TSTP Solution File: SEU104+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU104+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n014.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 08:46:37 EDT 2022
% Result : Theorem 67.27s 40.36s
% Output : Proof 117.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU104+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.14/0.33 % Computer : n014.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 600
% 0.14/0.33 % DateTime : Sun Jun 19 08:39:18 EDT 2022
% 0.14/0.33 % CPUTime :
% 0.51/0.58 ____ _
% 0.51/0.58 ___ / __ \_____(_)___ ________ __________
% 0.51/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.51/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.51/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.51/0.58
% 0.51/0.58 A Theorem Prover for First-Order Logic
% 0.51/0.58 (ePrincess v.1.0)
% 0.51/0.58
% 0.51/0.58 (c) Philipp Rümmer, 2009-2015
% 0.51/0.58 (c) Peter Backeman, 2014-2015
% 0.51/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.51/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.51/0.58 Bug reports to peter@backeman.se
% 0.51/0.58
% 0.51/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.51/0.58
% 0.51/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.51/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.60/0.97 Prover 0: Preprocessing ...
% 2.27/1.23 Prover 0: Warning: ignoring some quantifiers
% 2.57/1.25 Prover 0: Constructing countermodel ...
% 3.36/1.45 Prover 0: gave up
% 3.36/1.45 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 3.49/1.49 Prover 1: Preprocessing ...
% 4.07/1.63 Prover 1: Warning: ignoring some quantifiers
% 4.07/1.64 Prover 1: Constructing countermodel ...
% 5.81/2.01 Prover 1: gave up
% 5.81/2.01 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 6.08/2.04 Prover 2: Preprocessing ...
% 6.46/2.14 Prover 2: Warning: ignoring some quantifiers
% 6.46/2.15 Prover 2: Constructing countermodel ...
% 15.09/4.20 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 15.09/4.24 Prover 3: Preprocessing ...
% 15.36/4.28 Prover 3: Warning: ignoring some quantifiers
% 15.36/4.29 Prover 3: Constructing countermodel ...
% 15.36/4.35 Prover 3: gave up
% 15.36/4.35 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 15.79/4.38 Prover 4: Preprocessing ...
% 16.15/4.47 Prover 4: Warning: ignoring some quantifiers
% 16.15/4.47 Prover 4: Constructing countermodel ...
% 19.98/5.37 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 19.98/5.39 Prover 5: Preprocessing ...
% 20.22/5.44 Prover 5: Warning: ignoring some quantifiers
% 20.22/5.44 Prover 5: Constructing countermodel ...
% 44.07/20.82 Prover 5: stopped
% 44.46/21.02 Prover 6: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 44.46/21.04 Prover 6: Preprocessing ...
% 44.65/21.08 Prover 6: Warning: ignoring some quantifiers
% 44.65/21.08 Prover 6: Constructing countermodel ...
% 67.27/40.36 Prover 4: proved (1748ms)
% 67.27/40.36 Prover 2: stopped
% 67.27/40.36 Prover 6: stopped
% 67.27/40.36
% 67.27/40.36 No countermodel exists, formula is valid
% 67.27/40.36 % SZS status Theorem for theBenchmark
% 67.27/40.36
% 67.27/40.36 Generating proof ... Warning: ignoring some quantifiers
% 116.71/72.90 found it (size 102)
% 116.71/72.90
% 116.71/72.90 % SZS output start Proof for theBenchmark
% 116.71/72.90 Assumed formulas after preprocessing and simplification:
% 116.71/72.90 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ( ~ (v9 = 0) & ~ (v7 = 0) & ~ (v4 = 0) & ~ (v2 = 0) & ~ (v1 = 0) & cap_closed(v6) = 0 & preboolean(v6) = 0 & preboolean(v0) = v2 & cup_closed(v6) = 0 & diff_closed(v6) = 0 & empty(v8) = v9 & empty(v6) = v7 & empty(v5) = 0 & empty(v3) = v4 & empty(v0) = v1 & empty(empty_set) = 0 & finite(v8) = 0 & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (powerset(v12) = v13) | ~ (element(v11, v13) = 0) | ~ (element(v10, v12) = v14) | ? [v15] : ( ~ (v15 = 0) & in(v10, v11) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (powerset(v11) = v12) | ~ (element(v10, v12) = v13) | ? [v14] : ( ~ (v14 = 0) & subset(v10, v11) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (powerset(v10) = v11) | ~ (finite(v12) = v13) | ? [v14] : (( ~ (v14 = 0) & element(v12, v11) = v14) | ( ~ (v14 = 0) & finite(v10) = v14))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (element(v10, v12) = v13) | ~ (in(v10, v11) = 0) | ? [v14] : ? [v15] : ( ~ (v15 = 0) & powerset(v12) = v14 & element(v11, v14) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (subset(v13, v12) = v11) | ~ (subset(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (set_difference(v13, v12) = v11) | ~ (set_difference(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (symmetric_difference(v13, v12) = v11) | ~ (symmetric_difference(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (set_union2(v13, v12) = v11) | ~ (set_union2(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (element(v13, v12) = v11) | ~ (element(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (in(v13, v12) = v11) | ~ (in(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (set_difference(v11, v12) = v13) | ~ (preboolean(v10) = 0) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : (set_union2(v11, v12) = v16 & in(v16, v10) = v17 & in(v13, v10) = v18 & in(v12, v10) = v15 & in(v11, v10) = v14 & ( ~ (v15 = 0) | ~ (v14 = 0) | (v18 = 0 & v17 = 0)))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (set_union2(v11, v12) = v13) | ~ (preboolean(v10) = 0) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : (set_difference(v11, v12) = v17 & in(v17, v10) = v18 & in(v13, v10) = v16 & in(v12, v10) = v15 & in(v11, v10) = v14 & ( ~ (v15 = 0) | ~ (v14 = 0) | (v18 = 0 & v16 = 0)))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (powerset(v12) = v13) | ~ (element(v11, v13) = 0) | ~ (in(v10, v11) = 0) | element(v10, v12) = 0) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (powerset(v12) = v13) | ~ (element(v11, v13) = 0) | ~ (in(v10, v11) = 0) | ? [v14] : ( ~ (v14 = 0) & empty(v12) = v14)) & ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (subset(v10, v11) = v12) | ? [v13] : ? [v14] : ( ~ (v14 = 0) & powerset(v11) = v13 & element(v10, v13) = v14)) & ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (element(v10, v11) = v12) | ? [v13] : ( ~ (v13 = 0) & in(v10, v11) = v13)) & ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (in(v10, v11) = v12) | ? [v13] : ? [v14] : (element(v10, v11) = v13 & empty(v11) = v14 & ( ~ (v13 = 0) | v14 = 0))) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (relation(v12) = v11) | ~ (relation(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (function(v12) = v11) | ~ (function(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (one_to_one(v12) = v11) | ~ (one_to_one(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (epsilon_transitive(v12) = v11) | ~ (epsilon_transitive(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (epsilon_connected(v12) = v11) | ~ (epsilon_connected(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (ordinal(v12) = v11) | ~ (ordinal(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (natural(v12) = v11) | ~ (natural(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (cap_closed(v12) = v11) | ~ (cap_closed(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (powerset(v12) = v11) | ~ (powerset(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (preboolean(v12) = v11) | ~ (preboolean(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (cup_closed(v12) = v11) | ~ (cup_closed(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (diff_closed(v12) = v11) | ~ (diff_closed(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (empty(v12) = v11) | ~ (empty(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (finite(v12) = v11) | ~ (finite(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (set_difference(v11, v10) = v12) | ? [v13] : ? [v14] : (set_difference(v10, v11) = v14 & symmetric_difference(v10, v11) = v13 & set_union2(v14, v12) = v13)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (set_difference(v11, v10) = v12) | ? [v13] : (symmetric_difference(v10, v12) = v13 & set_union2(v10, v11) = v13)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (set_difference(v10, v11) = v12) | ~ (element(v10, v0) = 0) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : (symmetric_difference(v10, v11) = v14 & element(v11, v0) = v13 & in(v14, v0) = v15 & in(v12, v0) = v16 & ( ~ (v13 = 0) | (v16 = 0 & v15 = 0)))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (set_difference(v10, v11) = v12) | ? [v13] : ? [v14] : (set_difference(v11, v10) = v14 & symmetric_difference(v10, v11) = v13 & set_union2(v12, v14) = v13)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (set_difference(v10, v11) = v12) | ? [v13] : ? [v14] : (finite(v12) = v14 & finite(v10) = v13 & ( ~ (v13 = 0) | v14 = 0))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (symmetric_difference(v11, v10) = v12) | symmetric_difference(v10, v11) = v12) & ! [v10] : ! [v11] : ! [v12] : ( ~ (symmetric_difference(v10, v11) = v12) | ~ (element(v10, v0) = 0) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : (set_difference(v10, v11) = v15 & element(v11, v0) = v13 & in(v15, v0) = v16 & in(v12, v0) = v14 & ( ~ (v13 = 0) | (v16 = 0 & v14 = 0)))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (symmetric_difference(v10, v11) = v12) | symmetric_difference(v11, v10) = v12) & ! [v10] : ! [v11] : ! [v12] : ( ~ (symmetric_difference(v10, v11) = v12) | ? [v13] : ? [v14] : ? [v15] : (finite(v12) = v15 & finite(v11) = v14 & finite(v10) = v13 & ( ~ (v14 = 0) | ~ (v13 = 0) | v15 = 0))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (symmetric_difference(v10, v11) = v12) | ? [v13] : ? [v14] : (set_difference(v11, v10) = v14 & set_difference(v10, v11) = v13 & set_union2(v13, v14) = v12)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (set_union2(v11, v10) = v12) | set_union2(v10, v11) = v12) & ! [v10] : ! [v11] : ! [v12] : ( ~ (set_union2(v11, v10) = v12) | ? [v13] : ? [v14] : (empty(v12) = v14 & empty(v10) = v13 & ( ~ (v14 = 0) | v13 = 0))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (set_union2(v10, v11) = v12) | set_union2(v11, v10) = v12) & ! [v10] : ! [v11] : ! [v12] : ( ~ (set_union2(v10, v11) = v12) | ? [v13] : ? [v14] : ? [v15] : (finite(v12) = v15 & finite(v11) = v14 & finite(v10) = v13 & ( ~ (v14 = 0) | ~ (v13 = 0) | v15 = 0))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (set_union2(v10, v11) = v12) | ? [v13] : ? [v14] : (empty(v12) = v14 & empty(v10) = v13 & ( ~ (v14 = 0) | v13 = 0))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (set_union2(v10, v11) = v12) | ? [v13] : (set_difference(v11, v10) = v13 & symmetric_difference(v10, v13) = v12)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (powerset(v11) = v12) | ~ (element(v10, v12) = 0) | subset(v10, v11) = 0) & ! [v10] : ! [v11] : ! [v12] : ( ~ (powerset(v10) = v11) | ~ (element(v12, v11) = 0) | ? [v13] : ((v13 = 0 & finite(v12) = 0) | ( ~ (v13 = 0) & finite(v10) = v13))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (empty(v12) = 0) | ~ (in(v10, v11) = 0) | ? [v13] : ? [v14] : ( ~ (v14 = 0) & powerset(v12) = v13 & element(v11, v13) = v14)) & ! [v10] : ! [v11] : (v11 = v10 | ~ (set_difference(v10, empty_set) = v11)) & ! [v10] : ! [v11] : (v11 = v10 | ~ (symmetric_difference(v10, empty_set) = v11)) & ! [v10] : ! [v11] : (v11 = v10 | ~ (set_union2(v10, v10) = v11)) & ! [v10] : ! [v11] : (v11 = v10 | ~ (set_union2(v10, empty_set) = v11)) & ! [v10] : ! [v11] : (v11 = v10 | ~ (empty(v11) = 0) | ~ (empty(v10) = 0)) & ! [v10] : ! [v11] : (v11 = empty_set | ~ (set_difference(empty_set, v10) = v11)) & ! [v10] : ! [v11] : (v11 = 0 | ~ (subset(v10, v10) = v11)) & ! [v10] : ! [v11] : (v11 = 0 | ~ (preboolean(v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : (set_difference(v12, v13) = v16 & set_union2(v12, v13) = v14 & in(v16, v10) = v17 & in(v14, v10) = v15 & in(v13, v10) = 0 & in(v12, v10) = 0 & ( ~ (v17 = 0) | ~ (v15 = 0)))) & ! [v10] : ! [v11] : (v11 = 0 | ~ (preboolean(v10) = v11) | ? [v12] : ? [v13] : (cup_closed(v10) = v12 & diff_closed(v10) = v13 & ( ~ (v13 = 0) | ~ (v12 = 0)))) & ! [v10] : ! [v11] : (v11 = 0 | ~ (empty(v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ( ~ (v14 = 0) & powerset(v10) = v12 & element(v13, v12) = 0 & empty(v13) = v14 & finite(v13) = 0)) & ! [v10] : ! [v11] : (v11 = 0 | ~ (empty(v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ( ~ (v14 = 0) & powerset(v10) = v12 & element(v13, v12) = 0 & empty(v13) = v14)) & ! [v10] : ! [v11] : (v11 = 0 | ~ (finite(v10) = v11) | ? [v12] : ( ~ (v12 = 0) & empty(v10) = v12)) & ! [v10] : ! [v11] : ( ~ (subset(v10, v11) = 0) | ? [v12] : (powerset(v11) = v12 & element(v10, v12) = 0)) & ! [v10] : ! [v11] : ( ~ (powerset(v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : ((v15 = 0 & v13 = 0 & ~ (v14 = 0) & element(v12, v11) = 0 & empty(v12) = v14 & finite(v12) = 0) | (v12 = 0 & empty(v10) = 0))) & ! [v10] : ! [v11] : ( ~ (powerset(v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ((v13 = 0 & ~ (v14 = 0) & element(v12, v11) = 0 & empty(v12) = v14) | (v12 = 0 & empty(v10) = 0))) & ! [v10] : ! [v11] : ( ~ (powerset(v10) = v11) | ? [v12] : ( ~ (v12 = 0) & empty(v11) = v12)) & ! [v10] : ! [v11] : ( ~ (powerset(v10) = v11) | ? [v12] : (relation(v12) = 0 & function(v12) = 0 & one_to_one(v12) = 0 & epsilon_transitive(v12) = 0 & epsilon_connected(v12) = 0 & ordinal(v12) = 0 & natural(v12) = 0 & element(v12, v11) = 0 & empty(v12) = 0 & finite(v12) = 0)) & ! [v10] : ! [v11] : ( ~ (powerset(v10) = v11) | ? [v12] : (element(v12, v11) = 0 & empty(v12) = 0)) & ! [v10] : ! [v11] : ( ~ (element(v11, v0) = 0) | ~ (element(v10, v0) = 0) | ? [v12] : ? [v13] : (set_difference(v10, v11) = v13 & symmetric_difference(v10, v11) = v12 & in(v13, v0) = 0 & in(v12, v0) = 0)) & ! [v10] : ! [v11] : ( ~ (element(v10, v11) = 0) | ? [v12] : ? [v13] : (empty(v11) = v12 & in(v10, v11) = v13 & (v13 = 0 | v12 = 0))) & ! [v10] : ! [v11] : ( ~ (cup_closed(v10) = v11) | ? [v12] : ? [v13] : (preboolean(v10) = v12 & diff_closed(v10) = v13 & ( ~ (v12 = 0) | (v13 = 0 & v11 = 0)))) & ! [v10] : ! [v11] : ( ~ (diff_closed(v10) = v11) | ? [v12] : ? [v13] : (preboolean(v10) = v12 & cup_closed(v10) = v13 & ( ~ (v12 = 0) | (v13 = 0 & v11 = 0)))) & ! [v10] : ! [v11] : ( ~ (in(v11, v10) = 0) | ? [v12] : ( ~ (v12 = 0) & in(v10, v11) = v12)) & ! [v10] : ! [v11] : ( ~ (in(v10, v11) = 0) | element(v10, v11) = 0) & ! [v10] : ! [v11] : ( ~ (in(v10, v11) = 0) | ? [v12] : ( ~ (v12 = 0) & empty(v11) = v12)) & ! [v10] : ! [v11] : ( ~ (in(v10, v11) = 0) | ? [v12] : ( ~ (v12 = 0) & in(v11, v10) = v12)) & ! [v10] : (v10 = empty_set | ~ (empty(v10) = 0)) & ! [v10] : ( ~ (preboolean(v10) = 0) | (cup_closed(v10) = 0 & diff_closed(v10) = 0)) & ! [v10] : ( ~ (cup_closed(v10) = 0) | ? [v11] : ? [v12] : (preboolean(v10) = v12 & diff_closed(v10) = v11 & ( ~ (v11 = 0) | v12 = 0))) & ! [v10] : ( ~ (diff_closed(v10) = 0) | ? [v11] : ? [v12] : (preboolean(v10) = v12 & cup_closed(v10) = v11 & ( ~ (v11 = 0) | v12 = 0))) & ! [v10] : ( ~ (empty(v10) = 0) | finite(v10) = 0) & ! [v10] : ( ~ (finite(v10) = 0) | ? [v11] : (powerset(v10) = v11 & ! [v12] : ! [v13] : (v13 = 0 | ~ (finite(v12) = v13) | ? [v14] : ( ~ (v14 = 0) & element(v12, v11) = v14)) & ! [v12] : ( ~ (element(v12, v11) = 0) | finite(v12) = 0))) & ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : (powerset(v12) = v14 & element(v11, v14) = v15 & element(v10, v12) = v16 & in(v10, v11) = v13 & ( ~ (v15 = 0) | ~ (v13 = 0) | v16 = 0)) & ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : (symmetric_difference(v10, v11) = v14 & finite(v14) = v15 & finite(v11) = v13 & finite(v10) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0) | v15 = 0)) & ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (subset(v10, v11) = v12 & powerset(v11) = v13 & element(v10, v13) = v14 & ( ~ (v12 = 0) | v14 = 0)) & ? [v10] : ? [v11] : ? [v12] : ? [v13] : (set_difference(v11, v10) = v13 & symmetric_difference(v10, v13) = v12 & set_union2(v10, v11) = v12) & ? [v10] : ? [v11] : ? [v12] : ? [v13] : (preboolean(v10) = v13 & cup_closed(v10) = v11 & diff_closed(v10) = v12 & ( ~ (v12 = 0) | ~ (v11 = 0) | v13 = 0)) & ? [v10] : ? [v11] : ? [v12] : ? [v13] : (empty(v11) = v13 & in(v10, v11) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0))) & ? [v10] : ? [v11] : ? [v12] : (relation(v12) = 0 & function(v12) = 0 & one_to_one(v12) = 0 & epsilon_transitive(v12) = 0 & epsilon_connected(v12) = 0 & ordinal(v12) = 0 & natural(v12) = 0 & powerset(v10) = v11 & element(v12, v11) = 0 & empty(v12) = 0 & finite(v12) = 0) & ? [v10] : ? [v11] : element(v11, v10) = 0)
% 116.76/72.97 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9 yields:
% 116.76/72.97 | (1) ~ (all_0_0_0 = 0) & ~ (all_0_2_2 = 0) & ~ (all_0_5_5 = 0) & ~ (all_0_7_7 = 0) & ~ (all_0_8_8 = 0) & cap_closed(all_0_3_3) = 0 & preboolean(all_0_3_3) = 0 & preboolean(all_0_9_9) = all_0_7_7 & cup_closed(all_0_3_3) = 0 & diff_closed(all_0_3_3) = 0 & empty(all_0_1_1) = all_0_0_0 & empty(all_0_3_3) = all_0_2_2 & 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 & finite(all_0_1_1) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (element(v0, v2) = v4) | ? [v5] : ( ~ (v5 = 0) & in(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v0) = v1) | ~ (finite(v2) = v3) | ? [v4] : (( ~ (v4 = 0) & element(v2, v1) = v4) | ( ~ (v4 = 0) & finite(v0) = 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 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (symmetric_difference(v3, v2) = v1) | ~ (symmetric_difference(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 | ~ (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] : ( ~ (set_difference(v1, v2) = v3) | ~ (preboolean(v0) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (set_union2(v1, v2) = v6 & in(v6, v0) = v7 & in(v3, v0) = v8 & in(v2, v0) = v5 & in(v1, v0) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0) | (v8 = 0 & v7 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v1, v2) = v3) | ~ (preboolean(v0) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (set_difference(v1, v2) = v7 & in(v7, v0) = v8 & in(v3, v0) = v6 & in(v2, v0) = v5 & in(v1, v0) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0) | (v8 = 0 & v6 = 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(v2) = v1) | ~ (relation(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (epsilon_transitive(v2) = v1) | ~ (epsilon_transitive(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (epsilon_connected(v2) = v1) | ~ (epsilon_connected(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ordinal(v2) = v1) | ~ (ordinal(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (natural(v2) = v1) | ~ (natural(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cap_closed(v2) = v1) | ~ (cap_closed(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (preboolean(v2) = v1) | ~ (preboolean(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cup_closed(v2) = v1) | ~ (cup_closed(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (diff_closed(v2) = v1) | ~ (diff_closed(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (finite(v2) = v1) | ~ (finite(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v1, v0) = v2) | ? [v3] : ? [v4] : (set_difference(v0, v1) = v4 & symmetric_difference(v0, v1) = v3 & set_union2(v4, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v1, v0) = v2) | ? [v3] : (symmetric_difference(v0, v2) = v3 & set_union2(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ (element(v0, all_0_9_9) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (symmetric_difference(v0, v1) = v4 & element(v1, all_0_9_9) = v3 & in(v4, all_0_9_9) = v5 & in(v2, all_0_9_9) = v6 & ( ~ (v3 = 0) | (v6 = 0 & v5 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ? [v3] : ? [v4] : (set_difference(v1, v0) = v4 & symmetric_difference(v0, v1) = v3 & set_union2(v2, v4) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ? [v3] : ? [v4] : (finite(v2) = v4 & finite(v0) = v3 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (symmetric_difference(v1, v0) = v2) | symmetric_difference(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (symmetric_difference(v0, v1) = v2) | ~ (element(v0, all_0_9_9) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (set_difference(v0, v1) = v5 & element(v1, all_0_9_9) = v3 & in(v5, all_0_9_9) = v6 & in(v2, all_0_9_9) = v4 & ( ~ (v3 = 0) | (v6 = 0 & v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (symmetric_difference(v0, v1) = v2) | symmetric_difference(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (symmetric_difference(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (finite(v2) = v5 & finite(v1) = v4 & finite(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (symmetric_difference(v0, v1) = v2) | ? [v3] : ? [v4] : (set_difference(v1, v0) = v4 & set_difference(v0, v1) = v3 & set_union2(v3, v4) = v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ? [v3] : ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (finite(v2) = v5 & finite(v1) = v4 & finite(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : (set_difference(v1, v0) = v3 & symmetric_difference(v0, v3) = v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | subset(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ (element(v2, v1) = 0) | ? [v3] : ((v3 = 0 & finite(v2) = 0) | ( ~ (v3 = 0) & finite(v0) = 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_difference(v0, empty_set) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (symmetric_difference(v0, empty_set) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)) & ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_difference(empty_set, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (preboolean(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (set_difference(v2, v3) = v6 & set_union2(v2, v3) = v4 & in(v6, v0) = v7 & in(v4, v0) = v5 & in(v3, v0) = 0 & in(v2, v0) = 0 & ( ~ (v7 = 0) | ~ (v5 = 0)))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (preboolean(v0) = v1) | ? [v2] : ? [v3] : (cup_closed(v0) = v2 & diff_closed(v0) = v3 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (empty(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v0) = v2 & element(v3, v2) = 0 & empty(v3) = v4 & finite(v3) = 0)) & ! [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 | ~ (finite(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2)) & ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (powerset(v1) = v2 & element(v0, v2) = 0)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & v3 = 0 & ~ (v4 = 0) & element(v2, v1) = 0 & empty(v2) = v4 & finite(v2) = 0) | (v2 = 0 & empty(v0) = 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] : (relation(v2) = 0 & function(v2) = 0 & one_to_one(v2) = 0 & epsilon_transitive(v2) = 0 & epsilon_connected(v2) = 0 & ordinal(v2) = 0 & natural(v2) = 0 & element(v2, v1) = 0 & empty(v2) = 0 & finite(v2) = 0)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) = 0 & empty(v2) = 0)) & ! [v0] : ! [v1] : ( ~ (element(v1, all_0_9_9) = 0) | ~ (element(v0, all_0_9_9) = 0) | ? [v2] : ? [v3] : (set_difference(v0, v1) = v3 & symmetric_difference(v0, v1) = v2 & in(v3, all_0_9_9) = 0 & in(v2, all_0_9_9) = 0)) & ! [v0] : ! [v1] : ( ~ (element(v0, v1) = 0) | ? [v2] : ? [v3] : (empty(v1) = v2 & in(v0, v1) = v3 & (v3 = 0 | v2 = 0))) & ! [v0] : ! [v1] : ( ~ (cup_closed(v0) = v1) | ? [v2] : ? [v3] : (preboolean(v0) = v2 & diff_closed(v0) = v3 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0)))) & ! [v0] : ! [v1] : ( ~ (diff_closed(v0) = v1) | ? [v2] : ? [v3] : (preboolean(v0) = v2 & cup_closed(v0) = v3 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0)))) & ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | element(v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) & ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0)) & ! [v0] : ( ~ (preboolean(v0) = 0) | (cup_closed(v0) = 0 & diff_closed(v0) = 0)) & ! [v0] : ( ~ (cup_closed(v0) = 0) | ? [v1] : ? [v2] : (preboolean(v0) = v2 & diff_closed(v0) = v1 & ( ~ (v1 = 0) | v2 = 0))) & ! [v0] : ( ~ (diff_closed(v0) = 0) | ? [v1] : ? [v2] : (preboolean(v0) = v2 & cup_closed(v0) = v1 & ( ~ (v1 = 0) | v2 = 0))) & ! [v0] : ( ~ (empty(v0) = 0) | finite(v0) = 0) & ! [v0] : ( ~ (finite(v0) = 0) | ? [v1] : (powerset(v0) = v1 & ! [v2] : ! [v3] : (v3 = 0 | ~ (finite(v2) = v3) | ? [v4] : ( ~ (v4 = 0) & element(v2, v1) = v4)) & ! [v2] : ( ~ (element(v2, v1) = 0) | finite(v2) = 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] : (symmetric_difference(v0, v1) = v4 & finite(v4) = v5 & finite(v1) = v3 & finite(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | v5 = 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] : (set_difference(v1, v0) = v3 & symmetric_difference(v0, v3) = v2 & set_union2(v0, v1) = v2) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : (preboolean(v0) = v3 & cup_closed(v0) = v1 & diff_closed(v0) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0)) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : (empty(v1) = v3 & in(v0, v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))) & ? [v0] : ? [v1] : ? [v2] : (relation(v2) = 0 & function(v2) = 0 & one_to_one(v2) = 0 & epsilon_transitive(v2) = 0 & epsilon_connected(v2) = 0 & ordinal(v2) = 0 & natural(v2) = 0 & powerset(v0) = v1 & element(v2, v1) = 0 & empty(v2) = 0 & finite(v2) = 0) & ? [v0] : ? [v1] : element(v1, v0) = 0
% 116.76/72.99 |
% 116.76/72.99 | Applying alpha-rule on (1) yields:
% 116.76/72.99 | (2) empty(all_0_6_6) = all_0_5_5
% 116.76/72.99 | (3) ! [v0] : ( ~ (finite(v0) = 0) | ? [v1] : (powerset(v0) = v1 & ! [v2] : ! [v3] : (v3 = 0 | ~ (finite(v2) = v3) | ? [v4] : ( ~ (v4 = 0) & element(v2, v1) = v4)) & ! [v2] : ( ~ (element(v2, v1) = 0) | finite(v2) = 0)))
% 116.76/72.99 | (4) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (empty(v1) = v3 & in(v0, v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))
% 116.76/72.99 | (5) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (powerset(v1) = v2 & element(v0, v2) = 0))
% 116.76/72.99 | (6) ! [v0] : ! [v1] : (v1 = v0 | ~ (symmetric_difference(v0, empty_set) = v1))
% 116.76/72.99 | (7) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | subset(v0, v1) = 0)
% 116.76/72.99 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0))
% 116.76/72.99 | (9) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & v3 = 0 & ~ (v4 = 0) & element(v2, v1) = 0 & empty(v2) = v4 & finite(v2) = 0) | (v2 = 0 & empty(v0) = 0)))
% 116.76/72.99 | (10) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | element(v0, v1) = 0)
% 116.76/72.99 | (11) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3))
% 116.76/72.99 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 116.76/72.99 | (13) ! [v0] : ! [v1] : (v1 = 0 | ~ (empty(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v0) = v2 & element(v3, v2) = 0 & empty(v3) = v4 & finite(v3) = 0))
% 116.76/72.99 | (14) ! [v0] : ! [v1] : ! [v2] : ( ~ (empty(v2) = 0) | ~ (in(v0, v1) = 0) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v2) = v3 & element(v1, v3) = v4))
% 116.76/72.99 | (15) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ (element(v0, all_0_9_9) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (symmetric_difference(v0, v1) = v4 & element(v1, all_0_9_9) = v3 & in(v4, all_0_9_9) = v5 & in(v2, all_0_9_9) = v6 & ( ~ (v3 = 0) | (v6 = 0 & v5 = 0))))
% 116.76/72.99 | (16) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1))
% 116.76/72.99 | (17) empty(all_0_3_3) = all_0_2_2
% 116.76/72.99 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0))
% 116.76/72.99 | (19) ~ (all_0_7_7 = 0)
% 116.76/72.99 | (20) ! [v0] : ! [v1] : ! [v2] : ( ~ (symmetric_difference(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (finite(v2) = v5 & finite(v1) = v4 & finite(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0)))
% 116.76/72.99 | (21) empty(all_0_4_4) = 0
% 116.76/72.99 | (22) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1))
% 116.76/72.99 | (23) ! [v0] : ! [v1] : (v1 = 0 | ~ (preboolean(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (set_difference(v2, v3) = v6 & set_union2(v2, v3) = v4 & in(v6, v0) = v7 & in(v4, v0) = v5 & in(v3, v0) = 0 & in(v2, v0) = 0 & ( ~ (v7 = 0) | ~ (v5 = 0))))
% 116.76/73.00 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v1, v2) = v3) | ~ (preboolean(v0) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (set_union2(v1, v2) = v6 & in(v6, v0) = v7 & in(v3, v0) = v8 & in(v2, v0) = v5 & in(v1, v0) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0) | (v8 = 0 & v7 = 0))))
% 116.76/73.00 | (25) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0))
% 116.76/73.00 | (26) ! [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))
% 116.76/73.00 | (27) ! [v0] : ! [v1] : (v1 = 0 | ~ (finite(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2))
% 116.76/73.00 | (28) ? [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))
% 116.76/73.00 | (29) ! [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))
% 116.76/73.00 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4))
% 116.76/73.00 | (31) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (preboolean(v0) = v3 & cup_closed(v0) = v1 & diff_closed(v0) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0))
% 116.76/73.00 | (32) ! [v0] : ! [v1] : ( ~ (element(v1, all_0_9_9) = 0) | ~ (element(v0, all_0_9_9) = 0) | ? [v2] : ? [v3] : (set_difference(v0, v1) = v3 & symmetric_difference(v0, v1) = v2 & in(v3, all_0_9_9) = 0 & in(v2, all_0_9_9) = 0))
% 116.76/73.00 | (33) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ? [v3] : ? [v4] : (finite(v2) = v4 & finite(v0) = v3 & ( ~ (v3 = 0) | v4 = 0)))
% 116.76/73.00 | (34) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_difference(v0, empty_set) = v1))
% 116.76/73.00 | (35) ! [v0] : ( ~ (preboolean(v0) = 0) | (cup_closed(v0) = 0 & diff_closed(v0) = 0))
% 116.76/73.00 | (36) ! [v0] : ( ~ (empty(v0) = 0) | finite(v0) = 0)
% 116.76/73.00 | (37) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (epsilon_connected(v2) = v1) | ~ (epsilon_connected(v2) = v0))
% 116.76/73.00 | (38) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0))
% 116.76/73.00 | (39) diff_closed(all_0_3_3) = 0
% 116.76/73.00 | (40) ! [v0] : ( ~ (diff_closed(v0) = 0) | ? [v1] : ? [v2] : (preboolean(v0) = v2 & cup_closed(v0) = v1 & ( ~ (v1 = 0) | v2 = 0)))
% 116.76/73.00 | (41) ! [v0] : ( ~ (cup_closed(v0) = 0) | ? [v1] : ? [v2] : (preboolean(v0) = v2 & diff_closed(v0) = v1 & ( ~ (v1 = 0) | v2 = 0)))
% 116.76/73.00 | (42) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v1, v0) = v2) | ? [v3] : ? [v4] : (set_difference(v0, v1) = v4 & symmetric_difference(v0, v1) = v3 & set_union2(v4, v2) = v3))
% 116.76/73.00 | (43) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0))
% 116.76/73.00 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (symmetric_difference(v3, v2) = v1) | ~ (symmetric_difference(v3, v2) = v0))
% 116.76/73.00 | (45) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v1) = v3 & element(v0, v3) = v4))
% 116.76/73.00 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0))
% 116.76/73.00 | (47) cap_closed(all_0_3_3) = 0
% 116.76/73.00 | (48) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cup_closed(v2) = v1) | ~ (cup_closed(v2) = v0))
% 116.76/73.00 | (49) ~ (all_0_5_5 = 0)
% 116.76/73.00 | (50) ! [v0] : ! [v1] : ! [v2] : ( ~ (symmetric_difference(v0, v1) = v2) | symmetric_difference(v1, v0) = v2)
% 116.76/73.00 | (51) ! [v0] : ! [v1] : ! [v2] : ( ~ (symmetric_difference(v1, v0) = v2) | symmetric_difference(v0, v1) = v2)
% 116.76/73.00 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v1, v2) = v3) | ~ (preboolean(v0) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (set_difference(v1, v2) = v7 & in(v7, v0) = v8 & in(v3, v0) = v6 & in(v2, v0) = v5 & in(v1, v0) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0) | (v8 = 0 & v6 = 0))))
% 116.76/73.00 | (53) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0))
% 116.76/73.00 | (54) ! [v0] : ! [v1] : (v1 = 0 | ~ (preboolean(v0) = v1) | ? [v2] : ? [v3] : (cup_closed(v0) = v2 & diff_closed(v0) = v3 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 116.76/73.00 | (55) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (diff_closed(v2) = v1) | ~ (diff_closed(v2) = v0))
% 116.76/73.01 | (56) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0)))
% 116.76/73.01 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | element(v0, v2) = 0)
% 116.76/73.01 | (58) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 116.76/73.01 | (59) finite(all_0_1_1) = 0
% 116.76/73.01 | (60) ? [v0] : ? [v1] : ? [v2] : (relation(v2) = 0 & function(v2) = 0 & one_to_one(v2) = 0 & epsilon_transitive(v2) = 0 & epsilon_connected(v2) = 0 & ordinal(v2) = 0 & natural(v2) = 0 & powerset(v0) = v1 & element(v2, v1) = 0 & empty(v2) = 0 & finite(v2) = 0)
% 117.21/73.01 | (61) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (natural(v2) = v1) | ~ (natural(v2) = v0))
% 117.21/73.01 | (62) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (preboolean(v2) = v1) | ~ (preboolean(v2) = v0))
% 117.21/73.01 | (63) empty(all_0_1_1) = all_0_0_0
% 117.21/73.01 | (64) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 117.21/73.01 | (65) ! [v0] : ! [v1] : ! [v2] : ( ~ (symmetric_difference(v0, v1) = v2) | ~ (element(v0, all_0_9_9) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (set_difference(v0, v1) = v5 & element(v1, all_0_9_9) = v3 & in(v5, all_0_9_9) = v6 & in(v2, all_0_9_9) = v4 & ( ~ (v3 = 0) | (v6 = 0 & v4 = 0))))
% 117.21/73.01 | (66) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 117.21/73.01 | (67) ! [v0] : ! [v1] : ( ~ (diff_closed(v0) = v1) | ? [v2] : ? [v3] : (preboolean(v0) = v2 & cup_closed(v0) = v3 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0))))
% 117.21/73.01 | (68) ! [v0] : ! [v1] : ( ~ (cup_closed(v0) = v1) | ? [v2] : ? [v3] : (preboolean(v0) = v2 & diff_closed(v0) = v3 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0))))
% 117.21/73.01 | (69) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cap_closed(v2) = v1) | ~ (cap_closed(v2) = v0))
% 117.21/73.01 | (70) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0))
% 117.21/73.01 | (71) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ? [v3] : ? [v4] : (set_difference(v1, v0) = v4 & symmetric_difference(v0, v1) = v3 & set_union2(v2, v4) = v3))
% 117.21/73.01 | (72) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (epsilon_transitive(v2) = v1) | ~ (epsilon_transitive(v2) = v0))
% 117.21/73.01 | (73) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (symmetric_difference(v0, v1) = v4 & finite(v4) = v5 & finite(v1) = v3 & finite(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | v5 = 0))
% 117.21/73.01 | (74) ~ (all_0_8_8 = 0)
% 117.21/73.01 | (75) empty(empty_set) = 0
% 117.21/73.01 | (76) ! [v0] : ! [v1] : (v1 = 0 | ~ (empty(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v0) = v2 & element(v3, v2) = 0 & empty(v3) = v4))
% 117.21/73.01 | (77) preboolean(all_0_3_3) = 0
% 117.21/73.01 | (78) ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2))
% 117.21/73.01 | (79) ~ (all_0_2_2 = 0)
% 117.21/73.01 | (80) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) = 0 & empty(v2) = 0))
% 117.21/73.01 | (81) ! [v0] : ! [v1] : ! [v2] : ( ~ (symmetric_difference(v0, v1) = v2) | ? [v3] : ? [v4] : (set_difference(v1, v0) = v4 & set_difference(v0, v1) = v3 & set_union2(v3, v4) = v2))
% 117.21/73.01 | (82) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v3 = 0 & ~ (v4 = 0) & element(v2, v1) = 0 & empty(v2) = v4) | (v2 = 0 & empty(v0) = 0)))
% 117.21/73.01 | (83) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ? [v3] : ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0)))
% 117.21/73.01 | (84) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (finite(v2) = v5 & finite(v1) = v4 & finite(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0)))
% 117.21/73.01 | (85) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (set_difference(v1, v0) = v3 & symmetric_difference(v0, v3) = v2 & set_union2(v0, v1) = v2)
% 117.21/73.01 | (86) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_difference(empty_set, v0) = v1))
% 117.21/73.01 | (87) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ (element(v2, v1) = 0) | ? [v3] : ((v3 = 0 & finite(v2) = 0) | ( ~ (v3 = 0) & finite(v0) = v3)))
% 117.21/73.01 | (88) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (relation(v2) = 0 & function(v2) = 0 & one_to_one(v2) = 0 & epsilon_transitive(v2) = 0 & epsilon_connected(v2) = 0 & ordinal(v2) = 0 & natural(v2) = 0 & element(v2, v1) = 0 & empty(v2) = 0 & finite(v2) = 0))
% 117.21/73.02 | (89) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v1, v0) = v2) | ? [v3] : (symmetric_difference(v0, v2) = v3 & set_union2(v0, v1) = v3))
% 117.21/73.02 | (90) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2)
% 117.21/73.02 | (91) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2)
% 117.21/73.02 | (92) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 117.21/73.02 | (93) ~ (all_0_0_0 = 0)
% 117.21/73.02 | (94) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0))
% 117.21/73.02 | (95) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : (set_difference(v1, v0) = v3 & symmetric_difference(v0, v3) = v2))
% 117.21/73.02 | (96) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ordinal(v2) = v1) | ~ (ordinal(v2) = v0))
% 117.21/73.02 | (97) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (subset(v0, v1) = v2 & powerset(v1) = v3 & element(v0, v3) = v4 & ( ~ (v2 = 0) | v4 = 0))
% 117.21/73.02 | (98) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 117.21/73.02 | (99) cup_closed(all_0_3_3) = 0
% 117.21/73.02 | (100) ? [v0] : ? [v1] : element(v1, v0) = 0
% 117.21/73.02 | (101) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1))
% 117.21/73.02 | (102) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v0, v1) = v2) | ? [v3] : ? [v4] : (element(v0, v1) = v3 & empty(v1) = v4 & ( ~ (v3 = 0) | v4 = 0)))
% 117.21/73.02 | (103) empty(all_0_9_9) = all_0_8_8
% 117.21/73.02 | (104) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v0) = v1) | ~ (finite(v2) = v3) | ? [v4] : (( ~ (v4 = 0) & element(v2, v1) = v4) | ( ~ (v4 = 0) & finite(v0) = v4)))
% 117.21/73.02 | (105) preboolean(all_0_9_9) = all_0_7_7
% 117.21/73.02 | (106) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 117.21/73.02 | (107) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (finite(v2) = v1) | ~ (finite(v2) = v0))
% 117.21/73.02 | (108) ! [v0] : ! [v1] : ( ~ (element(v0, v1) = 0) | ? [v2] : ? [v3] : (empty(v1) = v2 & in(v0, v1) = v3 & (v3 = 0 | v2 = 0)))
% 117.21/73.02 |
% 117.21/73.02 | Instantiating formula (23) with all_0_7_7, all_0_9_9 and discharging atoms preboolean(all_0_9_9) = all_0_7_7, yields:
% 117.21/73.02 | (109) all_0_7_7 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (set_difference(v0, v1) = v4 & set_union2(v0, v1) = v2 & in(v4, all_0_9_9) = v5 & in(v2, all_0_9_9) = v3 & in(v1, all_0_9_9) = 0 & in(v0, all_0_9_9) = 0 & ( ~ (v5 = 0) | ~ (v3 = 0)))
% 117.21/73.02 |
% 117.21/73.02 +-Applying beta-rule and splitting (109), into two cases.
% 117.21/73.02 |-Branch one:
% 117.21/73.02 | (110) all_0_7_7 = 0
% 117.21/73.02 |
% 117.21/73.02 | Equations (110) can reduce 19 to:
% 117.21/73.02 | (111) $false
% 117.21/73.02 |
% 117.21/73.02 |-The branch is then unsatisfiable
% 117.21/73.02 |-Branch two:
% 117.21/73.02 | (19) ~ (all_0_7_7 = 0)
% 117.21/73.02 | (113) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (set_difference(v0, v1) = v4 & set_union2(v0, v1) = v2 & in(v4, all_0_9_9) = v5 & in(v2, all_0_9_9) = v3 & in(v1, all_0_9_9) = 0 & in(v0, all_0_9_9) = 0 & ( ~ (v5 = 0) | ~ (v3 = 0)))
% 117.21/73.02 |
% 117.21/73.02 | Instantiating (113) with all_136_0_143, all_136_1_144, all_136_2_145, all_136_3_146, all_136_4_147, all_136_5_148 yields:
% 117.21/73.02 | (114) set_difference(all_136_5_148, all_136_4_147) = all_136_1_144 & set_union2(all_136_5_148, all_136_4_147) = all_136_3_146 & in(all_136_1_144, all_0_9_9) = all_136_0_143 & in(all_136_3_146, all_0_9_9) = all_136_2_145 & in(all_136_4_147, all_0_9_9) = 0 & in(all_136_5_148, all_0_9_9) = 0 & ( ~ (all_136_0_143 = 0) | ~ (all_136_2_145 = 0))
% 117.21/73.02 |
% 117.21/73.02 | Applying alpha-rule on (114) yields:
% 117.21/73.02 | (115) ~ (all_136_0_143 = 0) | ~ (all_136_2_145 = 0)
% 117.21/73.02 | (116) set_difference(all_136_5_148, all_136_4_147) = all_136_1_144
% 117.21/73.02 | (117) in(all_136_5_148, all_0_9_9) = 0
% 117.21/73.02 | (118) in(all_136_4_147, all_0_9_9) = 0
% 117.21/73.02 | (119) in(all_136_1_144, all_0_9_9) = all_136_0_143
% 117.21/73.02 | (120) set_union2(all_136_5_148, all_136_4_147) = all_136_3_146
% 117.21/73.02 | (121) in(all_136_3_146, all_0_9_9) = all_136_2_145
% 117.21/73.02 |
% 117.21/73.02 | Instantiating formula (42) with all_136_1_144, all_136_5_148, all_136_4_147 and discharging atoms set_difference(all_136_5_148, all_136_4_147) = all_136_1_144, yields:
% 117.21/73.02 | (122) ? [v0] : ? [v1] : (set_difference(all_136_4_147, all_136_5_148) = v1 & symmetric_difference(all_136_4_147, all_136_5_148) = v0 & set_union2(v1, all_136_1_144) = v0)
% 117.21/73.03 |
% 117.21/73.03 | Instantiating formula (89) with all_136_1_144, all_136_5_148, all_136_4_147 and discharging atoms set_difference(all_136_5_148, all_136_4_147) = all_136_1_144, yields:
% 117.21/73.03 | (123) ? [v0] : (symmetric_difference(all_136_4_147, all_136_1_144) = v0 & set_union2(all_136_4_147, all_136_5_148) = v0)
% 117.21/73.03 |
% 117.21/73.03 | Instantiating formula (71) with all_136_1_144, all_136_4_147, all_136_5_148 and discharging atoms set_difference(all_136_5_148, all_136_4_147) = all_136_1_144, yields:
% 117.21/73.03 | (124) ? [v0] : ? [v1] : (set_difference(all_136_4_147, all_136_5_148) = v1 & symmetric_difference(all_136_5_148, all_136_4_147) = v0 & set_union2(all_136_1_144, v1) = v0)
% 117.21/73.03 |
% 117.21/73.03 | Instantiating formula (52) with all_136_3_146, all_136_4_147, all_136_5_148, all_0_3_3 and discharging atoms set_union2(all_136_5_148, all_136_4_147) = all_136_3_146, preboolean(all_0_3_3) = 0, yields:
% 117.21/73.03 | (125) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (set_difference(all_136_5_148, all_136_4_147) = v3 & in(v3, all_0_3_3) = v4 & in(all_136_3_146, all_0_3_3) = v2 & in(all_136_4_147, all_0_3_3) = v1 & in(all_136_5_148, all_0_3_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | (v4 = 0 & v2 = 0)))
% 117.21/73.03 |
% 117.21/73.03 | Instantiating formula (91) with all_136_3_146, all_136_5_148, all_136_4_147 and discharging atoms set_union2(all_136_5_148, all_136_4_147) = all_136_3_146, yields:
% 117.21/73.03 | (126) set_union2(all_136_4_147, all_136_5_148) = all_136_3_146
% 117.21/73.03 |
% 117.21/73.03 | Instantiating formula (95) with all_136_3_146, all_136_4_147, all_136_5_148 and discharging atoms set_union2(all_136_5_148, all_136_4_147) = all_136_3_146, yields:
% 117.21/73.03 | (127) ? [v0] : (set_difference(all_136_4_147, all_136_5_148) = v0 & symmetric_difference(all_136_5_148, v0) = all_136_3_146)
% 117.21/73.03 |
% 117.21/73.03 | Instantiating formula (10) with all_0_9_9, all_136_4_147 and discharging atoms in(all_136_4_147, all_0_9_9) = 0, yields:
% 117.21/73.03 | (128) element(all_136_4_147, all_0_9_9) = 0
% 117.21/73.03 |
% 117.21/73.03 | Instantiating formula (10) with all_0_9_9, all_136_5_148 and discharging atoms in(all_136_5_148, all_0_9_9) = 0, yields:
% 117.21/73.03 | (129) element(all_136_5_148, all_0_9_9) = 0
% 117.21/73.03 |
% 117.21/73.03 | Instantiating (125) with all_192_0_181, all_192_1_182, all_192_2_183, all_192_3_184, all_192_4_185 yields:
% 117.21/73.03 | (130) set_difference(all_136_5_148, all_136_4_147) = all_192_1_182 & in(all_192_1_182, all_0_3_3) = all_192_0_181 & in(all_136_3_146, all_0_3_3) = all_192_2_183 & in(all_136_4_147, all_0_3_3) = all_192_3_184 & in(all_136_5_148, all_0_3_3) = all_192_4_185 & ( ~ (all_192_3_184 = 0) | ~ (all_192_4_185 = 0) | (all_192_0_181 = 0 & all_192_2_183 = 0))
% 117.21/73.03 |
% 117.21/73.03 | Applying alpha-rule on (130) yields:
% 117.21/73.03 | (131) in(all_136_5_148, all_0_3_3) = all_192_4_185
% 117.21/73.03 | (132) in(all_192_1_182, all_0_3_3) = all_192_0_181
% 117.21/73.03 | (133) ~ (all_192_3_184 = 0) | ~ (all_192_4_185 = 0) | (all_192_0_181 = 0 & all_192_2_183 = 0)
% 117.21/73.03 | (134) in(all_136_4_147, all_0_3_3) = all_192_3_184
% 117.21/73.03 | (135) set_difference(all_136_5_148, all_136_4_147) = all_192_1_182
% 117.21/73.03 | (136) in(all_136_3_146, all_0_3_3) = all_192_2_183
% 117.21/73.03 |
% 117.21/73.03 | Instantiating (127) with all_210_0_207 yields:
% 117.21/73.03 | (137) set_difference(all_136_4_147, all_136_5_148) = all_210_0_207 & symmetric_difference(all_136_5_148, all_210_0_207) = all_136_3_146
% 117.21/73.03 |
% 117.21/73.03 | Applying alpha-rule on (137) yields:
% 117.21/73.03 | (138) set_difference(all_136_4_147, all_136_5_148) = all_210_0_207
% 117.21/73.03 | (139) symmetric_difference(all_136_5_148, all_210_0_207) = all_136_3_146
% 117.21/73.03 |
% 117.21/73.03 | Instantiating (124) with all_356_0_376, all_356_1_377 yields:
% 117.21/73.03 | (140) set_difference(all_136_4_147, all_136_5_148) = all_356_0_376 & symmetric_difference(all_136_5_148, all_136_4_147) = all_356_1_377 & set_union2(all_136_1_144, all_356_0_376) = all_356_1_377
% 117.21/73.03 |
% 117.21/73.03 | Applying alpha-rule on (140) yields:
% 117.21/73.03 | (141) set_difference(all_136_4_147, all_136_5_148) = all_356_0_376
% 117.21/73.03 | (142) symmetric_difference(all_136_5_148, all_136_4_147) = all_356_1_377
% 117.21/73.03 | (143) set_union2(all_136_1_144, all_356_0_376) = all_356_1_377
% 117.21/73.03 |
% 117.21/73.03 | Instantiating (123) with all_358_0_378 yields:
% 117.21/73.03 | (144) symmetric_difference(all_136_4_147, all_136_1_144) = all_358_0_378 & set_union2(all_136_4_147, all_136_5_148) = all_358_0_378
% 117.21/73.03 |
% 117.21/73.03 | Applying alpha-rule on (144) yields:
% 117.21/73.03 | (145) symmetric_difference(all_136_4_147, all_136_1_144) = all_358_0_378
% 117.21/73.03 | (146) set_union2(all_136_4_147, all_136_5_148) = all_358_0_378
% 117.21/73.03 |
% 117.21/73.03 | Instantiating (122) with all_360_0_379, all_360_1_380 yields:
% 117.21/73.03 | (147) set_difference(all_136_4_147, all_136_5_148) = all_360_0_379 & symmetric_difference(all_136_4_147, all_136_5_148) = all_360_1_380 & set_union2(all_360_0_379, all_136_1_144) = all_360_1_380
% 117.21/73.03 |
% 117.21/73.03 | Applying alpha-rule on (147) yields:
% 117.21/73.03 | (148) set_difference(all_136_4_147, all_136_5_148) = all_360_0_379
% 117.21/73.03 | (149) symmetric_difference(all_136_4_147, all_136_5_148) = all_360_1_380
% 117.21/73.03 | (150) set_union2(all_360_0_379, all_136_1_144) = all_360_1_380
% 117.21/73.03 |
% 117.21/73.03 | Instantiating formula (18) with all_136_4_147, all_136_5_148, all_356_0_376, all_360_0_379 and discharging atoms set_difference(all_136_4_147, all_136_5_148) = all_360_0_379, set_difference(all_136_4_147, all_136_5_148) = all_356_0_376, yields:
% 117.21/73.03 | (151) all_360_0_379 = all_356_0_376
% 117.21/73.03 |
% 117.21/73.03 | Instantiating formula (18) with all_136_4_147, all_136_5_148, all_210_0_207, all_360_0_379 and discharging atoms set_difference(all_136_4_147, all_136_5_148) = all_360_0_379, set_difference(all_136_4_147, all_136_5_148) = all_210_0_207, yields:
% 117.21/73.03 | (152) all_360_0_379 = all_210_0_207
% 117.21/73.03 |
% 117.21/73.03 | Instantiating formula (18) with all_136_5_148, all_136_4_147, all_192_1_182, all_136_1_144 and discharging atoms set_difference(all_136_5_148, all_136_4_147) = all_192_1_182, set_difference(all_136_5_148, all_136_4_147) = all_136_1_144, yields:
% 117.21/73.03 | (153) all_192_1_182 = all_136_1_144
% 117.21/73.03 |
% 117.21/73.03 | Instantiating formula (46) with all_136_4_147, all_136_5_148, all_136_3_146, all_358_0_378 and discharging atoms set_union2(all_136_4_147, all_136_5_148) = all_358_0_378, set_union2(all_136_4_147, all_136_5_148) = all_136_3_146, yields:
% 117.21/73.03 | (154) all_358_0_378 = all_136_3_146
% 117.21/73.03 |
% 117.21/73.03 | Combining equations (151,152) yields a new equation:
% 117.21/73.03 | (155) all_356_0_376 = all_210_0_207
% 117.21/73.03 |
% 117.21/73.03 | Simplifying 155 yields:
% 117.21/73.03 | (156) all_356_0_376 = all_210_0_207
% 117.21/73.03 |
% 117.21/73.03 | From (156) and (141) follows:
% 117.21/73.03 | (138) set_difference(all_136_4_147, all_136_5_148) = all_210_0_207
% 117.21/73.03 |
% 117.21/73.03 | From (153) and (135) follows:
% 117.21/73.03 | (116) set_difference(all_136_5_148, all_136_4_147) = all_136_1_144
% 117.21/73.03 |
% 117.21/73.03 | From (154) and (145) follows:
% 117.21/73.03 | (159) symmetric_difference(all_136_4_147, all_136_1_144) = all_136_3_146
% 117.21/73.03 |
% 117.21/73.03 | Instantiating formula (81) with all_136_3_146, all_210_0_207, all_136_5_148 and discharging atoms symmetric_difference(all_136_5_148, all_210_0_207) = all_136_3_146, yields:
% 117.21/73.03 | (160) ? [v0] : ? [v1] : (set_difference(all_210_0_207, all_136_5_148) = v1 & set_difference(all_136_5_148, all_210_0_207) = v0 & set_union2(v0, v1) = all_136_3_146)
% 117.21/73.03 |
% 117.21/73.03 | Instantiating formula (15) with all_210_0_207, all_136_5_148, all_136_4_147 and discharging atoms set_difference(all_136_4_147, all_136_5_148) = all_210_0_207, element(all_136_4_147, all_0_9_9) = 0, yields:
% 117.21/73.03 | (161) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (symmetric_difference(all_136_4_147, all_136_5_148) = v1 & element(all_136_5_148, all_0_9_9) = v0 & in(v1, all_0_9_9) = v2 & in(all_210_0_207, all_0_9_9) = v3 & ( ~ (v0 = 0) | (v3 = 0 & v2 = 0)))
% 117.21/73.03 |
% 117.21/73.03 | Instantiating formula (65) with all_136_3_146, all_136_1_144, all_136_4_147 and discharging atoms symmetric_difference(all_136_4_147, all_136_1_144) = all_136_3_146, element(all_136_4_147, all_0_9_9) = 0, yields:
% 117.21/73.03 | (162) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (set_difference(all_136_4_147, all_136_1_144) = v2 & element(all_136_1_144, all_0_9_9) = v0 & in(v2, all_0_9_9) = v3 & in(all_136_3_146, all_0_9_9) = v1 & ( ~ (v0 = 0) | (v3 = 0 & v1 = 0)))
% 117.21/73.04 |
% 117.21/73.04 | Instantiating formula (65) with all_360_1_380, all_136_5_148, all_136_4_147 and discharging atoms symmetric_difference(all_136_4_147, all_136_5_148) = all_360_1_380, element(all_136_4_147, all_0_9_9) = 0, yields:
% 117.21/73.04 | (163) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (set_difference(all_136_4_147, all_136_5_148) = v2 & element(all_136_5_148, all_0_9_9) = v0 & in(v2, all_0_9_9) = v3 & in(all_360_1_380, all_0_9_9) = v1 & ( ~ (v0 = 0) | (v3 = 0 & v1 = 0)))
% 117.21/73.04 |
% 117.21/73.04 | Instantiating formula (15) with all_136_1_144, all_136_4_147, all_136_5_148 and discharging atoms set_difference(all_136_5_148, all_136_4_147) = all_136_1_144, element(all_136_5_148, all_0_9_9) = 0, yields:
% 117.21/73.04 | (164) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (symmetric_difference(all_136_5_148, all_136_4_147) = v1 & element(all_136_4_147, all_0_9_9) = v0 & in(v1, all_0_9_9) = v2 & in(all_136_1_144, all_0_9_9) = v3 & ( ~ (v0 = 0) | (v3 = 0 & v2 = 0)))
% 117.21/73.04 |
% 117.21/73.04 | Instantiating formula (65) with all_136_3_146, all_210_0_207, all_136_5_148 and discharging atoms symmetric_difference(all_136_5_148, all_210_0_207) = all_136_3_146, element(all_136_5_148, all_0_9_9) = 0, yields:
% 117.21/73.04 | (165) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (set_difference(all_136_5_148, all_210_0_207) = v2 & element(all_210_0_207, all_0_9_9) = v0 & in(v2, all_0_9_9) = v3 & in(all_136_3_146, all_0_9_9) = v1 & ( ~ (v0 = 0) | (v3 = 0 & v1 = 0)))
% 117.21/73.04 |
% 117.21/73.04 | Instantiating formula (65) with all_356_1_377, all_136_4_147, all_136_5_148 and discharging atoms symmetric_difference(all_136_5_148, all_136_4_147) = all_356_1_377, element(all_136_5_148, all_0_9_9) = 0, yields:
% 117.21/73.04 | (166) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (set_difference(all_136_5_148, all_136_4_147) = v2 & element(all_136_4_147, all_0_9_9) = v0 & in(v2, all_0_9_9) = v3 & in(all_356_1_377, all_0_9_9) = v1 & ( ~ (v0 = 0) | (v3 = 0 & v1 = 0)))
% 117.21/73.04 |
% 117.21/73.04 | Instantiating (160) with all_972_0_563, all_972_1_564 yields:
% 117.21/73.04 | (167) set_difference(all_210_0_207, all_136_5_148) = all_972_0_563 & set_difference(all_136_5_148, all_210_0_207) = all_972_1_564 & set_union2(all_972_1_564, all_972_0_563) = all_136_3_146
% 117.21/73.04 |
% 117.21/73.04 | Applying alpha-rule on (167) yields:
% 117.21/73.04 | (168) set_difference(all_210_0_207, all_136_5_148) = all_972_0_563
% 117.21/73.04 | (169) set_difference(all_136_5_148, all_210_0_207) = all_972_1_564
% 117.21/73.04 | (170) set_union2(all_972_1_564, all_972_0_563) = all_136_3_146
% 117.21/73.04 |
% 117.21/73.04 | Instantiating (165) with all_1007_0_597, all_1007_1_598, all_1007_2_599, all_1007_3_600 yields:
% 117.21/73.04 | (171) set_difference(all_136_5_148, all_210_0_207) = all_1007_1_598 & element(all_210_0_207, all_0_9_9) = all_1007_3_600 & in(all_1007_1_598, all_0_9_9) = all_1007_0_597 & in(all_136_3_146, all_0_9_9) = all_1007_2_599 & ( ~ (all_1007_3_600 = 0) | (all_1007_0_597 = 0 & all_1007_2_599 = 0))
% 117.21/73.04 |
% 117.21/73.04 | Applying alpha-rule on (171) yields:
% 117.21/73.04 | (172) in(all_136_3_146, all_0_9_9) = all_1007_2_599
% 117.21/73.04 | (173) in(all_1007_1_598, all_0_9_9) = all_1007_0_597
% 117.21/73.04 | (174) element(all_210_0_207, all_0_9_9) = all_1007_3_600
% 117.21/73.04 | (175) set_difference(all_136_5_148, all_210_0_207) = all_1007_1_598
% 117.21/73.04 | (176) ~ (all_1007_3_600 = 0) | (all_1007_0_597 = 0 & all_1007_2_599 = 0)
% 117.21/73.04 |
% 117.21/73.04 | Instantiating (164) with all_1009_0_601, all_1009_1_602, all_1009_2_603, all_1009_3_604 yields:
% 117.21/73.04 | (177) symmetric_difference(all_136_5_148, all_136_4_147) = all_1009_2_603 & element(all_136_4_147, all_0_9_9) = all_1009_3_604 & in(all_1009_2_603, all_0_9_9) = all_1009_1_602 & in(all_136_1_144, all_0_9_9) = all_1009_0_601 & ( ~ (all_1009_3_604 = 0) | (all_1009_0_601 = 0 & all_1009_1_602 = 0))
% 117.21/73.04 |
% 117.21/73.04 | Applying alpha-rule on (177) yields:
% 117.21/73.04 | (178) in(all_1009_2_603, all_0_9_9) = all_1009_1_602
% 117.21/73.04 | (179) ~ (all_1009_3_604 = 0) | (all_1009_0_601 = 0 & all_1009_1_602 = 0)
% 117.21/73.04 | (180) symmetric_difference(all_136_5_148, all_136_4_147) = all_1009_2_603
% 117.21/73.04 | (181) element(all_136_4_147, all_0_9_9) = all_1009_3_604
% 117.21/73.04 | (182) in(all_136_1_144, all_0_9_9) = all_1009_0_601
% 117.21/73.04 |
% 117.21/73.04 | Instantiating (166) with all_1011_0_605, all_1011_1_606, all_1011_2_607, all_1011_3_608 yields:
% 117.21/73.04 | (183) set_difference(all_136_5_148, all_136_4_147) = all_1011_1_606 & element(all_136_4_147, all_0_9_9) = all_1011_3_608 & in(all_1011_1_606, all_0_9_9) = all_1011_0_605 & in(all_356_1_377, all_0_9_9) = all_1011_2_607 & ( ~ (all_1011_3_608 = 0) | (all_1011_0_605 = 0 & all_1011_2_607 = 0))
% 117.21/73.04 |
% 117.21/73.04 | Applying alpha-rule on (183) yields:
% 117.21/73.04 | (184) ~ (all_1011_3_608 = 0) | (all_1011_0_605 = 0 & all_1011_2_607 = 0)
% 117.21/73.04 | (185) in(all_356_1_377, all_0_9_9) = all_1011_2_607
% 117.21/73.04 | (186) element(all_136_4_147, all_0_9_9) = all_1011_3_608
% 117.21/73.04 | (187) set_difference(all_136_5_148, all_136_4_147) = all_1011_1_606
% 117.21/73.04 | (188) in(all_1011_1_606, all_0_9_9) = all_1011_0_605
% 117.21/73.04 |
% 117.21/73.04 | Instantiating (163) with all_1073_0_682, all_1073_1_683, all_1073_2_684, all_1073_3_685 yields:
% 117.21/73.04 | (189) set_difference(all_136_4_147, all_136_5_148) = all_1073_1_683 & element(all_136_5_148, all_0_9_9) = all_1073_3_685 & in(all_1073_1_683, all_0_9_9) = all_1073_0_682 & in(all_360_1_380, all_0_9_9) = all_1073_2_684 & ( ~ (all_1073_3_685 = 0) | (all_1073_0_682 = 0 & all_1073_2_684 = 0))
% 117.21/73.04 |
% 117.21/73.04 | Applying alpha-rule on (189) yields:
% 117.21/73.04 | (190) in(all_360_1_380, all_0_9_9) = all_1073_2_684
% 117.21/73.04 | (191) element(all_136_5_148, all_0_9_9) = all_1073_3_685
% 117.21/73.04 | (192) ~ (all_1073_3_685 = 0) | (all_1073_0_682 = 0 & all_1073_2_684 = 0)
% 117.21/73.04 | (193) set_difference(all_136_4_147, all_136_5_148) = all_1073_1_683
% 117.21/73.04 | (194) in(all_1073_1_683, all_0_9_9) = all_1073_0_682
% 117.21/73.04 |
% 117.21/73.04 | Instantiating (162) with all_1075_0_686, all_1075_1_687, all_1075_2_688, all_1075_3_689 yields:
% 117.21/73.04 | (195) set_difference(all_136_4_147, all_136_1_144) = all_1075_1_687 & element(all_136_1_144, all_0_9_9) = all_1075_3_689 & in(all_1075_1_687, all_0_9_9) = all_1075_0_686 & in(all_136_3_146, all_0_9_9) = all_1075_2_688 & ( ~ (all_1075_3_689 = 0) | (all_1075_0_686 = 0 & all_1075_2_688 = 0))
% 117.21/73.04 |
% 117.21/73.04 | Applying alpha-rule on (195) yields:
% 117.21/73.04 | (196) in(all_1075_1_687, all_0_9_9) = all_1075_0_686
% 117.21/73.04 | (197) ~ (all_1075_3_689 = 0) | (all_1075_0_686 = 0 & all_1075_2_688 = 0)
% 117.21/73.04 | (198) in(all_136_3_146, all_0_9_9) = all_1075_2_688
% 117.21/73.04 | (199) set_difference(all_136_4_147, all_136_1_144) = all_1075_1_687
% 117.21/73.04 | (200) element(all_136_1_144, all_0_9_9) = all_1075_3_689
% 117.21/73.04 |
% 117.21/73.04 | Instantiating (161) with all_1091_0_701, all_1091_1_702, all_1091_2_703, all_1091_3_704 yields:
% 117.21/73.04 | (201) symmetric_difference(all_136_4_147, all_136_5_148) = all_1091_2_703 & element(all_136_5_148, all_0_9_9) = all_1091_3_704 & in(all_1091_2_703, all_0_9_9) = all_1091_1_702 & in(all_210_0_207, all_0_9_9) = all_1091_0_701 & ( ~ (all_1091_3_704 = 0) | (all_1091_0_701 = 0 & all_1091_1_702 = 0))
% 117.21/73.04 |
% 117.21/73.04 | Applying alpha-rule on (201) yields:
% 117.21/73.04 | (202) symmetric_difference(all_136_4_147, all_136_5_148) = all_1091_2_703
% 117.21/73.04 | (203) ~ (all_1091_3_704 = 0) | (all_1091_0_701 = 0 & all_1091_1_702 = 0)
% 117.21/73.04 | (204) in(all_210_0_207, all_0_9_9) = all_1091_0_701
% 117.21/73.05 | (205) element(all_136_5_148, all_0_9_9) = all_1091_3_704
% 117.21/73.05 | (206) in(all_1091_2_703, all_0_9_9) = all_1091_1_702
% 117.21/73.05 |
% 117.21/73.05 | Instantiating formula (18) with all_136_5_148, all_210_0_207, all_972_1_564, all_1007_1_598 and discharging atoms set_difference(all_136_5_148, all_210_0_207) = all_1007_1_598, set_difference(all_136_5_148, all_210_0_207) = all_972_1_564, yields:
% 117.21/73.05 | (207) all_1007_1_598 = all_972_1_564
% 117.21/73.05 |
% 117.21/73.05 | Instantiating formula (8) with all_136_4_147, all_0_9_9, all_1011_3_608, 0 and discharging atoms element(all_136_4_147, all_0_9_9) = all_1011_3_608, element(all_136_4_147, all_0_9_9) = 0, yields:
% 117.21/73.05 | (208) all_1011_3_608 = 0
% 117.21/73.05 |
% 117.21/73.05 | Instantiating formula (8) with all_136_4_147, all_0_9_9, all_1009_3_604, all_1011_3_608 and discharging atoms element(all_136_4_147, all_0_9_9) = all_1011_3_608, element(all_136_4_147, all_0_9_9) = all_1009_3_604, yields:
% 117.21/73.05 | (209) all_1011_3_608 = all_1009_3_604
% 117.21/73.05 |
% 117.21/73.05 | Instantiating formula (8) with all_136_5_148, all_0_9_9, all_1091_3_704, 0 and discharging atoms element(all_136_5_148, all_0_9_9) = all_1091_3_704, element(all_136_5_148, all_0_9_9) = 0, yields:
% 117.21/73.05 | (210) all_1091_3_704 = 0
% 117.21/73.05 |
% 117.21/73.05 | Instantiating formula (8) with all_136_5_148, all_0_9_9, all_1073_3_685, all_1091_3_704 and discharging atoms element(all_136_5_148, all_0_9_9) = all_1091_3_704, element(all_136_5_148, all_0_9_9) = all_1073_3_685, yields:
% 117.21/73.05 | (211) all_1091_3_704 = all_1073_3_685
% 117.21/73.05 |
% 117.21/73.05 | Instantiating formula (92) with all_136_1_144, all_0_9_9, all_1009_0_601, all_136_0_143 and discharging atoms in(all_136_1_144, all_0_9_9) = all_1009_0_601, in(all_136_1_144, all_0_9_9) = all_136_0_143, yields:
% 117.21/73.05 | (212) all_1009_0_601 = all_136_0_143
% 117.21/73.05 |
% 117.21/73.05 | Instantiating formula (92) with all_136_3_146, all_0_9_9, all_1075_2_688, all_136_2_145 and discharging atoms in(all_136_3_146, all_0_9_9) = all_1075_2_688, in(all_136_3_146, all_0_9_9) = all_136_2_145, yields:
% 117.21/73.05 | (213) all_1075_2_688 = all_136_2_145
% 117.21/73.05 |
% 117.21/73.05 | Instantiating formula (92) with all_136_3_146, all_0_9_9, all_1007_2_599, all_1075_2_688 and discharging atoms in(all_136_3_146, all_0_9_9) = all_1075_2_688, in(all_136_3_146, all_0_9_9) = all_1007_2_599, yields:
% 117.21/73.05 | (214) all_1075_2_688 = all_1007_2_599
% 117.21/73.05 |
% 117.21/73.05 | Combining equations (211,210) yields a new equation:
% 117.21/73.05 | (215) all_1073_3_685 = 0
% 117.21/73.05 |
% 117.21/73.05 | Simplifying 215 yields:
% 117.21/73.05 | (216) all_1073_3_685 = 0
% 117.21/73.05 |
% 117.21/73.05 | Combining equations (214,213) yields a new equation:
% 117.21/73.05 | (217) all_1007_2_599 = all_136_2_145
% 117.21/73.05 |
% 117.21/73.05 | Simplifying 217 yields:
% 117.21/73.05 | (218) all_1007_2_599 = all_136_2_145
% 117.21/73.05 |
% 117.21/73.05 | Combining equations (208,209) yields a new equation:
% 117.21/73.05 | (219) all_1009_3_604 = 0
% 117.21/73.05 |
% 117.21/73.05 | From (207) and (175) follows:
% 117.21/73.05 | (169) set_difference(all_136_5_148, all_210_0_207) = all_972_1_564
% 117.21/73.05 |
% 117.21/73.05 | From (216) and (191) follows:
% 117.21/73.05 | (129) element(all_136_5_148, all_0_9_9) = 0
% 117.21/73.05 |
% 117.21/73.05 +-Applying beta-rule and splitting (179), into two cases.
% 117.21/73.05 |-Branch one:
% 117.21/73.05 | (222) ~ (all_1009_3_604 = 0)
% 117.21/73.05 |
% 117.21/73.05 | Equations (219) can reduce 222 to:
% 117.21/73.05 | (111) $false
% 117.21/73.05 |
% 117.21/73.05 |-The branch is then unsatisfiable
% 117.21/73.05 |-Branch two:
% 117.21/73.05 | (219) all_1009_3_604 = 0
% 117.21/73.05 | (225) all_1009_0_601 = 0 & all_1009_1_602 = 0
% 117.21/73.05 |
% 117.21/73.05 | Applying alpha-rule on (225) yields:
% 117.21/73.05 | (226) all_1009_0_601 = 0
% 117.21/73.05 | (227) all_1009_1_602 = 0
% 117.21/73.05 |
% 117.21/73.05 | Combining equations (226,212) yields a new equation:
% 117.21/73.05 | (228) all_136_0_143 = 0
% 117.21/73.05 |
% 117.21/73.05 +-Applying beta-rule and splitting (115), into two cases.
% 117.21/73.05 |-Branch one:
% 117.21/73.05 | (229) ~ (all_136_0_143 = 0)
% 117.21/73.05 |
% 117.21/73.05 | Equations (228) can reduce 229 to:
% 117.21/73.05 | (111) $false
% 117.21/73.05 |
% 117.21/73.05 |-The branch is then unsatisfiable
% 117.21/73.05 |-Branch two:
% 117.21/73.05 | (228) all_136_0_143 = 0
% 117.21/73.05 | (232) ~ (all_136_2_145 = 0)
% 117.21/73.05 |
% 117.21/73.05 +-Applying beta-rule and splitting (176), into two cases.
% 117.21/73.05 |-Branch one:
% 117.21/73.05 | (233) ~ (all_1007_3_600 = 0)
% 117.21/73.05 |
% 117.21/73.05 +-Applying beta-rule and splitting (203), into two cases.
% 117.21/73.05 |-Branch one:
% 117.21/73.05 | (234) ~ (all_1091_3_704 = 0)
% 117.21/73.05 |
% 117.21/73.05 | Equations (210) can reduce 234 to:
% 117.21/73.05 | (111) $false
% 117.21/73.05 |
% 117.21/73.05 |-The branch is then unsatisfiable
% 117.21/73.05 |-Branch two:
% 117.21/73.05 | (210) all_1091_3_704 = 0
% 117.21/73.05 | (237) all_1091_0_701 = 0 & all_1091_1_702 = 0
% 117.21/73.05 |
% 117.21/73.05 | Applying alpha-rule on (237) yields:
% 117.21/73.05 | (238) all_1091_0_701 = 0
% 117.21/73.05 | (239) all_1091_1_702 = 0
% 117.21/73.05 |
% 117.21/73.05 | From (238) and (204) follows:
% 117.21/73.05 | (240) in(all_210_0_207, all_0_9_9) = 0
% 117.21/73.05 |
% 117.21/73.05 | Instantiating formula (15) with all_972_1_564, all_210_0_207, all_136_5_148 and discharging atoms set_difference(all_136_5_148, all_210_0_207) = all_972_1_564, element(all_136_5_148, all_0_9_9) = 0, yields:
% 117.21/73.05 | (241) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (symmetric_difference(all_136_5_148, all_210_0_207) = v1 & element(all_210_0_207, all_0_9_9) = v0 & in(v1, all_0_9_9) = v2 & in(all_972_1_564, all_0_9_9) = v3 & ( ~ (v0 = 0) | (v3 = 0 & v2 = 0)))
% 117.21/73.05 |
% 117.21/73.05 | Instantiating formula (11) with all_1007_3_600, all_0_9_9, all_210_0_207 and discharging atoms element(all_210_0_207, all_0_9_9) = all_1007_3_600, yields:
% 117.21/73.05 | (242) all_1007_3_600 = 0 | ? [v0] : ( ~ (v0 = 0) & in(all_210_0_207, all_0_9_9) = v0)
% 117.21/73.05 |
% 117.21/73.05 | Instantiating formula (10) with all_0_9_9, all_210_0_207 and discharging atoms in(all_210_0_207, all_0_9_9) = 0, yields:
% 117.21/73.05 | (243) element(all_210_0_207, all_0_9_9) = 0
% 117.21/73.05 |
% 117.21/73.05 | Instantiating (241) with all_5827_0_3333, all_5827_1_3334, all_5827_2_3335, all_5827_3_3336 yields:
% 117.21/73.05 | (244) symmetric_difference(all_136_5_148, all_210_0_207) = all_5827_2_3335 & element(all_210_0_207, all_0_9_9) = all_5827_3_3336 & in(all_5827_2_3335, all_0_9_9) = all_5827_1_3334 & in(all_972_1_564, all_0_9_9) = all_5827_0_3333 & ( ~ (all_5827_3_3336 = 0) | (all_5827_0_3333 = 0 & all_5827_1_3334 = 0))
% 117.21/73.05 |
% 117.21/73.05 | Applying alpha-rule on (244) yields:
% 117.21/73.05 | (245) in(all_5827_2_3335, all_0_9_9) = all_5827_1_3334
% 117.21/73.05 | (246) in(all_972_1_564, all_0_9_9) = all_5827_0_3333
% 117.21/73.05 | (247) ~ (all_5827_3_3336 = 0) | (all_5827_0_3333 = 0 & all_5827_1_3334 = 0)
% 117.21/73.05 | (248) element(all_210_0_207, all_0_9_9) = all_5827_3_3336
% 117.21/73.05 | (249) symmetric_difference(all_136_5_148, all_210_0_207) = all_5827_2_3335
% 117.21/73.05 |
% 117.21/73.05 +-Applying beta-rule and splitting (242), into two cases.
% 117.21/73.05 |-Branch one:
% 117.21/73.05 | (250) all_1007_3_600 = 0
% 117.21/73.05 |
% 117.21/73.05 | Equations (250) can reduce 233 to:
% 117.21/73.05 | (111) $false
% 117.21/73.05 |
% 117.21/73.05 |-The branch is then unsatisfiable
% 117.21/73.05 |-Branch two:
% 117.21/73.05 | (233) ~ (all_1007_3_600 = 0)
% 117.21/73.05 | (253) ? [v0] : ( ~ (v0 = 0) & in(all_210_0_207, all_0_9_9) = v0)
% 117.21/73.05 |
% 117.21/73.05 | Instantiating formula (8) with all_210_0_207, all_0_9_9, all_5827_3_3336, all_1007_3_600 and discharging atoms element(all_210_0_207, all_0_9_9) = all_5827_3_3336, element(all_210_0_207, all_0_9_9) = all_1007_3_600, yields:
% 117.21/73.05 | (254) all_5827_3_3336 = all_1007_3_600
% 117.21/73.05 |
% 117.21/73.05 | Instantiating formula (8) with all_210_0_207, all_0_9_9, 0, all_5827_3_3336 and discharging atoms element(all_210_0_207, all_0_9_9) = all_5827_3_3336, element(all_210_0_207, all_0_9_9) = 0, yields:
% 117.21/73.06 | (255) all_5827_3_3336 = 0
% 117.21/73.06 |
% 117.21/73.06 | Combining equations (255,254) yields a new equation:
% 117.21/73.06 | (250) all_1007_3_600 = 0
% 117.21/73.06 |
% 117.21/73.06 | Equations (250) can reduce 233 to:
% 117.21/73.06 | (111) $false
% 117.21/73.06 |
% 117.21/73.06 |-The branch is then unsatisfiable
% 117.21/73.06 |-Branch two:
% 117.21/73.06 | (250) all_1007_3_600 = 0
% 117.21/73.06 | (259) all_1007_0_597 = 0 & all_1007_2_599 = 0
% 117.21/73.06 |
% 117.21/73.06 | Applying alpha-rule on (259) yields:
% 117.21/73.06 | (260) all_1007_0_597 = 0
% 117.21/73.06 | (261) all_1007_2_599 = 0
% 117.21/73.06 |
% 117.21/73.06 | Combining equations (261,218) yields a new equation:
% 117.21/73.06 | (262) all_136_2_145 = 0
% 117.21/73.06 |
% 117.21/73.06 | Equations (262) can reduce 232 to:
% 117.21/73.06 | (111) $false
% 117.21/73.06 |
% 117.21/73.06 |-The branch is then unsatisfiable
% 117.21/73.06 % SZS output end Proof for theBenchmark
% 117.21/73.06
% 117.21/73.06 72467ms
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