TSTP Solution File: SEU291+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU291+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 08:48:32 EDT 2022
% Result : Theorem 19.08s 5.18s
% Output : Proof 23.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU291+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.33 % Computer : n015.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jun 19 13:24:29 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.58 ____ _
% 0.20/0.58 ___ / __ \_____(_)___ ________ __________
% 0.20/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.20/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.20/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.20/0.58
% 0.20/0.58 A Theorem Prover for First-Order Logic
% 0.20/0.58 (ePrincess v.1.0)
% 0.20/0.58
% 0.20/0.58 (c) Philipp Rümmer, 2009-2015
% 0.20/0.58 (c) Peter Backeman, 2014-2015
% 0.20/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.20/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.20/0.58 Bug reports to peter@backeman.se
% 0.20/0.58
% 0.20/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.20/0.58
% 0.20/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.71/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.62/0.97 Prover 0: Preprocessing ...
% 2.30/1.20 Prover 0: Warning: ignoring some quantifiers
% 2.39/1.22 Prover 0: Constructing countermodel ...
% 3.60/1.52 Prover 0: gave up
% 3.60/1.52 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 3.74/1.56 Prover 1: Preprocessing ...
% 4.41/1.69 Prover 1: Warning: ignoring some quantifiers
% 4.41/1.70 Prover 1: Constructing countermodel ...
% 5.16/1.88 Prover 1: gave up
% 5.16/1.88 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 5.16/1.91 Prover 2: Preprocessing ...
% 5.70/2.03 Prover 2: Warning: ignoring some quantifiers
% 5.70/2.04 Prover 2: Constructing countermodel ...
% 14.54/4.10 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 14.69/4.14 Prover 3: Preprocessing ...
% 14.69/4.18 Prover 3: Warning: ignoring some quantifiers
% 14.69/4.18 Prover 3: Constructing countermodel ...
% 15.11/4.26 Prover 3: gave up
% 15.11/4.26 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 15.11/4.28 Prover 4: Preprocessing ...
% 15.44/4.36 Prover 4: Warning: ignoring some quantifiers
% 15.44/4.36 Prover 4: Constructing countermodel ...
% 19.08/5.17 Prover 4: proved (917ms)
% 19.08/5.18 Prover 2: stopped
% 19.08/5.18
% 19.08/5.18 No countermodel exists, formula is valid
% 19.08/5.18 % SZS status Theorem for theBenchmark
% 19.08/5.18
% 19.08/5.18 Generating proof ... Warning: ignoring some quantifiers
% 23.15/6.11 found it (size 139)
% 23.15/6.11
% 23.15/6.11 % SZS output start Proof for theBenchmark
% 23.15/6.11 Assumed formulas after preprocessing and simplification:
% 23.15/6.11 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ( ~ (v12 = 0) & ~ (v10 = 0) & subset(v1, v2) = 0 & relation_empty_yielding(v7) = 0 & relation_empty_yielding(v6) = 0 & relation_empty_yielding(empty_set) = 0 & relation_of2_as_subset(v3, v0, v2) = v5 & relation_of2_as_subset(v3, v0, v1) = 0 & quasi_total(v3, v0, v2) = v4 & quasi_total(v3, v0, v1) = 0 & one_to_one(v16) = 0 & one_to_one(v8) = 0 & relation(v17) = 0 & relation(v16) = 0 & relation(v15) = 0 & relation(v13) = 0 & relation(v11) = 0 & relation(v8) = 0 & relation(v7) = 0 & relation(v6) = 0 & relation(empty_set) = 0 & empty(v16) = 0 & empty(v15) = 0 & empty(v14) = 0 & empty(v13) = 0 & empty(v11) = v12 & empty(v9) = v10 & empty(empty_set) = 0 & function(v17) = 0 & function(v16) = 0 & function(v13) = 0 & function(v8) = 0 & function(v6) = 0 & function(v3) = 0 & ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v23 = 0 | ~ (cartesian_product2(v18, v19) = v21) | ~ (powerset(v21) = v22) | ~ (element(v20, v22) = v23) | ? [v24] : ( ~ (v24 = 0) & relation_of2_as_subset(v20, v18, v19) = v24)) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v22 = 0 | ~ (subset(v18, v19) = 0) | ~ (relation_of2_as_subset(v21, v20, v19) = v22) | ? [v23] : ( ~ (v23 = 0) & relation_of2_as_subset(v21, v20, v18) = v23)) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v22 = 0 | ~ (relation_of2_as_subset(v21, v20, v19) = v22) | ~ (relation_of2_as_subset(v21, v20, v18) = 0) | ? [v23] : ( ~ (v23 = 0) & subset(v18, v19) = v23)) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v22 = 0 | ~ (powerset(v20) = v21) | ~ (element(v19, v21) = 0) | ~ (element(v18, v20) = v22) | ? [v23] : ( ~ (v23 = 0) & in(v18, v19) = v23)) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v19 = v18 | ~ (relation_of2(v22, v21, v20) = v19) | ~ (relation_of2(v22, v21, v20) = v18)) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v19 = v18 | ~ (relation_of2_as_subset(v22, v21, v20) = v19) | ~ (relation_of2_as_subset(v22, v21, v20) = v18)) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v19 = v18 | ~ (quasi_total(v22, v21, v20) = v19) | ~ (quasi_total(v22, v21, v20) = v18)) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v19 = v18 | ~ (relation_dom_as_subset(v22, v21, v20) = v19) | ~ (relation_dom_as_subset(v22, v21, v20) = v18)) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (cartesian_product2(v18, v19) = v21) | ~ (powerset(v21) = v22) | ~ (element(v20, v22) = 0) | relation(v20) = 0) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v21 = 0 | ~ (relation_of2(v20, v18, v19) = v21) | ? [v22] : ( ~ (v22 = 0) & relation_of2_as_subset(v20, v18, v19) = v22)) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v21 = 0 | ~ (relation_of2_as_subset(v20, v18, v19) = v21) | ? [v22] : ( ~ (v22 = 0) & relation_of2(v20, v18, v19) = v22)) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v21 = 0 | ~ (powerset(v19) = v20) | ~ (element(v18, v20) = v21) | ? [v22] : ( ~ (v22 = 0) & subset(v18, v19) = v22)) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v21 = 0 | ~ (element(v18, v20) = v21) | ~ (in(v18, v19) = 0) | ? [v22] : ? [v23] : ( ~ (v23 = 0) & powerset(v20) = v22 & element(v19, v22) = v23)) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v19 = v18 | ~ (subset(v21, v20) = v19) | ~ (subset(v21, v20) = v18)) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v19 = v18 | ~ (cartesian_product2(v21, v20) = v19) | ~ (cartesian_product2(v21, v20) = v18)) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v19 = v18 | ~ (element(v21, v20) = v19) | ~ (element(v21, v20) = v18)) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v19 = v18 | ~ (in(v21, v20) = v19) | ~ (in(v21, v20) = v18)) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (subset(v18, v19) = 0) | ~ (relation_of2_as_subset(v21, v20, v18) = 0) | relation_of2_as_subset(v21, v20, v19) = 0) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (quasi_total(v20, v18, v19) = v21) | ? [v22] : ? [v23] : (relation_of2_as_subset(v20, v18, v19) = v22 & relation_dom_as_subset(v18, v19, v20) = v23 & ( ~ (v22 = 0) | (( ~ (v19 = empty_set) | v18 = empty_set | (( ~ (v21 = 0) | v20 = empty_set) & ( ~ (v20 = empty_set) | v21 = 0))) & ((v19 = empty_set & ~ (v18 = empty_set)) | (( ~ (v23 = v18) | v21 = 0) & ( ~ (v21 = 0) | v23 = v18))))))) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (relation_dom_as_subset(v18, v19, v20) = v21) | ? [v22] : ? [v23] : ? [v24] : (relation_of2(v20, v18, v19) = v22 & powerset(v18) = v23 & element(v21, v23) = v24 & ( ~ (v22 = 0) | v24 = 0))) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (relation_dom_as_subset(v18, v19, v20) = v21) | ? [v22] : ? [v23] : (relation_dom(v20) = v23 & relation_of2(v20, v18, v19) = v22 & ( ~ (v22 = 0) | v23 = v21))) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (relation_dom_as_subset(v18, v19, v20) = v21) | ? [v22] : ? [v23] : (relation_of2_as_subset(v20, v18, v19) = v22 & quasi_total(v20, v18, v19) = v23 & ( ~ (v22 = 0) | (( ~ (v19 = empty_set) | v18 = empty_set | (( ~ (v23 = 0) | v20 = empty_set) & ( ~ (v20 = empty_set) | v23 = 0))) & ((v19 = empty_set & ~ (v18 = empty_set)) | (( ~ (v23 = 0) | v21 = v18) & ( ~ (v21 = v18) | v23 = 0))))))) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (powerset(v20) = v21) | ~ (element(v19, v21) = 0) | ~ (in(v18, v19) = 0) | element(v18, v20) = 0) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (powerset(v20) = v21) | ~ (element(v19, v21) = 0) | ~ (in(v18, v19) = 0) | ? [v22] : ( ~ (v22 = 0) & empty(v20) = v22)) & ! [v18] : ! [v19] : ! [v20] : (v20 = 0 | ~ (subset(v18, v19) = v20) | ? [v21] : ? [v22] : ( ~ (v22 = 0) & powerset(v19) = v21 & element(v18, v21) = v22)) & ! [v18] : ! [v19] : ! [v20] : (v20 = 0 | ~ (element(v18, v19) = v20) | ? [v21] : ( ~ (v21 = 0) & in(v18, v19) = v21)) & ! [v18] : ! [v19] : ! [v20] : (v20 = 0 | ~ (in(v18, v19) = v20) | ? [v21] : ? [v22] : (element(v18, v19) = v21 & empty(v19) = v22 & ( ~ (v21 = 0) | v22 = 0))) & ! [v18] : ! [v19] : ! [v20] : (v19 = v18 | ~ (relation_empty_yielding(v20) = v19) | ~ (relation_empty_yielding(v20) = v18)) & ! [v18] : ! [v19] : ! [v20] : (v19 = v18 | ~ (relation_dom(v20) = v19) | ~ (relation_dom(v20) = v18)) & ! [v18] : ! [v19] : ! [v20] : (v19 = v18 | ~ (one_to_one(v20) = v19) | ~ (one_to_one(v20) = v18)) & ! [v18] : ! [v19] : ! [v20] : (v19 = v18 | ~ (powerset(v20) = v19) | ~ (powerset(v20) = v18)) & ! [v18] : ! [v19] : ! [v20] : (v19 = v18 | ~ (relation(v20) = v19) | ~ (relation(v20) = v18)) & ! [v18] : ! [v19] : ! [v20] : (v19 = v18 | ~ (empty(v20) = v19) | ~ (empty(v20) = v18)) & ! [v18] : ! [v19] : ! [v20] : (v19 = v18 | ~ (function(v20) = v19) | ~ (function(v20) = v18)) & ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_of2(v20, v18, v19) = 0) | relation_of2_as_subset(v20, v18, v19) = 0) & ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_of2(v20, v18, v19) = 0) | ? [v21] : ? [v22] : (relation_dom_as_subset(v18, v19, v20) = v21 & powerset(v18) = v22 & element(v21, v22) = 0)) & ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_of2(v20, v18, v19) = 0) | ? [v21] : (relation_dom(v20) = v21 & relation_dom_as_subset(v18, v19, v20) = v21)) & ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_of2_as_subset(v20, v18, v19) = 0) | relation_of2(v20, v18, v19) = 0) & ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_of2_as_subset(v20, v18, v19) = 0) | ? [v21] : ? [v22] : (quasi_total(v20, v18, v19) = v21 & relation_dom_as_subset(v18, v19, v20) = v22 & ( ~ (v19 = empty_set) | v18 = empty_set | (( ~ (v21 = 0) | v20 = empty_set) & ( ~ (v20 = empty_set) | v21 = 0))) & ((v19 = empty_set & ~ (v18 = empty_set)) | (( ~ (v22 = v18) | v21 = 0) & ( ~ (v21 = 0) | v22 = v18))))) & ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_of2_as_subset(v20, v18, v19) = 0) | ? [v21] : ? [v22] : (cartesian_product2(v18, v19) = v21 & powerset(v21) = v22 & element(v20, v22) = 0)) & ! [v18] : ! [v19] : ! [v20] : ( ~ (cartesian_product2(v18, v19) = v20) | ? [v21] : ? [v22] : ? [v23] : (empty(v20) = v23 & empty(v19) = v22 & empty(v18) = v21 & ( ~ (v23 = 0) | v22 = 0 | v21 = 0))) & ! [v18] : ! [v19] : ! [v20] : ( ~ (powerset(v19) = v20) | ~ (element(v18, v20) = 0) | subset(v18, v19) = 0) & ! [v18] : ! [v19] : ! [v20] : ( ~ (empty(v20) = 0) | ~ (in(v18, v19) = 0) | ? [v21] : ? [v22] : ( ~ (v22 = 0) & powerset(v20) = v21 & element(v19, v21) = v22)) & ! [v18] : ! [v19] : (v19 = v18 | ~ (empty(v19) = 0) | ~ (empty(v18) = 0)) & ! [v18] : ! [v19] : (v19 = 0 | ~ (subset(v18, v18) = v19)) & ! [v18] : ! [v19] : (v19 = 0 | ~ (relation(v18) = v19) | ? [v20] : ( ~ (v20 = 0) & empty(v18) = v20)) & ! [v18] : ! [v19] : (v19 = 0 | ~ (empty(v18) = v19) | ? [v20] : ? [v21] : ? [v22] : ( ~ (v22 = 0) & powerset(v18) = v20 & element(v21, v20) = 0 & empty(v21) = v22)) & ! [v18] : ! [v19] : (v19 = 0 | ~ (empty(v18) = v19) | ? [v20] : ? [v21] : ? [v22] : (relation_dom(v18) = v21 & relation(v18) = v20 & empty(v21) = v22 & ( ~ (v22 = 0) | ~ (v20 = 0)))) & ! [v18] : ! [v19] : (v19 = 0 | ~ (function(v18) = v19) | ? [v20] : ( ~ (v20 = 0) & empty(v18) = v20)) & ! [v18] : ! [v19] : ( ~ (subset(v18, v19) = 0) | ? [v20] : (powerset(v19) = v20 & element(v18, v20) = 0)) & ! [v18] : ! [v19] : ( ~ (relation_dom(v18) = v19) | ? [v20] : ? [v21] : ? [v22] : (relation(v19) = v22 & empty(v19) = v21 & empty(v18) = v20 & ( ~ (v20 = 0) | (v22 = 0 & v21 = 0)))) & ! [v18] : ! [v19] : ( ~ (relation_dom(v18) = v19) | ? [v20] : ? [v21] : ? [v22] : (relation(v18) = v21 & empty(v19) = v22 & empty(v18) = v20 & ( ~ (v22 = 0) | ~ (v21 = 0) | v20 = 0))) & ! [v18] : ! [v19] : ( ~ (one_to_one(v18) = v19) | ? [v20] : ? [v21] : ? [v22] : (relation(v18) = v20 & empty(v18) = v21 & function(v18) = v22 & ( ~ (v22 = 0) | ~ (v21 = 0) | ~ (v20 = 0) | v19 = 0))) & ! [v18] : ! [v19] : ( ~ (powerset(v18) = v19) | ? [v20] : ? [v21] : ? [v22] : ((v21 = 0 & ~ (v22 = 0) & element(v20, v19) = 0 & empty(v20) = v22) | (v20 = 0 & empty(v18) = 0))) & ! [v18] : ! [v19] : ( ~ (powerset(v18) = v19) | ? [v20] : ( ~ (v20 = 0) & empty(v19) = v20)) & ! [v18] : ! [v19] : ( ~ (powerset(v18) = v19) | ? [v20] : (element(v20, v19) = 0 & empty(v20) = 0)) & ! [v18] : ! [v19] : ( ~ (element(v18, v19) = 0) | ? [v20] : ? [v21] : (empty(v19) = v20 & in(v18, v19) = v21 & (v21 = 0 | v20 = 0))) & ! [v18] : ! [v19] : ( ~ (in(v19, v18) = 0) | ? [v20] : ( ~ (v20 = 0) & in(v18, v19) = v20)) & ! [v18] : ! [v19] : ( ~ (in(v18, v19) = 0) | element(v18, v19) = 0) & ! [v18] : ! [v19] : ( ~ (in(v18, v19) = 0) | ? [v20] : ( ~ (v20 = 0) & empty(v19) = v20)) & ! [v18] : ! [v19] : ( ~ (in(v18, v19) = 0) | ? [v20] : ( ~ (v20 = 0) & in(v19, v18) = v20)) & ! [v18] : (v18 = empty_set | ~ (subset(v18, empty_set) = 0)) & ! [v18] : (v18 = empty_set | ~ (empty(v18) = 0)) & ! [v18] : ( ~ (relation(v18) = 0) | ? [v19] : ? [v20] : ? [v21] : (relation_dom(v18) = v20 & empty(v20) = v21 & empty(v18) = v19 & ( ~ (v21 = 0) | v19 = 0))) & ! [v18] : ( ~ (relation(v18) = 0) | ? [v19] : ? [v20] : ? [v21] : (one_to_one(v18) = v21 & empty(v18) = v19 & function(v18) = v20 & ( ~ (v20 = 0) | ~ (v19 = 0) | v21 = 0))) & ! [v18] : ( ~ (empty(v18) = 0) | relation(v18) = 0) & ! [v18] : ( ~ (empty(v18) = 0) | function(v18) = 0) & ! [v18] : ( ~ (empty(v18) = 0) | ? [v19] : ? [v20] : ? [v21] : (one_to_one(v18) = v21 & relation(v18) = v19 & function(v18) = v20 & ( ~ (v20 = 0) | ~ (v19 = 0) | v21 = 0))) & ! [v18] : ( ~ (empty(v18) = 0) | ? [v19] : (relation_dom(v18) = v19 & relation(v19) = 0 & empty(v19) = 0)) & ! [v18] : ( ~ (function(v18) = 0) | ? [v19] : ? [v20] : ? [v21] : (one_to_one(v18) = v21 & relation(v18) = v19 & empty(v18) = v20 & ( ~ (v20 = 0) | ~ (v19 = 0) | v21 = 0))) & ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : (powerset(v20) = v22 & element(v19, v22) = v23 & element(v18, v20) = v24 & in(v18, v19) = v21 & ( ~ (v23 = 0) | ~ (v21 = 0) | v24 = 0)) & ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : (relation_dom(v20) = v23 & relation_of2(v20, v18, v19) = v21 & relation_dom_as_subset(v18, v19, v20) = v22 & ( ~ (v21 = 0) | v23 = v22)) & ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : (relation_of2_as_subset(v20, v18, v19) = v21 & quasi_total(v20, v18, v19) = v22 & relation_dom_as_subset(v18, v19, v20) = v23 & ( ~ (v21 = 0) | (( ~ (v19 = empty_set) | v18 = empty_set | (( ~ (v22 = 0) | v20 = empty_set) & ( ~ (v20 = empty_set) | v22 = 0))) & ((v19 = empty_set & ~ (v18 = empty_set)) | (( ~ (v23 = v18) | v22 = 0) & ( ~ (v22 = 0) | v23 = v18)))))) & ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : (cartesian_product2(v18, v19) = v22 & empty(v22) = v23 & empty(v19) = v21 & empty(v18) = v20 & ( ~ (v23 = 0) | v21 = 0 | v20 = 0)) & ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : (subset(v18, v19) = v20 & powerset(v19) = v21 & element(v18, v21) = v22 & ( ~ (v20 = 0) | v22 = 0)) & ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : (one_to_one(v18) = v22 & relation(v18) = v19 & empty(v18) = v20 & function(v18) = v21 & ( ~ (v21 = 0) | ~ (v20 = 0) | ~ (v19 = 0) | v22 = 0)) & ? [v18] : ? [v19] : ? [v20] : relation_of2(v20, v18, v19) = 0 & ? [v18] : ? [v19] : ? [v20] : relation_of2_as_subset(v20, v18, v19) = 0 & ? [v18] : ? [v19] : ? [v20] : (relation_of2(v20, v18, v19) = 0 & quasi_total(v20, v18, v19) = 0 & relation(v20) = 0 & function(v20) = 0) & ? [v18] : ? [v19] : ? [v20] : (relation_of2(v20, v18, v19) = 0 & relation(v20) = 0 & function(v20) = 0) & ? [v18] : ? [v19] : element(v19, v18) = 0 & ( ~ (v5 = 0) | ~ (v4 = 0)) & ( ~ (v1 = empty_set) | v0 = empty_set))
% 23.24/6.16 | 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, all_0_14_14, all_0_15_15, all_0_16_16, all_0_17_17 yields:
% 23.24/6.16 | (1) ~ (all_0_5_5 = 0) & ~ (all_0_7_7 = 0) & subset(all_0_16_16, all_0_15_15) = 0 & relation_empty_yielding(all_0_10_10) = 0 & relation_empty_yielding(all_0_11_11) = 0 & relation_empty_yielding(empty_set) = 0 & relation_of2_as_subset(all_0_14_14, all_0_17_17, all_0_15_15) = all_0_12_12 & relation_of2_as_subset(all_0_14_14, all_0_17_17, all_0_16_16) = 0 & quasi_total(all_0_14_14, all_0_17_17, all_0_15_15) = all_0_13_13 & quasi_total(all_0_14_14, all_0_17_17, all_0_16_16) = 0 & one_to_one(all_0_1_1) = 0 & one_to_one(all_0_9_9) = 0 & relation(all_0_0_0) = 0 & relation(all_0_1_1) = 0 & relation(all_0_2_2) = 0 & relation(all_0_4_4) = 0 & relation(all_0_6_6) = 0 & relation(all_0_9_9) = 0 & relation(all_0_10_10) = 0 & relation(all_0_11_11) = 0 & relation(empty_set) = 0 & empty(all_0_1_1) = 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_8_8) = all_0_7_7 & empty(empty_set) = 0 & function(all_0_0_0) = 0 & function(all_0_1_1) = 0 & function(all_0_4_4) = 0 & function(all_0_9_9) = 0 & function(all_0_11_11) = 0 & function(all_0_14_14) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (cartesian_product2(v0, v1) = v3) | ~ (powerset(v3) = v4) | ~ (element(v2, v4) = v5) | ? [v6] : ( ~ (v6 = 0) & relation_of2_as_subset(v2, v0, v1) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (subset(v0, v1) = 0) | ~ (relation_of2_as_subset(v3, v2, v1) = v4) | ? [v5] : ( ~ (v5 = 0) & relation_of2_as_subset(v3, v2, v0) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (relation_of2_as_subset(v3, v2, v1) = v4) | ~ (relation_of2_as_subset(v3, v2, v0) = 0) | ? [v5] : ( ~ (v5 = 0) & subset(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (element(v0, v2) = v4) | ? [v5] : ( ~ (v5 = 0) & in(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (relation_of2(v4, v3, v2) = v1) | ~ (relation_of2(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (relation_of2_as_subset(v4, v3, v2) = v1) | ~ (relation_of2_as_subset(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (quasi_total(v4, v3, v2) = v1) | ~ (quasi_total(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (relation_dom_as_subset(v4, v3, v2) = v1) | ~ (relation_dom_as_subset(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v0, v1) = v3) | ~ (powerset(v3) = v4) | ~ (element(v2, v4) = 0) | relation(v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (relation_of2(v2, v0, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & relation_of2_as_subset(v2, v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (relation_of2_as_subset(v2, v0, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & relation_of2(v2, v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (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 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset(v0, v1) = 0) | ~ (relation_of2_as_subset(v3, v2, v0) = 0) | relation_of2_as_subset(v3, v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (quasi_total(v2, v0, v1) = v3) | ? [v4] : ? [v5] : (relation_of2_as_subset(v2, v0, v1) = v4 & relation_dom_as_subset(v0, v1, v2) = v5 & ( ~ (v4 = 0) | (( ~ (v1 = empty_set) | v0 = empty_set | (( ~ (v3 = 0) | v2 = empty_set) & ( ~ (v2 = empty_set) | v3 = 0))) & ((v1 = empty_set & ~ (v0 = empty_set)) | (( ~ (v5 = v0) | v3 = 0) & ( ~ (v3 = 0) | v5 = v0))))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom_as_subset(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : (relation_of2(v2, v0, v1) = v4 & powerset(v0) = v5 & element(v3, v5) = v6 & ( ~ (v4 = 0) | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom_as_subset(v0, v1, v2) = v3) | ? [v4] : ? [v5] : (relation_dom(v2) = v5 & relation_of2(v2, v0, v1) = v4 & ( ~ (v4 = 0) | v5 = v3))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom_as_subset(v0, v1, v2) = v3) | ? [v4] : ? [v5] : (relation_of2_as_subset(v2, v0, v1) = v4 & quasi_total(v2, v0, v1) = v5 & ( ~ (v4 = 0) | (( ~ (v1 = empty_set) | v0 = empty_set | (( ~ (v5 = 0) | v2 = empty_set) & ( ~ (v2 = empty_set) | v5 = 0))) & ((v1 = empty_set & ~ (v0 = empty_set)) | (( ~ (v5 = 0) | v3 = v0) & ( ~ (v3 = v0) | v5 = 0))))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | element(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v1) = v3 & element(v0, v3) = v4)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v0, v1) = v2) | ? [v3] : ? [v4] : (element(v0, v1) = v3 & empty(v1) = v4 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (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 | ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_of2(v2, v0, v1) = 0) | relation_of2_as_subset(v2, v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_of2(v2, v0, v1) = 0) | ? [v3] : ? [v4] : (relation_dom_as_subset(v0, v1, v2) = v3 & powerset(v0) = v4 & element(v3, v4) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_of2(v2, v0, v1) = 0) | ? [v3] : (relation_dom(v2) = v3 & relation_dom_as_subset(v0, v1, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_of2_as_subset(v2, v0, v1) = 0) | relation_of2(v2, v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_of2_as_subset(v2, v0, v1) = 0) | ? [v3] : ? [v4] : (quasi_total(v2, v0, v1) = v3 & relation_dom_as_subset(v0, v1, v2) = v4 & ( ~ (v1 = empty_set) | v0 = empty_set | (( ~ (v3 = 0) | v2 = empty_set) & ( ~ (v2 = empty_set) | v3 = 0))) & ((v1 = empty_set & ~ (v0 = empty_set)) | (( ~ (v4 = v0) | v3 = 0) & ( ~ (v3 = 0) | v4 = v0))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_of2_as_subset(v2, v0, v1) = 0) | ? [v3] : ? [v4] : (cartesian_product2(v0, v1) = v3 & powerset(v3) = v4 & element(v2, v4) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (cartesian_product2(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (empty(v2) = v5 & empty(v1) = v4 & empty(v0) = v3 & ( ~ (v5 = 0) | v4 = 0 | v3 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | subset(v0, v1) = 0) & ! [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 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (relation(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (empty(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v0) = v2 & element(v3, v2) = 0 & empty(v3) = v4)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (empty(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation_dom(v0) = v3 & relation(v0) = v2 & empty(v3) = v4 & ( ~ (v4 = 0) | ~ (v2 = 0)))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (function(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2)) & ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (powerset(v1) = v2 & element(v0, v2) = 0)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation(v1) = v4 & empty(v1) = v3 & empty(v0) = v2 & ( ~ (v2 = 0) | (v4 = 0 & v3 = 0)))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation(v0) = v3 & empty(v1) = v4 & empty(v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2 = 0))) & ! [v0] : ! [v1] : ( ~ (one_to_one(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation(v0) = v2 & empty(v0) = v3 & function(v0) = v4 & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | v1 = 0))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v3 = 0 & ~ (v4 = 0) & element(v2, v1) = 0 & empty(v2) = v4) | (v2 = 0 & empty(v0) = 0))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) = 0 & empty(v2) = 0)) & ! [v0] : ! [v1] : ( ~ (element(v0, v1) = 0) | ? [v2] : ? [v3] : (empty(v1) = v2 & in(v0, v1) = v3 & (v3 = 0 | v2 = 0))) & ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | element(v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) & ! [v0] : (v0 = empty_set | ~ (subset(v0, empty_set) = 0)) & ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0)) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (relation_dom(v0) = v2 & empty(v2) = v3 & empty(v0) = v1 & ( ~ (v3 = 0) | v1 = 0))) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (one_to_one(v0) = v3 & empty(v0) = v1 & function(v0) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0))) & ! [v0] : ( ~ (empty(v0) = 0) | relation(v0) = 0) & ! [v0] : ( ~ (empty(v0) = 0) | function(v0) = 0) & ! [v0] : ( ~ (empty(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (one_to_one(v0) = v3 & relation(v0) = v1 & function(v0) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0))) & ! [v0] : ( ~ (empty(v0) = 0) | ? [v1] : (relation_dom(v0) = v1 & relation(v1) = 0 & empty(v1) = 0)) & ! [v0] : ( ~ (function(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (one_to_one(v0) = v3 & relation(v0) = v1 & empty(v0) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0))) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (powerset(v2) = v4 & element(v1, v4) = v5 & element(v0, v2) = v6 & in(v0, v1) = v3 & ( ~ (v5 = 0) | ~ (v3 = 0) | v6 = 0)) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_dom(v2) = v5 & relation_of2(v2, v0, v1) = v3 & relation_dom_as_subset(v0, v1, v2) = v4 & ( ~ (v3 = 0) | v5 = v4)) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_of2_as_subset(v2, v0, v1) = v3 & quasi_total(v2, v0, v1) = v4 & relation_dom_as_subset(v0, v1, v2) = v5 & ( ~ (v3 = 0) | (( ~ (v1 = empty_set) | v0 = empty_set | (( ~ (v4 = 0) | v2 = empty_set) & ( ~ (v2 = empty_set) | v4 = 0))) & ((v1 = empty_set & ~ (v0 = empty_set)) | (( ~ (v5 = v0) | v4 = 0) & ( ~ (v4 = 0) | v5 = v0)))))) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (cartesian_product2(v0, v1) = v4 & empty(v4) = v5 & empty(v1) = v3 & empty(v0) = v2 & ( ~ (v5 = 0) | v3 = 0 | v2 = 0)) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (subset(v0, v1) = v2 & powerset(v1) = v3 & element(v0, v3) = v4 & ( ~ (v2 = 0) | v4 = 0)) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (one_to_one(v0) = v4 & relation(v0) = v1 & empty(v0) = v2 & function(v0) = v3 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | v4 = 0)) & ? [v0] : ? [v1] : ? [v2] : relation_of2(v2, v0, v1) = 0 & ? [v0] : ? [v1] : ? [v2] : relation_of2_as_subset(v2, v0, v1) = 0 & ? [v0] : ? [v1] : ? [v2] : (relation_of2(v2, v0, v1) = 0 & quasi_total(v2, v0, v1) = 0 & relation(v2) = 0 & function(v2) = 0) & ? [v0] : ? [v1] : ? [v2] : (relation_of2(v2, v0, v1) = 0 & relation(v2) = 0 & function(v2) = 0) & ? [v0] : ? [v1] : element(v1, v0) = 0 & ( ~ (all_0_12_12 = 0) | ~ (all_0_13_13 = 0)) & ( ~ (all_0_16_16 = empty_set) | all_0_17_17 = empty_set)
% 23.24/6.18 |
% 23.24/6.18 | Applying alpha-rule on (1) yields:
% 23.24/6.18 | (2) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0))
% 23.24/6.18 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (relation_of2(v4, v3, v2) = v1) | ~ (relation_of2(v4, v3, v2) = v0))
% 23.24/6.18 | (4) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v0, v1) = v2) | ? [v3] : ? [v4] : (element(v0, v1) = v3 & empty(v1) = v4 & ( ~ (v3 = 0) | v4 = 0)))
% 23.24/6.18 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (cartesian_product2(v0, v1) = v3) | ~ (powerset(v3) = v4) | ~ (element(v2, v4) = v5) | ? [v6] : ( ~ (v6 = 0) & relation_of2_as_subset(v2, v0, v1) = v6))
% 23.24/6.18 | (6) ! [v0] : ( ~ (empty(v0) = 0) | function(v0) = 0)
% 23.24/6.18 | (7) function(all_0_0_0) = 0
% 23.24/6.18 | (8) function(all_0_4_4) = 0
% 23.24/6.18 | (9) quasi_total(all_0_14_14, all_0_17_17, all_0_16_16) = 0
% 23.24/6.18 | (10) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation(v0) = v3 & empty(v1) = v4 & empty(v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2 = 0)))
% 23.24/6.18 | (11) function(all_0_1_1) = 0
% 23.24/6.18 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (empty(v2) = 0) | ~ (in(v0, v1) = 0) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v2) = v3 & element(v1, v3) = v4))
% 23.24/6.18 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (subset(v0, v1) = 0) | ~ (relation_of2_as_subset(v3, v2, v1) = v4) | ? [v5] : ( ~ (v5 = 0) & relation_of2_as_subset(v3, v2, v0) = v5))
% 23.24/6.19 | (14) relation(empty_set) = 0
% 23.24/6.19 | (15) relation(all_0_9_9) = 0
% 23.24/6.19 | (16) relation_empty_yielding(all_0_10_10) = 0
% 23.24/6.19 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 23.24/6.19 | (18) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) = 0 & empty(v2) = 0))
% 23.24/6.19 | (19) relation(all_0_6_6) = 0
% 23.24/6.19 | (20) relation_of2_as_subset(all_0_14_14, all_0_17_17, all_0_15_15) = all_0_12_12
% 23.24/6.19 | (21) ~ (all_0_12_12 = 0) | ~ (all_0_13_13 = 0)
% 23.24/6.19 | (22) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0))
% 23.24/6.19 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (relation_of2_as_subset(v3, v2, v1) = v4) | ~ (relation_of2_as_subset(v3, v2, v0) = 0) | ? [v5] : ( ~ (v5 = 0) & subset(v0, v1) = v5))
% 23.24/6.19 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset(v0, v1) = 0) | ~ (relation_of2_as_subset(v3, v2, v0) = 0) | relation_of2_as_subset(v3, v2, v1) = 0)
% 23.24/6.19 | (25) relation(all_0_10_10) = 0
% 23.24/6.19 | (26) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0))
% 23.24/6.19 | (27) empty(all_0_4_4) = 0
% 23.24/6.19 | (28) ! [v0] : ! [v1] : (v1 = 0 | ~ (empty(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v0) = v2 & element(v3, v2) = 0 & empty(v3) = v4))
% 23.24/6.19 | (29) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_empty_yielding(v2) = v1) | ~ (relation_empty_yielding(v2) = v0))
% 23.24/6.19 | (30) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (one_to_one(v0) = v3 & empty(v0) = v1 & function(v0) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0)))
% 23.24/6.19 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (relation_of2_as_subset(v2, v0, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & relation_of2(v2, v0, v1) = v4))
% 23.24/6.19 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (relation_of2(v2, v0, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & relation_of2_as_subset(v2, v0, v1) = v4))
% 23.24/6.19 | (33) ! [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))
% 23.24/6.19 | (34) quasi_total(all_0_14_14, all_0_17_17, all_0_15_15) = all_0_13_13
% 23.24/6.19 | (35) one_to_one(all_0_1_1) = 0
% 23.24/6.19 | (36) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (subset(v0, v1) = v2 & powerset(v1) = v3 & element(v0, v3) = v4 & ( ~ (v2 = 0) | v4 = 0))
% 23.24/6.19 | (37) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 23.24/6.19 | (38) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (cartesian_product2(v0, v1) = v4 & empty(v4) = v5 & empty(v1) = v3 & empty(v0) = v2 & ( ~ (v5 = 0) | v3 = 0 | v2 = 0))
% 23.24/6.19 | (39) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (one_to_one(v0) = v4 & relation(v0) = v1 & empty(v0) = v2 & function(v0) = v3 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | v4 = 0))
% 23.24/6.19 | (40) ! [v0] : ! [v1] : ! [v2] : ( ~ (cartesian_product2(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (empty(v2) = v5 & empty(v1) = v4 & empty(v0) = v3 & ( ~ (v5 = 0) | v4 = 0 | v3 = 0)))
% 23.24/6.19 | (41) ~ (all_0_5_5 = 0)
% 23.24/6.19 | (42) function(all_0_9_9) = 0
% 23.24/6.19 | (43) function(all_0_11_11) = 0
% 23.24/6.19 | (44) empty(empty_set) = 0
% 23.24/6.19 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom_as_subset(v0, v1, v2) = v3) | ? [v4] : ? [v5] : (relation_dom(v2) = v5 & relation_of2(v2, v0, v1) = v4 & ( ~ (v4 = 0) | v5 = v3)))
% 23.24/6.19 | (46) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v3 = 0 & ~ (v4 = 0) & element(v2, v1) = 0 & empty(v2) = v4) | (v2 = 0 & empty(v0) = 0)))
% 23.24/6.19 | (47) ? [v0] : ? [v1] : ? [v2] : relation_of2_as_subset(v2, v0, v1) = 0
% 23.24/6.19 | (48) ? [v0] : ? [v1] : ? [v2] : (relation_of2(v2, v0, v1) = 0 & quasi_total(v2, v0, v1) = 0 & relation(v2) = 0 & function(v2) = 0)
% 23.24/6.19 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0))
% 23.24/6.19 | (50) empty(all_0_3_3) = 0
% 23.24/6.19 | (51) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (powerset(v2) = v4 & element(v1, v4) = v5 & element(v0, v2) = v6 & in(v0, v1) = v3 & ( ~ (v5 = 0) | ~ (v3 = 0) | v6 = 0))
% 23.24/6.19 | (52) ? [v0] : ? [v1] : ? [v2] : (relation_of2(v2, v0, v1) = 0 & relation(v2) = 0 & function(v2) = 0)
% 23.24/6.19 | (53) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 23.24/6.19 | (54) relation(all_0_2_2) = 0
% 23.24/6.19 | (55) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_of2_as_subset(v2, v0, v1) = 0) | relation_of2(v2, v0, v1) = 0)
% 23.24/6.20 | (56) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_of2(v2, v0, v1) = 0) | relation_of2_as_subset(v2, v0, v1) = 0)
% 23.24/6.20 | (57) ! [v0] : ( ~ (function(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (one_to_one(v0) = v3 & relation(v0) = v1 & empty(v0) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0)))
% 23.24/6.20 | (58) ! [v0] : ( ~ (empty(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (one_to_one(v0) = v3 & relation(v0) = v1 & function(v0) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0)))
% 23.24/6.20 | (59) ! [v0] : ! [v1] : (v1 = 0 | ~ (empty(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation_dom(v0) = v3 & relation(v0) = v2 & empty(v3) = v4 & ( ~ (v4 = 0) | ~ (v2 = 0))))
% 23.24/6.20 | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (relation_dom_as_subset(v4, v3, v2) = v1) | ~ (relation_dom_as_subset(v4, v3, v2) = v0))
% 23.24/6.20 | (61) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0))
% 23.24/6.20 | (62) relation(all_0_4_4) = 0
% 23.24/6.20 | (63) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0))
% 23.24/6.20 | (64) ! [v0] : ! [v1] : ( ~ (element(v0, v1) = 0) | ? [v2] : ? [v3] : (empty(v1) = v2 & in(v0, v1) = v3 & (v3 = 0 | v2 = 0)))
% 23.24/6.20 | (65) ! [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))
% 23.24/6.20 | (66) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (relation_of2_as_subset(v4, v3, v2) = v1) | ~ (relation_of2_as_subset(v4, v3, v2) = v0))
% 23.24/6.20 | (67) ! [v0] : (v0 = empty_set | ~ (subset(v0, empty_set) = 0))
% 23.24/6.20 | (68) empty(all_0_8_8) = all_0_7_7
% 23.24/6.20 | (69) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | element(v0, v2) = 0)
% 23.24/6.20 | (70) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom_as_subset(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : (relation_of2(v2, v0, v1) = v4 & powerset(v0) = v5 & element(v3, v5) = v6 & ( ~ (v4 = 0) | v6 = 0)))
% 23.24/6.20 | (71) ~ (all_0_16_16 = empty_set) | all_0_17_17 = empty_set
% 23.24/6.20 | (72) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v0, v1) = v3) | ~ (powerset(v3) = v4) | ~ (element(v2, v4) = 0) | relation(v2) = 0)
% 23.24/6.20 | (73) relation(all_0_1_1) = 0
% 23.24/6.20 | (74) relation_empty_yielding(empty_set) = 0
% 23.24/6.20 | (75) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (relation_dom(v0) = v2 & empty(v2) = v3 & empty(v0) = v1 & ( ~ (v3 = 0) | v1 = 0)))
% 23.24/6.20 | (76) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3))
% 23.24/6.20 | (77) ~ (all_0_7_7 = 0)
% 23.24/6.20 | (78) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4))
% 23.24/6.20 | (79) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_of2(v2, v0, v1) = 0) | ? [v3] : ? [v4] : (relation_dom_as_subset(v0, v1, v2) = v3 & powerset(v0) = v4 & element(v3, v4) = 0))
% 23.24/6.20 | (80) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom_as_subset(v0, v1, v2) = v3) | ? [v4] : ? [v5] : (relation_of2_as_subset(v2, v0, v1) = v4 & quasi_total(v2, v0, v1) = v5 & ( ~ (v4 = 0) | (( ~ (v1 = empty_set) | v0 = empty_set | (( ~ (v5 = 0) | v2 = empty_set) & ( ~ (v2 = empty_set) | v5 = 0))) & ((v1 = empty_set & ~ (v0 = empty_set)) | (( ~ (v5 = 0) | v3 = v0) & ( ~ (v3 = v0) | v5 = 0)))))))
% 23.24/6.20 | (81) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0))
% 23.24/6.20 | (82) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_of2_as_subset(v2, v0, v1) = v3 & quasi_total(v2, v0, v1) = v4 & relation_dom_as_subset(v0, v1, v2) = v5 & ( ~ (v3 = 0) | (( ~ (v1 = empty_set) | v0 = empty_set | (( ~ (v4 = 0) | v2 = empty_set) & ( ~ (v2 = empty_set) | v4 = 0))) & ((v1 = empty_set & ~ (v0 = empty_set)) | (( ~ (v5 = v0) | v4 = 0) & ( ~ (v4 = 0) | v5 = v0))))))
% 23.24/6.20 | (83) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (powerset(v1) = v2 & element(v0, v2) = 0))
% 23.24/6.21 | (84) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1))
% 23.24/6.21 | (85) relation_of2_as_subset(all_0_14_14, all_0_17_17, all_0_16_16) = 0
% 23.24/6.21 | (86) empty(all_0_6_6) = all_0_5_5
% 23.24/6.21 | (87) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0))
% 23.24/6.21 | (88) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0))
% 23.24/6.21 | (89) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | element(v0, v1) = 0)
% 23.24/6.21 | (90) relation_empty_yielding(all_0_11_11) = 0
% 23.24/6.21 | (91) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 23.24/6.21 | (92) empty(all_0_1_1) = 0
% 23.24/6.21 | (93) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_dom(v2) = v5 & relation_of2(v2, v0, v1) = v3 & relation_dom_as_subset(v0, v1, v2) = v4 & ( ~ (v3 = 0) | v5 = v4))
% 23.24/6.21 | (94) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation(v1) = v4 & empty(v1) = v3 & empty(v0) = v2 & ( ~ (v2 = 0) | (v4 = 0 & v3 = 0))))
% 23.24/6.21 | (95) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (quasi_total(v4, v3, v2) = v1) | ~ (quasi_total(v4, v3, v2) = v0))
% 23.24/6.21 | (96) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_of2_as_subset(v2, v0, v1) = 0) | ? [v3] : ? [v4] : (cartesian_product2(v0, v1) = v3 & powerset(v3) = v4 & element(v2, v4) = 0))
% 23.24/6.21 | (97) function(all_0_14_14) = 0
% 23.24/6.21 | (98) subset(all_0_16_16, all_0_15_15) = 0
% 23.24/6.21 | (99) one_to_one(all_0_9_9) = 0
% 23.24/6.21 | (100) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v1) = v3 & element(v0, v3) = v4))
% 23.24/6.21 | (101) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (quasi_total(v2, v0, v1) = v3) | ? [v4] : ? [v5] : (relation_of2_as_subset(v2, v0, v1) = v4 & relation_dom_as_subset(v0, v1, v2) = v5 & ( ~ (v4 = 0) | (( ~ (v1 = empty_set) | v0 = empty_set | (( ~ (v3 = 0) | v2 = empty_set) & ( ~ (v2 = empty_set) | v3 = 0))) & ((v1 = empty_set & ~ (v0 = empty_set)) | (( ~ (v5 = v0) | v3 = 0) & ( ~ (v3 = 0) | v5 = v0)))))))
% 23.24/6.21 | (102) ? [v0] : ? [v1] : element(v1, v0) = 0
% 23.24/6.21 | (103) ? [v0] : ? [v1] : ? [v2] : relation_of2(v2, v0, v1) = 0
% 23.24/6.21 | (104) relation(all_0_0_0) = 0
% 23.24/6.21 | (105) relation(all_0_11_11) = 0
% 23.24/6.21 | (106) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 23.24/6.21 | (107) ! [v0] : ! [v1] : ( ~ (one_to_one(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation(v0) = v2 & empty(v0) = v3 & function(v0) = v4 & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | v1 = 0)))
% 23.24/6.21 | (108) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 23.24/6.21 | (109) ! [v0] : ! [v1] : (v1 = 0 | ~ (function(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2))
% 23.24/6.21 | (110) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 23.24/6.21 | (111) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_of2(v2, v0, v1) = 0) | ? [v3] : (relation_dom(v2) = v3 & relation_dom_as_subset(v0, v1, v2) = v3))
% 23.24/6.21 | (112) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | subset(v0, v1) = 0)
% 23.24/6.21 | (113) ! [v0] : ( ~ (empty(v0) = 0) | ? [v1] : (relation_dom(v0) = v1 & relation(v1) = 0 & empty(v1) = 0))
% 23.24/6.21 | (114) ! [v0] : ( ~ (empty(v0) = 0) | relation(v0) = 0)
% 23.24/6.21 | (115) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_of2_as_subset(v2, v0, v1) = 0) | ? [v3] : ? [v4] : (quasi_total(v2, v0, v1) = v3 & relation_dom_as_subset(v0, v1, v2) = v4 & ( ~ (v1 = empty_set) | v0 = empty_set | (( ~ (v3 = 0) | v2 = empty_set) & ( ~ (v2 = empty_set) | v3 = 0))) & ((v1 = empty_set & ~ (v0 = empty_set)) | (( ~ (v4 = v0) | v3 = 0) & ( ~ (v3 = 0) | v4 = v0)))))
% 23.24/6.21 | (116) empty(all_0_2_2) = 0
% 23.24/6.21 | (117) ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2))
% 23.24/6.21 | (118) ! [v0] : ! [v1] : (v1 = 0 | ~ (relation(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2))
% 23.24/6.21 |
% 23.24/6.21 | Instantiating formula (13) with all_0_12_12, all_0_14_14, all_0_17_17, all_0_15_15, all_0_16_16 and discharging atoms subset(all_0_16_16, all_0_15_15) = 0, relation_of2_as_subset(all_0_14_14, all_0_17_17, all_0_15_15) = all_0_12_12, yields:
% 23.24/6.21 | (119) all_0_12_12 = 0 | ? [v0] : ( ~ (v0 = 0) & relation_of2_as_subset(all_0_14_14, all_0_17_17, all_0_16_16) = v0)
% 23.24/6.21 |
% 23.24/6.21 | Instantiating formula (31) with all_0_12_12, all_0_14_14, all_0_15_15, all_0_17_17 and discharging atoms relation_of2_as_subset(all_0_14_14, all_0_17_17, all_0_15_15) = all_0_12_12, yields:
% 23.24/6.21 | (120) all_0_12_12 = 0 | ? [v0] : ( ~ (v0 = 0) & relation_of2(all_0_14_14, all_0_17_17, all_0_15_15) = v0)
% 23.24/6.21 |
% 23.24/6.21 | Instantiating formula (23) with all_0_12_12, all_0_14_14, all_0_17_17, all_0_15_15, all_0_16_16 and discharging atoms relation_of2_as_subset(all_0_14_14, all_0_17_17, all_0_15_15) = all_0_12_12, relation_of2_as_subset(all_0_14_14, all_0_17_17, all_0_16_16) = 0, yields:
% 23.24/6.21 | (121) all_0_12_12 = 0 | ? [v0] : ( ~ (v0 = 0) & subset(all_0_16_16, all_0_15_15) = v0)
% 23.24/6.21 |
% 23.24/6.21 | Instantiating formula (24) with all_0_14_14, all_0_17_17, all_0_15_15, all_0_16_16 and discharging atoms subset(all_0_16_16, all_0_15_15) = 0, relation_of2_as_subset(all_0_14_14, all_0_17_17, all_0_16_16) = 0, yields:
% 23.24/6.21 | (122) relation_of2_as_subset(all_0_14_14, all_0_17_17, all_0_15_15) = 0
% 23.24/6.22 |
% 23.24/6.22 | Instantiating formula (55) with all_0_14_14, all_0_16_16, all_0_17_17 and discharging atoms relation_of2_as_subset(all_0_14_14, all_0_17_17, all_0_16_16) = 0, yields:
% 23.24/6.22 | (123) relation_of2(all_0_14_14, all_0_17_17, all_0_16_16) = 0
% 23.24/6.22 |
% 23.24/6.22 | Instantiating formula (115) with all_0_14_14, all_0_16_16, all_0_17_17 and discharging atoms relation_of2_as_subset(all_0_14_14, all_0_17_17, all_0_16_16) = 0, yields:
% 23.24/6.22 | (124) ? [v0] : ? [v1] : (quasi_total(all_0_14_14, all_0_17_17, all_0_16_16) = v0 & relation_dom_as_subset(all_0_17_17, all_0_16_16, all_0_14_14) = v1 & ( ~ (all_0_16_16 = empty_set) | all_0_17_17 = empty_set | (( ~ (v0 = 0) | all_0_14_14 = empty_set) & ( ~ (all_0_14_14 = empty_set) | v0 = 0))) & ((all_0_16_16 = empty_set & ~ (all_0_17_17 = empty_set)) | (( ~ (v1 = all_0_17_17) | v0 = 0) & ( ~ (v0 = 0) | v1 = all_0_17_17))))
% 23.24/6.22 |
% 23.24/6.22 | Instantiating formula (101) with all_0_13_13, all_0_14_14, all_0_15_15, all_0_17_17 and discharging atoms quasi_total(all_0_14_14, all_0_17_17, all_0_15_15) = all_0_13_13, yields:
% 23.24/6.22 | (125) ? [v0] : ? [v1] : (relation_of2_as_subset(all_0_14_14, all_0_17_17, all_0_15_15) = v0 & relation_dom_as_subset(all_0_17_17, all_0_15_15, all_0_14_14) = v1 & ( ~ (v0 = 0) | (( ~ (all_0_15_15 = empty_set) | all_0_17_17 = empty_set | (( ~ (all_0_13_13 = 0) | all_0_14_14 = empty_set) & ( ~ (all_0_14_14 = empty_set) | all_0_13_13 = 0))) & ((all_0_15_15 = empty_set & ~ (all_0_17_17 = empty_set)) | (( ~ (v1 = all_0_17_17) | all_0_13_13 = 0) & ( ~ (all_0_13_13 = 0) | v1 = all_0_17_17))))))
% 23.24/6.22 |
% 23.24/6.22 | Instantiating formula (101) with 0, all_0_14_14, all_0_16_16, all_0_17_17 and discharging atoms quasi_total(all_0_14_14, all_0_17_17, all_0_16_16) = 0, yields:
% 23.24/6.22 | (126) ? [v0] : ? [v1] : (relation_of2_as_subset(all_0_14_14, all_0_17_17, all_0_16_16) = v0 & relation_dom_as_subset(all_0_17_17, all_0_16_16, all_0_14_14) = v1 & ( ~ (v0 = 0) | (( ~ (all_0_16_16 = empty_set) | all_0_14_14 = empty_set | all_0_17_17 = empty_set) & (v1 = all_0_17_17 | (all_0_16_16 = empty_set & ~ (all_0_17_17 = empty_set))))))
% 23.24/6.22 |
% 23.24/6.22 | Instantiating (124) with all_73_0_119, all_73_1_120 yields:
% 23.24/6.22 | (127) quasi_total(all_0_14_14, all_0_17_17, all_0_16_16) = all_73_1_120 & relation_dom_as_subset(all_0_17_17, all_0_16_16, all_0_14_14) = all_73_0_119 & ( ~ (all_0_16_16 = empty_set) | all_0_17_17 = empty_set | (( ~ (all_73_1_120 = 0) | all_0_14_14 = empty_set) & ( ~ (all_0_14_14 = empty_set) | all_73_1_120 = 0))) & ((all_0_16_16 = empty_set & ~ (all_0_17_17 = empty_set)) | (( ~ (all_73_0_119 = all_0_17_17) | all_73_1_120 = 0) & ( ~ (all_73_1_120 = 0) | all_73_0_119 = all_0_17_17)))
% 23.24/6.22 |
% 23.24/6.22 | Applying alpha-rule on (127) yields:
% 23.24/6.22 | (128) quasi_total(all_0_14_14, all_0_17_17, all_0_16_16) = all_73_1_120
% 23.24/6.22 | (129) relation_dom_as_subset(all_0_17_17, all_0_16_16, all_0_14_14) = all_73_0_119
% 23.24/6.22 | (130) ~ (all_0_16_16 = empty_set) | all_0_17_17 = empty_set | (( ~ (all_73_1_120 = 0) | all_0_14_14 = empty_set) & ( ~ (all_0_14_14 = empty_set) | all_73_1_120 = 0))
% 23.24/6.22 | (131) (all_0_16_16 = empty_set & ~ (all_0_17_17 = empty_set)) | (( ~ (all_73_0_119 = all_0_17_17) | all_73_1_120 = 0) & ( ~ (all_73_1_120 = 0) | all_73_0_119 = all_0_17_17))
% 23.24/6.22 |
% 23.24/6.22 | Instantiating (125) with all_129_0_182, all_129_1_183 yields:
% 23.24/6.22 | (132) relation_of2_as_subset(all_0_14_14, all_0_17_17, all_0_15_15) = all_129_1_183 & relation_dom_as_subset(all_0_17_17, all_0_15_15, all_0_14_14) = all_129_0_182 & ( ~ (all_129_1_183 = 0) | (( ~ (all_0_15_15 = empty_set) | all_0_17_17 = empty_set | (( ~ (all_0_13_13 = 0) | all_0_14_14 = empty_set) & ( ~ (all_0_14_14 = empty_set) | all_0_13_13 = 0))) & ((all_0_15_15 = empty_set & ~ (all_0_17_17 = empty_set)) | (( ~ (all_129_0_182 = all_0_17_17) | all_0_13_13 = 0) & ( ~ (all_0_13_13 = 0) | all_129_0_182 = all_0_17_17)))))
% 23.24/6.22 |
% 23.24/6.22 | Applying alpha-rule on (132) yields:
% 23.24/6.22 | (133) relation_of2_as_subset(all_0_14_14, all_0_17_17, all_0_15_15) = all_129_1_183
% 23.24/6.22 | (134) relation_dom_as_subset(all_0_17_17, all_0_15_15, all_0_14_14) = all_129_0_182
% 23.24/6.22 | (135) ~ (all_129_1_183 = 0) | (( ~ (all_0_15_15 = empty_set) | all_0_17_17 = empty_set | (( ~ (all_0_13_13 = 0) | all_0_14_14 = empty_set) & ( ~ (all_0_14_14 = empty_set) | all_0_13_13 = 0))) & ((all_0_15_15 = empty_set & ~ (all_0_17_17 = empty_set)) | (( ~ (all_129_0_182 = all_0_17_17) | all_0_13_13 = 0) & ( ~ (all_0_13_13 = 0) | all_129_0_182 = all_0_17_17))))
% 23.24/6.22 |
% 23.24/6.22 | Instantiating (126) with all_141_0_196, all_141_1_197 yields:
% 23.24/6.22 | (136) relation_of2_as_subset(all_0_14_14, all_0_17_17, all_0_16_16) = all_141_1_197 & relation_dom_as_subset(all_0_17_17, all_0_16_16, all_0_14_14) = all_141_0_196 & ( ~ (all_141_1_197 = 0) | (( ~ (all_0_16_16 = empty_set) | all_0_14_14 = empty_set | all_0_17_17 = empty_set) & (all_141_0_196 = all_0_17_17 | (all_0_16_16 = empty_set & ~ (all_0_17_17 = empty_set)))))
% 23.66/6.22 |
% 23.66/6.22 | Applying alpha-rule on (136) yields:
% 23.66/6.22 | (137) relation_of2_as_subset(all_0_14_14, all_0_17_17, all_0_16_16) = all_141_1_197
% 23.66/6.22 | (138) relation_dom_as_subset(all_0_17_17, all_0_16_16, all_0_14_14) = all_141_0_196
% 23.66/6.22 | (139) ~ (all_141_1_197 = 0) | (( ~ (all_0_16_16 = empty_set) | all_0_14_14 = empty_set | all_0_17_17 = empty_set) & (all_141_0_196 = all_0_17_17 | (all_0_16_16 = empty_set & ~ (all_0_17_17 = empty_set))))
% 23.66/6.22 |
% 23.66/6.22 +-Applying beta-rule and splitting (121), into two cases.
% 23.66/6.22 |-Branch one:
% 23.66/6.22 | (140) all_0_12_12 = 0
% 23.66/6.22 |
% 23.66/6.22 | From (140) and (20) follows:
% 23.66/6.22 | (122) relation_of2_as_subset(all_0_14_14, all_0_17_17, all_0_15_15) = 0
% 23.66/6.22 |
% 23.66/6.22 +-Applying beta-rule and splitting (21), into two cases.
% 23.66/6.22 |-Branch one:
% 23.66/6.22 | (142) ~ (all_0_12_12 = 0)
% 23.66/6.22 |
% 23.66/6.22 | Equations (140) can reduce 142 to:
% 23.66/6.22 | (143) $false
% 23.66/6.22 |
% 23.66/6.22 |-The branch is then unsatisfiable
% 23.66/6.22 |-Branch two:
% 23.66/6.22 | (140) all_0_12_12 = 0
% 23.66/6.22 | (145) ~ (all_0_13_13 = 0)
% 23.66/6.22 |
% 23.66/6.22 | Instantiating formula (66) with all_0_14_14, all_0_17_17, all_0_15_15, 0, all_129_1_183 and discharging atoms relation_of2_as_subset(all_0_14_14, all_0_17_17, all_0_15_15) = all_129_1_183, relation_of2_as_subset(all_0_14_14, all_0_17_17, all_0_15_15) = 0, yields:
% 23.66/6.22 | (146) all_129_1_183 = 0
% 23.66/6.22 |
% 23.66/6.22 | Instantiating formula (66) with all_0_14_14, all_0_17_17, all_0_16_16, all_141_1_197, 0 and discharging atoms relation_of2_as_subset(all_0_14_14, all_0_17_17, all_0_16_16) = all_141_1_197, relation_of2_as_subset(all_0_14_14, all_0_17_17, all_0_16_16) = 0, yields:
% 23.66/6.22 | (147) all_141_1_197 = 0
% 23.66/6.22 |
% 23.66/6.22 | Instantiating formula (95) with all_0_14_14, all_0_17_17, all_0_16_16, all_73_1_120, 0 and discharging atoms quasi_total(all_0_14_14, all_0_17_17, all_0_16_16) = all_73_1_120, quasi_total(all_0_14_14, all_0_17_17, all_0_16_16) = 0, yields:
% 23.66/6.22 | (148) all_73_1_120 = 0
% 23.66/6.22 |
% 23.66/6.22 | Instantiating formula (60) with all_0_17_17, all_0_16_16, all_0_14_14, all_73_0_119, all_141_0_196 and discharging atoms relation_dom_as_subset(all_0_17_17, all_0_16_16, all_0_14_14) = all_141_0_196, relation_dom_as_subset(all_0_17_17, all_0_16_16, all_0_14_14) = all_73_0_119, yields:
% 23.66/6.22 | (149) all_141_0_196 = all_73_0_119
% 23.66/6.22 |
% 23.66/6.22 | From (146) and (133) follows:
% 23.66/6.22 | (122) relation_of2_as_subset(all_0_14_14, all_0_17_17, all_0_15_15) = 0
% 23.66/6.22 |
% 23.66/6.22 | From (147) and (137) follows:
% 23.66/6.22 | (85) relation_of2_as_subset(all_0_14_14, all_0_17_17, all_0_16_16) = 0
% 23.66/6.22 |
% 23.66/6.22 | From (148) and (128) follows:
% 23.66/6.22 | (9) quasi_total(all_0_14_14, all_0_17_17, all_0_16_16) = 0
% 23.66/6.22 |
% 23.66/6.22 | From (149) and (138) follows:
% 23.66/6.22 | (129) relation_dom_as_subset(all_0_17_17, all_0_16_16, all_0_14_14) = all_73_0_119
% 23.66/6.22 |
% 23.66/6.22 | Instantiating formula (79) with all_0_14_14, all_0_16_16, all_0_17_17 and discharging atoms relation_of2(all_0_14_14, all_0_17_17, all_0_16_16) = 0, yields:
% 23.66/6.22 | (154) ? [v0] : ? [v1] : (relation_dom_as_subset(all_0_17_17, all_0_16_16, all_0_14_14) = v0 & powerset(all_0_17_17) = v1 & element(v0, v1) = 0)
% 23.66/6.22 |
% 23.66/6.22 | Instantiating formula (111) with all_0_14_14, all_0_16_16, all_0_17_17 and discharging atoms relation_of2(all_0_14_14, all_0_17_17, all_0_16_16) = 0, yields:
% 23.66/6.22 | (155) ? [v0] : (relation_dom(all_0_14_14) = v0 & relation_dom_as_subset(all_0_17_17, all_0_16_16, all_0_14_14) = v0)
% 23.66/6.22 |
% 23.66/6.22 | Instantiating formula (55) with all_0_14_14, all_0_15_15, all_0_17_17 and discharging atoms relation_of2_as_subset(all_0_14_14, all_0_17_17, all_0_15_15) = 0, yields:
% 23.66/6.22 | (156) relation_of2(all_0_14_14, all_0_17_17, all_0_15_15) = 0
% 23.66/6.22 |
% 23.66/6.22 | Instantiating formula (115) with all_0_14_14, all_0_15_15, all_0_17_17 and discharging atoms relation_of2_as_subset(all_0_14_14, all_0_17_17, all_0_15_15) = 0, yields:
% 23.66/6.22 | (157) ? [v0] : ? [v1] : (quasi_total(all_0_14_14, all_0_17_17, all_0_15_15) = v0 & relation_dom_as_subset(all_0_17_17, all_0_15_15, all_0_14_14) = v1 & ( ~ (all_0_15_15 = empty_set) | all_0_17_17 = empty_set | (( ~ (v0 = 0) | all_0_14_14 = empty_set) & ( ~ (all_0_14_14 = empty_set) | v0 = 0))) & ((all_0_15_15 = empty_set & ~ (all_0_17_17 = empty_set)) | (( ~ (v1 = all_0_17_17) | v0 = 0) & ( ~ (v0 = 0) | v1 = all_0_17_17))))
% 23.66/6.22 |
% 23.66/6.22 | Instantiating formula (70) with all_129_0_182, all_0_14_14, all_0_15_15, all_0_17_17 and discharging atoms relation_dom_as_subset(all_0_17_17, all_0_15_15, all_0_14_14) = all_129_0_182, yields:
% 23.66/6.22 | (158) ? [v0] : ? [v1] : ? [v2] : (relation_of2(all_0_14_14, all_0_17_17, all_0_15_15) = v0 & powerset(all_0_17_17) = v1 & element(all_129_0_182, v1) = v2 & ( ~ (v0 = 0) | v2 = 0))
% 23.66/6.22 |
% 23.66/6.22 | Instantiating formula (45) with all_129_0_182, all_0_14_14, all_0_15_15, all_0_17_17 and discharging atoms relation_dom_as_subset(all_0_17_17, all_0_15_15, all_0_14_14) = all_129_0_182, yields:
% 23.66/6.22 | (159) ? [v0] : ? [v1] : (relation_dom(all_0_14_14) = v1 & relation_of2(all_0_14_14, all_0_17_17, all_0_15_15) = v0 & ( ~ (v0 = 0) | v1 = all_129_0_182))
% 23.66/6.23 |
% 23.66/6.23 | Instantiating formula (45) with all_73_0_119, all_0_14_14, all_0_16_16, all_0_17_17 and discharging atoms relation_dom_as_subset(all_0_17_17, all_0_16_16, all_0_14_14) = all_73_0_119, yields:
% 23.66/6.23 | (160) ? [v0] : ? [v1] : (relation_dom(all_0_14_14) = v1 & relation_of2(all_0_14_14, all_0_17_17, all_0_16_16) = v0 & ( ~ (v0 = 0) | v1 = all_73_0_119))
% 23.66/6.23 |
% 23.66/6.23 | Instantiating formula (80) with all_73_0_119, all_0_14_14, all_0_16_16, all_0_17_17 and discharging atoms relation_dom_as_subset(all_0_17_17, all_0_16_16, all_0_14_14) = all_73_0_119, yields:
% 23.66/6.23 | (161) ? [v0] : ? [v1] : (relation_of2_as_subset(all_0_14_14, all_0_17_17, all_0_16_16) = v0 & quasi_total(all_0_14_14, all_0_17_17, all_0_16_16) = v1 & ( ~ (v0 = 0) | (( ~ (all_0_16_16 = empty_set) | all_0_17_17 = empty_set | (( ~ (v1 = 0) | all_0_14_14 = empty_set) & ( ~ (all_0_14_14 = empty_set) | v1 = 0))) & ((all_0_16_16 = empty_set & ~ (all_0_17_17 = empty_set)) | (( ~ (v1 = 0) | all_73_0_119 = all_0_17_17) & ( ~ (all_73_0_119 = all_0_17_17) | v1 = 0))))))
% 23.66/6.23 |
% 23.66/6.23 | Instantiating (155) with all_295_0_327 yields:
% 23.66/6.23 | (162) relation_dom(all_0_14_14) = all_295_0_327 & relation_dom_as_subset(all_0_17_17, all_0_16_16, all_0_14_14) = all_295_0_327
% 23.66/6.23 |
% 23.66/6.23 | Applying alpha-rule on (162) yields:
% 23.66/6.23 | (163) relation_dom(all_0_14_14) = all_295_0_327
% 23.66/6.23 | (164) relation_dom_as_subset(all_0_17_17, all_0_16_16, all_0_14_14) = all_295_0_327
% 23.66/6.23 |
% 23.66/6.23 | Instantiating (161) with all_302_0_334, all_302_1_335 yields:
% 23.66/6.23 | (165) relation_of2_as_subset(all_0_14_14, all_0_17_17, all_0_16_16) = all_302_1_335 & quasi_total(all_0_14_14, all_0_17_17, all_0_16_16) = all_302_0_334 & ( ~ (all_302_1_335 = 0) | (( ~ (all_0_16_16 = empty_set) | all_0_17_17 = empty_set | (( ~ (all_302_0_334 = 0) | all_0_14_14 = empty_set) & ( ~ (all_0_14_14 = empty_set) | all_302_0_334 = 0))) & ((all_0_16_16 = empty_set & ~ (all_0_17_17 = empty_set)) | (( ~ (all_302_0_334 = 0) | all_73_0_119 = all_0_17_17) & ( ~ (all_73_0_119 = all_0_17_17) | all_302_0_334 = 0)))))
% 23.66/6.23 |
% 23.66/6.23 | Applying alpha-rule on (165) yields:
% 23.66/6.23 | (166) relation_of2_as_subset(all_0_14_14, all_0_17_17, all_0_16_16) = all_302_1_335
% 23.66/6.23 | (167) quasi_total(all_0_14_14, all_0_17_17, all_0_16_16) = all_302_0_334
% 23.66/6.23 | (168) ~ (all_302_1_335 = 0) | (( ~ (all_0_16_16 = empty_set) | all_0_17_17 = empty_set | (( ~ (all_302_0_334 = 0) | all_0_14_14 = empty_set) & ( ~ (all_0_14_14 = empty_set) | all_302_0_334 = 0))) & ((all_0_16_16 = empty_set & ~ (all_0_17_17 = empty_set)) | (( ~ (all_302_0_334 = 0) | all_73_0_119 = all_0_17_17) & ( ~ (all_73_0_119 = all_0_17_17) | all_302_0_334 = 0))))
% 23.66/6.23 |
% 23.66/6.23 | Instantiating (160) with all_324_0_360, all_324_1_361 yields:
% 23.66/6.23 | (169) relation_dom(all_0_14_14) = all_324_0_360 & relation_of2(all_0_14_14, all_0_17_17, all_0_16_16) = all_324_1_361 & ( ~ (all_324_1_361 = 0) | all_324_0_360 = all_73_0_119)
% 23.66/6.23 |
% 23.66/6.23 | Applying alpha-rule on (169) yields:
% 23.66/6.23 | (170) relation_dom(all_0_14_14) = all_324_0_360
% 23.66/6.23 | (171) relation_of2(all_0_14_14, all_0_17_17, all_0_16_16) = all_324_1_361
% 23.66/6.23 | (172) ~ (all_324_1_361 = 0) | all_324_0_360 = all_73_0_119
% 23.66/6.23 |
% 23.66/6.23 | Instantiating (154) with all_336_0_370, all_336_1_371 yields:
% 23.66/6.23 | (173) relation_dom_as_subset(all_0_17_17, all_0_16_16, all_0_14_14) = all_336_1_371 & powerset(all_0_17_17) = all_336_0_370 & element(all_336_1_371, all_336_0_370) = 0
% 23.66/6.23 |
% 23.66/6.23 | Applying alpha-rule on (173) yields:
% 23.66/6.23 | (174) relation_dom_as_subset(all_0_17_17, all_0_16_16, all_0_14_14) = all_336_1_371
% 23.66/6.23 | (175) powerset(all_0_17_17) = all_336_0_370
% 23.66/6.23 | (176) element(all_336_1_371, all_336_0_370) = 0
% 23.66/6.23 |
% 23.66/6.23 | Instantiating (159) with all_340_0_375, all_340_1_376 yields:
% 23.66/6.23 | (177) relation_dom(all_0_14_14) = all_340_0_375 & relation_of2(all_0_14_14, all_0_17_17, all_0_15_15) = all_340_1_376 & ( ~ (all_340_1_376 = 0) | all_340_0_375 = all_129_0_182)
% 23.66/6.23 |
% 23.66/6.23 | Applying alpha-rule on (177) yields:
% 23.66/6.23 | (178) relation_dom(all_0_14_14) = all_340_0_375
% 23.66/6.23 | (179) relation_of2(all_0_14_14, all_0_17_17, all_0_15_15) = all_340_1_376
% 23.66/6.23 | (180) ~ (all_340_1_376 = 0) | all_340_0_375 = all_129_0_182
% 23.66/6.23 |
% 23.66/6.23 | Instantiating (158) with all_342_0_377, all_342_1_378, all_342_2_379 yields:
% 23.66/6.23 | (181) relation_of2(all_0_14_14, all_0_17_17, all_0_15_15) = all_342_2_379 & powerset(all_0_17_17) = all_342_1_378 & element(all_129_0_182, all_342_1_378) = all_342_0_377 & ( ~ (all_342_2_379 = 0) | all_342_0_377 = 0)
% 23.66/6.23 |
% 23.66/6.23 | Applying alpha-rule on (181) yields:
% 23.66/6.23 | (182) relation_of2(all_0_14_14, all_0_17_17, all_0_15_15) = all_342_2_379
% 23.66/6.23 | (183) powerset(all_0_17_17) = all_342_1_378
% 23.66/6.23 | (184) element(all_129_0_182, all_342_1_378) = all_342_0_377
% 23.66/6.23 | (185) ~ (all_342_2_379 = 0) | all_342_0_377 = 0
% 23.66/6.23 |
% 23.66/6.23 | Instantiating (157) with all_359_0_402, all_359_1_403 yields:
% 23.66/6.23 | (186) quasi_total(all_0_14_14, all_0_17_17, all_0_15_15) = all_359_1_403 & relation_dom_as_subset(all_0_17_17, all_0_15_15, all_0_14_14) = all_359_0_402 & ( ~ (all_0_15_15 = empty_set) | all_0_17_17 = empty_set | (( ~ (all_359_1_403 = 0) | all_0_14_14 = empty_set) & ( ~ (all_0_14_14 = empty_set) | all_359_1_403 = 0))) & ((all_0_15_15 = empty_set & ~ (all_0_17_17 = empty_set)) | (( ~ (all_359_0_402 = all_0_17_17) | all_359_1_403 = 0) & ( ~ (all_359_1_403 = 0) | all_359_0_402 = all_0_17_17)))
% 23.66/6.23 |
% 23.66/6.23 | Applying alpha-rule on (186) yields:
% 23.66/6.23 | (187) quasi_total(all_0_14_14, all_0_17_17, all_0_15_15) = all_359_1_403
% 23.66/6.23 | (188) relation_dom_as_subset(all_0_17_17, all_0_15_15, all_0_14_14) = all_359_0_402
% 23.66/6.23 | (189) ~ (all_0_15_15 = empty_set) | all_0_17_17 = empty_set | (( ~ (all_359_1_403 = 0) | all_0_14_14 = empty_set) & ( ~ (all_0_14_14 = empty_set) | all_359_1_403 = 0))
% 23.66/6.23 | (190) (all_0_15_15 = empty_set & ~ (all_0_17_17 = empty_set)) | (( ~ (all_359_0_402 = all_0_17_17) | all_359_1_403 = 0) & ( ~ (all_359_1_403 = 0) | all_359_0_402 = all_0_17_17))
% 23.66/6.23 |
% 23.66/6.23 | Instantiating formula (87) with all_0_14_14, all_324_0_360, all_340_0_375 and discharging atoms relation_dom(all_0_14_14) = all_340_0_375, relation_dom(all_0_14_14) = all_324_0_360, yields:
% 23.66/6.23 | (191) all_340_0_375 = all_324_0_360
% 23.66/6.23 |
% 23.66/6.23 | Instantiating formula (87) with all_0_14_14, all_295_0_327, all_340_0_375 and discharging atoms relation_dom(all_0_14_14) = all_340_0_375, relation_dom(all_0_14_14) = all_295_0_327, yields:
% 23.66/6.23 | (192) all_340_0_375 = all_295_0_327
% 23.66/6.23 |
% 23.66/6.23 | Instantiating formula (3) with all_0_14_14, all_0_17_17, all_0_15_15, all_340_1_376, all_342_2_379 and discharging atoms relation_of2(all_0_14_14, all_0_17_17, all_0_15_15) = all_342_2_379, relation_of2(all_0_14_14, all_0_17_17, all_0_15_15) = all_340_1_376, yields:
% 23.66/6.23 | (193) all_342_2_379 = all_340_1_376
% 23.66/6.23 |
% 23.66/6.23 | Instantiating formula (3) with all_0_14_14, all_0_17_17, all_0_15_15, 0, all_342_2_379 and discharging atoms relation_of2(all_0_14_14, all_0_17_17, all_0_15_15) = all_342_2_379, relation_of2(all_0_14_14, all_0_17_17, all_0_15_15) = 0, yields:
% 23.66/6.23 | (194) all_342_2_379 = 0
% 23.66/6.23 |
% 23.66/6.23 | Instantiating formula (66) with all_0_14_14, all_0_17_17, all_0_16_16, all_302_1_335, 0 and discharging atoms relation_of2_as_subset(all_0_14_14, all_0_17_17, all_0_16_16) = all_302_1_335, relation_of2_as_subset(all_0_14_14, all_0_17_17, all_0_16_16) = 0, yields:
% 23.66/6.23 | (195) all_302_1_335 = 0
% 23.66/6.23 |
% 23.66/6.23 | Instantiating formula (95) with all_0_14_14, all_0_17_17, all_0_15_15, all_359_1_403, all_0_13_13 and discharging atoms quasi_total(all_0_14_14, all_0_17_17, all_0_15_15) = all_359_1_403, quasi_total(all_0_14_14, all_0_17_17, all_0_15_15) = all_0_13_13, yields:
% 23.66/6.23 | (196) all_359_1_403 = all_0_13_13
% 23.66/6.23 |
% 23.66/6.23 | Instantiating formula (95) with all_0_14_14, all_0_17_17, all_0_16_16, all_302_0_334, 0 and discharging atoms quasi_total(all_0_14_14, all_0_17_17, all_0_16_16) = all_302_0_334, quasi_total(all_0_14_14, all_0_17_17, all_0_16_16) = 0, yields:
% 23.66/6.23 | (197) all_302_0_334 = 0
% 23.66/6.23 |
% 23.66/6.23 | Instantiating formula (60) with all_0_17_17, all_0_15_15, all_0_14_14, all_359_0_402, all_129_0_182 and discharging atoms relation_dom_as_subset(all_0_17_17, all_0_15_15, all_0_14_14) = all_359_0_402, relation_dom_as_subset(all_0_17_17, all_0_15_15, all_0_14_14) = all_129_0_182, yields:
% 23.66/6.23 | (198) all_359_0_402 = all_129_0_182
% 23.66/6.23 |
% 23.66/6.23 | Instantiating formula (60) with all_0_17_17, all_0_16_16, all_0_14_14, all_336_1_371, all_73_0_119 and discharging atoms relation_dom_as_subset(all_0_17_17, all_0_16_16, all_0_14_14) = all_336_1_371, relation_dom_as_subset(all_0_17_17, all_0_16_16, all_0_14_14) = all_73_0_119, yields:
% 23.66/6.23 | (199) all_336_1_371 = all_73_0_119
% 23.66/6.23 |
% 23.66/6.23 | Instantiating formula (60) with all_0_17_17, all_0_16_16, all_0_14_14, all_295_0_327, all_336_1_371 and discharging atoms relation_dom_as_subset(all_0_17_17, all_0_16_16, all_0_14_14) = all_336_1_371, relation_dom_as_subset(all_0_17_17, all_0_16_16, all_0_14_14) = all_295_0_327, yields:
% 23.66/6.23 | (200) all_336_1_371 = all_295_0_327
% 23.66/6.23 |
% 23.66/6.23 | Combining equations (193,194) yields a new equation:
% 23.66/6.23 | (201) all_340_1_376 = 0
% 23.66/6.23 |
% 23.66/6.23 | Simplifying 201 yields:
% 23.66/6.23 | (202) all_340_1_376 = 0
% 23.66/6.23 |
% 23.66/6.23 | Combining equations (192,191) yields a new equation:
% 23.66/6.23 | (203) all_324_0_360 = all_295_0_327
% 23.66/6.23 |
% 23.66/6.23 | Combining equations (200,199) yields a new equation:
% 23.66/6.23 | (204) all_295_0_327 = all_73_0_119
% 23.66/6.23 |
% 23.66/6.23 | Simplifying 204 yields:
% 23.66/6.23 | (205) all_295_0_327 = all_73_0_119
% 23.66/6.23 |
% 23.66/6.23 | Combining equations (205,203) yields a new equation:
% 23.66/6.23 | (206) all_324_0_360 = all_73_0_119
% 23.66/6.23 |
% 23.66/6.23 | Combining equations (206,191) yields a new equation:
% 23.66/6.23 | (207) all_340_0_375 = all_73_0_119
% 23.66/6.23 |
% 23.66/6.23 +-Applying beta-rule and splitting (180), into two cases.
% 23.66/6.23 |-Branch one:
% 23.66/6.23 | (208) ~ (all_340_1_376 = 0)
% 23.66/6.23 |
% 23.66/6.23 | Equations (202) can reduce 208 to:
% 23.66/6.23 | (143) $false
% 23.66/6.23 |
% 23.66/6.23 |-The branch is then unsatisfiable
% 23.66/6.23 |-Branch two:
% 23.66/6.23 | (202) all_340_1_376 = 0
% 23.66/6.23 | (211) all_340_0_375 = all_129_0_182
% 23.66/6.23 |
% 23.66/6.23 | Combining equations (211,207) yields a new equation:
% 23.66/6.23 | (212) all_129_0_182 = all_73_0_119
% 23.66/6.23 |
% 23.66/6.23 | Simplifying 212 yields:
% 23.66/6.23 | (213) all_129_0_182 = all_73_0_119
% 23.66/6.23 |
% 23.66/6.23 | Combining equations (213,198) yields a new equation:
% 23.66/6.23 | (214) all_359_0_402 = all_73_0_119
% 23.66/6.23 |
% 23.66/6.23 +-Applying beta-rule and splitting (71), into two cases.
% 23.66/6.23 |-Branch one:
% 23.66/6.23 | (215) ~ (all_0_16_16 = empty_set)
% 23.66/6.23 |
% 23.66/6.23 +-Applying beta-rule and splitting (168), into two cases.
% 23.66/6.23 |-Branch one:
% 23.66/6.23 | (216) ~ (all_302_1_335 = 0)
% 23.66/6.23 |
% 23.66/6.23 | Equations (195) can reduce 216 to:
% 23.66/6.23 | (143) $false
% 23.66/6.23 |
% 23.66/6.23 |-The branch is then unsatisfiable
% 23.66/6.23 |-Branch two:
% 23.66/6.23 | (195) all_302_1_335 = 0
% 23.66/6.23 | (219) ( ~ (all_0_16_16 = empty_set) | all_0_17_17 = empty_set | (( ~ (all_302_0_334 = 0) | all_0_14_14 = empty_set) & ( ~ (all_0_14_14 = empty_set) | all_302_0_334 = 0))) & ((all_0_16_16 = empty_set & ~ (all_0_17_17 = empty_set)) | (( ~ (all_302_0_334 = 0) | all_73_0_119 = all_0_17_17) & ( ~ (all_73_0_119 = all_0_17_17) | all_302_0_334 = 0)))
% 23.66/6.23 |
% 23.66/6.23 | Applying alpha-rule on (219) yields:
% 23.66/6.23 | (220) ~ (all_0_16_16 = empty_set) | all_0_17_17 = empty_set | (( ~ (all_302_0_334 = 0) | all_0_14_14 = empty_set) & ( ~ (all_0_14_14 = empty_set) | all_302_0_334 = 0))
% 23.66/6.24 | (221) (all_0_16_16 = empty_set & ~ (all_0_17_17 = empty_set)) | (( ~ (all_302_0_334 = 0) | all_73_0_119 = all_0_17_17) & ( ~ (all_73_0_119 = all_0_17_17) | all_302_0_334 = 0))
% 23.66/6.24 |
% 23.66/6.24 +-Applying beta-rule and splitting (221), into two cases.
% 23.66/6.24 |-Branch one:
% 23.66/6.24 | (222) all_0_16_16 = empty_set & ~ (all_0_17_17 = empty_set)
% 23.66/6.24 |
% 23.66/6.24 | Applying alpha-rule on (222) yields:
% 23.66/6.24 | (223) all_0_16_16 = empty_set
% 23.66/6.24 | (224) ~ (all_0_17_17 = empty_set)
% 23.66/6.24 |
% 23.66/6.24 | Equations (223) can reduce 215 to:
% 23.66/6.24 | (143) $false
% 23.66/6.24 |
% 23.66/6.24 |-The branch is then unsatisfiable
% 23.66/6.24 |-Branch two:
% 23.66/6.24 | (226) ( ~ (all_302_0_334 = 0) | all_73_0_119 = all_0_17_17) & ( ~ (all_73_0_119 = all_0_17_17) | all_302_0_334 = 0)
% 23.66/6.24 |
% 23.66/6.24 | Applying alpha-rule on (226) yields:
% 23.66/6.24 | (227) ~ (all_302_0_334 = 0) | all_73_0_119 = all_0_17_17
% 23.66/6.24 | (228) ~ (all_73_0_119 = all_0_17_17) | all_302_0_334 = 0
% 23.66/6.24 |
% 23.66/6.24 +-Applying beta-rule and splitting (227), into two cases.
% 23.66/6.24 |-Branch one:
% 23.66/6.24 | (229) ~ (all_302_0_334 = 0)
% 23.66/6.24 |
% 23.66/6.24 | Equations (197) can reduce 229 to:
% 23.66/6.24 | (143) $false
% 23.66/6.24 |
% 23.66/6.24 |-The branch is then unsatisfiable
% 23.66/6.24 |-Branch two:
% 23.66/6.24 | (197) all_302_0_334 = 0
% 23.66/6.24 | (232) all_73_0_119 = all_0_17_17
% 23.66/6.24 |
% 23.66/6.24 | Combining equations (232,214) yields a new equation:
% 23.66/6.24 | (233) all_359_0_402 = all_0_17_17
% 23.66/6.24 |
% 23.66/6.24 +-Applying beta-rule and splitting (190), into two cases.
% 23.66/6.24 |-Branch one:
% 23.66/6.24 | (234) all_0_15_15 = empty_set & ~ (all_0_17_17 = empty_set)
% 23.66/6.24 |
% 23.66/6.24 | Applying alpha-rule on (234) yields:
% 23.66/6.24 | (235) all_0_15_15 = empty_set
% 23.66/6.24 | (224) ~ (all_0_17_17 = empty_set)
% 23.66/6.24 |
% 23.66/6.24 | From (235) and (98) follows:
% 23.66/6.24 | (237) subset(all_0_16_16, empty_set) = 0
% 23.66/6.24 |
% 23.66/6.24 | Instantiating formula (67) with all_0_16_16 and discharging atoms subset(all_0_16_16, empty_set) = 0, yields:
% 23.66/6.24 | (223) all_0_16_16 = empty_set
% 23.66/6.24 |
% 23.66/6.24 | Equations (223) can reduce 215 to:
% 23.66/6.24 | (143) $false
% 23.66/6.24 |
% 23.66/6.24 |-The branch is then unsatisfiable
% 23.66/6.24 |-Branch two:
% 23.66/6.24 | (240) ( ~ (all_359_0_402 = all_0_17_17) | all_359_1_403 = 0) & ( ~ (all_359_1_403 = 0) | all_359_0_402 = all_0_17_17)
% 23.66/6.24 |
% 23.66/6.24 | Applying alpha-rule on (240) yields:
% 23.66/6.24 | (241) ~ (all_359_0_402 = all_0_17_17) | all_359_1_403 = 0
% 23.66/6.24 | (242) ~ (all_359_1_403 = 0) | all_359_0_402 = all_0_17_17
% 23.66/6.24 |
% 23.66/6.24 +-Applying beta-rule and splitting (241), into two cases.
% 23.66/6.24 |-Branch one:
% 23.66/6.24 | (243) ~ (all_359_0_402 = all_0_17_17)
% 23.66/6.24 |
% 23.66/6.24 | Equations (233) can reduce 243 to:
% 23.66/6.24 | (143) $false
% 23.66/6.24 |
% 23.66/6.24 |-The branch is then unsatisfiable
% 23.66/6.24 |-Branch two:
% 23.66/6.24 | (233) all_359_0_402 = all_0_17_17
% 23.66/6.24 | (246) all_359_1_403 = 0
% 23.66/6.24 |
% 23.66/6.24 | Combining equations (246,196) yields a new equation:
% 23.66/6.24 | (247) all_0_13_13 = 0
% 23.66/6.24 |
% 23.66/6.24 | Equations (247) can reduce 145 to:
% 23.66/6.24 | (143) $false
% 23.66/6.24 |
% 23.66/6.24 |-The branch is then unsatisfiable
% 23.66/6.24 |-Branch two:
% 23.66/6.24 | (223) all_0_16_16 = empty_set
% 23.66/6.24 | (250) all_0_17_17 = empty_set
% 23.66/6.24 |
% 23.66/6.24 +-Applying beta-rule and splitting (168), into two cases.
% 23.66/6.24 |-Branch one:
% 23.66/6.24 | (216) ~ (all_302_1_335 = 0)
% 23.66/6.24 |
% 23.66/6.24 | Equations (195) can reduce 216 to:
% 23.66/6.24 | (143) $false
% 23.66/6.24 |
% 23.66/6.24 |-The branch is then unsatisfiable
% 23.66/6.24 |-Branch two:
% 23.66/6.24 | (195) all_302_1_335 = 0
% 23.66/6.24 | (219) ( ~ (all_0_16_16 = empty_set) | all_0_17_17 = empty_set | (( ~ (all_302_0_334 = 0) | all_0_14_14 = empty_set) & ( ~ (all_0_14_14 = empty_set) | all_302_0_334 = 0))) & ((all_0_16_16 = empty_set & ~ (all_0_17_17 = empty_set)) | (( ~ (all_302_0_334 = 0) | all_73_0_119 = all_0_17_17) & ( ~ (all_73_0_119 = all_0_17_17) | all_302_0_334 = 0)))
% 23.66/6.24 |
% 23.66/6.24 | Applying alpha-rule on (219) yields:
% 23.66/6.24 | (220) ~ (all_0_16_16 = empty_set) | all_0_17_17 = empty_set | (( ~ (all_302_0_334 = 0) | all_0_14_14 = empty_set) & ( ~ (all_0_14_14 = empty_set) | all_302_0_334 = 0))
% 23.66/6.24 | (221) (all_0_16_16 = empty_set & ~ (all_0_17_17 = empty_set)) | (( ~ (all_302_0_334 = 0) | all_73_0_119 = all_0_17_17) & ( ~ (all_73_0_119 = all_0_17_17) | all_302_0_334 = 0))
% 23.66/6.24 |
% 23.66/6.24 +-Applying beta-rule and splitting (221), into two cases.
% 23.66/6.24 |-Branch one:
% 23.66/6.24 | (222) all_0_16_16 = empty_set & ~ (all_0_17_17 = empty_set)
% 23.66/6.24 |
% 23.66/6.24 | Applying alpha-rule on (222) yields:
% 23.66/6.24 | (223) all_0_16_16 = empty_set
% 23.66/6.24 | (224) ~ (all_0_17_17 = empty_set)
% 23.66/6.24 |
% 23.66/6.24 | Equations (250) can reduce 224 to:
% 23.66/6.24 | (143) $false
% 23.66/6.24 |
% 23.66/6.24 |-The branch is then unsatisfiable
% 23.66/6.24 |-Branch two:
% 23.66/6.24 | (226) ( ~ (all_302_0_334 = 0) | all_73_0_119 = all_0_17_17) & ( ~ (all_73_0_119 = all_0_17_17) | all_302_0_334 = 0)
% 23.66/6.24 |
% 23.66/6.24 | Applying alpha-rule on (226) yields:
% 23.66/6.24 | (227) ~ (all_302_0_334 = 0) | all_73_0_119 = all_0_17_17
% 23.66/6.24 | (228) ~ (all_73_0_119 = all_0_17_17) | all_302_0_334 = 0
% 23.66/6.24 |
% 23.66/6.24 +-Applying beta-rule and splitting (227), into two cases.
% 23.66/6.24 |-Branch one:
% 23.66/6.24 | (229) ~ (all_302_0_334 = 0)
% 23.66/6.24 |
% 23.66/6.24 | Equations (197) can reduce 229 to:
% 23.66/6.24 | (143) $false
% 23.66/6.24 |
% 23.66/6.24 |-The branch is then unsatisfiable
% 23.66/6.24 |-Branch two:
% 23.66/6.24 | (197) all_302_0_334 = 0
% 23.66/6.24 | (232) all_73_0_119 = all_0_17_17
% 23.66/6.24 |
% 23.66/6.24 | Combining equations (250,232) yields a new equation:
% 23.66/6.24 | (268) all_73_0_119 = empty_set
% 23.66/6.24 |
% 23.66/6.24 | Combining equations (268,214) yields a new equation:
% 23.66/6.24 | (269) all_359_0_402 = empty_set
% 23.66/6.24 |
% 23.66/6.24 +-Applying beta-rule and splitting (190), into two cases.
% 23.66/6.24 |-Branch one:
% 23.66/6.24 | (234) all_0_15_15 = empty_set & ~ (all_0_17_17 = empty_set)
% 23.66/6.24 |
% 23.66/6.24 | Applying alpha-rule on (234) yields:
% 23.66/6.24 | (235) all_0_15_15 = empty_set
% 23.66/6.24 | (224) ~ (all_0_17_17 = empty_set)
% 23.66/6.24 |
% 23.66/6.24 | Equations (250) can reduce 224 to:
% 23.66/6.24 | (143) $false
% 23.66/6.24 |
% 23.66/6.24 |-The branch is then unsatisfiable
% 23.66/6.24 |-Branch two:
% 23.66/6.24 | (240) ( ~ (all_359_0_402 = all_0_17_17) | all_359_1_403 = 0) & ( ~ (all_359_1_403 = 0) | all_359_0_402 = all_0_17_17)
% 23.66/6.24 |
% 23.66/6.24 | Applying alpha-rule on (240) yields:
% 23.66/6.24 | (241) ~ (all_359_0_402 = all_0_17_17) | all_359_1_403 = 0
% 23.66/6.24 | (242) ~ (all_359_1_403 = 0) | all_359_0_402 = all_0_17_17
% 23.66/6.24 |
% 23.66/6.24 +-Applying beta-rule and splitting (241), into two cases.
% 23.66/6.24 |-Branch one:
% 23.66/6.24 | (243) ~ (all_359_0_402 = all_0_17_17)
% 23.66/6.24 |
% 23.66/6.24 | Equations (269,250) can reduce 243 to:
% 23.66/6.24 | (143) $false
% 23.66/6.24 |
% 23.66/6.24 |-The branch is then unsatisfiable
% 23.66/6.24 |-Branch two:
% 23.66/6.24 | (233) all_359_0_402 = all_0_17_17
% 23.66/6.24 | (246) all_359_1_403 = 0
% 23.66/6.24 |
% 23.66/6.24 | Combining equations (196,246) yields a new equation:
% 23.66/6.24 | (281) all_0_13_13 = 0
% 23.66/6.24 |
% 23.66/6.24 | Simplifying 281 yields:
% 23.66/6.24 | (247) all_0_13_13 = 0
% 23.66/6.24 |
% 23.66/6.24 | Equations (247) can reduce 145 to:
% 23.66/6.24 | (143) $false
% 23.66/6.24 |
% 23.66/6.24 |-The branch is then unsatisfiable
% 23.66/6.24 |-Branch two:
% 23.66/6.24 | (142) ~ (all_0_12_12 = 0)
% 23.66/6.24 | (285) ? [v0] : ( ~ (v0 = 0) & subset(all_0_16_16, all_0_15_15) = v0)
% 23.66/6.24 |
% 23.66/6.24 +-Applying beta-rule and splitting (119), into two cases.
% 23.66/6.24 |-Branch one:
% 23.66/6.24 | (140) all_0_12_12 = 0
% 23.66/6.24 |
% 23.66/6.24 | Equations (140) can reduce 142 to:
% 23.66/6.24 | (143) $false
% 23.66/6.24 |
% 23.66/6.24 |-The branch is then unsatisfiable
% 23.66/6.24 |-Branch two:
% 23.66/6.24 | (142) ~ (all_0_12_12 = 0)
% 23.66/6.24 | (289) ? [v0] : ( ~ (v0 = 0) & relation_of2_as_subset(all_0_14_14, all_0_17_17, all_0_16_16) = v0)
% 23.66/6.24 |
% 23.66/6.24 +-Applying beta-rule and splitting (120), into two cases.
% 23.66/6.24 |-Branch one:
% 23.66/6.24 | (140) all_0_12_12 = 0
% 23.66/6.24 |
% 23.66/6.24 | Equations (140) can reduce 142 to:
% 23.66/6.24 | (143) $false
% 23.66/6.24 |
% 23.66/6.24 |-The branch is then unsatisfiable
% 23.66/6.24 |-Branch two:
% 23.66/6.24 | (142) ~ (all_0_12_12 = 0)
% 23.66/6.24 | (293) ? [v0] : ( ~ (v0 = 0) & relation_of2(all_0_14_14, all_0_17_17, all_0_15_15) = v0)
% 23.66/6.24 |
% 23.66/6.24 | Instantiating formula (66) with all_0_14_14, all_0_17_17, all_0_15_15, all_129_1_183, all_0_12_12 and discharging atoms relation_of2_as_subset(all_0_14_14, all_0_17_17, all_0_15_15) = all_129_1_183, relation_of2_as_subset(all_0_14_14, all_0_17_17, all_0_15_15) = all_0_12_12, yields:
% 23.66/6.24 | (294) all_129_1_183 = all_0_12_12
% 23.66/6.24 |
% 23.66/6.24 | Instantiating formula (66) with all_0_14_14, all_0_17_17, all_0_15_15, 0, all_129_1_183 and discharging atoms relation_of2_as_subset(all_0_14_14, all_0_17_17, all_0_15_15) = all_129_1_183, relation_of2_as_subset(all_0_14_14, all_0_17_17, all_0_15_15) = 0, yields:
% 23.66/6.24 | (146) all_129_1_183 = 0
% 23.66/6.24 |
% 23.66/6.24 | Combining equations (294,146) yields a new equation:
% 23.66/6.24 | (296) all_0_12_12 = 0
% 23.66/6.24 |
% 23.66/6.24 | Simplifying 296 yields:
% 23.66/6.24 | (140) all_0_12_12 = 0
% 23.66/6.24 |
% 23.66/6.24 | Equations (140) can reduce 142 to:
% 23.66/6.24 | (143) $false
% 23.66/6.24 |
% 23.66/6.24 |-The branch is then unsatisfiable
% 23.66/6.24 % SZS output end Proof for theBenchmark
% 23.66/6.24
% 23.66/6.24 5639ms
%------------------------------------------------------------------------------