%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU326+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n017.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 08:48:53 EDT 2022 % Result : Theorem 21.15s 5.81s % Output : Proof 30.12s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.11 % Problem : SEU326+1 : TPTP v8.1.0. Released v3.3.0. % 0.06/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n017.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 : Sun Jun 19 18:30:58 EDT 2022 % 0.12/0.33 % CPUTime : % 0.18/0.57 ____ _ % 0.18/0.57 ___ / __ \_____(_)___ ________ __________ % 0.18/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.18/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.18/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.18/0.57 % 0.18/0.57 A Theorem Prover for First-Order Logic % 0.18/0.57 (ePrincess v.1.0) % 0.18/0.57 % 0.18/0.57 (c) Philipp Rümmer, 2009-2015 % 0.18/0.57 (c) Peter Backeman, 2014-2015 % 0.18/0.57 (contributions by Angelo Brillout, Peter Baumgartner) % 0.18/0.57 Free software under GNU Lesser General Public License (LGPL). % 0.18/0.57 Bug reports to peter@backeman.se % 0.18/0.57 % 0.18/0.57 For more information, visit http://user.uu.se/~petba168/breu/ % 0.18/0.57 % 0.18/0.57 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.73/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.71/0.94 Prover 0: Preprocessing ... % 2.15/1.17 Prover 0: Warning: ignoring some quantifiers % 2.46/1.19 Prover 0: Constructing countermodel ... % 4.72/1.73 Prover 0: gave up % 4.72/1.73 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 4.72/1.77 Prover 1: Preprocessing ... % 5.53/1.89 Prover 1: Warning: ignoring some quantifiers % 5.53/1.90 Prover 1: Constructing countermodel ... % 17.83/5.00 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 17.83/5.02 Prover 2: Preprocessing ... % 18.63/5.17 Prover 2: Warning: ignoring some quantifiers % 18.63/5.18 Prover 2: Constructing countermodel ... % 21.15/5.81 Prover 2: proved (814ms) % 21.15/5.81 Prover 1: stopped % 21.15/5.81 % 21.15/5.81 No countermodel exists, formula is valid % 21.15/5.81 % SZS status Theorem for theBenchmark % 21.15/5.81 % 21.15/5.81 Generating proof ... Warning: ignoring some quantifiers % 29.22/7.74 found it (size 64) % 29.22/7.74 % 29.22/7.74 % SZS output start Proof for theBenchmark % 29.22/7.74 Assumed formulas after preprocessing and simplification: % 29.22/7.74 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = 0) & complements_of_subsets(v0, v1) = v4 & powerset(v2) = v3 & powerset(v0) = v2 & empty(v5) = v6 & empty(empty_set) = 0 & v5_membered(v5) = 0 & v5_membered(empty_set) = 0 & v4_membered(v5) = 0 & v4_membered(empty_set) = 0 & v3_membered(v5) = 0 & v3_membered(empty_set) = 0 & v2_membered(v5) = 0 & v2_membered(empty_set) = 0 & v1_membered(v5) = 0 & v1_membered(empty_set) = 0 & element(v1, v3) = 0 & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (powerset(v9) = v10) | ~ (element(v8, v10) = 0) | ~ (element(v7, v9) = v11) | ? [v12] : ( ~ (v12 = 0) & in(v7, v8) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (powerset(v8) = v9) | ~ (element(v7, v9) = v10) | ? [v11] : ( ~ (v11 = 0) & subset(v7, v8) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (powerset(v7) = v8) | ~ (v1_membered(v9) = v10) | ? [v11] : (( ~ (v11 = 0) & v1_membered(v7) = v11) | ( ~ (v11 = 0) & element(v9, v8) = v11))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (element(v7, v9) = v10) | ~ (in(v7, v8) = 0) | ? [v11] : ? [v12] : ( ~ (v12 = 0) & powerset(v9) = v11 & element(v8, v11) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (subset(v10, v9) = v8) | ~ (subset(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (complements_of_subsets(v10, v9) = v8) | ~ (complements_of_subsets(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (element(v10, v9) = v8) | ~ (element(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (in(v10, v9) = v8) | ~ (in(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = empty_set | ~ (powerset(v9) = v10) | ~ (powerset(v7) = v9) | ~ (element(v8, v10) = 0) | ? [v11] : ( ~ (v11 = empty_set) & complements_of_subsets(v7, v8) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (powerset(v9) = v10) | ~ (powerset(v7) = v9) | ~ (element(v8, v10) = 0) | ? [v11] : (complements_of_subsets(v7, v11) = v8 & complements_of_subsets(v7, v8) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (powerset(v9) = v10) | ~ (powerset(v7) = v9) | ~ (element(v8, v10) = 0) | ? [v11] : (complements_of_subsets(v7, v8) = v11 & element(v11, v10) = 0)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (powerset(v9) = v10) | ~ (element(v8, v10) = 0) | ~ (in(v7, v8) = 0) | element(v7, v9) = 0) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (powerset(v9) = v10) | ~ (element(v8, v10) = 0) | ~ (in(v7, v8) = 0) | ? [v11] : ( ~ (v11 = 0) & empty(v9) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (powerset(v7) = v8) | ~ (v5_membered(v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : ((v14 = 0 & v13 = 0 & v12 = 0 & v11 = 0 & v10 = 0 & v4_membered(v9) = 0 & v3_membered(v9) = 0 & v2_membered(v9) = 0 & v1_membered(v9) = 0) | ( ~ (v11 = 0) & v5_membered(v7) = v11) | ( ~ (v11 = 0) & element(v9, v8) = v11))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (powerset(v7) = v8) | ~ (v4_membered(v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : ((v14 = 0 & v13 = 0 & v12 = 0 & v11 = 0 & v10 = 0 & v5_membered(v9) = 0 & v3_membered(v9) = 0 & v2_membered(v9) = 0 & v1_membered(v9) = 0) | ( ~ (v11 = 0) & v5_membered(v7) = v11) | ( ~ (v11 = 0) & element(v9, v8) = v11))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (powerset(v7) = v8) | ~ (v4_membered(v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ((v13 = 0 & v12 = 0 & v11 = 0 & v10 = 0 & v3_membered(v9) = 0 & v2_membered(v9) = 0 & v1_membered(v9) = 0) | ( ~ (v11 = 0) & v4_membered(v7) = v11) | ( ~ (v11 = 0) & element(v9, v8) = v11))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (powerset(v7) = v8) | ~ (v3_membered(v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : ((v14 = 0 & v13 = 0 & v12 = 0 & v11 = 0 & v10 = 0 & v5_membered(v9) = 0 & v4_membered(v9) = 0 & v2_membered(v9) = 0 & v1_membered(v9) = 0) | ( ~ (v11 = 0) & v5_membered(v7) = v11) | ( ~ (v11 = 0) & element(v9, v8) = v11))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (powerset(v7) = v8) | ~ (v3_membered(v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ((v13 = 0 & v12 = 0 & v11 = 0 & v10 = 0 & v4_membered(v9) = 0 & v2_membered(v9) = 0 & v1_membered(v9) = 0) | ( ~ (v11 = 0) & v4_membered(v7) = v11) | ( ~ (v11 = 0) & element(v9, v8) = v11))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (powerset(v7) = v8) | ~ (v3_membered(v9) = v10) | ? [v11] : ? [v12] : ((v12 = 0 & v11 = 0 & v10 = 0 & v2_membered(v9) = 0 & v1_membered(v9) = 0) | ( ~ (v11 = 0) & v3_membered(v7) = v11) | ( ~ (v11 = 0) & element(v9, v8) = v11))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (powerset(v7) = v8) | ~ (v2_membered(v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : ((v14 = 0 & v13 = 0 & v12 = 0 & v11 = 0 & v10 = 0 & v5_membered(v9) = 0 & v4_membered(v9) = 0 & v3_membered(v9) = 0 & v1_membered(v9) = 0) | ( ~ (v11 = 0) & v5_membered(v7) = v11) | ( ~ (v11 = 0) & element(v9, v8) = v11))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (powerset(v7) = v8) | ~ (v2_membered(v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ((v13 = 0 & v12 = 0 & v11 = 0 & v10 = 0 & v4_membered(v9) = 0 & v3_membered(v9) = 0 & v1_membered(v9) = 0) | ( ~ (v11 = 0) & v4_membered(v7) = v11) | ( ~ (v11 = 0) & element(v9, v8) = v11))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (powerset(v7) = v8) | ~ (v2_membered(v9) = v10) | ? [v11] : ? [v12] : ((v12 = 0 & v11 = 0 & v10 = 0 & v3_membered(v9) = 0 & v1_membered(v9) = 0) | ( ~ (v11 = 0) & v3_membered(v7) = v11) | ( ~ (v11 = 0) & element(v9, v8) = v11))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (powerset(v7) = v8) | ~ (v2_membered(v9) = v10) | ? [v11] : ((v11 = 0 & v10 = 0 & v1_membered(v9) = 0) | ( ~ (v11 = 0) & v2_membered(v7) = v11) | ( ~ (v11 = 0) & element(v9, v8) = v11))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (powerset(v7) = v8) | ~ (v1_membered(v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : ((v14 = 0 & v13 = 0 & v12 = 0 & v11 = 0 & v10 = 0 & v5_membered(v9) = 0 & v4_membered(v9) = 0 & v3_membered(v9) = 0 & v2_membered(v9) = 0) | ( ~ (v11 = 0) & v5_membered(v7) = v11) | ( ~ (v11 = 0) & element(v9, v8) = v11))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (powerset(v7) = v8) | ~ (v1_membered(v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ((v13 = 0 & v12 = 0 & v11 = 0 & v10 = 0 & v4_membered(v9) = 0 & v3_membered(v9) = 0 & v2_membered(v9) = 0) | ( ~ (v11 = 0) & v4_membered(v7) = v11) | ( ~ (v11 = 0) & element(v9, v8) = v11))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (powerset(v7) = v8) | ~ (v1_membered(v9) = v10) | ? [v11] : ? [v12] : ((v12 = 0 & v11 = 0 & v10 = 0 & v3_membered(v9) = 0 & v2_membered(v9) = 0) | ( ~ (v11 = 0) & v3_membered(v7) = v11) | ( ~ (v11 = 0) & element(v9, v8) = v11))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (powerset(v7) = v8) | ~ (v1_membered(v9) = v10) | ? [v11] : ((v11 = 0 & v10 = 0 & v2_membered(v9) = 0) | ( ~ (v11 = 0) & v2_membered(v7) = v11) | ( ~ (v11 = 0) & element(v9, v8) = v11))) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (subset(v7, v8) = v9) | ? [v10] : ? [v11] : ( ~ (v11 = 0) & powerset(v8) = v10 & element(v7, v10) = v11)) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (v1_membered(v7) = 0) | ~ (v1_xcmplx_0(v8) = v9) | ? [v10] : ( ~ (v10 = 0) & element(v8, v7) = v10)) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (element(v7, v8) = v9) | ? [v10] : ( ~ (v10 = 0) & in(v7, v8) = v10)) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (in(v7, v8) = v9) | ? [v10] : ((v10 = 0 & empty(v8) = 0) | ( ~ (v10 = 0) & element(v7, v8) = v10))) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (powerset(v9) = v8) | ~ (powerset(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (empty(v9) = v8) | ~ (empty(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (v5_membered(v9) = v8) | ~ (v5_membered(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (natural(v9) = v8) | ~ (natural(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (v4_membered(v9) = v8) | ~ (v4_membered(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (v1_int_1(v9) = v8) | ~ (v1_int_1(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (v3_membered(v9) = v8) | ~ (v3_membered(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (v1_rat_1(v9) = v8) | ~ (v1_rat_1(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (v2_membered(v9) = v8) | ~ (v2_membered(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (v1_xreal_0(v9) = v8) | ~ (v1_xreal_0(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (v1_membered(v9) = v8) | ~ (v1_membered(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (v1_xcmplx_0(v9) = v8) | ~ (v1_xcmplx_0(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (complements_of_subsets(v7, v8) = v9) | ? [v10] : ? [v11] : ? [v12] : (powerset(v10) = v11 & powerset(v7) = v10 & ((v12 = 0 & element(v9, v11) = 0) | ( ~ (v12 = 0) & element(v8, v11) = v12)))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (complements_of_subsets(v7, v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ((v10 = v8 & complements_of_subsets(v7, v9) = v8) | ( ~ (v12 = 0) & powerset(v10) = v11 & powerset(v7) = v10 & element(v8, v11) = v12))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (powerset(v8) = v9) | ~ (element(v7, v9) = 0) | subset(v7, v8) = 0) & ! [v7] : ! [v8] : ! [v9] : ( ~ (powerset(v7) = v8) | ~ (element(v9, v8) = 0) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ((v14 = 0 & v13 = 0 & v12 = 0 & v11 = 0 & v10 = 0 & v5_membered(v9) = 0 & v4_membered(v9) = 0 & v3_membered(v9) = 0 & v2_membered(v9) = 0 & v1_membered(v9) = 0) | ( ~ (v10 = 0) & v5_membered(v7) = v10))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (powerset(v7) = v8) | ~ (element(v9, v8) = 0) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : ((v13 = 0 & v12 = 0 & v11 = 0 & v10 = 0 & v4_membered(v9) = 0 & v3_membered(v9) = 0 & v2_membered(v9) = 0 & v1_membered(v9) = 0) | ( ~ (v10 = 0) & v4_membered(v7) = v10))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (powerset(v7) = v8) | ~ (element(v9, v8) = 0) | ? [v10] : ? [v11] : ? [v12] : ((v12 = 0 & v11 = 0 & v10 = 0 & v3_membered(v9) = 0 & v2_membered(v9) = 0 & v1_membered(v9) = 0) | ( ~ (v10 = 0) & v3_membered(v7) = v10))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (powerset(v7) = v8) | ~ (element(v9, v8) = 0) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & v2_membered(v9) = 0 & v1_membered(v9) = 0) | ( ~ (v10 = 0) & v2_membered(v7) = v10))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (powerset(v7) = v8) | ~ (element(v9, v8) = 0) | ? [v10] : ((v10 = 0 & v1_membered(v9) = 0) | ( ~ (v10 = 0) & v1_membered(v7) = v10))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (empty(v9) = 0) | ~ (in(v7, v8) = 0) | ? [v10] : ? [v11] : ( ~ (v11 = 0) & powerset(v9) = v10 & element(v8, v10) = v11)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (v5_membered(v7) = 0) | ~ (natural(v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : ((v13 = 0 & v12 = 0 & v11 = 0 & v10 = 0 & v9 = 0 & v1_int_1(v8) = 0 & v1_rat_1(v8) = 0 & v1_xreal_0(v8) = 0 & v1_xcmplx_0(v8) = 0) | ( ~ (v10 = 0) & element(v8, v7) = v10))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (v5_membered(v7) = 0) | ~ (v1_int_1(v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : ((v13 = 0 & v12 = 0 & v11 = 0 & v10 = 0 & v9 = 0 & natural(v8) = 0 & v1_rat_1(v8) = 0 & v1_xreal_0(v8) = 0 & v1_xcmplx_0(v8) = 0) | ( ~ (v10 = 0) & element(v8, v7) = v10))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (v5_membered(v7) = 0) | ~ (v1_rat_1(v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : ((v13 = 0 & v12 = 0 & v11 = 0 & v10 = 0 & v9 = 0 & natural(v8) = 0 & v1_int_1(v8) = 0 & v1_xreal_0(v8) = 0 & v1_xcmplx_0(v8) = 0) | ( ~ (v10 = 0) & element(v8, v7) = v10))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (v5_membered(v7) = 0) | ~ (v1_xreal_0(v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : ((v13 = 0 & v12 = 0 & v11 = 0 & v10 = 0 & v9 = 0 & natural(v8) = 0 & v1_int_1(v8) = 0 & v1_rat_1(v8) = 0 & v1_xcmplx_0(v8) = 0) | ( ~ (v10 = 0) & element(v8, v7) = v10))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (v5_membered(v7) = 0) | ~ (v1_xcmplx_0(v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : ((v13 = 0 & v12 = 0 & v11 = 0 & v10 = 0 & v9 = 0 & natural(v8) = 0 & v1_int_1(v8) = 0 & v1_rat_1(v8) = 0 & v1_xreal_0(v8) = 0) | ( ~ (v10 = 0) & element(v8, v7) = v10))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (v4_membered(v7) = 0) | ~ (v1_int_1(v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ((v12 = 0 & v11 = 0 & v10 = 0 & v9 = 0 & v1_rat_1(v8) = 0 & v1_xreal_0(v8) = 0 & v1_xcmplx_0(v8) = 0) | ( ~ (v10 = 0) & element(v8, v7) = v10))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (v4_membered(v7) = 0) | ~ (v1_rat_1(v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ((v12 = 0 & v11 = 0 & v10 = 0 & v9 = 0 & v1_int_1(v8) = 0 & v1_xreal_0(v8) = 0 & v1_xcmplx_0(v8) = 0) | ( ~ (v10 = 0) & element(v8, v7) = v10))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (v4_membered(v7) = 0) | ~ (v1_xreal_0(v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ((v12 = 0 & v11 = 0 & v10 = 0 & v9 = 0 & v1_int_1(v8) = 0 & v1_rat_1(v8) = 0 & v1_xcmplx_0(v8) = 0) | ( ~ (v10 = 0) & element(v8, v7) = v10))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (v4_membered(v7) = 0) | ~ (v1_xcmplx_0(v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ((v12 = 0 & v11 = 0 & v10 = 0 & v9 = 0 & v1_int_1(v8) = 0 & v1_rat_1(v8) = 0 & v1_xreal_0(v8) = 0) | ( ~ (v10 = 0) & element(v8, v7) = v10))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (v3_membered(v7) = 0) | ~ (v1_rat_1(v8) = v9) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & v9 = 0 & v1_xreal_0(v8) = 0 & v1_xcmplx_0(v8) = 0) | ( ~ (v10 = 0) & element(v8, v7) = v10))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (v3_membered(v7) = 0) | ~ (v1_xreal_0(v8) = v9) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & v9 = 0 & v1_rat_1(v8) = 0 & v1_xcmplx_0(v8) = 0) | ( ~ (v10 = 0) & element(v8, v7) = v10))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (v3_membered(v7) = 0) | ~ (v1_xcmplx_0(v8) = v9) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & v9 = 0 & v1_rat_1(v8) = 0 & v1_xreal_0(v8) = 0) | ( ~ (v10 = 0) & element(v8, v7) = v10))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (v2_membered(v7) = 0) | ~ (v1_xreal_0(v8) = v9) | ? [v10] : ((v10 = 0 & v9 = 0 & v1_xcmplx_0(v8) = 0) | ( ~ (v10 = 0) & element(v8, v7) = v10))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (v2_membered(v7) = 0) | ~ (v1_xcmplx_0(v8) = v9) | ? [v10] : ((v10 = 0 & v9 = 0 & v1_xreal_0(v8) = 0) | ( ~ (v10 = 0) & element(v8, v7) = v10))) & ! [v7] : ! [v8] : (v8 = v7 | ~ (empty(v8) = 0) | ~ (empty(v7) = 0)) & ! [v7] : ! [v8] : (v8 = empty_set | ~ (complements_of_subsets(v7, v8) = empty_set) | ? [v9] : ? [v10] : ? [v11] : ( ~ (v11 = 0) & powerset(v9) = v10 & powerset(v7) = v9 & element(v8, v10) = v11)) & ! [v7] : ! [v8] : (v8 = 0 | ~ (subset(v7, v7) = v8)) & ! [v7] : ! [v8] : (v8 = 0 | ~ (empty(v7) = v8) | ? [v9] : ? [v10] : ? [v11] : ( ~ (v11 = 0) & powerset(v7) = v9 & empty(v10) = v11 & element(v10, v9) = 0)) & ! [v7] : ! [v8] : (v8 = 0 | ~ (v4_membered(v7) = v8) | ? [v9] : ( ~ (v9 = 0) & v5_membered(v7) = v9)) & ! [v7] : ! [v8] : (v8 = 0 | ~ (v3_membered(v7) = v8) | ? [v9] : ( ~ (v9 = 0) & v4_membered(v7) = v9)) & ! [v7] : ! [v8] : (v8 = 0 | ~ (v2_membered(v7) = v8) | ? [v9] : ( ~ (v9 = 0) & v3_membered(v7) = v9)) & ! [v7] : ! [v8] : (v8 = 0 | ~ (v1_membered(v7) = v8) | ? [v9] : ( ~ (v9 = 0) & v2_membered(v7) = v9)) & ! [v7] : ! [v8] : ( ~ (subset(v7, v8) = 0) | ? [v9] : (powerset(v8) = v9 & element(v7, v9) = 0)) & ! [v7] : ! [v8] : ( ~ (powerset(v7) = v8) | ? [v9] : ? [v10] : ? [v11] : ((v10 = 0 & ~ (v11 = 0) & empty(v9) = v11 & element(v9, v8) = 0) | (v9 = 0 & empty(v7) = 0))) & ! [v7] : ! [v8] : ( ~ (powerset(v7) = v8) | ? [v9] : ( ~ (v9 = 0) & empty(v8) = v9)) & ! [v7] : ! [v8] : ( ~ (powerset(v7) = v8) | ? [v9] : (empty(v9) = 0 & element(v9, v8) = 0)) & ! [v7] : ! [v8] : ( ~ (v5_membered(v7) = v8) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : ((v12 = 0 & v11 = 0 & v10 = 0 & v9 = 0 & v8 = 0 & v4_membered(v7) = 0 & v3_membered(v7) = 0 & v2_membered(v7) = 0 & v1_membered(v7) = 0) | ( ~ (v9 = 0) & empty(v7) = v9))) & ! [v7] : ! [v8] : ( ~ (v5_membered(v7) = 0) | ~ (element(v8, v7) = 0) | (natural(v8) = 0 & v1_int_1(v8) = 0 & v1_rat_1(v8) = 0 & v1_xreal_0(v8) = 0 & v1_xcmplx_0(v8) = 0)) & ! [v7] : ! [v8] : ( ~ (v4_membered(v7) = v8) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : ((v12 = 0 & v11 = 0 & v10 = 0 & v9 = 0 & v8 = 0 & v5_membered(v7) = 0 & v3_membered(v7) = 0 & v2_membered(v7) = 0 & v1_membered(v7) = 0) | ( ~ (v9 = 0) & empty(v7) = v9))) & ! [v7] : ! [v8] : ( ~ (v4_membered(v7) = 0) | ~ (element(v8, v7) = 0) | (v1_int_1(v8) = 0 & v1_rat_1(v8) = 0 & v1_xreal_0(v8) = 0 & v1_xcmplx_0(v8) = 0)) & ! [v7] : ! [v8] : ( ~ (v3_membered(v7) = v8) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : ((v12 = 0 & v11 = 0 & v10 = 0 & v9 = 0 & v8 = 0 & v5_membered(v7) = 0 & v4_membered(v7) = 0 & v2_membered(v7) = 0 & v1_membered(v7) = 0) | ( ~ (v9 = 0) & empty(v7) = v9))) & ! [v7] : ! [v8] : ( ~ (v3_membered(v7) = 0) | ~ (element(v8, v7) = 0) | (v1_rat_1(v8) = 0 & v1_xreal_0(v8) = 0 & v1_xcmplx_0(v8) = 0)) & ! [v7] : ! [v8] : ( ~ (v2_membered(v7) = v8) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : ((v12 = 0 & v11 = 0 & v10 = 0 & v9 = 0 & v8 = 0 & v5_membered(v7) = 0 & v4_membered(v7) = 0 & v3_membered(v7) = 0 & v1_membered(v7) = 0) | ( ~ (v9 = 0) & empty(v7) = v9))) & ! [v7] : ! [v8] : ( ~ (v2_membered(v7) = 0) | ~ (element(v8, v7) = 0) | (v1_xreal_0(v8) = 0 & v1_xcmplx_0(v8) = 0)) & ! [v7] : ! [v8] : ( ~ (v1_membered(v7) = v8) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : ((v12 = 0 & v11 = 0 & v10 = 0 & v9 = 0 & v8 = 0 & v5_membered(v7) = 0 & v4_membered(v7) = 0 & v3_membered(v7) = 0 & v2_membered(v7) = 0) | ( ~ (v9 = 0) & empty(v7) = v9))) & ! [v7] : ! [v8] : ( ~ (v1_membered(v7) = 0) | ~ (element(v8, v7) = 0) | v1_xcmplx_0(v8) = 0) & ! [v7] : ! [v8] : ( ~ (element(v7, v8) = 0) | ? [v9] : ((v9 = 0 & empty(v8) = 0) | (v9 = 0 & in(v7, v8) = 0))) & ! [v7] : ! [v8] : ( ~ (in(v8, v7) = 0) | ? [v9] : ( ~ (v9 = 0) & in(v7, v8) = v9)) & ! [v7] : ! [v8] : ( ~ (in(v7, v8) = 0) | element(v7, v8) = 0) & ! [v7] : ! [v8] : ( ~ (in(v7, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & empty(v8) = v9)) & ! [v7] : ! [v8] : ( ~ (in(v7, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & in(v8, v7) = v9)) & ! [v7] : (v7 = empty_set | ~ (empty(v7) = 0)) & ! [v7] : ( ~ (empty(v7) = 0) | (v5_membered(v7) = 0 & v4_membered(v7) = 0 & v3_membered(v7) = 0 & v2_membered(v7) = 0 & v1_membered(v7) = 0)) & ! [v7] : ( ~ (v5_membered(v7) = 0) | v4_membered(v7) = 0) & ! [v7] : ( ~ (v5_membered(v7) = 0) | ? [v8] : (powerset(v7) = v8 & ! [v9] : ! [v10] : ( ~ (v5_membered(v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : ((v14 = 0 & v13 = 0 & v12 = 0 & v11 = 0 & v10 = 0 & v4_membered(v9) = 0 & v3_membered(v9) = 0 & v2_membered(v9) = 0 & v1_membered(v9) = 0) | ( ~ (v11 = 0) & element(v9, v8) = v11))) & ! [v9] : ! [v10] : ( ~ (v4_membered(v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : ((v14 = 0 & v13 = 0 & v12 = 0 & v11 = 0 & v10 = 0 & v5_membered(v9) = 0 & v3_membered(v9) = 0 & v2_membered(v9) = 0 & v1_membered(v9) = 0) | ( ~ (v11 = 0) & element(v9, v8) = v11))) & ! [v9] : ! [v10] : ( ~ (v3_membered(v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : ((v14 = 0 & v13 = 0 & v12 = 0 & v11 = 0 & v10 = 0 & v5_membered(v9) = 0 & v4_membered(v9) = 0 & v2_membered(v9) = 0 & v1_membered(v9) = 0) | ( ~ (v11 = 0) & element(v9, v8) = v11))) & ! [v9] : ! [v10] : ( ~ (v2_membered(v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : ((v14 = 0 & v13 = 0 & v12 = 0 & v11 = 0 & v10 = 0 & v5_membered(v9) = 0 & v4_membered(v9) = 0 & v3_membered(v9) = 0 & v1_membered(v9) = 0) | ( ~ (v11 = 0) & element(v9, v8) = v11))) & ! [v9] : ! [v10] : ( ~ (v1_membered(v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : ((v14 = 0 & v13 = 0 & v12 = 0 & v11 = 0 & v10 = 0 & v5_membered(v9) = 0 & v4_membered(v9) = 0 & v3_membered(v9) = 0 & v2_membered(v9) = 0) | ( ~ (v11 = 0) & element(v9, v8) = v11))) & ! [v9] : ( ~ (element(v9, v8) = 0) | (v5_membered(v9) = 0 & v4_membered(v9) = 0 & v3_membered(v9) = 0 & v2_membered(v9) = 0 & v1_membered(v9) = 0)))) & ! [v7] : ( ~ (v4_membered(v7) = 0) | v3_membered(v7) = 0) & ! [v7] : ( ~ (v4_membered(v7) = 0) | ? [v8] : (powerset(v7) = v8 & ! [v9] : ! [v10] : ( ~ (v4_membered(v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ((v13 = 0 & v12 = 0 & v11 = 0 & v10 = 0 & v3_membered(v9) = 0 & v2_membered(v9) = 0 & v1_membered(v9) = 0) | ( ~ (v11 = 0) & element(v9, v8) = v11))) & ! [v9] : ! [v10] : ( ~ (v3_membered(v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ((v13 = 0 & v12 = 0 & v11 = 0 & v10 = 0 & v4_membered(v9) = 0 & v2_membered(v9) = 0 & v1_membered(v9) = 0) | ( ~ (v11 = 0) & element(v9, v8) = v11))) & ! [v9] : ! [v10] : ( ~ (v2_membered(v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ((v13 = 0 & v12 = 0 & v11 = 0 & v10 = 0 & v4_membered(v9) = 0 & v3_membered(v9) = 0 & v1_membered(v9) = 0) | ( ~ (v11 = 0) & element(v9, v8) = v11))) & ! [v9] : ! [v10] : ( ~ (v1_membered(v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ((v13 = 0 & v12 = 0 & v11 = 0 & v10 = 0 & v4_membered(v9) = 0 & v3_membered(v9) = 0 & v2_membered(v9) = 0) | ( ~ (v11 = 0) & element(v9, v8) = v11))) & ! [v9] : ( ~ (element(v9, v8) = 0) | (v4_membered(v9) = 0 & v3_membered(v9) = 0 & v2_membered(v9) = 0 & v1_membered(v9) = 0)))) & ! [v7] : ( ~ (v3_membered(v7) = 0) | v2_membered(v7) = 0) & ! [v7] : ( ~ (v3_membered(v7) = 0) | ? [v8] : (powerset(v7) = v8 & ! [v9] : ! [v10] : ( ~ (v3_membered(v9) = v10) | ? [v11] : ? [v12] : ((v12 = 0 & v11 = 0 & v10 = 0 & v2_membered(v9) = 0 & v1_membered(v9) = 0) | ( ~ (v11 = 0) & element(v9, v8) = v11))) & ! [v9] : ! [v10] : ( ~ (v2_membered(v9) = v10) | ? [v11] : ? [v12] : ((v12 = 0 & v11 = 0 & v10 = 0 & v3_membered(v9) = 0 & v1_membered(v9) = 0) | ( ~ (v11 = 0) & element(v9, v8) = v11))) & ! [v9] : ! [v10] : ( ~ (v1_membered(v9) = v10) | ? [v11] : ? [v12] : ((v12 = 0 & v11 = 0 & v10 = 0 & v3_membered(v9) = 0 & v2_membered(v9) = 0) | ( ~ (v11 = 0) & element(v9, v8) = v11))) & ! [v9] : ( ~ (element(v9, v8) = 0) | (v3_membered(v9) = 0 & v2_membered(v9) = 0 & v1_membered(v9) = 0)))) & ! [v7] : ( ~ (v2_membered(v7) = 0) | v1_membered(v7) = 0) & ! [v7] : ( ~ (v2_membered(v7) = 0) | ? [v8] : (powerset(v7) = v8 & ! [v9] : ! [v10] : ( ~ (v2_membered(v9) = v10) | ? [v11] : ((v11 = 0 & v10 = 0 & v1_membered(v9) = 0) | ( ~ (v11 = 0) & element(v9, v8) = v11))) & ! [v9] : ! [v10] : ( ~ (v1_membered(v9) = v10) | ? [v11] : ((v11 = 0 & v10 = 0 & v2_membered(v9) = 0) | ( ~ (v11 = 0) & element(v9, v8) = v11))) & ! [v9] : ( ~ (element(v9, v8) = 0) | (v2_membered(v9) = 0 & v1_membered(v9) = 0)))) & ! [v7] : ( ~ (v1_membered(v7) = 0) | ? [v8] : (powerset(v7) = v8 & ! [v9] : ! [v10] : (v10 = 0 | ~ (v1_membered(v9) = v10) | ? [v11] : ( ~ (v11 = 0) & element(v9, v8) = v11)) & ! [v9] : ( ~ (element(v9, v8) = 0) | v1_membered(v9) = 0))) & ? [v7] : ? [v8] : ? [v9] : subset(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : complements_of_subsets(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : element(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : in(v8, v7) = v9 & ? [v7] : ? [v8] : powerset(v7) = v8 & ? [v7] : ? [v8] : empty(v7) = v8 & ? [v7] : ? [v8] : v5_membered(v7) = v8 & ? [v7] : ? [v8] : natural(v7) = v8 & ? [v7] : ? [v8] : v4_membered(v7) = v8 & ? [v7] : ? [v8] : v1_int_1(v7) = v8 & ? [v7] : ? [v8] : v3_membered(v7) = v8 & ? [v7] : ? [v8] : v1_rat_1(v7) = v8 & ? [v7] : ? [v8] : v2_membered(v7) = v8 & ? [v7] : ? [v8] : v1_xreal_0(v7) = v8 & ? [v7] : ? [v8] : v1_membered(v7) = v8 & ? [v7] : ? [v8] : v1_xcmplx_0(v7) = v8 & ? [v7] : ? [v8] : element(v8, v7) = 0 & ((v4 = empty_set & ~ (v1 = empty_set)) | (v1 = empty_set & ~ (v4 = empty_set)))) % 29.53/7.83 | 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 yields: % 29.53/7.83 | (1) ~ (all_0_0_0 = 0) & complements_of_subsets(all_0_6_6, all_0_5_5) = all_0_2_2 & powerset(all_0_4_4) = all_0_3_3 & powerset(all_0_6_6) = all_0_4_4 & empty(all_0_1_1) = all_0_0_0 & empty(empty_set) = 0 & v5_membered(all_0_1_1) = 0 & v5_membered(empty_set) = 0 & v4_membered(all_0_1_1) = 0 & v4_membered(empty_set) = 0 & v3_membered(all_0_1_1) = 0 & v3_membered(empty_set) = 0 & v2_membered(all_0_1_1) = 0 & v2_membered(empty_set) = 0 & v1_membered(all_0_1_1) = 0 & v1_membered(empty_set) = 0 & element(all_0_5_5, all_0_3_3) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (element(v0, v2) = v4) | ? [v5] : ( ~ (v5 = 0) & in(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v0) = v1) | ~ (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 | ~ (complements_of_subsets(v3, v2) = v1) | ~ (complements_of_subsets(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] : (v1 = empty_set | ~ (powerset(v2) = v3) | ~ (powerset(v0) = v2) | ~ (element(v1, v3) = 0) | ? [v4] : ( ~ (v4 = empty_set) & complements_of_subsets(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (powerset(v0) = v2) | ~ (element(v1, v3) = 0) | ? [v4] : (complements_of_subsets(v0, v4) = v1 & complements_of_subsets(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (powerset(v0) = v2) | ~ (element(v1, v3) = 0) | ? [v4] : (complements_of_subsets(v0, v1) = v4 & element(v4, v3) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | element(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [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 | ~ (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 | ~ (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] : ( ~ (complements_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (powerset(v3) = v4 & powerset(v0) = v3 & ((v5 = 0 & element(v2, v4) = 0) | ( ~ (v5 = 0) & element(v1, v4) = v5)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (complements_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ((v3 = v1 & complements_of_subsets(v0, v2) = v1) | ( ~ (v5 = 0) & powerset(v3) = v4 & powerset(v0) = v3 & element(v1, v4) = v5))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | subset(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ (element(v2, v1) = 0) | ? [v3] : ? [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 = empty_set | ~ (complements_of_subsets(v0, v1) = empty_set) | ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v2) = v3 & powerset(v0) = v2 & element(v1, v3) = v4)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (empty(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v0) = v2 & empty(v3) = v4 & element(v3, v2) = 0)) & ! [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] : ( ~ (powerset(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v3 = 0 & ~ (v4 = 0) & empty(v2) = v4 & element(v2, v1) = 0) | (v2 = 0 & empty(v0) = 0))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (empty(v2) = 0 & element(v2, v1) = 0)) & ! [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] : ( ~ (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] : complements_of_subsets(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : element(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2 & ? [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 & ((all_0_2_2 = empty_set & ~ (all_0_5_5 = empty_set)) | (all_0_5_5 = empty_set & ~ (all_0_2_2 = empty_set))) % 29.96/7.87 | % 29.96/7.87 | Applying alpha-rule on (1) yields: % 29.96/7.87 | (2) ! [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))) % 29.96/7.87 | (3) ! [v0] : ( ~ (v2_membered(v0) = 0) | v1_membered(v0) = 0) % 29.96/7.87 | (4) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (v1_membered(v0) = 0) | ~ (v1_xcmplx_0(v1) = v2) | ? [v3] : ( ~ (v3 = 0) & element(v1, v0) = v3)) % 29.96/7.87 | (5) ? [v0] : ? [v1] : v1_xreal_0(v0) = v1 % 29.96/7.87 | (6) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (v3_membered(v2) = v1) | ~ (v3_membered(v2) = v0)) % 29.96/7.87 | (7) complements_of_subsets(all_0_6_6, all_0_5_5) = all_0_2_2 % 29.96/7.87 | (8) ! [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))) % 29.96/7.87 | (9) ? [v0] : ? [v1] : v5_membered(v0) = v1 % 29.96/7.87 | (10) ? [v0] : ? [v1] : v1_membered(v0) = v1 % 29.96/7.87 | (11) ! [v0] : ! [v1] : (v1 = 0 | ~ (empty(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v0) = v2 & empty(v3) = v4 & element(v3, v2) = 0)) % 29.96/7.87 | (12) ! [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))) % 29.96/7.87 | (13) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) % 29.96/7.87 | (14) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v0, v1) = v2) | ? [v3] : ((v3 = 0 & empty(v1) = 0) | ( ~ (v3 = 0) & element(v0, v1) = v3))) % 29.96/7.87 | (15) ! [v0] : ! [v1] : ! [v2] : ( ~ (complements_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ((v3 = v1 & complements_of_subsets(v0, v2) = v1) | ( ~ (v5 = 0) & powerset(v3) = v4 & powerset(v0) = v3 & element(v1, v4) = v5))) % 29.96/7.87 | (16) ! [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))) % 29.96/7.88 | (17) ! [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))) % 29.96/7.88 | (18) ? [v0] : ? [v1] : ? [v2] : complements_of_subsets(v1, v0) = v2 % 29.96/7.88 | (19) empty(empty_set) = 0 % 29.96/7.88 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | element(v0, v2) = 0) % 29.96/7.88 | (21) v5_membered(all_0_1_1) = 0 % 29.96/7.88 | (22) ? [v0] : ? [v1] : v1_int_1(v0) = v1 % 29.96/7.88 | (23) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (v5_membered(v2) = v1) | ~ (v5_membered(v2) = v0)) % 29.96/7.88 | (24) ! [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))) % 29.96/7.88 | (25) powerset(all_0_4_4) = all_0_3_3 % 29.96/7.88 | (26) ! [v0] : ! [v1] : (v1 = 0 | ~ (v3_membered(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & v4_membered(v0) = v2)) % 29.96/7.88 | (27) ! [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))) % 29.96/7.88 | (28) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) % 29.96/7.88 | (29) ! [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))) % 29.96/7.88 | (30) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v3 = 0 & ~ (v4 = 0) & empty(v2) = v4 & element(v2, v1) = 0) | (v2 = 0 & empty(v0) = 0))) % 29.96/7.88 | (31) v1_membered(all_0_1_1) = 0 % 29.96/7.88 | (32) ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2 % 29.96/7.88 | (33) v2_membered(empty_set) = 0 % 29.96/7.88 | (34) ! [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)) % 29.96/7.88 | (35) ? [v0] : ? [v1] : v2_membered(v0) = v1 % 29.96/7.88 | (36) ? [v0] : ? [v1] : v1_xcmplx_0(v0) = v1 % 29.96/7.88 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) % 29.96/7.88 | (38) ! [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)))) % 29.96/7.88 | (39) ! [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))) % 29.96/7.89 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4)) % 29.96/7.89 | (41) ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2)) % 29.96/7.89 | (42) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (v1_int_1(v2) = v1) | ~ (v1_int_1(v2) = v0)) % 29.96/7.89 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) % 29.96/7.89 | (44) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ (element(v2, v1) = 0) | ? [v3] : ((v3 = 0 & v1_membered(v2) = 0) | ( ~ (v3 = 0) & v1_membered(v0) = v3))) % 29.96/7.89 | (45) ! [v0] : ( ~ (v4_membered(v0) = 0) | v3_membered(v0) = 0) % 29.96/7.89 | (46) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (v4_membered(v2) = v1) | ~ (v4_membered(v2) = v0)) % 29.96/7.89 | (47) ! [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))) % 29.96/7.89 | (48) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (v2_membered(v2) = v1) | ~ (v2_membered(v2) = v0)) % 29.96/7.89 | (49) v4_membered(empty_set) = 0 % 29.96/7.89 | (50) ! [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))) % 29.96/7.89 | (51) ! [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)) % 29.96/7.89 | (52) v2_membered(all_0_1_1) = 0 % 29.96/7.89 | (53) ! [v0] : ! [v1] : ! [v2] : ( ~ (complements_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (powerset(v3) = v4 & powerset(v0) = v3 & ((v5 = 0 & element(v2, v4) = 0) | ( ~ (v5 = 0) & element(v1, v4) = v5)))) % 29.96/7.89 | (54) ! [v0] : ! [v1] : ( ~ (v1_membered(v0) = 0) | ~ (element(v1, v0) = 0) | v1_xcmplx_0(v1) = 0) % 29.96/7.89 | (55) ! [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))) % 29.96/7.89 | (56) ? [v0] : ? [v1] : natural(v0) = v1 % 29.96/7.89 | (57) ! [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))) % 29.96/7.89 | (58) ! [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))) % 29.96/7.89 | (59) ! [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))) % 29.96/7.89 | (60) ! [v0] : ! [v1] : (v1 = 0 | ~ (v2_membered(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & v3_membered(v0) = v2)) % 29.96/7.89 | (61) v3_membered(empty_set) = 0 % 29.96/7.89 | (62) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (complements_of_subsets(v3, v2) = v1) | ~ (complements_of_subsets(v3, v2) = v0)) % 29.96/7.89 | (63) ! [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))) % 29.96/7.89 | (64) v4_membered(all_0_1_1) = 0 % 29.96/7.89 | (65) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (empty(v2) = 0 & element(v2, v1) = 0)) % 29.96/7.89 | (66) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) % 29.96/7.89 | (67) ? [v0] : ? [v1] : powerset(v0) = v1 % 29.96/7.89 | (68) ! [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)))) % 29.96/7.89 | (69) ! [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))) % 29.96/7.89 | (70) ? [v0] : ? [v1] : ? [v2] : element(v1, v0) = v2 % 29.96/7.89 | (71) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) % 29.96/7.89 | (72) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0)) % 29.96/7.89 | (73) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v1) = v3 & element(v0, v3) = v4)) % 29.96/7.90 | (74) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) % 29.96/7.90 | (75) ! [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)) % 29.96/7.90 | (76) ! [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))) % 29.96/7.90 | (77) ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2 % 29.96/7.90 | (78) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) % 29.96/7.90 | (79) ? [v0] : ? [v1] : element(v1, v0) = 0 % 29.96/7.90 | (80) powerset(all_0_6_6) = all_0_4_4 % 29.96/7.90 | (81) ! [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)) % 29.96/7.90 | (82) ! [v0] : ! [v1] : ( ~ (v2_membered(v0) = 0) | ~ (element(v1, v0) = 0) | (v1_xreal_0(v1) = 0 & v1_xcmplx_0(v1) = 0)) % 29.96/7.90 | (83) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (powerset(v0) = v2) | ~ (element(v1, v3) = 0) | ? [v4] : (complements_of_subsets(v0, v1) = v4 & element(v4, v3) = 0)) % 29.96/7.90 | (84) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (v1_xreal_0(v2) = v1) | ~ (v1_xreal_0(v2) = v0)) % 29.96/7.90 | (85) empty(all_0_1_1) = all_0_0_0 % 29.96/7.90 | (86) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 29.96/7.90 | (87) ! [v0] : ( ~ (v3_membered(v0) = 0) | v2_membered(v0) = 0) % 29.96/7.90 | (88) ! [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))) % 29.96/7.90 | (89) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (natural(v2) = v1) | ~ (natural(v2) = v0)) % 29.96/7.90 | (90) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (powerset(v0) = v2) | ~ (element(v1, v3) = 0) | ? [v4] : (complements_of_subsets(v0, v4) = v1 & complements_of_subsets(v0, v1) = v4)) % 29.96/7.90 | (91) ! [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))) % 29.96/7.90 | (92) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = empty_set | ~ (powerset(v2) = v3) | ~ (powerset(v0) = v2) | ~ (element(v1, v3) = 0) | ? [v4] : ( ~ (v4 = empty_set) & complements_of_subsets(v0, v1) = v4)) % 29.96/7.90 | (93) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3)) % 30.12/7.90 | (94) ! [v0] : ( ~ (v5_membered(v0) = 0) | v4_membered(v0) = 0) % 30.12/7.90 | (95) ? [v0] : ? [v1] : v3_membered(v0) = v1 % 30.12/7.90 | (96) ! [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))) % 30.12/7.90 | (97) ! [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))) % 30.12/7.90 | (98) ! [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)))) % 30.12/7.90 | (99) ! [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))) % 30.12/7.90 | (100) ! [v0] : ! [v1] : ! [v2] : ( ~ (empty(v2) = 0) | ~ (in(v0, v1) = 0) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v2) = v3 & element(v1, v3) = v4)) % 30.12/7.90 | (101) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | element(v0, v1) = 0) % 30.12/7.90 | (102) ! [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))) % 30.12/7.90 | (103) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (powerset(v1) = v2 & element(v0, v2) = 0)) % 30.12/7.90 | (104) ! [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))) % 30.12/7.90 | (105) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (v1_xcmplx_0(v2) = v1) | ~ (v1_xcmplx_0(v2) = v0)) % 30.12/7.90 | (106) ! [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)) % 30.12/7.90 | (107) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) % 30.12/7.90 | (108) (all_0_2_2 = empty_set & ~ (all_0_5_5 = empty_set)) | (all_0_5_5 = empty_set & ~ (all_0_2_2 = empty_set)) % 30.12/7.90 | (109) ~ (all_0_0_0 = 0) % 30.12/7.90 | (110) ! [v0] : ( ~ (empty(v0) = 0) | (v5_membered(v0) = 0 & v4_membered(v0) = 0 & v3_membered(v0) = 0 & v2_membered(v0) = 0 & v1_membered(v0) = 0)) % 30.12/7.91 | (111) ! [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))) % 30.12/7.91 | (112) ! [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))) % 30.12/7.91 | (113) ! [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))) % 30.12/7.91 | (114) element(all_0_5_5, all_0_3_3) = 0 % 30.12/7.91 | (115) ! [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))) % 30.12/7.91 | (116) v1_membered(empty_set) = 0 % 30.12/7.91 | (117) ! [v0] : ! [v1] : (v1 = 0 | ~ (v4_membered(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & v5_membered(v0) = v2)) % 30.12/7.91 | (118) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | subset(v0, v1) = 0) % 30.12/7.91 | (119) ! [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))) % 30.12/7.91 | (120) ! [v0] : ! [v1] : (v1 = 0 | ~ (v1_membered(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & v2_membered(v0) = v2)) % 30.12/7.91 | (121) ? [v0] : ? [v1] : empty(v0) = v1 % 30.12/7.91 | (122) ? [v0] : ? [v1] : v1_rat_1(v0) = v1 % 30.12/7.91 | (123) v5_membered(empty_set) = 0 % 30.12/7.91 | (124) ! [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))) % 30.12/7.91 | (125) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)) % 30.12/7.91 | (126) ! [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))) % 30.12/7.91 | (127) ! [v0] : ! [v1] : ( ~ (element(v0, v1) = 0) | ? [v2] : ((v2 = 0 & empty(v1) = 0) | (v2 = 0 & in(v0, v1) = 0))) % 30.12/7.91 | (128) ! [v0] : ! [v1] : (v1 = empty_set | ~ (complements_of_subsets(v0, v1) = empty_set) | ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v2) = v3 & powerset(v0) = v2 & element(v1, v3) = v4)) % 30.12/7.91 | (129) v3_membered(all_0_1_1) = 0 % 30.12/7.91 | (130) ! [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))) % 30.12/7.91 | (131) ! [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))) % 30.12/7.91 | (132) ! [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))) % 30.12/7.91 | (133) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (v1_membered(v2) = v1) | ~ (v1_membered(v2) = v0)) % 30.12/7.91 | (134) ! [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))) % 30.12/7.91 | (135) ! [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))) % 30.12/7.91 | (136) ! [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)))) % 30.12/7.91 | (137) ? [v0] : ? [v1] : v4_membered(v0) = v1 % 30.12/7.91 | (138) ! [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))) % 30.12/7.91 | (139) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (v1_rat_1(v2) = v1) | ~ (v1_rat_1(v2) = v0)) % 30.12/7.91 | (140) ! [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))) % 30.12/7.91 | % 30.12/7.92 | Instantiating formula (53) with all_0_2_2, all_0_5_5, all_0_6_6 and discharging atoms complements_of_subsets(all_0_6_6, all_0_5_5) = all_0_2_2, yields: % 30.12/7.92 | (141) ? [v0] : ? [v1] : ? [v2] : (powerset(v0) = v1 & powerset(all_0_6_6) = v0 & ((v2 = 0 & element(all_0_2_2, v1) = 0) | ( ~ (v2 = 0) & element(all_0_5_5, v1) = v2))) % 30.12/7.92 | % 30.12/7.92 | Instantiating formula (15) with all_0_2_2, all_0_5_5, all_0_6_6 and discharging atoms complements_of_subsets(all_0_6_6, all_0_5_5) = all_0_2_2, yields: % 30.12/7.92 | (142) ? [v0] : ? [v1] : ? [v2] : ((v0 = all_0_5_5 & complements_of_subsets(all_0_6_6, all_0_2_2) = all_0_5_5) | ( ~ (v2 = 0) & powerset(v0) = v1 & powerset(all_0_6_6) = v0 & element(all_0_5_5, v1) = v2)) % 30.12/7.92 | % 30.12/7.92 | Instantiating formula (92) with all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6 and discharging atoms powerset(all_0_4_4) = all_0_3_3, powerset(all_0_6_6) = all_0_4_4, element(all_0_5_5, all_0_3_3) = 0, yields: % 30.12/7.92 | (143) all_0_5_5 = empty_set | ? [v0] : ( ~ (v0 = empty_set) & complements_of_subsets(all_0_6_6, all_0_5_5) = v0) % 30.12/7.92 | % 30.12/7.92 | Instantiating formula (90) with all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6 and discharging atoms powerset(all_0_4_4) = all_0_3_3, powerset(all_0_6_6) = all_0_4_4, element(all_0_5_5, all_0_3_3) = 0, yields: % 30.12/7.92 | (144) ? [v0] : (complements_of_subsets(all_0_6_6, v0) = all_0_5_5 & complements_of_subsets(all_0_6_6, all_0_5_5) = v0) % 30.12/7.92 | % 30.12/7.92 | Instantiating formula (83) with all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6 and discharging atoms powerset(all_0_4_4) = all_0_3_3, powerset(all_0_6_6) = all_0_4_4, element(all_0_5_5, all_0_3_3) = 0, yields: % 30.12/7.92 | (145) ? [v0] : (complements_of_subsets(all_0_6_6, all_0_5_5) = v0 & element(v0, all_0_3_3) = 0) % 30.12/7.92 | % 30.12/7.92 | Instantiating (145) with all_43_0_45 yields: % 30.12/7.92 | (146) complements_of_subsets(all_0_6_6, all_0_5_5) = all_43_0_45 & element(all_43_0_45, all_0_3_3) = 0 % 30.12/7.92 | % 30.12/7.92 | Applying alpha-rule on (146) yields: % 30.12/7.92 | (147) complements_of_subsets(all_0_6_6, all_0_5_5) = all_43_0_45 % 30.12/7.92 | (148) element(all_43_0_45, all_0_3_3) = 0 % 30.12/7.92 | % 30.12/7.92 | Instantiating (144) with all_48_0_54 yields: % 30.12/7.92 | (149) complements_of_subsets(all_0_6_6, all_48_0_54) = all_0_5_5 & complements_of_subsets(all_0_6_6, all_0_5_5) = all_48_0_54 % 30.12/7.92 | % 30.12/7.92 | Applying alpha-rule on (149) yields: % 30.12/7.92 | (150) complements_of_subsets(all_0_6_6, all_48_0_54) = all_0_5_5 % 30.12/7.92 | (151) complements_of_subsets(all_0_6_6, all_0_5_5) = all_48_0_54 % 30.12/7.92 | % 30.12/7.92 | Instantiating (142) with all_98_0_150, all_98_1_151, all_98_2_152 yields: % 30.12/7.92 | (152) (all_98_2_152 = all_0_5_5 & complements_of_subsets(all_0_6_6, all_0_2_2) = all_0_5_5) | ( ~ (all_98_0_150 = 0) & powerset(all_98_2_152) = all_98_1_151 & powerset(all_0_6_6) = all_98_2_152 & element(all_0_5_5, all_98_1_151) = all_98_0_150) % 30.12/7.92 | % 30.12/7.92 | Instantiating (141) with all_119_0_193, all_119_1_194, all_119_2_195 yields: % 30.12/7.92 | (153) powerset(all_119_2_195) = all_119_1_194 & powerset(all_0_6_6) = all_119_2_195 & ((all_119_0_193 = 0 & element(all_0_2_2, all_119_1_194) = 0) | ( ~ (all_119_0_193 = 0) & element(all_0_5_5, all_119_1_194) = all_119_0_193)) % 30.12/7.92 | % 30.12/7.92 | Applying alpha-rule on (153) yields: % 30.12/7.92 | (154) powerset(all_119_2_195) = all_119_1_194 % 30.12/7.92 | (155) powerset(all_0_6_6) = all_119_2_195 % 30.12/7.92 | (156) (all_119_0_193 = 0 & element(all_0_2_2, all_119_1_194) = 0) | ( ~ (all_119_0_193 = 0) & element(all_0_5_5, all_119_1_194) = all_119_0_193) % 30.12/7.92 | % 30.12/7.92 | Instantiating formula (62) with all_0_6_6, all_0_5_5, all_48_0_54, all_0_2_2 and discharging atoms complements_of_subsets(all_0_6_6, all_0_5_5) = all_48_0_54, complements_of_subsets(all_0_6_6, all_0_5_5) = all_0_2_2, yields: % 30.12/7.92 | (157) all_48_0_54 = all_0_2_2 % 30.12/7.92 | % 30.12/7.92 | Instantiating formula (62) with all_0_6_6, all_0_5_5, all_43_0_45, all_48_0_54 and discharging atoms complements_of_subsets(all_0_6_6, all_0_5_5) = all_48_0_54, complements_of_subsets(all_0_6_6, all_0_5_5) = all_43_0_45, yields: % 30.12/7.92 | (158) all_48_0_54 = all_43_0_45 % 30.12/7.92 | % 30.12/7.92 | Instantiating formula (107) with all_0_6_6, all_119_2_195, all_0_4_4 and discharging atoms powerset(all_0_6_6) = all_119_2_195, powerset(all_0_6_6) = all_0_4_4, yields: % 30.12/7.92 | (159) all_119_2_195 = all_0_4_4 % 30.12/7.92 | % 30.12/7.92 | Combining equations (158,157) yields a new equation: % 30.12/7.92 | (160) all_43_0_45 = all_0_2_2 % 30.12/7.92 | % 30.12/7.92 | Simplifying 160 yields: % 30.12/7.92 | (161) all_43_0_45 = all_0_2_2 % 30.12/7.92 | % 30.12/7.92 | From (161) and (147) follows: % 30.12/7.92 | (7) complements_of_subsets(all_0_6_6, all_0_5_5) = all_0_2_2 % 30.12/7.92 | % 30.12/7.92 | From (159) and (154) follows: % 30.12/7.92 | (163) powerset(all_0_4_4) = all_119_1_194 % 30.12/7.92 | % 30.12/7.92 | From (159) and (155) follows: % 30.12/7.92 | (80) powerset(all_0_6_6) = all_0_4_4 % 30.12/7.92 | % 30.12/7.92 | Instantiating formula (107) with all_0_4_4, all_119_1_194, all_0_3_3 and discharging atoms powerset(all_0_4_4) = all_119_1_194, powerset(all_0_4_4) = all_0_3_3, yields: % 30.12/7.92 | (165) all_119_1_194 = all_0_3_3 % 30.12/7.92 | % 30.12/7.92 | From (165) and (163) follows: % 30.12/7.92 | (25) powerset(all_0_4_4) = all_0_3_3 % 30.12/7.92 | % 30.12/7.92 +-Applying beta-rule and splitting (156), into two cases. % 30.12/7.92 |-Branch one: % 30.12/7.92 | (167) all_119_0_193 = 0 & element(all_0_2_2, all_119_1_194) = 0 % 30.12/7.92 | % 30.12/7.92 | Applying alpha-rule on (167) yields: % 30.12/7.92 | (168) all_119_0_193 = 0 % 30.12/7.92 | (169) element(all_0_2_2, all_119_1_194) = 0 % 30.12/7.92 | % 30.12/7.92 | From (165) and (169) follows: % 30.12/7.92 | (170) element(all_0_2_2, all_0_3_3) = 0 % 30.12/7.92 | % 30.12/7.92 +-Applying beta-rule and splitting (152), into two cases. % 30.12/7.92 |-Branch one: % 30.12/7.92 | (171) all_98_2_152 = all_0_5_5 & complements_of_subsets(all_0_6_6, all_0_2_2) = all_0_5_5 % 30.12/7.92 | % 30.12/7.92 | Applying alpha-rule on (171) yields: % 30.12/7.92 | (172) all_98_2_152 = all_0_5_5 % 30.12/7.92 | (173) complements_of_subsets(all_0_6_6, all_0_2_2) = all_0_5_5 % 30.12/7.92 | % 30.12/7.92 | Instantiating formula (92) with all_0_3_3, all_0_4_4, all_0_2_2, all_0_6_6 and discharging atoms powerset(all_0_4_4) = all_0_3_3, powerset(all_0_6_6) = all_0_4_4, element(all_0_2_2, all_0_3_3) = 0, yields: % 30.12/7.92 | (174) all_0_2_2 = empty_set | ? [v0] : ( ~ (v0 = empty_set) & complements_of_subsets(all_0_6_6, all_0_2_2) = v0) % 30.12/7.92 | % 30.12/7.92 +-Applying beta-rule and splitting (108), into two cases. % 30.12/7.92 |-Branch one: % 30.12/7.92 | (175) all_0_2_2 = empty_set & ~ (all_0_5_5 = empty_set) % 30.12/7.92 | % 30.12/7.92 | Applying alpha-rule on (175) yields: % 30.12/7.92 | (176) all_0_2_2 = empty_set % 30.12/7.92 | (177) ~ (all_0_5_5 = empty_set) % 30.12/7.92 | % 30.12/7.92 | From (176) and (7) follows: % 30.12/7.92 | (178) complements_of_subsets(all_0_6_6, all_0_5_5) = empty_set % 30.12/7.92 | % 30.12/7.92 +-Applying beta-rule and splitting (143), into two cases. % 30.12/7.92 |-Branch one: % 30.12/7.92 | (179) all_0_5_5 = empty_set % 30.12/7.92 | % 30.12/7.92 | Equations (179) can reduce 177 to: % 30.12/7.92 | (180) $false % 30.12/7.92 | % 30.12/7.92 |-The branch is then unsatisfiable % 30.12/7.92 |-Branch two: % 30.12/7.92 | (177) ~ (all_0_5_5 = empty_set) % 30.12/7.92 | (182) ? [v0] : ( ~ (v0 = empty_set) & complements_of_subsets(all_0_6_6, all_0_5_5) = v0) % 30.12/7.92 | % 30.12/7.92 | Instantiating (182) with all_671_0_717 yields: % 30.12/7.92 | (183) ~ (all_671_0_717 = empty_set) & complements_of_subsets(all_0_6_6, all_0_5_5) = all_671_0_717 % 30.12/7.92 | % 30.12/7.92 | Applying alpha-rule on (183) yields: % 30.12/7.92 | (184) ~ (all_671_0_717 = empty_set) % 30.12/7.92 | (185) complements_of_subsets(all_0_6_6, all_0_5_5) = all_671_0_717 % 30.12/7.92 | % 30.12/7.92 | Instantiating formula (62) with all_0_6_6, all_0_5_5, empty_set, all_671_0_717 and discharging atoms complements_of_subsets(all_0_6_6, all_0_5_5) = all_671_0_717, complements_of_subsets(all_0_6_6, all_0_5_5) = empty_set, yields: % 30.12/7.92 | (186) all_671_0_717 = empty_set % 30.12/7.92 | % 30.12/7.92 | Equations (186) can reduce 184 to: % 30.12/7.92 | (180) $false % 30.12/7.92 | % 30.12/7.92 |-The branch is then unsatisfiable % 30.12/7.92 |-Branch two: % 30.12/7.92 | (188) all_0_5_5 = empty_set & ~ (all_0_2_2 = empty_set) % 30.12/7.92 | % 30.12/7.92 | Applying alpha-rule on (188) yields: % 30.12/7.92 | (179) all_0_5_5 = empty_set % 30.12/7.92 | (190) ~ (all_0_2_2 = empty_set) % 30.12/7.92 | % 30.12/7.92 | From (179) and (173) follows: % 30.12/7.92 | (191) complements_of_subsets(all_0_6_6, all_0_2_2) = empty_set % 30.12/7.92 | % 30.12/7.92 +-Applying beta-rule and splitting (174), into two cases. % 30.12/7.92 |-Branch one: % 30.12/7.92 | (176) all_0_2_2 = empty_set % 30.12/7.92 | % 30.12/7.92 | Equations (176) can reduce 190 to: % 30.12/7.93 | (180) $false % 30.12/7.93 | % 30.12/7.93 |-The branch is then unsatisfiable % 30.12/7.93 |-Branch two: % 30.12/7.93 | (190) ~ (all_0_2_2 = empty_set) % 30.12/7.93 | (195) ? [v0] : ( ~ (v0 = empty_set) & complements_of_subsets(all_0_6_6, all_0_2_2) = v0) % 30.12/7.93 | % 30.12/7.93 | Instantiating (195) with all_671_0_718 yields: % 30.12/7.93 | (196) ~ (all_671_0_718 = empty_set) & complements_of_subsets(all_0_6_6, all_0_2_2) = all_671_0_718 % 30.12/7.93 | % 30.12/7.93 | Applying alpha-rule on (196) yields: % 30.12/7.93 | (197) ~ (all_671_0_718 = empty_set) % 30.12/7.93 | (198) complements_of_subsets(all_0_6_6, all_0_2_2) = all_671_0_718 % 30.12/7.93 | % 30.12/7.93 | Instantiating formula (62) with all_0_6_6, all_0_2_2, empty_set, all_671_0_718 and discharging atoms complements_of_subsets(all_0_6_6, all_0_2_2) = all_671_0_718, complements_of_subsets(all_0_6_6, all_0_2_2) = empty_set, yields: % 30.12/7.93 | (199) all_671_0_718 = empty_set % 30.12/7.93 | % 30.12/7.93 | Equations (199) can reduce 197 to: % 30.12/7.93 | (180) $false % 30.12/7.93 | % 30.12/7.93 |-The branch is then unsatisfiable % 30.12/7.93 |-Branch two: % 30.12/7.93 | (201) ~ (all_98_0_150 = 0) & powerset(all_98_2_152) = all_98_1_151 & powerset(all_0_6_6) = all_98_2_152 & element(all_0_5_5, all_98_1_151) = all_98_0_150 % 30.12/7.93 | % 30.12/7.93 | Applying alpha-rule on (201) yields: % 30.12/7.93 | (202) ~ (all_98_0_150 = 0) % 30.12/7.93 | (203) powerset(all_98_2_152) = all_98_1_151 % 30.12/7.93 | (204) powerset(all_0_6_6) = all_98_2_152 % 30.12/7.93 | (205) element(all_0_5_5, all_98_1_151) = all_98_0_150 % 30.12/7.93 | % 30.12/7.93 | Instantiating formula (107) with all_0_6_6, all_98_2_152, all_0_4_4 and discharging atoms powerset(all_0_6_6) = all_98_2_152, powerset(all_0_6_6) = all_0_4_4, yields: % 30.12/7.93 | (206) all_98_2_152 = all_0_4_4 % 30.12/7.93 | % 30.12/7.93 | From (206) and (203) follows: % 30.12/7.93 | (207) powerset(all_0_4_4) = all_98_1_151 % 30.12/7.93 | % 30.12/7.93 | Instantiating formula (107) with all_0_4_4, all_98_1_151, all_0_3_3 and discharging atoms powerset(all_0_4_4) = all_98_1_151, powerset(all_0_4_4) = all_0_3_3, yields: % 30.12/7.93 | (208) all_98_1_151 = all_0_3_3 % 30.12/7.93 | % 30.12/7.93 | From (208) and (205) follows: % 30.12/7.93 | (209) element(all_0_5_5, all_0_3_3) = all_98_0_150 % 30.12/7.93 | % 30.12/7.93 | Instantiating formula (43) with all_0_5_5, all_0_3_3, all_98_0_150, 0 and discharging atoms element(all_0_5_5, all_0_3_3) = all_98_0_150, element(all_0_5_5, all_0_3_3) = 0, yields: % 30.12/7.93 | (210) all_98_0_150 = 0 % 30.12/7.93 | % 30.12/7.93 | Equations (210) can reduce 202 to: % 30.12/7.93 | (180) $false % 30.12/7.93 | % 30.12/7.93 |-The branch is then unsatisfiable % 30.12/7.93 |-Branch two: % 30.12/7.93 | (212) ~ (all_119_0_193 = 0) & element(all_0_5_5, all_119_1_194) = all_119_0_193 % 30.12/7.93 | % 30.12/7.93 | Applying alpha-rule on (212) yields: % 30.12/7.93 | (213) ~ (all_119_0_193 = 0) % 30.12/7.93 | (214) element(all_0_5_5, all_119_1_194) = all_119_0_193 % 30.12/7.93 | % 30.12/7.93 | From (165) and (214) follows: % 30.12/7.93 | (215) element(all_0_5_5, all_0_3_3) = all_119_0_193 % 30.12/7.93 | % 30.12/7.93 | Instantiating formula (43) with all_0_5_5, all_0_3_3, all_119_0_193, 0 and discharging atoms element(all_0_5_5, all_0_3_3) = all_119_0_193, element(all_0_5_5, all_0_3_3) = 0, yields: % 30.12/7.93 | (168) all_119_0_193 = 0 % 30.12/7.93 | % 30.12/7.93 | Equations (168) can reduce 213 to: % 30.12/7.93 | (180) $false % 30.12/7.93 | % 30.12/7.93 |-The branch is then unsatisfiable % 30.12/7.93 % SZS output end Proof for theBenchmark % 30.12/7.93 % 30.12/7.93 7343ms %------------------------------------------------------------------------------