TSTP Solution File: SEU270+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU270+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 08:48:21 EDT 2022
% Result : Theorem 8.62s 2.60s
% Output : Proof 28.78s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SEU270+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.32 % Computer : n006.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 600
% 0.12/0.32 % DateTime : Mon Jun 20 06:32:25 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.55/0.56 ____ _
% 0.55/0.56 ___ / __ \_____(_)___ ________ __________
% 0.55/0.56 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.55/0.56 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.55/0.56 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.55/0.56
% 0.55/0.56 A Theorem Prover for First-Order Logic
% 0.55/0.57 (ePrincess v.1.0)
% 0.55/0.57
% 0.55/0.57 (c) Philipp Rümmer, 2009-2015
% 0.55/0.57 (c) Peter Backeman, 2014-2015
% 0.55/0.57 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.55/0.57 Free software under GNU Lesser General Public License (LGPL).
% 0.55/0.57 Bug reports to peter@backeman.se
% 0.55/0.57
% 0.55/0.57 For more information, visit http://user.uu.se/~petba168/breu/
% 0.55/0.57
% 0.55/0.57 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.55/0.61 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.65/0.93 Prover 0: Preprocessing ...
% 2.35/1.22 Prover 0: Warning: ignoring some quantifiers
% 2.53/1.24 Prover 0: Constructing countermodel ...
% 4.54/1.74 Prover 0: gave up
% 4.54/1.74 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 4.93/1.79 Prover 1: Preprocessing ...
% 5.29/1.91 Prover 1: Warning: ignoring some quantifiers
% 5.29/1.91 Prover 1: Constructing countermodel ...
% 5.93/2.04 Prover 1: gave up
% 5.93/2.05 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 6.32/2.08 Prover 2: Preprocessing ...
% 6.72/2.22 Prover 2: Warning: ignoring some quantifiers
% 6.72/2.23 Prover 2: Constructing countermodel ...
% 8.38/2.60 Prover 2: proved (550ms)
% 8.62/2.60
% 8.62/2.60 No countermodel exists, formula is valid
% 8.62/2.60 % SZS status Theorem for theBenchmark
% 8.62/2.60
% 8.62/2.60 Generating proof ... Warning: ignoring some quantifiers
% 27.89/7.91 found it (size 251)
% 27.89/7.91
% 27.89/7.91 % SZS output start Proof for theBenchmark
% 27.89/7.91 Assumed formulas after preprocessing and simplification:
% 27.89/7.91 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ( ~ (v8 = 0) & ~ (v5 = 0) & ~ (v2 = 0) & relation_empty_yielding(v3) = 0 & relation_empty_yielding(empty_set) = 0 & inclusion_relation(v0) = v1 & connected(v1) = v2 & one_to_one(v9) = 0 & one_to_one(v6) = 0 & one_to_one(empty_set) = 0 & relation(v13) = 0 & relation(v10) = 0 & relation(v9) = 0 & relation(v6) = 0 & relation(v3) = 0 & relation(empty_set) = 0 & epsilon_transitive(v12) = 0 & epsilon_transitive(v9) = 0 & epsilon_transitive(v4) = 0 & epsilon_transitive(empty_set) = 0 & ordinal(v12) = 0 & ordinal(v9) = 0 & ordinal(v4) = 0 & ordinal(v0) = 0 & ordinal(empty_set) = 0 & epsilon_connected(v12) = 0 & epsilon_connected(v9) = 0 & epsilon_connected(v4) = 0 & epsilon_connected(empty_set) = 0 & function(v13) = 0 & function(v10) = 0 & function(v9) = 0 & function(v6) = 0 & function(v3) = 0 & function(empty_set) = 0 & empty(v11) = 0 & empty(v10) = 0 & empty(v9) = 0 & empty(v7) = v8 & empty(v4) = v5 & empty(empty_set) = 0 & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (inclusion_relation(v14) = v15) | ~ (subset(v17, v18) = v19) | ~ (relation_field(v15) = v16) | ? [v20] : ? [v21] : (( ~ (v20 = 0) & relation(v15) = v20) | ( ~ (v20 = 0) & in(v18, v14) = v20) | ( ~ (v20 = 0) & in(v17, v14) = v20) | (( ~ (v19 = 0) | (v21 = 0 & ordered_pair(v17, v18) = v20 & in(v20, v15) = 0)) & (v19 = 0 | ( ~ (v21 = 0) & ordered_pair(v17, v18) = v20 & in(v20, v15) = v21))))) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (inclusion_relation(v14) = v15) | ~ (ordered_pair(v17, v18) = v19) | ~ (relation_field(v15) = v16) | ? [v20] : ? [v21] : (( ~ (v20 = 0) & relation(v15) = v20) | ( ~ (v20 = 0) & in(v18, v14) = v20) | ( ~ (v20 = 0) & in(v17, v14) = v20) | (((v21 = 0 & subset(v17, v18) = 0) | ( ~ (v20 = 0) & in(v19, v15) = v20)) & ((v20 = 0 & in(v19, v15) = 0) | ( ~ (v21 = 0) & subset(v17, v18) = v21))))) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = 0 | ~ (powerset(v16) = v17) | ~ (element(v15, v17) = 0) | ~ (element(v14, v16) = v18) | ? [v19] : ( ~ (v19 = 0) & in(v14, v15) = v19)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v17 = v16 | ~ (ordered_pair(v17, v16) = v18) | ~ (is_connected_in(v14, v15) = 0) | ~ (relation(v14) = 0) | ? [v19] : ? [v20] : ((v20 = 0 & ordered_pair(v16, v17) = v19 & in(v19, v14) = 0) | (v19 = 0 & in(v18, v14) = 0) | ( ~ (v19 = 0) & in(v17, v15) = v19) | ( ~ (v19 = 0) & in(v16, v15) = v19))) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v17 = v16 | ~ (ordered_pair(v16, v17) = v18) | ~ (is_connected_in(v14, v15) = 0) | ~ (relation(v14) = 0) | ? [v19] : ? [v20] : ((v20 = 0 & ordered_pair(v17, v16) = v19 & in(v19, v14) = 0) | (v19 = 0 & in(v18, v14) = 0) | ( ~ (v19 = 0) & in(v17, v15) = v19) | ( ~ (v19 = 0) & in(v16, v15) = v19))) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v17 = 0 | ~ (powerset(v15) = v16) | ~ (element(v14, v16) = v17) | ? [v18] : ( ~ (v18 = 0) & subset(v14, v15) = v18)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v17 = 0 | ~ (element(v14, v16) = v17) | ~ (in(v14, v15) = 0) | ? [v18] : ? [v19] : ( ~ (v19 = 0) & powerset(v16) = v18 & element(v15, v18) = v19)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v15 = v14 | ~ (element(v17, v16) = v15) | ~ (element(v17, v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v15 = v14 | ~ (subset(v17, v16) = v15) | ~ (subset(v17, v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v15 = v14 | ~ (ordered_pair(v17, v16) = v15) | ~ (ordered_pair(v17, v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v15 = v14 | ~ (is_connected_in(v17, v16) = v15) | ~ (is_connected_in(v17, v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v15 = v14 | ~ (ordinal_subset(v17, v16) = v15) | ~ (ordinal_subset(v17, v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v15 = v14 | ~ (set_union2(v17, v16) = v15) | ~ (set_union2(v17, v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v15 = v14 | ~ (unordered_pair(v17, v16) = v15) | ~ (unordered_pair(v17, v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v15 = v14 | ~ (in(v17, v16) = v15) | ~ (in(v17, v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (powerset(v16) = v17) | ~ (element(v15, v17) = 0) | ~ (in(v14, v15) = 0) | element(v14, v16) = 0) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (powerset(v16) = v17) | ~ (element(v15, v17) = 0) | ~ (in(v14, v15) = 0) | ? [v18] : ( ~ (v18 = 0) & empty(v16) = v18)) & ! [v14] : ! [v15] : ! [v16] : (v16 = v15 | ~ (inclusion_relation(v14) = v16) | ~ (relation_field(v15) = v14) | ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ((v20 = 0 & v19 = 0 & in(v18, v14) = 0 & in(v17, v14) = 0 & ((v23 = 0 & subset(v17, v18) = 0) | (v22 = 0 & ordered_pair(v17, v18) = v21 & in(v21, v15) = 0)) & (( ~ (v23 = 0) & subset(v17, v18) = v23) | ( ~ (v22 = 0) & ordered_pair(v17, v18) = v21 & in(v21, v15) = v22))) | ( ~ (v17 = 0) & relation(v15) = v17))) & ! [v14] : ! [v15] : ! [v16] : (v16 = v14 | ~ (inclusion_relation(v14) = v15) | ~ (relation_field(v15) = v16) | ? [v17] : ( ~ (v17 = 0) & relation(v15) = v17)) & ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (element(v14, v15) = v16) | ? [v17] : ( ~ (v17 = 0) & in(v14, v15) = v17)) & ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (subset(v14, v15) = v16) | ? [v17] : ? [v18] : ( ~ (v18 = 0) & powerset(v15) = v17 & element(v14, v17) = v18)) & ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (is_connected_in(v14, v15) = v16) | ~ (relation(v14) = 0) | ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ( ~ (v22 = 0) & ~ (v20 = 0) & ~ (v18 = v17) & ordered_pair(v18, v17) = v21 & ordered_pair(v17, v18) = v19 & in(v21, v14) = v22 & in(v19, v14) = v20 & in(v18, v15) = 0 & in(v17, v15) = 0)) & ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (ordinal_subset(v15, v14) = v16) | ? [v17] : ((v17 = 0 & ordinal_subset(v14, v15) = 0) | ( ~ (v17 = 0) & ordinal(v15) = v17) | ( ~ (v17 = 0) & ordinal(v14) = v17))) & ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (ordinal_subset(v14, v15) = v16) | ? [v17] : ((v17 = 0 & ordinal_subset(v15, v14) = 0) | ( ~ (v17 = 0) & ordinal(v15) = v17) | ( ~ (v17 = 0) & ordinal(v14) = v17))) & ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (ordinal_subset(v14, v14) = v16) | ~ (ordinal(v15) = 0) | ? [v17] : ( ~ (v17 = 0) & ordinal(v14) = v17)) & ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (in(v14, v15) = v16) | ? [v17] : ((v17 = 0 & empty(v15) = 0) | ( ~ (v17 = 0) & element(v14, v15) = v17))) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (powerset(v16) = v15) | ~ (powerset(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (relation_empty_yielding(v16) = v15) | ~ (relation_empty_yielding(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (relation_dom(v16) = v15) | ~ (relation_dom(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (relation_rng(v16) = v15) | ~ (relation_rng(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (singleton(v16) = v15) | ~ (singleton(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (inclusion_relation(v16) = v15) | ~ (inclusion_relation(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (relation_field(v16) = v15) | ~ (relation_field(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (connected(v16) = v15) | ~ (connected(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (one_to_one(v16) = v15) | ~ (one_to_one(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (relation(v16) = v15) | ~ (relation(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (epsilon_transitive(v16) = v15) | ~ (epsilon_transitive(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (ordinal(v16) = v15) | ~ (ordinal(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (epsilon_connected(v16) = v15) | ~ (epsilon_connected(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (function(v16) = v15) | ~ (function(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (empty(v16) = v15) | ~ (empty(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : ( ~ (powerset(v15) = v16) | ~ (element(v14, v16) = 0) | subset(v14, v15) = 0) & ! [v14] : ! [v15] : ! [v16] : ( ~ (inclusion_relation(v14) = v16) | ~ (relation(v15) = 0) | ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : (( ~ (v16 = v15) | (v17 = v14 & relation_field(v15) = v14 & ! [v25] : ! [v26] : ! [v27] : ( ~ (subset(v25, v26) = v27) | ? [v28] : ? [v29] : (( ~ (v28 = 0) & in(v26, v14) = v28) | ( ~ (v28 = 0) & in(v25, v14) = v28) | (( ~ (v27 = 0) | (v29 = 0 & ordered_pair(v25, v26) = v28 & in(v28, v15) = 0)) & (v27 = 0 | ( ~ (v29 = 0) & ordered_pair(v25, v26) = v28 & in(v28, v15) = v29))))) & ! [v25] : ! [v26] : ! [v27] : ( ~ (ordered_pair(v25, v26) = v27) | ? [v28] : ? [v29] : (( ~ (v28 = 0) & in(v26, v14) = v28) | ( ~ (v28 = 0) & in(v25, v14) = v28) | (((v29 = 0 & subset(v25, v26) = 0) | ( ~ (v28 = 0) & in(v27, v15) = v28)) & ((v28 = 0 & in(v27, v15) = 0) | ( ~ (v29 = 0) & subset(v25, v26) = v29))))))) & (v16 = v15 | (v21 = 0 & v20 = 0 & in(v19, v14) = 0 & in(v18, v14) = 0 & ((v24 = 0 & subset(v18, v19) = 0) | (v23 = 0 & ordered_pair(v18, v19) = v22 & in(v22, v15) = 0)) & (( ~ (v24 = 0) & subset(v18, v19) = v24) | ( ~ (v23 = 0) & ordered_pair(v18, v19) = v22 & in(v22, v15) = v23))) | ( ~ (v17 = v14) & relation_field(v15) = v17)))) & ! [v14] : ! [v15] : ! [v16] : ( ~ (subset(v14, v15) = v16) | ? [v17] : (( ~ (v17 = 0) & ordinal(v15) = v17) | ( ~ (v17 = 0) & ordinal(v14) = v17) | (( ~ (v16 = 0) | (v17 = 0 & ordinal_subset(v14, v15) = 0)) & (v16 = 0 | ( ~ (v17 = 0) & ordinal_subset(v14, v15) = v17))))) & ! [v14] : ! [v15] : ! [v16] : ( ~ (ordered_pair(v14, v15) = v16) | ? [v17] : ? [v18] : (singleton(v14) = v18 & unordered_pair(v17, v18) = v16 & unordered_pair(v14, v15) = v17)) & ! [v14] : ! [v15] : ! [v16] : ( ~ (ordered_pair(v14, v15) = v16) | ? [v17] : ( ~ (v17 = 0) & empty(v16) = v17)) & ! [v14] : ! [v15] : ! [v16] : ( ~ (ordinal_subset(v14, v15) = v16) | ? [v17] : (( ~ (v17 = 0) & ordinal(v15) = v17) | ( ~ (v17 = 0) & ordinal(v14) = v17) | (( ~ (v16 = 0) | (v17 = 0 & subset(v14, v15) = 0)) & (v16 = 0 | ( ~ (v17 = 0) & subset(v14, v15) = v17))))) & ! [v14] : ! [v15] : ! [v16] : ( ~ (set_union2(v15, v14) = v16) | set_union2(v14, v15) = v16) & ! [v14] : ! [v15] : ! [v16] : ( ~ (set_union2(v15, v14) = v16) | ? [v17] : ((v17 = 0 & empty(v14) = 0) | ( ~ (v17 = 0) & empty(v16) = v17))) & ! [v14] : ! [v15] : ! [v16] : ( ~ (set_union2(v14, v15) = v16) | set_union2(v15, v14) = v16) & ! [v14] : ! [v15] : ! [v16] : ( ~ (set_union2(v14, v15) = v16) | ? [v17] : ((v17 = 0 & empty(v14) = 0) | ( ~ (v17 = 0) & empty(v16) = v17))) & ! [v14] : ! [v15] : ! [v16] : ( ~ (unordered_pair(v15, v14) = v16) | unordered_pair(v14, v15) = v16) & ! [v14] : ! [v15] : ! [v16] : ( ~ (unordered_pair(v14, v15) = v16) | unordered_pair(v15, v14) = v16) & ! [v14] : ! [v15] : ! [v16] : ( ~ (unordered_pair(v14, v15) = v16) | ? [v17] : ? [v18] : (singleton(v14) = v18 & ordered_pair(v14, v15) = v17 & unordered_pair(v16, v18) = v17)) & ! [v14] : ! [v15] : ! [v16] : ( ~ (empty(v16) = 0) | ~ (in(v14, v15) = 0) | ? [v17] : ? [v18] : ( ~ (v18 = 0) & powerset(v16) = v17 & element(v15, v17) = v18)) & ! [v14] : ! [v15] : (v15 = v14 | ~ (set_union2(v14, v14) = v15)) & ! [v14] : ! [v15] : (v15 = v14 | ~ (set_union2(v14, empty_set) = v15)) & ! [v14] : ! [v15] : (v15 = v14 | ~ (empty(v15) = 0) | ~ (empty(v14) = 0)) & ! [v14] : ! [v15] : (v15 = 0 | ~ (subset(v14, v14) = v15)) & ! [v14] : ! [v15] : (v15 = 0 | ~ (ordinal(v14) = v15) | ? [v16] : (( ~ (v16 = 0) & epsilon_transitive(v14) = v16) | ( ~ (v16 = 0) & epsilon_connected(v14) = v16))) & ! [v14] : ! [v15] : (v15 = 0 | ~ (function(v14) = v15) | ? [v16] : ( ~ (v16 = 0) & empty(v14) = v16)) & ! [v14] : ! [v15] : ( ~ (element(v14, v15) = 0) | ? [v16] : ((v16 = 0 & empty(v15) = 0) | (v16 = 0 & in(v14, v15) = 0))) & ! [v14] : ! [v15] : ( ~ (relation_dom(v14) = v15) | ? [v16] : ? [v17] : ? [v18] : ((v18 = v16 & relation_rng(v14) = v17 & relation_field(v14) = v16 & set_union2(v15, v17) = v16) | ( ~ (v16 = 0) & relation(v14) = v16))) & ! [v14] : ! [v15] : ( ~ (relation_rng(v14) = v15) | ? [v16] : ? [v17] : ? [v18] : ((v18 = v16 & relation_dom(v14) = v17 & relation_field(v14) = v16 & set_union2(v17, v15) = v16) | ( ~ (v16 = 0) & relation(v14) = v16))) & ! [v14] : ! [v15] : ( ~ (inclusion_relation(v14) = v15) | relation(v15) = 0) & ! [v14] : ! [v15] : ( ~ (subset(v14, v15) = 0) | ? [v16] : (powerset(v15) = v16 & element(v14, v16) = 0)) & ! [v14] : ! [v15] : ( ~ (relation_field(v14) = v15) | ? [v16] : ? [v17] : ? [v18] : ((v18 = v15 & relation_dom(v14) = v16 & relation_rng(v14) = v17 & set_union2(v16, v17) = v15) | ( ~ (v16 = 0) & relation(v14) = v16))) & ! [v14] : ! [v15] : ( ~ (relation_field(v14) = v15) | ? [v16] : ? [v17] : (( ~ (v16 = 0) & relation(v14) = v16) | (((v17 = 0 & is_connected_in(v14, v15) = 0) | ( ~ (v16 = 0) & connected(v14) = v16)) & ((v16 = 0 & connected(v14) = 0) | ( ~ (v17 = 0) & is_connected_in(v14, v15) = v17))))) & ! [v14] : ! [v15] : ( ~ (connected(v14) = v15) | ? [v16] : ? [v17] : (( ~ (v16 = 0) & relation(v14) = v16) | (( ~ (v15 = 0) | (v17 = 0 & relation_field(v14) = v16 & is_connected_in(v14, v16) = 0)) & (v15 = 0 | ( ~ (v17 = 0) & relation_field(v14) = v16 & is_connected_in(v14, v16) = v17))))) & ! [v14] : ! [v15] : ( ~ (one_to_one(v14) = v15) | ? [v16] : ? [v17] : ((v17 = 0 & v16 = 0 & v15 = 0 & relation(v14) = 0 & function(v14) = 0) | ( ~ (v16 = 0) & relation(v14) = v16) | ( ~ (v16 = 0) & function(v14) = v16) | ( ~ (v16 = 0) & empty(v14) = v16))) & ! [v14] : ! [v15] : ( ~ (epsilon_transitive(v14) = v15) | ? [v16] : ? [v17] : ((v17 = 0 & v16 = 0 & v15 = 0 & ordinal(v14) = 0 & epsilon_connected(v14) = 0) | ( ~ (v16 = 0) & empty(v14) = v16))) & ! [v14] : ! [v15] : ( ~ (epsilon_transitive(v14) = v15) | ? [v16] : ((v16 = 0 & v15 = 0 & epsilon_connected(v14) = 0) | ( ~ (v16 = 0) & ordinal(v14) = v16))) & ! [v14] : ! [v15] : ( ~ (ordinal(v15) = 0) | ~ (ordinal(v14) = 0) | ordinal_subset(v14, v14) = 0) & ! [v14] : ! [v15] : ( ~ (ordinal(v14) = v15) | ? [v16] : ? [v17] : ((v17 = 0 & v16 = 0 & v15 = 0 & epsilon_transitive(v14) = 0 & epsilon_connected(v14) = 0) | ( ~ (v16 = 0) & empty(v14) = v16))) & ! [v14] : ! [v15] : ( ~ (epsilon_connected(v14) = v15) | ? [v16] : ? [v17] : ((v17 = 0 & v16 = 0 & v15 = 0 & epsilon_transitive(v14) = 0 & ordinal(v14) = 0) | ( ~ (v16 = 0) & empty(v14) = v16))) & ! [v14] : ! [v15] : ( ~ (epsilon_connected(v14) = v15) | ? [v16] : ((v16 = 0 & v15 = 0 & epsilon_transitive(v14) = 0) | ( ~ (v16 = 0) & ordinal(v14) = v16))) & ! [v14] : ! [v15] : ( ~ (in(v15, v14) = 0) | ? [v16] : ( ~ (v16 = 0) & in(v14, v15) = v16)) & ! [v14] : ! [v15] : ( ~ (in(v14, v15) = 0) | element(v14, v15) = 0) & ! [v14] : ! [v15] : ( ~ (in(v14, v15) = 0) | ? [v16] : ( ~ (v16 = 0) & empty(v15) = v16)) & ! [v14] : ! [v15] : ( ~ (in(v14, v15) = 0) | ? [v16] : ( ~ (v16 = 0) & in(v15, v14) = v16)) & ! [v14] : ! [v15] : ( ~ (in(v14, v15) = 0) | ? [v16] : ((v16 = 0 & ordinal(v14) = 0) | ( ~ (v16 = 0) & ordinal(v15) = v16))) & ! [v14] : (v14 = empty_set | ~ (empty(v14) = 0)) & ! [v14] : ( ~ (relation(v14) = 0) | ? [v15] : ? [v16] : ? [v17] : (relation_dom(v14) = v16 & relation_rng(v14) = v17 & relation_field(v14) = v15 & set_union2(v16, v17) = v15)) & ! [v14] : ( ~ (relation(v14) = 0) | ? [v15] : ? [v16] : ? [v17] : (((v17 = 0 & relation_field(v14) = v16 & is_connected_in(v14, v16) = 0) | ( ~ (v15 = 0) & connected(v14) = v15)) & ((v15 = 0 & connected(v14) = 0) | ( ~ (v17 = 0) & relation_field(v14) = v16 & is_connected_in(v14, v16) = v17)))) & ! [v14] : ( ~ (relation(v14) = 0) | ? [v15] : ? [v16] : ((v16 = 0 & v15 = 0 & one_to_one(v14) = 0 & function(v14) = 0) | ( ~ (v15 = 0) & function(v14) = v15) | ( ~ (v15 = 0) & empty(v14) = v15))) & ! [v14] : ( ~ (epsilon_transitive(v14) = 0) | ? [v15] : ((v15 = 0 & ordinal(v14) = 0) | ( ~ (v15 = 0) & epsilon_connected(v14) = v15))) & ! [v14] : ( ~ (ordinal(v14) = 0) | (epsilon_transitive(v14) = 0 & epsilon_connected(v14) = 0)) & ! [v14] : ( ~ (epsilon_connected(v14) = 0) | ? [v15] : ((v15 = 0 & ordinal(v14) = 0) | ( ~ (v15 = 0) & epsilon_transitive(v14) = v15))) & ! [v14] : ( ~ (function(v14) = 0) | ? [v15] : ? [v16] : ((v16 = 0 & v15 = 0 & one_to_one(v14) = 0 & relation(v14) = 0) | ( ~ (v15 = 0) & relation(v14) = v15) | ( ~ (v15 = 0) & empty(v14) = v15))) & ! [v14] : ( ~ (empty(v14) = 0) | function(v14) = 0) & ! [v14] : ( ~ (empty(v14) = 0) | ? [v15] : ? [v16] : ? [v17] : ((v17 = 0 & v16 = 0 & v15 = 0 & one_to_one(v14) = 0 & relation(v14) = 0 & function(v14) = 0) | ( ~ (v15 = 0) & relation(v14) = v15) | ( ~ (v15 = 0) & function(v14) = v15))) & ! [v14] : ( ~ (empty(v14) = 0) | (epsilon_transitive(v14) = 0 & ordinal(v14) = 0 & epsilon_connected(v14) = 0)) & ? [v14] : ? [v15] : ? [v16] : element(v15, v14) = v16 & ? [v14] : ? [v15] : ? [v16] : subset(v15, v14) = v16 & ? [v14] : ? [v15] : ? [v16] : ordered_pair(v15, v14) = v16 & ? [v14] : ? [v15] : ? [v16] : is_connected_in(v15, v14) = v16 & ? [v14] : ? [v15] : ? [v16] : ordinal_subset(v15, v14) = v16 & ? [v14] : ? [v15] : ? [v16] : set_union2(v15, v14) = v16 & ? [v14] : ? [v15] : ? [v16] : unordered_pair(v15, v14) = v16 & ? [v14] : ? [v15] : ? [v16] : in(v15, v14) = v16 & ? [v14] : ? [v15] : powerset(v14) = v15 & ? [v14] : ? [v15] : relation_empty_yielding(v14) = v15 & ? [v14] : ? [v15] : element(v15, v14) = 0 & ? [v14] : ? [v15] : relation_dom(v14) = v15 & ? [v14] : ? [v15] : relation_rng(v14) = v15 & ? [v14] : ? [v15] : singleton(v14) = v15 & ? [v14] : ? [v15] : inclusion_relation(v14) = v15 & ? [v14] : ? [v15] : relation_field(v14) = v15 & ? [v14] : ? [v15] : connected(v14) = v15 & ? [v14] : ? [v15] : one_to_one(v14) = v15 & ? [v14] : ? [v15] : relation(v14) = v15 & ? [v14] : ? [v15] : epsilon_transitive(v14) = v15 & ? [v14] : ? [v15] : ordinal(v14) = v15 & ? [v14] : ? [v15] : epsilon_connected(v14) = v15 & ? [v14] : ? [v15] : function(v14) = v15 & ? [v14] : ? [v15] : empty(v14) = v15)
% 28.19/7.99 | 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, all_0_10_10, all_0_11_11, all_0_12_12, all_0_13_13 yields:
% 28.19/7.99 | (1) ~ (all_0_5_5 = 0) & ~ (all_0_8_8 = 0) & ~ (all_0_11_11 = 0) & relation_empty_yielding(all_0_10_10) = 0 & relation_empty_yielding(empty_set) = 0 & inclusion_relation(all_0_13_13) = all_0_12_12 & connected(all_0_12_12) = all_0_11_11 & one_to_one(all_0_4_4) = 0 & one_to_one(all_0_7_7) = 0 & one_to_one(empty_set) = 0 & relation(all_0_0_0) = 0 & relation(all_0_3_3) = 0 & relation(all_0_4_4) = 0 & relation(all_0_7_7) = 0 & relation(all_0_10_10) = 0 & relation(empty_set) = 0 & epsilon_transitive(all_0_1_1) = 0 & epsilon_transitive(all_0_4_4) = 0 & epsilon_transitive(all_0_9_9) = 0 & epsilon_transitive(empty_set) = 0 & ordinal(all_0_1_1) = 0 & ordinal(all_0_4_4) = 0 & ordinal(all_0_9_9) = 0 & ordinal(all_0_13_13) = 0 & ordinal(empty_set) = 0 & epsilon_connected(all_0_1_1) = 0 & epsilon_connected(all_0_4_4) = 0 & epsilon_connected(all_0_9_9) = 0 & epsilon_connected(empty_set) = 0 & function(all_0_0_0) = 0 & function(all_0_3_3) = 0 & function(all_0_4_4) = 0 & function(all_0_7_7) = 0 & function(all_0_10_10) = 0 & function(empty_set) = 0 & empty(all_0_2_2) = 0 & empty(all_0_3_3) = 0 & empty(all_0_4_4) = 0 & empty(all_0_6_6) = all_0_5_5 & empty(all_0_9_9) = all_0_8_8 & empty(empty_set) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (inclusion_relation(v0) = v1) | ~ (subset(v3, v4) = v5) | ~ (relation_field(v1) = v2) | ? [v6] : ? [v7] : (( ~ (v6 = 0) & relation(v1) = v6) | ( ~ (v6 = 0) & in(v4, v0) = v6) | ( ~ (v6 = 0) & in(v3, v0) = v6) | (( ~ (v5 = 0) | (v7 = 0 & ordered_pair(v3, v4) = v6 & in(v6, v1) = 0)) & (v5 = 0 | ( ~ (v7 = 0) & ordered_pair(v3, v4) = v6 & in(v6, v1) = v7))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (inclusion_relation(v0) = v1) | ~ (ordered_pair(v3, v4) = v5) | ~ (relation_field(v1) = v2) | ? [v6] : ? [v7] : (( ~ (v6 = 0) & relation(v1) = v6) | ( ~ (v6 = 0) & in(v4, v0) = v6) | ( ~ (v6 = 0) & in(v3, v0) = v6) | (((v7 = 0 & subset(v3, v4) = 0) | ( ~ (v6 = 0) & in(v5, v1) = v6)) & ((v6 = 0 & in(v5, v1) = 0) | ( ~ (v7 = 0) & subset(v3, v4) = v7))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (element(v0, v2) = v4) | ? [v5] : ( ~ (v5 = 0) & in(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (ordered_pair(v3, v2) = v4) | ~ (is_connected_in(v0, v1) = 0) | ~ (relation(v0) = 0) | ? [v5] : ? [v6] : ((v6 = 0 & ordered_pair(v2, v3) = v5 & in(v5, v0) = 0) | (v5 = 0 & in(v4, v0) = 0) | ( ~ (v5 = 0) & in(v3, v1) = v5) | ( ~ (v5 = 0) & in(v2, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (ordered_pair(v2, v3) = v4) | ~ (is_connected_in(v0, v1) = 0) | ~ (relation(v0) = 0) | ? [v5] : ? [v6] : ((v6 = 0 & ordered_pair(v3, v2) = v5 & in(v5, v0) = 0) | (v5 = 0 & in(v4, v0) = 0) | ( ~ (v5 = 0) & in(v3, v1) = v5) | ( ~ (v5 = 0) & in(v2, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (element(v0, v2) = v3) | ~ (in(v0, v1) = 0) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & powerset(v2) = v4 & element(v1, v4) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(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 | ~ (is_connected_in(v3, v2) = v1) | ~ (is_connected_in(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordinal_subset(v3, v2) = v1) | ~ (ordinal_subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (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] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | element(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (inclusion_relation(v0) = v2) | ~ (relation_field(v1) = v0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ((v6 = 0 & v5 = 0 & in(v4, v0) = 0 & in(v3, v0) = 0 & ((v9 = 0 & subset(v3, v4) = 0) | (v8 = 0 & ordered_pair(v3, v4) = v7 & in(v7, v1) = 0)) & (( ~ (v9 = 0) & subset(v3, v4) = v9) | ( ~ (v8 = 0) & ordered_pair(v3, v4) = v7 & in(v7, v1) = v8))) | ( ~ (v3 = 0) & relation(v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (inclusion_relation(v0) = v1) | ~ (relation_field(v1) = v2) | ? [v3] : ( ~ (v3 = 0) & relation(v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v1) = v3 & element(v0, v3) = v4)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (is_connected_in(v0, v1) = v2) | ~ (relation(v0) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ( ~ (v8 = 0) & ~ (v6 = 0) & ~ (v4 = v3) & ordered_pair(v4, v3) = v7 & ordered_pair(v3, v4) = v5 & in(v7, v0) = v8 & in(v5, v0) = v6 & in(v4, v1) = 0 & in(v3, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (ordinal_subset(v1, v0) = v2) | ? [v3] : ((v3 = 0 & ordinal_subset(v0, v1) = 0) | ( ~ (v3 = 0) & ordinal(v1) = v3) | ( ~ (v3 = 0) & ordinal(v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (ordinal_subset(v0, v1) = v2) | ? [v3] : ((v3 = 0 & ordinal_subset(v1, v0) = 0) | ( ~ (v3 = 0) & ordinal(v1) = v3) | ( ~ (v3 = 0) & ordinal(v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (ordinal_subset(v0, v0) = v2) | ~ (ordinal(v1) = 0) | ? [v3] : ( ~ (v3 = 0) & ordinal(v0) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v0, v1) = v2) | ? [v3] : ((v3 = 0 & empty(v1) = 0) | ( ~ (v3 = 0) & element(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_empty_yielding(v2) = v1) | ~ (relation_empty_yielding(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 | ~ (inclusion_relation(v2) = v1) | ~ (inclusion_relation(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_field(v2) = v1) | ~ (relation_field(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (connected(v2) = v1) | ~ (connected(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (epsilon_transitive(v2) = v1) | ~ (epsilon_transitive(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ordinal(v2) = v1) | ~ (ordinal(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (epsilon_connected(v2) = v1) | ~ (epsilon_connected(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | subset(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (inclusion_relation(v0) = v2) | ~ (relation(v1) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (( ~ (v2 = v1) | (v3 = v0 & relation_field(v1) = v0 & ! [v11] : ! [v12] : ! [v13] : ( ~ (subset(v11, v12) = v13) | ? [v14] : ? [v15] : (( ~ (v14 = 0) & in(v12, v0) = v14) | ( ~ (v14 = 0) & in(v11, v0) = v14) | (( ~ (v13 = 0) | (v15 = 0 & ordered_pair(v11, v12) = v14 & in(v14, v1) = 0)) & (v13 = 0 | ( ~ (v15 = 0) & ordered_pair(v11, v12) = v14 & in(v14, v1) = v15))))) & ! [v11] : ! [v12] : ! [v13] : ( ~ (ordered_pair(v11, v12) = v13) | ? [v14] : ? [v15] : (( ~ (v14 = 0) & in(v12, v0) = v14) | ( ~ (v14 = 0) & in(v11, v0) = v14) | (((v15 = 0 & subset(v11, v12) = 0) | ( ~ (v14 = 0) & in(v13, v1) = v14)) & ((v14 = 0 & in(v13, v1) = 0) | ( ~ (v15 = 0) & subset(v11, v12) = v15))))))) & (v2 = v1 | (v7 = 0 & v6 = 0 & in(v5, v0) = 0 & in(v4, v0) = 0 & ((v10 = 0 & subset(v4, v5) = 0) | (v9 = 0 & ordered_pair(v4, v5) = v8 & in(v8, v1) = 0)) & (( ~ (v10 = 0) & subset(v4, v5) = v10) | ( ~ (v9 = 0) & ordered_pair(v4, v5) = v8 & in(v8, v1) = v9))) | ( ~ (v3 = v0) & relation_field(v1) = v3)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & ordinal(v1) = v3) | ( ~ (v3 = 0) & ordinal(v0) = v3) | (( ~ (v2 = 0) | (v3 = 0 & ordinal_subset(v0, v1) = 0)) & (v2 = 0 | ( ~ (v3 = 0) & ordinal_subset(v0, v1) = 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] : ( ~ (ordinal_subset(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & ordinal(v1) = v3) | ( ~ (v3 = 0) & ordinal(v0) = v3) | (( ~ (v2 = 0) | (v3 = 0 & subset(v0, v1) = 0)) & (v2 = 0 | ( ~ (v3 = 0) & subset(v0, v1) = v3))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ? [v3] : ((v3 = 0 & empty(v0) = 0) | ( ~ (v3 = 0) & empty(v2) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : ((v3 = 0 & empty(v0) = 0) | ( ~ (v3 = 0) & empty(v2) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & ordered_pair(v0, v1) = v3 & unordered_pair(v2, v4) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (empty(v2) = 0) | ~ (in(v0, v1) = 0) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v2) = v3 & element(v1, v3) = v4)) & ! [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 = 0 | ~ (subset(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (ordinal(v0) = v1) | ? [v2] : (( ~ (v2 = 0) & epsilon_transitive(v0) = v2) | ( ~ (v2 = 0) & epsilon_connected(v0) = v2))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (function(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2)) & ! [v0] : ! [v1] : ( ~ (element(v0, v1) = 0) | ? [v2] : ((v2 = 0 & empty(v1) = 0) | (v2 = 0 & in(v0, v1) = 0))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v2 & relation_rng(v0) = v3 & relation_field(v0) = v2 & set_union2(v1, v3) = v2) | ( ~ (v2 = 0) & relation(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v2 & relation_dom(v0) = v3 & relation_field(v0) = v2 & set_union2(v3, v1) = v2) | ( ~ (v2 = 0) & relation(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (inclusion_relation(v0) = v1) | relation(v1) = 0) & ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (powerset(v1) = v2 & element(v0, v2) = 0)) & ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v1 & relation_dom(v0) = v2 & relation_rng(v0) = v3 & set_union2(v2, v3) = v1) | ( ~ (v2 = 0) & relation(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ? [v2] : ? [v3] : (( ~ (v2 = 0) & relation(v0) = v2) | (((v3 = 0 & is_connected_in(v0, v1) = 0) | ( ~ (v2 = 0) & connected(v0) = v2)) & ((v2 = 0 & connected(v0) = 0) | ( ~ (v3 = 0) & is_connected_in(v0, v1) = v3))))) & ! [v0] : ! [v1] : ( ~ (connected(v0) = v1) | ? [v2] : ? [v3] : (( ~ (v2 = 0) & relation(v0) = v2) | (( ~ (v1 = 0) | (v3 = 0 & relation_field(v0) = v2 & is_connected_in(v0, v2) = 0)) & (v1 = 0 | ( ~ (v3 = 0) & relation_field(v0) = v2 & is_connected_in(v0, v2) = v3))))) & ! [v0] : ! [v1] : ( ~ (one_to_one(v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & relation(v0) = 0 & function(v0) = 0) | ( ~ (v2 = 0) & relation(v0) = v2) | ( ~ (v2 = 0) & function(v0) = v2) | ( ~ (v2 = 0) & empty(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (epsilon_transitive(v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & ordinal(v0) = 0 & epsilon_connected(v0) = 0) | ( ~ (v2 = 0) & empty(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (epsilon_transitive(v0) = v1) | ? [v2] : ((v2 = 0 & v1 = 0 & epsilon_connected(v0) = 0) | ( ~ (v2 = 0) & ordinal(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (ordinal(v1) = 0) | ~ (ordinal(v0) = 0) | ordinal_subset(v0, v0) = 0) & ! [v0] : ! [v1] : ( ~ (ordinal(v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & epsilon_transitive(v0) = 0 & epsilon_connected(v0) = 0) | ( ~ (v2 = 0) & empty(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (epsilon_connected(v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & epsilon_transitive(v0) = 0 & ordinal(v0) = 0) | ( ~ (v2 = 0) & empty(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (epsilon_connected(v0) = v1) | ? [v2] : ((v2 = 0 & v1 = 0 & epsilon_transitive(v0) = 0) | ( ~ (v2 = 0) & ordinal(v0) = v2))) & ! [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] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ((v2 = 0 & ordinal(v0) = 0) | ( ~ (v2 = 0) & ordinal(v1) = v2))) & ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0)) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (relation_dom(v0) = v2 & relation_rng(v0) = v3 & relation_field(v0) = v1 & set_union2(v2, v3) = v1)) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (((v3 = 0 & relation_field(v0) = v2 & is_connected_in(v0, v2) = 0) | ( ~ (v1 = 0) & connected(v0) = v1)) & ((v1 = 0 & connected(v0) = 0) | ( ~ (v3 = 0) & relation_field(v0) = v2 & is_connected_in(v0, v2) = v3)))) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ((v2 = 0 & v1 = 0 & one_to_one(v0) = 0 & function(v0) = 0) | ( ~ (v1 = 0) & function(v0) = v1) | ( ~ (v1 = 0) & empty(v0) = v1))) & ! [v0] : ( ~ (epsilon_transitive(v0) = 0) | ? [v1] : ((v1 = 0 & ordinal(v0) = 0) | ( ~ (v1 = 0) & epsilon_connected(v0) = v1))) & ! [v0] : ( ~ (ordinal(v0) = 0) | (epsilon_transitive(v0) = 0 & epsilon_connected(v0) = 0)) & ! [v0] : ( ~ (epsilon_connected(v0) = 0) | ? [v1] : ((v1 = 0 & ordinal(v0) = 0) | ( ~ (v1 = 0) & epsilon_transitive(v0) = v1))) & ! [v0] : ( ~ (function(v0) = 0) | ? [v1] : ? [v2] : ((v2 = 0 & v1 = 0 & one_to_one(v0) = 0 & relation(v0) = 0) | ( ~ (v1 = 0) & relation(v0) = v1) | ( ~ (v1 = 0) & empty(v0) = v1))) & ! [v0] : ( ~ (empty(v0) = 0) | function(v0) = 0) & ! [v0] : ( ~ (empty(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & one_to_one(v0) = 0 & relation(v0) = 0 & function(v0) = 0) | ( ~ (v1 = 0) & relation(v0) = v1) | ( ~ (v1 = 0) & function(v0) = v1))) & ! [v0] : ( ~ (empty(v0) = 0) | (epsilon_transitive(v0) = 0 & ordinal(v0) = 0 & epsilon_connected(v0) = 0)) & ? [v0] : ? [v1] : ? [v2] : element(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : ordered_pair(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : is_connected_in(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : ordinal_subset(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : set_union2(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : unordered_pair(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2 & ? [v0] : ? [v1] : powerset(v0) = v1 & ? [v0] : ? [v1] : relation_empty_yielding(v0) = v1 & ? [v0] : ? [v1] : element(v1, v0) = 0 & ? [v0] : ? [v1] : relation_dom(v0) = v1 & ? [v0] : ? [v1] : relation_rng(v0) = v1 & ? [v0] : ? [v1] : singleton(v0) = v1 & ? [v0] : ? [v1] : inclusion_relation(v0) = v1 & ? [v0] : ? [v1] : relation_field(v0) = v1 & ? [v0] : ? [v1] : connected(v0) = v1 & ? [v0] : ? [v1] : one_to_one(v0) = v1 & ? [v0] : ? [v1] : relation(v0) = v1 & ? [v0] : ? [v1] : epsilon_transitive(v0) = v1 & ? [v0] : ? [v1] : ordinal(v0) = v1 & ? [v0] : ? [v1] : epsilon_connected(v0) = v1 & ? [v0] : ? [v1] : function(v0) = v1 & ? [v0] : ? [v1] : empty(v0) = v1
% 28.19/8.02 |
% 28.19/8.02 | Applying alpha-rule on (1) yields:
% 28.19/8.02 | (2) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0))
% 28.19/8.02 | (3) function(all_0_10_10) = 0
% 28.19/8.02 | (4) empty(all_0_4_4) = 0
% 28.19/8.02 | (5) ! [v0] : ( ~ (empty(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & one_to_one(v0) = 0 & relation(v0) = 0 & function(v0) = 0) | ( ~ (v1 = 0) & relation(v0) = v1) | ( ~ (v1 = 0) & function(v0) = v1)))
% 28.19/8.02 | (6) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | subset(v0, v1) = 0)
% 28.19/8.02 | (7) ? [v0] : ? [v1] : ? [v2] : unordered_pair(v1, v0) = v2
% 28.19/8.02 | (8) ? [v0] : ? [v1] : epsilon_connected(v0) = v1
% 28.19/8.02 | (9) ? [v0] : ? [v1] : ? [v2] : element(v1, v0) = v2
% 28.19/8.02 | (10) ! [v0] : ! [v1] : ( ~ (one_to_one(v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & relation(v0) = 0 & function(v0) = 0) | ( ~ (v2 = 0) & relation(v0) = v2) | ( ~ (v2 = 0) & function(v0) = v2) | ( ~ (v2 = 0) & empty(v0) = v2)))
% 28.19/8.02 | (11) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v2 & relation_rng(v0) = v3 & relation_field(v0) = v2 & set_union2(v1, v3) = v2) | ( ~ (v2 = 0) & relation(v0) = v2)))
% 28.19/8.02 | (12) ? [v0] : ? [v1] : relation_field(v0) = v1
% 28.19/8.02 | (13) ! [v0] : ! [v1] : ( ~ (connected(v0) = v1) | ? [v2] : ? [v3] : (( ~ (v2 = 0) & relation(v0) = v2) | (( ~ (v1 = 0) | (v3 = 0 & relation_field(v0) = v2 & is_connected_in(v0, v2) = 0)) & (v1 = 0 | ( ~ (v3 = 0) & relation_field(v0) = v2 & is_connected_in(v0, v2) = v3)))))
% 28.19/8.02 | (14) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v2 & relation_dom(v0) = v3 & relation_field(v0) = v2 & set_union2(v3, v1) = v2) | ( ~ (v2 = 0) & relation(v0) = v2)))
% 28.19/8.02 | (15) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0))
% 28.19/8.02 | (16) relation(all_0_4_4) = 0
% 28.19/8.02 | (17) empty(all_0_6_6) = all_0_5_5
% 28.19/8.02 | (18) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1))
% 28.19/8.02 | (19) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (ordinal_subset(v1, v0) = v2) | ? [v3] : ((v3 = 0 & ordinal_subset(v0, v1) = 0) | ( ~ (v3 = 0) & ordinal(v1) = v3) | ( ~ (v3 = 0) & ordinal(v0) = v3)))
% 28.19/8.02 | (20) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0))
% 28.19/8.02 | (21) ? [v0] : ? [v1] : ? [v2] : ordered_pair(v1, v0) = v2
% 28.19/8.02 | (22) ? [v0] : ? [v1] : function(v0) = v1
% 28.19/8.02 | (23) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (((v3 = 0 & relation_field(v0) = v2 & is_connected_in(v0, v2) = 0) | ( ~ (v1 = 0) & connected(v0) = v1)) & ((v1 = 0 & connected(v0) = 0) | ( ~ (v3 = 0) & relation_field(v0) = v2 & is_connected_in(v0, v2) = v3))))
% 28.19/8.02 | (24) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (connected(v2) = v1) | ~ (connected(v2) = v0))
% 28.19/8.02 | (25) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 28.19/8.03 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 28.19/8.03 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4))
% 28.19/8.03 | (28) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (inclusion_relation(v0) = v2) | ~ (relation_field(v1) = v0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ((v6 = 0 & v5 = 0 & in(v4, v0) = 0 & in(v3, v0) = 0 & ((v9 = 0 & subset(v3, v4) = 0) | (v8 = 0 & ordered_pair(v3, v4) = v7 & in(v7, v1) = 0)) & (( ~ (v9 = 0) & subset(v3, v4) = v9) | ( ~ (v8 = 0) & ordered_pair(v3, v4) = v7 & in(v7, v1) = v8))) | ( ~ (v3 = 0) & relation(v1) = v3)))
% 28.19/8.03 | (29) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0))
% 28.19/8.03 | (30) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (inclusion_relation(v2) = v1) | ~ (inclusion_relation(v2) = v0))
% 28.19/8.03 | (31) ? [v0] : ? [v1] : relation_dom(v0) = v1
% 28.19/8.03 | (32) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3))
% 28.19/8.03 | (33) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2)
% 28.19/8.03 | (34) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2)
% 28.19/8.03 | (35) ! [v0] : ! [v1] : ( ~ (inclusion_relation(v0) = v1) | relation(v1) = 0)
% 28.19/8.03 | (36) ? [v0] : ? [v1] : relation_rng(v0) = v1
% 28.19/8.03 | (37) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (epsilon_transitive(v2) = v1) | ~ (epsilon_transitive(v2) = v0))
% 28.19/8.03 | (38) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0))
% 28.19/8.03 | (39) epsilon_transitive(all_0_4_4) = 0
% 28.19/8.03 | (40) ordinal(all_0_4_4) = 0
% 28.19/8.03 | (41) function(all_0_4_4) = 0
% 28.19/8.03 | (42) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ordinal(v2) = v1) | ~ (ordinal(v2) = v0))
% 28.19/8.03 | (43) epsilon_transitive(all_0_1_1) = 0
% 28.19/8.03 | (44) empty(all_0_3_3) = 0
% 28.19/8.03 | (45) ? [v0] : ? [v1] : inclusion_relation(v0) = v1
% 28.19/8.03 | (46) function(all_0_7_7) = 0
% 28.19/8.03 | (47) function(all_0_0_0) = 0
% 28.19/8.03 | (48) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (is_connected_in(v0, v1) = v2) | ~ (relation(v0) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ( ~ (v8 = 0) & ~ (v6 = 0) & ~ (v4 = v3) & ordered_pair(v4, v3) = v7 & ordered_pair(v3, v4) = v5 & in(v7, v0) = v8 & in(v5, v0) = v6 & in(v4, v1) = 0 & in(v3, v1) = 0))
% 28.19/8.03 | (49) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 28.19/8.03 | (50) ? [v0] : ? [v1] : singleton(v0) = v1
% 28.19/8.03 | (51) relation(all_0_10_10) = 0
% 28.19/8.03 | (52) epsilon_transitive(all_0_9_9) = 0
% 28.19/8.03 | (53) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3))
% 28.19/8.03 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 28.19/8.03 | (55) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v0, v1) = v2) | ? [v3] : ((v3 = 0 & empty(v1) = 0) | ( ~ (v3 = 0) & element(v0, v1) = v3)))
% 28.19/8.03 | (56) ! [v0] : ! [v1] : ( ~ (ordinal(v1) = 0) | ~ (ordinal(v0) = 0) | ordinal_subset(v0, v0) = 0)
% 28.19/8.03 | (57) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 28.19/8.03 | (58) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1))
% 28.19/8.03 | (59) function(empty_set) = 0
% 28.19/8.03 | (60) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (relation_dom(v0) = v2 & relation_rng(v0) = v3 & relation_field(v0) = v1 & set_union2(v2, v3) = v1))
% 28.19/8.03 | (61) relation(all_0_3_3) = 0
% 28.19/8.03 | (62) ? [v0] : ? [v1] : empty(v0) = v1
% 28.19/8.03 | (63) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 28.19/8.03 | (64) epsilon_transitive(empty_set) = 0
% 28.19/8.03 | (65) one_to_one(empty_set) = 0
% 28.19/8.03 | (66) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : ((v3 = 0 & empty(v0) = 0) | ( ~ (v3 = 0) & empty(v2) = v3)))
% 28.19/8.03 | (67) ! [v0] : ( ~ (empty(v0) = 0) | function(v0) = 0)
% 28.19/8.03 | (68) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (element(v0, v2) = v4) | ? [v5] : ( ~ (v5 = 0) & in(v0, v1) = v5))
% 28.19/8.04 | (69) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v1) = v3 & element(v0, v3) = v4))
% 28.19/8.04 | (70) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | element(v0, v1) = 0)
% 28.19/8.04 | (71) ? [v0] : ? [v1] : one_to_one(v0) = v1
% 28.19/8.04 | (72) ! [v0] : ! [v1] : (v1 = 0 | ~ (ordinal(v0) = v1) | ? [v2] : (( ~ (v2 = 0) & epsilon_transitive(v0) = v2) | ( ~ (v2 = 0) & epsilon_connected(v0) = v2)))
% 28.19/8.04 | (73) connected(all_0_12_12) = all_0_11_11
% 28.19/8.04 | (74) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2)
% 28.19/8.04 | (75) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2)
% 28.19/8.04 | (76) ~ (all_0_11_11 = 0)
% 28.19/8.04 | (77) epsilon_connected(empty_set) = 0
% 28.19/8.04 | (78) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ((v2 = 0 & v1 = 0 & one_to_one(v0) = 0 & function(v0) = 0) | ( ~ (v1 = 0) & function(v0) = v1) | ( ~ (v1 = 0) & empty(v0) = v1)))
% 28.19/8.04 | (79) ? [v0] : ? [v1] : powerset(v0) = v1
% 28.19/8.04 | (80) ~ (all_0_5_5 = 0)
% 28.19/8.04 | (81) ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2
% 28.19/8.04 | (82) inclusion_relation(all_0_13_13) = all_0_12_12
% 28.19/8.04 | (83) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (ordered_pair(v3, v2) = v4) | ~ (is_connected_in(v0, v1) = 0) | ~ (relation(v0) = 0) | ? [v5] : ? [v6] : ((v6 = 0 & ordered_pair(v2, v3) = v5 & in(v5, v0) = 0) | (v5 = 0 & in(v4, v0) = 0) | ( ~ (v5 = 0) & in(v3, v1) = v5) | ( ~ (v5 = 0) & in(v2, v1) = v5)))
% 28.19/8.04 | (84) epsilon_connected(all_0_1_1) = 0
% 28.56/8.04 | (85) ! [v0] : ! [v1] : ( ~ (epsilon_transitive(v0) = v1) | ? [v2] : ((v2 = 0 & v1 = 0 & epsilon_connected(v0) = 0) | ( ~ (v2 = 0) & ordinal(v0) = v2)))
% 28.56/8.04 | (86) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (inclusion_relation(v0) = v1) | ~ (subset(v3, v4) = v5) | ~ (relation_field(v1) = v2) | ? [v6] : ? [v7] : (( ~ (v6 = 0) & relation(v1) = v6) | ( ~ (v6 = 0) & in(v4, v0) = v6) | ( ~ (v6 = 0) & in(v3, v0) = v6) | (( ~ (v5 = 0) | (v7 = 0 & ordered_pair(v3, v4) = v6 & in(v6, v1) = 0)) & (v5 = 0 | ( ~ (v7 = 0) & ordered_pair(v3, v4) = v6 & in(v6, v1) = v7)))))
% 28.56/8.04 | (87) ? [v0] : ? [v1] : ? [v2] : set_union2(v1, v0) = v2
% 28.56/8.04 | (88) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & ordered_pair(v0, v1) = v3 & unordered_pair(v2, v4) = v3))
% 28.56/8.04 | (89) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0))
% 28.56/8.04 | (90) ? [v0] : ? [v1] : ordinal(v0) = v1
% 28.56/8.04 | (91) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (ordinal_subset(v0, v0) = v2) | ~ (ordinal(v1) = 0) | ? [v3] : ( ~ (v3 = 0) & ordinal(v0) = v3))
% 28.56/8.04 | (92) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordinal_subset(v3, v2) = v1) | ~ (ordinal_subset(v3, v2) = v0))
% 28.56/8.04 | (93) ! [v0] : ( ~ (ordinal(v0) = 0) | (epsilon_transitive(v0) = 0 & epsilon_connected(v0) = 0))
% 28.56/8.04 | (94) ordinal(all_0_13_13) = 0
% 28.56/8.04 | (95) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0))
% 28.56/8.04 | (96) relation(all_0_7_7) = 0
% 28.56/8.04 | (97) ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v1 & relation_dom(v0) = v2 & relation_rng(v0) = v3 & set_union2(v2, v3) = v1) | ( ~ (v2 = 0) & relation(v0) = v2)))
% 28.56/8.04 | (98) ! [v0] : ! [v1] : ( ~ (epsilon_connected(v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & epsilon_transitive(v0) = 0 & ordinal(v0) = 0) | ( ~ (v2 = 0) & empty(v0) = v2)))
% 28.56/8.04 | (99) ? [v0] : ? [v1] : ? [v2] : ordinal_subset(v1, v0) = v2
% 28.56/8.04 | (100) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | element(v0, v2) = 0)
% 28.56/8.04 | (101) epsilon_connected(all_0_9_9) = 0
% 28.56/8.04 | (102) ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2))
% 28.56/8.04 | (103) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (powerset(v1) = v2 & element(v0, v2) = 0))
% 28.56/8.05 | (104) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ((v2 = 0 & ordinal(v0) = 0) | ( ~ (v2 = 0) & ordinal(v1) = v2)))
% 28.56/8.05 | (105) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0))
% 28.56/8.05 | (106) ! [v0] : ! [v1] : (v1 = 0 | ~ (function(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2))
% 28.56/8.05 | (107) ! [v0] : ! [v1] : ( ~ (ordinal(v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & epsilon_transitive(v0) = 0 & epsilon_connected(v0) = 0) | ( ~ (v2 = 0) & empty(v0) = v2)))
% 28.56/8.05 | (108) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (inclusion_relation(v0) = v1) | ~ (ordered_pair(v3, v4) = v5) | ~ (relation_field(v1) = v2) | ? [v6] : ? [v7] : (( ~ (v6 = 0) & relation(v1) = v6) | ( ~ (v6 = 0) & in(v4, v0) = v6) | ( ~ (v6 = 0) & in(v3, v0) = v6) | (((v7 = 0 & subset(v3, v4) = 0) | ( ~ (v6 = 0) & in(v5, v1) = v6)) & ((v6 = 0 & in(v5, v1) = 0) | ( ~ (v7 = 0) & subset(v3, v4) = v7)))))
% 28.56/8.05 | (109) function(all_0_3_3) = 0
% 28.56/8.05 | (110) ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2
% 28.56/8.05 | (111) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 28.56/8.05 | (112) ordinal(all_0_1_1) = 0
% 28.56/8.05 | (113) empty(all_0_2_2) = 0
% 28.56/8.05 | (114) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (ordinal_subset(v0, v1) = v2) | ? [v3] : ((v3 = 0 & ordinal_subset(v1, v0) = 0) | ( ~ (v3 = 0) & ordinal(v1) = v3) | ( ~ (v3 = 0) & ordinal(v0) = v3)))
% 28.56/8.05 | (115) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_empty_yielding(v2) = v1) | ~ (relation_empty_yielding(v2) = v0))
% 28.56/8.05 | (116) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1))
% 28.56/8.05 | (117) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0))
% 28.56/8.05 | (118) ! [v0] : ! [v1] : ! [v2] : ( ~ (inclusion_relation(v0) = v2) | ~ (relation(v1) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (( ~ (v2 = v1) | (v3 = v0 & relation_field(v1) = v0 & ! [v11] : ! [v12] : ! [v13] : ( ~ (subset(v11, v12) = v13) | ? [v14] : ? [v15] : (( ~ (v14 = 0) & in(v12, v0) = v14) | ( ~ (v14 = 0) & in(v11, v0) = v14) | (( ~ (v13 = 0) | (v15 = 0 & ordered_pair(v11, v12) = v14 & in(v14, v1) = 0)) & (v13 = 0 | ( ~ (v15 = 0) & ordered_pair(v11, v12) = v14 & in(v14, v1) = v15))))) & ! [v11] : ! [v12] : ! [v13] : ( ~ (ordered_pair(v11, v12) = v13) | ? [v14] : ? [v15] : (( ~ (v14 = 0) & in(v12, v0) = v14) | ( ~ (v14 = 0) & in(v11, v0) = v14) | (((v15 = 0 & subset(v11, v12) = 0) | ( ~ (v14 = 0) & in(v13, v1) = v14)) & ((v14 = 0 & in(v13, v1) = 0) | ( ~ (v15 = 0) & subset(v11, v12) = v15))))))) & (v2 = v1 | (v7 = 0 & v6 = 0 & in(v5, v0) = 0 & in(v4, v0) = 0 & ((v10 = 0 & subset(v4, v5) = 0) | (v9 = 0 & ordered_pair(v4, v5) = v8 & in(v8, v1) = 0)) & (( ~ (v10 = 0) & subset(v4, v5) = v10) | ( ~ (v9 = 0) & ordered_pair(v4, v5) = v8 & in(v8, v1) = v9))) | ( ~ (v3 = v0) & relation_field(v1) = v3))))
% 28.56/8.05 | (119) ! [v0] : ! [v1] : ( ~ (epsilon_connected(v0) = v1) | ? [v2] : ((v2 = 0 & v1 = 0 & epsilon_transitive(v0) = 0) | ( ~ (v2 = 0) & ordinal(v0) = v2)))
% 28.56/8.05 | (120) relation(all_0_0_0) = 0
% 28.56/8.05 | (121) one_to_one(all_0_4_4) = 0
% 28.56/8.05 | (122) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_field(v2) = v1) | ~ (relation_field(v2) = v0))
% 28.56/8.05 | (123) ? [v0] : ? [v1] : epsilon_transitive(v0) = v1
% 28.56/8.05 | (124) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordinal_subset(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & ordinal(v1) = v3) | ( ~ (v3 = 0) & ordinal(v0) = v3) | (( ~ (v2 = 0) | (v3 = 0 & subset(v0, v1) = 0)) & (v2 = 0 | ( ~ (v3 = 0) & subset(v0, v1) = v3)))))
% 28.56/8.05 | (125) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3))
% 28.56/8.05 | (126) relation_empty_yielding(all_0_10_10) = 0
% 28.56/8.05 | (127) ? [v0] : ? [v1] : connected(v0) = v1
% 28.56/8.05 | (128) relation_empty_yielding(empty_set) = 0
% 28.56/8.05 | (129) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 28.56/8.06 | (130) ~ (all_0_8_8 = 0)
% 28.56/8.06 | (131) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0))
% 28.56/8.06 | (132) empty(all_0_9_9) = all_0_8_8
% 28.56/8.06 | (133) ? [v0] : ? [v1] : ? [v2] : is_connected_in(v1, v0) = v2
% 28.56/8.06 | (134) ? [v0] : ? [v1] : relation(v0) = v1
% 28.56/8.06 | (135) one_to_one(all_0_7_7) = 0
% 28.56/8.06 | (136) ! [v0] : ( ~ (epsilon_connected(v0) = 0) | ? [v1] : ((v1 = 0 & ordinal(v0) = 0) | ( ~ (v1 = 0) & epsilon_transitive(v0) = v1)))
% 28.56/8.06 | (137) ! [v0] : ( ~ (epsilon_transitive(v0) = 0) | ? [v1] : ((v1 = 0 & ordinal(v0) = 0) | ( ~ (v1 = 0) & epsilon_connected(v0) = v1)))
% 28.56/8.06 | (138) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (is_connected_in(v3, v2) = v1) | ~ (is_connected_in(v3, v2) = v0))
% 28.56/8.06 | (139) ! [v0] : ! [v1] : ! [v2] : ( ~ (empty(v2) = 0) | ~ (in(v0, v1) = 0) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v2) = v3 & element(v1, v3) = v4))
% 28.56/8.06 | (140) ? [v0] : ? [v1] : element(v1, v0) = 0
% 28.56/8.06 | (141) ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ? [v2] : ? [v3] : (( ~ (v2 = 0) & relation(v0) = v2) | (((v3 = 0 & is_connected_in(v0, v1) = 0) | ( ~ (v2 = 0) & connected(v0) = v2)) & ((v2 = 0 & connected(v0) = 0) | ( ~ (v3 = 0) & is_connected_in(v0, v1) = v3)))))
% 28.56/8.06 | (142) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (epsilon_connected(v2) = v1) | ~ (epsilon_connected(v2) = v0))
% 28.56/8.06 | (143) relation(empty_set) = 0
% 28.56/8.06 | (144) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0))
% 28.56/8.06 | (145) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ? [v3] : ((v3 = 0 & empty(v0) = 0) | ( ~ (v3 = 0) & empty(v2) = v3)))
% 28.56/8.06 | (146) ! [v0] : ! [v1] : ( ~ (element(v0, v1) = 0) | ? [v2] : ((v2 = 0 & empty(v1) = 0) | (v2 = 0 & in(v0, v1) = 0)))
% 28.56/8.06 | (147) empty(empty_set) = 0
% 28.56/8.06 | (148) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (ordered_pair(v2, v3) = v4) | ~ (is_connected_in(v0, v1) = 0) | ~ (relation(v0) = 0) | ? [v5] : ? [v6] : ((v6 = 0 & ordered_pair(v3, v2) = v5 & in(v5, v0) = 0) | (v5 = 0 & in(v4, v0) = 0) | ( ~ (v5 = 0) & in(v3, v1) = v5) | ( ~ (v5 = 0) & in(v2, v1) = v5)))
% 28.56/8.06 | (149) ? [v0] : ? [v1] : relation_empty_yielding(v0) = v1
% 28.56/8.06 | (150) epsilon_connected(all_0_4_4) = 0
% 28.56/8.06 | (151) ordinal(all_0_9_9) = 0
% 28.56/8.06 | (152) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & ordinal(v1) = v3) | ( ~ (v3 = 0) & ordinal(v0) = v3) | (( ~ (v2 = 0) | (v3 = 0 & ordinal_subset(v0, v1) = 0)) & (v2 = 0 | ( ~ (v3 = 0) & ordinal_subset(v0, v1) = v3)))))
% 28.56/8.06 | (153) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (element(v0, v2) = v3) | ~ (in(v0, v1) = 0) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & powerset(v2) = v4 & element(v1, v4) = v5))
% 28.56/8.06 | (154) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (inclusion_relation(v0) = v1) | ~ (relation_field(v1) = v2) | ? [v3] : ( ~ (v3 = 0) & relation(v1) = v3))
% 28.56/8.06 | (155) ordinal(empty_set) = 0
% 28.56/8.06 | (156) ! [v0] : ( ~ (empty(v0) = 0) | (epsilon_transitive(v0) = 0 & ordinal(v0) = 0 & epsilon_connected(v0) = 0))
% 28.56/8.06 | (157) ! [v0] : ! [v1] : ( ~ (epsilon_transitive(v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & ordinal(v0) = 0 & epsilon_connected(v0) = 0) | ( ~ (v2 = 0) & empty(v0) = v2)))
% 28.56/8.06 | (158) ! [v0] : ( ~ (function(v0) = 0) | ? [v1] : ? [v2] : ((v2 = 0 & v1 = 0 & one_to_one(v0) = 0 & relation(v0) = 0) | ( ~ (v1 = 0) & relation(v0) = v1) | ( ~ (v1 = 0) & empty(v0) = v1)))
% 28.56/8.06 |
% 28.56/8.06 | Instantiating formula (35) with all_0_12_12, all_0_13_13 and discharging atoms inclusion_relation(all_0_13_13) = all_0_12_12, yields:
% 28.56/8.06 | (159) relation(all_0_12_12) = 0
% 28.56/8.06 |
% 28.56/8.06 | Instantiating formula (13) with all_0_11_11, all_0_12_12 and discharging atoms connected(all_0_12_12) = all_0_11_11, yields:
% 28.56/8.06 | (160) ? [v0] : ? [v1] : (( ~ (v0 = 0) & relation(all_0_12_12) = v0) | (( ~ (all_0_11_11 = 0) | (v1 = 0 & relation_field(all_0_12_12) = v0 & is_connected_in(all_0_12_12, v0) = 0)) & (all_0_11_11 = 0 | ( ~ (v1 = 0) & relation_field(all_0_12_12) = v0 & is_connected_in(all_0_12_12, v0) = v1))))
% 28.56/8.07 |
% 28.56/8.07 | Instantiating (160) with all_81_0_116, all_81_1_117 yields:
% 28.56/8.07 | (161) ( ~ (all_81_1_117 = 0) & relation(all_0_12_12) = all_81_1_117) | (( ~ (all_0_11_11 = 0) | (all_81_0_116 = 0 & relation_field(all_0_12_12) = all_81_1_117 & is_connected_in(all_0_12_12, all_81_1_117) = 0)) & (all_0_11_11 = 0 | ( ~ (all_81_0_116 = 0) & relation_field(all_0_12_12) = all_81_1_117 & is_connected_in(all_0_12_12, all_81_1_117) = all_81_0_116)))
% 28.56/8.07 |
% 28.56/8.07 +-Applying beta-rule and splitting (161), into two cases.
% 28.56/8.07 |-Branch one:
% 28.56/8.07 | (162) ~ (all_81_1_117 = 0) & relation(all_0_12_12) = all_81_1_117
% 28.56/8.07 |
% 28.56/8.07 | Applying alpha-rule on (162) yields:
% 28.56/8.07 | (163) ~ (all_81_1_117 = 0)
% 28.56/8.07 | (164) relation(all_0_12_12) = all_81_1_117
% 28.56/8.07 |
% 28.56/8.07 | Instantiating formula (29) with all_0_12_12, 0, all_81_1_117 and discharging atoms relation(all_0_12_12) = all_81_1_117, relation(all_0_12_12) = 0, yields:
% 28.56/8.07 | (165) all_81_1_117 = 0
% 28.56/8.07 |
% 28.56/8.07 | Equations (165) can reduce 163 to:
% 28.56/8.07 | (166) $false
% 28.56/8.07 |
% 28.56/8.07 |-The branch is then unsatisfiable
% 28.56/8.07 |-Branch two:
% 28.56/8.07 | (167) ( ~ (all_0_11_11 = 0) | (all_81_0_116 = 0 & relation_field(all_0_12_12) = all_81_1_117 & is_connected_in(all_0_12_12, all_81_1_117) = 0)) & (all_0_11_11 = 0 | ( ~ (all_81_0_116 = 0) & relation_field(all_0_12_12) = all_81_1_117 & is_connected_in(all_0_12_12, all_81_1_117) = all_81_0_116))
% 28.56/8.07 |
% 28.56/8.07 | Applying alpha-rule on (167) yields:
% 28.56/8.07 | (168) ~ (all_0_11_11 = 0) | (all_81_0_116 = 0 & relation_field(all_0_12_12) = all_81_1_117 & is_connected_in(all_0_12_12, all_81_1_117) = 0)
% 28.56/8.07 | (169) all_0_11_11 = 0 | ( ~ (all_81_0_116 = 0) & relation_field(all_0_12_12) = all_81_1_117 & is_connected_in(all_0_12_12, all_81_1_117) = all_81_0_116)
% 28.56/8.07 |
% 28.56/8.07 +-Applying beta-rule and splitting (169), into two cases.
% 28.56/8.07 |-Branch one:
% 28.56/8.07 | (170) all_0_11_11 = 0
% 28.56/8.07 |
% 28.56/8.07 | Equations (170) can reduce 76 to:
% 28.56/8.07 | (166) $false
% 28.56/8.07 |
% 28.56/8.07 |-The branch is then unsatisfiable
% 28.56/8.07 |-Branch two:
% 28.56/8.07 | (76) ~ (all_0_11_11 = 0)
% 28.56/8.07 | (173) ~ (all_81_0_116 = 0) & relation_field(all_0_12_12) = all_81_1_117 & is_connected_in(all_0_12_12, all_81_1_117) = all_81_0_116
% 28.56/8.07 |
% 28.56/8.07 | Applying alpha-rule on (173) yields:
% 28.56/8.07 | (174) ~ (all_81_0_116 = 0)
% 28.56/8.07 | (175) relation_field(all_0_12_12) = all_81_1_117
% 28.56/8.07 | (176) is_connected_in(all_0_12_12, all_81_1_117) = all_81_0_116
% 28.56/8.07 |
% 28.56/8.07 | Instantiating formula (154) with all_81_1_117, all_0_12_12, all_0_13_13 and discharging atoms inclusion_relation(all_0_13_13) = all_0_12_12, relation_field(all_0_12_12) = all_81_1_117, yields:
% 28.56/8.07 | (177) all_81_1_117 = all_0_13_13 | ? [v0] : ( ~ (v0 = 0) & relation(all_0_12_12) = v0)
% 28.56/8.07 |
% 28.56/8.07 | Instantiating formula (48) with all_81_0_116, all_81_1_117, all_0_12_12 and discharging atoms is_connected_in(all_0_12_12, all_81_1_117) = all_81_0_116, relation(all_0_12_12) = 0, yields:
% 28.56/8.07 | (178) all_81_0_116 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = 0) & ~ (v3 = 0) & ~ (v1 = v0) & ordered_pair(v1, v0) = v4 & ordered_pair(v0, v1) = v2 & in(v4, all_0_12_12) = v5 & in(v2, all_0_12_12) = v3 & in(v1, all_81_1_117) = 0 & in(v0, all_81_1_117) = 0)
% 28.56/8.07 |
% 28.56/8.07 | Instantiating formula (118) with all_0_12_12, all_0_12_12, all_0_13_13 and discharging atoms inclusion_relation(all_0_13_13) = all_0_12_12, relation(all_0_12_12) = 0, yields:
% 28.56/8.07 | (179) relation_field(all_0_12_12) = all_0_13_13 & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : (( ~ (v3 = 0) & in(v1, all_0_13_13) = v3) | ( ~ (v3 = 0) & in(v0, all_0_13_13) = v3) | (( ~ (v2 = 0) | (v4 = 0 & ordered_pair(v0, v1) = v3 & in(v3, all_0_12_12) = 0)) & (v2 = 0 | ( ~ (v4 = 0) & ordered_pair(v0, v1) = v3 & in(v3, all_0_12_12) = v4))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (( ~ (v3 = 0) & in(v1, all_0_13_13) = v3) | ( ~ (v3 = 0) & in(v0, all_0_13_13) = v3) | (((v4 = 0 & subset(v0, v1) = 0) | ( ~ (v3 = 0) & in(v2, all_0_12_12) = v3)) & ((v3 = 0 & in(v2, all_0_12_12) = 0) | ( ~ (v4 = 0) & subset(v0, v1) = v4)))))
% 28.56/8.07 |
% 28.56/8.07 | Applying alpha-rule on (179) yields:
% 28.56/8.07 | (180) relation_field(all_0_12_12) = all_0_13_13
% 28.56/8.07 | (181) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : (( ~ (v3 = 0) & in(v1, all_0_13_13) = v3) | ( ~ (v3 = 0) & in(v0, all_0_13_13) = v3) | (( ~ (v2 = 0) | (v4 = 0 & ordered_pair(v0, v1) = v3 & in(v3, all_0_12_12) = 0)) & (v2 = 0 | ( ~ (v4 = 0) & ordered_pair(v0, v1) = v3 & in(v3, all_0_12_12) = v4)))))
% 28.56/8.07 | (182) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (( ~ (v3 = 0) & in(v1, all_0_13_13) = v3) | ( ~ (v3 = 0) & in(v0, all_0_13_13) = v3) | (((v4 = 0 & subset(v0, v1) = 0) | ( ~ (v3 = 0) & in(v2, all_0_12_12) = v3)) & ((v3 = 0 & in(v2, all_0_12_12) = 0) | ( ~ (v4 = 0) & subset(v0, v1) = v4)))))
% 28.56/8.07 |
% 28.56/8.07 | Instantiating formula (60) with all_0_12_12 and discharging atoms relation(all_0_12_12) = 0, yields:
% 28.56/8.07 | (183) ? [v0] : ? [v1] : ? [v2] : (relation_dom(all_0_12_12) = v1 & relation_rng(all_0_12_12) = v2 & relation_field(all_0_12_12) = v0 & set_union2(v1, v2) = v0)
% 28.56/8.07 |
% 28.56/8.07 | Instantiating (183) with all_116_0_170, all_116_1_171, all_116_2_172 yields:
% 28.56/8.07 | (184) relation_dom(all_0_12_12) = all_116_1_171 & relation_rng(all_0_12_12) = all_116_0_170 & relation_field(all_0_12_12) = all_116_2_172 & set_union2(all_116_1_171, all_116_0_170) = all_116_2_172
% 28.56/8.07 |
% 28.56/8.07 | Applying alpha-rule on (184) yields:
% 28.56/8.07 | (185) relation_dom(all_0_12_12) = all_116_1_171
% 28.56/8.07 | (186) relation_rng(all_0_12_12) = all_116_0_170
% 28.56/8.07 | (187) relation_field(all_0_12_12) = all_116_2_172
% 28.56/8.07 | (188) set_union2(all_116_1_171, all_116_0_170) = all_116_2_172
% 28.56/8.07 |
% 28.56/8.07 +-Applying beta-rule and splitting (177), into two cases.
% 28.56/8.07 |-Branch one:
% 28.56/8.07 | (189) all_81_1_117 = all_0_13_13
% 28.56/8.07 |
% 28.56/8.07 | From (189) and (175) follows:
% 28.56/8.08 | (180) relation_field(all_0_12_12) = all_0_13_13
% 28.56/8.08 |
% 28.56/8.08 +-Applying beta-rule and splitting (178), into two cases.
% 28.56/8.08 |-Branch one:
% 28.56/8.08 | (191) all_81_0_116 = 0
% 28.56/8.08 |
% 28.56/8.08 | Equations (191) can reduce 174 to:
% 28.56/8.08 | (166) $false
% 28.56/8.08 |
% 28.56/8.08 |-The branch is then unsatisfiable
% 28.56/8.08 |-Branch two:
% 28.56/8.08 | (174) ~ (all_81_0_116 = 0)
% 28.56/8.08 | (194) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = 0) & ~ (v3 = 0) & ~ (v1 = v0) & ordered_pair(v1, v0) = v4 & ordered_pair(v0, v1) = v2 & in(v4, all_0_12_12) = v5 & in(v2, all_0_12_12) = v3 & in(v1, all_81_1_117) = 0 & in(v0, all_81_1_117) = 0)
% 28.56/8.08 |
% 28.56/8.08 | Instantiating (194) with all_147_0_189, all_147_1_190, all_147_2_191, all_147_3_192, all_147_4_193, all_147_5_194 yields:
% 28.56/8.08 | (195) ~ (all_147_0_189 = 0) & ~ (all_147_2_191 = 0) & ~ (all_147_4_193 = all_147_5_194) & ordered_pair(all_147_4_193, all_147_5_194) = all_147_1_190 & ordered_pair(all_147_5_194, all_147_4_193) = all_147_3_192 & in(all_147_1_190, all_0_12_12) = all_147_0_189 & in(all_147_3_192, all_0_12_12) = all_147_2_191 & in(all_147_4_193, all_81_1_117) = 0 & in(all_147_5_194, all_81_1_117) = 0
% 28.56/8.08 |
% 28.56/8.08 | Applying alpha-rule on (195) yields:
% 28.56/8.08 | (196) ~ (all_147_4_193 = all_147_5_194)
% 28.56/8.08 | (197) ~ (all_147_2_191 = 0)
% 28.56/8.08 | (198) in(all_147_3_192, all_0_12_12) = all_147_2_191
% 28.56/8.08 | (199) ordered_pair(all_147_5_194, all_147_4_193) = all_147_3_192
% 28.56/8.08 | (200) in(all_147_5_194, all_81_1_117) = 0
% 28.56/8.08 | (201) ordered_pair(all_147_4_193, all_147_5_194) = all_147_1_190
% 28.56/8.08 | (202) in(all_147_4_193, all_81_1_117) = 0
% 28.56/8.08 | (203) in(all_147_1_190, all_0_12_12) = all_147_0_189
% 28.56/8.08 | (204) ~ (all_147_0_189 = 0)
% 28.56/8.08 |
% 28.56/8.08 | From (189) and (202) follows:
% 28.56/8.08 | (205) in(all_147_4_193, all_0_13_13) = 0
% 28.56/8.08 |
% 28.56/8.08 | From (189) and (200) follows:
% 28.56/8.08 | (206) in(all_147_5_194, all_0_13_13) = 0
% 28.56/8.08 |
% 28.56/8.08 | Instantiating formula (122) with all_0_12_12, all_0_13_13, all_116_2_172 and discharging atoms relation_field(all_0_12_12) = all_116_2_172, relation_field(all_0_12_12) = all_0_13_13, yields:
% 28.56/8.08 | (207) all_116_2_172 = all_0_13_13
% 28.56/8.08 |
% 28.56/8.08 | From (207) and (187) follows:
% 28.56/8.08 | (180) relation_field(all_0_12_12) = all_0_13_13
% 28.56/8.08 |
% 28.56/8.08 | Instantiating formula (182) with all_147_1_190, all_147_5_194, all_147_4_193 and discharging atoms ordered_pair(all_147_4_193, all_147_5_194) = all_147_1_190, yields:
% 28.56/8.08 | (209) ? [v0] : ? [v1] : (( ~ (v0 = 0) & in(all_147_4_193, all_0_13_13) = v0) | ( ~ (v0 = 0) & in(all_147_5_194, all_0_13_13) = v0) | (((v1 = 0 & subset(all_147_4_193, all_147_5_194) = 0) | ( ~ (v0 = 0) & in(all_147_1_190, all_0_12_12) = v0)) & ((v0 = 0 & in(all_147_1_190, all_0_12_12) = 0) | ( ~ (v1 = 0) & subset(all_147_4_193, all_147_5_194) = v1))))
% 28.56/8.08 |
% 28.56/8.08 | Instantiating formula (182) with all_147_3_192, all_147_4_193, all_147_5_194 and discharging atoms ordered_pair(all_147_5_194, all_147_4_193) = all_147_3_192, yields:
% 28.56/8.08 | (210) ? [v0] : ? [v1] : (( ~ (v0 = 0) & in(all_147_4_193, all_0_13_13) = v0) | ( ~ (v0 = 0) & in(all_147_5_194, all_0_13_13) = v0) | (((v1 = 0 & subset(all_147_5_194, all_147_4_193) = 0) | ( ~ (v0 = 0) & in(all_147_3_192, all_0_12_12) = v0)) & ((v0 = 0 & in(all_147_3_192, all_0_12_12) = 0) | ( ~ (v1 = 0) & subset(all_147_5_194, all_147_4_193) = v1))))
% 28.56/8.08 |
% 28.56/8.08 | Instantiating formula (108) with all_147_1_190, all_147_5_194, all_147_4_193, all_0_13_13, all_0_12_12, all_0_13_13 and discharging atoms inclusion_relation(all_0_13_13) = all_0_12_12, ordered_pair(all_147_4_193, all_147_5_194) = all_147_1_190, relation_field(all_0_12_12) = all_0_13_13, yields:
% 28.56/8.08 | (211) ? [v0] : ? [v1] : (( ~ (v0 = 0) & relation(all_0_12_12) = v0) | ( ~ (v0 = 0) & in(all_147_4_193, all_0_13_13) = v0) | ( ~ (v0 = 0) & in(all_147_5_194, all_0_13_13) = v0) | (((v1 = 0 & subset(all_147_4_193, all_147_5_194) = 0) | ( ~ (v0 = 0) & in(all_147_1_190, all_0_12_12) = v0)) & ((v0 = 0 & in(all_147_1_190, all_0_12_12) = 0) | ( ~ (v1 = 0) & subset(all_147_4_193, all_147_5_194) = v1))))
% 28.56/8.08 |
% 28.56/8.08 | Instantiating formula (108) with all_147_3_192, all_147_4_193, all_147_5_194, all_0_13_13, all_0_12_12, all_0_13_13 and discharging atoms inclusion_relation(all_0_13_13) = all_0_12_12, ordered_pair(all_147_5_194, all_147_4_193) = all_147_3_192, relation_field(all_0_12_12) = all_0_13_13, yields:
% 28.56/8.08 | (212) ? [v0] : ? [v1] : (( ~ (v0 = 0) & relation(all_0_12_12) = v0) | ( ~ (v0 = 0) & in(all_147_4_193, all_0_13_13) = v0) | ( ~ (v0 = 0) & in(all_147_5_194, all_0_13_13) = v0) | (((v1 = 0 & subset(all_147_5_194, all_147_4_193) = 0) | ( ~ (v0 = 0) & in(all_147_3_192, all_0_12_12) = v0)) & ((v0 = 0 & in(all_147_3_192, all_0_12_12) = 0) | ( ~ (v1 = 0) & subset(all_147_5_194, all_147_4_193) = v1))))
% 28.56/8.08 |
% 28.56/8.08 | Instantiating formula (55) with all_147_0_189, all_0_12_12, all_147_1_190 and discharging atoms in(all_147_1_190, all_0_12_12) = all_147_0_189, yields:
% 28.56/8.08 | (213) all_147_0_189 = 0 | ? [v0] : ((v0 = 0 & empty(all_0_12_12) = 0) | ( ~ (v0 = 0) & element(all_147_1_190, all_0_12_12) = v0))
% 28.56/8.08 |
% 28.56/8.08 | Instantiating formula (55) with all_147_2_191, all_0_12_12, all_147_3_192 and discharging atoms in(all_147_3_192, all_0_12_12) = all_147_2_191, yields:
% 28.56/8.08 | (214) all_147_2_191 = 0 | ? [v0] : ((v0 = 0 & empty(all_0_12_12) = 0) | ( ~ (v0 = 0) & element(all_147_3_192, all_0_12_12) = v0))
% 28.56/8.08 |
% 28.56/8.08 | Instantiating formula (104) with all_0_13_13, all_147_4_193 and discharging atoms in(all_147_4_193, all_0_13_13) = 0, yields:
% 28.56/8.08 | (215) ? [v0] : ((v0 = 0 & ordinal(all_147_4_193) = 0) | ( ~ (v0 = 0) & ordinal(all_0_13_13) = v0))
% 28.56/8.08 |
% 28.56/8.08 | Instantiating formula (104) with all_0_13_13, all_147_5_194 and discharging atoms in(all_147_5_194, all_0_13_13) = 0, yields:
% 28.56/8.08 | (216) ? [v0] : ((v0 = 0 & ordinal(all_147_5_194) = 0) | ( ~ (v0 = 0) & ordinal(all_0_13_13) = v0))
% 28.56/8.08 |
% 28.56/8.08 | Instantiating (212) with all_167_0_195, all_167_1_196 yields:
% 28.56/8.08 | (217) ( ~ (all_167_1_196 = 0) & relation(all_0_12_12) = all_167_1_196) | ( ~ (all_167_1_196 = 0) & in(all_147_4_193, all_0_13_13) = all_167_1_196) | ( ~ (all_167_1_196 = 0) & in(all_147_5_194, all_0_13_13) = all_167_1_196) | (((all_167_0_195 = 0 & subset(all_147_5_194, all_147_4_193) = 0) | ( ~ (all_167_1_196 = 0) & in(all_147_3_192, all_0_12_12) = all_167_1_196)) & ((all_167_1_196 = 0 & in(all_147_3_192, all_0_12_12) = 0) | ( ~ (all_167_0_195 = 0) & subset(all_147_5_194, all_147_4_193) = all_167_0_195)))
% 28.56/8.08 |
% 28.56/8.08 | Instantiating (211) with all_168_0_197, all_168_1_198 yields:
% 28.56/8.08 | (218) ( ~ (all_168_1_198 = 0) & relation(all_0_12_12) = all_168_1_198) | ( ~ (all_168_1_198 = 0) & in(all_147_4_193, all_0_13_13) = all_168_1_198) | ( ~ (all_168_1_198 = 0) & in(all_147_5_194, all_0_13_13) = all_168_1_198) | (((all_168_0_197 = 0 & subset(all_147_4_193, all_147_5_194) = 0) | ( ~ (all_168_1_198 = 0) & in(all_147_1_190, all_0_12_12) = all_168_1_198)) & ((all_168_1_198 = 0 & in(all_147_1_190, all_0_12_12) = 0) | ( ~ (all_168_0_197 = 0) & subset(all_147_4_193, all_147_5_194) = all_168_0_197)))
% 28.56/8.08 |
% 28.56/8.08 | Instantiating (216) with all_173_0_204 yields:
% 28.56/8.08 | (219) (all_173_0_204 = 0 & ordinal(all_147_5_194) = 0) | ( ~ (all_173_0_204 = 0) & ordinal(all_0_13_13) = all_173_0_204)
% 28.56/8.08 |
% 28.56/8.08 | Instantiating (210) with all_191_0_221, all_191_1_222 yields:
% 28.56/8.08 | (220) ( ~ (all_191_1_222 = 0) & in(all_147_4_193, all_0_13_13) = all_191_1_222) | ( ~ (all_191_1_222 = 0) & in(all_147_5_194, all_0_13_13) = all_191_1_222) | (((all_191_0_221 = 0 & subset(all_147_5_194, all_147_4_193) = 0) | ( ~ (all_191_1_222 = 0) & in(all_147_3_192, all_0_12_12) = all_191_1_222)) & ((all_191_1_222 = 0 & in(all_147_3_192, all_0_12_12) = 0) | ( ~ (all_191_0_221 = 0) & subset(all_147_5_194, all_147_4_193) = all_191_0_221)))
% 28.56/8.09 |
% 28.56/8.09 | Instantiating (215) with all_205_0_237 yields:
% 28.56/8.09 | (221) (all_205_0_237 = 0 & ordinal(all_147_4_193) = 0) | ( ~ (all_205_0_237 = 0) & ordinal(all_0_13_13) = all_205_0_237)
% 28.56/8.09 |
% 28.56/8.09 | Instantiating (209) with all_210_0_241, all_210_1_242 yields:
% 28.56/8.09 | (222) ( ~ (all_210_1_242 = 0) & in(all_147_4_193, all_0_13_13) = all_210_1_242) | ( ~ (all_210_1_242 = 0) & in(all_147_5_194, all_0_13_13) = all_210_1_242) | (((all_210_0_241 = 0 & subset(all_147_4_193, all_147_5_194) = 0) | ( ~ (all_210_1_242 = 0) & in(all_147_1_190, all_0_12_12) = all_210_1_242)) & ((all_210_1_242 = 0 & in(all_147_1_190, all_0_12_12) = 0) | ( ~ (all_210_0_241 = 0) & subset(all_147_4_193, all_147_5_194) = all_210_0_241)))
% 28.56/8.09 |
% 28.56/8.09 +-Applying beta-rule and splitting (217), into two cases.
% 28.56/8.09 |-Branch one:
% 28.56/8.09 | (223) ( ~ (all_167_1_196 = 0) & relation(all_0_12_12) = all_167_1_196) | ( ~ (all_167_1_196 = 0) & in(all_147_4_193, all_0_13_13) = all_167_1_196) | ( ~ (all_167_1_196 = 0) & in(all_147_5_194, all_0_13_13) = all_167_1_196)
% 28.56/8.09 |
% 28.56/8.09 +-Applying beta-rule and splitting (223), into two cases.
% 28.56/8.09 |-Branch one:
% 28.56/8.09 | (224) ( ~ (all_167_1_196 = 0) & relation(all_0_12_12) = all_167_1_196) | ( ~ (all_167_1_196 = 0) & in(all_147_4_193, all_0_13_13) = all_167_1_196)
% 28.56/8.09 |
% 28.56/8.09 +-Applying beta-rule and splitting (224), into two cases.
% 28.56/8.09 |-Branch one:
% 28.56/8.09 | (225) ~ (all_167_1_196 = 0) & relation(all_0_12_12) = all_167_1_196
% 28.56/8.09 |
% 28.56/8.09 | Applying alpha-rule on (225) yields:
% 28.56/8.09 | (226) ~ (all_167_1_196 = 0)
% 28.78/8.09 | (227) relation(all_0_12_12) = all_167_1_196
% 28.78/8.09 |
% 28.78/8.09 | Instantiating formula (29) with all_0_12_12, all_167_1_196, 0 and discharging atoms relation(all_0_12_12) = all_167_1_196, relation(all_0_12_12) = 0, yields:
% 28.78/8.09 | (228) all_167_1_196 = 0
% 28.78/8.09 |
% 28.78/8.09 | Equations (228) can reduce 226 to:
% 28.78/8.09 | (166) $false
% 28.78/8.09 |
% 28.78/8.09 |-The branch is then unsatisfiable
% 28.78/8.09 |-Branch two:
% 28.78/8.09 | (230) ~ (all_167_1_196 = 0) & in(all_147_4_193, all_0_13_13) = all_167_1_196
% 28.78/8.09 |
% 28.78/8.09 | Applying alpha-rule on (230) yields:
% 28.78/8.09 | (226) ~ (all_167_1_196 = 0)
% 28.78/8.09 | (232) in(all_147_4_193, all_0_13_13) = all_167_1_196
% 28.78/8.09 |
% 28.78/8.09 | Instantiating formula (26) with all_147_4_193, all_0_13_13, all_167_1_196, 0 and discharging atoms in(all_147_4_193, all_0_13_13) = all_167_1_196, in(all_147_4_193, all_0_13_13) = 0, yields:
% 28.78/8.09 | (228) all_167_1_196 = 0
% 28.78/8.09 |
% 28.78/8.09 | Equations (228) can reduce 226 to:
% 28.78/8.09 | (166) $false
% 28.78/8.09 |
% 28.78/8.09 |-The branch is then unsatisfiable
% 28.78/8.09 |-Branch two:
% 28.78/8.09 | (235) ~ (all_167_1_196 = 0) & in(all_147_5_194, all_0_13_13) = all_167_1_196
% 28.78/8.09 |
% 28.78/8.09 | Applying alpha-rule on (235) yields:
% 28.78/8.09 | (226) ~ (all_167_1_196 = 0)
% 28.78/8.09 | (237) in(all_147_5_194, all_0_13_13) = all_167_1_196
% 28.78/8.09 |
% 28.78/8.09 | Instantiating formula (26) with all_147_5_194, all_0_13_13, all_167_1_196, 0 and discharging atoms in(all_147_5_194, all_0_13_13) = all_167_1_196, in(all_147_5_194, all_0_13_13) = 0, yields:
% 28.78/8.09 | (228) all_167_1_196 = 0
% 28.78/8.09 |
% 28.78/8.09 | Equations (228) can reduce 226 to:
% 28.78/8.09 | (166) $false
% 28.78/8.09 |
% 28.78/8.09 |-The branch is then unsatisfiable
% 28.78/8.09 |-Branch two:
% 28.78/8.09 | (240) ((all_167_0_195 = 0 & subset(all_147_5_194, all_147_4_193) = 0) | ( ~ (all_167_1_196 = 0) & in(all_147_3_192, all_0_12_12) = all_167_1_196)) & ((all_167_1_196 = 0 & in(all_147_3_192, all_0_12_12) = 0) | ( ~ (all_167_0_195 = 0) & subset(all_147_5_194, all_147_4_193) = all_167_0_195))
% 28.78/8.09 |
% 28.78/8.09 | Applying alpha-rule on (240) yields:
% 28.78/8.09 | (241) (all_167_0_195 = 0 & subset(all_147_5_194, all_147_4_193) = 0) | ( ~ (all_167_1_196 = 0) & in(all_147_3_192, all_0_12_12) = all_167_1_196)
% 28.78/8.09 | (242) (all_167_1_196 = 0 & in(all_147_3_192, all_0_12_12) = 0) | ( ~ (all_167_0_195 = 0) & subset(all_147_5_194, all_147_4_193) = all_167_0_195)
% 28.78/8.09 |
% 28.78/8.09 +-Applying beta-rule and splitting (242), into two cases.
% 28.78/8.09 |-Branch one:
% 28.78/8.09 | (243) all_167_1_196 = 0 & in(all_147_3_192, all_0_12_12) = 0
% 28.78/8.09 |
% 28.78/8.09 | Applying alpha-rule on (243) yields:
% 28.78/8.09 | (228) all_167_1_196 = 0
% 28.78/8.09 | (245) in(all_147_3_192, all_0_12_12) = 0
% 28.78/8.09 |
% 28.78/8.09 +-Applying beta-rule and splitting (214), into two cases.
% 28.78/8.09 |-Branch one:
% 28.78/8.09 | (246) all_147_2_191 = 0
% 28.78/8.09 |
% 28.78/8.09 | Equations (246) can reduce 197 to:
% 28.78/8.09 | (166) $false
% 28.78/8.09 |
% 28.78/8.09 |-The branch is then unsatisfiable
% 28.78/8.09 |-Branch two:
% 28.78/8.09 | (197) ~ (all_147_2_191 = 0)
% 28.78/8.09 | (249) ? [v0] : ((v0 = 0 & empty(all_0_12_12) = 0) | ( ~ (v0 = 0) & element(all_147_3_192, all_0_12_12) = v0))
% 28.78/8.09 |
% 28.78/8.09 | Instantiating formula (26) with all_147_3_192, all_0_12_12, 0, all_147_2_191 and discharging atoms in(all_147_3_192, all_0_12_12) = all_147_2_191, in(all_147_3_192, all_0_12_12) = 0, yields:
% 28.78/8.09 | (246) all_147_2_191 = 0
% 28.78/8.09 |
% 28.78/8.09 | Equations (246) can reduce 197 to:
% 28.78/8.09 | (166) $false
% 28.78/8.09 |
% 28.78/8.09 |-The branch is then unsatisfiable
% 28.78/8.09 |-Branch two:
% 28.78/8.09 | (252) ~ (all_167_0_195 = 0) & subset(all_147_5_194, all_147_4_193) = all_167_0_195
% 28.78/8.09 |
% 28.78/8.09 | Applying alpha-rule on (252) yields:
% 28.78/8.09 | (253) ~ (all_167_0_195 = 0)
% 28.78/8.09 | (254) subset(all_147_5_194, all_147_4_193) = all_167_0_195
% 28.78/8.09 |
% 28.78/8.09 +-Applying beta-rule and splitting (219), into two cases.
% 28.78/8.09 |-Branch one:
% 28.78/8.09 | (255) all_173_0_204 = 0 & ordinal(all_147_5_194) = 0
% 28.78/8.09 |
% 28.78/8.09 | Applying alpha-rule on (255) yields:
% 28.78/8.09 | (256) all_173_0_204 = 0
% 28.78/8.09 | (257) ordinal(all_147_5_194) = 0
% 28.78/8.09 |
% 28.78/8.09 +-Applying beta-rule and splitting (221), into two cases.
% 28.78/8.09 |-Branch one:
% 28.78/8.09 | (258) all_205_0_237 = 0 & ordinal(all_147_4_193) = 0
% 28.78/8.09 |
% 28.78/8.09 | Applying alpha-rule on (258) yields:
% 28.78/8.09 | (259) all_205_0_237 = 0
% 28.78/8.09 | (260) ordinal(all_147_4_193) = 0
% 28.78/8.09 |
% 28.78/8.09 +-Applying beta-rule and splitting (241), into two cases.
% 28.78/8.09 |-Branch one:
% 28.78/8.09 | (261) all_167_0_195 = 0 & subset(all_147_5_194, all_147_4_193) = 0
% 28.78/8.09 |
% 28.78/8.09 | Applying alpha-rule on (261) yields:
% 28.78/8.09 | (262) all_167_0_195 = 0
% 28.78/8.09 | (263) subset(all_147_5_194, all_147_4_193) = 0
% 28.78/8.09 |
% 28.78/8.09 | Equations (262) can reduce 253 to:
% 28.78/8.09 | (166) $false
% 28.78/8.09 |
% 28.78/8.09 |-The branch is then unsatisfiable
% 28.78/8.09 |-Branch two:
% 28.78/8.09 | (265) ~ (all_167_1_196 = 0) & in(all_147_3_192, all_0_12_12) = all_167_1_196
% 28.78/8.09 |
% 28.78/8.09 | Applying alpha-rule on (265) yields:
% 28.78/8.09 | (226) ~ (all_167_1_196 = 0)
% 28.78/8.09 | (267) in(all_147_3_192, all_0_12_12) = all_167_1_196
% 28.78/8.09 |
% 28.78/8.09 +-Applying beta-rule and splitting (222), into two cases.
% 28.78/8.09 |-Branch one:
% 28.78/8.09 | (268) ( ~ (all_210_1_242 = 0) & in(all_147_4_193, all_0_13_13) = all_210_1_242) | ( ~ (all_210_1_242 = 0) & in(all_147_5_194, all_0_13_13) = all_210_1_242)
% 28.78/8.09 |
% 28.78/8.09 +-Applying beta-rule and splitting (268), into two cases.
% 28.78/8.09 |-Branch one:
% 28.78/8.09 | (269) ~ (all_210_1_242 = 0) & in(all_147_4_193, all_0_13_13) = all_210_1_242
% 28.78/8.09 |
% 28.78/8.09 | Applying alpha-rule on (269) yields:
% 28.78/8.09 | (270) ~ (all_210_1_242 = 0)
% 28.78/8.09 | (271) in(all_147_4_193, all_0_13_13) = all_210_1_242
% 28.78/8.09 |
% 28.78/8.09 | Instantiating formula (26) with all_147_4_193, all_0_13_13, all_210_1_242, 0 and discharging atoms in(all_147_4_193, all_0_13_13) = all_210_1_242, in(all_147_4_193, all_0_13_13) = 0, yields:
% 28.78/8.09 | (272) all_210_1_242 = 0
% 28.78/8.09 |
% 28.78/8.09 | Equations (272) can reduce 270 to:
% 28.78/8.09 | (166) $false
% 28.78/8.09 |
% 28.78/8.09 |-The branch is then unsatisfiable
% 28.78/8.09 |-Branch two:
% 28.78/8.09 | (274) ~ (all_210_1_242 = 0) & in(all_147_5_194, all_0_13_13) = all_210_1_242
% 28.78/8.09 |
% 28.78/8.09 | Applying alpha-rule on (274) yields:
% 28.78/8.09 | (270) ~ (all_210_1_242 = 0)
% 28.78/8.09 | (276) in(all_147_5_194, all_0_13_13) = all_210_1_242
% 28.78/8.09 |
% 28.78/8.09 | Instantiating formula (26) with all_147_5_194, all_0_13_13, all_210_1_242, 0 and discharging atoms in(all_147_5_194, all_0_13_13) = all_210_1_242, in(all_147_5_194, all_0_13_13) = 0, yields:
% 28.78/8.09 | (272) all_210_1_242 = 0
% 28.78/8.09 |
% 28.78/8.09 | Equations (272) can reduce 270 to:
% 28.78/8.09 | (166) $false
% 28.78/8.09 |
% 28.78/8.09 |-The branch is then unsatisfiable
% 28.78/8.09 |-Branch two:
% 28.78/8.09 | (279) ((all_210_0_241 = 0 & subset(all_147_4_193, all_147_5_194) = 0) | ( ~ (all_210_1_242 = 0) & in(all_147_1_190, all_0_12_12) = all_210_1_242)) & ((all_210_1_242 = 0 & in(all_147_1_190, all_0_12_12) = 0) | ( ~ (all_210_0_241 = 0) & subset(all_147_4_193, all_147_5_194) = all_210_0_241))
% 28.78/8.09 |
% 28.78/8.09 | Applying alpha-rule on (279) yields:
% 28.78/8.09 | (280) (all_210_0_241 = 0 & subset(all_147_4_193, all_147_5_194) = 0) | ( ~ (all_210_1_242 = 0) & in(all_147_1_190, all_0_12_12) = all_210_1_242)
% 28.78/8.09 | (281) (all_210_1_242 = 0 & in(all_147_1_190, all_0_12_12) = 0) | ( ~ (all_210_0_241 = 0) & subset(all_147_4_193, all_147_5_194) = all_210_0_241)
% 28.78/8.09 |
% 28.78/8.09 +-Applying beta-rule and splitting (218), into two cases.
% 28.78/8.09 |-Branch one:
% 28.78/8.09 | (282) ( ~ (all_168_1_198 = 0) & relation(all_0_12_12) = all_168_1_198) | ( ~ (all_168_1_198 = 0) & in(all_147_4_193, all_0_13_13) = all_168_1_198) | ( ~ (all_168_1_198 = 0) & in(all_147_5_194, all_0_13_13) = all_168_1_198)
% 28.78/8.09 |
% 28.78/8.09 +-Applying beta-rule and splitting (282), into two cases.
% 28.78/8.09 |-Branch one:
% 28.78/8.09 | (283) ( ~ (all_168_1_198 = 0) & relation(all_0_12_12) = all_168_1_198) | ( ~ (all_168_1_198 = 0) & in(all_147_4_193, all_0_13_13) = all_168_1_198)
% 28.78/8.09 |
% 28.78/8.09 +-Applying beta-rule and splitting (283), into two cases.
% 28.78/8.09 |-Branch one:
% 28.78/8.09 | (284) ~ (all_168_1_198 = 0) & relation(all_0_12_12) = all_168_1_198
% 28.78/8.10 |
% 28.78/8.10 | Applying alpha-rule on (284) yields:
% 28.78/8.10 | (285) ~ (all_168_1_198 = 0)
% 28.78/8.10 | (286) relation(all_0_12_12) = all_168_1_198
% 28.78/8.10 |
% 28.78/8.10 | Instantiating formula (29) with all_0_12_12, all_168_1_198, 0 and discharging atoms relation(all_0_12_12) = all_168_1_198, relation(all_0_12_12) = 0, yields:
% 28.78/8.10 | (287) all_168_1_198 = 0
% 28.78/8.10 |
% 28.78/8.10 | Equations (287) can reduce 285 to:
% 28.78/8.10 | (166) $false
% 28.78/8.10 |
% 28.78/8.10 |-The branch is then unsatisfiable
% 28.78/8.10 |-Branch two:
% 28.78/8.10 | (289) ~ (all_168_1_198 = 0) & in(all_147_4_193, all_0_13_13) = all_168_1_198
% 28.78/8.10 |
% 28.78/8.10 | Applying alpha-rule on (289) yields:
% 28.78/8.10 | (285) ~ (all_168_1_198 = 0)
% 28.78/8.10 | (291) in(all_147_4_193, all_0_13_13) = all_168_1_198
% 28.78/8.10 |
% 28.78/8.10 | Instantiating formula (26) with all_147_4_193, all_0_13_13, all_168_1_198, 0 and discharging atoms in(all_147_4_193, all_0_13_13) = all_168_1_198, in(all_147_4_193, all_0_13_13) = 0, yields:
% 28.78/8.10 | (287) all_168_1_198 = 0
% 28.78/8.10 |
% 28.78/8.10 | Equations (287) can reduce 285 to:
% 28.78/8.10 | (166) $false
% 28.78/8.10 |
% 28.78/8.10 |-The branch is then unsatisfiable
% 28.78/8.10 |-Branch two:
% 28.78/8.10 | (294) ~ (all_168_1_198 = 0) & in(all_147_5_194, all_0_13_13) = all_168_1_198
% 28.78/8.10 |
% 28.78/8.10 | Applying alpha-rule on (294) yields:
% 28.78/8.10 | (285) ~ (all_168_1_198 = 0)
% 28.78/8.10 | (296) in(all_147_5_194, all_0_13_13) = all_168_1_198
% 28.78/8.10 |
% 28.78/8.10 | Instantiating formula (26) with all_147_5_194, all_0_13_13, all_168_1_198, 0 and discharging atoms in(all_147_5_194, all_0_13_13) = all_168_1_198, in(all_147_5_194, all_0_13_13) = 0, yields:
% 28.78/8.10 | (287) all_168_1_198 = 0
% 28.78/8.10 |
% 28.78/8.10 | Equations (287) can reduce 285 to:
% 28.78/8.10 | (166) $false
% 28.78/8.10 |
% 28.78/8.10 |-The branch is then unsatisfiable
% 28.78/8.10 |-Branch two:
% 28.78/8.10 | (299) ((all_168_0_197 = 0 & subset(all_147_4_193, all_147_5_194) = 0) | ( ~ (all_168_1_198 = 0) & in(all_147_1_190, all_0_12_12) = all_168_1_198)) & ((all_168_1_198 = 0 & in(all_147_1_190, all_0_12_12) = 0) | ( ~ (all_168_0_197 = 0) & subset(all_147_4_193, all_147_5_194) = all_168_0_197))
% 28.78/8.10 |
% 28.78/8.10 | Applying alpha-rule on (299) yields:
% 28.78/8.10 | (300) (all_168_0_197 = 0 & subset(all_147_4_193, all_147_5_194) = 0) | ( ~ (all_168_1_198 = 0) & in(all_147_1_190, all_0_12_12) = all_168_1_198)
% 28.78/8.10 | (301) (all_168_1_198 = 0 & in(all_147_1_190, all_0_12_12) = 0) | ( ~ (all_168_0_197 = 0) & subset(all_147_4_193, all_147_5_194) = all_168_0_197)
% 28.78/8.10 |
% 28.78/8.10 +-Applying beta-rule and splitting (213), into two cases.
% 28.78/8.10 |-Branch one:
% 28.78/8.10 | (302) all_147_0_189 = 0
% 28.78/8.10 |
% 28.78/8.10 | Equations (302) can reduce 204 to:
% 28.78/8.10 | (166) $false
% 28.78/8.10 |
% 28.78/8.10 |-The branch is then unsatisfiable
% 28.78/8.10 |-Branch two:
% 28.78/8.10 | (204) ~ (all_147_0_189 = 0)
% 28.78/8.10 | (305) ? [v0] : ((v0 = 0 & empty(all_0_12_12) = 0) | ( ~ (v0 = 0) & element(all_147_1_190, all_0_12_12) = v0))
% 28.78/8.10 |
% 28.78/8.10 +-Applying beta-rule and splitting (214), into two cases.
% 28.78/8.10 |-Branch one:
% 28.78/8.10 | (246) all_147_2_191 = 0
% 28.78/8.10 |
% 28.78/8.10 | Equations (246) can reduce 197 to:
% 28.78/8.10 | (166) $false
% 28.78/8.10 |
% 28.78/8.10 |-The branch is then unsatisfiable
% 28.78/8.10 |-Branch two:
% 28.78/8.10 | (197) ~ (all_147_2_191 = 0)
% 28.78/8.10 | (249) ? [v0] : ((v0 = 0 & empty(all_0_12_12) = 0) | ( ~ (v0 = 0) & element(all_147_3_192, all_0_12_12) = v0))
% 28.78/8.10 |
% 28.78/8.10 +-Applying beta-rule and splitting (301), into two cases.
% 28.78/8.10 |-Branch one:
% 28.78/8.10 | (310) all_168_1_198 = 0 & in(all_147_1_190, all_0_12_12) = 0
% 28.78/8.10 |
% 28.78/8.10 | Applying alpha-rule on (310) yields:
% 28.78/8.10 | (287) all_168_1_198 = 0
% 28.78/8.10 | (312) in(all_147_1_190, all_0_12_12) = 0
% 28.78/8.10 |
% 28.78/8.10 +-Applying beta-rule and splitting (281), into two cases.
% 28.78/8.10 |-Branch one:
% 28.78/8.10 | (313) all_210_1_242 = 0 & in(all_147_1_190, all_0_12_12) = 0
% 28.78/8.10 |
% 28.78/8.10 | Applying alpha-rule on (313) yields:
% 28.78/8.10 | (272) all_210_1_242 = 0
% 28.78/8.10 | (312) in(all_147_1_190, all_0_12_12) = 0
% 28.78/8.10 |
% 28.78/8.10 | Instantiating formula (26) with all_147_1_190, all_0_12_12, 0, all_147_0_189 and discharging atoms in(all_147_1_190, all_0_12_12) = all_147_0_189, in(all_147_1_190, all_0_12_12) = 0, yields:
% 28.78/8.10 | (302) all_147_0_189 = 0
% 28.78/8.10 |
% 28.78/8.10 | Equations (302) can reduce 204 to:
% 28.78/8.10 | (166) $false
% 28.78/8.10 |
% 28.78/8.10 |-The branch is then unsatisfiable
% 28.78/8.10 |-Branch two:
% 28.78/8.10 | (318) ~ (all_210_0_241 = 0) & subset(all_147_4_193, all_147_5_194) = all_210_0_241
% 28.78/8.10 |
% 28.78/8.10 | Applying alpha-rule on (318) yields:
% 28.78/8.10 | (319) ~ (all_210_0_241 = 0)
% 28.78/8.10 | (320) subset(all_147_4_193, all_147_5_194) = all_210_0_241
% 28.78/8.10 |
% 28.78/8.10 +-Applying beta-rule and splitting (280), into two cases.
% 28.78/8.10 |-Branch one:
% 28.78/8.10 | (321) all_210_0_241 = 0 & subset(all_147_4_193, all_147_5_194) = 0
% 28.78/8.10 |
% 28.78/8.10 | Applying alpha-rule on (321) yields:
% 28.78/8.10 | (322) all_210_0_241 = 0
% 28.78/8.10 | (323) subset(all_147_4_193, all_147_5_194) = 0
% 28.78/8.10 |
% 28.78/8.10 | Equations (322) can reduce 319 to:
% 28.78/8.10 | (166) $false
% 28.78/8.10 |
% 28.78/8.10 |-The branch is then unsatisfiable
% 28.78/8.10 |-Branch two:
% 28.78/8.10 | (325) ~ (all_210_1_242 = 0) & in(all_147_1_190, all_0_12_12) = all_210_1_242
% 28.78/8.10 |
% 28.78/8.10 | Applying alpha-rule on (325) yields:
% 28.78/8.10 | (270) ~ (all_210_1_242 = 0)
% 28.78/8.10 | (327) in(all_147_1_190, all_0_12_12) = all_210_1_242
% 28.78/8.10 |
% 28.78/8.10 | Instantiating formula (26) with all_147_1_190, all_0_12_12, all_210_1_242, all_147_0_189 and discharging atoms in(all_147_1_190, all_0_12_12) = all_210_1_242, in(all_147_1_190, all_0_12_12) = all_147_0_189, yields:
% 28.78/8.10 | (328) all_210_1_242 = all_147_0_189
% 28.78/8.10 |
% 28.78/8.10 | Instantiating formula (26) with all_147_1_190, all_0_12_12, 0, all_210_1_242 and discharging atoms in(all_147_1_190, all_0_12_12) = all_210_1_242, in(all_147_1_190, all_0_12_12) = 0, yields:
% 28.78/8.10 | (272) all_210_1_242 = 0
% 28.78/8.10 |
% 28.78/8.10 | Combining equations (328,272) yields a new equation:
% 28.78/8.10 | (330) all_147_0_189 = 0
% 28.78/8.10 |
% 28.78/8.10 | Simplifying 330 yields:
% 28.78/8.10 | (302) all_147_0_189 = 0
% 28.78/8.10 |
% 28.78/8.10 | Equations (302) can reduce 204 to:
% 28.78/8.10 | (166) $false
% 28.78/8.10 |
% 28.78/8.10 |-The branch is then unsatisfiable
% 28.78/8.10 |-Branch two:
% 28.78/8.10 | (333) ~ (all_168_0_197 = 0) & subset(all_147_4_193, all_147_5_194) = all_168_0_197
% 28.78/8.10 |
% 28.78/8.10 | Applying alpha-rule on (333) yields:
% 28.78/8.10 | (334) ~ (all_168_0_197 = 0)
% 28.78/8.10 | (335) subset(all_147_4_193, all_147_5_194) = all_168_0_197
% 28.78/8.10 |
% 28.78/8.10 +-Applying beta-rule and splitting (300), into two cases.
% 28.78/8.10 |-Branch one:
% 28.78/8.10 | (336) all_168_0_197 = 0 & subset(all_147_4_193, all_147_5_194) = 0
% 28.78/8.10 |
% 28.78/8.10 | Applying alpha-rule on (336) yields:
% 28.78/8.10 | (337) all_168_0_197 = 0
% 28.78/8.10 | (323) subset(all_147_4_193, all_147_5_194) = 0
% 28.78/8.10 |
% 28.78/8.10 | Equations (337) can reduce 334 to:
% 28.78/8.10 | (166) $false
% 28.78/8.10 |
% 28.78/8.10 |-The branch is then unsatisfiable
% 28.78/8.10 |-Branch two:
% 28.78/8.10 | (340) ~ (all_168_1_198 = 0) & in(all_147_1_190, all_0_12_12) = all_168_1_198
% 28.78/8.10 |
% 28.78/8.10 | Applying alpha-rule on (340) yields:
% 28.78/8.10 | (285) ~ (all_168_1_198 = 0)
% 28.78/8.10 | (342) in(all_147_1_190, all_0_12_12) = all_168_1_198
% 28.78/8.10 |
% 28.78/8.10 +-Applying beta-rule and splitting (281), into two cases.
% 28.78/8.10 |-Branch one:
% 28.78/8.10 | (313) all_210_1_242 = 0 & in(all_147_1_190, all_0_12_12) = 0
% 28.78/8.10 |
% 28.78/8.10 | Applying alpha-rule on (313) yields:
% 28.78/8.10 | (272) all_210_1_242 = 0
% 28.78/8.10 | (312) in(all_147_1_190, all_0_12_12) = 0
% 28.78/8.10 |
% 28.78/8.10 | Instantiating formula (26) with all_147_1_190, all_0_12_12, all_168_1_198, all_147_0_189 and discharging atoms in(all_147_1_190, all_0_12_12) = all_168_1_198, in(all_147_1_190, all_0_12_12) = all_147_0_189, yields:
% 28.78/8.10 | (346) all_168_1_198 = all_147_0_189
% 28.78/8.10 |
% 28.78/8.10 | Instantiating formula (26) with all_147_1_190, all_0_12_12, 0, all_168_1_198 and discharging atoms in(all_147_1_190, all_0_12_12) = all_168_1_198, in(all_147_1_190, all_0_12_12) = 0, yields:
% 28.78/8.10 | (287) all_168_1_198 = 0
% 28.78/8.10 |
% 28.78/8.10 | Combining equations (287,346) yields a new equation:
% 28.78/8.10 | (302) all_147_0_189 = 0
% 28.78/8.10 |
% 28.78/8.10 | Equations (302) can reduce 204 to:
% 28.78/8.10 | (166) $false
% 28.78/8.10 |
% 28.78/8.10 |-The branch is then unsatisfiable
% 28.78/8.10 |-Branch two:
% 28.78/8.10 | (318) ~ (all_210_0_241 = 0) & subset(all_147_4_193, all_147_5_194) = all_210_0_241
% 28.78/8.10 |
% 28.78/8.10 | Applying alpha-rule on (318) yields:
% 28.78/8.10 | (319) ~ (all_210_0_241 = 0)
% 28.78/8.10 | (320) subset(all_147_4_193, all_147_5_194) = all_210_0_241
% 28.78/8.10 |
% 28.78/8.10 +-Applying beta-rule and splitting (220), into two cases.
% 28.78/8.10 |-Branch one:
% 28.78/8.10 | (353) ( ~ (all_191_1_222 = 0) & in(all_147_4_193, all_0_13_13) = all_191_1_222) | ( ~ (all_191_1_222 = 0) & in(all_147_5_194, all_0_13_13) = all_191_1_222)
% 28.78/8.10 |
% 28.78/8.10 +-Applying beta-rule and splitting (353), into two cases.
% 28.78/8.10 |-Branch one:
% 28.78/8.10 | (354) ~ (all_191_1_222 = 0) & in(all_147_4_193, all_0_13_13) = all_191_1_222
% 28.78/8.10 |
% 28.78/8.10 | Applying alpha-rule on (354) yields:
% 28.78/8.10 | (355) ~ (all_191_1_222 = 0)
% 28.78/8.10 | (356) in(all_147_4_193, all_0_13_13) = all_191_1_222
% 28.78/8.10 |
% 28.78/8.10 | Instantiating formula (26) with all_147_4_193, all_0_13_13, all_191_1_222, 0 and discharging atoms in(all_147_4_193, all_0_13_13) = all_191_1_222, in(all_147_4_193, all_0_13_13) = 0, yields:
% 28.78/8.10 | (357) all_191_1_222 = 0
% 28.78/8.10 |
% 28.78/8.10 | Equations (357) can reduce 355 to:
% 28.78/8.10 | (166) $false
% 28.78/8.10 |
% 28.78/8.10 |-The branch is then unsatisfiable
% 28.78/8.10 |-Branch two:
% 28.78/8.10 | (359) ~ (all_191_1_222 = 0) & in(all_147_5_194, all_0_13_13) = all_191_1_222
% 28.78/8.10 |
% 28.78/8.10 | Applying alpha-rule on (359) yields:
% 28.78/8.10 | (355) ~ (all_191_1_222 = 0)
% 28.78/8.10 | (361) in(all_147_5_194, all_0_13_13) = all_191_1_222
% 28.78/8.10 |
% 28.78/8.10 | Instantiating formula (26) with all_147_5_194, all_0_13_13, all_191_1_222, 0 and discharging atoms in(all_147_5_194, all_0_13_13) = all_191_1_222, in(all_147_5_194, all_0_13_13) = 0, yields:
% 28.78/8.11 | (357) all_191_1_222 = 0
% 28.78/8.11 |
% 28.78/8.11 | Equations (357) can reduce 355 to:
% 28.78/8.11 | (166) $false
% 28.78/8.11 |
% 28.78/8.11 |-The branch is then unsatisfiable
% 28.78/8.11 |-Branch two:
% 28.78/8.11 | (364) ((all_191_0_221 = 0 & subset(all_147_5_194, all_147_4_193) = 0) | ( ~ (all_191_1_222 = 0) & in(all_147_3_192, all_0_12_12) = all_191_1_222)) & ((all_191_1_222 = 0 & in(all_147_3_192, all_0_12_12) = 0) | ( ~ (all_191_0_221 = 0) & subset(all_147_5_194, all_147_4_193) = all_191_0_221))
% 28.78/8.11 |
% 28.78/8.11 | Applying alpha-rule on (364) yields:
% 28.78/8.11 | (365) (all_191_0_221 = 0 & subset(all_147_5_194, all_147_4_193) = 0) | ( ~ (all_191_1_222 = 0) & in(all_147_3_192, all_0_12_12) = all_191_1_222)
% 28.78/8.11 | (366) (all_191_1_222 = 0 & in(all_147_3_192, all_0_12_12) = 0) | ( ~ (all_191_0_221 = 0) & subset(all_147_5_194, all_147_4_193) = all_191_0_221)
% 28.78/8.11 |
% 28.78/8.11 +-Applying beta-rule and splitting (366), into two cases.
% 28.78/8.11 |-Branch one:
% 28.78/8.11 | (367) all_191_1_222 = 0 & in(all_147_3_192, all_0_12_12) = 0
% 28.78/8.11 |
% 28.78/8.11 | Applying alpha-rule on (367) yields:
% 28.78/8.11 | (357) all_191_1_222 = 0
% 28.78/8.11 | (245) in(all_147_3_192, all_0_12_12) = 0
% 28.78/8.11 |
% 28.78/8.11 | Instantiating formula (26) with all_147_3_192, all_0_12_12, all_167_1_196, all_147_2_191 and discharging atoms in(all_147_3_192, all_0_12_12) = all_167_1_196, in(all_147_3_192, all_0_12_12) = all_147_2_191, yields:
% 28.78/8.11 | (370) all_167_1_196 = all_147_2_191
% 28.78/8.11 |
% 28.78/8.11 | Instantiating formula (26) with all_147_3_192, all_0_12_12, 0, all_167_1_196 and discharging atoms in(all_147_3_192, all_0_12_12) = all_167_1_196, in(all_147_3_192, all_0_12_12) = 0, yields:
% 28.78/8.11 | (228) all_167_1_196 = 0
% 28.78/8.11 |
% 28.78/8.11 | Combining equations (370,228) yields a new equation:
% 28.78/8.11 | (372) all_147_2_191 = 0
% 28.78/8.11 |
% 28.78/8.11 | Simplifying 372 yields:
% 28.78/8.11 | (246) all_147_2_191 = 0
% 28.78/8.11 |
% 28.78/8.11 | Equations (246) can reduce 197 to:
% 28.78/8.11 | (166) $false
% 28.78/8.11 |
% 28.78/8.11 |-The branch is then unsatisfiable
% 28.78/8.11 |-Branch two:
% 28.78/8.11 | (375) ~ (all_191_0_221 = 0) & subset(all_147_5_194, all_147_4_193) = all_191_0_221
% 28.78/8.11 |
% 28.78/8.11 | Applying alpha-rule on (375) yields:
% 28.78/8.11 | (376) ~ (all_191_0_221 = 0)
% 28.78/8.11 | (377) subset(all_147_5_194, all_147_4_193) = all_191_0_221
% 28.78/8.11 |
% 28.78/8.11 | Instantiating formula (54) with all_147_4_193, all_147_5_194, all_168_0_197, all_210_0_241 and discharging atoms subset(all_147_4_193, all_147_5_194) = all_210_0_241, subset(all_147_4_193, all_147_5_194) = all_168_0_197, yields:
% 28.78/8.11 | (378) all_210_0_241 = all_168_0_197
% 28.78/8.11 |
% 28.78/8.11 | Instantiating formula (54) with all_147_5_194, all_147_4_193, all_167_0_195, all_191_0_221 and discharging atoms subset(all_147_5_194, all_147_4_193) = all_191_0_221, subset(all_147_5_194, all_147_4_193) = all_167_0_195, yields:
% 28.78/8.11 | (379) all_191_0_221 = all_167_0_195
% 28.78/8.11 |
% 28.78/8.11 | Equations (378) can reduce 319 to:
% 28.78/8.11 | (334) ~ (all_168_0_197 = 0)
% 28.78/8.11 |
% 28.78/8.11 | Equations (379) can reduce 376 to:
% 28.78/8.11 | (253) ~ (all_167_0_195 = 0)
% 28.78/8.11 |
% 28.78/8.11 | From (378) and (320) follows:
% 28.78/8.11 | (335) subset(all_147_4_193, all_147_5_194) = all_168_0_197
% 28.78/8.11 |
% 28.78/8.11 | From (379) and (377) follows:
% 28.78/8.11 | (254) subset(all_147_5_194, all_147_4_193) = all_167_0_195
% 28.78/8.11 |
% 28.78/8.11 | Instantiating formula (69) with all_168_0_197, all_147_5_194, all_147_4_193 and discharging atoms subset(all_147_4_193, all_147_5_194) = all_168_0_197, yields:
% 28.78/8.11 | (384) all_168_0_197 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & powerset(all_147_5_194) = v0 & element(all_147_4_193, v0) = v1)
% 28.78/8.11 |
% 28.78/8.11 | Instantiating formula (152) with all_168_0_197, all_147_5_194, all_147_4_193 and discharging atoms subset(all_147_4_193, all_147_5_194) = all_168_0_197, yields:
% 28.78/8.11 | (385) ? [v0] : (( ~ (v0 = 0) & ordinal(all_147_4_193) = v0) | ( ~ (v0 = 0) & ordinal(all_147_5_194) = v0) | (( ~ (all_168_0_197 = 0) | (v0 = 0 & ordinal_subset(all_147_4_193, all_147_5_194) = 0)) & (all_168_0_197 = 0 | ( ~ (v0 = 0) & ordinal_subset(all_147_4_193, all_147_5_194) = v0))))
% 28.78/8.11 |
% 28.78/8.11 | Instantiating formula (69) with all_167_0_195, all_147_4_193, all_147_5_194 and discharging atoms subset(all_147_5_194, all_147_4_193) = all_167_0_195, yields:
% 28.78/8.11 | (386) all_167_0_195 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & powerset(all_147_4_193) = v0 & element(all_147_5_194, v0) = v1)
% 28.78/8.11 |
% 28.78/8.11 | Instantiating formula (152) with all_167_0_195, all_147_4_193, all_147_5_194 and discharging atoms subset(all_147_5_194, all_147_4_193) = all_167_0_195, yields:
% 28.78/8.11 | (387) ? [v0] : (( ~ (v0 = 0) & ordinal(all_147_4_193) = v0) | ( ~ (v0 = 0) & ordinal(all_147_5_194) = v0) | (( ~ (all_167_0_195 = 0) | (v0 = 0 & ordinal_subset(all_147_5_194, all_147_4_193) = 0)) & (all_167_0_195 = 0 | ( ~ (v0 = 0) & ordinal_subset(all_147_5_194, all_147_4_193) = v0))))
% 28.78/8.11 |
% 28.78/8.11 | Instantiating (385) with all_293_0_297 yields:
% 28.78/8.11 | (388) ( ~ (all_293_0_297 = 0) & ordinal(all_147_4_193) = all_293_0_297) | ( ~ (all_293_0_297 = 0) & ordinal(all_147_5_194) = all_293_0_297) | (( ~ (all_168_0_197 = 0) | (all_293_0_297 = 0 & ordinal_subset(all_147_4_193, all_147_5_194) = 0)) & (all_168_0_197 = 0 | ( ~ (all_293_0_297 = 0) & ordinal_subset(all_147_4_193, all_147_5_194) = all_293_0_297)))
% 28.78/8.11 |
% 28.78/8.11 | Instantiating (387) with all_316_0_321 yields:
% 28.78/8.11 | (389) ( ~ (all_316_0_321 = 0) & ordinal(all_147_4_193) = all_316_0_321) | ( ~ (all_316_0_321 = 0) & ordinal(all_147_5_194) = all_316_0_321) | (( ~ (all_167_0_195 = 0) | (all_316_0_321 = 0 & ordinal_subset(all_147_5_194, all_147_4_193) = 0)) & (all_167_0_195 = 0 | ( ~ (all_316_0_321 = 0) & ordinal_subset(all_147_5_194, all_147_4_193) = all_316_0_321)))
% 28.78/8.11 |
% 28.78/8.11 +-Applying beta-rule and splitting (388), into two cases.
% 28.78/8.11 |-Branch one:
% 28.78/8.11 | (390) ( ~ (all_293_0_297 = 0) & ordinal(all_147_4_193) = all_293_0_297) | ( ~ (all_293_0_297 = 0) & ordinal(all_147_5_194) = all_293_0_297)
% 28.78/8.11 |
% 28.78/8.11 +-Applying beta-rule and splitting (390), into two cases.
% 28.78/8.11 |-Branch one:
% 28.78/8.11 | (391) ~ (all_293_0_297 = 0) & ordinal(all_147_4_193) = all_293_0_297
% 28.78/8.11 |
% 28.78/8.11 | Applying alpha-rule on (391) yields:
% 28.78/8.11 | (392) ~ (all_293_0_297 = 0)
% 28.78/8.11 | (393) ordinal(all_147_4_193) = all_293_0_297
% 28.78/8.11 |
% 28.78/8.11 | Instantiating formula (42) with all_147_4_193, all_293_0_297, 0 and discharging atoms ordinal(all_147_4_193) = all_293_0_297, ordinal(all_147_4_193) = 0, yields:
% 28.78/8.11 | (394) all_293_0_297 = 0
% 28.78/8.11 |
% 28.78/8.11 | Equations (394) can reduce 392 to:
% 28.78/8.11 | (166) $false
% 28.78/8.11 |
% 28.78/8.11 |-The branch is then unsatisfiable
% 28.78/8.11 |-Branch two:
% 28.78/8.11 | (396) ~ (all_293_0_297 = 0) & ordinal(all_147_5_194) = all_293_0_297
% 28.78/8.11 |
% 28.78/8.11 | Applying alpha-rule on (396) yields:
% 28.78/8.11 | (392) ~ (all_293_0_297 = 0)
% 28.78/8.11 | (398) ordinal(all_147_5_194) = all_293_0_297
% 28.78/8.11 |
% 28.78/8.11 | Instantiating formula (42) with all_147_5_194, all_293_0_297, 0 and discharging atoms ordinal(all_147_5_194) = all_293_0_297, ordinal(all_147_5_194) = 0, yields:
% 28.78/8.11 | (394) all_293_0_297 = 0
% 28.78/8.11 |
% 28.78/8.11 | Equations (394) can reduce 392 to:
% 28.78/8.11 | (166) $false
% 28.78/8.11 |
% 28.78/8.11 |-The branch is then unsatisfiable
% 28.78/8.11 |-Branch two:
% 28.78/8.11 | (401) ( ~ (all_168_0_197 = 0) | (all_293_0_297 = 0 & ordinal_subset(all_147_4_193, all_147_5_194) = 0)) & (all_168_0_197 = 0 | ( ~ (all_293_0_297 = 0) & ordinal_subset(all_147_4_193, all_147_5_194) = all_293_0_297))
% 28.78/8.11 |
% 28.78/8.11 | Applying alpha-rule on (401) yields:
% 28.78/8.11 | (402) ~ (all_168_0_197 = 0) | (all_293_0_297 = 0 & ordinal_subset(all_147_4_193, all_147_5_194) = 0)
% 28.78/8.11 | (403) all_168_0_197 = 0 | ( ~ (all_293_0_297 = 0) & ordinal_subset(all_147_4_193, all_147_5_194) = all_293_0_297)
% 28.78/8.11 |
% 28.78/8.11 +-Applying beta-rule and splitting (389), into two cases.
% 28.78/8.11 |-Branch one:
% 28.78/8.11 | (404) ( ~ (all_316_0_321 = 0) & ordinal(all_147_4_193) = all_316_0_321) | ( ~ (all_316_0_321 = 0) & ordinal(all_147_5_194) = all_316_0_321)
% 28.78/8.11 |
% 28.78/8.11 +-Applying beta-rule and splitting (404), into two cases.
% 28.78/8.11 |-Branch one:
% 28.78/8.11 | (405) ~ (all_316_0_321 = 0) & ordinal(all_147_4_193) = all_316_0_321
% 28.78/8.11 |
% 28.78/8.11 | Applying alpha-rule on (405) yields:
% 28.78/8.11 | (406) ~ (all_316_0_321 = 0)
% 28.78/8.11 | (407) ordinal(all_147_4_193) = all_316_0_321
% 28.78/8.11 |
% 28.78/8.11 | Instantiating formula (42) with all_147_4_193, all_316_0_321, 0 and discharging atoms ordinal(all_147_4_193) = all_316_0_321, ordinal(all_147_4_193) = 0, yields:
% 28.78/8.11 | (408) all_316_0_321 = 0
% 28.78/8.11 |
% 28.78/8.11 | Equations (408) can reduce 406 to:
% 28.78/8.11 | (166) $false
% 28.78/8.11 |
% 28.78/8.11 |-The branch is then unsatisfiable
% 28.78/8.11 |-Branch two:
% 28.78/8.11 | (410) ~ (all_316_0_321 = 0) & ordinal(all_147_5_194) = all_316_0_321
% 28.78/8.11 |
% 28.78/8.11 | Applying alpha-rule on (410) yields:
% 28.78/8.11 | (406) ~ (all_316_0_321 = 0)
% 28.78/8.11 | (412) ordinal(all_147_5_194) = all_316_0_321
% 28.78/8.11 |
% 28.78/8.11 | Instantiating formula (42) with all_147_5_194, all_316_0_321, 0 and discharging atoms ordinal(all_147_5_194) = all_316_0_321, ordinal(all_147_5_194) = 0, yields:
% 28.78/8.11 | (408) all_316_0_321 = 0
% 28.78/8.11 |
% 28.78/8.11 | Equations (408) can reduce 406 to:
% 28.78/8.11 | (166) $false
% 28.78/8.11 |
% 28.78/8.11 |-The branch is then unsatisfiable
% 28.78/8.11 |-Branch two:
% 28.78/8.11 | (415) ( ~ (all_167_0_195 = 0) | (all_316_0_321 = 0 & ordinal_subset(all_147_5_194, all_147_4_193) = 0)) & (all_167_0_195 = 0 | ( ~ (all_316_0_321 = 0) & ordinal_subset(all_147_5_194, all_147_4_193) = all_316_0_321))
% 28.78/8.11 |
% 28.78/8.11 | Applying alpha-rule on (415) yields:
% 28.78/8.11 | (416) ~ (all_167_0_195 = 0) | (all_316_0_321 = 0 & ordinal_subset(all_147_5_194, all_147_4_193) = 0)
% 28.78/8.11 | (417) all_167_0_195 = 0 | ( ~ (all_316_0_321 = 0) & ordinal_subset(all_147_5_194, all_147_4_193) = all_316_0_321)
% 28.78/8.11 |
% 28.78/8.11 +-Applying beta-rule and splitting (386), into two cases.
% 28.78/8.11 |-Branch one:
% 28.78/8.11 | (262) all_167_0_195 = 0
% 28.78/8.11 |
% 28.78/8.11 | Equations (262) can reduce 253 to:
% 28.78/8.11 | (166) $false
% 28.78/8.11 |
% 28.78/8.11 |-The branch is then unsatisfiable
% 28.78/8.11 |-Branch two:
% 28.78/8.11 | (253) ~ (all_167_0_195 = 0)
% 28.78/8.11 | (421) ? [v0] : ? [v1] : ( ~ (v1 = 0) & powerset(all_147_4_193) = v0 & element(all_147_5_194, v0) = v1)
% 28.78/8.11 |
% 28.78/8.11 +-Applying beta-rule and splitting (384), into two cases.
% 28.78/8.11 |-Branch one:
% 28.78/8.11 | (337) all_168_0_197 = 0
% 28.78/8.11 |
% 28.78/8.11 | Equations (337) can reduce 334 to:
% 28.78/8.11 | (166) $false
% 28.78/8.11 |
% 28.78/8.11 |-The branch is then unsatisfiable
% 28.78/8.11 |-Branch two:
% 28.78/8.11 | (334) ~ (all_168_0_197 = 0)
% 28.78/8.11 | (425) ? [v0] : ? [v1] : ( ~ (v1 = 0) & powerset(all_147_5_194) = v0 & element(all_147_4_193, v0) = v1)
% 28.78/8.11 |
% 28.78/8.11 +-Applying beta-rule and splitting (403), into two cases.
% 28.78/8.11 |-Branch one:
% 28.78/8.11 | (337) all_168_0_197 = 0
% 28.78/8.11 |
% 28.78/8.11 | Equations (337) can reduce 334 to:
% 28.78/8.11 | (166) $false
% 28.78/8.11 |
% 28.78/8.11 |-The branch is then unsatisfiable
% 28.78/8.11 |-Branch two:
% 28.78/8.11 | (334) ~ (all_168_0_197 = 0)
% 28.78/8.12 | (429) ~ (all_293_0_297 = 0) & ordinal_subset(all_147_4_193, all_147_5_194) = all_293_0_297
% 28.78/8.12 |
% 28.78/8.12 | Applying alpha-rule on (429) yields:
% 28.78/8.12 | (392) ~ (all_293_0_297 = 0)
% 28.78/8.12 | (431) ordinal_subset(all_147_4_193, all_147_5_194) = all_293_0_297
% 28.78/8.12 |
% 28.78/8.12 +-Applying beta-rule and splitting (417), into two cases.
% 28.78/8.12 |-Branch one:
% 28.78/8.12 | (262) all_167_0_195 = 0
% 28.78/8.12 |
% 28.78/8.12 | Equations (262) can reduce 253 to:
% 28.78/8.12 | (166) $false
% 28.78/8.12 |
% 28.78/8.12 |-The branch is then unsatisfiable
% 28.78/8.12 |-Branch two:
% 28.78/8.12 | (253) ~ (all_167_0_195 = 0)
% 28.78/8.12 | (435) ~ (all_316_0_321 = 0) & ordinal_subset(all_147_5_194, all_147_4_193) = all_316_0_321
% 28.78/8.12 |
% 28.78/8.12 | Applying alpha-rule on (435) yields:
% 28.78/8.12 | (406) ~ (all_316_0_321 = 0)
% 28.78/8.12 | (437) ordinal_subset(all_147_5_194, all_147_4_193) = all_316_0_321
% 28.78/8.12 |
% 28.78/8.12 | Instantiating formula (19) with all_293_0_297, all_147_4_193, all_147_5_194 and discharging atoms ordinal_subset(all_147_4_193, all_147_5_194) = all_293_0_297, yields:
% 28.78/8.12 | (438) all_293_0_297 = 0 | ? [v0] : ((v0 = 0 & ordinal_subset(all_147_5_194, all_147_4_193) = 0) | ( ~ (v0 = 0) & ordinal(all_147_4_193) = v0) | ( ~ (v0 = 0) & ordinal(all_147_5_194) = v0))
% 28.78/8.12 |
% 28.78/8.12 | Instantiating formula (19) with all_316_0_321, all_147_5_194, all_147_4_193 and discharging atoms ordinal_subset(all_147_5_194, all_147_4_193) = all_316_0_321, yields:
% 28.78/8.12 | (439) all_316_0_321 = 0 | ? [v0] : ((v0 = 0 & ordinal_subset(all_147_4_193, all_147_5_194) = 0) | ( ~ (v0 = 0) & ordinal(all_147_4_193) = v0) | ( ~ (v0 = 0) & ordinal(all_147_5_194) = v0))
% 28.78/8.12 |
% 28.78/8.12 +-Applying beta-rule and splitting (439), into two cases.
% 28.78/8.12 |-Branch one:
% 28.78/8.12 | (408) all_316_0_321 = 0
% 28.78/8.12 |
% 28.78/8.12 | Equations (408) can reduce 406 to:
% 28.78/8.12 | (166) $false
% 28.78/8.12 |
% 28.78/8.12 |-The branch is then unsatisfiable
% 28.78/8.12 |-Branch two:
% 28.78/8.12 | (406) ~ (all_316_0_321 = 0)
% 28.78/8.12 | (443) ? [v0] : ((v0 = 0 & ordinal_subset(all_147_4_193, all_147_5_194) = 0) | ( ~ (v0 = 0) & ordinal(all_147_4_193) = v0) | ( ~ (v0 = 0) & ordinal(all_147_5_194) = v0))
% 28.78/8.12 |
% 28.78/8.12 | Instantiating (443) with all_987_0_1189 yields:
% 28.78/8.12 | (444) (all_987_0_1189 = 0 & ordinal_subset(all_147_4_193, all_147_5_194) = 0) | ( ~ (all_987_0_1189 = 0) & ordinal(all_147_4_193) = all_987_0_1189) | ( ~ (all_987_0_1189 = 0) & ordinal(all_147_5_194) = all_987_0_1189)
% 28.78/8.12 |
% 28.78/8.12 +-Applying beta-rule and splitting (444), into two cases.
% 28.78/8.12 |-Branch one:
% 28.78/8.12 | (445) (all_987_0_1189 = 0 & ordinal_subset(all_147_4_193, all_147_5_194) = 0) | ( ~ (all_987_0_1189 = 0) & ordinal(all_147_4_193) = all_987_0_1189)
% 28.78/8.12 |
% 28.78/8.12 +-Applying beta-rule and splitting (445), into two cases.
% 28.78/8.12 |-Branch one:
% 28.78/8.12 | (446) all_987_0_1189 = 0 & ordinal_subset(all_147_4_193, all_147_5_194) = 0
% 28.78/8.12 |
% 28.78/8.12 | Applying alpha-rule on (446) yields:
% 28.78/8.12 | (447) all_987_0_1189 = 0
% 28.78/8.12 | (448) ordinal_subset(all_147_4_193, all_147_5_194) = 0
% 28.78/8.12 |
% 28.78/8.12 +-Applying beta-rule and splitting (438), into two cases.
% 28.78/8.12 |-Branch one:
% 28.78/8.12 | (394) all_293_0_297 = 0
% 28.78/8.12 |
% 28.78/8.12 | Equations (394) can reduce 392 to:
% 28.78/8.12 | (166) $false
% 28.78/8.12 |
% 28.78/8.12 |-The branch is then unsatisfiable
% 28.78/8.12 |-Branch two:
% 28.78/8.12 | (392) ~ (all_293_0_297 = 0)
% 28.78/8.12 | (452) ? [v0] : ((v0 = 0 & ordinal_subset(all_147_5_194, all_147_4_193) = 0) | ( ~ (v0 = 0) & ordinal(all_147_4_193) = v0) | ( ~ (v0 = 0) & ordinal(all_147_5_194) = v0))
% 28.78/8.12 |
% 28.78/8.12 | Instantiating formula (92) with all_147_4_193, all_147_5_194, 0, all_293_0_297 and discharging atoms ordinal_subset(all_147_4_193, all_147_5_194) = all_293_0_297, ordinal_subset(all_147_4_193, all_147_5_194) = 0, yields:
% 28.78/8.12 | (394) all_293_0_297 = 0
% 28.78/8.12 |
% 28.78/8.12 | Equations (394) can reduce 392 to:
% 28.78/8.12 | (166) $false
% 28.78/8.12 |
% 28.78/8.12 |-The branch is then unsatisfiable
% 28.78/8.12 |-Branch two:
% 28.78/8.12 | (455) ~ (all_987_0_1189 = 0) & ordinal(all_147_4_193) = all_987_0_1189
% 28.78/8.12 |
% 28.78/8.12 | Applying alpha-rule on (455) yields:
% 28.78/8.12 | (456) ~ (all_987_0_1189 = 0)
% 28.78/8.12 | (457) ordinal(all_147_4_193) = all_987_0_1189
% 28.78/8.12 |
% 28.78/8.12 | Instantiating formula (42) with all_147_4_193, all_987_0_1189, 0 and discharging atoms ordinal(all_147_4_193) = all_987_0_1189, ordinal(all_147_4_193) = 0, yields:
% 28.78/8.12 | (447) all_987_0_1189 = 0
% 28.78/8.12 |
% 28.78/8.12 | Equations (447) can reduce 456 to:
% 28.78/8.12 | (166) $false
% 28.78/8.12 |
% 28.78/8.12 |-The branch is then unsatisfiable
% 28.78/8.12 |-Branch two:
% 28.78/8.12 | (460) ~ (all_987_0_1189 = 0) & ordinal(all_147_5_194) = all_987_0_1189
% 28.78/8.12 |
% 28.78/8.12 | Applying alpha-rule on (460) yields:
% 28.78/8.12 | (456) ~ (all_987_0_1189 = 0)
% 28.78/8.12 | (462) ordinal(all_147_5_194) = all_987_0_1189
% 28.78/8.12 |
% 28.78/8.12 | Instantiating formula (42) with all_147_5_194, all_987_0_1189, 0 and discharging atoms ordinal(all_147_5_194) = all_987_0_1189, ordinal(all_147_5_194) = 0, yields:
% 28.78/8.12 | (447) all_987_0_1189 = 0
% 28.78/8.12 |
% 28.78/8.12 | Equations (447) can reduce 456 to:
% 28.78/8.12 | (166) $false
% 28.78/8.12 |
% 28.78/8.12 |-The branch is then unsatisfiable
% 28.78/8.12 |-Branch two:
% 28.78/8.12 | (465) ~ (all_205_0_237 = 0) & ordinal(all_0_13_13) = all_205_0_237
% 28.78/8.12 |
% 28.78/8.12 | Applying alpha-rule on (465) yields:
% 28.78/8.12 | (466) ~ (all_205_0_237 = 0)
% 28.78/8.12 | (467) ordinal(all_0_13_13) = all_205_0_237
% 28.78/8.12 |
% 28.78/8.12 | Instantiating formula (42) with all_0_13_13, all_205_0_237, 0 and discharging atoms ordinal(all_0_13_13) = all_205_0_237, ordinal(all_0_13_13) = 0, yields:
% 28.78/8.12 | (259) all_205_0_237 = 0
% 28.78/8.12 |
% 28.78/8.12 | Equations (259) can reduce 466 to:
% 28.78/8.12 | (166) $false
% 28.78/8.12 |
% 28.78/8.12 |-The branch is then unsatisfiable
% 28.78/8.12 |-Branch two:
% 28.78/8.12 | (470) ~ (all_173_0_204 = 0) & ordinal(all_0_13_13) = all_173_0_204
% 28.78/8.12 |
% 28.78/8.12 | Applying alpha-rule on (470) yields:
% 28.78/8.12 | (471) ~ (all_173_0_204 = 0)
% 28.78/8.12 | (472) ordinal(all_0_13_13) = all_173_0_204
% 28.78/8.12 |
% 28.78/8.12 | Instantiating formula (42) with all_0_13_13, all_173_0_204, 0 and discharging atoms ordinal(all_0_13_13) = all_173_0_204, ordinal(all_0_13_13) = 0, yields:
% 28.78/8.12 | (256) all_173_0_204 = 0
% 28.78/8.12 |
% 28.78/8.12 | Equations (256) can reduce 471 to:
% 28.78/8.12 | (166) $false
% 28.78/8.12 |
% 28.78/8.12 |-The branch is then unsatisfiable
% 28.78/8.12 |-Branch two:
% 28.78/8.12 | (475) ~ (all_81_1_117 = all_0_13_13)
% 28.78/8.12 | (476) ? [v0] : ( ~ (v0 = 0) & relation(all_0_12_12) = v0)
% 28.78/8.12 |
% 28.78/8.12 | Instantiating formula (122) with all_0_12_12, all_116_2_172, all_81_1_117 and discharging atoms relation_field(all_0_12_12) = all_116_2_172, relation_field(all_0_12_12) = all_81_1_117, yields:
% 28.78/8.12 | (477) all_116_2_172 = all_81_1_117
% 28.78/8.12 |
% 28.78/8.12 | Instantiating formula (122) with all_0_12_12, all_0_13_13, all_116_2_172 and discharging atoms relation_field(all_0_12_12) = all_116_2_172, relation_field(all_0_12_12) = all_0_13_13, yields:
% 28.78/8.12 | (207) all_116_2_172 = all_0_13_13
% 28.78/8.12 |
% 28.78/8.12 | Combining equations (207,477) yields a new equation:
% 28.78/8.12 | (189) all_81_1_117 = all_0_13_13
% 28.78/8.12 |
% 28.78/8.12 | Equations (189) can reduce 475 to:
% 28.78/8.12 | (166) $false
% 28.78/8.12 |
% 28.78/8.12 |-The branch is then unsatisfiable
% 28.78/8.12 % SZS output end Proof for theBenchmark
% 28.78/8.12
% 28.78/8.12 7549ms
%------------------------------------------------------------------------------