TSTP Solution File: CSR017+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : CSR017+1 : TPTP v8.1.0. Bugfixed v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n032.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 : Fri Jul 15 02:50:14 EDT 2022
% Result : Theorem 24.69s 6.37s
% Output : Proof 33.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : CSR017+1 : TPTP v8.1.0. Bugfixed v3.1.0.
% 0.09/0.10 % Command : ePrincess-casc -timeout=%d %s
% 0.09/0.28 % Computer : n032.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8042.1875MB
% 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28 % CPULimit : 300
% 0.09/0.28 % WCLimit : 600
% 0.09/0.28 % DateTime : Fri Jun 10 05:01:08 EDT 2022
% 0.09/0.29 % CPUTime :
% 0.13/0.49 ____ _
% 0.13/0.49 ___ / __ \_____(_)___ ________ __________
% 0.13/0.49 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.13/0.49 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.13/0.49 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.13/0.49
% 0.13/0.49 A Theorem Prover for First-Order Logic
% 0.13/0.49 (ePrincess v.1.0)
% 0.13/0.49
% 0.13/0.49 (c) Philipp Rümmer, 2009-2015
% 0.13/0.49 (c) Peter Backeman, 2014-2015
% 0.13/0.49 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.13/0.49 Free software under GNU Lesser General Public License (LGPL).
% 0.13/0.49 Bug reports to peter@backeman.se
% 0.13/0.49
% 0.13/0.49 For more information, visit http://user.uu.se/~petba168/breu/
% 0.13/0.49
% 0.13/0.49 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.56/0.54 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.34/0.85 Prover 0: Preprocessing ...
% 4.22/1.52 Prover 0: Warning: ignoring some quantifiers
% 4.54/1.57 Prover 0: Constructing countermodel ...
% 7.55/2.30 Prover 0: gave up
% 7.55/2.30 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 7.87/2.35 Prover 1: Preprocessing ...
% 8.22/2.47 Prover 1: Constructing countermodel ...
% 8.83/2.56 Prover 1: gave up
% 8.83/2.56 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 8.83/2.60 Prover 2: Preprocessing ...
% 9.58/2.73 Prover 2: Warning: ignoring some quantifiers
% 9.58/2.73 Prover 2: Constructing countermodel ...
% 17.54/4.64 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 17.85/4.69 Prover 3: Preprocessing ...
% 18.30/4.81 Prover 3: Warning: ignoring some quantifiers
% 18.40/4.81 Prover 3: Constructing countermodel ...
% 19.76/5.22 Prover 3: gave up
% 19.76/5.22 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 20.14/5.24 Prover 4: Preprocessing ...
% 20.41/5.34 Prover 4: Warning: ignoring some quantifiers
% 20.41/5.34 Prover 4: Constructing countermodel ...
% 24.01/6.19 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 24.01/6.23 Prover 5: Preprocessing ...
% 24.56/6.30 Prover 5: Constructing countermodel ...
% 24.69/6.37 Prover 5: proved (175ms)
% 24.69/6.37 Prover 4: stopped
% 24.69/6.37 Prover 2: stopped
% 24.69/6.37
% 24.69/6.37 No countermodel exists, formula is valid
% 24.69/6.37 % SZS status Theorem for theBenchmark
% 24.69/6.37
% 24.69/6.37 Generating proof ... found it (size 743)
% 32.59/8.25
% 32.59/8.25 % SZS output start Proof for theBenchmark
% 32.59/8.25 Assumed formulas after preprocessing and simplification:
% 32.59/8.25 | (0) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (antitrajectory(v5, v4, v3, v2) = v1) | ~ (antitrajectory(v5, v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (trajectory(v5, v4, v3, v2) = v1) | ~ (trajectory(v5, v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (releases(v4, v3, v2) = v1) | ~ (releases(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (startedIn(v4, v3, v2) = v1) | ~ (startedIn(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (initiates(v4, v3, v2) = v1) | ~ (initiates(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (stoppedIn(v4, v3, v2) = v1) | ~ (stoppedIn(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (terminates(v4, v3, v2) = v1) | ~ (terminates(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (less_or_equal(v3, v2) = v1) | ~ (less_or_equal(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (releasedAt(v3, v2) = v1) | ~ (releasedAt(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (plus(v3, v2) = v1) | ~ (plus(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (holdsAt(v3, v2) = v1) | ~ (holdsAt(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (happens(v3, v2) = v1) | ~ (happens(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (less(v3, v2) = v1) | ~ (less(v3, v2) = v0)) & ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = 0) & ~ (v1 = 0) & ~ (v0 = 0) & ~ (spinning = backwards) & ~ (spinning = forwards) & ~ (backwards = forwards) & ~ (pull = push) & plus(n3, n3) = n6 & plus(n2, n3) = n5 & plus(n2, n2) = n4 & plus(n1, n3) = n4 & plus(n1, n2) = n3 & plus(n1, n1) = n2 & plus(n0, n3) = n3 & plus(n0, n2) = n2 & plus(n0, n1) = n1 & plus(n0, n0) = n0 & holdsAt(spinning, n1) = 0 & holdsAt(spinning, n0) = v2 & holdsAt(backwards, n0) = v1 & holdsAt(forwards, n0) = v0 & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (plus(v4, v7) = v8) | ~ (holdsAt(v6, v8) = v10) | ~ (stoppedIn(v4, v5, v8) = v9) | ~ (happens(v3, v4) = 0) | ? [v11] : ? [v12] : ? [v13] : (trajectory(v5, v4, v6, v7) = v13 & initiates(v3, v5, v4) = v11 & less(n0, v7) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0)))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (plus(v4, v6) = v8) | ~ (holdsAt(v7, v8) = v10) | ~ (startedIn(v4, v5, v8) = v9) | ~ (happens(v3, v4) = 0) | ? [v11] : ? [v12] : ? [v13] : (antitrajectory(v5, v4, v7, v6) = v13 & less(n0, v6) = v12 & terminates(v3, v5, v4) = v11 & ( ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0)))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (plus(v4, v7) = v8) | ~ (holdsAt(v6, v8) = v9) | ~ (initiates(v3, v5, v4) = 0) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : (trajectory(v5, v4, v6, v7) = v12 & stoppedIn(v4, v5, v8) = v13 & happens(v3, v4) = v10 & less(n0, v7) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0) | ~ (v10 = 0) | v13 = 0))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (plus(v4, v6) = v8) | ~ (holdsAt(v7, v8) = v9) | ~ (terminates(v3, v5, v4) = 0) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : (antitrajectory(v5, v4, v7, v6) = v12 & startedIn(v4, v5, v8) = v13 & happens(v3, v4) = v10 & less(n0, v6) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0) | ~ (v10 = 0) | v13 = 0))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (releasedAt(v5, v6) = v7) | ~ (plus(v4, n1) = v6) | ~ (happens(v3, v4) = 0) | ? [v8] : ( ~ (v8 = 0) & releases(v3, v5, v4) = v8)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (plus(v4, n1) = v6) | ~ (holdsAt(v5, v6) = v7) | ~ (happens(v3, v4) = 0) | ? [v8] : ( ~ (v8 = 0) & initiates(v3, v5, v4) = v8)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (antitrajectory(v5, v4, v7, v6) = 0) | ~ (happens(v3, v4) = 0) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : (plus(v4, v6) = v10 & holdsAt(v7, v10) = v12 & startedIn(v4, v5, v10) = v11 & less(n0, v6) = v9 & terminates(v3, v5, v4) = v8 & ( ~ (v9 = 0) | ~ (v8 = 0) | v12 = 0 | v11 = 0))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (antitrajectory(v5, v4, v7, v6) = 0) | ~ (terminates(v3, v5, v4) = 0) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : (plus(v4, v6) = v10 & holdsAt(v7, v10) = v12 & startedIn(v4, v5, v10) = v11 & happens(v3, v4) = v8 & less(n0, v6) = v9 & ( ~ (v9 = 0) | ~ (v8 = 0) | v12 = 0 | v11 = 0))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (trajectory(v5, v4, v6, v7) = 0) | ~ (initiates(v3, v5, v4) = 0) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : (plus(v4, v7) = v10 & holdsAt(v6, v10) = v12 & stoppedIn(v4, v5, v10) = v11 & happens(v3, v4) = v8 & less(n0, v7) = v9 & ( ~ (v9 = 0) | ~ (v8 = 0) | v12 = 0 | v11 = 0))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (trajectory(v5, v4, v6, v7) = 0) | ~ (happens(v3, v4) = 0) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : (plus(v4, v7) = v10 & holdsAt(v6, v10) = v12 & initiates(v3, v5, v4) = v8 & stoppedIn(v4, v5, v10) = v11 & less(n0, v7) = v9 & ( ~ (v9 = 0) | ~ (v8 = 0) | v12 = 0 | v11 = 0))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (releasedAt(v3, v5) = v6) | ~ (plus(v4, n1) = v5) | ? [v7] : ? [v8] : ? [v9] : (initiates(v7, v3, v4) = v8 & happens(v7, v4) = 0 & terminates(v7, v3, v4) = v9 & (v9 = 0 | v8 = 0)) | ? [v7] : ( ~ (v7 = 0) & releasedAt(v3, v4) = v7)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (releasedAt(v3, v5) = v6) | ~ (plus(v4, n1) = v5) | ? [v7] : ? [v8] : (holdsAt(v3, v5) = v8 & holdsAt(v3, v4) = v7 & ( ~ (v8 = 0) | v7 = 0)) | ? [v7] : (initiates(v7, v3, v4) = 0 & happens(v7, v4) = 0)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (releasedAt(v3, v5) = v6) | ~ (plus(v4, n1) = v5) | ? [v7] : ? [v8] : (holdsAt(v3, v5) = v8 & holdsAt(v3, v4) = v7 & ( ~ (v7 = 0) | v8 = 0)) | ? [v7] : (happens(v7, v4) = 0 & terminates(v7, v3, v4) = 0)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (plus(v4, n1) = v5) | ~ (holdsAt(v3, v5) = v6) | ? [v7] : ? [v8] : (releasedAt(v3, v5) = v8 & holdsAt(v3, v4) = v7 & ( ~ (v7 = 0) | v8 = 0)) | ? [v7] : (happens(v7, v4) = 0 & terminates(v7, v3, v4) = 0)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (startedIn(v3, v5, v4) = v6) | ( ! [v7] : ! [v8] : ( ~ (initiates(v7, v5, v8) = 0) | ? [v9] : ? [v10] : ? [v11] : (happens(v7, v8) = v9 & less(v8, v4) = v11 & less(v3, v8) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0) | ~ (v9 = 0)))) & ! [v7] : ! [v8] : ( ~ (happens(v7, v8) = 0) | ? [v9] : ? [v10] : ? [v11] : (initiates(v7, v5, v8) = v11 & less(v8, v4) = v10 & less(v3, v8) = v9 & ( ~ (v11 = 0) | ~ (v10 = 0) | ~ (v9 = 0)))))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (initiates(v3, v4, v5) = v6) | ? [v7] : ? [v8] : (happens(pull, v5) = v7 & happens(push, v5) = v8 & ( ~ (v8 = 0) | ~ (v4 = spinning) | ~ (v3 = pull)) & ( ~ (v4 = backwards) | ~ (v3 = pull) | v8 = 0) & ( ~ (v4 = forwards) | ~ (v3 = push) | v7 = 0))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (stoppedIn(v3, v4, v5) = v6) | ( ! [v7] : ! [v8] : ( ~ (happens(v7, v8) = 0) | ? [v9] : ? [v10] : ? [v11] : (less(v8, v5) = v10 & less(v3, v8) = v9 & terminates(v7, v4, v8) = v11 & ( ~ (v11 = 0) | ~ (v10 = 0) | ~ (v9 = 0)))) & ! [v7] : ! [v8] : ( ~ (terminates(v7, v4, v8) = 0) | ? [v9] : ? [v10] : ? [v11] : (happens(v7, v8) = v9 & less(v8, v5) = v11 & less(v3, v8) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0) | ~ (v9 = 0)))))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (terminates(v3, v4, v5) = v6) | ? [v7] : ? [v8] : (happens(pull, v5) = v7 & happens(push, v5) = v8 & ( ~ (v8 = 0) | ~ (v4 = backwards) | ~ (v3 = pull)) & ( ~ (v8 = 0) | ~ (v4 = forwards) | ~ (v3 = pull)) & ( ~ (v4 = spinning) | ~ (v3 = pull) | v8 = 0) & ( ~ (v4 = spinning) | ~ (v3 = push) | v7 = 0) & ( ~ (v4 = backwards) | ~ (v3 = push) | v7 = 0) & ( ~ (v4 = forwards) | ~ (v3 = pull) | v8 = 0))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (releasedAt(v5, v6) = 0) | ~ (plus(v4, n1) = v6) | ~ (happens(v3, v4) = 0) | ? [v7] : ? [v8] : ( ~ (v8 = 0) & ~ (v7 = 0) & initiates(v3, v5, v4) = v7 & terminates(v3, v5, v4) = v8)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (plus(v4, n1) = v6) | ~ (holdsAt(v5, v6) = 0) | ~ (happens(v3, v4) = 0) | ? [v7] : ( ~ (v7 = 0) & terminates(v3, v5, v4) = v7)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (initiates(v3, v5, v4) = v6) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : (releasedAt(v5, v9) = v10 & plus(v4, n1) = v9 & happens(v3, v4) = v7 & terminates(v3, v5, v4) = v8 & ( ~ (v10 = 0) | ~ (v7 = 0) | ( ~ (v8 = 0) & ~ (v6 = 0))))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (terminates(v3, v5, v4) = v6) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : (releasedAt(v5, v9) = v10 & plus(v4, n1) = v9 & initiates(v3, v5, v4) = v8 & happens(v3, v4) = v7 & ( ~ (v10 = 0) | ~ (v7 = 0) | ( ~ (v8 = 0) & ~ (v6 = 0))))) & ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = v3 | ~ (less(v4, v3) = v5) | less(v3, v4) = 0) & ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = v3 | ~ (less(v3, v4) = v5) | less(v4, v3) = 0) & ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = v3 | ~ (less(v3, v4) = v5) | ? [v6] : ( ~ (v6 = 0) & less_or_equal(v3, v4) = v6)) & ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (less_or_equal(v3, v4) = v5) | ( ~ (v4 = v3) & ? [v6] : ( ~ (v6 = 0) & less(v3, v4) = v6))) & ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (releasedAt(v3, v4) = v5) | ? [v6] : ? [v7] : ( ~ (v7 = 0) & releasedAt(v3, v6) = v7 & plus(v4, n1) = v6) | ? [v6] : (releases(v6, v3, v4) = 0 & happens(v6, v4) = 0)) & ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (holdsAt(v3, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : (releasedAt(v3, v6) = v7 & plus(v4, n1) = v6 & holdsAt(v3, v6) = v8 & ( ~ (v8 = 0) | v7 = 0)) | ? [v6] : (initiates(v6, v3, v4) = 0 & happens(v6, v4) = 0)) & ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (happens(v3, v4) = v5) | (( ~ (v4 = n2) | ~ (v3 = pull)) & ( ~ (v4 = n2) | ~ (v3 = push)) & ( ~ (v4 = n1) | ~ (v3 = pull)) & ( ~ (v4 = n0) | ~ (v3 = push)))) & ! [v3] : ! [v4] : ! [v5] : ( ~ (releases(v3, v5, v4) = 0) | ? [v6] : ? [v7] : ? [v8] : (releasedAt(v5, v7) = v8 & plus(v4, n1) = v7 & happens(v3, v4) = v6 & ( ~ (v6 = 0) | v8 = 0))) & ! [v3] : ! [v4] : ! [v5] : ~ (releases(v3, v4, v5) = 0) & ! [v3] : ! [v4] : ! [v5] : ( ~ (releasedAt(v3, v5) = 0) | ~ (plus(v4, n1) = v5) | releasedAt(v3, v4) = 0 | ? [v6] : (releases(v6, v3, v4) = 0 & happens(v6, v4) = 0)) & ! [v3] : ! [v4] : ! [v5] : ( ~ (plus(v4, v3) = v5) | plus(v3, v4) = v5) & ! [v3] : ! [v4] : ! [v5] : ( ~ (plus(v4, n1) = v5) | ~ (holdsAt(v3, v5) = 0) | ? [v6] : ? [v7] : (releasedAt(v3, v5) = v7 & holdsAt(v3, v4) = v6 & (v7 = 0 | v6 = 0)) | ? [v6] : (initiates(v6, v3, v4) = 0 & happens(v6, v4) = 0)) & ! [v3] : ! [v4] : ! [v5] : ( ~ (plus(v3, v4) = v5) | plus(v4, v3) = v5) & ! [v3] : ! [v4] : ! [v5] : ( ~ (startedIn(v3, v5, v4) = 0) | ? [v6] : ? [v7] : (initiates(v6, v5, v7) = 0 & happens(v6, v7) = 0 & less(v7, v4) = 0 & less(v3, v7) = 0)) & ! [v3] : ! [v4] : ! [v5] : ( ~ (initiates(v3, v5, v4) = 0) | ? [v6] : ? [v7] : ? [v8] : (plus(v4, n1) = v7 & holdsAt(v5, v7) = v8 & happens(v3, v4) = v6 & ( ~ (v6 = 0) | v8 = 0))) & ! [v3] : ! [v4] : ! [v5] : ( ~ (initiates(v3, v4, v5) = 0) | ? [v6] : ? [v7] : (happens(pull, v5) = v6 & happens(push, v5) = v7 & ((v7 = 0 & v4 = spinning & v3 = pull) | (v4 = backwards & v3 = pull & ~ (v7 = 0)) | (v4 = forwards & v3 = push & ~ (v6 = 0))))) & ! [v3] : ! [v4] : ! [v5] : ( ~ (stoppedIn(v3, v4, v5) = 0) | ? [v6] : ? [v7] : (happens(v6, v7) = 0 & less(v7, v5) = 0 & less(v3, v7) = 0 & terminates(v6, v4, v7) = 0)) & ! [v3] : ! [v4] : ! [v5] : ( ~ (less(v4, v3) = v5) | ? [v6] : ( ~ (v6 = 0) & less(v3, v4) = v6) | ( ~ (v5 = 0) & ~ (v4 = v3))) & ! [v3] : ! [v4] : ! [v5] : ( ~ (less(v3, v4) = v5) | less_or_equal(v3, v4) = 0 | ( ~ (v5 = 0) & ~ (v4 = v3))) & ! [v3] : ! [v4] : ! [v5] : ( ~ (terminates(v3, v5, v4) = 0) | ? [v6] : ? [v7] : ? [v8] : (plus(v4, n1) = v7 & holdsAt(v5, v7) = v8 & happens(v3, v4) = v6 & ( ~ (v8 = 0) | ~ (v6 = 0)))) & ! [v3] : ! [v4] : ! [v5] : ( ~ (terminates(v3, v4, v5) = 0) | ? [v6] : ? [v7] : (happens(pull, v5) = v6 & happens(push, v5) = v7 & ((v7 = 0 & v4 = backwards & v3 = pull) | (v7 = 0 & v4 = forwards & v3 = pull) | (v4 = spinning & v3 = pull & ~ (v7 = 0)) | (v4 = spinning & v3 = push & ~ (v6 = 0)) | (v4 = backwards & v3 = push & ~ (v6 = 0)) | (v4 = forwards & v3 = pull & ~ (v7 = 0))))) & ! [v3] : ! [v4] : (v4 = v3 | ~ (less_or_equal(v3, v4) = 0) | less(v3, v4) = 0) & ! [v3] : ! [v4] : (v4 = 0 | ~ (less_or_equal(v3, n8) = v4) | ? [v5] : ( ~ (v5 = 0) & less(v3, n9) = v5)) & ! [v3] : ! [v4] : (v4 = 0 | ~ (less_or_equal(v3, n7) = v4) | ? [v5] : ( ~ (v5 = 0) & less(v3, n8) = v5)) & ! [v3] : ! [v4] : (v4 = 0 | ~ (less_or_equal(v3, n6) = v4) | ? [v5] : ( ~ (v5 = 0) & less(v3, n7) = v5)) & ! [v3] : ! [v4] : (v4 = 0 | ~ (less_or_equal(v3, n5) = v4) | ? [v5] : ( ~ (v5 = 0) & less(v3, n6) = v5)) & ! [v3] : ! [v4] : (v4 = 0 | ~ (less_or_equal(v3, n4) = v4) | ? [v5] : ( ~ (v5 = 0) & less(v3, n5) = v5)) & ! [v3] : ! [v4] : (v4 = 0 | ~ (less_or_equal(v3, n3) = v4) | ? [v5] : ( ~ (v5 = 0) & less(v3, n4) = v5)) & ! [v3] : ! [v4] : (v4 = 0 | ~ (less_or_equal(v3, n2) = v4) | ? [v5] : ( ~ (v5 = 0) & less(v3, n3) = v5)) & ! [v3] : ! [v4] : (v4 = 0 | ~ (less_or_equal(v3, n1) = v4) | ? [v5] : ( ~ (v5 = 0) & less(v3, n2) = v5)) & ! [v3] : ! [v4] : (v4 = 0 | ~ (less_or_equal(v3, n0) = v4) | ? [v5] : ( ~ (v5 = 0) & less(v3, n1) = v5)) & ! [v3] : ! [v4] : (v4 = 0 | ~ (less(v3, n9) = v4) | ? [v5] : ( ~ (v5 = 0) & less_or_equal(v3, n8) = v5)) & ! [v3] : ! [v4] : (v4 = 0 | ~ (less(v3, n8) = v4) | ? [v5] : ( ~ (v5 = 0) & less_or_equal(v3, n7) = v5)) & ! [v3] : ! [v4] : (v4 = 0 | ~ (less(v3, n7) = v4) | ? [v5] : ( ~ (v5 = 0) & less_or_equal(v3, n6) = v5)) & ! [v3] : ! [v4] : (v4 = 0 | ~ (less(v3, n6) = v4) | ? [v5] : ( ~ (v5 = 0) & less_or_equal(v3, n5) = v5)) & ! [v3] : ! [v4] : (v4 = 0 | ~ (less(v3, n5) = v4) | ? [v5] : ( ~ (v5 = 0) & less_or_equal(v3, n4) = v5)) & ! [v3] : ! [v4] : (v4 = 0 | ~ (less(v3, n4) = v4) | ? [v5] : ( ~ (v5 = 0) & less_or_equal(v3, n3) = v5)) & ! [v3] : ! [v4] : (v4 = 0 | ~ (less(v3, n3) = v4) | ? [v5] : ( ~ (v5 = 0) & less_or_equal(v3, n2) = v5)) & ! [v3] : ! [v4] : (v4 = 0 | ~ (less(v3, n2) = v4) | ? [v5] : ( ~ (v5 = 0) & less_or_equal(v3, n1) = v5)) & ! [v3] : ! [v4] : (v4 = 0 | ~ (less(v3, n1) = v4) | ? [v5] : ( ~ (v5 = 0) & less_or_equal(v3, n0) = v5)) & ! [v3] : ! [v4] : ( ~ (releasedAt(v3, v4) = 0) | ? [v5] : ? [v6] : ? [v7] : (initiates(v5, v3, v4) = v6 & happens(v5, v4) = 0 & terminates(v5, v3, v4) = v7 & (v7 = 0 | v6 = 0)) | ? [v5] : (releasedAt(v3, v5) = 0 & plus(v4, n1) = v5)) & ! [v3] : ! [v4] : ~ (releasedAt(v3, v4) = 0) & ! [v3] : ! [v4] : ( ~ (holdsAt(v3, v4) = 0) | ? [v5] : ? [v6] : ? [v7] : (releasedAt(v3, v5) = v6 & plus(v4, n1) = v5 & holdsAt(v3, v5) = v7 & (v7 = 0 | v6 = 0)) | ? [v5] : (happens(v5, v4) = 0 & terminates(v5, v3, v4) = 0)) & ! [v3] : ! [v4] : ( ~ (happens(v3, v4) = 0) | (v4 = n2 & v3 = pull) | (v4 = n2 & v3 = push) | (v4 = n1 & v3 = pull) | (v4 = n0 & v3 = push)) & ! [v3] : ! [v4] : ( ~ (less(v3, v4) = 0) | ( ~ (v4 = v3) & ? [v5] : ( ~ (v5 = 0) & less(v4, v3) = v5))) & ! [v3] : ( ~ (less_or_equal(v3, n8) = 0) | less(v3, n9) = 0) & ! [v3] : ( ~ (less_or_equal(v3, n7) = 0) | less(v3, n8) = 0) & ! [v3] : ( ~ (less_or_equal(v3, n6) = 0) | less(v3, n7) = 0) & ! [v3] : ( ~ (less_or_equal(v3, n5) = 0) | less(v3, n6) = 0) & ! [v3] : ( ~ (less_or_equal(v3, n4) = 0) | less(v3, n5) = 0) & ! [v3] : ( ~ (less_or_equal(v3, n3) = 0) | less(v3, n4) = 0) & ! [v3] : ( ~ (less_or_equal(v3, n2) = 0) | less(v3, n3) = 0) & ! [v3] : ( ~ (less_or_equal(v3, n1) = 0) | less(v3, n2) = 0) & ! [v3] : ( ~ (less_or_equal(v3, n0) = 0) | less(v3, n1) = 0) & ! [v3] : ( ~ (less(v3, n9) = 0) | less_or_equal(v3, n8) = 0) & ! [v3] : ( ~ (less(v3, n8) = 0) | less_or_equal(v3, n7) = 0) & ! [v3] : ( ~ (less(v3, n7) = 0) | less_or_equal(v3, n6) = 0) & ! [v3] : ( ~ (less(v3, n6) = 0) | less_or_equal(v3, n5) = 0) & ! [v3] : ( ~ (less(v3, n5) = 0) | less_or_equal(v3, n4) = 0) & ! [v3] : ( ~ (less(v3, n4) = 0) | less_or_equal(v3, n3) = 0) & ! [v3] : ( ~ (less(v3, n3) = 0) | less_or_equal(v3, n2) = 0) & ! [v3] : ( ~ (less(v3, n2) = 0) | less_or_equal(v3, n1) = 0) & ! [v3] : ( ~ (less(v3, n1) = 0) | less_or_equal(v3, n0) = 0) & ! [v3] : ~ (less(v3, n0) = 0))
% 32.88/8.32 | Applying alpha-rule on (0) yields:
% 32.88/8.32 | (1) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (terminates(v4, v3, v2) = v1) | ~ (terminates(v4, v3, v2) = v0))
% 32.88/8.32 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (less_or_equal(v3, v2) = v1) | ~ (less_or_equal(v3, v2) = v0))
% 32.88/8.32 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (antitrajectory(v5, v4, v3, v2) = v1) | ~ (antitrajectory(v5, v4, v3, v2) = v0))
% 32.88/8.32 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (holdsAt(v3, v2) = v1) | ~ (holdsAt(v3, v2) = v0))
% 32.88/8.32 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (trajectory(v5, v4, v3, v2) = v1) | ~ (trajectory(v5, v4, v3, v2) = v0))
% 32.88/8.32 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (stoppedIn(v4, v3, v2) = v1) | ~ (stoppedIn(v4, v3, v2) = v0))
% 32.88/8.32 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (releasedAt(v3, v2) = v1) | ~ (releasedAt(v3, v2) = v0))
% 32.88/8.32 | (8) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = 0) & ~ (v1 = 0) & ~ (v0 = 0) & ~ (spinning = backwards) & ~ (spinning = forwards) & ~ (backwards = forwards) & ~ (pull = push) & plus(n3, n3) = n6 & plus(n2, n3) = n5 & plus(n2, n2) = n4 & plus(n1, n3) = n4 & plus(n1, n2) = n3 & plus(n1, n1) = n2 & plus(n0, n3) = n3 & plus(n0, n2) = n2 & plus(n0, n1) = n1 & plus(n0, n0) = n0 & holdsAt(spinning, n1) = 0 & holdsAt(spinning, n0) = v2 & holdsAt(backwards, n0) = v1 & holdsAt(forwards, n0) = v0 & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (plus(v4, v7) = v8) | ~ (holdsAt(v6, v8) = v10) | ~ (stoppedIn(v4, v5, v8) = v9) | ~ (happens(v3, v4) = 0) | ? [v11] : ? [v12] : ? [v13] : (trajectory(v5, v4, v6, v7) = v13 & initiates(v3, v5, v4) = v11 & less(n0, v7) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0)))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (plus(v4, v6) = v8) | ~ (holdsAt(v7, v8) = v10) | ~ (startedIn(v4, v5, v8) = v9) | ~ (happens(v3, v4) = 0) | ? [v11] : ? [v12] : ? [v13] : (antitrajectory(v5, v4, v7, v6) = v13 & less(n0, v6) = v12 & terminates(v3, v5, v4) = v11 & ( ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0)))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (plus(v4, v7) = v8) | ~ (holdsAt(v6, v8) = v9) | ~ (initiates(v3, v5, v4) = 0) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : (trajectory(v5, v4, v6, v7) = v12 & stoppedIn(v4, v5, v8) = v13 & happens(v3, v4) = v10 & less(n0, v7) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0) | ~ (v10 = 0) | v13 = 0))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (plus(v4, v6) = v8) | ~ (holdsAt(v7, v8) = v9) | ~ (terminates(v3, v5, v4) = 0) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : (antitrajectory(v5, v4, v7, v6) = v12 & startedIn(v4, v5, v8) = v13 & happens(v3, v4) = v10 & less(n0, v6) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0) | ~ (v10 = 0) | v13 = 0))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (releasedAt(v5, v6) = v7) | ~ (plus(v4, n1) = v6) | ~ (happens(v3, v4) = 0) | ? [v8] : ( ~ (v8 = 0) & releases(v3, v5, v4) = v8)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (plus(v4, n1) = v6) | ~ (holdsAt(v5, v6) = v7) | ~ (happens(v3, v4) = 0) | ? [v8] : ( ~ (v8 = 0) & initiates(v3, v5, v4) = v8)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (antitrajectory(v5, v4, v7, v6) = 0) | ~ (happens(v3, v4) = 0) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : (plus(v4, v6) = v10 & holdsAt(v7, v10) = v12 & startedIn(v4, v5, v10) = v11 & less(n0, v6) = v9 & terminates(v3, v5, v4) = v8 & ( ~ (v9 = 0) | ~ (v8 = 0) | v12 = 0 | v11 = 0))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (antitrajectory(v5, v4, v7, v6) = 0) | ~ (terminates(v3, v5, v4) = 0) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : (plus(v4, v6) = v10 & holdsAt(v7, v10) = v12 & startedIn(v4, v5, v10) = v11 & happens(v3, v4) = v8 & less(n0, v6) = v9 & ( ~ (v9 = 0) | ~ (v8 = 0) | v12 = 0 | v11 = 0))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (trajectory(v5, v4, v6, v7) = 0) | ~ (initiates(v3, v5, v4) = 0) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : (plus(v4, v7) = v10 & holdsAt(v6, v10) = v12 & stoppedIn(v4, v5, v10) = v11 & happens(v3, v4) = v8 & less(n0, v7) = v9 & ( ~ (v9 = 0) | ~ (v8 = 0) | v12 = 0 | v11 = 0))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (trajectory(v5, v4, v6, v7) = 0) | ~ (happens(v3, v4) = 0) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : (plus(v4, v7) = v10 & holdsAt(v6, v10) = v12 & initiates(v3, v5, v4) = v8 & stoppedIn(v4, v5, v10) = v11 & less(n0, v7) = v9 & ( ~ (v9 = 0) | ~ (v8 = 0) | v12 = 0 | v11 = 0))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (releasedAt(v3, v5) = v6) | ~ (plus(v4, n1) = v5) | ? [v7] : ? [v8] : ? [v9] : (initiates(v7, v3, v4) = v8 & happens(v7, v4) = 0 & terminates(v7, v3, v4) = v9 & (v9 = 0 | v8 = 0)) | ? [v7] : ( ~ (v7 = 0) & releasedAt(v3, v4) = v7)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (releasedAt(v3, v5) = v6) | ~ (plus(v4, n1) = v5) | ? [v7] : ? [v8] : (holdsAt(v3, v5) = v8 & holdsAt(v3, v4) = v7 & ( ~ (v8 = 0) | v7 = 0)) | ? [v7] : (initiates(v7, v3, v4) = 0 & happens(v7, v4) = 0)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (releasedAt(v3, v5) = v6) | ~ (plus(v4, n1) = v5) | ? [v7] : ? [v8] : (holdsAt(v3, v5) = v8 & holdsAt(v3, v4) = v7 & ( ~ (v7 = 0) | v8 = 0)) | ? [v7] : (happens(v7, v4) = 0 & terminates(v7, v3, v4) = 0)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (plus(v4, n1) = v5) | ~ (holdsAt(v3, v5) = v6) | ? [v7] : ? [v8] : (releasedAt(v3, v5) = v8 & holdsAt(v3, v4) = v7 & ( ~ (v7 = 0) | v8 = 0)) | ? [v7] : (happens(v7, v4) = 0 & terminates(v7, v3, v4) = 0)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (startedIn(v3, v5, v4) = v6) | ( ! [v7] : ! [v8] : ( ~ (initiates(v7, v5, v8) = 0) | ? [v9] : ? [v10] : ? [v11] : (happens(v7, v8) = v9 & less(v8, v4) = v11 & less(v3, v8) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0) | ~ (v9 = 0)))) & ! [v7] : ! [v8] : ( ~ (happens(v7, v8) = 0) | ? [v9] : ? [v10] : ? [v11] : (initiates(v7, v5, v8) = v11 & less(v8, v4) = v10 & less(v3, v8) = v9 & ( ~ (v11 = 0) | ~ (v10 = 0) | ~ (v9 = 0)))))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (initiates(v3, v4, v5) = v6) | ? [v7] : ? [v8] : (happens(pull, v5) = v7 & happens(push, v5) = v8 & ( ~ (v8 = 0) | ~ (v4 = spinning) | ~ (v3 = pull)) & ( ~ (v4 = backwards) | ~ (v3 = pull) | v8 = 0) & ( ~ (v4 = forwards) | ~ (v3 = push) | v7 = 0))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (stoppedIn(v3, v4, v5) = v6) | ( ! [v7] : ! [v8] : ( ~ (happens(v7, v8) = 0) | ? [v9] : ? [v10] : ? [v11] : (less(v8, v5) = v10 & less(v3, v8) = v9 & terminates(v7, v4, v8) = v11 & ( ~ (v11 = 0) | ~ (v10 = 0) | ~ (v9 = 0)))) & ! [v7] : ! [v8] : ( ~ (terminates(v7, v4, v8) = 0) | ? [v9] : ? [v10] : ? [v11] : (happens(v7, v8) = v9 & less(v8, v5) = v11 & less(v3, v8) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0) | ~ (v9 = 0)))))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (terminates(v3, v4, v5) = v6) | ? [v7] : ? [v8] : (happens(pull, v5) = v7 & happens(push, v5) = v8 & ( ~ (v8 = 0) | ~ (v4 = backwards) | ~ (v3 = pull)) & ( ~ (v8 = 0) | ~ (v4 = forwards) | ~ (v3 = pull)) & ( ~ (v4 = spinning) | ~ (v3 = pull) | v8 = 0) & ( ~ (v4 = spinning) | ~ (v3 = push) | v7 = 0) & ( ~ (v4 = backwards) | ~ (v3 = push) | v7 = 0) & ( ~ (v4 = forwards) | ~ (v3 = pull) | v8 = 0))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (releasedAt(v5, v6) = 0) | ~ (plus(v4, n1) = v6) | ~ (happens(v3, v4) = 0) | ? [v7] : ? [v8] : ( ~ (v8 = 0) & ~ (v7 = 0) & initiates(v3, v5, v4) = v7 & terminates(v3, v5, v4) = v8)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (plus(v4, n1) = v6) | ~ (holdsAt(v5, v6) = 0) | ~ (happens(v3, v4) = 0) | ? [v7] : ( ~ (v7 = 0) & terminates(v3, v5, v4) = v7)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (initiates(v3, v5, v4) = v6) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : (releasedAt(v5, v9) = v10 & plus(v4, n1) = v9 & happens(v3, v4) = v7 & terminates(v3, v5, v4) = v8 & ( ~ (v10 = 0) | ~ (v7 = 0) | ( ~ (v8 = 0) & ~ (v6 = 0))))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (terminates(v3, v5, v4) = v6) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : (releasedAt(v5, v9) = v10 & plus(v4, n1) = v9 & initiates(v3, v5, v4) = v8 & happens(v3, v4) = v7 & ( ~ (v10 = 0) | ~ (v7 = 0) | ( ~ (v8 = 0) & ~ (v6 = 0))))) & ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = v3 | ~ (less(v4, v3) = v5) | less(v3, v4) = 0) & ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = v3 | ~ (less(v3, v4) = v5) | less(v4, v3) = 0) & ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = v3 | ~ (less(v3, v4) = v5) | ? [v6] : ( ~ (v6 = 0) & less_or_equal(v3, v4) = v6)) & ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (less_or_equal(v3, v4) = v5) | ( ~ (v4 = v3) & ? [v6] : ( ~ (v6 = 0) & less(v3, v4) = v6))) & ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (releasedAt(v3, v4) = v5) | ? [v6] : ? [v7] : ( ~ (v7 = 0) & releasedAt(v3, v6) = v7 & plus(v4, n1) = v6) | ? [v6] : (releases(v6, v3, v4) = 0 & happens(v6, v4) = 0)) & ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (holdsAt(v3, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : (releasedAt(v3, v6) = v7 & plus(v4, n1) = v6 & holdsAt(v3, v6) = v8 & ( ~ (v8 = 0) | v7 = 0)) | ? [v6] : (initiates(v6, v3, v4) = 0 & happens(v6, v4) = 0)) & ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (happens(v3, v4) = v5) | (( ~ (v4 = n2) | ~ (v3 = pull)) & ( ~ (v4 = n2) | ~ (v3 = push)) & ( ~ (v4 = n1) | ~ (v3 = pull)) & ( ~ (v4 = n0) | ~ (v3 = push)))) & ! [v3] : ! [v4] : ! [v5] : ( ~ (releases(v3, v5, v4) = 0) | ? [v6] : ? [v7] : ? [v8] : (releasedAt(v5, v7) = v8 & plus(v4, n1) = v7 & happens(v3, v4) = v6 & ( ~ (v6 = 0) | v8 = 0))) & ! [v3] : ! [v4] : ! [v5] : ~ (releases(v3, v4, v5) = 0) & ! [v3] : ! [v4] : ! [v5] : ( ~ (releasedAt(v3, v5) = 0) | ~ (plus(v4, n1) = v5) | releasedAt(v3, v4) = 0 | ? [v6] : (releases(v6, v3, v4) = 0 & happens(v6, v4) = 0)) & ! [v3] : ! [v4] : ! [v5] : ( ~ (plus(v4, v3) = v5) | plus(v3, v4) = v5) & ! [v3] : ! [v4] : ! [v5] : ( ~ (plus(v4, n1) = v5) | ~ (holdsAt(v3, v5) = 0) | ? [v6] : ? [v7] : (releasedAt(v3, v5) = v7 & holdsAt(v3, v4) = v6 & (v7 = 0 | v6 = 0)) | ? [v6] : (initiates(v6, v3, v4) = 0 & happens(v6, v4) = 0)) & ! [v3] : ! [v4] : ! [v5] : ( ~ (plus(v3, v4) = v5) | plus(v4, v3) = v5) & ! [v3] : ! [v4] : ! [v5] : ( ~ (startedIn(v3, v5, v4) = 0) | ? [v6] : ? [v7] : (initiates(v6, v5, v7) = 0 & happens(v6, v7) = 0 & less(v7, v4) = 0 & less(v3, v7) = 0)) & ! [v3] : ! [v4] : ! [v5] : ( ~ (initiates(v3, v5, v4) = 0) | ? [v6] : ? [v7] : ? [v8] : (plus(v4, n1) = v7 & holdsAt(v5, v7) = v8 & happens(v3, v4) = v6 & ( ~ (v6 = 0) | v8 = 0))) & ! [v3] : ! [v4] : ! [v5] : ( ~ (initiates(v3, v4, v5) = 0) | ? [v6] : ? [v7] : (happens(pull, v5) = v6 & happens(push, v5) = v7 & ((v7 = 0 & v4 = spinning & v3 = pull) | (v4 = backwards & v3 = pull & ~ (v7 = 0)) | (v4 = forwards & v3 = push & ~ (v6 = 0))))) & ! [v3] : ! [v4] : ! [v5] : ( ~ (stoppedIn(v3, v4, v5) = 0) | ? [v6] : ? [v7] : (happens(v6, v7) = 0 & less(v7, v5) = 0 & less(v3, v7) = 0 & terminates(v6, v4, v7) = 0)) & ! [v3] : ! [v4] : ! [v5] : ( ~ (less(v4, v3) = v5) | ? [v6] : ( ~ (v6 = 0) & less(v3, v4) = v6) | ( ~ (v5 = 0) & ~ (v4 = v3))) & ! [v3] : ! [v4] : ! [v5] : ( ~ (less(v3, v4) = v5) | less_or_equal(v3, v4) = 0 | ( ~ (v5 = 0) & ~ (v4 = v3))) & ! [v3] : ! [v4] : ! [v5] : ( ~ (terminates(v3, v5, v4) = 0) | ? [v6] : ? [v7] : ? [v8] : (plus(v4, n1) = v7 & holdsAt(v5, v7) = v8 & happens(v3, v4) = v6 & ( ~ (v8 = 0) | ~ (v6 = 0)))) & ! [v3] : ! [v4] : ! [v5] : ( ~ (terminates(v3, v4, v5) = 0) | ? [v6] : ? [v7] : (happens(pull, v5) = v6 & happens(push, v5) = v7 & ((v7 = 0 & v4 = backwards & v3 = pull) | (v7 = 0 & v4 = forwards & v3 = pull) | (v4 = spinning & v3 = pull & ~ (v7 = 0)) | (v4 = spinning & v3 = push & ~ (v6 = 0)) | (v4 = backwards & v3 = push & ~ (v6 = 0)) | (v4 = forwards & v3 = pull & ~ (v7 = 0))))) & ! [v3] : ! [v4] : (v4 = v3 | ~ (less_or_equal(v3, v4) = 0) | less(v3, v4) = 0) & ! [v3] : ! [v4] : (v4 = 0 | ~ (less_or_equal(v3, n8) = v4) | ? [v5] : ( ~ (v5 = 0) & less(v3, n9) = v5)) & ! [v3] : ! [v4] : (v4 = 0 | ~ (less_or_equal(v3, n7) = v4) | ? [v5] : ( ~ (v5 = 0) & less(v3, n8) = v5)) & ! [v3] : ! [v4] : (v4 = 0 | ~ (less_or_equal(v3, n6) = v4) | ? [v5] : ( ~ (v5 = 0) & less(v3, n7) = v5)) & ! [v3] : ! [v4] : (v4 = 0 | ~ (less_or_equal(v3, n5) = v4) | ? [v5] : ( ~ (v5 = 0) & less(v3, n6) = v5)) & ! [v3] : ! [v4] : (v4 = 0 | ~ (less_or_equal(v3, n4) = v4) | ? [v5] : ( ~ (v5 = 0) & less(v3, n5) = v5)) & ! [v3] : ! [v4] : (v4 = 0 | ~ (less_or_equal(v3, n3) = v4) | ? [v5] : ( ~ (v5 = 0) & less(v3, n4) = v5)) & ! [v3] : ! [v4] : (v4 = 0 | ~ (less_or_equal(v3, n2) = v4) | ? [v5] : ( ~ (v5 = 0) & less(v3, n3) = v5)) & ! [v3] : ! [v4] : (v4 = 0 | ~ (less_or_equal(v3, n1) = v4) | ? [v5] : ( ~ (v5 = 0) & less(v3, n2) = v5)) & ! [v3] : ! [v4] : (v4 = 0 | ~ (less_or_equal(v3, n0) = v4) | ? [v5] : ( ~ (v5 = 0) & less(v3, n1) = v5)) & ! [v3] : ! [v4] : (v4 = 0 | ~ (less(v3, n9) = v4) | ? [v5] : ( ~ (v5 = 0) & less_or_equal(v3, n8) = v5)) & ! [v3] : ! [v4] : (v4 = 0 | ~ (less(v3, n8) = v4) | ? [v5] : ( ~ (v5 = 0) & less_or_equal(v3, n7) = v5)) & ! [v3] : ! [v4] : (v4 = 0 | ~ (less(v3, n7) = v4) | ? [v5] : ( ~ (v5 = 0) & less_or_equal(v3, n6) = v5)) & ! [v3] : ! [v4] : (v4 = 0 | ~ (less(v3, n6) = v4) | ? [v5] : ( ~ (v5 = 0) & less_or_equal(v3, n5) = v5)) & ! [v3] : ! [v4] : (v4 = 0 | ~ (less(v3, n5) = v4) | ? [v5] : ( ~ (v5 = 0) & less_or_equal(v3, n4) = v5)) & ! [v3] : ! [v4] : (v4 = 0 | ~ (less(v3, n4) = v4) | ? [v5] : ( ~ (v5 = 0) & less_or_equal(v3, n3) = v5)) & ! [v3] : ! [v4] : (v4 = 0 | ~ (less(v3, n3) = v4) | ? [v5] : ( ~ (v5 = 0) & less_or_equal(v3, n2) = v5)) & ! [v3] : ! [v4] : (v4 = 0 | ~ (less(v3, n2) = v4) | ? [v5] : ( ~ (v5 = 0) & less_or_equal(v3, n1) = v5)) & ! [v3] : ! [v4] : (v4 = 0 | ~ (less(v3, n1) = v4) | ? [v5] : ( ~ (v5 = 0) & less_or_equal(v3, n0) = v5)) & ! [v3] : ! [v4] : ( ~ (releasedAt(v3, v4) = 0) | ? [v5] : ? [v6] : ? [v7] : (initiates(v5, v3, v4) = v6 & happens(v5, v4) = 0 & terminates(v5, v3, v4) = v7 & (v7 = 0 | v6 = 0)) | ? [v5] : (releasedAt(v3, v5) = 0 & plus(v4, n1) = v5)) & ! [v3] : ! [v4] : ~ (releasedAt(v3, v4) = 0) & ! [v3] : ! [v4] : ( ~ (holdsAt(v3, v4) = 0) | ? [v5] : ? [v6] : ? [v7] : (releasedAt(v3, v5) = v6 & plus(v4, n1) = v5 & holdsAt(v3, v5) = v7 & (v7 = 0 | v6 = 0)) | ? [v5] : (happens(v5, v4) = 0 & terminates(v5, v3, v4) = 0)) & ! [v3] : ! [v4] : ( ~ (happens(v3, v4) = 0) | (v4 = n2 & v3 = pull) | (v4 = n2 & v3 = push) | (v4 = n1 & v3 = pull) | (v4 = n0 & v3 = push)) & ! [v3] : ! [v4] : ( ~ (less(v3, v4) = 0) | ( ~ (v4 = v3) & ? [v5] : ( ~ (v5 = 0) & less(v4, v3) = v5))) & ! [v3] : ( ~ (less_or_equal(v3, n8) = 0) | less(v3, n9) = 0) & ! [v3] : ( ~ (less_or_equal(v3, n7) = 0) | less(v3, n8) = 0) & ! [v3] : ( ~ (less_or_equal(v3, n6) = 0) | less(v3, n7) = 0) & ! [v3] : ( ~ (less_or_equal(v3, n5) = 0) | less(v3, n6) = 0) & ! [v3] : ( ~ (less_or_equal(v3, n4) = 0) | less(v3, n5) = 0) & ! [v3] : ( ~ (less_or_equal(v3, n3) = 0) | less(v3, n4) = 0) & ! [v3] : ( ~ (less_or_equal(v3, n2) = 0) | less(v3, n3) = 0) & ! [v3] : ( ~ (less_or_equal(v3, n1) = 0) | less(v3, n2) = 0) & ! [v3] : ( ~ (less_or_equal(v3, n0) = 0) | less(v3, n1) = 0) & ! [v3] : ( ~ (less(v3, n9) = 0) | less_or_equal(v3, n8) = 0) & ! [v3] : ( ~ (less(v3, n8) = 0) | less_or_equal(v3, n7) = 0) & ! [v3] : ( ~ (less(v3, n7) = 0) | less_or_equal(v3, n6) = 0) & ! [v3] : ( ~ (less(v3, n6) = 0) | less_or_equal(v3, n5) = 0) & ! [v3] : ( ~ (less(v3, n5) = 0) | less_or_equal(v3, n4) = 0) & ! [v3] : ( ~ (less(v3, n4) = 0) | less_or_equal(v3, n3) = 0) & ! [v3] : ( ~ (less(v3, n3) = 0) | less_or_equal(v3, n2) = 0) & ! [v3] : ( ~ (less(v3, n2) = 0) | less_or_equal(v3, n1) = 0) & ! [v3] : ( ~ (less(v3, n1) = 0) | less_or_equal(v3, n0) = 0) & ! [v3] : ~ (less(v3, n0) = 0))
% 32.88/8.34 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (plus(v3, v2) = v1) | ~ (plus(v3, v2) = v0))
% 32.88/8.34 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (happens(v3, v2) = v1) | ~ (happens(v3, v2) = v0))
% 32.88/8.34 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (initiates(v4, v3, v2) = v1) | ~ (initiates(v4, v3, v2) = v0))
% 32.88/8.34 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (releases(v4, v3, v2) = v1) | ~ (releases(v4, v3, v2) = v0))
% 32.88/8.34 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (startedIn(v4, v3, v2) = v1) | ~ (startedIn(v4, v3, v2) = v0))
% 32.88/8.34 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (less(v3, v2) = v1) | ~ (less(v3, v2) = v0))
% 32.88/8.34 |
% 32.88/8.34 | Instantiating (8) with all_1_0_0, all_1_1_1, all_1_2_2 yields:
% 32.88/8.34 | (15) ~ (all_1_0_0 = 0) & ~ (all_1_1_1 = 0) & ~ (all_1_2_2 = 0) & ~ (spinning = backwards) & ~ (spinning = forwards) & ~ (backwards = forwards) & ~ (pull = push) & plus(n3, n3) = n6 & plus(n2, n3) = n5 & plus(n2, n2) = n4 & plus(n1, n3) = n4 & plus(n1, n2) = n3 & plus(n1, n1) = n2 & plus(n0, n3) = n3 & plus(n0, n2) = n2 & plus(n0, n1) = n1 & plus(n0, n0) = n0 & holdsAt(spinning, n1) = 0 & holdsAt(spinning, n0) = all_1_0_0 & holdsAt(backwards, n0) = all_1_1_1 & holdsAt(forwards, n0) = all_1_2_2 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v6 = 0 | ~ (plus(v1, v4) = v5) | ~ (holdsAt(v3, v5) = v7) | ~ (stoppedIn(v1, v2, v5) = v6) | ~ (happens(v0, v1) = 0) | ? [v8] : ? [v9] : ? [v10] : (trajectory(v2, v1, v3, v4) = v10 & initiates(v0, v2, v1) = v8 & less(n0, v4) = v9 & ( ~ (v10 = 0) | ~ (v9 = 0) | ~ (v8 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v6 = 0 | ~ (plus(v1, v3) = v5) | ~ (holdsAt(v4, v5) = v7) | ~ (startedIn(v1, v2, v5) = v6) | ~ (happens(v0, v1) = 0) | ? [v8] : ? [v9] : ? [v10] : (antitrajectory(v2, v1, v4, v3) = v10 & less(n0, v3) = v9 & terminates(v0, v2, v1) = v8 & ( ~ (v10 = 0) | ~ (v9 = 0) | ~ (v8 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (plus(v1, v4) = v5) | ~ (holdsAt(v3, v5) = v6) | ~ (initiates(v0, v2, v1) = 0) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : (trajectory(v2, v1, v3, v4) = v9 & stoppedIn(v1, v2, v5) = v10 & happens(v0, v1) = v7 & less(n0, v4) = v8 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | v10 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (plus(v1, v3) = v5) | ~ (holdsAt(v4, v5) = v6) | ~ (terminates(v0, v2, v1) = 0) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : (antitrajectory(v2, v1, v4, v3) = v9 & startedIn(v1, v2, v5) = v10 & happens(v0, v1) = v7 & less(n0, v3) = v8 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | v10 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (releasedAt(v2, v3) = v4) | ~ (plus(v1, n1) = v3) | ~ (happens(v0, v1) = 0) | ? [v5] : ( ~ (v5 = 0) & releases(v0, v2, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (plus(v1, n1) = v3) | ~ (holdsAt(v2, v3) = v4) | ~ (happens(v0, v1) = 0) | ? [v5] : ( ~ (v5 = 0) & initiates(v0, v2, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (antitrajectory(v2, v1, v4, v3) = 0) | ~ (happens(v0, v1) = 0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (plus(v1, v3) = v7 & holdsAt(v4, v7) = v9 & startedIn(v1, v2, v7) = v8 & less(n0, v3) = v6 & terminates(v0, v2, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | v9 = 0 | v8 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (antitrajectory(v2, v1, v4, v3) = 0) | ~ (terminates(v0, v2, v1) = 0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (plus(v1, v3) = v7 & holdsAt(v4, v7) = v9 & startedIn(v1, v2, v7) = v8 & happens(v0, v1) = v5 & less(n0, v3) = v6 & ( ~ (v6 = 0) | ~ (v5 = 0) | v9 = 0 | v8 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (trajectory(v2, v1, v3, v4) = 0) | ~ (initiates(v0, v2, v1) = 0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (plus(v1, v4) = v7 & holdsAt(v3, v7) = v9 & stoppedIn(v1, v2, v7) = v8 & happens(v0, v1) = v5 & less(n0, v4) = v6 & ( ~ (v6 = 0) | ~ (v5 = 0) | v9 = 0 | v8 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (trajectory(v2, v1, v3, v4) = 0) | ~ (happens(v0, v1) = 0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (plus(v1, v4) = v7 & holdsAt(v3, v7) = v9 & initiates(v0, v2, v1) = v5 & stoppedIn(v1, v2, v7) = v8 & less(n0, v4) = v6 & ( ~ (v6 = 0) | ~ (v5 = 0) | v9 = 0 | v8 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (releasedAt(v0, v2) = v3) | ~ (plus(v1, n1) = v2) | ? [v4] : ? [v5] : ? [v6] : (initiates(v4, v0, v1) = v5 & happens(v4, v1) = 0 & terminates(v4, v0, v1) = v6 & (v6 = 0 | v5 = 0)) | ? [v4] : ( ~ (v4 = 0) & releasedAt(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (releasedAt(v0, v2) = v3) | ~ (plus(v1, n1) = v2) | ? [v4] : ? [v5] : (holdsAt(v0, v2) = v5 & holdsAt(v0, v1) = v4 & ( ~ (v5 = 0) | v4 = 0)) | ? [v4] : (initiates(v4, v0, v1) = 0 & happens(v4, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (releasedAt(v0, v2) = v3) | ~ (plus(v1, n1) = v2) | ? [v4] : ? [v5] : (holdsAt(v0, v2) = v5 & holdsAt(v0, v1) = v4 & ( ~ (v4 = 0) | v5 = 0)) | ? [v4] : (happens(v4, v1) = 0 & terminates(v4, v0, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (plus(v1, n1) = v2) | ~ (holdsAt(v0, v2) = v3) | ? [v4] : ? [v5] : (releasedAt(v0, v2) = v5 & holdsAt(v0, v1) = v4 & ( ~ (v4 = 0) | v5 = 0)) | ? [v4] : (happens(v4, v1) = 0 & terminates(v4, v0, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (startedIn(v0, v2, v1) = v3) | ( ! [v4] : ! [v5] : ( ~ (initiates(v4, v2, v5) = 0) | ? [v6] : ? [v7] : ? [v8] : (happens(v4, v5) = v6 & less(v5, v1) = v8 & less(v0, v5) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v4] : ! [v5] : ( ~ (happens(v4, v5) = 0) | ? [v6] : ? [v7] : ? [v8] : (initiates(v4, v2, v5) = v8 & less(v5, v1) = v7 & less(v0, v5) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0)))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (initiates(v0, v1, v2) = v3) | ? [v4] : ? [v5] : (happens(pull, v2) = v4 & happens(push, v2) = v5 & ( ~ (v5 = 0) | ~ (v1 = spinning) | ~ (v0 = pull)) & ( ~ (v1 = backwards) | ~ (v0 = pull) | v5 = 0) & ( ~ (v1 = forwards) | ~ (v0 = push) | v4 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (stoppedIn(v0, v1, v2) = v3) | ( ! [v4] : ! [v5] : ( ~ (happens(v4, v5) = 0) | ? [v6] : ? [v7] : ? [v8] : (less(v5, v2) = v7 & less(v0, v5) = v6 & terminates(v4, v1, v5) = v8 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v4] : ! [v5] : ( ~ (terminates(v4, v1, v5) = 0) | ? [v6] : ? [v7] : ? [v8] : (happens(v4, v5) = v6 & less(v5, v2) = v8 & less(v0, v5) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0)))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (terminates(v0, v1, v2) = v3) | ? [v4] : ? [v5] : (happens(pull, v2) = v4 & happens(push, v2) = v5 & ( ~ (v5 = 0) | ~ (v1 = backwards) | ~ (v0 = pull)) & ( ~ (v5 = 0) | ~ (v1 = forwards) | ~ (v0 = pull)) & ( ~ (v1 = spinning) | ~ (v0 = pull) | v5 = 0) & ( ~ (v1 = spinning) | ~ (v0 = push) | v4 = 0) & ( ~ (v1 = backwards) | ~ (v0 = push) | v4 = 0) & ( ~ (v1 = forwards) | ~ (v0 = pull) | v5 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (releasedAt(v2, v3) = 0) | ~ (plus(v1, n1) = v3) | ~ (happens(v0, v1) = 0) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & ~ (v4 = 0) & initiates(v0, v2, v1) = v4 & terminates(v0, v2, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (plus(v1, n1) = v3) | ~ (holdsAt(v2, v3) = 0) | ~ (happens(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & terminates(v0, v2, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (initiates(v0, v2, v1) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (releasedAt(v2, v6) = v7 & plus(v1, n1) = v6 & happens(v0, v1) = v4 & terminates(v0, v2, v1) = v5 & ( ~ (v7 = 0) | ~ (v4 = 0) | ( ~ (v5 = 0) & ~ (v3 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (terminates(v0, v2, v1) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (releasedAt(v2, v6) = v7 & plus(v1, n1) = v6 & initiates(v0, v2, v1) = v5 & happens(v0, v1) = v4 & ( ~ (v7 = 0) | ~ (v4 = 0) | ( ~ (v5 = 0) & ~ (v3 = 0))))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (less(v1, v0) = v2) | less(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (less(v0, v1) = v2) | less(v1, v0) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (less(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & less_or_equal(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (less_or_equal(v0, v1) = v2) | ( ~ (v1 = v0) & ? [v3] : ( ~ (v3 = 0) & less(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (releasedAt(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & releasedAt(v0, v3) = v4 & plus(v1, n1) = v3) | ? [v3] : (releases(v3, v0, v1) = 0 & happens(v3, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (holdsAt(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (releasedAt(v0, v3) = v4 & plus(v1, n1) = v3 & holdsAt(v0, v3) = v5 & ( ~ (v5 = 0) | v4 = 0)) | ? [v3] : (initiates(v3, v0, v1) = 0 & happens(v3, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (happens(v0, v1) = v2) | (( ~ (v1 = n2) | ~ (v0 = pull)) & ( ~ (v1 = n2) | ~ (v0 = push)) & ( ~ (v1 = n1) | ~ (v0 = pull)) & ( ~ (v1 = n0) | ~ (v0 = push)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (releases(v0, v2, v1) = 0) | ? [v3] : ? [v4] : ? [v5] : (releasedAt(v2, v4) = v5 & plus(v1, n1) = v4 & happens(v0, v1) = v3 & ( ~ (v3 = 0) | v5 = 0))) & ! [v0] : ! [v1] : ! [v2] : ~ (releases(v0, v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (releasedAt(v0, v2) = 0) | ~ (plus(v1, n1) = v2) | releasedAt(v0, v1) = 0 | ? [v3] : (releases(v3, v0, v1) = 0 & happens(v3, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (plus(v1, v0) = v2) | plus(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (plus(v1, n1) = v2) | ~ (holdsAt(v0, v2) = 0) | ? [v3] : ? [v4] : (releasedAt(v0, v2) = v4 & holdsAt(v0, v1) = v3 & (v4 = 0 | v3 = 0)) | ? [v3] : (initiates(v3, v0, v1) = 0 & happens(v3, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (plus(v0, v1) = v2) | plus(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (startedIn(v0, v2, v1) = 0) | ? [v3] : ? [v4] : (initiates(v3, v2, v4) = 0 & happens(v3, v4) = 0 & less(v4, v1) = 0 & less(v0, v4) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (initiates(v0, v2, v1) = 0) | ? [v3] : ? [v4] : ? [v5] : (plus(v1, n1) = v4 & holdsAt(v2, v4) = v5 & happens(v0, v1) = v3 & ( ~ (v3 = 0) | v5 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (initiates(v0, v1, v2) = 0) | ? [v3] : ? [v4] : (happens(pull, v2) = v3 & happens(push, v2) = v4 & ((v4 = 0 & v1 = spinning & v0 = pull) | (v1 = backwards & v0 = pull & ~ (v4 = 0)) | (v1 = forwards & v0 = push & ~ (v3 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (stoppedIn(v0, v1, v2) = 0) | ? [v3] : ? [v4] : (happens(v3, v4) = 0 & less(v4, v2) = 0 & less(v0, v4) = 0 & terminates(v3, v1, v4) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (less(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & less(v0, v1) = v3) | ( ~ (v2 = 0) & ~ (v1 = v0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (less(v0, v1) = v2) | less_or_equal(v0, v1) = 0 | ( ~ (v2 = 0) & ~ (v1 = v0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (terminates(v0, v2, v1) = 0) | ? [v3] : ? [v4] : ? [v5] : (plus(v1, n1) = v4 & holdsAt(v2, v4) = v5 & happens(v0, v1) = v3 & ( ~ (v5 = 0) | ~ (v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (terminates(v0, v1, v2) = 0) | ? [v3] : ? [v4] : (happens(pull, v2) = v3 & happens(push, v2) = v4 & ((v4 = 0 & v1 = backwards & v0 = pull) | (v4 = 0 & v1 = forwards & v0 = pull) | (v1 = spinning & v0 = pull & ~ (v4 = 0)) | (v1 = spinning & v0 = push & ~ (v3 = 0)) | (v1 = backwards & v0 = push & ~ (v3 = 0)) | (v1 = forwards & v0 = pull & ~ (v4 = 0))))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (less_or_equal(v0, v1) = 0) | less(v0, v1) = 0) & ! [v0] : ! [v1] : (v1 = 0 | ~ (less_or_equal(v0, n8) = v1) | ? [v2] : ( ~ (v2 = 0) & less(v0, n9) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (less_or_equal(v0, n7) = v1) | ? [v2] : ( ~ (v2 = 0) & less(v0, n8) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (less_or_equal(v0, n6) = v1) | ? [v2] : ( ~ (v2 = 0) & less(v0, n7) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (less_or_equal(v0, n5) = v1) | ? [v2] : ( ~ (v2 = 0) & less(v0, n6) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (less_or_equal(v0, n4) = v1) | ? [v2] : ( ~ (v2 = 0) & less(v0, n5) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (less_or_equal(v0, n3) = v1) | ? [v2] : ( ~ (v2 = 0) & less(v0, n4) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (less_or_equal(v0, n2) = v1) | ? [v2] : ( ~ (v2 = 0) & less(v0, n3) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (less_or_equal(v0, n1) = v1) | ? [v2] : ( ~ (v2 = 0) & less(v0, n2) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (less_or_equal(v0, n0) = v1) | ? [v2] : ( ~ (v2 = 0) & less(v0, n1) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (less(v0, n9) = v1) | ? [v2] : ( ~ (v2 = 0) & less_or_equal(v0, n8) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (less(v0, n8) = v1) | ? [v2] : ( ~ (v2 = 0) & less_or_equal(v0, n7) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (less(v0, n7) = v1) | ? [v2] : ( ~ (v2 = 0) & less_or_equal(v0, n6) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (less(v0, n6) = v1) | ? [v2] : ( ~ (v2 = 0) & less_or_equal(v0, n5) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (less(v0, n5) = v1) | ? [v2] : ( ~ (v2 = 0) & less_or_equal(v0, n4) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (less(v0, n4) = v1) | ? [v2] : ( ~ (v2 = 0) & less_or_equal(v0, n3) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (less(v0, n3) = v1) | ? [v2] : ( ~ (v2 = 0) & less_or_equal(v0, n2) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (less(v0, n2) = v1) | ? [v2] : ( ~ (v2 = 0) & less_or_equal(v0, n1) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (less(v0, n1) = v1) | ? [v2] : ( ~ (v2 = 0) & less_or_equal(v0, n0) = v2)) & ! [v0] : ! [v1] : ( ~ (releasedAt(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : (initiates(v2, v0, v1) = v3 & happens(v2, v1) = 0 & terminates(v2, v0, v1) = v4 & (v4 = 0 | v3 = 0)) | ? [v2] : (releasedAt(v0, v2) = 0 & plus(v1, n1) = v2)) & ! [v0] : ! [v1] : ~ (releasedAt(v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (holdsAt(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : (releasedAt(v0, v2) = v3 & plus(v1, n1) = v2 & holdsAt(v0, v2) = v4 & (v4 = 0 | v3 = 0)) | ? [v2] : (happens(v2, v1) = 0 & terminates(v2, v0, v1) = 0)) & ! [v0] : ! [v1] : ( ~ (happens(v0, v1) = 0) | (v1 = n2 & v0 = pull) | (v1 = n2 & v0 = push) | (v1 = n1 & v0 = pull) | (v1 = n0 & v0 = push)) & ! [v0] : ! [v1] : ( ~ (less(v0, v1) = 0) | ( ~ (v1 = v0) & ? [v2] : ( ~ (v2 = 0) & less(v1, v0) = v2))) & ! [v0] : ( ~ (less_or_equal(v0, n8) = 0) | less(v0, n9) = 0) & ! [v0] : ( ~ (less_or_equal(v0, n7) = 0) | less(v0, n8) = 0) & ! [v0] : ( ~ (less_or_equal(v0, n6) = 0) | less(v0, n7) = 0) & ! [v0] : ( ~ (less_or_equal(v0, n5) = 0) | less(v0, n6) = 0) & ! [v0] : ( ~ (less_or_equal(v0, n4) = 0) | less(v0, n5) = 0) & ! [v0] : ( ~ (less_or_equal(v0, n3) = 0) | less(v0, n4) = 0) & ! [v0] : ( ~ (less_or_equal(v0, n2) = 0) | less(v0, n3) = 0) & ! [v0] : ( ~ (less_or_equal(v0, n1) = 0) | less(v0, n2) = 0) & ! [v0] : ( ~ (less_or_equal(v0, n0) = 0) | less(v0, n1) = 0) & ! [v0] : ( ~ (less(v0, n9) = 0) | less_or_equal(v0, n8) = 0) & ! [v0] : ( ~ (less(v0, n8) = 0) | less_or_equal(v0, n7) = 0) & ! [v0] : ( ~ (less(v0, n7) = 0) | less_or_equal(v0, n6) = 0) & ! [v0] : ( ~ (less(v0, n6) = 0) | less_or_equal(v0, n5) = 0) & ! [v0] : ( ~ (less(v0, n5) = 0) | less_or_equal(v0, n4) = 0) & ! [v0] : ( ~ (less(v0, n4) = 0) | less_or_equal(v0, n3) = 0) & ! [v0] : ( ~ (less(v0, n3) = 0) | less_or_equal(v0, n2) = 0) & ! [v0] : ( ~ (less(v0, n2) = 0) | less_or_equal(v0, n1) = 0) & ! [v0] : ( ~ (less(v0, n1) = 0) | less_or_equal(v0, n0) = 0) & ! [v0] : ~ (less(v0, n0) = 0)
% 32.88/8.36 |
% 32.88/8.36 | Applying alpha-rule on (15) yields:
% 32.88/8.36 | (16) ! [v0] : ! [v1] : ! [v2] : ( ~ (initiates(v0, v2, v1) = 0) | ? [v3] : ? [v4] : ? [v5] : (plus(v1, n1) = v4 & holdsAt(v2, v4) = v5 & happens(v0, v1) = v3 & ( ~ (v3 = 0) | v5 = 0)))
% 32.88/8.36 | (17) ! [v0] : ! [v1] : (v1 = 0 | ~ (less(v0, n1) = v1) | ? [v2] : ( ~ (v2 = 0) & less_or_equal(v0, n0) = v2))
% 32.88/8.36 | (18) ! [v0] : ! [v1] : (v1 = 0 | ~ (less_or_equal(v0, n0) = v1) | ? [v2] : ( ~ (v2 = 0) & less(v0, n1) = v2))
% 32.88/8.36 | (19) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (less(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & less_or_equal(v0, v1) = v3))
% 32.88/8.36 | (20) ! [v0] : ! [v1] : ! [v2] : ( ~ (plus(v0, v1) = v2) | plus(v1, v0) = v2)
% 32.88/8.36 | (21) ! [v0] : ! [v1] : ! [v2] : ( ~ (plus(v1, v0) = v2) | plus(v0, v1) = v2)
% 33.25/8.36 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (antitrajectory(v2, v1, v4, v3) = 0) | ~ (happens(v0, v1) = 0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (plus(v1, v3) = v7 & holdsAt(v4, v7) = v9 & startedIn(v1, v2, v7) = v8 & less(n0, v3) = v6 & terminates(v0, v2, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | v9 = 0 | v8 = 0)))
% 33.25/8.36 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (terminates(v0, v1, v2) = v3) | ? [v4] : ? [v5] : (happens(pull, v2) = v4 & happens(push, v2) = v5 & ( ~ (v5 = 0) | ~ (v1 = backwards) | ~ (v0 = pull)) & ( ~ (v5 = 0) | ~ (v1 = forwards) | ~ (v0 = pull)) & ( ~ (v1 = spinning) | ~ (v0 = pull) | v5 = 0) & ( ~ (v1 = spinning) | ~ (v0 = push) | v4 = 0) & ( ~ (v1 = backwards) | ~ (v0 = push) | v4 = 0) & ( ~ (v1 = forwards) | ~ (v0 = pull) | v5 = 0)))
% 33.25/8.36 | (24) ! [v0] : ! [v1] : ! [v2] : ( ~ (startedIn(v0, v2, v1) = 0) | ? [v3] : ? [v4] : (initiates(v3, v2, v4) = 0 & happens(v3, v4) = 0 & less(v4, v1) = 0 & less(v0, v4) = 0))
% 33.25/8.36 | (25) ! [v0] : ( ~ (less(v0, n3) = 0) | less_or_equal(v0, n2) = 0)
% 33.25/8.36 | (26) ! [v0] : ( ~ (less_or_equal(v0, n2) = 0) | less(v0, n3) = 0)
% 33.25/8.36 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (releasedAt(v2, v3) = v4) | ~ (plus(v1, n1) = v3) | ~ (happens(v0, v1) = 0) | ? [v5] : ( ~ (v5 = 0) & releases(v0, v2, v1) = v5))
% 33.25/8.36 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (terminates(v0, v2, v1) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (releasedAt(v2, v6) = v7 & plus(v1, n1) = v6 & initiates(v0, v2, v1) = v5 & happens(v0, v1) = v4 & ( ~ (v7 = 0) | ~ (v4 = 0) | ( ~ (v5 = 0) & ~ (v3 = 0)))))
% 33.25/8.36 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (plus(v1, v4) = v5) | ~ (holdsAt(v3, v5) = v6) | ~ (initiates(v0, v2, v1) = 0) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : (trajectory(v2, v1, v3, v4) = v9 & stoppedIn(v1, v2, v5) = v10 & happens(v0, v1) = v7 & less(n0, v4) = v8 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | v10 = 0)))
% 33.25/8.36 | (30) ! [v0] : ! [v1] : ~ (releasedAt(v0, v1) = 0)
% 33.25/8.36 | (31) ! [v0] : ~ (less(v0, n0) = 0)
% 33.25/8.36 | (32) plus(n1, n2) = n3
% 33.25/8.36 | (33) ~ (spinning = forwards)
% 33.25/8.36 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v6 = 0 | ~ (plus(v1, v4) = v5) | ~ (holdsAt(v3, v5) = v7) | ~ (stoppedIn(v1, v2, v5) = v6) | ~ (happens(v0, v1) = 0) | ? [v8] : ? [v9] : ? [v10] : (trajectory(v2, v1, v3, v4) = v10 & initiates(v0, v2, v1) = v8 & less(n0, v4) = v9 & ( ~ (v10 = 0) | ~ (v9 = 0) | ~ (v8 = 0))))
% 33.25/8.36 | (35) ! [v0] : ( ~ (less(v0, n1) = 0) | less_or_equal(v0, n0) = 0)
% 33.25/8.36 | (36) ! [v0] : ( ~ (less_or_equal(v0, n0) = 0) | less(v0, n1) = 0)
% 33.25/8.36 | (37) ! [v0] : ! [v1] : (v1 = 0 | ~ (less(v0, n3) = v1) | ? [v2] : ( ~ (v2 = 0) & less_or_equal(v0, n2) = v2))
% 33.25/8.36 | (38) ! [v0] : ! [v1] : (v1 = 0 | ~ (less_or_equal(v0, n2) = v1) | ? [v2] : ( ~ (v2 = 0) & less(v0, n3) = v2))
% 33.25/8.36 | (39) ! [v0] : ( ~ (less(v0, n4) = 0) | less_or_equal(v0, n3) = 0)
% 33.25/8.36 | (40) ! [v0] : ( ~ (less_or_equal(v0, n3) = 0) | less(v0, n4) = 0)
% 33.25/8.36 | (41) plus(n1, n3) = n4
% 33.25/8.36 | (42) ~ (all_1_0_0 = 0)
% 33.25/8.36 | (43) ! [v0] : ! [v1] : ! [v2] : ( ~ (stoppedIn(v0, v1, v2) = 0) | ? [v3] : ? [v4] : (happens(v3, v4) = 0 & less(v4, v2) = 0 & less(v0, v4) = 0 & terminates(v3, v1, v4) = 0))
% 33.25/8.36 | (44) ~ (backwards = forwards)
% 33.25/8.36 | (45) plus(n0, n3) = n3
% 33.25/8.36 | (46) ! [v0] : ! [v1] : ( ~ (releasedAt(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : (initiates(v2, v0, v1) = v3 & happens(v2, v1) = 0 & terminates(v2, v0, v1) = v4 & (v4 = 0 | v3 = 0)) | ? [v2] : (releasedAt(v0, v2) = 0 & plus(v1, n1) = v2))
% 33.25/8.37 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (startedIn(v0, v2, v1) = v3) | ( ! [v4] : ! [v5] : ( ~ (initiates(v4, v2, v5) = 0) | ? [v6] : ? [v7] : ? [v8] : (happens(v4, v5) = v6 & less(v5, v1) = v8 & less(v0, v5) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v4] : ! [v5] : ( ~ (happens(v4, v5) = 0) | ? [v6] : ? [v7] : ? [v8] : (initiates(v4, v2, v5) = v8 & less(v5, v1) = v7 & less(v0, v5) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0))))))
% 33.25/8.37 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (initiates(v0, v2, v1) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (releasedAt(v2, v6) = v7 & plus(v1, n1) = v6 & happens(v0, v1) = v4 & terminates(v0, v2, v1) = v5 & ( ~ (v7 = 0) | ~ (v4 = 0) | ( ~ (v5 = 0) & ~ (v3 = 0)))))
% 33.25/8.37 | (49) ! [v0] : ( ~ (less(v0, n9) = 0) | less_or_equal(v0, n8) = 0)
% 33.25/8.37 | (50) ! [v0] : ( ~ (less_or_equal(v0, n8) = 0) | less(v0, n9) = 0)
% 33.25/8.37 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (plus(v1, v3) = v5) | ~ (holdsAt(v4, v5) = v6) | ~ (terminates(v0, v2, v1) = 0) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : (antitrajectory(v2, v1, v4, v3) = v9 & startedIn(v1, v2, v5) = v10 & happens(v0, v1) = v7 & less(n0, v3) = v8 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | v10 = 0)))
% 33.25/8.37 | (52) ~ (spinning = backwards)
% 33.25/8.37 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (plus(v1, n1) = v3) | ~ (holdsAt(v2, v3) = 0) | ~ (happens(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & terminates(v0, v2, v1) = v4))
% 33.25/8.37 | (54) ! [v0] : ! [v1] : (v1 = 0 | ~ (less(v0, n7) = v1) | ? [v2] : ( ~ (v2 = 0) & less_or_equal(v0, n6) = v2))
% 33.25/8.37 | (55) ! [v0] : ! [v1] : (v1 = 0 | ~ (less_or_equal(v0, n6) = v1) | ? [v2] : ( ~ (v2 = 0) & less(v0, n7) = v2))
% 33.25/8.37 | (56) ! [v0] : ! [v1] : ! [v2] : ( ~ (releases(v0, v2, v1) = 0) | ? [v3] : ? [v4] : ? [v5] : (releasedAt(v2, v4) = v5 & plus(v1, n1) = v4 & happens(v0, v1) = v3 & ( ~ (v3 = 0) | v5 = 0)))
% 33.25/8.37 | (57) ! [v0] : ! [v1] : (v1 = 0 | ~ (less(v0, n9) = v1) | ? [v2] : ( ~ (v2 = 0) & less_or_equal(v0, n8) = v2))
% 33.25/8.37 | (58) ! [v0] : ! [v1] : (v1 = 0 | ~ (less_or_equal(v0, n8) = v1) | ? [v2] : ( ~ (v2 = 0) & less(v0, n9) = v2))
% 33.25/8.37 | (59) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (releasedAt(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & releasedAt(v0, v3) = v4 & plus(v1, n1) = v3) | ? [v3] : (releases(v3, v0, v1) = 0 & happens(v3, v1) = 0))
% 33.25/8.37 | (60) ! [v0] : ! [v1] : ! [v2] : ( ~ (plus(v1, n1) = v2) | ~ (holdsAt(v0, v2) = 0) | ? [v3] : ? [v4] : (releasedAt(v0, v2) = v4 & holdsAt(v0, v1) = v3 & (v4 = 0 | v3 = 0)) | ? [v3] : (initiates(v3, v0, v1) = 0 & happens(v3, v1) = 0))
% 33.25/8.37 | (61) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (trajectory(v2, v1, v3, v4) = 0) | ~ (initiates(v0, v2, v1) = 0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (plus(v1, v4) = v7 & holdsAt(v3, v7) = v9 & stoppedIn(v1, v2, v7) = v8 & happens(v0, v1) = v5 & less(n0, v4) = v6 & ( ~ (v6 = 0) | ~ (v5 = 0) | v9 = 0 | v8 = 0)))
% 33.25/8.37 | (62) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (releasedAt(v0, v2) = v3) | ~ (plus(v1, n1) = v2) | ? [v4] : ? [v5] : ? [v6] : (initiates(v4, v0, v1) = v5 & happens(v4, v1) = 0 & terminates(v4, v0, v1) = v6 & (v6 = 0 | v5 = 0)) | ? [v4] : ( ~ (v4 = 0) & releasedAt(v0, v1) = v4))
% 33.25/8.37 | (63) plus(n0, n2) = n2
% 33.25/8.37 | (64) ! [v0] : ! [v1] : ! [v2] : ( ~ (initiates(v0, v1, v2) = 0) | ? [v3] : ? [v4] : (happens(pull, v2) = v3 & happens(push, v2) = v4 & ((v4 = 0 & v1 = spinning & v0 = pull) | (v1 = backwards & v0 = pull & ~ (v4 = 0)) | (v1 = forwards & v0 = push & ~ (v3 = 0)))))
% 33.25/8.37 | (65) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (releasedAt(v0, v2) = v3) | ~ (plus(v1, n1) = v2) | ? [v4] : ? [v5] : (holdsAt(v0, v2) = v5 & holdsAt(v0, v1) = v4 & ( ~ (v5 = 0) | v4 = 0)) | ? [v4] : (initiates(v4, v0, v1) = 0 & happens(v4, v1) = 0))
% 33.25/8.37 | (66) holdsAt(spinning, n0) = all_1_0_0
% 33.25/8.37 | (67) ! [v0] : ( ~ (less(v0, n5) = 0) | less_or_equal(v0, n4) = 0)
% 33.25/8.37 | (68) ! [v0] : ( ~ (less_or_equal(v0, n4) = 0) | less(v0, n5) = 0)
% 33.25/8.37 | (69) ! [v0] : ! [v1] : ! [v2] : ( ~ (less(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & less(v0, v1) = v3) | ( ~ (v2 = 0) & ~ (v1 = v0)))
% 33.31/8.37 | (70) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (plus(v1, n1) = v2) | ~ (holdsAt(v0, v2) = v3) | ? [v4] : ? [v5] : (releasedAt(v0, v2) = v5 & holdsAt(v0, v1) = v4 & ( ~ (v4 = 0) | v5 = 0)) | ? [v4] : (happens(v4, v1) = 0 & terminates(v4, v0, v1) = 0))
% 33.31/8.37 | (71) ~ (all_1_2_2 = 0)
% 33.31/8.37 | (72) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (less_or_equal(v0, v1) = v2) | ( ~ (v1 = v0) & ? [v3] : ( ~ (v3 = 0) & less(v0, v1) = v3)))
% 33.31/8.37 | (73) ! [v0] : ! [v1] : ( ~ (less(v0, v1) = 0) | ( ~ (v1 = v0) & ? [v2] : ( ~ (v2 = 0) & less(v1, v0) = v2)))
% 33.31/8.37 | (74) ! [v0] : ! [v1] : ( ~ (holdsAt(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : (releasedAt(v0, v2) = v3 & plus(v1, n1) = v2 & holdsAt(v0, v2) = v4 & (v4 = 0 | v3 = 0)) | ? [v2] : (happens(v2, v1) = 0 & terminates(v2, v0, v1) = 0))
% 33.31/8.37 | (75) ! [v0] : ! [v1] : (v1 = 0 | ~ (less(v0, n6) = v1) | ? [v2] : ( ~ (v2 = 0) & less_or_equal(v0, n5) = v2))
% 33.31/8.37 | (76) ! [v0] : ! [v1] : (v1 = 0 | ~ (less_or_equal(v0, n5) = v1) | ? [v2] : ( ~ (v2 = 0) & less(v0, n6) = v2))
% 33.31/8.37 | (77) ! [v0] : ! [v1] : ! [v2] : ~ (releases(v0, v1, v2) = 0)
% 33.31/8.37 | (78) plus(n1, n1) = n2
% 33.31/8.37 | (79) plus(n0, n1) = n1
% 33.31/8.37 | (80) ! [v0] : ! [v1] : ( ~ (happens(v0, v1) = 0) | (v1 = n2 & v0 = pull) | (v1 = n2 & v0 = push) | (v1 = n1 & v0 = pull) | (v1 = n0 & v0 = push))
% 33.31/8.37 | (81) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (stoppedIn(v0, v1, v2) = v3) | ( ! [v4] : ! [v5] : ( ~ (happens(v4, v5) = 0) | ? [v6] : ? [v7] : ? [v8] : (less(v5, v2) = v7 & less(v0, v5) = v6 & terminates(v4, v1, v5) = v8 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v4] : ! [v5] : ( ~ (terminates(v4, v1, v5) = 0) | ? [v6] : ? [v7] : ? [v8] : (happens(v4, v5) = v6 & less(v5, v2) = v8 & less(v0, v5) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0))))))
% 33.31/8.37 | (82) ! [v0] : ( ~ (less(v0, n6) = 0) | less_or_equal(v0, n5) = 0)
% 33.31/8.37 | (83) ! [v0] : ( ~ (less_or_equal(v0, n5) = 0) | less(v0, n6) = 0)
% 33.31/8.37 | (84) plus(n2, n3) = n5
% 33.31/8.37 | (85) ! [v0] : ! [v1] : ! [v2] : ( ~ (terminates(v0, v1, v2) = 0) | ? [v3] : ? [v4] : (happens(pull, v2) = v3 & happens(push, v2) = v4 & ((v4 = 0 & v1 = backwards & v0 = pull) | (v4 = 0 & v1 = forwards & v0 = pull) | (v1 = spinning & v0 = pull & ~ (v4 = 0)) | (v1 = spinning & v0 = push & ~ (v3 = 0)) | (v1 = backwards & v0 = push & ~ (v3 = 0)) | (v1 = forwards & v0 = pull & ~ (v4 = 0)))))
% 33.31/8.37 | (86) ! [v0] : ! [v1] : (v1 = 0 | ~ (less(v0, n5) = v1) | ? [v2] : ( ~ (v2 = 0) & less_or_equal(v0, n4) = v2))
% 33.31/8.37 | (87) ! [v0] : ! [v1] : (v1 = 0 | ~ (less_or_equal(v0, n4) = v1) | ? [v2] : ( ~ (v2 = 0) & less(v0, n5) = v2))
% 33.31/8.38 | (88) ! [v0] : ! [v1] : ! [v2] : ( ~ (terminates(v0, v2, v1) = 0) | ? [v3] : ? [v4] : ? [v5] : (plus(v1, n1) = v4 & holdsAt(v2, v4) = v5 & happens(v0, v1) = v3 & ( ~ (v5 = 0) | ~ (v3 = 0))))
% 33.31/8.38 | (89) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (trajectory(v2, v1, v3, v4) = 0) | ~ (happens(v0, v1) = 0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (plus(v1, v4) = v7 & holdsAt(v3, v7) = v9 & initiates(v0, v2, v1) = v5 & stoppedIn(v1, v2, v7) = v8 & less(n0, v4) = v6 & ( ~ (v6 = 0) | ~ (v5 = 0) | v9 = 0 | v8 = 0)))
% 33.31/8.38 | (90) ! [v0] : ( ~ (less(v0, n7) = 0) | less_or_equal(v0, n6) = 0)
% 33.31/8.38 | (91) ! [v0] : ( ~ (less_or_equal(v0, n6) = 0) | less(v0, n7) = 0)
% 33.31/8.38 | (92) ! [v0] : ! [v1] : (v1 = 0 | ~ (less(v0, n2) = v1) | ? [v2] : ( ~ (v2 = 0) & less_or_equal(v0, n1) = v2))
% 33.31/8.38 | (93) ! [v0] : ! [v1] : (v1 = 0 | ~ (less_or_equal(v0, n1) = v1) | ? [v2] : ( ~ (v2 = 0) & less(v0, n2) = v2))
% 33.31/8.38 | (94) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (releasedAt(v0, v2) = v3) | ~ (plus(v1, n1) = v2) | ? [v4] : ? [v5] : (holdsAt(v0, v2) = v5 & holdsAt(v0, v1) = v4 & ( ~ (v4 = 0) | v5 = 0)) | ? [v4] : (happens(v4, v1) = 0 & terminates(v4, v0, v1) = 0))
% 33.31/8.38 | (95) plus(n2, n2) = n4
% 33.31/8.38 | (96) ! [v0] : ( ~ (less(v0, n2) = 0) | less_or_equal(v0, n1) = 0)
% 33.31/8.38 | (97) ! [v0] : ( ~ (less_or_equal(v0, n1) = 0) | less(v0, n2) = 0)
% 33.31/8.38 | (98) plus(n3, n3) = n6
% 33.31/8.38 | (99) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (antitrajectory(v2, v1, v4, v3) = 0) | ~ (terminates(v0, v2, v1) = 0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (plus(v1, v3) = v7 & holdsAt(v4, v7) = v9 & startedIn(v1, v2, v7) = v8 & happens(v0, v1) = v5 & less(n0, v3) = v6 & ( ~ (v6 = 0) | ~ (v5 = 0) | v9 = 0 | v8 = 0)))
% 33.31/8.38 | (100) holdsAt(spinning, n1) = 0
% 33.31/8.38 | (101) plus(n0, n0) = n0
% 33.31/8.38 | (102) ~ (pull = push)
% 33.31/8.38 | (103) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v6 = 0 | ~ (plus(v1, v3) = v5) | ~ (holdsAt(v4, v5) = v7) | ~ (startedIn(v1, v2, v5) = v6) | ~ (happens(v0, v1) = 0) | ? [v8] : ? [v9] : ? [v10] : (antitrajectory(v2, v1, v4, v3) = v10 & less(n0, v3) = v9 & terminates(v0, v2, v1) = v8 & ( ~ (v10 = 0) | ~ (v9 = 0) | ~ (v8 = 0))))
% 33.31/8.38 | (104) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (holdsAt(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (releasedAt(v0, v3) = v4 & plus(v1, n1) = v3 & holdsAt(v0, v3) = v5 & ( ~ (v5 = 0) | v4 = 0)) | ? [v3] : (initiates(v3, v0, v1) = 0 & happens(v3, v1) = 0))
% 33.31/8.38 | (105) ! [v0] : ! [v1] : (v1 = 0 | ~ (less(v0, n4) = v1) | ? [v2] : ( ~ (v2 = 0) & less_or_equal(v0, n3) = v2))
% 33.31/8.38 | (106) ! [v0] : ! [v1] : (v1 = 0 | ~ (less_or_equal(v0, n3) = v1) | ? [v2] : ( ~ (v2 = 0) & less(v0, n4) = v2))
% 33.31/8.38 | (107) ! [v0] : ! [v1] : ! [v2] : ( ~ (releasedAt(v0, v2) = 0) | ~ (plus(v1, n1) = v2) | releasedAt(v0, v1) = 0 | ? [v3] : (releases(v3, v0, v1) = 0 & happens(v3, v1) = 0))
% 33.31/8.38 | (108) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (releasedAt(v2, v3) = 0) | ~ (plus(v1, n1) = v3) | ~ (happens(v0, v1) = 0) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & ~ (v4 = 0) & initiates(v0, v2, v1) = v4 & terminates(v0, v2, v1) = v5))
% 33.31/8.38 | (109) ! [v0] : ! [v1] : (v1 = 0 | ~ (less(v0, n8) = v1) | ? [v2] : ( ~ (v2 = 0) & less_or_equal(v0, n7) = v2))
% 33.31/8.38 | (110) ! [v0] : ! [v1] : (v1 = 0 | ~ (less_or_equal(v0, n7) = v1) | ? [v2] : ( ~ (v2 = 0) & less(v0, n8) = v2))
% 33.31/8.38 | (111) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (plus(v1, n1) = v3) | ~ (holdsAt(v2, v3) = v4) | ~ (happens(v0, v1) = 0) | ? [v5] : ( ~ (v5 = 0) & initiates(v0, v2, v1) = v5))
% 33.31/8.38 | (112) holdsAt(forwards, n0) = all_1_2_2
% 33.31/8.38 | (113) holdsAt(backwards, n0) = all_1_1_1
% 33.31/8.38 | (114) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (less(v0, v1) = v2) | less(v1, v0) = 0)
% 33.31/8.38 | (115) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (less(v1, v0) = v2) | less(v0, v1) = 0)
% 33.31/8.38 | (116) ! [v0] : ( ~ (less(v0, n8) = 0) | less_or_equal(v0, n7) = 0)
% 33.31/8.38 | (117) ! [v0] : ( ~ (less_or_equal(v0, n7) = 0) | less(v0, n8) = 0)
% 33.31/8.38 | (118) ~ (all_1_1_1 = 0)
% 33.31/8.38 | (119) ! [v0] : ! [v1] : ! [v2] : ( ~ (less(v0, v1) = v2) | less_or_equal(v0, v1) = 0 | ( ~ (v2 = 0) & ~ (v1 = v0)))
% 33.31/8.38 | (120) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (initiates(v0, v1, v2) = v3) | ? [v4] : ? [v5] : (happens(pull, v2) = v4 & happens(push, v2) = v5 & ( ~ (v5 = 0) | ~ (v1 = spinning) | ~ (v0 = pull)) & ( ~ (v1 = backwards) | ~ (v0 = pull) | v5 = 0) & ( ~ (v1 = forwards) | ~ (v0 = push) | v4 = 0)))
% 33.31/8.38 | (121) ! [v0] : ! [v1] : (v1 = v0 | ~ (less_or_equal(v0, v1) = 0) | less(v0, v1) = 0)
% 33.31/8.38 | (122) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (happens(v0, v1) = v2) | (( ~ (v1 = n2) | ~ (v0 = pull)) & ( ~ (v1 = n2) | ~ (v0 = push)) & ( ~ (v1 = n1) | ~ (v0 = pull)) & ( ~ (v1 = n0) | ~ (v0 = push))))
% 33.31/8.38 |
% 33.31/8.38 | Instantiating formula (9) with n2, n2, n5, n6 yields:
% 33.31/8.38 | (123) n6 = n5 | ~ (plus(n2, n2) = n6) | ~ (plus(n2, n2) = n5)
% 33.31/8.38 |
% 33.31/8.38 | Instantiating formula (9) with n2, n2, n4, n5 and discharging atoms plus(n2, n2) = n4, yields:
% 33.31/8.38 | (124) n5 = n4 | ~ (plus(n2, n2) = n5)
% 33.31/8.38 |
% 33.31/8.38 | Instantiating formula (9) with n1, n1, n4, n6 yields:
% 33.31/8.38 | (125) n6 = n4 | ~ (plus(n1, n1) = n6) | ~ (plus(n1, n1) = n4)
% 33.31/8.38 |
% 33.31/8.38 | Instantiating formula (9) with n1, n3, n4, n5 and discharging atoms plus(n1, n3) = n4, yields:
% 33.31/8.38 | (126) n5 = n4 | ~ (plus(n1, n3) = n5)
% 33.31/8.38 |
% 33.31/8.38 | Instantiating formula (9) with n1, n1, n3, n4 yields:
% 33.31/8.38 | (127) n4 = n3 | ~ (plus(n1, n1) = n4) | ~ (plus(n1, n1) = n3)
% 33.31/8.38 |
% 33.31/8.38 | Instantiating formula (9) with n1, n2, n2, n4 yields:
% 33.31/8.38 | (128) n4 = n2 | ~ (plus(n1, n2) = n4) | ~ (plus(n1, n2) = n2)
% 33.31/8.38 |
% 33.31/8.38 | Instantiating formula (9) with n1, n1, n2, n4 and discharging atoms plus(n1, n1) = n2, yields:
% 33.31/8.38 | (129) n4 = n2 | ~ (plus(n1, n1) = n4)
% 33.31/8.38 |
% 33.31/8.38 | Instantiating formula (9) with n1, n1, n1, n3 yields:
% 33.31/8.38 | (130) n3 = n1 | ~ (plus(n1, n1) = n3) | ~ (plus(n1, n1) = n1)
% 33.31/8.38 |
% 33.31/8.38 | Instantiating formula (9) with n0, n0, n0, n6 and discharging atoms plus(n0, n0) = n0, yields:
% 33.31/8.38 | (131) n6 = n0 | ~ (plus(n0, n0) = n6)
% 33.31/8.38 |
% 33.31/8.38 | Instantiating formula (9) with n0, n3, n3, n5 and discharging atoms plus(n0, n3) = n3, yields:
% 33.31/8.38 | (132) n5 = n3 | ~ (plus(n0, n3) = n5)
% 33.31/8.38 |
% 33.31/8.38 | Instantiating formula (9) with n0, n3, n3, n4 and discharging atoms plus(n0, n3) = n3, yields:
% 33.31/8.38 | (133) n4 = n3 | ~ (plus(n0, n3) = n4)
% 33.31/8.38 |
% 33.31/8.38 | Instantiating formula (9) with n0, n0, n0, n4 and discharging atoms plus(n0, n0) = n0, yields:
% 33.31/8.38 | (134) n4 = n0 | ~ (plus(n0, n0) = n4)
% 33.31/8.38 |
% 33.31/8.38 | Instantiating formula (9) with n0, n2, n2, n3 and discharging atoms plus(n0, n2) = n2, yields:
% 33.31/8.38 | (135) n3 = n2 | ~ (plus(n0, n2) = n3)
% 33.31/8.38 |
% 33.31/8.38 | Instantiating formula (9) with n0, n0, n0, n2 and discharging atoms plus(n0, n0) = n0, yields:
% 33.31/8.38 | (136) n2 = n0 | ~ (plus(n0, n0) = n2)
% 33.31/8.39 |
% 33.31/8.39 | Instantiating formula (4) with spinning, n0, all_1_0_0, 0 and discharging atoms holdsAt(spinning, n0) = all_1_0_0, yields:
% 33.31/8.39 | (137) all_1_0_0 = 0 | ~ (holdsAt(spinning, n0) = 0)
% 33.31/8.39 |
% 33.31/8.39 | Instantiating formula (21) with n4, n1, n3 and discharging atoms plus(n1, n3) = n4, yields:
% 33.31/8.39 | (138) plus(n3, n1) = n4
% 33.31/8.39 |
% 33.31/8.39 | Instantiating formula (21) with n3, n1, n2 and discharging atoms plus(n1, n2) = n3, yields:
% 33.31/8.39 | (139) plus(n2, n1) = n3
% 33.31/8.39 |
% 33.31/8.39 | Instantiating formula (21) with n2, n0, n2 and discharging atoms plus(n0, n2) = n2, yields:
% 33.31/8.39 | (140) plus(n2, n0) = n2
% 33.31/8.39 |
% 33.31/8.39 | Instantiating formula (21) with n1, n0, n1 and discharging atoms plus(n0, n1) = n1, yields:
% 33.31/8.39 | (141) plus(n1, n0) = n1
% 33.31/8.39 |
% 33.31/8.39 | Instantiating formula (60) with n1, n0, spinning and discharging atoms plus(n0, n1) = n1, holdsAt(spinning, n1) = 0, yields:
% 33.31/8.39 | (142) ? [v0] : ? [v1] : (releasedAt(spinning, n1) = v1 & holdsAt(spinning, n0) = v0 & (v1 = 0 | v0 = 0)) | ? [v0] : (initiates(v0, spinning, n0) = 0 & happens(v0, n0) = 0)
% 33.31/8.39 |
% 33.31/8.39 | Instantiating formula (74) with n1, spinning and discharging atoms holdsAt(spinning, n1) = 0, yields:
% 33.31/8.39 | (143) ? [v0] : ? [v1] : ? [v2] : (releasedAt(spinning, v0) = v1 & plus(n1, n1) = v0 & holdsAt(spinning, v0) = v2 & (v2 = 0 | v1 = 0)) | ? [v0] : (happens(v0, n1) = 0 & terminates(v0, spinning, n1) = 0)
% 33.31/8.39 |
% 33.31/8.39 | Instantiating formula (104) with all_1_0_0, n0, spinning and discharging atoms holdsAt(spinning, n0) = all_1_0_0, yields:
% 33.31/8.39 | (144) all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : (releasedAt(spinning, v0) = v1 & plus(n0, n1) = v0 & holdsAt(spinning, v0) = v2 & ( ~ (v2 = 0) | v1 = 0)) | ? [v0] : (initiates(v0, spinning, n0) = 0 & happens(v0, n0) = 0)
% 33.31/8.39 |
% 33.31/8.39 | Instantiating formula (9) with n0, n1, n3, n1 and discharging atoms plus(n0, n1) = n1, yields:
% 33.31/8.39 | (145) n3 = n1 | ~ (plus(n0, n1) = n3)
% 33.31/8.39 |
% 33.31/8.39 | Instantiating formula (9) with n1, n0, n1, n3 and discharging atoms plus(n1, n0) = n1, yields:
% 33.31/8.39 | (146) n3 = n1 | ~ (plus(n1, n0) = n3)
% 33.31/8.39 |
% 33.31/8.39 | Instantiating formula (60) with n1, n2, spinning and discharging atoms holdsAt(spinning, n1) = 0, yields:
% 33.31/8.39 | (147) ~ (plus(n2, n1) = n1) | ? [v0] : ? [v1] : (releasedAt(spinning, n1) = v1 & holdsAt(spinning, n2) = v0 & (v1 = 0 | v0 = 0)) | ? [v0] : (initiates(v0, spinning, n2) = 0 & happens(v0, n2) = 0)
% 33.31/8.39 |
% 33.31/8.39 +-Applying beta-rule and splitting (126), into two cases.
% 33.31/8.39 |-Branch one:
% 33.31/8.39 | (148) ~ (plus(n1, n3) = n5)
% 33.31/8.39 |
% 33.31/8.39 | Using (41) and (148) yields:
% 33.31/8.39 | (149) ~ (n5 = n4)
% 33.31/8.39 |
% 33.31/8.39 +-Applying beta-rule and splitting (129), into two cases.
% 33.31/8.39 |-Branch one:
% 33.31/8.39 | (150) ~ (plus(n1, n1) = n4)
% 33.31/8.39 |
% 33.31/8.39 | Using (78) and (150) yields:
% 33.31/8.39 | (151) ~ (n4 = n2)
% 33.31/8.39 |
% 33.31/8.39 +-Applying beta-rule and splitting (132), into two cases.
% 33.31/8.39 |-Branch one:
% 33.31/8.39 | (152) ~ (plus(n0, n3) = n5)
% 33.31/8.39 |
% 33.31/8.39 | Using (84) and (152) yields:
% 33.31/8.39 | (153) ~ (n2 = n0)
% 33.31/8.39 |
% 33.31/8.39 +-Applying beta-rule and splitting (142), into two cases.
% 33.31/8.39 |-Branch one:
% 33.31/8.39 | (154) ? [v0] : ? [v1] : (releasedAt(spinning, n1) = v1 & holdsAt(spinning, n0) = v0 & (v1 = 0 | v0 = 0))
% 33.31/8.39 |
% 33.31/8.39 | Instantiating (154) with all_103_0_3, all_103_1_4 yields:
% 33.31/8.39 | (155) releasedAt(spinning, n1) = all_103_0_3 & holdsAt(spinning, n0) = all_103_1_4 & (all_103_0_3 = 0 | all_103_1_4 = 0)
% 33.31/8.39 |
% 33.31/8.39 | Applying alpha-rule on (155) yields:
% 33.31/8.39 | (156) releasedAt(spinning, n1) = all_103_0_3
% 33.31/8.39 | (157) holdsAt(spinning, n0) = all_103_1_4
% 33.31/8.39 | (158) all_103_0_3 = 0 | all_103_1_4 = 0
% 33.31/8.39 |
% 33.31/8.39 | Instantiating formula (30) with n1, spinning yields:
% 33.31/8.39 | (159) ~ (releasedAt(spinning, n1) = 0)
% 33.31/8.39 |
% 33.31/8.39 | Instantiating formula (4) with spinning, n0, all_103_1_4, all_1_0_0 and discharging atoms holdsAt(spinning, n0) = all_103_1_4, holdsAt(spinning, n0) = all_1_0_0, yields:
% 33.31/8.39 | (160) all_103_1_4 = all_1_0_0
% 33.31/8.39 |
% 33.31/8.39 +-Applying beta-rule and splitting (158), into two cases.
% 33.31/8.39 |-Branch one:
% 33.31/8.39 | (161) all_103_0_3 = 0
% 33.31/8.39 |
% 33.31/8.39 | From (161) and (156) follows:
% 33.31/8.39 | (162) releasedAt(spinning, n1) = 0
% 33.31/8.39 |
% 33.31/8.39 | Using (162) and (159) yields:
% 33.31/8.39 | (163) $false
% 33.31/8.39 |
% 33.31/8.39 |-The branch is then unsatisfiable
% 33.31/8.39 |-Branch two:
% 33.31/8.39 | (164) ~ (all_103_0_3 = 0)
% 33.31/8.39 | (165) all_103_1_4 = 0
% 33.31/8.39 |
% 33.31/8.39 | Combining equations (165,160) yields a new equation:
% 33.31/8.39 | (166) all_1_0_0 = 0
% 33.31/8.39 |
% 33.31/8.39 | Equations (166) can reduce 42 to:
% 33.31/8.39 | (167) $false
% 33.31/8.39 |
% 33.31/8.39 |-The branch is then unsatisfiable
% 33.31/8.39 |-Branch two:
% 33.31/8.39 | (168) ? [v0] : (initiates(v0, spinning, n0) = 0 & happens(v0, n0) = 0)
% 33.31/8.39 |
% 33.31/8.39 | Instantiating (168) with all_103_0_5 yields:
% 33.31/8.39 | (169) initiates(all_103_0_5, spinning, n0) = 0 & happens(all_103_0_5, n0) = 0
% 33.31/8.39 |
% 33.31/8.39 | Applying alpha-rule on (169) yields:
% 33.31/8.39 | (170) initiates(all_103_0_5, spinning, n0) = 0
% 33.31/8.39 | (171) happens(all_103_0_5, n0) = 0
% 33.31/8.39 |
% 33.31/8.39 | Instantiating formula (80) with n0, all_103_0_5 and discharging atoms happens(all_103_0_5, n0) = 0, yields:
% 33.31/8.39 | (172) all_103_0_5 = push | (all_103_0_5 = pull & n2 = n0) | (all_103_0_5 = pull & n1 = n0)
% 33.31/8.39 |
% 33.31/8.39 | Instantiating formula (29) with all_1_0_0, n0, n0, spinning, spinning, n0, all_103_0_5 and discharging atoms plus(n0, n0) = n0, holdsAt(spinning, n0) = all_1_0_0, initiates(all_103_0_5, spinning, n0) = 0, yields:
% 33.31/8.39 | (173) all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (trajectory(spinning, n0, spinning, n0) = v2 & stoppedIn(n0, spinning, n0) = v3 & happens(all_103_0_5, n0) = v0 & less(n0, n0) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0))
% 33.31/8.39 |
% 33.31/8.39 | Instantiating formula (64) with n0, spinning, all_103_0_5 and discharging atoms initiates(all_103_0_5, spinning, n0) = 0, yields:
% 33.31/8.39 | (174) ? [v0] : ? [v1] : (happens(pull, n0) = v0 & happens(push, n0) = v1 & ((v1 = 0 & all_103_0_5 = pull) | (all_103_0_5 = pull & spinning = backwards & ~ (v1 = 0)) | (all_103_0_5 = push & spinning = forwards & ~ (v0 = 0))))
% 33.31/8.39 |
% 33.31/8.39 | Instantiating (174) with all_114_0_11, all_114_1_12 yields:
% 33.31/8.39 | (175) happens(pull, n0) = all_114_1_12 & happens(push, n0) = all_114_0_11 & ((all_114_0_11 = 0 & all_103_0_5 = pull) | (all_103_0_5 = pull & spinning = backwards & ~ (all_114_0_11 = 0)) | (all_103_0_5 = push & spinning = forwards & ~ (all_114_1_12 = 0)))
% 33.31/8.39 |
% 33.31/8.39 | Applying alpha-rule on (175) yields:
% 33.31/8.39 | (176) happens(pull, n0) = all_114_1_12
% 33.31/8.39 | (177) happens(push, n0) = all_114_0_11
% 33.31/8.39 | (178) (all_114_0_11 = 0 & all_103_0_5 = pull) | (all_103_0_5 = pull & spinning = backwards & ~ (all_114_0_11 = 0)) | (all_103_0_5 = push & spinning = forwards & ~ (all_114_1_12 = 0))
% 33.31/8.39 |
% 33.31/8.39 +-Applying beta-rule and splitting (173), into two cases.
% 33.31/8.39 |-Branch one:
% 33.31/8.39 | (166) all_1_0_0 = 0
% 33.31/8.39 |
% 33.31/8.39 | Equations (166) can reduce 42 to:
% 33.31/8.39 | (167) $false
% 33.31/8.39 |
% 33.31/8.39 |-The branch is then unsatisfiable
% 33.31/8.39 |-Branch two:
% 33.31/8.39 | (42) ~ (all_1_0_0 = 0)
% 33.31/8.39 | (182) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (trajectory(spinning, n0, spinning, n0) = v2 & stoppedIn(n0, spinning, n0) = v3 & happens(all_103_0_5, n0) = v0 & less(n0, n0) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0))
% 33.31/8.39 |
% 33.31/8.39 +-Applying beta-rule and splitting (178), into two cases.
% 33.31/8.39 |-Branch one:
% 33.31/8.39 | (183) (all_114_0_11 = 0 & all_103_0_5 = pull) | (all_103_0_5 = pull & spinning = backwards & ~ (all_114_0_11 = 0))
% 33.31/8.39 |
% 33.31/8.39 +-Applying beta-rule and splitting (183), into two cases.
% 33.31/8.39 |-Branch one:
% 33.31/8.39 | (184) all_114_0_11 = 0 & all_103_0_5 = pull
% 33.31/8.39 |
% 33.31/8.39 | Applying alpha-rule on (184) yields:
% 33.31/8.39 | (185) all_114_0_11 = 0
% 33.31/8.39 | (186) all_103_0_5 = pull
% 33.31/8.39 |
% 33.31/8.39 +-Applying beta-rule and splitting (172), into two cases.
% 33.31/8.39 |-Branch one:
% 33.31/8.39 | (187) all_103_0_5 = push
% 33.31/8.39 |
% 33.31/8.39 | Combining equations (186,187) yields a new equation:
% 33.31/8.39 | (188) pull = push
% 33.31/8.39 |
% 33.31/8.39 | Simplifying 188 yields:
% 33.31/8.39 | (189) pull = push
% 33.31/8.39 |
% 33.31/8.39 | Equations (189) can reduce 102 to:
% 33.31/8.39 | (167) $false
% 33.31/8.39 |
% 33.31/8.39 |-The branch is then unsatisfiable
% 33.31/8.39 |-Branch two:
% 33.31/8.39 | (191) ~ (all_103_0_5 = push)
% 33.31/8.40 | (192) (all_103_0_5 = pull & n2 = n0) | (all_103_0_5 = pull & n1 = n0)
% 33.31/8.40 |
% 33.31/8.40 +-Applying beta-rule and splitting (192), into two cases.
% 33.31/8.40 |-Branch one:
% 33.31/8.40 | (193) all_103_0_5 = pull & n2 = n0
% 33.31/8.40 |
% 33.31/8.40 | Applying alpha-rule on (193) yields:
% 33.31/8.40 | (186) all_103_0_5 = pull
% 33.31/8.40 | (195) n2 = n0
% 33.31/8.40 |
% 33.31/8.40 | Equations (195) can reduce 153 to:
% 33.31/8.40 | (167) $false
% 33.31/8.40 |
% 33.31/8.40 |-The branch is then unsatisfiable
% 33.31/8.40 |-Branch two:
% 33.31/8.40 | (197) all_103_0_5 = pull & n1 = n0
% 33.31/8.40 |
% 33.31/8.40 | Applying alpha-rule on (197) yields:
% 33.31/8.40 | (186) all_103_0_5 = pull
% 33.31/8.40 | (199) n1 = n0
% 33.31/8.40 |
% 33.31/8.40 | From (199) and (100) follows:
% 33.31/8.40 | (200) holdsAt(spinning, n0) = 0
% 33.31/8.40 |
% 33.31/8.40 +-Applying beta-rule and splitting (137), into two cases.
% 33.31/8.40 |-Branch one:
% 33.31/8.40 | (201) ~ (holdsAt(spinning, n0) = 0)
% 33.31/8.40 |
% 33.31/8.40 | Using (200) and (201) yields:
% 33.31/8.40 | (163) $false
% 33.31/8.40 |
% 33.31/8.40 |-The branch is then unsatisfiable
% 33.31/8.40 |-Branch two:
% 33.31/8.40 | (200) holdsAt(spinning, n0) = 0
% 33.31/8.40 | (166) all_1_0_0 = 0
% 33.31/8.40 |
% 33.31/8.40 | Equations (166) can reduce 42 to:
% 33.31/8.40 | (167) $false
% 33.31/8.40 |
% 33.31/8.40 |-The branch is then unsatisfiable
% 33.31/8.40 |-Branch two:
% 33.31/8.40 | (206) all_103_0_5 = pull & spinning = backwards & ~ (all_114_0_11 = 0)
% 33.31/8.40 |
% 33.31/8.40 | Applying alpha-rule on (206) yields:
% 33.31/8.40 | (186) all_103_0_5 = pull
% 33.31/8.40 | (208) spinning = backwards
% 33.31/8.40 | (209) ~ (all_114_0_11 = 0)
% 33.31/8.40 |
% 33.31/8.40 | Equations (208) can reduce 52 to:
% 33.31/8.40 | (167) $false
% 33.31/8.40 |
% 33.31/8.40 |-The branch is then unsatisfiable
% 33.31/8.40 |-Branch two:
% 33.31/8.40 | (211) all_103_0_5 = push & spinning = forwards & ~ (all_114_1_12 = 0)
% 33.31/8.40 |
% 33.31/8.40 | Applying alpha-rule on (211) yields:
% 33.31/8.40 | (187) all_103_0_5 = push
% 33.31/8.40 | (213) spinning = forwards
% 33.31/8.40 | (214) ~ (all_114_1_12 = 0)
% 33.31/8.40 |
% 33.31/8.40 | Equations (213) can reduce 33 to:
% 33.31/8.40 | (167) $false
% 33.31/8.40 |
% 33.31/8.40 |-The branch is then unsatisfiable
% 33.31/8.40 |-Branch two:
% 33.31/8.40 | (216) plus(n0, n3) = n5
% 33.31/8.40 | (217) n5 = n3
% 33.31/8.40 |
% 33.31/8.40 | From (217) and (216) follows:
% 33.31/8.40 | (45) plus(n0, n3) = n3
% 33.31/8.40 |
% 33.31/8.40 | From (217) and (148) follows:
% 33.31/8.40 | (219) ~ (plus(n1, n3) = n3)
% 33.31/8.40 |
% 33.31/8.40 | Using (45) and (219) yields:
% 33.31/8.40 | (220) ~ (n1 = n0)
% 33.31/8.40 |
% 33.31/8.40 +-Applying beta-rule and splitting (134), into two cases.
% 33.31/8.40 |-Branch one:
% 33.31/8.40 | (221) ~ (plus(n0, n0) = n4)
% 33.31/8.40 |
% 33.31/8.40 +-Applying beta-rule and splitting (137), into two cases.
% 33.31/8.40 |-Branch one:
% 33.31/8.40 | (201) ~ (holdsAt(spinning, n0) = 0)
% 33.31/8.40 |
% 33.31/8.40 +-Applying beta-rule and splitting (136), into two cases.
% 33.31/8.40 |-Branch one:
% 33.31/8.40 | (223) ~ (plus(n0, n0) = n2)
% 33.31/8.40 |
% 33.31/8.40 | Using (140) and (223) yields:
% 33.31/8.40 | (153) ~ (n2 = n0)
% 33.31/8.40 |
% 33.31/8.40 +-Applying beta-rule and splitting (142), into two cases.
% 33.31/8.40 |-Branch one:
% 33.31/8.40 | (154) ? [v0] : ? [v1] : (releasedAt(spinning, n1) = v1 & holdsAt(spinning, n0) = v0 & (v1 = 0 | v0 = 0))
% 33.31/8.40 |
% 33.31/8.40 | Instantiating (154) with all_136_0_29, all_136_1_30 yields:
% 33.31/8.40 | (226) releasedAt(spinning, n1) = all_136_0_29 & holdsAt(spinning, n0) = all_136_1_30 & (all_136_0_29 = 0 | all_136_1_30 = 0)
% 33.31/8.40 |
% 33.31/8.40 | Applying alpha-rule on (226) yields:
% 33.31/8.40 | (227) releasedAt(spinning, n1) = all_136_0_29
% 33.31/8.40 | (228) holdsAt(spinning, n0) = all_136_1_30
% 33.31/8.40 | (229) all_136_0_29 = 0 | all_136_1_30 = 0
% 33.31/8.40 |
% 33.31/8.40 | Instantiating formula (30) with n1, spinning yields:
% 33.31/8.40 | (159) ~ (releasedAt(spinning, n1) = 0)
% 33.31/8.40 |
% 33.31/8.40 | Instantiating formula (4) with spinning, n0, all_136_1_30, all_1_0_0 and discharging atoms holdsAt(spinning, n0) = all_136_1_30, holdsAt(spinning, n0) = all_1_0_0, yields:
% 33.31/8.40 | (231) all_136_1_30 = all_1_0_0
% 33.31/8.40 |
% 33.31/8.40 | Using (228) and (201) yields:
% 33.31/8.40 | (232) ~ (all_136_1_30 = 0)
% 33.31/8.40 |
% 33.31/8.40 | Equations (231) can reduce 232 to:
% 33.31/8.40 | (42) ~ (all_1_0_0 = 0)
% 33.31/8.40 |
% 33.31/8.40 +-Applying beta-rule and splitting (229), into two cases.
% 33.31/8.40 |-Branch one:
% 33.31/8.40 | (234) all_136_0_29 = 0
% 33.31/8.40 |
% 33.31/8.40 | From (234) and (227) follows:
% 33.31/8.40 | (162) releasedAt(spinning, n1) = 0
% 33.31/8.40 |
% 33.31/8.40 | Using (162) and (159) yields:
% 33.31/8.40 | (163) $false
% 33.31/8.40 |
% 33.31/8.40 |-The branch is then unsatisfiable
% 33.31/8.40 |-Branch two:
% 33.31/8.40 | (237) ~ (all_136_0_29 = 0)
% 33.31/8.40 | (238) all_136_1_30 = 0
% 33.31/8.40 |
% 33.31/8.40 | Combining equations (238,231) yields a new equation:
% 33.31/8.40 | (166) all_1_0_0 = 0
% 33.31/8.40 |
% 33.31/8.40 | Equations (166) can reduce 42 to:
% 33.31/8.40 | (167) $false
% 33.31/8.40 |
% 33.31/8.40 |-The branch is then unsatisfiable
% 33.31/8.40 |-Branch two:
% 33.31/8.40 | (168) ? [v0] : (initiates(v0, spinning, n0) = 0 & happens(v0, n0) = 0)
% 33.31/8.40 |
% 33.31/8.40 | Instantiating (168) with all_136_0_31 yields:
% 33.31/8.40 | (242) initiates(all_136_0_31, spinning, n0) = 0 & happens(all_136_0_31, n0) = 0
% 33.31/8.40 |
% 33.31/8.40 | Applying alpha-rule on (242) yields:
% 33.31/8.40 | (243) initiates(all_136_0_31, spinning, n0) = 0
% 33.31/8.40 | (244) happens(all_136_0_31, n0) = 0
% 33.31/8.40 |
% 33.31/8.40 | Instantiating formula (80) with n0, all_136_0_31 and discharging atoms happens(all_136_0_31, n0) = 0, yields:
% 33.31/8.40 | (245) all_136_0_31 = push | (all_136_0_31 = pull & n2 = n0) | (all_136_0_31 = pull & n1 = n0)
% 33.31/8.40 |
% 33.31/8.40 +-Applying beta-rule and splitting (245), into two cases.
% 33.31/8.40 |-Branch one:
% 33.31/8.40 | (246) all_136_0_31 = push
% 33.31/8.40 |
% 33.31/8.40 | From (246) and (243) follows:
% 33.31/8.40 | (247) initiates(push, spinning, n0) = 0
% 33.31/8.40 |
% 33.31/8.40 | Instantiating formula (64) with n0, spinning, push and discharging atoms initiates(push, spinning, n0) = 0, yields:
% 33.31/8.40 | (248) ? [v0] : ? [v1] : (happens(pull, n0) = v0 & happens(push, n0) = v1 & ((v1 = 0 & pull = push) | (spinning = backwards & pull = push & ~ (v1 = 0)) | (spinning = forwards & ~ (v0 = 0))))
% 33.31/8.40 |
% 33.31/8.40 | Instantiating (248) with all_248_0_40, all_248_1_41 yields:
% 33.31/8.40 | (249) happens(pull, n0) = all_248_1_41 & happens(push, n0) = all_248_0_40 & ((all_248_0_40 = 0 & pull = push) | (spinning = backwards & pull = push & ~ (all_248_0_40 = 0)) | (spinning = forwards & ~ (all_248_1_41 = 0)))
% 33.31/8.40 |
% 33.31/8.40 | Applying alpha-rule on (249) yields:
% 33.31/8.40 | (250) happens(pull, n0) = all_248_1_41
% 33.31/8.40 | (251) happens(push, n0) = all_248_0_40
% 33.31/8.40 | (252) (all_248_0_40 = 0 & pull = push) | (spinning = backwards & pull = push & ~ (all_248_0_40 = 0)) | (spinning = forwards & ~ (all_248_1_41 = 0))
% 33.31/8.40 |
% 33.31/8.40 +-Applying beta-rule and splitting (252), into two cases.
% 33.31/8.40 |-Branch one:
% 33.31/8.40 | (253) (all_248_0_40 = 0 & pull = push) | (spinning = backwards & pull = push & ~ (all_248_0_40 = 0))
% 33.31/8.40 |
% 33.31/8.40 +-Applying beta-rule and splitting (253), into two cases.
% 33.31/8.40 |-Branch one:
% 33.31/8.40 | (254) all_248_0_40 = 0 & pull = push
% 33.31/8.40 |
% 33.31/8.40 | Applying alpha-rule on (254) yields:
% 33.31/8.40 | (255) all_248_0_40 = 0
% 33.31/8.40 | (189) pull = push
% 33.31/8.40 |
% 33.31/8.40 | Equations (189) can reduce 102 to:
% 33.31/8.40 | (167) $false
% 33.31/8.40 |
% 33.31/8.40 |-The branch is then unsatisfiable
% 33.31/8.40 |-Branch two:
% 33.31/8.40 | (258) spinning = backwards & pull = push & ~ (all_248_0_40 = 0)
% 33.31/8.40 |
% 33.31/8.40 | Applying alpha-rule on (258) yields:
% 33.31/8.40 | (208) spinning = backwards
% 33.31/8.40 | (189) pull = push
% 33.31/8.40 | (261) ~ (all_248_0_40 = 0)
% 33.31/8.40 |
% 33.31/8.40 | Equations (189) can reduce 102 to:
% 33.31/8.40 | (167) $false
% 33.31/8.40 |
% 33.31/8.40 |-The branch is then unsatisfiable
% 33.31/8.40 |-Branch two:
% 33.31/8.40 | (263) spinning = forwards & ~ (all_248_1_41 = 0)
% 33.31/8.40 |
% 33.31/8.40 | Applying alpha-rule on (263) yields:
% 33.31/8.40 | (213) spinning = forwards
% 33.31/8.40 | (265) ~ (all_248_1_41 = 0)
% 33.31/8.40 |
% 33.31/8.40 | Equations (213) can reduce 33 to:
% 33.31/8.40 | (167) $false
% 33.31/8.40 |
% 33.31/8.40 |-The branch is then unsatisfiable
% 33.31/8.40 |-Branch two:
% 33.31/8.40 | (267) ~ (all_136_0_31 = push)
% 33.31/8.40 | (268) (all_136_0_31 = pull & n2 = n0) | (all_136_0_31 = pull & n1 = n0)
% 33.31/8.40 |
% 33.31/8.40 +-Applying beta-rule and splitting (268), into two cases.
% 33.31/8.40 |-Branch one:
% 33.31/8.40 | (269) all_136_0_31 = pull & n2 = n0
% 33.31/8.40 |
% 33.31/8.40 | Applying alpha-rule on (269) yields:
% 33.31/8.40 | (270) all_136_0_31 = pull
% 33.31/8.40 | (195) n2 = n0
% 33.31/8.40 |
% 33.31/8.40 | Equations (195) can reduce 153 to:
% 33.31/8.40 | (167) $false
% 33.31/8.40 |
% 33.31/8.40 |-The branch is then unsatisfiable
% 33.31/8.40 |-Branch two:
% 33.31/8.40 | (273) all_136_0_31 = pull & n1 = n0
% 33.31/8.40 |
% 33.31/8.40 | Applying alpha-rule on (273) yields:
% 33.31/8.40 | (270) all_136_0_31 = pull
% 33.31/8.40 | (199) n1 = n0
% 33.31/8.40 |
% 33.31/8.40 | Equations (199) can reduce 220 to:
% 33.31/8.40 | (167) $false
% 33.31/8.40 |
% 33.31/8.40 |-The branch is then unsatisfiable
% 33.31/8.40 |-Branch two:
% 33.31/8.40 | (277) plus(n0, n0) = n2
% 33.31/8.40 | (195) n2 = n0
% 33.31/8.40 |
% 33.31/8.40 | From (195)(195) and (95) follows:
% 33.31/8.40 | (279) plus(n0, n0) = n4
% 33.31/8.40 |
% 33.31/8.40 | Using (279) and (221) yields:
% 33.31/8.40 | (163) $false
% 33.31/8.40 |
% 33.31/8.40 |-The branch is then unsatisfiable
% 33.31/8.40 |-Branch two:
% 33.31/8.40 | (200) holdsAt(spinning, n0) = 0
% 33.31/8.40 | (166) all_1_0_0 = 0
% 33.31/8.40 |
% 33.31/8.40 | Equations (166) can reduce 42 to:
% 33.31/8.40 | (167) $false
% 33.31/8.40 |
% 33.31/8.40 |-The branch is then unsatisfiable
% 33.31/8.40 |-Branch two:
% 33.31/8.40 | (279) plus(n0, n0) = n4
% 33.31/8.40 | (285) n4 = n0
% 33.31/8.40 |
% 33.31/8.40 | Equations (285) can reduce 151 to:
% 33.31/8.40 | (286) ~ (n2 = n0)
% 33.31/8.40 |
% 33.31/8.40 | Simplifying 286 yields:
% 33.31/8.40 | (153) ~ (n2 = n0)
% 33.31/8.40 |
% 33.31/8.40 +-Applying beta-rule and splitting (137), into two cases.
% 33.31/8.40 |-Branch one:
% 33.31/8.40 | (201) ~ (holdsAt(spinning, n0) = 0)
% 33.31/8.40 |
% 33.31/8.40 +-Applying beta-rule and splitting (142), into two cases.
% 33.31/8.40 |-Branch one:
% 33.31/8.40 | (154) ? [v0] : ? [v1] : (releasedAt(spinning, n1) = v1 & holdsAt(spinning, n0) = v0 & (v1 = 0 | v0 = 0))
% 33.31/8.40 |
% 33.31/8.40 | Instantiating (154) with all_134_0_42, all_134_1_43 yields:
% 33.31/8.40 | (290) releasedAt(spinning, n1) = all_134_0_42 & holdsAt(spinning, n0) = all_134_1_43 & (all_134_0_42 = 0 | all_134_1_43 = 0)
% 33.31/8.40 |
% 33.31/8.40 | Applying alpha-rule on (290) yields:
% 33.31/8.40 | (291) releasedAt(spinning, n1) = all_134_0_42
% 33.31/8.40 | (292) holdsAt(spinning, n0) = all_134_1_43
% 33.31/8.41 | (293) all_134_0_42 = 0 | all_134_1_43 = 0
% 33.31/8.41 |
% 33.31/8.41 | Instantiating formula (30) with n1, spinning yields:
% 33.31/8.41 | (159) ~ (releasedAt(spinning, n1) = 0)
% 33.31/8.41 |
% 33.31/8.41 | Instantiating formula (4) with spinning, n0, all_134_1_43, all_1_0_0 and discharging atoms holdsAt(spinning, n0) = all_134_1_43, holdsAt(spinning, n0) = all_1_0_0, yields:
% 33.31/8.41 | (295) all_134_1_43 = all_1_0_0
% 33.31/8.41 |
% 33.31/8.41 | Using (292) and (201) yields:
% 33.31/8.41 | (296) ~ (all_134_1_43 = 0)
% 33.31/8.41 |
% 33.31/8.41 | Equations (295) can reduce 296 to:
% 33.31/8.41 | (42) ~ (all_1_0_0 = 0)
% 33.31/8.41 |
% 33.31/8.41 +-Applying beta-rule and splitting (293), into two cases.
% 33.31/8.41 |-Branch one:
% 33.31/8.41 | (298) all_134_0_42 = 0
% 33.31/8.41 |
% 33.31/8.41 | From (298) and (291) follows:
% 33.31/8.41 | (162) releasedAt(spinning, n1) = 0
% 33.31/8.41 |
% 33.31/8.41 | Using (162) and (159) yields:
% 33.31/8.41 | (163) $false
% 33.31/8.41 |
% 33.31/8.41 |-The branch is then unsatisfiable
% 33.31/8.41 |-Branch two:
% 33.31/8.41 | (301) ~ (all_134_0_42 = 0)
% 33.31/8.41 | (302) all_134_1_43 = 0
% 33.31/8.41 |
% 33.31/8.41 | Combining equations (302,295) yields a new equation:
% 33.31/8.41 | (166) all_1_0_0 = 0
% 33.31/8.41 |
% 33.31/8.41 | Equations (166) can reduce 42 to:
% 33.31/8.41 | (167) $false
% 33.31/8.41 |
% 33.31/8.41 |-The branch is then unsatisfiable
% 33.31/8.41 |-Branch two:
% 33.31/8.41 | (168) ? [v0] : (initiates(v0, spinning, n0) = 0 & happens(v0, n0) = 0)
% 33.31/8.41 |
% 33.31/8.41 | Instantiating (168) with all_134_0_44 yields:
% 33.31/8.41 | (306) initiates(all_134_0_44, spinning, n0) = 0 & happens(all_134_0_44, n0) = 0
% 33.31/8.41 |
% 33.31/8.41 | Applying alpha-rule on (306) yields:
% 33.31/8.41 | (307) initiates(all_134_0_44, spinning, n0) = 0
% 33.31/8.41 | (308) happens(all_134_0_44, n0) = 0
% 33.31/8.41 |
% 33.31/8.41 | Instantiating formula (80) with n0, all_134_0_44 and discharging atoms happens(all_134_0_44, n0) = 0, yields:
% 33.31/8.41 | (309) all_134_0_44 = push | (all_134_0_44 = pull & n2 = n0) | (all_134_0_44 = pull & n1 = n0)
% 33.31/8.41 |
% 33.31/8.41 +-Applying beta-rule and splitting (309), into two cases.
% 33.31/8.41 |-Branch one:
% 33.31/8.41 | (310) all_134_0_44 = push
% 33.31/8.41 |
% 33.31/8.41 | From (310) and (307) follows:
% 33.31/8.41 | (247) initiates(push, spinning, n0) = 0
% 33.31/8.41 |
% 33.31/8.41 | Instantiating formula (64) with n0, spinning, push and discharging atoms initiates(push, spinning, n0) = 0, yields:
% 33.31/8.41 | (248) ? [v0] : ? [v1] : (happens(pull, n0) = v0 & happens(push, n0) = v1 & ((v1 = 0 & pull = push) | (spinning = backwards & pull = push & ~ (v1 = 0)) | (spinning = forwards & ~ (v0 = 0))))
% 33.46/8.41 |
% 33.46/8.41 | Instantiating (248) with all_228_0_53, all_228_1_54 yields:
% 33.46/8.41 | (313) happens(pull, n0) = all_228_1_54 & happens(push, n0) = all_228_0_53 & ((all_228_0_53 = 0 & pull = push) | (spinning = backwards & pull = push & ~ (all_228_0_53 = 0)) | (spinning = forwards & ~ (all_228_1_54 = 0)))
% 33.46/8.41 |
% 33.46/8.41 | Applying alpha-rule on (313) yields:
% 33.46/8.41 | (314) happens(pull, n0) = all_228_1_54
% 33.46/8.41 | (315) happens(push, n0) = all_228_0_53
% 33.46/8.41 | (316) (all_228_0_53 = 0 & pull = push) | (spinning = backwards & pull = push & ~ (all_228_0_53 = 0)) | (spinning = forwards & ~ (all_228_1_54 = 0))
% 33.46/8.41 |
% 33.46/8.41 +-Applying beta-rule and splitting (316), into two cases.
% 33.46/8.41 |-Branch one:
% 33.46/8.41 | (317) (all_228_0_53 = 0 & pull = push) | (spinning = backwards & pull = push & ~ (all_228_0_53 = 0))
% 33.46/8.41 |
% 33.46/8.41 +-Applying beta-rule and splitting (317), into two cases.
% 33.46/8.41 |-Branch one:
% 33.46/8.41 | (318) all_228_0_53 = 0 & pull = push
% 33.46/8.41 |
% 33.46/8.41 | Applying alpha-rule on (318) yields:
% 33.46/8.41 | (319) all_228_0_53 = 0
% 33.46/8.41 | (189) pull = push
% 33.46/8.41 |
% 33.46/8.41 | Equations (189) can reduce 102 to:
% 33.46/8.41 | (167) $false
% 33.46/8.41 |
% 33.46/8.41 |-The branch is then unsatisfiable
% 33.46/8.41 |-Branch two:
% 33.46/8.41 | (322) spinning = backwards & pull = push & ~ (all_228_0_53 = 0)
% 33.46/8.41 |
% 33.46/8.41 | Applying alpha-rule on (322) yields:
% 33.46/8.41 | (208) spinning = backwards
% 33.46/8.41 | (189) pull = push
% 33.46/8.41 | (325) ~ (all_228_0_53 = 0)
% 33.46/8.41 |
% 33.46/8.41 | Equations (189) can reduce 102 to:
% 33.46/8.41 | (167) $false
% 33.46/8.41 |
% 33.46/8.41 |-The branch is then unsatisfiable
% 33.46/8.41 |-Branch two:
% 33.46/8.41 | (327) spinning = forwards & ~ (all_228_1_54 = 0)
% 33.46/8.41 |
% 33.46/8.41 | Applying alpha-rule on (327) yields:
% 33.46/8.41 | (213) spinning = forwards
% 33.46/8.41 | (329) ~ (all_228_1_54 = 0)
% 33.46/8.41 |
% 33.46/8.41 | Equations (213) can reduce 33 to:
% 33.46/8.41 | (167) $false
% 33.46/8.41 |
% 33.46/8.41 |-The branch is then unsatisfiable
% 33.46/8.41 |-Branch two:
% 33.46/8.41 | (331) ~ (all_134_0_44 = push)
% 33.46/8.41 | (332) (all_134_0_44 = pull & n2 = n0) | (all_134_0_44 = pull & n1 = n0)
% 33.46/8.41 |
% 33.46/8.41 +-Applying beta-rule and splitting (332), into two cases.
% 33.46/8.41 |-Branch one:
% 33.46/8.41 | (333) all_134_0_44 = pull & n2 = n0
% 33.46/8.41 |
% 33.46/8.41 | Applying alpha-rule on (333) yields:
% 33.46/8.41 | (334) all_134_0_44 = pull
% 33.46/8.41 | (195) n2 = n0
% 33.46/8.41 |
% 33.46/8.41 | Equations (195) can reduce 153 to:
% 33.46/8.41 | (167) $false
% 33.46/8.41 |
% 33.46/8.41 |-The branch is then unsatisfiable
% 33.46/8.41 |-Branch two:
% 33.46/8.41 | (337) all_134_0_44 = pull & n1 = n0
% 33.46/8.41 |
% 33.46/8.41 | Applying alpha-rule on (337) yields:
% 33.46/8.41 | (334) all_134_0_44 = pull
% 33.46/8.41 | (199) n1 = n0
% 33.46/8.41 |
% 33.46/8.41 | Equations (199) can reduce 220 to:
% 33.46/8.41 | (167) $false
% 33.46/8.41 |
% 33.46/8.41 |-The branch is then unsatisfiable
% 33.46/8.41 |-Branch two:
% 33.46/8.41 | (200) holdsAt(spinning, n0) = 0
% 33.46/8.41 | (166) all_1_0_0 = 0
% 33.46/8.41 |
% 33.46/8.41 | Equations (166) can reduce 42 to:
% 33.46/8.41 | (167) $false
% 33.46/8.41 |
% 33.46/8.41 |-The branch is then unsatisfiable
% 33.46/8.41 |-Branch two:
% 33.46/8.41 | (344) plus(n1, n1) = n4
% 33.46/8.41 | (345) n4 = n2
% 33.46/8.41 |
% 33.46/8.41 | Equations (345) can reduce 149 to:
% 33.46/8.41 | (346) ~ (n5 = n2)
% 33.46/8.41 |
% 33.46/8.41 | From (345) and (41) follows:
% 33.46/8.41 | (347) plus(n1, n3) = n2
% 33.46/8.41 |
% 33.46/8.41 | From (345) and (344) follows:
% 33.46/8.41 | (78) plus(n1, n1) = n2
% 33.46/8.41 |
% 33.46/8.41 +-Applying beta-rule and splitting (125), into two cases.
% 33.46/8.41 |-Branch one:
% 33.46/8.41 | (349) ~ (plus(n1, n1) = n6)
% 33.46/8.41 |
% 33.46/8.41 +-Applying beta-rule and splitting (130), into two cases.
% 33.46/8.41 |-Branch one:
% 33.46/8.41 | (350) ~ (plus(n1, n1) = n3)
% 33.46/8.41 |
% 33.46/8.41 | Using (78) and (350) yields:
% 33.46/8.41 | (351) ~ (n3 = n2)
% 33.46/8.41 |
% 33.46/8.41 +-Applying beta-rule and splitting (128), into two cases.
% 33.46/8.41 |-Branch one:
% 33.46/8.41 | (352) ~ (plus(n1, n2) = n4)
% 33.46/8.41 |
% 33.46/8.41 | From (345) and (352) follows:
% 33.46/8.41 | (353) ~ (plus(n1, n2) = n2)
% 33.46/8.41 |
% 33.46/8.41 | Using (63) and (353) yields:
% 33.46/8.41 | (220) ~ (n1 = n0)
% 33.46/8.41 |
% 33.46/8.41 +-Applying beta-rule and splitting (137), into two cases.
% 33.46/8.41 |-Branch one:
% 33.46/8.41 | (201) ~ (holdsAt(spinning, n0) = 0)
% 33.46/8.41 |
% 33.46/8.41 +-Applying beta-rule and splitting (134), into two cases.
% 33.46/8.41 |-Branch one:
% 33.46/8.41 | (221) ~ (plus(n0, n0) = n4)
% 33.46/8.41 |
% 33.46/8.41 | From (345) and (221) follows:
% 33.46/8.41 | (223) ~ (plus(n0, n0) = n2)
% 33.46/8.41 |
% 33.46/8.41 | Using (140) and (223) yields:
% 33.46/8.41 | (153) ~ (n2 = n0)
% 33.46/8.41 |
% 33.46/8.41 +-Applying beta-rule and splitting (142), into two cases.
% 33.46/8.41 |-Branch one:
% 33.46/8.41 | (154) ? [v0] : ? [v1] : (releasedAt(spinning, n1) = v1 & holdsAt(spinning, n0) = v0 & (v1 = 0 | v0 = 0))
% 33.46/8.41 |
% 33.46/8.41 | Instantiating (154) with all_129_0_55, all_129_1_56 yields:
% 33.46/8.41 | (360) releasedAt(spinning, n1) = all_129_0_55 & holdsAt(spinning, n0) = all_129_1_56 & (all_129_0_55 = 0 | all_129_1_56 = 0)
% 33.46/8.41 |
% 33.46/8.41 | Applying alpha-rule on (360) yields:
% 33.46/8.41 | (361) releasedAt(spinning, n1) = all_129_0_55
% 33.46/8.41 | (362) holdsAt(spinning, n0) = all_129_1_56
% 33.46/8.41 | (363) all_129_0_55 = 0 | all_129_1_56 = 0
% 33.46/8.41 |
% 33.46/8.41 | Instantiating formula (30) with n1, spinning yields:
% 33.46/8.41 | (159) ~ (releasedAt(spinning, n1) = 0)
% 33.46/8.41 |
% 33.46/8.41 | Instantiating formula (4) with spinning, n0, all_129_1_56, all_1_0_0 and discharging atoms holdsAt(spinning, n0) = all_129_1_56, holdsAt(spinning, n0) = all_1_0_0, yields:
% 33.46/8.41 | (365) all_129_1_56 = all_1_0_0
% 33.46/8.41 |
% 33.46/8.41 | Using (362) and (201) yields:
% 33.46/8.41 | (366) ~ (all_129_1_56 = 0)
% 33.46/8.41 |
% 33.46/8.41 | Equations (365) can reduce 366 to:
% 33.46/8.41 | (42) ~ (all_1_0_0 = 0)
% 33.46/8.41 |
% 33.46/8.41 +-Applying beta-rule and splitting (363), into two cases.
% 33.46/8.41 |-Branch one:
% 33.46/8.41 | (368) all_129_0_55 = 0
% 33.46/8.41 |
% 33.46/8.41 | From (368) and (361) follows:
% 33.46/8.41 | (162) releasedAt(spinning, n1) = 0
% 33.46/8.41 |
% 33.46/8.41 | Using (162) and (159) yields:
% 33.46/8.41 | (163) $false
% 33.46/8.41 |
% 33.46/8.41 |-The branch is then unsatisfiable
% 33.46/8.41 |-Branch two:
% 33.46/8.41 | (371) ~ (all_129_0_55 = 0)
% 33.46/8.41 | (372) all_129_1_56 = 0
% 33.46/8.41 |
% 33.46/8.41 | Combining equations (372,365) yields a new equation:
% 33.46/8.41 | (166) all_1_0_0 = 0
% 33.46/8.41 |
% 33.46/8.41 | Equations (166) can reduce 42 to:
% 33.46/8.41 | (167) $false
% 33.46/8.41 |
% 33.46/8.41 |-The branch is then unsatisfiable
% 33.46/8.41 |-Branch two:
% 33.46/8.41 | (168) ? [v0] : (initiates(v0, spinning, n0) = 0 & happens(v0, n0) = 0)
% 33.46/8.41 |
% 33.46/8.41 | Instantiating (168) with all_129_0_57 yields:
% 33.46/8.41 | (376) initiates(all_129_0_57, spinning, n0) = 0 & happens(all_129_0_57, n0) = 0
% 33.46/8.41 |
% 33.46/8.41 | Applying alpha-rule on (376) yields:
% 33.46/8.41 | (377) initiates(all_129_0_57, spinning, n0) = 0
% 33.46/8.41 | (378) happens(all_129_0_57, n0) = 0
% 33.46/8.41 |
% 33.46/8.41 | Instantiating formula (80) with n0, all_129_0_57 and discharging atoms happens(all_129_0_57, n0) = 0, yields:
% 33.46/8.41 | (379) all_129_0_57 = push | (all_129_0_57 = pull & n2 = n0) | (all_129_0_57 = pull & n1 = n0)
% 33.46/8.41 |
% 33.46/8.41 +-Applying beta-rule and splitting (379), into two cases.
% 33.46/8.41 |-Branch one:
% 33.46/8.41 | (380) all_129_0_57 = push
% 33.46/8.41 |
% 33.46/8.41 | From (380) and (377) follows:
% 33.46/8.41 | (247) initiates(push, spinning, n0) = 0
% 33.46/8.41 |
% 33.46/8.41 | Instantiating formula (64) with n0, spinning, push and discharging atoms initiates(push, spinning, n0) = 0, yields:
% 33.46/8.41 | (248) ? [v0] : ? [v1] : (happens(pull, n0) = v0 & happens(push, n0) = v1 & ((v1 = 0 & pull = push) | (spinning = backwards & pull = push & ~ (v1 = 0)) | (spinning = forwards & ~ (v0 = 0))))
% 33.46/8.41 |
% 33.46/8.41 | Instantiating (248) with all_283_0_66, all_283_1_67 yields:
% 33.46/8.41 | (383) happens(pull, n0) = all_283_1_67 & happens(push, n0) = all_283_0_66 & ((all_283_0_66 = 0 & pull = push) | (spinning = backwards & pull = push & ~ (all_283_0_66 = 0)) | (spinning = forwards & ~ (all_283_1_67 = 0)))
% 33.46/8.41 |
% 33.46/8.41 | Applying alpha-rule on (383) yields:
% 33.46/8.41 | (384) happens(pull, n0) = all_283_1_67
% 33.46/8.41 | (385) happens(push, n0) = all_283_0_66
% 33.46/8.41 | (386) (all_283_0_66 = 0 & pull = push) | (spinning = backwards & pull = push & ~ (all_283_0_66 = 0)) | (spinning = forwards & ~ (all_283_1_67 = 0))
% 33.46/8.41 |
% 33.46/8.41 +-Applying beta-rule and splitting (386), into two cases.
% 33.46/8.41 |-Branch one:
% 33.46/8.41 | (387) (all_283_0_66 = 0 & pull = push) | (spinning = backwards & pull = push & ~ (all_283_0_66 = 0))
% 33.46/8.41 |
% 33.46/8.41 +-Applying beta-rule and splitting (387), into two cases.
% 33.46/8.41 |-Branch one:
% 33.46/8.42 | (388) all_283_0_66 = 0 & pull = push
% 33.46/8.42 |
% 33.46/8.42 | Applying alpha-rule on (388) yields:
% 33.46/8.42 | (389) all_283_0_66 = 0
% 33.46/8.42 | (189) pull = push
% 33.46/8.42 |
% 33.46/8.42 | Equations (189) can reduce 102 to:
% 33.46/8.42 | (167) $false
% 33.46/8.42 |
% 33.46/8.42 |-The branch is then unsatisfiable
% 33.46/8.42 |-Branch two:
% 33.46/8.42 | (392) spinning = backwards & pull = push & ~ (all_283_0_66 = 0)
% 33.46/8.42 |
% 33.46/8.42 | Applying alpha-rule on (392) yields:
% 33.46/8.42 | (208) spinning = backwards
% 33.46/8.42 | (189) pull = push
% 33.46/8.42 | (395) ~ (all_283_0_66 = 0)
% 33.46/8.42 |
% 33.46/8.42 | Equations (189) can reduce 102 to:
% 33.46/8.42 | (167) $false
% 33.46/8.42 |
% 33.46/8.42 |-The branch is then unsatisfiable
% 33.46/8.42 |-Branch two:
% 33.46/8.42 | (397) spinning = forwards & ~ (all_283_1_67 = 0)
% 33.46/8.42 |
% 33.46/8.42 | Applying alpha-rule on (397) yields:
% 33.46/8.42 | (213) spinning = forwards
% 33.46/8.42 | (399) ~ (all_283_1_67 = 0)
% 33.46/8.42 |
% 33.46/8.42 | Equations (213) can reduce 33 to:
% 33.46/8.42 | (167) $false
% 33.46/8.42 |
% 33.46/8.42 |-The branch is then unsatisfiable
% 33.46/8.42 |-Branch two:
% 33.46/8.42 | (401) ~ (all_129_0_57 = push)
% 33.46/8.42 | (402) (all_129_0_57 = pull & n2 = n0) | (all_129_0_57 = pull & n1 = n0)
% 33.46/8.42 |
% 33.46/8.42 +-Applying beta-rule and splitting (402), into two cases.
% 33.46/8.42 |-Branch one:
% 33.46/8.42 | (403) all_129_0_57 = pull & n2 = n0
% 33.46/8.42 |
% 33.46/8.42 | Applying alpha-rule on (403) yields:
% 33.46/8.42 | (404) all_129_0_57 = pull
% 33.46/8.42 | (195) n2 = n0
% 33.46/8.42 |
% 33.46/8.42 | Equations (195) can reduce 153 to:
% 33.46/8.42 | (167) $false
% 33.46/8.42 |
% 33.46/8.42 |-The branch is then unsatisfiable
% 33.46/8.42 |-Branch two:
% 33.46/8.42 | (407) all_129_0_57 = pull & n1 = n0
% 33.46/8.42 |
% 33.46/8.42 | Applying alpha-rule on (407) yields:
% 33.46/8.42 | (404) all_129_0_57 = pull
% 33.46/8.42 | (199) n1 = n0
% 33.46/8.42 |
% 33.46/8.42 | Equations (199) can reduce 220 to:
% 33.46/8.42 | (167) $false
% 33.46/8.42 |
% 33.46/8.42 |-The branch is then unsatisfiable
% 33.46/8.42 |-Branch two:
% 33.46/8.42 | (279) plus(n0, n0) = n4
% 33.46/8.42 | (285) n4 = n0
% 33.46/8.42 |
% 33.46/8.42 | Combining equations (285,345) yields a new equation:
% 33.46/8.42 | (195) n2 = n0
% 33.46/8.42 |
% 33.46/8.42 | From (195) and (32) follows:
% 33.46/8.42 | (414) plus(n1, n0) = n3
% 33.46/8.42 |
% 33.46/8.42 +-Applying beta-rule and splitting (146), into two cases.
% 33.46/8.42 |-Branch one:
% 33.46/8.42 | (415) ~ (plus(n1, n0) = n3)
% 33.46/8.42 |
% 33.46/8.42 | Using (414) and (415) yields:
% 33.46/8.42 | (163) $false
% 33.46/8.42 |
% 33.46/8.42 |-The branch is then unsatisfiable
% 33.46/8.42 |-Branch two:
% 33.46/8.42 | (414) plus(n1, n0) = n3
% 33.46/8.42 | (418) n3 = n1
% 33.46/8.42 |
% 33.46/8.42 | From (418)(418) and (98) follows:
% 33.46/8.42 | (419) plus(n1, n1) = n6
% 33.46/8.42 |
% 33.46/8.42 | Using (419) and (349) yields:
% 33.46/8.42 | (163) $false
% 33.46/8.42 |
% 33.46/8.42 |-The branch is then unsatisfiable
% 33.46/8.42 |-Branch two:
% 33.46/8.42 | (200) holdsAt(spinning, n0) = 0
% 33.46/8.42 | (166) all_1_0_0 = 0
% 33.46/8.42 |
% 33.46/8.42 | Equations (166) can reduce 42 to:
% 33.46/8.42 | (167) $false
% 33.46/8.42 |
% 33.46/8.42 |-The branch is then unsatisfiable
% 33.46/8.42 |-Branch two:
% 33.46/8.42 | (424) plus(n1, n2) = n4
% 33.46/8.42 | (425) n4 = n2 | ~ (plus(n1, n2) = n2)
% 33.46/8.42 |
% 33.46/8.42 | From (345) and (424) follows:
% 33.46/8.42 | (426) plus(n1, n2) = n2
% 33.46/8.42 |
% 33.46/8.42 | Instantiating formula (9) with n1, n2, n2, n3 and discharging atoms plus(n1, n2) = n3, plus(n1, n2) = n2, yields:
% 33.46/8.42 | (427) n3 = n2
% 33.46/8.42 |
% 33.46/8.42 | Equations (427) can reduce 351 to:
% 33.46/8.42 | (167) $false
% 33.46/8.42 |
% 33.46/8.42 |-The branch is then unsatisfiable
% 33.46/8.42 |-Branch two:
% 33.46/8.42 | (429) plus(n1, n1) = n3
% 33.46/8.42 | (430) n3 = n1 | ~ (plus(n1, n1) = n1)
% 33.46/8.42 |
% 33.46/8.42 +-Applying beta-rule and splitting (127), into two cases.
% 33.46/8.42 |-Branch one:
% 33.46/8.42 | (150) ~ (plus(n1, n1) = n4)
% 33.46/8.42 |
% 33.46/8.42 | From (345) and (150) follows:
% 33.46/8.42 | (432) ~ (plus(n1, n1) = n2)
% 33.46/8.42 |
% 33.46/8.42 | Using (78) and (432) yields:
% 33.46/8.42 | (163) $false
% 33.46/8.42 |
% 33.46/8.42 |-The branch is then unsatisfiable
% 33.46/8.42 |-Branch two:
% 33.46/8.42 | (344) plus(n1, n1) = n4
% 33.46/8.42 | (435) n4 = n3 | ~ (plus(n1, n1) = n3)
% 33.46/8.42 |
% 33.46/8.42 +-Applying beta-rule and splitting (435), into two cases.
% 33.46/8.42 |-Branch one:
% 33.46/8.42 | (350) ~ (plus(n1, n1) = n3)
% 33.46/8.42 |
% 33.46/8.42 | Using (429) and (350) yields:
% 33.46/8.42 | (163) $false
% 33.46/8.42 |
% 33.46/8.42 |-The branch is then unsatisfiable
% 33.46/8.42 |-Branch two:
% 33.46/8.42 | (429) plus(n1, n1) = n3
% 33.46/8.42 | (439) n4 = n3
% 33.46/8.42 |
% 33.46/8.42 | Combining equations (439,345) yields a new equation:
% 33.46/8.42 | (440) n3 = n2
% 33.46/8.42 |
% 33.46/8.42 | Simplifying 440 yields:
% 33.46/8.42 | (427) n3 = n2
% 33.46/8.42 |
% 33.46/8.42 | From (427) and (84) follows:
% 33.46/8.42 | (442) plus(n2, n2) = n5
% 33.46/8.42 |
% 33.46/8.42 +-Applying beta-rule and splitting (124), into two cases.
% 33.46/8.42 |-Branch one:
% 33.46/8.42 | (443) ~ (plus(n2, n2) = n5)
% 33.46/8.42 |
% 33.46/8.42 | Using (442) and (443) yields:
% 33.46/8.42 | (163) $false
% 33.46/8.42 |
% 33.46/8.42 |-The branch is then unsatisfiable
% 33.46/8.42 |-Branch two:
% 33.46/8.42 | (442) plus(n2, n2) = n5
% 33.46/8.42 | (446) n5 = n4
% 33.46/8.42 |
% 33.46/8.42 | Combining equations (345,446) yields a new equation:
% 33.46/8.42 | (447) n5 = n2
% 33.46/8.42 |
% 33.46/8.42 | Equations (447) can reduce 346 to:
% 33.46/8.42 | (167) $false
% 33.46/8.42 |
% 33.46/8.42 |-The branch is then unsatisfiable
% 33.46/8.42 |-Branch two:
% 33.46/8.42 | (419) plus(n1, n1) = n6
% 33.46/8.42 | (450) n6 = n4 | ~ (plus(n1, n1) = n4)
% 33.46/8.42 |
% 33.46/8.42 +-Applying beta-rule and splitting (450), into two cases.
% 33.46/8.42 |-Branch one:
% 33.46/8.42 | (150) ~ (plus(n1, n1) = n4)
% 33.46/8.42 |
% 33.46/8.42 | From (345) and (150) follows:
% 33.46/8.42 | (432) ~ (plus(n1, n1) = n2)
% 33.46/8.42 |
% 33.46/8.42 | Using (78) and (432) yields:
% 33.46/8.42 | (163) $false
% 33.46/8.42 |
% 33.46/8.42 |-The branch is then unsatisfiable
% 33.46/8.42 |-Branch two:
% 33.46/8.42 | (344) plus(n1, n1) = n4
% 33.46/8.42 | (455) n6 = n4
% 33.46/8.42 |
% 33.46/8.42 | Combining equations (345,455) yields a new equation:
% 33.46/8.42 | (456) n6 = n2
% 33.46/8.42 |
% 33.46/8.42 | From (345) and (344) follows:
% 33.46/8.42 | (78) plus(n1, n1) = n2
% 33.46/8.42 |
% 33.46/8.42 +-Applying beta-rule and splitting (130), into two cases.
% 33.46/8.42 |-Branch one:
% 33.46/8.42 | (350) ~ (plus(n1, n1) = n3)
% 33.46/8.42 |
% 33.46/8.42 | Using (78) and (350) yields:
% 33.46/8.42 | (351) ~ (n3 = n2)
% 33.46/8.42 |
% 33.46/8.42 +-Applying beta-rule and splitting (128), into two cases.
% 33.46/8.42 |-Branch one:
% 33.46/8.42 | (352) ~ (plus(n1, n2) = n4)
% 33.46/8.42 |
% 33.46/8.42 | From (345) and (352) follows:
% 33.46/8.42 | (353) ~ (plus(n1, n2) = n2)
% 33.46/8.42 |
% 33.46/8.42 | Using (63) and (353) yields:
% 33.46/8.42 | (220) ~ (n1 = n0)
% 33.46/8.42 |
% 33.46/8.42 +-Applying beta-rule and splitting (131), into two cases.
% 33.46/8.42 |-Branch one:
% 33.46/8.42 | (463) ~ (plus(n0, n0) = n6)
% 33.46/8.42 |
% 33.46/8.42 | From (456) and (463) follows:
% 33.46/8.42 | (223) ~ (plus(n0, n0) = n2)
% 33.46/8.42 |
% 33.46/8.42 | Using (140) and (223) yields:
% 33.46/8.42 | (153) ~ (n2 = n0)
% 33.46/8.42 |
% 33.46/8.42 +-Applying beta-rule and splitting (142), into two cases.
% 33.46/8.42 |-Branch one:
% 33.46/8.42 | (154) ? [v0] : ? [v1] : (releasedAt(spinning, n1) = v1 & holdsAt(spinning, n0) = v0 & (v1 = 0 | v0 = 0))
% 33.46/8.42 |
% 33.46/8.42 | Instantiating (154) with all_110_0_68, all_110_1_69 yields:
% 33.46/8.42 | (467) releasedAt(spinning, n1) = all_110_0_68 & holdsAt(spinning, n0) = all_110_1_69 & (all_110_0_68 = 0 | all_110_1_69 = 0)
% 33.46/8.42 |
% 33.46/8.42 | Applying alpha-rule on (467) yields:
% 33.46/8.42 | (468) releasedAt(spinning, n1) = all_110_0_68
% 33.46/8.42 | (469) holdsAt(spinning, n0) = all_110_1_69
% 33.46/8.42 | (470) all_110_0_68 = 0 | all_110_1_69 = 0
% 33.46/8.42 |
% 33.46/8.42 | Instantiating formula (30) with n1, spinning yields:
% 33.46/8.42 | (159) ~ (releasedAt(spinning, n1) = 0)
% 33.46/8.42 |
% 33.46/8.42 | Instantiating formula (4) with spinning, n0, all_110_1_69, all_1_0_0 and discharging atoms holdsAt(spinning, n0) = all_110_1_69, holdsAt(spinning, n0) = all_1_0_0, yields:
% 33.46/8.42 | (472) all_110_1_69 = all_1_0_0
% 33.46/8.42 |
% 33.46/8.42 +-Applying beta-rule and splitting (470), into two cases.
% 33.46/8.42 |-Branch one:
% 33.46/8.42 | (473) all_110_0_68 = 0
% 33.46/8.42 |
% 33.46/8.42 | From (473) and (468) follows:
% 33.46/8.42 | (162) releasedAt(spinning, n1) = 0
% 33.46/8.42 |
% 33.46/8.42 | Using (162) and (159) yields:
% 33.46/8.42 | (163) $false
% 33.46/8.42 |
% 33.46/8.42 |-The branch is then unsatisfiable
% 33.46/8.42 |-Branch two:
% 33.46/8.42 | (476) ~ (all_110_0_68 = 0)
% 33.46/8.42 | (477) all_110_1_69 = 0
% 33.46/8.42 |
% 33.46/8.42 | Combining equations (477,472) yields a new equation:
% 33.46/8.42 | (166) all_1_0_0 = 0
% 33.46/8.42 |
% 33.46/8.42 | Equations (166) can reduce 42 to:
% 33.46/8.42 | (167) $false
% 33.46/8.42 |
% 33.46/8.42 |-The branch is then unsatisfiable
% 33.46/8.42 |-Branch two:
% 33.46/8.42 | (168) ? [v0] : (initiates(v0, spinning, n0) = 0 & happens(v0, n0) = 0)
% 33.46/8.42 |
% 33.46/8.42 | Instantiating (168) with all_110_0_70 yields:
% 33.46/8.42 | (481) initiates(all_110_0_70, spinning, n0) = 0 & happens(all_110_0_70, n0) = 0
% 33.46/8.43 |
% 33.46/8.43 | Applying alpha-rule on (481) yields:
% 33.46/8.43 | (482) initiates(all_110_0_70, spinning, n0) = 0
% 33.46/8.43 | (483) happens(all_110_0_70, n0) = 0
% 33.46/8.43 |
% 33.46/8.43 | Instantiating formula (80) with n0, all_110_0_70 and discharging atoms happens(all_110_0_70, n0) = 0, yields:
% 33.46/8.43 | (484) all_110_0_70 = push | (all_110_0_70 = pull & n2 = n0) | (all_110_0_70 = pull & n1 = n0)
% 33.46/8.43 |
% 33.46/8.43 +-Applying beta-rule and splitting (484), into two cases.
% 33.46/8.43 |-Branch one:
% 33.46/8.43 | (485) all_110_0_70 = push
% 33.46/8.43 |
% 33.46/8.43 | From (485) and (482) follows:
% 33.46/8.43 | (247) initiates(push, spinning, n0) = 0
% 33.46/8.43 |
% 33.46/8.43 | Instantiating formula (64) with n0, spinning, push and discharging atoms initiates(push, spinning, n0) = 0, yields:
% 33.46/8.43 | (248) ? [v0] : ? [v1] : (happens(pull, n0) = v0 & happens(push, n0) = v1 & ((v1 = 0 & pull = push) | (spinning = backwards & pull = push & ~ (v1 = 0)) | (spinning = forwards & ~ (v0 = 0))))
% 33.46/8.43 |
% 33.46/8.43 | Instantiating (248) with all_248_0_79, all_248_1_80 yields:
% 33.46/8.43 | (488) happens(pull, n0) = all_248_1_80 & happens(push, n0) = all_248_0_79 & ((all_248_0_79 = 0 & pull = push) | (spinning = backwards & pull = push & ~ (all_248_0_79 = 0)) | (spinning = forwards & ~ (all_248_1_80 = 0)))
% 33.46/8.43 |
% 33.46/8.43 | Applying alpha-rule on (488) yields:
% 33.46/8.43 | (489) happens(pull, n0) = all_248_1_80
% 33.46/8.43 | (490) happens(push, n0) = all_248_0_79
% 33.46/8.43 | (491) (all_248_0_79 = 0 & pull = push) | (spinning = backwards & pull = push & ~ (all_248_0_79 = 0)) | (spinning = forwards & ~ (all_248_1_80 = 0))
% 33.46/8.43 |
% 33.46/8.43 +-Applying beta-rule and splitting (491), into two cases.
% 33.46/8.43 |-Branch one:
% 33.46/8.43 | (492) (all_248_0_79 = 0 & pull = push) | (spinning = backwards & pull = push & ~ (all_248_0_79 = 0))
% 33.46/8.43 |
% 33.46/8.43 +-Applying beta-rule and splitting (492), into two cases.
% 33.46/8.43 |-Branch one:
% 33.46/8.43 | (493) all_248_0_79 = 0 & pull = push
% 33.46/8.43 |
% 33.46/8.43 | Applying alpha-rule on (493) yields:
% 33.46/8.43 | (494) all_248_0_79 = 0
% 33.46/8.43 | (189) pull = push
% 33.46/8.43 |
% 33.46/8.43 | Equations (189) can reduce 102 to:
% 33.46/8.43 | (167) $false
% 33.46/8.43 |
% 33.46/8.43 |-The branch is then unsatisfiable
% 33.46/8.43 |-Branch two:
% 33.46/8.43 | (497) spinning = backwards & pull = push & ~ (all_248_0_79 = 0)
% 33.46/8.43 |
% 33.46/8.43 | Applying alpha-rule on (497) yields:
% 33.46/8.43 | (208) spinning = backwards
% 33.46/8.43 | (189) pull = push
% 33.46/8.43 | (500) ~ (all_248_0_79 = 0)
% 33.46/8.43 |
% 33.46/8.43 | Equations (189) can reduce 102 to:
% 33.46/8.43 | (167) $false
% 33.46/8.43 |
% 33.46/8.43 |-The branch is then unsatisfiable
% 33.46/8.43 |-Branch two:
% 33.46/8.43 | (502) spinning = forwards & ~ (all_248_1_80 = 0)
% 33.46/8.43 |
% 33.46/8.43 | Applying alpha-rule on (502) yields:
% 33.46/8.43 | (213) spinning = forwards
% 33.46/8.43 | (504) ~ (all_248_1_80 = 0)
% 33.46/8.43 |
% 33.46/8.43 | Equations (213) can reduce 33 to:
% 33.46/8.43 | (167) $false
% 33.46/8.43 |
% 33.46/8.43 |-The branch is then unsatisfiable
% 33.46/8.43 |-Branch two:
% 33.46/8.43 | (506) ~ (all_110_0_70 = push)
% 33.46/8.43 | (507) (all_110_0_70 = pull & n2 = n0) | (all_110_0_70 = pull & n1 = n0)
% 33.46/8.43 |
% 33.46/8.43 +-Applying beta-rule and splitting (507), into two cases.
% 33.46/8.43 |-Branch one:
% 33.46/8.43 | (508) all_110_0_70 = pull & n2 = n0
% 33.46/8.43 |
% 33.46/8.43 | Applying alpha-rule on (508) yields:
% 33.46/8.43 | (509) all_110_0_70 = pull
% 33.46/8.43 | (195) n2 = n0
% 33.46/8.43 |
% 33.46/8.43 | Equations (195) can reduce 153 to:
% 33.46/8.43 | (167) $false
% 33.46/8.43 |
% 33.46/8.43 |-The branch is then unsatisfiable
% 33.46/8.43 |-Branch two:
% 33.46/8.43 | (512) all_110_0_70 = pull & n1 = n0
% 33.46/8.43 |
% 33.46/8.43 | Applying alpha-rule on (512) yields:
% 33.46/8.43 | (509) all_110_0_70 = pull
% 33.46/8.43 | (199) n1 = n0
% 33.46/8.43 |
% 33.46/8.43 | Equations (199) can reduce 220 to:
% 33.46/8.43 | (167) $false
% 33.46/8.43 |
% 33.46/8.43 |-The branch is then unsatisfiable
% 33.46/8.43 |-Branch two:
% 33.46/8.43 | (516) plus(n0, n0) = n6
% 33.46/8.43 | (517) n6 = n0
% 33.46/8.43 |
% 33.46/8.43 | Combining equations (517,456) yields a new equation:
% 33.46/8.43 | (195) n2 = n0
% 33.46/8.43 |
% 33.46/8.43 | Combining equations (195,345) yields a new equation:
% 33.46/8.43 | (285) n4 = n0
% 33.46/8.43 |
% 33.46/8.43 | Combining equations (195,456) yields a new equation:
% 33.46/8.43 | (517) n6 = n0
% 33.46/8.43 |
% 33.46/8.43 | Equations (195) can reduce 346 to:
% 33.46/8.43 | (521) ~ (n5 = n0)
% 33.46/8.43 |
% 33.46/8.43 | From (195) and (84) follows:
% 33.46/8.43 | (216) plus(n0, n3) = n5
% 33.46/8.43 |
% 33.46/8.43 | From (195) and (139) follows:
% 33.46/8.43 | (523) plus(n0, n1) = n3
% 33.46/8.43 |
% 33.46/8.43 | From (195) and (347) follows:
% 33.46/8.43 | (524) plus(n1, n3) = n0
% 33.46/8.43 |
% 33.46/8.43 | From (517) and (516) follows:
% 33.46/8.43 | (101) plus(n0, n0) = n0
% 33.46/8.43 |
% 33.46/8.43 +-Applying beta-rule and splitting (132), into two cases.
% 33.46/8.43 |-Branch one:
% 33.46/8.43 | (152) ~ (plus(n0, n3) = n5)
% 33.46/8.43 |
% 33.46/8.43 | Using (216) and (152) yields:
% 33.46/8.43 | (163) $false
% 33.46/8.43 |
% 33.46/8.43 |-The branch is then unsatisfiable
% 33.46/8.43 |-Branch two:
% 33.46/8.43 | (216) plus(n0, n3) = n5
% 33.46/8.43 | (217) n5 = n3
% 33.46/8.43 |
% 33.46/8.43 | Equations (217) can reduce 521 to:
% 33.46/8.43 | (530) ~ (n3 = n0)
% 33.46/8.43 |
% 33.46/8.43 +-Applying beta-rule and splitting (145), into two cases.
% 33.46/8.43 |-Branch one:
% 33.46/8.43 | (531) ~ (plus(n0, n1) = n3)
% 33.46/8.43 |
% 33.46/8.43 | Using (523) and (531) yields:
% 33.46/8.43 | (163) $false
% 33.46/8.43 |
% 33.46/8.43 |-The branch is then unsatisfiable
% 33.46/8.43 |-Branch two:
% 33.46/8.43 | (523) plus(n0, n1) = n3
% 33.46/8.43 | (418) n3 = n1
% 33.46/8.43 |
% 33.46/8.43 | Equations (418) can reduce 530 to:
% 33.46/8.43 | (220) ~ (n1 = n0)
% 33.46/8.43 |
% 33.46/8.43 | From (418) and (524) follows:
% 33.46/8.43 | (536) plus(n1, n1) = n0
% 33.46/8.43 |
% 33.46/8.43 | From (418) and (523) follows:
% 33.46/8.43 | (79) plus(n0, n1) = n1
% 33.46/8.43 |
% 33.46/8.43 +-Applying beta-rule and splitting (142), into two cases.
% 33.46/8.43 |-Branch one:
% 33.46/8.43 | (154) ? [v0] : ? [v1] : (releasedAt(spinning, n1) = v1 & holdsAt(spinning, n0) = v0 & (v1 = 0 | v0 = 0))
% 33.46/8.43 |
% 33.46/8.43 | Instantiating (154) with all_100_0_81, all_100_1_82 yields:
% 33.46/8.43 | (539) releasedAt(spinning, n1) = all_100_0_81 & holdsAt(spinning, n0) = all_100_1_82 & (all_100_0_81 = 0 | all_100_1_82 = 0)
% 33.46/8.43 |
% 33.46/8.43 | Applying alpha-rule on (539) yields:
% 33.46/8.43 | (540) releasedAt(spinning, n1) = all_100_0_81
% 33.46/8.43 | (541) holdsAt(spinning, n0) = all_100_1_82
% 33.46/8.43 | (542) all_100_0_81 = 0 | all_100_1_82 = 0
% 33.46/8.43 |
% 33.46/8.43 | Instantiating formula (30) with n1, spinning yields:
% 33.46/8.43 | (159) ~ (releasedAt(spinning, n1) = 0)
% 33.46/8.43 |
% 33.46/8.43 | Instantiating formula (4) with spinning, n0, all_100_1_82, all_1_0_0 and discharging atoms holdsAt(spinning, n0) = all_100_1_82, holdsAt(spinning, n0) = all_1_0_0, yields:
% 33.46/8.43 | (544) all_100_1_82 = all_1_0_0
% 33.46/8.43 |
% 33.46/8.43 +-Applying beta-rule and splitting (542), into two cases.
% 33.46/8.43 |-Branch one:
% 33.46/8.43 | (545) all_100_0_81 = 0
% 33.46/8.43 |
% 33.46/8.43 | From (545) and (540) follows:
% 33.46/8.43 | (162) releasedAt(spinning, n1) = 0
% 33.46/8.43 |
% 33.46/8.43 | Using (162) and (159) yields:
% 33.46/8.43 | (163) $false
% 33.46/8.43 |
% 33.46/8.43 |-The branch is then unsatisfiable
% 33.46/8.43 |-Branch two:
% 33.46/8.43 | (548) ~ (all_100_0_81 = 0)
% 33.46/8.43 | (549) all_100_1_82 = 0
% 33.46/8.43 |
% 33.46/8.43 | Combining equations (549,544) yields a new equation:
% 33.46/8.43 | (166) all_1_0_0 = 0
% 33.46/8.43 |
% 33.46/8.43 | Equations (166) can reduce 42 to:
% 33.46/8.43 | (167) $false
% 33.56/8.43 |
% 33.56/8.43 |-The branch is then unsatisfiable
% 33.56/8.43 |-Branch two:
% 33.56/8.43 | (168) ? [v0] : (initiates(v0, spinning, n0) = 0 & happens(v0, n0) = 0)
% 33.56/8.43 |
% 33.56/8.43 | Instantiating (168) with all_100_0_83 yields:
% 33.56/8.43 | (553) initiates(all_100_0_83, spinning, n0) = 0 & happens(all_100_0_83, n0) = 0
% 33.56/8.43 |
% 33.56/8.43 | Applying alpha-rule on (553) yields:
% 33.56/8.43 | (554) initiates(all_100_0_83, spinning, n0) = 0
% 33.56/8.43 | (555) happens(all_100_0_83, n0) = 0
% 33.56/8.43 |
% 33.56/8.43 | Instantiating formula (29) with all_1_0_0, n0, n0, spinning, spinning, n0, all_100_0_83 and discharging atoms plus(n0, n0) = n0, holdsAt(spinning, n0) = all_1_0_0, initiates(all_100_0_83, spinning, n0) = 0, yields:
% 33.56/8.43 | (556) all_1_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (trajectory(spinning, n0, spinning, n0) = v2 & stoppedIn(n0, spinning, n0) = v3 & happens(all_100_0_83, n0) = v0 & less(n0, n0) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0))
% 33.56/8.43 |
% 33.56/8.43 | Instantiating formula (29) with all_1_1_1, n0, n0, backwards, spinning, n0, all_100_0_83 and discharging atoms plus(n0, n0) = n0, holdsAt(backwards, n0) = all_1_1_1, initiates(all_100_0_83, spinning, n0) = 0, yields:
% 33.56/8.43 | (557) all_1_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (trajectory(spinning, n0, backwards, n0) = v2 & stoppedIn(n0, spinning, n0) = v3 & happens(all_100_0_83, n0) = v0 & less(n0, n0) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0))
% 33.56/8.43 |
% 33.56/8.43 | Instantiating formula (64) with n0, spinning, all_100_0_83 and discharging atoms initiates(all_100_0_83, spinning, n0) = 0, yields:
% 33.56/8.43 | (558) ? [v0] : ? [v1] : (happens(pull, n0) = v0 & happens(push, n0) = v1 & ((v1 = 0 & all_100_0_83 = pull) | (all_100_0_83 = pull & spinning = backwards & ~ (v1 = 0)) | (all_100_0_83 = push & spinning = forwards & ~ (v0 = 0))))
% 33.56/8.43 |
% 33.56/8.43 | Instantiating formula (48) with 0, spinning, n0, all_100_0_83 and discharging atoms initiates(all_100_0_83, spinning, n0) = 0, yields:
% 33.56/8.43 | (559) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (releasedAt(spinning, v2) = v3 & plus(n0, n1) = v2 & happens(all_100_0_83, n0) = v0 & terminates(all_100_0_83, spinning, n0) = v1 & ( ~ (v3 = 0) | ~ (v0 = 0)))
% 33.56/8.43 |
% 33.56/8.43 | Instantiating (558) with all_109_0_85, all_109_1_86 yields:
% 33.56/8.43 | (560) happens(pull, n0) = all_109_1_86 & happens(push, n0) = all_109_0_85 & ((all_109_0_85 = 0 & all_100_0_83 = pull) | (all_100_0_83 = pull & spinning = backwards & ~ (all_109_0_85 = 0)) | (all_100_0_83 = push & spinning = forwards & ~ (all_109_1_86 = 0)))
% 33.56/8.43 |
% 33.56/8.43 | Applying alpha-rule on (560) yields:
% 33.56/8.43 | (561) happens(pull, n0) = all_109_1_86
% 33.56/8.43 | (562) happens(push, n0) = all_109_0_85
% 33.56/8.43 | (563) (all_109_0_85 = 0 & all_100_0_83 = pull) | (all_100_0_83 = pull & spinning = backwards & ~ (all_109_0_85 = 0)) | (all_100_0_83 = push & spinning = forwards & ~ (all_109_1_86 = 0))
% 33.56/8.43 |
% 33.56/8.43 | Instantiating (559) with all_111_0_87, all_111_1_88, all_111_2_89, all_111_3_90 yields:
% 33.56/8.43 | (564) releasedAt(spinning, all_111_1_88) = all_111_0_87 & plus(n0, n1) = all_111_1_88 & happens(all_100_0_83, n0) = all_111_3_90 & terminates(all_100_0_83, spinning, n0) = all_111_2_89 & ( ~ (all_111_0_87 = 0) | ~ (all_111_3_90 = 0))
% 33.56/8.43 |
% 33.56/8.43 | Applying alpha-rule on (564) yields:
% 33.56/8.43 | (565) terminates(all_100_0_83, spinning, n0) = all_111_2_89
% 33.56/8.43 | (566) ~ (all_111_0_87 = 0) | ~ (all_111_3_90 = 0)
% 33.56/8.43 | (567) plus(n0, n1) = all_111_1_88
% 33.56/8.43 | (568) happens(all_100_0_83, n0) = all_111_3_90
% 33.56/8.43 | (569) releasedAt(spinning, all_111_1_88) = all_111_0_87
% 33.56/8.44 |
% 33.56/8.44 +-Applying beta-rule and splitting (563), into two cases.
% 33.56/8.44 |-Branch one:
% 33.56/8.44 | (570) (all_109_0_85 = 0 & all_100_0_83 = pull) | (all_100_0_83 = pull & spinning = backwards & ~ (all_109_0_85 = 0))
% 33.56/8.44 |
% 33.56/8.44 +-Applying beta-rule and splitting (570), into two cases.
% 33.56/8.44 |-Branch one:
% 33.56/8.44 | (571) all_109_0_85 = 0 & all_100_0_83 = pull
% 33.56/8.44 |
% 33.56/8.44 | Applying alpha-rule on (571) yields:
% 33.56/8.44 | (572) all_109_0_85 = 0
% 33.56/8.44 | (573) all_100_0_83 = pull
% 33.56/8.44 |
% 33.56/8.44 | From (573) and (554) follows:
% 33.56/8.44 | (574) initiates(pull, spinning, n0) = 0
% 33.56/8.44 |
% 33.56/8.44 | From (573) and (568) follows:
% 33.56/8.44 | (575) happens(pull, n0) = all_111_3_90
% 33.56/8.44 |
% 33.56/8.44 | From (573) and (555) follows:
% 33.56/8.44 | (576) happens(pull, n0) = 0
% 33.56/8.44 |
% 33.56/8.44 +-Applying beta-rule and splitting (556), into two cases.
% 33.56/8.44 |-Branch one:
% 33.56/8.44 | (166) all_1_0_0 = 0
% 33.56/8.44 |
% 33.56/8.44 | Equations (166) can reduce 42 to:
% 33.56/8.44 | (167) $false
% 33.56/8.44 |
% 33.56/8.44 |-The branch is then unsatisfiable
% 33.56/8.44 |-Branch two:
% 33.56/8.44 | (42) ~ (all_1_0_0 = 0)
% 33.56/8.44 | (580) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (trajectory(spinning, n0, spinning, n0) = v2 & stoppedIn(n0, spinning, n0) = v3 & happens(all_100_0_83, n0) = v0 & less(n0, n0) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0))
% 33.56/8.44 |
% 33.56/8.44 +-Applying beta-rule and splitting (557), into two cases.
% 33.56/8.44 |-Branch one:
% 33.56/8.44 | (581) all_1_1_1 = 0
% 33.56/8.44 |
% 33.56/8.44 | Equations (581) can reduce 118 to:
% 33.56/8.44 | (167) $false
% 33.56/8.44 |
% 33.56/8.44 |-The branch is then unsatisfiable
% 33.56/8.44 |-Branch two:
% 33.56/8.44 | (118) ~ (all_1_1_1 = 0)
% 33.56/8.44 | (584) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (trajectory(spinning, n0, backwards, n0) = v2 & stoppedIn(n0, spinning, n0) = v3 & happens(all_100_0_83, n0) = v0 & less(n0, n0) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0))
% 33.56/8.44 |
% 33.56/8.44 | Instantiating formula (30) with all_111_1_88, spinning yields:
% 33.56/8.44 | (585) ~ (releasedAt(spinning, all_111_1_88) = 0)
% 33.56/8.44 |
% 33.56/8.44 | Instantiating formula (9) with n0, n1, all_111_1_88, n1 and discharging atoms plus(n0, n1) = all_111_1_88, plus(n0, n1) = n1, yields:
% 33.56/8.44 | (586) all_111_1_88 = n1
% 33.56/8.44 |
% 33.56/8.44 | Instantiating formula (10) with pull, n0, 0, all_111_3_90 and discharging atoms happens(pull, n0) = all_111_3_90, happens(pull, n0) = 0, yields:
% 33.56/8.44 | (587) all_111_3_90 = 0
% 33.56/8.44 |
% 33.56/8.44 | From (586) and (569) follows:
% 33.56/8.44 | (588) releasedAt(spinning, n1) = all_111_0_87
% 33.56/8.44 |
% 33.56/8.44 | From (586) and (567) follows:
% 33.56/8.44 | (79) plus(n0, n1) = n1
% 33.56/8.44 |
% 33.56/8.44 | From (586) and (585) follows:
% 33.56/8.44 | (159) ~ (releasedAt(spinning, n1) = 0)
% 33.56/8.44 |
% 33.56/8.44 +-Applying beta-rule and splitting (566), into two cases.
% 33.56/8.44 |-Branch one:
% 33.56/8.44 | (591) ~ (all_111_0_87 = 0)
% 33.56/8.44 |
% 33.56/8.44 +-Applying beta-rule and splitting (144), into two cases.
% 33.56/8.44 |-Branch one:
% 33.56/8.44 | (166) all_1_0_0 = 0
% 33.56/8.44 |
% 33.56/8.44 | Equations (166) can reduce 42 to:
% 33.56/8.44 | (167) $false
% 33.56/8.44 |
% 33.56/8.44 |-The branch is then unsatisfiable
% 33.56/8.44 |-Branch two:
% 33.56/8.44 | (42) ~ (all_1_0_0 = 0)
% 33.56/8.44 | (595) ? [v0] : ? [v1] : ? [v2] : (releasedAt(spinning, v0) = v1 & plus(n0, n1) = v0 & holdsAt(spinning, v0) = v2 & ( ~ (v2 = 0) | v1 = 0)) | ? [v0] : (initiates(v0, spinning, n0) = 0 & happens(v0, n0) = 0)
% 33.56/8.44 |
% 33.56/8.44 +-Applying beta-rule and splitting (147), into two cases.
% 33.56/8.44 |-Branch one:
% 33.56/8.44 | (596) ~ (plus(n2, n1) = n1)
% 33.56/8.44 |
% 33.56/8.44 | From (195) and (596) follows:
% 33.56/8.44 | (597) ~ (plus(n0, n1) = n1)
% 33.56/8.44 |
% 33.56/8.44 | Using (79) and (597) yields:
% 33.56/8.44 | (163) $false
% 33.56/8.44 |
% 33.56/8.44 |-The branch is then unsatisfiable
% 33.56/8.44 |-Branch two:
% 33.56/8.44 | (599) plus(n2, n1) = n1
% 33.56/8.44 | (600) ? [v0] : ? [v1] : (releasedAt(spinning, n1) = v1 & holdsAt(spinning, n2) = v0 & (v1 = 0 | v0 = 0)) | ? [v0] : (initiates(v0, spinning, n2) = 0 & happens(v0, n2) = 0)
% 33.56/8.44 |
% 33.56/8.44 | From (195) and (599) follows:
% 33.56/8.44 | (79) plus(n0, n1) = n1
% 33.56/8.44 |
% 33.56/8.44 +-Applying beta-rule and splitting (595), into two cases.
% 33.56/8.44 |-Branch one:
% 33.56/8.44 | (602) ? [v0] : ? [v1] : ? [v2] : (releasedAt(spinning, v0) = v1 & plus(n0, n1) = v0 & holdsAt(spinning, v0) = v2 & ( ~ (v2 = 0) | v1 = 0))
% 33.56/8.44 |
% 33.56/8.44 | Instantiating (602) with all_150_0_103, all_150_1_104, all_150_2_105 yields:
% 33.56/8.44 | (603) releasedAt(spinning, all_150_2_105) = all_150_1_104 & plus(n0, n1) = all_150_2_105 & holdsAt(spinning, all_150_2_105) = all_150_0_103 & ( ~ (all_150_0_103 = 0) | all_150_1_104 = 0)
% 33.56/8.44 |
% 33.56/8.44 | Applying alpha-rule on (603) yields:
% 33.56/8.44 | (604) releasedAt(spinning, all_150_2_105) = all_150_1_104
% 33.56/8.44 | (605) plus(n0, n1) = all_150_2_105
% 33.56/8.44 | (606) holdsAt(spinning, all_150_2_105) = all_150_0_103
% 33.56/8.44 | (607) ~ (all_150_0_103 = 0) | all_150_1_104 = 0
% 33.56/8.44 |
% 33.56/8.44 | Instantiating formula (7) with spinning, n1, all_111_0_87, all_150_1_104 and discharging atoms releasedAt(spinning, n1) = all_111_0_87, yields:
% 33.56/8.44 | (608) all_150_1_104 = all_111_0_87 | ~ (releasedAt(spinning, n1) = all_150_1_104)
% 33.56/8.44 |
% 33.56/8.44 | Instantiating formula (9) with n0, n1, all_150_2_105, n1 and discharging atoms plus(n0, n1) = all_150_2_105, plus(n0, n1) = n1, yields:
% 33.56/8.44 | (609) all_150_2_105 = n1
% 33.56/8.44 |
% 33.56/8.44 | Instantiating formula (4) with spinning, n1, all_150_0_103, 0 and discharging atoms holdsAt(spinning, n1) = 0, yields:
% 33.56/8.44 | (610) all_150_0_103 = 0 | ~ (holdsAt(spinning, n1) = all_150_0_103)
% 33.56/8.44 |
% 33.56/8.44 | From (609) and (604) follows:
% 33.56/8.44 | (611) releasedAt(spinning, n1) = all_150_1_104
% 33.56/8.44 |
% 33.56/8.44 | From (609) and (606) follows:
% 33.56/8.44 | (612) holdsAt(spinning, n1) = all_150_0_103
% 33.56/8.44 |
% 33.56/8.44 +-Applying beta-rule and splitting (610), into two cases.
% 33.56/8.44 |-Branch one:
% 33.56/8.44 | (613) ~ (holdsAt(spinning, n1) = all_150_0_103)
% 33.56/8.44 |
% 33.56/8.44 | Using (612) and (613) yields:
% 33.56/8.44 | (163) $false
% 33.56/8.44 |
% 33.56/8.44 |-The branch is then unsatisfiable
% 33.56/8.44 |-Branch two:
% 33.56/8.44 | (612) holdsAt(spinning, n1) = all_150_0_103
% 33.56/8.44 | (616) all_150_0_103 = 0
% 33.56/8.44 |
% 33.56/8.44 +-Applying beta-rule and splitting (608), into two cases.
% 33.56/8.44 |-Branch one:
% 33.56/8.44 | (617) ~ (releasedAt(spinning, n1) = all_150_1_104)
% 33.56/8.44 |
% 33.56/8.44 | Using (611) and (617) yields:
% 33.56/8.44 | (163) $false
% 33.56/8.44 |
% 33.56/8.44 |-The branch is then unsatisfiable
% 33.56/8.44 |-Branch two:
% 33.56/8.44 | (611) releasedAt(spinning, n1) = all_150_1_104
% 33.56/8.44 | (620) all_150_1_104 = all_111_0_87
% 33.56/8.44 |
% 33.56/8.44 +-Applying beta-rule and splitting (607), into two cases.
% 33.56/8.44 |-Branch one:
% 33.56/8.44 | (621) ~ (all_150_0_103 = 0)
% 33.56/8.44 |
% 33.56/8.44 | Equations (616) can reduce 621 to:
% 33.56/8.44 | (167) $false
% 33.56/8.44 |
% 33.56/8.44 |-The branch is then unsatisfiable
% 33.56/8.44 |-Branch two:
% 33.56/8.44 | (616) all_150_0_103 = 0
% 33.56/8.44 | (624) all_150_1_104 = 0
% 33.56/8.44 |
% 33.56/8.44 | Combining equations (624,620) yields a new equation:
% 33.56/8.44 | (625) all_111_0_87 = 0
% 33.56/8.44 |
% 33.56/8.44 | Equations (625) can reduce 591 to:
% 33.56/8.44 | (167) $false
% 33.56/8.44 |
% 33.56/8.44 |-The branch is then unsatisfiable
% 33.56/8.44 |-Branch two:
% 33.56/8.44 | (168) ? [v0] : (initiates(v0, spinning, n0) = 0 & happens(v0, n0) = 0)
% 33.56/8.44 |
% 33.56/8.44 | Instantiating (168) with all_150_0_109 yields:
% 33.56/8.44 | (628) initiates(all_150_0_109, spinning, n0) = 0 & happens(all_150_0_109, n0) = 0
% 33.56/8.44 |
% 33.56/8.44 | Applying alpha-rule on (628) yields:
% 33.56/8.44 | (629) initiates(all_150_0_109, spinning, n0) = 0
% 33.56/8.44 | (630) happens(all_150_0_109, n0) = 0
% 33.56/8.44 |
% 33.56/8.44 +-Applying beta-rule and splitting (600), into two cases.
% 33.56/8.44 |-Branch one:
% 33.56/8.44 | (631) ? [v0] : ? [v1] : (releasedAt(spinning, n1) = v1 & holdsAt(spinning, n2) = v0 & (v1 = 0 | v0 = 0))
% 33.56/8.44 |
% 33.56/8.44 | Instantiating (631) with all_154_0_110, all_154_1_111 yields:
% 33.56/8.44 | (632) releasedAt(spinning, n1) = all_154_0_110 & holdsAt(spinning, n2) = all_154_1_111 & (all_154_0_110 = 0 | all_154_1_111 = 0)
% 33.56/8.44 |
% 33.56/8.44 | Applying alpha-rule on (632) yields:
% 33.56/8.44 | (633) releasedAt(spinning, n1) = all_154_0_110
% 33.56/8.44 | (634) holdsAt(spinning, n2) = all_154_1_111
% 33.56/8.44 | (635) all_154_0_110 = 0 | all_154_1_111 = 0
% 33.56/8.44 |
% 33.56/8.44 | From (195) and (634) follows:
% 33.56/8.44 | (636) holdsAt(spinning, n0) = all_154_1_111
% 33.56/8.44 |
% 33.56/8.44 | Instantiating formula (7) with spinning, n1, all_111_0_87, all_154_0_110 and discharging atoms releasedAt(spinning, n1) = all_154_0_110, releasedAt(spinning, n1) = all_111_0_87, yields:
% 33.56/8.44 | (637) all_154_0_110 = all_111_0_87
% 33.56/8.44 |
% 33.56/8.44 | Instantiating formula (4) with spinning, n0, all_154_1_111, all_1_0_0 and discharging atoms holdsAt(spinning, n0) = all_154_1_111, holdsAt(spinning, n0) = all_1_0_0, yields:
% 33.56/8.44 | (638) all_154_1_111 = all_1_0_0
% 33.56/8.44 |
% 33.56/8.44 | Using (633) and (159) yields:
% 33.56/8.44 | (639) ~ (all_154_0_110 = 0)
% 33.56/8.44 |
% 33.56/8.44 | Equations (637) can reduce 639 to:
% 33.56/8.44 | (591) ~ (all_111_0_87 = 0)
% 33.56/8.44 |
% 33.56/8.44 +-Applying beta-rule and splitting (635), into two cases.
% 33.56/8.44 |-Branch one:
% 33.56/8.44 | (641) all_154_0_110 = 0
% 33.56/8.44 |
% 33.56/8.44 | Combining equations (641,637) yields a new equation:
% 33.56/8.44 | (625) all_111_0_87 = 0
% 33.56/8.44 |
% 33.56/8.44 | Equations (625) can reduce 591 to:
% 33.56/8.44 | (167) $false
% 33.56/8.44 |
% 33.56/8.44 |-The branch is then unsatisfiable
% 33.56/8.44 |-Branch two:
% 33.56/8.44 | (639) ~ (all_154_0_110 = 0)
% 33.56/8.44 | (645) all_154_1_111 = 0
% 33.56/8.44 |
% 33.56/8.44 | Combining equations (645,638) yields a new equation:
% 33.56/8.44 | (166) all_1_0_0 = 0
% 33.56/8.44 |
% 33.56/8.44 | Equations (166) can reduce 42 to:
% 33.56/8.44 | (167) $false
% 33.56/8.44 |
% 33.56/8.44 |-The branch is then unsatisfiable
% 33.56/8.44 |-Branch two:
% 33.56/8.44 | (648) ? [v0] : (initiates(v0, spinning, n2) = 0 & happens(v0, n2) = 0)
% 33.56/8.44 |
% 33.56/8.44 | Instantiating (648) with all_154_0_112 yields:
% 33.56/8.44 | (649) initiates(all_154_0_112, spinning, n2) = 0 & happens(all_154_0_112, n2) = 0
% 33.56/8.44 |
% 33.56/8.44 | Applying alpha-rule on (649) yields:
% 33.56/8.44 | (650) initiates(all_154_0_112, spinning, n2) = 0
% 33.56/8.44 | (651) happens(all_154_0_112, n2) = 0
% 33.56/8.44 |
% 33.56/8.44 | From (195) and (650) follows:
% 33.56/8.44 | (652) initiates(all_154_0_112, spinning, n0) = 0
% 33.56/8.44 |
% 33.56/8.44 +-Applying beta-rule and splitting (136), into two cases.
% 33.56/8.44 |-Branch one:
% 33.56/8.44 | (223) ~ (plus(n0, n0) = n2)
% 33.56/8.44 |
% 33.56/8.44 | From (195) and (223) follows:
% 33.56/8.44 | (654) ~ (plus(n0, n0) = n0)
% 33.56/8.45 |
% 33.56/8.45 | Using (101) and (654) yields:
% 33.56/8.45 | (163) $false
% 33.56/8.45 |
% 33.56/8.45 |-The branch is then unsatisfiable
% 33.56/8.45 |-Branch two:
% 33.56/8.45 | (277) plus(n0, n0) = n2
% 33.56/8.45 | (195) n2 = n0
% 33.56/8.45 |
% 33.56/8.45 | From (195) and (277) follows:
% 33.56/8.45 | (101) plus(n0, n0) = n0
% 33.56/8.45 |
% 33.56/8.45 +-Applying beta-rule and splitting (134), into two cases.
% 33.56/8.45 |-Branch one:
% 33.56/8.45 | (221) ~ (plus(n0, n0) = n4)
% 33.56/8.45 |
% 33.56/8.45 | From (285) and (221) follows:
% 33.56/8.45 | (654) ~ (plus(n0, n0) = n0)
% 33.56/8.45 |
% 33.56/8.45 | Using (101) and (654) yields:
% 33.56/8.45 | (163) $false
% 33.56/8.45 |
% 33.56/8.45 |-The branch is then unsatisfiable
% 33.56/8.45 |-Branch two:
% 33.56/8.45 | (279) plus(n0, n0) = n4
% 33.56/8.45 | (285) n4 = n0
% 33.56/8.45 |
% 33.56/8.45 | From (285) and (279) follows:
% 33.56/8.45 | (101) plus(n0, n0) = n0
% 33.56/8.45 |
% 33.56/8.45 +-Applying beta-rule and splitting (143), into two cases.
% 33.56/8.45 |-Branch one:
% 33.56/8.45 | (665) ? [v0] : ? [v1] : ? [v2] : (releasedAt(spinning, v0) = v1 & plus(n1, n1) = v0 & holdsAt(spinning, v0) = v2 & (v2 = 0 | v1 = 0))
% 33.56/8.45 |
% 33.56/8.45 | Instantiating (665) with all_195_0_113, all_195_1_114, all_195_2_115 yields:
% 33.56/8.45 | (666) releasedAt(spinning, all_195_2_115) = all_195_1_114 & plus(n1, n1) = all_195_2_115 & holdsAt(spinning, all_195_2_115) = all_195_0_113 & (all_195_0_113 = 0 | all_195_1_114 = 0)
% 33.56/8.45 |
% 33.56/8.45 | Applying alpha-rule on (666) yields:
% 33.56/8.45 | (667) releasedAt(spinning, all_195_2_115) = all_195_1_114
% 33.56/8.45 | (668) plus(n1, n1) = all_195_2_115
% 33.56/8.45 | (669) holdsAt(spinning, all_195_2_115) = all_195_0_113
% 33.56/8.45 | (670) all_195_0_113 = 0 | all_195_1_114 = 0
% 33.56/8.45 |
% 33.56/8.45 | Instantiating formula (30) with all_195_2_115, spinning yields:
% 33.56/8.45 | (671) ~ (releasedAt(spinning, all_195_2_115) = 0)
% 33.56/8.45 |
% 33.56/8.45 | Instantiating formula (9) with n1, n1, all_195_2_115, n0 and discharging atoms plus(n1, n1) = all_195_2_115, plus(n1, n1) = n0, yields:
% 33.56/8.45 | (672) all_195_2_115 = n0
% 33.56/8.45 |
% 33.56/8.45 | Instantiating formula (4) with spinning, n0, all_195_0_113, all_1_0_0 and discharging atoms holdsAt(spinning, n0) = all_1_0_0, yields:
% 33.56/8.45 | (673) all_195_0_113 = all_1_0_0 | ~ (holdsAt(spinning, n0) = all_195_0_113)
% 33.56/8.45 |
% 33.56/8.45 | From (672) and (667) follows:
% 33.56/8.45 | (674) releasedAt(spinning, n0) = all_195_1_114
% 33.56/8.45 |
% 33.56/8.45 | From (672) and (669) follows:
% 33.56/8.45 | (675) holdsAt(spinning, n0) = all_195_0_113
% 33.56/8.45 |
% 33.56/8.45 | From (672) and (671) follows:
% 33.56/8.45 | (676) ~ (releasedAt(spinning, n0) = 0)
% 33.56/8.45 |
% 33.56/8.45 +-Applying beta-rule and splitting (673), into two cases.
% 33.56/8.45 |-Branch one:
% 33.56/8.45 | (677) ~ (holdsAt(spinning, n0) = all_195_0_113)
% 33.56/8.45 |
% 33.56/8.45 | Using (675) and (677) yields:
% 33.56/8.45 | (163) $false
% 33.56/8.45 |
% 33.56/8.45 |-The branch is then unsatisfiable
% 33.56/8.45 |-Branch two:
% 33.56/8.45 | (675) holdsAt(spinning, n0) = all_195_0_113
% 33.56/8.45 | (680) all_195_0_113 = all_1_0_0
% 33.56/8.45 |
% 33.56/8.45 +-Applying beta-rule and splitting (670), into two cases.
% 33.56/8.45 |-Branch one:
% 33.56/8.45 | (681) all_195_0_113 = 0
% 33.56/8.45 |
% 33.56/8.45 | Combining equations (681,680) yields a new equation:
% 33.56/8.45 | (166) all_1_0_0 = 0
% 33.56/8.45 |
% 33.56/8.45 | Equations (166) can reduce 42 to:
% 33.56/8.45 | (167) $false
% 33.56/8.45 |
% 33.56/8.45 |-The branch is then unsatisfiable
% 33.56/8.45 |-Branch two:
% 33.56/8.45 | (684) ~ (all_195_0_113 = 0)
% 33.56/8.45 | (685) all_195_1_114 = 0
% 33.56/8.45 |
% 33.56/8.45 | From (685) and (674) follows:
% 33.56/8.45 | (686) releasedAt(spinning, n0) = 0
% 33.56/8.45 |
% 33.56/8.45 | Using (686) and (676) yields:
% 33.56/8.45 | (163) $false
% 33.56/8.45 |
% 33.56/8.45 |-The branch is then unsatisfiable
% 33.56/8.45 |-Branch two:
% 33.56/8.45 | (688) ? [v0] : (happens(v0, n1) = 0 & terminates(v0, spinning, n1) = 0)
% 33.56/8.45 |
% 33.56/8.45 | Instantiating (688) with all_195_0_116 yields:
% 33.56/8.45 | (689) happens(all_195_0_116, n1) = 0 & terminates(all_195_0_116, spinning, n1) = 0
% 33.56/8.45 |
% 33.56/8.45 | Applying alpha-rule on (689) yields:
% 33.56/8.45 | (690) happens(all_195_0_116, n1) = 0
% 33.56/8.45 | (691) terminates(all_195_0_116, spinning, n1) = 0
% 33.56/8.45 |
% 33.56/8.45 | Instantiating formula (80) with n1, all_195_0_116 and discharging atoms happens(all_195_0_116, n1) = 0, yields:
% 33.56/8.45 | (692) all_195_0_116 = pull | (all_195_0_116 = push & n2 = n1) | (all_195_0_116 = push & n1 = n0)
% 33.56/8.45 |
% 33.56/8.45 +-Applying beta-rule and splitting (123), into two cases.
% 33.56/8.45 |-Branch one:
% 33.56/8.45 | (693) ~ (plus(n2, n2) = n6)
% 33.56/8.45 |
% 33.56/8.45 | From (195)(195)(517) and (693) follows:
% 33.56/8.45 | (654) ~ (plus(n0, n0) = n0)
% 33.56/8.45 |
% 33.56/8.45 | Using (101) and (654) yields:
% 33.56/8.45 | (163) $false
% 33.56/8.45 |
% 33.56/8.45 |-The branch is then unsatisfiable
% 33.56/8.45 |-Branch two:
% 33.56/8.45 | (696) plus(n2, n2) = n6
% 33.56/8.45 | (697) n6 = n5 | ~ (plus(n2, n2) = n5)
% 33.56/8.45 |
% 33.56/8.45 | From (195)(195)(517) and (696) follows:
% 33.56/8.45 | (101) plus(n0, n0) = n0
% 33.56/8.45 |
% 33.56/8.45 +-Applying beta-rule and splitting (692), into two cases.
% 33.56/8.45 |-Branch one:
% 33.56/8.45 | (699) all_195_0_116 = pull
% 33.56/8.45 |
% 33.56/8.45 | From (699) and (690) follows:
% 33.56/8.45 | (700) happens(pull, n1) = 0
% 33.56/8.45 |
% 33.56/8.45 | From (699) and (691) follows:
% 33.56/8.45 | (701) terminates(pull, spinning, n1) = 0
% 33.56/8.45 |
% 33.56/8.45 | Instantiating formula (29) with all_1_1_1, n0, n0, backwards, spinning, n0, all_154_0_112 and discharging atoms plus(n0, n0) = n0, holdsAt(backwards, n0) = all_1_1_1, initiates(all_154_0_112, spinning, n0) = 0, yields:
% 33.56/8.45 | (702) all_1_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (trajectory(spinning, n0, backwards, n0) = v2 & stoppedIn(n0, spinning, n0) = v3 & happens(all_154_0_112, n0) = v0 & less(n0, n0) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0))
% 33.56/8.45 |
% 33.56/8.45 | Instantiating formula (29) with all_1_1_1, n0, n0, backwards, spinning, n0, all_150_0_109 and discharging atoms plus(n0, n0) = n0, holdsAt(backwards, n0) = all_1_1_1, initiates(all_150_0_109, spinning, n0) = 0, yields:
% 33.56/8.45 | (703) all_1_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (trajectory(spinning, n0, backwards, n0) = v2 & stoppedIn(n0, spinning, n0) = v3 & happens(all_150_0_109, n0) = v0 & less(n0, n0) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0))
% 33.56/8.45 |
% 33.56/8.45 | Instantiating formula (29) with all_1_1_1, n0, n0, backwards, spinning, n0, pull and discharging atoms plus(n0, n0) = n0, holdsAt(backwards, n0) = all_1_1_1, initiates(pull, spinning, n0) = 0, yields:
% 33.56/8.45 | (704) all_1_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (trajectory(spinning, n0, backwards, n0) = v2 & stoppedIn(n0, spinning, n0) = v3 & happens(pull, n0) = v0 & less(n0, n0) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0))
% 33.56/8.45 |
% 33.56/8.45 | Instantiating formula (111) with all_1_1_1, n0, backwards, n1, pull and discharging atoms plus(n1, n1) = n0, holdsAt(backwards, n0) = all_1_1_1, happens(pull, n1) = 0, yields:
% 33.56/8.45 | (705) all_1_1_1 = 0 | ? [v0] : ( ~ (v0 = 0) & initiates(pull, backwards, n1) = v0)
% 33.56/8.45 |
% 33.56/8.45 | Instantiating formula (85) with n1, spinning, pull and discharging atoms terminates(pull, spinning, n1) = 0, yields:
% 33.56/8.45 | (706) ? [v0] : ? [v1] : (happens(pull, n1) = v0 & happens(push, n1) = v1 & ( ~ (v1 = 0) | spinning = backwards | spinning = forwards | (pull = push & ~ (v0 = 0))))
% 33.56/8.45 |
% 33.56/8.45 | Instantiating (706) with all_229_0_136, all_229_1_137 yields:
% 33.56/8.45 | (707) happens(pull, n1) = all_229_1_137 & happens(push, n1) = all_229_0_136 & ( ~ (all_229_0_136 = 0) | spinning = backwards | spinning = forwards | (pull = push & ~ (all_229_1_137 = 0)))
% 33.56/8.45 |
% 33.56/8.45 | Applying alpha-rule on (707) yields:
% 33.56/8.45 | (708) happens(pull, n1) = all_229_1_137
% 33.56/8.45 | (709) happens(push, n1) = all_229_0_136
% 33.56/8.45 | (710) ~ (all_229_0_136 = 0) | spinning = backwards | spinning = forwards | (pull = push & ~ (all_229_1_137 = 0))
% 33.56/8.45 |
% 33.56/8.45 +-Applying beta-rule and splitting (702), into two cases.
% 33.56/8.45 |-Branch one:
% 33.56/8.45 | (581) all_1_1_1 = 0
% 33.56/8.45 |
% 33.56/8.45 | Equations (581) can reduce 118 to:
% 33.56/8.45 | (167) $false
% 33.56/8.45 |
% 33.56/8.45 |-The branch is then unsatisfiable
% 33.56/8.45 |-Branch two:
% 33.56/8.45 | (118) ~ (all_1_1_1 = 0)
% 33.56/8.45 | (714) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (trajectory(spinning, n0, backwards, n0) = v2 & stoppedIn(n0, spinning, n0) = v3 & happens(all_154_0_112, n0) = v0 & less(n0, n0) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0))
% 33.56/8.45 |
% 33.56/8.45 +-Applying beta-rule and splitting (704), into two cases.
% 33.56/8.45 |-Branch one:
% 33.56/8.45 | (581) all_1_1_1 = 0
% 33.56/8.45 |
% 33.56/8.45 | Equations (581) can reduce 118 to:
% 33.56/8.45 | (167) $false
% 33.56/8.45 |
% 33.56/8.45 |-The branch is then unsatisfiable
% 33.56/8.45 |-Branch two:
% 33.56/8.45 | (118) ~ (all_1_1_1 = 0)
% 33.56/8.45 | (718) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (trajectory(spinning, n0, backwards, n0) = v2 & stoppedIn(n0, spinning, n0) = v3 & happens(pull, n0) = v0 & less(n0, n0) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0))
% 33.56/8.45 |
% 33.56/8.45 +-Applying beta-rule and splitting (703), into two cases.
% 33.56/8.45 |-Branch one:
% 33.56/8.45 | (581) all_1_1_1 = 0
% 33.56/8.45 |
% 33.56/8.45 | Equations (581) can reduce 118 to:
% 33.56/8.45 | (167) $false
% 33.56/8.45 |
% 33.56/8.45 |-The branch is then unsatisfiable
% 33.56/8.45 |-Branch two:
% 33.56/8.45 | (118) ~ (all_1_1_1 = 0)
% 33.56/8.45 | (722) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (trajectory(spinning, n0, backwards, n0) = v2 & stoppedIn(n0, spinning, n0) = v3 & happens(all_150_0_109, n0) = v0 & less(n0, n0) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0))
% 33.56/8.45 |
% 33.56/8.46 +-Applying beta-rule and splitting (705), into two cases.
% 33.56/8.46 |-Branch one:
% 33.56/8.46 | (581) all_1_1_1 = 0
% 33.56/8.46 |
% 33.56/8.46 | Equations (581) can reduce 118 to:
% 33.56/8.46 | (167) $false
% 33.56/8.46 |
% 33.56/8.46 |-The branch is then unsatisfiable
% 33.56/8.46 |-Branch two:
% 33.56/8.46 | (118) ~ (all_1_1_1 = 0)
% 33.56/8.46 | (726) ? [v0] : ( ~ (v0 = 0) & initiates(pull, backwards, n1) = v0)
% 33.56/8.46 |
% 33.56/8.46 | Instantiating (726) with all_280_0_163 yields:
% 33.56/8.46 | (727) ~ (all_280_0_163 = 0) & initiates(pull, backwards, n1) = all_280_0_163
% 33.56/8.46 |
% 33.56/8.46 | Applying alpha-rule on (727) yields:
% 33.56/8.46 | (728) ~ (all_280_0_163 = 0)
% 33.56/8.46 | (729) initiates(pull, backwards, n1) = all_280_0_163
% 33.56/8.46 |
% 33.56/8.46 +-Applying beta-rule and splitting (710), into two cases.
% 33.56/8.46 |-Branch one:
% 33.56/8.46 | (730) ~ (all_229_0_136 = 0)
% 33.56/8.46 |
% 33.56/8.46 | Instantiating formula (10) with push, n1, 0, all_229_0_136 and discharging atoms happens(push, n1) = all_229_0_136, yields:
% 33.56/8.46 | (731) all_229_0_136 = 0 | ~ (happens(push, n1) = 0)
% 33.56/8.46 |
% 33.56/8.46 | Instantiating formula (120) with all_280_0_163, n1, backwards, pull and discharging atoms initiates(pull, backwards, n1) = all_280_0_163, yields:
% 33.56/8.46 | (732) all_280_0_163 = 0 | ? [v0] : ( ~ (spinning = backwards) & happens(pull, n1) = v0 & happens(push, n1) = 0 & ( ~ (backwards = forwards) | ~ (pull = push) | v0 = 0))
% 33.56/8.46 |
% 33.56/8.46 +-Applying beta-rule and splitting (732), into two cases.
% 33.56/8.46 |-Branch one:
% 33.56/8.46 | (733) all_280_0_163 = 0
% 33.56/8.46 |
% 33.56/8.46 | Equations (733) can reduce 728 to:
% 33.56/8.46 | (167) $false
% 33.56/8.46 |
% 33.56/8.46 |-The branch is then unsatisfiable
% 33.56/8.46 |-Branch two:
% 33.56/8.46 | (728) ~ (all_280_0_163 = 0)
% 33.56/8.46 | (736) ? [v0] : ( ~ (spinning = backwards) & happens(pull, n1) = v0 & happens(push, n1) = 0 & ( ~ (backwards = forwards) | ~ (pull = push) | v0 = 0))
% 33.56/8.46 |
% 33.56/8.46 | Instantiating (736) with all_557_0_212 yields:
% 33.56/8.46 | (737) ~ (spinning = backwards) & happens(pull, n1) = all_557_0_212 & happens(push, n1) = 0 & ( ~ (backwards = forwards) | ~ (pull = push) | all_557_0_212 = 0)
% 33.56/8.46 |
% 33.56/8.46 | Applying alpha-rule on (737) yields:
% 33.56/8.46 | (52) ~ (spinning = backwards)
% 33.56/8.46 | (739) happens(pull, n1) = all_557_0_212
% 33.56/8.46 | (740) happens(push, n1) = 0
% 33.56/8.46 | (741) ~ (backwards = forwards) | ~ (pull = push) | all_557_0_212 = 0
% 33.56/8.46 |
% 33.56/8.46 +-Applying beta-rule and splitting (731), into two cases.
% 33.56/8.46 |-Branch one:
% 33.56/8.46 | (742) ~ (happens(push, n1) = 0)
% 33.56/8.46 |
% 33.56/8.46 | Using (740) and (742) yields:
% 33.56/8.46 | (163) $false
% 33.56/8.46 |
% 33.56/8.46 |-The branch is then unsatisfiable
% 33.56/8.46 |-Branch two:
% 33.56/8.46 | (740) happens(push, n1) = 0
% 33.56/8.46 | (745) all_229_0_136 = 0
% 33.56/8.46 |
% 33.56/8.46 | Equations (745) can reduce 730 to:
% 33.56/8.46 | (167) $false
% 33.56/8.46 |
% 33.56/8.46 |-The branch is then unsatisfiable
% 33.56/8.46 |-Branch two:
% 33.56/8.46 | (745) all_229_0_136 = 0
% 33.56/8.46 | (748) spinning = backwards | spinning = forwards | (pull = push & ~ (all_229_1_137 = 0))
% 33.56/8.46 |
% 33.56/8.46 +-Applying beta-rule and splitting (748), into two cases.
% 33.56/8.46 |-Branch one:
% 33.56/8.46 | (208) spinning = backwards
% 33.56/8.46 |
% 33.56/8.46 | Equations (208) can reduce 52 to:
% 33.56/8.46 | (167) $false
% 33.56/8.46 |
% 33.56/8.46 |-The branch is then unsatisfiable
% 33.56/8.46 |-Branch two:
% 33.56/8.46 | (52) ~ (spinning = backwards)
% 33.56/8.46 | (752) spinning = forwards | (pull = push & ~ (all_229_1_137 = 0))
% 33.56/8.46 |
% 33.56/8.46 +-Applying beta-rule and splitting (752), into two cases.
% 33.56/8.46 |-Branch one:
% 33.56/8.46 | (213) spinning = forwards
% 33.56/8.46 |
% 33.56/8.46 | Equations (213) can reduce 33 to:
% 33.56/8.46 | (167) $false
% 33.56/8.46 |
% 33.56/8.46 |-The branch is then unsatisfiable
% 33.56/8.46 |-Branch two:
% 33.56/8.46 | (33) ~ (spinning = forwards)
% 33.56/8.46 | (756) pull = push & ~ (all_229_1_137 = 0)
% 33.56/8.46 |
% 33.56/8.46 | Applying alpha-rule on (756) yields:
% 33.56/8.46 | (189) pull = push
% 33.56/8.46 | (758) ~ (all_229_1_137 = 0)
% 33.56/8.46 |
% 33.56/8.46 | Equations (189) can reduce 102 to:
% 33.56/8.46 | (167) $false
% 33.56/8.46 |
% 33.56/8.46 |-The branch is then unsatisfiable
% 33.56/8.46 |-Branch two:
% 33.56/8.46 | (760) ~ (all_195_0_116 = pull)
% 33.56/8.46 | (761) (all_195_0_116 = push & n2 = n1) | (all_195_0_116 = push & n1 = n0)
% 33.56/8.46 |
% 33.56/8.46 +-Applying beta-rule and splitting (761), into two cases.
% 33.56/8.46 |-Branch one:
% 33.56/8.46 | (762) all_195_0_116 = push & n2 = n1
% 33.56/8.46 |
% 33.56/8.46 | Applying alpha-rule on (762) yields:
% 33.56/8.46 | (763) all_195_0_116 = push
% 33.56/8.46 | (764) n2 = n1
% 33.56/8.46 |
% 33.56/8.46 | Combining equations (764,195) yields a new equation:
% 33.56/8.46 | (765) n1 = n0
% 33.56/8.46 |
% 33.56/8.46 | Simplifying 765 yields:
% 33.56/8.46 | (199) n1 = n0
% 33.56/8.46 |
% 33.56/8.46 | Equations (199) can reduce 220 to:
% 33.56/8.46 | (167) $false
% 33.56/8.46 |
% 33.56/8.46 |-The branch is then unsatisfiable
% 33.56/8.46 |-Branch two:
% 33.56/8.46 | (768) all_195_0_116 = push & n1 = n0
% 33.56/8.46 |
% 33.56/8.46 | Applying alpha-rule on (768) yields:
% 33.56/8.46 | (763) all_195_0_116 = push
% 33.56/8.46 | (199) n1 = n0
% 33.56/8.46 |
% 33.56/8.46 | Equations (199) can reduce 220 to:
% 33.56/8.46 | (167) $false
% 33.56/8.46 |
% 33.56/8.46 |-The branch is then unsatisfiable
% 33.56/8.46 |-Branch two:
% 33.56/8.46 | (625) all_111_0_87 = 0
% 33.56/8.46 | (773) ~ (all_111_3_90 = 0)
% 33.56/8.46 |
% 33.56/8.46 | Equations (587) can reduce 773 to:
% 33.56/8.46 | (167) $false
% 33.56/8.46 |
% 33.56/8.46 |-The branch is then unsatisfiable
% 33.56/8.46 |-Branch two:
% 33.56/8.46 | (775) all_100_0_83 = pull & spinning = backwards & ~ (all_109_0_85 = 0)
% 33.56/8.46 |
% 33.56/8.46 | Applying alpha-rule on (775) yields:
% 33.56/8.46 | (573) all_100_0_83 = pull
% 33.56/8.46 | (208) spinning = backwards
% 33.56/8.46 | (778) ~ (all_109_0_85 = 0)
% 33.56/8.46 |
% 33.56/8.46 | Equations (208) can reduce 52 to:
% 33.56/8.46 | (167) $false
% 33.56/8.46 |
% 33.56/8.46 |-The branch is then unsatisfiable
% 33.56/8.46 |-Branch two:
% 33.56/8.46 | (780) all_100_0_83 = push & spinning = forwards & ~ (all_109_1_86 = 0)
% 33.56/8.46 |
% 33.56/8.46 | Applying alpha-rule on (780) yields:
% 33.56/8.46 | (781) all_100_0_83 = push
% 33.56/8.46 | (213) spinning = forwards
% 33.56/8.46 | (783) ~ (all_109_1_86 = 0)
% 33.56/8.46 |
% 33.56/8.46 | Equations (213) can reduce 33 to:
% 33.56/8.46 | (167) $false
% 33.56/8.46 |
% 33.56/8.46 |-The branch is then unsatisfiable
% 33.56/8.46 |-Branch two:
% 33.56/8.46 | (424) plus(n1, n2) = n4
% 33.56/8.46 | (425) n4 = n2 | ~ (plus(n1, n2) = n2)
% 33.56/8.46 |
% 33.56/8.46 | From (345) and (424) follows:
% 33.56/8.46 | (426) plus(n1, n2) = n2
% 33.56/8.46 |
% 33.56/8.46 | Instantiating formula (9) with n1, n2, n2, n3 and discharging atoms plus(n1, n2) = n3, plus(n1, n2) = n2, yields:
% 33.56/8.46 | (427) n3 = n2
% 33.56/8.46 |
% 33.56/8.46 | Equations (427) can reduce 351 to:
% 33.56/8.46 | (167) $false
% 33.56/8.46 |
% 33.56/8.46 |-The branch is then unsatisfiable
% 33.56/8.46 |-Branch two:
% 33.56/8.46 | (429) plus(n1, n1) = n3
% 33.56/8.46 | (430) n3 = n1 | ~ (plus(n1, n1) = n1)
% 33.56/8.46 |
% 33.56/8.46 +-Applying beta-rule and splitting (127), into two cases.
% 33.56/8.46 |-Branch one:
% 33.56/8.46 | (150) ~ (plus(n1, n1) = n4)
% 33.56/8.46 |
% 33.56/8.46 | From (345) and (150) follows:
% 33.56/8.46 | (432) ~ (plus(n1, n1) = n2)
% 33.56/8.46 |
% 33.56/8.46 | Using (78) and (432) yields:
% 33.56/8.46 | (163) $false
% 33.56/8.46 |
% 33.56/8.46 |-The branch is then unsatisfiable
% 33.56/8.46 |-Branch two:
% 33.56/8.46 | (344) plus(n1, n1) = n4
% 33.56/8.46 | (435) n4 = n3 | ~ (plus(n1, n1) = n3)
% 33.56/8.46 |
% 33.56/8.46 +-Applying beta-rule and splitting (435), into two cases.
% 33.56/8.46 |-Branch one:
% 33.56/8.46 | (350) ~ (plus(n1, n1) = n3)
% 33.56/8.46 |
% 33.56/8.46 | Using (429) and (350) yields:
% 33.56/8.46 | (163) $false
% 33.56/8.46 |
% 33.56/8.46 |-The branch is then unsatisfiable
% 33.56/8.46 |-Branch two:
% 33.56/8.46 | (429) plus(n1, n1) = n3
% 33.56/8.46 | (439) n4 = n3
% 33.56/8.46 |
% 33.56/8.46 | Combining equations (345,439) yields a new equation:
% 33.56/8.46 | (427) n3 = n2
% 33.56/8.46 |
% 33.56/8.46 | Combining equations (427,439) yields a new equation:
% 33.56/8.46 | (345) n4 = n2
% 33.56/8.46 |
% 33.56/8.46 | From (427) and (84) follows:
% 33.56/8.46 | (442) plus(n2, n2) = n5
% 33.56/8.46 |
% 33.56/8.46 +-Applying beta-rule and splitting (124), into two cases.
% 33.56/8.46 |-Branch one:
% 33.56/8.46 | (443) ~ (plus(n2, n2) = n5)
% 33.56/8.46 |
% 33.56/8.46 | Using (442) and (443) yields:
% 33.56/8.46 | (163) $false
% 33.56/8.46 |
% 33.56/8.46 |-The branch is then unsatisfiable
% 33.56/8.46 |-Branch two:
% 33.56/8.47 | (442) plus(n2, n2) = n5
% 33.56/8.47 | (446) n5 = n4
% 33.56/8.47 |
% 33.56/8.47 | Combining equations (345,446) yields a new equation:
% 33.56/8.47 | (447) n5 = n2
% 33.56/8.47 |
% 33.56/8.47 | Equations (447) can reduce 346 to:
% 33.56/8.47 | (167) $false
% 33.56/8.47 |
% 33.56/8.47 |-The branch is then unsatisfiable
% 33.56/8.47 |-Branch two:
% 33.56/8.47 | (810) plus(n1, n3) = n5
% 33.56/8.47 | (446) n5 = n4
% 33.56/8.47 |
% 33.56/8.47 | From (446) and (84) follows:
% 33.56/8.47 | (812) plus(n2, n3) = n4
% 33.56/8.47 |
% 33.56/8.47 | From (446) and (810) follows:
% 33.56/8.47 | (41) plus(n1, n3) = n4
% 33.56/8.47 |
% 33.56/8.47 +-Applying beta-rule and splitting (129), into two cases.
% 33.56/8.47 |-Branch one:
% 33.56/8.47 | (150) ~ (plus(n1, n1) = n4)
% 33.56/8.47 |
% 33.56/8.47 | Using (138) and (150) yields:
% 33.56/8.47 | (815) ~ (n3 = n1)
% 33.56/8.47 |
% 33.56/8.47 +-Applying beta-rule and splitting (127), into two cases.
% 33.56/8.47 |-Branch one:
% 33.56/8.47 | (150) ~ (plus(n1, n1) = n4)
% 33.56/8.47 |
% 33.56/8.47 +-Applying beta-rule and splitting (130), into two cases.
% 33.56/8.47 |-Branch one:
% 33.56/8.47 | (350) ~ (plus(n1, n1) = n3)
% 33.56/8.47 |
% 33.56/8.47 | Using (78) and (350) yields:
% 33.56/8.47 | (351) ~ (n3 = n2)
% 33.56/8.47 |
% 33.56/8.47 +-Applying beta-rule and splitting (135), into two cases.
% 33.56/8.47 |-Branch one:
% 33.56/8.47 | (819) ~ (plus(n0, n2) = n3)
% 33.56/8.47 |
% 33.56/8.47 | Using (32) and (819) yields:
% 33.56/8.47 | (220) ~ (n1 = n0)
% 33.56/8.47 |
% 33.56/8.47 +-Applying beta-rule and splitting (142), into two cases.
% 33.56/8.47 |-Branch one:
% 33.56/8.47 | (154) ? [v0] : ? [v1] : (releasedAt(spinning, n1) = v1 & holdsAt(spinning, n0) = v0 & (v1 = 0 | v0 = 0))
% 33.56/8.47 |
% 33.56/8.47 | Instantiating (154) with all_85_0_229, all_85_1_230 yields:
% 33.56/8.47 | (822) releasedAt(spinning, n1) = all_85_0_229 & holdsAt(spinning, n0) = all_85_1_230 & (all_85_0_229 = 0 | all_85_1_230 = 0)
% 33.56/8.47 |
% 33.56/8.47 | Applying alpha-rule on (822) yields:
% 33.56/8.47 | (823) releasedAt(spinning, n1) = all_85_0_229
% 33.56/8.47 | (824) holdsAt(spinning, n0) = all_85_1_230
% 33.56/8.47 | (825) all_85_0_229 = 0 | all_85_1_230 = 0
% 33.56/8.47 |
% 33.56/8.47 | Instantiating formula (30) with n1, spinning yields:
% 33.56/8.47 | (159) ~ (releasedAt(spinning, n1) = 0)
% 33.56/8.47 |
% 33.56/8.47 | Instantiating formula (4) with spinning, n0, all_85_1_230, all_1_0_0 and discharging atoms holdsAt(spinning, n0) = all_85_1_230, holdsAt(spinning, n0) = all_1_0_0, yields:
% 33.56/8.47 | (827) all_85_1_230 = all_1_0_0
% 33.56/8.47 |
% 33.56/8.47 +-Applying beta-rule and splitting (825), into two cases.
% 33.56/8.47 |-Branch one:
% 33.56/8.47 | (828) all_85_0_229 = 0
% 33.56/8.47 |
% 33.56/8.47 | From (828) and (823) follows:
% 33.56/8.47 | (162) releasedAt(spinning, n1) = 0
% 33.56/8.47 |
% 33.56/8.47 | Using (162) and (159) yields:
% 33.56/8.47 | (163) $false
% 33.56/8.47 |
% 33.56/8.47 |-The branch is then unsatisfiable
% 33.56/8.47 |-Branch two:
% 33.56/8.47 | (831) ~ (all_85_0_229 = 0)
% 33.56/8.47 | (832) all_85_1_230 = 0
% 33.56/8.47 |
% 33.56/8.47 | Combining equations (832,827) yields a new equation:
% 33.56/8.47 | (166) all_1_0_0 = 0
% 33.56/8.47 |
% 33.56/8.47 | Equations (166) can reduce 42 to:
% 33.56/8.47 | (167) $false
% 33.56/8.47 |
% 33.56/8.47 |-The branch is then unsatisfiable
% 33.56/8.47 |-Branch two:
% 33.56/8.47 | (168) ? [v0] : (initiates(v0, spinning, n0) = 0 & happens(v0, n0) = 0)
% 33.56/8.47 |
% 33.56/8.47 | Instantiating (168) with all_85_0_231 yields:
% 33.56/8.47 | (836) initiates(all_85_0_231, spinning, n0) = 0 & happens(all_85_0_231, n0) = 0
% 33.56/8.47 |
% 33.56/8.47 | Applying alpha-rule on (836) yields:
% 33.56/8.47 | (837) initiates(all_85_0_231, spinning, n0) = 0
% 33.56/8.47 | (838) happens(all_85_0_231, n0) = 0
% 33.56/8.47 |
% 33.56/8.47 | Instantiating formula (80) with n0, all_85_0_231 and discharging atoms happens(all_85_0_231, n0) = 0, yields:
% 33.56/8.47 | (839) all_85_0_231 = push | (all_85_0_231 = pull & n2 = n0) | (all_85_0_231 = pull & n1 = n0)
% 33.56/8.47 |
% 33.56/8.47 | Instantiating formula (64) with n0, spinning, all_85_0_231 and discharging atoms initiates(all_85_0_231, spinning, n0) = 0, yields:
% 33.56/8.47 | (840) ? [v0] : ? [v1] : (happens(pull, n0) = v0 & happens(push, n0) = v1 & ((v1 = 0 & all_85_0_231 = pull) | (all_85_0_231 = pull & spinning = backwards & ~ (v1 = 0)) | (all_85_0_231 = push & spinning = forwards & ~ (v0 = 0))))
% 33.56/8.47 |
% 33.56/8.47 | Instantiating (840) with all_94_0_233, all_94_1_234 yields:
% 33.56/8.47 | (841) happens(pull, n0) = all_94_1_234 & happens(push, n0) = all_94_0_233 & ((all_94_0_233 = 0 & all_85_0_231 = pull) | (all_85_0_231 = pull & spinning = backwards & ~ (all_94_0_233 = 0)) | (all_85_0_231 = push & spinning = forwards & ~ (all_94_1_234 = 0)))
% 33.56/8.47 |
% 33.56/8.47 | Applying alpha-rule on (841) yields:
% 33.56/8.47 | (842) happens(pull, n0) = all_94_1_234
% 33.56/8.47 | (843) happens(push, n0) = all_94_0_233
% 33.56/8.47 | (844) (all_94_0_233 = 0 & all_85_0_231 = pull) | (all_85_0_231 = pull & spinning = backwards & ~ (all_94_0_233 = 0)) | (all_85_0_231 = push & spinning = forwards & ~ (all_94_1_234 = 0))
% 33.56/8.47 |
% 33.56/8.47 +-Applying beta-rule and splitting (844), into two cases.
% 33.56/8.47 |-Branch one:
% 33.56/8.47 | (845) (all_94_0_233 = 0 & all_85_0_231 = pull) | (all_85_0_231 = pull & spinning = backwards & ~ (all_94_0_233 = 0))
% 33.56/8.47 |
% 33.56/8.47 +-Applying beta-rule and splitting (845), into two cases.
% 33.56/8.47 |-Branch one:
% 33.56/8.47 | (846) all_94_0_233 = 0 & all_85_0_231 = pull
% 33.56/8.47 |
% 33.56/8.47 | Applying alpha-rule on (846) yields:
% 33.56/8.47 | (847) all_94_0_233 = 0
% 33.56/8.47 | (848) all_85_0_231 = pull
% 33.56/8.47 |
% 33.56/8.47 +-Applying beta-rule and splitting (839), into two cases.
% 33.56/8.47 |-Branch one:
% 33.56/8.47 | (849) all_85_0_231 = push
% 33.56/8.47 |
% 33.56/8.47 | Combining equations (848,849) yields a new equation:
% 33.56/8.47 | (188) pull = push
% 33.56/8.47 |
% 33.56/8.47 | Simplifying 188 yields:
% 33.56/8.47 | (189) pull = push
% 33.56/8.47 |
% 33.56/8.47 | Equations (189) can reduce 102 to:
% 33.56/8.47 | (167) $false
% 33.56/8.47 |
% 33.56/8.47 |-The branch is then unsatisfiable
% 33.56/8.47 |-Branch two:
% 33.56/8.47 | (853) ~ (all_85_0_231 = push)
% 33.56/8.47 | (854) (all_85_0_231 = pull & n2 = n0) | (all_85_0_231 = pull & n1 = n0)
% 33.56/8.47 |
% 33.56/8.47 +-Applying beta-rule and splitting (854), into two cases.
% 33.56/8.47 |-Branch one:
% 33.56/8.47 | (855) all_85_0_231 = pull & n2 = n0
% 33.56/8.47 |
% 33.56/8.47 | Applying alpha-rule on (855) yields:
% 33.56/8.47 | (848) all_85_0_231 = pull
% 33.56/8.47 | (195) n2 = n0
% 33.56/8.47 |
% 33.56/8.47 | From (195) and (32) follows:
% 33.56/8.47 | (414) plus(n1, n0) = n3
% 33.56/8.47 |
% 33.56/8.47 +-Applying beta-rule and splitting (146), into two cases.
% 33.56/8.47 |-Branch one:
% 33.56/8.47 | (415) ~ (plus(n1, n0) = n3)
% 33.56/8.47 |
% 33.56/8.47 | Using (414) and (415) yields:
% 33.56/8.47 | (163) $false
% 33.56/8.47 |
% 33.56/8.47 |-The branch is then unsatisfiable
% 33.56/8.47 |-Branch two:
% 33.56/8.47 | (414) plus(n1, n0) = n3
% 33.56/8.47 | (418) n3 = n1
% 33.56/8.47 |
% 33.56/8.47 | Equations (418) can reduce 815 to:
% 33.56/8.47 | (167) $false
% 33.56/8.47 |
% 33.56/8.47 |-The branch is then unsatisfiable
% 33.56/8.47 |-Branch two:
% 33.56/8.47 | (864) all_85_0_231 = pull & n1 = n0
% 33.56/8.47 |
% 33.56/8.47 | Applying alpha-rule on (864) yields:
% 33.56/8.47 | (848) all_85_0_231 = pull
% 33.56/8.47 | (199) n1 = n0
% 33.56/8.47 |
% 33.56/8.47 | Equations (199) can reduce 220 to:
% 33.56/8.47 | (167) $false
% 33.56/8.47 |
% 33.56/8.47 |-The branch is then unsatisfiable
% 33.56/8.47 |-Branch two:
% 33.56/8.47 | (868) all_85_0_231 = pull & spinning = backwards & ~ (all_94_0_233 = 0)
% 33.56/8.47 |
% 33.56/8.47 | Applying alpha-rule on (868) yields:
% 33.56/8.47 | (848) all_85_0_231 = pull
% 33.56/8.47 | (208) spinning = backwards
% 33.56/8.47 | (871) ~ (all_94_0_233 = 0)
% 33.56/8.47 |
% 33.56/8.47 | Equations (208) can reduce 52 to:
% 33.56/8.47 | (167) $false
% 33.56/8.47 |
% 33.56/8.47 |-The branch is then unsatisfiable
% 33.56/8.47 |-Branch two:
% 33.56/8.47 | (873) all_85_0_231 = push & spinning = forwards & ~ (all_94_1_234 = 0)
% 33.56/8.47 |
% 33.56/8.47 | Applying alpha-rule on (873) yields:
% 33.56/8.47 | (849) all_85_0_231 = push
% 33.56/8.47 | (213) spinning = forwards
% 33.56/8.47 | (876) ~ (all_94_1_234 = 0)
% 33.56/8.47 |
% 33.56/8.47 | Equations (213) can reduce 33 to:
% 33.56/8.47 | (167) $false
% 33.56/8.47 |
% 33.56/8.47 |-The branch is then unsatisfiable
% 33.56/8.47 |-Branch two:
% 33.56/8.47 | (878) plus(n0, n2) = n3
% 33.56/8.47 | (427) n3 = n2
% 33.56/8.47 |
% 33.56/8.47 | Equations (427) can reduce 351 to:
% 33.56/8.47 | (167) $false
% 33.56/8.47 |
% 33.56/8.47 |-The branch is then unsatisfiable
% 33.56/8.47 |-Branch two:
% 33.56/8.47 | (429) plus(n1, n1) = n3
% 33.56/8.47 | (430) n3 = n1 | ~ (plus(n1, n1) = n1)
% 33.56/8.47 |
% 33.56/8.47 | Instantiating formula (9) with n1, n1, n3, n2 and discharging atoms plus(n1, n1) = n3, plus(n1, n1) = n2, yields:
% 33.56/8.47 | (427) n3 = n2
% 33.56/8.47 |
% 33.56/8.47 | Using (429) and (150) yields:
% 33.56/8.47 | (884) ~ (n4 = n3)
% 33.56/8.47 |
% 33.56/8.47 | Equations (427) can reduce 884 to:
% 33.56/8.47 | (151) ~ (n4 = n2)
% 33.56/8.47 |
% 33.56/8.47 | From (427) and (41) follows:
% 33.56/8.47 | (424) plus(n1, n2) = n4
% 33.56/8.47 |
% 33.56/8.47 | From (427) and (32) follows:
% 33.56/8.47 | (426) plus(n1, n2) = n2
% 33.56/8.47 |
% 33.56/8.47 +-Applying beta-rule and splitting (128), into two cases.
% 33.56/8.47 |-Branch one:
% 33.56/8.47 | (352) ~ (plus(n1, n2) = n4)
% 33.56/8.47 |
% 33.56/8.47 | Using (424) and (352) yields:
% 33.56/8.47 | (163) $false
% 33.56/8.47 |
% 33.56/8.47 |-The branch is then unsatisfiable
% 33.56/8.47 |-Branch two:
% 33.56/8.47 | (424) plus(n1, n2) = n4
% 33.56/8.47 | (425) n4 = n2 | ~ (plus(n1, n2) = n2)
% 33.56/8.48 |
% 33.56/8.48 +-Applying beta-rule and splitting (425), into two cases.
% 33.56/8.48 |-Branch one:
% 33.56/8.48 | (353) ~ (plus(n1, n2) = n2)
% 33.56/8.48 |
% 33.56/8.48 | Using (426) and (353) yields:
% 33.56/8.48 | (163) $false
% 33.56/8.48 |
% 33.56/8.48 |-The branch is then unsatisfiable
% 33.56/8.48 |-Branch two:
% 33.56/8.48 | (426) plus(n1, n2) = n2
% 33.56/8.48 | (345) n4 = n2
% 33.56/8.48 |
% 33.56/8.48 | Equations (345) can reduce 151 to:
% 33.56/8.48 | (167) $false
% 33.56/8.48 |
% 33.56/8.48 |-The branch is then unsatisfiable
% 33.56/8.48 |-Branch two:
% 33.56/8.48 | (344) plus(n1, n1) = n4
% 33.56/8.48 | (435) n4 = n3 | ~ (plus(n1, n1) = n3)
% 33.56/8.48 |
% 33.56/8.48 | Using (344) and (150) yields:
% 33.56/8.48 | (163) $false
% 33.56/8.48 |
% 33.56/8.48 |-The branch is then unsatisfiable
% 33.56/8.48 |-Branch two:
% 33.56/8.48 | (344) plus(n1, n1) = n4
% 33.56/8.48 | (345) n4 = n2
% 33.56/8.48 |
% 33.56/8.48 | Combining equations (345,446) yields a new equation:
% 33.56/8.48 | (447) n5 = n2
% 33.56/8.48 |
% 33.56/8.48 | From (345) and (812) follows:
% 33.56/8.48 | (903) plus(n2, n3) = n2
% 33.56/8.48 |
% 33.56/8.48 | From (345) and (344) follows:
% 33.56/8.48 | (78) plus(n1, n1) = n2
% 33.56/8.48 |
% 33.56/8.48 +-Applying beta-rule and splitting (130), into two cases.
% 33.56/8.48 |-Branch one:
% 33.56/8.48 | (350) ~ (plus(n1, n1) = n3)
% 33.56/8.48 |
% 33.56/8.48 | Using (78) and (350) yields:
% 33.56/8.48 | (351) ~ (n3 = n2)
% 33.56/8.48 |
% 33.56/8.48 +-Applying beta-rule and splitting (128), into two cases.
% 33.56/8.48 |-Branch one:
% 33.56/8.48 | (352) ~ (plus(n1, n2) = n4)
% 33.56/8.48 |
% 33.56/8.48 | From (345) and (352) follows:
% 33.56/8.48 | (353) ~ (plus(n1, n2) = n2)
% 33.56/8.48 |
% 33.56/8.48 | Using (63) and (353) yields:
% 33.56/8.48 | (220) ~ (n1 = n0)
% 33.56/8.48 |
% 33.56/8.48 +-Applying beta-rule and splitting (132), into two cases.
% 33.56/8.48 |-Branch one:
% 33.56/8.48 | (152) ~ (plus(n0, n3) = n5)
% 33.56/8.48 |
% 33.56/8.48 | From (447) and (152) follows:
% 33.56/8.48 | (911) ~ (plus(n0, n3) = n2)
% 33.56/8.48 |
% 33.56/8.48 | Using (903) and (911) yields:
% 33.56/8.48 | (153) ~ (n2 = n0)
% 33.56/8.48 |
% 33.56/8.48 +-Applying beta-rule and splitting (137), into two cases.
% 33.56/8.48 |-Branch one:
% 33.56/8.48 | (201) ~ (holdsAt(spinning, n0) = 0)
% 33.56/8.48 |
% 33.56/8.48 +-Applying beta-rule and splitting (142), into two cases.
% 33.56/8.48 |-Branch one:
% 33.56/8.48 | (154) ? [v0] : ? [v1] : (releasedAt(spinning, n1) = v1 & holdsAt(spinning, n0) = v0 & (v1 = 0 | v0 = 0))
% 33.56/8.48 |
% 33.56/8.48 | Instantiating (154) with all_109_0_247, all_109_1_248 yields:
% 33.56/8.48 | (915) releasedAt(spinning, n1) = all_109_0_247 & holdsAt(spinning, n0) = all_109_1_248 & (all_109_0_247 = 0 | all_109_1_248 = 0)
% 33.56/8.48 |
% 33.56/8.48 | Applying alpha-rule on (915) yields:
% 33.56/8.48 | (916) releasedAt(spinning, n1) = all_109_0_247
% 33.56/8.48 | (917) holdsAt(spinning, n0) = all_109_1_248
% 33.56/8.48 | (918) all_109_0_247 = 0 | all_109_1_248 = 0
% 33.56/8.48 |
% 33.56/8.48 | Instantiating formula (30) with n1, spinning yields:
% 33.56/8.48 | (159) ~ (releasedAt(spinning, n1) = 0)
% 33.56/8.48 |
% 33.56/8.48 | Instantiating formula (4) with spinning, n0, all_109_1_248, all_1_0_0 and discharging atoms holdsAt(spinning, n0) = all_109_1_248, holdsAt(spinning, n0) = all_1_0_0, yields:
% 33.56/8.48 | (920) all_109_1_248 = all_1_0_0
% 33.56/8.48 |
% 33.56/8.48 | Using (917) and (201) yields:
% 33.56/8.48 | (921) ~ (all_109_1_248 = 0)
% 33.56/8.48 |
% 33.56/8.48 | Equations (920) can reduce 921 to:
% 33.56/8.48 | (42) ~ (all_1_0_0 = 0)
% 33.56/8.48 |
% 33.56/8.48 +-Applying beta-rule and splitting (918), into two cases.
% 33.56/8.48 |-Branch one:
% 33.56/8.48 | (923) all_109_0_247 = 0
% 33.56/8.48 |
% 33.56/8.48 | From (923) and (916) follows:
% 33.56/8.48 | (162) releasedAt(spinning, n1) = 0
% 33.56/8.48 |
% 33.56/8.48 | Using (162) and (159) yields:
% 33.56/8.48 | (163) $false
% 33.56/8.48 |
% 33.56/8.48 |-The branch is then unsatisfiable
% 33.56/8.48 |-Branch two:
% 33.56/8.48 | (926) ~ (all_109_0_247 = 0)
% 33.56/8.48 | (927) all_109_1_248 = 0
% 33.56/8.48 |
% 33.56/8.48 | Combining equations (927,920) yields a new equation:
% 33.56/8.48 | (166) all_1_0_0 = 0
% 33.56/8.48 |
% 33.56/8.48 | Equations (166) can reduce 42 to:
% 33.56/8.48 | (167) $false
% 33.56/8.48 |
% 33.56/8.48 |-The branch is then unsatisfiable
% 33.56/8.48 |-Branch two:
% 33.56/8.48 | (168) ? [v0] : (initiates(v0, spinning, n0) = 0 & happens(v0, n0) = 0)
% 33.56/8.48 |
% 33.56/8.48 | Instantiating (168) with all_109_0_249 yields:
% 33.56/8.48 | (931) initiates(all_109_0_249, spinning, n0) = 0 & happens(all_109_0_249, n0) = 0
% 33.56/8.48 |
% 33.56/8.48 | Applying alpha-rule on (931) yields:
% 33.56/8.48 | (932) initiates(all_109_0_249, spinning, n0) = 0
% 33.56/8.48 | (933) happens(all_109_0_249, n0) = 0
% 33.56/8.48 |
% 33.56/8.48 | Instantiating formula (80) with n0, all_109_0_249 and discharging atoms happens(all_109_0_249, n0) = 0, yields:
% 33.56/8.48 | (934) all_109_0_249 = push | (all_109_0_249 = pull & n2 = n0) | (all_109_0_249 = pull & n1 = n0)
% 33.56/8.48 |
% 33.56/8.48 +-Applying beta-rule and splitting (934), into two cases.
% 33.56/8.48 |-Branch one:
% 33.56/8.48 | (935) all_109_0_249 = push
% 33.56/8.48 |
% 33.56/8.48 | From (935) and (932) follows:
% 33.56/8.48 | (247) initiates(push, spinning, n0) = 0
% 33.56/8.48 |
% 33.56/8.48 | Instantiating formula (64) with n0, spinning, push and discharging atoms initiates(push, spinning, n0) = 0, yields:
% 33.56/8.48 | (248) ? [v0] : ? [v1] : (happens(pull, n0) = v0 & happens(push, n0) = v1 & ((v1 = 0 & pull = push) | (spinning = backwards & pull = push & ~ (v1 = 0)) | (spinning = forwards & ~ (v0 = 0))))
% 33.56/8.48 |
% 33.56/8.48 | Instantiating (248) with all_229_0_258, all_229_1_259 yields:
% 33.56/8.48 | (938) happens(pull, n0) = all_229_1_259 & happens(push, n0) = all_229_0_258 & ((all_229_0_258 = 0 & pull = push) | (spinning = backwards & pull = push & ~ (all_229_0_258 = 0)) | (spinning = forwards & ~ (all_229_1_259 = 0)))
% 33.56/8.48 |
% 33.56/8.48 | Applying alpha-rule on (938) yields:
% 33.56/8.48 | (939) happens(pull, n0) = all_229_1_259
% 33.56/8.48 | (940) happens(push, n0) = all_229_0_258
% 33.56/8.48 | (941) (all_229_0_258 = 0 & pull = push) | (spinning = backwards & pull = push & ~ (all_229_0_258 = 0)) | (spinning = forwards & ~ (all_229_1_259 = 0))
% 33.56/8.48 |
% 33.56/8.48 +-Applying beta-rule and splitting (941), into two cases.
% 33.56/8.48 |-Branch one:
% 33.56/8.48 | (942) (all_229_0_258 = 0 & pull = push) | (spinning = backwards & pull = push & ~ (all_229_0_258 = 0))
% 33.56/8.48 |
% 33.56/8.48 +-Applying beta-rule and splitting (942), into two cases.
% 33.56/8.48 |-Branch one:
% 33.56/8.48 | (943) all_229_0_258 = 0 & pull = push
% 33.56/8.48 |
% 33.56/8.48 | Applying alpha-rule on (943) yields:
% 33.56/8.48 | (944) all_229_0_258 = 0
% 33.56/8.48 | (189) pull = push
% 33.56/8.48 |
% 33.56/8.48 | Equations (189) can reduce 102 to:
% 33.56/8.48 | (167) $false
% 33.56/8.48 |
% 33.56/8.48 |-The branch is then unsatisfiable
% 33.56/8.48 |-Branch two:
% 33.56/8.48 | (947) spinning = backwards & pull = push & ~ (all_229_0_258 = 0)
% 33.56/8.48 |
% 33.56/8.48 | Applying alpha-rule on (947) yields:
% 33.56/8.48 | (208) spinning = backwards
% 33.56/8.48 | (189) pull = push
% 33.56/8.48 | (950) ~ (all_229_0_258 = 0)
% 33.56/8.48 |
% 33.56/8.48 | Equations (189) can reduce 102 to:
% 33.56/8.48 | (167) $false
% 33.56/8.48 |
% 33.56/8.48 |-The branch is then unsatisfiable
% 33.56/8.48 |-Branch two:
% 33.56/8.48 | (952) spinning = forwards & ~ (all_229_1_259 = 0)
% 33.56/8.48 |
% 33.56/8.48 | Applying alpha-rule on (952) yields:
% 33.56/8.48 | (213) spinning = forwards
% 33.56/8.48 | (954) ~ (all_229_1_259 = 0)
% 33.56/8.48 |
% 33.56/8.48 | Equations (213) can reduce 33 to:
% 33.56/8.48 | (167) $false
% 33.56/8.48 |
% 33.56/8.48 |-The branch is then unsatisfiable
% 33.56/8.48 |-Branch two:
% 33.56/8.48 | (956) ~ (all_109_0_249 = push)
% 33.56/8.48 | (957) (all_109_0_249 = pull & n2 = n0) | (all_109_0_249 = pull & n1 = n0)
% 33.56/8.48 |
% 33.56/8.48 +-Applying beta-rule and splitting (957), into two cases.
% 33.56/8.48 |-Branch one:
% 33.56/8.48 | (958) all_109_0_249 = pull & n2 = n0
% 33.56/8.48 |
% 33.56/8.48 | Applying alpha-rule on (958) yields:
% 33.56/8.48 | (959) all_109_0_249 = pull
% 33.56/8.48 | (195) n2 = n0
% 33.56/8.48 |
% 33.56/8.48 | Equations (195) can reduce 153 to:
% 33.56/8.48 | (167) $false
% 33.56/8.48 |
% 33.56/8.48 |-The branch is then unsatisfiable
% 33.56/8.48 |-Branch two:
% 33.56/8.48 | (962) all_109_0_249 = pull & n1 = n0
% 33.56/8.48 |
% 33.56/8.48 | Applying alpha-rule on (962) yields:
% 33.56/8.48 | (959) all_109_0_249 = pull
% 33.56/8.48 | (199) n1 = n0
% 33.56/8.48 |
% 33.56/8.48 | Equations (199) can reduce 220 to:
% 33.56/8.48 | (167) $false
% 33.56/8.48 |
% 33.56/8.48 |-The branch is then unsatisfiable
% 33.56/8.48 |-Branch two:
% 33.56/8.48 | (200) holdsAt(spinning, n0) = 0
% 33.56/8.48 | (166) all_1_0_0 = 0
% 33.56/8.48 |
% 33.56/8.48 | Equations (166) can reduce 42 to:
% 33.56/8.48 | (167) $false
% 33.56/8.48 |
% 33.56/8.48 |-The branch is then unsatisfiable
% 33.56/8.48 |-Branch two:
% 33.56/8.48 | (216) plus(n0, n3) = n5
% 33.56/8.48 | (217) n5 = n3
% 33.56/8.48 |
% 33.56/8.48 | Combining equations (217,447) yields a new equation:
% 33.56/8.48 | (440) n3 = n2
% 33.56/8.48 |
% 33.56/8.48 | Simplifying 440 yields:
% 33.56/8.48 | (427) n3 = n2
% 33.56/8.48 |
% 33.56/8.48 | Equations (427) can reduce 351 to:
% 33.56/8.48 | (167) $false
% 33.56/8.48 |
% 33.56/8.48 |-The branch is then unsatisfiable
% 33.56/8.48 |-Branch two:
% 33.56/8.48 | (424) plus(n1, n2) = n4
% 33.56/8.48 | (425) n4 = n2 | ~ (plus(n1, n2) = n2)
% 33.56/8.48 |
% 33.56/8.48 | From (345) and (424) follows:
% 33.56/8.49 | (426) plus(n1, n2) = n2
% 33.56/8.49 |
% 33.56/8.49 | Instantiating formula (9) with n1, n2, n2, n3 and discharging atoms plus(n1, n2) = n3, plus(n1, n2) = n2, yields:
% 33.56/8.49 | (427) n3 = n2
% 33.56/8.49 |
% 33.56/8.49 | Equations (427) can reduce 351 to:
% 33.56/8.49 | (167) $false
% 33.56/8.49 |
% 33.56/8.49 |-The branch is then unsatisfiable
% 33.56/8.49 |-Branch two:
% 33.56/8.49 | (429) plus(n1, n1) = n3
% 33.56/8.49 | (430) n3 = n1 | ~ (plus(n1, n1) = n1)
% 33.56/8.49 |
% 33.56/8.49 +-Applying beta-rule and splitting (127), into two cases.
% 33.56/8.49 |-Branch one:
% 33.56/8.49 | (150) ~ (plus(n1, n1) = n4)
% 33.56/8.49 |
% 33.56/8.49 | From (345) and (150) follows:
% 33.56/8.49 | (432) ~ (plus(n1, n1) = n2)
% 33.56/8.49 |
% 33.56/8.49 | Using (78) and (432) yields:
% 33.56/8.49 | (163) $false
% 33.56/8.49 |
% 33.56/8.49 |-The branch is then unsatisfiable
% 33.56/8.49 |-Branch two:
% 33.56/8.49 | (344) plus(n1, n1) = n4
% 33.56/8.49 | (435) n4 = n3 | ~ (plus(n1, n1) = n3)
% 33.56/8.49 |
% 33.56/8.49 +-Applying beta-rule and splitting (435), into two cases.
% 33.56/8.49 |-Branch one:
% 33.56/8.49 | (350) ~ (plus(n1, n1) = n3)
% 33.56/8.49 |
% 33.56/8.49 | Using (429) and (350) yields:
% 33.56/8.49 | (163) $false
% 33.56/8.49 |
% 33.56/8.49 |-The branch is then unsatisfiable
% 33.56/8.49 |-Branch two:
% 33.56/8.49 | (429) plus(n1, n1) = n3
% 33.56/8.49 | (439) n4 = n3
% 33.56/8.49 |
% 33.56/8.49 | Combining equations (345,439) yields a new equation:
% 33.56/8.49 | (427) n3 = n2
% 33.56/8.49 |
% 33.56/8.49 | Combining equations (427,439) yields a new equation:
% 33.56/8.49 | (345) n4 = n2
% 33.56/8.49 |
% 33.56/8.49 | From (427) and (32) follows:
% 33.56/8.49 | (426) plus(n1, n2) = n2
% 33.56/8.49 |
% 33.56/8.49 | From (427)(427) and (45) follows:
% 33.56/8.49 | (63) plus(n0, n2) = n2
% 33.56/8.49 |
% 33.56/8.49 +-Applying beta-rule and splitting (128), into two cases.
% 33.56/8.49 |-Branch one:
% 33.56/8.49 | (352) ~ (plus(n1, n2) = n4)
% 33.56/8.49 |
% 33.56/8.49 | From (345) and (352) follows:
% 33.56/8.49 | (353) ~ (plus(n1, n2) = n2)
% 33.56/8.49 |
% 33.56/8.49 | Using (426) and (353) yields:
% 33.56/8.49 | (163) $false
% 33.56/8.49 |
% 33.56/8.49 |-The branch is then unsatisfiable
% 33.56/8.49 |-Branch two:
% 33.56/8.49 | (424) plus(n1, n2) = n4
% 33.56/8.49 | (425) n4 = n2 | ~ (plus(n1, n2) = n2)
% 33.56/8.49 |
% 33.56/8.49 | From (345) and (424) follows:
% 33.56/8.49 | (426) plus(n1, n2) = n2
% 33.56/8.49 |
% 33.56/8.49 +-Applying beta-rule and splitting (133), into two cases.
% 33.56/8.49 |-Branch one:
% 33.56/8.49 | (1000) ~ (plus(n0, n3) = n4)
% 33.56/8.49 |
% 33.56/8.49 | From (427)(345) and (1000) follows:
% 33.56/8.49 | (1001) ~ (plus(n0, n2) = n2)
% 33.56/8.49 |
% 33.56/8.49 | Using (63) and (1001) yields:
% 33.56/8.49 | (163) $false
% 33.56/8.49 |
% 33.56/8.49 |-The branch is then unsatisfiable
% 33.56/8.49 |-Branch two:
% 33.56/8.49 | (1003) plus(n0, n3) = n4
% 33.56/8.49 | (439) n4 = n3
% 33.56/8.49 |
% 33.56/8.49 | Combining equations (345,439) yields a new equation:
% 33.56/8.49 | (427) n3 = n2
% 33.56/8.49 |
% 33.56/8.49 +-Applying beta-rule and splitting (137), into two cases.
% 33.56/8.49 |-Branch one:
% 33.56/8.49 | (201) ~ (holdsAt(spinning, n0) = 0)
% 33.56/8.49 |
% 33.56/8.49 | Using (100) and (201) yields:
% 33.56/8.49 | (220) ~ (n1 = n0)
% 33.56/8.49 |
% 33.56/8.49 +-Applying beta-rule and splitting (142), into two cases.
% 33.56/8.49 |-Branch one:
% 33.56/8.49 | (154) ? [v0] : ? [v1] : (releasedAt(spinning, n1) = v1 & holdsAt(spinning, n0) = v0 & (v1 = 0 | v0 = 0))
% 33.56/8.49 |
% 33.56/8.49 | Instantiating (154) with all_85_0_260, all_85_1_261 yields:
% 33.56/8.49 | (1009) releasedAt(spinning, n1) = all_85_0_260 & holdsAt(spinning, n0) = all_85_1_261 & (all_85_0_260 = 0 | all_85_1_261 = 0)
% 33.56/8.49 |
% 33.56/8.49 | Applying alpha-rule on (1009) yields:
% 33.56/8.49 | (1010) releasedAt(spinning, n1) = all_85_0_260
% 33.56/8.49 | (1011) holdsAt(spinning, n0) = all_85_1_261
% 33.56/8.49 | (1012) all_85_0_260 = 0 | all_85_1_261 = 0
% 33.56/8.49 |
% 33.56/8.49 | Instantiating formula (30) with n1, spinning yields:
% 33.56/8.49 | (159) ~ (releasedAt(spinning, n1) = 0)
% 33.56/8.49 |
% 33.56/8.49 | Instantiating formula (4) with spinning, n0, all_85_1_261, all_1_0_0 and discharging atoms holdsAt(spinning, n0) = all_85_1_261, holdsAt(spinning, n0) = all_1_0_0, yields:
% 33.56/8.49 | (1014) all_85_1_261 = all_1_0_0
% 33.56/8.49 |
% 33.56/8.49 | Using (1011) and (201) yields:
% 33.56/8.49 | (1015) ~ (all_85_1_261 = 0)
% 33.56/8.49 |
% 33.56/8.49 | Equations (1014) can reduce 1015 to:
% 33.56/8.49 | (42) ~ (all_1_0_0 = 0)
% 33.56/8.49 |
% 33.56/8.49 +-Applying beta-rule and splitting (1012), into two cases.
% 33.56/8.49 |-Branch one:
% 33.56/8.49 | (1017) all_85_0_260 = 0
% 33.56/8.49 |
% 33.56/8.49 | From (1017) and (1010) follows:
% 33.56/8.49 | (162) releasedAt(spinning, n1) = 0
% 33.56/8.49 |
% 33.56/8.49 | Using (162) and (159) yields:
% 33.56/8.49 | (163) $false
% 33.56/8.49 |
% 33.56/8.49 |-The branch is then unsatisfiable
% 33.56/8.49 |-Branch two:
% 33.56/8.49 | (1020) ~ (all_85_0_260 = 0)
% 33.56/8.49 | (1021) all_85_1_261 = 0
% 33.56/8.49 |
% 33.56/8.49 | Combining equations (1021,1014) yields a new equation:
% 33.56/8.49 | (166) all_1_0_0 = 0
% 33.56/8.49 |
% 33.56/8.49 | Equations (166) can reduce 42 to:
% 33.56/8.49 | (167) $false
% 33.56/8.49 |
% 33.56/8.49 |-The branch is then unsatisfiable
% 33.56/8.49 |-Branch two:
% 33.56/8.49 | (168) ? [v0] : (initiates(v0, spinning, n0) = 0 & happens(v0, n0) = 0)
% 33.56/8.49 |
% 33.56/8.49 | Instantiating (168) with all_85_0_262 yields:
% 33.56/8.49 | (1025) initiates(all_85_0_262, spinning, n0) = 0 & happens(all_85_0_262, n0) = 0
% 33.56/8.49 |
% 33.56/8.49 | Applying alpha-rule on (1025) yields:
% 33.56/8.49 | (1026) initiates(all_85_0_262, spinning, n0) = 0
% 33.56/8.49 | (1027) happens(all_85_0_262, n0) = 0
% 33.56/8.49 |
% 33.56/8.49 | Instantiating formula (80) with n0, all_85_0_262 and discharging atoms happens(all_85_0_262, n0) = 0, yields:
% 33.56/8.49 | (1028) all_85_0_262 = push | (all_85_0_262 = pull & n2 = n0) | (all_85_0_262 = pull & n1 = n0)
% 33.56/8.49 |
% 33.56/8.49 | Instantiating formula (64) with n0, spinning, all_85_0_262 and discharging atoms initiates(all_85_0_262, spinning, n0) = 0, yields:
% 33.56/8.49 | (1029) ? [v0] : ? [v1] : (happens(pull, n0) = v0 & happens(push, n0) = v1 & ((v1 = 0 & all_85_0_262 = pull) | (all_85_0_262 = pull & spinning = backwards & ~ (v1 = 0)) | (all_85_0_262 = push & spinning = forwards & ~ (v0 = 0))))
% 33.56/8.49 |
% 33.56/8.49 | Instantiating (1029) with all_94_0_264, all_94_1_265 yields:
% 33.56/8.49 | (1030) happens(pull, n0) = all_94_1_265 & happens(push, n0) = all_94_0_264 & ((all_94_0_264 = 0 & all_85_0_262 = pull) | (all_85_0_262 = pull & spinning = backwards & ~ (all_94_0_264 = 0)) | (all_85_0_262 = push & spinning = forwards & ~ (all_94_1_265 = 0)))
% 33.56/8.49 |
% 33.56/8.49 | Applying alpha-rule on (1030) yields:
% 33.56/8.49 | (1031) happens(pull, n0) = all_94_1_265
% 33.56/8.49 | (1032) happens(push, n0) = all_94_0_264
% 33.56/8.49 | (1033) (all_94_0_264 = 0 & all_85_0_262 = pull) | (all_85_0_262 = pull & spinning = backwards & ~ (all_94_0_264 = 0)) | (all_85_0_262 = push & spinning = forwards & ~ (all_94_1_265 = 0))
% 33.56/8.49 |
% 33.56/8.49 +-Applying beta-rule and splitting (1033), into two cases.
% 33.56/8.49 |-Branch one:
% 33.56/8.49 | (1034) (all_94_0_264 = 0 & all_85_0_262 = pull) | (all_85_0_262 = pull & spinning = backwards & ~ (all_94_0_264 = 0))
% 33.56/8.49 |
% 33.56/8.49 +-Applying beta-rule and splitting (1034), into two cases.
% 33.56/8.49 |-Branch one:
% 33.56/8.49 | (1035) all_94_0_264 = 0 & all_85_0_262 = pull
% 33.56/8.49 |
% 33.56/8.49 | Applying alpha-rule on (1035) yields:
% 33.56/8.49 | (1036) all_94_0_264 = 0
% 33.56/8.49 | (1037) all_85_0_262 = pull
% 33.56/8.49 |
% 33.56/8.49 +-Applying beta-rule and splitting (1028), into two cases.
% 33.56/8.49 |-Branch one:
% 33.56/8.49 | (1038) all_85_0_262 = push
% 33.56/8.49 |
% 33.56/8.49 | Combining equations (1038,1037) yields a new equation:
% 33.56/8.50 | (189) pull = push
% 33.56/8.50 |
% 33.56/8.50 | Equations (189) can reduce 102 to:
% 33.56/8.50 | (167) $false
% 33.56/8.50 |
% 33.56/8.50 |-The branch is then unsatisfiable
% 33.56/8.50 |-Branch two:
% 33.56/8.50 | (1041) ~ (all_85_0_262 = push)
% 33.56/8.50 | (1042) (all_85_0_262 = pull & n2 = n0) | (all_85_0_262 = pull & n1 = n0)
% 33.56/8.50 |
% 33.56/8.50 +-Applying beta-rule and splitting (1042), into two cases.
% 33.56/8.50 |-Branch one:
% 33.56/8.50 | (1043) all_85_0_262 = pull & n2 = n0
% 33.56/8.50 |
% 33.56/8.50 | Applying alpha-rule on (1043) yields:
% 33.56/8.50 | (1037) all_85_0_262 = pull
% 33.56/8.50 | (195) n2 = n0
% 33.56/8.50 |
% 33.56/8.50 | Combining equations (195,427) yields a new equation:
% 33.56/8.50 | (1046) n3 = n0
% 33.56/8.50 |
% 33.56/8.50 | From (195)(195) and (426) follows:
% 33.56/8.50 | (1047) plus(n1, n0) = n0
% 33.56/8.50 |
% 33.56/8.50 +-Applying beta-rule and splitting (146), into two cases.
% 33.56/8.50 |-Branch one:
% 33.56/8.50 | (415) ~ (plus(n1, n0) = n3)
% 33.56/8.50 |
% 33.56/8.50 | From (1046) and (415) follows:
% 33.56/8.50 | (1049) ~ (plus(n1, n0) = n0)
% 33.56/8.50 |
% 33.56/8.50 | Using (1047) and (1049) yields:
% 33.56/8.50 | (163) $false
% 33.56/8.50 |
% 33.56/8.50 |-The branch is then unsatisfiable
% 33.56/8.50 |-Branch two:
% 33.56/8.50 | (414) plus(n1, n0) = n3
% 33.56/8.50 | (418) n3 = n1
% 33.56/8.50 |
% 33.56/8.50 | Combining equations (1046,418) yields a new equation:
% 33.56/8.50 | (199) n1 = n0
% 33.56/8.50 |
% 33.56/8.50 | Equations (199) can reduce 220 to:
% 33.56/8.50 | (167) $false
% 33.56/8.50 |
% 33.56/8.50 |-The branch is then unsatisfiable
% 33.56/8.50 |-Branch two:
% 33.56/8.50 | (1055) all_85_0_262 = pull & n1 = n0
% 33.56/8.50 |
% 33.56/8.50 | Applying alpha-rule on (1055) yields:
% 33.56/8.50 | (1037) all_85_0_262 = pull
% 33.56/8.50 | (199) n1 = n0
% 33.56/8.50 |
% 33.56/8.50 | Equations (199) can reduce 220 to:
% 33.56/8.50 | (167) $false
% 33.56/8.50 |
% 33.56/8.50 |-The branch is then unsatisfiable
% 33.56/8.50 |-Branch two:
% 33.56/8.50 | (1059) all_85_0_262 = pull & spinning = backwards & ~ (all_94_0_264 = 0)
% 33.56/8.50 |
% 33.56/8.50 | Applying alpha-rule on (1059) yields:
% 33.56/8.50 | (1037) all_85_0_262 = pull
% 33.56/8.50 | (208) spinning = backwards
% 33.56/8.50 | (1062) ~ (all_94_0_264 = 0)
% 33.56/8.50 |
% 33.56/8.50 | Equations (208) can reduce 52 to:
% 33.56/8.50 | (167) $false
% 33.56/8.50 |
% 33.56/8.50 |-The branch is then unsatisfiable
% 33.56/8.50 |-Branch two:
% 33.56/8.50 | (1064) all_85_0_262 = push & spinning = forwards & ~ (all_94_1_265 = 0)
% 33.56/8.50 |
% 33.56/8.50 | Applying alpha-rule on (1064) yields:
% 33.56/8.50 | (1038) all_85_0_262 = push
% 33.56/8.50 | (213) spinning = forwards
% 33.56/8.50 | (1067) ~ (all_94_1_265 = 0)
% 33.56/8.50 |
% 33.56/8.50 | Equations (213) can reduce 33 to:
% 33.56/8.50 | (167) $false
% 33.56/8.50 |
% 33.56/8.50 |-The branch is then unsatisfiable
% 33.56/8.50 |-Branch two:
% 33.56/8.50 | (200) holdsAt(spinning, n0) = 0
% 33.56/8.50 | (166) all_1_0_0 = 0
% 33.56/8.50 |
% 33.56/8.50 | Equations (166) can reduce 42 to:
% 33.56/8.50 | (167) $false
% 33.56/8.50 |
% 33.56/8.50 |-The branch is then unsatisfiable
% 33.56/8.50 % SZS output end Proof for theBenchmark
% 33.56/8.50
% 33.56/8.50 7999ms
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