TSTP Solution File: SEU253+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU253+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n024.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 08:48:10 EDT 2022
% Result : Theorem 30.70s 8.53s
% Output : Proof 42.51s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU253+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.11/0.33 % Computer : n024.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Mon Jun 20 00:04:02 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.57/0.57 ____ _
% 0.57/0.57 ___ / __ \_____(_)___ ________ __________
% 0.57/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.57/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.57/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.57/0.57
% 0.57/0.57 A Theorem Prover for First-Order Logic
% 0.57/0.57 (ePrincess v.1.0)
% 0.57/0.57
% 0.57/0.57 (c) Philipp Rümmer, 2009-2015
% 0.57/0.57 (c) Peter Backeman, 2014-2015
% 0.57/0.57 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.57/0.57 Free software under GNU Lesser General Public License (LGPL).
% 0.57/0.57 Bug reports to peter@backeman.se
% 0.57/0.57
% 0.57/0.57 For more information, visit http://user.uu.se/~petba168/breu/
% 0.57/0.57
% 0.57/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.57/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.55/0.92 Prover 0: Preprocessing ...
% 2.41/1.17 Prover 0: Warning: ignoring some quantifiers
% 2.55/1.19 Prover 0: Constructing countermodel ...
% 20.06/5.93 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 20.06/5.97 Prover 1: Preprocessing ...
% 20.78/6.09 Prover 1: Warning: ignoring some quantifiers
% 20.78/6.10 Prover 1: Constructing countermodel ...
% 22.11/6.37 Prover 1: gave up
% 22.11/6.37 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 22.11/6.40 Prover 2: Preprocessing ...
% 22.46/6.48 Prover 2: Warning: ignoring some quantifiers
% 22.46/6.48 Prover 2: Constructing countermodel ...
% 28.94/8.10 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 28.94/8.13 Prover 3: Preprocessing ...
% 29.21/8.17 Prover 3: Warning: ignoring some quantifiers
% 29.21/8.18 Prover 3: Constructing countermodel ...
% 29.63/8.26 Prover 3: gave up
% 29.63/8.26 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 29.63/8.27 Prover 4: Preprocessing ...
% 29.94/8.34 Prover 4: Warning: ignoring some quantifiers
% 29.94/8.35 Prover 4: Constructing countermodel ...
% 30.70/8.53 Prover 4: proved (269ms)
% 30.70/8.53 Prover 0: stopped
% 30.70/8.53 Prover 2: stopped
% 30.70/8.53
% 30.70/8.53 No countermodel exists, formula is valid
% 30.70/8.53 % SZS status Theorem for theBenchmark
% 30.70/8.53
% 30.70/8.53 Generating proof ... Warning: ignoring some quantifiers
% 41.55/12.27 found it (size 341)
% 41.55/12.27
% 41.55/12.27 % SZS output start Proof for theBenchmark
% 41.55/12.27 Assumed formulas after preprocessing and simplification:
% 41.55/12.27 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ( ~ (v6 = 0) & ~ (v3 = 0) & connected(v2) = v3 & connected(v1) = 0 & relation_restriction(v1, v0) = v2 & relation(v9) = 0 & relation(v7) = 0 & relation(v4) = 0 & relation(v1) = 0 & one_to_one(v4) = 0 & empty(v8) = 0 & empty(v7) = 0 & empty(v5) = v6 & empty(empty_set) = 0 & function(v9) = 0 & function(v7) = 0 & function(v4) = 0 & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (cartesian_product2(v12, v13) = v15) | ~ (ordered_pair(v10, v11) = v14) | ~ (in(v14, v15) = v16) | ? [v17] : ? [v18] : (in(v11, v13) = v18 & in(v10, v12) = v17 & ( ~ (v18 = 0) | ~ (v17 = 0)))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (cartesian_product2(v12, v13) = v15) | ~ (ordered_pair(v10, v11) = v14) | ~ (in(v14, v15) = 0) | (in(v11, v13) = 0 & in(v10, v12) = 0)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (relation_restriction(v12, v11) = v13) | ~ (relation_field(v13) = v14) | ~ (in(v10, v14) = 0) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : (relation_field(v12) = v16 & relation(v12) = v15 & in(v10, v16) = v17 & in(v10, v11) = v18 & ( ~ (v15 = 0) | (v18 = 0 & v17 = 0)))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (relation_restriction(v12, v11) = v13) | ~ (in(v10, v13) = v14) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : (cartesian_product2(v11, v11) = v17 & relation(v12) = v15 & in(v10, v17) = v18 & in(v10, v12) = v16 & ( ~ (v15 = 0) | (( ~ (v18 = 0) | ~ (v16 = 0) | v14 = 0) & ( ~ (v14 = 0) | (v18 = 0 & v16 = 0)))))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (element(v13, v12) = v11) | ~ (element(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (relation_restriction(v13, v12) = v11) | ~ (relation_restriction(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 | ~ (ordered_pair(v13, v12) = v11) | ~ (ordered_pair(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (set_intersection2(v13, v12) = v11) | ~ (set_intersection2(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (set_union2(v13, v12) = v11) | ~ (set_union2(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 | ~ (in(v13, v12) = v11) | ~ (in(v13, v12) = v10)) & ! [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] : ? [v14] : (element(v10, v11) = v13 & empty(v11) = v14 & ( ~ (v13 = 0) | v14 = 0))) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (connected(v12) = v11) | ~ (connected(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (relation_field(v12) = v11) | ~ (relation_field(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (relation_dom(v12) = v11) | ~ (relation_dom(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (relation_rng(v12) = v11) | ~ (relation_rng(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (singleton(v12) = v11) | ~ (singleton(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (relation(v12) = v11) | ~ (relation(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (one_to_one(v12) = v11) | ~ (one_to_one(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (empty(v12) = v11) | ~ (empty(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (function(v12) = v11) | ~ (function(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (relation_restriction(v10, v11) = v12) | ~ (relation(v10) = 0) | ? [v13] : (cartesian_product2(v11, v11) = v13 & set_intersection2(v10, v13) = v12)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (relation_restriction(v10, v11) = v12) | ? [v13] : ? [v14] : (relation(v12) = v14 & relation(v10) = v13 & ( ~ (v13 = 0) | v14 = 0))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (cartesian_product2(v11, v11) = v12) | ~ (relation(v10) = 0) | ? [v13] : (relation_restriction(v10, v11) = v13 & set_intersection2(v10, v12) = 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] : ( ~ (set_intersection2(v11, v10) = v12) | set_intersection2(v10, v11) = v12) & ! [v10] : ! [v11] : ! [v12] : ( ~ (set_intersection2(v10, v11) = v12) | set_intersection2(v11, v10) = v12) & ! [v10] : ! [v11] : ! [v12] : ( ~ (set_union2(v11, v10) = v12) | set_union2(v10, v11) = v12) & ! [v10] : ! [v11] : ! [v12] : ( ~ (set_union2(v11, v10) = v12) | ? [v13] : ? [v14] : (empty(v12) = v14 & empty(v10) = v13 & ( ~ (v14 = 0) | v13 = 0))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (set_union2(v10, v11) = v12) | set_union2(v11, v10) = v12) & ! [v10] : ! [v11] : ! [v12] : ( ~ (set_union2(v10, v11) = v12) | ? [v13] : ? [v14] : (empty(v12) = v14 & empty(v10) = v13 & ( ~ (v14 = 0) | v13 = 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] : (ordered_pair(v10, v11) = v13 & singleton(v10) = v14 & unordered_pair(v12, v14) = v13)) & ! [v10] : ! [v11] : (v11 = v10 | ~ (set_intersection2(v10, v10) = v11)) & ! [v10] : ! [v11] : (v11 = v10 | ~ (set_union2(v10, v10) = v11)) & ! [v10] : ! [v11] : (v11 = v10 | ~ (set_union2(v10, empty_set) = v11)) & ! [v10] : ! [v11] : (v11 = v10 | ~ (empty(v11) = 0) | ~ (empty(v10) = 0)) & ! [v10] : ! [v11] : (v11 = empty_set | ~ (set_intersection2(v10, empty_set) = v11)) & ! [v10] : ! [v11] : (v11 = 0 | ~ (function(v10) = v11) | ? [v12] : ( ~ (v12 = 0) & empty(v10) = v12)) & ! [v10] : ! [v11] : ( ~ (connected(v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : (relation_field(v10) = v13 & relation(v10) = v12 & ( ~ (v12 = 0) | (( ~ (v11 = 0) | ( ! [v22] : ! [v23] : ! [v24] : (v23 = v22 | ~ (ordered_pair(v23, v22) = v24) | ? [v25] : ? [v26] : ? [v27] : ? [v28] : ? [v29] : (ordered_pair(v22, v23) = v27 & in(v27, v10) = v28 & in(v24, v10) = v29 & in(v23, v13) = v26 & in(v22, v13) = v25 & ( ~ (v26 = 0) | ~ (v25 = 0) | v29 = 0 | v28 = 0))) & ! [v22] : ! [v23] : ! [v24] : (v23 = v22 | ~ (ordered_pair(v22, v23) = v24) | ? [v25] : ? [v26] : ? [v27] : ? [v28] : ? [v29] : (ordered_pair(v23, v22) = v28 & in(v28, v10) = v29 & in(v24, v10) = v27 & in(v23, v13) = v26 & in(v22, v13) = v25 & ( ~ (v26 = 0) | ~ (v25 = 0) | v29 = 0 | v27 = 0))))) & (v11 = 0 | (v17 = 0 & v16 = 0 & ~ (v21 = 0) & ~ (v19 = 0) & ~ (v15 = v14) & ordered_pair(v15, v14) = v20 & ordered_pair(v14, v15) = v18 & in(v20, v10) = v21 & in(v18, v10) = v19 & in(v15, v13) = 0 & in(v14, v13) = 0)))))) & ! [v10] : ! [v11] : ( ~ (element(v10, v11) = 0) | ? [v12] : ? [v13] : (empty(v11) = v12 & in(v10, v11) = v13 & (v13 = 0 | v12 = 0))) & ! [v10] : ! [v11] : ( ~ (relation_field(v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : (connected(v10) = v13 & relation(v10) = v12 & ( ~ (v12 = 0) | (( ~ (v13 = 0) | ( ! [v22] : ! [v23] : ! [v24] : (v23 = v22 | ~ (ordered_pair(v23, v22) = v24) | ? [v25] : ? [v26] : ? [v27] : ? [v28] : ? [v29] : (ordered_pair(v22, v23) = v27 & in(v27, v10) = v28 & in(v24, v10) = v29 & in(v23, v11) = v26 & in(v22, v11) = v25 & ( ~ (v26 = 0) | ~ (v25 = 0) | v29 = 0 | v28 = 0))) & ! [v22] : ! [v23] : ! [v24] : (v23 = v22 | ~ (ordered_pair(v22, v23) = v24) | ? [v25] : ? [v26] : ? [v27] : ? [v28] : ? [v29] : (ordered_pair(v23, v22) = v28 & in(v28, v10) = v29 & in(v24, v10) = v27 & in(v23, v11) = v26 & in(v22, v11) = v25 & ( ~ (v26 = 0) | ~ (v25 = 0) | v29 = 0 | v27 = 0))))) & (v13 = 0 | (v17 = 0 & v16 = 0 & ~ (v21 = 0) & ~ (v19 = 0) & ~ (v15 = v14) & ordered_pair(v15, v14) = v20 & ordered_pair(v14, v15) = v18 & in(v20, v10) = v21 & in(v18, v10) = v19 & in(v15, v11) = 0 & in(v14, v11) = 0)))))) & ! [v10] : ! [v11] : ( ~ (relation_field(v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : (relation_dom(v10) = v13 & relation_rng(v10) = v14 & set_union2(v13, v14) = v15 & relation(v10) = v12 & ( ~ (v12 = 0) | v15 = v11))) & ! [v10] : ! [v11] : ( ~ (relation_dom(v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : (relation_field(v10) = v13 & relation_rng(v10) = v14 & set_union2(v11, v14) = v15 & relation(v10) = v12 & ( ~ (v12 = 0) | v15 = v13))) & ! [v10] : ! [v11] : ( ~ (relation_rng(v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : (relation_field(v10) = v13 & relation_dom(v10) = v14 & set_union2(v14, v11) = v15 & relation(v10) = v12 & ( ~ (v12 = 0) | v15 = v13))) & ! [v10] : ! [v11] : ( ~ (one_to_one(v10) = v11) | ? [v12] : ? [v13] : ? [v14] : (relation(v10) = v12 & empty(v10) = v13 & function(v10) = v14 & ( ~ (v14 = 0) | ~ (v13 = 0) | ~ (v12 = 0) | 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] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : (connected(v10) = v11 & relation_field(v10) = v12 & ( ~ (v11 = 0) | ( ! [v21] : ! [v22] : ! [v23] : (v22 = v21 | ~ (ordered_pair(v22, v21) = v23) | ? [v24] : ? [v25] : ? [v26] : ? [v27] : ? [v28] : (ordered_pair(v21, v22) = v26 & in(v26, v10) = v27 & in(v23, v10) = v28 & in(v22, v12) = v25 & in(v21, v12) = v24 & ( ~ (v25 = 0) | ~ (v24 = 0) | v28 = 0 | v27 = 0))) & ! [v21] : ! [v22] : ! [v23] : (v22 = v21 | ~ (ordered_pair(v21, v22) = v23) | ? [v24] : ? [v25] : ? [v26] : ? [v27] : ? [v28] : (ordered_pair(v22, v21) = v27 & in(v27, v10) = v28 & in(v23, v10) = v26 & in(v22, v12) = v25 & in(v21, v12) = v24 & ( ~ (v25 = 0) | ~ (v24 = 0) | v28 = 0 | v26 = 0))))) & (v11 = 0 | (v16 = 0 & v15 = 0 & ~ (v20 = 0) & ~ (v18 = 0) & ~ (v14 = v13) & ordered_pair(v14, v13) = v19 & ordered_pair(v13, v14) = v17 & in(v19, v10) = v20 & in(v17, v10) = v18 & in(v14, v12) = 0 & in(v13, v12) = 0)))) & ! [v10] : ( ~ (relation(v10) = 0) | ? [v11] : ? [v12] : ? [v13] : (relation_field(v10) = v11 & relation_dom(v10) = v12 & relation_rng(v10) = v13 & set_union2(v12, v13) = v11)) & ! [v10] : ( ~ (relation(v10) = 0) | ? [v11] : ? [v12] : ? [v13] : (one_to_one(v10) = v13 & empty(v10) = v11 & function(v10) = v12 & ( ~ (v12 = 0) | ~ (v11 = 0) | v13 = 0))) & ! [v10] : ( ~ (empty(v10) = 0) | function(v10) = 0) & ! [v10] : ( ~ (empty(v10) = 0) | ? [v11] : ? [v12] : ? [v13] : (relation(v10) = v11 & one_to_one(v10) = v13 & function(v10) = v12 & ( ~ (v12 = 0) | ~ (v11 = 0) | v13 = 0))) & ! [v10] : ( ~ (function(v10) = 0) | ? [v11] : ? [v12] : ? [v13] : (relation(v10) = v11 & one_to_one(v10) = v13 & empty(v10) = v12 & ( ~ (v12 = 0) | ~ (v11 = 0) | v13 = 0))) & ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : (connected(v10) = v12 & relation_field(v10) = v13 & relation(v10) = v11 & ( ~ (v11 = 0) | (( ~ (v12 = 0) | ? [v22] : ? [v23] : (v23 = v22 | ? [v24] : ? [v25] : ? [v26] : ? [v27] : ? [v28] : ? [v29] : (ordered_pair(v23, v22) = v28 & ordered_pair(v22, v23) = v26 & in(v28, v10) = v29 & in(v26, v10) = v27 & in(v23, v13) = v25 & in(v22, v13) = v24 & ( ~ (v25 = 0) | ~ (v24 = 0) | v29 = 0 | v27 = 0)))) & (v12 = 0 | (v17 = 0 & v16 = 0 & ~ (v21 = 0) & ~ (v19 = 0) & ~ (v15 = v14) & ordered_pair(v15, v14) = v20 & ordered_pair(v14, v15) = v18 & in(v20, v10) = v21 & in(v18, v10) = v19 & in(v15, v13) = 0 & in(v14, v13) = 0))))) & ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : (relation_restriction(v12, v11) = v14 & relation_field(v14) = v15 & relation_field(v12) = v17 & relation(v12) = v13 & in(v10, v17) = v18 & in(v10, v15) = v16 & in(v10, v11) = v19 & ( ~ (v16 = 0) | ~ (v13 = 0) | (v19 = 0 & v18 = 0))) & ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : (cartesian_product2(v12, v13) = v17 & ordered_pair(v10, v11) = v16 & in(v16, v17) = v18 & in(v11, v13) = v15 & in(v10, v12) = v14 & ( ~ (v15 = 0) | ~ (v14 = 0) | v18 = 0)) & ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : (relation_field(v10) = v12 & relation_dom(v10) = v13 & relation_rng(v10) = v14 & set_union2(v13, v14) = v15 & relation(v10) = v11 & ( ~ (v11 = 0) | v15 = v12)) & ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (element(v10, v11) = v12 & empty(v11) = v13 & in(v10, v11) = v14 & ( ~ (v12 = 0) | v14 = 0 | v13 = 0)) & ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (ordered_pair(v10, v11) = v12 & singleton(v10) = v14 & unordered_pair(v13, v14) = v12 & unordered_pair(v10, v11) = v13) & ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (set_union2(v11, v10) = v13 & empty(v13) = v14 & empty(v10) = v12 & ( ~ (v14 = 0) | v12 = 0)) & ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (relation(v10) = v11 & one_to_one(v10) = v14 & empty(v10) = v12 & function(v10) = v13 & ( ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0) | v14 = 0)) & ? [v10] : ? [v11] : ? [v12] : (set_intersection2(v11, v10) = v12 & set_intersection2(v10, v11) = v12) & ? [v10] : ? [v11] : element(v11, v10) = 0)
% 41.77/12.34 | 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:
% 41.77/12.34 | (1) ~ (all_0_3_3 = 0) & ~ (all_0_6_6 = 0) & connected(all_0_7_7) = all_0_6_6 & connected(all_0_8_8) = 0 & relation_restriction(all_0_8_8, all_0_9_9) = all_0_7_7 & relation(all_0_0_0) = 0 & relation(all_0_2_2) = 0 & relation(all_0_5_5) = 0 & relation(all_0_8_8) = 0 & one_to_one(all_0_5_5) = 0 & empty(all_0_1_1) = 0 & empty(all_0_2_2) = 0 & empty(all_0_4_4) = all_0_3_3 & empty(empty_set) = 0 & function(all_0_0_0) = 0 & function(all_0_2_2) = 0 & function(all_0_5_5) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ (in(v4, v5) = v6) | ? [v7] : ? [v8] : (in(v1, v3) = v8 & in(v0, v2) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ (in(v4, v5) = 0) | (in(v1, v3) = 0 & in(v0, v2) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_restriction(v2, v1) = v3) | ~ (relation_field(v3) = v4) | ~ (in(v0, v4) = 0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (relation_field(v2) = v6 & relation(v2) = v5 & in(v0, v6) = v7 & in(v0, v1) = v8 & ( ~ (v5 = 0) | (v8 = 0 & v7 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_restriction(v2, v1) = v3) | ~ (in(v0, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (cartesian_product2(v1, v1) = v7 & relation(v2) = v5 & in(v0, v7) = v8 & in(v0, v2) = v6 & ( ~ (v5 = 0) | (( ~ (v8 = 0) | ~ (v6 = 0) | v4 = 0) & ( ~ (v4 = 0) | (v8 = 0 & v6 = 0)))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_restriction(v3, v2) = v1) | ~ (relation_restriction(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 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [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] : ? [v4] : (element(v0, v1) = v3 & empty(v1) = v4 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (connected(v2) = v1) | ~ (connected(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_field(v2) = v1) | ~ (relation_field(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_restriction(v0, v1) = v2) | ~ (relation(v0) = 0) | ? [v3] : (cartesian_product2(v1, v1) = v3 & set_intersection2(v0, v3) = v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_restriction(v0, v1) = v2) | ? [v3] : ? [v4] : (relation(v2) = v4 & relation(v0) = v3 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (cartesian_product2(v1, v1) = v2) | ~ (relation(v0) = 0) | ? [v3] : (relation_restriction(v0, v1) = v3 & set_intersection2(v0, v2) = 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] : ( ~ (set_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ? [v3] : ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (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] : (ordered_pair(v0, v1) = v3 & singleton(v0) = v4 & unordered_pair(v2, v4) = v3)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)) & ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (function(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2)) & ! [v0] : ! [v1] : ( ~ (connected(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : (relation_field(v0) = v3 & relation(v0) = v2 & ( ~ (v2 = 0) | (( ~ (v1 = 0) | ( ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (ordered_pair(v13, v12) = v14) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : (ordered_pair(v12, v13) = v17 & in(v17, v0) = v18 & in(v14, v0) = v19 & in(v13, v3) = v16 & in(v12, v3) = v15 & ( ~ (v16 = 0) | ~ (v15 = 0) | v19 = 0 | v18 = 0))) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (ordered_pair(v12, v13) = v14) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : (ordered_pair(v13, v12) = v18 & in(v18, v0) = v19 & in(v14, v0) = v17 & in(v13, v3) = v16 & in(v12, v3) = v15 & ( ~ (v16 = 0) | ~ (v15 = 0) | v19 = 0 | v17 = 0))))) & (v1 = 0 | (v7 = 0 & v6 = 0 & ~ (v11 = 0) & ~ (v9 = 0) & ~ (v5 = v4) & ordered_pair(v5, v4) = v10 & ordered_pair(v4, v5) = v8 & in(v10, v0) = v11 & in(v8, v0) = v9 & in(v5, v3) = 0 & in(v4, v3) = 0)))))) & ! [v0] : ! [v1] : ( ~ (element(v0, v1) = 0) | ? [v2] : ? [v3] : (empty(v1) = v2 & in(v0, v1) = v3 & (v3 = 0 | v2 = 0))) & ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : (connected(v0) = v3 & relation(v0) = v2 & ( ~ (v2 = 0) | (( ~ (v3 = 0) | ( ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (ordered_pair(v13, v12) = v14) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : (ordered_pair(v12, v13) = v17 & in(v17, v0) = v18 & in(v14, v0) = v19 & in(v13, v1) = v16 & in(v12, v1) = v15 & ( ~ (v16 = 0) | ~ (v15 = 0) | v19 = 0 | v18 = 0))) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (ordered_pair(v12, v13) = v14) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : (ordered_pair(v13, v12) = v18 & in(v18, v0) = v19 & in(v14, v0) = v17 & in(v13, v1) = v16 & in(v12, v1) = v15 & ( ~ (v16 = 0) | ~ (v15 = 0) | v19 = 0 | v17 = 0))))) & (v3 = 0 | (v7 = 0 & v6 = 0 & ~ (v11 = 0) & ~ (v9 = 0) & ~ (v5 = v4) & ordered_pair(v5, v4) = v10 & ordered_pair(v4, v5) = v8 & in(v10, v0) = v11 & in(v8, v0) = v9 & in(v5, v1) = 0 & in(v4, v1) = 0)))))) & ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_dom(v0) = v3 & relation_rng(v0) = v4 & set_union2(v3, v4) = v5 & relation(v0) = v2 & ( ~ (v2 = 0) | v5 = v1))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_field(v0) = v3 & relation_rng(v0) = v4 & set_union2(v1, v4) = v5 & relation(v0) = v2 & ( ~ (v2 = 0) | v5 = v3))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_field(v0) = v3 & relation_dom(v0) = v4 & set_union2(v4, v1) = v5 & relation(v0) = v2 & ( ~ (v2 = 0) | v5 = v3))) & ! [v0] : ! [v1] : ( ~ (one_to_one(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation(v0) = v2 & empty(v0) = v3 & function(v0) = v4 & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | 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] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (connected(v0) = v1 & relation_field(v0) = v2 & ( ~ (v1 = 0) | ( ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (ordered_pair(v12, v11) = v13) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : (ordered_pair(v11, v12) = v16 & in(v16, v0) = v17 & in(v13, v0) = v18 & in(v12, v2) = v15 & in(v11, v2) = v14 & ( ~ (v15 = 0) | ~ (v14 = 0) | v18 = 0 | v17 = 0))) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (ordered_pair(v11, v12) = v13) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : (ordered_pair(v12, v11) = v17 & in(v17, v0) = v18 & in(v13, v0) = v16 & in(v12, v2) = v15 & in(v11, v2) = v14 & ( ~ (v15 = 0) | ~ (v14 = 0) | v18 = 0 | v16 = 0))))) & (v1 = 0 | (v6 = 0 & v5 = 0 & ~ (v10 = 0) & ~ (v8 = 0) & ~ (v4 = v3) & ordered_pair(v4, v3) = v9 & ordered_pair(v3, v4) = v7 & in(v9, v0) = v10 & in(v7, v0) = v8 & in(v4, v2) = 0 & in(v3, v2) = 0)))) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (relation_field(v0) = v1 & relation_dom(v0) = v2 & relation_rng(v0) = v3 & set_union2(v2, v3) = v1)) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (one_to_one(v0) = v3 & empty(v0) = v1 & function(v0) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0))) & ! [v0] : ( ~ (empty(v0) = 0) | function(v0) = 0) & ! [v0] : ( ~ (empty(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (relation(v0) = v1 & one_to_one(v0) = v3 & function(v0) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0))) & ! [v0] : ( ~ (function(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (relation(v0) = v1 & one_to_one(v0) = v3 & empty(v0) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0))) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : (connected(v0) = v2 & relation_field(v0) = v3 & relation(v0) = v1 & ( ~ (v1 = 0) | (( ~ (v2 = 0) | ? [v12] : ? [v13] : (v13 = v12 | ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : (ordered_pair(v13, v12) = v18 & ordered_pair(v12, v13) = v16 & in(v18, v0) = v19 & in(v16, v0) = v17 & in(v13, v3) = v15 & in(v12, v3) = v14 & ( ~ (v15 = 0) | ~ (v14 = 0) | v19 = 0 | v17 = 0)))) & (v2 = 0 | (v7 = 0 & v6 = 0 & ~ (v11 = 0) & ~ (v9 = 0) & ~ (v5 = v4) & ordered_pair(v5, v4) = v10 & ordered_pair(v4, v5) = v8 & in(v10, v0) = v11 & in(v8, v0) = v9 & in(v5, v3) = 0 & in(v4, v3) = 0))))) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (relation_restriction(v2, v1) = v4 & relation_field(v4) = v5 & relation_field(v2) = v7 & relation(v2) = v3 & in(v0, v7) = v8 & in(v0, v5) = v6 & in(v0, v1) = v9 & ( ~ (v6 = 0) | ~ (v3 = 0) | (v9 = 0 & v8 = 0))) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (cartesian_product2(v2, v3) = v7 & ordered_pair(v0, v1) = v6 & in(v6, v7) = v8 & in(v1, v3) = v5 & in(v0, v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0) | v8 = 0)) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_field(v0) = v2 & relation_dom(v0) = v3 & relation_rng(v0) = v4 & set_union2(v3, v4) = v5 & relation(v0) = v1 & ( ~ (v1 = 0) | v5 = v2)) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (element(v0, v1) = v2 & empty(v1) = v3 & in(v0, v1) = v4 & ( ~ (v2 = 0) | v4 = 0 | v3 = 0)) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (ordered_pair(v0, v1) = v2 & singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (set_union2(v1, v0) = v3 & empty(v3) = v4 & empty(v0) = v2 & ( ~ (v4 = 0) | v2 = 0)) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (relation(v0) = v1 & one_to_one(v0) = v4 & empty(v0) = v2 & function(v0) = v3 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | v4 = 0)) & ? [v0] : ? [v1] : ? [v2] : (set_intersection2(v1, v0) = v2 & set_intersection2(v0, v1) = v2) & ? [v0] : ? [v1] : element(v1, v0) = 0
% 41.77/12.36 |
% 41.77/12.36 | Applying alpha-rule on (1) yields:
% 41.77/12.36 | (2) function(all_0_2_2) = 0
% 41.77/12.36 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ (in(v4, v5) = v6) | ? [v7] : ? [v8] : (in(v1, v3) = v8 & in(v0, v2) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0))))
% 41.77/12.36 | (4) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (connected(v0) = v1 & relation_field(v0) = v2 & ( ~ (v1 = 0) | ( ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (ordered_pair(v12, v11) = v13) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : (ordered_pair(v11, v12) = v16 & in(v16, v0) = v17 & in(v13, v0) = v18 & in(v12, v2) = v15 & in(v11, v2) = v14 & ( ~ (v15 = 0) | ~ (v14 = 0) | v18 = 0 | v17 = 0))) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (ordered_pair(v11, v12) = v13) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : (ordered_pair(v12, v11) = v17 & in(v17, v0) = v18 & in(v13, v0) = v16 & in(v12, v2) = v15 & in(v11, v2) = v14 & ( ~ (v15 = 0) | ~ (v14 = 0) | v18 = 0 | v16 = 0))))) & (v1 = 0 | (v6 = 0 & v5 = 0 & ~ (v10 = 0) & ~ (v8 = 0) & ~ (v4 = v3) & ordered_pair(v4, v3) = v9 & ordered_pair(v3, v4) = v7 & in(v9, v0) = v10 & in(v7, v0) = v8 & in(v4, v2) = 0 & in(v3, v2) = 0))))
% 41.77/12.37 | (5) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_restriction(v0, v1) = v2) | ~ (relation(v0) = 0) | ? [v3] : (cartesian_product2(v1, v1) = v3 & set_intersection2(v0, v3) = v2))
% 41.77/12.37 | (6) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (relation_field(v0) = v1 & relation_dom(v0) = v2 & relation_rng(v0) = v3 & set_union2(v2, v3) = v1))
% 41.77/12.37 | (7) ~ (all_0_3_3 = 0)
% 41.77/12.37 | (8) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_field(v0) = v3 & relation_rng(v0) = v4 & set_union2(v1, v4) = v5 & relation(v0) = v2 & ( ~ (v2 = 0) | v5 = v3)))
% 41.77/12.37 | (9) ! [v0] : ( ~ (function(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (relation(v0) = v1 & one_to_one(v0) = v3 & empty(v0) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0)))
% 41.77/12.37 | (10) ! [v0] : ( ~ (empty(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (relation(v0) = v1 & one_to_one(v0) = v3 & function(v0) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0)))
% 41.77/12.37 | (11) function(all_0_0_0) = 0
% 41.77/12.37 | (12) connected(all_0_8_8) = 0
% 41.77/12.37 | (13) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (connected(v2) = v1) | ~ (connected(v2) = v0))
% 41.77/12.37 | (14) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_field(v0) = v2 & relation_dom(v0) = v3 & relation_rng(v0) = v4 & set_union2(v3, v4) = v5 & relation(v0) = v1 & ( ~ (v1 = 0) | v5 = v2))
% 41.77/12.37 | (15) ~ (all_0_6_6 = 0)
% 41.77/12.37 | (16) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 41.77/12.37 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0))
% 41.77/12.37 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_restriction(v3, v2) = v1) | ~ (relation_restriction(v3, v2) = v0))
% 41.77/12.37 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0))
% 41.77/12.37 | (20) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : (connected(v0) = v2 & relation_field(v0) = v3 & relation(v0) = v1 & ( ~ (v1 = 0) | (( ~ (v2 = 0) | ? [v12] : ? [v13] : (v13 = v12 | ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : (ordered_pair(v13, v12) = v18 & ordered_pair(v12, v13) = v16 & in(v18, v0) = v19 & in(v16, v0) = v17 & in(v13, v3) = v15 & in(v12, v3) = v14 & ( ~ (v15 = 0) | ~ (v14 = 0) | v19 = 0 | v17 = 0)))) & (v2 = 0 | (v7 = 0 & v6 = 0 & ~ (v11 = 0) & ~ (v9 = 0) & ~ (v5 = v4) & ordered_pair(v5, v4) = v10 & ordered_pair(v4, v5) = v8 & in(v10, v0) = v11 & in(v8, v0) = v9 & in(v5, v3) = 0 & in(v4, v3) = 0)))))
% 41.77/12.37 | (21) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (cartesian_product2(v2, v3) = v7 & ordered_pair(v0, v1) = v6 & in(v6, v7) = v8 & in(v1, v3) = v5 & in(v0, v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0) | v8 = 0))
% 41.77/12.37 | (22) empty(all_0_2_2) = 0
% 41.77/12.37 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 41.77/12.37 | (24) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0))
% 41.77/12.37 | (25) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0))
% 41.77/12.37 | (26) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_field(v2) = v1) | ~ (relation_field(v2) = v0))
% 41.77/12.37 | (27) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (set_union2(v1, v0) = v3 & empty(v3) = v4 & empty(v0) = v2 & ( ~ (v4 = 0) | v2 = 0))
% 41.77/12.37 | (28) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1))
% 41.77/12.37 | (29) ! [v0] : ! [v1] : ( ~ (element(v0, v1) = 0) | ? [v2] : ? [v3] : (empty(v1) = v2 & in(v0, v1) = v3 & (v3 = 0 | v2 = 0)))
% 41.77/12.37 | (30) one_to_one(all_0_5_5) = 0
% 41.77/12.37 | (31) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0)))
% 41.77/12.37 | (32) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3))
% 41.77/12.37 | (33) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (one_to_one(v0) = v3 & empty(v0) = v1 & function(v0) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0)))
% 41.77/12.38 | (34) relation(all_0_2_2) = 0
% 41.77/12.38 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 41.77/12.38 | (36) ! [v0] : ! [v1] : ( ~ (one_to_one(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation(v0) = v2 & empty(v0) = v3 & function(v0) = v4 & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | v1 = 0)))
% 41.77/12.38 | (37) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3))
% 41.77/12.38 | (38) ? [v0] : ? [v1] : element(v1, v0) = 0
% 41.77/12.38 | (39) ! [v0] : ! [v1] : ( ~ (connected(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : (relation_field(v0) = v3 & relation(v0) = v2 & ( ~ (v2 = 0) | (( ~ (v1 = 0) | ( ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (ordered_pair(v13, v12) = v14) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : (ordered_pair(v12, v13) = v17 & in(v17, v0) = v18 & in(v14, v0) = v19 & in(v13, v3) = v16 & in(v12, v3) = v15 & ( ~ (v16 = 0) | ~ (v15 = 0) | v19 = 0 | v18 = 0))) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (ordered_pair(v12, v13) = v14) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : (ordered_pair(v13, v12) = v18 & in(v18, v0) = v19 & in(v14, v0) = v17 & in(v13, v3) = v16 & in(v12, v3) = v15 & ( ~ (v16 = 0) | ~ (v15 = 0) | v19 = 0 | v17 = 0))))) & (v1 = 0 | (v7 = 0 & v6 = 0 & ~ (v11 = 0) & ~ (v9 = 0) & ~ (v5 = v4) & ordered_pair(v5, v4) = v10 & ordered_pair(v4, v5) = v8 & in(v10, v0) = v11 & in(v8, v0) = v9 & in(v5, v3) = 0 & in(v4, v3) = 0))))))
% 42.25/12.38 | (40) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 42.25/12.38 | (41) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1))
% 42.25/12.38 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0))
% 42.25/12.38 | (43) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (element(v0, v1) = v2 & empty(v1) = v3 & in(v0, v1) = v4 & ( ~ (v2 = 0) | v4 = 0 | v3 = 0))
% 42.25/12.38 | (44) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (relation(v0) = v1 & one_to_one(v0) = v4 & empty(v0) = v2 & function(v0) = v3 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | v4 = 0))
% 42.25/12.38 | (45) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_field(v0) = v3 & relation_dom(v0) = v4 & set_union2(v4, v1) = v5 & relation(v0) = v2 & ( ~ (v2 = 0) | v5 = v3)))
% 42.25/12.38 | (46) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2)
% 42.25/12.38 | (47) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2)
% 42.25/12.38 | (48) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v0, v1) = v2) | ? [v3] : ? [v4] : (element(v0, v1) = v3 & empty(v1) = v4 & ( ~ (v3 = 0) | v4 = 0)))
% 42.25/12.38 | (49) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0))
% 42.25/12.38 | (50) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0))
% 42.25/12.38 | (51) empty(all_0_1_1) = 0
% 42.25/12.38 | (52) empty(empty_set) = 0
% 42.25/12.38 | (53) ! [v0] : ! [v1] : ! [v2] : ( ~ (cartesian_product2(v1, v1) = v2) | ~ (relation(v0) = 0) | ? [v3] : (relation_restriction(v0, v1) = v3 & set_intersection2(v0, v2) = v3))
% 42.25/12.38 | (54) ? [v0] : ? [v1] : ? [v2] : (set_intersection2(v1, v0) = v2 & set_intersection2(v0, v1) = v2)
% 42.25/12.38 | (55) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0))
% 42.25/12.38 | (56) ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_dom(v0) = v3 & relation_rng(v0) = v4 & set_union2(v3, v4) = v5 & relation(v0) = v2 & ( ~ (v2 = 0) | v5 = v1)))
% 42.25/12.38 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0))
% 42.25/12.38 | (58) ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : (connected(v0) = v3 & relation(v0) = v2 & ( ~ (v2 = 0) | (( ~ (v3 = 0) | ( ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (ordered_pair(v13, v12) = v14) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : (ordered_pair(v12, v13) = v17 & in(v17, v0) = v18 & in(v14, v0) = v19 & in(v13, v1) = v16 & in(v12, v1) = v15 & ( ~ (v16 = 0) | ~ (v15 = 0) | v19 = 0 | v18 = 0))) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (ordered_pair(v12, v13) = v14) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : (ordered_pair(v13, v12) = v18 & in(v18, v0) = v19 & in(v14, v0) = v17 & in(v13, v1) = v16 & in(v12, v1) = v15 & ( ~ (v16 = 0) | ~ (v15 = 0) | v19 = 0 | v17 = 0))))) & (v3 = 0 | (v7 = 0 & v6 = 0 & ~ (v11 = 0) & ~ (v9 = 0) & ~ (v5 = v4) & ordered_pair(v5, v4) = v10 & ordered_pair(v4, v5) = v8 & in(v10, v0) = v11 & in(v8, v0) = v9 & in(v5, v1) = 0 & in(v4, v1) = 0))))))
% 42.25/12.39 | (59) relation_restriction(all_0_8_8, all_0_9_9) = all_0_7_7
% 42.25/12.39 | (60) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0))
% 42.25/12.39 | (61) ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2))
% 42.25/12.39 | (62) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2)
% 42.25/12.39 | (63) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2)
% 42.25/12.39 | (64) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3))
% 42.25/12.39 | (65) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (relation_restriction(v2, v1) = v4 & relation_field(v4) = v5 & relation_field(v2) = v7 & relation(v2) = v3 & in(v0, v7) = v8 & in(v0, v5) = v6 & in(v0, v1) = v9 & ( ~ (v6 = 0) | ~ (v3 = 0) | (v9 = 0 & v8 = 0)))
% 42.25/12.39 | (66) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1))
% 42.25/12.39 | (67) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 42.25/12.39 | (68) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2)
% 42.25/12.39 | (69) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2)
% 42.25/12.39 | (70) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ? [v3] : ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0)))
% 42.25/12.39 | (71) connected(all_0_7_7) = all_0_6_6
% 42.25/12.39 | (72) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (ordered_pair(v0, v1) = v2 & singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3)
% 42.25/12.39 | (73) ! [v0] : ( ~ (empty(v0) = 0) | function(v0) = 0)
% 42.25/12.39 | (74) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_restriction(v0, v1) = v2) | ? [v3] : ? [v4] : (relation(v2) = v4 & relation(v0) = v3 & ( ~ (v3 = 0) | v4 = 0)))
% 42.25/12.39 | (75) relation(all_0_0_0) = 0
% 42.25/12.39 | (76) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ (in(v4, v5) = 0) | (in(v1, v3) = 0 & in(v0, v2) = 0))
% 42.25/12.39 | (77) relation(all_0_5_5) = 0
% 42.25/12.39 | (78) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (ordered_pair(v0, v1) = v3 & singleton(v0) = v4 & unordered_pair(v2, v4) = v3))
% 42.25/12.39 | (79) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_restriction(v2, v1) = v3) | ~ (in(v0, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (cartesian_product2(v1, v1) = v7 & relation(v2) = v5 & in(v0, v7) = v8 & in(v0, v2) = v6 & ( ~ (v5 = 0) | (( ~ (v8 = 0) | ~ (v6 = 0) | v4 = 0) & ( ~ (v4 = 0) | (v8 = 0 & v6 = 0))))))
% 42.25/12.39 | (80) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 42.25/12.39 | (81) empty(all_0_4_4) = all_0_3_3
% 42.25/12.39 | (82) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1))
% 42.25/12.39 | (83) relation(all_0_8_8) = 0
% 42.25/12.39 | (84) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | element(v0, v1) = 0)
% 42.25/12.39 | (85) ! [v0] : ! [v1] : (v1 = 0 | ~ (function(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2))
% 42.25/12.39 | (86) function(all_0_5_5) = 0
% 42.25/12.39 | (87) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_restriction(v2, v1) = v3) | ~ (relation_field(v3) = v4) | ~ (in(v0, v4) = 0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (relation_field(v2) = v6 & relation(v2) = v5 & in(v0, v6) = v7 & in(v0, v1) = v8 & ( ~ (v5 = 0) | (v8 = 0 & v7 = 0))))
% 42.25/12.39 | (88) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0))
% 42.25/12.39 | (89) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0))
% 42.25/12.39 |
% 42.25/12.39 | Instantiating formula (39) with all_0_6_6, all_0_7_7 and discharging atoms connected(all_0_7_7) = all_0_6_6, yields:
% 42.25/12.39 | (90) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (relation_field(all_0_7_7) = v1 & relation(all_0_7_7) = v0 & ( ~ (v0 = 0) | (( ~ (all_0_6_6 = 0) | ( ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (ordered_pair(v11, v10) = v12) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : (ordered_pair(v10, v11) = v15 & in(v15, all_0_7_7) = v16 & in(v12, all_0_7_7) = v17 & in(v11, v1) = v14 & in(v10, v1) = v13 & ( ~ (v14 = 0) | ~ (v13 = 0) | v17 = 0 | v16 = 0))) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (ordered_pair(v10, v11) = v12) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : (ordered_pair(v11, v10) = v16 & in(v16, all_0_7_7) = v17 & in(v12, all_0_7_7) = v15 & in(v11, v1) = v14 & in(v10, v1) = v13 & ( ~ (v14 = 0) | ~ (v13 = 0) | v17 = 0 | v15 = 0))))) & (all_0_6_6 = 0 | (v5 = 0 & v4 = 0 & ~ (v9 = 0) & ~ (v7 = 0) & ~ (v3 = v2) & ordered_pair(v3, v2) = v8 & ordered_pair(v2, v3) = v6 & in(v8, all_0_7_7) = v9 & in(v6, all_0_7_7) = v7 & in(v3, v1) = 0 & in(v2, v1) = 0)))))
% 42.34/12.40 |
% 42.34/12.40 | Instantiating formula (39) with 0, all_0_8_8 and discharging atoms connected(all_0_8_8) = 0, yields:
% 42.34/12.40 | (91) ? [v0] : ? [v1] : (relation_field(all_0_8_8) = v1 & relation(all_0_8_8) = v0 & ( ~ (v0 = 0) | ( ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (ordered_pair(v3, v2) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (ordered_pair(v2, v3) = v7 & in(v7, all_0_8_8) = v8 & in(v4, all_0_8_8) = v9 & in(v3, v1) = v6 & in(v2, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | v9 = 0 | v8 = 0))) & ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (ordered_pair(v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (ordered_pair(v3, v2) = v8 & in(v8, all_0_8_8) = v9 & in(v4, all_0_8_8) = v7 & in(v3, v1) = v6 & in(v2, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | v9 = 0 | v7 = 0))))))
% 42.34/12.40 |
% 42.34/12.40 | Instantiating formula (74) with all_0_7_7, all_0_9_9, all_0_8_8 and discharging atoms relation_restriction(all_0_8_8, all_0_9_9) = all_0_7_7, yields:
% 42.34/12.40 | (92) ? [v0] : ? [v1] : (relation(all_0_7_7) = v1 & relation(all_0_8_8) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 42.34/12.40 |
% 42.34/12.40 | Instantiating formula (5) with all_0_7_7, all_0_9_9, all_0_8_8 and discharging atoms relation_restriction(all_0_8_8, all_0_9_9) = all_0_7_7, relation(all_0_8_8) = 0, yields:
% 42.34/12.40 | (93) ? [v0] : (cartesian_product2(all_0_9_9, all_0_9_9) = v0 & set_intersection2(all_0_8_8, v0) = all_0_7_7)
% 42.34/12.40 |
% 42.34/12.40 | Instantiating formula (4) with all_0_8_8 and discharging atoms relation(all_0_8_8) = 0, yields:
% 42.34/12.40 | (94) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (connected(all_0_8_8) = v0 & relation_field(all_0_8_8) = v1 & ( ~ (v0 = 0) | ( ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (ordered_pair(v11, v10) = v12) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : (ordered_pair(v10, v11) = v15 & in(v15, all_0_8_8) = v16 & in(v12, all_0_8_8) = v17 & in(v11, v1) = v14 & in(v10, v1) = v13 & ( ~ (v14 = 0) | ~ (v13 = 0) | v17 = 0 | v16 = 0))) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (ordered_pair(v10, v11) = v12) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : (ordered_pair(v11, v10) = v16 & in(v16, all_0_8_8) = v17 & in(v12, all_0_8_8) = v15 & in(v11, v1) = v14 & in(v10, v1) = v13 & ( ~ (v14 = 0) | ~ (v13 = 0) | v17 = 0 | v15 = 0))))) & (v0 = 0 | (v5 = 0 & v4 = 0 & ~ (v9 = 0) & ~ (v7 = 0) & ~ (v3 = v2) & ordered_pair(v3, v2) = v8 & ordered_pair(v2, v3) = v6 & in(v8, all_0_8_8) = v9 & in(v6, all_0_8_8) = v7 & in(v3, v1) = 0 & in(v2, v1) = 0)))
% 42.34/12.40 |
% 42.34/12.40 | Instantiating formula (6) with all_0_8_8 and discharging atoms relation(all_0_8_8) = 0, yields:
% 42.34/12.40 | (95) ? [v0] : ? [v1] : ? [v2] : (relation_field(all_0_8_8) = v0 & relation_dom(all_0_8_8) = v1 & relation_rng(all_0_8_8) = v2 & set_union2(v1, v2) = v0)
% 42.34/12.40 |
% 42.34/12.40 | Instantiating formula (33) with all_0_8_8 and discharging atoms relation(all_0_8_8) = 0, yields:
% 42.34/12.40 | (96) ? [v0] : ? [v1] : ? [v2] : (one_to_one(all_0_8_8) = v2 & empty(all_0_8_8) = v0 & function(all_0_8_8) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 42.34/12.40 |
% 42.34/12.40 | Instantiating (95) with all_35_0_82, all_35_1_83, all_35_2_84 yields:
% 42.34/12.40 | (97) relation_field(all_0_8_8) = all_35_2_84 & relation_dom(all_0_8_8) = all_35_1_83 & relation_rng(all_0_8_8) = all_35_0_82 & set_union2(all_35_1_83, all_35_0_82) = all_35_2_84
% 42.34/12.40 |
% 42.34/12.40 | Applying alpha-rule on (97) yields:
% 42.34/12.40 | (98) relation_field(all_0_8_8) = all_35_2_84
% 42.34/12.40 | (99) relation_dom(all_0_8_8) = all_35_1_83
% 42.34/12.40 | (100) relation_rng(all_0_8_8) = all_35_0_82
% 42.34/12.40 | (101) set_union2(all_35_1_83, all_35_0_82) = all_35_2_84
% 42.34/12.40 |
% 42.34/12.40 | Instantiating (94) with all_37_0_85, all_37_1_86, all_37_2_87, all_37_3_88, all_37_4_89, all_37_5_90, all_37_6_91, all_37_7_92, all_37_8_93, all_37_9_94 yields:
% 42.34/12.40 | (102) connected(all_0_8_8) = all_37_9_94 & relation_field(all_0_8_8) = all_37_8_93 & ( ~ (all_37_9_94 = 0) | ( ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ordered_pair(v1, v0) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (ordered_pair(v0, v1) = v5 & in(v5, all_0_8_8) = v6 & in(v2, all_0_8_8) = v7 & in(v1, all_37_8_93) = v4 & in(v0, all_37_8_93) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v7 = 0 | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (ordered_pair(v1, v0) = v6 & in(v6, all_0_8_8) = v7 & in(v2, all_0_8_8) = v5 & in(v1, all_37_8_93) = v4 & in(v0, all_37_8_93) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v7 = 0 | v5 = 0))))) & (all_37_9_94 = 0 | (all_37_4_89 = 0 & all_37_5_90 = 0 & ~ (all_37_0_85 = 0) & ~ (all_37_2_87 = 0) & ~ (all_37_6_91 = all_37_7_92) & ordered_pair(all_37_6_91, all_37_7_92) = all_37_1_86 & ordered_pair(all_37_7_92, all_37_6_91) = all_37_3_88 & in(all_37_1_86, all_0_8_8) = all_37_0_85 & in(all_37_3_88, all_0_8_8) = all_37_2_87 & in(all_37_6_91, all_37_8_93) = 0 & in(all_37_7_92, all_37_8_93) = 0))
% 42.34/12.40 |
% 42.34/12.40 | Applying alpha-rule on (102) yields:
% 42.34/12.40 | (103) connected(all_0_8_8) = all_37_9_94
% 42.34/12.40 | (104) relation_field(all_0_8_8) = all_37_8_93
% 42.34/12.40 | (105) ~ (all_37_9_94 = 0) | ( ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ordered_pair(v1, v0) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (ordered_pair(v0, v1) = v5 & in(v5, all_0_8_8) = v6 & in(v2, all_0_8_8) = v7 & in(v1, all_37_8_93) = v4 & in(v0, all_37_8_93) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v7 = 0 | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (ordered_pair(v1, v0) = v6 & in(v6, all_0_8_8) = v7 & in(v2, all_0_8_8) = v5 & in(v1, all_37_8_93) = v4 & in(v0, all_37_8_93) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v7 = 0 | v5 = 0))))
% 42.34/12.41 | (106) all_37_9_94 = 0 | (all_37_4_89 = 0 & all_37_5_90 = 0 & ~ (all_37_0_85 = 0) & ~ (all_37_2_87 = 0) & ~ (all_37_6_91 = all_37_7_92) & ordered_pair(all_37_6_91, all_37_7_92) = all_37_1_86 & ordered_pair(all_37_7_92, all_37_6_91) = all_37_3_88 & in(all_37_1_86, all_0_8_8) = all_37_0_85 & in(all_37_3_88, all_0_8_8) = all_37_2_87 & in(all_37_6_91, all_37_8_93) = 0 & in(all_37_7_92, all_37_8_93) = 0)
% 42.34/12.41 |
% 42.34/12.41 | Instantiating (96) with all_39_0_95, all_39_1_96, all_39_2_97 yields:
% 42.34/12.41 | (107) one_to_one(all_0_8_8) = all_39_0_95 & empty(all_0_8_8) = all_39_2_97 & function(all_0_8_8) = all_39_1_96 & ( ~ (all_39_1_96 = 0) | ~ (all_39_2_97 = 0) | all_39_0_95 = 0)
% 42.34/12.41 |
% 42.34/12.41 | Applying alpha-rule on (107) yields:
% 42.34/12.41 | (108) one_to_one(all_0_8_8) = all_39_0_95
% 42.34/12.41 | (109) empty(all_0_8_8) = all_39_2_97
% 42.34/12.41 | (110) function(all_0_8_8) = all_39_1_96
% 42.34/12.41 | (111) ~ (all_39_1_96 = 0) | ~ (all_39_2_97 = 0) | all_39_0_95 = 0
% 42.34/12.41 |
% 42.34/12.41 | Instantiating (93) with all_45_0_103 yields:
% 42.34/12.41 | (112) cartesian_product2(all_0_9_9, all_0_9_9) = all_45_0_103 & set_intersection2(all_0_8_8, all_45_0_103) = all_0_7_7
% 42.34/12.41 |
% 42.34/12.41 | Applying alpha-rule on (112) yields:
% 42.34/12.41 | (113) cartesian_product2(all_0_9_9, all_0_9_9) = all_45_0_103
% 42.34/12.41 | (114) set_intersection2(all_0_8_8, all_45_0_103) = all_0_7_7
% 42.34/12.41 |
% 42.34/12.41 | Instantiating (92) with all_55_0_121, all_55_1_122 yields:
% 42.34/12.41 | (115) relation(all_0_7_7) = all_55_0_121 & relation(all_0_8_8) = all_55_1_122 & ( ~ (all_55_1_122 = 0) | all_55_0_121 = 0)
% 42.34/12.41 |
% 42.34/12.41 | Applying alpha-rule on (115) yields:
% 42.34/12.41 | (116) relation(all_0_7_7) = all_55_0_121
% 42.34/12.41 | (117) relation(all_0_8_8) = all_55_1_122
% 42.34/12.41 | (118) ~ (all_55_1_122 = 0) | all_55_0_121 = 0
% 42.34/12.41 |
% 42.34/12.41 | Instantiating (91) with all_57_0_123, all_57_1_124 yields:
% 42.34/12.41 | (119) relation_field(all_0_8_8) = all_57_0_123 & relation(all_0_8_8) = all_57_1_124 & ( ~ (all_57_1_124 = 0) | ( ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ordered_pair(v1, v0) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (ordered_pair(v0, v1) = v5 & in(v5, all_0_8_8) = v6 & in(v2, all_0_8_8) = v7 & in(v1, all_57_0_123) = v4 & in(v0, all_57_0_123) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v7 = 0 | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (ordered_pair(v1, v0) = v6 & in(v6, all_0_8_8) = v7 & in(v2, all_0_8_8) = v5 & in(v1, all_57_0_123) = v4 & in(v0, all_57_0_123) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v7 = 0 | v5 = 0)))))
% 42.34/12.41 |
% 42.34/12.41 | Applying alpha-rule on (119) yields:
% 42.34/12.41 | (120) relation_field(all_0_8_8) = all_57_0_123
% 42.34/12.41 | (121) relation(all_0_8_8) = all_57_1_124
% 42.34/12.41 | (122) ~ (all_57_1_124 = 0) | ( ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ordered_pair(v1, v0) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (ordered_pair(v0, v1) = v5 & in(v5, all_0_8_8) = v6 & in(v2, all_0_8_8) = v7 & in(v1, all_57_0_123) = v4 & in(v0, all_57_0_123) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v7 = 0 | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (ordered_pair(v1, v0) = v6 & in(v6, all_0_8_8) = v7 & in(v2, all_0_8_8) = v5 & in(v1, all_57_0_123) = v4 & in(v0, all_57_0_123) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v7 = 0 | v5 = 0))))
% 42.34/12.41 |
% 42.34/12.41 | Instantiating (90) with all_61_0_128, all_61_1_129, all_61_2_130, all_61_3_131, all_61_4_132, all_61_5_133, all_61_6_134, all_61_7_135, all_61_8_136, all_61_9_137 yields:
% 42.34/12.41 | (123) relation_field(all_0_7_7) = all_61_8_136 & relation(all_0_7_7) = all_61_9_137 & ( ~ (all_61_9_137 = 0) | (( ~ (all_0_6_6 = 0) | ( ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ordered_pair(v1, v0) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (ordered_pair(v0, v1) = v5 & in(v5, all_0_7_7) = v6 & in(v2, all_0_7_7) = v7 & in(v1, all_61_8_136) = v4 & in(v0, all_61_8_136) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v7 = 0 | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (ordered_pair(v1, v0) = v6 & in(v6, all_0_7_7) = v7 & in(v2, all_0_7_7) = v5 & in(v1, all_61_8_136) = v4 & in(v0, all_61_8_136) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v7 = 0 | v5 = 0))))) & (all_0_6_6 = 0 | (all_61_4_132 = 0 & all_61_5_133 = 0 & ~ (all_61_0_128 = 0) & ~ (all_61_2_130 = 0) & ~ (all_61_6_134 = all_61_7_135) & ordered_pair(all_61_6_134, all_61_7_135) = all_61_1_129 & ordered_pair(all_61_7_135, all_61_6_134) = all_61_3_131 & in(all_61_1_129, all_0_7_7) = all_61_0_128 & in(all_61_3_131, all_0_7_7) = all_61_2_130 & in(all_61_6_134, all_61_8_136) = 0 & in(all_61_7_135, all_61_8_136) = 0))))
% 42.34/12.41 |
% 42.34/12.41 | Applying alpha-rule on (123) yields:
% 42.34/12.41 | (124) relation_field(all_0_7_7) = all_61_8_136
% 42.34/12.41 | (125) relation(all_0_7_7) = all_61_9_137
% 42.34/12.41 | (126) ~ (all_61_9_137 = 0) | (( ~ (all_0_6_6 = 0) | ( ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ordered_pair(v1, v0) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (ordered_pair(v0, v1) = v5 & in(v5, all_0_7_7) = v6 & in(v2, all_0_7_7) = v7 & in(v1, all_61_8_136) = v4 & in(v0, all_61_8_136) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v7 = 0 | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (ordered_pair(v1, v0) = v6 & in(v6, all_0_7_7) = v7 & in(v2, all_0_7_7) = v5 & in(v1, all_61_8_136) = v4 & in(v0, all_61_8_136) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v7 = 0 | v5 = 0))))) & (all_0_6_6 = 0 | (all_61_4_132 = 0 & all_61_5_133 = 0 & ~ (all_61_0_128 = 0) & ~ (all_61_2_130 = 0) & ~ (all_61_6_134 = all_61_7_135) & ordered_pair(all_61_6_134, all_61_7_135) = all_61_1_129 & ordered_pair(all_61_7_135, all_61_6_134) = all_61_3_131 & in(all_61_1_129, all_0_7_7) = all_61_0_128 & in(all_61_3_131, all_0_7_7) = all_61_2_130 & in(all_61_6_134, all_61_8_136) = 0 & in(all_61_7_135, all_61_8_136) = 0)))
% 42.43/12.42 |
% 42.43/12.42 | Instantiating formula (13) with all_0_8_8, all_37_9_94, 0 and discharging atoms connected(all_0_8_8) = all_37_9_94, connected(all_0_8_8) = 0, yields:
% 42.43/12.42 | (127) all_37_9_94 = 0
% 42.43/12.42 |
% 42.43/12.42 | Instantiating formula (26) with all_0_8_8, all_37_8_93, all_57_0_123 and discharging atoms relation_field(all_0_8_8) = all_57_0_123, relation_field(all_0_8_8) = all_37_8_93, yields:
% 42.43/12.42 | (128) all_57_0_123 = all_37_8_93
% 42.43/12.42 |
% 42.43/12.42 | Instantiating formula (26) with all_0_8_8, all_35_2_84, all_57_0_123 and discharging atoms relation_field(all_0_8_8) = all_57_0_123, relation_field(all_0_8_8) = all_35_2_84, yields:
% 42.43/12.42 | (129) all_57_0_123 = all_35_2_84
% 42.43/12.42 |
% 42.43/12.42 | Instantiating formula (88) with all_0_7_7, all_55_0_121, all_61_9_137 and discharging atoms relation(all_0_7_7) = all_61_9_137, relation(all_0_7_7) = all_55_0_121, yields:
% 42.43/12.42 | (130) all_61_9_137 = all_55_0_121
% 42.43/12.42 |
% 42.43/12.42 | Instantiating formula (88) with all_0_8_8, all_57_1_124, 0 and discharging atoms relation(all_0_8_8) = all_57_1_124, relation(all_0_8_8) = 0, yields:
% 42.43/12.42 | (131) all_57_1_124 = 0
% 42.43/12.42 |
% 42.43/12.42 | Instantiating formula (88) with all_0_8_8, all_55_1_122, all_57_1_124 and discharging atoms relation(all_0_8_8) = all_57_1_124, relation(all_0_8_8) = all_55_1_122, yields:
% 42.43/12.42 | (132) all_57_1_124 = all_55_1_122
% 42.43/12.42 |
% 42.43/12.42 | Combining equations (129,128) yields a new equation:
% 42.43/12.42 | (133) all_37_8_93 = all_35_2_84
% 42.43/12.42 |
% 42.43/12.42 | Combining equations (131,132) yields a new equation:
% 42.43/12.42 | (134) all_55_1_122 = 0
% 42.43/12.42 |
% 42.43/12.42 | Combining equations (134,132) yields a new equation:
% 42.43/12.42 | (131) all_57_1_124 = 0
% 42.43/12.42 |
% 42.43/12.42 | Combining equations (133,128) yields a new equation:
% 42.43/12.42 | (129) all_57_0_123 = all_35_2_84
% 42.43/12.42 |
% 42.43/12.42 | From (133) and (104) follows:
% 42.43/12.42 | (98) relation_field(all_0_8_8) = all_35_2_84
% 42.43/12.42 |
% 42.43/12.42 | From (134) and (117) follows:
% 42.43/12.42 | (83) relation(all_0_8_8) = 0
% 42.43/12.42 |
% 42.43/12.42 +-Applying beta-rule and splitting (118), into two cases.
% 42.43/12.42 |-Branch one:
% 42.43/12.42 | (139) ~ (all_55_1_122 = 0)
% 42.43/12.42 |
% 42.43/12.42 | Equations (134) can reduce 139 to:
% 42.43/12.42 | (140) $false
% 42.43/12.42 |
% 42.43/12.42 |-The branch is then unsatisfiable
% 42.43/12.42 |-Branch two:
% 42.43/12.42 | (134) all_55_1_122 = 0
% 42.43/12.42 | (142) all_55_0_121 = 0
% 42.43/12.42 |
% 42.43/12.42 | Combining equations (142,130) yields a new equation:
% 42.43/12.42 | (143) all_61_9_137 = 0
% 42.43/12.42 |
% 42.43/12.42 +-Applying beta-rule and splitting (126), into two cases.
% 42.43/12.42 |-Branch one:
% 42.43/12.42 | (144) ~ (all_61_9_137 = 0)
% 42.43/12.42 |
% 42.43/12.42 | Equations (143) can reduce 144 to:
% 42.43/12.42 | (140) $false
% 42.43/12.42 |
% 42.43/12.42 |-The branch is then unsatisfiable
% 42.43/12.42 |-Branch two:
% 42.43/12.42 | (143) all_61_9_137 = 0
% 42.43/12.42 | (147) ( ~ (all_0_6_6 = 0) | ( ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ordered_pair(v1, v0) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (ordered_pair(v0, v1) = v5 & in(v5, all_0_7_7) = v6 & in(v2, all_0_7_7) = v7 & in(v1, all_61_8_136) = v4 & in(v0, all_61_8_136) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v7 = 0 | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (ordered_pair(v1, v0) = v6 & in(v6, all_0_7_7) = v7 & in(v2, all_0_7_7) = v5 & in(v1, all_61_8_136) = v4 & in(v0, all_61_8_136) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v7 = 0 | v5 = 0))))) & (all_0_6_6 = 0 | (all_61_4_132 = 0 & all_61_5_133 = 0 & ~ (all_61_0_128 = 0) & ~ (all_61_2_130 = 0) & ~ (all_61_6_134 = all_61_7_135) & ordered_pair(all_61_6_134, all_61_7_135) = all_61_1_129 & ordered_pair(all_61_7_135, all_61_6_134) = all_61_3_131 & in(all_61_1_129, all_0_7_7) = all_61_0_128 & in(all_61_3_131, all_0_7_7) = all_61_2_130 & in(all_61_6_134, all_61_8_136) = 0 & in(all_61_7_135, all_61_8_136) = 0))
% 42.43/12.42 |
% 42.43/12.42 | Applying alpha-rule on (147) yields:
% 42.43/12.42 | (148) ~ (all_0_6_6 = 0) | ( ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ordered_pair(v1, v0) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (ordered_pair(v0, v1) = v5 & in(v5, all_0_7_7) = v6 & in(v2, all_0_7_7) = v7 & in(v1, all_61_8_136) = v4 & in(v0, all_61_8_136) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v7 = 0 | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (ordered_pair(v1, v0) = v6 & in(v6, all_0_7_7) = v7 & in(v2, all_0_7_7) = v5 & in(v1, all_61_8_136) = v4 & in(v0, all_61_8_136) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v7 = 0 | v5 = 0))))
% 42.43/12.42 | (149) all_0_6_6 = 0 | (all_61_4_132 = 0 & all_61_5_133 = 0 & ~ (all_61_0_128 = 0) & ~ (all_61_2_130 = 0) & ~ (all_61_6_134 = all_61_7_135) & ordered_pair(all_61_6_134, all_61_7_135) = all_61_1_129 & ordered_pair(all_61_7_135, all_61_6_134) = all_61_3_131 & in(all_61_1_129, all_0_7_7) = all_61_0_128 & in(all_61_3_131, all_0_7_7) = all_61_2_130 & in(all_61_6_134, all_61_8_136) = 0 & in(all_61_7_135, all_61_8_136) = 0)
% 42.43/12.42 |
% 42.43/12.42 +-Applying beta-rule and splitting (122), into two cases.
% 42.43/12.42 |-Branch one:
% 42.43/12.42 | (150) ~ (all_57_1_124 = 0)
% 42.43/12.42 |
% 42.43/12.42 | Equations (131) can reduce 150 to:
% 42.43/12.42 | (140) $false
% 42.43/12.42 |
% 42.43/12.42 |-The branch is then unsatisfiable
% 42.43/12.42 |-Branch two:
% 42.43/12.42 | (131) all_57_1_124 = 0
% 42.43/12.42 | (153) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ordered_pair(v1, v0) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (ordered_pair(v0, v1) = v5 & in(v5, all_0_8_8) = v6 & in(v2, all_0_8_8) = v7 & in(v1, all_57_0_123) = v4 & in(v0, all_57_0_123) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v7 = 0 | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (ordered_pair(v1, v0) = v6 & in(v6, all_0_8_8) = v7 & in(v2, all_0_8_8) = v5 & in(v1, all_57_0_123) = v4 & in(v0, all_57_0_123) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v7 = 0 | v5 = 0)))
% 42.43/12.43 |
% 42.43/12.43 | Applying alpha-rule on (153) yields:
% 42.43/12.43 | (154) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ordered_pair(v1, v0) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (ordered_pair(v0, v1) = v5 & in(v5, all_0_8_8) = v6 & in(v2, all_0_8_8) = v7 & in(v1, all_57_0_123) = v4 & in(v0, all_57_0_123) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v7 = 0 | v6 = 0)))
% 42.43/12.43 | (155) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (ordered_pair(v1, v0) = v6 & in(v6, all_0_8_8) = v7 & in(v2, all_0_8_8) = v5 & in(v1, all_57_0_123) = v4 & in(v0, all_57_0_123) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v7 = 0 | v5 = 0)))
% 42.43/12.43 |
% 42.43/12.43 +-Applying beta-rule and splitting (149), into two cases.
% 42.43/12.43 |-Branch one:
% 42.43/12.43 | (156) all_0_6_6 = 0
% 42.43/12.43 |
% 42.43/12.43 | Equations (156) can reduce 15 to:
% 42.43/12.43 | (140) $false
% 42.43/12.43 |
% 42.43/12.43 |-The branch is then unsatisfiable
% 42.43/12.43 |-Branch two:
% 42.43/12.43 | (15) ~ (all_0_6_6 = 0)
% 42.43/12.43 | (159) all_61_4_132 = 0 & all_61_5_133 = 0 & ~ (all_61_0_128 = 0) & ~ (all_61_2_130 = 0) & ~ (all_61_6_134 = all_61_7_135) & ordered_pair(all_61_6_134, all_61_7_135) = all_61_1_129 & ordered_pair(all_61_7_135, all_61_6_134) = all_61_3_131 & in(all_61_1_129, all_0_7_7) = all_61_0_128 & in(all_61_3_131, all_0_7_7) = all_61_2_130 & in(all_61_6_134, all_61_8_136) = 0 & in(all_61_7_135, all_61_8_136) = 0
% 42.43/12.43 |
% 42.43/12.43 | Applying alpha-rule on (159) yields:
% 42.43/12.43 | (160) in(all_61_7_135, all_61_8_136) = 0
% 42.43/12.43 | (161) ~ (all_61_2_130 = 0)
% 42.43/12.43 | (162) all_61_4_132 = 0
% 42.43/12.43 | (163) in(all_61_6_134, all_61_8_136) = 0
% 42.43/12.43 | (164) ordered_pair(all_61_6_134, all_61_7_135) = all_61_1_129
% 42.43/12.43 | (165) in(all_61_3_131, all_0_7_7) = all_61_2_130
% 42.43/12.43 | (166) ~ (all_61_0_128 = 0)
% 42.43/12.43 | (167) ~ (all_61_6_134 = all_61_7_135)
% 42.43/12.43 | (168) ordered_pair(all_61_7_135, all_61_6_134) = all_61_3_131
% 42.43/12.43 | (169) all_61_5_133 = 0
% 42.43/12.43 | (170) in(all_61_1_129, all_0_7_7) = all_61_0_128
% 42.43/12.43 |
% 42.43/12.43 +-Applying beta-rule and splitting (105), into two cases.
% 42.43/12.43 |-Branch one:
% 42.43/12.43 | (171) ~ (all_37_9_94 = 0)
% 42.43/12.43 |
% 42.43/12.43 | Equations (127) can reduce 171 to:
% 42.43/12.43 | (140) $false
% 42.43/12.43 |
% 42.43/12.43 |-The branch is then unsatisfiable
% 42.43/12.43 |-Branch two:
% 42.43/12.43 | (127) all_37_9_94 = 0
% 42.43/12.43 | (174) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ordered_pair(v1, v0) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (ordered_pair(v0, v1) = v5 & in(v5, all_0_8_8) = v6 & in(v2, all_0_8_8) = v7 & in(v1, all_37_8_93) = v4 & in(v0, all_37_8_93) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v7 = 0 | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (ordered_pair(v1, v0) = v6 & in(v6, all_0_8_8) = v7 & in(v2, all_0_8_8) = v5 & in(v1, all_37_8_93) = v4 & in(v0, all_37_8_93) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v7 = 0 | v5 = 0)))
% 42.43/12.43 |
% 42.43/12.43 | Applying alpha-rule on (174) yields:
% 42.43/12.43 | (175) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ordered_pair(v1, v0) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (ordered_pair(v0, v1) = v5 & in(v5, all_0_8_8) = v6 & in(v2, all_0_8_8) = v7 & in(v1, all_37_8_93) = v4 & in(v0, all_37_8_93) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v7 = 0 | v6 = 0)))
% 42.43/12.43 | (176) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (ordered_pair(v1, v0) = v6 & in(v6, all_0_8_8) = v7 & in(v2, all_0_8_8) = v5 & in(v1, all_37_8_93) = v4 & in(v0, all_37_8_93) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v7 = 0 | v5 = 0)))
% 42.43/12.43 |
% 42.43/12.43 | Instantiating formula (58) with all_35_2_84, all_0_8_8 and discharging atoms relation_field(all_0_8_8) = all_35_2_84, yields:
% 42.43/12.43 | (177) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (connected(all_0_8_8) = v1 & relation(all_0_8_8) = v0 & ( ~ (v0 = 0) | (( ~ (v1 = 0) | ( ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (ordered_pair(v11, v10) = v12) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : (ordered_pair(v10, v11) = v15 & in(v15, all_0_8_8) = v16 & in(v12, all_0_8_8) = v17 & in(v11, all_35_2_84) = v14 & in(v10, all_35_2_84) = v13 & ( ~ (v14 = 0) | ~ (v13 = 0) | v17 = 0 | v16 = 0))) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (ordered_pair(v10, v11) = v12) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : (ordered_pair(v11, v10) = v16 & in(v16, all_0_8_8) = v17 & in(v12, all_0_8_8) = v15 & in(v11, all_35_2_84) = v14 & in(v10, all_35_2_84) = v13 & ( ~ (v14 = 0) | ~ (v13 = 0) | v17 = 0 | v15 = 0))))) & (v1 = 0 | (v5 = 0 & v4 = 0 & ~ (v9 = 0) & ~ (v7 = 0) & ~ (v3 = v2) & ordered_pair(v3, v2) = v8 & ordered_pair(v2, v3) = v6 & in(v8, all_0_8_8) = v9 & in(v6, all_0_8_8) = v7 & in(v3, all_35_2_84) = 0 & in(v2, all_35_2_84) = 0)))))
% 42.43/12.43 |
% 42.43/12.43 | Instantiating formula (154) with all_61_1_129, all_61_6_134, all_61_7_135 and discharging atoms ordered_pair(all_61_6_134, all_61_7_135) = all_61_1_129, yields:
% 42.43/12.43 | (178) all_61_6_134 = all_61_7_135 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (ordered_pair(all_61_7_135, all_61_6_134) = v2 & in(v2, all_0_8_8) = v3 & in(all_61_1_129, all_0_8_8) = v4 & in(all_61_6_134, all_57_0_123) = v1 & in(all_61_7_135, all_57_0_123) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v4 = 0 | v3 = 0))
% 42.43/12.43 |
% 42.43/12.43 | Instantiating formula (175) with all_61_1_129, all_61_6_134, all_61_7_135 and discharging atoms ordered_pair(all_61_6_134, all_61_7_135) = all_61_1_129, yields:
% 42.43/12.43 | (179) all_61_6_134 = all_61_7_135 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (ordered_pair(all_61_7_135, all_61_6_134) = v2 & in(v2, all_0_8_8) = v3 & in(all_61_1_129, all_0_8_8) = v4 & in(all_61_6_134, all_37_8_93) = v1 & in(all_61_7_135, all_37_8_93) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v4 = 0 | v3 = 0))
% 42.43/12.43 |
% 42.43/12.43 | Instantiating formula (155) with all_61_1_129, all_61_7_135, all_61_6_134 and discharging atoms ordered_pair(all_61_6_134, all_61_7_135) = all_61_1_129, yields:
% 42.43/12.43 | (180) all_61_6_134 = all_61_7_135 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (ordered_pair(all_61_7_135, all_61_6_134) = v3 & in(v3, all_0_8_8) = v4 & in(all_61_1_129, all_0_8_8) = v2 & in(all_61_6_134, all_57_0_123) = v0 & in(all_61_7_135, all_57_0_123) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v4 = 0 | v2 = 0))
% 42.43/12.43 |
% 42.43/12.43 | Instantiating formula (176) with all_61_1_129, all_61_7_135, all_61_6_134 and discharging atoms ordered_pair(all_61_6_134, all_61_7_135) = all_61_1_129, yields:
% 42.43/12.43 | (181) all_61_6_134 = all_61_7_135 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (ordered_pair(all_61_7_135, all_61_6_134) = v3 & in(v3, all_0_8_8) = v4 & in(all_61_1_129, all_0_8_8) = v2 & in(all_61_6_134, all_37_8_93) = v0 & in(all_61_7_135, all_37_8_93) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v4 = 0 | v2 = 0))
% 42.51/12.43 |
% 42.51/12.43 | Instantiating formula (154) with all_61_3_131, all_61_7_135, all_61_6_134 and discharging atoms ordered_pair(all_61_7_135, all_61_6_134) = all_61_3_131, yields:
% 42.51/12.43 | (182) all_61_6_134 = all_61_7_135 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (ordered_pair(all_61_6_134, all_61_7_135) = v2 & in(v2, all_0_8_8) = v3 & in(all_61_3_131, all_0_8_8) = v4 & in(all_61_6_134, all_57_0_123) = v0 & in(all_61_7_135, all_57_0_123) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v4 = 0 | v3 = 0))
% 42.51/12.43 |
% 42.51/12.43 | Instantiating formula (175) with all_61_3_131, all_61_7_135, all_61_6_134 and discharging atoms ordered_pair(all_61_7_135, all_61_6_134) = all_61_3_131, yields:
% 42.51/12.43 | (183) all_61_6_134 = all_61_7_135 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (ordered_pair(all_61_6_134, all_61_7_135) = v2 & in(v2, all_0_8_8) = v3 & in(all_61_3_131, all_0_8_8) = v4 & in(all_61_6_134, all_37_8_93) = v0 & in(all_61_7_135, all_37_8_93) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v4 = 0 | v3 = 0))
% 42.51/12.43 |
% 42.51/12.44 | Instantiating formula (155) with all_61_3_131, all_61_6_134, all_61_7_135 and discharging atoms ordered_pair(all_61_7_135, all_61_6_134) = all_61_3_131, yields:
% 42.51/12.44 | (184) all_61_6_134 = all_61_7_135 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (ordered_pair(all_61_6_134, all_61_7_135) = v3 & in(v3, all_0_8_8) = v4 & in(all_61_3_131, all_0_8_8) = v2 & in(all_61_6_134, all_57_0_123) = v1 & in(all_61_7_135, all_57_0_123) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v4 = 0 | v2 = 0))
% 42.51/12.44 |
% 42.51/12.44 | Instantiating formula (176) with all_61_3_131, all_61_6_134, all_61_7_135 and discharging atoms ordered_pair(all_61_7_135, all_61_6_134) = all_61_3_131, yields:
% 42.51/12.44 | (185) all_61_6_134 = all_61_7_135 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (ordered_pair(all_61_6_134, all_61_7_135) = v3 & in(v3, all_0_8_8) = v4 & in(all_61_3_131, all_0_8_8) = v2 & in(all_61_6_134, all_37_8_93) = v1 & in(all_61_7_135, all_37_8_93) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v4 = 0 | v2 = 0))
% 42.51/12.44 |
% 42.51/12.44 | Instantiating formula (36) with all_39_0_95, all_0_8_8 and discharging atoms one_to_one(all_0_8_8) = all_39_0_95, yields:
% 42.51/12.44 | (186) ? [v0] : ? [v1] : ? [v2] : (relation(all_0_8_8) = v0 & empty(all_0_8_8) = v1 & function(all_0_8_8) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | all_39_0_95 = 0))
% 42.51/12.44 |
% 42.51/12.44 | Instantiating formula (79) with all_61_0_128, all_0_7_7, all_0_8_8, all_0_9_9, all_61_1_129 and discharging atoms relation_restriction(all_0_8_8, all_0_9_9) = all_0_7_7, in(all_61_1_129, all_0_7_7) = all_61_0_128, yields:
% 42.51/12.44 | (187) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (cartesian_product2(all_0_9_9, all_0_9_9) = v2 & relation(all_0_8_8) = v0 & in(all_61_1_129, v2) = v3 & in(all_61_1_129, all_0_8_8) = v1 & ( ~ (v0 = 0) | (( ~ (v3 = 0) | ~ (v1 = 0) | all_61_0_128 = 0) & ( ~ (all_61_0_128 = 0) | (v3 = 0 & v1 = 0)))))
% 42.51/12.44 |
% 42.51/12.44 | Instantiating formula (48) with all_61_0_128, all_0_7_7, all_61_1_129 and discharging atoms in(all_61_1_129, all_0_7_7) = all_61_0_128, yields:
% 42.51/12.44 | (188) all_61_0_128 = 0 | ? [v0] : ? [v1] : (element(all_61_1_129, all_0_7_7) = v0 & empty(all_0_7_7) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 42.51/12.44 |
% 42.51/12.44 | Instantiating formula (79) with all_61_2_130, all_0_7_7, all_0_8_8, all_0_9_9, all_61_3_131 and discharging atoms relation_restriction(all_0_8_8, all_0_9_9) = all_0_7_7, in(all_61_3_131, all_0_7_7) = all_61_2_130, yields:
% 42.51/12.44 | (189) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (cartesian_product2(all_0_9_9, all_0_9_9) = v2 & relation(all_0_8_8) = v0 & in(all_61_3_131, v2) = v3 & in(all_61_3_131, all_0_8_8) = v1 & ( ~ (v0 = 0) | (( ~ (v3 = 0) | ~ (v1 = 0) | all_61_2_130 = 0) & ( ~ (all_61_2_130 = 0) | (v3 = 0 & v1 = 0)))))
% 42.51/12.44 |
% 42.51/12.44 | Instantiating formula (48) with all_61_2_130, all_0_7_7, all_61_3_131 and discharging atoms in(all_61_3_131, all_0_7_7) = all_61_2_130, yields:
% 42.51/12.44 | (190) all_61_2_130 = 0 | ? [v0] : ? [v1] : (element(all_61_3_131, all_0_7_7) = v0 & empty(all_0_7_7) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 42.51/12.44 |
% 42.51/12.44 | Instantiating formula (87) with all_61_8_136, all_0_7_7, all_0_8_8, all_0_9_9, all_61_6_134 and discharging atoms relation_restriction(all_0_8_8, all_0_9_9) = all_0_7_7, relation_field(all_0_7_7) = all_61_8_136, in(all_61_6_134, all_61_8_136) = 0, yields:
% 42.51/12.44 | (191) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (relation_field(all_0_8_8) = v1 & relation(all_0_8_8) = v0 & in(all_61_6_134, v1) = v2 & in(all_61_6_134, all_0_9_9) = v3 & ( ~ (v0 = 0) | (v3 = 0 & v2 = 0)))
% 42.51/12.44 |
% 42.51/12.44 | Instantiating formula (87) with all_61_8_136, all_0_7_7, all_0_8_8, all_0_9_9, all_61_7_135 and discharging atoms relation_restriction(all_0_8_8, all_0_9_9) = all_0_7_7, relation_field(all_0_7_7) = all_61_8_136, in(all_61_7_135, all_61_8_136) = 0, yields:
% 42.51/12.44 | (192) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (relation_field(all_0_8_8) = v1 & relation(all_0_8_8) = v0 & in(all_61_7_135, v1) = v2 & in(all_61_7_135, all_0_9_9) = v3 & ( ~ (v0 = 0) | (v3 = 0 & v2 = 0)))
% 42.51/12.44 |
% 42.51/12.44 | Instantiating (191) with all_175_0_274, all_175_1_275, all_175_2_276, all_175_3_277 yields:
% 42.51/12.44 | (193) relation_field(all_0_8_8) = all_175_2_276 & relation(all_0_8_8) = all_175_3_277 & in(all_61_6_134, all_175_2_276) = all_175_1_275 & in(all_61_6_134, all_0_9_9) = all_175_0_274 & ( ~ (all_175_3_277 = 0) | (all_175_0_274 = 0 & all_175_1_275 = 0))
% 42.51/12.44 |
% 42.51/12.44 | Applying alpha-rule on (193) yields:
% 42.51/12.44 | (194) in(all_61_6_134, all_0_9_9) = all_175_0_274
% 42.51/12.44 | (195) in(all_61_6_134, all_175_2_276) = all_175_1_275
% 42.51/12.44 | (196) relation(all_0_8_8) = all_175_3_277
% 42.51/12.44 | (197) ~ (all_175_3_277 = 0) | (all_175_0_274 = 0 & all_175_1_275 = 0)
% 42.51/12.44 | (198) relation_field(all_0_8_8) = all_175_2_276
% 42.51/12.44 |
% 42.51/12.44 | Instantiating (189) with all_181_0_286, all_181_1_287, all_181_2_288, all_181_3_289 yields:
% 42.51/12.44 | (199) cartesian_product2(all_0_9_9, all_0_9_9) = all_181_1_287 & relation(all_0_8_8) = all_181_3_289 & in(all_61_3_131, all_181_1_287) = all_181_0_286 & in(all_61_3_131, all_0_8_8) = all_181_2_288 & ( ~ (all_181_3_289 = 0) | (( ~ (all_181_0_286 = 0) | ~ (all_181_2_288 = 0) | all_61_2_130 = 0) & ( ~ (all_61_2_130 = 0) | (all_181_0_286 = 0 & all_181_2_288 = 0))))
% 42.51/12.44 |
% 42.51/12.44 | Applying alpha-rule on (199) yields:
% 42.51/12.44 | (200) ~ (all_181_3_289 = 0) | (( ~ (all_181_0_286 = 0) | ~ (all_181_2_288 = 0) | all_61_2_130 = 0) & ( ~ (all_61_2_130 = 0) | (all_181_0_286 = 0 & all_181_2_288 = 0)))
% 42.51/12.44 | (201) in(all_61_3_131, all_181_1_287) = all_181_0_286
% 42.51/12.44 | (202) in(all_61_3_131, all_0_8_8) = all_181_2_288
% 42.51/12.44 | (203) relation(all_0_8_8) = all_181_3_289
% 42.51/12.44 | (204) cartesian_product2(all_0_9_9, all_0_9_9) = all_181_1_287
% 42.51/12.44 |
% 42.51/12.44 | Instantiating (177) with all_193_0_326, all_193_1_327, all_193_2_328, all_193_3_329, all_193_4_330, all_193_5_331, all_193_6_332, all_193_7_333, all_193_8_334, all_193_9_335 yields:
% 42.51/12.44 | (205) connected(all_0_8_8) = all_193_8_334 & relation(all_0_8_8) = all_193_9_335 & ( ~ (all_193_9_335 = 0) | (( ~ (all_193_8_334 = 0) | ( ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ordered_pair(v1, v0) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (ordered_pair(v0, v1) = v5 & in(v5, all_0_8_8) = v6 & in(v2, all_0_8_8) = v7 & in(v1, all_35_2_84) = v4 & in(v0, all_35_2_84) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v7 = 0 | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (ordered_pair(v1, v0) = v6 & in(v6, all_0_8_8) = v7 & in(v2, all_0_8_8) = v5 & in(v1, all_35_2_84) = v4 & in(v0, all_35_2_84) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v7 = 0 | v5 = 0))))) & (all_193_8_334 = 0 | (all_193_4_330 = 0 & all_193_5_331 = 0 & ~ (all_193_0_326 = 0) & ~ (all_193_2_328 = 0) & ~ (all_193_6_332 = all_193_7_333) & ordered_pair(all_193_6_332, all_193_7_333) = all_193_1_327 & ordered_pair(all_193_7_333, all_193_6_332) = all_193_3_329 & in(all_193_1_327, all_0_8_8) = all_193_0_326 & in(all_193_3_329, all_0_8_8) = all_193_2_328 & in(all_193_6_332, all_35_2_84) = 0 & in(all_193_7_333, all_35_2_84) = 0))))
% 42.51/12.44 |
% 42.51/12.44 | Applying alpha-rule on (205) yields:
% 42.51/12.44 | (206) connected(all_0_8_8) = all_193_8_334
% 42.51/12.44 | (207) relation(all_0_8_8) = all_193_9_335
% 42.51/12.44 | (208) ~ (all_193_9_335 = 0) | (( ~ (all_193_8_334 = 0) | ( ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ordered_pair(v1, v0) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (ordered_pair(v0, v1) = v5 & in(v5, all_0_8_8) = v6 & in(v2, all_0_8_8) = v7 & in(v1, all_35_2_84) = v4 & in(v0, all_35_2_84) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v7 = 0 | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (ordered_pair(v1, v0) = v6 & in(v6, all_0_8_8) = v7 & in(v2, all_0_8_8) = v5 & in(v1, all_35_2_84) = v4 & in(v0, all_35_2_84) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v7 = 0 | v5 = 0))))) & (all_193_8_334 = 0 | (all_193_4_330 = 0 & all_193_5_331 = 0 & ~ (all_193_0_326 = 0) & ~ (all_193_2_328 = 0) & ~ (all_193_6_332 = all_193_7_333) & ordered_pair(all_193_6_332, all_193_7_333) = all_193_1_327 & ordered_pair(all_193_7_333, all_193_6_332) = all_193_3_329 & in(all_193_1_327, all_0_8_8) = all_193_0_326 & in(all_193_3_329, all_0_8_8) = all_193_2_328 & in(all_193_6_332, all_35_2_84) = 0 & in(all_193_7_333, all_35_2_84) = 0)))
% 42.51/12.44 |
% 42.51/12.44 | Instantiating (187) with all_225_0_418, all_225_1_419, all_225_2_420, all_225_3_421 yields:
% 42.51/12.44 | (209) cartesian_product2(all_0_9_9, all_0_9_9) = all_225_1_419 & relation(all_0_8_8) = all_225_3_421 & in(all_61_1_129, all_225_1_419) = all_225_0_418 & in(all_61_1_129, all_0_8_8) = all_225_2_420 & ( ~ (all_225_3_421 = 0) | (( ~ (all_225_0_418 = 0) | ~ (all_225_2_420 = 0) | all_61_0_128 = 0) & ( ~ (all_61_0_128 = 0) | (all_225_0_418 = 0 & all_225_2_420 = 0))))
% 42.51/12.44 |
% 42.51/12.44 | Applying alpha-rule on (209) yields:
% 42.51/12.44 | (210) in(all_61_1_129, all_0_8_8) = all_225_2_420
% 42.51/12.44 | (211) relation(all_0_8_8) = all_225_3_421
% 42.51/12.44 | (212) cartesian_product2(all_0_9_9, all_0_9_9) = all_225_1_419
% 42.51/12.44 | (213) in(all_61_1_129, all_225_1_419) = all_225_0_418
% 42.51/12.44 | (214) ~ (all_225_3_421 = 0) | (( ~ (all_225_0_418 = 0) | ~ (all_225_2_420 = 0) | all_61_0_128 = 0) & ( ~ (all_61_0_128 = 0) | (all_225_0_418 = 0 & all_225_2_420 = 0)))
% 42.51/12.44 |
% 42.51/12.44 | Instantiating (186) with all_227_0_422, all_227_1_423, all_227_2_424 yields:
% 42.51/12.44 | (215) relation(all_0_8_8) = all_227_2_424 & empty(all_0_8_8) = all_227_1_423 & function(all_0_8_8) = all_227_0_422 & ( ~ (all_227_0_422 = 0) | ~ (all_227_1_423 = 0) | ~ (all_227_2_424 = 0) | all_39_0_95 = 0)
% 42.51/12.44 |
% 42.51/12.44 | Applying alpha-rule on (215) yields:
% 42.51/12.44 | (216) relation(all_0_8_8) = all_227_2_424
% 42.51/12.44 | (217) empty(all_0_8_8) = all_227_1_423
% 42.51/12.44 | (218) function(all_0_8_8) = all_227_0_422
% 42.51/12.44 | (219) ~ (all_227_0_422 = 0) | ~ (all_227_1_423 = 0) | ~ (all_227_2_424 = 0) | all_39_0_95 = 0
% 42.51/12.44 |
% 42.51/12.44 | Instantiating (192) with all_251_0_445, all_251_1_446, all_251_2_447, all_251_3_448 yields:
% 42.51/12.44 | (220) relation_field(all_0_8_8) = all_251_2_447 & relation(all_0_8_8) = all_251_3_448 & in(all_61_7_135, all_251_2_447) = all_251_1_446 & in(all_61_7_135, all_0_9_9) = all_251_0_445 & ( ~ (all_251_3_448 = 0) | (all_251_0_445 = 0 & all_251_1_446 = 0))
% 42.51/12.44 |
% 42.51/12.44 | Applying alpha-rule on (220) yields:
% 42.51/12.44 | (221) relation(all_0_8_8) = all_251_3_448
% 42.51/12.44 | (222) relation_field(all_0_8_8) = all_251_2_447
% 42.51/12.44 | (223) in(all_61_7_135, all_0_9_9) = all_251_0_445
% 42.51/12.44 | (224) in(all_61_7_135, all_251_2_447) = all_251_1_446
% 42.51/12.45 | (225) ~ (all_251_3_448 = 0) | (all_251_0_445 = 0 & all_251_1_446 = 0)
% 42.51/12.45 |
% 42.51/12.45 +-Applying beta-rule and splitting (178), into two cases.
% 42.51/12.45 |-Branch one:
% 42.51/12.45 | (226) all_61_6_134 = all_61_7_135
% 42.51/12.45 |
% 42.51/12.45 | Equations (226) can reduce 167 to:
% 42.51/12.45 | (140) $false
% 42.51/12.45 |
% 42.51/12.45 |-The branch is then unsatisfiable
% 42.51/12.45 |-Branch two:
% 42.51/12.45 | (167) ~ (all_61_6_134 = all_61_7_135)
% 42.51/12.45 | (229) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (ordered_pair(all_61_7_135, all_61_6_134) = v2 & in(v2, all_0_8_8) = v3 & in(all_61_1_129, all_0_8_8) = v4 & in(all_61_6_134, all_57_0_123) = v1 & in(all_61_7_135, all_57_0_123) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v4 = 0 | v3 = 0))
% 42.51/12.45 |
% 42.51/12.45 | Instantiating (229) with all_287_0_495, all_287_1_496, all_287_2_497, all_287_3_498, all_287_4_499 yields:
% 42.51/12.45 | (230) ordered_pair(all_61_7_135, all_61_6_134) = all_287_2_497 & in(all_287_2_497, all_0_8_8) = all_287_1_496 & in(all_61_1_129, all_0_8_8) = all_287_0_495 & in(all_61_6_134, all_57_0_123) = all_287_3_498 & in(all_61_7_135, all_57_0_123) = all_287_4_499 & ( ~ (all_287_3_498 = 0) | ~ (all_287_4_499 = 0) | all_287_0_495 = 0 | all_287_1_496 = 0)
% 42.51/12.45 |
% 42.51/12.45 | Applying alpha-rule on (230) yields:
% 42.51/12.45 | (231) in(all_61_7_135, all_57_0_123) = all_287_4_499
% 42.51/12.45 | (232) in(all_61_6_134, all_57_0_123) = all_287_3_498
% 42.51/12.45 | (233) ~ (all_287_3_498 = 0) | ~ (all_287_4_499 = 0) | all_287_0_495 = 0 | all_287_1_496 = 0
% 42.51/12.45 | (234) in(all_287_2_497, all_0_8_8) = all_287_1_496
% 42.51/12.45 | (235) ordered_pair(all_61_7_135, all_61_6_134) = all_287_2_497
% 42.51/12.45 | (236) in(all_61_1_129, all_0_8_8) = all_287_0_495
% 42.51/12.45 |
% 42.51/12.45 | From (129) and (232) follows:
% 42.51/12.45 | (237) in(all_61_6_134, all_35_2_84) = all_287_3_498
% 42.51/12.45 |
% 42.51/12.45 | From (129) and (231) follows:
% 42.51/12.45 | (238) in(all_61_7_135, all_35_2_84) = all_287_4_499
% 42.51/12.45 |
% 42.51/12.45 +-Applying beta-rule and splitting (182), into two cases.
% 42.51/12.45 |-Branch one:
% 42.51/12.45 | (226) all_61_6_134 = all_61_7_135
% 42.51/12.45 |
% 42.51/12.45 | Equations (226) can reduce 167 to:
% 42.51/12.45 | (140) $false
% 42.51/12.45 |
% 42.51/12.45 |-The branch is then unsatisfiable
% 42.51/12.45 |-Branch two:
% 42.51/12.45 | (167) ~ (all_61_6_134 = all_61_7_135)
% 42.51/12.45 | (242) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (ordered_pair(all_61_6_134, all_61_7_135) = v2 & in(v2, all_0_8_8) = v3 & in(all_61_3_131, all_0_8_8) = v4 & in(all_61_6_134, all_57_0_123) = v0 & in(all_61_7_135, all_57_0_123) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v4 = 0 | v3 = 0))
% 42.51/12.45 |
% 42.51/12.45 | Instantiating (242) with all_292_0_500, all_292_1_501, all_292_2_502, all_292_3_503, all_292_4_504 yields:
% 42.51/12.45 | (243) ordered_pair(all_61_6_134, all_61_7_135) = all_292_2_502 & in(all_292_2_502, all_0_8_8) = all_292_1_501 & in(all_61_3_131, all_0_8_8) = all_292_0_500 & in(all_61_6_134, all_57_0_123) = all_292_4_504 & in(all_61_7_135, all_57_0_123) = all_292_3_503 & ( ~ (all_292_3_503 = 0) | ~ (all_292_4_504 = 0) | all_292_0_500 = 0 | all_292_1_501 = 0)
% 42.51/12.45 |
% 42.51/12.45 | Applying alpha-rule on (243) yields:
% 42.51/12.45 | (244) in(all_292_2_502, all_0_8_8) = all_292_1_501
% 42.51/12.45 | (245) in(all_61_7_135, all_57_0_123) = all_292_3_503
% 42.51/12.45 | (246) ordered_pair(all_61_6_134, all_61_7_135) = all_292_2_502
% 42.51/12.45 | (247) in(all_61_6_134, all_57_0_123) = all_292_4_504
% 42.51/12.45 | (248) in(all_61_3_131, all_0_8_8) = all_292_0_500
% 42.51/12.45 | (249) ~ (all_292_3_503 = 0) | ~ (all_292_4_504 = 0) | all_292_0_500 = 0 | all_292_1_501 = 0
% 42.51/12.45 |
% 42.51/12.45 | From (129) and (247) follows:
% 42.51/12.45 | (250) in(all_61_6_134, all_35_2_84) = all_292_4_504
% 42.51/12.45 |
% 42.51/12.45 | From (129) and (245) follows:
% 42.51/12.45 | (251) in(all_61_7_135, all_35_2_84) = all_292_3_503
% 42.51/12.45 |
% 42.51/12.45 +-Applying beta-rule and splitting (185), into two cases.
% 42.51/12.45 |-Branch one:
% 42.51/12.45 | (226) all_61_6_134 = all_61_7_135
% 42.51/12.45 |
% 42.51/12.45 | Equations (226) can reduce 167 to:
% 42.51/12.45 | (140) $false
% 42.51/12.45 |
% 42.51/12.45 |-The branch is then unsatisfiable
% 42.51/12.45 |-Branch two:
% 42.51/12.45 | (167) ~ (all_61_6_134 = all_61_7_135)
% 42.51/12.45 | (255) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (ordered_pair(all_61_6_134, all_61_7_135) = v3 & in(v3, all_0_8_8) = v4 & in(all_61_3_131, all_0_8_8) = v2 & in(all_61_6_134, all_37_8_93) = v1 & in(all_61_7_135, all_37_8_93) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v4 = 0 | v2 = 0))
% 42.51/12.45 |
% 42.51/12.45 | Instantiating (255) with all_297_0_505, all_297_1_506, all_297_2_507, all_297_3_508, all_297_4_509 yields:
% 42.51/12.45 | (256) ordered_pair(all_61_6_134, all_61_7_135) = all_297_1_506 & in(all_297_1_506, all_0_8_8) = all_297_0_505 & in(all_61_3_131, all_0_8_8) = all_297_2_507 & in(all_61_6_134, all_37_8_93) = all_297_3_508 & in(all_61_7_135, all_37_8_93) = all_297_4_509 & ( ~ (all_297_3_508 = 0) | ~ (all_297_4_509 = 0) | all_297_0_505 = 0 | all_297_2_507 = 0)
% 42.51/12.45 |
% 42.51/12.45 | Applying alpha-rule on (256) yields:
% 42.51/12.45 | (257) ordered_pair(all_61_6_134, all_61_7_135) = all_297_1_506
% 42.51/12.45 | (258) in(all_61_7_135, all_37_8_93) = all_297_4_509
% 42.51/12.45 | (259) in(all_61_6_134, all_37_8_93) = all_297_3_508
% 42.51/12.45 | (260) ~ (all_297_3_508 = 0) | ~ (all_297_4_509 = 0) | all_297_0_505 = 0 | all_297_2_507 = 0
% 42.51/12.45 | (261) in(all_297_1_506, all_0_8_8) = all_297_0_505
% 42.51/12.45 | (262) in(all_61_3_131, all_0_8_8) = all_297_2_507
% 42.51/12.45 |
% 42.51/12.45 | From (133) and (259) follows:
% 42.51/12.45 | (263) in(all_61_6_134, all_35_2_84) = all_297_3_508
% 42.51/12.45 |
% 42.51/12.45 | From (133) and (258) follows:
% 42.51/12.45 | (264) in(all_61_7_135, all_35_2_84) = all_297_4_509
% 42.51/12.45 |
% 42.51/12.45 +-Applying beta-rule and splitting (181), into two cases.
% 42.51/12.45 |-Branch one:
% 42.51/12.45 | (226) all_61_6_134 = all_61_7_135
% 42.51/12.45 |
% 42.51/12.45 | Equations (226) can reduce 167 to:
% 42.51/12.45 | (140) $false
% 42.51/12.45 |
% 42.51/12.45 |-The branch is then unsatisfiable
% 42.51/12.45 |-Branch two:
% 42.51/12.45 | (167) ~ (all_61_6_134 = all_61_7_135)
% 42.51/12.45 | (268) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (ordered_pair(all_61_7_135, all_61_6_134) = v3 & in(v3, all_0_8_8) = v4 & in(all_61_1_129, all_0_8_8) = v2 & in(all_61_6_134, all_37_8_93) = v0 & in(all_61_7_135, all_37_8_93) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v4 = 0 | v2 = 0))
% 42.51/12.45 |
% 42.51/12.45 | Instantiating (268) with all_302_0_510, all_302_1_511, all_302_2_512, all_302_3_513, all_302_4_514 yields:
% 42.51/12.45 | (269) ordered_pair(all_61_7_135, all_61_6_134) = all_302_1_511 & in(all_302_1_511, all_0_8_8) = all_302_0_510 & in(all_61_1_129, all_0_8_8) = all_302_2_512 & in(all_61_6_134, all_37_8_93) = all_302_4_514 & in(all_61_7_135, all_37_8_93) = all_302_3_513 & ( ~ (all_302_3_513 = 0) | ~ (all_302_4_514 = 0) | all_302_0_510 = 0 | all_302_2_512 = 0)
% 42.51/12.45 |
% 42.51/12.45 | Applying alpha-rule on (269) yields:
% 42.51/12.45 | (270) in(all_61_7_135, all_37_8_93) = all_302_3_513
% 42.51/12.45 | (271) in(all_61_1_129, all_0_8_8) = all_302_2_512
% 42.51/12.45 | (272) ~ (all_302_3_513 = 0) | ~ (all_302_4_514 = 0) | all_302_0_510 = 0 | all_302_2_512 = 0
% 42.51/12.45 | (273) in(all_302_1_511, all_0_8_8) = all_302_0_510
% 42.51/12.45 | (274) ordered_pair(all_61_7_135, all_61_6_134) = all_302_1_511
% 42.51/12.45 | (275) in(all_61_6_134, all_37_8_93) = all_302_4_514
% 42.51/12.45 |
% 42.51/12.45 | From (133) and (275) follows:
% 42.51/12.45 | (276) in(all_61_6_134, all_35_2_84) = all_302_4_514
% 42.51/12.45 |
% 42.51/12.45 | From (133) and (270) follows:
% 42.51/12.45 | (277) in(all_61_7_135, all_35_2_84) = all_302_3_513
% 42.51/12.45 |
% 42.51/12.45 +-Applying beta-rule and splitting (183), into two cases.
% 42.51/12.45 |-Branch one:
% 42.51/12.45 | (226) all_61_6_134 = all_61_7_135
% 42.51/12.45 |
% 42.51/12.45 | Equations (226) can reduce 167 to:
% 42.51/12.45 | (140) $false
% 42.51/12.45 |
% 42.51/12.45 |-The branch is then unsatisfiable
% 42.51/12.45 |-Branch two:
% 42.51/12.45 | (167) ~ (all_61_6_134 = all_61_7_135)
% 42.51/12.45 | (281) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (ordered_pair(all_61_6_134, all_61_7_135) = v2 & in(v2, all_0_8_8) = v3 & in(all_61_3_131, all_0_8_8) = v4 & in(all_61_6_134, all_37_8_93) = v0 & in(all_61_7_135, all_37_8_93) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v4 = 0 | v3 = 0))
% 42.51/12.45 |
% 42.51/12.45 | Instantiating (281) with all_307_0_515, all_307_1_516, all_307_2_517, all_307_3_518, all_307_4_519 yields:
% 42.51/12.45 | (282) ordered_pair(all_61_6_134, all_61_7_135) = all_307_2_517 & in(all_307_2_517, all_0_8_8) = all_307_1_516 & in(all_61_3_131, all_0_8_8) = all_307_0_515 & in(all_61_6_134, all_37_8_93) = all_307_4_519 & in(all_61_7_135, all_37_8_93) = all_307_3_518 & ( ~ (all_307_3_518 = 0) | ~ (all_307_4_519 = 0) | all_307_0_515 = 0 | all_307_1_516 = 0)
% 42.51/12.45 |
% 42.51/12.45 | Applying alpha-rule on (282) yields:
% 42.51/12.45 | (283) in(all_61_6_134, all_37_8_93) = all_307_4_519
% 42.51/12.45 | (284) in(all_307_2_517, all_0_8_8) = all_307_1_516
% 42.51/12.45 | (285) ordered_pair(all_61_6_134, all_61_7_135) = all_307_2_517
% 42.51/12.45 | (286) in(all_61_7_135, all_37_8_93) = all_307_3_518
% 42.51/12.45 | (287) in(all_61_3_131, all_0_8_8) = all_307_0_515
% 42.51/12.45 | (288) ~ (all_307_3_518 = 0) | ~ (all_307_4_519 = 0) | all_307_0_515 = 0 | all_307_1_516 = 0
% 42.51/12.45 |
% 42.51/12.45 | From (133) and (283) follows:
% 42.51/12.45 | (289) in(all_61_6_134, all_35_2_84) = all_307_4_519
% 42.51/12.45 |
% 42.51/12.45 | From (133) and (286) follows:
% 42.51/12.45 | (290) in(all_61_7_135, all_35_2_84) = all_307_3_518
% 42.51/12.45 |
% 42.51/12.45 +-Applying beta-rule and splitting (179), into two cases.
% 42.51/12.45 |-Branch one:
% 42.51/12.45 | (226) all_61_6_134 = all_61_7_135
% 42.51/12.45 |
% 42.51/12.45 | Equations (226) can reduce 167 to:
% 42.51/12.45 | (140) $false
% 42.51/12.45 |
% 42.51/12.45 |-The branch is then unsatisfiable
% 42.51/12.45 |-Branch two:
% 42.51/12.45 | (167) ~ (all_61_6_134 = all_61_7_135)
% 42.51/12.45 | (294) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (ordered_pair(all_61_7_135, all_61_6_134) = v2 & in(v2, all_0_8_8) = v3 & in(all_61_1_129, all_0_8_8) = v4 & in(all_61_6_134, all_37_8_93) = v1 & in(all_61_7_135, all_37_8_93) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v4 = 0 | v3 = 0))
% 42.51/12.45 |
% 42.51/12.45 | Instantiating (294) with all_312_0_520, all_312_1_521, all_312_2_522, all_312_3_523, all_312_4_524 yields:
% 42.51/12.45 | (295) ordered_pair(all_61_7_135, all_61_6_134) = all_312_2_522 & in(all_312_2_522, all_0_8_8) = all_312_1_521 & in(all_61_1_129, all_0_8_8) = all_312_0_520 & in(all_61_6_134, all_37_8_93) = all_312_3_523 & in(all_61_7_135, all_37_8_93) = all_312_4_524 & ( ~ (all_312_3_523 = 0) | ~ (all_312_4_524 = 0) | all_312_0_520 = 0 | all_312_1_521 = 0)
% 42.51/12.45 |
% 42.51/12.45 | Applying alpha-rule on (295) yields:
% 42.51/12.45 | (296) in(all_312_2_522, all_0_8_8) = all_312_1_521
% 42.51/12.45 | (297) in(all_61_7_135, all_37_8_93) = all_312_4_524
% 42.51/12.45 | (298) ~ (all_312_3_523 = 0) | ~ (all_312_4_524 = 0) | all_312_0_520 = 0 | all_312_1_521 = 0
% 42.51/12.45 | (299) in(all_61_1_129, all_0_8_8) = all_312_0_520
% 42.51/12.45 | (300) in(all_61_6_134, all_37_8_93) = all_312_3_523
% 42.51/12.45 | (301) ordered_pair(all_61_7_135, all_61_6_134) = all_312_2_522
% 42.51/12.45 |
% 42.51/12.45 | From (133) and (300) follows:
% 42.51/12.45 | (302) in(all_61_6_134, all_35_2_84) = all_312_3_523
% 42.51/12.46 |
% 42.51/12.46 | From (133) and (297) follows:
% 42.51/12.46 | (303) in(all_61_7_135, all_35_2_84) = all_312_4_524
% 42.51/12.46 |
% 42.51/12.46 +-Applying beta-rule and splitting (180), into two cases.
% 42.51/12.46 |-Branch one:
% 42.51/12.46 | (226) all_61_6_134 = all_61_7_135
% 42.51/12.46 |
% 42.51/12.46 | Equations (226) can reduce 167 to:
% 42.51/12.46 | (140) $false
% 42.51/12.46 |
% 42.51/12.46 |-The branch is then unsatisfiable
% 42.51/12.46 |-Branch two:
% 42.51/12.46 | (167) ~ (all_61_6_134 = all_61_7_135)
% 42.51/12.46 | (307) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (ordered_pair(all_61_7_135, all_61_6_134) = v3 & in(v3, all_0_8_8) = v4 & in(all_61_1_129, all_0_8_8) = v2 & in(all_61_6_134, all_57_0_123) = v0 & in(all_61_7_135, all_57_0_123) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v4 = 0 | v2 = 0))
% 42.51/12.46 |
% 42.51/12.46 | Instantiating (307) with all_317_0_525, all_317_1_526, all_317_2_527, all_317_3_528, all_317_4_529 yields:
% 42.51/12.46 | (308) ordered_pair(all_61_7_135, all_61_6_134) = all_317_1_526 & in(all_317_1_526, all_0_8_8) = all_317_0_525 & in(all_61_1_129, all_0_8_8) = all_317_2_527 & in(all_61_6_134, all_57_0_123) = all_317_4_529 & in(all_61_7_135, all_57_0_123) = all_317_3_528 & ( ~ (all_317_3_528 = 0) | ~ (all_317_4_529 = 0) | all_317_0_525 = 0 | all_317_2_527 = 0)
% 42.51/12.46 |
% 42.51/12.46 | Applying alpha-rule on (308) yields:
% 42.51/12.46 | (309) in(all_61_1_129, all_0_8_8) = all_317_2_527
% 42.51/12.46 | (310) ~ (all_317_3_528 = 0) | ~ (all_317_4_529 = 0) | all_317_0_525 = 0 | all_317_2_527 = 0
% 42.51/12.46 | (311) in(all_61_6_134, all_57_0_123) = all_317_4_529
% 42.51/12.46 | (312) ordered_pair(all_61_7_135, all_61_6_134) = all_317_1_526
% 42.51/12.46 | (313) in(all_61_7_135, all_57_0_123) = all_317_3_528
% 42.51/12.46 | (314) in(all_317_1_526, all_0_8_8) = all_317_0_525
% 42.51/12.46 |
% 42.51/12.46 | From (129) and (311) follows:
% 42.51/12.46 | (315) in(all_61_6_134, all_35_2_84) = all_317_4_529
% 42.51/12.46 |
% 42.51/12.46 | From (129) and (313) follows:
% 42.51/12.46 | (316) in(all_61_7_135, all_35_2_84) = all_317_3_528
% 42.51/12.46 |
% 42.51/12.46 +-Applying beta-rule and splitting (184), into two cases.
% 42.51/12.46 |-Branch one:
% 42.51/12.46 | (226) all_61_6_134 = all_61_7_135
% 42.51/12.46 |
% 42.51/12.46 | Equations (226) can reduce 167 to:
% 42.51/12.46 | (140) $false
% 42.51/12.46 |
% 42.51/12.46 |-The branch is then unsatisfiable
% 42.51/12.46 |-Branch two:
% 42.51/12.46 | (167) ~ (all_61_6_134 = all_61_7_135)
% 42.51/12.46 | (320) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (ordered_pair(all_61_6_134, all_61_7_135) = v3 & in(v3, all_0_8_8) = v4 & in(all_61_3_131, all_0_8_8) = v2 & in(all_61_6_134, all_57_0_123) = v1 & in(all_61_7_135, all_57_0_123) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v4 = 0 | v2 = 0))
% 42.51/12.46 |
% 42.51/12.46 | Instantiating (320) with all_322_0_530, all_322_1_531, all_322_2_532, all_322_3_533, all_322_4_534 yields:
% 42.51/12.46 | (321) ordered_pair(all_61_6_134, all_61_7_135) = all_322_1_531 & in(all_322_1_531, all_0_8_8) = all_322_0_530 & in(all_61_3_131, all_0_8_8) = all_322_2_532 & in(all_61_6_134, all_57_0_123) = all_322_3_533 & in(all_61_7_135, all_57_0_123) = all_322_4_534 & ( ~ (all_322_3_533 = 0) | ~ (all_322_4_534 = 0) | all_322_0_530 = 0 | all_322_2_532 = 0)
% 42.51/12.46 |
% 42.51/12.46 | Applying alpha-rule on (321) yields:
% 42.51/12.46 | (322) in(all_322_1_531, all_0_8_8) = all_322_0_530
% 42.51/12.46 | (323) in(all_61_3_131, all_0_8_8) = all_322_2_532
% 42.51/12.46 | (324) in(all_61_7_135, all_57_0_123) = all_322_4_534
% 42.51/12.46 | (325) ordered_pair(all_61_6_134, all_61_7_135) = all_322_1_531
% 42.51/12.46 | (326) in(all_61_6_134, all_57_0_123) = all_322_3_533
% 42.51/12.46 | (327) ~ (all_322_3_533 = 0) | ~ (all_322_4_534 = 0) | all_322_0_530 = 0 | all_322_2_532 = 0
% 42.51/12.46 |
% 42.51/12.46 | From (129) and (326) follows:
% 42.51/12.46 | (328) in(all_61_6_134, all_35_2_84) = all_322_3_533
% 42.51/12.46 |
% 42.51/12.46 | From (129) and (324) follows:
% 42.51/12.46 | (329) in(all_61_7_135, all_35_2_84) = all_322_4_534
% 42.51/12.46 |
% 42.51/12.46 +-Applying beta-rule and splitting (188), into two cases.
% 42.51/12.46 |-Branch one:
% 42.51/12.46 | (330) all_61_0_128 = 0
% 42.51/12.46 |
% 42.51/12.46 | Equations (330) can reduce 166 to:
% 42.51/12.46 | (140) $false
% 42.51/12.46 |
% 42.51/12.46 |-The branch is then unsatisfiable
% 42.51/12.46 |-Branch two:
% 42.51/12.46 | (166) ~ (all_61_0_128 = 0)
% 42.51/12.46 | (333) ? [v0] : ? [v1] : (element(all_61_1_129, all_0_7_7) = v0 & empty(all_0_7_7) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 42.51/12.46 |
% 42.51/12.46 +-Applying beta-rule and splitting (190), into two cases.
% 42.51/12.46 |-Branch one:
% 42.51/12.46 | (334) all_61_2_130 = 0
% 42.51/12.46 |
% 42.51/12.46 | Equations (334) can reduce 161 to:
% 42.51/12.46 | (140) $false
% 42.51/12.46 |
% 42.51/12.46 |-The branch is then unsatisfiable
% 42.51/12.46 |-Branch two:
% 42.51/12.46 | (161) ~ (all_61_2_130 = 0)
% 42.51/12.46 | (337) ? [v0] : ? [v1] : (element(all_61_3_131, all_0_7_7) = v0 & empty(all_0_7_7) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 42.51/12.46 |
% 42.51/12.46 | Instantiating formula (89) with all_0_9_9, all_0_9_9, all_225_1_419, all_45_0_103 and discharging atoms cartesian_product2(all_0_9_9, all_0_9_9) = all_225_1_419, cartesian_product2(all_0_9_9, all_0_9_9) = all_45_0_103, yields:
% 42.51/12.46 | (338) all_225_1_419 = all_45_0_103
% 42.51/12.46 |
% 42.51/12.46 | Instantiating formula (89) with all_0_9_9, all_0_9_9, all_181_1_287, all_225_1_419 and discharging atoms cartesian_product2(all_0_9_9, all_0_9_9) = all_225_1_419, cartesian_product2(all_0_9_9, all_0_9_9) = all_181_1_287, yields:
% 42.51/12.46 | (339) all_225_1_419 = all_181_1_287
% 42.51/12.46 |
% 42.51/12.46 | Instantiating formula (26) with all_0_8_8, all_251_2_447, all_35_2_84 and discharging atoms relation_field(all_0_8_8) = all_251_2_447, relation_field(all_0_8_8) = all_35_2_84, yields:
% 42.51/12.46 | (340) all_251_2_447 = all_35_2_84
% 42.51/12.46 |
% 42.51/12.46 | Instantiating formula (26) with all_0_8_8, all_175_2_276, all_251_2_447 and discharging atoms relation_field(all_0_8_8) = all_251_2_447, relation_field(all_0_8_8) = all_175_2_276, yields:
% 42.51/12.46 | (341) all_251_2_447 = all_175_2_276
% 42.51/12.46 |
% 42.51/12.46 | Instantiating formula (17) with all_61_6_134, all_61_7_135, all_307_2_517, all_61_1_129 and discharging atoms ordered_pair(all_61_6_134, all_61_7_135) = all_307_2_517, ordered_pair(all_61_6_134, all_61_7_135) = all_61_1_129, yields:
% 42.51/12.46 | (342) all_307_2_517 = all_61_1_129
% 42.51/12.46 |
% 42.51/12.46 | Instantiating formula (17) with all_61_6_134, all_61_7_135, all_307_2_517, all_322_1_531 and discharging atoms ordered_pair(all_61_6_134, all_61_7_135) = all_322_1_531, ordered_pair(all_61_6_134, all_61_7_135) = all_307_2_517, yields:
% 42.51/12.46 | (343) all_322_1_531 = all_307_2_517
% 42.51/12.46 |
% 42.51/12.46 | Instantiating formula (17) with all_61_6_134, all_61_7_135, all_297_1_506, all_322_1_531 and discharging atoms ordered_pair(all_61_6_134, all_61_7_135) = all_322_1_531, ordered_pair(all_61_6_134, all_61_7_135) = all_297_1_506, yields:
% 42.51/12.46 | (344) all_322_1_531 = all_297_1_506
% 42.51/12.46 |
% 42.51/12.46 | Instantiating formula (17) with all_61_6_134, all_61_7_135, all_292_2_502, all_307_2_517 and discharging atoms ordered_pair(all_61_6_134, all_61_7_135) = all_307_2_517, ordered_pair(all_61_6_134, all_61_7_135) = all_292_2_502, yields:
% 42.51/12.46 | (345) all_307_2_517 = all_292_2_502
% 42.51/12.46 |
% 42.51/12.46 | Instantiating formula (17) with all_61_7_135, all_61_6_134, all_317_1_526, all_61_3_131 and discharging atoms ordered_pair(all_61_7_135, all_61_6_134) = all_317_1_526, ordered_pair(all_61_7_135, all_61_6_134) = all_61_3_131, yields:
% 42.51/12.46 | (346) all_317_1_526 = all_61_3_131
% 42.51/12.46 |
% 42.51/12.46 | Instantiating formula (17) with all_61_7_135, all_61_6_134, all_312_2_522, all_317_1_526 and discharging atoms ordered_pair(all_61_7_135, all_61_6_134) = all_317_1_526, ordered_pair(all_61_7_135, all_61_6_134) = all_312_2_522, yields:
% 42.51/12.46 | (347) all_317_1_526 = all_312_2_522
% 42.51/12.46 |
% 42.51/12.46 | Instantiating formula (17) with all_61_7_135, all_61_6_134, all_302_1_511, all_317_1_526 and discharging atoms ordered_pair(all_61_7_135, all_61_6_134) = all_317_1_526, ordered_pair(all_61_7_135, all_61_6_134) = all_302_1_511, yields:
% 42.51/12.46 | (348) all_317_1_526 = all_302_1_511
% 42.51/12.46 |
% 42.51/12.46 | Instantiating formula (17) with all_61_7_135, all_61_6_134, all_287_2_497, all_302_1_511 and discharging atoms ordered_pair(all_61_7_135, all_61_6_134) = all_302_1_511, ordered_pair(all_61_7_135, all_61_6_134) = all_287_2_497, yields:
% 42.51/12.46 | (349) all_302_1_511 = all_287_2_497
% 42.51/12.46 |
% 42.51/12.46 | Instantiating formula (88) with all_0_8_8, all_227_2_424, all_251_3_448 and discharging atoms relation(all_0_8_8) = all_251_3_448, relation(all_0_8_8) = all_227_2_424, yields:
% 42.51/12.46 | (350) all_251_3_448 = all_227_2_424
% 42.51/12.46 |
% 42.51/12.46 | Instantiating formula (88) with all_0_8_8, all_225_3_421, all_227_2_424 and discharging atoms relation(all_0_8_8) = all_227_2_424, relation(all_0_8_8) = all_225_3_421, yields:
% 42.51/12.46 | (351) all_227_2_424 = all_225_3_421
% 42.51/12.46 |
% 42.51/12.46 | Instantiating formula (88) with all_0_8_8, all_193_9_335, all_225_3_421 and discharging atoms relation(all_0_8_8) = all_225_3_421, relation(all_0_8_8) = all_193_9_335, yields:
% 42.51/12.46 | (352) all_225_3_421 = all_193_9_335
% 42.51/12.46 |
% 42.51/12.46 | Instantiating formula (88) with all_0_8_8, all_181_3_289, 0 and discharging atoms relation(all_0_8_8) = all_181_3_289, relation(all_0_8_8) = 0, yields:
% 42.51/12.46 | (353) all_181_3_289 = 0
% 42.51/12.46 |
% 42.51/12.46 | Instantiating formula (88) with all_0_8_8, all_181_3_289, all_193_9_335 and discharging atoms relation(all_0_8_8) = all_193_9_335, relation(all_0_8_8) = all_181_3_289, yields:
% 42.51/12.46 | (354) all_193_9_335 = all_181_3_289
% 42.51/12.46 |
% 42.51/12.46 | Instantiating formula (88) with all_0_8_8, all_175_3_277, all_251_3_448 and discharging atoms relation(all_0_8_8) = all_251_3_448, relation(all_0_8_8) = all_175_3_277, yields:
% 42.51/12.46 | (355) all_251_3_448 = all_175_3_277
% 42.51/12.46 |
% 42.51/12.46 | Instantiating formula (23) with all_61_1_129, all_0_8_8, all_312_0_520, all_317_2_527 and discharging atoms in(all_61_1_129, all_0_8_8) = all_317_2_527, in(all_61_1_129, all_0_8_8) = all_312_0_520, yields:
% 42.51/12.46 | (356) all_317_2_527 = all_312_0_520
% 42.51/12.46 |
% 42.51/12.46 | Instantiating formula (23) with all_61_1_129, all_0_8_8, all_302_2_512, all_312_0_520 and discharging atoms in(all_61_1_129, all_0_8_8) = all_312_0_520, in(all_61_1_129, all_0_8_8) = all_302_2_512, yields:
% 42.51/12.46 | (357) all_312_0_520 = all_302_2_512
% 42.51/12.46 |
% 42.51/12.46 | Instantiating formula (23) with all_61_1_129, all_0_8_8, all_287_0_495, all_302_2_512 and discharging atoms in(all_61_1_129, all_0_8_8) = all_302_2_512, in(all_61_1_129, all_0_8_8) = all_287_0_495, yields:
% 42.51/12.46 | (358) all_302_2_512 = all_287_0_495
% 42.51/12.46 |
% 42.51/12.46 | Instantiating formula (23) with all_61_1_129, all_0_8_8, all_225_2_420, all_317_2_527 and discharging atoms in(all_61_1_129, all_0_8_8) = all_317_2_527, in(all_61_1_129, all_0_8_8) = all_225_2_420, yields:
% 42.51/12.46 | (359) all_317_2_527 = all_225_2_420
% 42.51/12.46 |
% 42.51/12.46 | Instantiating formula (23) with all_61_3_131, all_0_8_8, all_307_0_515, all_322_2_532 and discharging atoms in(all_61_3_131, all_0_8_8) = all_322_2_532, in(all_61_3_131, all_0_8_8) = all_307_0_515, yields:
% 42.51/12.46 | (360) all_322_2_532 = all_307_0_515
% 42.51/12.46 |
% 42.51/12.46 | Instantiating formula (23) with all_61_3_131, all_0_8_8, all_181_2_288, all_322_2_532 and discharging atoms in(all_61_3_131, all_0_8_8) = all_322_2_532, in(all_61_3_131, all_0_8_8) = all_181_2_288, yields:
% 42.51/12.46 | (361) all_322_2_532 = all_181_2_288
% 42.51/12.46 |
% 42.51/12.46 | Instantiating formula (23) with all_61_6_134, all_35_2_84, all_317_4_529, all_322_3_533 and discharging atoms in(all_61_6_134, all_35_2_84) = all_322_3_533, in(all_61_6_134, all_35_2_84) = all_317_4_529, yields:
% 42.51/12.46 | (362) all_322_3_533 = all_317_4_529
% 42.51/12.46 |
% 42.51/12.46 | Instantiating formula (23) with all_61_6_134, all_35_2_84, all_312_3_523, all_322_3_533 and discharging atoms in(all_61_6_134, all_35_2_84) = all_322_3_533, in(all_61_6_134, all_35_2_84) = all_312_3_523, yields:
% 42.51/12.46 | (363) all_322_3_533 = all_312_3_523
% 42.51/12.46 |
% 42.51/12.46 | Instantiating formula (23) with all_61_6_134, all_35_2_84, all_307_4_519, all_317_4_529 and discharging atoms in(all_61_6_134, all_35_2_84) = all_317_4_529, in(all_61_6_134, all_35_2_84) = all_307_4_519, yields:
% 42.51/12.46 | (364) all_317_4_529 = all_307_4_519
% 42.51/12.46 |
% 42.51/12.46 | Instantiating formula (23) with all_61_6_134, all_35_2_84, all_302_4_514, all_317_4_529 and discharging atoms in(all_61_6_134, all_35_2_84) = all_317_4_529, in(all_61_6_134, all_35_2_84) = all_302_4_514, yields:
% 42.51/12.46 | (365) all_317_4_529 = all_302_4_514
% 42.51/12.46 |
% 42.51/12.46 | Instantiating formula (23) with all_61_6_134, all_35_2_84, all_297_3_508, all_307_4_519 and discharging atoms in(all_61_6_134, all_35_2_84) = all_307_4_519, in(all_61_6_134, all_35_2_84) = all_297_3_508, yields:
% 42.51/12.46 | (366) all_307_4_519 = all_297_3_508
% 42.51/12.46 |
% 42.51/12.46 | Instantiating formula (23) with all_61_6_134, all_35_2_84, all_292_4_504, all_307_4_519 and discharging atoms in(all_61_6_134, all_35_2_84) = all_307_4_519, in(all_61_6_134, all_35_2_84) = all_292_4_504, yields:
% 42.51/12.46 | (367) all_307_4_519 = all_292_4_504
% 42.51/12.46 |
% 42.51/12.46 | Instantiating formula (23) with all_61_6_134, all_35_2_84, all_287_3_498, all_322_3_533 and discharging atoms in(all_61_6_134, all_35_2_84) = all_322_3_533, in(all_61_6_134, all_35_2_84) = all_287_3_498, yields:
% 42.51/12.46 | (368) all_322_3_533 = all_287_3_498
% 42.51/12.46 |
% 42.51/12.46 | Instantiating formula (23) with all_61_7_135, all_35_2_84, all_317_3_528, all_322_4_534 and discharging atoms in(all_61_7_135, all_35_2_84) = all_322_4_534, in(all_61_7_135, all_35_2_84) = all_317_3_528, yields:
% 42.51/12.46 | (369) all_322_4_534 = all_317_3_528
% 42.51/12.46 |
% 42.51/12.46 | Instantiating formula (23) with all_61_7_135, all_35_2_84, all_312_4_524, all_322_4_534 and discharging atoms in(all_61_7_135, all_35_2_84) = all_322_4_534, in(all_61_7_135, all_35_2_84) = all_312_4_524, yields:
% 42.51/12.46 | (370) all_322_4_534 = all_312_4_524
% 42.51/12.46 |
% 42.51/12.46 | Instantiating formula (23) with all_61_7_135, all_35_2_84, all_307_3_518, all_312_4_524 and discharging atoms in(all_61_7_135, all_35_2_84) = all_312_4_524, in(all_61_7_135, all_35_2_84) = all_307_3_518, yields:
% 42.51/12.46 | (371) all_312_4_524 = all_307_3_518
% 42.51/12.46 |
% 42.51/12.46 | Instantiating formula (23) with all_61_7_135, all_35_2_84, all_302_3_513, all_307_3_518 and discharging atoms in(all_61_7_135, all_35_2_84) = all_307_3_518, in(all_61_7_135, all_35_2_84) = all_302_3_513, yields:
% 42.51/12.46 | (372) all_307_3_518 = all_302_3_513
% 42.51/12.46 |
% 42.51/12.46 | Instantiating formula (23) with all_61_7_135, all_35_2_84, all_297_4_509, all_302_3_513 and discharging atoms in(all_61_7_135, all_35_2_84) = all_302_3_513, in(all_61_7_135, all_35_2_84) = all_297_4_509, yields:
% 42.51/12.46 | (373) all_302_3_513 = all_297_4_509
% 42.51/12.47 |
% 42.51/12.47 | Instantiating formula (23) with all_61_7_135, all_35_2_84, all_292_3_503, all_322_4_534 and discharging atoms in(all_61_7_135, all_35_2_84) = all_322_4_534, in(all_61_7_135, all_35_2_84) = all_292_3_503, yields:
% 42.51/12.47 | (374) all_322_4_534 = all_292_3_503
% 42.51/12.47 |
% 42.51/12.47 | Instantiating formula (23) with all_61_7_135, all_35_2_84, all_287_4_499, all_302_3_513 and discharging atoms in(all_61_7_135, all_35_2_84) = all_302_3_513, in(all_61_7_135, all_35_2_84) = all_287_4_499, yields:
% 42.51/12.47 | (375) all_302_3_513 = all_287_4_499
% 42.51/12.47 |
% 42.51/12.47 | Combining equations (343,344) yields a new equation:
% 42.51/12.47 | (376) all_307_2_517 = all_297_1_506
% 42.51/12.47 |
% 42.51/12.47 | Simplifying 376 yields:
% 42.51/12.47 | (377) all_307_2_517 = all_297_1_506
% 42.51/12.47 |
% 42.51/12.47 | Combining equations (361,360) yields a new equation:
% 42.51/12.47 | (378) all_307_0_515 = all_181_2_288
% 42.51/12.47 |
% 42.51/12.47 | Combining equations (368,363) yields a new equation:
% 42.51/12.47 | (379) all_312_3_523 = all_287_3_498
% 42.51/12.47 |
% 42.51/12.47 | Combining equations (362,363) yields a new equation:
% 42.51/12.47 | (380) all_317_4_529 = all_312_3_523
% 42.51/12.47 |
% 42.51/12.47 | Simplifying 380 yields:
% 42.51/12.47 | (381) all_317_4_529 = all_312_3_523
% 42.51/12.47 |
% 42.51/12.47 | Combining equations (374,369) yields a new equation:
% 42.51/12.47 | (382) all_317_3_528 = all_292_3_503
% 42.51/12.47 |
% 42.51/12.47 | Combining equations (370,369) yields a new equation:
% 42.51/12.47 | (383) all_317_3_528 = all_312_4_524
% 42.51/12.47 |
% 42.51/12.47 | Combining equations (346,347) yields a new equation:
% 42.51/12.47 | (384) all_312_2_522 = all_61_3_131
% 42.51/12.47 |
% 42.51/12.47 | Combining equations (348,347) yields a new equation:
% 42.51/12.47 | (385) all_312_2_522 = all_302_1_511
% 42.51/12.47 |
% 42.51/12.47 | Combining equations (356,359) yields a new equation:
% 42.51/12.47 | (386) all_312_0_520 = all_225_2_420
% 42.51/12.47 |
% 42.51/12.47 | Simplifying 386 yields:
% 42.51/12.47 | (387) all_312_0_520 = all_225_2_420
% 42.51/12.47 |
% 42.51/12.47 | Combining equations (383,382) yields a new equation:
% 42.51/12.47 | (388) all_312_4_524 = all_292_3_503
% 42.51/12.47 |
% 42.51/12.47 | Simplifying 388 yields:
% 42.51/12.47 | (389) all_312_4_524 = all_292_3_503
% 42.51/12.47 |
% 42.51/12.47 | Combining equations (364,365) yields a new equation:
% 42.51/12.47 | (390) all_307_4_519 = all_302_4_514
% 42.51/12.47 |
% 42.51/12.47 | Simplifying 390 yields:
% 42.51/12.47 | (391) all_307_4_519 = all_302_4_514
% 42.51/12.47 |
% 42.51/12.47 | Combining equations (381,365) yields a new equation:
% 42.51/12.47 | (392) all_312_3_523 = all_302_4_514
% 42.51/12.47 |
% 42.51/12.47 | Simplifying 392 yields:
% 42.51/12.47 | (393) all_312_3_523 = all_302_4_514
% 42.51/12.47 |
% 42.51/12.47 | Combining equations (357,387) yields a new equation:
% 42.51/12.47 | (394) all_302_2_512 = all_225_2_420
% 42.51/12.47 |
% 42.51/12.47 | Simplifying 394 yields:
% 42.51/12.47 | (395) all_302_2_512 = all_225_2_420
% 42.51/12.47 |
% 42.51/12.47 | Combining equations (385,384) yields a new equation:
% 42.51/12.47 | (396) all_302_1_511 = all_61_3_131
% 42.51/12.47 |
% 42.51/12.47 | Simplifying 396 yields:
% 42.51/12.47 | (397) all_302_1_511 = all_61_3_131
% 42.51/12.47 |
% 42.51/12.47 | Combining equations (393,379) yields a new equation:
% 42.51/12.47 | (398) all_302_4_514 = all_287_3_498
% 42.51/12.47 |
% 42.51/12.47 | Simplifying 398 yields:
% 42.51/12.47 | (399) all_302_4_514 = all_287_3_498
% 42.51/12.47 |
% 42.51/12.47 | Combining equations (371,389) yields a new equation:
% 42.51/12.47 | (400) all_307_3_518 = all_292_3_503
% 42.51/12.47 |
% 42.51/12.47 | Simplifying 400 yields:
% 42.51/12.47 | (401) all_307_3_518 = all_292_3_503
% 42.51/12.47 |
% 42.51/12.47 | Combining equations (345,377) yields a new equation:
% 42.51/12.47 | (402) all_297_1_506 = all_292_2_502
% 42.51/12.47 |
% 42.51/12.47 | Combining equations (342,377) yields a new equation:
% 42.51/12.47 | (403) all_297_1_506 = all_61_1_129
% 42.51/12.47 |
% 42.51/12.47 | Combining equations (372,401) yields a new equation:
% 42.51/12.47 | (404) all_302_3_513 = all_292_3_503
% 42.51/12.47 |
% 42.51/12.47 | Simplifying 404 yields:
% 42.51/12.47 | (405) all_302_3_513 = all_292_3_503
% 42.51/12.47 |
% 42.51/12.47 | Combining equations (367,366) yields a new equation:
% 42.51/12.47 | (406) all_297_3_508 = all_292_4_504
% 42.51/12.47 |
% 42.51/12.47 | Combining equations (391,366) yields a new equation:
% 42.51/12.47 | (407) all_302_4_514 = all_297_3_508
% 42.51/12.47 |
% 42.51/12.47 | Simplifying 407 yields:
% 42.51/12.47 | (408) all_302_4_514 = all_297_3_508
% 42.51/12.47 |
% 42.51/12.47 | Combining equations (349,397) yields a new equation:
% 42.51/12.47 | (409) all_287_2_497 = all_61_3_131
% 42.51/12.47 |
% 42.51/12.47 | Simplifying 409 yields:
% 42.51/12.47 | (410) all_287_2_497 = all_61_3_131
% 42.51/12.47 |
% 42.51/12.47 | Combining equations (358,395) yields a new equation:
% 42.51/12.47 | (411) all_287_0_495 = all_225_2_420
% 42.51/12.47 |
% 42.51/12.47 | Simplifying 411 yields:
% 42.51/12.47 | (412) all_287_0_495 = all_225_2_420
% 42.51/12.47 |
% 42.51/12.47 | Combining equations (375,373) yields a new equation:
% 42.51/12.47 | (413) all_297_4_509 = all_287_4_499
% 42.51/12.47 |
% 42.51/12.47 | Combining equations (405,373) yields a new equation:
% 42.51/12.47 | (414) all_297_4_509 = all_292_3_503
% 42.51/12.47 |
% 42.51/12.47 | Combining equations (408,399) yields a new equation:
% 42.51/12.47 | (415) all_297_3_508 = all_287_3_498
% 42.51/12.47 |
% 42.51/12.47 | Simplifying 415 yields:
% 42.51/12.47 | (416) all_297_3_508 = all_287_3_498
% 42.51/12.47 |
% 42.51/12.47 | Combining equations (403,402) yields a new equation:
% 42.51/12.47 | (417) all_292_2_502 = all_61_1_129
% 42.51/12.47 |
% 42.51/12.47 | Combining equations (406,416) yields a new equation:
% 42.51/12.47 | (418) all_292_4_504 = all_287_3_498
% 42.51/12.47 |
% 42.51/12.47 | Simplifying 418 yields:
% 42.51/12.47 | (419) all_292_4_504 = all_287_3_498
% 42.51/12.47 |
% 42.51/12.47 | Combining equations (413,414) yields a new equation:
% 42.51/12.47 | (420) all_292_3_503 = all_287_4_499
% 42.51/12.47 |
% 42.51/12.47 | Combining equations (341,340) yields a new equation:
% 42.51/12.47 | (421) all_175_2_276 = all_35_2_84
% 42.51/12.47 |
% 42.51/12.47 | Simplifying 421 yields:
% 42.51/12.47 | (422) all_175_2_276 = all_35_2_84
% 42.51/12.47 |
% 42.51/12.47 | Combining equations (350,355) yields a new equation:
% 42.51/12.47 | (423) all_227_2_424 = all_175_3_277
% 42.51/12.47 |
% 42.51/12.47 | Simplifying 423 yields:
% 42.51/12.47 | (424) all_227_2_424 = all_175_3_277
% 42.51/12.47 |
% 42.51/12.47 | Combining equations (351,424) yields a new equation:
% 42.51/12.47 | (425) all_225_3_421 = all_175_3_277
% 42.51/12.47 |
% 42.51/12.47 | Simplifying 425 yields:
% 42.51/12.47 | (426) all_225_3_421 = all_175_3_277
% 42.51/12.47 |
% 42.51/12.47 | Combining equations (338,339) yields a new equation:
% 42.51/12.47 | (427) all_181_1_287 = all_45_0_103
% 42.51/12.47 |
% 42.51/12.47 | Combining equations (352,426) yields a new equation:
% 42.51/12.47 | (428) all_193_9_335 = all_175_3_277
% 42.51/12.47 |
% 42.51/12.47 | Simplifying 428 yields:
% 42.51/12.47 | (429) all_193_9_335 = all_175_3_277
% 42.51/12.47 |
% 42.51/12.47 | Combining equations (354,429) yields a new equation:
% 42.51/12.47 | (430) all_181_3_289 = all_175_3_277
% 42.51/12.47 |
% 42.51/12.47 | Simplifying 430 yields:
% 42.51/12.47 | (431) all_181_3_289 = all_175_3_277
% 42.51/12.47 |
% 42.51/12.47 | Combining equations (353,431) yields a new equation:
% 42.51/12.47 | (432) all_175_3_277 = 0
% 42.51/12.47 |
% 42.51/12.47 | Combining equations (432,431) yields a new equation:
% 42.51/12.47 | (353) all_181_3_289 = 0
% 42.51/12.47 |
% 42.51/12.47 | Combining equations (432,426) yields a new equation:
% 42.51/12.47 | (434) all_225_3_421 = 0
% 42.51/12.47 |
% 42.51/12.47 | Combining equations (427,339) yields a new equation:
% 42.51/12.47 | (338) all_225_1_419 = all_45_0_103
% 42.51/12.47 |
% 42.51/12.47 | Combining equations (432,355) yields a new equation:
% 42.51/12.47 | (436) all_251_3_448 = 0
% 42.51/12.47 |
% 42.51/12.47 | Combining equations (417,402) yields a new equation:
% 42.51/12.47 | (403) all_297_1_506 = all_61_1_129
% 42.51/12.47 |
% 42.51/12.47 | Combining equations (416,366) yields a new equation:
% 42.51/12.47 | (438) all_307_4_519 = all_287_3_498
% 42.51/12.47 |
% 42.51/12.47 | Combining equations (420,401) yields a new equation:
% 42.51/12.47 | (439) all_307_3_518 = all_287_4_499
% 42.51/12.47 |
% 42.51/12.47 | Combining equations (403,377) yields a new equation:
% 42.51/12.47 | (342) all_307_2_517 = all_61_1_129
% 42.51/12.47 |
% 42.51/12.47 | Combining equations (403,344) yields a new equation:
% 42.51/12.47 | (441) all_322_1_531 = all_61_1_129
% 42.51/12.47 |
% 42.51/12.47 | From (427) and (204) follows:
% 42.51/12.47 | (113) cartesian_product2(all_0_9_9, all_0_9_9) = all_45_0_103
% 42.51/12.47 |
% 42.51/12.47 | From (417) and (246) follows:
% 42.51/12.47 | (164) ordered_pair(all_61_6_134, all_61_7_135) = all_61_1_129
% 42.51/12.47 |
% 42.51/12.47 | From (410) and (235) follows:
% 42.51/12.47 | (168) ordered_pair(all_61_7_135, all_61_6_134) = all_61_3_131
% 42.51/12.47 |
% 42.51/12.47 | From (441) and (322) follows:
% 42.51/12.47 | (445) in(all_61_1_129, all_0_8_8) = all_322_0_530
% 42.51/12.47 |
% 42.51/12.47 | From (342) and (284) follows:
% 42.51/12.47 | (446) in(all_61_1_129, all_0_8_8) = all_307_1_516
% 42.51/12.47 |
% 42.51/12.47 | From (403) and (261) follows:
% 42.51/12.47 | (447) in(all_61_1_129, all_0_8_8) = all_297_0_505
% 42.51/12.47 |
% 42.51/12.47 | From (338) and (213) follows:
% 42.51/12.47 | (448) in(all_61_1_129, all_45_0_103) = all_225_0_418
% 42.51/12.47 |
% 42.51/12.47 | From (412) and (236) follows:
% 42.51/12.47 | (210) in(all_61_1_129, all_0_8_8) = all_225_2_420
% 42.51/12.47 |
% 42.51/12.47 | From (427) and (201) follows:
% 42.51/12.47 | (450) in(all_61_3_131, all_45_0_103) = all_181_0_286
% 42.51/12.47 |
% 42.51/12.47 | From (422) and (195) follows:
% 42.51/12.47 | (451) in(all_61_6_134, all_35_2_84) = all_175_1_275
% 42.51/12.47 |
% 42.51/12.47 | From (419) and (250) follows:
% 42.51/12.47 | (237) in(all_61_6_134, all_35_2_84) = all_287_3_498
% 42.51/12.47 |
% 42.51/12.47 | From (340) and (224) follows:
% 42.51/12.47 | (453) in(all_61_7_135, all_35_2_84) = all_251_1_446
% 42.51/12.47 |
% 42.51/12.47 | From (420) and (251) follows:
% 42.51/12.47 | (238) in(all_61_7_135, all_35_2_84) = all_287_4_499
% 42.51/12.47 |
% 42.51/12.47 +-Applying beta-rule and splitting (197), into two cases.
% 42.51/12.47 |-Branch one:
% 42.51/12.47 | (455) ~ (all_175_3_277 = 0)
% 42.51/12.47 |
% 42.51/12.47 | Equations (432) can reduce 455 to:
% 42.51/12.47 | (140) $false
% 42.51/12.47 |
% 42.51/12.47 |-The branch is then unsatisfiable
% 42.51/12.47 |-Branch two:
% 42.51/12.47 | (432) all_175_3_277 = 0
% 42.51/12.47 | (458) all_175_0_274 = 0 & all_175_1_275 = 0
% 42.51/12.47 |
% 42.51/12.47 | Applying alpha-rule on (458) yields:
% 42.51/12.47 | (459) all_175_0_274 = 0
% 42.51/12.47 | (460) all_175_1_275 = 0
% 42.51/12.47 |
% 42.51/12.47 | From (460) and (451) follows:
% 42.51/12.47 | (461) in(all_61_6_134, all_35_2_84) = 0
% 42.51/12.47 |
% 42.51/12.47 | From (459) and (194) follows:
% 42.51/12.47 | (462) in(all_61_6_134, all_0_9_9) = 0
% 42.51/12.47 |
% 42.51/12.48 +-Applying beta-rule and splitting (225), into two cases.
% 42.51/12.48 |-Branch one:
% 42.51/12.48 | (463) ~ (all_251_3_448 = 0)
% 42.51/12.48 |
% 42.51/12.48 | Equations (436) can reduce 463 to:
% 42.51/12.48 | (140) $false
% 42.51/12.48 |
% 42.51/12.48 |-The branch is then unsatisfiable
% 42.51/12.48 |-Branch two:
% 42.51/12.48 | (436) all_251_3_448 = 0
% 42.51/12.48 | (466) all_251_0_445 = 0 & all_251_1_446 = 0
% 42.51/12.48 |
% 42.51/12.48 | Applying alpha-rule on (466) yields:
% 42.51/12.48 | (467) all_251_0_445 = 0
% 42.51/12.48 | (468) all_251_1_446 = 0
% 42.51/12.48 |
% 42.51/12.48 | From (468) and (453) follows:
% 42.51/12.48 | (469) in(all_61_7_135, all_35_2_84) = 0
% 42.51/12.48 |
% 42.51/12.48 | From (467) and (223) follows:
% 42.51/12.48 | (470) in(all_61_7_135, all_0_9_9) = 0
% 42.51/12.48 |
% 42.51/12.48 | Instantiating formula (23) with all_61_1_129, all_0_8_8, all_322_0_530, all_225_2_420 and discharging atoms in(all_61_1_129, all_0_8_8) = all_322_0_530, in(all_61_1_129, all_0_8_8) = all_225_2_420, yields:
% 42.51/12.48 | (471) all_322_0_530 = all_225_2_420
% 42.51/12.48 |
% 42.51/12.48 | Instantiating formula (23) with all_61_1_129, all_0_8_8, all_307_1_516, all_322_0_530 and discharging atoms in(all_61_1_129, all_0_8_8) = all_322_0_530, in(all_61_1_129, all_0_8_8) = all_307_1_516, yields:
% 42.51/12.48 | (472) all_322_0_530 = all_307_1_516
% 42.51/12.48 |
% 42.51/12.48 | Instantiating formula (23) with all_61_1_129, all_0_8_8, all_297_0_505, all_322_0_530 and discharging atoms in(all_61_1_129, all_0_8_8) = all_322_0_530, in(all_61_1_129, all_0_8_8) = all_297_0_505, yields:
% 42.51/12.48 | (473) all_322_0_530 = all_297_0_505
% 42.51/12.48 |
% 42.51/12.48 | Instantiating formula (23) with all_61_6_134, all_35_2_84, 0, all_287_3_498 and discharging atoms in(all_61_6_134, all_35_2_84) = all_287_3_498, in(all_61_6_134, all_35_2_84) = 0, yields:
% 42.51/12.48 | (474) all_287_3_498 = 0
% 42.51/12.48 |
% 42.51/12.48 | Instantiating formula (23) with all_61_7_135, all_35_2_84, 0, all_287_4_499 and discharging atoms in(all_61_7_135, all_35_2_84) = all_287_4_499, in(all_61_7_135, all_35_2_84) = 0, yields:
% 42.51/12.48 | (475) all_287_4_499 = 0
% 42.51/12.48 |
% 42.51/12.48 | Combining equations (471,472) yields a new equation:
% 42.51/12.48 | (476) all_307_1_516 = all_225_2_420
% 42.51/12.48 |
% 42.51/12.48 | Combining equations (473,472) yields a new equation:
% 42.51/12.48 | (477) all_307_1_516 = all_297_0_505
% 42.51/12.48 |
% 42.51/12.48 | Combining equations (476,477) yields a new equation:
% 42.51/12.48 | (478) all_297_0_505 = all_225_2_420
% 42.51/12.48 |
% 42.51/12.48 | Combining equations (474,438) yields a new equation:
% 42.51/12.48 | (479) all_307_4_519 = 0
% 42.51/12.48 |
% 42.51/12.48 | Combining equations (475,439) yields a new equation:
% 42.51/12.48 | (480) all_307_3_518 = 0
% 42.51/12.48 |
% 42.51/12.48 | Combining equations (478,477) yields a new equation:
% 42.51/12.48 | (476) all_307_1_516 = all_225_2_420
% 42.51/12.48 |
% 42.51/12.48 | Instantiating formula (3) with all_225_0_418, all_45_0_103, all_61_1_129, all_0_9_9, all_0_9_9, all_61_7_135, all_61_6_134 and discharging atoms cartesian_product2(all_0_9_9, all_0_9_9) = all_45_0_103, ordered_pair(all_61_6_134, all_61_7_135) = all_61_1_129, in(all_61_1_129, all_45_0_103) = all_225_0_418, yields:
% 42.51/12.48 | (482) all_225_0_418 = 0 | ? [v0] : ? [v1] : (in(all_61_6_134, all_0_9_9) = v0 & in(all_61_7_135, all_0_9_9) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 42.51/12.48 |
% 42.51/12.48 | Instantiating formula (3) with all_181_0_286, all_45_0_103, all_61_3_131, all_0_9_9, all_0_9_9, all_61_6_134, all_61_7_135 and discharging atoms cartesian_product2(all_0_9_9, all_0_9_9) = all_45_0_103, ordered_pair(all_61_7_135, all_61_6_134) = all_61_3_131, in(all_61_3_131, all_45_0_103) = all_181_0_286, yields:
% 42.51/12.48 | (483) all_181_0_286 = 0 | ? [v0] : ? [v1] : (in(all_61_6_134, all_0_9_9) = v1 & in(all_61_7_135, all_0_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 42.51/12.48 |
% 42.51/12.48 +-Applying beta-rule and splitting (482), into two cases.
% 42.51/12.48 |-Branch one:
% 42.51/12.48 | (484) all_225_0_418 = 0
% 42.51/12.48 |
% 42.51/12.48 +-Applying beta-rule and splitting (214), into two cases.
% 42.51/12.48 |-Branch one:
% 42.51/12.48 | (485) ~ (all_225_3_421 = 0)
% 42.51/12.48 |
% 42.51/12.48 | Equations (434) can reduce 485 to:
% 42.51/12.48 | (140) $false
% 42.51/12.48 |
% 42.51/12.48 |-The branch is then unsatisfiable
% 42.51/12.48 |-Branch two:
% 42.51/12.48 | (434) all_225_3_421 = 0
% 42.51/12.48 | (488) ( ~ (all_225_0_418 = 0) | ~ (all_225_2_420 = 0) | all_61_0_128 = 0) & ( ~ (all_61_0_128 = 0) | (all_225_0_418 = 0 & all_225_2_420 = 0))
% 42.51/12.48 |
% 42.51/12.48 | Applying alpha-rule on (488) yields:
% 42.51/12.48 | (489) ~ (all_225_0_418 = 0) | ~ (all_225_2_420 = 0) | all_61_0_128 = 0
% 42.51/12.48 | (490) ~ (all_61_0_128 = 0) | (all_225_0_418 = 0 & all_225_2_420 = 0)
% 42.51/12.48 |
% 42.51/12.48 +-Applying beta-rule and splitting (483), into two cases.
% 42.51/12.48 |-Branch one:
% 42.51/12.48 | (491) all_181_0_286 = 0
% 42.51/12.48 |
% 42.51/12.48 +-Applying beta-rule and splitting (200), into two cases.
% 42.51/12.48 |-Branch one:
% 42.51/12.48 | (492) ~ (all_181_3_289 = 0)
% 42.51/12.48 |
% 42.51/12.48 | Equations (353) can reduce 492 to:
% 42.51/12.48 | (140) $false
% 42.51/12.48 |
% 42.51/12.48 |-The branch is then unsatisfiable
% 42.51/12.48 |-Branch two:
% 42.51/12.48 | (353) all_181_3_289 = 0
% 42.51/12.48 | (495) ( ~ (all_181_0_286 = 0) | ~ (all_181_2_288 = 0) | all_61_2_130 = 0) & ( ~ (all_61_2_130 = 0) | (all_181_0_286 = 0 & all_181_2_288 = 0))
% 42.51/12.48 |
% 42.51/12.48 | Applying alpha-rule on (495) yields:
% 42.51/12.48 | (496) ~ (all_181_0_286 = 0) | ~ (all_181_2_288 = 0) | all_61_2_130 = 0
% 42.51/12.48 | (497) ~ (all_61_2_130 = 0) | (all_181_0_286 = 0 & all_181_2_288 = 0)
% 42.51/12.48 |
% 42.51/12.48 +-Applying beta-rule and splitting (496), into two cases.
% 42.51/12.48 |-Branch one:
% 42.51/12.48 | (498) ~ (all_181_0_286 = 0)
% 42.51/12.48 |
% 42.51/12.48 | Equations (491) can reduce 498 to:
% 42.51/12.48 | (140) $false
% 42.51/12.48 |
% 42.51/12.48 |-The branch is then unsatisfiable
% 42.51/12.48 |-Branch two:
% 42.51/12.48 | (491) all_181_0_286 = 0
% 42.51/12.48 | (501) ~ (all_181_2_288 = 0) | all_61_2_130 = 0
% 42.51/12.48 |
% 42.51/12.48 +-Applying beta-rule and splitting (489), into two cases.
% 42.51/12.48 |-Branch one:
% 42.51/12.48 | (502) ~ (all_225_0_418 = 0)
% 42.51/12.48 |
% 42.51/12.48 | Equations (484) can reduce 502 to:
% 42.51/12.48 | (140) $false
% 42.51/12.48 |
% 42.51/12.48 |-The branch is then unsatisfiable
% 42.51/12.48 |-Branch two:
% 42.51/12.48 | (484) all_225_0_418 = 0
% 42.51/12.48 | (505) ~ (all_225_2_420 = 0) | all_61_0_128 = 0
% 42.51/12.48 |
% 42.51/12.48 +-Applying beta-rule and splitting (501), into two cases.
% 42.51/12.48 |-Branch one:
% 42.51/12.48 | (506) ~ (all_181_2_288 = 0)
% 42.51/12.48 |
% 42.51/12.48 +-Applying beta-rule and splitting (505), into two cases.
% 42.51/12.48 |-Branch one:
% 42.51/12.48 | (507) ~ (all_225_2_420 = 0)
% 42.51/12.48 |
% 42.51/12.48 +-Applying beta-rule and splitting (288), into two cases.
% 42.51/12.48 |-Branch one:
% 42.51/12.48 | (508) ~ (all_307_3_518 = 0)
% 42.51/12.48 |
% 42.51/12.48 | Equations (480) can reduce 508 to:
% 42.51/12.48 | (140) $false
% 42.51/12.48 |
% 42.51/12.48 |-The branch is then unsatisfiable
% 42.51/12.48 |-Branch two:
% 42.51/12.48 | (480) all_307_3_518 = 0
% 42.51/12.48 | (511) ~ (all_307_4_519 = 0) | all_307_0_515 = 0 | all_307_1_516 = 0
% 42.51/12.48 |
% 42.51/12.48 +-Applying beta-rule and splitting (511), into two cases.
% 42.51/12.48 |-Branch one:
% 42.51/12.48 | (512) ~ (all_307_4_519 = 0)
% 42.51/12.48 |
% 42.51/12.48 | Equations (479) can reduce 512 to:
% 42.51/12.48 | (140) $false
% 42.51/12.48 |
% 42.51/12.48 |-The branch is then unsatisfiable
% 42.51/12.48 |-Branch two:
% 42.51/12.48 | (479) all_307_4_519 = 0
% 42.51/12.48 | (515) all_307_0_515 = 0 | all_307_1_516 = 0
% 42.51/12.48 |
% 42.51/12.48 +-Applying beta-rule and splitting (515), into two cases.
% 42.51/12.48 |-Branch one:
% 42.51/12.48 | (516) all_307_0_515 = 0
% 42.51/12.48 |
% 42.51/12.48 | Combining equations (378,516) yields a new equation:
% 42.51/12.48 | (517) all_181_2_288 = 0
% 42.51/12.48 |
% 42.51/12.48 | Simplifying 517 yields:
% 42.51/12.48 | (518) all_181_2_288 = 0
% 42.51/12.48 |
% 42.51/12.48 | Equations (518) can reduce 506 to:
% 42.51/12.48 | (140) $false
% 42.51/12.48 |
% 42.51/12.48 |-The branch is then unsatisfiable
% 42.51/12.48 |-Branch two:
% 42.51/12.48 | (520) ~ (all_307_0_515 = 0)
% 42.51/12.48 | (521) all_307_1_516 = 0
% 42.51/12.48 |
% 42.51/12.48 | Combining equations (521,476) yields a new equation:
% 42.51/12.48 | (522) all_225_2_420 = 0
% 42.51/12.48 |
% 42.51/12.48 | Equations (522) can reduce 507 to:
% 42.51/12.48 | (140) $false
% 42.51/12.48 |
% 42.51/12.48 |-The branch is then unsatisfiable
% 42.51/12.48 |-Branch two:
% 42.51/12.48 | (522) all_225_2_420 = 0
% 42.51/12.48 | (330) all_61_0_128 = 0
% 42.51/12.48 |
% 42.51/12.48 | Equations (330) can reduce 166 to:
% 42.51/12.48 | (140) $false
% 42.51/12.48 |
% 42.51/12.48 |-The branch is then unsatisfiable
% 42.51/12.48 |-Branch two:
% 42.51/12.48 | (518) all_181_2_288 = 0
% 42.51/12.48 | (334) all_61_2_130 = 0
% 42.51/12.48 |
% 42.51/12.48 | Equations (334) can reduce 161 to:
% 42.51/12.48 | (140) $false
% 42.51/12.48 |
% 42.51/12.48 |-The branch is then unsatisfiable
% 42.51/12.48 |-Branch two:
% 42.51/12.48 | (498) ~ (all_181_0_286 = 0)
% 42.51/12.48 | (531) ? [v0] : ? [v1] : (in(all_61_6_134, all_0_9_9) = v1 & in(all_61_7_135, all_0_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 42.51/12.48 |
% 42.51/12.48 | Instantiating (531) with all_876_0_1709, all_876_1_1710 yields:
% 42.51/12.48 | (532) in(all_61_6_134, all_0_9_9) = all_876_0_1709 & in(all_61_7_135, all_0_9_9) = all_876_1_1710 & ( ~ (all_876_0_1709 = 0) | ~ (all_876_1_1710 = 0))
% 42.51/12.48 |
% 42.51/12.48 | Applying alpha-rule on (532) yields:
% 42.51/12.48 | (533) in(all_61_6_134, all_0_9_9) = all_876_0_1709
% 42.51/12.48 | (534) in(all_61_7_135, all_0_9_9) = all_876_1_1710
% 42.51/12.48 | (535) ~ (all_876_0_1709 = 0) | ~ (all_876_1_1710 = 0)
% 42.51/12.48 |
% 42.51/12.48 | Instantiating formula (23) with all_61_6_134, all_0_9_9, all_876_0_1709, 0 and discharging atoms in(all_61_6_134, all_0_9_9) = all_876_0_1709, in(all_61_6_134, all_0_9_9) = 0, yields:
% 42.51/12.48 | (536) all_876_0_1709 = 0
% 42.51/12.48 |
% 42.51/12.48 | Instantiating formula (23) with all_61_7_135, all_0_9_9, all_876_1_1710, 0 and discharging atoms in(all_61_7_135, all_0_9_9) = all_876_1_1710, in(all_61_7_135, all_0_9_9) = 0, yields:
% 42.51/12.48 | (537) all_876_1_1710 = 0
% 42.51/12.48 |
% 42.51/12.48 +-Applying beta-rule and splitting (535), into two cases.
% 42.51/12.48 |-Branch one:
% 42.51/12.48 | (538) ~ (all_876_0_1709 = 0)
% 42.51/12.48 |
% 42.51/12.48 | Equations (536) can reduce 538 to:
% 42.51/12.48 | (140) $false
% 42.51/12.48 |
% 42.51/12.48 |-The branch is then unsatisfiable
% 42.51/12.48 |-Branch two:
% 42.51/12.48 | (536) all_876_0_1709 = 0
% 42.51/12.48 | (541) ~ (all_876_1_1710 = 0)
% 42.51/12.48 |
% 42.51/12.48 | Equations (537) can reduce 541 to:
% 42.51/12.48 | (140) $false
% 42.51/12.48 |
% 42.51/12.48 |-The branch is then unsatisfiable
% 42.51/12.48 |-Branch two:
% 42.51/12.48 | (502) ~ (all_225_0_418 = 0)
% 42.51/12.48 | (544) ? [v0] : ? [v1] : (in(all_61_6_134, all_0_9_9) = v0 & in(all_61_7_135, all_0_9_9) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 42.51/12.48 |
% 42.51/12.48 | Instantiating (544) with all_713_0_1825, all_713_1_1826 yields:
% 42.51/12.48 | (545) in(all_61_6_134, all_0_9_9) = all_713_1_1826 & in(all_61_7_135, all_0_9_9) = all_713_0_1825 & ( ~ (all_713_0_1825 = 0) | ~ (all_713_1_1826 = 0))
% 42.51/12.48 |
% 42.51/12.48 | Applying alpha-rule on (545) yields:
% 42.51/12.48 | (546) in(all_61_6_134, all_0_9_9) = all_713_1_1826
% 42.51/12.48 | (547) in(all_61_7_135, all_0_9_9) = all_713_0_1825
% 42.51/12.48 | (548) ~ (all_713_0_1825 = 0) | ~ (all_713_1_1826 = 0)
% 42.51/12.48 |
% 42.51/12.48 | Instantiating formula (23) with all_61_6_134, all_0_9_9, all_713_1_1826, 0 and discharging atoms in(all_61_6_134, all_0_9_9) = all_713_1_1826, in(all_61_6_134, all_0_9_9) = 0, yields:
% 42.51/12.48 | (549) all_713_1_1826 = 0
% 42.51/12.48 |
% 42.51/12.48 | Instantiating formula (23) with all_61_7_135, all_0_9_9, all_713_0_1825, 0 and discharging atoms in(all_61_7_135, all_0_9_9) = all_713_0_1825, in(all_61_7_135, all_0_9_9) = 0, yields:
% 42.51/12.48 | (550) all_713_0_1825 = 0
% 42.51/12.48 |
% 42.51/12.48 +-Applying beta-rule and splitting (548), into two cases.
% 42.51/12.48 |-Branch one:
% 42.51/12.48 | (551) ~ (all_713_0_1825 = 0)
% 42.51/12.48 |
% 42.51/12.48 | Equations (550) can reduce 551 to:
% 42.51/12.48 | (140) $false
% 42.51/12.48 |
% 42.51/12.48 |-The branch is then unsatisfiable
% 42.51/12.48 |-Branch two:
% 42.51/12.48 | (550) all_713_0_1825 = 0
% 42.51/12.48 | (554) ~ (all_713_1_1826 = 0)
% 42.51/12.48 |
% 42.51/12.48 | Equations (549) can reduce 554 to:
% 42.51/12.48 | (140) $false
% 42.51/12.48 |
% 42.51/12.48 |-The branch is then unsatisfiable
% 42.51/12.48 % SZS output end Proof for theBenchmark
% 42.51/12.48
% 42.51/12.48 11900ms
%------------------------------------------------------------------------------