%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU309+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n021.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 08:48:43 EDT 2022 % Result : Theorem 4.56s 1.73s % Output : Proof 7.75s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SEU309+1 : TPTP v8.1.0. Released v3.3.0. % 0.03/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.34 % Computer : n021.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 600 % 0.12/0.34 % DateTime : Mon Jun 20 13:51:18 EDT 2022 % 0.12/0.34 % CPUTime : % 0.55/0.60 ____ _ % 0.55/0.60 ___ / __ \_____(_)___ ________ __________ % 0.55/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.55/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.55/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.55/0.60 % 0.55/0.60 A Theorem Prover for First-Order Logic % 0.55/0.61 (ePrincess v.1.0) % 0.55/0.61 % 0.55/0.61 (c) Philipp Rümmer, 2009-2015 % 0.55/0.61 (c) Peter Backeman, 2014-2015 % 0.55/0.61 (contributions by Angelo Brillout, Peter Baumgartner) % 0.55/0.61 Free software under GNU Lesser General Public License (LGPL). % 0.55/0.61 Bug reports to peter@backeman.se % 0.55/0.61 % 0.55/0.61 For more information, visit http://user.uu.se/~petba168/breu/ % 0.55/0.61 % 0.55/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.71/0.68 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.89/1.05 Prover 0: Preprocessing ... % 3.19/1.42 Prover 0: Warning: ignoring some quantifiers % 3.19/1.46 Prover 0: Constructing countermodel ... % 4.56/1.73 Prover 0: proved (1048ms) % 4.56/1.73 % 4.56/1.73 No countermodel exists, formula is valid % 4.56/1.73 % SZS status Theorem for theBenchmark % 4.56/1.73 % 4.56/1.73 Generating proof ... Warning: ignoring some quantifiers % 7.00/2.26 found it (size 144) % 7.00/2.26 % 7.00/2.26 % SZS output start Proof for theBenchmark % 7.00/2.26 Assumed formulas after preprocessing and simplification: % 7.00/2.26 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ( ~ (v6 = v4) & subset_difference(v1, v3, v5) = v6 & subset_difference(v1, v3, v4) = v5 & cast_as_carrier_subset(v0) = v3 & the_carrier(v0) = v1 & powerset(v1) = v2 & one_sorted_str(v8) & one_sorted_str(v0) & empty(empty_set) & v5_membered(v7) & v5_membered(empty_set) & v4_membered(v7) & v4_membered(empty_set) & v3_membered(v7) & v3_membered(empty_set) & v2_membered(v7) & v2_membered(empty_set) & element(v4, v2) & v1_membered(v7) & v1_membered(empty_set) & ~ empty(v7) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v10 = v9 | ~ (subset_difference(v13, v12, v11) = v10) | ~ (subset_difference(v13, v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v10 = v9 | ~ (subset_intersection2(v13, v12, v11) = v10) | ~ (subset_intersection2(v13, v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (set_difference(v10, v11) = v13) | ~ (powerset(v9) = v12) | ~ element(v11, v12) | ~ element(v10, v12) | subset_difference(v9, v10, v11) = v13) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (set_intersection2(v10, v11) = v13) | ~ (powerset(v9) = v12) | ~ element(v11, v12) | ~ element(v10, v12) | subset_intersection2(v9, v10, v11) = v13) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (set_difference(v12, v11) = v10) | ~ (set_difference(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (set_intersection2(v12, v11) = v10) | ~ (set_intersection2(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (set_difference(v9, v11) = v12) | ~ (set_difference(v9, v10) = v11) | set_intersection2(v9, v10) = v12) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (subset_difference(v9, v10, v11) = v12) | ? [v13] : ? [v14] : (set_difference(v10, v11) = v14 & powerset(v9) = v13 & (v14 = v12 | ~ element(v11, v13) | ~ element(v10, v13)))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (subset_difference(v9, v10, v11) = v12) | ? [v13] : (powerset(v9) = v13 & ( ~ element(v11, v13) | ~ element(v10, v13) | element(v12, v13)))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (subset_intersection2(v9, v11, v10) = v12) | ? [v13] : ? [v14] : (subset_intersection2(v9, v10, v11) = v14 & powerset(v9) = v13 & (v14 = v12 | ~ element(v11, v13) | ~ element(v10, v13)))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (subset_intersection2(v9, v10, v11) = v12) | ? [v13] : ? [v14] : (subset_intersection2(v9, v11, v10) = v14 & powerset(v9) = v13 & (v14 = v12 | ~ element(v11, v13) | ~ element(v10, v13)))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (subset_intersection2(v9, v10, v11) = v12) | ? [v13] : ? [v14] : (set_intersection2(v10, v11) = v14 & powerset(v9) = v13 & (v14 = v12 | ~ element(v11, v13) | ~ element(v10, v13)))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (subset_intersection2(v9, v10, v11) = v12) | ? [v13] : (powerset(v9) = v13 & ( ~ element(v11, v13) | ~ element(v10, v13) | element(v12, v13)))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (powerset(v11) = v12) | ~ empty(v11) | ~ element(v10, v12) | ~ in(v9, v10)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (powerset(v11) = v12) | ~ element(v10, v12) | ~ in(v9, v10) | element(v9, v11)) & ? [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v11 | ~ (subset_intersection2(v10, v11, v11) = v12) | ? [v13] : (powerset(v10) = v13 & ( ~ element(v11, v13) | ~ element(v9, v13)))) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (cast_as_carrier_subset(v11) = v10) | ~ (cast_as_carrier_subset(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (the_carrier(v11) = v10) | ~ (the_carrier(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (powerset(v11) = v10) | ~ (powerset(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_difference(v9, v10) = v11) | ~ v5_membered(v9) | v5_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_difference(v9, v10) = v11) | ~ v5_membered(v9) | v4_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_difference(v9, v10) = v11) | ~ v5_membered(v9) | v3_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_difference(v9, v10) = v11) | ~ v5_membered(v9) | v2_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_difference(v9, v10) = v11) | ~ v5_membered(v9) | v1_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_difference(v9, v10) = v11) | ~ v4_membered(v9) | v4_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_difference(v9, v10) = v11) | ~ v4_membered(v9) | v3_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_difference(v9, v10) = v11) | ~ v4_membered(v9) | v2_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_difference(v9, v10) = v11) | ~ v4_membered(v9) | v1_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_difference(v9, v10) = v11) | ~ v3_membered(v9) | v3_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_difference(v9, v10) = v11) | ~ v3_membered(v9) | v2_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_difference(v9, v10) = v11) | ~ v3_membered(v9) | v1_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_difference(v9, v10) = v11) | ~ v2_membered(v9) | v2_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_difference(v9, v10) = v11) | ~ v2_membered(v9) | v1_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_difference(v9, v10) = v11) | ~ v1_membered(v9) | v1_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_intersection2(v10, v9) = v11) | ~ v5_membered(v9) | v5_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_intersection2(v10, v9) = v11) | ~ v5_membered(v9) | v4_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_intersection2(v10, v9) = v11) | ~ v5_membered(v9) | v3_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_intersection2(v10, v9) = v11) | ~ v5_membered(v9) | v2_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_intersection2(v10, v9) = v11) | ~ v5_membered(v9) | v1_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_intersection2(v10, v9) = v11) | ~ v4_membered(v9) | v4_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_intersection2(v10, v9) = v11) | ~ v4_membered(v9) | v3_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_intersection2(v10, v9) = v11) | ~ v4_membered(v9) | v2_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_intersection2(v10, v9) = v11) | ~ v4_membered(v9) | v1_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_intersection2(v10, v9) = v11) | ~ v3_membered(v9) | v3_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_intersection2(v10, v9) = v11) | ~ v3_membered(v9) | v2_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_intersection2(v10, v9) = v11) | ~ v3_membered(v9) | v1_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_intersection2(v10, v9) = v11) | ~ v2_membered(v9) | v2_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_intersection2(v10, v9) = v11) | ~ v2_membered(v9) | v1_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_intersection2(v10, v9) = v11) | ~ v1_membered(v9) | v1_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_intersection2(v10, v9) = v11) | set_intersection2(v9, v10) = v11) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_intersection2(v9, v10) = v11) | ~ v5_membered(v9) | v5_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_intersection2(v9, v10) = v11) | ~ v5_membered(v9) | v4_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_intersection2(v9, v10) = v11) | ~ v5_membered(v9) | v3_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_intersection2(v9, v10) = v11) | ~ v5_membered(v9) | v2_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_intersection2(v9, v10) = v11) | ~ v5_membered(v9) | v1_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_intersection2(v9, v10) = v11) | ~ v4_membered(v9) | v4_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_intersection2(v9, v10) = v11) | ~ v4_membered(v9) | v3_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_intersection2(v9, v10) = v11) | ~ v4_membered(v9) | v2_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_intersection2(v9, v10) = v11) | ~ v4_membered(v9) | v1_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_intersection2(v9, v10) = v11) | ~ v3_membered(v9) | v3_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_intersection2(v9, v10) = v11) | ~ v3_membered(v9) | v2_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_intersection2(v9, v10) = v11) | ~ v3_membered(v9) | v1_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_intersection2(v9, v10) = v11) | ~ v2_membered(v9) | v2_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_intersection2(v9, v10) = v11) | ~ v2_membered(v9) | v1_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_intersection2(v9, v10) = v11) | ~ v1_membered(v9) | v1_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_intersection2(v9, v10) = v11) | set_intersection2(v10, v9) = v11) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_intersection2(v9, v10) = v11) | ? [v12] : (set_difference(v9, v12) = v11 & set_difference(v9, v10) = v12)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (powerset(v10) = v11) | ~ subset(v9, v10) | element(v9, v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (powerset(v10) = v11) | ~ element(v9, v11) | subset(v9, v10)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (powerset(v9) = v10) | ~ v5_membered(v9) | ~ element(v11, v10) | v5_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (powerset(v9) = v10) | ~ v5_membered(v9) | ~ element(v11, v10) | v4_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (powerset(v9) = v10) | ~ v5_membered(v9) | ~ element(v11, v10) | v3_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (powerset(v9) = v10) | ~ v5_membered(v9) | ~ element(v11, v10) | v2_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (powerset(v9) = v10) | ~ v5_membered(v9) | ~ element(v11, v10) | v1_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (powerset(v9) = v10) | ~ v4_membered(v9) | ~ element(v11, v10) | v4_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (powerset(v9) = v10) | ~ v4_membered(v9) | ~ element(v11, v10) | v3_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (powerset(v9) = v10) | ~ v4_membered(v9) | ~ element(v11, v10) | v2_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (powerset(v9) = v10) | ~ v4_membered(v9) | ~ element(v11, v10) | v1_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (powerset(v9) = v10) | ~ v3_membered(v9) | ~ element(v11, v10) | v3_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (powerset(v9) = v10) | ~ v3_membered(v9) | ~ element(v11, v10) | v2_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (powerset(v9) = v10) | ~ v3_membered(v9) | ~ element(v11, v10) | v1_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (powerset(v9) = v10) | ~ v2_membered(v9) | ~ element(v11, v10) | v2_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (powerset(v9) = v10) | ~ v2_membered(v9) | ~ element(v11, v10) | v1_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (powerset(v9) = v10) | ~ element(v11, v10) | ~ v1_membered(v9) | v1_membered(v11)) & ! [v9] : ! [v10] : (v10 = v9 | ~ (set_difference(v9, empty_set) = v10)) & ! [v9] : ! [v10] : (v10 = v9 | ~ (set_intersection2(v9, v9) = v10)) & ! [v9] : ! [v10] : (v10 = v9 | ~ empty(v10) | ~ empty(v9)) & ! [v9] : ! [v10] : (v10 = empty_set | ~ (set_difference(empty_set, v9) = v10)) & ! [v9] : ! [v10] : (v10 = empty_set | ~ (set_intersection2(v9, empty_set) = v10)) & ! [v9] : ! [v10] : ( ~ (cast_as_carrier_subset(v9) = v10) | ~ one_sorted_str(v9) | the_carrier(v9) = v10) & ! [v9] : ! [v10] : ( ~ (cast_as_carrier_subset(v9) = v10) | ~ one_sorted_str(v9) | ? [v11] : ? [v12] : (the_carrier(v9) = v11 & powerset(v11) = v12 & element(v10, v12))) & ! [v9] : ! [v10] : ( ~ (cast_as_carrier_subset(v9) = v10) | ~ one_sorted_str(v9) | ? [v11] : ? [v12] : (the_carrier(v9) = v11 & powerset(v11) = v12 & ! [v13] : ! [v14] : (v14 = v13 | ~ (subset_intersection2(v11, v13, v10) = v14) | ~ element(v13, v12)))) & ! [v9] : ! [v10] : ( ~ (the_carrier(v9) = v10) | ~ one_sorted_str(v9) | cast_as_carrier_subset(v9) = v10) & ! [v9] : ! [v10] : ( ~ (the_carrier(v9) = v10) | ~ one_sorted_str(v9) | ? [v11] : ? [v12] : (cast_as_carrier_subset(v9) = v12 & powerset(v10) = v11 & ! [v13] : ! [v14] : (v14 = v13 | ~ (subset_intersection2(v10, v13, v12) = v14) | ~ element(v13, v11)))) & ! [v9] : ! [v10] : ( ~ (the_carrier(v9) = v10) | ~ one_sorted_str(v9) | ? [v11] : ? [v12] : (cast_as_carrier_subset(v9) = v11 & powerset(v10) = v12 & element(v11, v12))) & ! [v9] : ! [v10] : ( ~ (powerset(v9) = v10) | ~ empty(v10)) & ! [v9] : ! [v10] : ( ~ (powerset(v9) = v10) | empty(v9) | ? [v11] : (element(v11, v10) & ~ empty(v11))) & ! [v9] : ! [v10] : ( ~ (powerset(v9) = v10) | ? [v11] : (empty(v11) & element(v11, v10))) & ! [v9] : ! [v10] : ( ~ empty(v10) | ~ in(v9, v10)) & ! [v9] : ! [v10] : ( ~ v5_membered(v9) | ~ element(v10, v9) | natural(v10)) & ! [v9] : ! [v10] : ( ~ v5_membered(v9) | ~ element(v10, v9) | v1_int_1(v10)) & ! [v9] : ! [v10] : ( ~ v5_membered(v9) | ~ element(v10, v9) | v1_rat_1(v10)) & ! [v9] : ! [v10] : ( ~ v5_membered(v9) | ~ element(v10, v9) | v1_xreal_0(v10)) & ! [v9] : ! [v10] : ( ~ v5_membered(v9) | ~ element(v10, v9) | v1_xcmplx_0(v10)) & ! [v9] : ! [v10] : ( ~ v4_membered(v9) | ~ element(v10, v9) | v1_int_1(v10)) & ! [v9] : ! [v10] : ( ~ v4_membered(v9) | ~ element(v10, v9) | v1_rat_1(v10)) & ! [v9] : ! [v10] : ( ~ v4_membered(v9) | ~ element(v10, v9) | v1_xreal_0(v10)) & ! [v9] : ! [v10] : ( ~ v4_membered(v9) | ~ element(v10, v9) | v1_xcmplx_0(v10)) & ! [v9] : ! [v10] : ( ~ v3_membered(v9) | ~ element(v10, v9) | v1_rat_1(v10)) & ! [v9] : ! [v10] : ( ~ v3_membered(v9) | ~ element(v10, v9) | v1_xreal_0(v10)) & ! [v9] : ! [v10] : ( ~ v3_membered(v9) | ~ element(v10, v9) | v1_xcmplx_0(v10)) & ! [v9] : ! [v10] : ( ~ v2_membered(v9) | ~ element(v10, v9) | v1_xreal_0(v10)) & ! [v9] : ! [v10] : ( ~ v2_membered(v9) | ~ element(v10, v9) | v1_xcmplx_0(v10)) & ! [v9] : ! [v10] : ( ~ element(v10, v9) | ~ v1_membered(v9) | v1_xcmplx_0(v10)) & ! [v9] : ! [v10] : ( ~ element(v9, v10) | empty(v10) | in(v9, v10)) & ! [v9] : ! [v10] : ( ~ in(v10, v9) | ~ in(v9, v10)) & ! [v9] : ! [v10] : ( ~ in(v9, v10) | element(v9, v10)) & ! [v9] : (v9 = empty_set | ~ empty(v9)) & ! [v9] : ( ~ empty(v9) | v5_membered(v9)) & ! [v9] : ( ~ empty(v9) | v4_membered(v9)) & ! [v9] : ( ~ empty(v9) | v3_membered(v9)) & ! [v9] : ( ~ empty(v9) | v2_membered(v9)) & ! [v9] : ( ~ empty(v9) | v1_membered(v9)) & ! [v9] : ( ~ v5_membered(v9) | v4_membered(v9)) & ! [v9] : ( ~ v4_membered(v9) | v3_membered(v9)) & ! [v9] : ( ~ v3_membered(v9) | v2_membered(v9)) & ! [v9] : ( ~ v2_membered(v9) | v1_membered(v9)) & ? [v9] : ? [v10] : element(v10, v9) & ? [v9] : subset(v9, v9)) % 7.37/2.32 | 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 yields: % 7.37/2.32 | (1) ~ (all_0_2_2 = all_0_4_4) & subset_difference(all_0_7_7, all_0_5_5, all_0_3_3) = all_0_2_2 & subset_difference(all_0_7_7, all_0_5_5, all_0_4_4) = all_0_3_3 & cast_as_carrier_subset(all_0_8_8) = all_0_5_5 & the_carrier(all_0_8_8) = all_0_7_7 & powerset(all_0_7_7) = all_0_6_6 & one_sorted_str(all_0_0_0) & one_sorted_str(all_0_8_8) & empty(empty_set) & v5_membered(all_0_1_1) & v5_membered(empty_set) & v4_membered(all_0_1_1) & v4_membered(empty_set) & v3_membered(all_0_1_1) & v3_membered(empty_set) & v2_membered(all_0_1_1) & v2_membered(empty_set) & element(all_0_4_4, all_0_6_6) & v1_membered(all_0_1_1) & v1_membered(empty_set) & ~ empty(all_0_1_1) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (subset_difference(v4, v3, v2) = v1) | ~ (subset_difference(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (subset_intersection2(v4, v3, v2) = v1) | ~ (subset_intersection2(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v1, v2) = v4) | ~ (powerset(v0) = v3) | ~ element(v2, v3) | ~ element(v1, v3) | subset_difference(v0, v1, v2) = v4) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_intersection2(v1, v2) = v4) | ~ (powerset(v0) = v3) | ~ element(v2, v3) | ~ element(v1, v3) | subset_intersection2(v0, v1, v2) = v4) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v2) = v3) | ~ (set_difference(v0, v1) = v2) | set_intersection2(v0, v1) = v3) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_difference(v0, v1, v2) = v3) | ? [v4] : ? [v5] : (set_difference(v1, v2) = v5 & powerset(v0) = v4 & (v5 = v3 | ~ element(v2, v4) | ~ element(v1, v4)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_difference(v0, v1, v2) = v3) | ? [v4] : (powerset(v0) = v4 & ( ~ element(v2, v4) | ~ element(v1, v4) | element(v3, v4)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_intersection2(v0, v2, v1) = v3) | ? [v4] : ? [v5] : (subset_intersection2(v0, v1, v2) = v5 & powerset(v0) = v4 & (v5 = v3 | ~ element(v2, v4) | ~ element(v1, v4)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_intersection2(v0, v1, v2) = v3) | ? [v4] : ? [v5] : (subset_intersection2(v0, v2, v1) = v5 & powerset(v0) = v4 & (v5 = v3 | ~ element(v2, v4) | ~ element(v1, v4)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_intersection2(v0, v1, v2) = v3) | ? [v4] : ? [v5] : (set_intersection2(v1, v2) = v5 & powerset(v0) = v4 & (v5 = v3 | ~ element(v2, v4) | ~ element(v1, v4)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_intersection2(v0, v1, v2) = v3) | ? [v4] : (powerset(v0) = v4 & ( ~ element(v2, v4) | ~ element(v1, v4) | element(v3, v4)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ empty(v2) | ~ element(v1, v3) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ in(v0, v1) | element(v0, v2)) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (subset_intersection2(v1, v2, v2) = v3) | ? [v4] : (powerset(v1) = v4 & ( ~ element(v2, v4) | ~ element(v0, v4)))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cast_as_carrier_subset(v2) = v1) | ~ (cast_as_carrier_subset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (the_carrier(v2) = v1) | ~ (the_carrier(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v5_membered(v0) | v5_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v5_membered(v0) | v4_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v5_membered(v0) | v3_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v5_membered(v0) | v2_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v5_membered(v0) | v1_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v4_membered(v0) | v4_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v4_membered(v0) | v3_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v4_membered(v0) | v2_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v4_membered(v0) | v1_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v3_membered(v0) | v3_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v3_membered(v0) | v2_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v3_membered(v0) | v1_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v2_membered(v0) | v2_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v2_membered(v0) | v1_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v1_membered(v0) | v1_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | ~ v5_membered(v0) | v5_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | ~ v5_membered(v0) | v4_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | ~ v5_membered(v0) | v3_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | ~ v5_membered(v0) | v2_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | ~ v5_membered(v0) | v1_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | ~ v4_membered(v0) | v4_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | ~ v4_membered(v0) | v3_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | ~ v4_membered(v0) | v2_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | ~ v4_membered(v0) | v1_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | ~ v3_membered(v0) | v3_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | ~ v3_membered(v0) | v2_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | ~ v3_membered(v0) | v1_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | ~ v2_membered(v0) | v2_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | ~ v2_membered(v0) | v1_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | ~ v1_membered(v0) | v1_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ v5_membered(v0) | v5_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ v5_membered(v0) | v4_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ v5_membered(v0) | v3_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ v5_membered(v0) | v2_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ v5_membered(v0) | v1_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ v4_membered(v0) | v4_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ v4_membered(v0) | v3_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ v4_membered(v0) | v2_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ v4_membered(v0) | v1_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ v3_membered(v0) | v3_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ v3_membered(v0) | v2_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ v3_membered(v0) | v1_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ v2_membered(v0) | v2_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ v2_membered(v0) | v1_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ v1_membered(v0) | v1_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ? [v3] : (set_difference(v0, v3) = v2 & set_difference(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ element(v0, v2) | subset(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v5_membered(v0) | ~ element(v2, v1) | v5_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v5_membered(v0) | ~ element(v2, v1) | v4_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v5_membered(v0) | ~ element(v2, v1) | v3_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v5_membered(v0) | ~ element(v2, v1) | v2_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v5_membered(v0) | ~ element(v2, v1) | v1_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v4_membered(v0) | ~ element(v2, v1) | v4_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v4_membered(v0) | ~ element(v2, v1) | v3_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v4_membered(v0) | ~ element(v2, v1) | v2_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v4_membered(v0) | ~ element(v2, v1) | v1_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v3_membered(v0) | ~ element(v2, v1) | v3_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v3_membered(v0) | ~ element(v2, v1) | v2_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v3_membered(v0) | ~ element(v2, v1) | v1_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v2_membered(v0) | ~ element(v2, v1) | v2_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v2_membered(v0) | ~ element(v2, v1) | v1_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ element(v2, v1) | ~ v1_membered(v0) | v1_membered(v2)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_difference(v0, empty_set) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) & ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_difference(empty_set, v0) = v1)) & ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1)) & ! [v0] : ! [v1] : ( ~ (cast_as_carrier_subset(v0) = v1) | ~ one_sorted_str(v0) | the_carrier(v0) = v1) & ! [v0] : ! [v1] : ( ~ (cast_as_carrier_subset(v0) = v1) | ~ one_sorted_str(v0) | ? [v2] : ? [v3] : (the_carrier(v0) = v2 & powerset(v2) = v3 & element(v1, v3))) & ! [v0] : ! [v1] : ( ~ (cast_as_carrier_subset(v0) = v1) | ~ one_sorted_str(v0) | ? [v2] : ? [v3] : (the_carrier(v0) = v2 & powerset(v2) = v3 & ! [v4] : ! [v5] : (v5 = v4 | ~ (subset_intersection2(v2, v4, v1) = v5) | ~ element(v4, v3)))) & ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ one_sorted_str(v0) | cast_as_carrier_subset(v0) = v1) & ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ one_sorted_str(v0) | ? [v2] : ? [v3] : (cast_as_carrier_subset(v0) = v3 & powerset(v1) = v2 & ! [v4] : ! [v5] : (v5 = v4 | ~ (subset_intersection2(v1, v4, v3) = v5) | ~ element(v4, v2)))) & ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ one_sorted_str(v0) | ? [v2] : ? [v3] : (cast_as_carrier_subset(v0) = v2 & powerset(v1) = v3 & element(v2, v3))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ empty(v1)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (element(v2, v1) & ~ empty(v2))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (empty(v2) & element(v2, v1))) & ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ( ~ v5_membered(v0) | ~ element(v1, v0) | natural(v1)) & ! [v0] : ! [v1] : ( ~ v5_membered(v0) | ~ element(v1, v0) | v1_int_1(v1)) & ! [v0] : ! [v1] : ( ~ v5_membered(v0) | ~ element(v1, v0) | v1_rat_1(v1)) & ! [v0] : ! [v1] : ( ~ v5_membered(v0) | ~ element(v1, v0) | v1_xreal_0(v1)) & ! [v0] : ! [v1] : ( ~ v5_membered(v0) | ~ element(v1, v0) | v1_xcmplx_0(v1)) & ! [v0] : ! [v1] : ( ~ v4_membered(v0) | ~ element(v1, v0) | v1_int_1(v1)) & ! [v0] : ! [v1] : ( ~ v4_membered(v0) | ~ element(v1, v0) | v1_rat_1(v1)) & ! [v0] : ! [v1] : ( ~ v4_membered(v0) | ~ element(v1, v0) | v1_xreal_0(v1)) & ! [v0] : ! [v1] : ( ~ v4_membered(v0) | ~ element(v1, v0) | v1_xcmplx_0(v1)) & ! [v0] : ! [v1] : ( ~ v3_membered(v0) | ~ element(v1, v0) | v1_rat_1(v1)) & ! [v0] : ! [v1] : ( ~ v3_membered(v0) | ~ element(v1, v0) | v1_xreal_0(v1)) & ! [v0] : ! [v1] : ( ~ v3_membered(v0) | ~ element(v1, v0) | v1_xcmplx_0(v1)) & ! [v0] : ! [v1] : ( ~ v2_membered(v0) | ~ element(v1, v0) | v1_xreal_0(v1)) & ! [v0] : ! [v1] : ( ~ v2_membered(v0) | ~ element(v1, v0) | v1_xcmplx_0(v1)) & ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ v1_membered(v0) | v1_xcmplx_0(v1)) & ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1)) & ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1)) & ! [v0] : (v0 = empty_set | ~ empty(v0)) & ! [v0] : ( ~ empty(v0) | v5_membered(v0)) & ! [v0] : ( ~ empty(v0) | v4_membered(v0)) & ! [v0] : ( ~ empty(v0) | v3_membered(v0)) & ! [v0] : ( ~ empty(v0) | v2_membered(v0)) & ! [v0] : ( ~ empty(v0) | v1_membered(v0)) & ! [v0] : ( ~ v5_membered(v0) | v4_membered(v0)) & ! [v0] : ( ~ v4_membered(v0) | v3_membered(v0)) & ! [v0] : ( ~ v3_membered(v0) | v2_membered(v0)) & ! [v0] : ( ~ v2_membered(v0) | v1_membered(v0)) & ? [v0] : ? [v1] : element(v1, v0) & ? [v0] : subset(v0, v0) % 7.37/2.36 | % 7.37/2.36 | Applying alpha-rule on (1) yields: % 7.37/2.36 | (2) ! [v0] : ! [v1] : ( ~ (cast_as_carrier_subset(v0) = v1) | ~ one_sorted_str(v0) | the_carrier(v0) = v1) % 7.37/2.36 | (3) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1)) % 7.37/2.36 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v4_membered(v0) | v4_membered(v2)) % 7.37/2.36 | (5) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ v2_membered(v0) | v1_membered(v2)) % 7.37/2.36 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_intersection2(v0, v2, v1) = v3) | ? [v4] : ? [v5] : (subset_intersection2(v0, v1, v2) = v5 & powerset(v0) = v4 & (v5 = v3 | ~ element(v2, v4) | ~ element(v1, v4)))) % 7.37/2.36 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) % 7.37/2.36 | (8) ! [v0] : ! [v1] : ( ~ (cast_as_carrier_subset(v0) = v1) | ~ one_sorted_str(v0) | ? [v2] : ? [v3] : (the_carrier(v0) = v2 & powerset(v2) = v3 & element(v1, v3))) % 7.37/2.36 | (9) ! [v0] : (v0 = empty_set | ~ empty(v0)) % 7.37/2.36 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ element(v2, v1) | ~ v1_membered(v0) | v1_membered(v2)) % 7.37/2.36 | (11) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | ~ v5_membered(v0) | v5_membered(v2)) % 7.37/2.36 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ v3_membered(v0) | v3_membered(v2)) % 7.37/2.36 | (13) ! [v0] : ! [v1] : ( ~ v5_membered(v0) | ~ element(v1, v0) | v1_xcmplx_0(v1)) % 7.37/2.36 | (14) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (element(v2, v1) & ~ empty(v2))) % 7.37/2.36 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_difference(v0, v1, v2) = v3) | ? [v4] : ? [v5] : (set_difference(v1, v2) = v5 & powerset(v0) = v4 & (v5 = v3 | ~ element(v2, v4) | ~ element(v1, v4)))) % 7.37/2.36 | (16) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ v4_membered(v0) | v1_membered(v2)) % 7.37/2.36 | (17) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ v2_membered(v0) | v2_membered(v2)) % 7.37/2.36 | (18) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v3_membered(v0) | v1_membered(v2)) % 7.37/2.36 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (subset_intersection2(v4, v3, v2) = v1) | ~ (subset_intersection2(v4, v3, v2) = v0)) % 7.37/2.36 | (20) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (subset_intersection2(v1, v2, v2) = v3) | ? [v4] : (powerset(v1) = v4 & ( ~ element(v2, v4) | ~ element(v0, v4)))) % 7.37/2.36 | (21) ! [v0] : ! [v1] : ( ~ v5_membered(v0) | ~ element(v1, v0) | v1_int_1(v1)) % 7.37/2.36 | (22) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v5_membered(v0) | v3_membered(v2)) % 7.37/2.36 | (23) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | ~ v2_membered(v0) | v1_membered(v2)) % 7.37/2.36 | (24) ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ one_sorted_str(v0) | ? [v2] : ? [v3] : (cast_as_carrier_subset(v0) = v3 & powerset(v1) = v2 & ! [v4] : ! [v5] : (v5 = v4 | ~ (subset_intersection2(v1, v4, v3) = v5) | ~ element(v4, v2)))) % 7.37/2.36 | (25) cast_as_carrier_subset(all_0_8_8) = all_0_5_5 % 7.37/2.36 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) % 7.37/2.36 | (27) subset_difference(all_0_7_7, all_0_5_5, all_0_4_4) = all_0_3_3 % 7.37/2.36 | (28) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_difference(empty_set, v0) = v1)) % 7.37/2.36 | (29) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1)) % 7.37/2.36 | (30) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | ~ v4_membered(v0) | v1_membered(v2)) % 7.37/2.36 | (31) v2_membered(empty_set) % 7.37/2.36 | (32) ! [v0] : ! [v1] : ( ~ v3_membered(v0) | ~ element(v1, v0) | v1_xcmplx_0(v1)) % 7.37/2.36 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v1, v2) = v4) | ~ (powerset(v0) = v3) | ~ element(v2, v3) | ~ element(v1, v3) | subset_difference(v0, v1, v2) = v4) % 7.37/2.36 | (34) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | ~ v4_membered(v0) | v3_membered(v2)) % 7.37/2.36 | (35) ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1)) % 7.37/2.37 | (36) one_sorted_str(all_0_0_0) % 7.37/2.37 | (37) ! [v0] : ( ~ v2_membered(v0) | v1_membered(v0)) % 7.37/2.37 | (38) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v4_membered(v0) | ~ element(v2, v1) | v1_membered(v2)) % 7.37/2.37 | (39) ! [v0] : ! [v1] : ( ~ v5_membered(v0) | ~ element(v1, v0) | v1_rat_1(v1)) % 7.37/2.37 | (40) ! [v0] : ! [v1] : ( ~ v3_membered(v0) | ~ element(v1, v0) | v1_xreal_0(v1)) % 7.37/2.37 | (41) ! [v0] : ( ~ empty(v0) | v1_membered(v0)) % 7.37/2.37 | (42) the_carrier(all_0_8_8) = all_0_7_7 % 7.37/2.37 | (43) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v5_membered(v0) | ~ element(v2, v1) | v4_membered(v2)) % 7.37/2.37 | (44) ! [v0] : ! [v1] : ( ~ v2_membered(v0) | ~ element(v1, v0) | v1_xcmplx_0(v1)) % 7.37/2.37 | (45) ! [v0] : ! [v1] : ( ~ v5_membered(v0) | ~ element(v1, v0) | v1_xreal_0(v1)) % 7.37/2.37 | (46) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v5_membered(v0) | ~ element(v2, v1) | v5_membered(v2)) % 7.37/2.37 | (47) v4_membered(empty_set) % 7.37/2.37 | (48) v4_membered(all_0_1_1) % 7.37/2.37 | (49) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v4_membered(v0) | v3_membered(v2)) % 7.37/2.37 | (50) ! [v0] : ! [v1] : ( ~ (cast_as_carrier_subset(v0) = v1) | ~ one_sorted_str(v0) | ? [v2] : ? [v3] : (the_carrier(v0) = v2 & powerset(v2) = v3 & ! [v4] : ! [v5] : (v5 = v4 | ~ (subset_intersection2(v2, v4, v1) = v5) | ~ element(v4, v3)))) % 7.37/2.37 | (51) ~ (all_0_2_2 = all_0_4_4) % 7.37/2.37 | (52) ~ empty(all_0_1_1) % 7.37/2.37 | (53) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v2_membered(v0) | ~ element(v2, v1) | v1_membered(v2)) % 7.37/2.37 | (54) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_difference(v0, empty_set) = v1)) % 7.37/2.37 | (55) v5_membered(all_0_1_1) % 7.37/2.37 | (56) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) % 7.37/2.37 | (57) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2) % 7.37/2.37 | (58) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) % 7.37/2.37 | (59) ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1)) % 7.37/2.37 | (60) ! [v0] : ( ~ v5_membered(v0) | v4_membered(v0)) % 7.37/2.37 | (61) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | ~ v4_membered(v0) | v2_membered(v2)) % 7.37/2.37 | (62) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v4_membered(v0) | v2_membered(v2)) % 7.37/2.37 | (63) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | ~ v5_membered(v0) | v2_membered(v2)) % 7.37/2.37 | (64) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ v3_membered(v0) | v1_membered(v2)) % 7.37/2.37 | (65) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v5_membered(v0) | v1_membered(v2)) % 7.37/2.37 | (66) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cast_as_carrier_subset(v2) = v1) | ~ (cast_as_carrier_subset(v2) = v0)) % 7.37/2.37 | (67) ! [v0] : ! [v1] : ( ~ v3_membered(v0) | ~ element(v1, v0) | v1_rat_1(v1)) % 7.37/2.37 | (68) ! [v0] : ! [v1] : ( ~ v4_membered(v0) | ~ element(v1, v0) | v1_xreal_0(v1)) % 7.37/2.37 | (69) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | ~ v5_membered(v0) | v1_membered(v2)) % 7.37/2.37 | (70) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | ~ v1_membered(v0) | v1_membered(v2)) % 7.37/2.37 | (71) ! [v0] : ! [v1] : ( ~ v4_membered(v0) | ~ element(v1, v0) | v1_rat_1(v1)) % 7.37/2.37 | (72) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ v3_membered(v0) | v2_membered(v2)) % 7.37/2.37 | (73) ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ one_sorted_str(v0) | ? [v2] : ? [v3] : (cast_as_carrier_subset(v0) = v2 & powerset(v1) = v3 & element(v2, v3))) % 7.37/2.37 | (74) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ v4_membered(v0) | v2_membered(v2)) % 7.37/2.37 | (75) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | ~ v5_membered(v0) | v4_membered(v2)) % 7.37/2.37 | (76) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_intersection2(v0, v1, v2) = v3) | ? [v4] : (powerset(v0) = v4 & ( ~ element(v2, v4) | ~ element(v1, v4) | element(v3, v4)))) % 7.37/2.37 | (77) v1_membered(all_0_1_1) % 7.37/2.37 | (78) subset_difference(all_0_7_7, all_0_5_5, all_0_3_3) = all_0_2_2 % 7.37/2.37 | (79) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v5_membered(v0) | ~ element(v2, v1) | v2_membered(v2)) % 7.37/2.37 | (80) ! [v0] : ( ~ empty(v0) | v2_membered(v0)) % 7.37/2.37 | (81) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v5_membered(v0) | v2_membered(v2)) % 7.37/2.37 | (82) ? [v0] : subset(v0, v0) % 7.37/2.37 | (83) ! [v0] : ! [v1] : ( ~ v2_membered(v0) | ~ element(v1, v0) | v1_xreal_0(v1)) % 7.37/2.37 | (84) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ v5_membered(v0) | v5_membered(v2)) % 7.37/2.37 | (85) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v4_membered(v0) | ~ element(v2, v1) | v4_membered(v2)) % 7.37/2.37 | (86) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v4_membered(v0) | ~ element(v2, v1) | v2_membered(v2)) % 7.37/2.37 | (87) ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ v1_membered(v0) | v1_xcmplx_0(v1)) % 7.37/2.37 | (88) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v2_membered(v0) | v2_membered(v2)) % 7.37/2.37 | (89) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v3_membered(v0) | ~ element(v2, v1) | v1_membered(v2)) % 7.37/2.38 | (90) v1_membered(empty_set) % 7.37/2.38 | (91) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_difference(v0, v1, v2) = v3) | ? [v4] : (powerset(v0) = v4 & ( ~ element(v2, v4) | ~ element(v1, v4) | element(v3, v4)))) % 7.37/2.38 | (92) ! [v0] : ! [v1] : ( ~ v4_membered(v0) | ~ element(v1, v0) | v1_xcmplx_0(v1)) % 7.37/2.38 | (93) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ element(v0, v2) | subset(v0, v1)) % 7.37/2.38 | (94) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2)) % 7.37/2.38 | (95) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v2_membered(v0) | ~ element(v2, v1) | v2_membered(v2)) % 7.37/2.38 | (96) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v2) = v3) | ~ (set_difference(v0, v1) = v2) | set_intersection2(v0, v1) = v3) % 7.37/2.38 | (97) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v5_membered(v0) | v4_membered(v2)) % 7.37/2.38 | (98) empty(empty_set) % 7.37/2.38 | (99) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v2_membered(v0) | v1_membered(v2)) % 7.37/2.38 | (100) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v5_membered(v0) | v5_membered(v2)) % 7.37/2.38 | (101) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v3_membered(v0) | ~ element(v2, v1) | v3_membered(v2)) % 7.37/2.38 | (102) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ empty(v2) | ~ element(v1, v3) | ~ in(v0, v1)) % 7.37/2.38 | (103) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ v4_membered(v0) | v3_membered(v2)) % 7.37/2.38 | (104) v5_membered(empty_set) % 7.37/2.38 | (105) element(all_0_4_4, all_0_6_6) % 7.37/2.38 | (106) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v3_membered(v0) | ~ element(v2, v1) | v2_membered(v2)) % 7.37/2.38 | (107) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v5_membered(v0) | ~ element(v2, v1) | v3_membered(v2)) % 7.37/2.38 | (108) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ v1_membered(v0) | v1_membered(v2)) % 7.37/2.38 | (109) powerset(all_0_7_7) = all_0_6_6 % 7.37/2.38 | (110) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) % 7.37/2.38 | (111) ! [v0] : ( ~ empty(v0) | v4_membered(v0)) % 7.37/2.38 | (112) v2_membered(all_0_1_1) % 7.37/2.38 | (113) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v3_membered(v0) | v2_membered(v2)) % 7.75/2.38 | (114) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | ~ v3_membered(v0) | v3_membered(v2)) % 7.75/2.38 | (115) v3_membered(all_0_1_1) % 7.75/2.38 | (116) ! [v0] : ( ~ v4_membered(v0) | v3_membered(v0)) % 7.75/2.38 | (117) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v1_membered(v0) | v1_membered(v2)) % 7.75/2.38 | (118) ! [v0] : ! [v1] : ( ~ v4_membered(v0) | ~ element(v1, v0) | v1_int_1(v1)) % 7.75/2.38 | (119) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v4_membered(v0) | v1_membered(v2)) % 7.75/2.38 | (120) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ v5_membered(v0) | v4_membered(v2)) % 7.75/2.38 | (121) ! [v0] : ( ~ v3_membered(v0) | v2_membered(v0)) % 7.75/2.38 | (122) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | ~ v3_membered(v0) | v1_membered(v2)) % 7.75/2.38 | (123) ! [v0] : ( ~ empty(v0) | v5_membered(v0)) % 7.75/2.38 | (124) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1)) % 7.75/2.38 | (125) v3_membered(empty_set) % 7.75/2.38 | (126) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | ~ v4_membered(v0) | v4_membered(v2)) % 7.75/2.38 | (127) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v5_membered(v0) | ~ element(v2, v1) | v1_membered(v2)) % 7.75/2.38 | (128) ! [v0] : ( ~ empty(v0) | v3_membered(v0)) % 7.75/2.38 | (129) ? [v0] : ? [v1] : element(v1, v0) % 7.75/2.38 | (130) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | ~ v3_membered(v0) | v2_membered(v2)) % 7.75/2.38 | (131) ! [v0] : ! [v1] : ( ~ v5_membered(v0) | ~ element(v1, v0) | natural(v1)) % 7.75/2.38 | (132) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ? [v3] : (set_difference(v0, v3) = v2 & set_difference(v0, v1) = v3)) % 7.75/2.38 | (133) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ v4_membered(v0) | v4_membered(v2)) % 7.75/2.38 | (134) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (empty(v2) & element(v2, v1))) % 7.75/2.38 | (135) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | ~ v5_membered(v0) | v3_membered(v2)) % 7.75/2.38 | (136) one_sorted_str(all_0_8_8) % 7.75/2.38 | (137) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ in(v0, v1) | element(v0, v2)) % 7.75/2.38 | (138) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ empty(v1)) % 7.75/2.38 | (139) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (subset_difference(v4, v3, v2) = v1) | ~ (subset_difference(v4, v3, v2) = v0)) % 7.75/2.38 | (140) ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ one_sorted_str(v0) | cast_as_carrier_subset(v0) = v1) % 7.75/2.38 | (141) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ v5_membered(v0) | v1_membered(v2)) % 7.75/2.38 | (142) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ v5_membered(v0) | v2_membered(v2)) % 7.75/2.38 | (143) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) % 7.75/2.38 | (144) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v4_membered(v0) | ~ element(v2, v1) | v3_membered(v2)) % 7.75/2.38 | (145) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_intersection2(v0, v1, v2) = v3) | ? [v4] : ? [v5] : (subset_intersection2(v0, v2, v1) = v5 & powerset(v0) = v4 & (v5 = v3 | ~ element(v2, v4) | ~ element(v1, v4)))) % 7.75/2.39 | (146) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v3_membered(v0) | v3_membered(v2)) % 7.75/2.39 | (147) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_intersection2(v1, v2) = v4) | ~ (powerset(v0) = v3) | ~ element(v2, v3) | ~ element(v1, v3) | subset_intersection2(v0, v1, v2) = v4) % 7.75/2.39 | (148) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_intersection2(v0, v1, v2) = v3) | ? [v4] : ? [v5] : (set_intersection2(v1, v2) = v5 & powerset(v0) = v4 & (v5 = v3 | ~ element(v2, v4) | ~ element(v1, v4)))) % 7.75/2.39 | (149) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (the_carrier(v2) = v1) | ~ (the_carrier(v2) = v0)) % 7.75/2.39 | (150) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | ~ v2_membered(v0) | v2_membered(v2)) % 7.75/2.39 | (151) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ v5_membered(v0) | v3_membered(v2)) % 7.75/2.39 | % 7.75/2.39 | Instantiating formula (15) with all_0_2_2, all_0_3_3, all_0_5_5, all_0_7_7 and discharging atoms subset_difference(all_0_7_7, all_0_5_5, all_0_3_3) = all_0_2_2, yields: % 7.75/2.39 | (152) ? [v0] : ? [v1] : (set_difference(all_0_5_5, all_0_3_3) = v1 & powerset(all_0_7_7) = v0 & (v1 = all_0_2_2 | ~ element(all_0_3_3, v0) | ~ element(all_0_5_5, v0))) % 7.75/2.39 | % 7.75/2.39 | Instantiating formula (91) with all_0_2_2, all_0_3_3, all_0_5_5, all_0_7_7 and discharging atoms subset_difference(all_0_7_7, all_0_5_5, all_0_3_3) = all_0_2_2, yields: % 7.75/2.39 | (153) ? [v0] : (powerset(all_0_7_7) = v0 & ( ~ element(all_0_3_3, v0) | ~ element(all_0_5_5, v0) | element(all_0_2_2, v0))) % 7.75/2.39 | % 7.75/2.39 | Instantiating formula (15) with all_0_3_3, all_0_4_4, all_0_5_5, all_0_7_7 and discharging atoms subset_difference(all_0_7_7, all_0_5_5, all_0_4_4) = all_0_3_3, yields: % 7.75/2.39 | (154) ? [v0] : ? [v1] : (set_difference(all_0_5_5, all_0_4_4) = v1 & powerset(all_0_7_7) = v0 & (v1 = all_0_3_3 | ~ element(all_0_4_4, v0) | ~ element(all_0_5_5, v0))) % 7.75/2.39 | % 7.75/2.39 | Instantiating formula (91) with all_0_3_3, all_0_4_4, all_0_5_5, all_0_7_7 and discharging atoms subset_difference(all_0_7_7, all_0_5_5, all_0_4_4) = all_0_3_3, yields: % 7.75/2.39 | (155) ? [v0] : (powerset(all_0_7_7) = v0 & ( ~ element(all_0_4_4, v0) | ~ element(all_0_5_5, v0) | element(all_0_3_3, v0))) % 7.75/2.39 | % 7.75/2.39 | Instantiating formula (2) with all_0_5_5, all_0_8_8 and discharging atoms cast_as_carrier_subset(all_0_8_8) = all_0_5_5, one_sorted_str(all_0_8_8), yields: % 7.75/2.39 | (156) the_carrier(all_0_8_8) = all_0_5_5 % 7.75/2.39 | % 7.75/2.39 | Instantiating formula (8) with all_0_5_5, all_0_8_8 and discharging atoms cast_as_carrier_subset(all_0_8_8) = all_0_5_5, one_sorted_str(all_0_8_8), yields: % 7.75/2.39 | (157) ? [v0] : ? [v1] : (the_carrier(all_0_8_8) = v0 & powerset(v0) = v1 & element(all_0_5_5, v1)) % 7.75/2.39 | % 7.75/2.39 | Instantiating formula (50) with all_0_5_5, all_0_8_8 and discharging atoms cast_as_carrier_subset(all_0_8_8) = all_0_5_5, one_sorted_str(all_0_8_8), yields: % 7.75/2.39 | (158) ? [v0] : ? [v1] : (the_carrier(all_0_8_8) = v0 & powerset(v0) = v1 & ! [v2] : ! [v3] : (v3 = v2 | ~ (subset_intersection2(v0, v2, all_0_5_5) = v3) | ~ element(v2, v1))) % 7.75/2.39 | % 7.75/2.39 | Instantiating formula (140) with all_0_7_7, all_0_8_8 and discharging atoms the_carrier(all_0_8_8) = all_0_7_7, one_sorted_str(all_0_8_8), yields: % 7.75/2.39 | (159) cast_as_carrier_subset(all_0_8_8) = all_0_7_7 % 7.75/2.39 | % 7.75/2.39 | Instantiating formula (24) with all_0_7_7, all_0_8_8 and discharging atoms the_carrier(all_0_8_8) = all_0_7_7, one_sorted_str(all_0_8_8), yields: % 7.75/2.39 | (160) ? [v0] : ? [v1] : (cast_as_carrier_subset(all_0_8_8) = v1 & powerset(all_0_7_7) = v0 & ! [v2] : ! [v3] : (v3 = v2 | ~ (subset_intersection2(all_0_7_7, v2, v1) = v3) | ~ element(v2, v0))) % 7.75/2.39 | % 7.75/2.39 | Instantiating formula (73) with all_0_7_7, all_0_8_8 and discharging atoms the_carrier(all_0_8_8) = all_0_7_7, one_sorted_str(all_0_8_8), yields: % 7.75/2.39 | (161) ? [v0] : ? [v1] : (cast_as_carrier_subset(all_0_8_8) = v0 & powerset(all_0_7_7) = v1 & element(v0, v1)) % 7.75/2.39 | % 7.75/2.39 | Instantiating (158) with all_15_0_13, all_15_1_14 yields: % 7.75/2.39 | (162) the_carrier(all_0_8_8) = all_15_1_14 & powerset(all_15_1_14) = all_15_0_13 & ! [v0] : ! [v1] : (v1 = v0 | ~ (subset_intersection2(all_15_1_14, v0, all_0_5_5) = v1) | ~ element(v0, all_15_0_13)) % 7.75/2.39 | % 7.75/2.39 | Applying alpha-rule on (162) yields: % 7.75/2.39 | (163) the_carrier(all_0_8_8) = all_15_1_14 % 7.75/2.39 | (164) powerset(all_15_1_14) = all_15_0_13 % 7.75/2.39 | (165) ! [v0] : ! [v1] : (v1 = v0 | ~ (subset_intersection2(all_15_1_14, v0, all_0_5_5) = v1) | ~ element(v0, all_15_0_13)) % 7.75/2.39 | % 7.75/2.39 | Instantiating (157) with all_18_0_15, all_18_1_16 yields: % 7.75/2.39 | (166) the_carrier(all_0_8_8) = all_18_1_16 & powerset(all_18_1_16) = all_18_0_15 & element(all_0_5_5, all_18_0_15) % 7.75/2.39 | % 7.75/2.39 | Applying alpha-rule on (166) yields: % 7.75/2.39 | (167) the_carrier(all_0_8_8) = all_18_1_16 % 7.75/2.39 | (168) powerset(all_18_1_16) = all_18_0_15 % 7.75/2.39 | (169) element(all_0_5_5, all_18_0_15) % 7.75/2.39 | % 7.75/2.39 | Instantiating (155) with all_20_0_17 yields: % 7.75/2.39 | (170) powerset(all_0_7_7) = all_20_0_17 & ( ~ element(all_0_4_4, all_20_0_17) | ~ element(all_0_5_5, all_20_0_17) | element(all_0_3_3, all_20_0_17)) % 7.75/2.39 | % 7.75/2.39 | Applying alpha-rule on (170) yields: % 7.75/2.39 | (171) powerset(all_0_7_7) = all_20_0_17 % 7.75/2.39 | (172) ~ element(all_0_4_4, all_20_0_17) | ~ element(all_0_5_5, all_20_0_17) | element(all_0_3_3, all_20_0_17) % 7.75/2.39 | % 7.75/2.39 | Instantiating (153) with all_22_0_18 yields: % 7.75/2.39 | (173) powerset(all_0_7_7) = all_22_0_18 & ( ~ element(all_0_3_3, all_22_0_18) | ~ element(all_0_5_5, all_22_0_18) | element(all_0_2_2, all_22_0_18)) % 7.75/2.39 | % 7.75/2.39 | Applying alpha-rule on (173) yields: % 7.75/2.39 | (174) powerset(all_0_7_7) = all_22_0_18 % 7.75/2.39 | (175) ~ element(all_0_3_3, all_22_0_18) | ~ element(all_0_5_5, all_22_0_18) | element(all_0_2_2, all_22_0_18) % 7.75/2.39 | % 7.75/2.39 | Instantiating (152) with all_24_0_19, all_24_1_20 yields: % 7.75/2.39 | (176) set_difference(all_0_5_5, all_0_3_3) = all_24_0_19 & powerset(all_0_7_7) = all_24_1_20 & (all_24_0_19 = all_0_2_2 | ~ element(all_0_3_3, all_24_1_20) | ~ element(all_0_5_5, all_24_1_20)) % 7.75/2.39 | % 7.75/2.39 | Applying alpha-rule on (176) yields: % 7.75/2.39 | (177) set_difference(all_0_5_5, all_0_3_3) = all_24_0_19 % 7.75/2.39 | (178) powerset(all_0_7_7) = all_24_1_20 % 7.75/2.39 | (179) all_24_0_19 = all_0_2_2 | ~ element(all_0_3_3, all_24_1_20) | ~ element(all_0_5_5, all_24_1_20) % 7.75/2.39 | % 7.75/2.39 | Instantiating (154) with all_26_0_21, all_26_1_22 yields: % 7.75/2.39 | (180) set_difference(all_0_5_5, all_0_4_4) = all_26_0_21 & powerset(all_0_7_7) = all_26_1_22 & (all_26_0_21 = all_0_3_3 | ~ element(all_0_4_4, all_26_1_22) | ~ element(all_0_5_5, all_26_1_22)) % 7.75/2.39 | % 7.75/2.39 | Applying alpha-rule on (180) yields: % 7.75/2.39 | (181) set_difference(all_0_5_5, all_0_4_4) = all_26_0_21 % 7.75/2.39 | (182) powerset(all_0_7_7) = all_26_1_22 % 7.75/2.39 | (183) all_26_0_21 = all_0_3_3 | ~ element(all_0_4_4, all_26_1_22) | ~ element(all_0_5_5, all_26_1_22) % 7.75/2.39 | % 7.75/2.39 | Instantiating (161) with all_28_0_23, all_28_1_24 yields: % 7.75/2.39 | (184) cast_as_carrier_subset(all_0_8_8) = all_28_1_24 & powerset(all_0_7_7) = all_28_0_23 & element(all_28_1_24, all_28_0_23) % 7.75/2.39 | % 7.75/2.39 | Applying alpha-rule on (184) yields: % 7.75/2.39 | (185) cast_as_carrier_subset(all_0_8_8) = all_28_1_24 % 7.75/2.39 | (186) powerset(all_0_7_7) = all_28_0_23 % 7.75/2.39 | (187) element(all_28_1_24, all_28_0_23) % 7.75/2.39 | % 7.75/2.39 | Instantiating (160) with all_30_0_25, all_30_1_26 yields: % 7.75/2.39 | (188) cast_as_carrier_subset(all_0_8_8) = all_30_0_25 & powerset(all_0_7_7) = all_30_1_26 & ! [v0] : ! [v1] : (v1 = v0 | ~ (subset_intersection2(all_0_7_7, v0, all_30_0_25) = v1) | ~ element(v0, all_30_1_26)) % 7.75/2.40 | % 7.75/2.40 | Applying alpha-rule on (188) yields: % 7.75/2.40 | (189) cast_as_carrier_subset(all_0_8_8) = all_30_0_25 % 7.75/2.40 | (190) powerset(all_0_7_7) = all_30_1_26 % 7.75/2.40 | (191) ! [v0] : ! [v1] : (v1 = v0 | ~ (subset_intersection2(all_0_7_7, v0, all_30_0_25) = v1) | ~ element(v0, all_30_1_26)) % 7.75/2.40 | % 7.75/2.40 | Instantiating formula (66) with all_0_8_8, all_28_1_24, all_30_0_25 and discharging atoms cast_as_carrier_subset(all_0_8_8) = all_30_0_25, cast_as_carrier_subset(all_0_8_8) = all_28_1_24, yields: % 7.75/2.40 | (192) all_30_0_25 = all_28_1_24 % 7.75/2.40 | % 7.75/2.40 | Instantiating formula (66) with all_0_8_8, all_0_7_7, all_30_0_25 and discharging atoms cast_as_carrier_subset(all_0_8_8) = all_30_0_25, cast_as_carrier_subset(all_0_8_8) = all_0_7_7, yields: % 7.75/2.40 | (193) all_30_0_25 = all_0_7_7 % 7.75/2.40 | % 7.75/2.40 | Instantiating formula (149) with all_0_8_8, all_18_1_16, all_0_7_7 and discharging atoms the_carrier(all_0_8_8) = all_18_1_16, the_carrier(all_0_8_8) = all_0_7_7, yields: % 7.75/2.40 | (194) all_18_1_16 = all_0_7_7 % 7.75/2.40 | % 7.75/2.40 | Instantiating formula (149) with all_0_8_8, all_15_1_14, all_18_1_16 and discharging atoms the_carrier(all_0_8_8) = all_18_1_16, the_carrier(all_0_8_8) = all_15_1_14, yields: % 7.75/2.40 | (195) all_18_1_16 = all_15_1_14 % 7.75/2.40 | % 7.75/2.40 | Instantiating formula (149) with all_0_8_8, all_0_5_5, all_18_1_16 and discharging atoms the_carrier(all_0_8_8) = all_18_1_16, the_carrier(all_0_8_8) = all_0_5_5, yields: % 7.75/2.40 | (196) all_18_1_16 = all_0_5_5 % 7.75/2.40 | % 7.75/2.40 | Instantiating formula (58) with all_0_7_7, all_30_1_26, all_0_6_6 and discharging atoms powerset(all_0_7_7) = all_30_1_26, powerset(all_0_7_7) = all_0_6_6, yields: % 7.75/2.40 | (197) all_30_1_26 = all_0_6_6 % 7.75/2.40 | % 7.75/2.40 | Instantiating formula (58) with all_0_7_7, all_26_1_22, all_30_1_26 and discharging atoms powerset(all_0_7_7) = all_30_1_26, powerset(all_0_7_7) = all_26_1_22, yields: % 7.75/2.40 | (198) all_30_1_26 = all_26_1_22 % 7.75/2.40 | % 7.75/2.40 | Instantiating formula (58) with all_0_7_7, all_26_1_22, all_28_0_23 and discharging atoms powerset(all_0_7_7) = all_28_0_23, powerset(all_0_7_7) = all_26_1_22, yields: % 7.75/2.40 | (199) all_28_0_23 = all_26_1_22 % 7.75/2.40 | % 7.75/2.40 | Instantiating formula (58) with all_0_7_7, all_24_1_20, all_30_1_26 and discharging atoms powerset(all_0_7_7) = all_30_1_26, powerset(all_0_7_7) = all_24_1_20, yields: % 7.75/2.40 | (200) all_30_1_26 = all_24_1_20 % 7.75/2.40 | % 7.75/2.40 | Instantiating formula (58) with all_0_7_7, all_22_0_18, all_28_0_23 and discharging atoms powerset(all_0_7_7) = all_28_0_23, powerset(all_0_7_7) = all_22_0_18, yields: % 7.75/2.40 | (201) all_28_0_23 = all_22_0_18 % 7.75/2.40 | % 7.75/2.40 | Instantiating formula (58) with all_0_7_7, all_20_0_17, all_30_1_26 and discharging atoms powerset(all_0_7_7) = all_30_1_26, powerset(all_0_7_7) = all_20_0_17, yields: % 7.75/2.40 | (202) all_30_1_26 = all_20_0_17 % 7.75/2.40 | % 7.75/2.40 | Combining equations (192,193) yields a new equation: % 7.75/2.40 | (203) all_28_1_24 = all_0_7_7 % 7.75/2.40 | % 7.75/2.40 | Simplifying 203 yields: % 7.75/2.40 | (204) all_28_1_24 = all_0_7_7 % 7.75/2.40 | % 7.75/2.40 | Combining equations (198,200) yields a new equation: % 7.75/2.40 | (205) all_26_1_22 = all_24_1_20 % 7.75/2.40 | % 7.75/2.40 | Simplifying 205 yields: % 7.75/2.40 | (206) all_26_1_22 = all_24_1_20 % 7.75/2.40 | % 7.75/2.40 | Combining equations (197,200) yields a new equation: % 7.75/2.40 | (207) all_24_1_20 = all_0_6_6 % 7.75/2.40 | % 7.75/2.40 | Combining equations (202,200) yields a new equation: % 7.75/2.40 | (208) all_24_1_20 = all_20_0_17 % 7.75/2.40 | % 7.75/2.40 | Combining equations (199,201) yields a new equation: % 7.75/2.40 | (209) all_26_1_22 = all_22_0_18 % 7.75/2.40 | % 7.75/2.40 | Simplifying 209 yields: % 7.75/2.40 | (210) all_26_1_22 = all_22_0_18 % 7.75/2.40 | % 7.75/2.40 | Combining equations (206,210) yields a new equation: % 7.75/2.40 | (211) all_24_1_20 = all_22_0_18 % 7.75/2.40 | % 7.75/2.40 | Simplifying 211 yields: % 7.75/2.40 | (212) all_24_1_20 = all_22_0_18 % 7.75/2.40 | % 7.75/2.40 | Combining equations (207,212) yields a new equation: % 7.75/2.40 | (213) all_22_0_18 = all_0_6_6 % 7.75/2.40 | % 7.75/2.40 | Combining equations (208,212) yields a new equation: % 7.75/2.40 | (214) all_22_0_18 = all_20_0_17 % 7.75/2.40 | % 7.75/2.40 | Combining equations (213,214) yields a new equation: % 7.75/2.40 | (215) all_20_0_17 = all_0_6_6 % 7.75/2.40 | % 7.75/2.40 | Combining equations (196,195) yields a new equation: % 7.75/2.40 | (216) all_15_1_14 = all_0_5_5 % 7.75/2.40 | % 7.75/2.40 | Combining equations (194,195) yields a new equation: % 7.75/2.40 | (217) all_15_1_14 = all_0_7_7 % 7.75/2.40 | % 7.75/2.40 | Combining equations (217,216) yields a new equation: % 7.75/2.40 | (218) all_0_5_5 = all_0_7_7 % 7.75/2.40 | % 7.75/2.40 | Combining equations (218,216) yields a new equation: % 7.75/2.40 | (217) all_15_1_14 = all_0_7_7 % 7.75/2.40 | % 7.75/2.40 | Combining equations (217,195) yields a new equation: % 7.75/2.40 | (194) all_18_1_16 = all_0_7_7 % 7.75/2.40 | % 7.75/2.40 | Combining equations (215,214) yields a new equation: % 7.75/2.40 | (213) all_22_0_18 = all_0_6_6 % 7.75/2.40 | % 7.75/2.40 | Combining equations (213,212) yields a new equation: % 7.75/2.40 | (207) all_24_1_20 = all_0_6_6 % 7.75/2.40 | % 7.75/2.40 | Combining equations (213,210) yields a new equation: % 7.75/2.40 | (223) all_26_1_22 = all_0_6_6 % 7.75/2.40 | % 7.75/2.40 | Combining equations (213,201) yields a new equation: % 7.75/2.40 | (224) all_28_0_23 = all_0_6_6 % 7.75/2.40 | % 7.75/2.40 | Combining equations (207,200) yields a new equation: % 7.75/2.40 | (197) all_30_1_26 = all_0_6_6 % 7.75/2.40 | % 7.75/2.40 | From (218) and (177) follows: % 7.75/2.40 | (226) set_difference(all_0_7_7, all_0_3_3) = all_24_0_19 % 7.75/2.40 | % 7.75/2.40 | From (218) and (181) follows: % 7.75/2.40 | (227) set_difference(all_0_7_7, all_0_4_4) = all_26_0_21 % 7.75/2.40 | % 7.75/2.40 | From (194) and (168) follows: % 7.75/2.40 | (228) powerset(all_0_7_7) = all_18_0_15 % 7.75/2.40 | % 7.75/2.40 | From (217) and (164) follows: % 7.75/2.40 | (229) powerset(all_0_7_7) = all_15_0_13 % 7.75/2.40 | % 7.75/2.40 | From (215) and (171) follows: % 7.75/2.40 | (109) powerset(all_0_7_7) = all_0_6_6 % 7.75/2.40 | % 7.75/2.40 | From (204)(224) and (187) follows: % 7.75/2.40 | (231) element(all_0_7_7, all_0_6_6) % 7.75/2.40 | % 7.75/2.40 | From (218) and (169) follows: % 7.75/2.40 | (232) element(all_0_7_7, all_18_0_15) % 7.75/2.40 | % 7.75/2.40 +-Applying beta-rule and splitting (183), into two cases. % 7.75/2.40 |-Branch one: % 7.75/2.40 | (233) ~ element(all_0_4_4, all_26_1_22) % 7.75/2.40 | % 7.75/2.40 | From (223) and (233) follows: % 7.75/2.40 | (234) ~ element(all_0_4_4, all_0_6_6) % 7.75/2.40 | % 7.75/2.40 | Using (105) and (234) yields: % 7.75/2.40 | (235) $false % 7.75/2.40 | % 7.75/2.40 |-The branch is then unsatisfiable % 7.75/2.40 |-Branch two: % 7.75/2.40 | (236) element(all_0_4_4, all_26_1_22) % 7.75/2.40 | (237) all_26_0_21 = all_0_3_3 | ~ element(all_0_5_5, all_26_1_22) % 7.75/2.40 | % 7.75/2.40 | From (223) and (236) follows: % 7.75/2.40 | (105) element(all_0_4_4, all_0_6_6) % 7.75/2.40 | % 7.75/2.40 +-Applying beta-rule and splitting (172), into two cases. % 7.75/2.40 |-Branch one: % 7.75/2.40 | (239) ~ element(all_0_4_4, all_20_0_17) % 7.75/2.40 | % 7.75/2.40 | From (215) and (239) follows: % 7.75/2.40 | (234) ~ element(all_0_4_4, all_0_6_6) % 7.75/2.40 | % 7.75/2.40 | Using (105) and (234) yields: % 7.75/2.40 | (235) $false % 7.75/2.40 | % 7.75/2.40 |-The branch is then unsatisfiable % 7.75/2.40 |-Branch two: % 7.75/2.40 | (242) element(all_0_4_4, all_20_0_17) % 7.75/2.40 | (243) ~ element(all_0_5_5, all_20_0_17) | element(all_0_3_3, all_20_0_17) % 7.75/2.40 | % 7.75/2.40 | From (215) and (242) follows: % 7.75/2.40 | (105) element(all_0_4_4, all_0_6_6) % 7.75/2.41 | % 7.75/2.41 +-Applying beta-rule and splitting (237), into two cases. % 7.75/2.41 |-Branch one: % 7.75/2.41 | (245) ~ element(all_0_5_5, all_26_1_22) % 7.75/2.41 | % 7.75/2.41 | From (218)(223) and (245) follows: % 7.75/2.41 | (246) ~ element(all_0_7_7, all_0_6_6) % 7.75/2.41 | % 7.75/2.41 | Using (231) and (246) yields: % 7.75/2.41 | (235) $false % 7.75/2.41 | % 7.75/2.41 |-The branch is then unsatisfiable % 7.75/2.41 |-Branch two: % 7.75/2.41 | (248) element(all_0_5_5, all_26_1_22) % 7.75/2.41 | (249) all_26_0_21 = all_0_3_3 % 7.75/2.41 | % 7.75/2.41 | From (249) and (227) follows: % 7.75/2.41 | (250) set_difference(all_0_7_7, all_0_4_4) = all_0_3_3 % 7.75/2.41 | % 7.75/2.41 | From (218)(223) and (248) follows: % 7.75/2.41 | (231) element(all_0_7_7, all_0_6_6) % 7.75/2.41 | % 7.75/2.41 +-Applying beta-rule and splitting (243), into two cases. % 7.75/2.41 |-Branch one: % 7.75/2.41 | (252) ~ element(all_0_5_5, all_20_0_17) % 7.75/2.41 | % 7.75/2.41 | From (218)(215) and (252) follows: % 7.75/2.41 | (246) ~ element(all_0_7_7, all_0_6_6) % 7.75/2.41 | % 7.75/2.41 | Using (231) and (246) yields: % 7.75/2.41 | (235) $false % 7.75/2.41 | % 7.75/2.41 |-The branch is then unsatisfiable % 7.75/2.41 |-Branch two: % 7.75/2.41 | (255) element(all_0_5_5, all_20_0_17) % 7.75/2.41 | (256) element(all_0_3_3, all_20_0_17) % 7.75/2.41 | % 7.75/2.41 | From (215) and (256) follows: % 7.75/2.41 | (257) element(all_0_3_3, all_0_6_6) % 7.75/2.41 | % 7.75/2.41 | From (218)(215) and (255) follows: % 7.75/2.41 | (231) element(all_0_7_7, all_0_6_6) % 7.75/2.41 | % 7.75/2.41 +-Applying beta-rule and splitting (175), into two cases. % 7.75/2.41 |-Branch one: % 7.75/2.41 | (259) ~ element(all_0_3_3, all_22_0_18) % 7.75/2.41 | % 7.75/2.41 | From (213) and (259) follows: % 7.75/2.41 | (260) ~ element(all_0_3_3, all_0_6_6) % 7.75/2.41 | % 7.75/2.41 | Using (257) and (260) yields: % 7.75/2.41 | (235) $false % 7.75/2.41 | % 7.75/2.41 |-The branch is then unsatisfiable % 7.75/2.41 |-Branch two: % 7.75/2.41 | (262) element(all_0_3_3, all_22_0_18) % 7.75/2.41 | (263) ~ element(all_0_5_5, all_22_0_18) | element(all_0_2_2, all_22_0_18) % 7.75/2.41 | % 7.75/2.41 | From (213) and (262) follows: % 7.75/2.41 | (257) element(all_0_3_3, all_0_6_6) % 7.75/2.41 | % 7.75/2.41 +-Applying beta-rule and splitting (179), into two cases. % 7.75/2.41 |-Branch one: % 7.75/2.41 | (265) ~ element(all_0_3_3, all_24_1_20) % 7.75/2.41 | % 7.75/2.41 | From (207) and (265) follows: % 7.75/2.41 | (260) ~ element(all_0_3_3, all_0_6_6) % 7.75/2.41 | % 7.75/2.41 | Using (257) and (260) yields: % 7.75/2.41 | (235) $false % 7.75/2.41 | % 7.75/2.41 |-The branch is then unsatisfiable % 7.75/2.41 |-Branch two: % 7.75/2.41 | (268) element(all_0_3_3, all_24_1_20) % 7.75/2.41 | (269) all_24_0_19 = all_0_2_2 | ~ element(all_0_5_5, all_24_1_20) % 7.75/2.41 | % 7.75/2.41 +-Applying beta-rule and splitting (269), into two cases. % 7.75/2.41 |-Branch one: % 7.75/2.41 | (270) ~ element(all_0_5_5, all_24_1_20) % 7.75/2.41 | % 7.75/2.41 | From (218)(207) and (270) follows: % 7.75/2.41 | (246) ~ element(all_0_7_7, all_0_6_6) % 7.75/2.41 | % 7.75/2.41 | Using (231) and (246) yields: % 7.75/2.41 | (235) $false % 7.75/2.41 | % 7.75/2.41 |-The branch is then unsatisfiable % 7.75/2.41 |-Branch two: % 7.75/2.41 | (273) element(all_0_5_5, all_24_1_20) % 7.75/2.41 | (274) all_24_0_19 = all_0_2_2 % 7.75/2.41 | % 7.75/2.41 | From (274) and (226) follows: % 7.75/2.41 | (275) set_difference(all_0_7_7, all_0_3_3) = all_0_2_2 % 7.75/2.41 | % 7.75/2.41 | Instantiating formula (58) with all_0_7_7, all_18_0_15, all_0_6_6 and discharging atoms powerset(all_0_7_7) = all_18_0_15, powerset(all_0_7_7) = all_0_6_6, yields: % 7.75/2.41 | (276) all_18_0_15 = all_0_6_6 % 7.75/2.41 | % 7.75/2.41 | Instantiating formula (58) with all_0_7_7, all_15_0_13, all_18_0_15 and discharging atoms powerset(all_0_7_7) = all_18_0_15, powerset(all_0_7_7) = all_15_0_13, yields: % 7.75/2.41 | (277) all_18_0_15 = all_15_0_13 % 7.75/2.41 | % 7.75/2.41 | Combining equations (277,276) yields a new equation: % 7.75/2.41 | (278) all_15_0_13 = all_0_6_6 % 7.75/2.41 | % 7.75/2.41 | Simplifying 278 yields: % 7.75/2.41 | (279) all_15_0_13 = all_0_6_6 % 7.75/2.41 | % 7.75/2.41 | From (279) and (229) follows: % 7.75/2.41 | (109) powerset(all_0_7_7) = all_0_6_6 % 7.75/2.41 | % 7.75/2.41 | From (276) and (232) follows: % 7.75/2.41 | (231) element(all_0_7_7, all_0_6_6) % 7.75/2.41 | % 7.75/2.41 | Instantiating formula (96) with all_0_2_2, all_0_3_3, all_0_4_4, all_0_7_7 and discharging atoms set_difference(all_0_7_7, all_0_3_3) = all_0_2_2, set_difference(all_0_7_7, all_0_4_4) = all_0_3_3, yields: % 7.75/2.41 | (282) set_intersection2(all_0_7_7, all_0_4_4) = all_0_2_2 % 7.75/2.41 | % 7.75/2.41 | Instantiating formula (147) with all_0_2_2, all_0_6_6, all_0_4_4, all_0_7_7, all_0_7_7 and discharging atoms set_intersection2(all_0_7_7, all_0_4_4) = all_0_2_2, powerset(all_0_7_7) = all_0_6_6, element(all_0_4_4, all_0_6_6), element(all_0_7_7, all_0_6_6), yields: % 7.75/2.41 | (283) subset_intersection2(all_0_7_7, all_0_7_7, all_0_4_4) = all_0_2_2 % 7.75/2.41 | % 7.75/2.41 | Instantiating formula (57) with all_0_2_2, all_0_7_7, all_0_4_4 and discharging atoms set_intersection2(all_0_7_7, all_0_4_4) = all_0_2_2, yields: % 7.75/2.41 | (284) set_intersection2(all_0_4_4, all_0_7_7) = all_0_2_2 % 7.75/2.41 | % 7.75/2.41 | Instantiating formula (6) with all_0_2_2, all_0_7_7, all_0_4_4, all_0_7_7 and discharging atoms subset_intersection2(all_0_7_7, all_0_7_7, all_0_4_4) = all_0_2_2, yields: % 7.75/2.41 | (285) ? [v0] : ? [v1] : (subset_intersection2(all_0_7_7, all_0_4_4, all_0_7_7) = v1 & powerset(all_0_7_7) = v0 & (v1 = all_0_2_2 | ~ element(all_0_4_4, v0) | ~ element(all_0_7_7, v0))) % 7.75/2.41 | % 7.75/2.41 | Instantiating formula (147) with all_0_2_2, all_0_6_6, all_0_7_7, all_0_4_4, all_0_7_7 and discharging atoms set_intersection2(all_0_4_4, all_0_7_7) = all_0_2_2, powerset(all_0_7_7) = all_0_6_6, element(all_0_4_4, all_0_6_6), element(all_0_7_7, all_0_6_6), yields: % 7.75/2.41 | (286) subset_intersection2(all_0_7_7, all_0_4_4, all_0_7_7) = all_0_2_2 % 7.75/2.41 | % 7.75/2.41 | Instantiating (285) with all_93_0_28, all_93_1_29 yields: % 7.75/2.41 | (287) subset_intersection2(all_0_7_7, all_0_4_4, all_0_7_7) = all_93_0_28 & powerset(all_0_7_7) = all_93_1_29 & (all_93_0_28 = all_0_2_2 | ~ element(all_0_4_4, all_93_1_29) | ~ element(all_0_7_7, all_93_1_29)) % 7.75/2.41 | % 7.75/2.41 | Applying alpha-rule on (287) yields: % 7.75/2.41 | (288) subset_intersection2(all_0_7_7, all_0_4_4, all_0_7_7) = all_93_0_28 % 7.75/2.41 | (289) powerset(all_0_7_7) = all_93_1_29 % 7.75/2.41 | (290) all_93_0_28 = all_0_2_2 | ~ element(all_0_4_4, all_93_1_29) | ~ element(all_0_7_7, all_93_1_29) % 7.75/2.41 | % 7.75/2.41 | Instantiating formula (165) with all_93_0_28, all_0_4_4 yields: % 7.75/2.41 | (291) all_93_0_28 = all_0_4_4 | ~ (subset_intersection2(all_15_1_14, all_0_4_4, all_0_5_5) = all_93_0_28) | ~ element(all_0_4_4, all_15_0_13) % 7.75/2.41 | % 7.75/2.41 | Instantiating formula (191) with all_93_0_28, all_0_4_4 yields: % 7.75/2.41 | (292) all_93_0_28 = all_0_4_4 | ~ (subset_intersection2(all_0_7_7, all_0_4_4, all_30_0_25) = all_93_0_28) | ~ element(all_0_4_4, all_30_1_26) % 7.75/2.41 | % 7.75/2.41 | Instantiating formula (19) with all_0_7_7, all_0_4_4, all_0_7_7, all_0_2_2, all_93_0_28 and discharging atoms subset_intersection2(all_0_7_7, all_0_4_4, all_0_7_7) = all_93_0_28, subset_intersection2(all_0_7_7, all_0_4_4, all_0_7_7) = all_0_2_2, yields: % 7.75/2.41 | (293) all_93_0_28 = all_0_2_2 % 7.75/2.41 | % 7.75/2.41 | Instantiating formula (165) with all_0_2_2, all_0_4_4 yields: % 7.75/2.41 | (294) all_0_2_2 = all_0_4_4 | ~ (subset_intersection2(all_15_1_14, all_0_4_4, all_0_5_5) = all_0_2_2) | ~ element(all_0_4_4, all_15_0_13) % 7.75/2.41 | % 7.75/2.41 | From (293) and (288) follows: % 7.75/2.41 | (286) subset_intersection2(all_0_7_7, all_0_4_4, all_0_7_7) = all_0_2_2 % 7.75/2.41 | % 7.75/2.41 +-Applying beta-rule and splitting (294), into two cases. % 7.75/2.41 |-Branch one: % 7.75/2.41 | (296) ~ element(all_0_4_4, all_15_0_13) % 7.75/2.41 | % 7.75/2.41 | From (279) and (296) follows: % 7.75/2.41 | (234) ~ element(all_0_4_4, all_0_6_6) % 7.75/2.42 | % 7.75/2.42 | Using (105) and (234) yields: % 7.75/2.42 | (235) $false % 7.75/2.42 | % 7.75/2.42 |-The branch is then unsatisfiable % 7.75/2.42 |-Branch two: % 7.75/2.42 | (299) element(all_0_4_4, all_15_0_13) % 7.75/2.42 | (300) all_0_2_2 = all_0_4_4 | ~ (subset_intersection2(all_15_1_14, all_0_4_4, all_0_5_5) = all_0_2_2) % 7.75/2.42 | % 7.75/2.42 | From (279) and (299) follows: % 7.75/2.42 | (105) element(all_0_4_4, all_0_6_6) % 7.75/2.42 | % 7.75/2.42 +-Applying beta-rule and splitting (292), into two cases. % 7.75/2.42 |-Branch one: % 7.75/2.42 | (302) ~ element(all_0_4_4, all_30_1_26) % 7.75/2.42 | % 7.75/2.42 | From (197) and (302) follows: % 7.75/2.42 | (234) ~ element(all_0_4_4, all_0_6_6) % 7.75/2.42 | % 7.75/2.42 | Using (105) and (234) yields: % 7.75/2.42 | (235) $false % 7.75/2.42 | % 7.75/2.42 |-The branch is then unsatisfiable % 7.75/2.42 |-Branch two: % 7.75/2.42 | (305) element(all_0_4_4, all_30_1_26) % 7.75/2.42 | (306) all_93_0_28 = all_0_4_4 | ~ (subset_intersection2(all_0_7_7, all_0_4_4, all_30_0_25) = all_93_0_28) % 7.75/2.42 | % 7.75/2.42 | From (197) and (305) follows: % 7.75/2.42 | (105) element(all_0_4_4, all_0_6_6) % 7.75/2.42 | % 7.75/2.42 +-Applying beta-rule and splitting (291), into two cases. % 7.75/2.42 |-Branch one: % 7.75/2.42 | (296) ~ element(all_0_4_4, all_15_0_13) % 7.75/2.42 | % 7.75/2.42 | From (279) and (296) follows: % 7.75/2.42 | (234) ~ element(all_0_4_4, all_0_6_6) % 7.75/2.42 | % 7.75/2.42 | Using (105) and (234) yields: % 7.75/2.42 | (235) $false % 7.75/2.42 | % 7.75/2.42 |-The branch is then unsatisfiable % 7.75/2.42 |-Branch two: % 7.75/2.42 | (299) element(all_0_4_4, all_15_0_13) % 7.75/2.42 | (312) all_93_0_28 = all_0_4_4 | ~ (subset_intersection2(all_15_1_14, all_0_4_4, all_0_5_5) = all_93_0_28) % 7.75/2.42 | % 7.75/2.42 +-Applying beta-rule and splitting (312), into two cases. % 7.75/2.42 |-Branch one: % 7.75/2.42 | (313) ~ (subset_intersection2(all_15_1_14, all_0_4_4, all_0_5_5) = all_93_0_28) % 7.75/2.42 | % 7.75/2.42 | From (217)(218)(293) and (313) follows: % 7.75/2.42 | (314) ~ (subset_intersection2(all_0_7_7, all_0_4_4, all_0_7_7) = all_0_2_2) % 7.75/2.42 | % 7.75/2.42 | Using (286) and (314) yields: % 7.75/2.42 | (235) $false % 7.75/2.42 | % 7.75/2.42 |-The branch is then unsatisfiable % 7.75/2.42 |-Branch two: % 7.75/2.42 | (316) subset_intersection2(all_15_1_14, all_0_4_4, all_0_5_5) = all_93_0_28 % 7.75/2.42 | (317) all_93_0_28 = all_0_4_4 % 7.75/2.42 | % 7.75/2.42 | Combining equations (317,293) yields a new equation: % 7.75/2.42 | (318) all_0_2_2 = all_0_4_4 % 7.75/2.42 | % 7.75/2.42 | Equations (318) can reduce 51 to: % 7.75/2.42 | (319) $false % 7.75/2.42 | % 7.75/2.42 |-The branch is then unsatisfiable % 7.75/2.42 % SZS output end Proof for theBenchmark % 7.75/2.42 % 7.75/2.42 1797ms %------------------------------------------------------------------------------