TSTP Solution File: SEU262+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU262+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n015.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 08:48:16 EDT 2022
% Result : Theorem 7.22s 2.39s
% Output : Proof 11.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : SEU262+1 : TPTP v8.1.0. Released v3.3.0.
% 0.04/0.14 % Command : ePrincess-casc -timeout=%d %s
% 0.14/0.36 % Computer : n015.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Mon Jun 20 13:07:16 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.63/0.64 ____ _
% 0.63/0.64 ___ / __ \_____(_)___ ________ __________
% 0.63/0.64 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.63/0.64 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.63/0.64 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.63/0.64
% 0.63/0.64 A Theorem Prover for First-Order Logic
% 0.63/0.64 (ePrincess v.1.0)
% 0.63/0.64
% 0.63/0.64 (c) Philipp Rümmer, 2009-2015
% 0.63/0.64 (c) Peter Backeman, 2014-2015
% 0.63/0.64 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.63/0.64 Free software under GNU Lesser General Public License (LGPL).
% 0.63/0.64 Bug reports to peter@backeman.se
% 0.63/0.64
% 0.63/0.64 For more information, visit http://user.uu.se/~petba168/breu/
% 0.63/0.64
% 0.63/0.64 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.79/0.69 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.56/0.98 Prover 0: Preprocessing ...
% 2.15/1.21 Prover 0: Warning: ignoring some quantifiers
% 2.33/1.24 Prover 0: Constructing countermodel ...
% 3.10/1.46 Prover 0: gave up
% 3.10/1.46 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 3.21/1.49 Prover 1: Preprocessing ...
% 3.69/1.61 Prover 1: Warning: ignoring some quantifiers
% 3.69/1.62 Prover 1: Constructing countermodel ...
% 5.61/2.02 Prover 1: gave up
% 5.61/2.02 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 5.61/2.04 Prover 2: Preprocessing ...
% 6.20/2.14 Prover 2: Warning: ignoring some quantifiers
% 6.20/2.14 Prover 2: Constructing countermodel ...
% 7.22/2.39 Prover 2: proved (369ms)
% 7.22/2.39
% 7.22/2.39 No countermodel exists, formula is valid
% 7.22/2.39 % SZS status Theorem for theBenchmark
% 7.22/2.39
% 7.22/2.39 Generating proof ... Warning: ignoring some quantifiers
% 10.46/3.15 found it (size 68)
% 10.46/3.15
% 10.46/3.15 % SZS output start Proof for theBenchmark
% 10.46/3.15 Assumed formulas after preprocessing and simplification:
% 10.46/3.15 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ( ~ (v8 = 0) & empty(v9) = 0 & empty(v7) = v8 & empty(empty_set) = 0 & relation_of2_as_subset(v2, v0, v1) = 0 & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (ordered_pair(v10, v11) = v14) | ~ (cartesian_product2(v12, v13) = v15) | ~ (in(v14, v15) = v16) | ? [v17] : (( ~ (v17 = 0) & in(v11, v13) = v17) | ( ~ (v17 = 0) & in(v10, v12) = v17))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (cartesian_product2(v10, v11) = v13) | ~ (powerset(v13) = v14) | ~ (element(v12, v14) = v15) | ? [v16] : ( ~ (v16 = 0) & relation_of2_as_subset(v12, v10, v11) = v16)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = 0 | ~ (relation_rng(v10) = v11) | ~ (ordered_pair(v14, v12) = v15) | ~ (in(v12, v11) = v13) | ? [v16] : (( ~ (v16 = 0) & relation(v10) = v16) | ( ~ (v16 = 0) & in(v15, v10) = v16))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = 0 | ~ (relation_dom(v10) = v11) | ~ (ordered_pair(v12, v14) = v15) | ~ (in(v12, v11) = v13) | ? [v16] : (( ~ (v16 = 0) & relation(v10) = v16) | ( ~ (v16 = 0) & in(v15, v10) = v16))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (ordered_pair(v10, v11) = v14) | ~ (cartesian_product2(v12, v13) = v15) | ~ (in(v14, v15) = 0) | (in(v11, v13) = 0 & in(v10, v12) = 0)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (powerset(v12) = v13) | ~ (element(v11, v13) = 0) | ~ (element(v10, v12) = v14) | ? [v15] : ( ~ (v15 = 0) & in(v10, v11) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v11 = v10 | ~ (relation_of2(v14, v13, v12) = v11) | ~ (relation_of2(v14, v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v11 = v10 | ~ (relation_of2_as_subset(v14, v13, v12) = v11) | ~ (relation_of2_as_subset(v14, v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (cartesian_product2(v10, v11) = v13) | ~ (powerset(v13) = v14) | ~ (element(v12, v14) = 0) | relation(v12) = 0) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (relation_of2(v12, v10, v11) = v13) | ? [v14] : ( ~ (v14 = 0) & relation_of2_as_subset(v12, v10, v11) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (relation_of2_as_subset(v12, v10, v11) = v13) | ? [v14] : ( ~ (v14 = 0) & relation_of2(v12, v10, v11) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (subset(v10, v11) = 0) | ~ (in(v12, v11) = v13) | ? [v14] : ( ~ (v14 = 0) & in(v12, v10) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (powerset(v11) = v12) | ~ (element(v10, v12) = v13) | ? [v14] : ( ~ (v14 = 0) & subset(v10, v11) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (element(v10, v12) = v13) | ~ (in(v10, v11) = 0) | ? [v14] : ? [v15] : ( ~ (v15 = 0) & powerset(v12) = v14 & element(v11, v14) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (ordered_pair(v13, v12) = v11) | ~ (ordered_pair(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (subset(v13, v12) = v11) | ~ (subset(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (unordered_pair(v13, v12) = v11) | ~ (unordered_pair(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (cartesian_product2(v13, v12) = v11) | ~ (cartesian_product2(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (element(v13, v12) = v11) | ~ (element(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (in(v13, v12) = v11) | ~ (in(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (powerset(v12) = v13) | ~ (element(v11, v13) = 0) | ~ (in(v10, v11) = 0) | element(v10, v12) = 0) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (powerset(v12) = v13) | ~ (element(v11, v13) = 0) | ~ (in(v10, v11) = 0) | ? [v14] : ( ~ (v14 = 0) & empty(v12) = v14)) & ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (subset(v10, v11) = v12) | ? [v13] : ? [v14] : ( ~ (v14 = 0) & powerset(v11) = v13 & element(v10, v13) = v14)) & ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (subset(v10, v11) = v12) | ? [v13] : ? [v14] : ( ~ (v14 = 0) & in(v13, v11) = v14 & in(v13, v10) = 0)) & ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (element(v10, v11) = v12) | ? [v13] : ( ~ (v13 = 0) & in(v10, v11) = v13)) & ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (in(v10, v11) = v12) | ? [v13] : ((v13 = 0 & empty(v11) = 0) | ( ~ (v13 = 0) & element(v10, v11) = v13))) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (empty(v12) = v11) | ~ (empty(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (singleton(v12) = v11) | ~ (singleton(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (relation_rng(v12) = v11) | ~ (relation_rng(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (relation_dom(v12) = v11) | ~ (relation_dom(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (powerset(v12) = v11) | ~ (powerset(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (relation(v12) = v11) | ~ (relation(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (empty(v12) = 0) | ~ (in(v10, v11) = 0) | ? [v13] : ? [v14] : ( ~ (v14 = 0) & powerset(v12) = v13 & element(v11, v13) = v14)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (relation_of2(v12, v10, v11) = 0) | relation_of2_as_subset(v12, v10, v11) = 0) & ! [v10] : ! [v11] : ! [v12] : ( ~ (relation_of2_as_subset(v12, v10, v11) = 0) | relation_of2(v12, v10, v11) = 0) & ! [v10] : ! [v11] : ! [v12] : ( ~ (relation_of2_as_subset(v12, v10, v11) = 0) | ? [v13] : ? [v14] : (cartesian_product2(v10, v11) = v13 & powerset(v13) = v14 & element(v12, v14) = 0)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (relation_rng(v10) = v11) | ~ (in(v12, v11) = 0) | ? [v13] : ? [v14] : ? [v15] : ((v15 = 0 & ordered_pair(v13, v12) = v14 & in(v14, v10) = 0) | ( ~ (v13 = 0) & relation(v10) = v13))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (relation_dom(v10) = v11) | ~ (in(v12, v11) = 0) | ? [v13] : ? [v14] : ? [v15] : ((v15 = 0 & ordered_pair(v12, v13) = v14 & in(v14, v10) = 0) | ( ~ (v13 = 0) & relation(v10) = v13))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (ordered_pair(v10, v11) = v12) | ? [v13] : ? [v14] : (singleton(v10) = v14 & unordered_pair(v13, v14) = v12 & unordered_pair(v10, v11) = v13)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (ordered_pair(v10, v11) = v12) | ? [v13] : ( ~ (v13 = 0) & empty(v12) = v13)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (subset(v10, v11) = 0) | ~ (in(v12, v10) = 0) | in(v12, v11) = 0) & ! [v10] : ! [v11] : ! [v12] : ( ~ (unordered_pair(v11, v10) = v12) | unordered_pair(v10, v11) = v12) & ! [v10] : ! [v11] : ! [v12] : ( ~ (unordered_pair(v10, v11) = v12) | unordered_pair(v11, v10) = v12) & ! [v10] : ! [v11] : ! [v12] : ( ~ (unordered_pair(v10, v11) = v12) | ? [v13] : ? [v14] : (singleton(v10) = v14 & ordered_pair(v10, v11) = v13 & unordered_pair(v12, v14) = v13)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (powerset(v11) = v12) | ~ (element(v10, v12) = 0) | subset(v10, v11) = 0) & ? [v10] : ! [v11] : ! [v12] : (v12 = v10 | ~ (relation_rng(v11) = v12) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : (( ~ (v13 = 0) & relation(v11) = v13) | (( ! [v18] : ! [v19] : ( ~ (ordered_pair(v18, v13) = v19) | ? [v20] : ( ~ (v20 = 0) & in(v19, v11) = v20)) | ( ~ (v14 = 0) & in(v13, v10) = v14)) & ((v17 = 0 & ordered_pair(v15, v13) = v16 & in(v16, v11) = 0) | (v14 = 0 & in(v13, v10) = 0))))) & ? [v10] : ! [v11] : ! [v12] : (v12 = v10 | ~ (relation_dom(v11) = v12) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : (( ~ (v13 = 0) & relation(v11) = v13) | (( ! [v18] : ! [v19] : ( ~ (ordered_pair(v13, v18) = v19) | ? [v20] : ( ~ (v20 = 0) & in(v19, v11) = v20)) | ( ~ (v14 = 0) & in(v13, v10) = v14)) & ((v17 = 0 & ordered_pair(v13, v15) = v16 & in(v16, v11) = 0) | (v14 = 0 & in(v13, v10) = 0))))) & ! [v10] : ! [v11] : (v11 = v10 | ~ (empty(v11) = 0) | ~ (empty(v10) = 0)) & ! [v10] : ! [v11] : (v11 = 0 | ~ (subset(v10, v10) = v11)) & ! [v10] : ! [v11] : ( ~ (subset(v10, v11) = 0) | ? [v12] : (powerset(v11) = v12 & element(v10, v12) = 0)) & ! [v10] : ! [v11] : ( ~ (element(v10, v11) = 0) | ? [v12] : ((v12 = 0 & empty(v11) = 0) | (v12 = 0 & in(v10, v11) = 0))) & ! [v10] : ! [v11] : ( ~ (in(v11, v10) = 0) | ? [v12] : ( ~ (v12 = 0) & in(v10, v11) = v12)) & ! [v10] : ! [v11] : ( ~ (in(v10, v11) = 0) | element(v10, v11) = 0) & ! [v10] : ! [v11] : ( ~ (in(v10, v11) = 0) | ? [v12] : ( ~ (v12 = 0) & empty(v11) = v12)) & ! [v10] : ! [v11] : ( ~ (in(v10, v11) = 0) | ? [v12] : ( ~ (v12 = 0) & in(v11, v10) = v12)) & ! [v10] : (v10 = empty_set | ~ (empty(v10) = 0)) & ! [v10] : ( ~ (relation(v10) = 0) | ? [v11] : (relation_rng(v10) = v11 & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = 0 | ~ (ordered_pair(v14, v12) = v15) | ~ (in(v12, v11) = v13) | ? [v16] : ( ~ (v16 = 0) & in(v15, v10) = v16)) & ! [v12] : ( ~ (in(v12, v11) = 0) | ? [v13] : ? [v14] : (ordered_pair(v13, v12) = v14 & in(v14, v10) = 0)) & ? [v12] : (v12 = v11 | ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : (( ! [v18] : ! [v19] : ( ~ (ordered_pair(v18, v13) = v19) | ? [v20] : ( ~ (v20 = 0) & in(v19, v10) = v20)) | ( ~ (v14 = 0) & in(v13, v12) = v14)) & ((v17 = 0 & ordered_pair(v15, v13) = v16 & in(v16, v10) = 0) | (v14 = 0 & in(v13, v12) = 0)))))) & ! [v10] : ( ~ (relation(v10) = 0) | ? [v11] : (relation_dom(v10) = v11 & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = 0 | ~ (ordered_pair(v12, v14) = v15) | ~ (in(v12, v11) = v13) | ? [v16] : ( ~ (v16 = 0) & in(v15, v10) = v16)) & ! [v12] : ( ~ (in(v12, v11) = 0) | ? [v13] : ? [v14] : (ordered_pair(v12, v13) = v14 & in(v14, v10) = 0)) & ? [v12] : (v12 = v11 | ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : (( ! [v18] : ! [v19] : ( ~ (ordered_pair(v13, v18) = v19) | ? [v20] : ( ~ (v20 = 0) & in(v19, v10) = v20)) | ( ~ (v14 = 0) & in(v13, v12) = v14)) & ((v17 = 0 & ordered_pair(v13, v15) = v16 & in(v16, v10) = 0) | (v14 = 0 & in(v13, v12) = 0)))))) & ? [v10] : ? [v11] : ? [v12] : ? [v13] : relation_of2(v12, v11, v10) = v13 & ? [v10] : ? [v11] : ? [v12] : ? [v13] : relation_of2_as_subset(v12, v11, v10) = v13 & ? [v10] : ? [v11] : ? [v12] : relation_of2(v12, v10, v11) = 0 & ? [v10] : ? [v11] : ? [v12] : relation_of2_as_subset(v12, v10, v11) = 0 & ? [v10] : ? [v11] : ? [v12] : ordered_pair(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : subset(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : unordered_pair(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : cartesian_product2(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : element(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : in(v11, v10) = v12 & ? [v10] : ? [v11] : empty(v10) = v11 & ? [v10] : ? [v11] : singleton(v10) = v11 & ? [v10] : ? [v11] : relation_rng(v10) = v11 & ? [v10] : ? [v11] : relation_dom(v10) = v11 & ? [v10] : ? [v11] : powerset(v10) = v11 & ? [v10] : ? [v11] : element(v11, v10) = 0 & ? [v10] : ? [v11] : relation(v10) = v11 & (( ~ (v6 = 0) & relation_rng(v2) = v5 & subset(v5, v1) = v6) | ( ~ (v4 = 0) & relation_dom(v2) = v3 & subset(v3, v0) = v4)))
% 10.95/3.21 | 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, all_0_9_9 yields:
% 10.95/3.21 | (1) ~ (all_0_1_1 = 0) & empty(all_0_0_0) = 0 & empty(all_0_2_2) = all_0_1_1 & empty(empty_set) = 0 & relation_of2_as_subset(all_0_7_7, all_0_9_9, all_0_8_8) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (ordered_pair(v0, v1) = v4) | ~ (cartesian_product2(v2, v3) = v5) | ~ (in(v4, v5) = v6) | ? [v7] : (( ~ (v7 = 0) & in(v1, v3) = v7) | ( ~ (v7 = 0) & in(v0, v2) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (cartesian_product2(v0, v1) = v3) | ~ (powerset(v3) = v4) | ~ (element(v2, v4) = v5) | ? [v6] : ( ~ (v6 = 0) & relation_of2_as_subset(v2, v0, v1) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = 0 | ~ (relation_rng(v0) = v1) | ~ (ordered_pair(v4, v2) = v5) | ~ (in(v2, v1) = v3) | ? [v6] : (( ~ (v6 = 0) & relation(v0) = v6) | ( ~ (v6 = 0) & in(v5, v0) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = 0 | ~ (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v4) = v5) | ~ (in(v2, v1) = v3) | ? [v6] : (( ~ (v6 = 0) & relation(v0) = v6) | ( ~ (v6 = 0) & in(v5, v0) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (ordered_pair(v0, v1) = v4) | ~ (cartesian_product2(v2, v3) = v5) | ~ (in(v4, v5) = 0) | (in(v1, v3) = 0 & in(v0, v2) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (element(v0, v2) = v4) | ? [v5] : ( ~ (v5 = 0) & in(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (relation_of2(v4, v3, v2) = v1) | ~ (relation_of2(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (relation_of2_as_subset(v4, v3, v2) = v1) | ~ (relation_of2_as_subset(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v0, v1) = v3) | ~ (powerset(v3) = v4) | ~ (element(v2, v4) = 0) | relation(v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (relation_of2(v2, v0, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & relation_of2_as_subset(v2, v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (relation_of2_as_subset(v2, v0, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & relation_of2(v2, v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v2, v0) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (element(v0, v2) = v3) | ~ (in(v0, v1) = 0) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & powerset(v2) = v4 & element(v1, v4) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | element(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v1) = v3 & element(v0, v3) = v4)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v0, v1) = v2) | ? [v3] : ((v3 = 0 & empty(v1) = 0) | ( ~ (v3 = 0) & element(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (empty(v2) = 0) | ~ (in(v0, v1) = 0) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v2) = v3 & element(v1, v3) = v4)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_of2(v2, v0, v1) = 0) | relation_of2_as_subset(v2, v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_of2_as_subset(v2, v0, v1) = 0) | relation_of2(v2, v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_of2_as_subset(v2, v0, v1) = 0) | ? [v3] : ? [v4] : (cartesian_product2(v0, v1) = v3 & powerset(v3) = v4 & element(v2, v4) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng(v0) = v1) | ~ (in(v2, v1) = 0) | ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & ordered_pair(v3, v2) = v4 & in(v4, v0) = 0) | ( ~ (v3 = 0) & relation(v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom(v0) = v1) | ~ (in(v2, v1) = 0) | ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & ordered_pair(v2, v3) = v4 & in(v4, v0) = 0) | ( ~ (v3 = 0) & relation(v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & ordered_pair(v0, v1) = v3 & unordered_pair(v2, v4) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | subset(v0, v1) = 0) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_rng(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (( ~ (v3 = 0) & relation(v1) = v3) | (( ! [v8] : ! [v9] : ( ~ (ordered_pair(v8, v3) = v9) | ? [v10] : ( ~ (v10 = 0) & in(v9, v1) = v10)) | ( ~ (v4 = 0) & in(v3, v0) = v4)) & ((v7 = 0 & ordered_pair(v5, v3) = v6 & in(v6, v1) = 0) | (v4 = 0 & in(v3, v0) = 0))))) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_dom(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (( ~ (v3 = 0) & relation(v1) = v3) | (( ! [v8] : ! [v9] : ( ~ (ordered_pair(v3, v8) = v9) | ? [v10] : ( ~ (v10 = 0) & in(v9, v1) = v10)) | ( ~ (v4 = 0) & in(v3, v0) = v4)) & ((v7 = 0 & ordered_pair(v3, v5) = v6 & in(v6, v1) = 0) | (v4 = 0 & in(v3, v0) = 0))))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (powerset(v1) = v2 & element(v0, v2) = 0)) & ! [v0] : ! [v1] : ( ~ (element(v0, v1) = 0) | ? [v2] : ((v2 = 0 & empty(v1) = 0) | (v2 = 0 & in(v0, v1) = 0))) & ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | element(v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) & ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0)) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : (relation_rng(v0) = v1 & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = 0 | ~ (ordered_pair(v4, v2) = v5) | ~ (in(v2, v1) = v3) | ? [v6] : ( ~ (v6 = 0) & in(v5, v0) = v6)) & ! [v2] : ( ~ (in(v2, v1) = 0) | ? [v3] : ? [v4] : (ordered_pair(v3, v2) = v4 & in(v4, v0) = 0)) & ? [v2] : (v2 = v1 | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (( ! [v8] : ! [v9] : ( ~ (ordered_pair(v8, v3) = v9) | ? [v10] : ( ~ (v10 = 0) & in(v9, v0) = v10)) | ( ~ (v4 = 0) & in(v3, v2) = v4)) & ((v7 = 0 & ordered_pair(v5, v3) = v6 & in(v6, v0) = 0) | (v4 = 0 & in(v3, v2) = 0)))))) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : (relation_dom(v0) = v1 & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = 0 | ~ (ordered_pair(v2, v4) = v5) | ~ (in(v2, v1) = v3) | ? [v6] : ( ~ (v6 = 0) & in(v5, v0) = v6)) & ! [v2] : ( ~ (in(v2, v1) = 0) | ? [v3] : ? [v4] : (ordered_pair(v2, v3) = v4 & in(v4, v0) = 0)) & ? [v2] : (v2 = v1 | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (( ! [v8] : ! [v9] : ( ~ (ordered_pair(v3, v8) = v9) | ? [v10] : ( ~ (v10 = 0) & in(v9, v0) = v10)) | ( ~ (v4 = 0) & in(v3, v2) = v4)) & ((v7 = 0 & ordered_pair(v3, v5) = v6 & in(v6, v0) = 0) | (v4 = 0 & in(v3, v2) = 0)))))) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : relation_of2(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : relation_of2_as_subset(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : relation_of2(v2, v0, v1) = 0 & ? [v0] : ? [v1] : ? [v2] : relation_of2_as_subset(v2, v0, v1) = 0 & ? [v0] : ? [v1] : ? [v2] : ordered_pair(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : unordered_pair(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : cartesian_product2(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : element(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2 & ? [v0] : ? [v1] : empty(v0) = v1 & ? [v0] : ? [v1] : singleton(v0) = v1 & ? [v0] : ? [v1] : relation_rng(v0) = v1 & ? [v0] : ? [v1] : relation_dom(v0) = v1 & ? [v0] : ? [v1] : powerset(v0) = v1 & ? [v0] : ? [v1] : element(v1, v0) = 0 & ? [v0] : ? [v1] : relation(v0) = v1 & (( ~ (all_0_3_3 = 0) & relation_rng(all_0_7_7) = all_0_4_4 & subset(all_0_4_4, all_0_8_8) = all_0_3_3) | ( ~ (all_0_5_5 = 0) & relation_dom(all_0_7_7) = all_0_6_6 & subset(all_0_6_6, all_0_9_9) = all_0_5_5))
% 10.95/3.22 |
% 10.95/3.22 | Applying alpha-rule on (1) yields:
% 10.95/3.22 | (2) ! [v0] : ! [v1] : ! [v2] : ( ~ (empty(v2) = 0) | ~ (in(v0, v1) = 0) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v2) = v3 & element(v1, v3) = v4))
% 10.95/3.22 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 10.95/3.23 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_of2_as_subset(v2, v0, v1) = 0) | relation_of2(v2, v0, v1) = 0)
% 10.95/3.23 | (5) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_of2(v2, v0, v1) = 0) | relation_of2_as_subset(v2, v0, v1) = 0)
% 10.95/3.23 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = 0 | ~ (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v4) = v5) | ~ (in(v2, v1) = v3) | ? [v6] : (( ~ (v6 = 0) & relation(v0) = v6) | ( ~ (v6 = 0) & in(v5, v0) = v6)))
% 10.95/3.23 | (7) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2)
% 10.95/3.23 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2)
% 10.95/3.23 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (ordered_pair(v0, v1) = v4) | ~ (cartesian_product2(v2, v3) = v5) | ~ (in(v4, v5) = v6) | ? [v7] : (( ~ (v7 = 0) & in(v1, v3) = v7) | ( ~ (v7 = 0) & in(v0, v2) = v7)))
% 10.95/3.23 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | element(v0, v2) = 0)
% 10.95/3.23 | (11) ? [v0] : ? [v1] : powerset(v0) = v1
% 10.95/3.23 | (12) ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2
% 10.95/3.23 | (13) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom(v0) = v1) | ~ (in(v2, v1) = 0) | ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & ordered_pair(v2, v3) = v4 & in(v4, v0) = 0) | ( ~ (v3 = 0) & relation(v0) = v3)))
% 10.95/3.23 | (14) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 11.09/3.23 | (15) ? [v0] : ? [v1] : relation(v0) = v1
% 11.09/3.23 | (16) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0))
% 11.09/3.23 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v2, v0) = v4))
% 11.09/3.23 | (18) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | subset(v0, v1) = 0)
% 11.09/3.23 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (relation_of2(v4, v3, v2) = v1) | ~ (relation_of2(v4, v3, v2) = v0))
% 11.09/3.23 | (20) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (powerset(v1) = v2 & element(v0, v2) = 0))
% 11.09/3.23 | (21) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_of2_as_subset(v2, v0, v1) = 0) | ? [v3] : ? [v4] : (cartesian_product2(v0, v1) = v3 & powerset(v3) = v4 & element(v2, v4) = 0))
% 11.09/3.23 | (22) ? [v0] : ? [v1] : relation_rng(v0) = v1
% 11.09/3.23 | (23) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0))
% 11.09/3.23 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0))
% 11.09/3.23 | (25) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3))
% 11.09/3.23 | (26) relation_of2_as_subset(all_0_7_7, all_0_9_9, all_0_8_8) = 0
% 11.09/3.23 | (27) ? [v0] : ? [v1] : ? [v2] : unordered_pair(v1, v0) = v2
% 11.09/3.23 | (28) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0))
% 11.09/3.23 | (29) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_dom(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (( ~ (v3 = 0) & relation(v1) = v3) | (( ! [v8] : ! [v9] : ( ~ (ordered_pair(v3, v8) = v9) | ? [v10] : ( ~ (v10 = 0) & in(v9, v1) = v10)) | ( ~ (v4 = 0) & in(v3, v0) = v4)) & ((v7 = 0 & ordered_pair(v3, v5) = v6 & in(v6, v1) = 0) | (v4 = 0 & in(v3, v0) = 0)))))
% 11.09/3.23 | (30) ? [v0] : ? [v1] : singleton(v0) = v1
% 11.09/3.23 | (31) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0))
% 11.09/3.23 | (32) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v1) = v3 & element(v0, v3) = v4))
% 11.09/3.23 | (33) ! [v0] : ! [v1] : ( ~ (element(v0, v1) = 0) | ? [v2] : ((v2 = 0 & empty(v1) = 0) | (v2 = 0 & in(v0, v1) = 0)))
% 11.09/3.23 | (34) ? [v0] : ? [v1] : ? [v2] : relation_of2(v2, v0, v1) = 0
% 11.09/3.23 | (35) ~ (all_0_1_1 = 0)
% 11.09/3.23 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 11.09/3.24 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (cartesian_product2(v0, v1) = v3) | ~ (powerset(v3) = v4) | ~ (element(v2, v4) = v5) | ? [v6] : ( ~ (v6 = 0) & relation_of2_as_subset(v2, v0, v1) = v6))
% 11.09/3.24 | (38) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & ordered_pair(v0, v1) = v3 & unordered_pair(v2, v4) = v3))
% 11.09/3.24 | (39) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0))
% 11.09/3.24 | (40) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 11.09/3.24 | (41) ? [v0] : ? [v1] : ? [v2] : relation_of2_as_subset(v2, v0, v1) = 0
% 11.09/3.24 | (42) ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2))
% 11.09/3.24 | (43) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3))
% 11.09/3.24 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 11.09/3.24 | (45) ? [v0] : ? [v1] : empty(v0) = v1
% 11.09/3.24 | (46) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : (relation_dom(v0) = v1 & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = 0 | ~ (ordered_pair(v2, v4) = v5) | ~ (in(v2, v1) = v3) | ? [v6] : ( ~ (v6 = 0) & in(v5, v0) = v6)) & ! [v2] : ( ~ (in(v2, v1) = 0) | ? [v3] : ? [v4] : (ordered_pair(v2, v3) = v4 & in(v4, v0) = 0)) & ? [v2] : (v2 = v1 | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (( ! [v8] : ! [v9] : ( ~ (ordered_pair(v3, v8) = v9) | ? [v10] : ( ~ (v10 = 0) & in(v9, v0) = v10)) | ( ~ (v4 = 0) & in(v3, v2) = v4)) & ((v7 = 0 & ordered_pair(v3, v5) = v6 & in(v6, v0) = 0) | (v4 = 0 & in(v3, v2) = 0))))))
% 11.09/3.24 | (47) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0))
% 11.09/3.24 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (ordered_pair(v0, v1) = v4) | ~ (cartesian_product2(v2, v3) = v5) | ~ (in(v4, v5) = 0) | (in(v1, v3) = 0 & in(v0, v2) = 0))
% 11.09/3.24 | (49) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | element(v0, v1) = 0)
% 11.09/3.24 | (50) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (element(v0, v2) = v3) | ~ (in(v0, v1) = 0) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & powerset(v2) = v4 & element(v1, v4) = v5))
% 11.09/3.24 | (51) empty(all_0_2_2) = all_0_1_1
% 11.09/3.24 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = 0 | ~ (relation_rng(v0) = v1) | ~ (ordered_pair(v4, v2) = v5) | ~ (in(v2, v1) = v3) | ? [v6] : (( ~ (v6 = 0) & relation(v0) = v6) | ( ~ (v6 = 0) & in(v5, v0) = v6)))
% 11.09/3.24 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 11.09/3.24 | (54) ? [v0] : ? [v1] : ? [v2] : ordered_pair(v1, v0) = v2
% 11.09/3.24 | (55) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 11.09/3.24 | (56) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0))
% 11.09/3.24 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (element(v0, v2) = v4) | ? [v5] : ( ~ (v5 = 0) & in(v0, v1) = v5))
% 11.09/3.24 | (58) ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2
% 11.09/3.24 | (59) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0)
% 11.09/3.24 | (60) ? [v0] : ? [v1] : ? [v2] : ? [v3] : relation_of2_as_subset(v2, v1, v0) = v3
% 11.09/3.24 | (61) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng(v0) = v1) | ~ (in(v2, v1) = 0) | ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & ordered_pair(v3, v2) = v4 & in(v4, v0) = 0) | ( ~ (v3 = 0) & relation(v0) = v3)))
% 11.09/3.24 | (62) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v0, v1) = v2) | ? [v3] : ((v3 = 0 & empty(v1) = 0) | ( ~ (v3 = 0) & element(v0, v1) = v3)))
% 11.09/3.24 | (63) ? [v0] : ? [v1] : element(v1, v0) = 0
% 11.09/3.24 | (64) ? [v0] : ? [v1] : ? [v2] : element(v1, v0) = v2
% 11.09/3.24 | (65) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1))
% 11.09/3.24 | (66) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3))
% 11.09/3.24 | (67) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (relation_of2_as_subset(v2, v0, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & relation_of2(v2, v0, v1) = v4))
% 11.09/3.24 | (68) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (relation_of2(v2, v0, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & relation_of2_as_subset(v2, v0, v1) = v4))
% 11.09/3.25 | (69) ? [v0] : ? [v1] : ? [v2] : ? [v3] : relation_of2(v2, v1, v0) = v3
% 11.09/3.25 | (70) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (relation_of2_as_subset(v4, v3, v2) = v1) | ~ (relation_of2_as_subset(v4, v3, v2) = v0))
% 11.09/3.25 | (71) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0))
% 11.09/3.25 | (72) ? [v0] : ? [v1] : relation_dom(v0) = v1
% 11.09/3.25 | (73) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 11.09/3.25 | (74) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_rng(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (( ~ (v3 = 0) & relation(v1) = v3) | (( ! [v8] : ! [v9] : ( ~ (ordered_pair(v8, v3) = v9) | ? [v10] : ( ~ (v10 = 0) & in(v9, v1) = v10)) | ( ~ (v4 = 0) & in(v3, v0) = v4)) & ((v7 = 0 & ordered_pair(v5, v3) = v6 & in(v6, v1) = 0) | (v4 = 0 & in(v3, v0) = 0)))))
% 11.09/3.25 | (75) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4))
% 11.09/3.25 | (76) ( ~ (all_0_3_3 = 0) & relation_rng(all_0_7_7) = all_0_4_4 & subset(all_0_4_4, all_0_8_8) = all_0_3_3) | ( ~ (all_0_5_5 = 0) & relation_dom(all_0_7_7) = all_0_6_6 & subset(all_0_6_6, all_0_9_9) = all_0_5_5)
% 11.09/3.25 | (77) empty(empty_set) = 0
% 11.09/3.25 | (78) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : (relation_rng(v0) = v1 & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = 0 | ~ (ordered_pair(v4, v2) = v5) | ~ (in(v2, v1) = v3) | ? [v6] : ( ~ (v6 = 0) & in(v5, v0) = v6)) & ! [v2] : ( ~ (in(v2, v1) = 0) | ? [v3] : ? [v4] : (ordered_pair(v3, v2) = v4 & in(v4, v0) = 0)) & ? [v2] : (v2 = v1 | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (( ! [v8] : ! [v9] : ( ~ (ordered_pair(v8, v3) = v9) | ? [v10] : ( ~ (v10 = 0) & in(v9, v0) = v10)) | ( ~ (v4 = 0) & in(v3, v2) = v4)) & ((v7 = 0 & ordered_pair(v5, v3) = v6 & in(v6, v0) = 0) | (v4 = 0 & in(v3, v2) = 0))))))
% 11.09/3.25 | (79) empty(all_0_0_0) = 0
% 11.09/3.25 | (80) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v0, v1) = v3) | ~ (powerset(v3) = v4) | ~ (element(v2, v4) = 0) | relation(v2) = 0)
% 11.09/3.25 | (81) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0))
% 11.09/3.25 | (82) ? [v0] : ? [v1] : ? [v2] : cartesian_product2(v1, v0) = v2
% 11.09/3.25 |
% 11.09/3.25 | Instantiating formula (21) with all_0_7_7, all_0_8_8, all_0_9_9 and discharging atoms relation_of2_as_subset(all_0_7_7, all_0_9_9, all_0_8_8) = 0, yields:
% 11.09/3.25 | (83) ? [v0] : ? [v1] : (cartesian_product2(all_0_9_9, all_0_8_8) = v0 & powerset(v0) = v1 & element(all_0_7_7, v1) = 0)
% 11.09/3.25 |
% 11.09/3.25 | Instantiating (83) with all_51_0_58, all_51_1_59 yields:
% 11.09/3.25 | (84) cartesian_product2(all_0_9_9, all_0_8_8) = all_51_1_59 & powerset(all_51_1_59) = all_51_0_58 & element(all_0_7_7, all_51_0_58) = 0
% 11.09/3.25 |
% 11.09/3.25 | Applying alpha-rule on (84) yields:
% 11.09/3.25 | (85) cartesian_product2(all_0_9_9, all_0_8_8) = all_51_1_59
% 11.09/3.25 | (86) powerset(all_51_1_59) = all_51_0_58
% 11.09/3.25 | (87) element(all_0_7_7, all_51_0_58) = 0
% 11.09/3.25 |
% 11.09/3.25 | Instantiating formula (18) with all_51_0_58, all_51_1_59, all_0_7_7 and discharging atoms powerset(all_51_1_59) = all_51_0_58, element(all_0_7_7, all_51_0_58) = 0, yields:
% 11.09/3.25 | (88) subset(all_0_7_7, all_51_1_59) = 0
% 11.09/3.25 |
% 11.09/3.25 | Instantiating formula (80) with all_51_0_58, all_51_1_59, all_0_7_7, all_0_8_8, all_0_9_9 and discharging atoms cartesian_product2(all_0_9_9, all_0_8_8) = all_51_1_59, powerset(all_51_1_59) = all_51_0_58, element(all_0_7_7, all_51_0_58) = 0, yields:
% 11.09/3.25 | (89) relation(all_0_7_7) = 0
% 11.09/3.25 |
% 11.09/3.25 | Instantiating formula (78) with all_0_7_7 and discharging atoms relation(all_0_7_7) = 0, yields:
% 11.09/3.25 | (90) ? [v0] : (relation_rng(all_0_7_7) = v0 & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = 0 | ~ (ordered_pair(v3, v1) = v4) | ~ (in(v1, v0) = v2) | ? [v5] : ( ~ (v5 = 0) & in(v4, all_0_7_7) = v5)) & ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ? [v3] : (ordered_pair(v2, v1) = v3 & in(v3, all_0_7_7) = 0)) & ? [v1] : (v1 = v0 | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (( ! [v7] : ! [v8] : ( ~ (ordered_pair(v7, v2) = v8) | ? [v9] : ( ~ (v9 = 0) & in(v8, all_0_7_7) = v9)) | ( ~ (v3 = 0) & in(v2, v1) = v3)) & ((v6 = 0 & ordered_pair(v4, v2) = v5 & in(v5, all_0_7_7) = 0) | (v3 = 0 & in(v2, v1) = 0)))))
% 11.09/3.26 |
% 11.09/3.26 | Instantiating formula (46) with all_0_7_7 and discharging atoms relation(all_0_7_7) = 0, yields:
% 11.09/3.26 | (91) ? [v0] : (relation_dom(all_0_7_7) = v0 & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = 0 | ~ (ordered_pair(v1, v3) = v4) | ~ (in(v1, v0) = v2) | ? [v5] : ( ~ (v5 = 0) & in(v4, all_0_7_7) = v5)) & ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ? [v3] : (ordered_pair(v1, v2) = v3 & in(v3, all_0_7_7) = 0)) & ? [v1] : (v1 = v0 | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (( ! [v7] : ! [v8] : ( ~ (ordered_pair(v2, v7) = v8) | ? [v9] : ( ~ (v9 = 0) & in(v8, all_0_7_7) = v9)) | ( ~ (v3 = 0) & in(v2, v1) = v3)) & ((v6 = 0 & ordered_pair(v2, v4) = v5 & in(v5, all_0_7_7) = 0) | (v3 = 0 & in(v2, v1) = 0)))))
% 11.09/3.26 |
% 11.09/3.26 | Instantiating (91) with all_72_0_67 yields:
% 11.09/3.26 | (92) relation_dom(all_0_7_7) = all_72_0_67 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = 0 | ~ (ordered_pair(v0, v2) = v3) | ~ (in(v0, all_72_0_67) = v1) | ? [v4] : ( ~ (v4 = 0) & in(v3, all_0_7_7) = v4)) & ! [v0] : ( ~ (in(v0, all_72_0_67) = 0) | ? [v1] : ? [v2] : (ordered_pair(v0, v1) = v2 & in(v2, all_0_7_7) = 0)) & ? [v0] : (v0 = all_72_0_67 | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (( ! [v6] : ! [v7] : ( ~ (ordered_pair(v1, v6) = v7) | ? [v8] : ( ~ (v8 = 0) & in(v7, all_0_7_7) = v8)) | ( ~ (v2 = 0) & in(v1, v0) = v2)) & ((v5 = 0 & ordered_pair(v1, v3) = v4 & in(v4, all_0_7_7) = 0) | (v2 = 0 & in(v1, v0) = 0))))
% 11.09/3.26 |
% 11.09/3.26 | Applying alpha-rule on (92) yields:
% 11.09/3.26 | (93) relation_dom(all_0_7_7) = all_72_0_67
% 11.09/3.26 | (94) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = 0 | ~ (ordered_pair(v0, v2) = v3) | ~ (in(v0, all_72_0_67) = v1) | ? [v4] : ( ~ (v4 = 0) & in(v3, all_0_7_7) = v4))
% 11.09/3.26 | (95) ! [v0] : ( ~ (in(v0, all_72_0_67) = 0) | ? [v1] : ? [v2] : (ordered_pair(v0, v1) = v2 & in(v2, all_0_7_7) = 0))
% 11.09/3.26 | (96) ? [v0] : (v0 = all_72_0_67 | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (( ! [v6] : ! [v7] : ( ~ (ordered_pair(v1, v6) = v7) | ? [v8] : ( ~ (v8 = 0) & in(v7, all_0_7_7) = v8)) | ( ~ (v2 = 0) & in(v1, v0) = v2)) & ((v5 = 0 & ordered_pair(v1, v3) = v4 & in(v4, all_0_7_7) = 0) | (v2 = 0 & in(v1, v0) = 0))))
% 11.09/3.26 |
% 11.09/3.26 | Instantiating (90) with all_79_0_70 yields:
% 11.09/3.26 | (97) relation_rng(all_0_7_7) = all_79_0_70 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = 0 | ~ (ordered_pair(v2, v0) = v3) | ~ (in(v0, all_79_0_70) = v1) | ? [v4] : ( ~ (v4 = 0) & in(v3, all_0_7_7) = v4)) & ! [v0] : ( ~ (in(v0, all_79_0_70) = 0) | ? [v1] : ? [v2] : (ordered_pair(v1, v0) = v2 & in(v2, all_0_7_7) = 0)) & ? [v0] : (v0 = all_79_0_70 | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (( ! [v6] : ! [v7] : ( ~ (ordered_pair(v6, v1) = v7) | ? [v8] : ( ~ (v8 = 0) & in(v7, all_0_7_7) = v8)) | ( ~ (v2 = 0) & in(v1, v0) = v2)) & ((v5 = 0 & ordered_pair(v3, v1) = v4 & in(v4, all_0_7_7) = 0) | (v2 = 0 & in(v1, v0) = 0))))
% 11.09/3.26 |
% 11.09/3.26 | Applying alpha-rule on (97) yields:
% 11.09/3.26 | (98) relation_rng(all_0_7_7) = all_79_0_70
% 11.09/3.26 | (99) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = 0 | ~ (ordered_pair(v2, v0) = v3) | ~ (in(v0, all_79_0_70) = v1) | ? [v4] : ( ~ (v4 = 0) & in(v3, all_0_7_7) = v4))
% 11.09/3.26 | (100) ! [v0] : ( ~ (in(v0, all_79_0_70) = 0) | ? [v1] : ? [v2] : (ordered_pair(v1, v0) = v2 & in(v2, all_0_7_7) = 0))
% 11.09/3.26 | (101) ? [v0] : (v0 = all_79_0_70 | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (( ! [v6] : ! [v7] : ( ~ (ordered_pair(v6, v1) = v7) | ? [v8] : ( ~ (v8 = 0) & in(v7, all_0_7_7) = v8)) | ( ~ (v2 = 0) & in(v1, v0) = v2)) & ((v5 = 0 & ordered_pair(v3, v1) = v4 & in(v4, all_0_7_7) = 0) | (v2 = 0 & in(v1, v0) = 0))))
% 11.09/3.26 |
% 11.09/3.26 +-Applying beta-rule and splitting (76), into two cases.
% 11.09/3.26 |-Branch one:
% 11.09/3.26 | (102) ~ (all_0_3_3 = 0) & relation_rng(all_0_7_7) = all_0_4_4 & subset(all_0_4_4, all_0_8_8) = all_0_3_3
% 11.09/3.26 |
% 11.09/3.26 | Applying alpha-rule on (102) yields:
% 11.09/3.26 | (103) ~ (all_0_3_3 = 0)
% 11.09/3.26 | (104) relation_rng(all_0_7_7) = all_0_4_4
% 11.09/3.26 | (105) subset(all_0_4_4, all_0_8_8) = all_0_3_3
% 11.09/3.26 |
% 11.09/3.26 | Instantiating formula (23) with all_0_7_7, all_0_4_4, all_79_0_70 and discharging atoms relation_rng(all_0_7_7) = all_79_0_70, relation_rng(all_0_7_7) = all_0_4_4, yields:
% 11.09/3.26 | (106) all_79_0_70 = all_0_4_4
% 11.09/3.26 |
% 11.09/3.26 | From (106) and (98) follows:
% 11.09/3.26 | (104) relation_rng(all_0_7_7) = all_0_4_4
% 11.09/3.26 |
% 11.09/3.26 | Instantiating formula (16) with all_0_3_3, all_0_8_8, all_0_4_4 and discharging atoms subset(all_0_4_4, all_0_8_8) = all_0_3_3, yields:
% 11.09/3.26 | (108) all_0_3_3 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_4_4) = 0 & in(v0, all_0_8_8) = v1)
% 11.09/3.26 |
% 11.09/3.26 +-Applying beta-rule and splitting (108), into two cases.
% 11.09/3.26 |-Branch one:
% 11.09/3.26 | (109) all_0_3_3 = 0
% 11.09/3.26 |
% 11.09/3.26 | Equations (109) can reduce 103 to:
% 11.09/3.26 | (110) $false
% 11.09/3.26 |
% 11.09/3.26 |-The branch is then unsatisfiable
% 11.09/3.26 |-Branch two:
% 11.09/3.26 | (103) ~ (all_0_3_3 = 0)
% 11.09/3.26 | (112) ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_4_4) = 0 & in(v0, all_0_8_8) = v1)
% 11.09/3.26 |
% 11.09/3.26 | Instantiating (112) with all_124_0_80, all_124_1_81 yields:
% 11.09/3.27 | (113) ~ (all_124_0_80 = 0) & in(all_124_1_81, all_0_4_4) = 0 & in(all_124_1_81, all_0_8_8) = all_124_0_80
% 11.09/3.27 |
% 11.09/3.27 | Applying alpha-rule on (113) yields:
% 11.09/3.27 | (114) ~ (all_124_0_80 = 0)
% 11.09/3.27 | (115) in(all_124_1_81, all_0_4_4) = 0
% 11.09/3.27 | (116) in(all_124_1_81, all_0_8_8) = all_124_0_80
% 11.09/3.27 |
% 11.09/3.27 | Instantiating formula (61) with all_124_1_81, all_0_4_4, all_0_7_7 and discharging atoms relation_rng(all_0_7_7) = all_0_4_4, in(all_124_1_81, all_0_4_4) = 0, yields:
% 11.09/3.27 | (117) ? [v0] : ? [v1] : ? [v2] : ((v2 = 0 & ordered_pair(v0, all_124_1_81) = v1 & in(v1, all_0_7_7) = 0) | ( ~ (v0 = 0) & relation(all_0_7_7) = v0))
% 11.09/3.27 |
% 11.09/3.27 | Instantiating formula (62) with all_124_0_80, all_0_8_8, all_124_1_81 and discharging atoms in(all_124_1_81, all_0_8_8) = all_124_0_80, yields:
% 11.09/3.27 | (118) all_124_0_80 = 0 | ? [v0] : ((v0 = 0 & empty(all_0_8_8) = 0) | ( ~ (v0 = 0) & element(all_124_1_81, all_0_8_8) = v0))
% 11.09/3.27 |
% 11.09/3.27 | Instantiating (117) with all_145_0_86, all_145_1_87, all_145_2_88 yields:
% 11.09/3.27 | (119) (all_145_0_86 = 0 & ordered_pair(all_145_2_88, all_124_1_81) = all_145_1_87 & in(all_145_1_87, all_0_7_7) = 0) | ( ~ (all_145_2_88 = 0) & relation(all_0_7_7) = all_145_2_88)
% 11.09/3.27 |
% 11.09/3.27 +-Applying beta-rule and splitting (119), into two cases.
% 11.09/3.27 |-Branch one:
% 11.09/3.27 | (120) all_145_0_86 = 0 & ordered_pair(all_145_2_88, all_124_1_81) = all_145_1_87 & in(all_145_1_87, all_0_7_7) = 0
% 11.09/3.27 |
% 11.09/3.27 | Applying alpha-rule on (120) yields:
% 11.09/3.27 | (121) all_145_0_86 = 0
% 11.09/3.27 | (122) ordered_pair(all_145_2_88, all_124_1_81) = all_145_1_87
% 11.09/3.27 | (123) in(all_145_1_87, all_0_7_7) = 0
% 11.09/3.27 |
% 11.09/3.27 +-Applying beta-rule and splitting (118), into two cases.
% 11.09/3.27 |-Branch one:
% 11.09/3.27 | (124) all_124_0_80 = 0
% 11.09/3.27 |
% 11.09/3.27 | Equations (124) can reduce 114 to:
% 11.09/3.27 | (110) $false
% 11.09/3.27 |
% 11.09/3.27 |-The branch is then unsatisfiable
% 11.09/3.27 |-Branch two:
% 11.09/3.27 | (114) ~ (all_124_0_80 = 0)
% 11.09/3.27 | (127) ? [v0] : ((v0 = 0 & empty(all_0_8_8) = 0) | ( ~ (v0 = 0) & element(all_124_1_81, all_0_8_8) = v0))
% 11.09/3.27 |
% 11.09/3.27 | Instantiating formula (59) with all_145_1_87, all_51_1_59, all_0_7_7 and discharging atoms subset(all_0_7_7, all_51_1_59) = 0, in(all_145_1_87, all_0_7_7) = 0, yields:
% 11.09/3.27 | (128) in(all_145_1_87, all_51_1_59) = 0
% 11.09/3.27 |
% 11.09/3.27 | Instantiating formula (48) with all_51_1_59, all_145_1_87, all_0_8_8, all_0_9_9, all_124_1_81, all_145_2_88 and discharging atoms ordered_pair(all_145_2_88, all_124_1_81) = all_145_1_87, cartesian_product2(all_0_9_9, all_0_8_8) = all_51_1_59, in(all_145_1_87, all_51_1_59) = 0, yields:
% 11.09/3.27 | (129) in(all_145_2_88, all_0_9_9) = 0 & in(all_124_1_81, all_0_8_8) = 0
% 11.09/3.27 |
% 11.09/3.27 | Applying alpha-rule on (129) yields:
% 11.09/3.27 | (130) in(all_145_2_88, all_0_9_9) = 0
% 11.09/3.27 | (131) in(all_124_1_81, all_0_8_8) = 0
% 11.09/3.27 |
% 11.09/3.27 | Instantiating formula (53) with all_124_1_81, all_0_8_8, 0, all_124_0_80 and discharging atoms in(all_124_1_81, all_0_8_8) = all_124_0_80, in(all_124_1_81, all_0_8_8) = 0, yields:
% 11.09/3.27 | (124) all_124_0_80 = 0
% 11.09/3.27 |
% 11.09/3.27 | Equations (124) can reduce 114 to:
% 11.09/3.27 | (110) $false
% 11.09/3.27 |
% 11.09/3.27 |-The branch is then unsatisfiable
% 11.09/3.27 |-Branch two:
% 11.09/3.27 | (134) ~ (all_145_2_88 = 0) & relation(all_0_7_7) = all_145_2_88
% 11.09/3.27 |
% 11.09/3.27 | Applying alpha-rule on (134) yields:
% 11.09/3.27 | (135) ~ (all_145_2_88 = 0)
% 11.09/3.27 | (136) relation(all_0_7_7) = all_145_2_88
% 11.09/3.27 |
% 11.09/3.27 | Instantiating formula (28) with all_0_7_7, all_145_2_88, 0 and discharging atoms relation(all_0_7_7) = all_145_2_88, relation(all_0_7_7) = 0, yields:
% 11.09/3.27 | (137) all_145_2_88 = 0
% 11.09/3.27 |
% 11.09/3.27 | Equations (137) can reduce 135 to:
% 11.09/3.27 | (110) $false
% 11.09/3.27 |
% 11.09/3.27 |-The branch is then unsatisfiable
% 11.09/3.27 |-Branch two:
% 11.09/3.27 | (139) ~ (all_0_5_5 = 0) & relation_dom(all_0_7_7) = all_0_6_6 & subset(all_0_6_6, all_0_9_9) = all_0_5_5
% 11.09/3.27 |
% 11.09/3.27 | Applying alpha-rule on (139) yields:
% 11.09/3.27 | (140) ~ (all_0_5_5 = 0)
% 11.09/3.27 | (141) relation_dom(all_0_7_7) = all_0_6_6
% 11.09/3.27 | (142) subset(all_0_6_6, all_0_9_9) = all_0_5_5
% 11.09/3.27 |
% 11.09/3.27 | Instantiating formula (39) with all_0_7_7, all_0_6_6, all_72_0_67 and discharging atoms relation_dom(all_0_7_7) = all_72_0_67, relation_dom(all_0_7_7) = all_0_6_6, yields:
% 11.09/3.27 | (143) all_72_0_67 = all_0_6_6
% 11.09/3.27 |
% 11.09/3.27 | From (143) and (93) follows:
% 11.09/3.27 | (141) relation_dom(all_0_7_7) = all_0_6_6
% 11.09/3.27 |
% 11.09/3.27 | Instantiating formula (16) with all_0_5_5, all_0_9_9, all_0_6_6 and discharging atoms subset(all_0_6_6, all_0_9_9) = all_0_5_5, yields:
% 11.09/3.27 | (145) all_0_5_5 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_6_6) = 0 & in(v0, all_0_9_9) = v1)
% 11.09/3.27 |
% 11.09/3.27 +-Applying beta-rule and splitting (145), into two cases.
% 11.09/3.27 |-Branch one:
% 11.09/3.27 | (146) all_0_5_5 = 0
% 11.09/3.27 |
% 11.09/3.27 | Equations (146) can reduce 140 to:
% 11.09/3.27 | (110) $false
% 11.09/3.27 |
% 11.09/3.27 |-The branch is then unsatisfiable
% 11.09/3.27 |-Branch two:
% 11.09/3.27 | (140) ~ (all_0_5_5 = 0)
% 11.09/3.27 | (149) ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_6_6) = 0 & in(v0, all_0_9_9) = v1)
% 11.09/3.27 |
% 11.09/3.27 | Instantiating (149) with all_124_0_131, all_124_1_132 yields:
% 11.09/3.27 | (150) ~ (all_124_0_131 = 0) & in(all_124_1_132, all_0_6_6) = 0 & in(all_124_1_132, all_0_9_9) = all_124_0_131
% 11.09/3.27 |
% 11.09/3.27 | Applying alpha-rule on (150) yields:
% 11.09/3.27 | (151) ~ (all_124_0_131 = 0)
% 11.09/3.27 | (152) in(all_124_1_132, all_0_6_6) = 0
% 11.09/3.27 | (153) in(all_124_1_132, all_0_9_9) = all_124_0_131
% 11.09/3.27 |
% 11.09/3.27 | Instantiating formula (13) with all_124_1_132, all_0_6_6, all_0_7_7 and discharging atoms relation_dom(all_0_7_7) = all_0_6_6, in(all_124_1_132, all_0_6_6) = 0, yields:
% 11.09/3.27 | (154) ? [v0] : ? [v1] : ? [v2] : ((v2 = 0 & ordered_pair(all_124_1_132, v0) = v1 & in(v1, all_0_7_7) = 0) | ( ~ (v0 = 0) & relation(all_0_7_7) = v0))
% 11.09/3.27 |
% 11.09/3.27 | Instantiating formula (62) with all_124_0_131, all_0_9_9, all_124_1_132 and discharging atoms in(all_124_1_132, all_0_9_9) = all_124_0_131, yields:
% 11.09/3.27 | (155) all_124_0_131 = 0 | ? [v0] : ((v0 = 0 & empty(all_0_9_9) = 0) | ( ~ (v0 = 0) & element(all_124_1_132, all_0_9_9) = v0))
% 11.09/3.27 |
% 11.09/3.27 | Instantiating (154) with all_145_0_137, all_145_1_138, all_145_2_139 yields:
% 11.09/3.27 | (156) (all_145_0_137 = 0 & ordered_pair(all_124_1_132, all_145_2_139) = all_145_1_138 & in(all_145_1_138, all_0_7_7) = 0) | ( ~ (all_145_2_139 = 0) & relation(all_0_7_7) = all_145_2_139)
% 11.09/3.27 |
% 11.09/3.27 +-Applying beta-rule and splitting (156), into two cases.
% 11.09/3.27 |-Branch one:
% 11.09/3.27 | (157) all_145_0_137 = 0 & ordered_pair(all_124_1_132, all_145_2_139) = all_145_1_138 & in(all_145_1_138, all_0_7_7) = 0
% 11.09/3.27 |
% 11.09/3.27 | Applying alpha-rule on (157) yields:
% 11.09/3.27 | (158) all_145_0_137 = 0
% 11.09/3.27 | (159) ordered_pair(all_124_1_132, all_145_2_139) = all_145_1_138
% 11.09/3.27 | (160) in(all_145_1_138, all_0_7_7) = 0
% 11.09/3.27 |
% 11.09/3.27 +-Applying beta-rule and splitting (155), into two cases.
% 11.09/3.27 |-Branch one:
% 11.09/3.27 | (161) all_124_0_131 = 0
% 11.09/3.27 |
% 11.09/3.27 | Equations (161) can reduce 151 to:
% 11.09/3.27 | (110) $false
% 11.09/3.27 |
% 11.09/3.27 |-The branch is then unsatisfiable
% 11.09/3.27 |-Branch two:
% 11.09/3.27 | (151) ~ (all_124_0_131 = 0)
% 11.09/3.27 | (164) ? [v0] : ((v0 = 0 & empty(all_0_9_9) = 0) | ( ~ (v0 = 0) & element(all_124_1_132, all_0_9_9) = v0))
% 11.09/3.27 |
% 11.09/3.27 | Instantiating formula (59) with all_145_1_138, all_51_1_59, all_0_7_7 and discharging atoms subset(all_0_7_7, all_51_1_59) = 0, in(all_145_1_138, all_0_7_7) = 0, yields:
% 11.09/3.27 | (165) in(all_145_1_138, all_51_1_59) = 0
% 11.09/3.27 |
% 11.09/3.27 | Instantiating formula (48) with all_51_1_59, all_145_1_138, all_0_8_8, all_0_9_9, all_145_2_139, all_124_1_132 and discharging atoms ordered_pair(all_124_1_132, all_145_2_139) = all_145_1_138, cartesian_product2(all_0_9_9, all_0_8_8) = all_51_1_59, in(all_145_1_138, all_51_1_59) = 0, yields:
% 11.09/3.27 | (166) in(all_145_2_139, all_0_8_8) = 0 & in(all_124_1_132, all_0_9_9) = 0
% 11.09/3.27 |
% 11.09/3.27 | Applying alpha-rule on (166) yields:
% 11.09/3.27 | (167) in(all_145_2_139, all_0_8_8) = 0
% 11.09/3.27 | (168) in(all_124_1_132, all_0_9_9) = 0
% 11.09/3.27 |
% 11.09/3.27 | Instantiating formula (53) with all_124_1_132, all_0_9_9, 0, all_124_0_131 and discharging atoms in(all_124_1_132, all_0_9_9) = all_124_0_131, in(all_124_1_132, all_0_9_9) = 0, yields:
% 11.09/3.27 | (161) all_124_0_131 = 0
% 11.09/3.27 |
% 11.09/3.27 | Equations (161) can reduce 151 to:
% 11.09/3.27 | (110) $false
% 11.09/3.27 |
% 11.09/3.27 |-The branch is then unsatisfiable
% 11.09/3.27 |-Branch two:
% 11.09/3.27 | (171) ~ (all_145_2_139 = 0) & relation(all_0_7_7) = all_145_2_139
% 11.09/3.27 |
% 11.09/3.27 | Applying alpha-rule on (171) yields:
% 11.09/3.27 | (172) ~ (all_145_2_139 = 0)
% 11.09/3.27 | (173) relation(all_0_7_7) = all_145_2_139
% 11.09/3.27 |
% 11.09/3.28 | Instantiating formula (28) with all_0_7_7, all_145_2_139, 0 and discharging atoms relation(all_0_7_7) = all_145_2_139, relation(all_0_7_7) = 0, yields:
% 11.09/3.28 | (174) all_145_2_139 = 0
% 11.09/3.28 |
% 11.09/3.28 | Equations (174) can reduce 172 to:
% 11.09/3.28 | (110) $false
% 11.09/3.28 |
% 11.09/3.28 |-The branch is then unsatisfiable
% 11.09/3.28 % SZS output end Proof for theBenchmark
% 11.09/3.28
% 11.09/3.28 2626ms
%------------------------------------------------------------------------------