TSTP Solution File: SEU322+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU322+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n004.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 08:48:50 EDT 2022
% Result : Theorem 24.82s 6.52s
% Output : Proof 51.39s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SEU322+1 : TPTP v8.1.0. Released v3.3.0.
% 0.04/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n004.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 20 02:48:53 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.51/0.59 ____ _
% 0.51/0.59 ___ / __ \_____(_)___ ________ __________
% 0.51/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.51/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.51/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.51/0.59
% 0.51/0.59 A Theorem Prover for First-Order Logic
% 0.51/0.60 (ePrincess v.1.0)
% 0.51/0.60
% 0.51/0.60 (c) Philipp Rümmer, 2009-2015
% 0.51/0.60 (c) Peter Backeman, 2014-2015
% 0.51/0.60 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.51/0.60 Free software under GNU Lesser General Public License (LGPL).
% 0.51/0.60 Bug reports to peter@backeman.se
% 0.51/0.60
% 0.51/0.60 For more information, visit http://user.uu.se/~petba168/breu/
% 0.51/0.60
% 0.51/0.60 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
% 1.85/0.98 Prover 0: Preprocessing ...
% 2.80/1.28 Prover 0: Warning: ignoring some quantifiers
% 2.80/1.31 Prover 0: Constructing countermodel ...
% 7.78/2.47 Prover 0: gave up
% 7.78/2.47 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 7.78/2.52 Prover 1: Preprocessing ...
% 8.54/2.65 Prover 1: Warning: ignoring some quantifiers
% 8.81/2.66 Prover 1: Constructing countermodel ...
% 20.87/5.58 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 21.05/5.64 Prover 2: Preprocessing ...
% 22.15/5.89 Prover 2: Warning: ignoring some quantifiers
% 22.34/5.91 Prover 2: Constructing countermodel ...
% 24.82/6.52 Prover 2: proved (941ms)
% 24.82/6.52 Prover 1: stopped
% 24.82/6.52
% 24.82/6.52 No countermodel exists, formula is valid
% 24.82/6.52 % SZS status Theorem for theBenchmark
% 24.82/6.52
% 24.82/6.52 Generating proof ... Warning: ignoring some quantifiers
% 50.20/19.66 found it (size 335)
% 50.20/19.66
% 50.20/19.66 % SZS output start Proof for theBenchmark
% 50.20/19.66 Assumed formulas after preprocessing and simplification:
% 50.20/19.66 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ( ~ (v9 = 0) & ~ (v7 = 0) & ~ (v5 = 0) & subset(v4, v3) = v5 & top_str(v11) = 0 & top_str(v0) = 0 & interior(v0, v3) = v4 & the_carrier(v0) = v1 & one_sorted_str(v10) = 0 & one_sorted_str(v6) = 0 & empty_carrier(v6) = v7 & powerset(v1) = v2 & empty(v8) = v9 & empty(empty_set) = 0 & v5_membered(v8) = 0 & v5_membered(empty_set) = 0 & v4_membered(v8) = 0 & v4_membered(empty_set) = 0 & v3_membered(v8) = 0 & v3_membered(empty_set) = 0 & v2_membered(v8) = 0 & v2_membered(empty_set) = 0 & v1_membered(v8) = 0 & v1_membered(empty_set) = 0 & element(v3, v2) = 0 & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (powerset(v14) = v15) | ~ (element(v13, v15) = 0) | ~ (element(v12, v14) = v16) | ? [v17] : ( ~ (v17 = 0) & in(v12, v13) = v17)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (subset(v12, v13) = 0) | ~ (in(v14, v13) = v15) | ? [v16] : ( ~ (v16 = 0) & in(v14, v12) = v16)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (powerset(v13) = v14) | ~ (element(v12, v14) = v15) | ? [v16] : ( ~ (v16 = 0) & subset(v12, v13) = v16)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (powerset(v12) = v13) | ~ (v1_membered(v14) = v15) | ? [v16] : (( ~ (v16 = 0) & v1_membered(v12) = v16) | ( ~ (v16 = 0) & element(v14, v13) = v16))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (element(v12, v14) = v15) | ~ (in(v12, v13) = 0) | ? [v16] : ? [v17] : ( ~ (v17 = 0) & powerset(v14) = v16 & element(v13, v16) = v17)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (subset(v15, v14) = v13) | ~ (subset(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (interior(v15, v14) = v13) | ~ (interior(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (topstr_closure(v15, v14) = v13) | ~ (topstr_closure(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (subset_complement(v15, v14) = v13) | ~ (subset_complement(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (element(v15, v14) = v13) | ~ (element(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (in(v15, v14) = v13) | ~ (in(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (subset_complement(v12, v14) = v15) | ~ (in(v13, v15) = 0) | ? [v16] : ? [v17] : (( ~ (v17 = 0) & powerset(v12) = v16 & element(v14, v16) = v17) | ( ~ (v16 = 0) & in(v13, v14) = v16))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (the_carrier(v12) = v14) | ~ (powerset(v14) = v15) | ~ (element(v13, v15) = 0) | ? [v16] : ? [v17] : ((v17 = 0 & interior(v12, v13) = v16 & element(v16, v15) = 0) | ( ~ (v16 = 0) & top_str(v12) = v16))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (the_carrier(v12) = v14) | ~ (powerset(v14) = v15) | ~ (element(v13, v15) = 0) | ? [v16] : ? [v17] : ((v17 = 0 & topstr_closure(v12, v13) = v16 & element(v16, v15) = 0) | ( ~ (v16 = 0) & top_str(v12) = v16))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (powerset(v14) = v15) | ~ (element(v13, v15) = 0) | ~ (in(v12, v13) = 0) | element(v12, v14) = 0) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (powerset(v14) = v15) | ~ (element(v13, v15) = 0) | ~ (in(v12, v13) = 0) | ? [v16] : ( ~ (v16 = 0) & empty(v14) = v16)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (powerset(v12) = v13) | ~ (v5_membered(v14) = v15) | ? [v16] : ? [v17] : ? [v18] : ? [v19] : ((v19 = 0 & v18 = 0 & v17 = 0 & v16 = 0 & v15 = 0 & v4_membered(v14) = 0 & v3_membered(v14) = 0 & v2_membered(v14) = 0 & v1_membered(v14) = 0) | ( ~ (v16 = 0) & v5_membered(v12) = v16) | ( ~ (v16 = 0) & element(v14, v13) = v16))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (powerset(v12) = v13) | ~ (v4_membered(v14) = v15) | ? [v16] : ? [v17] : ? [v18] : ? [v19] : ((v19 = 0 & v18 = 0 & v17 = 0 & v16 = 0 & v15 = 0 & v5_membered(v14) = 0 & v3_membered(v14) = 0 & v2_membered(v14) = 0 & v1_membered(v14) = 0) | ( ~ (v16 = 0) & v5_membered(v12) = v16) | ( ~ (v16 = 0) & element(v14, v13) = v16))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (powerset(v12) = v13) | ~ (v4_membered(v14) = v15) | ? [v16] : ? [v17] : ? [v18] : ((v18 = 0 & v17 = 0 & v16 = 0 & v15 = 0 & v3_membered(v14) = 0 & v2_membered(v14) = 0 & v1_membered(v14) = 0) | ( ~ (v16 = 0) & v4_membered(v12) = v16) | ( ~ (v16 = 0) & element(v14, v13) = v16))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (powerset(v12) = v13) | ~ (v3_membered(v14) = v15) | ? [v16] : ? [v17] : ? [v18] : ? [v19] : ((v19 = 0 & v18 = 0 & v17 = 0 & v16 = 0 & v15 = 0 & v5_membered(v14) = 0 & v4_membered(v14) = 0 & v2_membered(v14) = 0 & v1_membered(v14) = 0) | ( ~ (v16 = 0) & v5_membered(v12) = v16) | ( ~ (v16 = 0) & element(v14, v13) = v16))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (powerset(v12) = v13) | ~ (v3_membered(v14) = v15) | ? [v16] : ? [v17] : ? [v18] : ((v18 = 0 & v17 = 0 & v16 = 0 & v15 = 0 & v4_membered(v14) = 0 & v2_membered(v14) = 0 & v1_membered(v14) = 0) | ( ~ (v16 = 0) & v4_membered(v12) = v16) | ( ~ (v16 = 0) & element(v14, v13) = v16))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (powerset(v12) = v13) | ~ (v3_membered(v14) = v15) | ? [v16] : ? [v17] : ((v17 = 0 & v16 = 0 & v15 = 0 & v2_membered(v14) = 0 & v1_membered(v14) = 0) | ( ~ (v16 = 0) & v3_membered(v12) = v16) | ( ~ (v16 = 0) & element(v14, v13) = v16))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (powerset(v12) = v13) | ~ (v2_membered(v14) = v15) | ? [v16] : ? [v17] : ? [v18] : ? [v19] : ((v19 = 0 & v18 = 0 & v17 = 0 & v16 = 0 & v15 = 0 & v5_membered(v14) = 0 & v4_membered(v14) = 0 & v3_membered(v14) = 0 & v1_membered(v14) = 0) | ( ~ (v16 = 0) & v5_membered(v12) = v16) | ( ~ (v16 = 0) & element(v14, v13) = v16))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (powerset(v12) = v13) | ~ (v2_membered(v14) = v15) | ? [v16] : ? [v17] : ? [v18] : ((v18 = 0 & v17 = 0 & v16 = 0 & v15 = 0 & v4_membered(v14) = 0 & v3_membered(v14) = 0 & v1_membered(v14) = 0) | ( ~ (v16 = 0) & v4_membered(v12) = v16) | ( ~ (v16 = 0) & element(v14, v13) = v16))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (powerset(v12) = v13) | ~ (v2_membered(v14) = v15) | ? [v16] : ? [v17] : ((v17 = 0 & v16 = 0 & v15 = 0 & v3_membered(v14) = 0 & v1_membered(v14) = 0) | ( ~ (v16 = 0) & v3_membered(v12) = v16) | ( ~ (v16 = 0) & element(v14, v13) = v16))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (powerset(v12) = v13) | ~ (v2_membered(v14) = v15) | ? [v16] : ((v16 = 0 & v15 = 0 & v1_membered(v14) = 0) | ( ~ (v16 = 0) & v2_membered(v12) = v16) | ( ~ (v16 = 0) & element(v14, v13) = v16))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (powerset(v12) = v13) | ~ (v1_membered(v14) = v15) | ? [v16] : ? [v17] : ? [v18] : ? [v19] : ((v19 = 0 & v18 = 0 & v17 = 0 & v16 = 0 & v15 = 0 & v5_membered(v14) = 0 & v4_membered(v14) = 0 & v3_membered(v14) = 0 & v2_membered(v14) = 0) | ( ~ (v16 = 0) & v5_membered(v12) = v16) | ( ~ (v16 = 0) & element(v14, v13) = v16))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (powerset(v12) = v13) | ~ (v1_membered(v14) = v15) | ? [v16] : ? [v17] : ? [v18] : ((v18 = 0 & v17 = 0 & v16 = 0 & v15 = 0 & v4_membered(v14) = 0 & v3_membered(v14) = 0 & v2_membered(v14) = 0) | ( ~ (v16 = 0) & v4_membered(v12) = v16) | ( ~ (v16 = 0) & element(v14, v13) = v16))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (powerset(v12) = v13) | ~ (v1_membered(v14) = v15) | ? [v16] : ? [v17] : ((v17 = 0 & v16 = 0 & v15 = 0 & v3_membered(v14) = 0 & v2_membered(v14) = 0) | ( ~ (v16 = 0) & v3_membered(v12) = v16) | ( ~ (v16 = 0) & element(v14, v13) = v16))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (powerset(v12) = v13) | ~ (v1_membered(v14) = v15) | ? [v16] : ((v16 = 0 & v15 = 0 & v2_membered(v14) = 0) | ( ~ (v16 = 0) & v2_membered(v12) = v16) | ( ~ (v16 = 0) & element(v14, v13) = v16))) & ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (subset(v12, v13) = v14) | ? [v15] : ? [v16] : ( ~ (v16 = 0) & powerset(v13) = v15 & element(v12, v15) = v16)) & ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (subset(v12, v13) = v14) | ? [v15] : ? [v16] : ( ~ (v16 = 0) & in(v15, v13) = v16 & in(v15, v12) = 0)) & ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (v1_membered(v12) = 0) | ~ (v1_xcmplx_0(v13) = v14) | ? [v15] : ( ~ (v15 = 0) & element(v13, v12) = v15)) & ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (element(v12, v13) = v14) | ? [v15] : ( ~ (v15 = 0) & in(v12, v13) = v15)) & ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (in(v12, v13) = v14) | ? [v15] : ((v15 = 0 & empty(v13) = 0) | ( ~ (v15 = 0) & element(v12, v13) = v15))) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (top_str(v14) = v13) | ~ (top_str(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (the_carrier(v14) = v13) | ~ (the_carrier(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (one_sorted_str(v14) = v13) | ~ (one_sorted_str(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (empty_carrier(v14) = v13) | ~ (empty_carrier(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (powerset(v14) = v13) | ~ (powerset(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (empty(v14) = v13) | ~ (empty(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (v5_membered(v14) = v13) | ~ (v5_membered(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (natural(v14) = v13) | ~ (natural(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (v4_membered(v14) = v13) | ~ (v4_membered(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (v1_int_1(v14) = v13) | ~ (v1_int_1(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (v3_membered(v14) = v13) | ~ (v3_membered(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (v1_rat_1(v14) = v13) | ~ (v1_rat_1(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (v2_membered(v14) = v13) | ~ (v2_membered(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (v1_xreal_0(v14) = v13) | ~ (v1_xreal_0(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (v1_membered(v14) = v13) | ~ (v1_membered(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (v1_xcmplx_0(v14) = v13) | ~ (v1_xcmplx_0(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (subset(v12, v13) = 0) | ~ (in(v14, v12) = 0) | in(v14, v13) = 0) & ! [v12] : ! [v13] : ! [v14] : ( ~ (interior(v12, v13) = v14) | ? [v15] : ? [v16] : ? [v17] : ((v17 = 0 & the_carrier(v12) = v15 & powerset(v15) = v16 & element(v14, v16) = 0) | ( ~ (v17 = 0) & the_carrier(v12) = v15 & powerset(v15) = v16 & element(v13, v16) = v17) | ( ~ (v15 = 0) & top_str(v12) = v15))) & ! [v12] : ! [v13] : ! [v14] : ( ~ (topstr_closure(v12, v13) = v14) | ? [v15] : ? [v16] : ? [v17] : ((v17 = 0 & the_carrier(v12) = v15 & powerset(v15) = v16 & element(v14, v16) = 0) | ( ~ (v17 = 0) & the_carrier(v12) = v15 & powerset(v15) = v16 & element(v13, v16) = v17) | ( ~ (v15 = 0) & top_str(v12) = v15))) & ! [v12] : ! [v13] : ! [v14] : ( ~ (subset_complement(v12, v13) = v14) | ? [v15] : ? [v16] : (powerset(v12) = v15 & ((v16 = 0 & element(v14, v15) = 0) | ( ~ (v16 = 0) & element(v13, v15) = v16)))) & ! [v12] : ! [v13] : ! [v14] : ( ~ (subset_complement(v12, v13) = v14) | ? [v15] : ? [v16] : ((v15 = v13 & subset_complement(v12, v14) = v13) | ( ~ (v16 = 0) & powerset(v12) = v15 & element(v13, v15) = v16))) & ! [v12] : ! [v13] : ! [v14] : ( ~ (powerset(v13) = v14) | ~ (element(v12, v14) = 0) | subset(v12, v13) = 0) & ! [v12] : ! [v13] : ! [v14] : ( ~ (powerset(v12) = v14) | ~ (element(v13, v14) = 0) | ? [v15] : (subset_complement(v12, v15) = v13 & subset_complement(v12, v13) = v15)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (powerset(v12) = v14) | ~ (element(v13, v14) = 0) | ? [v15] : (subset_complement(v12, v13) = v15 & element(v15, v14) = 0)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (powerset(v12) = v13) | ~ (element(v14, v13) = 0) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ((v19 = 0 & v18 = 0 & v17 = 0 & v16 = 0 & v15 = 0 & v5_membered(v14) = 0 & v4_membered(v14) = 0 & v3_membered(v14) = 0 & v2_membered(v14) = 0 & v1_membered(v14) = 0) | ( ~ (v15 = 0) & v5_membered(v12) = v15))) & ! [v12] : ! [v13] : ! [v14] : ( ~ (powerset(v12) = v13) | ~ (element(v14, v13) = 0) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : ((v18 = 0 & v17 = 0 & v16 = 0 & v15 = 0 & v4_membered(v14) = 0 & v3_membered(v14) = 0 & v2_membered(v14) = 0 & v1_membered(v14) = 0) | ( ~ (v15 = 0) & v4_membered(v12) = v15))) & ! [v12] : ! [v13] : ! [v14] : ( ~ (powerset(v12) = v13) | ~ (element(v14, v13) = 0) | ? [v15] : ? [v16] : ? [v17] : ((v17 = 0 & v16 = 0 & v15 = 0 & v3_membered(v14) = 0 & v2_membered(v14) = 0 & v1_membered(v14) = 0) | ( ~ (v15 = 0) & v3_membered(v12) = v15))) & ! [v12] : ! [v13] : ! [v14] : ( ~ (powerset(v12) = v13) | ~ (element(v14, v13) = 0) | ? [v15] : ? [v16] : ((v16 = 0 & v15 = 0 & v2_membered(v14) = 0 & v1_membered(v14) = 0) | ( ~ (v15 = 0) & v2_membered(v12) = v15))) & ! [v12] : ! [v13] : ! [v14] : ( ~ (powerset(v12) = v13) | ~ (element(v14, v13) = 0) | ? [v15] : ((v15 = 0 & v1_membered(v14) = 0) | ( ~ (v15 = 0) & v1_membered(v12) = v15))) & ! [v12] : ! [v13] : ! [v14] : ( ~ (empty(v14) = 0) | ~ (in(v12, v13) = 0) | ? [v15] : ? [v16] : ( ~ (v16 = 0) & powerset(v14) = v15 & element(v13, v15) = v16)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (v5_membered(v12) = 0) | ~ (natural(v13) = v14) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : ((v18 = 0 & v17 = 0 & v16 = 0 & v15 = 0 & v14 = 0 & v1_int_1(v13) = 0 & v1_rat_1(v13) = 0 & v1_xreal_0(v13) = 0 & v1_xcmplx_0(v13) = 0) | ( ~ (v15 = 0) & element(v13, v12) = v15))) & ! [v12] : ! [v13] : ! [v14] : ( ~ (v5_membered(v12) = 0) | ~ (v1_int_1(v13) = v14) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : ((v18 = 0 & v17 = 0 & v16 = 0 & v15 = 0 & v14 = 0 & natural(v13) = 0 & v1_rat_1(v13) = 0 & v1_xreal_0(v13) = 0 & v1_xcmplx_0(v13) = 0) | ( ~ (v15 = 0) & element(v13, v12) = v15))) & ! [v12] : ! [v13] : ! [v14] : ( ~ (v5_membered(v12) = 0) | ~ (v1_rat_1(v13) = v14) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : ((v18 = 0 & v17 = 0 & v16 = 0 & v15 = 0 & v14 = 0 & natural(v13) = 0 & v1_int_1(v13) = 0 & v1_xreal_0(v13) = 0 & v1_xcmplx_0(v13) = 0) | ( ~ (v15 = 0) & element(v13, v12) = v15))) & ! [v12] : ! [v13] : ! [v14] : ( ~ (v5_membered(v12) = 0) | ~ (v1_xreal_0(v13) = v14) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : ((v18 = 0 & v17 = 0 & v16 = 0 & v15 = 0 & v14 = 0 & natural(v13) = 0 & v1_int_1(v13) = 0 & v1_rat_1(v13) = 0 & v1_xcmplx_0(v13) = 0) | ( ~ (v15 = 0) & element(v13, v12) = v15))) & ! [v12] : ! [v13] : ! [v14] : ( ~ (v5_membered(v12) = 0) | ~ (v1_xcmplx_0(v13) = v14) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : ((v18 = 0 & v17 = 0 & v16 = 0 & v15 = 0 & v14 = 0 & natural(v13) = 0 & v1_int_1(v13) = 0 & v1_rat_1(v13) = 0 & v1_xreal_0(v13) = 0) | ( ~ (v15 = 0) & element(v13, v12) = v15))) & ! [v12] : ! [v13] : ! [v14] : ( ~ (v4_membered(v12) = 0) | ~ (v1_int_1(v13) = v14) | ? [v15] : ? [v16] : ? [v17] : ((v17 = 0 & v16 = 0 & v15 = 0 & v14 = 0 & v1_rat_1(v13) = 0 & v1_xreal_0(v13) = 0 & v1_xcmplx_0(v13) = 0) | ( ~ (v15 = 0) & element(v13, v12) = v15))) & ! [v12] : ! [v13] : ! [v14] : ( ~ (v4_membered(v12) = 0) | ~ (v1_rat_1(v13) = v14) | ? [v15] : ? [v16] : ? [v17] : ((v17 = 0 & v16 = 0 & v15 = 0 & v14 = 0 & v1_int_1(v13) = 0 & v1_xreal_0(v13) = 0 & v1_xcmplx_0(v13) = 0) | ( ~ (v15 = 0) & element(v13, v12) = v15))) & ! [v12] : ! [v13] : ! [v14] : ( ~ (v4_membered(v12) = 0) | ~ (v1_xreal_0(v13) = v14) | ? [v15] : ? [v16] : ? [v17] : ((v17 = 0 & v16 = 0 & v15 = 0 & v14 = 0 & v1_int_1(v13) = 0 & v1_rat_1(v13) = 0 & v1_xcmplx_0(v13) = 0) | ( ~ (v15 = 0) & element(v13, v12) = v15))) & ! [v12] : ! [v13] : ! [v14] : ( ~ (v4_membered(v12) = 0) | ~ (v1_xcmplx_0(v13) = v14) | ? [v15] : ? [v16] : ? [v17] : ((v17 = 0 & v16 = 0 & v15 = 0 & v14 = 0 & v1_int_1(v13) = 0 & v1_rat_1(v13) = 0 & v1_xreal_0(v13) = 0) | ( ~ (v15 = 0) & element(v13, v12) = v15))) & ! [v12] : ! [v13] : ! [v14] : ( ~ (v3_membered(v12) = 0) | ~ (v1_rat_1(v13) = v14) | ? [v15] : ? [v16] : ((v16 = 0 & v15 = 0 & v14 = 0 & v1_xreal_0(v13) = 0 & v1_xcmplx_0(v13) = 0) | ( ~ (v15 = 0) & element(v13, v12) = v15))) & ! [v12] : ! [v13] : ! [v14] : ( ~ (v3_membered(v12) = 0) | ~ (v1_xreal_0(v13) = v14) | ? [v15] : ? [v16] : ((v16 = 0 & v15 = 0 & v14 = 0 & v1_rat_1(v13) = 0 & v1_xcmplx_0(v13) = 0) | ( ~ (v15 = 0) & element(v13, v12) = v15))) & ! [v12] : ! [v13] : ! [v14] : ( ~ (v3_membered(v12) = 0) | ~ (v1_xcmplx_0(v13) = v14) | ? [v15] : ? [v16] : ((v16 = 0 & v15 = 0 & v14 = 0 & v1_rat_1(v13) = 0 & v1_xreal_0(v13) = 0) | ( ~ (v15 = 0) & element(v13, v12) = v15))) & ! [v12] : ! [v13] : ! [v14] : ( ~ (v2_membered(v12) = 0) | ~ (v1_xreal_0(v13) = v14) | ? [v15] : ((v15 = 0 & v14 = 0 & v1_xcmplx_0(v13) = 0) | ( ~ (v15 = 0) & element(v13, v12) = v15))) & ! [v12] : ! [v13] : ! [v14] : ( ~ (v2_membered(v12) = 0) | ~ (v1_xcmplx_0(v13) = v14) | ? [v15] : ((v15 = 0 & v14 = 0 & v1_xreal_0(v13) = 0) | ( ~ (v15 = 0) & element(v13, v12) = v15))) & ! [v12] : ! [v13] : (v13 = v12 | ~ (empty(v13) = 0) | ~ (empty(v12) = 0)) & ! [v12] : ! [v13] : (v13 = 0 | ~ (subset(v12, v12) = v13)) & ! [v12] : ! [v13] : (v13 = 0 | ~ (one_sorted_str(v12) = v13) | ? [v14] : ( ~ (v14 = 0) & top_str(v12) = v14)) & ! [v12] : ! [v13] : (v13 = 0 | ~ (empty_carrier(v12) = v13) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ((v17 = 0 & ~ (v18 = 0) & the_carrier(v12) = v14 & powerset(v14) = v15 & empty(v16) = v18 & element(v16, v15) = 0) | ( ~ (v14 = 0) & one_sorted_str(v12) = v14))) & ! [v12] : ! [v13] : (v13 = 0 | ~ (empty_carrier(v12) = v13) | ? [v14] : ? [v15] : (( ~ (v15 = 0) & the_carrier(v12) = v14 & empty(v14) = v15) | ( ~ (v14 = 0) & one_sorted_str(v12) = v14))) & ! [v12] : ! [v13] : (v13 = 0 | ~ (empty_carrier(v12) = v13) | ? [v14] : ? [v15] : (( ~ (v14 = 0) & one_sorted_str(v12) = v14) | (the_carrier(v12) = v14 & powerset(v14) = v15 & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (subset_complement(v14, v16) = v17) | ~ (in(v18, v17) = v19) | ? [v20] : (( ~ (v20 = 0) & element(v18, v14) = v20) | ( ~ (v20 = 0) & element(v16, v15) = v20) | (( ~ (v19 = 0) | ( ~ (v20 = 0) & in(v18, v16) = v20)) & (v19 = 0 | (v20 = 0 & in(v18, v16) = 0))))) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (subset_complement(v14, v16) = v17) | ~ (in(v18, v16) = v19) | ? [v20] : (( ~ (v20 = 0) & element(v18, v14) = v20) | ( ~ (v20 = 0) & element(v16, v15) = v20) | (( ~ (v19 = 0) | ( ~ (v20 = 0) & in(v18, v17) = v20)) & (v19 = 0 | (v20 = 0 & in(v18, v17) = 0))))) & ! [v16] : ! [v17] : ! [v18] : ( ~ (subset_complement(v14, v16) = v17) | ~ (element(v18, v14) = 0) | ? [v19] : ? [v20] : (( ~ (v19 = 0) & element(v16, v15) = v19) | (((v20 = 0 & in(v18, v16) = 0) | (v19 = 0 & in(v18, v17) = 0)) & (( ~ (v20 = 0) & in(v18, v16) = v20) | ( ~ (v19 = 0) & in(v18, v17) = v19))))) & ! [v16] : ( ~ (element(v16, v15) = 0) | ? [v17] : (subset_complement(v14, v16) = v17 & ! [v18] : ! [v19] : ( ~ (in(v18, v17) = v19) | ? [v20] : (( ~ (v20 = 0) & element(v18, v14) = v20) | (( ~ (v19 = 0) | ( ~ (v20 = 0) & in(v18, v16) = v20)) & (v19 = 0 | (v20 = 0 & in(v18, v16) = 0))))) & ! [v18] : ! [v19] : ( ~ (in(v18, v16) = v19) | ? [v20] : (( ~ (v20 = 0) & element(v18, v14) = v20) | (( ~ (v19 = 0) | ( ~ (v20 = 0) & in(v18, v17) = v20)) & (v19 = 0 | (v20 = 0 & in(v18, v17) = 0))))) & ! [v18] : ( ~ (element(v18, v14) = 0) | ? [v19] : ? [v20] : (((v20 = 0 & in(v18, v16) = 0) | (v19 = 0 & in(v18, v17) = 0)) & (( ~ (v20 = 0) & in(v18, v16) = v20) | ( ~ (v19 = 0) & in(v18, v17) = v19))))))))) & ! [v12] : ! [v13] : (v13 = 0 | ~ (v4_membered(v12) = v13) | ? [v14] : ( ~ (v14 = 0) & v5_membered(v12) = v14)) & ! [v12] : ! [v13] : (v13 = 0 | ~ (v3_membered(v12) = v13) | ? [v14] : ( ~ (v14 = 0) & v4_membered(v12) = v14)) & ! [v12] : ! [v13] : (v13 = 0 | ~ (v2_membered(v12) = v13) | ? [v14] : ( ~ (v14 = 0) & v3_membered(v12) = v14)) & ! [v12] : ! [v13] : (v13 = 0 | ~ (v1_membered(v12) = v13) | ? [v14] : ( ~ (v14 = 0) & v2_membered(v12) = v14)) & ! [v12] : ! [v13] : ( ~ (subset(v12, v13) = 0) | ? [v14] : (powerset(v13) = v14 & element(v12, v14) = 0)) & ! [v12] : ! [v13] : ( ~ (the_carrier(v12) = v13) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : ((v16 = 0 & ~ (v17 = 0) & powerset(v13) = v14 & empty(v15) = v17 & element(v15, v14) = 0) | (v14 = 0 & empty_carrier(v12) = 0) | ( ~ (v14 = 0) & one_sorted_str(v12) = v14))) & ! [v12] : ! [v13] : ( ~ (the_carrier(v12) = v13) | ? [v14] : ? [v15] : (( ~ (v14 = 0) & one_sorted_str(v12) = v14) | (((v15 = 0 & empty(v13) = 0) | ( ~ (v14 = 0) & empty_carrier(v12) = v14)) & ((v14 = 0 & empty_carrier(v12) = 0) | ( ~ (v15 = 0) & empty(v13) = v15))))) & ! [v12] : ! [v13] : ( ~ (the_carrier(v12) = v13) | ? [v14] : ((v14 = 0 & empty_carrier(v12) = 0) | ( ~ (v14 = 0) & one_sorted_str(v12) = v14) | ( ~ (v14 = 0) & empty(v13) = v14))) & ! [v12] : ! [v13] : ( ~ (the_carrier(v12) = v13) | ? [v14] : ((v14 = 0 & empty_carrier(v12) = 0) | ( ~ (v14 = 0) & one_sorted_str(v12) = v14) | (powerset(v13) = v14 & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (subset_complement(v13, v15) = v16) | ~ (in(v17, v16) = v18) | ? [v19] : (( ~ (v19 = 0) & element(v17, v13) = v19) | ( ~ (v19 = 0) & element(v15, v14) = v19) | (( ~ (v18 = 0) | ( ~ (v19 = 0) & in(v17, v15) = v19)) & (v18 = 0 | (v19 = 0 & in(v17, v15) = 0))))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (subset_complement(v13, v15) = v16) | ~ (in(v17, v15) = v18) | ? [v19] : (( ~ (v19 = 0) & element(v17, v13) = v19) | ( ~ (v19 = 0) & element(v15, v14) = v19) | (( ~ (v18 = 0) | ( ~ (v19 = 0) & in(v17, v16) = v19)) & (v18 = 0 | (v19 = 0 & in(v17, v16) = 0))))) & ! [v15] : ! [v16] : ! [v17] : ( ~ (subset_complement(v13, v15) = v16) | ~ (element(v17, v13) = 0) | ? [v18] : ? [v19] : (( ~ (v18 = 0) & element(v15, v14) = v18) | (((v19 = 0 & in(v17, v15) = 0) | (v18 = 0 & in(v17, v16) = 0)) & (( ~ (v19 = 0) & in(v17, v15) = v19) | ( ~ (v18 = 0) & in(v17, v16) = v18))))) & ! [v15] : ( ~ (element(v15, v14) = 0) | ? [v16] : (subset_complement(v13, v15) = v16 & ! [v17] : ! [v18] : ( ~ (in(v17, v16) = v18) | ? [v19] : (( ~ (v19 = 0) & element(v17, v13) = v19) | (( ~ (v18 = 0) | ( ~ (v19 = 0) & in(v17, v15) = v19)) & (v18 = 0 | (v19 = 0 & in(v17, v15) = 0))))) & ! [v17] : ! [v18] : ( ~ (in(v17, v15) = v18) | ? [v19] : (( ~ (v19 = 0) & element(v17, v13) = v19) | (( ~ (v18 = 0) | ( ~ (v19 = 0) & in(v17, v16) = v19)) & (v18 = 0 | (v19 = 0 & in(v17, v16) = 0))))) & ! [v17] : ( ~ (element(v17, v13) = 0) | ? [v18] : ? [v19] : (((v19 = 0 & in(v17, v15) = 0) | (v18 = 0 & in(v17, v16) = 0)) & (( ~ (v19 = 0) & in(v17, v15) = v19) | ( ~ (v18 = 0) & in(v17, v16) = v18))))))))) & ! [v12] : ! [v13] : ( ~ (the_carrier(v12) = v13) | ? [v14] : (( ~ (v14 = 0) & top_str(v12) = v14) | (powerset(v13) = v14 & ! [v15] : ! [v16] : ( ~ (interior(v12, v15) = v16) | ? [v17] : ? [v18] : ? [v19] : ((v19 = v16 & topstr_closure(v12, v17) = v18 & subset_complement(v13, v18) = v16 & subset_complement(v13, v15) = v17) | ( ~ (v17 = 0) & element(v15, v14) = v17))) & ! [v15] : ! [v16] : ( ~ (subset_complement(v13, v15) = v16) | ? [v17] : ? [v18] : ? [v19] : ((v19 = v17 & interior(v12, v15) = v17 & topstr_closure(v12, v16) = v18 & subset_complement(v13, v18) = v17) | ( ~ (v17 = 0) & element(v15, v14) = v17))) & ! [v15] : ( ~ (element(v15, v14) = 0) | ? [v16] : ? [v17] : ? [v18] : (interior(v12, v15) = v16 & topstr_closure(v12, v17) = v18 & subset_complement(v13, v18) = v16 & subset_complement(v13, v15) = v17))))) & ! [v12] : ! [v13] : ( ~ (the_carrier(v12) = v13) | ? [v14] : (( ~ (v14 = 0) & top_str(v12) = v14) | (powerset(v13) = v14 & ! [v15] : ! [v16] : ( ~ (topstr_closure(v12, v15) = v16) | ? [v17] : ((v17 = 0 & subset(v15, v16) = 0) | ( ~ (v17 = 0) & element(v15, v14) = v17))) & ! [v15] : ( ~ (element(v15, v14) = 0) | ? [v16] : (subset(v15, v16) = 0 & topstr_closure(v12, v15) = v16))))) & ! [v12] : ! [v13] : ( ~ (empty_carrier(v12) = v13) | ? [v14] : ? [v15] : (( ~ (v14 = 0) & one_sorted_str(v12) = v14) | (( ~ (v13 = 0) | (v15 = 0 & the_carrier(v12) = v14 & empty(v14) = 0)) & (v13 = 0 | ( ~ (v15 = 0) & the_carrier(v12) = v14 & empty(v14) = v15))))) & ! [v12] : ! [v13] : ( ~ (v5_membered(v12) = v13) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : ((v17 = 0 & v16 = 0 & v15 = 0 & v14 = 0 & v13 = 0 & v4_membered(v12) = 0 & v3_membered(v12) = 0 & v2_membered(v12) = 0 & v1_membered(v12) = 0) | ( ~ (v14 = 0) & empty(v12) = v14))) & ! [v12] : ! [v13] : ( ~ (v5_membered(v12) = 0) | ~ (element(v13, v12) = 0) | (natural(v13) = 0 & v1_int_1(v13) = 0 & v1_rat_1(v13) = 0 & v1_xreal_0(v13) = 0 & v1_xcmplx_0(v13) = 0)) & ! [v12] : ! [v13] : ( ~ (v4_membered(v12) = v13) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : ((v17 = 0 & v16 = 0 & v15 = 0 & v14 = 0 & v13 = 0 & v5_membered(v12) = 0 & v3_membered(v12) = 0 & v2_membered(v12) = 0 & v1_membered(v12) = 0) | ( ~ (v14 = 0) & empty(v12) = v14))) & ! [v12] : ! [v13] : ( ~ (v4_membered(v12) = 0) | ~ (element(v13, v12) = 0) | (v1_int_1(v13) = 0 & v1_rat_1(v13) = 0 & v1_xreal_0(v13) = 0 & v1_xcmplx_0(v13) = 0)) & ! [v12] : ! [v13] : ( ~ (v3_membered(v12) = v13) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : ((v17 = 0 & v16 = 0 & v15 = 0 & v14 = 0 & v13 = 0 & v5_membered(v12) = 0 & v4_membered(v12) = 0 & v2_membered(v12) = 0 & v1_membered(v12) = 0) | ( ~ (v14 = 0) & empty(v12) = v14))) & ! [v12] : ! [v13] : ( ~ (v3_membered(v12) = 0) | ~ (element(v13, v12) = 0) | (v1_rat_1(v13) = 0 & v1_xreal_0(v13) = 0 & v1_xcmplx_0(v13) = 0)) & ! [v12] : ! [v13] : ( ~ (v2_membered(v12) = v13) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : ((v17 = 0 & v16 = 0 & v15 = 0 & v14 = 0 & v13 = 0 & v5_membered(v12) = 0 & v4_membered(v12) = 0 & v3_membered(v12) = 0 & v1_membered(v12) = 0) | ( ~ (v14 = 0) & empty(v12) = v14))) & ! [v12] : ! [v13] : ( ~ (v2_membered(v12) = 0) | ~ (element(v13, v12) = 0) | (v1_xreal_0(v13) = 0 & v1_xcmplx_0(v13) = 0)) & ! [v12] : ! [v13] : ( ~ (v1_membered(v12) = v13) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : ((v17 = 0 & v16 = 0 & v15 = 0 & v14 = 0 & v13 = 0 & v5_membered(v12) = 0 & v4_membered(v12) = 0 & v3_membered(v12) = 0 & v2_membered(v12) = 0) | ( ~ (v14 = 0) & empty(v12) = v14))) & ! [v12] : ! [v13] : ( ~ (v1_membered(v12) = 0) | ~ (element(v13, v12) = 0) | v1_xcmplx_0(v13) = 0) & ! [v12] : ! [v13] : ( ~ (element(v12, v13) = 0) | ? [v14] : ((v14 = 0 & empty(v13) = 0) | (v14 = 0 & in(v12, v13) = 0))) & ! [v12] : ! [v13] : ( ~ (in(v13, v12) = 0) | ? [v14] : ( ~ (v14 = 0) & in(v12, v13) = v14)) & ! [v12] : ! [v13] : ( ~ (in(v12, v13) = 0) | element(v12, v13) = 0) & ! [v12] : ! [v13] : ( ~ (in(v12, v13) = 0) | ? [v14] : ( ~ (v14 = 0) & empty(v13) = v14)) & ! [v12] : ! [v13] : ( ~ (in(v12, v13) = 0) | ? [v14] : ( ~ (v14 = 0) & in(v13, v12) = v14)) & ! [v12] : (v12 = empty_set | ~ (empty(v12) = 0)) & ! [v12] : ( ~ (top_str(v12) = 0) | one_sorted_str(v12) = 0) & ! [v12] : ( ~ (top_str(v12) = 0) | ? [v13] : ? [v14] : (the_carrier(v12) = v13 & powerset(v13) = v14 & ! [v15] : ! [v16] : ( ~ (interior(v12, v15) = v16) | ? [v17] : ? [v18] : ? [v19] : ((v19 = v16 & topstr_closure(v12, v17) = v18 & subset_complement(v13, v18) = v16 & subset_complement(v13, v15) = v17) | ( ~ (v17 = 0) & element(v15, v14) = v17))) & ! [v15] : ! [v16] : ( ~ (subset_complement(v13, v15) = v16) | ? [v17] : ? [v18] : ? [v19] : ((v19 = v17 & interior(v12, v15) = v17 & topstr_closure(v12, v16) = v18 & subset_complement(v13, v18) = v17) | ( ~ (v17 = 0) & element(v15, v14) = v17))) & ! [v15] : ( ~ (element(v15, v14) = 0) | ? [v16] : ? [v17] : ? [v18] : (interior(v12, v15) = v16 & topstr_closure(v12, v17) = v18 & subset_complement(v13, v18) = v16 & subset_complement(v13, v15) = v17)))) & ! [v12] : ( ~ (top_str(v12) = 0) | ? [v13] : ? [v14] : (the_carrier(v12) = v13 & powerset(v13) = v14 & ! [v15] : ! [v16] : ( ~ (topstr_closure(v12, v15) = v16) | ? [v17] : ((v17 = 0 & subset(v15, v16) = 0) | ( ~ (v17 = 0) & element(v15, v14) = v17))) & ! [v15] : ( ~ (element(v15, v14) = 0) | ? [v16] : (subset(v15, v16) = 0 & topstr_closure(v12, v15) = v16)))) & ! [v12] : ( ~ (one_sorted_str(v12) = 0) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ((v16 = 0 & ~ (v17 = 0) & the_carrier(v12) = v13 & powerset(v13) = v14 & empty(v15) = v17 & element(v15, v14) = 0) | (v13 = 0 & empty_carrier(v12) = 0))) & ! [v12] : ( ~ (one_sorted_str(v12) = 0) | ? [v13] : ? [v14] : ? [v15] : (((v15 = 0 & the_carrier(v12) = v14 & empty(v14) = 0) | ( ~ (v13 = 0) & empty_carrier(v12) = v13)) & ((v13 = 0 & empty_carrier(v12) = 0) | ( ~ (v15 = 0) & the_carrier(v12) = v14 & empty(v14) = v15)))) & ! [v12] : ( ~ (one_sorted_str(v12) = 0) | ? [v13] : ? [v14] : ((v13 = 0 & empty_carrier(v12) = 0) | ( ~ (v14 = 0) & the_carrier(v12) = v13 & empty(v13) = v14))) & ! [v12] : ( ~ (one_sorted_str(v12) = 0) | ? [v13] : ? [v14] : ((v13 = 0 & empty_carrier(v12) = 0) | (the_carrier(v12) = v13 & powerset(v13) = v14 & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (subset_complement(v13, v15) = v16) | ~ (in(v17, v16) = v18) | ? [v19] : (( ~ (v19 = 0) & element(v17, v13) = v19) | ( ~ (v19 = 0) & element(v15, v14) = v19) | (( ~ (v18 = 0) | ( ~ (v19 = 0) & in(v17, v15) = v19)) & (v18 = 0 | (v19 = 0 & in(v17, v15) = 0))))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (subset_complement(v13, v15) = v16) | ~ (in(v17, v15) = v18) | ? [v19] : (( ~ (v19 = 0) & element(v17, v13) = v19) | ( ~ (v19 = 0) & element(v15, v14) = v19) | (( ~ (v18 = 0) | ( ~ (v19 = 0) & in(v17, v16) = v19)) & (v18 = 0 | (v19 = 0 & in(v17, v16) = 0))))) & ! [v15] : ! [v16] : ! [v17] : ( ~ (subset_complement(v13, v15) = v16) | ~ (element(v17, v13) = 0) | ? [v18] : ? [v19] : (( ~ (v18 = 0) & element(v15, v14) = v18) | (((v19 = 0 & in(v17, v15) = 0) | (v18 = 0 & in(v17, v16) = 0)) & (( ~ (v19 = 0) & in(v17, v15) = v19) | ( ~ (v18 = 0) & in(v17, v16) = v18))))) & ! [v15] : ( ~ (element(v15, v14) = 0) | ? [v16] : (subset_complement(v13, v15) = v16 & ! [v17] : ! [v18] : ( ~ (in(v17, v16) = v18) | ? [v19] : (( ~ (v19 = 0) & element(v17, v13) = v19) | (( ~ (v18 = 0) | ( ~ (v19 = 0) & in(v17, v15) = v19)) & (v18 = 0 | (v19 = 0 & in(v17, v15) = 0))))) & ! [v17] : ! [v18] : ( ~ (in(v17, v15) = v18) | ? [v19] : (( ~ (v19 = 0) & element(v17, v13) = v19) | (( ~ (v18 = 0) | ( ~ (v19 = 0) & in(v17, v16) = v19)) & (v18 = 0 | (v19 = 0 & in(v17, v16) = 0))))) & ! [v17] : ( ~ (element(v17, v13) = 0) | ? [v18] : ? [v19] : (((v19 = 0 & in(v17, v15) = 0) | (v18 = 0 & in(v17, v16) = 0)) & (( ~ (v19 = 0) & in(v17, v15) = v19) | ( ~ (v18 = 0) & in(v17, v16) = v18))))))))) & ! [v12] : ( ~ (empty(v12) = 0) | (v5_membered(v12) = 0 & v4_membered(v12) = 0 & v3_membered(v12) = 0 & v2_membered(v12) = 0 & v1_membered(v12) = 0)) & ! [v12] : ( ~ (v5_membered(v12) = 0) | v4_membered(v12) = 0) & ! [v12] : ( ~ (v5_membered(v12) = 0) | ? [v13] : (powerset(v12) = v13 & ! [v14] : ! [v15] : ( ~ (v5_membered(v14) = v15) | ? [v16] : ? [v17] : ? [v18] : ? [v19] : ((v19 = 0 & v18 = 0 & v17 = 0 & v16 = 0 & v15 = 0 & v4_membered(v14) = 0 & v3_membered(v14) = 0 & v2_membered(v14) = 0 & v1_membered(v14) = 0) | ( ~ (v16 = 0) & element(v14, v13) = v16))) & ! [v14] : ! [v15] : ( ~ (v4_membered(v14) = v15) | ? [v16] : ? [v17] : ? [v18] : ? [v19] : ((v19 = 0 & v18 = 0 & v17 = 0 & v16 = 0 & v15 = 0 & v5_membered(v14) = 0 & v3_membered(v14) = 0 & v2_membered(v14) = 0 & v1_membered(v14) = 0) | ( ~ (v16 = 0) & element(v14, v13) = v16))) & ! [v14] : ! [v15] : ( ~ (v3_membered(v14) = v15) | ? [v16] : ? [v17] : ? [v18] : ? [v19] : ((v19 = 0 & v18 = 0 & v17 = 0 & v16 = 0 & v15 = 0 & v5_membered(v14) = 0 & v4_membered(v14) = 0 & v2_membered(v14) = 0 & v1_membered(v14) = 0) | ( ~ (v16 = 0) & element(v14, v13) = v16))) & ! [v14] : ! [v15] : ( ~ (v2_membered(v14) = v15) | ? [v16] : ? [v17] : ? [v18] : ? [v19] : ((v19 = 0 & v18 = 0 & v17 = 0 & v16 = 0 & v15 = 0 & v5_membered(v14) = 0 & v4_membered(v14) = 0 & v3_membered(v14) = 0 & v1_membered(v14) = 0) | ( ~ (v16 = 0) & element(v14, v13) = v16))) & ! [v14] : ! [v15] : ( ~ (v1_membered(v14) = v15) | ? [v16] : ? [v17] : ? [v18] : ? [v19] : ((v19 = 0 & v18 = 0 & v17 = 0 & v16 = 0 & v15 = 0 & v5_membered(v14) = 0 & v4_membered(v14) = 0 & v3_membered(v14) = 0 & v2_membered(v14) = 0) | ( ~ (v16 = 0) & element(v14, v13) = v16))) & ! [v14] : ( ~ (element(v14, v13) = 0) | (v5_membered(v14) = 0 & v4_membered(v14) = 0 & v3_membered(v14) = 0 & v2_membered(v14) = 0 & v1_membered(v14) = 0)))) & ! [v12] : ( ~ (v4_membered(v12) = 0) | v3_membered(v12) = 0) & ! [v12] : ( ~ (v4_membered(v12) = 0) | ? [v13] : (powerset(v12) = v13 & ! [v14] : ! [v15] : ( ~ (v4_membered(v14) = v15) | ? [v16] : ? [v17] : ? [v18] : ((v18 = 0 & v17 = 0 & v16 = 0 & v15 = 0 & v3_membered(v14) = 0 & v2_membered(v14) = 0 & v1_membered(v14) = 0) | ( ~ (v16 = 0) & element(v14, v13) = v16))) & ! [v14] : ! [v15] : ( ~ (v3_membered(v14) = v15) | ? [v16] : ? [v17] : ? [v18] : ((v18 = 0 & v17 = 0 & v16 = 0 & v15 = 0 & v4_membered(v14) = 0 & v2_membered(v14) = 0 & v1_membered(v14) = 0) | ( ~ (v16 = 0) & element(v14, v13) = v16))) & ! [v14] : ! [v15] : ( ~ (v2_membered(v14) = v15) | ? [v16] : ? [v17] : ? [v18] : ((v18 = 0 & v17 = 0 & v16 = 0 & v15 = 0 & v4_membered(v14) = 0 & v3_membered(v14) = 0 & v1_membered(v14) = 0) | ( ~ (v16 = 0) & element(v14, v13) = v16))) & ! [v14] : ! [v15] : ( ~ (v1_membered(v14) = v15) | ? [v16] : ? [v17] : ? [v18] : ((v18 = 0 & v17 = 0 & v16 = 0 & v15 = 0 & v4_membered(v14) = 0 & v3_membered(v14) = 0 & v2_membered(v14) = 0) | ( ~ (v16 = 0) & element(v14, v13) = v16))) & ! [v14] : ( ~ (element(v14, v13) = 0) | (v4_membered(v14) = 0 & v3_membered(v14) = 0 & v2_membered(v14) = 0 & v1_membered(v14) = 0)))) & ! [v12] : ( ~ (v3_membered(v12) = 0) | v2_membered(v12) = 0) & ! [v12] : ( ~ (v3_membered(v12) = 0) | ? [v13] : (powerset(v12) = v13 & ! [v14] : ! [v15] : ( ~ (v3_membered(v14) = v15) | ? [v16] : ? [v17] : ((v17 = 0 & v16 = 0 & v15 = 0 & v2_membered(v14) = 0 & v1_membered(v14) = 0) | ( ~ (v16 = 0) & element(v14, v13) = v16))) & ! [v14] : ! [v15] : ( ~ (v2_membered(v14) = v15) | ? [v16] : ? [v17] : ((v17 = 0 & v16 = 0 & v15 = 0 & v3_membered(v14) = 0 & v1_membered(v14) = 0) | ( ~ (v16 = 0) & element(v14, v13) = v16))) & ! [v14] : ! [v15] : ( ~ (v1_membered(v14) = v15) | ? [v16] : ? [v17] : ((v17 = 0 & v16 = 0 & v15 = 0 & v3_membered(v14) = 0 & v2_membered(v14) = 0) | ( ~ (v16 = 0) & element(v14, v13) = v16))) & ! [v14] : ( ~ (element(v14, v13) = 0) | (v3_membered(v14) = 0 & v2_membered(v14) = 0 & v1_membered(v14) = 0)))) & ! [v12] : ( ~ (v2_membered(v12) = 0) | v1_membered(v12) = 0) & ! [v12] : ( ~ (v2_membered(v12) = 0) | ? [v13] : (powerset(v12) = v13 & ! [v14] : ! [v15] : ( ~ (v2_membered(v14) = v15) | ? [v16] : ((v16 = 0 & v15 = 0 & v1_membered(v14) = 0) | ( ~ (v16 = 0) & element(v14, v13) = v16))) & ! [v14] : ! [v15] : ( ~ (v1_membered(v14) = v15) | ? [v16] : ((v16 = 0 & v15 = 0 & v2_membered(v14) = 0) | ( ~ (v16 = 0) & element(v14, v13) = v16))) & ! [v14] : ( ~ (element(v14, v13) = 0) | (v2_membered(v14) = 0 & v1_membered(v14) = 0)))) & ! [v12] : ( ~ (v1_membered(v12) = 0) | ? [v13] : (powerset(v12) = v13 & ! [v14] : ! [v15] : (v15 = 0 | ~ (v1_membered(v14) = v15) | ? [v16] : ( ~ (v16 = 0) & element(v14, v13) = v16)) & ! [v14] : ( ~ (element(v14, v13) = 0) | v1_membered(v14) = 0))) & ? [v12] : ? [v13] : ? [v14] : subset(v13, v12) = v14 & ? [v12] : ? [v13] : ? [v14] : interior(v13, v12) = v14 & ? [v12] : ? [v13] : ? [v14] : topstr_closure(v13, v12) = v14 & ? [v12] : ? [v13] : ? [v14] : subset_complement(v13, v12) = v14 & ? [v12] : ? [v13] : ? [v14] : element(v13, v12) = v14 & ? [v12] : ? [v13] : ? [v14] : in(v13, v12) = v14 & ? [v12] : ? [v13] : top_str(v12) = v13 & ? [v12] : ? [v13] : the_carrier(v12) = v13 & ? [v12] : ? [v13] : one_sorted_str(v12) = v13 & ? [v12] : ? [v13] : empty_carrier(v12) = v13 & ? [v12] : ? [v13] : powerset(v12) = v13 & ? [v12] : ? [v13] : empty(v12) = v13 & ? [v12] : ? [v13] : v5_membered(v12) = v13 & ? [v12] : ? [v13] : natural(v12) = v13 & ? [v12] : ? [v13] : v4_membered(v12) = v13 & ? [v12] : ? [v13] : v1_int_1(v12) = v13 & ? [v12] : ? [v13] : v3_membered(v12) = v13 & ? [v12] : ? [v13] : v1_rat_1(v12) = v13 & ? [v12] : ? [v13] : v2_membered(v12) = v13 & ? [v12] : ? [v13] : v1_xreal_0(v12) = v13 & ? [v12] : ? [v13] : v1_membered(v12) = v13 & ? [v12] : ? [v13] : v1_xcmplx_0(v12) = v13 & ? [v12] : ? [v13] : element(v13, v12) = 0)
% 50.52/19.78 | 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 yields:
% 50.52/19.78 | (1) ~ (all_0_2_2 = 0) & ~ (all_0_4_4 = 0) & ~ (all_0_6_6 = 0) & subset(all_0_7_7, all_0_8_8) = all_0_6_6 & top_str(all_0_0_0) = 0 & top_str(all_0_11_11) = 0 & interior(all_0_11_11, all_0_8_8) = all_0_7_7 & the_carrier(all_0_11_11) = all_0_10_10 & one_sorted_str(all_0_1_1) = 0 & one_sorted_str(all_0_5_5) = 0 & empty_carrier(all_0_5_5) = all_0_4_4 & powerset(all_0_10_10) = all_0_9_9 & empty(all_0_3_3) = all_0_2_2 & empty(empty_set) = 0 & v5_membered(all_0_3_3) = 0 & v5_membered(empty_set) = 0 & v4_membered(all_0_3_3) = 0 & v4_membered(empty_set) = 0 & v3_membered(all_0_3_3) = 0 & v3_membered(empty_set) = 0 & v2_membered(all_0_3_3) = 0 & v2_membered(empty_set) = 0 & v1_membered(all_0_3_3) = 0 & v1_membered(empty_set) = 0 & element(all_0_8_8, all_0_9_9) = 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 | ~ (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v2, v0) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v0) = v1) | ~ (v1_membered(v2) = v3) | ? [v4] : (( ~ (v4 = 0) & v1_membered(v0) = v4) | ( ~ (v4 = 0) & element(v2, 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 | ~ (interior(v3, v2) = v1) | ~ (interior(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (topstr_closure(v3, v2) = v1) | ~ (topstr_closure(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset_complement(v3, v2) = v1) | ~ (subset_complement(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_complement(v0, v2) = v3) | ~ (in(v1, v3) = 0) | ? [v4] : ? [v5] : (( ~ (v5 = 0) & powerset(v0) = v4 & element(v2, v4) = v5) | ( ~ (v4 = 0) & in(v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (the_carrier(v0) = v2) | ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & interior(v0, v1) = v4 & element(v4, v3) = 0) | ( ~ (v4 = 0) & top_str(v0) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (the_carrier(v0) = v2) | ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & topstr_closure(v0, v1) = v4 & element(v4, v3) = 0) | ( ~ (v4 = 0) & top_str(v0) = v4))) & ! [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] : ! [v3] : ( ~ (powerset(v0) = v1) | ~ (v5_membered(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & v4_membered(v2) = 0 & v3_membered(v2) = 0 & v2_membered(v2) = 0 & v1_membered(v2) = 0) | ( ~ (v4 = 0) & v5_membered(v0) = v4) | ( ~ (v4 = 0) & element(v2, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v0) = v1) | ~ (v4_membered(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & v5_membered(v2) = 0 & v3_membered(v2) = 0 & v2_membered(v2) = 0 & v1_membered(v2) = 0) | ( ~ (v4 = 0) & v5_membered(v0) = v4) | ( ~ (v4 = 0) & element(v2, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v0) = v1) | ~ (v4_membered(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & v3_membered(v2) = 0 & v2_membered(v2) = 0 & v1_membered(v2) = 0) | ( ~ (v4 = 0) & v4_membered(v0) = v4) | ( ~ (v4 = 0) & element(v2, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v0) = v1) | ~ (v3_membered(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & v5_membered(v2) = 0 & v4_membered(v2) = 0 & v2_membered(v2) = 0 & v1_membered(v2) = 0) | ( ~ (v4 = 0) & v5_membered(v0) = v4) | ( ~ (v4 = 0) & element(v2, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v0) = v1) | ~ (v3_membered(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & v4_membered(v2) = 0 & v2_membered(v2) = 0 & v1_membered(v2) = 0) | ( ~ (v4 = 0) & v4_membered(v0) = v4) | ( ~ (v4 = 0) & element(v2, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v0) = v1) | ~ (v3_membered(v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & v3 = 0 & v2_membered(v2) = 0 & v1_membered(v2) = 0) | ( ~ (v4 = 0) & v3_membered(v0) = v4) | ( ~ (v4 = 0) & element(v2, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v0) = v1) | ~ (v2_membered(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & v5_membered(v2) = 0 & v4_membered(v2) = 0 & v3_membered(v2) = 0 & v1_membered(v2) = 0) | ( ~ (v4 = 0) & v5_membered(v0) = v4) | ( ~ (v4 = 0) & element(v2, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v0) = v1) | ~ (v2_membered(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & v4_membered(v2) = 0 & v3_membered(v2) = 0 & v1_membered(v2) = 0) | ( ~ (v4 = 0) & v4_membered(v0) = v4) | ( ~ (v4 = 0) & element(v2, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v0) = v1) | ~ (v2_membered(v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & v3 = 0 & v3_membered(v2) = 0 & v1_membered(v2) = 0) | ( ~ (v4 = 0) & v3_membered(v0) = v4) | ( ~ (v4 = 0) & element(v2, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v0) = v1) | ~ (v2_membered(v2) = v3) | ? [v4] : ((v4 = 0 & v3 = 0 & v1_membered(v2) = 0) | ( ~ (v4 = 0) & v2_membered(v0) = v4) | ( ~ (v4 = 0) & element(v2, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v0) = v1) | ~ (v1_membered(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & v5_membered(v2) = 0 & v4_membered(v2) = 0 & v3_membered(v2) = 0 & v2_membered(v2) = 0) | ( ~ (v4 = 0) & v5_membered(v0) = v4) | ( ~ (v4 = 0) & element(v2, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v0) = v1) | ~ (v1_membered(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & v4_membered(v2) = 0 & v3_membered(v2) = 0 & v2_membered(v2) = 0) | ( ~ (v4 = 0) & v4_membered(v0) = v4) | ( ~ (v4 = 0) & element(v2, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v0) = v1) | ~ (v1_membered(v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & v3 = 0 & v3_membered(v2) = 0 & v2_membered(v2) = 0) | ( ~ (v4 = 0) & v3_membered(v0) = v4) | ( ~ (v4 = 0) & element(v2, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v0) = v1) | ~ (v1_membered(v2) = v3) | ? [v4] : ((v4 = 0 & v3 = 0 & v2_membered(v2) = 0) | ( ~ (v4 = 0) & v2_membered(v0) = v4) | ( ~ (v4 = 0) & element(v2, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v1) = v3 & element(v0, v3) = v4)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (v1_membered(v0) = 0) | ~ (v1_xcmplx_0(v1) = v2) | ? [v3] : ( ~ (v3 = 0) & element(v1, v0) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v0, v1) = v2) | ? [v3] : ((v3 = 0 & empty(v1) = 0) | ( ~ (v3 = 0) & element(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (top_str(v2) = v1) | ~ (top_str(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (the_carrier(v2) = v1) | ~ (the_carrier(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (one_sorted_str(v2) = v1) | ~ (one_sorted_str(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty_carrier(v2) = v1) | ~ (empty_carrier(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (v5_membered(v2) = v1) | ~ (v5_membered(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (natural(v2) = v1) | ~ (natural(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (v4_membered(v2) = v1) | ~ (v4_membered(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (v1_int_1(v2) = v1) | ~ (v1_int_1(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (v3_membered(v2) = v1) | ~ (v3_membered(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (v1_rat_1(v2) = v1) | ~ (v1_rat_1(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (v2_membered(v2) = v1) | ~ (v2_membered(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (v1_xreal_0(v2) = v1) | ~ (v1_xreal_0(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (v1_membered(v2) = v1) | ~ (v1_membered(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (v1_xcmplx_0(v2) = v1) | ~ (v1_xcmplx_0(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (interior(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & the_carrier(v0) = v3 & powerset(v3) = v4 & element(v2, v4) = 0) | ( ~ (v5 = 0) & the_carrier(v0) = v3 & powerset(v3) = v4 & element(v1, v4) = v5) | ( ~ (v3 = 0) & top_str(v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (topstr_closure(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & the_carrier(v0) = v3 & powerset(v3) = v4 & element(v2, v4) = 0) | ( ~ (v5 = 0) & the_carrier(v0) = v3 & powerset(v3) = v4 & element(v1, v4) = v5) | ( ~ (v3 = 0) & top_str(v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_complement(v0, v1) = v2) | ? [v3] : ? [v4] : (powerset(v0) = v3 & ((v4 = 0 & element(v2, v3) = 0) | ( ~ (v4 = 0) & element(v1, v3) = v4)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_complement(v0, v1) = v2) | ? [v3] : ? [v4] : ((v3 = v1 & subset_complement(v0, v2) = v1) | ( ~ (v4 = 0) & powerset(v0) = v3 & element(v1, v3) = v4))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | subset(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v2) | ~ (element(v1, v2) = 0) | ? [v3] : (subset_complement(v0, v3) = v1 & subset_complement(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v2) | ~ (element(v1, v2) = 0) | ? [v3] : (subset_complement(v0, v1) = v3 & element(v3, v2) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ (element(v2, v1) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & v5_membered(v2) = 0 & v4_membered(v2) = 0 & v3_membered(v2) = 0 & v2_membered(v2) = 0 & v1_membered(v2) = 0) | ( ~ (v3 = 0) & v5_membered(v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ (element(v2, v1) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & v4_membered(v2) = 0 & v3_membered(v2) = 0 & v2_membered(v2) = 0 & v1_membered(v2) = 0) | ( ~ (v3 = 0) & v4_membered(v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ (element(v2, v1) = 0) | ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & v3 = 0 & v3_membered(v2) = 0 & v2_membered(v2) = 0 & v1_membered(v2) = 0) | ( ~ (v3 = 0) & v3_membered(v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ (element(v2, v1) = 0) | ? [v3] : ? [v4] : ((v4 = 0 & v3 = 0 & v2_membered(v2) = 0 & v1_membered(v2) = 0) | ( ~ (v3 = 0) & v2_membered(v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ (element(v2, v1) = 0) | ? [v3] : ((v3 = 0 & v1_membered(v2) = 0) | ( ~ (v3 = 0) & v1_membered(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] : ! [v2] : ( ~ (v5_membered(v0) = 0) | ~ (natural(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & v2 = 0 & v1_int_1(v1) = 0 & v1_rat_1(v1) = 0 & v1_xreal_0(v1) = 0 & v1_xcmplx_0(v1) = 0) | ( ~ (v3 = 0) & element(v1, v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (v5_membered(v0) = 0) | ~ (v1_int_1(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & v2 = 0 & natural(v1) = 0 & v1_rat_1(v1) = 0 & v1_xreal_0(v1) = 0 & v1_xcmplx_0(v1) = 0) | ( ~ (v3 = 0) & element(v1, v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (v5_membered(v0) = 0) | ~ (v1_rat_1(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & v2 = 0 & natural(v1) = 0 & v1_int_1(v1) = 0 & v1_xreal_0(v1) = 0 & v1_xcmplx_0(v1) = 0) | ( ~ (v3 = 0) & element(v1, v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (v5_membered(v0) = 0) | ~ (v1_xreal_0(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & v2 = 0 & natural(v1) = 0 & v1_int_1(v1) = 0 & v1_rat_1(v1) = 0 & v1_xcmplx_0(v1) = 0) | ( ~ (v3 = 0) & element(v1, v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (v5_membered(v0) = 0) | ~ (v1_xcmplx_0(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & v2 = 0 & natural(v1) = 0 & v1_int_1(v1) = 0 & v1_rat_1(v1) = 0 & v1_xreal_0(v1) = 0) | ( ~ (v3 = 0) & element(v1, v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (v4_membered(v0) = 0) | ~ (v1_int_1(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & v3 = 0 & v2 = 0 & v1_rat_1(v1) = 0 & v1_xreal_0(v1) = 0 & v1_xcmplx_0(v1) = 0) | ( ~ (v3 = 0) & element(v1, v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (v4_membered(v0) = 0) | ~ (v1_rat_1(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & v3 = 0 & v2 = 0 & v1_int_1(v1) = 0 & v1_xreal_0(v1) = 0 & v1_xcmplx_0(v1) = 0) | ( ~ (v3 = 0) & element(v1, v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (v4_membered(v0) = 0) | ~ (v1_xreal_0(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & v3 = 0 & v2 = 0 & v1_int_1(v1) = 0 & v1_rat_1(v1) = 0 & v1_xcmplx_0(v1) = 0) | ( ~ (v3 = 0) & element(v1, v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (v4_membered(v0) = 0) | ~ (v1_xcmplx_0(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & v3 = 0 & v2 = 0 & v1_int_1(v1) = 0 & v1_rat_1(v1) = 0 & v1_xreal_0(v1) = 0) | ( ~ (v3 = 0) & element(v1, v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (v3_membered(v0) = 0) | ~ (v1_rat_1(v1) = v2) | ? [v3] : ? [v4] : ((v4 = 0 & v3 = 0 & v2 = 0 & v1_xreal_0(v1) = 0 & v1_xcmplx_0(v1) = 0) | ( ~ (v3 = 0) & element(v1, v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (v3_membered(v0) = 0) | ~ (v1_xreal_0(v1) = v2) | ? [v3] : ? [v4] : ((v4 = 0 & v3 = 0 & v2 = 0 & v1_rat_1(v1) = 0 & v1_xcmplx_0(v1) = 0) | ( ~ (v3 = 0) & element(v1, v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (v3_membered(v0) = 0) | ~ (v1_xcmplx_0(v1) = v2) | ? [v3] : ? [v4] : ((v4 = 0 & v3 = 0 & v2 = 0 & v1_rat_1(v1) = 0 & v1_xreal_0(v1) = 0) | ( ~ (v3 = 0) & element(v1, v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (v2_membered(v0) = 0) | ~ (v1_xreal_0(v1) = v2) | ? [v3] : ((v3 = 0 & v2 = 0 & v1_xcmplx_0(v1) = 0) | ( ~ (v3 = 0) & element(v1, v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (v2_membered(v0) = 0) | ~ (v1_xcmplx_0(v1) = v2) | ? [v3] : ((v3 = 0 & v2 = 0 & v1_xreal_0(v1) = 0) | ( ~ (v3 = 0) & element(v1, v0) = v3))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (one_sorted_str(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & top_str(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (empty_carrier(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ((v5 = 0 & ~ (v6 = 0) & the_carrier(v0) = v2 & powerset(v2) = v3 & empty(v4) = v6 & element(v4, v3) = 0) | ( ~ (v2 = 0) & one_sorted_str(v0) = v2))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (empty_carrier(v0) = v1) | ? [v2] : ? [v3] : (( ~ (v3 = 0) & the_carrier(v0) = v2 & empty(v2) = v3) | ( ~ (v2 = 0) & one_sorted_str(v0) = v2))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (empty_carrier(v0) = v1) | ? [v2] : ? [v3] : (( ~ (v2 = 0) & one_sorted_str(v0) = v2) | (the_carrier(v0) = v2 & powerset(v2) = v3 & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (subset_complement(v2, v4) = v5) | ~ (in(v6, v5) = v7) | ? [v8] : (( ~ (v8 = 0) & element(v6, v2) = v8) | ( ~ (v8 = 0) & element(v4, v3) = v8) | (( ~ (v7 = 0) | ( ~ (v8 = 0) & in(v6, v4) = v8)) & (v7 = 0 | (v8 = 0 & in(v6, v4) = 0))))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (subset_complement(v2, v4) = v5) | ~ (in(v6, v4) = v7) | ? [v8] : (( ~ (v8 = 0) & element(v6, v2) = v8) | ( ~ (v8 = 0) & element(v4, v3) = v8) | (( ~ (v7 = 0) | ( ~ (v8 = 0) & in(v6, v5) = v8)) & (v7 = 0 | (v8 = 0 & in(v6, v5) = 0))))) & ! [v4] : ! [v5] : ! [v6] : ( ~ (subset_complement(v2, v4) = v5) | ~ (element(v6, v2) = 0) | ? [v7] : ? [v8] : (( ~ (v7 = 0) & element(v4, v3) = v7) | (((v8 = 0 & in(v6, v4) = 0) | (v7 = 0 & in(v6, v5) = 0)) & (( ~ (v8 = 0) & in(v6, v4) = v8) | ( ~ (v7 = 0) & in(v6, v5) = v7))))) & ! [v4] : ( ~ (element(v4, v3) = 0) | ? [v5] : (subset_complement(v2, v4) = v5 & ! [v6] : ! [v7] : ( ~ (in(v6, v5) = v7) | ? [v8] : (( ~ (v8 = 0) & element(v6, v2) = v8) | (( ~ (v7 = 0) | ( ~ (v8 = 0) & in(v6, v4) = v8)) & (v7 = 0 | (v8 = 0 & in(v6, v4) = 0))))) & ! [v6] : ! [v7] : ( ~ (in(v6, v4) = v7) | ? [v8] : (( ~ (v8 = 0) & element(v6, v2) = v8) | (( ~ (v7 = 0) | ( ~ (v8 = 0) & in(v6, v5) = v8)) & (v7 = 0 | (v8 = 0 & in(v6, v5) = 0))))) & ! [v6] : ( ~ (element(v6, v2) = 0) | ? [v7] : ? [v8] : (((v8 = 0 & in(v6, v4) = 0) | (v7 = 0 & in(v6, v5) = 0)) & (( ~ (v8 = 0) & in(v6, v4) = v8) | ( ~ (v7 = 0) & in(v6, v5) = v7))))))))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (v4_membered(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & v5_membered(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (v3_membered(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & v4_membered(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (v2_membered(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & v3_membered(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (v1_membered(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & v2_membered(v0) = v2)) & ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (powerset(v1) = v2 & element(v0, v2) = 0)) & ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ((v4 = 0 & ~ (v5 = 0) & powerset(v1) = v2 & empty(v3) = v5 & element(v3, v2) = 0) | (v2 = 0 & empty_carrier(v0) = 0) | ( ~ (v2 = 0) & one_sorted_str(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ? [v2] : ? [v3] : (( ~ (v2 = 0) & one_sorted_str(v0) = v2) | (((v3 = 0 & empty(v1) = 0) | ( ~ (v2 = 0) & empty_carrier(v0) = v2)) & ((v2 = 0 & empty_carrier(v0) = 0) | ( ~ (v3 = 0) & empty(v1) = v3))))) & ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ? [v2] : ((v2 = 0 & empty_carrier(v0) = 0) | ( ~ (v2 = 0) & one_sorted_str(v0) = v2) | ( ~ (v2 = 0) & empty(v1) = v2))) & ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ? [v2] : ((v2 = 0 & empty_carrier(v0) = 0) | ( ~ (v2 = 0) & one_sorted_str(v0) = v2) | (powerset(v1) = v2 & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (subset_complement(v1, v3) = v4) | ~ (in(v5, v4) = v6) | ? [v7] : (( ~ (v7 = 0) & element(v5, v1) = v7) | ( ~ (v7 = 0) & element(v3, v2) = v7) | (( ~ (v6 = 0) | ( ~ (v7 = 0) & in(v5, v3) = v7)) & (v6 = 0 | (v7 = 0 & in(v5, v3) = 0))))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (subset_complement(v1, v3) = v4) | ~ (in(v5, v3) = v6) | ? [v7] : (( ~ (v7 = 0) & element(v5, v1) = v7) | ( ~ (v7 = 0) & element(v3, v2) = v7) | (( ~ (v6 = 0) | ( ~ (v7 = 0) & in(v5, v4) = v7)) & (v6 = 0 | (v7 = 0 & in(v5, v4) = 0))))) & ! [v3] : ! [v4] : ! [v5] : ( ~ (subset_complement(v1, v3) = v4) | ~ (element(v5, v1) = 0) | ? [v6] : ? [v7] : (( ~ (v6 = 0) & element(v3, v2) = v6) | (((v7 = 0 & in(v5, v3) = 0) | (v6 = 0 & in(v5, v4) = 0)) & (( ~ (v7 = 0) & in(v5, v3) = v7) | ( ~ (v6 = 0) & in(v5, v4) = v6))))) & ! [v3] : ( ~ (element(v3, v2) = 0) | ? [v4] : (subset_complement(v1, v3) = v4 & ! [v5] : ! [v6] : ( ~ (in(v5, v4) = v6) | ? [v7] : (( ~ (v7 = 0) & element(v5, v1) = v7) | (( ~ (v6 = 0) | ( ~ (v7 = 0) & in(v5, v3) = v7)) & (v6 = 0 | (v7 = 0 & in(v5, v3) = 0))))) & ! [v5] : ! [v6] : ( ~ (in(v5, v3) = v6) | ? [v7] : (( ~ (v7 = 0) & element(v5, v1) = v7) | (( ~ (v6 = 0) | ( ~ (v7 = 0) & in(v5, v4) = v7)) & (v6 = 0 | (v7 = 0 & in(v5, v4) = 0))))) & ! [v5] : ( ~ (element(v5, v1) = 0) | ? [v6] : ? [v7] : (((v7 = 0 & in(v5, v3) = 0) | (v6 = 0 & in(v5, v4) = 0)) & (( ~ (v7 = 0) & in(v5, v3) = v7) | ( ~ (v6 = 0) & in(v5, v4) = v6))))))))) & ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ? [v2] : (( ~ (v2 = 0) & top_str(v0) = v2) | (powerset(v1) = v2 & ! [v3] : ! [v4] : ( ~ (interior(v0, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ((v7 = v4 & topstr_closure(v0, v5) = v6 & subset_complement(v1, v6) = v4 & subset_complement(v1, v3) = v5) | ( ~ (v5 = 0) & element(v3, v2) = v5))) & ! [v3] : ! [v4] : ( ~ (subset_complement(v1, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ((v7 = v5 & interior(v0, v3) = v5 & topstr_closure(v0, v4) = v6 & subset_complement(v1, v6) = v5) | ( ~ (v5 = 0) & element(v3, v2) = v5))) & ! [v3] : ( ~ (element(v3, v2) = 0) | ? [v4] : ? [v5] : ? [v6] : (interior(v0, v3) = v4 & topstr_closure(v0, v5) = v6 & subset_complement(v1, v6) = v4 & subset_complement(v1, v3) = v5))))) & ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ? [v2] : (( ~ (v2 = 0) & top_str(v0) = v2) | (powerset(v1) = v2 & ! [v3] : ! [v4] : ( ~ (topstr_closure(v0, v3) = v4) | ? [v5] : ((v5 = 0 & subset(v3, v4) = 0) | ( ~ (v5 = 0) & element(v3, v2) = v5))) & ! [v3] : ( ~ (element(v3, v2) = 0) | ? [v4] : (subset(v3, v4) = 0 & topstr_closure(v0, v3) = v4))))) & ! [v0] : ! [v1] : ( ~ (empty_carrier(v0) = v1) | ? [v2] : ? [v3] : (( ~ (v2 = 0) & one_sorted_str(v0) = v2) | (( ~ (v1 = 0) | (v3 = 0 & the_carrier(v0) = v2 & empty(v2) = 0)) & (v1 = 0 | ( ~ (v3 = 0) & the_carrier(v0) = v2 & empty(v2) = v3))))) & ! [v0] : ! [v1] : ( ~ (v5_membered(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & v3 = 0 & v2 = 0 & v1 = 0 & v4_membered(v0) = 0 & v3_membered(v0) = 0 & v2_membered(v0) = 0 & v1_membered(v0) = 0) | ( ~ (v2 = 0) & empty(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (v5_membered(v0) = 0) | ~ (element(v1, v0) = 0) | (natural(v1) = 0 & v1_int_1(v1) = 0 & v1_rat_1(v1) = 0 & v1_xreal_0(v1) = 0 & v1_xcmplx_0(v1) = 0)) & ! [v0] : ! [v1] : ( ~ (v4_membered(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & v3 = 0 & v2 = 0 & v1 = 0 & v5_membered(v0) = 0 & v3_membered(v0) = 0 & v2_membered(v0) = 0 & v1_membered(v0) = 0) | ( ~ (v2 = 0) & empty(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (v4_membered(v0) = 0) | ~ (element(v1, v0) = 0) | (v1_int_1(v1) = 0 & v1_rat_1(v1) = 0 & v1_xreal_0(v1) = 0 & v1_xcmplx_0(v1) = 0)) & ! [v0] : ! [v1] : ( ~ (v3_membered(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & v3 = 0 & v2 = 0 & v1 = 0 & v5_membered(v0) = 0 & v4_membered(v0) = 0 & v2_membered(v0) = 0 & v1_membered(v0) = 0) | ( ~ (v2 = 0) & empty(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (v3_membered(v0) = 0) | ~ (element(v1, v0) = 0) | (v1_rat_1(v1) = 0 & v1_xreal_0(v1) = 0 & v1_xcmplx_0(v1) = 0)) & ! [v0] : ! [v1] : ( ~ (v2_membered(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & v3 = 0 & v2 = 0 & v1 = 0 & v5_membered(v0) = 0 & v4_membered(v0) = 0 & v3_membered(v0) = 0 & v1_membered(v0) = 0) | ( ~ (v2 = 0) & empty(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (v2_membered(v0) = 0) | ~ (element(v1, v0) = 0) | (v1_xreal_0(v1) = 0 & v1_xcmplx_0(v1) = 0)) & ! [v0] : ! [v1] : ( ~ (v1_membered(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & v3 = 0 & v2 = 0 & v1 = 0 & v5_membered(v0) = 0 & v4_membered(v0) = 0 & v3_membered(v0) = 0 & v2_membered(v0) = 0) | ( ~ (v2 = 0) & empty(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (v1_membered(v0) = 0) | ~ (element(v1, v0) = 0) | v1_xcmplx_0(v1) = 0) & ! [v0] : ! [v1] : ( ~ (element(v0, v1) = 0) | ? [v2] : ((v2 = 0 & empty(v1) = 0) | (v2 = 0 & in(v0, v1) = 0))) & ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | element(v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) & ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0)) & ! [v0] : ( ~ (top_str(v0) = 0) | one_sorted_str(v0) = 0) & ! [v0] : ( ~ (top_str(v0) = 0) | ? [v1] : ? [v2] : (the_carrier(v0) = v1 & powerset(v1) = v2 & ! [v3] : ! [v4] : ( ~ (interior(v0, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ((v7 = v4 & topstr_closure(v0, v5) = v6 & subset_complement(v1, v6) = v4 & subset_complement(v1, v3) = v5) | ( ~ (v5 = 0) & element(v3, v2) = v5))) & ! [v3] : ! [v4] : ( ~ (subset_complement(v1, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ((v7 = v5 & interior(v0, v3) = v5 & topstr_closure(v0, v4) = v6 & subset_complement(v1, v6) = v5) | ( ~ (v5 = 0) & element(v3, v2) = v5))) & ! [v3] : ( ~ (element(v3, v2) = 0) | ? [v4] : ? [v5] : ? [v6] : (interior(v0, v3) = v4 & topstr_closure(v0, v5) = v6 & subset_complement(v1, v6) = v4 & subset_complement(v1, v3) = v5)))) & ! [v0] : ( ~ (top_str(v0) = 0) | ? [v1] : ? [v2] : (the_carrier(v0) = v1 & powerset(v1) = v2 & ! [v3] : ! [v4] : ( ~ (topstr_closure(v0, v3) = v4) | ? [v5] : ((v5 = 0 & subset(v3, v4) = 0) | ( ~ (v5 = 0) & element(v3, v2) = v5))) & ! [v3] : ( ~ (element(v3, v2) = 0) | ? [v4] : (subset(v3, v4) = 0 & topstr_closure(v0, v3) = v4)))) & ! [v0] : ( ~ (one_sorted_str(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ((v4 = 0 & ~ (v5 = 0) & the_carrier(v0) = v1 & powerset(v1) = v2 & empty(v3) = v5 & element(v3, v2) = 0) | (v1 = 0 & empty_carrier(v0) = 0))) & ! [v0] : ( ~ (one_sorted_str(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (((v3 = 0 & the_carrier(v0) = v2 & empty(v2) = 0) | ( ~ (v1 = 0) & empty_carrier(v0) = v1)) & ((v1 = 0 & empty_carrier(v0) = 0) | ( ~ (v3 = 0) & the_carrier(v0) = v2 & empty(v2) = v3)))) & ! [v0] : ( ~ (one_sorted_str(v0) = 0) | ? [v1] : ? [v2] : ((v1 = 0 & empty_carrier(v0) = 0) | ( ~ (v2 = 0) & the_carrier(v0) = v1 & empty(v1) = v2))) & ! [v0] : ( ~ (one_sorted_str(v0) = 0) | ? [v1] : ? [v2] : ((v1 = 0 & empty_carrier(v0) = 0) | (the_carrier(v0) = v1 & powerset(v1) = v2 & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (subset_complement(v1, v3) = v4) | ~ (in(v5, v4) = v6) | ? [v7] : (( ~ (v7 = 0) & element(v5, v1) = v7) | ( ~ (v7 = 0) & element(v3, v2) = v7) | (( ~ (v6 = 0) | ( ~ (v7 = 0) & in(v5, v3) = v7)) & (v6 = 0 | (v7 = 0 & in(v5, v3) = 0))))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (subset_complement(v1, v3) = v4) | ~ (in(v5, v3) = v6) | ? [v7] : (( ~ (v7 = 0) & element(v5, v1) = v7) | ( ~ (v7 = 0) & element(v3, v2) = v7) | (( ~ (v6 = 0) | ( ~ (v7 = 0) & in(v5, v4) = v7)) & (v6 = 0 | (v7 = 0 & in(v5, v4) = 0))))) & ! [v3] : ! [v4] : ! [v5] : ( ~ (subset_complement(v1, v3) = v4) | ~ (element(v5, v1) = 0) | ? [v6] : ? [v7] : (( ~ (v6 = 0) & element(v3, v2) = v6) | (((v7 = 0 & in(v5, v3) = 0) | (v6 = 0 & in(v5, v4) = 0)) & (( ~ (v7 = 0) & in(v5, v3) = v7) | ( ~ (v6 = 0) & in(v5, v4) = v6))))) & ! [v3] : ( ~ (element(v3, v2) = 0) | ? [v4] : (subset_complement(v1, v3) = v4 & ! [v5] : ! [v6] : ( ~ (in(v5, v4) = v6) | ? [v7] : (( ~ (v7 = 0) & element(v5, v1) = v7) | (( ~ (v6 = 0) | ( ~ (v7 = 0) & in(v5, v3) = v7)) & (v6 = 0 | (v7 = 0 & in(v5, v3) = 0))))) & ! [v5] : ! [v6] : ( ~ (in(v5, v3) = v6) | ? [v7] : (( ~ (v7 = 0) & element(v5, v1) = v7) | (( ~ (v6 = 0) | ( ~ (v7 = 0) & in(v5, v4) = v7)) & (v6 = 0 | (v7 = 0 & in(v5, v4) = 0))))) & ! [v5] : ( ~ (element(v5, v1) = 0) | ? [v6] : ? [v7] : (((v7 = 0 & in(v5, v3) = 0) | (v6 = 0 & in(v5, v4) = 0)) & (( ~ (v7 = 0) & in(v5, v3) = v7) | ( ~ (v6 = 0) & in(v5, v4) = v6))))))))) & ! [v0] : ( ~ (empty(v0) = 0) | (v5_membered(v0) = 0 & v4_membered(v0) = 0 & v3_membered(v0) = 0 & v2_membered(v0) = 0 & v1_membered(v0) = 0)) & ! [v0] : ( ~ (v5_membered(v0) = 0) | v4_membered(v0) = 0) & ! [v0] : ( ~ (v5_membered(v0) = 0) | ? [v1] : (powerset(v0) = v1 & ! [v2] : ! [v3] : ( ~ (v5_membered(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & v4_membered(v2) = 0 & v3_membered(v2) = 0 & v2_membered(v2) = 0 & v1_membered(v2) = 0) | ( ~ (v4 = 0) & element(v2, v1) = v4))) & ! [v2] : ! [v3] : ( ~ (v4_membered(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & v5_membered(v2) = 0 & v3_membered(v2) = 0 & v2_membered(v2) = 0 & v1_membered(v2) = 0) | ( ~ (v4 = 0) & element(v2, v1) = v4))) & ! [v2] : ! [v3] : ( ~ (v3_membered(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & v5_membered(v2) = 0 & v4_membered(v2) = 0 & v2_membered(v2) = 0 & v1_membered(v2) = 0) | ( ~ (v4 = 0) & element(v2, v1) = v4))) & ! [v2] : ! [v3] : ( ~ (v2_membered(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & v5_membered(v2) = 0 & v4_membered(v2) = 0 & v3_membered(v2) = 0 & v1_membered(v2) = 0) | ( ~ (v4 = 0) & element(v2, v1) = v4))) & ! [v2] : ! [v3] : ( ~ (v1_membered(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & v5_membered(v2) = 0 & v4_membered(v2) = 0 & v3_membered(v2) = 0 & v2_membered(v2) = 0) | ( ~ (v4 = 0) & element(v2, v1) = v4))) & ! [v2] : ( ~ (element(v2, v1) = 0) | (v5_membered(v2) = 0 & v4_membered(v2) = 0 & v3_membered(v2) = 0 & v2_membered(v2) = 0 & v1_membered(v2) = 0)))) & ! [v0] : ( ~ (v4_membered(v0) = 0) | v3_membered(v0) = 0) & ! [v0] : ( ~ (v4_membered(v0) = 0) | ? [v1] : (powerset(v0) = v1 & ! [v2] : ! [v3] : ( ~ (v4_membered(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & v3_membered(v2) = 0 & v2_membered(v2) = 0 & v1_membered(v2) = 0) | ( ~ (v4 = 0) & element(v2, v1) = v4))) & ! [v2] : ! [v3] : ( ~ (v3_membered(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & v4_membered(v2) = 0 & v2_membered(v2) = 0 & v1_membered(v2) = 0) | ( ~ (v4 = 0) & element(v2, v1) = v4))) & ! [v2] : ! [v3] : ( ~ (v2_membered(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & v4_membered(v2) = 0 & v3_membered(v2) = 0 & v1_membered(v2) = 0) | ( ~ (v4 = 0) & element(v2, v1) = v4))) & ! [v2] : ! [v3] : ( ~ (v1_membered(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & v4_membered(v2) = 0 & v3_membered(v2) = 0 & v2_membered(v2) = 0) | ( ~ (v4 = 0) & element(v2, v1) = v4))) & ! [v2] : ( ~ (element(v2, v1) = 0) | (v4_membered(v2) = 0 & v3_membered(v2) = 0 & v2_membered(v2) = 0 & v1_membered(v2) = 0)))) & ! [v0] : ( ~ (v3_membered(v0) = 0) | v2_membered(v0) = 0) & ! [v0] : ( ~ (v3_membered(v0) = 0) | ? [v1] : (powerset(v0) = v1 & ! [v2] : ! [v3] : ( ~ (v3_membered(v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & v3 = 0 & v2_membered(v2) = 0 & v1_membered(v2) = 0) | ( ~ (v4 = 0) & element(v2, v1) = v4))) & ! [v2] : ! [v3] : ( ~ (v2_membered(v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & v3 = 0 & v3_membered(v2) = 0 & v1_membered(v2) = 0) | ( ~ (v4 = 0) & element(v2, v1) = v4))) & ! [v2] : ! [v3] : ( ~ (v1_membered(v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & v3 = 0 & v3_membered(v2) = 0 & v2_membered(v2) = 0) | ( ~ (v4 = 0) & element(v2, v1) = v4))) & ! [v2] : ( ~ (element(v2, v1) = 0) | (v3_membered(v2) = 0 & v2_membered(v2) = 0 & v1_membered(v2) = 0)))) & ! [v0] : ( ~ (v2_membered(v0) = 0) | v1_membered(v0) = 0) & ! [v0] : ( ~ (v2_membered(v0) = 0) | ? [v1] : (powerset(v0) = v1 & ! [v2] : ! [v3] : ( ~ (v2_membered(v2) = v3) | ? [v4] : ((v4 = 0 & v3 = 0 & v1_membered(v2) = 0) | ( ~ (v4 = 0) & element(v2, v1) = v4))) & ! [v2] : ! [v3] : ( ~ (v1_membered(v2) = v3) | ? [v4] : ((v4 = 0 & v3 = 0 & v2_membered(v2) = 0) | ( ~ (v4 = 0) & element(v2, v1) = v4))) & ! [v2] : ( ~ (element(v2, v1) = 0) | (v2_membered(v2) = 0 & v1_membered(v2) = 0)))) & ! [v0] : ( ~ (v1_membered(v0) = 0) | ? [v1] : (powerset(v0) = v1 & ! [v2] : ! [v3] : (v3 = 0 | ~ (v1_membered(v2) = v3) | ? [v4] : ( ~ (v4 = 0) & element(v2, v1) = v4)) & ! [v2] : ( ~ (element(v2, v1) = 0) | v1_membered(v2) = 0))) & ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : interior(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : topstr_closure(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : subset_complement(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : element(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2 & ? [v0] : ? [v1] : top_str(v0) = v1 & ? [v0] : ? [v1] : the_carrier(v0) = v1 & ? [v0] : ? [v1] : one_sorted_str(v0) = v1 & ? [v0] : ? [v1] : empty_carrier(v0) = v1 & ? [v0] : ? [v1] : powerset(v0) = v1 & ? [v0] : ? [v1] : empty(v0) = v1 & ? [v0] : ? [v1] : v5_membered(v0) = v1 & ? [v0] : ? [v1] : natural(v0) = v1 & ? [v0] : ? [v1] : v4_membered(v0) = v1 & ? [v0] : ? [v1] : v1_int_1(v0) = v1 & ? [v0] : ? [v1] : v3_membered(v0) = v1 & ? [v0] : ? [v1] : v1_rat_1(v0) = v1 & ? [v0] : ? [v1] : v2_membered(v0) = v1 & ? [v0] : ? [v1] : v1_xreal_0(v0) = v1 & ? [v0] : ? [v1] : v1_membered(v0) = v1 & ? [v0] : ? [v1] : v1_xcmplx_0(v0) = v1 & ? [v0] : ? [v1] : element(v1, v0) = 0
% 50.76/19.84 |
% 50.76/19.84 | Applying alpha-rule on (1) yields:
% 50.76/19.84 | (2) ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ((v4 = 0 & ~ (v5 = 0) & powerset(v1) = v2 & empty(v3) = v5 & element(v3, v2) = 0) | (v2 = 0 & empty_carrier(v0) = 0) | ( ~ (v2 = 0) & one_sorted_str(v0) = v2)))
% 50.76/19.84 | (3) ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2))
% 50.76/19.84 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ (v5_membered(v0) = 0) | ~ (v1_rat_1(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & v2 = 0 & natural(v1) = 0 & v1_int_1(v1) = 0 & v1_xreal_0(v1) = 0 & v1_xcmplx_0(v1) = 0) | ( ~ (v3 = 0) & element(v1, v0) = v3)))
% 50.76/19.84 | (5) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (v1_membered(v2) = v1) | ~ (v1_membered(v2) = v0))
% 50.76/19.84 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v0) = v1) | ~ (v1_membered(v2) = v3) | ? [v4] : (( ~ (v4 = 0) & v1_membered(v0) = v4) | ( ~ (v4 = 0) & element(v2, v1) = v4)))
% 50.76/19.84 | (7) ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ? [v2] : (( ~ (v2 = 0) & top_str(v0) = v2) | (powerset(v1) = v2 & ! [v3] : ! [v4] : ( ~ (interior(v0, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ((v7 = v4 & topstr_closure(v0, v5) = v6 & subset_complement(v1, v6) = v4 & subset_complement(v1, v3) = v5) | ( ~ (v5 = 0) & element(v3, v2) = v5))) & ! [v3] : ! [v4] : ( ~ (subset_complement(v1, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ((v7 = v5 & interior(v0, v3) = v5 & topstr_closure(v0, v4) = v6 & subset_complement(v1, v6) = v5) | ( ~ (v5 = 0) & element(v3, v2) = v5))) & ! [v3] : ( ~ (element(v3, v2) = 0) | ? [v4] : ? [v5] : ? [v6] : (interior(v0, v3) = v4 & topstr_closure(v0, v5) = v6 & subset_complement(v1, v6) = v4 & subset_complement(v1, v3) = v5)))))
% 50.76/19.84 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ (v4_membered(v0) = 0) | ~ (v1_int_1(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & v3 = 0 & v2 = 0 & v1_rat_1(v1) = 0 & v1_xreal_0(v1) = 0 & v1_xcmplx_0(v1) = 0) | ( ~ (v3 = 0) & element(v1, v0) = v3)))
% 50.76/19.84 | (9) ! [v0] : ( ~ (v4_membered(v0) = 0) | v3_membered(v0) = 0)
% 50.76/19.84 | (10) ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ? [v2] : ? [v3] : (( ~ (v2 = 0) & one_sorted_str(v0) = v2) | (((v3 = 0 & empty(v1) = 0) | ( ~ (v2 = 0) & empty_carrier(v0) = v2)) & ((v2 = 0 & empty_carrier(v0) = 0) | ( ~ (v3 = 0) & empty(v1) = v3)))))
% 50.76/19.84 | (11) ? [v0] : ? [v1] : empty_carrier(v0) = v1
% 50.76/19.84 | (12) ! [v0] : ! [v1] : ( ~ (v1_membered(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & v3 = 0 & v2 = 0 & v1 = 0 & v5_membered(v0) = 0 & v4_membered(v0) = 0 & v3_membered(v0) = 0 & v2_membered(v0) = 0) | ( ~ (v2 = 0) & empty(v0) = v2)))
% 50.76/19.84 | (13) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | element(v0, v1) = 0)
% 50.76/19.84 | (14) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0))
% 50.76/19.84 | (15) ! [v0] : ! [v1] : ( ~ (v2_membered(v0) = 0) | ~ (element(v1, v0) = 0) | (v1_xreal_0(v1) = 0 & v1_xcmplx_0(v1) = 0))
% 50.76/19.84 | (16) ? [v0] : ? [v1] : v1_xreal_0(v0) = v1
% 50.76/19.84 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (topstr_closure(v3, v2) = v1) | ~ (topstr_closure(v3, v2) = v0))
% 50.76/19.84 | (18) ? [v0] : ? [v1] : ? [v2] : topstr_closure(v1, v0) = v2
% 50.76/19.84 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v0) = v1) | ~ (v2_membered(v2) = v3) | ? [v4] : ((v4 = 0 & v3 = 0 & v1_membered(v2) = 0) | ( ~ (v4 = 0) & v2_membered(v0) = v4) | ( ~ (v4 = 0) & element(v2, v1) = v4)))
% 50.76/19.84 | (20) ? [v0] : ? [v1] : v4_membered(v0) = v1
% 50.76/19.84 | (21) ! [v0] : ! [v1] : ! [v2] : ( ~ (v4_membered(v0) = 0) | ~ (v1_xcmplx_0(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & v3 = 0 & v2 = 0 & v1_int_1(v1) = 0 & v1_rat_1(v1) = 0 & v1_xreal_0(v1) = 0) | ( ~ (v3 = 0) & element(v1, v0) = v3)))
% 50.76/19.84 | (22) ? [v0] : ? [v1] : v2_membered(v0) = v1
% 50.76/19.84 | (23) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (v1_rat_1(v2) = v1) | ~ (v1_rat_1(v2) = v0))
% 50.76/19.84 | (24) one_sorted_str(all_0_5_5) = 0
% 50.76/19.84 | (25) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (v1_xcmplx_0(v2) = v1) | ~ (v1_xcmplx_0(v2) = v0))
% 50.76/19.84 | (26) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (v2_membered(v2) = v1) | ~ (v2_membered(v2) = v0))
% 50.76/19.84 | (27) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1))
% 50.76/19.84 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 50.76/19.84 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_complement(v0, v2) = v3) | ~ (in(v1, v3) = 0) | ? [v4] : ? [v5] : (( ~ (v5 = 0) & powerset(v0) = v4 & element(v2, v4) = v5) | ( ~ (v4 = 0) & in(v1, v2) = v4)))
% 50.76/19.84 | (30) ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2
% 50.76/19.84 | (31) ! [v0] : ! [v1] : ! [v2] : ( ~ (v5_membered(v0) = 0) | ~ (v1_xreal_0(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & v2 = 0 & natural(v1) = 0 & v1_int_1(v1) = 0 & v1_rat_1(v1) = 0 & v1_xcmplx_0(v1) = 0) | ( ~ (v3 = 0) & element(v1, v0) = v3)))
% 50.98/19.85 | (32) ! [v0] : ! [v1] : ( ~ (v4_membered(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & v3 = 0 & v2 = 0 & v1 = 0 & v5_membered(v0) = 0 & v3_membered(v0) = 0 & v2_membered(v0) = 0 & v1_membered(v0) = 0) | ( ~ (v2 = 0) & empty(v0) = v2)))
% 50.98/19.85 | (33) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_complement(v0, v1) = v2) | ? [v3] : ? [v4] : (powerset(v0) = v3 & ((v4 = 0 & element(v2, v3) = 0) | ( ~ (v4 = 0) & element(v1, v3) = v4))))
% 50.98/19.85 | (34) the_carrier(all_0_11_11) = all_0_10_10
% 50.98/19.85 | (35) ! [v0] : ! [v1] : ! [v2] : ( ~ (v3_membered(v0) = 0) | ~ (v1_xreal_0(v1) = v2) | ? [v3] : ? [v4] : ((v4 = 0 & v3 = 0 & v2 = 0 & v1_rat_1(v1) = 0 & v1_xcmplx_0(v1) = 0) | ( ~ (v3 = 0) & element(v1, v0) = v3)))
% 50.98/19.85 | (36) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v2) | ~ (element(v1, v2) = 0) | ? [v3] : (subset_complement(v0, v1) = v3 & element(v3, v2) = 0))
% 50.98/19.85 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (the_carrier(v0) = v2) | ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & topstr_closure(v0, v1) = v4 & element(v4, v3) = 0) | ( ~ (v4 = 0) & top_str(v0) = v4)))
% 50.98/19.85 | (38) ~ (all_0_6_6 = 0)
% 50.98/19.85 | (39) ! [v0] : ! [v1] : ! [v2] : ( ~ (empty(v2) = 0) | ~ (in(v0, v1) = 0) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v2) = v3 & element(v1, v3) = v4))
% 50.98/19.85 | (40) empty_carrier(all_0_5_5) = all_0_4_4
% 50.98/19.85 | (41) ! [v0] : ! [v1] : ! [v2] : ( ~ (interior(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & the_carrier(v0) = v3 & powerset(v3) = v4 & element(v2, v4) = 0) | ( ~ (v5 = 0) & the_carrier(v0) = v3 & powerset(v3) = v4 & element(v1, v4) = v5) | ( ~ (v3 = 0) & top_str(v0) = v3)))
% 50.98/19.85 | (42) v5_membered(all_0_3_3) = 0
% 50.98/19.85 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v0) = v1) | ~ (v3_membered(v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & v3 = 0 & v2_membered(v2) = 0 & v1_membered(v2) = 0) | ( ~ (v4 = 0) & v3_membered(v0) = v4) | ( ~ (v4 = 0) & element(v2, v1) = v4)))
% 50.98/19.85 | (44) ? [v0] : ? [v1] : empty(v0) = v1
% 50.98/19.85 | (45) v3_membered(empty_set) = 0
% 50.98/19.85 | (46) ! [v0] : ! [v1] : ( ~ (v5_membered(v0) = 0) | ~ (element(v1, v0) = 0) | (natural(v1) = 0 & v1_int_1(v1) = 0 & v1_rat_1(v1) = 0 & v1_xreal_0(v1) = 0 & v1_xcmplx_0(v1) = 0))
% 50.98/19.85 | (47) ! [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))
% 50.98/19.85 | (48) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty_carrier(v2) = v1) | ~ (empty_carrier(v2) = v0))
% 50.98/19.85 | (49) ! [v0] : ! [v1] : ( ~ (v5_membered(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & v3 = 0 & v2 = 0 & v1 = 0 & v4_membered(v0) = 0 & v3_membered(v0) = 0 & v2_membered(v0) = 0 & v1_membered(v0) = 0) | ( ~ (v2 = 0) & empty(v0) = v2)))
% 50.98/19.85 | (50) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 50.98/19.85 | (51) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (v4_membered(v2) = v1) | ~ (v4_membered(v2) = v0))
% 50.98/19.85 | (52) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 50.98/19.85 | (53) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (one_sorted_str(v2) = v1) | ~ (one_sorted_str(v2) = v0))
% 50.98/19.85 | (54) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v1) = v3 & element(v0, v3) = v4))
% 50.98/19.85 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v2, v0) = v4))
% 50.98/19.85 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v0) = v1) | ~ (v1_membered(v2) = v3) | ? [v4] : ((v4 = 0 & v3 = 0 & v2_membered(v2) = 0) | ( ~ (v4 = 0) & v2_membered(v0) = v4) | ( ~ (v4 = 0) & element(v2, v1) = v4)))
% 50.98/19.85 | (57) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (v1_int_1(v2) = v1) | ~ (v1_int_1(v2) = v0))
% 50.98/19.85 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v0) = v1) | ~ (v1_membered(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & v5_membered(v2) = 0 & v4_membered(v2) = 0 & v3_membered(v2) = 0 & v2_membered(v2) = 0) | ( ~ (v4 = 0) & v5_membered(v0) = v4) | ( ~ (v4 = 0) & element(v2, v1) = v4)))
% 50.98/19.85 | (59) ? [v0] : ? [v1] : v1_membered(v0) = v1
% 50.98/19.85 | (60) ! [v0] : ! [v1] : ! [v2] : ( ~ (v2_membered(v0) = 0) | ~ (v1_xcmplx_0(v1) = v2) | ? [v3] : ((v3 = 0 & v2 = 0 & v1_xreal_0(v1) = 0) | ( ~ (v3 = 0) & element(v1, v0) = v3)))
% 50.98/19.85 | (61) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0))
% 50.98/19.85 | (62) ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ? [v2] : (( ~ (v2 = 0) & top_str(v0) = v2) | (powerset(v1) = v2 & ! [v3] : ! [v4] : ( ~ (topstr_closure(v0, v3) = v4) | ? [v5] : ((v5 = 0 & subset(v3, v4) = 0) | ( ~ (v5 = 0) & element(v3, v2) = v5))) & ! [v3] : ( ~ (element(v3, v2) = 0) | ? [v4] : (subset(v3, v4) = 0 & topstr_closure(v0, v3) = v4)))))
% 50.98/19.85 | (63) top_str(all_0_11_11) = 0
% 50.98/19.85 | (64) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ (element(v2, v1) = 0) | ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & v3 = 0 & v3_membered(v2) = 0 & v2_membered(v2) = 0 & v1_membered(v2) = 0) | ( ~ (v3 = 0) & v3_membered(v0) = v3)))
% 50.98/19.85 | (65) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | element(v0, v2) = 0)
% 50.98/19.85 | (66) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (interior(v3, v2) = v1) | ~ (interior(v3, v2) = v0))
% 50.98/19.85 | (67) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3))
% 50.98/19.85 | (68) ? [v0] : ? [v1] : ? [v2] : element(v1, v0) = v2
% 50.98/19.85 | (69) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ (element(v2, v1) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & v4_membered(v2) = 0 & v3_membered(v2) = 0 & v2_membered(v2) = 0 & v1_membered(v2) = 0) | ( ~ (v3 = 0) & v4_membered(v0) = v3)))
% 50.98/19.85 | (70) v5_membered(empty_set) = 0
% 50.98/19.85 | (71) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v0) = v1) | ~ (v3_membered(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & v4_membered(v2) = 0 & v2_membered(v2) = 0 & v1_membered(v2) = 0) | ( ~ (v4 = 0) & v4_membered(v0) = v4) | ( ~ (v4 = 0) & element(v2, v1) = v4)))
% 50.98/19.85 | (72) ? [v0] : ? [v1] : ? [v2] : subset_complement(v1, v0) = v2
% 50.98/19.85 | (73) ! [v0] : ! [v1] : ( ~ (v3_membered(v0) = 0) | ~ (element(v1, v0) = 0) | (v1_rat_1(v1) = 0 & v1_xreal_0(v1) = 0 & v1_xcmplx_0(v1) = 0))
% 50.98/19.86 | (74) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0))
% 50.98/19.86 | (75) ? [v0] : ? [v1] : top_str(v0) = v1
% 50.98/19.86 | (76) ! [v0] : ! [v1] : ! [v2] : ( ~ (v5_membered(v0) = 0) | ~ (natural(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & v2 = 0 & v1_int_1(v1) = 0 & v1_rat_1(v1) = 0 & v1_xreal_0(v1) = 0 & v1_xcmplx_0(v1) = 0) | ( ~ (v3 = 0) & element(v1, v0) = v3)))
% 50.98/19.86 | (77) ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ? [v2] : ((v2 = 0 & empty_carrier(v0) = 0) | ( ~ (v2 = 0) & one_sorted_str(v0) = v2) | (powerset(v1) = v2 & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (subset_complement(v1, v3) = v4) | ~ (in(v5, v4) = v6) | ? [v7] : (( ~ (v7 = 0) & element(v5, v1) = v7) | ( ~ (v7 = 0) & element(v3, v2) = v7) | (( ~ (v6 = 0) | ( ~ (v7 = 0) & in(v5, v3) = v7)) & (v6 = 0 | (v7 = 0 & in(v5, v3) = 0))))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (subset_complement(v1, v3) = v4) | ~ (in(v5, v3) = v6) | ? [v7] : (( ~ (v7 = 0) & element(v5, v1) = v7) | ( ~ (v7 = 0) & element(v3, v2) = v7) | (( ~ (v6 = 0) | ( ~ (v7 = 0) & in(v5, v4) = v7)) & (v6 = 0 | (v7 = 0 & in(v5, v4) = 0))))) & ! [v3] : ! [v4] : ! [v5] : ( ~ (subset_complement(v1, v3) = v4) | ~ (element(v5, v1) = 0) | ? [v6] : ? [v7] : (( ~ (v6 = 0) & element(v3, v2) = v6) | (((v7 = 0 & in(v5, v3) = 0) | (v6 = 0 & in(v5, v4) = 0)) & (( ~ (v7 = 0) & in(v5, v3) = v7) | ( ~ (v6 = 0) & in(v5, v4) = v6))))) & ! [v3] : ( ~ (element(v3, v2) = 0) | ? [v4] : (subset_complement(v1, v3) = v4 & ! [v5] : ! [v6] : ( ~ (in(v5, v4) = v6) | ? [v7] : (( ~ (v7 = 0) & element(v5, v1) = v7) | (( ~ (v6 = 0) | ( ~ (v7 = 0) & in(v5, v3) = v7)) & (v6 = 0 | (v7 = 0 & in(v5, v3) = 0))))) & ! [v5] : ! [v6] : ( ~ (in(v5, v3) = v6) | ? [v7] : (( ~ (v7 = 0) & element(v5, v1) = v7) | (( ~ (v6 = 0) | ( ~ (v7 = 0) & in(v5, v4) = v7)) & (v6 = 0 | (v7 = 0 & in(v5, v4) = 0))))) & ! [v5] : ( ~ (element(v5, v1) = 0) | ? [v6] : ? [v7] : (((v7 = 0 & in(v5, v3) = 0) | (v6 = 0 & in(v5, v4) = 0)) & (( ~ (v7 = 0) & in(v5, v3) = v7) | ( ~ (v6 = 0) & in(v5, v4) = v6)))))))))
% 50.98/19.86 | (78) v1_membered(all_0_3_3) = 0
% 50.98/19.86 | (79) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (v3_membered(v2) = v1) | ~ (v3_membered(v2) = v0))
% 50.98/19.86 | (80) v1_membered(empty_set) = 0
% 50.98/19.86 | (81) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset_complement(v3, v2) = v1) | ~ (subset_complement(v3, v2) = v0))
% 50.98/19.86 | (82) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v0, v1) = v2) | ? [v3] : ((v3 = 0 & empty(v1) = 0) | ( ~ (v3 = 0) & element(v0, v1) = v3)))
% 50.98/19.86 | (83) ! [v0] : ! [v1] : (v1 = 0 | ~ (empty_carrier(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ((v5 = 0 & ~ (v6 = 0) & the_carrier(v0) = v2 & powerset(v2) = v3 & empty(v4) = v6 & element(v4, v3) = 0) | ( ~ (v2 = 0) & one_sorted_str(v0) = v2)))
% 50.98/19.86 | (84) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (v1_membered(v0) = 0) | ~ (v1_xcmplx_0(v1) = v2) | ? [v3] : ( ~ (v3 = 0) & element(v1, v0) = v3))
% 50.98/19.86 | (85) ! [v0] : ! [v1] : ( ~ (v4_membered(v0) = 0) | ~ (element(v1, v0) = 0) | (v1_int_1(v1) = 0 & v1_rat_1(v1) = 0 & v1_xreal_0(v1) = 0 & v1_xcmplx_0(v1) = 0))
% 50.98/19.86 | (86) one_sorted_str(all_0_1_1) = 0
% 50.98/19.86 | (87) ! [v0] : ! [v1] : ( ~ (v1_membered(v0) = 0) | ~ (element(v1, v0) = 0) | v1_xcmplx_0(v1) = 0)
% 50.98/19.86 | (88) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (v1_xreal_0(v2) = v1) | ~ (v1_xreal_0(v2) = v0))
% 50.98/19.86 | (89) ? [v0] : ? [v1] : v3_membered(v0) = v1
% 50.98/19.86 | (90) ! [v0] : ! [v1] : ( ~ (v2_membered(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & v3 = 0 & v2 = 0 & v1 = 0 & v5_membered(v0) = 0 & v4_membered(v0) = 0 & v3_membered(v0) = 0 & v1_membered(v0) = 0) | ( ~ (v2 = 0) & empty(v0) = v2)))
% 50.98/19.86 | (91) ! [v0] : ! [v1] : ( ~ (element(v0, v1) = 0) | ? [v2] : ((v2 = 0 & empty(v1) = 0) | (v2 = 0 & in(v0, v1) = 0)))
% 50.98/19.86 | (92) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v0) = v1) | ~ (v2_membered(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & v4_membered(v2) = 0 & v3_membered(v2) = 0 & v1_membered(v2) = 0) | ( ~ (v4 = 0) & v4_membered(v0) = v4) | ( ~ (v4 = 0) & element(v2, v1) = v4)))
% 50.98/19.86 | (93) ! [v0] : ( ~ (top_str(v0) = 0) | one_sorted_str(v0) = 0)
% 50.98/19.86 | (94) ! [v0] : ! [v1] : (v1 = 0 | ~ (v2_membered(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & v3_membered(v0) = v2))
% 50.98/19.86 | (95) ! [v0] : ! [v1] : ! [v2] : ( ~ (v2_membered(v0) = 0) | ~ (v1_xreal_0(v1) = v2) | ? [v3] : ((v3 = 0 & v2 = 0 & v1_xcmplx_0(v1) = 0) | ( ~ (v3 = 0) & element(v1, v0) = v3)))
% 50.98/19.86 | (96) subset(all_0_7_7, all_0_8_8) = all_0_6_6
% 50.98/19.86 | (97) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v0) = v1) | ~ (v4_membered(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & v3_membered(v2) = 0 & v2_membered(v2) = 0 & v1_membered(v2) = 0) | ( ~ (v4 = 0) & v4_membered(v0) = v4) | ( ~ (v4 = 0) & element(v2, v1) = v4)))
% 50.98/19.86 | (98) ! [v0] : ( ~ (one_sorted_str(v0) = 0) | ? [v1] : ? [v2] : ((v1 = 0 & empty_carrier(v0) = 0) | ( ~ (v2 = 0) & the_carrier(v0) = v1 & empty(v1) = v2)))
% 50.98/19.86 | (99) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0)
% 50.98/19.86 | (100) ~ (all_0_4_4 = 0)
% 50.98/19.86 | (101) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4))
% 50.98/19.86 | (102) ! [v0] : ( ~ (one_sorted_str(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (((v3 = 0 & the_carrier(v0) = v2 & empty(v2) = 0) | ( ~ (v1 = 0) & empty_carrier(v0) = v1)) & ((v1 = 0 & empty_carrier(v0) = 0) | ( ~ (v3 = 0) & the_carrier(v0) = v2 & empty(v2) = v3))))
% 50.98/19.86 | (103) ? [v0] : ? [v1] : v5_membered(v0) = v1
% 50.98/19.86 | (104) ! [v0] : ! [v1] : (v1 = 0 | ~ (one_sorted_str(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & top_str(v0) = v2))
% 50.98/19.86 | (105) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (powerset(v1) = v2 & element(v0, v2) = 0))
% 50.98/19.86 | (106) ! [v0] : ( ~ (top_str(v0) = 0) | ? [v1] : ? [v2] : (the_carrier(v0) = v1 & powerset(v1) = v2 & ! [v3] : ! [v4] : ( ~ (topstr_closure(v0, v3) = v4) | ? [v5] : ((v5 = 0 & subset(v3, v4) = 0) | ( ~ (v5 = 0) & element(v3, v2) = v5))) & ! [v3] : ( ~ (element(v3, v2) = 0) | ? [v4] : (subset(v3, v4) = 0 & topstr_closure(v0, v3) = v4))))
% 50.98/19.86 | (107) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v0) = v1) | ~ (v1_membered(v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & v3 = 0 & v3_membered(v2) = 0 & v2_membered(v2) = 0) | ( ~ (v4 = 0) & v3_membered(v0) = v4) | ( ~ (v4 = 0) & element(v2, v1) = v4)))
% 50.98/19.86 | (108) element(all_0_8_8, all_0_9_9) = 0
% 50.98/19.86 | (109) ? [v0] : ? [v1] : one_sorted_str(v0) = v1
% 50.98/19.86 | (110) ? [v0] : ? [v1] : v1_xcmplx_0(v0) = v1
% 50.98/19.86 | (111) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 50.98/19.87 | (112) ? [v0] : ? [v1] : natural(v0) = v1
% 50.98/19.87 | (113) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_complement(v0, v1) = v2) | ? [v3] : ? [v4] : ((v3 = v1 & subset_complement(v0, v2) = v1) | ( ~ (v4 = 0) & powerset(v0) = v3 & element(v1, v3) = v4)))
% 50.98/19.87 | (114) ! [v0] : ! [v1] : ! [v2] : ( ~ (v3_membered(v0) = 0) | ~ (v1_rat_1(v1) = v2) | ? [v3] : ? [v4] : ((v4 = 0 & v3 = 0 & v2 = 0 & v1_xreal_0(v1) = 0 & v1_xcmplx_0(v1) = 0) | ( ~ (v3 = 0) & element(v1, v0) = v3)))
% 50.98/19.87 | (115) ? [v0] : ? [v1] : the_carrier(v0) = v1
% 50.98/19.87 | (116) ! [v0] : ( ~ (v5_membered(v0) = 0) | v4_membered(v0) = 0)
% 50.98/19.87 | (117) ? [v0] : ? [v1] : element(v1, v0) = 0
% 50.98/19.87 | (118) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v0) = v1) | ~ (v5_membered(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & v4_membered(v2) = 0 & v3_membered(v2) = 0 & v2_membered(v2) = 0 & v1_membered(v2) = 0) | ( ~ (v4 = 0) & v5_membered(v0) = v4) | ( ~ (v4 = 0) & element(v2, v1) = v4)))
% 50.98/19.87 | (119) ! [v0] : ! [v1] : ! [v2] : ( ~ (v5_membered(v0) = 0) | ~ (v1_xcmplx_0(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & v2 = 0 & natural(v1) = 0 & v1_int_1(v1) = 0 & v1_rat_1(v1) = 0 & v1_xreal_0(v1) = 0) | ( ~ (v3 = 0) & element(v1, v0) = v3)))
% 50.98/19.87 | (120) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0))
% 50.98/19.87 | (121) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0))
% 50.98/19.87 | (122) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (natural(v2) = v1) | ~ (natural(v2) = v0))
% 50.98/19.87 | (123) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v2) | ~ (element(v1, v2) = 0) | ? [v3] : (subset_complement(v0, v3) = v1 & subset_complement(v0, v1) = v3))
% 50.98/19.87 | (124) ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2
% 50.98/19.87 | (125) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v0) = v1) | ~ (v2_membered(v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & v3 = 0 & v3_membered(v2) = 0 & v1_membered(v2) = 0) | ( ~ (v4 = 0) & v3_membered(v0) = v4) | ( ~ (v4 = 0) & element(v2, v1) = v4)))
% 50.98/19.87 | (126) ! [v0] : ( ~ (one_sorted_str(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ((v4 = 0 & ~ (v5 = 0) & the_carrier(v0) = v1 & powerset(v1) = v2 & empty(v3) = v5 & element(v3, v2) = 0) | (v1 = 0 & empty_carrier(v0) = 0)))
% 50.98/19.87 | (127) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (v5_membered(v2) = v1) | ~ (v5_membered(v2) = v0))
% 50.98/19.87 | (128) ! [v0] : ( ~ (v2_membered(v0) = 0) | v1_membered(v0) = 0)
% 50.98/19.87 | (129) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (top_str(v2) = v1) | ~ (top_str(v2) = v0))
% 50.98/19.87 | (130) ! [v0] : ( ~ (v2_membered(v0) = 0) | ? [v1] : (powerset(v0) = v1 & ! [v2] : ! [v3] : ( ~ (v2_membered(v2) = v3) | ? [v4] : ((v4 = 0 & v3 = 0 & v1_membered(v2) = 0) | ( ~ (v4 = 0) & element(v2, v1) = v4))) & ! [v2] : ! [v3] : ( ~ (v1_membered(v2) = v3) | ? [v4] : ((v4 = 0 & v3 = 0 & v2_membered(v2) = 0) | ( ~ (v4 = 0) & element(v2, v1) = v4))) & ! [v2] : ( ~ (element(v2, v1) = 0) | (v2_membered(v2) = 0 & v1_membered(v2) = 0))))
% 50.98/19.87 | (131) ? [v0] : ? [v1] : v1_rat_1(v0) = v1
% 50.98/19.87 | (132) ! [v0] : ( ~ (one_sorted_str(v0) = 0) | ? [v1] : ? [v2] : ((v1 = 0 & empty_carrier(v0) = 0) | (the_carrier(v0) = v1 & powerset(v1) = v2 & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (subset_complement(v1, v3) = v4) | ~ (in(v5, v4) = v6) | ? [v7] : (( ~ (v7 = 0) & element(v5, v1) = v7) | ( ~ (v7 = 0) & element(v3, v2) = v7) | (( ~ (v6 = 0) | ( ~ (v7 = 0) & in(v5, v3) = v7)) & (v6 = 0 | (v7 = 0 & in(v5, v3) = 0))))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (subset_complement(v1, v3) = v4) | ~ (in(v5, v3) = v6) | ? [v7] : (( ~ (v7 = 0) & element(v5, v1) = v7) | ( ~ (v7 = 0) & element(v3, v2) = v7) | (( ~ (v6 = 0) | ( ~ (v7 = 0) & in(v5, v4) = v7)) & (v6 = 0 | (v7 = 0 & in(v5, v4) = 0))))) & ! [v3] : ! [v4] : ! [v5] : ( ~ (subset_complement(v1, v3) = v4) | ~ (element(v5, v1) = 0) | ? [v6] : ? [v7] : (( ~ (v6 = 0) & element(v3, v2) = v6) | (((v7 = 0 & in(v5, v3) = 0) | (v6 = 0 & in(v5, v4) = 0)) & (( ~ (v7 = 0) & in(v5, v3) = v7) | ( ~ (v6 = 0) & in(v5, v4) = v6))))) & ! [v3] : ( ~ (element(v3, v2) = 0) | ? [v4] : (subset_complement(v1, v3) = v4 & ! [v5] : ! [v6] : ( ~ (in(v5, v4) = v6) | ? [v7] : (( ~ (v7 = 0) & element(v5, v1) = v7) | (( ~ (v6 = 0) | ( ~ (v7 = 0) & in(v5, v3) = v7)) & (v6 = 0 | (v7 = 0 & in(v5, v3) = 0))))) & ! [v5] : ! [v6] : ( ~ (in(v5, v3) = v6) | ? [v7] : (( ~ (v7 = 0) & element(v5, v1) = v7) | (( ~ (v6 = 0) | ( ~ (v7 = 0) & in(v5, v4) = v7)) & (v6 = 0 | (v7 = 0 & in(v5, v4) = 0))))) & ! [v5] : ( ~ (element(v5, v1) = 0) | ? [v6] : ? [v7] : (((v7 = 0 & in(v5, v3) = 0) | (v6 = 0 & in(v5, v4) = 0)) & (( ~ (v7 = 0) & in(v5, v3) = v7) | ( ~ (v6 = 0) & in(v5, v4) = v6)))))))))
% 50.98/19.87 | (133) ! [v0] : ( ~ (empty(v0) = 0) | (v5_membered(v0) = 0 & v4_membered(v0) = 0 & v3_membered(v0) = 0 & v2_membered(v0) = 0 & v1_membered(v0) = 0))
% 50.98/19.87 | (134) ! [v0] : ! [v1] : ( ~ (v3_membered(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & v3 = 0 & v2 = 0 & v1 = 0 & v5_membered(v0) = 0 & v4_membered(v0) = 0 & v2_membered(v0) = 0 & v1_membered(v0) = 0) | ( ~ (v2 = 0) & empty(v0) = v2)))
% 50.98/19.87 | (135) ! [v0] : ( ~ (v1_membered(v0) = 0) | ? [v1] : (powerset(v0) = v1 & ! [v2] : ! [v3] : (v3 = 0 | ~ (v1_membered(v2) = v3) | ? [v4] : ( ~ (v4 = 0) & element(v2, v1) = v4)) & ! [v2] : ( ~ (element(v2, v1) = 0) | v1_membered(v2) = 0)))
% 50.98/19.87 | (136) ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ? [v2] : ((v2 = 0 & empty_carrier(v0) = 0) | ( ~ (v2 = 0) & one_sorted_str(v0) = v2) | ( ~ (v2 = 0) & empty(v1) = v2)))
% 50.98/19.87 | (137) ! [v0] : ! [v1] : ! [v2] : ( ~ (v4_membered(v0) = 0) | ~ (v1_rat_1(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & v3 = 0 & v2 = 0 & v1_int_1(v1) = 0 & v1_xreal_0(v1) = 0 & v1_xcmplx_0(v1) = 0) | ( ~ (v3 = 0) & element(v1, v0) = v3)))
% 50.98/19.87 | (138) v2_membered(empty_set) = 0
% 50.98/19.87 | (139) ! [v0] : ( ~ (v4_membered(v0) = 0) | ? [v1] : (powerset(v0) = v1 & ! [v2] : ! [v3] : ( ~ (v4_membered(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & v3_membered(v2) = 0 & v2_membered(v2) = 0 & v1_membered(v2) = 0) | ( ~ (v4 = 0) & element(v2, v1) = v4))) & ! [v2] : ! [v3] : ( ~ (v3_membered(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & v4_membered(v2) = 0 & v2_membered(v2) = 0 & v1_membered(v2) = 0) | ( ~ (v4 = 0) & element(v2, v1) = v4))) & ! [v2] : ! [v3] : ( ~ (v2_membered(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & v4_membered(v2) = 0 & v3_membered(v2) = 0 & v1_membered(v2) = 0) | ( ~ (v4 = 0) & element(v2, v1) = v4))) & ! [v2] : ! [v3] : ( ~ (v1_membered(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & v4_membered(v2) = 0 & v3_membered(v2) = 0 & v2_membered(v2) = 0) | ( ~ (v4 = 0) & element(v2, v1) = v4))) & ! [v2] : ( ~ (element(v2, v1) = 0) | (v4_membered(v2) = 0 & v3_membered(v2) = 0 & v2_membered(v2) = 0 & v1_membered(v2) = 0))))
% 50.98/19.87 | (140) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 50.98/19.87 | (141) powerset(all_0_10_10) = all_0_9_9
% 50.98/19.87 | (142) ? [v0] : ? [v1] : v1_int_1(v0) = v1
% 50.98/19.87 | (143) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ (element(v2, v1) = 0) | ? [v3] : ? [v4] : ((v4 = 0 & v3 = 0 & v2_membered(v2) = 0 & v1_membered(v2) = 0) | ( ~ (v3 = 0) & v2_membered(v0) = v3)))
% 50.98/19.87 | (144) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v0) = v1) | ~ (v4_membered(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & v5_membered(v2) = 0 & v3_membered(v2) = 0 & v2_membered(v2) = 0 & v1_membered(v2) = 0) | ( ~ (v4 = 0) & v5_membered(v0) = v4) | ( ~ (v4 = 0) & element(v2, v1) = v4)))
% 50.98/19.88 | (145) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (the_carrier(v2) = v1) | ~ (the_carrier(v2) = v0))
% 50.98/19.88 | (146) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | subset(v0, v1) = 0)
% 50.98/19.88 | (147) v4_membered(empty_set) = 0
% 50.98/19.88 | (148) ! [v0] : ! [v1] : (v1 = 0 | ~ (v4_membered(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & v5_membered(v0) = v2))
% 50.98/19.88 | (149) ! [v0] : ! [v1] : (v1 = 0 | ~ (v1_membered(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & v2_membered(v0) = v2))
% 50.98/19.88 | (150) ? [v0] : ? [v1] : ? [v2] : interior(v1, v0) = v2
% 50.98/19.88 | (151) ! [v0] : ! [v1] : ! [v2] : ( ~ (v3_membered(v0) = 0) | ~ (v1_xcmplx_0(v1) = v2) | ? [v3] : ? [v4] : ((v4 = 0 & v3 = 0 & v2 = 0 & v1_rat_1(v1) = 0 & v1_xreal_0(v1) = 0) | ( ~ (v3 = 0) & element(v1, v0) = v3)))
% 50.98/19.88 | (152) ! [v0] : ! [v1] : ! [v2] : ( ~ (topstr_closure(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & the_carrier(v0) = v3 & powerset(v3) = v4 & element(v2, v4) = 0) | ( ~ (v5 = 0) & the_carrier(v0) = v3 & powerset(v3) = v4 & element(v1, v4) = v5) | ( ~ (v3 = 0) & top_str(v0) = v3)))
% 50.98/19.88 | (153) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v0) = v1) | ~ (v2_membered(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & v5_membered(v2) = 0 & v4_membered(v2) = 0 & v3_membered(v2) = 0 & v1_membered(v2) = 0) | ( ~ (v4 = 0) & v5_membered(v0) = v4) | ( ~ (v4 = 0) & element(v2, v1) = v4)))
% 50.98/19.88 | (154) ? [v0] : ? [v1] : powerset(v0) = v1
% 50.98/19.88 | (155) interior(all_0_11_11, all_0_8_8) = all_0_7_7
% 50.98/19.88 | (156) v2_membered(all_0_3_3) = 0
% 50.98/19.88 | (157) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v0) = v1) | ~ (v1_membered(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & v4_membered(v2) = 0 & v3_membered(v2) = 0 & v2_membered(v2) = 0) | ( ~ (v4 = 0) & v4_membered(v0) = v4) | ( ~ (v4 = 0) & element(v2, v1) = v4)))
% 50.98/19.88 | (158) ! [v0] : ! [v1] : (v1 = 0 | ~ (empty_carrier(v0) = v1) | ? [v2] : ? [v3] : (( ~ (v3 = 0) & the_carrier(v0) = v2 & empty(v2) = v3) | ( ~ (v2 = 0) & one_sorted_str(v0) = v2)))
% 50.98/19.88 | (159) ! [v0] : ( ~ (v3_membered(v0) = 0) | v2_membered(v0) = 0)
% 50.98/19.88 | (160) ~ (all_0_2_2 = 0)
% 50.98/19.88 | (161) ! [v0] : ! [v1] : (v1 = 0 | ~ (v3_membered(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & v4_membered(v0) = v2))
% 50.98/19.88 | (162) empty(all_0_3_3) = all_0_2_2
% 50.98/19.88 | (163) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 50.98/19.88 | (164) ! [v0] : ! [v1] : (v1 = 0 | ~ (empty_carrier(v0) = v1) | ? [v2] : ? [v3] : (( ~ (v2 = 0) & one_sorted_str(v0) = v2) | (the_carrier(v0) = v2 & powerset(v2) = v3 & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (subset_complement(v2, v4) = v5) | ~ (in(v6, v5) = v7) | ? [v8] : (( ~ (v8 = 0) & element(v6, v2) = v8) | ( ~ (v8 = 0) & element(v4, v3) = v8) | (( ~ (v7 = 0) | ( ~ (v8 = 0) & in(v6, v4) = v8)) & (v7 = 0 | (v8 = 0 & in(v6, v4) = 0))))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (subset_complement(v2, v4) = v5) | ~ (in(v6, v4) = v7) | ? [v8] : (( ~ (v8 = 0) & element(v6, v2) = v8) | ( ~ (v8 = 0) & element(v4, v3) = v8) | (( ~ (v7 = 0) | ( ~ (v8 = 0) & in(v6, v5) = v8)) & (v7 = 0 | (v8 = 0 & in(v6, v5) = 0))))) & ! [v4] : ! [v5] : ! [v6] : ( ~ (subset_complement(v2, v4) = v5) | ~ (element(v6, v2) = 0) | ? [v7] : ? [v8] : (( ~ (v7 = 0) & element(v4, v3) = v7) | (((v8 = 0 & in(v6, v4) = 0) | (v7 = 0 & in(v6, v5) = 0)) & (( ~ (v8 = 0) & in(v6, v4) = v8) | ( ~ (v7 = 0) & in(v6, v5) = v7))))) & ! [v4] : ( ~ (element(v4, v3) = 0) | ? [v5] : (subset_complement(v2, v4) = v5 & ! [v6] : ! [v7] : ( ~ (in(v6, v5) = v7) | ? [v8] : (( ~ (v8 = 0) & element(v6, v2) = v8) | (( ~ (v7 = 0) | ( ~ (v8 = 0) & in(v6, v4) = v8)) & (v7 = 0 | (v8 = 0 & in(v6, v4) = 0))))) & ! [v6] : ! [v7] : ( ~ (in(v6, v4) = v7) | ? [v8] : (( ~ (v8 = 0) & element(v6, v2) = v8) | (( ~ (v7 = 0) | ( ~ (v8 = 0) & in(v6, v5) = v8)) & (v7 = 0 | (v8 = 0 & in(v6, v5) = 0))))) & ! [v6] : ( ~ (element(v6, v2) = 0) | ? [v7] : ? [v8] : (((v8 = 0 & in(v6, v4) = 0) | (v7 = 0 & in(v6, v5) = 0)) & (( ~ (v8 = 0) & in(v6, v4) = v8) | ( ~ (v7 = 0) & in(v6, v5) = v7)))))))))
% 50.98/19.88 | (165) ! [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))
% 50.98/19.88 | (166) v3_membered(all_0_3_3) = 0
% 50.98/19.88 | (167) top_str(all_0_0_0) = 0
% 50.98/19.88 | (168) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ (element(v2, v1) = 0) | ? [v3] : ((v3 = 0 & v1_membered(v2) = 0) | ( ~ (v3 = 0) & v1_membered(v0) = v3)))
% 50.98/19.88 | (169) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v0) = v1) | ~ (v3_membered(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & v5_membered(v2) = 0 & v4_membered(v2) = 0 & v2_membered(v2) = 0 & v1_membered(v2) = 0) | ( ~ (v4 = 0) & v5_membered(v0) = v4) | ( ~ (v4 = 0) & element(v2, v1) = v4)))
% 50.98/19.88 | (170) ! [v0] : ! [v1] : ! [v2] : ( ~ (v5_membered(v0) = 0) | ~ (v1_int_1(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & v2 = 0 & natural(v1) = 0 & v1_rat_1(v1) = 0 & v1_xreal_0(v1) = 0 & v1_xcmplx_0(v1) = 0) | ( ~ (v3 = 0) & element(v1, v0) = v3)))
% 50.98/19.88 | (171) ! [v0] : ( ~ (top_str(v0) = 0) | ? [v1] : ? [v2] : (the_carrier(v0) = v1 & powerset(v1) = v2 & ! [v3] : ! [v4] : ( ~ (interior(v0, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ((v7 = v4 & topstr_closure(v0, v5) = v6 & subset_complement(v1, v6) = v4 & subset_complement(v1, v3) = v5) | ( ~ (v5 = 0) & element(v3, v2) = v5))) & ! [v3] : ! [v4] : ( ~ (subset_complement(v1, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ((v7 = v5 & interior(v0, v3) = v5 & topstr_closure(v0, v4) = v6 & subset_complement(v1, v6) = v5) | ( ~ (v5 = 0) & element(v3, v2) = v5))) & ! [v3] : ( ~ (element(v3, v2) = 0) | ? [v4] : ? [v5] : ? [v6] : (interior(v0, v3) = v4 & topstr_closure(v0, v5) = v6 & subset_complement(v1, v6) = v4 & subset_complement(v1, v3) = v5))))
% 50.98/19.88 | (172) ! [v0] : ( ~ (v5_membered(v0) = 0) | ? [v1] : (powerset(v0) = v1 & ! [v2] : ! [v3] : ( ~ (v5_membered(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & v4_membered(v2) = 0 & v3_membered(v2) = 0 & v2_membered(v2) = 0 & v1_membered(v2) = 0) | ( ~ (v4 = 0) & element(v2, v1) = v4))) & ! [v2] : ! [v3] : ( ~ (v4_membered(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & v5_membered(v2) = 0 & v3_membered(v2) = 0 & v2_membered(v2) = 0 & v1_membered(v2) = 0) | ( ~ (v4 = 0) & element(v2, v1) = v4))) & ! [v2] : ! [v3] : ( ~ (v3_membered(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & v5_membered(v2) = 0 & v4_membered(v2) = 0 & v2_membered(v2) = 0 & v1_membered(v2) = 0) | ( ~ (v4 = 0) & element(v2, v1) = v4))) & ! [v2] : ! [v3] : ( ~ (v2_membered(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & v5_membered(v2) = 0 & v4_membered(v2) = 0 & v3_membered(v2) = 0 & v1_membered(v2) = 0) | ( ~ (v4 = 0) & element(v2, v1) = v4))) & ! [v2] : ! [v3] : ( ~ (v1_membered(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & v5_membered(v2) = 0 & v4_membered(v2) = 0 & v3_membered(v2) = 0 & v2_membered(v2) = 0) | ( ~ (v4 = 0) & element(v2, v1) = v4))) & ! [v2] : ( ~ (element(v2, v1) = 0) | (v5_membered(v2) = 0 & v4_membered(v2) = 0 & v3_membered(v2) = 0 & v2_membered(v2) = 0 & v1_membered(v2) = 0))))
% 50.98/19.88 | (173) ! [v0] : ! [v1] : ( ~ (empty_carrier(v0) = v1) | ? [v2] : ? [v3] : (( ~ (v2 = 0) & one_sorted_str(v0) = v2) | (( ~ (v1 = 0) | (v3 = 0 & the_carrier(v0) = v2 & empty(v2) = 0)) & (v1 = 0 | ( ~ (v3 = 0) & the_carrier(v0) = v2 & empty(v2) = v3)))))
% 50.98/19.89 | (174) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ (element(v2, v1) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & v5_membered(v2) = 0 & v4_membered(v2) = 0 & v3_membered(v2) = 0 & v2_membered(v2) = 0 & v1_membered(v2) = 0) | ( ~ (v3 = 0) & v5_membered(v0) = v3)))
% 50.98/19.89 | (175) v4_membered(all_0_3_3) = 0
% 50.98/19.89 | (176) empty(empty_set) = 0
% 50.98/19.89 | (177) ! [v0] : ! [v1] : ! [v2] : ( ~ (v4_membered(v0) = 0) | ~ (v1_xreal_0(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & v3 = 0 & v2 = 0 & v1_int_1(v1) = 0 & v1_rat_1(v1) = 0 & v1_xcmplx_0(v1) = 0) | ( ~ (v3 = 0) & element(v1, v0) = v3)))
% 50.98/19.89 | (178) ! [v0] : ( ~ (v3_membered(v0) = 0) | ? [v1] : (powerset(v0) = v1 & ! [v2] : ! [v3] : ( ~ (v3_membered(v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & v3 = 0 & v2_membered(v2) = 0 & v1_membered(v2) = 0) | ( ~ (v4 = 0) & element(v2, v1) = v4))) & ! [v2] : ! [v3] : ( ~ (v2_membered(v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & v3 = 0 & v3_membered(v2) = 0 & v1_membered(v2) = 0) | ( ~ (v4 = 0) & element(v2, v1) = v4))) & ! [v2] : ! [v3] : ( ~ (v1_membered(v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & v3 = 0 & v3_membered(v2) = 0 & v2_membered(v2) = 0) | ( ~ (v4 = 0) & element(v2, v1) = v4))) & ! [v2] : ( ~ (element(v2, v1) = 0) | (v3_membered(v2) = 0 & v2_membered(v2) = 0 & v1_membered(v2) = 0))))
% 50.98/19.89 | (179) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (the_carrier(v0) = v2) | ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & interior(v0, v1) = v4 & element(v4, v3) = 0) | ( ~ (v4 = 0) & top_str(v0) = v4)))
% 50.98/19.89 |
% 50.98/19.89 | Instantiating formula (54) with all_0_6_6, all_0_8_8, all_0_7_7 and discharging atoms subset(all_0_7_7, all_0_8_8) = all_0_6_6, yields:
% 50.98/19.89 | (180) all_0_6_6 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & powerset(all_0_8_8) = v0 & element(all_0_7_7, v0) = v1)
% 50.98/19.89 |
% 50.98/19.89 | Instantiating formula (120) with all_0_6_6, all_0_8_8, all_0_7_7 and discharging atoms subset(all_0_7_7, all_0_8_8) = all_0_6_6, yields:
% 50.98/19.89 | (181) all_0_6_6 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_7_7) = 0 & in(v0, all_0_8_8) = v1)
% 50.98/19.89 |
% 50.98/19.89 | Instantiating formula (93) with all_0_11_11 and discharging atoms top_str(all_0_11_11) = 0, yields:
% 50.98/19.89 | (182) one_sorted_str(all_0_11_11) = 0
% 50.98/19.89 |
% 50.98/19.89 | Instantiating formula (171) with all_0_11_11 and discharging atoms top_str(all_0_11_11) = 0, yields:
% 50.98/19.89 | (183) ? [v0] : ? [v1] : (the_carrier(all_0_11_11) = v0 & powerset(v0) = v1 & ! [v2] : ! [v3] : ( ~ (interior(all_0_11_11, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ((v6 = v3 & topstr_closure(all_0_11_11, v4) = v5 & subset_complement(v0, v5) = v3 & subset_complement(v0, v2) = v4) | ( ~ (v4 = 0) & element(v2, v1) = v4))) & ! [v2] : ! [v3] : ( ~ (subset_complement(v0, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ((v6 = v4 & interior(all_0_11_11, v2) = v4 & topstr_closure(all_0_11_11, v3) = v5 & subset_complement(v0, v5) = v4) | ( ~ (v4 = 0) & element(v2, v1) = v4))) & ! [v2] : ( ~ (element(v2, v1) = 0) | ? [v3] : ? [v4] : ? [v5] : (interior(all_0_11_11, v2) = v3 & topstr_closure(all_0_11_11, v4) = v5 & subset_complement(v0, v5) = v3 & subset_complement(v0, v2) = v4)))
% 50.98/19.89 |
% 50.98/19.89 | Instantiating formula (106) with all_0_11_11 and discharging atoms top_str(all_0_11_11) = 0, yields:
% 50.98/19.89 | (184) ? [v0] : ? [v1] : (the_carrier(all_0_11_11) = v0 & powerset(v0) = v1 & ! [v2] : ! [v3] : ( ~ (topstr_closure(all_0_11_11, v2) = v3) | ? [v4] : ((v4 = 0 & subset(v2, v3) = 0) | ( ~ (v4 = 0) & element(v2, v1) = v4))) & ! [v2] : ( ~ (element(v2, v1) = 0) | ? [v3] : (subset(v2, v3) = 0 & topstr_closure(all_0_11_11, v2) = v3)))
% 50.98/19.89 |
% 50.98/19.89 | Instantiating formula (41) with all_0_7_7, all_0_8_8, all_0_11_11 and discharging atoms interior(all_0_11_11, all_0_8_8) = all_0_7_7, yields:
% 50.98/19.89 | (185) ? [v0] : ? [v1] : ? [v2] : ((v2 = 0 & the_carrier(all_0_11_11) = v0 & powerset(v0) = v1 & element(all_0_7_7, v1) = 0) | ( ~ (v2 = 0) & the_carrier(all_0_11_11) = v0 & powerset(v0) = v1 & element(all_0_8_8, v1) = v2) | ( ~ (v0 = 0) & top_str(all_0_11_11) = v0))
% 50.98/19.89 |
% 50.98/19.89 | Instantiating formula (2) with all_0_10_10, all_0_11_11 and discharging atoms the_carrier(all_0_11_11) = all_0_10_10, yields:
% 50.98/19.89 | (186) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ((v2 = 0 & ~ (v3 = 0) & powerset(all_0_10_10) = v0 & empty(v1) = v3 & element(v1, v0) = 0) | (v0 = 0 & empty_carrier(all_0_11_11) = 0) | ( ~ (v0 = 0) & one_sorted_str(all_0_11_11) = v0))
% 50.98/19.89 |
% 50.98/19.89 | Instantiating formula (10) with all_0_10_10, all_0_11_11 and discharging atoms the_carrier(all_0_11_11) = all_0_10_10, yields:
% 50.98/19.89 | (187) ? [v0] : ? [v1] : (( ~ (v0 = 0) & one_sorted_str(all_0_11_11) = v0) | (((v1 = 0 & empty(all_0_10_10) = 0) | ( ~ (v0 = 0) & empty_carrier(all_0_11_11) = v0)) & ((v0 = 0 & empty_carrier(all_0_11_11) = 0) | ( ~ (v1 = 0) & empty(all_0_10_10) = v1))))
% 50.98/19.89 |
% 50.98/19.89 | Instantiating formula (77) with all_0_10_10, all_0_11_11 and discharging atoms the_carrier(all_0_11_11) = all_0_10_10, yields:
% 50.98/19.89 | (188) ? [v0] : ((v0 = 0 & empty_carrier(all_0_11_11) = 0) | ( ~ (v0 = 0) & one_sorted_str(all_0_11_11) = v0) | (powerset(all_0_10_10) = v0 & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (subset_complement(all_0_10_10, v1) = v2) | ~ (in(v3, v2) = v4) | ? [v5] : (( ~ (v5 = 0) & element(v3, all_0_10_10) = v5) | ( ~ (v5 = 0) & element(v1, v0) = v5) | (( ~ (v4 = 0) | ( ~ (v5 = 0) & in(v3, v1) = v5)) & (v4 = 0 | (v5 = 0 & in(v3, v1) = 0))))) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (subset_complement(all_0_10_10, v1) = v2) | ~ (in(v3, v1) = v4) | ? [v5] : (( ~ (v5 = 0) & element(v3, all_0_10_10) = v5) | ( ~ (v5 = 0) & element(v1, v0) = v5) | (( ~ (v4 = 0) | ( ~ (v5 = 0) & in(v3, v2) = v5)) & (v4 = 0 | (v5 = 0 & in(v3, v2) = 0))))) & ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_complement(all_0_10_10, v1) = v2) | ~ (element(v3, all_0_10_10) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & element(v1, v0) = v4) | (((v5 = 0 & in(v3, v1) = 0) | (v4 = 0 & in(v3, v2) = 0)) & (( ~ (v5 = 0) & in(v3, v1) = v5) | ( ~ (v4 = 0) & in(v3, v2) = v4))))) & ! [v1] : ( ~ (element(v1, v0) = 0) | ? [v2] : (subset_complement(all_0_10_10, v1) = v2 & ! [v3] : ! [v4] : ( ~ (in(v3, v2) = v4) | ? [v5] : (( ~ (v5 = 0) & element(v3, all_0_10_10) = v5) | (( ~ (v4 = 0) | ( ~ (v5 = 0) & in(v3, v1) = v5)) & (v4 = 0 | (v5 = 0 & in(v3, v1) = 0))))) & ! [v3] : ! [v4] : ( ~ (in(v3, v1) = v4) | ? [v5] : (( ~ (v5 = 0) & element(v3, all_0_10_10) = v5) | (( ~ (v4 = 0) | ( ~ (v5 = 0) & in(v3, v2) = v5)) & (v4 = 0 | (v5 = 0 & in(v3, v2) = 0))))) & ! [v3] : ( ~ (element(v3, all_0_10_10) = 0) | ? [v4] : ? [v5] : (((v5 = 0 & in(v3, v1) = 0) | (v4 = 0 & in(v3, v2) = 0)) & (( ~ (v5 = 0) & in(v3, v1) = v5) | ( ~ (v4 = 0) & in(v3, v2) = v4))))))))
% 50.98/19.89 |
% 50.98/19.89 | Instantiating formula (7) with all_0_10_10, all_0_11_11 and discharging atoms the_carrier(all_0_11_11) = all_0_10_10, yields:
% 50.98/19.89 | (189) ? [v0] : (( ~ (v0 = 0) & top_str(all_0_11_11) = v0) | (powerset(all_0_10_10) = v0 & ! [v1] : ! [v2] : ( ~ (interior(all_0_11_11, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ((v5 = v2 & topstr_closure(all_0_11_11, v3) = v4 & subset_complement(all_0_10_10, v4) = v2 & subset_complement(all_0_10_10, v1) = v3) | ( ~ (v3 = 0) & element(v1, v0) = v3))) & ! [v1] : ! [v2] : ( ~ (subset_complement(all_0_10_10, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ((v5 = v3 & interior(all_0_11_11, v1) = v3 & topstr_closure(all_0_11_11, v2) = v4 & subset_complement(all_0_10_10, v4) = v3) | ( ~ (v3 = 0) & element(v1, v0) = v3))) & ! [v1] : ( ~ (element(v1, v0) = 0) | ? [v2] : ? [v3] : ? [v4] : (interior(all_0_11_11, v1) = v2 & topstr_closure(all_0_11_11, v3) = v4 & subset_complement(all_0_10_10, v4) = v2 & subset_complement(all_0_10_10, v1) = v3))))
% 50.98/19.89 |
% 50.98/19.89 | Instantiating formula (62) with all_0_10_10, all_0_11_11 and discharging atoms the_carrier(all_0_11_11) = all_0_10_10, yields:
% 50.98/19.89 | (190) ? [v0] : (( ~ (v0 = 0) & top_str(all_0_11_11) = v0) | (powerset(all_0_10_10) = v0 & ! [v1] : ! [v2] : ( ~ (topstr_closure(all_0_11_11, v1) = v2) | ? [v3] : ((v3 = 0 & subset(v1, v2) = 0) | ( ~ (v3 = 0) & element(v1, v0) = v3))) & ! [v1] : ( ~ (element(v1, v0) = 0) | ? [v2] : (subset(v1, v2) = 0 & topstr_closure(all_0_11_11, v1) = v2))))
% 50.98/19.89 |
% 50.98/19.90 | Instantiating formula (123) with all_0_9_9, all_0_8_8, all_0_10_10 and discharging atoms powerset(all_0_10_10) = all_0_9_9, element(all_0_8_8, all_0_9_9) = 0, yields:
% 50.98/19.90 | (191) ? [v0] : (subset_complement(all_0_10_10, v0) = all_0_8_8 & subset_complement(all_0_10_10, all_0_8_8) = v0)
% 50.98/19.90 |
% 50.98/19.90 | Instantiating formula (36) with all_0_9_9, all_0_8_8, all_0_10_10 and discharging atoms powerset(all_0_10_10) = all_0_9_9, element(all_0_8_8, all_0_9_9) = 0, yields:
% 50.98/19.90 | (192) ? [v0] : (subset_complement(all_0_10_10, all_0_8_8) = v0 & element(v0, all_0_9_9) = 0)
% 50.98/19.90 |
% 50.98/19.90 | Instantiating (192) with all_79_0_101 yields:
% 50.98/19.90 | (193) subset_complement(all_0_10_10, all_0_8_8) = all_79_0_101 & element(all_79_0_101, all_0_9_9) = 0
% 50.98/19.90 |
% 50.98/19.90 | Applying alpha-rule on (193) yields:
% 50.98/19.90 | (194) subset_complement(all_0_10_10, all_0_8_8) = all_79_0_101
% 50.98/19.90 | (195) element(all_79_0_101, all_0_9_9) = 0
% 50.98/19.90 |
% 50.98/19.90 | Instantiating (191) with all_81_0_102 yields:
% 50.98/19.90 | (196) subset_complement(all_0_10_10, all_81_0_102) = all_0_8_8 & subset_complement(all_0_10_10, all_0_8_8) = all_81_0_102
% 50.98/19.90 |
% 50.98/19.90 | Applying alpha-rule on (196) yields:
% 50.98/19.90 | (197) subset_complement(all_0_10_10, all_81_0_102) = all_0_8_8
% 50.98/19.90 | (198) subset_complement(all_0_10_10, all_0_8_8) = all_81_0_102
% 50.98/19.90 |
% 50.98/19.90 | Instantiating (189) with all_92_0_126 yields:
% 50.98/19.90 | (199) ( ~ (all_92_0_126 = 0) & top_str(all_0_11_11) = all_92_0_126) | (powerset(all_0_10_10) = all_92_0_126 & ! [v0] : ! [v1] : ( ~ (interior(all_0_11_11, v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v1 & topstr_closure(all_0_11_11, v2) = v3 & subset_complement(all_0_10_10, v3) = v1 & subset_complement(all_0_10_10, v0) = v2) | ( ~ (v2 = 0) & element(v0, all_92_0_126) = v2))) & ! [v0] : ! [v1] : ( ~ (subset_complement(all_0_10_10, v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v2 & interior(all_0_11_11, v0) = v2 & topstr_closure(all_0_11_11, v1) = v3 & subset_complement(all_0_10_10, v3) = v2) | ( ~ (v2 = 0) & element(v0, all_92_0_126) = v2))) & ! [v0] : ( ~ (element(v0, all_92_0_126) = 0) | ? [v1] : ? [v2] : ? [v3] : (interior(all_0_11_11, v0) = v1 & topstr_closure(all_0_11_11, v2) = v3 & subset_complement(all_0_10_10, v3) = v1 & subset_complement(all_0_10_10, v0) = v2)))
% 50.98/19.90 |
% 50.98/19.90 | Instantiating (188) with all_93_0_127 yields:
% 50.98/19.90 | (200) (all_93_0_127 = 0 & empty_carrier(all_0_11_11) = 0) | ( ~ (all_93_0_127 = 0) & one_sorted_str(all_0_11_11) = all_93_0_127) | (powerset(all_0_10_10) = all_93_0_127 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_complement(all_0_10_10, v0) = v1) | ~ (in(v2, v1) = v3) | ? [v4] : (( ~ (v4 = 0) & element(v2, all_0_10_10) = v4) | ( ~ (v4 = 0) & element(v0, all_93_0_127) = v4) | (( ~ (v3 = 0) | ( ~ (v4 = 0) & in(v2, v0) = v4)) & (v3 = 0 | (v4 = 0 & in(v2, v0) = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_complement(all_0_10_10, v0) = v1) | ~ (in(v2, v0) = v3) | ? [v4] : (( ~ (v4 = 0) & element(v2, all_0_10_10) = v4) | ( ~ (v4 = 0) & element(v0, all_93_0_127) = v4) | (( ~ (v3 = 0) | ( ~ (v4 = 0) & in(v2, v1) = v4)) & (v3 = 0 | (v4 = 0 & in(v2, v1) = 0))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_complement(all_0_10_10, v0) = v1) | ~ (element(v2, all_0_10_10) = 0) | ? [v3] : ? [v4] : (( ~ (v3 = 0) & element(v0, all_93_0_127) = v3) | (((v4 = 0 & in(v2, v0) = 0) | (v3 = 0 & in(v2, v1) = 0)) & (( ~ (v4 = 0) & in(v2, v0) = v4) | ( ~ (v3 = 0) & in(v2, v1) = v3))))) & ! [v0] : ( ~ (element(v0, all_93_0_127) = 0) | ? [v1] : (subset_complement(all_0_10_10, v0) = v1 & ! [v2] : ! [v3] : ( ~ (in(v2, v1) = v3) | ? [v4] : (( ~ (v4 = 0) & element(v2, all_0_10_10) = v4) | (( ~ (v3 = 0) | ( ~ (v4 = 0) & in(v2, v0) = v4)) & (v3 = 0 | (v4 = 0 & in(v2, v0) = 0))))) & ! [v2] : ! [v3] : ( ~ (in(v2, v0) = v3) | ? [v4] : (( ~ (v4 = 0) & element(v2, all_0_10_10) = v4) | (( ~ (v3 = 0) | ( ~ (v4 = 0) & in(v2, v1) = v4)) & (v3 = 0 | (v4 = 0 & in(v2, v1) = 0))))) & ! [v2] : ( ~ (element(v2, all_0_10_10) = 0) | ? [v3] : ? [v4] : (((v4 = 0 & in(v2, v0) = 0) | (v3 = 0 & in(v2, v1) = 0)) & (( ~ (v4 = 0) & in(v2, v0) = v4) | ( ~ (v3 = 0) & in(v2, v1) = v3)))))))
% 50.98/19.90 |
% 50.98/19.90 | Instantiating (184) with all_94_0_128, all_94_1_129 yields:
% 50.98/19.90 | (201) the_carrier(all_0_11_11) = all_94_1_129 & powerset(all_94_1_129) = all_94_0_128 & ! [v0] : ! [v1] : ( ~ (topstr_closure(all_0_11_11, v0) = v1) | ? [v2] : ((v2 = 0 & subset(v0, v1) = 0) | ( ~ (v2 = 0) & element(v0, all_94_0_128) = v2))) & ! [v0] : ( ~ (element(v0, all_94_0_128) = 0) | ? [v1] : (subset(v0, v1) = 0 & topstr_closure(all_0_11_11, v0) = v1))
% 50.98/19.90 |
% 50.98/19.90 | Applying alpha-rule on (201) yields:
% 50.98/19.90 | (202) the_carrier(all_0_11_11) = all_94_1_129
% 50.98/19.90 | (203) powerset(all_94_1_129) = all_94_0_128
% 50.98/19.90 | (204) ! [v0] : ! [v1] : ( ~ (topstr_closure(all_0_11_11, v0) = v1) | ? [v2] : ((v2 = 0 & subset(v0, v1) = 0) | ( ~ (v2 = 0) & element(v0, all_94_0_128) = v2)))
% 50.98/19.90 | (205) ! [v0] : ( ~ (element(v0, all_94_0_128) = 0) | ? [v1] : (subset(v0, v1) = 0 & topstr_closure(all_0_11_11, v0) = v1))
% 50.98/19.90 |
% 50.98/19.90 | Instantiating (183) with all_99_0_133, all_99_1_134 yields:
% 50.98/19.90 | (206) the_carrier(all_0_11_11) = all_99_1_134 & powerset(all_99_1_134) = all_99_0_133 & ! [v0] : ! [v1] : ( ~ (interior(all_0_11_11, v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v1 & topstr_closure(all_0_11_11, v2) = v3 & subset_complement(all_99_1_134, v3) = v1 & subset_complement(all_99_1_134, v0) = v2) | ( ~ (v2 = 0) & element(v0, all_99_0_133) = v2))) & ! [v0] : ! [v1] : ( ~ (subset_complement(all_99_1_134, v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v2 & interior(all_0_11_11, v0) = v2 & topstr_closure(all_0_11_11, v1) = v3 & subset_complement(all_99_1_134, v3) = v2) | ( ~ (v2 = 0) & element(v0, all_99_0_133) = v2))) & ! [v0] : ( ~ (element(v0, all_99_0_133) = 0) | ? [v1] : ? [v2] : ? [v3] : (interior(all_0_11_11, v0) = v1 & topstr_closure(all_0_11_11, v2) = v3 & subset_complement(all_99_1_134, v3) = v1 & subset_complement(all_99_1_134, v0) = v2))
% 50.98/19.90 |
% 50.98/19.90 | Applying alpha-rule on (206) yields:
% 50.98/19.90 | (207) ! [v0] : ! [v1] : ( ~ (subset_complement(all_99_1_134, v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v2 & interior(all_0_11_11, v0) = v2 & topstr_closure(all_0_11_11, v1) = v3 & subset_complement(all_99_1_134, v3) = v2) | ( ~ (v2 = 0) & element(v0, all_99_0_133) = v2)))
% 50.98/19.90 | (208) ! [v0] : ! [v1] : ( ~ (interior(all_0_11_11, v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v1 & topstr_closure(all_0_11_11, v2) = v3 & subset_complement(all_99_1_134, v3) = v1 & subset_complement(all_99_1_134, v0) = v2) | ( ~ (v2 = 0) & element(v0, all_99_0_133) = v2)))
% 50.98/19.90 | (209) powerset(all_99_1_134) = all_99_0_133
% 50.98/19.90 | (210) ! [v0] : ( ~ (element(v0, all_99_0_133) = 0) | ? [v1] : ? [v2] : ? [v3] : (interior(all_0_11_11, v0) = v1 & topstr_closure(all_0_11_11, v2) = v3 & subset_complement(all_99_1_134, v3) = v1 & subset_complement(all_99_1_134, v0) = v2))
% 50.98/19.90 | (211) the_carrier(all_0_11_11) = all_99_1_134
% 50.98/19.90 |
% 50.98/19.90 | Instantiating formula (208) with all_0_7_7, all_0_8_8 and discharging atoms interior(all_0_11_11, all_0_8_8) = all_0_7_7, yields:
% 50.98/19.90 | (212) ? [v0] : ? [v1] : ? [v2] : ((v2 = all_0_7_7 & topstr_closure(all_0_11_11, v0) = v1 & subset_complement(all_99_1_134, v1) = all_0_7_7 & subset_complement(all_99_1_134, all_0_8_8) = v0) | ( ~ (v0 = 0) & element(all_0_8_8, all_99_0_133) = v0))
% 50.98/19.90 |
% 50.98/19.90 | Instantiating (190) with all_102_0_135 yields:
% 50.98/19.90 | (213) ( ~ (all_102_0_135 = 0) & top_str(all_0_11_11) = all_102_0_135) | (powerset(all_0_10_10) = all_102_0_135 & ! [v0] : ! [v1] : ( ~ (topstr_closure(all_0_11_11, v0) = v1) | ? [v2] : ((v2 = 0 & subset(v0, v1) = 0) | ( ~ (v2 = 0) & element(v0, all_102_0_135) = v2))) & ! [v0] : ( ~ (element(v0, all_102_0_135) = 0) | ? [v1] : (subset(v0, v1) = 0 & topstr_closure(all_0_11_11, v0) = v1)))
% 50.98/19.90 |
% 50.98/19.90 | Instantiating (187) with all_104_0_137, all_104_1_138 yields:
% 50.98/19.90 | (214) ( ~ (all_104_1_138 = 0) & one_sorted_str(all_0_11_11) = all_104_1_138) | (((all_104_0_137 = 0 & empty(all_0_10_10) = 0) | ( ~ (all_104_1_138 = 0) & empty_carrier(all_0_11_11) = all_104_1_138)) & ((all_104_1_138 = 0 & empty_carrier(all_0_11_11) = 0) | ( ~ (all_104_0_137 = 0) & empty(all_0_10_10) = all_104_0_137)))
% 50.98/19.90 |
% 50.98/19.90 | Instantiating (186) with all_105_0_139, all_105_1_140, all_105_2_141, all_105_3_142 yields:
% 50.98/19.90 | (215) (all_105_1_140 = 0 & ~ (all_105_0_139 = 0) & powerset(all_0_10_10) = all_105_3_142 & empty(all_105_2_141) = all_105_0_139 & element(all_105_2_141, all_105_3_142) = 0) | (all_105_3_142 = 0 & empty_carrier(all_0_11_11) = 0) | ( ~ (all_105_3_142 = 0) & one_sorted_str(all_0_11_11) = all_105_3_142)
% 50.98/19.90 |
% 50.98/19.90 | Instantiating (185) with all_106_0_143, all_106_1_144, all_106_2_145 yields:
% 50.98/19.90 | (216) (all_106_0_143 = 0 & the_carrier(all_0_11_11) = all_106_2_145 & powerset(all_106_2_145) = all_106_1_144 & element(all_0_7_7, all_106_1_144) = 0) | ( ~ (all_106_0_143 = 0) & the_carrier(all_0_11_11) = all_106_2_145 & powerset(all_106_2_145) = all_106_1_144 & element(all_0_8_8, all_106_1_144) = all_106_0_143) | ( ~ (all_106_2_145 = 0) & top_str(all_0_11_11) = all_106_2_145)
% 50.98/19.90 |
% 50.98/19.90 | Instantiating (212) with all_169_0_260, all_169_1_261, all_169_2_262 yields:
% 50.98/19.90 | (217) (all_169_0_260 = all_0_7_7 & topstr_closure(all_0_11_11, all_169_2_262) = all_169_1_261 & subset_complement(all_99_1_134, all_169_1_261) = all_0_7_7 & subset_complement(all_99_1_134, all_0_8_8) = all_169_2_262) | ( ~ (all_169_2_262 = 0) & element(all_0_8_8, all_99_0_133) = all_169_2_262)
% 50.98/19.90 |
% 50.98/19.90 +-Applying beta-rule and splitting (213), into two cases.
% 50.98/19.90 |-Branch one:
% 50.98/19.90 | (218) ~ (all_102_0_135 = 0) & top_str(all_0_11_11) = all_102_0_135
% 50.98/19.90 |
% 50.98/19.90 | Applying alpha-rule on (218) yields:
% 50.98/19.90 | (219) ~ (all_102_0_135 = 0)
% 50.98/19.90 | (220) top_str(all_0_11_11) = all_102_0_135
% 50.98/19.90 |
% 50.98/19.90 | Instantiating formula (129) with all_0_11_11, all_102_0_135, 0 and discharging atoms top_str(all_0_11_11) = all_102_0_135, top_str(all_0_11_11) = 0, yields:
% 50.98/19.90 | (221) all_102_0_135 = 0
% 50.98/19.90 |
% 50.98/19.91 | Equations (221) can reduce 219 to:
% 50.98/19.91 | (222) $false
% 50.98/19.91 |
% 50.98/19.91 |-The branch is then unsatisfiable
% 50.98/19.91 |-Branch two:
% 50.98/19.91 | (223) powerset(all_0_10_10) = all_102_0_135 & ! [v0] : ! [v1] : ( ~ (topstr_closure(all_0_11_11, v0) = v1) | ? [v2] : ((v2 = 0 & subset(v0, v1) = 0) | ( ~ (v2 = 0) & element(v0, all_102_0_135) = v2))) & ! [v0] : ( ~ (element(v0, all_102_0_135) = 0) | ? [v1] : (subset(v0, v1) = 0 & topstr_closure(all_0_11_11, v0) = v1))
% 50.98/19.91 |
% 50.98/19.91 | Applying alpha-rule on (223) yields:
% 50.98/19.91 | (224) powerset(all_0_10_10) = all_102_0_135
% 50.98/19.91 | (225) ! [v0] : ! [v1] : ( ~ (topstr_closure(all_0_11_11, v0) = v1) | ? [v2] : ((v2 = 0 & subset(v0, v1) = 0) | ( ~ (v2 = 0) & element(v0, all_102_0_135) = v2)))
% 50.98/19.91 | (226) ! [v0] : ( ~ (element(v0, all_102_0_135) = 0) | ? [v1] : (subset(v0, v1) = 0 & topstr_closure(all_0_11_11, v0) = v1))
% 50.98/19.91 |
% 50.98/19.91 +-Applying beta-rule and splitting (180), into two cases.
% 50.98/19.91 |-Branch one:
% 50.98/19.91 | (227) all_0_6_6 = 0
% 50.98/19.91 |
% 50.98/19.91 | Equations (227) can reduce 38 to:
% 50.98/19.91 | (222) $false
% 50.98/19.91 |
% 50.98/19.91 |-The branch is then unsatisfiable
% 50.98/19.91 |-Branch two:
% 50.98/19.91 | (38) ~ (all_0_6_6 = 0)
% 50.98/19.91 | (230) ? [v0] : ? [v1] : ( ~ (v1 = 0) & powerset(all_0_8_8) = v0 & element(all_0_7_7, v0) = v1)
% 50.98/19.91 |
% 50.98/19.91 +-Applying beta-rule and splitting (181), into two cases.
% 50.98/19.91 |-Branch one:
% 50.98/19.91 | (227) all_0_6_6 = 0
% 50.98/19.91 |
% 50.98/19.91 | Equations (227) can reduce 38 to:
% 50.98/19.91 | (222) $false
% 50.98/19.91 |
% 50.98/19.91 |-The branch is then unsatisfiable
% 50.98/19.91 |-Branch two:
% 50.98/19.91 | (38) ~ (all_0_6_6 = 0)
% 50.98/19.91 | (234) ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_7_7) = 0 & in(v0, all_0_8_8) = v1)
% 50.98/19.91 |
% 50.98/19.91 | Instantiating (234) with all_259_0_453, all_259_1_454 yields:
% 50.98/19.91 | (235) ~ (all_259_0_453 = 0) & in(all_259_1_454, all_0_7_7) = 0 & in(all_259_1_454, all_0_8_8) = all_259_0_453
% 50.98/19.91 |
% 50.98/19.91 | Applying alpha-rule on (235) yields:
% 50.98/19.91 | (236) ~ (all_259_0_453 = 0)
% 50.98/19.91 | (237) in(all_259_1_454, all_0_7_7) = 0
% 50.98/19.91 | (238) in(all_259_1_454, all_0_8_8) = all_259_0_453
% 50.98/19.91 |
% 50.98/19.91 +-Applying beta-rule and splitting (199), into two cases.
% 50.98/19.91 |-Branch one:
% 50.98/19.91 | (239) ~ (all_92_0_126 = 0) & top_str(all_0_11_11) = all_92_0_126
% 50.98/19.91 |
% 50.98/19.91 | Applying alpha-rule on (239) yields:
% 50.98/19.91 | (240) ~ (all_92_0_126 = 0)
% 50.98/19.91 | (241) top_str(all_0_11_11) = all_92_0_126
% 50.98/19.91 |
% 50.98/19.91 | Instantiating formula (129) with all_0_11_11, all_92_0_126, 0 and discharging atoms top_str(all_0_11_11) = all_92_0_126, top_str(all_0_11_11) = 0, yields:
% 50.98/19.91 | (242) all_92_0_126 = 0
% 50.98/19.91 |
% 50.98/19.91 | Equations (242) can reduce 240 to:
% 50.98/19.91 | (222) $false
% 50.98/19.91 |
% 50.98/19.91 |-The branch is then unsatisfiable
% 50.98/19.91 |-Branch two:
% 50.98/19.91 | (244) powerset(all_0_10_10) = all_92_0_126 & ! [v0] : ! [v1] : ( ~ (interior(all_0_11_11, v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v1 & topstr_closure(all_0_11_11, v2) = v3 & subset_complement(all_0_10_10, v3) = v1 & subset_complement(all_0_10_10, v0) = v2) | ( ~ (v2 = 0) & element(v0, all_92_0_126) = v2))) & ! [v0] : ! [v1] : ( ~ (subset_complement(all_0_10_10, v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v2 & interior(all_0_11_11, v0) = v2 & topstr_closure(all_0_11_11, v1) = v3 & subset_complement(all_0_10_10, v3) = v2) | ( ~ (v2 = 0) & element(v0, all_92_0_126) = v2))) & ! [v0] : ( ~ (element(v0, all_92_0_126) = 0) | ? [v1] : ? [v2] : ? [v3] : (interior(all_0_11_11, v0) = v1 & topstr_closure(all_0_11_11, v2) = v3 & subset_complement(all_0_10_10, v3) = v1 & subset_complement(all_0_10_10, v0) = v2))
% 50.98/19.91 |
% 50.98/19.91 | Applying alpha-rule on (244) yields:
% 50.98/19.91 | (245) powerset(all_0_10_10) = all_92_0_126
% 50.98/19.91 | (246) ! [v0] : ! [v1] : ( ~ (interior(all_0_11_11, v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v1 & topstr_closure(all_0_11_11, v2) = v3 & subset_complement(all_0_10_10, v3) = v1 & subset_complement(all_0_10_10, v0) = v2) | ( ~ (v2 = 0) & element(v0, all_92_0_126) = v2)))
% 50.98/19.91 | (247) ! [v0] : ! [v1] : ( ~ (subset_complement(all_0_10_10, v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v2 & interior(all_0_11_11, v0) = v2 & topstr_closure(all_0_11_11, v1) = v3 & subset_complement(all_0_10_10, v3) = v2) | ( ~ (v2 = 0) & element(v0, all_92_0_126) = v2)))
% 50.98/19.91 | (248) ! [v0] : ( ~ (element(v0, all_92_0_126) = 0) | ? [v1] : ? [v2] : ? [v3] : (interior(all_0_11_11, v0) = v1 & topstr_closure(all_0_11_11, v2) = v3 & subset_complement(all_0_10_10, v3) = v1 & subset_complement(all_0_10_10, v0) = v2))
% 50.98/19.91 |
% 50.98/19.91 | Instantiating formula (246) with all_0_7_7, all_0_8_8 and discharging atoms interior(all_0_11_11, all_0_8_8) = all_0_7_7, yields:
% 50.98/19.91 | (249) ? [v0] : ? [v1] : ? [v2] : ((v2 = all_0_7_7 & topstr_closure(all_0_11_11, v0) = v1 & subset_complement(all_0_10_10, v1) = all_0_7_7 & subset_complement(all_0_10_10, all_0_8_8) = v0) | ( ~ (v0 = 0) & element(all_0_8_8, all_92_0_126) = v0))
% 50.98/19.91 |
% 50.98/19.91 | Instantiating (249) with all_274_0_457, all_274_1_458, all_274_2_459 yields:
% 50.98/19.91 | (250) (all_274_0_457 = all_0_7_7 & topstr_closure(all_0_11_11, all_274_2_459) = all_274_1_458 & subset_complement(all_0_10_10, all_274_1_458) = all_0_7_7 & subset_complement(all_0_10_10, all_0_8_8) = all_274_2_459) | ( ~ (all_274_2_459 = 0) & element(all_0_8_8, all_92_0_126) = all_274_2_459)
% 50.98/19.91 |
% 50.98/19.91 | Instantiating formula (81) with all_0_10_10, all_0_8_8, all_79_0_101, all_81_0_102 and discharging atoms subset_complement(all_0_10_10, all_0_8_8) = all_81_0_102, subset_complement(all_0_10_10, all_0_8_8) = all_79_0_101, yields:
% 50.98/19.91 | (251) all_81_0_102 = all_79_0_101
% 50.98/19.91 |
% 50.98/19.91 | Instantiating formula (145) with all_0_11_11, all_99_1_134, all_0_10_10 and discharging atoms the_carrier(all_0_11_11) = all_99_1_134, the_carrier(all_0_11_11) = all_0_10_10, yields:
% 50.98/19.91 | (252) all_99_1_134 = all_0_10_10
% 50.98/19.91 |
% 50.98/19.91 | Instantiating formula (145) with all_0_11_11, all_94_1_129, all_99_1_134 and discharging atoms the_carrier(all_0_11_11) = all_99_1_134, the_carrier(all_0_11_11) = all_94_1_129, yields:
% 50.98/19.91 | (253) all_99_1_134 = all_94_1_129
% 50.98/19.91 |
% 50.98/19.91 | Instantiating formula (74) with all_0_10_10, all_102_0_135, all_0_9_9 and discharging atoms powerset(all_0_10_10) = all_102_0_135, powerset(all_0_10_10) = all_0_9_9, yields:
% 50.98/19.91 | (254) all_102_0_135 = all_0_9_9
% 50.98/19.91 |
% 50.98/19.91 | Instantiating formula (74) with all_0_10_10, all_92_0_126, all_102_0_135 and discharging atoms powerset(all_0_10_10) = all_102_0_135, powerset(all_0_10_10) = all_92_0_126, yields:
% 50.98/19.91 | (255) all_102_0_135 = all_92_0_126
% 50.98/19.91 |
% 50.98/19.91 | Combining equations (254,255) yields a new equation:
% 50.98/19.91 | (256) all_92_0_126 = all_0_9_9
% 50.98/19.91 |
% 50.98/19.91 | Combining equations (252,253) yields a new equation:
% 50.98/19.91 | (257) all_94_1_129 = all_0_10_10
% 50.98/19.91 |
% 50.98/19.91 | Combining equations (257,253) yields a new equation:
% 50.98/19.91 | (252) all_99_1_134 = all_0_10_10
% 50.98/19.91 |
% 50.98/19.91 | Combining equations (256,255) yields a new equation:
% 50.98/19.91 | (254) all_102_0_135 = all_0_9_9
% 50.98/19.91 |
% 50.98/19.91 | From (251) and (197) follows:
% 50.98/19.91 | (260) subset_complement(all_0_10_10, all_79_0_101) = all_0_8_8
% 50.98/19.91 |
% 50.98/19.91 | From (251) and (198) follows:
% 50.98/19.91 | (194) subset_complement(all_0_10_10, all_0_8_8) = all_79_0_101
% 50.98/19.91 |
% 50.98/19.91 | From (257) and (202) follows:
% 50.98/19.91 | (34) the_carrier(all_0_11_11) = all_0_10_10
% 50.98/19.91 |
% 50.98/19.91 | From (252) and (209) follows:
% 50.98/19.91 | (263) powerset(all_0_10_10) = all_99_0_133
% 50.98/19.91 |
% 50.98/19.91 | From (257) and (203) follows:
% 50.98/19.91 | (264) powerset(all_0_10_10) = all_94_0_128
% 50.98/19.91 |
% 50.98/19.91 | From (256) and (245) follows:
% 50.98/19.91 | (141) powerset(all_0_10_10) = all_0_9_9
% 50.98/19.91 |
% 50.98/19.91 +-Applying beta-rule and splitting (250), into two cases.
% 50.98/19.91 |-Branch one:
% 50.98/19.91 | (266) all_274_0_457 = all_0_7_7 & topstr_closure(all_0_11_11, all_274_2_459) = all_274_1_458 & subset_complement(all_0_10_10, all_274_1_458) = all_0_7_7 & subset_complement(all_0_10_10, all_0_8_8) = all_274_2_459
% 50.98/19.91 |
% 50.98/19.91 | Applying alpha-rule on (266) yields:
% 50.98/19.91 | (267) all_274_0_457 = all_0_7_7
% 50.98/19.91 | (268) topstr_closure(all_0_11_11, all_274_2_459) = all_274_1_458
% 50.98/19.91 | (269) subset_complement(all_0_10_10, all_274_1_458) = all_0_7_7
% 50.98/19.91 | (270) subset_complement(all_0_10_10, all_0_8_8) = all_274_2_459
% 50.98/19.91 |
% 50.98/19.91 | Instantiating formula (81) with all_0_10_10, all_0_8_8, all_274_2_459, all_79_0_101 and discharging atoms subset_complement(all_0_10_10, all_0_8_8) = all_274_2_459, subset_complement(all_0_10_10, all_0_8_8) = all_79_0_101, yields:
% 50.98/19.92 | (271) all_274_2_459 = all_79_0_101
% 50.98/19.92 |
% 50.98/19.92 | Instantiating formula (74) with all_0_10_10, all_99_0_133, all_0_9_9 and discharging atoms powerset(all_0_10_10) = all_99_0_133, powerset(all_0_10_10) = all_0_9_9, yields:
% 50.98/19.92 | (272) all_99_0_133 = all_0_9_9
% 50.98/19.92 |
% 50.98/19.92 | Instantiating formula (74) with all_0_10_10, all_94_0_128, all_99_0_133 and discharging atoms powerset(all_0_10_10) = all_99_0_133, powerset(all_0_10_10) = all_94_0_128, yields:
% 50.98/19.92 | (273) all_99_0_133 = all_94_0_128
% 50.98/19.92 |
% 50.98/19.92 | Combining equations (272,273) yields a new equation:
% 50.98/19.92 | (274) all_94_0_128 = all_0_9_9
% 50.98/19.92 |
% 50.98/19.92 | Combining equations (274,273) yields a new equation:
% 50.98/19.92 | (272) all_99_0_133 = all_0_9_9
% 50.98/19.92 |
% 50.98/19.92 | From (271) and (268) follows:
% 50.98/19.92 | (276) topstr_closure(all_0_11_11, all_79_0_101) = all_274_1_458
% 50.98/19.92 |
% 50.98/19.92 | From (271) and (270) follows:
% 50.98/19.92 | (194) subset_complement(all_0_10_10, all_0_8_8) = all_79_0_101
% 50.98/19.92 |
% 50.98/19.92 | From (274) and (264) follows:
% 50.98/19.92 | (141) powerset(all_0_10_10) = all_0_9_9
% 50.98/19.92 |
% 50.98/19.92 +-Applying beta-rule and splitting (217), into two cases.
% 50.98/19.92 |-Branch one:
% 50.98/19.92 | (279) all_169_0_260 = all_0_7_7 & topstr_closure(all_0_11_11, all_169_2_262) = all_169_1_261 & subset_complement(all_99_1_134, all_169_1_261) = all_0_7_7 & subset_complement(all_99_1_134, all_0_8_8) = all_169_2_262
% 50.98/19.92 |
% 50.98/19.92 | Applying alpha-rule on (279) yields:
% 50.98/19.92 | (280) all_169_0_260 = all_0_7_7
% 50.98/19.92 | (281) topstr_closure(all_0_11_11, all_169_2_262) = all_169_1_261
% 50.98/19.92 | (282) subset_complement(all_99_1_134, all_169_1_261) = all_0_7_7
% 50.98/19.92 | (283) subset_complement(all_99_1_134, all_0_8_8) = all_169_2_262
% 50.98/19.92 |
% 50.98/19.92 | From (252) and (283) follows:
% 50.98/19.92 | (284) subset_complement(all_0_10_10, all_0_8_8) = all_169_2_262
% 50.98/19.92 |
% 50.98/19.92 +-Applying beta-rule and splitting (216), into two cases.
% 50.98/19.92 |-Branch one:
% 50.98/19.92 | (285) (all_106_0_143 = 0 & the_carrier(all_0_11_11) = all_106_2_145 & powerset(all_106_2_145) = all_106_1_144 & element(all_0_7_7, all_106_1_144) = 0) | ( ~ (all_106_0_143 = 0) & the_carrier(all_0_11_11) = all_106_2_145 & powerset(all_106_2_145) = all_106_1_144 & element(all_0_8_8, all_106_1_144) = all_106_0_143)
% 50.98/19.92 |
% 50.98/19.92 +-Applying beta-rule and splitting (285), into two cases.
% 50.98/19.92 |-Branch one:
% 50.98/19.92 | (286) all_106_0_143 = 0 & the_carrier(all_0_11_11) = all_106_2_145 & powerset(all_106_2_145) = all_106_1_144 & element(all_0_7_7, all_106_1_144) = 0
% 50.98/19.92 |
% 50.98/19.92 | Applying alpha-rule on (286) yields:
% 50.98/19.92 | (287) all_106_0_143 = 0
% 50.98/19.92 | (288) the_carrier(all_0_11_11) = all_106_2_145
% 50.98/19.92 | (289) powerset(all_106_2_145) = all_106_1_144
% 50.98/19.92 | (290) element(all_0_7_7, all_106_1_144) = 0
% 50.98/19.92 |
% 50.98/19.92 | Instantiating formula (81) with all_0_10_10, all_0_8_8, all_169_2_262, all_79_0_101 and discharging atoms subset_complement(all_0_10_10, all_0_8_8) = all_169_2_262, subset_complement(all_0_10_10, all_0_8_8) = all_79_0_101, yields:
% 50.98/19.92 | (291) all_169_2_262 = all_79_0_101
% 50.98/19.92 |
% 50.98/19.92 | Instantiating formula (145) with all_0_11_11, all_106_2_145, all_0_10_10 and discharging atoms the_carrier(all_0_11_11) = all_106_2_145, the_carrier(all_0_11_11) = all_0_10_10, yields:
% 50.98/19.92 | (292) all_106_2_145 = all_0_10_10
% 50.98/19.92 |
% 50.98/19.92 | From (291) and (281) follows:
% 50.98/19.92 | (293) topstr_closure(all_0_11_11, all_79_0_101) = all_169_1_261
% 50.98/19.92 |
% 50.98/19.92 | From (291) and (284) follows:
% 50.98/19.92 | (194) subset_complement(all_0_10_10, all_0_8_8) = all_79_0_101
% 50.98/19.92 |
% 50.98/19.92 | From (292) and (288) follows:
% 50.98/19.92 | (34) the_carrier(all_0_11_11) = all_0_10_10
% 50.98/19.92 |
% 50.98/19.92 | From (292) and (289) follows:
% 50.98/19.92 | (296) powerset(all_0_10_10) = all_106_1_144
% 50.98/19.92 |
% 50.98/19.92 | Instantiating formula (17) with all_0_11_11, all_79_0_101, all_169_1_261, all_274_1_458 and discharging atoms topstr_closure(all_0_11_11, all_79_0_101) = all_274_1_458, topstr_closure(all_0_11_11, all_79_0_101) = all_169_1_261, yields:
% 50.98/19.92 | (297) all_274_1_458 = all_169_1_261
% 50.98/19.92 |
% 50.98/19.92 | Instantiating formula (74) with all_0_10_10, all_106_1_144, all_0_9_9 and discharging atoms powerset(all_0_10_10) = all_106_1_144, powerset(all_0_10_10) = all_0_9_9, yields:
% 50.98/19.92 | (298) all_106_1_144 = all_0_9_9
% 50.98/19.92 |
% 50.98/19.92 | From (297) and (276) follows:
% 50.98/19.92 | (293) topstr_closure(all_0_11_11, all_79_0_101) = all_169_1_261
% 50.98/19.92 |
% 50.98/19.92 | From (297) and (269) follows:
% 50.98/19.92 | (300) subset_complement(all_0_10_10, all_169_1_261) = all_0_7_7
% 50.98/19.92 |
% 50.98/19.92 | From (298) and (296) follows:
% 50.98/19.92 | (141) powerset(all_0_10_10) = all_0_9_9
% 50.98/19.92 |
% 50.98/19.92 | From (298) and (290) follows:
% 50.98/19.92 | (302) element(all_0_7_7, all_0_9_9) = 0
% 50.98/19.92 |
% 50.98/19.92 | Instantiating formula (33) with all_0_7_7, all_169_1_261, all_0_10_10 and discharging atoms subset_complement(all_0_10_10, all_169_1_261) = all_0_7_7, yields:
% 50.98/19.92 | (303) ? [v0] : ? [v1] : (powerset(all_0_10_10) = v0 & ((v1 = 0 & element(all_0_7_7, v0) = 0) | ( ~ (v1 = 0) & element(all_169_1_261, v0) = v1)))
% 50.98/19.92 |
% 50.98/19.92 | Instantiating formula (126) with all_0_11_11 and discharging atoms one_sorted_str(all_0_11_11) = 0, yields:
% 50.98/19.92 | (304) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ((v3 = 0 & ~ (v4 = 0) & the_carrier(all_0_11_11) = v0 & powerset(v0) = v1 & empty(v2) = v4 & element(v2, v1) = 0) | (v0 = 0 & empty_carrier(all_0_11_11) = 0))
% 50.98/19.92 |
% 50.98/19.92 | Instantiating formula (102) with all_0_11_11 and discharging atoms one_sorted_str(all_0_11_11) = 0, yields:
% 50.98/19.92 | (305) ? [v0] : ? [v1] : ? [v2] : (((v2 = 0 & the_carrier(all_0_11_11) = v1 & empty(v1) = 0) | ( ~ (v0 = 0) & empty_carrier(all_0_11_11) = v0)) & ((v0 = 0 & empty_carrier(all_0_11_11) = 0) | ( ~ (v2 = 0) & the_carrier(all_0_11_11) = v1 & empty(v1) = v2)))
% 50.98/19.92 |
% 50.98/19.92 | Instantiating formula (98) with all_0_11_11 and discharging atoms one_sorted_str(all_0_11_11) = 0, yields:
% 50.98/19.92 | (306) ? [v0] : ? [v1] : ((v0 = 0 & empty_carrier(all_0_11_11) = 0) | ( ~ (v1 = 0) & the_carrier(all_0_11_11) = v0 & empty(v0) = v1))
% 50.98/19.92 |
% 50.98/19.92 | Instantiating formula (132) with all_0_11_11 and discharging atoms one_sorted_str(all_0_11_11) = 0, yields:
% 50.98/19.92 | (307) ? [v0] : ? [v1] : ((v0 = 0 & empty_carrier(all_0_11_11) = 0) | (the_carrier(all_0_11_11) = v0 & powerset(v0) = v1 & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (subset_complement(v0, v2) = v3) | ~ (in(v4, v3) = v5) | ? [v6] : (( ~ (v6 = 0) & element(v4, v0) = v6) | ( ~ (v6 = 0) & element(v2, v1) = v6) | (( ~ (v5 = 0) | ( ~ (v6 = 0) & in(v4, v2) = v6)) & (v5 = 0 | (v6 = 0 & in(v4, v2) = 0))))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (subset_complement(v0, v2) = v3) | ~ (in(v4, v2) = v5) | ? [v6] : (( ~ (v6 = 0) & element(v4, v0) = v6) | ( ~ (v6 = 0) & element(v2, v1) = v6) | (( ~ (v5 = 0) | ( ~ (v6 = 0) & in(v4, v3) = v6)) & (v5 = 0 | (v6 = 0 & in(v4, v3) = 0))))) & ! [v2] : ! [v3] : ! [v4] : ( ~ (subset_complement(v0, v2) = v3) | ~ (element(v4, v0) = 0) | ? [v5] : ? [v6] : (( ~ (v5 = 0) & element(v2, v1) = v5) | (((v6 = 0 & in(v4, v2) = 0) | (v5 = 0 & in(v4, v3) = 0)) & (( ~ (v6 = 0) & in(v4, v2) = v6) | ( ~ (v5 = 0) & in(v4, v3) = v5))))) & ! [v2] : ( ~ (element(v2, v1) = 0) | ? [v3] : (subset_complement(v0, v2) = v3 & ! [v4] : ! [v5] : ( ~ (in(v4, v3) = v5) | ? [v6] : (( ~ (v6 = 0) & element(v4, v0) = v6) | (( ~ (v5 = 0) | ( ~ (v6 = 0) & in(v4, v2) = v6)) & (v5 = 0 | (v6 = 0 & in(v4, v2) = 0))))) & ! [v4] : ! [v5] : ( ~ (in(v4, v2) = v5) | ? [v6] : (( ~ (v6 = 0) & element(v4, v0) = v6) | (( ~ (v5 = 0) | ( ~ (v6 = 0) & in(v4, v3) = v6)) & (v5 = 0 | (v6 = 0 & in(v4, v3) = 0))))) & ! [v4] : ( ~ (element(v4, v0) = 0) | ? [v5] : ? [v6] : (((v6 = 0 & in(v4, v2) = 0) | (v5 = 0 & in(v4, v3) = 0)) & (( ~ (v6 = 0) & in(v4, v2) = v6) | ( ~ (v5 = 0) & in(v4, v3) = v5))))))))
% 50.98/19.92 |
% 50.98/19.92 | Instantiating formula (37) with all_0_9_9, all_0_10_10, all_79_0_101, all_0_11_11 and discharging atoms the_carrier(all_0_11_11) = all_0_10_10, powerset(all_0_10_10) = all_0_9_9, element(all_79_0_101, all_0_9_9) = 0, yields:
% 50.98/19.92 | (308) ? [v0] : ? [v1] : ((v1 = 0 & topstr_closure(all_0_11_11, all_79_0_101) = v0 & element(v0, all_0_9_9) = 0) | ( ~ (v0 = 0) & top_str(all_0_11_11) = v0))
% 50.98/19.92 |
% 50.98/19.92 | Instantiating formula (226) with all_79_0_101 yields:
% 50.98/19.92 | (309) ~ (element(all_79_0_101, all_102_0_135) = 0) | ? [v0] : (subset(all_79_0_101, v0) = 0 & topstr_closure(all_0_11_11, all_79_0_101) = v0)
% 50.98/19.92 |
% 50.98/19.92 | Instantiating formula (29) with all_0_7_7, all_169_1_261, all_259_1_454, all_0_10_10 and discharging atoms subset_complement(all_0_10_10, all_169_1_261) = all_0_7_7, in(all_259_1_454, all_0_7_7) = 0, yields:
% 50.98/19.92 | (310) ? [v0] : ? [v1] : (( ~ (v1 = 0) & powerset(all_0_10_10) = v0 & element(all_169_1_261, v0) = v1) | ( ~ (v0 = 0) & in(all_259_1_454, all_169_1_261) = v0))
% 50.98/19.92 |
% 50.98/19.92 | Instantiating formula (65) with all_0_9_9, all_0_10_10, all_0_7_7, all_259_1_454 and discharging atoms powerset(all_0_10_10) = all_0_9_9, element(all_0_7_7, all_0_9_9) = 0, in(all_259_1_454, all_0_7_7) = 0, yields:
% 50.98/19.92 | (311) element(all_259_1_454, all_0_10_10) = 0
% 50.98/19.92 |
% 50.98/19.92 | Instantiating formula (101) with all_0_9_9, all_0_10_10, all_0_7_7, all_259_1_454 and discharging atoms powerset(all_0_10_10) = all_0_9_9, element(all_0_7_7, all_0_9_9) = 0, in(all_259_1_454, all_0_7_7) = 0, yields:
% 50.98/19.92 | (312) ? [v0] : ( ~ (v0 = 0) & empty(all_0_10_10) = v0)
% 50.98/19.92 |
% 50.98/19.92 | Instantiating formula (82) with all_259_0_453, all_0_8_8, all_259_1_454 and discharging atoms in(all_259_1_454, all_0_8_8) = all_259_0_453, yields:
% 50.98/19.92 | (313) all_259_0_453 = 0 | ? [v0] : ((v0 = 0 & empty(all_0_8_8) = 0) | ( ~ (v0 = 0) & element(all_259_1_454, all_0_8_8) = v0))
% 50.98/19.92 |
% 50.98/19.93 | Instantiating (310) with all_372_0_543, all_372_1_544 yields:
% 50.98/19.93 | (314) ( ~ (all_372_0_543 = 0) & powerset(all_0_10_10) = all_372_1_544 & element(all_169_1_261, all_372_1_544) = all_372_0_543) | ( ~ (all_372_1_544 = 0) & in(all_259_1_454, all_169_1_261) = all_372_1_544)
% 50.98/19.93 |
% 50.98/19.93 | Instantiating (312) with all_382_0_554 yields:
% 50.98/19.93 | (315) ~ (all_382_0_554 = 0) & empty(all_0_10_10) = all_382_0_554
% 50.98/19.93 |
% 50.98/19.93 | Applying alpha-rule on (315) yields:
% 50.98/19.93 | (316) ~ (all_382_0_554 = 0)
% 50.98/19.93 | (317) empty(all_0_10_10) = all_382_0_554
% 50.98/19.93 |
% 50.98/19.93 | Instantiating (307) with all_434_0_702, all_434_1_703 yields:
% 50.98/19.93 | (318) (all_434_1_703 = 0 & empty_carrier(all_0_11_11) = 0) | (the_carrier(all_0_11_11) = all_434_1_703 & powerset(all_434_1_703) = all_434_0_702 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_complement(all_434_1_703, v0) = v1) | ~ (in(v2, v1) = v3) | ? [v4] : (( ~ (v4 = 0) & element(v2, all_434_1_703) = v4) | ( ~ (v4 = 0) & element(v0, all_434_0_702) = v4) | (( ~ (v3 = 0) | ( ~ (v4 = 0) & in(v2, v0) = v4)) & (v3 = 0 | (v4 = 0 & in(v2, v0) = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_complement(all_434_1_703, v0) = v1) | ~ (in(v2, v0) = v3) | ? [v4] : (( ~ (v4 = 0) & element(v2, all_434_1_703) = v4) | ( ~ (v4 = 0) & element(v0, all_434_0_702) = v4) | (( ~ (v3 = 0) | ( ~ (v4 = 0) & in(v2, v1) = v4)) & (v3 = 0 | (v4 = 0 & in(v2, v1) = 0))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_complement(all_434_1_703, v0) = v1) | ~ (element(v2, all_434_1_703) = 0) | ? [v3] : ? [v4] : (( ~ (v3 = 0) & element(v0, all_434_0_702) = v3) | (((v4 = 0 & in(v2, v0) = 0) | (v3 = 0 & in(v2, v1) = 0)) & (( ~ (v4 = 0) & in(v2, v0) = v4) | ( ~ (v3 = 0) & in(v2, v1) = v3))))) & ! [v0] : ( ~ (element(v0, all_434_0_702) = 0) | ? [v1] : (subset_complement(all_434_1_703, v0) = v1 & ! [v2] : ! [v3] : ( ~ (in(v2, v1) = v3) | ? [v4] : (( ~ (v4 = 0) & element(v2, all_434_1_703) = v4) | (( ~ (v3 = 0) | ( ~ (v4 = 0) & in(v2, v0) = v4)) & (v3 = 0 | (v4 = 0 & in(v2, v0) = 0))))) & ! [v2] : ! [v3] : ( ~ (in(v2, v0) = v3) | ? [v4] : (( ~ (v4 = 0) & element(v2, all_434_1_703) = v4) | (( ~ (v3 = 0) | ( ~ (v4 = 0) & in(v2, v1) = v4)) & (v3 = 0 | (v4 = 0 & in(v2, v1) = 0))))) & ! [v2] : ( ~ (element(v2, all_434_1_703) = 0) | ? [v3] : ? [v4] : (((v4 = 0 & in(v2, v0) = 0) | (v3 = 0 & in(v2, v1) = 0)) & (( ~ (v4 = 0) & in(v2, v0) = v4) | ( ~ (v3 = 0) & in(v2, v1) = v3)))))))
% 50.98/19.93 |
% 50.98/19.93 | Instantiating (303) with all_439_0_711, all_439_1_712 yields:
% 50.98/19.93 | (319) powerset(all_0_10_10) = all_439_1_712 & ((all_439_0_711 = 0 & element(all_0_7_7, all_439_1_712) = 0) | ( ~ (all_439_0_711 = 0) & element(all_169_1_261, all_439_1_712) = all_439_0_711))
% 50.98/19.93 |
% 50.98/19.93 | Applying alpha-rule on (319) yields:
% 50.98/19.93 | (320) powerset(all_0_10_10) = all_439_1_712
% 50.98/19.93 | (321) (all_439_0_711 = 0 & element(all_0_7_7, all_439_1_712) = 0) | ( ~ (all_439_0_711 = 0) & element(all_169_1_261, all_439_1_712) = all_439_0_711)
% 50.98/19.93 |
% 50.98/19.93 | Instantiating (306) with all_451_0_733, all_451_1_734 yields:
% 50.98/19.93 | (322) (all_451_1_734 = 0 & empty_carrier(all_0_11_11) = 0) | ( ~ (all_451_0_733 = 0) & the_carrier(all_0_11_11) = all_451_1_734 & empty(all_451_1_734) = all_451_0_733)
% 50.98/19.93 |
% 50.98/19.93 | Instantiating (305) with all_452_0_735, all_452_1_736, all_452_2_737 yields:
% 50.98/19.93 | (323) ((all_452_0_735 = 0 & the_carrier(all_0_11_11) = all_452_1_736 & empty(all_452_1_736) = 0) | ( ~ (all_452_2_737 = 0) & empty_carrier(all_0_11_11) = all_452_2_737)) & ((all_452_2_737 = 0 & empty_carrier(all_0_11_11) = 0) | ( ~ (all_452_0_735 = 0) & the_carrier(all_0_11_11) = all_452_1_736 & empty(all_452_1_736) = all_452_0_735))
% 50.98/19.93 |
% 50.98/19.93 | Applying alpha-rule on (323) yields:
% 50.98/19.93 | (324) (all_452_0_735 = 0 & the_carrier(all_0_11_11) = all_452_1_736 & empty(all_452_1_736) = 0) | ( ~ (all_452_2_737 = 0) & empty_carrier(all_0_11_11) = all_452_2_737)
% 50.98/19.93 | (325) (all_452_2_737 = 0 & empty_carrier(all_0_11_11) = 0) | ( ~ (all_452_0_735 = 0) & the_carrier(all_0_11_11) = all_452_1_736 & empty(all_452_1_736) = all_452_0_735)
% 50.98/19.93 |
% 50.98/19.93 | Instantiating (304) with all_458_0_750, all_458_1_751, all_458_2_752, all_458_3_753, all_458_4_754 yields:
% 50.98/19.93 | (326) (all_458_1_751 = 0 & ~ (all_458_0_750 = 0) & the_carrier(all_0_11_11) = all_458_4_754 & powerset(all_458_4_754) = all_458_3_753 & empty(all_458_2_752) = all_458_0_750 & element(all_458_2_752, all_458_3_753) = 0) | (all_458_4_754 = 0 & empty_carrier(all_0_11_11) = 0)
% 50.98/19.93 |
% 50.98/19.93 | Instantiating (308) with all_503_0_867, all_503_1_868 yields:
% 50.98/19.93 | (327) (all_503_0_867 = 0 & topstr_closure(all_0_11_11, all_79_0_101) = all_503_1_868 & element(all_503_1_868, all_0_9_9) = 0) | ( ~ (all_503_1_868 = 0) & top_str(all_0_11_11) = all_503_1_868)
% 50.98/19.93 |
% 50.98/19.93 +-Applying beta-rule and splitting (214), into two cases.
% 50.98/19.93 |-Branch one:
% 50.98/19.93 | (328) ~ (all_104_1_138 = 0) & one_sorted_str(all_0_11_11) = all_104_1_138
% 50.98/19.93 |
% 50.98/19.93 | Applying alpha-rule on (328) yields:
% 50.98/19.93 | (329) ~ (all_104_1_138 = 0)
% 50.98/19.93 | (330) one_sorted_str(all_0_11_11) = all_104_1_138
% 50.98/19.93 |
% 50.98/19.93 | Instantiating formula (53) with all_0_11_11, all_104_1_138, 0 and discharging atoms one_sorted_str(all_0_11_11) = all_104_1_138, one_sorted_str(all_0_11_11) = 0, yields:
% 50.98/19.93 | (331) all_104_1_138 = 0
% 50.98/19.93 |
% 50.98/19.93 | Equations (331) can reduce 329 to:
% 50.98/19.93 | (222) $false
% 50.98/19.93 |
% 50.98/19.93 |-The branch is then unsatisfiable
% 50.98/19.93 |-Branch two:
% 50.98/19.93 | (333) ((all_104_0_137 = 0 & empty(all_0_10_10) = 0) | ( ~ (all_104_1_138 = 0) & empty_carrier(all_0_11_11) = all_104_1_138)) & ((all_104_1_138 = 0 & empty_carrier(all_0_11_11) = 0) | ( ~ (all_104_0_137 = 0) & empty(all_0_10_10) = all_104_0_137))
% 50.98/19.93 |
% 50.98/19.93 | Applying alpha-rule on (333) yields:
% 50.98/19.93 | (334) (all_104_0_137 = 0 & empty(all_0_10_10) = 0) | ( ~ (all_104_1_138 = 0) & empty_carrier(all_0_11_11) = all_104_1_138)
% 50.98/19.93 | (335) (all_104_1_138 = 0 & empty_carrier(all_0_11_11) = 0) | ( ~ (all_104_0_137 = 0) & empty(all_0_10_10) = all_104_0_137)
% 50.98/19.93 |
% 50.98/19.93 +-Applying beta-rule and splitting (334), into two cases.
% 50.98/19.93 |-Branch one:
% 50.98/19.93 | (336) all_104_0_137 = 0 & empty(all_0_10_10) = 0
% 50.98/19.93 |
% 50.98/19.93 | Applying alpha-rule on (336) yields:
% 50.98/19.93 | (337) all_104_0_137 = 0
% 50.98/19.93 | (338) empty(all_0_10_10) = 0
% 50.98/19.93 |
% 50.98/19.93 | Instantiating formula (163) with all_0_10_10, 0, all_382_0_554 and discharging atoms empty(all_0_10_10) = all_382_0_554, empty(all_0_10_10) = 0, yields:
% 50.98/19.93 | (339) all_382_0_554 = 0
% 50.98/19.93 |
% 50.98/19.93 | Equations (339) can reduce 316 to:
% 50.98/19.93 | (222) $false
% 50.98/19.93 |
% 50.98/19.93 |-The branch is then unsatisfiable
% 50.98/19.93 |-Branch two:
% 50.98/19.93 | (341) ~ (all_104_1_138 = 0) & empty_carrier(all_0_11_11) = all_104_1_138
% 50.98/19.93 |
% 50.98/19.93 | Applying alpha-rule on (341) yields:
% 50.98/19.93 | (329) ~ (all_104_1_138 = 0)
% 50.98/19.93 | (343) empty_carrier(all_0_11_11) = all_104_1_138
% 50.98/19.93 |
% 50.98/19.93 +-Applying beta-rule and splitting (325), into two cases.
% 50.98/19.93 |-Branch one:
% 50.98/19.93 | (344) all_452_2_737 = 0 & empty_carrier(all_0_11_11) = 0
% 50.98/19.93 |
% 50.98/19.93 | Applying alpha-rule on (344) yields:
% 50.98/19.93 | (345) all_452_2_737 = 0
% 50.98/19.93 | (346) empty_carrier(all_0_11_11) = 0
% 50.98/19.93 |
% 50.98/19.93 | Instantiating formula (48) with all_0_11_11, 0, all_104_1_138 and discharging atoms empty_carrier(all_0_11_11) = all_104_1_138, empty_carrier(all_0_11_11) = 0, yields:
% 50.98/19.93 | (331) all_104_1_138 = 0
% 50.98/19.93 |
% 50.98/19.93 | Equations (331) can reduce 329 to:
% 50.98/19.93 | (222) $false
% 50.98/19.93 |
% 50.98/19.93 |-The branch is then unsatisfiable
% 50.98/19.93 |-Branch two:
% 50.98/19.93 | (349) ~ (all_452_0_735 = 0) & the_carrier(all_0_11_11) = all_452_1_736 & empty(all_452_1_736) = all_452_0_735
% 50.98/19.93 |
% 50.98/19.93 | Applying alpha-rule on (349) yields:
% 50.98/19.93 | (350) ~ (all_452_0_735 = 0)
% 50.98/19.93 | (351) the_carrier(all_0_11_11) = all_452_1_736
% 50.98/19.93 | (352) empty(all_452_1_736) = all_452_0_735
% 50.98/19.93 |
% 50.98/19.93 +-Applying beta-rule and splitting (200), into two cases.
% 50.98/19.93 |-Branch one:
% 50.98/19.93 | (353) (all_93_0_127 = 0 & empty_carrier(all_0_11_11) = 0) | ( ~ (all_93_0_127 = 0) & one_sorted_str(all_0_11_11) = all_93_0_127)
% 50.98/19.93 |
% 50.98/19.93 +-Applying beta-rule and splitting (353), into two cases.
% 50.98/19.93 |-Branch one:
% 50.98/19.93 | (354) all_93_0_127 = 0 & empty_carrier(all_0_11_11) = 0
% 50.98/19.93 |
% 50.98/19.93 | Applying alpha-rule on (354) yields:
% 50.98/19.93 | (355) all_93_0_127 = 0
% 50.98/19.93 | (346) empty_carrier(all_0_11_11) = 0
% 50.98/19.93 |
% 50.98/19.93 +-Applying beta-rule and splitting (324), into two cases.
% 50.98/19.93 |-Branch one:
% 50.98/19.93 | (357) all_452_0_735 = 0 & the_carrier(all_0_11_11) = all_452_1_736 & empty(all_452_1_736) = 0
% 50.98/19.93 |
% 50.98/19.93 | Applying alpha-rule on (357) yields:
% 50.98/19.93 | (358) all_452_0_735 = 0
% 50.98/19.93 | (351) the_carrier(all_0_11_11) = all_452_1_736
% 50.98/19.93 | (360) empty(all_452_1_736) = 0
% 50.98/19.93 |
% 50.98/19.93 | Equations (358) can reduce 350 to:
% 50.98/19.93 | (222) $false
% 50.98/19.93 |
% 50.98/19.93 |-The branch is then unsatisfiable
% 50.98/19.93 |-Branch two:
% 50.98/19.93 | (362) ~ (all_452_2_737 = 0) & empty_carrier(all_0_11_11) = all_452_2_737
% 50.98/19.93 |
% 50.98/19.93 | Applying alpha-rule on (362) yields:
% 50.98/19.93 | (363) ~ (all_452_2_737 = 0)
% 50.98/19.93 | (364) empty_carrier(all_0_11_11) = all_452_2_737
% 50.98/19.93 |
% 50.98/19.93 | Instantiating formula (48) with all_0_11_11, all_104_1_138, all_452_2_737 and discharging atoms empty_carrier(all_0_11_11) = all_452_2_737, empty_carrier(all_0_11_11) = all_104_1_138, yields:
% 50.98/19.93 | (365) all_452_2_737 = all_104_1_138
% 50.98/19.93 |
% 50.98/19.93 | Instantiating formula (48) with all_0_11_11, 0, all_452_2_737 and discharging atoms empty_carrier(all_0_11_11) = all_452_2_737, empty_carrier(all_0_11_11) = 0, yields:
% 50.98/19.93 | (345) all_452_2_737 = 0
% 50.98/19.93 |
% 50.98/19.93 | Combining equations (345,365) yields a new equation:
% 50.98/19.93 | (331) all_104_1_138 = 0
% 50.98/19.93 |
% 50.98/19.93 | Equations (331) can reduce 329 to:
% 50.98/19.93 | (222) $false
% 50.98/19.93 |
% 50.98/19.93 |-The branch is then unsatisfiable
% 50.98/19.93 |-Branch two:
% 50.98/19.93 | (369) ~ (all_93_0_127 = 0) & one_sorted_str(all_0_11_11) = all_93_0_127
% 50.98/19.93 |
% 50.98/19.93 | Applying alpha-rule on (369) yields:
% 50.98/19.94 | (370) ~ (all_93_0_127 = 0)
% 50.98/19.94 | (371) one_sorted_str(all_0_11_11) = all_93_0_127
% 50.98/19.94 |
% 50.98/19.94 | Instantiating formula (53) with all_0_11_11, all_93_0_127, 0 and discharging atoms one_sorted_str(all_0_11_11) = all_93_0_127, one_sorted_str(all_0_11_11) = 0, yields:
% 50.98/19.94 | (355) all_93_0_127 = 0
% 50.98/19.94 |
% 50.98/19.94 | Equations (355) can reduce 370 to:
% 50.98/19.94 | (222) $false
% 50.98/19.94 |
% 50.98/19.94 |-The branch is then unsatisfiable
% 50.98/19.94 |-Branch two:
% 50.98/19.94 | (374) powerset(all_0_10_10) = all_93_0_127 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_complement(all_0_10_10, v0) = v1) | ~ (in(v2, v1) = v3) | ? [v4] : (( ~ (v4 = 0) & element(v2, all_0_10_10) = v4) | ( ~ (v4 = 0) & element(v0, all_93_0_127) = v4) | (( ~ (v3 = 0) | ( ~ (v4 = 0) & in(v2, v0) = v4)) & (v3 = 0 | (v4 = 0 & in(v2, v0) = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_complement(all_0_10_10, v0) = v1) | ~ (in(v2, v0) = v3) | ? [v4] : (( ~ (v4 = 0) & element(v2, all_0_10_10) = v4) | ( ~ (v4 = 0) & element(v0, all_93_0_127) = v4) | (( ~ (v3 = 0) | ( ~ (v4 = 0) & in(v2, v1) = v4)) & (v3 = 0 | (v4 = 0 & in(v2, v1) = 0))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_complement(all_0_10_10, v0) = v1) | ~ (element(v2, all_0_10_10) = 0) | ? [v3] : ? [v4] : (( ~ (v3 = 0) & element(v0, all_93_0_127) = v3) | (((v4 = 0 & in(v2, v0) = 0) | (v3 = 0 & in(v2, v1) = 0)) & (( ~ (v4 = 0) & in(v2, v0) = v4) | ( ~ (v3 = 0) & in(v2, v1) = v3))))) & ! [v0] : ( ~ (element(v0, all_93_0_127) = 0) | ? [v1] : (subset_complement(all_0_10_10, v0) = v1 & ! [v2] : ! [v3] : ( ~ (in(v2, v1) = v3) | ? [v4] : (( ~ (v4 = 0) & element(v2, all_0_10_10) = v4) | (( ~ (v3 = 0) | ( ~ (v4 = 0) & in(v2, v0) = v4)) & (v3 = 0 | (v4 = 0 & in(v2, v0) = 0))))) & ! [v2] : ! [v3] : ( ~ (in(v2, v0) = v3) | ? [v4] : (( ~ (v4 = 0) & element(v2, all_0_10_10) = v4) | (( ~ (v3 = 0) | ( ~ (v4 = 0) & in(v2, v1) = v4)) & (v3 = 0 | (v4 = 0 & in(v2, v1) = 0))))) & ! [v2] : ( ~ (element(v2, all_0_10_10) = 0) | ? [v3] : ? [v4] : (((v4 = 0 & in(v2, v0) = 0) | (v3 = 0 & in(v2, v1) = 0)) & (( ~ (v4 = 0) & in(v2, v0) = v4) | ( ~ (v3 = 0) & in(v2, v1) = v3))))))
% 50.98/19.94 |
% 50.98/19.94 | Applying alpha-rule on (374) yields:
% 50.98/19.94 | (375) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_complement(all_0_10_10, v0) = v1) | ~ (in(v2, v0) = v3) | ? [v4] : (( ~ (v4 = 0) & element(v2, all_0_10_10) = v4) | ( ~ (v4 = 0) & element(v0, all_93_0_127) = v4) | (( ~ (v3 = 0) | ( ~ (v4 = 0) & in(v2, v1) = v4)) & (v3 = 0 | (v4 = 0 & in(v2, v1) = 0)))))
% 50.98/19.94 | (376) powerset(all_0_10_10) = all_93_0_127
% 50.98/19.94 | (377) ! [v0] : ( ~ (element(v0, all_93_0_127) = 0) | ? [v1] : (subset_complement(all_0_10_10, v0) = v1 & ! [v2] : ! [v3] : ( ~ (in(v2, v1) = v3) | ? [v4] : (( ~ (v4 = 0) & element(v2, all_0_10_10) = v4) | (( ~ (v3 = 0) | ( ~ (v4 = 0) & in(v2, v0) = v4)) & (v3 = 0 | (v4 = 0 & in(v2, v0) = 0))))) & ! [v2] : ! [v3] : ( ~ (in(v2, v0) = v3) | ? [v4] : (( ~ (v4 = 0) & element(v2, all_0_10_10) = v4) | (( ~ (v3 = 0) | ( ~ (v4 = 0) & in(v2, v1) = v4)) & (v3 = 0 | (v4 = 0 & in(v2, v1) = 0))))) & ! [v2] : ( ~ (element(v2, all_0_10_10) = 0) | ? [v3] : ? [v4] : (((v4 = 0 & in(v2, v0) = 0) | (v3 = 0 & in(v2, v1) = 0)) & (( ~ (v4 = 0) & in(v2, v0) = v4) | ( ~ (v3 = 0) & in(v2, v1) = v3))))))
% 50.98/19.94 | (378) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_complement(all_0_10_10, v0) = v1) | ~ (element(v2, all_0_10_10) = 0) | ? [v3] : ? [v4] : (( ~ (v3 = 0) & element(v0, all_93_0_127) = v3) | (((v4 = 0 & in(v2, v0) = 0) | (v3 = 0 & in(v2, v1) = 0)) & (( ~ (v4 = 0) & in(v2, v0) = v4) | ( ~ (v3 = 0) & in(v2, v1) = v3)))))
% 50.98/19.94 | (379) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_complement(all_0_10_10, v0) = v1) | ~ (in(v2, v1) = v3) | ? [v4] : (( ~ (v4 = 0) & element(v2, all_0_10_10) = v4) | ( ~ (v4 = 0) & element(v0, all_93_0_127) = v4) | (( ~ (v3 = 0) | ( ~ (v4 = 0) & in(v2, v0) = v4)) & (v3 = 0 | (v4 = 0 & in(v2, v0) = 0)))))
% 50.98/19.94 |
% 50.98/19.94 | Instantiating formula (379) with 0, all_259_1_454, all_0_7_7, all_169_1_261 and discharging atoms subset_complement(all_0_10_10, all_169_1_261) = all_0_7_7, in(all_259_1_454, all_0_7_7) = 0, yields:
% 50.98/19.94 | (380) ? [v0] : (( ~ (v0 = 0) & element(all_259_1_454, all_0_10_10) = v0) | ( ~ (v0 = 0) & element(all_169_1_261, all_93_0_127) = v0) | ( ~ (v0 = 0) & in(all_259_1_454, all_169_1_261) = v0))
% 50.98/19.94 |
% 50.98/19.94 | Instantiating formula (379) with all_259_0_453, all_259_1_454, all_0_8_8, all_79_0_101 and discharging atoms subset_complement(all_0_10_10, all_79_0_101) = all_0_8_8, in(all_259_1_454, all_0_8_8) = all_259_0_453, yields:
% 50.98/19.94 | (381) ? [v0] : (( ~ (v0 = 0) & element(all_259_1_454, all_0_10_10) = v0) | ( ~ (v0 = 0) & element(all_79_0_101, all_93_0_127) = v0) | (( ~ (all_259_0_453 = 0) | ( ~ (v0 = 0) & in(all_259_1_454, all_79_0_101) = v0)) & (all_259_0_453 = 0 | (v0 = 0 & in(all_259_1_454, all_79_0_101) = 0))))
% 50.98/19.94 |
% 50.98/19.94 | Instantiating formula (375) with all_259_0_453, all_259_1_454, all_79_0_101, all_0_8_8 and discharging atoms subset_complement(all_0_10_10, all_0_8_8) = all_79_0_101, in(all_259_1_454, all_0_8_8) = all_259_0_453, yields:
% 50.98/19.94 | (382) ? [v0] : (( ~ (v0 = 0) & element(all_259_1_454, all_0_10_10) = v0) | ( ~ (v0 = 0) & element(all_0_8_8, all_93_0_127) = v0) | (( ~ (all_259_0_453 = 0) | ( ~ (v0 = 0) & in(all_259_1_454, all_79_0_101) = v0)) & (all_259_0_453 = 0 | (v0 = 0 & in(all_259_1_454, all_79_0_101) = 0))))
% 50.98/19.94 |
% 50.98/19.94 | Instantiating (382) with all_589_0_1139 yields:
% 50.98/19.94 | (383) ( ~ (all_589_0_1139 = 0) & element(all_259_1_454, all_0_10_10) = all_589_0_1139) | ( ~ (all_589_0_1139 = 0) & element(all_0_8_8, all_93_0_127) = all_589_0_1139) | (( ~ (all_259_0_453 = 0) | ( ~ (all_589_0_1139 = 0) & in(all_259_1_454, all_79_0_101) = all_589_0_1139)) & (all_259_0_453 = 0 | (all_589_0_1139 = 0 & in(all_259_1_454, all_79_0_101) = 0)))
% 50.98/19.94 |
% 50.98/19.94 | Instantiating (381) with all_590_0_1140 yields:
% 50.98/19.94 | (384) ( ~ (all_590_0_1140 = 0) & element(all_259_1_454, all_0_10_10) = all_590_0_1140) | ( ~ (all_590_0_1140 = 0) & element(all_79_0_101, all_93_0_127) = all_590_0_1140) | (( ~ (all_259_0_453 = 0) | ( ~ (all_590_0_1140 = 0) & in(all_259_1_454, all_79_0_101) = all_590_0_1140)) & (all_259_0_453 = 0 | (all_590_0_1140 = 0 & in(all_259_1_454, all_79_0_101) = 0)))
% 50.98/19.94 |
% 50.98/19.94 | Instantiating (380) with all_591_0_1141 yields:
% 50.98/19.94 | (385) ( ~ (all_591_0_1141 = 0) & element(all_259_1_454, all_0_10_10) = all_591_0_1141) | ( ~ (all_591_0_1141 = 0) & element(all_169_1_261, all_93_0_127) = all_591_0_1141) | ( ~ (all_591_0_1141 = 0) & in(all_259_1_454, all_169_1_261) = all_591_0_1141)
% 51.39/19.94 |
% 51.39/19.94 +-Applying beta-rule and splitting (324), into two cases.
% 51.39/19.94 |-Branch one:
% 51.39/19.94 | (357) all_452_0_735 = 0 & the_carrier(all_0_11_11) = all_452_1_736 & empty(all_452_1_736) = 0
% 51.39/19.94 |
% 51.39/19.94 | Applying alpha-rule on (357) yields:
% 51.39/19.94 | (358) all_452_0_735 = 0
% 51.39/19.94 | (351) the_carrier(all_0_11_11) = all_452_1_736
% 51.39/19.94 | (360) empty(all_452_1_736) = 0
% 51.39/19.94 |
% 51.39/19.94 | Equations (358) can reduce 350 to:
% 51.39/19.94 | (222) $false
% 51.39/19.94 |
% 51.39/19.94 |-The branch is then unsatisfiable
% 51.39/19.94 |-Branch two:
% 51.39/19.94 | (362) ~ (all_452_2_737 = 0) & empty_carrier(all_0_11_11) = all_452_2_737
% 51.39/19.94 |
% 51.39/19.94 | Applying alpha-rule on (362) yields:
% 51.39/19.94 | (363) ~ (all_452_2_737 = 0)
% 51.39/19.94 | (364) empty_carrier(all_0_11_11) = all_452_2_737
% 51.39/19.94 |
% 51.39/19.94 +-Applying beta-rule and splitting (215), into two cases.
% 51.39/19.94 |-Branch one:
% 51.39/19.94 | (394) (all_105_1_140 = 0 & ~ (all_105_0_139 = 0) & powerset(all_0_10_10) = all_105_3_142 & empty(all_105_2_141) = all_105_0_139 & element(all_105_2_141, all_105_3_142) = 0) | (all_105_3_142 = 0 & empty_carrier(all_0_11_11) = 0)
% 51.39/19.94 |
% 51.39/19.94 +-Applying beta-rule and splitting (394), into two cases.
% 51.39/19.94 |-Branch one:
% 51.39/19.94 | (395) all_105_1_140 = 0 & ~ (all_105_0_139 = 0) & powerset(all_0_10_10) = all_105_3_142 & empty(all_105_2_141) = all_105_0_139 & element(all_105_2_141, all_105_3_142) = 0
% 51.39/19.94 |
% 51.39/19.94 | Applying alpha-rule on (395) yields:
% 51.39/19.94 | (396) powerset(all_0_10_10) = all_105_3_142
% 51.39/19.94 | (397) all_105_1_140 = 0
% 51.39/19.94 | (398) ~ (all_105_0_139 = 0)
% 51.39/19.94 | (399) element(all_105_2_141, all_105_3_142) = 0
% 51.39/19.94 | (400) empty(all_105_2_141) = all_105_0_139
% 51.39/19.94 |
% 51.39/19.94 +-Applying beta-rule and splitting (318), into two cases.
% 51.39/19.94 |-Branch one:
% 51.39/19.94 | (401) all_434_1_703 = 0 & empty_carrier(all_0_11_11) = 0
% 51.39/19.94 |
% 51.39/19.94 | Applying alpha-rule on (401) yields:
% 51.39/19.94 | (402) all_434_1_703 = 0
% 51.39/19.94 | (346) empty_carrier(all_0_11_11) = 0
% 51.39/19.94 |
% 51.39/19.94 | Instantiating formula (48) with all_0_11_11, all_104_1_138, all_452_2_737 and discharging atoms empty_carrier(all_0_11_11) = all_452_2_737, empty_carrier(all_0_11_11) = all_104_1_138, yields:
% 51.39/19.94 | (365) all_452_2_737 = all_104_1_138
% 51.39/19.95 |
% 51.39/19.95 | Instantiating formula (48) with all_0_11_11, 0, all_452_2_737 and discharging atoms empty_carrier(all_0_11_11) = all_452_2_737, empty_carrier(all_0_11_11) = 0, yields:
% 51.39/19.95 | (345) all_452_2_737 = 0
% 51.39/19.95 |
% 51.39/19.95 | Combining equations (365,345) yields a new equation:
% 51.39/19.95 | (406) all_104_1_138 = 0
% 51.39/19.95 |
% 51.39/19.95 | Simplifying 406 yields:
% 51.39/19.95 | (331) all_104_1_138 = 0
% 51.39/19.95 |
% 51.39/19.95 | Equations (331) can reduce 329 to:
% 51.39/19.95 | (222) $false
% 51.39/19.95 |
% 51.39/19.95 |-The branch is then unsatisfiable
% 51.39/19.95 |-Branch two:
% 51.39/19.95 | (409) the_carrier(all_0_11_11) = all_434_1_703 & powerset(all_434_1_703) = all_434_0_702 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_complement(all_434_1_703, v0) = v1) | ~ (in(v2, v1) = v3) | ? [v4] : (( ~ (v4 = 0) & element(v2, all_434_1_703) = v4) | ( ~ (v4 = 0) & element(v0, all_434_0_702) = v4) | (( ~ (v3 = 0) | ( ~ (v4 = 0) & in(v2, v0) = v4)) & (v3 = 0 | (v4 = 0 & in(v2, v0) = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_complement(all_434_1_703, v0) = v1) | ~ (in(v2, v0) = v3) | ? [v4] : (( ~ (v4 = 0) & element(v2, all_434_1_703) = v4) | ( ~ (v4 = 0) & element(v0, all_434_0_702) = v4) | (( ~ (v3 = 0) | ( ~ (v4 = 0) & in(v2, v1) = v4)) & (v3 = 0 | (v4 = 0 & in(v2, v1) = 0))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_complement(all_434_1_703, v0) = v1) | ~ (element(v2, all_434_1_703) = 0) | ? [v3] : ? [v4] : (( ~ (v3 = 0) & element(v0, all_434_0_702) = v3) | (((v4 = 0 & in(v2, v0) = 0) | (v3 = 0 & in(v2, v1) = 0)) & (( ~ (v4 = 0) & in(v2, v0) = v4) | ( ~ (v3 = 0) & in(v2, v1) = v3))))) & ! [v0] : ( ~ (element(v0, all_434_0_702) = 0) | ? [v1] : (subset_complement(all_434_1_703, v0) = v1 & ! [v2] : ! [v3] : ( ~ (in(v2, v1) = v3) | ? [v4] : (( ~ (v4 = 0) & element(v2, all_434_1_703) = v4) | (( ~ (v3 = 0) | ( ~ (v4 = 0) & in(v2, v0) = v4)) & (v3 = 0 | (v4 = 0 & in(v2, v0) = 0))))) & ! [v2] : ! [v3] : ( ~ (in(v2, v0) = v3) | ? [v4] : (( ~ (v4 = 0) & element(v2, all_434_1_703) = v4) | (( ~ (v3 = 0) | ( ~ (v4 = 0) & in(v2, v1) = v4)) & (v3 = 0 | (v4 = 0 & in(v2, v1) = 0))))) & ! [v2] : ( ~ (element(v2, all_434_1_703) = 0) | ? [v3] : ? [v4] : (((v4 = 0 & in(v2, v0) = 0) | (v3 = 0 & in(v2, v1) = 0)) & (( ~ (v4 = 0) & in(v2, v0) = v4) | ( ~ (v3 = 0) & in(v2, v1) = v3))))))
% 51.39/19.95 |
% 51.39/19.95 | Applying alpha-rule on (409) yields:
% 51.39/19.95 | (410) the_carrier(all_0_11_11) = all_434_1_703
% 51.39/19.95 | (411) powerset(all_434_1_703) = all_434_0_702
% 51.39/19.95 | (412) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_complement(all_434_1_703, v0) = v1) | ~ (element(v2, all_434_1_703) = 0) | ? [v3] : ? [v4] : (( ~ (v3 = 0) & element(v0, all_434_0_702) = v3) | (((v4 = 0 & in(v2, v0) = 0) | (v3 = 0 & in(v2, v1) = 0)) & (( ~ (v4 = 0) & in(v2, v0) = v4) | ( ~ (v3 = 0) & in(v2, v1) = v3)))))
% 51.39/19.95 | (413) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_complement(all_434_1_703, v0) = v1) | ~ (in(v2, v0) = v3) | ? [v4] : (( ~ (v4 = 0) & element(v2, all_434_1_703) = v4) | ( ~ (v4 = 0) & element(v0, all_434_0_702) = v4) | (( ~ (v3 = 0) | ( ~ (v4 = 0) & in(v2, v1) = v4)) & (v3 = 0 | (v4 = 0 & in(v2, v1) = 0)))))
% 51.39/19.95 | (414) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_complement(all_434_1_703, v0) = v1) | ~ (in(v2, v1) = v3) | ? [v4] : (( ~ (v4 = 0) & element(v2, all_434_1_703) = v4) | ( ~ (v4 = 0) & element(v0, all_434_0_702) = v4) | (( ~ (v3 = 0) | ( ~ (v4 = 0) & in(v2, v0) = v4)) & (v3 = 0 | (v4 = 0 & in(v2, v0) = 0)))))
% 51.39/19.95 | (415) ! [v0] : ( ~ (element(v0, all_434_0_702) = 0) | ? [v1] : (subset_complement(all_434_1_703, v0) = v1 & ! [v2] : ! [v3] : ( ~ (in(v2, v1) = v3) | ? [v4] : (( ~ (v4 = 0) & element(v2, all_434_1_703) = v4) | (( ~ (v3 = 0) | ( ~ (v4 = 0) & in(v2, v0) = v4)) & (v3 = 0 | (v4 = 0 & in(v2, v0) = 0))))) & ! [v2] : ! [v3] : ( ~ (in(v2, v0) = v3) | ? [v4] : (( ~ (v4 = 0) & element(v2, all_434_1_703) = v4) | (( ~ (v3 = 0) | ( ~ (v4 = 0) & in(v2, v1) = v4)) & (v3 = 0 | (v4 = 0 & in(v2, v1) = 0))))) & ! [v2] : ( ~ (element(v2, all_434_1_703) = 0) | ? [v3] : ? [v4] : (((v4 = 0 & in(v2, v0) = 0) | (v3 = 0 & in(v2, v1) = 0)) & (( ~ (v4 = 0) & in(v2, v0) = v4) | ( ~ (v3 = 0) & in(v2, v1) = v3))))))
% 51.39/19.95 |
% 51.39/19.95 +-Applying beta-rule and splitting (326), into two cases.
% 51.39/19.95 |-Branch one:
% 51.39/19.95 | (416) all_458_1_751 = 0 & ~ (all_458_0_750 = 0) & the_carrier(all_0_11_11) = all_458_4_754 & powerset(all_458_4_754) = all_458_3_753 & empty(all_458_2_752) = all_458_0_750 & element(all_458_2_752, all_458_3_753) = 0
% 51.39/19.95 |
% 51.39/19.95 | Applying alpha-rule on (416) yields:
% 51.39/19.95 | (417) powerset(all_458_4_754) = all_458_3_753
% 51.39/19.95 | (418) ~ (all_458_0_750 = 0)
% 51.39/19.95 | (419) element(all_458_2_752, all_458_3_753) = 0
% 51.39/19.95 | (420) the_carrier(all_0_11_11) = all_458_4_754
% 51.39/19.95 | (421) all_458_1_751 = 0
% 51.39/19.95 | (422) empty(all_458_2_752) = all_458_0_750
% 51.39/19.95 |
% 51.39/19.95 +-Applying beta-rule and splitting (309), into two cases.
% 51.39/19.95 |-Branch one:
% 51.39/19.95 | (423) ~ (element(all_79_0_101, all_102_0_135) = 0)
% 51.39/19.95 |
% 51.39/19.95 | From (254) and (423) follows:
% 51.39/19.95 | (424) ~ (element(all_79_0_101, all_0_9_9) = 0)
% 51.39/19.95 |
% 51.39/19.95 | Using (195) and (424) yields:
% 51.39/19.95 | (425) $false
% 51.39/19.95 |
% 51.39/19.95 |-The branch is then unsatisfiable
% 51.39/19.95 |-Branch two:
% 51.39/19.95 | (426) element(all_79_0_101, all_102_0_135) = 0
% 51.39/19.95 | (427) ? [v0] : (subset(all_79_0_101, v0) = 0 & topstr_closure(all_0_11_11, all_79_0_101) = v0)
% 51.39/19.95 |
% 51.39/19.95 | Instantiating (427) with all_674_0_1231 yields:
% 51.39/19.95 | (428) subset(all_79_0_101, all_674_0_1231) = 0 & topstr_closure(all_0_11_11, all_79_0_101) = all_674_0_1231
% 51.39/19.95 |
% 51.39/19.95 | Applying alpha-rule on (428) yields:
% 51.39/19.95 | (429) subset(all_79_0_101, all_674_0_1231) = 0
% 51.39/19.95 | (430) topstr_closure(all_0_11_11, all_79_0_101) = all_674_0_1231
% 51.39/19.95 |
% 51.39/19.95 | From (254) and (426) follows:
% 51.39/19.95 | (195) element(all_79_0_101, all_0_9_9) = 0
% 51.39/19.95 |
% 51.39/19.95 +-Applying beta-rule and splitting (313), into two cases.
% 51.39/19.95 |-Branch one:
% 51.39/19.95 | (432) all_259_0_453 = 0
% 51.39/19.95 |
% 51.39/19.95 | Equations (432) can reduce 236 to:
% 51.39/19.95 | (222) $false
% 51.39/19.95 |
% 51.39/19.95 |-The branch is then unsatisfiable
% 51.39/19.95 |-Branch two:
% 51.39/19.95 | (236) ~ (all_259_0_453 = 0)
% 51.39/19.95 | (435) ? [v0] : ((v0 = 0 & empty(all_0_8_8) = 0) | ( ~ (v0 = 0) & element(all_259_1_454, all_0_8_8) = v0))
% 51.39/19.95 |
% 51.39/19.95 +-Applying beta-rule and splitting (327), into two cases.
% 51.39/19.95 |-Branch one:
% 51.39/19.95 | (436) all_503_0_867 = 0 & topstr_closure(all_0_11_11, all_79_0_101) = all_503_1_868 & element(all_503_1_868, all_0_9_9) = 0
% 51.39/19.95 |
% 51.39/19.95 | Applying alpha-rule on (436) yields:
% 51.39/19.95 | (437) all_503_0_867 = 0
% 51.39/19.95 | (438) topstr_closure(all_0_11_11, all_79_0_101) = all_503_1_868
% 51.39/19.95 | (439) element(all_503_1_868, all_0_9_9) = 0
% 51.39/19.95 |
% 51.39/19.95 +-Applying beta-rule and splitting (322), into two cases.
% 51.39/19.95 |-Branch one:
% 51.39/19.95 | (440) all_451_1_734 = 0 & empty_carrier(all_0_11_11) = 0
% 51.39/19.95 |
% 51.39/19.95 | Applying alpha-rule on (440) yields:
% 51.39/19.95 | (441) all_451_1_734 = 0
% 51.39/19.95 | (346) empty_carrier(all_0_11_11) = 0
% 51.39/19.95 |
% 51.39/19.95 | Instantiating formula (48) with all_0_11_11, all_104_1_138, all_452_2_737 and discharging atoms empty_carrier(all_0_11_11) = all_452_2_737, empty_carrier(all_0_11_11) = all_104_1_138, yields:
% 51.39/19.95 | (365) all_452_2_737 = all_104_1_138
% 51.39/19.95 |
% 51.39/19.95 | Instantiating formula (48) with all_0_11_11, 0, all_452_2_737 and discharging atoms empty_carrier(all_0_11_11) = all_452_2_737, empty_carrier(all_0_11_11) = 0, yields:
% 51.39/19.95 | (345) all_452_2_737 = 0
% 51.39/19.95 |
% 51.39/19.95 | Combining equations (365,345) yields a new equation:
% 51.39/19.95 | (406) all_104_1_138 = 0
% 51.39/19.95 |
% 51.39/19.95 | Simplifying 406 yields:
% 51.39/19.95 | (331) all_104_1_138 = 0
% 51.39/19.95 |
% 51.39/19.95 | Equations (331) can reduce 329 to:
% 51.39/19.95 | (222) $false
% 51.39/19.95 |
% 51.39/19.95 |-The branch is then unsatisfiable
% 51.39/19.95 |-Branch two:
% 51.39/19.95 | (448) ~ (all_451_0_733 = 0) & the_carrier(all_0_11_11) = all_451_1_734 & empty(all_451_1_734) = all_451_0_733
% 51.39/19.95 |
% 51.39/19.95 | Applying alpha-rule on (448) yields:
% 51.39/19.95 | (449) ~ (all_451_0_733 = 0)
% 51.39/19.95 | (450) the_carrier(all_0_11_11) = all_451_1_734
% 51.39/19.96 | (451) empty(all_451_1_734) = all_451_0_733
% 51.39/19.96 |
% 51.39/19.96 | Instantiating formula (17) with all_0_11_11, all_79_0_101, all_674_0_1231, all_169_1_261 and discharging atoms topstr_closure(all_0_11_11, all_79_0_101) = all_674_0_1231, topstr_closure(all_0_11_11, all_79_0_101) = all_169_1_261, yields:
% 51.39/19.96 | (452) all_674_0_1231 = all_169_1_261
% 51.39/19.96 |
% 51.39/19.96 | Instantiating formula (17) with all_0_11_11, all_79_0_101, all_503_1_868, all_674_0_1231 and discharging atoms topstr_closure(all_0_11_11, all_79_0_101) = all_674_0_1231, topstr_closure(all_0_11_11, all_79_0_101) = all_503_1_868, yields:
% 51.39/19.96 | (453) all_674_0_1231 = all_503_1_868
% 51.39/19.96 |
% 51.39/19.96 | Instantiating formula (145) with all_0_11_11, all_452_1_736, all_458_4_754 and discharging atoms the_carrier(all_0_11_11) = all_458_4_754, the_carrier(all_0_11_11) = all_452_1_736, yields:
% 51.39/19.96 | (454) all_458_4_754 = all_452_1_736
% 51.39/19.96 |
% 51.39/19.96 | Instantiating formula (145) with all_0_11_11, all_451_1_734, all_0_10_10 and discharging atoms the_carrier(all_0_11_11) = all_451_1_734, the_carrier(all_0_11_11) = all_0_10_10, yields:
% 51.39/19.96 | (455) all_451_1_734 = all_0_10_10
% 51.39/19.96 |
% 51.39/19.96 | Instantiating formula (145) with all_0_11_11, all_451_1_734, all_452_1_736 and discharging atoms the_carrier(all_0_11_11) = all_452_1_736, the_carrier(all_0_11_11) = all_451_1_734, yields:
% 51.39/19.96 | (456) all_452_1_736 = all_451_1_734
% 51.39/19.96 |
% 51.39/19.96 | Instantiating formula (145) with all_0_11_11, all_434_1_703, all_458_4_754 and discharging atoms the_carrier(all_0_11_11) = all_458_4_754, the_carrier(all_0_11_11) = all_434_1_703, yields:
% 51.39/19.96 | (457) all_458_4_754 = all_434_1_703
% 51.39/19.96 |
% 51.39/19.96 | Instantiating formula (74) with all_0_10_10, all_439_1_712, all_0_9_9 and discharging atoms powerset(all_0_10_10) = all_439_1_712, powerset(all_0_10_10) = all_0_9_9, yields:
% 51.39/19.96 | (458) all_439_1_712 = all_0_9_9
% 51.39/19.96 |
% 51.39/19.96 | Instantiating formula (74) with all_0_10_10, all_105_3_142, all_439_1_712 and discharging atoms powerset(all_0_10_10) = all_439_1_712, powerset(all_0_10_10) = all_105_3_142, yields:
% 51.39/19.96 | (459) all_439_1_712 = all_105_3_142
% 51.39/19.96 |
% 51.39/19.96 | Instantiating formula (74) with all_0_10_10, all_93_0_127, all_439_1_712 and discharging atoms powerset(all_0_10_10) = all_439_1_712, powerset(all_0_10_10) = all_93_0_127, yields:
% 51.39/19.96 | (460) all_439_1_712 = all_93_0_127
% 51.39/19.96 |
% 51.39/19.96 | Combining equations (452,453) yields a new equation:
% 51.39/19.96 | (461) all_503_1_868 = all_169_1_261
% 51.39/19.96 |
% 51.39/19.96 | Combining equations (454,457) yields a new equation:
% 51.39/19.96 | (462) all_452_1_736 = all_434_1_703
% 51.39/19.96 |
% 51.39/19.96 | Simplifying 462 yields:
% 51.39/19.96 | (463) all_452_1_736 = all_434_1_703
% 51.39/19.96 |
% 51.39/19.96 | Combining equations (456,463) yields a new equation:
% 51.39/19.96 | (464) all_451_1_734 = all_434_1_703
% 51.39/19.96 |
% 51.39/19.96 | Simplifying 464 yields:
% 51.39/19.96 | (465) all_451_1_734 = all_434_1_703
% 51.39/19.96 |
% 51.39/19.96 | Combining equations (465,455) yields a new equation:
% 51.39/19.96 | (466) all_434_1_703 = all_0_10_10
% 51.39/19.96 |
% 51.39/19.96 | Simplifying 466 yields:
% 51.39/19.96 | (467) all_434_1_703 = all_0_10_10
% 51.39/19.96 |
% 51.39/19.96 | Combining equations (458,459) yields a new equation:
% 51.39/19.96 | (468) all_105_3_142 = all_0_9_9
% 51.39/19.96 |
% 51.39/19.96 | Combining equations (460,459) yields a new equation:
% 51.39/19.96 | (469) all_105_3_142 = all_93_0_127
% 51.39/19.96 |
% 51.39/19.96 | Combining equations (468,469) yields a new equation:
% 51.39/19.96 | (470) all_93_0_127 = all_0_9_9
% 51.39/19.96 |
% 51.39/19.96 | Combining equations (467,457) yields a new equation:
% 51.39/19.96 | (471) all_458_4_754 = all_0_10_10
% 51.39/19.96 |
% 51.39/19.96 | Combining equations (461,453) yields a new equation:
% 51.39/19.96 | (452) all_674_0_1231 = all_169_1_261
% 51.39/19.96 |
% 51.39/19.96 | From (452) and (429) follows:
% 51.39/19.96 | (473) subset(all_79_0_101, all_169_1_261) = 0
% 51.39/19.96 |
% 51.39/19.96 | From (471) and (417) follows:
% 51.39/19.96 | (474) powerset(all_0_10_10) = all_458_3_753
% 51.39/19.96 |
% 51.39/19.96 | From (467) and (411) follows:
% 51.39/19.96 | (475) powerset(all_0_10_10) = all_434_0_702
% 51.39/19.96 |
% 51.39/19.96 | From (470) and (376) follows:
% 51.39/19.96 | (141) powerset(all_0_10_10) = all_0_9_9
% 51.39/19.96 |
% 51.39/19.96 | From (461) and (439) follows:
% 51.39/19.96 | (477) element(all_169_1_261, all_0_9_9) = 0
% 51.39/19.96 |
% 51.39/19.96 +-Applying beta-rule and splitting (384), into two cases.
% 51.39/19.96 |-Branch one:
% 51.39/19.96 | (478) ( ~ (all_590_0_1140 = 0) & element(all_259_1_454, all_0_10_10) = all_590_0_1140) | ( ~ (all_590_0_1140 = 0) & element(all_79_0_101, all_93_0_127) = all_590_0_1140)
% 51.39/19.96 |
% 51.39/19.96 +-Applying beta-rule and splitting (478), into two cases.
% 51.39/19.96 |-Branch one:
% 51.39/19.96 | (479) ~ (all_590_0_1140 = 0) & element(all_259_1_454, all_0_10_10) = all_590_0_1140
% 51.39/19.96 |
% 51.39/19.96 | Applying alpha-rule on (479) yields:
% 51.39/19.96 | (480) ~ (all_590_0_1140 = 0)
% 51.39/19.96 | (481) element(all_259_1_454, all_0_10_10) = all_590_0_1140
% 51.39/19.96 |
% 51.39/19.96 | Instantiating formula (121) with all_259_1_454, all_0_10_10, all_590_0_1140, 0 and discharging atoms element(all_259_1_454, all_0_10_10) = all_590_0_1140, element(all_259_1_454, all_0_10_10) = 0, yields:
% 51.39/19.96 | (482) all_590_0_1140 = 0
% 51.39/19.96 |
% 51.39/19.96 | Equations (482) can reduce 480 to:
% 51.39/19.96 | (222) $false
% 51.39/19.96 |
% 51.39/19.96 |-The branch is then unsatisfiable
% 51.39/19.96 |-Branch two:
% 51.39/19.96 | (484) ~ (all_590_0_1140 = 0) & element(all_79_0_101, all_93_0_127) = all_590_0_1140
% 51.39/19.96 |
% 51.39/19.96 | Applying alpha-rule on (484) yields:
% 51.39/19.96 | (480) ~ (all_590_0_1140 = 0)
% 51.39/19.96 | (486) element(all_79_0_101, all_93_0_127) = all_590_0_1140
% 51.39/19.96 |
% 51.39/19.96 | From (470) and (486) follows:
% 51.39/19.96 | (487) element(all_79_0_101, all_0_9_9) = all_590_0_1140
% 51.39/19.96 |
% 51.39/19.96 | Instantiating formula (121) with all_79_0_101, all_0_9_9, all_590_0_1140, 0 and discharging atoms element(all_79_0_101, all_0_9_9) = all_590_0_1140, element(all_79_0_101, all_0_9_9) = 0, yields:
% 51.39/19.96 | (482) all_590_0_1140 = 0
% 51.39/19.96 |
% 51.39/19.96 | Equations (482) can reduce 480 to:
% 51.39/19.96 | (222) $false
% 51.39/19.96 |
% 51.39/19.96 |-The branch is then unsatisfiable
% 51.39/19.96 |-Branch two:
% 51.39/19.96 | (490) ( ~ (all_259_0_453 = 0) | ( ~ (all_590_0_1140 = 0) & in(all_259_1_454, all_79_0_101) = all_590_0_1140)) & (all_259_0_453 = 0 | (all_590_0_1140 = 0 & in(all_259_1_454, all_79_0_101) = 0))
% 51.39/19.96 |
% 51.39/19.96 | Applying alpha-rule on (490) yields:
% 51.39/19.96 | (491) ~ (all_259_0_453 = 0) | ( ~ (all_590_0_1140 = 0) & in(all_259_1_454, all_79_0_101) = all_590_0_1140)
% 51.39/19.96 | (492) all_259_0_453 = 0 | (all_590_0_1140 = 0 & in(all_259_1_454, all_79_0_101) = 0)
% 51.39/19.96 |
% 51.39/19.96 +-Applying beta-rule and splitting (383), into two cases.
% 51.39/19.96 |-Branch one:
% 51.39/19.96 | (493) ( ~ (all_589_0_1139 = 0) & element(all_259_1_454, all_0_10_10) = all_589_0_1139) | ( ~ (all_589_0_1139 = 0) & element(all_0_8_8, all_93_0_127) = all_589_0_1139)
% 51.39/19.96 |
% 51.39/19.96 +-Applying beta-rule and splitting (493), into two cases.
% 51.39/19.96 |-Branch one:
% 51.39/19.96 | (494) ~ (all_589_0_1139 = 0) & element(all_259_1_454, all_0_10_10) = all_589_0_1139
% 51.39/19.96 |
% 51.39/19.96 | Applying alpha-rule on (494) yields:
% 51.39/19.96 | (495) ~ (all_589_0_1139 = 0)
% 51.39/19.96 | (496) element(all_259_1_454, all_0_10_10) = all_589_0_1139
% 51.39/19.96 |
% 51.39/19.96 | Instantiating formula (121) with all_259_1_454, all_0_10_10, all_589_0_1139, 0 and discharging atoms element(all_259_1_454, all_0_10_10) = all_589_0_1139, element(all_259_1_454, all_0_10_10) = 0, yields:
% 51.39/19.96 | (497) all_589_0_1139 = 0
% 51.39/19.96 |
% 51.39/19.96 | Equations (497) can reduce 495 to:
% 51.39/19.96 | (222) $false
% 51.39/19.96 |
% 51.39/19.96 |-The branch is then unsatisfiable
% 51.39/19.96 |-Branch two:
% 51.39/19.96 | (499) ~ (all_589_0_1139 = 0) & element(all_0_8_8, all_93_0_127) = all_589_0_1139
% 51.39/19.96 |
% 51.39/19.96 | Applying alpha-rule on (499) yields:
% 51.39/19.96 | (495) ~ (all_589_0_1139 = 0)
% 51.39/19.96 | (501) element(all_0_8_8, all_93_0_127) = all_589_0_1139
% 51.39/19.96 |
% 51.39/19.96 | From (470) and (501) follows:
% 51.39/19.96 | (502) element(all_0_8_8, all_0_9_9) = all_589_0_1139
% 51.39/19.96 |
% 51.39/19.96 | Instantiating formula (121) with all_0_8_8, all_0_9_9, all_589_0_1139, 0 and discharging atoms element(all_0_8_8, all_0_9_9) = all_589_0_1139, element(all_0_8_8, all_0_9_9) = 0, yields:
% 51.39/19.96 | (497) all_589_0_1139 = 0
% 51.39/19.96 |
% 51.39/19.96 | Equations (497) can reduce 495 to:
% 51.39/19.96 | (222) $false
% 51.39/19.96 |
% 51.39/19.96 |-The branch is then unsatisfiable
% 51.39/19.96 |-Branch two:
% 51.39/19.96 | (505) ( ~ (all_259_0_453 = 0) | ( ~ (all_589_0_1139 = 0) & in(all_259_1_454, all_79_0_101) = all_589_0_1139)) & (all_259_0_453 = 0 | (all_589_0_1139 = 0 & in(all_259_1_454, all_79_0_101) = 0))
% 51.39/19.96 |
% 51.39/19.96 | Applying alpha-rule on (505) yields:
% 51.39/19.96 | (506) ~ (all_259_0_453 = 0) | ( ~ (all_589_0_1139 = 0) & in(all_259_1_454, all_79_0_101) = all_589_0_1139)
% 51.39/19.96 | (507) all_259_0_453 = 0 | (all_589_0_1139 = 0 & in(all_259_1_454, all_79_0_101) = 0)
% 51.39/19.96 |
% 51.39/19.96 +-Applying beta-rule and splitting (492), into two cases.
% 51.39/19.96 |-Branch one:
% 51.39/19.96 | (432) all_259_0_453 = 0
% 51.39/19.96 |
% 51.39/19.96 | Equations (432) can reduce 236 to:
% 51.39/19.96 | (222) $false
% 51.39/19.96 |
% 51.39/19.96 |-The branch is then unsatisfiable
% 51.39/19.96 |-Branch two:
% 51.39/19.96 | (236) ~ (all_259_0_453 = 0)
% 51.39/19.96 | (511) all_590_0_1140 = 0 & in(all_259_1_454, all_79_0_101) = 0
% 51.39/19.96 |
% 51.39/19.96 +-Applying beta-rule and splitting (507), into two cases.
% 51.39/19.96 |-Branch one:
% 51.39/19.96 | (432) all_259_0_453 = 0
% 51.39/19.96 |
% 51.39/19.96 | Equations (432) can reduce 236 to:
% 51.39/19.96 | (222) $false
% 51.39/19.96 |
% 51.39/19.96 |-The branch is then unsatisfiable
% 51.39/19.96 |-Branch two:
% 51.39/19.96 | (236) ~ (all_259_0_453 = 0)
% 51.39/19.96 | (515) all_589_0_1139 = 0 & in(all_259_1_454, all_79_0_101) = 0
% 51.39/19.97 |
% 51.39/19.97 | Applying alpha-rule on (515) yields:
% 51.39/19.97 | (497) all_589_0_1139 = 0
% 51.39/19.97 | (517) in(all_259_1_454, all_79_0_101) = 0
% 51.39/19.97 |
% 51.39/19.97 +-Applying beta-rule and splitting (385), into two cases.
% 51.39/19.97 |-Branch one:
% 51.39/19.97 | (518) ( ~ (all_591_0_1141 = 0) & element(all_259_1_454, all_0_10_10) = all_591_0_1141) | ( ~ (all_591_0_1141 = 0) & element(all_169_1_261, all_93_0_127) = all_591_0_1141)
% 51.39/19.97 |
% 51.39/19.97 +-Applying beta-rule and splitting (518), into two cases.
% 51.39/19.97 |-Branch one:
% 51.39/19.97 | (519) ~ (all_591_0_1141 = 0) & element(all_259_1_454, all_0_10_10) = all_591_0_1141
% 51.39/19.97 |
% 51.39/19.97 | Applying alpha-rule on (519) yields:
% 51.39/19.97 | (520) ~ (all_591_0_1141 = 0)
% 51.39/19.97 | (521) element(all_259_1_454, all_0_10_10) = all_591_0_1141
% 51.39/19.97 |
% 51.39/19.97 | Instantiating formula (121) with all_259_1_454, all_0_10_10, all_591_0_1141, 0 and discharging atoms element(all_259_1_454, all_0_10_10) = all_591_0_1141, element(all_259_1_454, all_0_10_10) = 0, yields:
% 51.39/19.97 | (522) all_591_0_1141 = 0
% 51.39/19.97 |
% 51.39/19.97 | Equations (522) can reduce 520 to:
% 51.39/19.97 | (222) $false
% 51.39/19.97 |
% 51.39/19.97 |-The branch is then unsatisfiable
% 51.39/19.97 |-Branch two:
% 51.39/19.97 | (524) ~ (all_591_0_1141 = 0) & element(all_169_1_261, all_93_0_127) = all_591_0_1141
% 51.39/19.97 |
% 51.39/19.97 | Applying alpha-rule on (524) yields:
% 51.39/19.97 | (520) ~ (all_591_0_1141 = 0)
% 51.39/19.97 | (526) element(all_169_1_261, all_93_0_127) = all_591_0_1141
% 51.39/19.97 |
% 51.39/19.97 | From (470) and (526) follows:
% 51.39/19.97 | (527) element(all_169_1_261, all_0_9_9) = all_591_0_1141
% 51.39/19.97 |
% 51.39/19.97 | Instantiating formula (121) with all_169_1_261, all_0_9_9, 0, all_591_0_1141 and discharging atoms element(all_169_1_261, all_0_9_9) = all_591_0_1141, element(all_169_1_261, all_0_9_9) = 0, yields:
% 51.39/19.97 | (522) all_591_0_1141 = 0
% 51.39/19.97 |
% 51.39/19.97 | Equations (522) can reduce 520 to:
% 51.39/19.97 | (222) $false
% 51.39/19.97 |
% 51.39/19.97 |-The branch is then unsatisfiable
% 51.39/19.97 |-Branch two:
% 51.39/19.97 | (530) ~ (all_591_0_1141 = 0) & in(all_259_1_454, all_169_1_261) = all_591_0_1141
% 51.39/19.97 |
% 51.39/19.97 | Applying alpha-rule on (530) yields:
% 51.39/19.97 | (520) ~ (all_591_0_1141 = 0)
% 51.39/19.97 | (532) in(all_259_1_454, all_169_1_261) = all_591_0_1141
% 51.39/19.97 |
% 51.39/19.97 | Instantiating formula (74) with all_0_10_10, all_458_3_753, all_0_9_9 and discharging atoms powerset(all_0_10_10) = all_458_3_753, powerset(all_0_10_10) = all_0_9_9, yields:
% 51.39/19.97 | (533) all_458_3_753 = all_0_9_9
% 51.39/19.97 |
% 51.39/19.97 | Instantiating formula (74) with all_0_10_10, all_434_0_702, all_458_3_753 and discharging atoms powerset(all_0_10_10) = all_458_3_753, powerset(all_0_10_10) = all_434_0_702, yields:
% 51.39/19.97 | (534) all_458_3_753 = all_434_0_702
% 51.39/19.97 |
% 51.39/19.97 | Combining equations (533,534) yields a new equation:
% 51.39/19.97 | (535) all_434_0_702 = all_0_9_9
% 51.39/19.97 |
% 51.39/19.97 | From (535) and (475) follows:
% 51.39/19.97 | (141) powerset(all_0_10_10) = all_0_9_9
% 51.39/19.97 |
% 51.39/19.97 +-Applying beta-rule and splitting (314), into two cases.
% 51.39/19.97 |-Branch one:
% 51.39/19.97 | (537) ~ (all_372_0_543 = 0) & powerset(all_0_10_10) = all_372_1_544 & element(all_169_1_261, all_372_1_544) = all_372_0_543
% 51.39/19.97 |
% 51.39/19.97 | Applying alpha-rule on (537) yields:
% 51.39/19.97 | (538) ~ (all_372_0_543 = 0)
% 51.39/19.97 | (539) powerset(all_0_10_10) = all_372_1_544
% 51.39/19.97 | (540) element(all_169_1_261, all_372_1_544) = all_372_0_543
% 51.39/19.97 |
% 51.39/19.97 | Instantiating formula (74) with all_0_10_10, all_372_1_544, all_0_9_9 and discharging atoms powerset(all_0_10_10) = all_372_1_544, powerset(all_0_10_10) = all_0_9_9, yields:
% 51.39/19.97 | (541) all_372_1_544 = all_0_9_9
% 51.39/19.97 |
% 51.39/19.97 | From (541) and (540) follows:
% 51.39/19.97 | (542) element(all_169_1_261, all_0_9_9) = all_372_0_543
% 51.39/19.97 |
% 51.39/19.97 | Instantiating formula (121) with all_169_1_261, all_0_9_9, all_372_0_543, 0 and discharging atoms element(all_169_1_261, all_0_9_9) = all_372_0_543, element(all_169_1_261, all_0_9_9) = 0, yields:
% 51.39/19.97 | (543) all_372_0_543 = 0
% 51.39/19.97 |
% 51.39/19.97 | Equations (543) can reduce 538 to:
% 51.39/19.97 | (222) $false
% 51.39/19.97 |
% 51.39/19.97 |-The branch is then unsatisfiable
% 51.39/19.97 |-Branch two:
% 51.39/19.97 | (545) ~ (all_372_1_544 = 0) & in(all_259_1_454, all_169_1_261) = all_372_1_544
% 51.39/19.97 |
% 51.39/19.97 | Applying alpha-rule on (545) yields:
% 51.39/19.97 | (546) ~ (all_372_1_544 = 0)
% 51.39/19.97 | (547) in(all_259_1_454, all_169_1_261) = all_372_1_544
% 51.39/19.97 |
% 51.39/19.97 | Instantiating formula (140) with all_259_1_454, all_169_1_261, all_372_1_544, all_591_0_1141 and discharging atoms in(all_259_1_454, all_169_1_261) = all_591_0_1141, in(all_259_1_454, all_169_1_261) = all_372_1_544, yields:
% 51.39/19.97 | (548) all_591_0_1141 = all_372_1_544
% 51.39/19.97 |
% 51.39/19.97 | Equations (548) can reduce 520 to:
% 51.39/19.97 | (546) ~ (all_372_1_544 = 0)
% 51.39/19.97 |
% 51.39/19.97 | From (548) and (532) follows:
% 51.39/19.97 | (547) in(all_259_1_454, all_169_1_261) = all_372_1_544
% 51.39/19.97 |
% 51.39/19.97 | Instantiating formula (82) with all_372_1_544, all_169_1_261, all_259_1_454 and discharging atoms in(all_259_1_454, all_169_1_261) = all_372_1_544, yields:
% 51.39/19.97 | (551) all_372_1_544 = 0 | ? [v0] : ((v0 = 0 & empty(all_169_1_261) = 0) | ( ~ (v0 = 0) & element(all_259_1_454, all_169_1_261) = v0))
% 51.39/19.97 |
% 51.39/19.97 | Instantiating formula (99) with all_259_1_454, all_169_1_261, all_79_0_101 and discharging atoms subset(all_79_0_101, all_169_1_261) = 0, in(all_259_1_454, all_79_0_101) = 0, yields:
% 51.39/19.97 | (552) in(all_259_1_454, all_169_1_261) = 0
% 51.39/19.97 |
% 51.39/19.97 +-Applying beta-rule and splitting (551), into two cases.
% 51.39/19.97 |-Branch one:
% 51.39/19.97 | (553) all_372_1_544 = 0
% 51.39/19.97 |
% 51.39/19.97 | Equations (553) can reduce 546 to:
% 51.39/19.97 | (222) $false
% 51.39/19.97 |
% 51.39/19.97 |-The branch is then unsatisfiable
% 51.39/19.97 |-Branch two:
% 51.39/19.97 | (546) ~ (all_372_1_544 = 0)
% 51.39/19.97 | (556) ? [v0] : ((v0 = 0 & empty(all_169_1_261) = 0) | ( ~ (v0 = 0) & element(all_259_1_454, all_169_1_261) = v0))
% 51.39/19.97 |
% 51.39/19.97 | Instantiating formula (140) with all_259_1_454, all_169_1_261, 0, all_372_1_544 and discharging atoms in(all_259_1_454, all_169_1_261) = all_372_1_544, in(all_259_1_454, all_169_1_261) = 0, yields:
% 51.39/19.97 | (553) all_372_1_544 = 0
% 51.39/19.97 |
% 51.39/19.97 | Equations (553) can reduce 546 to:
% 51.39/19.97 | (222) $false
% 51.39/19.97 |
% 51.39/19.97 |-The branch is then unsatisfiable
% 51.39/19.97 |-Branch two:
% 51.39/19.97 | (559) ~ (all_503_1_868 = 0) & top_str(all_0_11_11) = all_503_1_868
% 51.39/19.97 |
% 51.39/19.97 | Applying alpha-rule on (559) yields:
% 51.39/19.97 | (560) ~ (all_503_1_868 = 0)
% 51.39/19.97 | (561) top_str(all_0_11_11) = all_503_1_868
% 51.39/19.97 |
% 51.39/19.97 | Instantiating formula (129) with all_0_11_11, all_503_1_868, 0 and discharging atoms top_str(all_0_11_11) = all_503_1_868, top_str(all_0_11_11) = 0, yields:
% 51.39/19.97 | (562) all_503_1_868 = 0
% 51.39/19.97 |
% 51.39/19.97 | Equations (562) can reduce 560 to:
% 51.39/19.97 | (222) $false
% 51.39/19.97 |
% 51.39/19.97 |-The branch is then unsatisfiable
% 51.39/19.97 |-Branch two:
% 51.39/19.97 | (564) all_458_4_754 = 0 & empty_carrier(all_0_11_11) = 0
% 51.39/19.97 |
% 51.39/19.97 | Applying alpha-rule on (564) yields:
% 51.39/19.97 | (565) all_458_4_754 = 0
% 51.39/19.97 | (346) empty_carrier(all_0_11_11) = 0
% 51.39/19.97 |
% 51.39/19.97 | Instantiating formula (48) with all_0_11_11, all_104_1_138, all_452_2_737 and discharging atoms empty_carrier(all_0_11_11) = all_452_2_737, empty_carrier(all_0_11_11) = all_104_1_138, yields:
% 51.39/19.97 | (365) all_452_2_737 = all_104_1_138
% 51.39/19.97 |
% 51.39/19.97 | Instantiating formula (48) with all_0_11_11, 0, all_452_2_737 and discharging atoms empty_carrier(all_0_11_11) = all_452_2_737, empty_carrier(all_0_11_11) = 0, yields:
% 51.39/19.97 | (345) all_452_2_737 = 0
% 51.39/19.97 |
% 51.39/19.97 | Combining equations (345,365) yields a new equation:
% 51.39/19.97 | (331) all_104_1_138 = 0
% 51.39/19.97 |
% 51.39/19.97 | Equations (331) can reduce 329 to:
% 51.39/19.97 | (222) $false
% 51.39/19.97 |
% 51.39/19.97 |-The branch is then unsatisfiable
% 51.39/19.97 |-Branch two:
% 51.39/19.97 | (571) all_105_3_142 = 0 & empty_carrier(all_0_11_11) = 0
% 51.39/19.97 |
% 51.39/19.97 | Applying alpha-rule on (571) yields:
% 51.39/19.97 | (572) all_105_3_142 = 0
% 51.39/19.97 | (346) empty_carrier(all_0_11_11) = 0
% 51.39/19.97 |
% 51.39/19.97 | Instantiating formula (48) with all_0_11_11, all_104_1_138, all_452_2_737 and discharging atoms empty_carrier(all_0_11_11) = all_452_2_737, empty_carrier(all_0_11_11) = all_104_1_138, yields:
% 51.39/19.97 | (365) all_452_2_737 = all_104_1_138
% 51.39/19.97 |
% 51.39/19.97 | Instantiating formula (48) with all_0_11_11, 0, all_452_2_737 and discharging atoms empty_carrier(all_0_11_11) = all_452_2_737, empty_carrier(all_0_11_11) = 0, yields:
% 51.39/19.97 | (345) all_452_2_737 = 0
% 51.39/19.97 |
% 51.39/19.98 | Combining equations (365,345) yields a new equation:
% 51.39/19.98 | (406) all_104_1_138 = 0
% 51.39/19.98 |
% 51.39/19.98 | Simplifying 406 yields:
% 51.39/19.98 | (331) all_104_1_138 = 0
% 51.39/19.98 |
% 51.39/19.98 | Equations (331) can reduce 329 to:
% 51.39/19.98 | (222) $false
% 51.39/19.98 |
% 51.39/19.98 |-The branch is then unsatisfiable
% 51.39/19.98 |-Branch two:
% 51.39/19.98 | (579) ~ (all_105_3_142 = 0) & one_sorted_str(all_0_11_11) = all_105_3_142
% 51.39/19.98 |
% 51.39/19.98 | Applying alpha-rule on (579) yields:
% 51.39/19.98 | (580) ~ (all_105_3_142 = 0)
% 51.39/19.98 | (581) one_sorted_str(all_0_11_11) = all_105_3_142
% 51.39/19.98 |
% 51.39/19.98 | Instantiating formula (53) with all_0_11_11, all_105_3_142, 0 and discharging atoms one_sorted_str(all_0_11_11) = all_105_3_142, one_sorted_str(all_0_11_11) = 0, yields:
% 51.39/19.98 | (572) all_105_3_142 = 0
% 51.39/19.98 |
% 51.39/19.98 | Equations (572) can reduce 580 to:
% 51.39/19.98 | (222) $false
% 51.39/19.98 |
% 51.39/19.98 |-The branch is then unsatisfiable
% 51.39/19.98 |-Branch two:
% 51.39/19.98 | (584) ~ (all_106_0_143 = 0) & the_carrier(all_0_11_11) = all_106_2_145 & powerset(all_106_2_145) = all_106_1_144 & element(all_0_8_8, all_106_1_144) = all_106_0_143
% 51.39/19.98 |
% 51.39/19.98 | Applying alpha-rule on (584) yields:
% 51.39/19.98 | (585) ~ (all_106_0_143 = 0)
% 51.39/19.98 | (288) the_carrier(all_0_11_11) = all_106_2_145
% 51.39/19.98 | (289) powerset(all_106_2_145) = all_106_1_144
% 51.39/19.98 | (588) element(all_0_8_8, all_106_1_144) = all_106_0_143
% 51.39/19.98 |
% 51.39/19.98 | Instantiating formula (145) with all_0_11_11, all_106_2_145, all_0_10_10 and discharging atoms the_carrier(all_0_11_11) = all_106_2_145, the_carrier(all_0_11_11) = all_0_10_10, yields:
% 51.39/19.98 | (292) all_106_2_145 = all_0_10_10
% 51.39/19.98 |
% 51.39/19.98 | From (292) and (289) follows:
% 51.39/19.98 | (296) powerset(all_0_10_10) = all_106_1_144
% 51.39/19.98 |
% 51.39/19.98 | Instantiating formula (74) with all_0_10_10, all_106_1_144, all_0_9_9 and discharging atoms powerset(all_0_10_10) = all_106_1_144, powerset(all_0_10_10) = all_0_9_9, yields:
% 51.39/19.98 | (298) all_106_1_144 = all_0_9_9
% 51.39/19.98 |
% 51.39/19.98 | From (298) and (588) follows:
% 51.39/19.98 | (592) element(all_0_8_8, all_0_9_9) = all_106_0_143
% 51.39/19.98 |
% 51.39/19.98 | Instantiating formula (121) with all_0_8_8, all_0_9_9, all_106_0_143, 0 and discharging atoms element(all_0_8_8, all_0_9_9) = all_106_0_143, element(all_0_8_8, all_0_9_9) = 0, yields:
% 51.39/19.98 | (287) all_106_0_143 = 0
% 51.39/19.98 |
% 51.39/19.98 | Equations (287) can reduce 585 to:
% 51.39/19.98 | (222) $false
% 51.39/19.98 |
% 51.39/19.98 |-The branch is then unsatisfiable
% 51.39/19.98 |-Branch two:
% 51.39/19.98 | (595) ~ (all_106_2_145 = 0) & top_str(all_0_11_11) = all_106_2_145
% 51.39/19.98 |
% 51.39/19.98 | Applying alpha-rule on (595) yields:
% 51.39/19.98 | (596) ~ (all_106_2_145 = 0)
% 51.39/19.98 | (597) top_str(all_0_11_11) = all_106_2_145
% 51.39/19.98 |
% 51.39/19.98 | Instantiating formula (129) with all_0_11_11, all_106_2_145, 0 and discharging atoms top_str(all_0_11_11) = all_106_2_145, top_str(all_0_11_11) = 0, yields:
% 51.39/19.98 | (598) all_106_2_145 = 0
% 51.39/19.98 |
% 51.39/19.98 | Equations (598) can reduce 596 to:
% 51.39/19.98 | (222) $false
% 51.39/19.98 |
% 51.39/19.98 |-The branch is then unsatisfiable
% 51.39/19.98 |-Branch two:
% 51.39/19.98 | (600) ~ (all_169_2_262 = 0) & element(all_0_8_8, all_99_0_133) = all_169_2_262
% 51.39/19.98 |
% 51.39/19.98 | Applying alpha-rule on (600) yields:
% 51.39/19.98 | (601) ~ (all_169_2_262 = 0)
% 51.39/19.98 | (602) element(all_0_8_8, all_99_0_133) = all_169_2_262
% 51.39/19.98 |
% 51.39/19.98 | From (272) and (602) follows:
% 51.39/19.98 | (603) element(all_0_8_8, all_0_9_9) = all_169_2_262
% 51.39/19.98 |
% 51.39/19.98 | Instantiating formula (121) with all_0_8_8, all_0_9_9, all_169_2_262, 0 and discharging atoms element(all_0_8_8, all_0_9_9) = all_169_2_262, element(all_0_8_8, all_0_9_9) = 0, yields:
% 51.39/19.98 | (604) all_169_2_262 = 0
% 51.39/19.98 |
% 51.39/19.98 | Equations (604) can reduce 601 to:
% 51.39/19.98 | (222) $false
% 51.39/19.98 |
% 51.39/19.98 |-The branch is then unsatisfiable
% 51.39/19.98 |-Branch two:
% 51.39/19.98 | (606) ~ (all_274_2_459 = 0) & element(all_0_8_8, all_92_0_126) = all_274_2_459
% 51.39/19.98 |
% 51.39/19.98 | Applying alpha-rule on (606) yields:
% 51.39/19.98 | (607) ~ (all_274_2_459 = 0)
% 51.39/19.98 | (608) element(all_0_8_8, all_92_0_126) = all_274_2_459
% 51.39/19.98 |
% 51.39/19.98 | From (256) and (608) follows:
% 51.39/19.98 | (609) element(all_0_8_8, all_0_9_9) = all_274_2_459
% 51.39/19.98 |
% 51.39/19.98 | Instantiating formula (121) with all_0_8_8, all_0_9_9, all_274_2_459, 0 and discharging atoms element(all_0_8_8, all_0_9_9) = all_274_2_459, element(all_0_8_8, all_0_9_9) = 0, yields:
% 51.39/19.98 | (610) all_274_2_459 = 0
% 51.39/19.98 |
% 51.39/19.98 | Equations (610) can reduce 607 to:
% 51.39/19.98 | (222) $false
% 51.39/19.98 |
% 51.39/19.98 |-The branch is then unsatisfiable
% 51.39/19.98 % SZS output end Proof for theBenchmark
% 51.39/19.98
% 51.39/19.98 19376ms
%------------------------------------------------------------------------------