TSTP Solution File: SEU320+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU320+1 : TPTP v8.1.0. Released v3.3.0.
% 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 08:48:49 EDT 2022
% Result : Theorem 4.05s 1.75s
% Output : Proof 10.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SEU320+1 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.13 % 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 : Mon Jun 20 11:16:40 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.55/0.62 ____ _
% 0.55/0.62 ___ / __ \_____(_)___ ________ __________
% 0.55/0.62 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.55/0.62 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.55/0.62 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.55/0.62
% 0.55/0.62 A Theorem Prover for First-Order Logic
% 0.55/0.62 (ePrincess v.1.0)
% 0.55/0.62
% 0.55/0.62 (c) Philipp Rümmer, 2009-2015
% 0.55/0.62 (c) Peter Backeman, 2014-2015
% 0.55/0.62 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.55/0.62 Free software under GNU Lesser General Public License (LGPL).
% 0.55/0.62 Bug reports to peter@backeman.se
% 0.55/0.62
% 0.55/0.62 For more information, visit http://user.uu.se/~petba168/breu/
% 0.55/0.62
% 0.55/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.65/0.67 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.45/0.96 Prover 0: Preprocessing ...
% 1.80/1.09 Prover 0: Warning: ignoring some quantifiers
% 1.80/1.11 Prover 0: Constructing countermodel ...
% 2.56/1.33 Prover 0: gave up
% 2.56/1.33 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.56/1.35 Prover 1: Preprocessing ...
% 2.81/1.41 Prover 1: Warning: ignoring some quantifiers
% 2.81/1.42 Prover 1: Constructing countermodel ...
% 3.27/1.54 Prover 1: gave up
% 3.27/1.55 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 3.27/1.56 Prover 2: Preprocessing ...
% 3.66/1.64 Prover 2: Warning: ignoring some quantifiers
% 3.66/1.65 Prover 2: Constructing countermodel ...
% 4.05/1.75 Prover 2: proved (208ms)
% 4.05/1.75
% 4.05/1.75 No countermodel exists, formula is valid
% 4.05/1.75 % SZS status Theorem for theBenchmark
% 4.05/1.75
% 4.05/1.75 Generating proof ... Warning: ignoring some quantifiers
% 10.08/3.15 found it (size 219)
% 10.08/3.15
% 10.08/3.15 % SZS output start Proof for theBenchmark
% 10.08/3.15 Assumed formulas after preprocessing and simplification:
% 10.08/3.15 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (the_carrier(v0) = v1 & closed_subset(v5, v0) = v6 & open_subset(v3, v0) = v4 & one_sorted_str(v7) = 0 & top_str(v8) = 0 & top_str(v0) = 0 & subset_complement(v1, v3) = v5 & powerset(v1) = v2 & element(v3, v2) = 0 & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (powerset(v10) = v11) | ~ (element(v9, v11) = v12) | ? [v13] : ( ~ (v13 = 0) & subset(v9, v10) = v13)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (closed_subset(v12, v11) = v10) | ~ (closed_subset(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (open_subset(v12, v11) = v10) | ~ (open_subset(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (subset(v12, v11) = v10) | ~ (subset(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (subset_complement(v12, v11) = v10) | ~ (subset_complement(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (element(v12, v11) = v10) | ~ (element(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (subset(v9, v10) = v11) | ? [v12] : ? [v13] : ( ~ (v13 = 0) & powerset(v10) = v12 & element(v9, v12) = v13)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (the_carrier(v11) = v10) | ~ (the_carrier(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (one_sorted_str(v11) = v10) | ~ (one_sorted_str(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (top_str(v11) = v10) | ~ (top_str(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (powerset(v11) = v10) | ~ (powerset(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (subset_complement(v9, v10) = v11) | ? [v12] : ? [v13] : (powerset(v9) = v12 & ((v13 = 0 & element(v11, v12) = 0) | ( ~ (v13 = 0) & element(v10, v12) = v13)))) & ! [v9] : ! [v10] : ! [v11] : ( ~ (subset_complement(v9, v10) = v11) | ? [v12] : ? [v13] : ((v12 = v10 & subset_complement(v9, v11) = v10) | ( ~ (v13 = 0) & powerset(v9) = v12 & element(v10, v12) = v13))) & ! [v9] : ! [v10] : ! [v11] : ( ~ (powerset(v10) = v11) | ~ (element(v9, v11) = 0) | subset(v9, v10) = 0) & ! [v9] : ! [v10] : ! [v11] : ( ~ (powerset(v9) = v11) | ~ (element(v10, v11) = 0) | ? [v12] : (subset_complement(v9, v12) = v10 & subset_complement(v9, v10) = v12)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (powerset(v9) = v11) | ~ (element(v10, v11) = 0) | ? [v12] : (subset_complement(v9, v10) = v12 & element(v12, v11) = 0)) & ! [v9] : ! [v10] : (v10 = 0 | ~ (subset(v9, v9) = v10)) & ! [v9] : ! [v10] : (v10 = 0 | ~ (one_sorted_str(v9) = v10) | ? [v11] : ( ~ (v11 = 0) & top_str(v9) = v11)) & ! [v9] : ! [v10] : ( ~ (the_carrier(v9) = v10) | ? [v11] : (( ~ (v11 = 0) & top_str(v9) = v11) | (powerset(v10) = v11 & ! [v12] : ! [v13] : ( ~ (closed_subset(v12, v9) = v13) | ? [v14] : ? [v15] : (( ~ (v14 = 0) & element(v12, v11) = v14) | (( ~ (v13 = 0) | (v15 = 0 & open_subset(v14, v9) = 0 & subset_complement(v10, v12) = v14)) & (v13 = 0 | ( ~ (v15 = 0) & open_subset(v14, v9) = v15 & subset_complement(v10, v12) = v14))))) & ! [v12] : ! [v13] : ( ~ (subset_complement(v10, v12) = v13) | ? [v14] : ? [v15] : (( ~ (v14 = 0) & element(v12, v11) = v14) | (((v15 = 0 & open_subset(v13, v9) = 0) | ( ~ (v14 = 0) & closed_subset(v12, v9) = v14)) & ((v14 = 0 & closed_subset(v12, v9) = 0) | ( ~ (v15 = 0) & open_subset(v13, v9) = v15))))) & ! [v12] : ( ~ (element(v12, v11) = 0) | ? [v13] : ? [v14] : ? [v15] : (((v15 = 0 & open_subset(v14, v9) = 0 & subset_complement(v10, v12) = v14) | ( ~ (v13 = 0) & closed_subset(v12, v9) = v13)) & ((v13 = 0 & closed_subset(v12, v9) = 0) | ( ~ (v15 = 0) & open_subset(v14, v9) = v15 & subset_complement(v10, v12) = v14))))))) & ! [v9] : ! [v10] : ( ~ (subset(v9, v10) = 0) | ? [v11] : (powerset(v10) = v11 & element(v9, v11) = 0)) & ! [v9] : ( ~ (top_str(v9) = 0) | one_sorted_str(v9) = 0) & ! [v9] : ( ~ (top_str(v9) = 0) | ? [v10] : ? [v11] : (the_carrier(v9) = v10 & powerset(v10) = v11 & ! [v12] : ! [v13] : ( ~ (closed_subset(v12, v9) = v13) | ? [v14] : ? [v15] : (( ~ (v14 = 0) & element(v12, v11) = v14) | (( ~ (v13 = 0) | (v15 = 0 & open_subset(v14, v9) = 0 & subset_complement(v10, v12) = v14)) & (v13 = 0 | ( ~ (v15 = 0) & open_subset(v14, v9) = v15 & subset_complement(v10, v12) = v14))))) & ! [v12] : ! [v13] : ( ~ (subset_complement(v10, v12) = v13) | ? [v14] : ? [v15] : (( ~ (v14 = 0) & element(v12, v11) = v14) | (((v15 = 0 & open_subset(v13, v9) = 0) | ( ~ (v14 = 0) & closed_subset(v12, v9) = v14)) & ((v14 = 0 & closed_subset(v12, v9) = 0) | ( ~ (v15 = 0) & open_subset(v13, v9) = v15))))) & ! [v12] : ( ~ (element(v12, v11) = 0) | ? [v13] : ? [v14] : ? [v15] : (((v15 = 0 & open_subset(v14, v9) = 0 & subset_complement(v10, v12) = v14) | ( ~ (v13 = 0) & closed_subset(v12, v9) = v13)) & ((v13 = 0 & closed_subset(v12, v9) = 0) | ( ~ (v15 = 0) & open_subset(v14, v9) = v15 & subset_complement(v10, v12) = v14)))))) & ? [v9] : ? [v10] : ? [v11] : closed_subset(v10, v9) = v11 & ? [v9] : ? [v10] : ? [v11] : open_subset(v10, v9) = v11 & ? [v9] : ? [v10] : ? [v11] : subset(v10, v9) = v11 & ? [v9] : ? [v10] : ? [v11] : subset_complement(v10, v9) = v11 & ? [v9] : ? [v10] : ? [v11] : element(v10, v9) = v11 & ? [v9] : ? [v10] : the_carrier(v9) = v10 & ? [v9] : ? [v10] : one_sorted_str(v9) = v10 & ? [v9] : ? [v10] : top_str(v9) = v10 & ? [v9] : ? [v10] : powerset(v9) = v10 & ? [v9] : ? [v10] : element(v10, v9) = 0 & ((v6 = 0 & ~ (v4 = 0)) | (v4 = 0 & ~ (v6 = 0))))
% 10.59/3.20 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8 yields:
% 10.59/3.20 | (1) the_carrier(all_0_8_8) = all_0_7_7 & closed_subset(all_0_3_3, all_0_8_8) = all_0_2_2 & open_subset(all_0_5_5, all_0_8_8) = all_0_4_4 & one_sorted_str(all_0_1_1) = 0 & top_str(all_0_0_0) = 0 & top_str(all_0_8_8) = 0 & subset_complement(all_0_7_7, all_0_5_5) = all_0_3_3 & powerset(all_0_7_7) = all_0_6_6 & element(all_0_5_5, all_0_6_6) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (closed_subset(v3, v2) = v1) | ~ (closed_subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (open_subset(v3, v2) = v1) | ~ (open_subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset_complement(v3, v2) = v1) | ~ (subset_complement(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v1) = v3 & element(v0, v3) = v4)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (the_carrier(v2) = v1) | ~ (the_carrier(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (one_sorted_str(v2) = v1) | ~ (one_sorted_str(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (top_str(v2) = v1) | ~ (top_str(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_complement(v0, v1) = v2) | ? [v3] : ? [v4] : (powerset(v0) = v3 & ((v4 = 0 & element(v2, v3) = 0) | ( ~ (v4 = 0) & element(v1, v3) = v4)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_complement(v0, v1) = v2) | ? [v3] : ? [v4] : ((v3 = v1 & subset_complement(v0, v2) = v1) | ( ~ (v4 = 0) & powerset(v0) = v3 & element(v1, v3) = v4))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | subset(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v2) | ~ (element(v1, v2) = 0) | ? [v3] : (subset_complement(v0, v3) = v1 & subset_complement(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v2) | ~ (element(v1, v2) = 0) | ? [v3] : (subset_complement(v0, v1) = v3 & element(v3, v2) = 0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (one_sorted_str(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & top_str(v0) = v2)) & ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ? [v2] : (( ~ (v2 = 0) & top_str(v0) = v2) | (powerset(v1) = v2 & ! [v3] : ! [v4] : ( ~ (closed_subset(v3, v0) = v4) | ? [v5] : ? [v6] : (( ~ (v5 = 0) & element(v3, v2) = v5) | (( ~ (v4 = 0) | (v6 = 0 & open_subset(v5, v0) = 0 & subset_complement(v1, v3) = v5)) & (v4 = 0 | ( ~ (v6 = 0) & open_subset(v5, v0) = v6 & subset_complement(v1, v3) = v5))))) & ! [v3] : ! [v4] : ( ~ (subset_complement(v1, v3) = v4) | ? [v5] : ? [v6] : (( ~ (v5 = 0) & element(v3, v2) = v5) | (((v6 = 0 & open_subset(v4, v0) = 0) | ( ~ (v5 = 0) & closed_subset(v3, v0) = v5)) & ((v5 = 0 & closed_subset(v3, v0) = 0) | ( ~ (v6 = 0) & open_subset(v4, v0) = v6))))) & ! [v3] : ( ~ (element(v3, v2) = 0) | ? [v4] : ? [v5] : ? [v6] : (((v6 = 0 & open_subset(v5, v0) = 0 & subset_complement(v1, v3) = v5) | ( ~ (v4 = 0) & closed_subset(v3, v0) = v4)) & ((v4 = 0 & closed_subset(v3, v0) = 0) | ( ~ (v6 = 0) & open_subset(v5, v0) = v6 & subset_complement(v1, v3) = v5))))))) & ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (powerset(v1) = v2 & element(v0, v2) = 0)) & ! [v0] : ( ~ (top_str(v0) = 0) | one_sorted_str(v0) = 0) & ! [v0] : ( ~ (top_str(v0) = 0) | ? [v1] : ? [v2] : (the_carrier(v0) = v1 & powerset(v1) = v2 & ! [v3] : ! [v4] : ( ~ (closed_subset(v3, v0) = v4) | ? [v5] : ? [v6] : (( ~ (v5 = 0) & element(v3, v2) = v5) | (( ~ (v4 = 0) | (v6 = 0 & open_subset(v5, v0) = 0 & subset_complement(v1, v3) = v5)) & (v4 = 0 | ( ~ (v6 = 0) & open_subset(v5, v0) = v6 & subset_complement(v1, v3) = v5))))) & ! [v3] : ! [v4] : ( ~ (subset_complement(v1, v3) = v4) | ? [v5] : ? [v6] : (( ~ (v5 = 0) & element(v3, v2) = v5) | (((v6 = 0 & open_subset(v4, v0) = 0) | ( ~ (v5 = 0) & closed_subset(v3, v0) = v5)) & ((v5 = 0 & closed_subset(v3, v0) = 0) | ( ~ (v6 = 0) & open_subset(v4, v0) = v6))))) & ! [v3] : ( ~ (element(v3, v2) = 0) | ? [v4] : ? [v5] : ? [v6] : (((v6 = 0 & open_subset(v5, v0) = 0 & subset_complement(v1, v3) = v5) | ( ~ (v4 = 0) & closed_subset(v3, v0) = v4)) & ((v4 = 0 & closed_subset(v3, v0) = 0) | ( ~ (v6 = 0) & open_subset(v5, v0) = v6 & subset_complement(v1, v3) = v5)))))) & ? [v0] : ? [v1] : ? [v2] : closed_subset(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : open_subset(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : subset_complement(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : element(v1, v0) = v2 & ? [v0] : ? [v1] : the_carrier(v0) = v1 & ? [v0] : ? [v1] : one_sorted_str(v0) = v1 & ? [v0] : ? [v1] : top_str(v0) = v1 & ? [v0] : ? [v1] : powerset(v0) = v1 & ? [v0] : ? [v1] : element(v1, v0) = 0 & ((all_0_2_2 = 0 & ~ (all_0_4_4 = 0)) | (all_0_4_4 = 0 & ~ (all_0_2_2 = 0)))
% 10.70/3.22 |
% 10.70/3.22 | Applying alpha-rule on (1) yields:
% 10.71/3.22 | (2) ? [v0] : ? [v1] : the_carrier(v0) = v1
% 10.71/3.22 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 10.71/3.22 | (4) one_sorted_str(all_0_1_1) = 0
% 10.71/3.22 | (5) element(all_0_5_5, all_0_6_6) = 0
% 10.71/3.22 | (6) ! [v0] : ! [v1] : (v1 = 0 | ~ (one_sorted_str(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & top_str(v0) = v2))
% 10.71/3.22 | (7) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_complement(v0, v1) = v2) | ? [v3] : ? [v4] : (powerset(v0) = v3 & ((v4 = 0 & element(v2, v3) = 0) | ( ~ (v4 = 0) & element(v1, v3) = v4))))
% 10.71/3.22 | (8) powerset(all_0_7_7) = all_0_6_6
% 10.71/3.22 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (open_subset(v3, v2) = v1) | ~ (open_subset(v3, v2) = v0))
% 10.71/3.22 | (10) top_str(all_0_0_0) = 0
% 10.71/3.22 | (11) ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ? [v2] : (( ~ (v2 = 0) & top_str(v0) = v2) | (powerset(v1) = v2 & ! [v3] : ! [v4] : ( ~ (closed_subset(v3, v0) = v4) | ? [v5] : ? [v6] : (( ~ (v5 = 0) & element(v3, v2) = v5) | (( ~ (v4 = 0) | (v6 = 0 & open_subset(v5, v0) = 0 & subset_complement(v1, v3) = v5)) & (v4 = 0 | ( ~ (v6 = 0) & open_subset(v5, v0) = v6 & subset_complement(v1, v3) = v5))))) & ! [v3] : ! [v4] : ( ~ (subset_complement(v1, v3) = v4) | ? [v5] : ? [v6] : (( ~ (v5 = 0) & element(v3, v2) = v5) | (((v6 = 0 & open_subset(v4, v0) = 0) | ( ~ (v5 = 0) & closed_subset(v3, v0) = v5)) & ((v5 = 0 & closed_subset(v3, v0) = 0) | ( ~ (v6 = 0) & open_subset(v4, v0) = v6))))) & ! [v3] : ( ~ (element(v3, v2) = 0) | ? [v4] : ? [v5] : ? [v6] : (((v6 = 0 & open_subset(v5, v0) = 0 & subset_complement(v1, v3) = v5) | ( ~ (v4 = 0) & closed_subset(v3, v0) = v4)) & ((v4 = 0 & closed_subset(v3, v0) = 0) | ( ~ (v6 = 0) & open_subset(v5, v0) = v6 & subset_complement(v1, v3) = v5)))))))
% 10.71/3.22 | (12) ? [v0] : ? [v1] : ? [v2] : closed_subset(v1, v0) = v2
% 10.71/3.22 | (13) ? [v0] : ? [v1] : one_sorted_str(v0) = v1
% 10.71/3.22 | (14) closed_subset(all_0_3_3, all_0_8_8) = all_0_2_2
% 10.71/3.22 | (15) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v1) = v3 & element(v0, v3) = v4))
% 10.71/3.22 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset_complement(v3, v2) = v1) | ~ (subset_complement(v3, v2) = v0))
% 10.71/3.22 | (17) ? [v0] : ? [v1] : top_str(v0) = v1
% 10.71/3.22 | (18) ? [v0] : ? [v1] : ? [v2] : open_subset(v1, v0) = v2
% 10.71/3.22 | (19) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0))
% 10.71/3.22 | (20) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v2) | ~ (element(v1, v2) = 0) | ? [v3] : (subset_complement(v0, v1) = v3 & element(v3, v2) = 0))
% 10.71/3.22 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (closed_subset(v3, v2) = v1) | ~ (closed_subset(v3, v2) = v0))
% 10.71/3.22 | (22) ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2
% 10.71/3.23 | (23) open_subset(all_0_5_5, all_0_8_8) = all_0_4_4
% 10.71/3.23 | (24) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_complement(v0, v1) = v2) | ? [v3] : ? [v4] : ((v3 = v1 & subset_complement(v0, v2) = v1) | ( ~ (v4 = 0) & powerset(v0) = v3 & element(v1, v3) = v4)))
% 10.71/3.23 | (25) ! [v0] : ( ~ (top_str(v0) = 0) | one_sorted_str(v0) = 0)
% 10.71/3.23 | (26) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (one_sorted_str(v2) = v1) | ~ (one_sorted_str(v2) = v0))
% 10.71/3.23 | (27) ? [v0] : ? [v1] : powerset(v0) = v1
% 10.71/3.23 | (28) ? [v0] : ? [v1] : ? [v2] : subset_complement(v1, v0) = v2
% 10.71/3.23 | (29) top_str(all_0_8_8) = 0
% 10.71/3.23 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 10.71/3.23 | (31) ! [v0] : ( ~ (top_str(v0) = 0) | ? [v1] : ? [v2] : (the_carrier(v0) = v1 & powerset(v1) = v2 & ! [v3] : ! [v4] : ( ~ (closed_subset(v3, v0) = v4) | ? [v5] : ? [v6] : (( ~ (v5 = 0) & element(v3, v2) = v5) | (( ~ (v4 = 0) | (v6 = 0 & open_subset(v5, v0) = 0 & subset_complement(v1, v3) = v5)) & (v4 = 0 | ( ~ (v6 = 0) & open_subset(v5, v0) = v6 & subset_complement(v1, v3) = v5))))) & ! [v3] : ! [v4] : ( ~ (subset_complement(v1, v3) = v4) | ? [v5] : ? [v6] : (( ~ (v5 = 0) & element(v3, v2) = v5) | (((v6 = 0 & open_subset(v4, v0) = 0) | ( ~ (v5 = 0) & closed_subset(v3, v0) = v5)) & ((v5 = 0 & closed_subset(v3, v0) = 0) | ( ~ (v6 = 0) & open_subset(v4, v0) = v6))))) & ! [v3] : ( ~ (element(v3, v2) = 0) | ? [v4] : ? [v5] : ? [v6] : (((v6 = 0 & open_subset(v5, v0) = 0 & subset_complement(v1, v3) = v5) | ( ~ (v4 = 0) & closed_subset(v3, v0) = v4)) & ((v4 = 0 & closed_subset(v3, v0) = 0) | ( ~ (v6 = 0) & open_subset(v5, v0) = v6 & subset_complement(v1, v3) = v5))))))
% 10.71/3.23 | (32) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1))
% 10.71/3.23 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0))
% 10.71/3.23 | (34) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (powerset(v1) = v2 & element(v0, v2) = 0))
% 10.71/3.23 | (35) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (the_carrier(v2) = v1) | ~ (the_carrier(v2) = v0))
% 10.71/3.23 | (36) (all_0_2_2 = 0 & ~ (all_0_4_4 = 0)) | (all_0_4_4 = 0 & ~ (all_0_2_2 = 0))
% 10.71/3.23 | (37) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | subset(v0, v1) = 0)
% 10.71/3.23 | (38) ? [v0] : ? [v1] : ? [v2] : element(v1, v0) = v2
% 10.71/3.23 | (39) subset_complement(all_0_7_7, all_0_5_5) = all_0_3_3
% 10.71/3.23 | (40) ? [v0] : ? [v1] : element(v1, v0) = 0
% 10.71/3.23 | (41) the_carrier(all_0_8_8) = all_0_7_7
% 10.71/3.23 | (42) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (top_str(v2) = v1) | ~ (top_str(v2) = v0))
% 10.71/3.23 | (43) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v2) | ~ (element(v1, v2) = 0) | ? [v3] : (subset_complement(v0, v3) = v1 & subset_complement(v0, v1) = v3))
% 10.71/3.23 |
% 10.71/3.23 | Instantiating formula (11) with all_0_7_7, all_0_8_8 and discharging atoms the_carrier(all_0_8_8) = all_0_7_7, yields:
% 10.71/3.23 | (44) ? [v0] : (( ~ (v0 = 0) & top_str(all_0_8_8) = v0) | (powerset(all_0_7_7) = v0 & ! [v1] : ! [v2] : ( ~ (closed_subset(v1, all_0_8_8) = v2) | ? [v3] : ? [v4] : (( ~ (v3 = 0) & element(v1, v0) = v3) | (( ~ (v2 = 0) | (v4 = 0 & open_subset(v3, all_0_8_8) = 0 & subset_complement(all_0_7_7, v1) = v3)) & (v2 = 0 | ( ~ (v4 = 0) & open_subset(v3, all_0_8_8) = v4 & subset_complement(all_0_7_7, v1) = v3))))) & ! [v1] : ! [v2] : ( ~ (subset_complement(all_0_7_7, v1) = v2) | ? [v3] : ? [v4] : (( ~ (v3 = 0) & element(v1, v0) = v3) | (((v4 = 0 & open_subset(v2, all_0_8_8) = 0) | ( ~ (v3 = 0) & closed_subset(v1, all_0_8_8) = v3)) & ((v3 = 0 & closed_subset(v1, all_0_8_8) = 0) | ( ~ (v4 = 0) & open_subset(v2, all_0_8_8) = v4))))) & ! [v1] : ( ~ (element(v1, v0) = 0) | ? [v2] : ? [v3] : ? [v4] : (((v4 = 0 & open_subset(v3, all_0_8_8) = 0 & subset_complement(all_0_7_7, v1) = v3) | ( ~ (v2 = 0) & closed_subset(v1, all_0_8_8) = v2)) & ((v2 = 0 & closed_subset(v1, all_0_8_8) = 0) | ( ~ (v4 = 0) & open_subset(v3, all_0_8_8) = v4 & subset_complement(all_0_7_7, v1) = v3))))))
% 10.71/3.23 |
% 10.71/3.23 | Instantiating formula (31) with all_0_8_8 and discharging atoms top_str(all_0_8_8) = 0, yields:
% 10.71/3.23 | (45) ? [v0] : ? [v1] : (the_carrier(all_0_8_8) = v0 & powerset(v0) = v1 & ! [v2] : ! [v3] : ( ~ (closed_subset(v2, all_0_8_8) = v3) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & element(v2, v1) = v4) | (( ~ (v3 = 0) | (v5 = 0 & open_subset(v4, all_0_8_8) = 0 & subset_complement(v0, v2) = v4)) & (v3 = 0 | ( ~ (v5 = 0) & open_subset(v4, all_0_8_8) = v5 & subset_complement(v0, v2) = v4))))) & ! [v2] : ! [v3] : ( ~ (subset_complement(v0, v2) = v3) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & element(v2, v1) = v4) | (((v5 = 0 & open_subset(v3, all_0_8_8) = 0) | ( ~ (v4 = 0) & closed_subset(v2, all_0_8_8) = v4)) & ((v4 = 0 & closed_subset(v2, all_0_8_8) = 0) | ( ~ (v5 = 0) & open_subset(v3, all_0_8_8) = v5))))) & ! [v2] : ( ~ (element(v2, v1) = 0) | ? [v3] : ? [v4] : ? [v5] : (((v5 = 0 & open_subset(v4, all_0_8_8) = 0 & subset_complement(v0, v2) = v4) | ( ~ (v3 = 0) & closed_subset(v2, all_0_8_8) = v3)) & ((v3 = 0 & closed_subset(v2, all_0_8_8) = 0) | ( ~ (v5 = 0) & open_subset(v4, all_0_8_8) = v5 & subset_complement(v0, v2) = v4)))))
% 10.71/3.24 |
% 10.71/3.24 | Instantiating formula (7) with all_0_3_3, all_0_5_5, all_0_7_7 and discharging atoms subset_complement(all_0_7_7, all_0_5_5) = all_0_3_3, yields:
% 10.71/3.24 | (46) ? [v0] : ? [v1] : (powerset(all_0_7_7) = v0 & ((v1 = 0 & element(all_0_3_3, v0) = 0) | ( ~ (v1 = 0) & element(all_0_5_5, v0) = v1)))
% 10.71/3.24 |
% 10.71/3.24 | Instantiating formula (24) with all_0_3_3, all_0_5_5, all_0_7_7 and discharging atoms subset_complement(all_0_7_7, all_0_5_5) = all_0_3_3, yields:
% 10.71/3.24 | (47) ? [v0] : ? [v1] : ((v0 = all_0_5_5 & subset_complement(all_0_7_7, all_0_3_3) = all_0_5_5) | ( ~ (v1 = 0) & powerset(all_0_7_7) = v0 & element(all_0_5_5, v0) = v1))
% 10.71/3.24 |
% 10.71/3.24 | Instantiating (45) with all_33_0_36, all_33_1_37 yields:
% 10.71/3.24 | (48) the_carrier(all_0_8_8) = all_33_1_37 & powerset(all_33_1_37) = all_33_0_36 & ! [v0] : ! [v1] : ( ~ (closed_subset(v0, all_0_8_8) = v1) | ? [v2] : ? [v3] : (( ~ (v2 = 0) & element(v0, all_33_0_36) = v2) | (( ~ (v1 = 0) | (v3 = 0 & open_subset(v2, all_0_8_8) = 0 & subset_complement(all_33_1_37, v0) = v2)) & (v1 = 0 | ( ~ (v3 = 0) & open_subset(v2, all_0_8_8) = v3 & subset_complement(all_33_1_37, v0) = v2))))) & ! [v0] : ! [v1] : ( ~ (subset_complement(all_33_1_37, v0) = v1) | ? [v2] : ? [v3] : (( ~ (v2 = 0) & element(v0, all_33_0_36) = v2) | (((v3 = 0 & open_subset(v1, all_0_8_8) = 0) | ( ~ (v2 = 0) & closed_subset(v0, all_0_8_8) = v2)) & ((v2 = 0 & closed_subset(v0, all_0_8_8) = 0) | ( ~ (v3 = 0) & open_subset(v1, all_0_8_8) = v3))))) & ! [v0] : ( ~ (element(v0, all_33_0_36) = 0) | ? [v1] : ? [v2] : ? [v3] : (((v3 = 0 & open_subset(v2, all_0_8_8) = 0 & subset_complement(all_33_1_37, v0) = v2) | ( ~ (v1 = 0) & closed_subset(v0, all_0_8_8) = v1)) & ((v1 = 0 & closed_subset(v0, all_0_8_8) = 0) | ( ~ (v3 = 0) & open_subset(v2, all_0_8_8) = v3 & subset_complement(all_33_1_37, v0) = v2))))
% 10.71/3.24 |
% 10.71/3.24 | Applying alpha-rule on (48) yields:
% 10.71/3.24 | (49) powerset(all_33_1_37) = all_33_0_36
% 10.71/3.24 | (50) ! [v0] : ( ~ (element(v0, all_33_0_36) = 0) | ? [v1] : ? [v2] : ? [v3] : (((v3 = 0 & open_subset(v2, all_0_8_8) = 0 & subset_complement(all_33_1_37, v0) = v2) | ( ~ (v1 = 0) & closed_subset(v0, all_0_8_8) = v1)) & ((v1 = 0 & closed_subset(v0, all_0_8_8) = 0) | ( ~ (v3 = 0) & open_subset(v2, all_0_8_8) = v3 & subset_complement(all_33_1_37, v0) = v2))))
% 10.71/3.24 | (51) ! [v0] : ! [v1] : ( ~ (subset_complement(all_33_1_37, v0) = v1) | ? [v2] : ? [v3] : (( ~ (v2 = 0) & element(v0, all_33_0_36) = v2) | (((v3 = 0 & open_subset(v1, all_0_8_8) = 0) | ( ~ (v2 = 0) & closed_subset(v0, all_0_8_8) = v2)) & ((v2 = 0 & closed_subset(v0, all_0_8_8) = 0) | ( ~ (v3 = 0) & open_subset(v1, all_0_8_8) = v3)))))
% 10.71/3.24 | (52) the_carrier(all_0_8_8) = all_33_1_37
% 10.71/3.24 | (53) ! [v0] : ! [v1] : ( ~ (closed_subset(v0, all_0_8_8) = v1) | ? [v2] : ? [v3] : (( ~ (v2 = 0) & element(v0, all_33_0_36) = v2) | (( ~ (v1 = 0) | (v3 = 0 & open_subset(v2, all_0_8_8) = 0 & subset_complement(all_33_1_37, v0) = v2)) & (v1 = 0 | ( ~ (v3 = 0) & open_subset(v2, all_0_8_8) = v3 & subset_complement(all_33_1_37, v0) = v2)))))
% 10.71/3.24 |
% 10.71/3.24 | Instantiating formula (53) with all_0_2_2, all_0_3_3 and discharging atoms closed_subset(all_0_3_3, all_0_8_8) = all_0_2_2, yields:
% 10.71/3.24 | (54) ? [v0] : ? [v1] : (( ~ (v0 = 0) & element(all_0_3_3, all_33_0_36) = v0) | (( ~ (all_0_2_2 = 0) | (v1 = 0 & open_subset(v0, all_0_8_8) = 0 & subset_complement(all_33_1_37, all_0_3_3) = v0)) & (all_0_2_2 = 0 | ( ~ (v1 = 0) & open_subset(v0, all_0_8_8) = v1 & subset_complement(all_33_1_37, all_0_3_3) = v0))))
% 10.71/3.24 |
% 10.71/3.24 | Instantiating (47) with all_36_0_38, all_36_1_39 yields:
% 10.71/3.24 | (55) (all_36_1_39 = all_0_5_5 & subset_complement(all_0_7_7, all_0_3_3) = all_0_5_5) | ( ~ (all_36_0_38 = 0) & powerset(all_0_7_7) = all_36_1_39 & element(all_0_5_5, all_36_1_39) = all_36_0_38)
% 10.71/3.24 |
% 10.71/3.24 | Instantiating (44) with all_37_0_40 yields:
% 10.71/3.24 | (56) ( ~ (all_37_0_40 = 0) & top_str(all_0_8_8) = all_37_0_40) | (powerset(all_0_7_7) = all_37_0_40 & ! [v0] : ! [v1] : ( ~ (closed_subset(v0, all_0_8_8) = v1) | ? [v2] : ? [v3] : (( ~ (v2 = 0) & element(v0, all_37_0_40) = v2) | (( ~ (v1 = 0) | (v3 = 0 & open_subset(v2, all_0_8_8) = 0 & subset_complement(all_0_7_7, v0) = v2)) & (v1 = 0 | ( ~ (v3 = 0) & open_subset(v2, all_0_8_8) = v3 & subset_complement(all_0_7_7, v0) = v2))))) & ! [v0] : ! [v1] : ( ~ (subset_complement(all_0_7_7, v0) = v1) | ? [v2] : ? [v3] : (( ~ (v2 = 0) & element(v0, all_37_0_40) = v2) | (((v3 = 0 & open_subset(v1, all_0_8_8) = 0) | ( ~ (v2 = 0) & closed_subset(v0, all_0_8_8) = v2)) & ((v2 = 0 & closed_subset(v0, all_0_8_8) = 0) | ( ~ (v3 = 0) & open_subset(v1, all_0_8_8) = v3))))) & ! [v0] : ( ~ (element(v0, all_37_0_40) = 0) | ? [v1] : ? [v2] : ? [v3] : (((v3 = 0 & open_subset(v2, all_0_8_8) = 0 & subset_complement(all_0_7_7, v0) = v2) | ( ~ (v1 = 0) & closed_subset(v0, all_0_8_8) = v1)) & ((v1 = 0 & closed_subset(v0, all_0_8_8) = 0) | ( ~ (v3 = 0) & open_subset(v2, all_0_8_8) = v3 & subset_complement(all_0_7_7, v0) = v2)))))
% 10.71/3.24 |
% 10.71/3.24 | Instantiating (46) with all_38_0_41, all_38_1_42 yields:
% 10.71/3.24 | (57) powerset(all_0_7_7) = all_38_1_42 & ((all_38_0_41 = 0 & element(all_0_3_3, all_38_1_42) = 0) | ( ~ (all_38_0_41 = 0) & element(all_0_5_5, all_38_1_42) = all_38_0_41))
% 10.71/3.24 |
% 10.71/3.24 | Applying alpha-rule on (57) yields:
% 10.71/3.24 | (58) powerset(all_0_7_7) = all_38_1_42
% 10.71/3.24 | (59) (all_38_0_41 = 0 & element(all_0_3_3, all_38_1_42) = 0) | ( ~ (all_38_0_41 = 0) & element(all_0_5_5, all_38_1_42) = all_38_0_41)
% 10.71/3.24 |
% 10.71/3.24 | Instantiating (54) with all_43_0_45, all_43_1_46 yields:
% 10.71/3.24 | (60) ( ~ (all_43_1_46 = 0) & element(all_0_3_3, all_33_0_36) = all_43_1_46) | (( ~ (all_0_2_2 = 0) | (all_43_0_45 = 0 & open_subset(all_43_1_46, all_0_8_8) = 0 & subset_complement(all_33_1_37, all_0_3_3) = all_43_1_46)) & (all_0_2_2 = 0 | ( ~ (all_43_0_45 = 0) & open_subset(all_43_1_46, all_0_8_8) = all_43_0_45 & subset_complement(all_33_1_37, all_0_3_3) = all_43_1_46)))
% 10.71/3.25 |
% 10.71/3.25 +-Applying beta-rule and splitting (56), into two cases.
% 10.71/3.25 |-Branch one:
% 10.71/3.25 | (61) ~ (all_37_0_40 = 0) & top_str(all_0_8_8) = all_37_0_40
% 10.71/3.25 |
% 10.71/3.25 | Applying alpha-rule on (61) yields:
% 10.71/3.25 | (62) ~ (all_37_0_40 = 0)
% 10.71/3.25 | (63) top_str(all_0_8_8) = all_37_0_40
% 10.71/3.25 |
% 10.71/3.25 | Instantiating formula (42) with all_0_8_8, all_37_0_40, 0 and discharging atoms top_str(all_0_8_8) = all_37_0_40, top_str(all_0_8_8) = 0, yields:
% 10.71/3.25 | (64) all_37_0_40 = 0
% 10.71/3.25 |
% 10.71/3.25 | Equations (64) can reduce 62 to:
% 10.71/3.25 | (65) $false
% 10.71/3.25 |
% 10.71/3.25 |-The branch is then unsatisfiable
% 10.71/3.25 |-Branch two:
% 10.71/3.25 | (66) powerset(all_0_7_7) = all_37_0_40 & ! [v0] : ! [v1] : ( ~ (closed_subset(v0, all_0_8_8) = v1) | ? [v2] : ? [v3] : (( ~ (v2 = 0) & element(v0, all_37_0_40) = v2) | (( ~ (v1 = 0) | (v3 = 0 & open_subset(v2, all_0_8_8) = 0 & subset_complement(all_0_7_7, v0) = v2)) & (v1 = 0 | ( ~ (v3 = 0) & open_subset(v2, all_0_8_8) = v3 & subset_complement(all_0_7_7, v0) = v2))))) & ! [v0] : ! [v1] : ( ~ (subset_complement(all_0_7_7, v0) = v1) | ? [v2] : ? [v3] : (( ~ (v2 = 0) & element(v0, all_37_0_40) = v2) | (((v3 = 0 & open_subset(v1, all_0_8_8) = 0) | ( ~ (v2 = 0) & closed_subset(v0, all_0_8_8) = v2)) & ((v2 = 0 & closed_subset(v0, all_0_8_8) = 0) | ( ~ (v3 = 0) & open_subset(v1, all_0_8_8) = v3))))) & ! [v0] : ( ~ (element(v0, all_37_0_40) = 0) | ? [v1] : ? [v2] : ? [v3] : (((v3 = 0 & open_subset(v2, all_0_8_8) = 0 & subset_complement(all_0_7_7, v0) = v2) | ( ~ (v1 = 0) & closed_subset(v0, all_0_8_8) = v1)) & ((v1 = 0 & closed_subset(v0, all_0_8_8) = 0) | ( ~ (v3 = 0) & open_subset(v2, all_0_8_8) = v3 & subset_complement(all_0_7_7, v0) = v2))))
% 10.71/3.25 |
% 10.71/3.25 | Applying alpha-rule on (66) yields:
% 10.71/3.25 | (67) powerset(all_0_7_7) = all_37_0_40
% 10.71/3.25 | (68) ! [v0] : ! [v1] : ( ~ (closed_subset(v0, all_0_8_8) = v1) | ? [v2] : ? [v3] : (( ~ (v2 = 0) & element(v0, all_37_0_40) = v2) | (( ~ (v1 = 0) | (v3 = 0 & open_subset(v2, all_0_8_8) = 0 & subset_complement(all_0_7_7, v0) = v2)) & (v1 = 0 | ( ~ (v3 = 0) & open_subset(v2, all_0_8_8) = v3 & subset_complement(all_0_7_7, v0) = v2)))))
% 10.71/3.25 | (69) ! [v0] : ! [v1] : ( ~ (subset_complement(all_0_7_7, v0) = v1) | ? [v2] : ? [v3] : (( ~ (v2 = 0) & element(v0, all_37_0_40) = v2) | (((v3 = 0 & open_subset(v1, all_0_8_8) = 0) | ( ~ (v2 = 0) & closed_subset(v0, all_0_8_8) = v2)) & ((v2 = 0 & closed_subset(v0, all_0_8_8) = 0) | ( ~ (v3 = 0) & open_subset(v1, all_0_8_8) = v3)))))
% 10.71/3.25 | (70) ! [v0] : ( ~ (element(v0, all_37_0_40) = 0) | ? [v1] : ? [v2] : ? [v3] : (((v3 = 0 & open_subset(v2, all_0_8_8) = 0 & subset_complement(all_0_7_7, v0) = v2) | ( ~ (v1 = 0) & closed_subset(v0, all_0_8_8) = v1)) & ((v1 = 0 & closed_subset(v0, all_0_8_8) = 0) | ( ~ (v3 = 0) & open_subset(v2, all_0_8_8) = v3 & subset_complement(all_0_7_7, v0) = v2))))
% 10.71/3.25 |
% 10.71/3.25 | Instantiating formula (35) with all_0_8_8, all_33_1_37, all_0_7_7 and discharging atoms the_carrier(all_0_8_8) = all_33_1_37, the_carrier(all_0_8_8) = all_0_7_7, yields:
% 10.71/3.25 | (71) all_33_1_37 = all_0_7_7
% 10.71/3.25 |
% 10.71/3.25 | Instantiating formula (19) with all_0_7_7, all_38_1_42, all_0_6_6 and discharging atoms powerset(all_0_7_7) = all_38_1_42, powerset(all_0_7_7) = all_0_6_6, yields:
% 10.71/3.25 | (72) all_38_1_42 = all_0_6_6
% 10.71/3.25 |
% 10.71/3.25 | Instantiating formula (19) with all_0_7_7, all_37_0_40, all_38_1_42 and discharging atoms powerset(all_0_7_7) = all_38_1_42, powerset(all_0_7_7) = all_37_0_40, yields:
% 10.71/3.25 | (73) all_38_1_42 = all_37_0_40
% 10.71/3.25 |
% 10.71/3.25 | Combining equations (72,73) yields a new equation:
% 10.71/3.25 | (74) all_37_0_40 = all_0_6_6
% 10.71/3.25 |
% 10.71/3.25 | Combining equations (74,73) yields a new equation:
% 10.71/3.25 | (72) all_38_1_42 = all_0_6_6
% 10.71/3.25 |
% 10.71/3.25 | From (71) and (49) follows:
% 10.71/3.25 | (76) powerset(all_0_7_7) = all_33_0_36
% 10.71/3.25 |
% 10.71/3.25 | From (74) and (67) follows:
% 10.71/3.25 | (8) powerset(all_0_7_7) = all_0_6_6
% 10.71/3.25 |
% 10.71/3.25 +-Applying beta-rule and splitting (59), into two cases.
% 10.71/3.25 |-Branch one:
% 10.71/3.25 | (78) all_38_0_41 = 0 & element(all_0_3_3, all_38_1_42) = 0
% 10.71/3.25 |
% 10.71/3.25 | Applying alpha-rule on (78) yields:
% 10.71/3.25 | (79) all_38_0_41 = 0
% 10.71/3.25 | (80) element(all_0_3_3, all_38_1_42) = 0
% 10.71/3.25 |
% 10.71/3.25 | From (72) and (80) follows:
% 10.71/3.25 | (81) element(all_0_3_3, all_0_6_6) = 0
% 10.71/3.25 |
% 10.71/3.25 | Instantiating formula (19) with all_0_7_7, all_33_0_36, all_0_6_6 and discharging atoms powerset(all_0_7_7) = all_33_0_36, powerset(all_0_7_7) = all_0_6_6, yields:
% 10.71/3.25 | (82) all_33_0_36 = all_0_6_6
% 10.71/3.25 |
% 10.71/3.25 | From (82) and (76) follows:
% 10.71/3.25 | (8) powerset(all_0_7_7) = all_0_6_6
% 10.71/3.25 |
% 10.71/3.25 +-Applying beta-rule and splitting (55), into two cases.
% 10.71/3.25 |-Branch one:
% 10.71/3.25 | (84) all_36_1_39 = all_0_5_5 & subset_complement(all_0_7_7, all_0_3_3) = all_0_5_5
% 10.71/3.25 |
% 10.71/3.25 | Applying alpha-rule on (84) yields:
% 10.71/3.25 | (85) all_36_1_39 = all_0_5_5
% 10.71/3.25 | (86) subset_complement(all_0_7_7, all_0_3_3) = all_0_5_5
% 10.71/3.26 |
% 10.71/3.26 | Instantiating formula (69) with all_0_5_5, all_0_3_3 and discharging atoms subset_complement(all_0_7_7, all_0_3_3) = all_0_5_5, yields:
% 10.71/3.26 | (87) ? [v0] : ? [v1] : (( ~ (v0 = 0) & element(all_0_3_3, all_37_0_40) = v0) | (((v1 = 0 & open_subset(all_0_5_5, all_0_8_8) = 0) | ( ~ (v0 = 0) & closed_subset(all_0_3_3, all_0_8_8) = v0)) & ((v0 = 0 & closed_subset(all_0_3_3, all_0_8_8) = 0) | ( ~ (v1 = 0) & open_subset(all_0_5_5, all_0_8_8) = v1))))
% 10.71/3.26 |
% 10.71/3.26 | Instantiating formula (70) with all_0_3_3 yields:
% 10.71/3.26 | (88) ~ (element(all_0_3_3, all_37_0_40) = 0) | ? [v0] : ? [v1] : ? [v2] : (((v2 = 0 & open_subset(v1, all_0_8_8) = 0 & subset_complement(all_0_7_7, all_0_3_3) = v1) | ( ~ (v0 = 0) & closed_subset(all_0_3_3, all_0_8_8) = v0)) & ((v0 = 0 & closed_subset(all_0_3_3, all_0_8_8) = 0) | ( ~ (v2 = 0) & open_subset(v1, all_0_8_8) = v2 & subset_complement(all_0_7_7, all_0_3_3) = v1)))
% 10.71/3.26 |
% 10.71/3.26 | Instantiating formula (50) with all_0_3_3 yields:
% 10.71/3.26 | (89) ~ (element(all_0_3_3, all_33_0_36) = 0) | ? [v0] : ? [v1] : ? [v2] : (((v2 = 0 & open_subset(v1, all_0_8_8) = 0 & subset_complement(all_33_1_37, all_0_3_3) = v1) | ( ~ (v0 = 0) & closed_subset(all_0_3_3, all_0_8_8) = v0)) & ((v0 = 0 & closed_subset(all_0_3_3, all_0_8_8) = 0) | ( ~ (v2 = 0) & open_subset(v1, all_0_8_8) = v2 & subset_complement(all_33_1_37, all_0_3_3) = v1)))
% 10.71/3.26 |
% 10.71/3.26 | Instantiating (87) with all_74_0_52, all_74_1_53 yields:
% 10.71/3.26 | (90) ( ~ (all_74_1_53 = 0) & element(all_0_3_3, all_37_0_40) = all_74_1_53) | (((all_74_0_52 = 0 & open_subset(all_0_5_5, all_0_8_8) = 0) | ( ~ (all_74_1_53 = 0) & closed_subset(all_0_3_3, all_0_8_8) = all_74_1_53)) & ((all_74_1_53 = 0 & closed_subset(all_0_3_3, all_0_8_8) = 0) | ( ~ (all_74_0_52 = 0) & open_subset(all_0_5_5, all_0_8_8) = all_74_0_52)))
% 10.71/3.26 |
% 10.71/3.26 +-Applying beta-rule and splitting (88), into two cases.
% 10.71/3.26 |-Branch one:
% 10.71/3.26 | (91) ~ (element(all_0_3_3, all_37_0_40) = 0)
% 10.71/3.26 |
% 10.71/3.26 | From (74) and (91) follows:
% 10.71/3.26 | (92) ~ (element(all_0_3_3, all_0_6_6) = 0)
% 10.71/3.26 |
% 10.71/3.26 | Using (81) and (92) yields:
% 10.71/3.26 | (93) $false
% 10.71/3.26 |
% 10.71/3.26 |-The branch is then unsatisfiable
% 10.71/3.26 |-Branch two:
% 10.71/3.26 | (94) element(all_0_3_3, all_37_0_40) = 0
% 10.71/3.26 | (95) ? [v0] : ? [v1] : ? [v2] : (((v2 = 0 & open_subset(v1, all_0_8_8) = 0 & subset_complement(all_0_7_7, all_0_3_3) = v1) | ( ~ (v0 = 0) & closed_subset(all_0_3_3, all_0_8_8) = v0)) & ((v0 = 0 & closed_subset(all_0_3_3, all_0_8_8) = 0) | ( ~ (v2 = 0) & open_subset(v1, all_0_8_8) = v2 & subset_complement(all_0_7_7, all_0_3_3) = v1)))
% 10.71/3.26 |
% 10.71/3.26 | Instantiating (95) with all_88_0_64, all_88_1_65, all_88_2_66 yields:
% 10.71/3.26 | (96) ((all_88_0_64 = 0 & open_subset(all_88_1_65, all_0_8_8) = 0 & subset_complement(all_0_7_7, all_0_3_3) = all_88_1_65) | ( ~ (all_88_2_66 = 0) & closed_subset(all_0_3_3, all_0_8_8) = all_88_2_66)) & ((all_88_2_66 = 0 & closed_subset(all_0_3_3, all_0_8_8) = 0) | ( ~ (all_88_0_64 = 0) & open_subset(all_88_1_65, all_0_8_8) = all_88_0_64 & subset_complement(all_0_7_7, all_0_3_3) = all_88_1_65))
% 10.71/3.26 |
% 10.71/3.26 | Applying alpha-rule on (96) yields:
% 10.71/3.26 | (97) (all_88_0_64 = 0 & open_subset(all_88_1_65, all_0_8_8) = 0 & subset_complement(all_0_7_7, all_0_3_3) = all_88_1_65) | ( ~ (all_88_2_66 = 0) & closed_subset(all_0_3_3, all_0_8_8) = all_88_2_66)
% 10.71/3.26 | (98) (all_88_2_66 = 0 & closed_subset(all_0_3_3, all_0_8_8) = 0) | ( ~ (all_88_0_64 = 0) & open_subset(all_88_1_65, all_0_8_8) = all_88_0_64 & subset_complement(all_0_7_7, all_0_3_3) = all_88_1_65)
% 10.71/3.26 |
% 10.71/3.26 | From (74) and (94) follows:
% 10.71/3.26 | (81) element(all_0_3_3, all_0_6_6) = 0
% 10.71/3.26 |
% 10.71/3.26 +-Applying beta-rule and splitting (89), into two cases.
% 10.71/3.26 |-Branch one:
% 10.71/3.26 | (100) ~ (element(all_0_3_3, all_33_0_36) = 0)
% 10.71/3.26 |
% 10.71/3.26 | From (82) and (100) follows:
% 10.71/3.26 | (92) ~ (element(all_0_3_3, all_0_6_6) = 0)
% 10.71/3.26 |
% 10.71/3.26 | Using (81) and (92) yields:
% 10.71/3.26 | (93) $false
% 10.71/3.26 |
% 10.71/3.26 |-The branch is then unsatisfiable
% 10.71/3.26 |-Branch two:
% 10.71/3.26 | (103) element(all_0_3_3, all_33_0_36) = 0
% 10.71/3.26 | (104) ? [v0] : ? [v1] : ? [v2] : (((v2 = 0 & open_subset(v1, all_0_8_8) = 0 & subset_complement(all_33_1_37, all_0_3_3) = v1) | ( ~ (v0 = 0) & closed_subset(all_0_3_3, all_0_8_8) = v0)) & ((v0 = 0 & closed_subset(all_0_3_3, all_0_8_8) = 0) | ( ~ (v2 = 0) & open_subset(v1, all_0_8_8) = v2 & subset_complement(all_33_1_37, all_0_3_3) = v1)))
% 10.71/3.26 |
% 10.71/3.26 | Instantiating (104) with all_92_0_67, all_92_1_68, all_92_2_69 yields:
% 10.71/3.26 | (105) ((all_92_0_67 = 0 & open_subset(all_92_1_68, all_0_8_8) = 0 & subset_complement(all_33_1_37, all_0_3_3) = all_92_1_68) | ( ~ (all_92_2_69 = 0) & closed_subset(all_0_3_3, all_0_8_8) = all_92_2_69)) & ((all_92_2_69 = 0 & closed_subset(all_0_3_3, all_0_8_8) = 0) | ( ~ (all_92_0_67 = 0) & open_subset(all_92_1_68, all_0_8_8) = all_92_0_67 & subset_complement(all_33_1_37, all_0_3_3) = all_92_1_68))
% 10.71/3.26 |
% 10.71/3.26 | Applying alpha-rule on (105) yields:
% 10.71/3.26 | (106) (all_92_0_67 = 0 & open_subset(all_92_1_68, all_0_8_8) = 0 & subset_complement(all_33_1_37, all_0_3_3) = all_92_1_68) | ( ~ (all_92_2_69 = 0) & closed_subset(all_0_3_3, all_0_8_8) = all_92_2_69)
% 10.71/3.26 | (107) (all_92_2_69 = 0 & closed_subset(all_0_3_3, all_0_8_8) = 0) | ( ~ (all_92_0_67 = 0) & open_subset(all_92_1_68, all_0_8_8) = all_92_0_67 & subset_complement(all_33_1_37, all_0_3_3) = all_92_1_68)
% 10.71/3.26 |
% 10.71/3.26 | From (82) and (103) follows:
% 10.71/3.26 | (81) element(all_0_3_3, all_0_6_6) = 0
% 10.71/3.26 |
% 10.71/3.26 +-Applying beta-rule and splitting (36), into two cases.
% 10.71/3.26 |-Branch one:
% 10.71/3.26 | (109) all_0_2_2 = 0 & ~ (all_0_4_4 = 0)
% 10.71/3.26 |
% 10.71/3.26 | Applying alpha-rule on (109) yields:
% 10.71/3.26 | (110) all_0_2_2 = 0
% 10.71/3.26 | (111) ~ (all_0_4_4 = 0)
% 10.71/3.26 |
% 10.71/3.26 | From (110) and (14) follows:
% 10.71/3.26 | (112) closed_subset(all_0_3_3, all_0_8_8) = 0
% 10.71/3.26 |
% 10.71/3.26 +-Applying beta-rule and splitting (97), into two cases.
% 10.71/3.26 |-Branch one:
% 10.71/3.26 | (113) all_88_0_64 = 0 & open_subset(all_88_1_65, all_0_8_8) = 0 & subset_complement(all_0_7_7, all_0_3_3) = all_88_1_65
% 10.71/3.26 |
% 10.71/3.26 | Applying alpha-rule on (113) yields:
% 10.71/3.26 | (114) all_88_0_64 = 0
% 10.71/3.26 | (115) open_subset(all_88_1_65, all_0_8_8) = 0
% 10.71/3.26 | (116) subset_complement(all_0_7_7, all_0_3_3) = all_88_1_65
% 10.71/3.27 |
% 10.71/3.27 +-Applying beta-rule and splitting (90), into two cases.
% 10.71/3.27 |-Branch one:
% 10.71/3.27 | (117) ~ (all_74_1_53 = 0) & element(all_0_3_3, all_37_0_40) = all_74_1_53
% 10.71/3.27 |
% 10.71/3.27 | Applying alpha-rule on (117) yields:
% 10.71/3.27 | (118) ~ (all_74_1_53 = 0)
% 10.71/3.27 | (119) element(all_0_3_3, all_37_0_40) = all_74_1_53
% 10.71/3.27 |
% 10.71/3.27 | From (74) and (119) follows:
% 10.71/3.27 | (120) element(all_0_3_3, all_0_6_6) = all_74_1_53
% 10.71/3.27 |
% 10.71/3.27 | Instantiating formula (33) with all_0_3_3, all_0_6_6, all_74_1_53, 0 and discharging atoms element(all_0_3_3, all_0_6_6) = all_74_1_53, element(all_0_3_3, all_0_6_6) = 0, yields:
% 10.71/3.27 | (121) all_74_1_53 = 0
% 10.71/3.27 |
% 10.71/3.27 | Equations (121) can reduce 118 to:
% 10.71/3.27 | (65) $false
% 10.71/3.27 |
% 10.71/3.27 |-The branch is then unsatisfiable
% 10.71/3.27 |-Branch two:
% 10.71/3.27 | (123) ((all_74_0_52 = 0 & open_subset(all_0_5_5, all_0_8_8) = 0) | ( ~ (all_74_1_53 = 0) & closed_subset(all_0_3_3, all_0_8_8) = all_74_1_53)) & ((all_74_1_53 = 0 & closed_subset(all_0_3_3, all_0_8_8) = 0) | ( ~ (all_74_0_52 = 0) & open_subset(all_0_5_5, all_0_8_8) = all_74_0_52))
% 10.71/3.27 |
% 10.71/3.27 | Applying alpha-rule on (123) yields:
% 10.71/3.27 | (124) (all_74_0_52 = 0 & open_subset(all_0_5_5, all_0_8_8) = 0) | ( ~ (all_74_1_53 = 0) & closed_subset(all_0_3_3, all_0_8_8) = all_74_1_53)
% 10.71/3.27 | (125) (all_74_1_53 = 0 & closed_subset(all_0_3_3, all_0_8_8) = 0) | ( ~ (all_74_0_52 = 0) & open_subset(all_0_5_5, all_0_8_8) = all_74_0_52)
% 10.71/3.27 |
% 10.71/3.27 +-Applying beta-rule and splitting (124), into two cases.
% 10.71/3.27 |-Branch one:
% 10.71/3.27 | (126) all_74_0_52 = 0 & open_subset(all_0_5_5, all_0_8_8) = 0
% 10.71/3.27 |
% 10.71/3.27 | Applying alpha-rule on (126) yields:
% 10.71/3.27 | (127) all_74_0_52 = 0
% 10.71/3.27 | (128) open_subset(all_0_5_5, all_0_8_8) = 0
% 10.71/3.27 |
% 10.71/3.27 | Instantiating formula (9) with all_0_5_5, all_0_8_8, 0, all_0_4_4 and discharging atoms open_subset(all_0_5_5, all_0_8_8) = all_0_4_4, open_subset(all_0_5_5, all_0_8_8) = 0, yields:
% 10.71/3.27 | (129) all_0_4_4 = 0
% 10.71/3.27 |
% 10.71/3.27 | Equations (129) can reduce 111 to:
% 10.71/3.27 | (65) $false
% 10.71/3.27 |
% 10.71/3.27 |-The branch is then unsatisfiable
% 10.71/3.27 |-Branch two:
% 10.71/3.27 | (131) ~ (all_74_1_53 = 0) & closed_subset(all_0_3_3, all_0_8_8) = all_74_1_53
% 10.71/3.27 |
% 10.71/3.27 | Applying alpha-rule on (131) yields:
% 10.71/3.27 | (118) ~ (all_74_1_53 = 0)
% 10.71/3.27 | (133) closed_subset(all_0_3_3, all_0_8_8) = all_74_1_53
% 10.71/3.27 |
% 10.71/3.27 +-Applying beta-rule and splitting (98), into two cases.
% 10.71/3.27 |-Branch one:
% 10.71/3.27 | (134) all_88_2_66 = 0 & closed_subset(all_0_3_3, all_0_8_8) = 0
% 10.71/3.27 |
% 10.71/3.27 | Applying alpha-rule on (134) yields:
% 10.71/3.27 | (135) all_88_2_66 = 0
% 10.71/3.27 | (112) closed_subset(all_0_3_3, all_0_8_8) = 0
% 10.71/3.27 |
% 10.71/3.27 +-Applying beta-rule and splitting (107), into two cases.
% 10.71/3.27 |-Branch one:
% 10.71/3.27 | (137) all_92_2_69 = 0 & closed_subset(all_0_3_3, all_0_8_8) = 0
% 10.71/3.27 |
% 10.71/3.27 | Applying alpha-rule on (137) yields:
% 10.71/3.27 | (138) all_92_2_69 = 0
% 10.71/3.27 | (112) closed_subset(all_0_3_3, all_0_8_8) = 0
% 10.71/3.27 |
% 10.71/3.27 | Instantiating formula (21) with all_0_3_3, all_0_8_8, 0, all_74_1_53 and discharging atoms closed_subset(all_0_3_3, all_0_8_8) = all_74_1_53, closed_subset(all_0_3_3, all_0_8_8) = 0, yields:
% 10.71/3.27 | (121) all_74_1_53 = 0
% 10.71/3.27 |
% 10.71/3.27 | Equations (121) can reduce 118 to:
% 10.71/3.27 | (65) $false
% 10.71/3.27 |
% 10.71/3.27 |-The branch is then unsatisfiable
% 10.71/3.27 |-Branch two:
% 10.71/3.27 | (142) ~ (all_92_0_67 = 0) & open_subset(all_92_1_68, all_0_8_8) = all_92_0_67 & subset_complement(all_33_1_37, all_0_3_3) = all_92_1_68
% 10.71/3.27 |
% 10.71/3.27 | Applying alpha-rule on (142) yields:
% 10.71/3.27 | (143) ~ (all_92_0_67 = 0)
% 10.71/3.27 | (144) open_subset(all_92_1_68, all_0_8_8) = all_92_0_67
% 10.71/3.27 | (145) subset_complement(all_33_1_37, all_0_3_3) = all_92_1_68
% 10.71/3.27 |
% 10.71/3.27 +-Applying beta-rule and splitting (106), into two cases.
% 10.71/3.27 |-Branch one:
% 10.71/3.27 | (146) all_92_0_67 = 0 & open_subset(all_92_1_68, all_0_8_8) = 0 & subset_complement(all_33_1_37, all_0_3_3) = all_92_1_68
% 10.71/3.27 |
% 10.71/3.27 | Applying alpha-rule on (146) yields:
% 10.71/3.27 | (147) all_92_0_67 = 0
% 10.71/3.27 | (148) open_subset(all_92_1_68, all_0_8_8) = 0
% 10.71/3.27 | (145) subset_complement(all_33_1_37, all_0_3_3) = all_92_1_68
% 10.71/3.27 |
% 10.71/3.27 | Equations (147) can reduce 143 to:
% 10.71/3.27 | (65) $false
% 10.71/3.27 |
% 10.71/3.27 |-The branch is then unsatisfiable
% 10.71/3.27 |-Branch two:
% 10.71/3.27 | (151) ~ (all_92_2_69 = 0) & closed_subset(all_0_3_3, all_0_8_8) = all_92_2_69
% 10.71/3.27 |
% 10.71/3.27 | Applying alpha-rule on (151) yields:
% 10.71/3.27 | (152) ~ (all_92_2_69 = 0)
% 10.71/3.27 | (153) closed_subset(all_0_3_3, all_0_8_8) = all_92_2_69
% 10.71/3.27 |
% 10.71/3.27 | Instantiating formula (21) with all_0_3_3, all_0_8_8, all_74_1_53, all_92_2_69 and discharging atoms closed_subset(all_0_3_3, all_0_8_8) = all_92_2_69, closed_subset(all_0_3_3, all_0_8_8) = all_74_1_53, yields:
% 10.71/3.27 | (154) all_92_2_69 = all_74_1_53
% 10.71/3.27 |
% 10.71/3.27 | Instantiating formula (21) with all_0_3_3, all_0_8_8, 0, all_92_2_69 and discharging atoms closed_subset(all_0_3_3, all_0_8_8) = all_92_2_69, closed_subset(all_0_3_3, all_0_8_8) = 0, yields:
% 10.71/3.27 | (138) all_92_2_69 = 0
% 10.71/3.27 |
% 10.71/3.27 | Combining equations (154,138) yields a new equation:
% 10.71/3.27 | (156) all_74_1_53 = 0
% 10.71/3.27 |
% 10.71/3.27 | Simplifying 156 yields:
% 10.71/3.27 | (121) all_74_1_53 = 0
% 10.71/3.27 |
% 10.71/3.27 | Equations (121) can reduce 118 to:
% 10.71/3.27 | (65) $false
% 10.71/3.27 |
% 10.71/3.27 |-The branch is then unsatisfiable
% 10.71/3.27 |-Branch two:
% 10.71/3.27 | (159) ~ (all_88_0_64 = 0) & open_subset(all_88_1_65, all_0_8_8) = all_88_0_64 & subset_complement(all_0_7_7, all_0_3_3) = all_88_1_65
% 10.71/3.27 |
% 10.71/3.27 | Applying alpha-rule on (159) yields:
% 10.71/3.27 | (160) ~ (all_88_0_64 = 0)
% 10.71/3.27 | (161) open_subset(all_88_1_65, all_0_8_8) = all_88_0_64
% 10.71/3.27 | (116) subset_complement(all_0_7_7, all_0_3_3) = all_88_1_65
% 10.71/3.27 |
% 10.71/3.27 | Equations (114) can reduce 160 to:
% 10.71/3.27 | (65) $false
% 10.71/3.27 |
% 10.71/3.27 |-The branch is then unsatisfiable
% 10.71/3.27 |-Branch two:
% 10.71/3.27 | (164) ~ (all_88_2_66 = 0) & closed_subset(all_0_3_3, all_0_8_8) = all_88_2_66
% 10.71/3.27 |
% 10.71/3.27 | Applying alpha-rule on (164) yields:
% 10.71/3.27 | (165) ~ (all_88_2_66 = 0)
% 10.71/3.27 | (166) closed_subset(all_0_3_3, all_0_8_8) = all_88_2_66
% 10.71/3.27 |
% 10.71/3.27 +-Applying beta-rule and splitting (90), into two cases.
% 10.71/3.27 |-Branch one:
% 10.71/3.27 | (117) ~ (all_74_1_53 = 0) & element(all_0_3_3, all_37_0_40) = all_74_1_53
% 10.71/3.27 |
% 10.71/3.27 | Applying alpha-rule on (117) yields:
% 10.71/3.27 | (118) ~ (all_74_1_53 = 0)
% 10.71/3.27 | (119) element(all_0_3_3, all_37_0_40) = all_74_1_53
% 10.71/3.27 |
% 10.71/3.27 | From (74) and (119) follows:
% 10.71/3.27 | (120) element(all_0_3_3, all_0_6_6) = all_74_1_53
% 10.71/3.27 |
% 10.71/3.27 | Instantiating formula (33) with all_0_3_3, all_0_6_6, all_74_1_53, 0 and discharging atoms element(all_0_3_3, all_0_6_6) = all_74_1_53, element(all_0_3_3, all_0_6_6) = 0, yields:
% 10.71/3.27 | (121) all_74_1_53 = 0
% 10.71/3.27 |
% 10.71/3.27 | Equations (121) can reduce 118 to:
% 10.71/3.27 | (65) $false
% 10.71/3.27 |
% 10.71/3.27 |-The branch is then unsatisfiable
% 10.71/3.27 |-Branch two:
% 10.71/3.27 | (123) ((all_74_0_52 = 0 & open_subset(all_0_5_5, all_0_8_8) = 0) | ( ~ (all_74_1_53 = 0) & closed_subset(all_0_3_3, all_0_8_8) = all_74_1_53)) & ((all_74_1_53 = 0 & closed_subset(all_0_3_3, all_0_8_8) = 0) | ( ~ (all_74_0_52 = 0) & open_subset(all_0_5_5, all_0_8_8) = all_74_0_52))
% 10.71/3.27 |
% 10.71/3.27 | Applying alpha-rule on (123) yields:
% 10.71/3.27 | (124) (all_74_0_52 = 0 & open_subset(all_0_5_5, all_0_8_8) = 0) | ( ~ (all_74_1_53 = 0) & closed_subset(all_0_3_3, all_0_8_8) = all_74_1_53)
% 10.71/3.27 | (125) (all_74_1_53 = 0 & closed_subset(all_0_3_3, all_0_8_8) = 0) | ( ~ (all_74_0_52 = 0) & open_subset(all_0_5_5, all_0_8_8) = all_74_0_52)
% 10.71/3.27 |
% 10.71/3.27 +-Applying beta-rule and splitting (124), into two cases.
% 10.71/3.27 |-Branch one:
% 10.71/3.27 | (126) all_74_0_52 = 0 & open_subset(all_0_5_5, all_0_8_8) = 0
% 10.71/3.28 |
% 10.71/3.28 | Applying alpha-rule on (126) yields:
% 10.71/3.28 | (127) all_74_0_52 = 0
% 10.71/3.28 | (128) open_subset(all_0_5_5, all_0_8_8) = 0
% 10.71/3.28 |
% 10.71/3.28 | Instantiating formula (9) with all_0_5_5, all_0_8_8, 0, all_0_4_4 and discharging atoms open_subset(all_0_5_5, all_0_8_8) = all_0_4_4, open_subset(all_0_5_5, all_0_8_8) = 0, yields:
% 10.71/3.28 | (129) all_0_4_4 = 0
% 10.71/3.28 |
% 10.71/3.28 | Equations (129) can reduce 111 to:
% 10.71/3.28 | (65) $false
% 10.71/3.28 |
% 10.71/3.28 |-The branch is then unsatisfiable
% 10.71/3.28 |-Branch two:
% 10.71/3.28 | (131) ~ (all_74_1_53 = 0) & closed_subset(all_0_3_3, all_0_8_8) = all_74_1_53
% 10.71/3.28 |
% 10.71/3.28 | Applying alpha-rule on (131) yields:
% 10.71/3.28 | (118) ~ (all_74_1_53 = 0)
% 10.71/3.28 | (133) closed_subset(all_0_3_3, all_0_8_8) = all_74_1_53
% 10.71/3.28 |
% 10.71/3.28 +-Applying beta-rule and splitting (106), into two cases.
% 10.71/3.28 |-Branch one:
% 10.71/3.28 | (146) all_92_0_67 = 0 & open_subset(all_92_1_68, all_0_8_8) = 0 & subset_complement(all_33_1_37, all_0_3_3) = all_92_1_68
% 10.71/3.28 |
% 10.71/3.28 | Applying alpha-rule on (146) yields:
% 10.71/3.28 | (147) all_92_0_67 = 0
% 10.71/3.28 | (148) open_subset(all_92_1_68, all_0_8_8) = 0
% 10.71/3.28 | (145) subset_complement(all_33_1_37, all_0_3_3) = all_92_1_68
% 10.71/3.28 |
% 10.71/3.28 +-Applying beta-rule and splitting (107), into two cases.
% 10.71/3.28 |-Branch one:
% 10.71/3.28 | (137) all_92_2_69 = 0 & closed_subset(all_0_3_3, all_0_8_8) = 0
% 10.71/3.28 |
% 10.71/3.28 | Applying alpha-rule on (137) yields:
% 10.71/3.28 | (138) all_92_2_69 = 0
% 10.71/3.28 | (112) closed_subset(all_0_3_3, all_0_8_8) = 0
% 10.71/3.28 |
% 10.71/3.28 | Instantiating formula (21) with all_0_3_3, all_0_8_8, all_74_1_53, all_88_2_66 and discharging atoms closed_subset(all_0_3_3, all_0_8_8) = all_88_2_66, closed_subset(all_0_3_3, all_0_8_8) = all_74_1_53, yields:
% 10.71/3.28 | (191) all_88_2_66 = all_74_1_53
% 10.71/3.28 |
% 10.71/3.28 | Instantiating formula (21) with all_0_3_3, all_0_8_8, 0, all_88_2_66 and discharging atoms closed_subset(all_0_3_3, all_0_8_8) = all_88_2_66, closed_subset(all_0_3_3, all_0_8_8) = 0, yields:
% 10.71/3.28 | (135) all_88_2_66 = 0
% 10.71/3.28 |
% 10.71/3.28 | Combining equations (191,135) yields a new equation:
% 10.71/3.28 | (156) all_74_1_53 = 0
% 10.71/3.28 |
% 10.71/3.28 | Simplifying 156 yields:
% 10.71/3.28 | (121) all_74_1_53 = 0
% 10.71/3.28 |
% 10.71/3.28 | Equations (121) can reduce 118 to:
% 10.71/3.28 | (65) $false
% 10.71/3.28 |
% 10.71/3.28 |-The branch is then unsatisfiable
% 10.71/3.28 |-Branch two:
% 10.71/3.28 | (142) ~ (all_92_0_67 = 0) & open_subset(all_92_1_68, all_0_8_8) = all_92_0_67 & subset_complement(all_33_1_37, all_0_3_3) = all_92_1_68
% 10.71/3.28 |
% 10.71/3.28 | Applying alpha-rule on (142) yields:
% 10.71/3.28 | (143) ~ (all_92_0_67 = 0)
% 10.71/3.28 | (144) open_subset(all_92_1_68, all_0_8_8) = all_92_0_67
% 10.71/3.28 | (145) subset_complement(all_33_1_37, all_0_3_3) = all_92_1_68
% 10.71/3.28 |
% 10.71/3.28 | Equations (147) can reduce 143 to:
% 10.71/3.28 | (65) $false
% 10.71/3.28 |
% 10.71/3.28 |-The branch is then unsatisfiable
% 10.71/3.28 |-Branch two:
% 10.71/3.28 | (151) ~ (all_92_2_69 = 0) & closed_subset(all_0_3_3, all_0_8_8) = all_92_2_69
% 10.71/3.28 |
% 10.71/3.28 | Applying alpha-rule on (151) yields:
% 10.71/3.28 | (152) ~ (all_92_2_69 = 0)
% 10.71/3.28 | (153) closed_subset(all_0_3_3, all_0_8_8) = all_92_2_69
% 10.71/3.28 |
% 10.71/3.28 | Instantiating formula (21) with all_0_3_3, all_0_8_8, all_88_2_66, all_92_2_69 and discharging atoms closed_subset(all_0_3_3, all_0_8_8) = all_92_2_69, closed_subset(all_0_3_3, all_0_8_8) = all_88_2_66, yields:
% 10.71/3.28 | (204) all_92_2_69 = all_88_2_66
% 10.71/3.28 |
% 10.71/3.28 | Instantiating formula (21) with all_0_3_3, all_0_8_8, all_74_1_53, all_92_2_69 and discharging atoms closed_subset(all_0_3_3, all_0_8_8) = all_92_2_69, closed_subset(all_0_3_3, all_0_8_8) = all_74_1_53, yields:
% 10.71/3.28 | (154) all_92_2_69 = all_74_1_53
% 10.71/3.28 |
% 10.71/3.28 | Instantiating formula (21) with all_0_3_3, all_0_8_8, 0, all_92_2_69 and discharging atoms closed_subset(all_0_3_3, all_0_8_8) = all_92_2_69, closed_subset(all_0_3_3, all_0_8_8) = 0, yields:
% 10.71/3.28 | (138) all_92_2_69 = 0
% 10.71/3.28 |
% 10.71/3.28 | Combining equations (154,204) yields a new equation:
% 10.71/3.28 | (191) all_88_2_66 = all_74_1_53
% 10.71/3.28 |
% 10.71/3.28 | Combining equations (138,204) yields a new equation:
% 10.71/3.28 | (135) all_88_2_66 = 0
% 10.71/3.28 |
% 10.71/3.28 | Combining equations (135,191) yields a new equation:
% 10.71/3.28 | (121) all_74_1_53 = 0
% 10.71/3.28 |
% 10.71/3.28 | Equations (121) can reduce 118 to:
% 10.71/3.28 | (65) $false
% 10.71/3.28 |
% 10.71/3.28 |-The branch is then unsatisfiable
% 10.71/3.28 |-Branch two:
% 10.71/3.28 | (211) all_0_4_4 = 0 & ~ (all_0_2_2 = 0)
% 10.71/3.28 |
% 10.71/3.28 | Applying alpha-rule on (211) yields:
% 10.71/3.28 | (129) all_0_4_4 = 0
% 10.71/3.28 | (213) ~ (all_0_2_2 = 0)
% 10.71/3.28 |
% 10.71/3.28 | From (129) and (23) follows:
% 10.71/3.28 | (128) open_subset(all_0_5_5, all_0_8_8) = 0
% 10.71/3.28 |
% 10.71/3.28 +-Applying beta-rule and splitting (60), into two cases.
% 10.71/3.28 |-Branch one:
% 10.71/3.28 | (215) ~ (all_43_1_46 = 0) & element(all_0_3_3, all_33_0_36) = all_43_1_46
% 10.71/3.28 |
% 10.71/3.28 | Applying alpha-rule on (215) yields:
% 10.71/3.28 | (216) ~ (all_43_1_46 = 0)
% 10.71/3.28 | (217) element(all_0_3_3, all_33_0_36) = all_43_1_46
% 10.71/3.28 |
% 10.71/3.28 | From (82) and (217) follows:
% 10.71/3.28 | (218) element(all_0_3_3, all_0_6_6) = all_43_1_46
% 10.71/3.28 |
% 10.71/3.28 | Instantiating formula (33) with all_0_3_3, all_0_6_6, all_43_1_46, 0 and discharging atoms element(all_0_3_3, all_0_6_6) = all_43_1_46, element(all_0_3_3, all_0_6_6) = 0, yields:
% 10.71/3.28 | (219) all_43_1_46 = 0
% 10.71/3.28 |
% 10.71/3.28 | Equations (219) can reduce 216 to:
% 10.71/3.28 | (65) $false
% 10.71/3.28 |
% 10.71/3.28 |-The branch is then unsatisfiable
% 10.71/3.28 |-Branch two:
% 10.71/3.28 | (221) ( ~ (all_0_2_2 = 0) | (all_43_0_45 = 0 & open_subset(all_43_1_46, all_0_8_8) = 0 & subset_complement(all_33_1_37, all_0_3_3) = all_43_1_46)) & (all_0_2_2 = 0 | ( ~ (all_43_0_45 = 0) & open_subset(all_43_1_46, all_0_8_8) = all_43_0_45 & subset_complement(all_33_1_37, all_0_3_3) = all_43_1_46))
% 10.71/3.28 |
% 10.71/3.28 | Applying alpha-rule on (221) yields:
% 10.71/3.28 | (222) ~ (all_0_2_2 = 0) | (all_43_0_45 = 0 & open_subset(all_43_1_46, all_0_8_8) = 0 & subset_complement(all_33_1_37, all_0_3_3) = all_43_1_46)
% 10.71/3.28 | (223) all_0_2_2 = 0 | ( ~ (all_43_0_45 = 0) & open_subset(all_43_1_46, all_0_8_8) = all_43_0_45 & subset_complement(all_33_1_37, all_0_3_3) = all_43_1_46)
% 10.71/3.28 |
% 10.71/3.28 +-Applying beta-rule and splitting (90), into two cases.
% 10.71/3.28 |-Branch one:
% 10.71/3.28 | (117) ~ (all_74_1_53 = 0) & element(all_0_3_3, all_37_0_40) = all_74_1_53
% 10.71/3.28 |
% 10.71/3.28 | Applying alpha-rule on (117) yields:
% 10.71/3.28 | (118) ~ (all_74_1_53 = 0)
% 10.71/3.28 | (119) element(all_0_3_3, all_37_0_40) = all_74_1_53
% 10.71/3.28 |
% 10.71/3.28 | From (74) and (119) follows:
% 10.71/3.28 | (120) element(all_0_3_3, all_0_6_6) = all_74_1_53
% 10.71/3.28 |
% 10.71/3.28 | Instantiating formula (33) with all_0_3_3, all_0_6_6, all_74_1_53, 0 and discharging atoms element(all_0_3_3, all_0_6_6) = all_74_1_53, element(all_0_3_3, all_0_6_6) = 0, yields:
% 10.71/3.28 | (121) all_74_1_53 = 0
% 10.71/3.28 |
% 10.71/3.28 | Equations (121) can reduce 118 to:
% 10.71/3.28 | (65) $false
% 10.71/3.28 |
% 10.71/3.28 |-The branch is then unsatisfiable
% 10.71/3.28 |-Branch two:
% 10.71/3.28 | (123) ((all_74_0_52 = 0 & open_subset(all_0_5_5, all_0_8_8) = 0) | ( ~ (all_74_1_53 = 0) & closed_subset(all_0_3_3, all_0_8_8) = all_74_1_53)) & ((all_74_1_53 = 0 & closed_subset(all_0_3_3, all_0_8_8) = 0) | ( ~ (all_74_0_52 = 0) & open_subset(all_0_5_5, all_0_8_8) = all_74_0_52))
% 10.71/3.28 |
% 10.71/3.28 | Applying alpha-rule on (123) yields:
% 10.71/3.28 | (124) (all_74_0_52 = 0 & open_subset(all_0_5_5, all_0_8_8) = 0) | ( ~ (all_74_1_53 = 0) & closed_subset(all_0_3_3, all_0_8_8) = all_74_1_53)
% 10.71/3.28 | (125) (all_74_1_53 = 0 & closed_subset(all_0_3_3, all_0_8_8) = 0) | ( ~ (all_74_0_52 = 0) & open_subset(all_0_5_5, all_0_8_8) = all_74_0_52)
% 10.71/3.28 |
% 10.71/3.28 +-Applying beta-rule and splitting (125), into two cases.
% 10.71/3.28 |-Branch one:
% 10.71/3.28 | (233) all_74_1_53 = 0 & closed_subset(all_0_3_3, all_0_8_8) = 0
% 10.71/3.28 |
% 10.71/3.28 | Applying alpha-rule on (233) yields:
% 10.71/3.28 | (121) all_74_1_53 = 0
% 10.71/3.28 | (112) closed_subset(all_0_3_3, all_0_8_8) = 0
% 10.71/3.28 |
% 10.71/3.28 +-Applying beta-rule and splitting (98), into two cases.
% 10.71/3.28 |-Branch one:
% 10.71/3.28 | (134) all_88_2_66 = 0 & closed_subset(all_0_3_3, all_0_8_8) = 0
% 10.71/3.28 |
% 10.71/3.28 | Applying alpha-rule on (134) yields:
% 10.71/3.28 | (135) all_88_2_66 = 0
% 10.71/3.28 | (112) closed_subset(all_0_3_3, all_0_8_8) = 0
% 10.71/3.28 |
% 10.71/3.28 +-Applying beta-rule and splitting (107), into two cases.
% 10.71/3.28 |-Branch one:
% 10.71/3.28 | (137) all_92_2_69 = 0 & closed_subset(all_0_3_3, all_0_8_8) = 0
% 10.71/3.28 |
% 10.71/3.28 | Applying alpha-rule on (137) yields:
% 10.71/3.28 | (138) all_92_2_69 = 0
% 10.71/3.28 | (112) closed_subset(all_0_3_3, all_0_8_8) = 0
% 10.71/3.28 |
% 10.71/3.28 +-Applying beta-rule and splitting (223), into two cases.
% 10.71/3.28 |-Branch one:
% 10.71/3.28 | (110) all_0_2_2 = 0
% 10.71/3.28 |
% 10.71/3.28 | Equations (110) can reduce 213 to:
% 10.71/3.28 | (65) $false
% 10.71/3.28 |
% 10.71/3.28 |-The branch is then unsatisfiable
% 10.71/3.28 |-Branch two:
% 10.71/3.28 | (213) ~ (all_0_2_2 = 0)
% 10.71/3.28 | (245) ~ (all_43_0_45 = 0) & open_subset(all_43_1_46, all_0_8_8) = all_43_0_45 & subset_complement(all_33_1_37, all_0_3_3) = all_43_1_46
% 10.71/3.28 |
% 10.71/3.28 | Instantiating formula (21) with all_0_3_3, all_0_8_8, 0, all_0_2_2 and discharging atoms closed_subset(all_0_3_3, all_0_8_8) = all_0_2_2, closed_subset(all_0_3_3, all_0_8_8) = 0, yields:
% 10.71/3.28 | (110) all_0_2_2 = 0
% 10.71/3.28 |
% 10.71/3.28 | Equations (110) can reduce 213 to:
% 10.71/3.28 | (65) $false
% 10.71/3.28 |
% 10.71/3.28 |-The branch is then unsatisfiable
% 10.71/3.28 |-Branch two:
% 10.71/3.28 | (142) ~ (all_92_0_67 = 0) & open_subset(all_92_1_68, all_0_8_8) = all_92_0_67 & subset_complement(all_33_1_37, all_0_3_3) = all_92_1_68
% 10.71/3.28 |
% 10.71/3.28 | Applying alpha-rule on (142) yields:
% 10.71/3.28 | (143) ~ (all_92_0_67 = 0)
% 10.71/3.28 | (144) open_subset(all_92_1_68, all_0_8_8) = all_92_0_67
% 10.71/3.28 | (145) subset_complement(all_33_1_37, all_0_3_3) = all_92_1_68
% 10.71/3.28 |
% 10.71/3.28 +-Applying beta-rule and splitting (106), into two cases.
% 10.71/3.28 |-Branch one:
% 10.71/3.28 | (146) all_92_0_67 = 0 & open_subset(all_92_1_68, all_0_8_8) = 0 & subset_complement(all_33_1_37, all_0_3_3) = all_92_1_68
% 10.71/3.28 |
% 10.71/3.28 | Applying alpha-rule on (146) yields:
% 10.71/3.28 | (147) all_92_0_67 = 0
% 10.71/3.28 | (148) open_subset(all_92_1_68, all_0_8_8) = 0
% 10.71/3.28 | (145) subset_complement(all_33_1_37, all_0_3_3) = all_92_1_68
% 10.71/3.28 |
% 10.71/3.28 | Equations (147) can reduce 143 to:
% 10.71/3.28 | (65) $false
% 10.71/3.28 |
% 10.71/3.28 |-The branch is then unsatisfiable
% 10.71/3.28 |-Branch two:
% 10.71/3.28 | (151) ~ (all_92_2_69 = 0) & closed_subset(all_0_3_3, all_0_8_8) = all_92_2_69
% 10.71/3.28 |
% 10.71/3.28 | Applying alpha-rule on (151) yields:
% 10.71/3.28 | (152) ~ (all_92_2_69 = 0)
% 10.71/3.28 | (153) closed_subset(all_0_3_3, all_0_8_8) = all_92_2_69
% 10.71/3.28 |
% 10.71/3.28 +-Applying beta-rule and splitting (223), into two cases.
% 10.71/3.28 |-Branch one:
% 10.71/3.28 | (110) all_0_2_2 = 0
% 10.71/3.28 |
% 10.71/3.28 | Equations (110) can reduce 213 to:
% 10.71/3.28 | (65) $false
% 10.71/3.28 |
% 10.71/3.28 |-The branch is then unsatisfiable
% 10.71/3.28 |-Branch two:
% 10.71/3.28 | (213) ~ (all_0_2_2 = 0)
% 10.71/3.29 | (245) ~ (all_43_0_45 = 0) & open_subset(all_43_1_46, all_0_8_8) = all_43_0_45 & subset_complement(all_33_1_37, all_0_3_3) = all_43_1_46
% 10.71/3.29 |
% 10.71/3.29 | Instantiating formula (21) with all_0_3_3, all_0_8_8, all_92_2_69, all_0_2_2 and discharging atoms closed_subset(all_0_3_3, all_0_8_8) = all_92_2_69, closed_subset(all_0_3_3, all_0_8_8) = all_0_2_2, yields:
% 10.71/3.29 | (264) all_92_2_69 = all_0_2_2
% 10.71/3.29 |
% 10.71/3.29 | Instantiating formula (21) with all_0_3_3, all_0_8_8, 0, all_92_2_69 and discharging atoms closed_subset(all_0_3_3, all_0_8_8) = all_92_2_69, closed_subset(all_0_3_3, all_0_8_8) = 0, yields:
% 10.71/3.29 | (138) all_92_2_69 = 0
% 10.71/3.29 |
% 10.71/3.29 | Combining equations (138,264) yields a new equation:
% 10.71/3.29 | (110) all_0_2_2 = 0
% 10.71/3.29 |
% 10.71/3.29 | Equations (110) can reduce 213 to:
% 10.71/3.29 | (65) $false
% 10.71/3.29 |
% 10.71/3.29 |-The branch is then unsatisfiable
% 10.71/3.29 |-Branch two:
% 10.71/3.29 | (159) ~ (all_88_0_64 = 0) & open_subset(all_88_1_65, all_0_8_8) = all_88_0_64 & subset_complement(all_0_7_7, all_0_3_3) = all_88_1_65
% 10.71/3.29 |
% 10.71/3.29 | Applying alpha-rule on (159) yields:
% 10.71/3.29 | (160) ~ (all_88_0_64 = 0)
% 10.71/3.29 | (161) open_subset(all_88_1_65, all_0_8_8) = all_88_0_64
% 10.71/3.29 | (116) subset_complement(all_0_7_7, all_0_3_3) = all_88_1_65
% 10.71/3.29 |
% 10.71/3.29 +-Applying beta-rule and splitting (97), into two cases.
% 10.71/3.29 |-Branch one:
% 10.71/3.29 | (113) all_88_0_64 = 0 & open_subset(all_88_1_65, all_0_8_8) = 0 & subset_complement(all_0_7_7, all_0_3_3) = all_88_1_65
% 10.71/3.29 |
% 10.71/3.29 | Applying alpha-rule on (113) yields:
% 10.71/3.29 | (114) all_88_0_64 = 0
% 10.71/3.29 | (115) open_subset(all_88_1_65, all_0_8_8) = 0
% 10.71/3.29 | (116) subset_complement(all_0_7_7, all_0_3_3) = all_88_1_65
% 10.71/3.29 |
% 10.71/3.29 | Equations (114) can reduce 160 to:
% 10.71/3.29 | (65) $false
% 10.71/3.29 |
% 10.71/3.29 |-The branch is then unsatisfiable
% 10.71/3.29 |-Branch two:
% 10.71/3.29 | (164) ~ (all_88_2_66 = 0) & closed_subset(all_0_3_3, all_0_8_8) = all_88_2_66
% 10.71/3.29 |
% 10.71/3.29 | Applying alpha-rule on (164) yields:
% 10.71/3.29 | (165) ~ (all_88_2_66 = 0)
% 10.71/3.29 | (166) closed_subset(all_0_3_3, all_0_8_8) = all_88_2_66
% 10.71/3.29 |
% 10.71/3.29 +-Applying beta-rule and splitting (106), into two cases.
% 10.71/3.29 |-Branch one:
% 10.71/3.29 | (146) all_92_0_67 = 0 & open_subset(all_92_1_68, all_0_8_8) = 0 & subset_complement(all_33_1_37, all_0_3_3) = all_92_1_68
% 10.71/3.29 |
% 10.71/3.29 | Applying alpha-rule on (146) yields:
% 10.71/3.29 | (147) all_92_0_67 = 0
% 10.71/3.29 | (148) open_subset(all_92_1_68, all_0_8_8) = 0
% 10.71/3.29 | (145) subset_complement(all_33_1_37, all_0_3_3) = all_92_1_68
% 10.71/3.29 |
% 10.71/3.29 +-Applying beta-rule and splitting (223), into two cases.
% 10.71/3.29 |-Branch one:
% 10.71/3.29 | (110) all_0_2_2 = 0
% 10.71/3.29 |
% 10.71/3.29 | Equations (110) can reduce 213 to:
% 10.71/3.29 | (65) $false
% 10.71/3.29 |
% 10.71/3.29 |-The branch is then unsatisfiable
% 10.71/3.29 |-Branch two:
% 10.71/3.29 | (213) ~ (all_0_2_2 = 0)
% 10.71/3.29 | (245) ~ (all_43_0_45 = 0) & open_subset(all_43_1_46, all_0_8_8) = all_43_0_45 & subset_complement(all_33_1_37, all_0_3_3) = all_43_1_46
% 10.71/3.29 |
% 10.71/3.29 +-Applying beta-rule and splitting (107), into two cases.
% 10.71/3.29 |-Branch one:
% 10.71/3.29 | (137) all_92_2_69 = 0 & closed_subset(all_0_3_3, all_0_8_8) = 0
% 10.71/3.29 |
% 10.71/3.29 | Applying alpha-rule on (137) yields:
% 10.71/3.29 | (138) all_92_2_69 = 0
% 10.71/3.29 | (112) closed_subset(all_0_3_3, all_0_8_8) = 0
% 10.71/3.29 |
% 10.71/3.29 | Instantiating formula (21) with all_0_3_3, all_0_8_8, all_88_2_66, all_0_2_2 and discharging atoms closed_subset(all_0_3_3, all_0_8_8) = all_88_2_66, closed_subset(all_0_3_3, all_0_8_8) = all_0_2_2, yields:
% 10.71/3.29 | (291) all_88_2_66 = all_0_2_2
% 10.71/3.29 |
% 10.71/3.29 | Instantiating formula (21) with all_0_3_3, all_0_8_8, 0, all_88_2_66 and discharging atoms closed_subset(all_0_3_3, all_0_8_8) = all_88_2_66, closed_subset(all_0_3_3, all_0_8_8) = 0, yields:
% 10.71/3.29 | (135) all_88_2_66 = 0
% 10.71/3.29 |
% 10.71/3.29 | Combining equations (135,291) yields a new equation:
% 10.71/3.29 | (110) all_0_2_2 = 0
% 10.71/3.29 |
% 10.71/3.29 | Equations (110) can reduce 213 to:
% 10.71/3.29 | (65) $false
% 10.71/3.29 |
% 10.71/3.29 |-The branch is then unsatisfiable
% 10.71/3.29 |-Branch two:
% 10.71/3.29 | (142) ~ (all_92_0_67 = 0) & open_subset(all_92_1_68, all_0_8_8) = all_92_0_67 & subset_complement(all_33_1_37, all_0_3_3) = all_92_1_68
% 10.71/3.29 |
% 10.71/3.29 | Applying alpha-rule on (142) yields:
% 10.71/3.29 | (143) ~ (all_92_0_67 = 0)
% 10.71/3.29 | (144) open_subset(all_92_1_68, all_0_8_8) = all_92_0_67
% 10.71/3.29 | (145) subset_complement(all_33_1_37, all_0_3_3) = all_92_1_68
% 10.71/3.29 |
% 10.71/3.29 | Equations (147) can reduce 143 to:
% 10.71/3.29 | (65) $false
% 10.71/3.29 |
% 10.71/3.29 |-The branch is then unsatisfiable
% 10.71/3.29 |-Branch two:
% 10.71/3.29 | (151) ~ (all_92_2_69 = 0) & closed_subset(all_0_3_3, all_0_8_8) = all_92_2_69
% 10.71/3.29 |
% 10.71/3.29 | Applying alpha-rule on (151) yields:
% 10.71/3.29 | (152) ~ (all_92_2_69 = 0)
% 10.71/3.29 | (153) closed_subset(all_0_3_3, all_0_8_8) = all_92_2_69
% 10.71/3.29 |
% 10.71/3.29 +-Applying beta-rule and splitting (223), into two cases.
% 10.71/3.29 |-Branch one:
% 10.71/3.29 | (110) all_0_2_2 = 0
% 10.71/3.29 |
% 10.71/3.29 | Equations (110) can reduce 213 to:
% 10.71/3.29 | (65) $false
% 10.71/3.29 |
% 10.71/3.29 |-The branch is then unsatisfiable
% 10.71/3.29 |-Branch two:
% 10.71/3.29 | (213) ~ (all_0_2_2 = 0)
% 10.71/3.29 | (245) ~ (all_43_0_45 = 0) & open_subset(all_43_1_46, all_0_8_8) = all_43_0_45 & subset_complement(all_33_1_37, all_0_3_3) = all_43_1_46
% 10.71/3.29 |
% 10.71/3.29 | Instantiating formula (21) with all_0_3_3, all_0_8_8, all_88_2_66, all_0_2_2 and discharging atoms closed_subset(all_0_3_3, all_0_8_8) = all_88_2_66, closed_subset(all_0_3_3, all_0_8_8) = all_0_2_2, yields:
% 10.71/3.29 | (291) all_88_2_66 = all_0_2_2
% 10.71/3.29 |
% 10.71/3.29 | Instantiating formula (21) with all_0_3_3, all_0_8_8, all_88_2_66, all_92_2_69 and discharging atoms closed_subset(all_0_3_3, all_0_8_8) = all_92_2_69, closed_subset(all_0_3_3, all_0_8_8) = all_88_2_66, yields:
% 10.71/3.29 | (204) all_92_2_69 = all_88_2_66
% 10.71/3.29 |
% 10.71/3.29 | Instantiating formula (21) with all_0_3_3, all_0_8_8, 0, all_92_2_69 and discharging atoms closed_subset(all_0_3_3, all_0_8_8) = all_92_2_69, closed_subset(all_0_3_3, all_0_8_8) = 0, yields:
% 10.71/3.29 | (138) all_92_2_69 = 0
% 10.71/3.29 |
% 10.71/3.29 | Combining equations (204,138) yields a new equation:
% 10.71/3.29 | (310) all_88_2_66 = 0
% 10.71/3.29 |
% 10.71/3.29 | Simplifying 310 yields:
% 10.71/3.29 | (135) all_88_2_66 = 0
% 10.71/3.29 |
% 10.71/3.29 | Combining equations (291,135) yields a new equation:
% 10.71/3.29 | (312) all_0_2_2 = 0
% 10.71/3.29 |
% 10.71/3.29 | Simplifying 312 yields:
% 10.71/3.29 | (110) all_0_2_2 = 0
% 10.71/3.29 |
% 10.71/3.29 | Equations (110) can reduce 213 to:
% 10.71/3.29 | (65) $false
% 10.71/3.29 |
% 10.71/3.29 |-The branch is then unsatisfiable
% 10.71/3.29 |-Branch two:
% 10.71/3.29 | (315) ~ (all_74_0_52 = 0) & open_subset(all_0_5_5, all_0_8_8) = all_74_0_52
% 10.71/3.29 |
% 10.71/3.29 | Applying alpha-rule on (315) yields:
% 10.71/3.29 | (316) ~ (all_74_0_52 = 0)
% 10.71/3.29 | (317) open_subset(all_0_5_5, all_0_8_8) = all_74_0_52
% 10.71/3.29 |
% 10.71/3.29 | Instantiating formula (9) with all_0_5_5, all_0_8_8, 0, all_74_0_52 and discharging atoms open_subset(all_0_5_5, all_0_8_8) = all_74_0_52, open_subset(all_0_5_5, all_0_8_8) = 0, yields:
% 10.71/3.29 | (127) all_74_0_52 = 0
% 10.71/3.29 |
% 10.71/3.29 | Equations (127) can reduce 316 to:
% 10.71/3.29 | (65) $false
% 10.71/3.29 |
% 10.71/3.29 |-The branch is then unsatisfiable
% 10.71/3.29 |-Branch two:
% 10.71/3.29 | (320) ~ (all_36_0_38 = 0) & powerset(all_0_7_7) = all_36_1_39 & element(all_0_5_5, all_36_1_39) = all_36_0_38
% 10.71/3.29 |
% 10.71/3.29 | Applying alpha-rule on (320) yields:
% 10.71/3.29 | (321) ~ (all_36_0_38 = 0)
% 10.71/3.29 | (322) powerset(all_0_7_7) = all_36_1_39
% 10.71/3.29 | (323) element(all_0_5_5, all_36_1_39) = all_36_0_38
% 10.71/3.29 |
% 10.71/3.29 | Instantiating formula (19) with all_0_7_7, all_36_1_39, all_0_6_6 and discharging atoms powerset(all_0_7_7) = all_36_1_39, powerset(all_0_7_7) = all_0_6_6, yields:
% 10.71/3.29 | (324) all_36_1_39 = all_0_6_6
% 10.71/3.29 |
% 10.71/3.29 | From (324) and (323) follows:
% 10.71/3.29 | (325) element(all_0_5_5, all_0_6_6) = all_36_0_38
% 10.71/3.29 |
% 10.71/3.29 | Instantiating formula (33) with all_0_5_5, all_0_6_6, all_36_0_38, 0 and discharging atoms element(all_0_5_5, all_0_6_6) = all_36_0_38, element(all_0_5_5, all_0_6_6) = 0, yields:
% 10.71/3.29 | (326) all_36_0_38 = 0
% 10.71/3.29 |
% 10.71/3.29 | Equations (326) can reduce 321 to:
% 10.71/3.29 | (65) $false
% 10.71/3.29 |
% 10.71/3.29 |-The branch is then unsatisfiable
% 10.71/3.29 |-Branch two:
% 10.71/3.29 | (328) ~ (all_38_0_41 = 0) & element(all_0_5_5, all_38_1_42) = all_38_0_41
% 10.71/3.29 |
% 10.71/3.29 | Applying alpha-rule on (328) yields:
% 10.71/3.29 | (329) ~ (all_38_0_41 = 0)
% 10.71/3.29 | (330) element(all_0_5_5, all_38_1_42) = all_38_0_41
% 10.71/3.29 |
% 10.71/3.29 | From (72) and (330) follows:
% 10.71/3.29 | (331) element(all_0_5_5, all_0_6_6) = all_38_0_41
% 10.71/3.29 |
% 10.71/3.29 | Instantiating formula (33) with all_0_5_5, all_0_6_6, all_38_0_41, 0 and discharging atoms element(all_0_5_5, all_0_6_6) = all_38_0_41, element(all_0_5_5, all_0_6_6) = 0, yields:
% 10.71/3.29 | (79) all_38_0_41 = 0
% 10.71/3.29 |
% 10.71/3.29 | Equations (79) can reduce 329 to:
% 10.71/3.29 | (65) $false
% 10.71/3.29 |
% 10.71/3.29 |-The branch is then unsatisfiable
% 10.71/3.29 % SZS output end Proof for theBenchmark
% 10.71/3.29
% 10.71/3.29 2664ms
%------------------------------------------------------------------------------