TSTP Solution File: SET935+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET935+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n006.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 : Tue Jul 19 00:23:18 EDT 2022
% Result : Theorem 24.82s 6.59s
% Output : Proof 50.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET935+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.34 % Computer : n006.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sat Jul 9 23:23:36 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.51/0.61 ____ _
% 0.51/0.61 ___ / __ \_____(_)___ ________ __________
% 0.51/0.61 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.51/0.61 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.51/0.61 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.51/0.61
% 0.51/0.61 A Theorem Prover for First-Order Logic
% 0.51/0.61 (ePrincess v.1.0)
% 0.51/0.61
% 0.51/0.61 (c) Philipp Rümmer, 2009-2015
% 0.51/0.61 (c) Peter Backeman, 2014-2015
% 0.51/0.61 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.51/0.61 Free software under GNU Lesser General Public License (LGPL).
% 0.51/0.61 Bug reports to peter@backeman.se
% 0.51/0.61
% 0.51/0.61 For more information, visit http://user.uu.se/~petba168/breu/
% 0.51/0.61
% 0.51/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.67/0.66 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.53/0.93 Prover 0: Preprocessing ...
% 1.93/1.13 Prover 0: Warning: ignoring some quantifiers
% 2.10/1.15 Prover 0: Constructing countermodel ...
% 7.68/2.51 Prover 0: gave up
% 7.68/2.51 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 7.88/2.53 Prover 1: Preprocessing ...
% 7.90/2.59 Prover 1: Warning: ignoring some quantifiers
% 7.90/2.60 Prover 1: Constructing countermodel ...
% 8.92/2.76 Prover 1: gave up
% 8.92/2.76 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 8.92/2.78 Prover 2: Preprocessing ...
% 9.37/2.85 Prover 2: Warning: ignoring some quantifiers
% 9.37/2.86 Prover 2: Constructing countermodel ...
% 17.26/4.83 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 17.56/4.86 Prover 3: Preprocessing ...
% 17.65/4.90 Prover 3: Warning: ignoring some quantifiers
% 17.65/4.90 Prover 3: Constructing countermodel ...
% 19.95/5.43 Prover 3: gave up
% 19.95/5.43 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 19.95/5.44 Prover 4: Preprocessing ...
% 20.43/5.50 Prover 4: Warning: ignoring some quantifiers
% 20.43/5.50 Prover 4: Constructing countermodel ...
% 23.94/6.40 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 23.94/6.42 Prover 5: Preprocessing ...
% 24.35/6.47 Prover 5: Warning: ignoring some quantifiers
% 24.35/6.47 Prover 5: Constructing countermodel ...
% 24.82/6.59 Prover 5: proved (187ms)
% 24.82/6.59 Prover 4: stopped
% 24.82/6.59 Prover 2: stopped
% 24.82/6.59
% 24.82/6.59 No countermodel exists, formula is valid
% 24.82/6.59 % SZS status Theorem for theBenchmark
% 24.82/6.59
% 24.82/6.59 Generating proof ... Warning: ignoring some quantifiers
% 49.98/19.17 found it (size 218)
% 49.98/19.17
% 49.98/19.17 % SZS output start Proof for theBenchmark
% 49.98/19.17 Assumed formulas after preprocessing and simplification:
% 49.98/19.17 | (0) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (inclusion_comparable(v3, v2) = v1) | ~ (inclusion_comparable(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_union2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & ( ~ (v5 = 0) | ( ~ (v7 = 0) & ~ (v6 = 0))) & (v7 = 0 | v6 = 0 | v5 = 0))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (inclusion_comparable(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & inclusion_comparable(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (inclusion_comparable(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & ~ (v3 = 0) & subset(v1, v0) = v4 & subset(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v1, v0) = v2) | ? [v3] : ? [v4] : (inclusion_comparable(v0, v1) = v3 & subset(v0, v1) = v4 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : (inclusion_comparable(v0, v1) = v3 & subset(v1, v0) = v4 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v1, v0) = v2) | ? [v3] : ? [v4] : (inclusion_comparable(v0, v1) = v4 & subset(v0, v1) = v3 & (v4 = 0 | ( ~ (v3 = 0) & ~ (v2 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : (inclusion_comparable(v0, v1) = v4 & subset(v1, v0) = v3 & (v4 = 0 | ( ~ (v3 = 0) & ~ (v2 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ? [v3] : ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | subset(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ( ! [v3] : ! [v4] : (v4 = 0 | ~ (in(v3, v2) = v4) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & ~ (v5 = 0) & in(v3, v1) = v6 & in(v3, v0) = v5)) & ! [v3] : ! [v4] : (v4 = 0 | ~ (in(v3, v1) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v5 & in(v3, v0) = v6 & ( ~ (v5 = 0) | v6 = 0))) & ! [v3] : ! [v4] : (v4 = 0 | ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | v6 = 0))) & ! [v3] : ! [v4] : ( ~ (in(v3, v1) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v6 & in(v3, v0) = v5 & (v6 = 0 | ( ~ (v5 = 0) & ~ (v4 = 0))))) & ! [v3] : ! [v4] : ( ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v6 & in(v3, v1) = v5 & (v6 = 0 | ( ~ (v5 = 0) & ~ (v4 = 0))))) & ! [v3] : ( ~ (in(v3, v2) = 0) | ? [v4] : ? [v5] : (in(v3, v1) = v5 & in(v3, v0) = v4 & (v5 = 0 | v4 = 0))))) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (powerset(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (subset(v3, v1) = v5 & in(v3, v0) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)) & (v5 = 0 | v4 = 0))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (subset(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v0, v1) = v2)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v1, v0) = v2)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (inclusion_comparable(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (inclusion_comparable(v0, v1) = 0) | inclusion_comparable(v1, v0) = 0) & ! [v0] : ! [v1] : ( ~ (inclusion_comparable(v0, v1) = 0) | ? [v2] : ? [v3] : (subset(v1, v0) = v3 & subset(v0, v1) = v2 & (v3 = 0 | v2 = 0))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ( ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v2, v0) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v2, v1) = v4)) & ! [v2] : ! [v3] : (v3 = 0 | ~ (in(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v2, v0) = v4)) & ! [v2] : ( ~ (subset(v2, v0) = 0) | in(v2, v1) = 0) & ! [v2] : ( ~ (in(v2, v1) = 0) | subset(v2, v0) = 0))) & ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = 0) & inclusion_comparable(v0, v1) = v6 & powerset(v5) = v4 & powerset(v1) = v3 & powerset(v0) = v2 & set_union2(v2, v3) = v4 & set_union2(v0, v1) = v5) & ? [v0] : ? [v1] : ( ~ (v1 = 0) & empty(v0) = v1) & ? [v0] : empty(v0) = 0
% 50.14/19.21 | Applying alpha-rule on (0) yields:
% 50.14/19.21 | (1) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (inclusion_comparable(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & ~ (v3 = 0) & subset(v1, v0) = v4 & subset(v0, v1) = v3))
% 50.14/19.21 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0))
% 50.14/19.21 | (3) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 50.14/19.21 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 50.14/19.21 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (inclusion_comparable(v3, v2) = v1) | ~ (inclusion_comparable(v3, v2) = v0))
% 50.14/19.21 | (6) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v1, v0) = v2) | ? [v3] : ? [v4] : (inclusion_comparable(v0, v1) = v3 & subset(v0, v1) = v4 & ( ~ (v3 = 0) | v4 = 0)))
% 50.14/19.22 | (7) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (powerset(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (subset(v3, v1) = v5 & in(v3, v0) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)) & (v5 = 0 | v4 = 0)))
% 50.14/19.22 | (8) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = 0) & inclusion_comparable(v0, v1) = v6 & powerset(v5) = v4 & powerset(v1) = v3 & powerset(v0) = v2 & set_union2(v2, v3) = v4 & set_union2(v0, v1) = v5)
% 50.14/19.22 | (9) ! [v0] : ! [v1] : ( ~ (inclusion_comparable(v0, v1) = 0) | ? [v2] : ? [v3] : (subset(v1, v0) = v3 & subset(v0, v1) = v2 & (v3 = 0 | v2 = 0)))
% 50.14/19.22 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v1, v0) = v2) | ? [v3] : ? [v4] : (inclusion_comparable(v0, v1) = v4 & subset(v0, v1) = v3 & (v4 = 0 | ( ~ (v3 = 0) & ~ (v2 = 0)))))
% 50.14/19.22 | (11) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2)
% 50.14/19.22 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2)
% 50.14/19.22 | (13) ! [v0] : ! [v1] : ( ~ (inclusion_comparable(v0, v1) = 0) | inclusion_comparable(v1, v0) = 0)
% 50.14/19.22 | (14) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_union2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & ( ~ (v5 = 0) | ( ~ (v7 = 0) & ~ (v6 = 0))) & (v7 = 0 | v6 = 0 | v5 = 0)))
% 50.14/19.22 | (15) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (inclusion_comparable(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & inclusion_comparable(v0, v1) = v3))
% 50.14/19.22 | (16) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0)))
% 50.14/19.22 | (17) ? [v0] : ? [v1] : ( ~ (v1 = 0) & empty(v0) = v1)
% 50.14/19.22 | (18) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1))
% 50.14/19.22 | (19) ! [v0] : ! [v1] : (v1 = v0 | ~ (subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v1, v0) = v2))
% 50.14/19.22 | (20) ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2))
% 50.14/19.22 | (21) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : (inclusion_comparable(v0, v1) = v3 & subset(v1, v0) = v4 & ( ~ (v3 = 0) | v4 = 0)))
% 50.14/19.22 | (22) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | subset(v0, v2) = 0)
% 50.14/19.22 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 50.14/19.22 | (24) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : (inclusion_comparable(v0, v1) = v4 & subset(v1, v0) = v3 & (v4 = 0 | ( ~ (v3 = 0) & ~ (v2 = 0)))))
% 50.14/19.22 | (25) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 50.14/19.23 | (26) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ( ! [v3] : ! [v4] : (v4 = 0 | ~ (in(v3, v2) = v4) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & ~ (v5 = 0) & in(v3, v1) = v6 & in(v3, v0) = v5)) & ! [v3] : ! [v4] : (v4 = 0 | ~ (in(v3, v1) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v5 & in(v3, v0) = v6 & ( ~ (v5 = 0) | v6 = 0))) & ! [v3] : ! [v4] : (v4 = 0 | ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | v6 = 0))) & ! [v3] : ! [v4] : ( ~ (in(v3, v1) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v6 & in(v3, v0) = v5 & (v6 = 0 | ( ~ (v5 = 0) & ~ (v4 = 0))))) & ! [v3] : ! [v4] : ( ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v6 & in(v3, v1) = v5 & (v6 = 0 | ( ~ (v5 = 0) & ~ (v4 = 0))))) & ! [v3] : ( ~ (in(v3, v2) = 0) | ? [v4] : ? [v5] : (in(v3, v1) = v5 & in(v3, v0) = v4 & (v5 = 0 | v4 = 0)))))
% 50.14/19.23 | (27) ! [v0] : ! [v1] : (v1 = 0 | ~ (inclusion_comparable(v0, v0) = v1))
% 50.14/19.23 | (28) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1))
% 50.14/19.23 | (29) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ? [v3] : ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0)))
% 50.14/19.23 | (30) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0))
% 50.14/19.23 | (31) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ( ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v2, v0) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v2, v1) = v4)) & ! [v2] : ! [v3] : (v3 = 0 | ~ (in(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v2, v0) = v4)) & ! [v2] : ( ~ (subset(v2, v0) = 0) | in(v2, v1) = 0) & ! [v2] : ( ~ (in(v2, v1) = 0) | subset(v2, v0) = 0)))
% 50.14/19.23 | (32) ! [v0] : ! [v1] : (v1 = v0 | ~ (subset(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v0, v1) = v2))
% 50.14/19.23 | (33) ? [v0] : empty(v0) = 0
% 50.14/19.23 |
% 50.14/19.23 | Instantiating (8) with all_3_0_2, all_3_1_3, all_3_2_4, all_3_3_5, all_3_4_6, all_3_5_7, all_3_6_8 yields:
% 50.14/19.23 | (34) ~ (all_3_0_2 = 0) & inclusion_comparable(all_3_6_8, all_3_5_7) = all_3_0_2 & powerset(all_3_1_3) = all_3_2_4 & powerset(all_3_5_7) = all_3_3_5 & powerset(all_3_6_8) = all_3_4_6 & set_union2(all_3_4_6, all_3_3_5) = all_3_2_4 & set_union2(all_3_6_8, all_3_5_7) = all_3_1_3
% 50.14/19.23 |
% 50.14/19.23 | Applying alpha-rule on (34) yields:
% 50.14/19.23 | (35) inclusion_comparable(all_3_6_8, all_3_5_7) = all_3_0_2
% 50.14/19.23 | (36) powerset(all_3_5_7) = all_3_3_5
% 50.14/19.23 | (37) powerset(all_3_1_3) = all_3_2_4
% 50.14/19.23 | (38) set_union2(all_3_4_6, all_3_3_5) = all_3_2_4
% 50.14/19.23 | (39) set_union2(all_3_6_8, all_3_5_7) = all_3_1_3
% 50.14/19.23 | (40) powerset(all_3_6_8) = all_3_4_6
% 50.14/19.23 | (41) ~ (all_3_0_2 = 0)
% 50.14/19.23 |
% 50.14/19.23 | Instantiating formula (30) with all_3_5_7, all_3_3_5, all_3_2_4 and discharging atoms powerset(all_3_5_7) = all_3_3_5, yields:
% 50.14/19.23 | (42) all_3_2_4 = all_3_3_5 | ~ (powerset(all_3_5_7) = all_3_2_4)
% 50.14/19.23 |
% 50.14/19.23 | Instantiating formula (30) with all_3_6_8, all_3_4_6, all_3_2_4 and discharging atoms powerset(all_3_6_8) = all_3_4_6, yields:
% 50.14/19.23 | (43) all_3_2_4 = all_3_4_6 | ~ (powerset(all_3_6_8) = all_3_2_4)
% 50.14/19.23 |
% 50.14/19.23 | Instantiating formula (1) with all_3_0_2, all_3_5_7, all_3_6_8 and discharging atoms inclusion_comparable(all_3_6_8, all_3_5_7) = all_3_0_2, yields:
% 50.14/19.23 | (44) all_3_0_2 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & subset(all_3_5_7, all_3_6_8) = v1 & subset(all_3_6_8, all_3_5_7) = v0)
% 50.14/19.23 |
% 50.14/19.23 | Instantiating formula (31) with all_3_2_4, all_3_1_3 and discharging atoms powerset(all_3_1_3) = all_3_2_4, yields:
% 50.14/19.23 | (45) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, all_3_1_3) = v1) | ? [v2] : ( ~ (v2 = 0) & in(v0, all_3_2_4) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (in(v0, all_3_2_4) = v1) | ? [v2] : ( ~ (v2 = 0) & subset(v0, all_3_1_3) = v2)) & ! [v0] : ( ~ (subset(v0, all_3_1_3) = 0) | in(v0, all_3_2_4) = 0) & ! [v0] : ( ~ (in(v0, all_3_2_4) = 0) | subset(v0, all_3_1_3) = 0)
% 50.14/19.24 |
% 50.14/19.24 | Applying alpha-rule on (45) yields:
% 50.14/19.24 | (46) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, all_3_1_3) = v1) | ? [v2] : ( ~ (v2 = 0) & in(v0, all_3_2_4) = v2))
% 50.14/19.24 | (47) ! [v0] : ! [v1] : (v1 = 0 | ~ (in(v0, all_3_2_4) = v1) | ? [v2] : ( ~ (v2 = 0) & subset(v0, all_3_1_3) = v2))
% 50.14/19.24 | (48) ! [v0] : ( ~ (subset(v0, all_3_1_3) = 0) | in(v0, all_3_2_4) = 0)
% 50.14/19.24 | (49) ! [v0] : ( ~ (in(v0, all_3_2_4) = 0) | subset(v0, all_3_1_3) = 0)
% 50.14/19.24 |
% 50.14/19.24 | Instantiating formula (31) with all_3_3_5, all_3_5_7 and discharging atoms powerset(all_3_5_7) = all_3_3_5, yields:
% 50.14/19.24 | (50) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, all_3_5_7) = v1) | ? [v2] : ( ~ (v2 = 0) & in(v0, all_3_3_5) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (in(v0, all_3_3_5) = v1) | ? [v2] : ( ~ (v2 = 0) & subset(v0, all_3_5_7) = v2)) & ! [v0] : ( ~ (subset(v0, all_3_5_7) = 0) | in(v0, all_3_3_5) = 0) & ! [v0] : ( ~ (in(v0, all_3_3_5) = 0) | subset(v0, all_3_5_7) = 0)
% 50.14/19.24 |
% 50.14/19.24 | Applying alpha-rule on (50) yields:
% 50.14/19.24 | (51) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, all_3_5_7) = v1) | ? [v2] : ( ~ (v2 = 0) & in(v0, all_3_3_5) = v2))
% 50.14/19.24 | (52) ! [v0] : ! [v1] : (v1 = 0 | ~ (in(v0, all_3_3_5) = v1) | ? [v2] : ( ~ (v2 = 0) & subset(v0, all_3_5_7) = v2))
% 50.14/19.24 | (53) ! [v0] : ( ~ (subset(v0, all_3_5_7) = 0) | in(v0, all_3_3_5) = 0)
% 50.14/19.24 | (54) ! [v0] : ( ~ (in(v0, all_3_3_5) = 0) | subset(v0, all_3_5_7) = 0)
% 50.14/19.24 |
% 50.14/19.24 | Instantiating formula (31) with all_3_4_6, all_3_6_8 and discharging atoms powerset(all_3_6_8) = all_3_4_6, yields:
% 50.14/19.24 | (55) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, all_3_6_8) = v1) | ? [v2] : ( ~ (v2 = 0) & in(v0, all_3_4_6) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (in(v0, all_3_4_6) = v1) | ? [v2] : ( ~ (v2 = 0) & subset(v0, all_3_6_8) = v2)) & ! [v0] : ( ~ (subset(v0, all_3_6_8) = 0) | in(v0, all_3_4_6) = 0) & ! [v0] : ( ~ (in(v0, all_3_4_6) = 0) | subset(v0, all_3_6_8) = 0)
% 50.14/19.24 |
% 50.14/19.24 | Applying alpha-rule on (55) yields:
% 50.14/19.24 | (56) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, all_3_6_8) = v1) | ? [v2] : ( ~ (v2 = 0) & in(v0, all_3_4_6) = v2))
% 50.14/19.24 | (57) ! [v0] : ! [v1] : (v1 = 0 | ~ (in(v0, all_3_4_6) = v1) | ? [v2] : ( ~ (v2 = 0) & subset(v0, all_3_6_8) = v2))
% 50.14/19.24 | (58) ! [v0] : ( ~ (subset(v0, all_3_6_8) = 0) | in(v0, all_3_4_6) = 0)
% 50.14/19.24 | (59) ! [v0] : ( ~ (in(v0, all_3_4_6) = 0) | subset(v0, all_3_6_8) = 0)
% 50.14/19.24 |
% 50.14/19.24 | Instantiating formula (12) with all_3_2_4, all_3_4_6, all_3_3_5 and discharging atoms set_union2(all_3_4_6, all_3_3_5) = all_3_2_4, yields:
% 50.14/19.24 | (60) set_union2(all_3_3_5, all_3_4_6) = all_3_2_4
% 50.14/19.24 |
% 50.14/19.24 | Instantiating formula (22) with all_3_2_4, all_3_3_5, all_3_4_6 and discharging atoms set_union2(all_3_4_6, all_3_3_5) = all_3_2_4, yields:
% 50.14/19.24 | (61) subset(all_3_4_6, all_3_2_4) = 0
% 50.14/19.24 |
% 50.14/19.24 | Instantiating formula (26) with all_3_2_4, all_3_3_5, all_3_4_6 and discharging atoms set_union2(all_3_4_6, all_3_3_5) = all_3_2_4, yields:
% 50.14/19.24 | (62) ! [v0] : ! [v1] : (v1 = 0 | ~ (in(v0, all_3_2_4) = v1) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & ~ (v2 = 0) & in(v0, all_3_3_5) = v3 & in(v0, all_3_4_6) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (in(v0, all_3_3_5) = v1) | ? [v2] : ? [v3] : (in(v0, all_3_2_4) = v2 & in(v0, all_3_4_6) = v3 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (in(v0, all_3_4_6) = v1) | ? [v2] : ? [v3] : (in(v0, all_3_2_4) = v2 & in(v0, all_3_3_5) = v3 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0] : ! [v1] : ( ~ (in(v0, all_3_3_5) = v1) | ? [v2] : ? [v3] : (in(v0, all_3_2_4) = v3 & in(v0, all_3_4_6) = v2 & (v3 = 0 | ( ~ (v2 = 0) & ~ (v1 = 0))))) & ! [v0] : ! [v1] : ( ~ (in(v0, all_3_4_6) = v1) | ? [v2] : ? [v3] : (in(v0, all_3_2_4) = v3 & in(v0, all_3_3_5) = v2 & (v3 = 0 | ( ~ (v2 = 0) & ~ (v1 = 0))))) & ! [v0] : ( ~ (in(v0, all_3_2_4) = 0) | ? [v1] : ? [v2] : (in(v0, all_3_3_5) = v2 & in(v0, all_3_4_6) = v1 & (v2 = 0 | v1 = 0)))
% 50.14/19.24 |
% 50.14/19.24 | Applying alpha-rule on (62) yields:
% 50.14/19.24 | (63) ! [v0] : ! [v1] : (v1 = 0 | ~ (in(v0, all_3_2_4) = v1) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & ~ (v2 = 0) & in(v0, all_3_3_5) = v3 & in(v0, all_3_4_6) = v2))
% 50.14/19.24 | (64) ! [v0] : ! [v1] : ( ~ (in(v0, all_3_4_6) = v1) | ? [v2] : ? [v3] : (in(v0, all_3_2_4) = v3 & in(v0, all_3_3_5) = v2 & (v3 = 0 | ( ~ (v2 = 0) & ~ (v1 = 0)))))
% 50.14/19.24 | (65) ! [v0] : ! [v1] : ( ~ (in(v0, all_3_3_5) = v1) | ? [v2] : ? [v3] : (in(v0, all_3_2_4) = v3 & in(v0, all_3_4_6) = v2 & (v3 = 0 | ( ~ (v2 = 0) & ~ (v1 = 0)))))
% 50.14/19.24 | (66) ! [v0] : ( ~ (in(v0, all_3_2_4) = 0) | ? [v1] : ? [v2] : (in(v0, all_3_3_5) = v2 & in(v0, all_3_4_6) = v1 & (v2 = 0 | v1 = 0)))
% 50.14/19.25 | (67) ! [v0] : ! [v1] : (v1 = 0 | ~ (in(v0, all_3_4_6) = v1) | ? [v2] : ? [v3] : (in(v0, all_3_2_4) = v2 & in(v0, all_3_3_5) = v3 & ( ~ (v2 = 0) | v3 = 0)))
% 50.14/19.25 | (68) ! [v0] : ! [v1] : (v1 = 0 | ~ (in(v0, all_3_3_5) = v1) | ? [v2] : ? [v3] : (in(v0, all_3_2_4) = v2 & in(v0, all_3_4_6) = v3 & ( ~ (v2 = 0) | v3 = 0)))
% 50.14/19.25 |
% 50.14/19.25 | Instantiating formula (12) with all_3_1_3, all_3_6_8, all_3_5_7 and discharging atoms set_union2(all_3_6_8, all_3_5_7) = all_3_1_3, yields:
% 50.14/19.25 | (69) set_union2(all_3_5_7, all_3_6_8) = all_3_1_3
% 50.14/19.25 |
% 50.14/19.25 | Instantiating formula (22) with all_3_1_3, all_3_5_7, all_3_6_8 and discharging atoms set_union2(all_3_6_8, all_3_5_7) = all_3_1_3, yields:
% 50.14/19.25 | (70) subset(all_3_6_8, all_3_1_3) = 0
% 50.14/19.25 |
% 50.14/19.25 +-Applying beta-rule and splitting (44), into two cases.
% 50.14/19.25 |-Branch one:
% 50.14/19.25 | (71) all_3_0_2 = 0
% 50.14/19.25 |
% 50.14/19.25 | Equations (71) can reduce 41 to:
% 50.14/19.25 | (72) $false
% 50.14/19.25 |
% 50.14/19.25 |-The branch is then unsatisfiable
% 50.14/19.25 |-Branch two:
% 50.14/19.25 | (41) ~ (all_3_0_2 = 0)
% 50.14/19.25 | (74) ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & subset(all_3_5_7, all_3_6_8) = v1 & subset(all_3_6_8, all_3_5_7) = v0)
% 50.14/19.25 |
% 50.14/19.25 | Instantiating (74) with all_37_0_20, all_37_1_21 yields:
% 50.14/19.25 | (75) ~ (all_37_0_20 = 0) & ~ (all_37_1_21 = 0) & subset(all_3_5_7, all_3_6_8) = all_37_0_20 & subset(all_3_6_8, all_3_5_7) = all_37_1_21
% 50.14/19.25 |
% 50.14/19.25 | Applying alpha-rule on (75) yields:
% 50.14/19.25 | (76) ~ (all_37_0_20 = 0)
% 50.14/19.25 | (77) ~ (all_37_1_21 = 0)
% 50.14/19.25 | (78) subset(all_3_5_7, all_3_6_8) = all_37_0_20
% 50.14/19.25 | (79) subset(all_3_6_8, all_3_5_7) = all_37_1_21
% 50.14/19.25 |
% 50.14/19.25 | Instantiating formula (32) with all_3_4_6, all_3_2_4 and discharging atoms subset(all_3_4_6, all_3_2_4) = 0, yields:
% 50.14/19.25 | (80) all_3_2_4 = all_3_4_6 | ? [v0] : ( ~ (v0 = 0) & subset(all_3_2_4, all_3_4_6) = v0)
% 50.14/19.25 |
% 50.14/19.25 | Instantiating formula (56) with all_37_0_20, all_3_5_7 and discharging atoms subset(all_3_5_7, all_3_6_8) = all_37_0_20, yields:
% 50.14/19.25 | (81) all_37_0_20 = 0 | ? [v0] : ( ~ (v0 = 0) & in(all_3_5_7, all_3_4_6) = v0)
% 50.14/19.25 |
% 50.14/19.25 | Instantiating formula (48) with all_3_6_8 and discharging atoms subset(all_3_6_8, all_3_1_3) = 0, yields:
% 50.14/19.25 | (82) in(all_3_6_8, all_3_2_4) = 0
% 50.14/19.25 |
% 50.14/19.25 | Instantiating formula (32) with all_3_6_8, all_3_1_3 and discharging atoms subset(all_3_6_8, all_3_1_3) = 0, yields:
% 50.14/19.25 | (83) all_3_1_3 = all_3_6_8 | ? [v0] : ( ~ (v0 = 0) & subset(all_3_1_3, all_3_6_8) = v0)
% 50.14/19.25 |
% 50.14/19.25 | Instantiating formula (10) with 0, all_3_6_8, all_3_1_3 and discharging atoms subset(all_3_6_8, all_3_1_3) = 0, yields:
% 50.14/19.25 | (84) ? [v0] : (inclusion_comparable(all_3_1_3, all_3_6_8) = 0 & subset(all_3_1_3, all_3_6_8) = v0)
% 50.14/19.25 |
% 50.14/19.25 | Instantiating formula (24) with 0, all_3_1_3, all_3_6_8 and discharging atoms subset(all_3_6_8, all_3_1_3) = 0, yields:
% 50.14/19.25 | (85) ? [v0] : (inclusion_comparable(all_3_6_8, all_3_1_3) = 0 & subset(all_3_1_3, all_3_6_8) = v0)
% 50.14/19.25 |
% 50.14/19.25 | Instantiating formula (51) with all_37_1_21, all_3_6_8 and discharging atoms subset(all_3_6_8, all_3_5_7) = all_37_1_21, yields:
% 50.14/19.25 | (86) all_37_1_21 = 0 | ? [v0] : ( ~ (v0 = 0) & in(all_3_6_8, all_3_3_5) = v0)
% 50.14/19.25 |
% 50.14/19.25 | Instantiating formula (22) with all_3_2_4, all_3_4_6, all_3_3_5 and discharging atoms set_union2(all_3_3_5, all_3_4_6) = all_3_2_4, yields:
% 50.14/19.25 | (87) subset(all_3_3_5, all_3_2_4) = 0
% 50.14/19.25 |
% 50.14/19.25 | Instantiating formula (26) with all_3_2_4, all_3_4_6, all_3_3_5 and discharging atoms set_union2(all_3_3_5, all_3_4_6) = all_3_2_4, yields:
% 50.14/19.25 | (88) ! [v0] : ! [v1] : (v1 = 0 | ~ (in(v0, all_3_2_4) = v1) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & ~ (v2 = 0) & in(v0, all_3_3_5) = v2 & in(v0, all_3_4_6) = v3)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (in(v0, all_3_3_5) = v1) | ? [v2] : ? [v3] : (in(v0, all_3_2_4) = v2 & in(v0, all_3_4_6) = v3 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (in(v0, all_3_4_6) = v1) | ? [v2] : ? [v3] : (in(v0, all_3_2_4) = v2 & in(v0, all_3_3_5) = v3 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0] : ! [v1] : ( ~ (in(v0, all_3_3_5) = v1) | ? [v2] : ? [v3] : (in(v0, all_3_2_4) = v3 & in(v0, all_3_4_6) = v2 & (v3 = 0 | ( ~ (v2 = 0) & ~ (v1 = 0))))) & ! [v0] : ! [v1] : ( ~ (in(v0, all_3_4_6) = v1) | ? [v2] : ? [v3] : (in(v0, all_3_2_4) = v3 & in(v0, all_3_3_5) = v2 & (v3 = 0 | ( ~ (v2 = 0) & ~ (v1 = 0))))) & ! [v0] : ( ~ (in(v0, all_3_2_4) = 0) | ? [v1] : ? [v2] : (in(v0, all_3_3_5) = v1 & in(v0, all_3_4_6) = v2 & (v2 = 0 | v1 = 0)))
% 50.14/19.25 |
% 50.14/19.25 | Applying alpha-rule on (88) yields:
% 50.14/19.25 | (89) ! [v0] : ! [v1] : (v1 = 0 | ~ (in(v0, all_3_2_4) = v1) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & ~ (v2 = 0) & in(v0, all_3_3_5) = v2 & in(v0, all_3_4_6) = v3))
% 50.14/19.25 | (90) ! [v0] : ( ~ (in(v0, all_3_2_4) = 0) | ? [v1] : ? [v2] : (in(v0, all_3_3_5) = v1 & in(v0, all_3_4_6) = v2 & (v2 = 0 | v1 = 0)))
% 50.14/19.25 | (64) ! [v0] : ! [v1] : ( ~ (in(v0, all_3_4_6) = v1) | ? [v2] : ? [v3] : (in(v0, all_3_2_4) = v3 & in(v0, all_3_3_5) = v2 & (v3 = 0 | ( ~ (v2 = 0) & ~ (v1 = 0)))))
% 50.14/19.26 | (65) ! [v0] : ! [v1] : ( ~ (in(v0, all_3_3_5) = v1) | ? [v2] : ? [v3] : (in(v0, all_3_2_4) = v3 & in(v0, all_3_4_6) = v2 & (v3 = 0 | ( ~ (v2 = 0) & ~ (v1 = 0)))))
% 50.14/19.26 | (67) ! [v0] : ! [v1] : (v1 = 0 | ~ (in(v0, all_3_4_6) = v1) | ? [v2] : ? [v3] : (in(v0, all_3_2_4) = v2 & in(v0, all_3_3_5) = v3 & ( ~ (v2 = 0) | v3 = 0)))
% 50.14/19.26 | (68) ! [v0] : ! [v1] : (v1 = 0 | ~ (in(v0, all_3_3_5) = v1) | ? [v2] : ? [v3] : (in(v0, all_3_2_4) = v2 & in(v0, all_3_4_6) = v3 & ( ~ (v2 = 0) | v3 = 0)))
% 50.14/19.26 |
% 50.14/19.26 | Instantiating formula (22) with all_3_1_3, all_3_6_8, all_3_5_7 and discharging atoms set_union2(all_3_5_7, all_3_6_8) = all_3_1_3, yields:
% 50.14/19.26 | (95) subset(all_3_5_7, all_3_1_3) = 0
% 50.14/19.26 |
% 50.14/19.26 | Instantiating (85) with all_76_0_29 yields:
% 50.14/19.26 | (96) inclusion_comparable(all_3_6_8, all_3_1_3) = 0 & subset(all_3_1_3, all_3_6_8) = all_76_0_29
% 50.14/19.26 |
% 50.14/19.26 | Applying alpha-rule on (96) yields:
% 50.14/19.26 | (97) inclusion_comparable(all_3_6_8, all_3_1_3) = 0
% 50.14/19.26 | (98) subset(all_3_1_3, all_3_6_8) = all_76_0_29
% 50.14/19.26 |
% 50.14/19.26 | Instantiating (84) with all_78_0_30 yields:
% 50.14/19.26 | (99) inclusion_comparable(all_3_1_3, all_3_6_8) = 0 & subset(all_3_1_3, all_3_6_8) = all_78_0_30
% 50.14/19.26 |
% 50.14/19.26 | Applying alpha-rule on (99) yields:
% 50.14/19.26 | (100) inclusion_comparable(all_3_1_3, all_3_6_8) = 0
% 50.14/19.26 | (101) subset(all_3_1_3, all_3_6_8) = all_78_0_30
% 50.14/19.26 |
% 50.14/19.26 +-Applying beta-rule and splitting (86), into two cases.
% 50.14/19.26 |-Branch one:
% 50.14/19.26 | (102) all_37_1_21 = 0
% 50.14/19.26 |
% 50.14/19.26 | Equations (102) can reduce 77 to:
% 50.14/19.26 | (72) $false
% 50.14/19.26 |
% 50.14/19.26 |-The branch is then unsatisfiable
% 50.14/19.26 |-Branch two:
% 50.14/19.26 | (77) ~ (all_37_1_21 = 0)
% 50.14/19.26 | (105) ? [v0] : ( ~ (v0 = 0) & in(all_3_6_8, all_3_3_5) = v0)
% 50.14/19.26 |
% 50.14/19.26 | Instantiating (105) with all_88_0_35 yields:
% 50.14/19.26 | (106) ~ (all_88_0_35 = 0) & in(all_3_6_8, all_3_3_5) = all_88_0_35
% 50.14/19.26 |
% 50.14/19.26 | Applying alpha-rule on (106) yields:
% 50.14/19.26 | (107) ~ (all_88_0_35 = 0)
% 50.14/19.26 | (108) in(all_3_6_8, all_3_3_5) = all_88_0_35
% 50.14/19.26 |
% 50.14/19.26 +-Applying beta-rule and splitting (81), into two cases.
% 50.14/19.26 |-Branch one:
% 50.14/19.26 | (109) all_37_0_20 = 0
% 50.14/19.26 |
% 50.14/19.26 | Equations (109) can reduce 76 to:
% 50.14/19.26 | (72) $false
% 50.14/19.26 |
% 50.14/19.26 |-The branch is then unsatisfiable
% 50.14/19.26 |-Branch two:
% 50.14/19.26 | (76) ~ (all_37_0_20 = 0)
% 50.14/19.26 | (112) ? [v0] : ( ~ (v0 = 0) & in(all_3_5_7, all_3_4_6) = v0)
% 50.14/19.26 |
% 50.14/19.26 | Instantiating (112) with all_93_0_36 yields:
% 50.14/19.26 | (113) ~ (all_93_0_36 = 0) & in(all_3_5_7, all_3_4_6) = all_93_0_36
% 50.14/19.26 |
% 50.14/19.26 | Applying alpha-rule on (113) yields:
% 50.14/19.26 | (114) ~ (all_93_0_36 = 0)
% 50.14/19.26 | (115) in(all_3_5_7, all_3_4_6) = all_93_0_36
% 50.14/19.26 |
% 50.14/19.26 | Instantiating formula (23) with all_3_1_3, all_3_6_8, all_76_0_29, all_78_0_30 and discharging atoms subset(all_3_1_3, all_3_6_8) = all_78_0_30, subset(all_3_1_3, all_3_6_8) = all_76_0_29, yields:
% 50.14/19.26 | (116) all_78_0_30 = all_76_0_29
% 50.14/19.26 |
% 50.14/19.26 | From (116) and (101) follows:
% 50.45/19.26 | (98) subset(all_3_1_3, all_3_6_8) = all_76_0_29
% 50.45/19.26 |
% 50.45/19.26 | Instantiating formula (56) with all_76_0_29, all_3_1_3 and discharging atoms subset(all_3_1_3, all_3_6_8) = all_76_0_29, yields:
% 50.45/19.26 | (118) all_76_0_29 = 0 | ? [v0] : ( ~ (v0 = 0) & in(all_3_1_3, all_3_4_6) = v0)
% 50.45/19.26 |
% 50.45/19.26 | Instantiating formula (32) with all_3_3_5, all_3_2_4 and discharging atoms subset(all_3_3_5, all_3_2_4) = 0, yields:
% 50.45/19.26 | (119) all_3_2_4 = all_3_3_5 | ? [v0] : ( ~ (v0 = 0) & subset(all_3_2_4, all_3_3_5) = v0)
% 50.45/19.26 |
% 50.45/19.26 | Instantiating formula (48) with all_3_5_7 and discharging atoms subset(all_3_5_7, all_3_1_3) = 0, yields:
% 50.45/19.26 | (120) in(all_3_5_7, all_3_2_4) = 0
% 50.45/19.26 |
% 50.45/19.26 | Instantiating formula (32) with all_3_5_7, all_3_1_3 and discharging atoms subset(all_3_5_7, all_3_1_3) = 0, yields:
% 50.45/19.26 | (121) all_3_1_3 = all_3_5_7 | ? [v0] : ( ~ (v0 = 0) & subset(all_3_1_3, all_3_5_7) = v0)
% 50.45/19.26 |
% 50.45/19.26 | Instantiating formula (10) with 0, all_3_5_7, all_3_1_3 and discharging atoms subset(all_3_5_7, all_3_1_3) = 0, yields:
% 50.45/19.26 | (122) ? [v0] : (inclusion_comparable(all_3_1_3, all_3_5_7) = 0 & subset(all_3_1_3, all_3_5_7) = v0)
% 50.45/19.26 |
% 50.45/19.26 | Instantiating formula (24) with 0, all_3_1_3, all_3_5_7 and discharging atoms subset(all_3_5_7, all_3_1_3) = 0, yields:
% 50.45/19.26 | (123) ? [v0] : (inclusion_comparable(all_3_5_7, all_3_1_3) = 0 & subset(all_3_1_3, all_3_5_7) = v0)
% 50.45/19.26 |
% 50.45/19.26 | Instantiating formula (63) with all_93_0_36, all_3_5_7 yields:
% 50.45/19.26 | (124) all_93_0_36 = 0 | ~ (in(all_3_5_7, all_3_2_4) = all_93_0_36) | ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & in(all_3_5_7, all_3_3_5) = v1 & in(all_3_5_7, all_3_4_6) = v0)
% 50.47/19.26 |
% 50.47/19.26 | Instantiating formula (89) with all_93_0_36, all_3_5_7 yields:
% 50.47/19.26 | (125) all_93_0_36 = 0 | ~ (in(all_3_5_7, all_3_2_4) = all_93_0_36) | ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & in(all_3_5_7, all_3_3_5) = v0 & in(all_3_5_7, all_3_4_6) = v1)
% 50.47/19.26 |
% 50.47/19.26 | Instantiating formula (47) with all_93_0_36, all_3_5_7 yields:
% 50.47/19.26 | (126) all_93_0_36 = 0 | ~ (in(all_3_5_7, all_3_2_4) = all_93_0_36) | ? [v0] : ( ~ (v0 = 0) & subset(all_3_5_7, all_3_1_3) = v0)
% 50.47/19.26 |
% 50.47/19.26 | Instantiating formula (67) with all_93_0_36, all_3_5_7 and discharging atoms in(all_3_5_7, all_3_4_6) = all_93_0_36, yields:
% 50.47/19.26 | (127) all_93_0_36 = 0 | ? [v0] : ? [v1] : (in(all_3_5_7, all_3_2_4) = v0 & in(all_3_5_7, all_3_3_5) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 50.47/19.26 |
% 50.47/19.27 | Instantiating formula (64) with all_93_0_36, all_3_5_7 and discharging atoms in(all_3_5_7, all_3_4_6) = all_93_0_36, yields:
% 50.47/19.27 | (128) ? [v0] : ? [v1] : (in(all_3_5_7, all_3_2_4) = v1 & in(all_3_5_7, all_3_3_5) = v0 & (v1 = 0 | ( ~ (v0 = 0) & ~ (all_93_0_36 = 0))))
% 50.47/19.27 |
% 50.47/19.27 | Instantiating formula (63) with all_88_0_35, all_3_6_8 yields:
% 50.47/19.27 | (129) all_88_0_35 = 0 | ~ (in(all_3_6_8, all_3_2_4) = all_88_0_35) | ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & in(all_3_6_8, all_3_3_5) = v1 & in(all_3_6_8, all_3_4_6) = v0)
% 50.47/19.27 |
% 50.47/19.27 | Instantiating formula (89) with all_88_0_35, all_3_6_8 yields:
% 50.47/19.27 | (130) all_88_0_35 = 0 | ~ (in(all_3_6_8, all_3_2_4) = all_88_0_35) | ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & in(all_3_6_8, all_3_3_5) = v0 & in(all_3_6_8, all_3_4_6) = v1)
% 50.47/19.27 |
% 50.47/19.27 | Instantiating formula (47) with all_88_0_35, all_3_6_8 yields:
% 50.47/19.27 | (131) all_88_0_35 = 0 | ~ (in(all_3_6_8, all_3_2_4) = all_88_0_35) | ? [v0] : ( ~ (v0 = 0) & subset(all_3_6_8, all_3_1_3) = v0)
% 50.47/19.27 |
% 50.47/19.27 | Instantiating formula (68) with all_88_0_35, all_3_6_8 and discharging atoms in(all_3_6_8, all_3_3_5) = all_88_0_35, yields:
% 50.47/19.27 | (132) all_88_0_35 = 0 | ? [v0] : ? [v1] : (in(all_3_6_8, all_3_2_4) = v0 & in(all_3_6_8, all_3_4_6) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 50.47/19.27 |
% 50.47/19.27 | Instantiating formula (65) with all_88_0_35, all_3_6_8 and discharging atoms in(all_3_6_8, all_3_3_5) = all_88_0_35, yields:
% 50.47/19.27 | (133) ? [v0] : ? [v1] : (in(all_3_6_8, all_3_2_4) = v1 & in(all_3_6_8, all_3_4_6) = v0 & (v1 = 0 | ( ~ (v0 = 0) & ~ (all_88_0_35 = 0))))
% 50.47/19.27 |
% 50.47/19.27 | Instantiating (128) with all_105_0_37, all_105_1_38 yields:
% 50.47/19.27 | (134) in(all_3_5_7, all_3_2_4) = all_105_0_37 & in(all_3_5_7, all_3_3_5) = all_105_1_38 & (all_105_0_37 = 0 | ( ~ (all_105_1_38 = 0) & ~ (all_93_0_36 = 0)))
% 50.47/19.27 |
% 50.47/19.27 | Applying alpha-rule on (134) yields:
% 50.47/19.27 | (135) in(all_3_5_7, all_3_2_4) = all_105_0_37
% 50.47/19.27 | (136) in(all_3_5_7, all_3_3_5) = all_105_1_38
% 50.47/19.27 | (137) all_105_0_37 = 0 | ( ~ (all_105_1_38 = 0) & ~ (all_93_0_36 = 0))
% 50.47/19.27 |
% 50.47/19.27 | Instantiating (133) with all_107_0_39, all_107_1_40 yields:
% 50.47/19.27 | (138) in(all_3_6_8, all_3_2_4) = all_107_0_39 & in(all_3_6_8, all_3_4_6) = all_107_1_40 & (all_107_0_39 = 0 | ( ~ (all_107_1_40 = 0) & ~ (all_88_0_35 = 0)))
% 50.47/19.27 |
% 50.47/19.27 | Applying alpha-rule on (138) yields:
% 50.47/19.27 | (139) in(all_3_6_8, all_3_2_4) = all_107_0_39
% 50.47/19.27 | (140) in(all_3_6_8, all_3_4_6) = all_107_1_40
% 50.47/19.27 | (141) all_107_0_39 = 0 | ( ~ (all_107_1_40 = 0) & ~ (all_88_0_35 = 0))
% 50.47/19.27 |
% 50.47/19.27 | Instantiating (123) with all_119_0_48 yields:
% 50.47/19.27 | (142) inclusion_comparable(all_3_5_7, all_3_1_3) = 0 & subset(all_3_1_3, all_3_5_7) = all_119_0_48
% 50.47/19.27 |
% 50.47/19.27 | Applying alpha-rule on (142) yields:
% 50.47/19.27 | (143) inclusion_comparable(all_3_5_7, all_3_1_3) = 0
% 50.47/19.27 | (144) subset(all_3_1_3, all_3_5_7) = all_119_0_48
% 50.47/19.27 |
% 50.47/19.27 | Instantiating (122) with all_121_0_49 yields:
% 50.47/19.27 | (145) inclusion_comparable(all_3_1_3, all_3_5_7) = 0 & subset(all_3_1_3, all_3_5_7) = all_121_0_49
% 50.47/19.27 |
% 50.47/19.27 | Applying alpha-rule on (145) yields:
% 50.47/19.27 | (146) inclusion_comparable(all_3_1_3, all_3_5_7) = 0
% 50.47/19.27 | (147) subset(all_3_1_3, all_3_5_7) = all_121_0_49
% 50.47/19.27 |
% 50.47/19.27 +-Applying beta-rule and splitting (131), into two cases.
% 50.47/19.27 |-Branch one:
% 50.47/19.27 | (148) ~ (in(all_3_6_8, all_3_2_4) = all_88_0_35)
% 50.47/19.27 |
% 50.47/19.27 +-Applying beta-rule and splitting (126), into two cases.
% 50.47/19.27 |-Branch one:
% 50.47/19.27 | (149) ~ (in(all_3_5_7, all_3_2_4) = all_93_0_36)
% 50.47/19.27 |
% 50.47/19.27 | Instantiating formula (23) with all_3_1_3, all_3_5_7, all_119_0_48, all_121_0_49 and discharging atoms subset(all_3_1_3, all_3_5_7) = all_121_0_49, subset(all_3_1_3, all_3_5_7) = all_119_0_48, yields:
% 50.47/19.27 | (150) all_121_0_49 = all_119_0_48
% 50.47/19.27 |
% 50.47/19.27 | Using (115) and (149) yields:
% 50.47/19.27 | (151) ~ (all_3_2_4 = all_3_4_6)
% 50.47/19.27 |
% 50.47/19.27 | Using (108) and (148) yields:
% 50.47/19.27 | (152) ~ (all_3_2_4 = all_3_3_5)
% 50.47/19.27 |
% 50.47/19.27 | From (150) and (147) follows:
% 50.47/19.27 | (144) subset(all_3_1_3, all_3_5_7) = all_119_0_48
% 50.47/19.27 |
% 50.47/19.27 +-Applying beta-rule and splitting (119), into two cases.
% 50.47/19.27 |-Branch one:
% 50.47/19.27 | (154) all_3_2_4 = all_3_3_5
% 50.47/19.27 |
% 50.47/19.27 | Equations (154) can reduce 152 to:
% 50.47/19.27 | (72) $false
% 50.47/19.27 |
% 50.47/19.27 |-The branch is then unsatisfiable
% 50.47/19.27 |-Branch two:
% 50.47/19.27 | (152) ~ (all_3_2_4 = all_3_3_5)
% 50.47/19.27 | (157) ? [v0] : ( ~ (v0 = 0) & subset(all_3_2_4, all_3_3_5) = v0)
% 50.47/19.27 |
% 50.47/19.27 +-Applying beta-rule and splitting (80), into two cases.
% 50.47/19.27 |-Branch one:
% 50.47/19.27 | (158) all_3_2_4 = all_3_4_6
% 50.47/19.27 |
% 50.47/19.27 | Equations (158) can reduce 151 to:
% 50.47/19.27 | (72) $false
% 50.47/19.27 |
% 50.47/19.27 |-The branch is then unsatisfiable
% 50.47/19.27 |-Branch two:
% 50.47/19.27 | (151) ~ (all_3_2_4 = all_3_4_6)
% 50.47/19.27 | (161) ? [v0] : ( ~ (v0 = 0) & subset(all_3_2_4, all_3_4_6) = v0)
% 50.47/19.27 |
% 50.47/19.27 | Instantiating formula (51) with all_119_0_48, all_3_1_3 and discharging atoms subset(all_3_1_3, all_3_5_7) = all_119_0_48, yields:
% 50.47/19.27 | (162) all_119_0_48 = 0 | ? [v0] : ( ~ (v0 = 0) & in(all_3_1_3, all_3_3_5) = v0)
% 50.47/19.27 |
% 50.47/19.27 +-Applying beta-rule and splitting (42), into two cases.
% 50.47/19.27 |-Branch one:
% 50.47/19.27 | (163) ~ (powerset(all_3_5_7) = all_3_2_4)
% 50.47/19.27 |
% 50.47/19.27 | Using (37) and (163) yields:
% 50.47/19.27 | (164) ~ (all_3_1_3 = all_3_5_7)
% 50.47/19.27 |
% 50.47/19.27 +-Applying beta-rule and splitting (121), into two cases.
% 50.47/19.27 |-Branch one:
% 50.47/19.27 | (165) all_3_1_3 = all_3_5_7
% 50.47/19.27 |
% 50.47/19.27 | Equations (165) can reduce 164 to:
% 50.47/19.27 | (72) $false
% 50.47/19.27 |
% 50.47/19.27 |-The branch is then unsatisfiable
% 50.47/19.27 |-Branch two:
% 50.47/19.27 | (164) ~ (all_3_1_3 = all_3_5_7)
% 50.47/19.27 | (168) ? [v0] : ( ~ (v0 = 0) & subset(all_3_1_3, all_3_5_7) = v0)
% 50.47/19.28 |
% 50.47/19.28 | Instantiating (168) with all_247_0_64 yields:
% 50.47/19.28 | (169) ~ (all_247_0_64 = 0) & subset(all_3_1_3, all_3_5_7) = all_247_0_64
% 50.47/19.28 |
% 50.47/19.28 | Applying alpha-rule on (169) yields:
% 50.47/19.28 | (170) ~ (all_247_0_64 = 0)
% 50.47/19.28 | (171) subset(all_3_1_3, all_3_5_7) = all_247_0_64
% 50.47/19.28 |
% 50.47/19.28 | Instantiating formula (23) with all_3_1_3, all_3_5_7, all_247_0_64, all_119_0_48 and discharging atoms subset(all_3_1_3, all_3_5_7) = all_247_0_64, subset(all_3_1_3, all_3_5_7) = all_119_0_48, yields:
% 50.47/19.28 | (172) all_247_0_64 = all_119_0_48
% 50.47/19.28 |
% 50.47/19.28 | Equations (172) can reduce 170 to:
% 50.47/19.28 | (173) ~ (all_119_0_48 = 0)
% 50.47/19.28 |
% 50.47/19.28 +-Applying beta-rule and splitting (162), into two cases.
% 50.47/19.28 |-Branch one:
% 50.47/19.28 | (174) all_119_0_48 = 0
% 50.47/19.28 |
% 50.47/19.28 | Equations (174) can reduce 173 to:
% 50.47/19.28 | (72) $false
% 50.47/19.28 |
% 50.47/19.28 |-The branch is then unsatisfiable
% 50.47/19.28 |-Branch two:
% 50.47/19.28 | (173) ~ (all_119_0_48 = 0)
% 50.47/19.28 | (177) ? [v0] : ( ~ (v0 = 0) & in(all_3_1_3, all_3_3_5) = v0)
% 50.47/19.28 |
% 50.47/19.28 | Instantiating (177) with all_261_0_65 yields:
% 50.47/19.28 | (178) ~ (all_261_0_65 = 0) & in(all_3_1_3, all_3_3_5) = all_261_0_65
% 50.47/19.28 |
% 50.47/19.28 | Applying alpha-rule on (178) yields:
% 50.47/19.28 | (179) ~ (all_261_0_65 = 0)
% 50.47/19.28 | (180) in(all_3_1_3, all_3_3_5) = all_261_0_65
% 50.47/19.28 |
% 50.47/19.28 +-Applying beta-rule and splitting (43), into two cases.
% 50.47/19.28 |-Branch one:
% 50.47/19.28 | (181) ~ (powerset(all_3_6_8) = all_3_2_4)
% 50.47/19.28 |
% 50.47/19.28 | Using (37) and (181) yields:
% 50.47/19.28 | (182) ~ (all_3_1_3 = all_3_6_8)
% 50.47/19.28 |
% 50.47/19.28 +-Applying beta-rule and splitting (83), into two cases.
% 50.47/19.28 |-Branch one:
% 50.47/19.28 | (183) all_3_1_3 = all_3_6_8
% 50.47/19.28 |
% 50.47/19.28 | Equations (183) can reduce 182 to:
% 50.47/19.28 | (72) $false
% 50.47/19.28 |
% 50.47/19.28 |-The branch is then unsatisfiable
% 50.47/19.28 |-Branch two:
% 50.47/19.28 | (182) ~ (all_3_1_3 = all_3_6_8)
% 50.47/19.28 | (186) ? [v0] : ( ~ (v0 = 0) & subset(all_3_1_3, all_3_6_8) = v0)
% 50.47/19.28 |
% 50.47/19.28 | Instantiating (186) with all_303_0_66 yields:
% 50.47/19.28 | (187) ~ (all_303_0_66 = 0) & subset(all_3_1_3, all_3_6_8) = all_303_0_66
% 50.47/19.28 |
% 50.47/19.28 | Applying alpha-rule on (187) yields:
% 50.47/19.28 | (188) ~ (all_303_0_66 = 0)
% 50.47/19.28 | (189) subset(all_3_1_3, all_3_6_8) = all_303_0_66
% 50.47/19.28 |
% 50.47/19.28 | Instantiating formula (23) with all_3_1_3, all_3_6_8, all_303_0_66, all_76_0_29 and discharging atoms subset(all_3_1_3, all_3_6_8) = all_303_0_66, subset(all_3_1_3, all_3_6_8) = all_76_0_29, yields:
% 50.47/19.28 | (190) all_303_0_66 = all_76_0_29
% 50.47/19.28 |
% 50.47/19.28 | Equations (190) can reduce 188 to:
% 50.47/19.28 | (191) ~ (all_76_0_29 = 0)
% 50.47/19.28 |
% 50.47/19.28 +-Applying beta-rule and splitting (118), into two cases.
% 50.47/19.28 |-Branch one:
% 50.47/19.28 | (192) all_76_0_29 = 0
% 50.47/19.28 |
% 50.47/19.28 | Equations (192) can reduce 191 to:
% 50.47/19.28 | (72) $false
% 50.47/19.28 |
% 50.47/19.28 |-The branch is then unsatisfiable
% 50.47/19.28 |-Branch two:
% 50.47/19.28 | (191) ~ (all_76_0_29 = 0)
% 50.47/19.28 | (195) ? [v0] : ( ~ (v0 = 0) & in(all_3_1_3, all_3_4_6) = v0)
% 50.47/19.28 |
% 50.47/19.28 | Instantiating (195) with all_313_0_67 yields:
% 50.47/19.28 | (196) ~ (all_313_0_67 = 0) & in(all_3_1_3, all_3_4_6) = all_313_0_67
% 50.47/19.28 |
% 50.47/19.28 | Applying alpha-rule on (196) yields:
% 50.47/19.28 | (197) ~ (all_313_0_67 = 0)
% 50.47/19.28 | (198) in(all_3_1_3, all_3_4_6) = all_313_0_67
% 50.47/19.28 |
% 50.47/19.28 | Instantiating formula (68) with all_261_0_65, all_3_1_3 and discharging atoms in(all_3_1_3, all_3_3_5) = all_261_0_65, yields:
% 50.47/19.28 | (199) all_261_0_65 = 0 | ? [v0] : ? [v1] : (in(all_3_1_3, all_3_2_4) = v0 & in(all_3_1_3, all_3_4_6) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 50.47/19.28 |
% 50.47/19.28 | Instantiating formula (65) with all_261_0_65, all_3_1_3 and discharging atoms in(all_3_1_3, all_3_3_5) = all_261_0_65, yields:
% 50.47/19.28 | (200) ? [v0] : ? [v1] : (in(all_3_1_3, all_3_2_4) = v1 & in(all_3_1_3, all_3_4_6) = v0 & (v1 = 0 | ( ~ (v0 = 0) & ~ (all_261_0_65 = 0))))
% 50.47/19.28 |
% 50.47/19.28 | Instantiating formula (67) with all_313_0_67, all_3_1_3 and discharging atoms in(all_3_1_3, all_3_4_6) = all_313_0_67, yields:
% 50.47/19.28 | (201) all_313_0_67 = 0 | ? [v0] : ? [v1] : (in(all_3_1_3, all_3_2_4) = v0 & in(all_3_1_3, all_3_3_5) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 50.47/19.28 |
% 50.47/19.28 | Instantiating formula (64) with all_313_0_67, all_3_1_3 and discharging atoms in(all_3_1_3, all_3_4_6) = all_313_0_67, yields:
% 50.47/19.28 | (202) ? [v0] : ? [v1] : (in(all_3_1_3, all_3_2_4) = v1 & in(all_3_1_3, all_3_3_5) = v0 & (v1 = 0 | ( ~ (v0 = 0) & ~ (all_313_0_67 = 0))))
% 50.47/19.28 |
% 50.47/19.28 | Instantiating (202) with all_1382_0_580, all_1382_1_581 yields:
% 50.47/19.28 | (203) in(all_3_1_3, all_3_2_4) = all_1382_0_580 & in(all_3_1_3, all_3_3_5) = all_1382_1_581 & (all_1382_0_580 = 0 | ( ~ (all_1382_1_581 = 0) & ~ (all_313_0_67 = 0)))
% 50.47/19.28 |
% 50.47/19.28 | Applying alpha-rule on (203) yields:
% 50.47/19.28 | (204) in(all_3_1_3, all_3_2_4) = all_1382_0_580
% 50.47/19.28 | (205) in(all_3_1_3, all_3_3_5) = all_1382_1_581
% 50.47/19.28 | (206) all_1382_0_580 = 0 | ( ~ (all_1382_1_581 = 0) & ~ (all_313_0_67 = 0))
% 50.47/19.28 |
% 50.47/19.28 | Instantiating (200) with all_1396_0_591, all_1396_1_592 yields:
% 50.47/19.28 | (207) in(all_3_1_3, all_3_2_4) = all_1396_0_591 & in(all_3_1_3, all_3_4_6) = all_1396_1_592 & (all_1396_0_591 = 0 | ( ~ (all_1396_1_592 = 0) & ~ (all_261_0_65 = 0)))
% 50.47/19.28 |
% 50.47/19.28 | Applying alpha-rule on (207) yields:
% 50.47/19.28 | (208) in(all_3_1_3, all_3_2_4) = all_1396_0_591
% 50.47/19.28 | (209) in(all_3_1_3, all_3_4_6) = all_1396_1_592
% 50.47/19.28 | (210) all_1396_0_591 = 0 | ( ~ (all_1396_1_592 = 0) & ~ (all_261_0_65 = 0))
% 50.47/19.28 |
% 50.47/19.28 | Instantiating formula (4) with all_3_1_3, all_3_2_4, all_1382_0_580, all_1396_0_591 and discharging atoms in(all_3_1_3, all_3_2_4) = all_1396_0_591, in(all_3_1_3, all_3_2_4) = all_1382_0_580, yields:
% 50.47/19.28 | (211) all_1396_0_591 = all_1382_0_580
% 50.47/19.28 |
% 50.47/19.28 | Instantiating formula (4) with all_3_1_3, all_3_3_5, all_1382_1_581, all_261_0_65 and discharging atoms in(all_3_1_3, all_3_3_5) = all_1382_1_581, in(all_3_1_3, all_3_3_5) = all_261_0_65, yields:
% 50.47/19.28 | (212) all_1382_1_581 = all_261_0_65
% 50.47/19.29 |
% 50.47/19.29 | From (211) and (208) follows:
% 50.47/19.29 | (204) in(all_3_1_3, all_3_2_4) = all_1382_0_580
% 50.47/19.29 |
% 50.47/19.29 | From (212) and (205) follows:
% 50.47/19.29 | (180) in(all_3_1_3, all_3_3_5) = all_261_0_65
% 50.47/19.29 |
% 50.47/19.29 +-Applying beta-rule and splitting (201), into two cases.
% 50.47/19.29 |-Branch one:
% 50.47/19.29 | (215) all_313_0_67 = 0
% 50.47/19.29 |
% 50.47/19.29 | Equations (215) can reduce 197 to:
% 50.47/19.29 | (72) $false
% 50.47/19.29 |
% 50.47/19.29 |-The branch is then unsatisfiable
% 50.47/19.29 |-Branch two:
% 50.47/19.29 | (197) ~ (all_313_0_67 = 0)
% 50.47/19.29 | (218) ? [v0] : ? [v1] : (in(all_3_1_3, all_3_2_4) = v0 & in(all_3_1_3, all_3_3_5) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 50.47/19.29 |
% 50.47/19.29 | Instantiating (218) with all_1428_0_610, all_1428_1_611 yields:
% 50.47/19.29 | (219) in(all_3_1_3, all_3_2_4) = all_1428_1_611 & in(all_3_1_3, all_3_3_5) = all_1428_0_610 & ( ~ (all_1428_1_611 = 0) | all_1428_0_610 = 0)
% 50.47/19.29 |
% 50.47/19.29 | Applying alpha-rule on (219) yields:
% 50.47/19.29 | (220) in(all_3_1_3, all_3_2_4) = all_1428_1_611
% 50.47/19.29 | (221) in(all_3_1_3, all_3_3_5) = all_1428_0_610
% 50.47/19.29 | (222) ~ (all_1428_1_611 = 0) | all_1428_0_610 = 0
% 50.47/19.29 |
% 50.47/19.29 +-Applying beta-rule and splitting (199), into two cases.
% 50.47/19.29 |-Branch one:
% 50.47/19.29 | (223) all_261_0_65 = 0
% 50.47/19.29 |
% 50.47/19.29 | Equations (223) can reduce 179 to:
% 50.47/19.29 | (72) $false
% 50.47/19.29 |
% 50.47/19.29 |-The branch is then unsatisfiable
% 50.47/19.29 |-Branch two:
% 50.47/19.29 | (179) ~ (all_261_0_65 = 0)
% 50.47/19.29 | (226) ? [v0] : ? [v1] : (in(all_3_1_3, all_3_2_4) = v0 & in(all_3_1_3, all_3_4_6) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 50.47/19.29 |
% 50.47/19.29 | Instantiating (226) with all_1434_0_612, all_1434_1_613 yields:
% 50.47/19.29 | (227) in(all_3_1_3, all_3_2_4) = all_1434_1_613 & in(all_3_1_3, all_3_4_6) = all_1434_0_612 & ( ~ (all_1434_1_613 = 0) | all_1434_0_612 = 0)
% 50.47/19.29 |
% 50.47/19.29 | Applying alpha-rule on (227) yields:
% 50.47/19.29 | (228) in(all_3_1_3, all_3_2_4) = all_1434_1_613
% 50.47/19.29 | (229) in(all_3_1_3, all_3_4_6) = all_1434_0_612
% 50.47/19.29 | (230) ~ (all_1434_1_613 = 0) | all_1434_0_612 = 0
% 50.47/19.29 |
% 50.47/19.29 | Instantiating formula (4) with all_3_1_3, all_3_2_4, all_1434_1_613, all_1382_0_580 and discharging atoms in(all_3_1_3, all_3_2_4) = all_1434_1_613, in(all_3_1_3, all_3_2_4) = all_1382_0_580, yields:
% 50.47/19.29 | (231) all_1434_1_613 = all_1382_0_580
% 50.47/19.29 |
% 50.47/19.29 | Instantiating formula (4) with all_3_1_3, all_3_2_4, all_1428_1_611, all_1434_1_613 and discharging atoms in(all_3_1_3, all_3_2_4) = all_1434_1_613, in(all_3_1_3, all_3_2_4) = all_1428_1_611, yields:
% 50.47/19.29 | (232) all_1434_1_613 = all_1428_1_611
% 50.47/19.29 |
% 50.47/19.29 | Instantiating formula (4) with all_3_1_3, all_3_3_5, all_1428_0_610, all_261_0_65 and discharging atoms in(all_3_1_3, all_3_3_5) = all_1428_0_610, in(all_3_1_3, all_3_3_5) = all_261_0_65, yields:
% 50.47/19.29 | (233) all_1428_0_610 = all_261_0_65
% 50.47/19.29 |
% 50.47/19.29 | Combining equations (231,232) yields a new equation:
% 50.47/19.29 | (234) all_1428_1_611 = all_1382_0_580
% 50.47/19.29 |
% 50.47/19.29 | From (234) and (220) follows:
% 50.47/19.29 | (204) in(all_3_1_3, all_3_2_4) = all_1382_0_580
% 50.47/19.29 |
% 50.47/19.29 +-Applying beta-rule and splitting (222), into two cases.
% 50.47/19.29 |-Branch one:
% 50.47/19.29 | (236) ~ (all_1428_1_611 = 0)
% 50.47/19.29 |
% 50.47/19.29 | Equations (234) can reduce 236 to:
% 50.47/19.29 | (237) ~ (all_1382_0_580 = 0)
% 50.47/19.29 |
% 50.47/19.29 | Instantiating formula (47) with all_1382_0_580, all_3_1_3 and discharging atoms in(all_3_1_3, all_3_2_4) = all_1382_0_580, yields:
% 50.47/19.29 | (238) all_1382_0_580 = 0 | ? [v0] : ( ~ (v0 = 0) & subset(all_3_1_3, all_3_1_3) = v0)
% 50.47/19.29 |
% 50.47/19.29 +-Applying beta-rule and splitting (238), into two cases.
% 50.47/19.29 |-Branch one:
% 50.47/19.29 | (239) all_1382_0_580 = 0
% 50.47/19.29 |
% 50.47/19.29 | Equations (239) can reduce 237 to:
% 50.47/19.29 | (72) $false
% 50.47/19.29 |
% 50.47/19.29 |-The branch is then unsatisfiable
% 50.47/19.29 |-Branch two:
% 50.47/19.29 | (237) ~ (all_1382_0_580 = 0)
% 50.47/19.29 | (242) ? [v0] : ( ~ (v0 = 0) & subset(all_3_1_3, all_3_1_3) = v0)
% 50.47/19.29 |
% 50.47/19.29 | Instantiating (242) with all_2407_0_678 yields:
% 50.47/19.29 | (243) ~ (all_2407_0_678 = 0) & subset(all_3_1_3, all_3_1_3) = all_2407_0_678
% 50.47/19.29 |
% 50.47/19.29 | Applying alpha-rule on (243) yields:
% 50.47/19.29 | (244) ~ (all_2407_0_678 = 0)
% 50.47/19.29 | (245) subset(all_3_1_3, all_3_1_3) = all_2407_0_678
% 50.47/19.29 |
% 50.47/19.29 | Instantiating formula (28) with all_2407_0_678, all_3_1_3 and discharging atoms subset(all_3_1_3, all_3_1_3) = all_2407_0_678, yields:
% 50.47/19.29 | (246) all_2407_0_678 = 0
% 50.47/19.29 |
% 50.47/19.29 | Equations (246) can reduce 244 to:
% 50.47/19.29 | (72) $false
% 50.47/19.29 |
% 50.47/19.29 |-The branch is then unsatisfiable
% 50.47/19.29 |-Branch two:
% 50.47/19.29 | (248) all_1428_1_611 = 0
% 50.47/19.29 | (249) all_1428_0_610 = 0
% 50.47/19.29 |
% 50.47/19.29 | Combining equations (233,249) yields a new equation:
% 50.47/19.29 | (250) all_261_0_65 = 0
% 50.47/19.29 |
% 50.47/19.29 | Simplifying 250 yields:
% 50.47/19.29 | (223) all_261_0_65 = 0
% 50.47/19.29 |
% 50.47/19.29 | Equations (223) can reduce 179 to:
% 50.47/19.29 | (72) $false
% 50.47/19.29 |
% 50.47/19.29 |-The branch is then unsatisfiable
% 50.47/19.29 |-Branch two:
% 50.47/19.29 | (253) powerset(all_3_6_8) = all_3_2_4
% 50.47/19.29 | (158) all_3_2_4 = all_3_4_6
% 50.47/19.29 |
% 50.47/19.29 | Equations (158) can reduce 151 to:
% 50.47/19.29 | (72) $false
% 50.47/19.29 |
% 50.47/19.29 |-The branch is then unsatisfiable
% 50.47/19.30 |-Branch two:
% 50.47/19.30 | (256) powerset(all_3_5_7) = all_3_2_4
% 50.47/19.30 | (154) all_3_2_4 = all_3_3_5
% 50.47/19.30 |
% 50.47/19.30 | Equations (154) can reduce 152 to:
% 50.47/19.30 | (72) $false
% 50.47/19.30 |
% 50.47/19.30 |-The branch is then unsatisfiable
% 50.47/19.30 |-Branch two:
% 50.47/19.30 | (259) in(all_3_5_7, all_3_2_4) = all_93_0_36
% 50.47/19.30 | (260) all_93_0_36 = 0 | ? [v0] : ( ~ (v0 = 0) & subset(all_3_5_7, all_3_1_3) = v0)
% 50.47/19.30 |
% 50.47/19.30 +-Applying beta-rule and splitting (125), into two cases.
% 50.47/19.30 |-Branch one:
% 50.47/19.30 | (149) ~ (in(all_3_5_7, all_3_2_4) = all_93_0_36)
% 50.47/19.30 |
% 50.47/19.30 | Using (259) and (149) yields:
% 50.47/19.30 | (262) $false
% 50.47/19.30 |
% 50.47/19.30 |-The branch is then unsatisfiable
% 50.47/19.30 |-Branch two:
% 50.47/19.30 | (259) in(all_3_5_7, all_3_2_4) = all_93_0_36
% 50.47/19.30 | (264) all_93_0_36 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & in(all_3_5_7, all_3_3_5) = v0 & in(all_3_5_7, all_3_4_6) = v1)
% 50.47/19.30 |
% 50.47/19.30 +-Applying beta-rule and splitting (260), into two cases.
% 50.47/19.30 |-Branch one:
% 50.47/19.30 | (265) all_93_0_36 = 0
% 50.47/19.30 |
% 50.47/19.30 | Equations (265) can reduce 114 to:
% 50.47/19.30 | (72) $false
% 50.47/19.30 |
% 50.47/19.30 |-The branch is then unsatisfiable
% 50.47/19.30 |-Branch two:
% 50.47/19.30 | (114) ~ (all_93_0_36 = 0)
% 50.47/19.30 | (268) ? [v0] : ( ~ (v0 = 0) & subset(all_3_5_7, all_3_1_3) = v0)
% 50.47/19.30 |
% 50.47/19.30 +-Applying beta-rule and splitting (264), into two cases.
% 50.47/19.30 |-Branch one:
% 50.47/19.30 | (265) all_93_0_36 = 0
% 50.47/19.30 |
% 50.47/19.30 | Equations (265) can reduce 114 to:
% 50.47/19.30 | (72) $false
% 50.47/19.30 |
% 50.47/19.30 |-The branch is then unsatisfiable
% 50.47/19.30 |-Branch two:
% 50.47/19.30 | (114) ~ (all_93_0_36 = 0)
% 50.47/19.30 | (272) ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & in(all_3_5_7, all_3_3_5) = v0 & in(all_3_5_7, all_3_4_6) = v1)
% 50.47/19.30 |
% 50.47/19.30 +-Applying beta-rule and splitting (127), into two cases.
% 50.47/19.30 |-Branch one:
% 50.47/19.30 | (265) all_93_0_36 = 0
% 50.47/19.30 |
% 50.47/19.30 | Equations (265) can reduce 114 to:
% 50.47/19.30 | (72) $false
% 50.47/19.30 |
% 50.47/19.30 |-The branch is then unsatisfiable
% 50.47/19.30 |-Branch two:
% 50.47/19.30 | (114) ~ (all_93_0_36 = 0)
% 50.47/19.30 | (276) ? [v0] : ? [v1] : (in(all_3_5_7, all_3_2_4) = v0 & in(all_3_5_7, all_3_3_5) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 50.47/19.30 |
% 50.47/19.30 | Instantiating (276) with all_151_0_689, all_151_1_690 yields:
% 50.47/19.30 | (277) in(all_3_5_7, all_3_2_4) = all_151_1_690 & in(all_3_5_7, all_3_3_5) = all_151_0_689 & ( ~ (all_151_1_690 = 0) | all_151_0_689 = 0)
% 50.65/19.30 |
% 50.65/19.30 | Applying alpha-rule on (277) yields:
% 50.65/19.30 | (278) in(all_3_5_7, all_3_2_4) = all_151_1_690
% 50.65/19.30 | (279) in(all_3_5_7, all_3_3_5) = all_151_0_689
% 50.65/19.30 | (280) ~ (all_151_1_690 = 0) | all_151_0_689 = 0
% 50.65/19.30 |
% 50.65/19.30 +-Applying beta-rule and splitting (124), into two cases.
% 50.65/19.30 |-Branch one:
% 50.65/19.30 | (149) ~ (in(all_3_5_7, all_3_2_4) = all_93_0_36)
% 50.65/19.30 |
% 50.65/19.30 | Using (259) and (149) yields:
% 50.65/19.30 | (262) $false
% 50.65/19.30 |
% 50.65/19.30 |-The branch is then unsatisfiable
% 50.65/19.30 |-Branch two:
% 50.65/19.30 | (259) in(all_3_5_7, all_3_2_4) = all_93_0_36
% 50.65/19.30 | (284) all_93_0_36 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & in(all_3_5_7, all_3_3_5) = v1 & in(all_3_5_7, all_3_4_6) = v0)
% 50.65/19.30 |
% 50.65/19.30 +-Applying beta-rule and splitting (284), into two cases.
% 50.65/19.30 |-Branch one:
% 50.65/19.30 | (265) all_93_0_36 = 0
% 50.65/19.30 |
% 50.65/19.30 | Equations (265) can reduce 114 to:
% 50.65/19.30 | (72) $false
% 50.65/19.30 |
% 50.65/19.30 |-The branch is then unsatisfiable
% 50.65/19.30 |-Branch two:
% 50.65/19.30 | (114) ~ (all_93_0_36 = 0)
% 50.65/19.30 | (288) ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & in(all_3_5_7, all_3_3_5) = v1 & in(all_3_5_7, all_3_4_6) = v0)
% 50.65/19.30 |
% 50.65/19.30 | Instantiating formula (4) with all_3_5_7, all_3_2_4, all_105_0_37, all_151_1_690 and discharging atoms in(all_3_5_7, all_3_2_4) = all_151_1_690, in(all_3_5_7, all_3_2_4) = all_105_0_37, yields:
% 50.65/19.30 | (289) all_151_1_690 = all_105_0_37
% 50.65/19.30 |
% 50.65/19.30 | Instantiating formula (4) with all_3_5_7, all_3_2_4, all_93_0_36, all_151_1_690 and discharging atoms in(all_3_5_7, all_3_2_4) = all_151_1_690, in(all_3_5_7, all_3_2_4) = all_93_0_36, yields:
% 50.65/19.30 | (290) all_151_1_690 = all_93_0_36
% 50.65/19.30 |
% 50.65/19.30 | Instantiating formula (4) with all_3_5_7, all_3_2_4, 0, all_151_1_690 and discharging atoms in(all_3_5_7, all_3_2_4) = all_151_1_690, in(all_3_5_7, all_3_2_4) = 0, yields:
% 50.65/19.30 | (291) all_151_1_690 = 0
% 50.65/19.30 |
% 50.65/19.30 | Combining equations (290,289) yields a new equation:
% 50.65/19.30 | (292) all_105_0_37 = all_93_0_36
% 50.65/19.30 |
% 50.65/19.30 | Combining equations (291,289) yields a new equation:
% 50.65/19.30 | (293) all_105_0_37 = 0
% 50.65/19.30 |
% 50.65/19.30 | Combining equations (292,293) yields a new equation:
% 50.65/19.30 | (294) all_93_0_36 = 0
% 50.65/19.30 |
% 50.65/19.30 | Simplifying 294 yields:
% 50.65/19.30 | (265) all_93_0_36 = 0
% 50.65/19.30 |
% 50.65/19.30 | Equations (265) can reduce 114 to:
% 50.65/19.30 | (72) $false
% 50.65/19.30 |
% 50.65/19.30 |-The branch is then unsatisfiable
% 50.65/19.31 |-Branch two:
% 50.65/19.31 | (297) in(all_3_6_8, all_3_2_4) = all_88_0_35
% 50.65/19.31 | (298) all_88_0_35 = 0 | ? [v0] : ( ~ (v0 = 0) & subset(all_3_6_8, all_3_1_3) = v0)
% 50.65/19.31 |
% 50.65/19.31 +-Applying beta-rule and splitting (130), into two cases.
% 50.65/19.31 |-Branch one:
% 50.65/19.31 | (148) ~ (in(all_3_6_8, all_3_2_4) = all_88_0_35)
% 50.65/19.31 |
% 50.65/19.31 | Using (297) and (148) yields:
% 50.65/19.31 | (262) $false
% 50.65/19.31 |
% 50.65/19.31 |-The branch is then unsatisfiable
% 50.65/19.31 |-Branch two:
% 50.65/19.31 | (297) in(all_3_6_8, all_3_2_4) = all_88_0_35
% 50.65/19.31 | (302) all_88_0_35 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & in(all_3_6_8, all_3_3_5) = v0 & in(all_3_6_8, all_3_4_6) = v1)
% 50.65/19.31 |
% 50.65/19.31 +-Applying beta-rule and splitting (298), into two cases.
% 50.65/19.31 |-Branch one:
% 50.65/19.31 | (303) all_88_0_35 = 0
% 50.65/19.31 |
% 50.65/19.31 | Equations (303) can reduce 107 to:
% 50.65/19.31 | (72) $false
% 50.65/19.31 |
% 50.65/19.31 |-The branch is then unsatisfiable
% 50.65/19.31 |-Branch two:
% 50.65/19.31 | (107) ~ (all_88_0_35 = 0)
% 50.65/19.31 | (306) ? [v0] : ( ~ (v0 = 0) & subset(all_3_6_8, all_3_1_3) = v0)
% 50.65/19.31 |
% 50.65/19.31 +-Applying beta-rule and splitting (129), into two cases.
% 50.65/19.31 |-Branch one:
% 50.65/19.31 | (148) ~ (in(all_3_6_8, all_3_2_4) = all_88_0_35)
% 50.65/19.31 |
% 50.65/19.31 | Using (297) and (148) yields:
% 50.65/19.31 | (262) $false
% 50.65/19.31 |
% 50.65/19.31 |-The branch is then unsatisfiable
% 50.65/19.31 |-Branch two:
% 50.65/19.31 | (297) in(all_3_6_8, all_3_2_4) = all_88_0_35
% 50.65/19.31 | (310) all_88_0_35 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & in(all_3_6_8, all_3_3_5) = v1 & in(all_3_6_8, all_3_4_6) = v0)
% 50.65/19.31 |
% 50.65/19.31 +-Applying beta-rule and splitting (310), into two cases.
% 50.65/19.31 |-Branch one:
% 50.65/19.31 | (303) all_88_0_35 = 0
% 50.65/19.31 |
% 50.65/19.31 | Equations (303) can reduce 107 to:
% 50.65/19.31 | (72) $false
% 50.65/19.31 |
% 50.65/19.31 |-The branch is then unsatisfiable
% 50.65/19.31 |-Branch two:
% 50.65/19.31 | (107) ~ (all_88_0_35 = 0)
% 50.65/19.31 | (314) ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & in(all_3_6_8, all_3_3_5) = v1 & in(all_3_6_8, all_3_4_6) = v0)
% 50.65/19.31 |
% 50.65/19.31 +-Applying beta-rule and splitting (132), into two cases.
% 50.65/19.31 |-Branch one:
% 50.65/19.31 | (303) all_88_0_35 = 0
% 50.65/19.31 |
% 50.65/19.31 | Equations (303) can reduce 107 to:
% 50.65/19.31 | (72) $false
% 50.65/19.31 |
% 50.65/19.31 |-The branch is then unsatisfiable
% 50.65/19.31 |-Branch two:
% 50.65/19.31 | (107) ~ (all_88_0_35 = 0)
% 50.65/19.31 | (318) ? [v0] : ? [v1] : (in(all_3_6_8, all_3_2_4) = v0 & in(all_3_6_8, all_3_4_6) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 50.65/19.31 |
% 50.65/19.31 | Instantiating (318) with all_155_0_696, all_155_1_697 yields:
% 50.65/19.31 | (319) in(all_3_6_8, all_3_2_4) = all_155_1_697 & in(all_3_6_8, all_3_4_6) = all_155_0_696 & ( ~ (all_155_1_697 = 0) | all_155_0_696 = 0)
% 50.65/19.31 |
% 50.65/19.31 | Applying alpha-rule on (319) yields:
% 50.65/19.31 | (320) in(all_3_6_8, all_3_2_4) = all_155_1_697
% 50.65/19.31 | (321) in(all_3_6_8, all_3_4_6) = all_155_0_696
% 50.65/19.31 | (322) ~ (all_155_1_697 = 0) | all_155_0_696 = 0
% 50.65/19.31 |
% 50.65/19.31 +-Applying beta-rule and splitting (302), into two cases.
% 50.65/19.31 |-Branch one:
% 50.65/19.31 | (303) all_88_0_35 = 0
% 50.65/19.31 |
% 50.65/19.31 | Equations (303) can reduce 107 to:
% 50.65/19.31 | (72) $false
% 50.65/19.31 |
% 50.65/19.31 |-The branch is then unsatisfiable
% 50.65/19.31 |-Branch two:
% 50.65/19.31 | (107) ~ (all_88_0_35 = 0)
% 50.65/19.31 | (326) ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & in(all_3_6_8, all_3_3_5) = v0 & in(all_3_6_8, all_3_4_6) = v1)
% 50.65/19.31 |
% 50.65/19.31 | Instantiating formula (4) with all_3_6_8, all_3_2_4, all_107_0_39, 0 and discharging atoms in(all_3_6_8, all_3_2_4) = all_107_0_39, in(all_3_6_8, all_3_2_4) = 0, yields:
% 50.65/19.31 | (327) all_107_0_39 = 0
% 50.65/19.31 |
% 50.65/19.31 | Instantiating formula (4) with all_3_6_8, all_3_2_4, all_107_0_39, all_155_1_697 and discharging atoms in(all_3_6_8, all_3_2_4) = all_155_1_697, in(all_3_6_8, all_3_2_4) = all_107_0_39, yields:
% 50.65/19.31 | (328) all_155_1_697 = all_107_0_39
% 50.65/19.31 |
% 50.65/19.31 | Instantiating formula (4) with all_3_6_8, all_3_2_4, all_88_0_35, all_155_1_697 and discharging atoms in(all_3_6_8, all_3_2_4) = all_155_1_697, in(all_3_6_8, all_3_2_4) = all_88_0_35, yields:
% 50.65/19.31 | (329) all_155_1_697 = all_88_0_35
% 50.65/19.31 |
% 50.65/19.31 | Combining equations (328,329) yields a new equation:
% 50.65/19.31 | (330) all_107_0_39 = all_88_0_35
% 50.65/19.31 |
% 50.65/19.32 | Simplifying 330 yields:
% 50.65/19.32 | (331) all_107_0_39 = all_88_0_35
% 50.65/19.32 |
% 50.65/19.32 | Combining equations (327,331) yields a new equation:
% 50.65/19.32 | (303) all_88_0_35 = 0
% 50.65/19.32 |
% 50.65/19.32 | Equations (303) can reduce 107 to:
% 50.65/19.32 | (72) $false
% 50.65/19.32 |
% 50.65/19.32 |-The branch is then unsatisfiable
% 50.65/19.32 % SZS output end Proof for theBenchmark
% 50.65/19.32
% 50.65/19.32 18694ms
%------------------------------------------------------------------------------