2_1_1, false2 and discharging atoms impl(false2, all_2_1_1) = all_292_0_201, yields:
% 211.03/152.63  					| (721)  ? [v0] :  ? [v1] : (phi(false2) = v1 & bool(false2) = v0 & (v1 = all_292_0_201 | v0 = 0))
% 211.03/152.63  					|
% 211.03/152.63  					| Instantiating (721) with all_318_0_214, all_318_1_215 yields:
% 211.03/152.63  					| (722) phi(false2) = all_318_0_214 & bool(false2) = all_318_1_215 & (all_318_0_214 = all_292_0_201 | all_318_1_215 = 0)
% 211.03/152.63  					|
% 211.03/152.63  					| Applying alpha-rule on (722) yields:
% 211.03/152.63  					| (723) phi(false2) = all_318_0_214
% 211.03/152.63  					| (724) bool(false2) = all_318_1_215
% 211.03/152.63  					| (725) all_318_0_214 = all_292_0_201 | all_318_1_215 = 0
% 211.03/152.63  					|
% 211.03/152.63  					| Instantiating (720) with all_324_0_222, all_324_1_223, all_324_2_224 yields:
% 211.03/152.63  					| (726) f2(true, all_2_1_1, all_2_1_1) = all_324_2_224 & lazy_impl(all_324_1_223, all_324_0_222) = all_324_2_224 & impl(all_298_2_210, all_2_1_1) = all_324_0_222 & prop(all_2_1_1) = all_324_1_223
% 211.03/152.63  					|
% 211.03/152.63  					| Applying alpha-rule on (726) yields:
% 211.03/152.63  					| (727) f2(true, all_2_1_1, all_2_1_1) = all_324_2_224
% 211.03/152.63  					| (728) lazy_impl(all_324_1_223, all_324_0_222) = all_324_2_224
% 211.03/152.63  					| (729) impl(all_298_2_210, all_2_1_1) = all_324_0_222
% 211.03/152.63  					| (730) prop(all_2_1_1) = all_324_1_223
% 211.03/152.63  					|
% 211.03/152.63  					| Instantiating formula (67) with false2, all_318_0_214, false2 and discharging atoms phi(false2) = all_318_0_214, phi(false2) = false2, yields:
% 211.03/152.63  					| (731) all_318_0_214 = false2
% 211.03/152.63  					|
% 211.03/152.63  					| Instantiating formula (116) with false2, all_318_1_215, all_63_1_76 and discharging atoms bool(false2) = all_318_1_215, bool(false2) = all_63_1_76, yields:
% 211.03/152.63  					| (732) all_318_1_215 = all_63_1_76
% 211.03/152.63  					|
% 211.03/152.63  					| From (731) and (723) follows:
% 211.03/152.63  					| (614) phi(false2) = false2
% 211.03/152.63  					|
% 211.03/152.63  					+-Applying beta-rule and splitting (725), into two cases.
% 211.03/152.63  					|-Branch one:
% 211.03/152.63  					| (734) all_318_1_215 = 0
% 211.03/152.63  					|
% 211.03/152.63  						| Combining equations (732,734) yields a new equation:
% 211.03/152.63  						| (735) all_63_1_76 = 0
% 211.03/152.63  						|
% 211.03/152.63  						| Simplifying 735 yields:
% 211.03/152.63  						| (565) all_63_1_76 = 0
% 211.03/152.63  						|
% 211.03/152.63  						| Equations (565) can reduce 600 to:
% 211.03/152.63  						| (576) $false
% 211.03/152.63  						|
% 211.03/152.63  						|-The branch is then unsatisfiable
% 211.03/152.63  					|-Branch two:
% 211.03/152.63  					| (738)  ~ (all_318_1_215 = 0)
% 211.03/152.63  					| (739) all_318_0_214 = all_292_0_201
% 211.03/152.63  					|
% 211.03/152.63  						| Combining equations (731,739) yields a new equation:
% 211.03/152.63  						| (740) all_292_0_201 = false2
% 211.03/152.63  						|
% 211.03/152.63  						| From (740) and (719) follows:
% 211.03/152.63  						| (741) phi(false2) = all_292_2_203
% 211.03/152.63  						|
% 211.03/152.63  						| Instantiating formula (67) with false2, all_292_2_203, false2 and discharging atoms phi(false2) = all_292_2_203, phi(false2) = false2, yields:
% 211.03/152.63  						| (742) all_292_2_203 = false2
% 211.03/152.63  						|
% 211.03/152.63  						| From (742) and (656) follows:
% 211.03/152.63  						| (743) f2(true, true, all_2_1_1) = false2
% 211.03/152.63  						|
% 211.03/152.63  						+-Applying beta-rule and splitting (623), into two cases.
% 211.03/152.63  						|-Branch one:
% 211.03/152.63  						| (744) all_2_1_1 = true
% 211.03/152.63  						|
% 211.03/152.63  							| From (744)(744) and (727) follows:
% 211.03/152.63  							| (745) f2(true, true, true) = all_324_2_224
% 211.03/152.63  							|
% 211.03/152.63  							| From (744) and (743) follows:
% 211.03/152.63  							| (746) f2(true, true, true) = false2
% 211.03/152.63  							|
% 211.03/152.63  							+-Applying beta-rule and splitting (662), into two cases.
% 211.03/152.63  							|-Branch one:
% 211.03/152.63  							| (747) all_294_0_204 = 0 & all_2_1_1 = false2
% 211.03/152.63  							|
% 211.03/152.63  								| Applying alpha-rule on (747) yields:
% 211.03/152.63  								| (748) all_294_0_204 = 0
% 211.03/152.63  								| (749) all_2_1_1 = false2
% 211.03/152.63  								|
% 211.03/152.63  								| Combining equations (744,749) yields a new equation:
% 211.03/152.63  								| (573) false2 = true
% 211.03/152.63  								|
% 211.03/152.63  								| Equations (573) can reduce 611 to:
% 211.03/152.63  								| (576) $false
% 211.03/152.63  								|
% 211.03/152.63  								|-The branch is then unsatisfiable
% 211.03/152.63  							|-Branch two:
% 211.03/152.63  							| (752) false2 = err &  ~ (all_294_0_204 = 0)
% 211.03/152.63  							|
% 211.03/152.63  								| Applying alpha-rule on (752) yields:
% 211.03/152.63  								| (582) false2 = err
% 211.03/152.63  								| (754)  ~ (all_294_0_204 = 0)
% 211.03/152.63  								|
% 211.03/152.63  								| Equations (582) can reduce 611 to:
% 211.03/152.63  								| (119)  ~ (err = true)
% 211.03/152.63  								|
% 211.03/152.63  								| From (582) and (746) follows:
% 211.03/152.63  								| (756) f2(true, true, true) = err
% 211.03/152.63  								|
% 211.03/152.63  								| Instantiating formula (73) with true, true, true, all_324_2_224, true and discharging atoms f2(true, true, true) = all_324_2_224, f2(true, true, true) = true, yields:
% 211.03/152.63  								| (757) all_324_2_224 = true
% 211.03/152.63  								|
% 211.03/152.63  								| Instantiating formula (73) with true, true, true, err, all_324_2_224 and discharging atoms f2(true, true, true) = all_324_2_224, f2(true, true, true) = err, yields:
% 211.03/152.63  								| (758) all_324_2_224 = err
% 211.03/152.63  								|
% 211.03/152.63  								| Combining equations (757,758) yields a new equation:
% 211.03/152.63  								| (759) err = true
% 211.03/152.63  								|
% 211.03/152.63  								| Equations (759) can reduce 119 to:
% 211.03/152.63  								| (576) $false
% 211.03/152.63  								|
% 211.03/152.63  								|-The branch is then unsatisfiable
% 211.03/152.63  						|-Branch two:
% 211.03/152.63  						| (761)  ~ (all_2_1_1 = true)
% 211.03/152.63  						| (762) all_2_1_1 = false
% 211.03/152.63  						|
% 211.03/152.63  							| Equations (762) can reduce 761 to:
% 211.03/152.63  							| (763)  ~ (true = false)
% 211.03/152.63  							|
% 211.03/152.63  							| Simplifying 763 yields:
% 211.03/152.63  							| (122)  ~ (true = false)
% 211.03/152.63  							|
% 211.03/152.63  							| From (762)(762) and (727) follows:
% 211.03/152.63  							| (765) f2(true, false, false) = all_324_2_224
% 211.03/152.63  							|
% 211.03/152.63  							| From (762) and (743) follows:
% 211.03/152.63  							| (766) f2(true, true, false) = false2
% 211.03/152.63  							|
% 211.03/152.63  							| From (762) and (718) follows:
% 211.03/152.63  							| (767) f2(true, false, false) = false2
% 211.03/152.63  							|
% 211.03/152.63  							+-Applying beta-rule and splitting (662), into two cases.
% 211.03/152.63  							|-Branch one:
% 211.03/152.63  							| (747) all_294_0_204 = 0 & all_2_1_1 = false2
% 211.03/152.63  							|
% 211.03/152.63  								| Applying alpha-rule on (747) yields:
% 211.03/152.63  								| (748) all_294_0_204 = 0
% 211.03/152.63  								| (749) all_2_1_1 = false2
% 211.03/152.63  								|
% 211.03/152.63  								| Combining equations (762,749) yields a new equation:
% 211.03/152.63  								| (579) false2 = false
% 211.03/152.63  								|
% 211.03/152.63  								| Equations (579) can reduce 41 to:
% 211.03/152.63  								| (576) $false
% 211.03/152.63  								|
% 211.03/152.63  								|-The branch is then unsatisfiable
% 211.03/152.63  							|-Branch two:
% 211.03/152.63  							| (752) false2 = err &  ~ (all_294_0_204 = 0)
% 211.03/152.63  							|
% 211.03/152.63  								| Applying alpha-rule on (752) yields:
% 211.03/152.63  								| (582) false2 = err
% 211.03/152.63  								| (754)  ~ (all_294_0_204 = 0)
% 211.03/152.63  								|
% 211.03/152.63  								| From (582) and (766) follows:
% 211.03/152.63  								| (776) f2(true, true, false) = err
% 211.03/152.63  								|
% 211.03/152.63  								| From (582) and (767) follows:
% 211.03/152.63  								| (777) f2(true, false, false) = err
% 211.03/152.63  								|
% 211.03/152.63  								| Instantiating formula (73) with true, true, false, err, true and discharging atoms f2(true, true, false) = err, f2(true, true, false) = true, yields:
% 211.03/152.63  								| (759) err = true
% 211.03/152.63  								|
% 211.03/152.63  								| Instantiating formula (73) with true, false, false, all_324_2_224, false and discharging atoms f2(true, false, false) = all_324_2_224, f2(true, false, false) = false, yields:
% 211.03/152.63  								| (779) all_324_2_224 = false
% 211.03/152.63  								|
% 211.03/152.63  								| Instantiating formula (73) with true, false, false, err, all_324_2_224 and discharging atoms f2(true, false, false) = all_324_2_224, f2(true, false, false) = err, yields:
% 211.03/152.63  								| (758) all_324_2_224 = err
% 211.03/152.63  								|
% 211.03/152.63  								| Combining equations (758,779) yields a new equation:
% 211.03/152.63  								| (781) err = false
% 211.03/152.63  								|
% 211.03/152.63  								| Simplifying 781 yields:
% 211.03/152.63  								| (598) err = false
% 211.03/152.63  								|
% 211.03/152.63  								| Combining equations (759,598) yields a new equation:
% 211.03/152.63  								| (783) true = false
% 211.03/152.63  								|
% 211.03/152.63  								| Simplifying 783 yields:
% 211.03/152.63  								| (784) true = false
% 211.03/152.63  								|
% 211.03/152.63  								| Equations (784) can reduce 122 to:
% 211.03/152.63  								| (576) $false
% 211.03/152.63  								|
% 211.03/152.63  								|-The branch is then unsatisfiable
% 211.03/152.63  				|-Branch two:
% 211.03/152.63  				| (786)  ~ (all_73_0_83 = true)
% 211.03/152.63  				| (787)  ? [v0] : ( ~ (v0 = 0) & bool(all_2_1_1) = v0)
% 211.03/152.63  				|
% 211.03/152.63  					| Instantiating (787) with all_246_0_262 yields:
% 211.03/152.63  					| (788)  ~ (all_246_0_262 = 0) & bool(all_2_1_1) = all_246_0_262
% 211.03/152.63  					|
% 211.03/152.63  					| Applying alpha-rule on (788) yields:
% 211.03/152.63  					| (789)  ~ (all_246_0_262 = 0)
% 211.03/152.63  					| (790) bool(all_2_1_1) = all_246_0_262
% 211.03/152.63  					|
% 211.03/152.63  					| Instantiating formula (116) with all_2_1_1, 0, all_246_0_262 and discharging atoms bool(all_2_1_1) = all_246_0_262, bool(all_2_1_1) = 0, yields:
% 211.03/152.63  					| (791) all_246_0_262 = 0
% 211.03/152.63  					|
% 211.03/152.63  					| Equations (791) can reduce 789 to:
% 211.03/152.63  					| (576) $false
% 211.03/152.63  					|
% 211.03/152.63  					|-The branch is then unsatisfiable
% 211.03/152.63  			|-Branch two:
% 211.03/152.63  			| (793)  ~ (bool(all_2_1_1) = 0)
% 211.03/152.63  			| (794) all_73_0_83 = false
% 211.03/152.63  			|
% 211.03/152.63  				| From (794) and (613) follows:
% 211.03/152.63  				| (795) lazy_impl(false, all_2_1_1) = false2
% 211.03/152.63  				|
% 211.03/152.63  				| Instantiating formula (22) with false2, all_2_1_1 and discharging atoms lazy_impl(false, all_2_1_1) = false2, yields:
% 211.03/152.63  				| (573) false2 = true
% 211.03/152.63  				|
% 211.03/152.63  				| Equations (573) can reduce 611 to:
% 211.03/152.63  				| (576) $false
% 211.03/152.63  				|
% 211.03/152.63  				|-The branch is then unsatisfiable
% 211.03/152.63  		|-Branch two:
% 211.03/152.63  		| (581) false2 = err &  ~ (all_65_0_77 = 0)
% 211.03/152.63  		|
% 211.03/152.63  			| Applying alpha-rule on (581) yields:
% 211.03/152.63  			| (582) false2 = err
% 211.03/152.63  			| (583)  ~ (all_65_0_77 = 0)
% 211.03/152.63  			|
% 211.03/152.63  			| From (582) and (131) follows:
% 211.03/152.63  			| (585) phi(all_2_0_0) = err
% 211.03/152.63  			|
% 211.03/152.63  			+-Applying beta-rule and splitting (171), into two cases.
% 211.03/152.63  			|-Branch one:
% 211.03/152.63  			| (616) bool(all_2_1_1) = 0
% 211.03/152.63  			|
% 211.03/152.63  				+-Applying beta-rule and splitting (170), into two cases.
% 211.03/152.63  				|-Branch one:
% 211.03/152.63  				| (617) all_73_0_83 = true
% 211.03/152.63  				|
% 211.03/152.63  					| From (617) and (157) follows:
% 211.03/152.63  					| (804) lazy_impl(true, all_2_1_1) = all_2_0_0
% 211.03/152.63  					|
% 211.03/152.63  					| From (617) and (238) follows:
% 211.03/152.63  					| (619) lazy_impl(true, true) = all_93_0_89
% 211.03/152.63  					|
% 211.03/152.63  					| From (617) and (158) follows:
% 211.03/152.63  					| (620) prop(all_2_1_1) = true
% 211.03/152.63  					|
% 211.03/152.63  					| From (617) and (198) follows:
% 211.03/152.63  					| (621) phi(true) = all_93_0_89
% 211.03/152.63  					|
% 211.03/152.63  					| Instantiating formula (67) with true, all_93_0_89, true and discharging atoms phi(true) = all_93_0_89, phi(true) = true, yields:
% 211.03/152.63  					| (622) all_93_0_89 = true
% 211.03/152.63  					|
% 211.03/152.63  					| Instantiating formula (69) with all_2_1_1 and discharging atoms bool(all_2_1_1) = 0, yields:
% 211.03/152.63  					| (623) all_2_1_1 = true | all_2_1_1 = false
% 211.03/152.63  					|
% 211.03/152.63  					| From (622) and (619) follows:
% 211.03/152.63  					| (173) lazy_impl(true, true) = true
% 211.03/152.63  					|
% 211.03/152.63  					| Instantiating formula (34) with all_2_0_0, all_2_1_1 and discharging atoms lazy_impl(true, all_2_1_1) = all_2_0_0, yields:
% 211.03/152.63  					| (811) phi(all_2_1_1) = all_2_0_0
% 211.03/152.63  					|
% 211.03/152.63  					| Instantiating formula (105) with all_2_1_1 and discharging atoms bool(all_2_1_1) = 0, yields:
% 211.03/152.63  					| (626) impl(true, all_2_1_1) = all_2_1_1
% 211.03/152.63  					|
% 211.03/152.63  					| Instantiating formula (57) with all_2_1_1 and discharging atoms bool(all_2_1_1) = 0, yields:
% 211.03/152.63  					| (627) impl(false, all_2_1_1) = true
% 211.03/152.63  					|
% 211.03/152.63  					| Instantiating formula (10) with all_2_1_1, all_2_1_1, all_2_1_1, true, true and discharging atoms impl(true, all_2_1_1) = all_2_1_1, yields:
% 211.03/152.63  					| (628)  ? [v0] :  ? [v1] :  ? [v2] : (f1(true, true, all_2_1_1) = v0 & lazy_impl(v1, v2) = v0 & impl(all_2_1_1, all_2_1_1) = v2 & prop(all_2_1_1) = v1)
% 211.03/152.63  					|
% 211.03/152.63  					| Instantiating formula (51) with all_2_0_0, all_2_1_1, all_2_1_1, true, true and discharging atoms lazy_impl(true, all_2_1_1) = all_2_0_0, impl(true, all_2_1_1) = all_2_1_1, yields:
% 211.03/152.64  					| (815)  ? [v0] :  ? [v1] :  ? [v2] : (f2(true, true, all_2_1_1) = v0 & lazy_impl(v1, v2) = v0 & impl(all_2_0_0, all_2_1_1) = v2 & prop(all_2_1_1) = v1)
% 211.03/152.64  					|
% 211.03/152.64  					| Instantiating formula (10) with true, true, all_2_1_1, false, true and discharging atoms impl(true, true) = true, impl(false, all_2_1_1) = true, yields:
% 211.03/152.64  					| (630)  ? [v0] :  ? [v1] :  ? [v2] : (f1(true, false, all_2_1_1) = v0 & lazy_impl(v1, v2) = v0 & impl(true, all_2_1_1) = v2 & prop(all_2_1_1) = v1)
% 211.03/152.64  					|
% 211.03/152.64  					| Instantiating formula (10) with true, true, all_2_1_1, false, false and discharging atoms impl(false, all_2_1_1) = true, impl(false, true) = true, yields:
% 211.03/152.64  					| (631)  ? [v0] :  ? [v1] :  ? [v2] : (f1(false, false, all_2_1_1) = v0 & lazy_impl(v1, v2) = v0 & impl(true, all_2_1_1) = v2 & prop(all_2_1_1) = v1)
% 211.03/152.64  					|
% 211.03/152.64  					| Instantiating formula (10) with true, all_2_1_1, all_2_1_1, true, false and discharging atoms impl(true, all_2_1_1) = all_2_1_1, impl(false, all_2_1_1) = true, yields:
% 211.03/152.64  					| (632)  ? [v0] :  ? [v1] :  ? [v2] : (f1(false, true, all_2_1_1) = v0 & lazy_impl(v1, v2) = v0 & impl(true, all_2_1_1) = v2 & prop(all_2_1_1) = v1)
% 211.03/152.64  					|
% 211.03/152.64  					| Instantiating formula (102) with all_2_1_1, all_2_1_1, true, true, all_2_1_1, false, false and discharging atoms impl(true, all_2_1_1) = all_2_1_1, impl(false, all_2_1_1) = true, yields:
% 211.03/152.64  					| (633)  ? [v0] :  ? [v1] : (f3(false, false, all_2_1_1) = v0 & lazy_impl(v1, all_2_1_1) = v0 & prop(all_2_1_1) = v1)
% 211.03/152.64  					|
% 211.03/152.64  					| Instantiating formula (51) with true, true, all_2_1_1, false, true and discharging atoms lazy_impl(true, true) = true, impl(false, all_2_1_1) = true, yields:
% 211.03/152.64  					| (634)  ? [v0] :  ? [v1] :  ? [v2] : (f2(true, false, all_2_1_1) = v0 & lazy_impl(v1, v2) = v0 & impl(true, all_2_1_1) = v2 & prop(all_2_1_1) = v1)
% 211.03/152.64  					|
% 211.03/152.64  					| Instantiating formula (98) with all_2_0_0, all_2_1_1 and discharging atoms phi(all_2_1_1) = all_2_0_0, yields:
% 211.03/152.64  					| (821)  ? [v0] : (d(all_2_1_1) = v0 & ((v0 = 0 & all_2_0_0 = all_2_1_1) | (all_2_0_0 = err &  ~ (v0 = 0))))
% 211.03/152.64  					|
% 211.03/152.64  					| Instantiating (633) with all_284_0_271, all_284_1_272 yields:
% 211.03/152.64  					| (822) f3(false, false, all_2_1_1) = all_284_1_272 & lazy_impl(all_284_0_271, all_2_1_1) = all_284_1_272 & prop(all_2_1_1) = all_284_0_271
% 211.03/152.64  					|
% 211.03/152.64  					| Applying alpha-rule on (822) yields:
% 211.03/152.64  					| (823) f3(false, false, all_2_1_1) = all_284_1_272
% 211.03/152.64  					| (824) lazy_impl(all_284_0_271, all_2_1_1) = all_284_1_272
% 211.03/152.64  					| (825) prop(all_2_1_1) = all_284_0_271
% 211.03/152.64  					|
% 211.03/152.64  					| Instantiating (632) with all_286_0_273, all_286_1_274, all_286_2_275 yields:
% 211.03/152.64  					| (826) f1(false, true, all_2_1_1) = all_286_2_275 & lazy_impl(all_286_1_274, all_286_0_273) = all_286_2_275 & impl(true, all_2_1_1) = all_286_0_273 & prop(all_2_1_1) = all_286_1_274
% 211.03/152.64  					|
% 211.03/152.64  					| Applying alpha-rule on (826) yields:
% 211.03/152.64  					| (827) f1(false, true, all_2_1_1) = all_286_2_275
% 211.03/152.64  					| (828) lazy_impl(all_286_1_274, all_286_0_273) = all_286_2_275
% 211.03/152.64  					| (829) impl(true, all_2_1_1) = all_286_0_273
% 211.03/152.64  					| (830) prop(all_2_1_1) = all_286_1_274
% 211.03/152.64  					|
% 211.03/152.64  					| Instantiating (631) with all_288_0_276, all_288_1_277, all_288_2_278 yields:
% 211.03/152.64  					| (831) f1(false, false, all_2_1_1) = all_288_2_278 & lazy_impl(all_288_1_277, all_288_0_276) = all_288_2_278 & impl(true, all_2_1_1) = all_288_0_276 & prop(all_2_1_1) = all_288_1_277
% 211.03/152.64  					|
% 211.03/152.64  					| Applying alpha-rule on (831) yields:
% 211.03/152.64  					| (832) f1(false, false, all_2_1_1) = all_288_2_278
% 211.03/152.64  					| (833) lazy_impl(all_288_1_277, all_288_0_276) = all_288_2_278
% 211.03/152.64  					| (834) impl(true, all_2_1_1) = all_288_0_276
% 211.03/152.64  					| (835) prop(all_2_1_1) = all_288_1_277
% 211.03/152.64  					|
% 211.03/152.64  					| Instantiating (630) with all_290_0_279, all_290_1_280, all_290_2_281 yields:
% 211.03/152.64  					| (836) f1(true, false, all_2_1_1) = all_290_2_281 & lazy_impl(all_290_1_280, all_290_0_279) = all_290_2_281 & impl(true, all_2_1_1) = all_290_0_279 & prop(all_2_1_1) = all_290_1_280
% 211.03/152.64  					|
% 211.03/152.64  					| Applying alpha-rule on (836) yields:
% 211.03/152.64  					| (837) f1(true, false, all_2_1_1) = all_290_2_281
% 211.03/152.64  					| (838) lazy_impl(all_290_1_280, all_290_0_279) = all_290_2_281
% 211.03/152.64  					| (839) impl(true, all_2_1_1) = all_290_0_279
% 211.03/152.64  					| (840) prop(all_2_1_1) = all_290_1_280
% 211.03/152.64  					|
% 211.03/152.64  					| Instantiating (815) with all_292_0_282, all_292_1_283, all_292_2_284 yields:
% 211.03/152.64  					| (841) f2(true, true, all_2_1_1) = all_292_2_284 & lazy_impl(all_292_1_283, all_292_0_282) = all_292_2_284 & impl(all_2_0_0, all_2_1_1) = all_292_0_282 & prop(all_2_1_1) = all_292_1_283
% 211.03/152.64  					|
% 211.03/152.64  					| Applying alpha-rule on (841) yields:
% 211.03/152.64  					| (842) f2(true, true, all_2_1_1) = all_292_2_284
% 211.03/152.64  					| (843) lazy_impl(all_292_1_283, all_292_0_282) = all_292_2_284
% 211.03/152.64  					| (844) impl(all_2_0_0, all_2_1_1) = all_292_0_282
% 211.03/152.64  					| (845) prop(all_2_1_1) = all_292_1_283
% 211.03/152.64  					|
% 211.03/152.64  					| Instantiating (821) with all_294_0_285 yields:
% 211.03/152.64  					| (846) d(all_2_1_1) = all_294_0_285 & ((all_294_0_285 = 0 & all_2_0_0 = all_2_1_1) | (all_2_0_0 = err &  ~ (all_294_0_285 = 0)))
% 211.03/152.64  					|
% 211.03/152.64  					| Applying alpha-rule on (846) yields:
% 211.03/152.64  					| (847) d(all_2_1_1) = all_294_0_285
% 211.03/152.64  					| (848) (all_294_0_285 = 0 & all_2_0_0 = all_2_1_1) | (all_2_0_0 = err &  ~ (all_294_0_285 = 0))
% 211.03/152.64  					|
% 211.03/152.64  					| Instantiating (634) with all_296_0_286, all_296_1_287, all_296_2_288 yields:
% 211.03/152.64  					| (849) f2(true, false, all_2_1_1) = all_296_2_288 & lazy_impl(all_296_1_287, all_296_0_286) = all_296_2_288 & impl(true, all_2_1_1) = all_296_0_286 & prop(all_2_1_1) = all_296_1_287
% 211.03/152.64  					|
% 211.03/152.64  					| Applying alpha-rule on (849) yields:
% 211.03/152.64  					| (850) f2(true, false, all_2_1_1) = all_296_2_288
% 211.03/152.64  					| (851) lazy_impl(all_296_1_287, all_296_0_286) = all_296_2_288
% 211.03/152.64  					| (852) impl(true, all_2_1_1) = all_296_0_286
% 211.03/152.64  					| (853) prop(all_2_1_1) = all_296_1_287
% 211.03/152.64  					|
% 211.03/152.64  					| Instantiating (628) with all_298_0_289, all_298_1_290, all_298_2_291 yields:
% 211.03/152.64  					| (854) f1(true, true, all_2_1_1) = all_298_2_291 & lazy_impl(all_298_1_290, all_298_0_289) = all_298_2_291 & impl(all_2_1_1, all_2_1_1) = all_298_0_289 & prop(all_2_1_1) = all_298_1_290
% 211.03/152.64  					|
% 211.03/152.64  					| Applying alpha-rule on (854) yields:
% 211.03/152.64  					| (855) f1(true, true, all_2_1_1) = all_298_2_291
% 211.03/152.64  					| (856) lazy_impl(all_298_1_290, all_298_0_289) = all_298_2_291
% 211.03/152.64  					| (857) impl(all_2_1_1, all_2_1_1) = all_298_0_289
% 211.03/152.64  					| (858) prop(all_2_1_1) = all_298_1_290
% 211.03/152.64  					|
% 211.03/152.64  					| Instantiating formula (63) with true, all_2_1_1, all_296_0_286, all_2_1_1 and discharging atoms impl(true, all_2_1_1) = all_296_0_286, impl(true, all_2_1_1) = all_2_1_1, yields:
% 211.03/152.64  					| (859) all_296_0_286 = all_2_1_1
% 211.03/152.64  					|
% 211.03/152.64  					| Instantiating formula (63) with true, all_2_1_1, all_290_0_279, all_296_0_286 and discharging atoms impl(true, all_2_1_1) = all_296_0_286, impl(true, all_2_1_1) = all_290_0_279, yields:
% 211.03/152.64  					| (860) all_296_0_286 = all_290_0_279
% 211.03/152.64  					|
% 211.03/152.64  					| Instantiating formula (63) with true, all_2_1_1, all_288_0_276, all_290_0_279 and discharging atoms impl(true, all_2_1_1) = all_290_0_279, impl(true, all_2_1_1) = all_288_0_276, yields:
% 211.03/152.64  					| (861) all_290_0_279 = all_288_0_276
% 211.03/152.64  					|
% 211.03/152.64  					| Instantiating formula (63) with true, all_2_1_1, all_286_0_273, all_288_0_276 and discharging atoms impl(true, all_2_1_1) = all_288_0_276, impl(true, all_2_1_1) = all_286_0_273, yields:
% 211.03/152.64  					| (862) all_288_0_276 = all_286_0_273
% 211.03/152.64  					|
% 211.03/152.64  					| Instantiating formula (6) with all_2_1_1, all_292_1_283, all_296_1_287 and discharging atoms prop(all_2_1_1) = all_296_1_287, prop(all_2_1_1) = all_292_1_283, yields:
% 211.03/152.64  					| (863) all_296_1_287 = all_292_1_283
% 211.03/152.64  					|
% 211.03/152.64  					| Instantiating formula (6) with all_2_1_1, all_290_1_280, all_298_1_290 and discharging atoms prop(all_2_1_1) = all_298_1_290, prop(all_2_1_1) = all_290_1_280, yields:
% 211.03/152.64  					| (864) all_298_1_290 = all_290_1_280
% 211.03/152.64  					|
% 211.03/152.64  					| Instantiating formula (6) with all_2_1_1, all_288_1_277, true and discharging atoms prop(all_2_1_1) = all_288_1_277, prop(all_2_1_1) = true, yields:
% 211.03/152.64  					| (865) all_288_1_277 = true
% 211.03/152.64  					|
% 211.03/152.64  					| Instantiating formula (6) with all_2_1_1, all_288_1_277, all_298_1_290 and discharging atoms prop(all_2_1_1) = all_298_1_290, prop(all_2_1_1) = all_288_1_277, yields:
% 211.03/152.64  					| (866) all_298_1_290 = all_288_1_277
% 211.03/152.64  					|
% 211.03/152.64  					| Instantiating formula (6) with all_2_1_1, all_288_1_277, all_296_1_287 and discharging atoms prop(all_2_1_1) = all_296_1_287, prop(all_2_1_1) = all_288_1_277, yields:
% 211.03/152.64  					| (867) all_296_1_287 = all_288_1_277
% 211.03/152.64  					|
% 211.03/152.64  					| Instantiating formula (6) with all_2_1_1, all_286_1_274, all_296_1_287 and discharging atoms prop(all_2_1_1) = all_296_1_287, prop(all_2_1_1) = all_286_1_274, yields:
% 211.03/152.64  					| (868) all_296_1_287 = all_286_1_274
% 211.03/152.64  					|
% 211.03/152.64  					| Instantiating formula (6) with all_2_1_1, all_284_0_271, all_298_1_290 and discharging atoms prop(all_2_1_1) = all_298_1_290, prop(all_2_1_1) = all_284_0_271, yields:
% 211.03/152.64  					| (869) all_298_1_290 = all_284_0_271
% 211.03/152.64  					|
% 211.03/152.64  					| Combining equations (869,864) yields a new equation:
% 211.03/152.64  					| (870) all_290_1_280 = all_284_0_271
% 211.03/152.64  					|
% 211.03/152.64  					| Combining equations (866,864) yields a new equation:
% 211.03/152.64  					| (871) all_290_1_280 = all_288_1_277
% 211.03/152.64  					|
% 211.03/152.64  					| Combining equations (860,859) yields a new equation:
% 211.03/152.64  					| (872) all_290_0_279 = all_2_1_1
% 211.03/152.64  					|
% 211.03/152.64  					| Simplifying 872 yields:
% 211.03/152.64  					| (873) all_290_0_279 = all_2_1_1
% 211.03/152.64  					|
% 211.03/152.64  					| Combining equations (867,863) yields a new equation:
% 211.03/152.64  					| (874) all_292_1_283 = all_288_1_277
% 211.03/152.64  					|
% 211.03/152.64  					| Combining equations (868,863) yields a new equation:
% 211.03/152.64  					| (875) all_292_1_283 = all_286_1_274
% 211.03/152.64  					|
% 211.03/152.64  					| Combining equations (874,875) yields a new equation:
% 211.03/152.64  					| (876) all_288_1_277 = all_286_1_274
% 211.03/152.64  					|
% 211.03/152.64  					| Simplifying 876 yields:
% 211.03/152.64  					| (877) all_288_1_277 = all_286_1_274
% 211.03/152.64  					|
% 211.03/152.64  					| Combining equations (861,873) yields a new equation:
% 211.03/152.64  					| (878) all_288_0_276 = all_2_1_1
% 211.03/152.64  					|
% 211.03/152.64  					| Simplifying 878 yields:
% 211.03/152.64  					| (879) all_288_0_276 = all_2_1_1
% 211.03/152.64  					|
% 211.03/152.64  					| Combining equations (871,870) yields a new equation:
% 211.03/152.64  					| (880) all_288_1_277 = all_284_0_271
% 211.03/152.64  					|
% 211.03/152.64  					| Simplifying 880 yields:
% 211.03/152.64  					| (881) all_288_1_277 = all_284_0_271
% 211.03/152.64  					|
% 211.03/152.64  					| Combining equations (879,862) yields a new equation:
% 211.03/152.64  					| (882) all_286_0_273 = all_2_1_1
% 211.03/152.64  					|
% 211.03/152.64  					| Combining equations (865,877) yields a new equation:
% 211.03/152.64  					| (883) all_286_1_274 = true
% 211.03/152.64  					|
% 211.03/152.64  					| Combining equations (881,877) yields a new equation:
% 211.03/152.64  					| (884) all_286_1_274 = all_284_0_271
% 211.03/152.64  					|
% 211.03/152.64  					| Combining equations (883,884) yields a new equation:
% 211.03/152.64  					| (885) all_284_0_271 = true
% 211.03/152.64  					|
% 211.03/152.64  					| Combining equations (885,884) yields a new equation:
% 211.03/152.64  					| (883) all_286_1_274 = true
% 211.03/152.64  					|
% 211.03/152.64  					| Combining equations (885,870) yields a new equation:
% 211.03/152.64  					| (887) all_290_1_280 = true
% 211.03/152.64  					|
% 211.03/152.64  					| Combining equations (883,875) yields a new equation:
% 211.03/152.64  					| (888) all_292_1_283 = true
% 211.03/152.64  					|
% 211.03/152.64  					| Combining equations (888,863) yields a new equation:
% 211.03/152.64  					| (889) all_296_1_287 = true
% 211.03/152.64  					|
% 211.03/152.64  					| Combining equations (887,864) yields a new equation:
% 211.03/152.64  					| (890) all_298_1_290 = true
% 211.03/152.64  					|
% 211.03/152.64  					| From (890) and (856) follows:
% 211.03/152.64  					| (891) lazy_impl(true, all_298_0_289) = all_298_2_291
% 211.03/152.64  					|
% 211.03/152.64  					| From (889)(859) and (851) follows:
% 211.03/152.64  					| (892) lazy_impl(true, all_2_1_1) = all_296_2_288
% 211.03/152.64  					|
% 211.03/152.64  					| From (888) and (843) follows:
% 211.03/152.64  					| (893) lazy_impl(true, all_292_0_282) = all_292_2_284
% 211.03/152.64  					|
% 211.03/152.64  					| From (887)(873) and (838) follows:
% 211.03/152.64  					| (894) lazy_impl(true, all_2_1_1) = all_290_2_281
% 211.03/152.64  					|
% 211.03/152.64  					| From (883)(882) and (828) follows:
% 211.03/152.64  					| (895) lazy_impl(true, all_2_1_1) = all_286_2_275
% 211.03/152.64  					|
% 211.03/152.64  					| Instantiating formula (103) with true, all_2_1_1, all_290_2_281, all_2_0_0 and discharging atoms lazy_impl(true, all_2_1_1) = all_290_2_281, lazy_impl(true, all_2_1_1) = all_2_0_0, yields:
% 211.03/152.64  					| (896) all_290_2_281 = all_2_0_0
% 211.03/152.64  					|
% 211.03/152.64  					| Instantiating formula (103) with true, all_2_1_1, all_290_2_281, all_296_2_288 and discharging atoms lazy_impl(true, all_2_1_1) = all_296_2_288, lazy_impl(true, all_2_1_1) = all_290_2_281, yields:
% 211.03/152.64  					| (897) all_296_2_288 = all_290_2_281
% 211.03/152.64  					|
% 211.03/152.64  					| Instantiating formula (103) with true, all_2_1_1, all_286_2_275, all_296_2_288 and discharging atoms lazy_impl(true, all_2_1_1) = all_296_2_288, lazy_impl(true, all_2_1_1) = all_286_2_275, yields:
% 211.03/152.64  					| (898) all_296_2_288 = all_286_2_275
% 211.03/152.64  					|
% 211.03/152.64  					| Combining equations (897,898) yields a new equation:
% 211.03/152.64  					| (899) all_290_2_281 = all_286_2_275
% 211.03/152.64  					|
% 211.03/152.64  					| Simplifying 899 yields:
% 211.03/152.64  					| (900) all_290_2_281 = all_286_2_275
% 211.03/152.64  					|
% 211.03/152.64  					| Combining equations (900,896) yields a new equation:
% 211.03/152.64  					| (901) all_286_2_275 = all_2_0_0
% 211.03/152.64  					|
% 211.03/152.64  					| Simplifying 901 yields:
% 211.03/152.64  					| (902) all_286_2_275 = all_2_0_0
% 211.03/152.64  					|
% 211.03/152.64  					| Combining equations (902,898) yields a new equation:
% 211.03/152.64  					| (903) all_296_2_288 = all_2_0_0
% 211.03/152.64  					|
% 211.03/152.64  					| From (903) and (850) follows:
% 211.03/152.64  					| (904) f2(true, false, all_2_1_1) = all_2_0_0
% 211.03/152.64  					|
% 211.03/152.64  					| Instantiating formula (34) with all_292_2_284, all_292_0_282 and discharging atoms lazy_impl(true, all_292_0_282) = all_292_2_284, yields:
% 211.03/152.65  					| (905) phi(all_292_0_282) = all_292_2_284
% 211.03/152.65  					|
% 211.03/152.65  					| Instantiating formula (54) with all_292_0_282, all_2_1_1, all_2_0_0 and discharging atoms impl(all_2_0_0, all_2_1_1) = all_292_0_282, yields:
% 211.03/152.65  					| (906)  ? [v0] :  ? [v1] : (phi(all_2_0_0) = v1 & bool(all_2_0_0) = v0 & (v1 = all_292_0_282 | v0 = 0))
% 211.03/152.65  					|
% 211.03/152.65  					| Instantiating formula (51) with all_298_2_291, all_298_0_289, all_2_1_1, all_2_1_1, true and discharging atoms lazy_impl(true, all_298_0_289) = all_298_2_291, impl(all_2_1_1, all_2_1_1) = all_298_0_289, yields:
% 211.03/152.65  					| (907)  ? [v0] :  ? [v1] :  ? [v2] : (f2(true, all_2_1_1, all_2_1_1) = v0 & lazy_impl(v1, v2) = v0 & impl(all_298_2_291, all_2_1_1) = v2 & prop(all_2_1_1) = v1)
% 211.03/152.65  					|
% 211.03/152.65  					| Instantiating formula (58) with all_294_0_285, all_2_1_1 and discharging atoms d(all_2_1_1) = all_294_0_285, yields:
% 211.03/152.65  					| (908)  ? [v0] : (phi(all_2_1_1) = v0 & ((v0 = all_2_1_1 & all_294_0_285 = 0) | (v0 = err &  ~ (all_294_0_285 = 0))))
% 211.03/152.65  					|
% 211.03/152.65  					| Instantiating (908) with all_316_0_294 yields:
% 211.03/152.65  					| (909) phi(all_2_1_1) = all_316_0_294 & ((all_316_0_294 = all_2_1_1 & all_294_0_285 = 0) | (all_316_0_294 = err &  ~ (all_294_0_285 = 0)))
% 211.03/152.65  					|
% 211.03/152.65  					| Applying alpha-rule on (909) yields:
% 211.03/152.65  					| (910) phi(all_2_1_1) = all_316_0_294
% 211.03/152.65  					| (911) (all_316_0_294 = all_2_1_1 & all_294_0_285 = 0) | (all_316_0_294 = err &  ~ (all_294_0_285 = 0))
% 211.03/152.65  					|
% 211.03/152.65  					| Instantiating (907) with all_318_0_295, all_318_1_296, all_318_2_297 yields:
% 211.03/152.65  					| (912) f2(true, all_2_1_1, all_2_1_1) = all_318_2_297 & lazy_impl(all_318_1_296, all_318_0_295) = all_318_2_297 & impl(all_298_2_291, all_2_1_1) = all_318_0_295 & prop(all_2_1_1) = all_318_1_296
% 211.03/152.65  					|
% 211.03/152.65  					| Applying alpha-rule on (912) yields:
% 211.03/152.65  					| (913) f2(true, all_2_1_1, all_2_1_1) = all_318_2_297
% 211.03/152.65  					| (914) lazy_impl(all_318_1_296, all_318_0_295) = all_318_2_297
% 211.03/152.65  					| (915) impl(all_298_2_291, all_2_1_1) = all_318_0_295
% 211.03/152.65  					| (916) prop(all_2_1_1) = all_318_1_296
% 211.03/152.65  					|
% 211.03/152.65  					| Instantiating (906) with all_324_0_303, all_324_1_304 yields:
% 211.03/152.65  					| (917) phi(all_2_0_0) = all_324_0_303 & bool(all_2_0_0) = all_324_1_304 & (all_324_0_303 = all_292_0_282 | all_324_1_304 = 0)
% 211.03/152.65  					|
% 211.03/152.65  					| Applying alpha-rule on (917) yields:
% 211.03/152.65  					| (918) phi(all_2_0_0) = all_324_0_303
% 211.03/152.65  					| (919) bool(all_2_0_0) = all_324_1_304
% 211.03/152.65  					| (920) all_324_0_303 = all_292_0_282 | all_324_1_304 = 0
% 211.03/152.65  					|
% 211.03/152.65  					| Instantiating formula (67) with all_2_0_0, all_324_0_303, err and discharging atoms phi(all_2_0_0) = all_324_0_303, phi(all_2_0_0) = err, yields:
% 211.03/152.65  					| (921) all_324_0_303 = err
% 211.03/152.65  					|
% 211.03/152.65  					| Instantiating formula (67) with all_2_1_1, all_316_0_294, all_2_0_0 and discharging atoms phi(all_2_1_1) = all_316_0_294, phi(all_2_1_1) = all_2_0_0, yields:
% 211.03/152.65  					| (922) all_316_0_294 = all_2_0_0
% 211.03/152.65  					|
% 211.03/152.65  					| Instantiating formula (116) with all_2_0_0, all_324_1_304, all_63_1_76 and discharging atoms bool(all_2_0_0) = all_324_1_304, bool(all_2_0_0) = all_63_1_76, yields:
% 211.03/152.65  					| (923) all_324_1_304 = all_63_1_76
% 211.03/152.65  					|
% 211.03/152.65  					+-Applying beta-rule and splitting (920), into two cases.
% 211.03/152.65  					|-Branch one:
% 211.03/152.65  					| (924) all_324_1_304 = 0
% 211.03/152.65  					|
% 211.03/152.65  						| Combining equations (924,923) yields a new equation:
% 211.03/152.65  						| (565) all_63_1_76 = 0
% 211.03/152.65  						|
% 211.03/152.65  						| Equations (565) can reduce 600 to:
% 211.03/152.65  						| (576) $false
% 211.03/152.65  						|
% 211.03/152.65  						|-The branch is then unsatisfiable
% 211.03/152.65  					|-Branch two:
% 211.03/152.65  					| (927)  ~ (all_324_1_304 = 0)
% 211.03/152.65  					| (928) all_324_0_303 = all_292_0_282
% 211.03/152.65  					|
% 211.03/152.65  						| Combining equations (921,928) yields a new equation:
% 211.03/152.65  						| (929) all_292_0_282 = err
% 211.03/152.65  						|
% 211.03/152.65  						| From (929) and (905) follows:
% 211.03/152.65  						| (930) phi(err) = all_292_2_284
% 211.03/152.65  						|
% 211.03/152.65  						| Instantiating formula (67) with err, all_292_2_284, err and discharging atoms phi(err) = all_292_2_284, phi(err) = err, yields:
% 211.03/152.65  						| (931) all_292_2_284 = err
% 211.03/152.65  						|
% 211.03/152.65  						| From (931) and (842) follows:
% 211.03/152.65  						| (932) f2(true, true, all_2_1_1) = err
% 211.03/152.65  						|
% 211.03/152.65  						+-Applying beta-rule and splitting (623), into two cases.
% 211.03/152.65  						|-Branch one:
% 211.03/152.65  						| (744) all_2_1_1 = true
% 211.03/152.65  						|
% 211.03/152.65  							| From (744)(744) and (913) follows:
% 211.03/152.65  							| (934) f2(true, true, true) = all_318_2_297
% 211.03/152.65  							|
% 211.03/152.65  							| From (744) and (932) follows:
% 211.03/152.65  							| (756) f2(true, true, true) = err
% 211.03/152.65  							|
% 211.03/152.65  							+-Applying beta-rule and splitting (911), into two cases.
% 211.03/152.65  							|-Branch one:
% 211.03/152.65  							| (936) all_316_0_294 = all_2_1_1 & all_294_0_285 = 0
% 211.03/152.65  							|
% 211.03/152.65  								| Applying alpha-rule on (936) yields:
% 211.03/152.65  								| (937) all_316_0_294 = all_2_1_1
% 211.03/152.65  								| (938) all_294_0_285 = 0
% 211.03/152.65  								|
% 211.03/152.65  								| Combining equations (922,937) yields a new equation:
% 211.03/152.65  								| (939) all_2_0_0 = all_2_1_1
% 211.03/152.65  								|
% 211.03/152.65  								| Simplifying 939 yields:
% 211.03/152.65  								| (940) all_2_0_0 = all_2_1_1
% 211.03/152.65  								|
% 211.03/152.65  								| Combining equations (744,940) yields a new equation:
% 211.03/152.65  								| (572) all_2_0_0 = true
% 211.03/152.65  								|
% 211.03/152.65  								| Equations (572) can reduce 577 to:
% 211.03/152.65  								| (576) $false
% 211.03/152.65  								|
% 211.03/152.65  								|-The branch is then unsatisfiable
% 211.03/152.65  							|-Branch two:
% 211.03/152.65  							| (943) all_316_0_294 = err &  ~ (all_294_0_285 = 0)
% 211.03/152.65  							|
% 211.03/152.65  								| Applying alpha-rule on (943) yields:
% 211.03/152.65  								| (944) all_316_0_294 = err
% 211.03/152.65  								| (945)  ~ (all_294_0_285 = 0)
% 211.03/152.65  								|
% 211.03/152.65  								| Combining equations (944,922) yields a new equation:
% 211.03/152.65  								| (946) all_2_0_0 = err
% 211.03/152.65  								|
% 211.03/152.65  								| Equations (946) can reduce 577 to:
% 211.03/152.65  								| (119)  ~ (err = true)
% 211.03/152.65  								|
% 211.03/152.65  								| Instantiating formula (73) with true, true, true, all_318_2_297, true and discharging atoms f2(true, true, true) = all_318_2_297, f2(true, true, true) = true, yields:
% 211.03/152.65  								| (948) all_318_2_297 = true
% 211.03/152.65  								|
% 211.03/152.65  								| Instantiating formula (73) with true, true, true, err, all_318_2_297 and discharging atoms f2(true, true, true) = all_318_2_297, f2(true, true, true) = err, yields:
% 211.03/152.65  								| (949) all_318_2_297 = err
% 211.03/152.65  								|
% 211.03/152.65  								| Combining equations (948,949) yields a new equation:
% 211.03/152.65  								| (759) err = true
% 211.03/152.65  								|
% 211.03/152.65  								| Equations (759) can reduce 119 to:
% 211.03/152.65  								| (576) $false
% 211.03/152.65  								|
% 211.03/152.65  								|-The branch is then unsatisfiable
% 211.03/152.65  						|-Branch two:
% 211.03/152.65  						| (761)  ~ (all_2_1_1 = true)
% 211.03/152.65  						| (762) all_2_1_1 = false
% 211.03/152.65  						|
% 211.03/152.65  							| Equations (762) can reduce 761 to:
% 211.03/152.65  							| (763)  ~ (true = false)
% 211.03/152.65  							|
% 211.03/152.65  							| Simplifying 763 yields:
% 211.03/152.65  							| (122)  ~ (true = false)
% 211.03/152.65  							|
% 211.03/152.65  							| From (762)(762) and (913) follows:
% 211.03/152.65  							| (956) f2(true, false, false) = all_318_2_297
% 211.03/152.65  							|
% 211.03/152.65  							| From (762) and (932) follows:
% 211.03/152.65  							| (776) f2(true, true, false) = err
% 211.03/152.65  							|
% 211.03/152.65  							| From (762) and (904) follows:
% 211.03/152.65  							| (958) f2(true, false, false) = all_2_0_0
% 211.03/152.65  							|
% 211.03/152.65  							+-Applying beta-rule and splitting (911), into two cases.
% 211.03/152.65  							|-Branch one:
% 211.03/152.65  							| (936) all_316_0_294 = all_2_1_1 & all_294_0_285 = 0
% 211.03/152.65  							|
% 211.03/152.65  								| Applying alpha-rule on (936) yields:
% 211.03/152.65  								| (937) all_316_0_294 = all_2_1_1
% 211.03/152.65  								| (938) all_294_0_285 = 0
% 211.03/152.65  								|
% 211.03/152.65  								| Combining equations (922,937) yields a new equation:
% 211.03/152.65  								| (939) all_2_0_0 = all_2_1_1
% 211.03/152.65  								|
% 211.03/152.65  								| Simplifying 939 yields:
% 211.03/152.65  								| (940) all_2_0_0 = all_2_1_1
% 211.03/152.65  								|
% 211.03/152.65  								| Combining equations (762,940) yields a new equation:
% 211.03/152.65  								| (578) all_2_0_0 = false
% 211.03/152.65  								|
% 211.03/152.65  								| Equations (578) can reduce 607 to:
% 211.03/152.65  								| (576) $false
% 211.03/152.65  								|
% 211.03/152.65  								|-The branch is then unsatisfiable
% 211.03/152.65  							|-Branch two:
% 211.03/152.65  							| (943) all_316_0_294 = err &  ~ (all_294_0_285 = 0)
% 211.03/152.65  							|
% 211.03/152.65  								| Applying alpha-rule on (943) yields:
% 211.03/152.65  								| (944) all_316_0_294 = err
% 211.03/152.65  								| (945)  ~ (all_294_0_285 = 0)
% 211.03/152.65  								|
% 211.03/152.65  								| Combining equations (944,922) yields a new equation:
% 211.03/152.65  								| (946) all_2_0_0 = err
% 211.03/152.65  								|
% 211.03/152.65  								| From (946) and (958) follows:
% 211.03/152.65  								| (777) f2(true, false, false) = err
% 211.03/152.65  								|
% 211.03/152.65  								| Instantiating formula (73) with true, true, false, err, true and discharging atoms f2(true, true, false) = err, f2(true, true, false) = true, yields:
% 211.03/152.65  								| (759) err = true
% 211.03/152.65  								|
% 211.03/152.65  								| Instantiating formula (73) with true, false, false, all_318_2_297, false and discharging atoms f2(true, false, false) = all_318_2_297, f2(true, false, false) = false, yields:
% 211.03/152.65  								| (972) all_318_2_297 = false
% 211.03/152.65  								|
% 211.03/152.65  								| Instantiating formula (73) with true, false, false, err, all_318_2_297 and discharging atoms f2(true, false, false) = all_318_2_297, f2(true, false, false) = err, yields:
% 211.03/152.65  								| (949) all_318_2_297 = err
% 211.03/152.65  								|
% 211.03/152.65  								| Combining equations (949,972) yields a new equation:
% 211.03/152.65  								| (781) err = false
% 211.03/152.65  								|
% 211.03/152.65  								| Simplifying 781 yields:
% 211.03/152.65  								| (598) err = false
% 211.03/152.65  								|
% 211.03/152.65  								| Combining equations (759,598) yields a new equation:
% 211.03/152.65  								| (783) true = false
% 211.03/152.65  								|
% 211.03/152.65  								| Simplifying 783 yields:
% 211.03/152.65  								| (784) true = false
% 211.03/152.65  								|
% 211.03/152.65  								| Equations (784) can reduce 122 to:
% 211.03/152.65  								| (576) $false
% 211.03/152.65  								|
% 211.03/152.65  								|-The branch is then unsatisfiable
% 211.03/152.65  				|-Branch two:
% 211.03/152.65  				| (786)  ~ (all_73_0_83 = true)
% 211.03/152.65  				| (787)  ? [v0] : ( ~ (v0 = 0) & bool(all_2_1_1) = v0)
% 211.03/152.65  				|
% 211.03/152.65  					| Instantiating (787) with all_246_0_351 yields:
% 211.03/152.65  					| (981)  ~ (all_246_0_351 = 0) & bool(all_2_1_1) = all_246_0_351
% 211.03/152.65  					|
% 211.03/152.65  					| Applying alpha-rule on (981) yields:
% 211.03/152.65  					| (982)  ~ (all_246_0_351 = 0)
% 211.03/152.65  					| (983) bool(all_2_1_1) = all_246_0_351
% 211.03/152.65  					|
% 211.03/152.65  					| Instantiating formula (116) with all_2_1_1, 0, all_246_0_351 and discharging atoms bool(all_2_1_1) = all_246_0_351, bool(all_2_1_1) = 0, yields:
% 211.03/152.65  					| (984) all_246_0_351 = 0
% 211.03/152.65  					|
% 211.03/152.65  					| Equations (984) can reduce 982 to:
% 211.03/152.65  					| (576) $false
% 211.03/152.65  					|
% 211.03/152.65  					|-The branch is then unsatisfiable
% 211.03/152.65  			|-Branch two:
% 211.03/152.65  			| (793)  ~ (bool(all_2_1_1) = 0)
% 211.03/152.65  			| (794) all_73_0_83 = false
% 211.03/152.65  			|
% 211.03/152.65  				| From (794) and (157) follows:
% 211.03/152.65  				| (988) lazy_impl(false, all_2_1_1) = all_2_0_0
% 211.03/152.65  				|
% 211.03/152.65  				| Instantiating formula (22) with all_2_0_0, all_2_1_1 and discharging atoms lazy_impl(false, all_2_1_1) = all_2_0_0, yields:
% 211.03/152.65  				| (572) all_2_0_0 = true
% 211.03/152.65  				|
% 211.03/152.65  				| Equations (572) can reduce 577 to:
% 211.03/152.65  				| (576) $false
% 211.03/152.65  				|
% 211.03/152.65  				|-The branch is then unsatisfiable
% 211.03/152.65  % SZS output end Proof for theBenchmark
% 211.03/152.65  
% 211.03/152.65  152061ms
%------------------------------------------------------------------------------