%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU308+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n025.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 3.61s 1.48s % Output : Proof 6.04s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SEU308+1 : TPTP v8.1.0. Released v3.3.0. % 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.33 % Computer : n025.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 600 % 0.13/0.33 % DateTime : Sun Jun 19 01:44:28 EDT 2022 % 0.13/0.34 % CPUTime : % 0.55/0.58 ____ _ % 0.55/0.58 ___ / __ \_____(_)___ ________ __________ % 0.55/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.55/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.55/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.55/0.58 % 0.55/0.58 A Theorem Prover for First-Order Logic % 0.55/0.58 (ePrincess v.1.0) % 0.55/0.58 % 0.55/0.58 (c) Philipp Rümmer, 2009-2015 % 0.55/0.58 (c) Peter Backeman, 2014-2015 % 0.55/0.58 (contributions by Angelo Brillout, Peter Baumgartner) % 0.55/0.58 Free software under GNU Lesser General Public License (LGPL). % 0.55/0.58 Bug reports to peter@backeman.se % 0.55/0.58 % 0.55/0.58 For more information, visit http://user.uu.se/~petba168/breu/ % 0.55/0.58 % 0.55/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.77/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.83/0.97 Prover 0: Preprocessing ... % 2.78/1.28 Prover 0: Warning: ignoring some quantifiers % 2.78/1.31 Prover 0: Constructing countermodel ... % 3.61/1.48 Prover 0: proved (843ms) % 3.61/1.48 % 3.61/1.48 No countermodel exists, formula is valid % 3.61/1.48 % SZS status Theorem for theBenchmark % 3.76/1.48 % 3.76/1.48 Generating proof ... Warning: ignoring some quantifiers % 5.41/1.90 found it (size 72) % 5.41/1.90 % 5.41/1.90 % SZS output start Proof for theBenchmark % 5.41/1.90 Assumed formulas after preprocessing and simplification: % 5.41/1.90 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ( ~ (v6 = v5) & the_carrier(v0) = v1 & cast_as_carrier_subset(v0) = v3 & subset_difference(v1, v3, v4) = v6 & subset_complement(v1, v4) = v5 & powerset(v1) = v2 & one_sorted_str(v7) & one_sorted_str(v0) & element(v4, v2) & empty(empty_set) & v1_membered(v8) & v1_membered(empty_set) & v2_membered(v8) & v2_membered(empty_set) & v3_membered(v8) & v3_membered(empty_set) & v4_membered(v8) & v4_membered(empty_set) & v5_membered(v8) & v5_membered(empty_set) & ~ empty(v8) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v10 = v9 | ~ (subset_difference(v13, v12, v11) = v10) | ~ (subset_difference(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] : (v12 = v10 | ~ (subset_complement(v9, v11) = v12) | ~ (subset_complement(v9, v10) = v11) | ? [v13] : (powerset(v9) = v13 & ~ element(v10, v13))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (subset_complement(v12, v11) = v10) | ~ (subset_complement(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (set_difference(v12, v11) = v10) | ~ (set_difference(v12, v11) = v9)) & ! [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] : ( ~ (powerset(v11) = v12) | ~ element(v10, v12) | ~ empty(v11) | ~ in(v9, v10)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (powerset(v11) = v12) | ~ element(v10, v12) | ~ in(v9, v10) | element(v9, v11)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (the_carrier(v11) = v10) | ~ (the_carrier(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (cast_as_carrier_subset(v11) = v10) | ~ (cast_as_carrier_subset(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (powerset(v11) = v10) | ~ (powerset(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (subset_complement(v9, v10) = v11) | ? [v12] : ? [v13] : (set_difference(v9, v10) = v13 & powerset(v9) = v12 & (v13 = v11 | ~ element(v10, v12)))) & ! [v9] : ! [v10] : ! [v11] : ( ~ (subset_complement(v9, v10) = v11) | ? [v12] : (powerset(v9) = v12 & ( ~ element(v10, v12) | element(v11, v12)))) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_difference(v9, v10) = v11) | ~ v1_membered(v9) | v1_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_difference(v9, v10) = v11) | ~ v2_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) | ~ v3_membered(v9) | v1_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) | v3_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_difference(v9, v10) = v11) | ~ v4_membered(v9) | v1_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) | v3_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_difference(v9, v10) = v11) | ~ v4_membered(v9) | v4_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_difference(v9, v10) = v11) | ~ v5_membered(v9) | v1_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) | v3_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) | v5_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_difference(v9, v10) = v11) | ? [v12] : ? [v13] : (subset_complement(v9, v10) = v13 & powerset(v9) = v12 & (v13 = v11 | ~ element(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) | ~ element(v11, v10) | ~ v1_membered(v9) | v1_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (powerset(v9) = v10) | ~ element(v11, v10) | ~ v2_membered(v9) | v1_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (powerset(v9) = v10) | ~ element(v11, v10) | ~ v2_membered(v9) | v2_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (powerset(v9) = v10) | ~ element(v11, v10) | ~ v3_membered(v9) | v1_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (powerset(v9) = v10) | ~ element(v11, v10) | ~ v3_membered(v9) | v2_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (powerset(v9) = v10) | ~ element(v11, v10) | ~ v3_membered(v9) | v3_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (powerset(v9) = v10) | ~ element(v11, v10) | ~ v4_membered(v9) | v1_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (powerset(v9) = v10) | ~ element(v11, v10) | ~ v4_membered(v9) | v2_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (powerset(v9) = v10) | ~ element(v11, v10) | ~ v4_membered(v9) | v3_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (powerset(v9) = v10) | ~ element(v11, v10) | ~ v4_membered(v9) | v4_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (powerset(v9) = v10) | ~ element(v11, v10) | ~ v5_membered(v9) | v1_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (powerset(v9) = v10) | ~ element(v11, v10) | ~ v5_membered(v9) | v2_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (powerset(v9) = v10) | ~ element(v11, v10) | ~ v5_membered(v9) | v3_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (powerset(v9) = v10) | ~ element(v11, v10) | ~ v5_membered(v9) | v4_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (powerset(v9) = v10) | ~ element(v11, v10) | ~ v5_membered(v9) | v5_membered(v11)) & ! [v9] : ! [v10] : (v10 = v9 | ~ (set_difference(v9, empty_set) = v10)) & ! [v9] : ! [v10] : (v10 = v9 | ~ empty(v10) | ~ empty(v9)) & ! [v9] : ! [v10] : (v10 = empty_set | ~ (set_difference(empty_set, v9) = v10)) & ! [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) = v11 & powerset(v10) = v12 & element(v11, v12))) & ! [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] : ( ~ (powerset(v9) = v10) | ~ empty(v10)) & ! [v9] : ! [v10] : ( ~ (powerset(v9) = v10) | empty(v9) | ? [v11] : (element(v11, v10) & ~ empty(v11))) & ! [v9] : ! [v10] : ( ~ (powerset(v9) = v10) | ? [v11] : (element(v11, v10) & empty(v11))) & ! [v9] : ! [v10] : ( ~ element(v10, v9) | ~ v1_membered(v9) | v1_xcmplx_0(v10)) & ! [v9] : ! [v10] : ( ~ element(v10, v9) | ~ v2_membered(v9) | v1_xreal_0(v10)) & ! [v9] : ! [v10] : ( ~ element(v10, v9) | ~ v2_membered(v9) | v1_xcmplx_0(v10)) & ! [v9] : ! [v10] : ( ~ element(v10, v9) | ~ v3_membered(v9) | v1_rat_1(v10)) & ! [v9] : ! [v10] : ( ~ element(v10, v9) | ~ v3_membered(v9) | v1_xreal_0(v10)) & ! [v9] : ! [v10] : ( ~ element(v10, v9) | ~ v3_membered(v9) | v1_xcmplx_0(v10)) & ! [v9] : ! [v10] : ( ~ element(v10, v9) | ~ v4_membered(v9) | v1_int_1(v10)) & ! [v9] : ! [v10] : ( ~ element(v10, v9) | ~ v4_membered(v9) | v1_rat_1(v10)) & ! [v9] : ! [v10] : ( ~ element(v10, v9) | ~ v4_membered(v9) | v1_xreal_0(v10)) & ! [v9] : ! [v10] : ( ~ element(v10, v9) | ~ v4_membered(v9) | v1_xcmplx_0(v10)) & ! [v9] : ! [v10] : ( ~ element(v10, v9) | ~ v5_membered(v9) | natural(v10)) & ! [v9] : ! [v10] : ( ~ element(v10, v9) | ~ v5_membered(v9) | v1_int_1(v10)) & ! [v9] : ! [v10] : ( ~ element(v10, v9) | ~ v5_membered(v9) | v1_rat_1(v10)) & ! [v9] : ! [v10] : ( ~ element(v10, v9) | ~ v5_membered(v9) | v1_xreal_0(v10)) & ! [v9] : ! [v10] : ( ~ element(v10, v9) | ~ v5_membered(v9) | v1_xcmplx_0(v10)) & ! [v9] : ! [v10] : ( ~ element(v9, v10) | empty(v10) | in(v9, v10)) & ! [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) | v1_membered(v9)) & ! [v9] : ( ~ empty(v9) | v2_membered(v9)) & ! [v9] : ( ~ empty(v9) | v3_membered(v9)) & ! [v9] : ( ~ empty(v9) | v4_membered(v9)) & ! [v9] : ( ~ empty(v9) | v5_membered(v9)) & ! [v9] : ( ~ v2_membered(v9) | v1_membered(v9)) & ! [v9] : ( ~ v3_membered(v9) | v2_membered(v9)) & ! [v9] : ( ~ v4_membered(v9) | v3_membered(v9)) & ! [v9] : ( ~ v5_membered(v9) | v4_membered(v9)) & ? [v9] : ? [v10] : element(v10, v9) & ? [v9] : subset(v9, v9)) % 5.78/1.95 | 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: % 5.78/1.95 | (1) ~ (all_0_2_2 = all_0_3_3) & the_carrier(all_0_8_8) = all_0_7_7 & cast_as_carrier_subset(all_0_8_8) = all_0_5_5 & subset_difference(all_0_7_7, all_0_5_5, all_0_4_4) = all_0_2_2 & subset_complement(all_0_7_7, all_0_4_4) = all_0_3_3 & powerset(all_0_7_7) = all_0_6_6 & one_sorted_str(all_0_1_1) & one_sorted_str(all_0_8_8) & element(all_0_4_4, all_0_6_6) & empty(empty_set) & v1_membered(all_0_0_0) & v1_membered(empty_set) & v2_membered(all_0_0_0) & v2_membered(empty_set) & v3_membered(all_0_0_0) & v3_membered(empty_set) & v4_membered(all_0_0_0) & v4_membered(empty_set) & v5_membered(all_0_0_0) & v5_membered(empty_set) & ~ empty(all_0_0_0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (subset_difference(v4, v3, v2) = v1) | ~ (subset_difference(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] : (v3 = v1 | ~ (subset_complement(v0, v2) = v3) | ~ (subset_complement(v0, v1) = v2) | ? [v4] : (powerset(v0) = v4 & ~ element(v1, v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset_complement(v3, v2) = v1) | ~ (subset_complement(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [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] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ empty(v2) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ in(v0, v1) | element(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (the_carrier(v2) = v1) | ~ (the_carrier(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cast_as_carrier_subset(v2) = v1) | ~ (cast_as_carrier_subset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_complement(v0, v1) = v2) | ? [v3] : ? [v4] : (set_difference(v0, v1) = v4 & powerset(v0) = v3 & (v4 = v2 | ~ element(v1, v3)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_complement(v0, v1) = v2) | ? [v3] : (powerset(v0) = v3 & ( ~ element(v1, v3) | element(v2, v3)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v1_membered(v0) | v1_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v2_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) | ~ v3_membered(v0) | v1_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) | v3_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v4_membered(v0) | v1_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) | v3_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v4_membered(v0) | v4_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v5_membered(v0) | v1_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) | v3_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) | v5_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ? [v3] : ? [v4] : (subset_complement(v0, v1) = v4 & powerset(v0) = v3 & (v4 = v2 | ~ element(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) | ~ element(v2, v1) | ~ v1_membered(v0) | v1_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ element(v2, v1) | ~ v2_membered(v0) | v1_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ element(v2, v1) | ~ v2_membered(v0) | v2_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ element(v2, v1) | ~ v3_membered(v0) | v1_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ element(v2, v1) | ~ v3_membered(v0) | v2_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ element(v2, v1) | ~ v3_membered(v0) | v3_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ element(v2, v1) | ~ v4_membered(v0) | v1_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ element(v2, v1) | ~ v4_membered(v0) | v2_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ element(v2, v1) | ~ v4_membered(v0) | v3_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ element(v2, v1) | ~ v4_membered(v0) | v4_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ element(v2, v1) | ~ v5_membered(v0) | v1_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ element(v2, v1) | ~ v5_membered(v0) | v2_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ element(v2, v1) | ~ v5_membered(v0) | v3_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ element(v2, v1) | ~ v5_membered(v0) | v4_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ element(v2, v1) | ~ v5_membered(v0) | v5_membered(v2)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_difference(v0, empty_set) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) & ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_difference(empty_set, v0) = v1)) & ! [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) = v2 & powerset(v1) = v3 & element(v2, v3))) & ! [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] : ( ~ (powerset(v0) = v1) | ~ empty(v1)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (element(v2, v1) & ~ empty(v2))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) & empty(v2))) & ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ v1_membered(v0) | v1_xcmplx_0(v1)) & ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ v2_membered(v0) | v1_xreal_0(v1)) & ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ v2_membered(v0) | v1_xcmplx_0(v1)) & ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ v3_membered(v0) | v1_rat_1(v1)) & ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ v3_membered(v0) | v1_xreal_0(v1)) & ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ v3_membered(v0) | v1_xcmplx_0(v1)) & ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ v4_membered(v0) | v1_int_1(v1)) & ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ v4_membered(v0) | v1_rat_1(v1)) & ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ v4_membered(v0) | v1_xreal_0(v1)) & ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ v4_membered(v0) | v1_xcmplx_0(v1)) & ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ v5_membered(v0) | natural(v1)) & ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ v5_membered(v0) | v1_int_1(v1)) & ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ v5_membered(v0) | v1_rat_1(v1)) & ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ v5_membered(v0) | v1_xreal_0(v1)) & ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ v5_membered(v0) | v1_xcmplx_0(v1)) & ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1)) & ! [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) | v1_membered(v0)) & ! [v0] : ( ~ empty(v0) | v2_membered(v0)) & ! [v0] : ( ~ empty(v0) | v3_membered(v0)) & ! [v0] : ( ~ empty(v0) | v4_membered(v0)) & ! [v0] : ( ~ empty(v0) | v5_membered(v0)) & ! [v0] : ( ~ v2_membered(v0) | v1_membered(v0)) & ! [v0] : ( ~ v3_membered(v0) | v2_membered(v0)) & ! [v0] : ( ~ v4_membered(v0) | v3_membered(v0)) & ! [v0] : ( ~ v5_membered(v0) | v4_membered(v0)) & ? [v0] : ? [v1] : element(v1, v0) & ? [v0] : subset(v0, v0) % 5.78/1.98 | % 5.78/1.98 | Applying alpha-rule on (1) yields: % 6.04/1.98 | (2) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v4_membered(v0) | v3_membered(v2)) % 6.04/1.98 | (3) ! [v0] : ( ~ empty(v0) | v3_membered(v0)) % 6.04/1.98 | (4) ! [v0] : ( ~ empty(v0) | v5_membered(v0)) % 6.04/1.98 | (5) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_difference(empty_set, v0) = v1)) % 6.04/1.98 | (6) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v3_membered(v0) | v1_membered(v2)) % 6.04/1.98 | (7) ? [v0] : ? [v1] : element(v1, v0) % 6.04/1.98 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset_complement(v3, v2) = v1) | ~ (subset_complement(v3, v2) = v0)) % 6.04/1.98 | (9) empty(empty_set) % 6.04/1.98 | (10) v3_membered(empty_set) % 6.04/1.98 | (11) ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ v3_membered(v0) | v1_xcmplx_0(v1)) % 6.04/1.98 | (12) ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ v1_membered(v0) | v1_xcmplx_0(v1)) % 6.04/1.98 | (13) v1_membered(all_0_0_0) % 6.04/1.98 | (14) ! [v0] : (v0 = empty_set | ~ empty(v0)) % 6.04/1.98 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ in(v0, v1) | element(v0, v2)) % 6.04/1.98 | (16) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (element(v2, v1) & ~ empty(v2))) % 6.04/1.98 | (17) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ element(v2, v1) | ~ v5_membered(v0) | v1_membered(v2)) % 6.04/1.98 | (18) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ element(v2, v1) | ~ v3_membered(v0) | v3_membered(v2)) % 6.04/1.98 | (19) ~ empty(all_0_0_0) % 6.04/1.98 | (20) ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ v4_membered(v0) | v1_int_1(v1)) % 6.04/1.98 | (21) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ element(v2, v1) | ~ v5_membered(v0) | v3_membered(v2)) % 6.04/1.98 | (22) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ element(v2, v1) | ~ v1_membered(v0) | v1_membered(v2)) % 6.04/1.98 | (23) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v4_membered(v0) | v1_membered(v2)) % 6.04/1.99 | (24) powerset(all_0_7_7) = all_0_6_6 % 6.04/1.99 | (25) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ empty(v1)) % 6.04/1.99 | (26) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ element(v2, v1) | ~ v4_membered(v0) | v3_membered(v2)) % 6.04/1.99 | (27) ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ v5_membered(v0) | v1_int_1(v1)) % 6.04/1.99 | (28) ! [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) % 6.04/1.99 | (29) v3_membered(all_0_0_0) % 6.04/1.99 | (30) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) & empty(v2))) % 6.04/1.99 | (31) v2_membered(all_0_0_0) % 6.04/1.99 | (32) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v2_membered(v0) | v1_membered(v2)) % 6.04/1.99 | (33) one_sorted_str(all_0_8_8) % 6.04/1.99 | (34) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v2_membered(v0) | v2_membered(v2)) % 6.04/1.99 | (35) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) % 6.04/1.99 | (36) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) % 6.04/1.99 | (37) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v1_membered(v0) | v1_membered(v2)) % 6.04/1.99 | (38) ! [v0] : ( ~ v5_membered(v0) | v4_membered(v0)) % 6.04/1.99 | (39) ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ v2_membered(v0) | v1_xreal_0(v1)) % 6.04/1.99 | (40) ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ v4_membered(v0) | v1_xcmplx_0(v1)) % 6.04/1.99 | (41) ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1)) % 6.04/1.99 | (42) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v5_membered(v0) | v5_membered(v2)) % 6.04/1.99 | (43) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ element(v2, v1) | ~ v5_membered(v0) | v4_membered(v2)) % 6.04/1.99 | (44) v4_membered(empty_set) % 6.04/1.99 | (45) v5_membered(empty_set) % 6.04/1.99 | (46) one_sorted_str(all_0_1_1) % 6.04/1.99 | (47) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ element(v2, v1) | ~ v2_membered(v0) | v1_membered(v2)) % 6.04/1.99 | (48) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ element(v2, v1) | ~ v5_membered(v0) | v2_membered(v2)) % 6.04/1.99 | (49) v2_membered(empty_set) % 6.04/1.99 | (50) ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ one_sorted_str(v0) | ? [v2] : ? [v3] : (cast_as_carrier_subset(v0) = v2 & powerset(v1) = v3 & element(v2, v3))) % 6.04/1.99 | (51) ? [v0] : subset(v0, v0) % 6.04/1.99 | (52) ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ v3_membered(v0) | v1_xreal_0(v1)) % 6.04/1.99 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (subset_difference(v4, v3, v2) = v1) | ~ (subset_difference(v4, v3, v2) = v0)) % 6.04/1.99 | (54) ! [v0] : ( ~ empty(v0) | v4_membered(v0)) % 6.04/1.99 | (55) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (the_carrier(v2) = v1) | ~ (the_carrier(v2) = v0)) % 6.04/1.99 | (56) v4_membered(all_0_0_0) % 6.04/1.99 | (57) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v4_membered(v0) | v4_membered(v2)) % 6.04/1.99 | (58) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ element(v2, v1) | ~ v2_membered(v0) | v2_membered(v2)) % 6.04/1.99 | (59) subset_complement(all_0_7_7, all_0_4_4) = all_0_3_3 % 6.04/1.99 | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) % 6.04/1.99 | (61) ! [v0] : ! [v1] : ( ~ (cast_as_carrier_subset(v0) = v1) | ~ one_sorted_str(v0) | the_carrier(v0) = v1) % 6.04/1.99 | (62) ! [v0] : ( ~ v3_membered(v0) | v2_membered(v0)) % 6.04/2.00 | (63) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ element(v2, v1) | ~ v4_membered(v0) | v1_membered(v2)) % 6.04/2.00 | (64) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v3_membered(v0) | v2_membered(v2)) % 6.04/2.00 | (65) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v3_membered(v0) | v3_membered(v2)) % 6.04/2.00 | (66) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ element(v2, v1) | ~ v3_membered(v0) | v1_membered(v2)) % 6.04/2.00 | (67) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ element(v2, v1) | ~ v4_membered(v0) | v4_membered(v2)) % 6.04/2.00 | (68) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v5_membered(v0) | v1_membered(v2)) % 6.04/2.00 | (69) cast_as_carrier_subset(all_0_8_8) = all_0_5_5 % 6.04/2.00 | (70) ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ v5_membered(v0) | v1_xreal_0(v1)) % 6.04/2.00 | (71) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ element(v2, v1) | ~ v4_membered(v0) | v2_membered(v2)) % 6.04/2.00 | (72) ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ v5_membered(v0) | v1_xcmplx_0(v1)) % 6.04/2.00 | (73) ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1)) % 6.04/2.00 | (74) ~ (all_0_2_2 = all_0_3_3) % 6.04/2.00 | (75) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v5_membered(v0) | v2_membered(v2)) % 6.04/2.00 | (76) ! [v0] : ( ~ v4_membered(v0) | v3_membered(v0)) % 6.04/2.00 | (77) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ element(v2, v1) | ~ v3_membered(v0) | v2_membered(v2)) % 6.04/2.00 | (78) ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ v5_membered(v0) | natural(v1)) % 6.04/2.00 | (79) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v4_membered(v0) | v2_membered(v2)) % 6.04/2.00 | (80) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_complement(v0, v1) = v2) | ? [v3] : ? [v4] : (set_difference(v0, v1) = v4 & powerset(v0) = v3 & (v4 = v2 | ~ element(v1, v3)))) % 6.04/2.00 | (81) ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ one_sorted_str(v0) | cast_as_carrier_subset(v0) = v1) % 6.04/2.00 | (82) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v5_membered(v0) | v4_membered(v2)) % 6.04/2.00 | (83) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ element(v0, v2) | subset(v0, v1)) % 6.04/2.00 | (84) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2)) % 6.04/2.00 | (85) ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ v4_membered(v0) | v1_xreal_0(v1)) % 6.04/2.00 | (86) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (subset_complement(v0, v2) = v3) | ~ (subset_complement(v0, v1) = v2) | ? [v4] : (powerset(v0) = v4 & ~ element(v1, v4))) % 6.04/2.00 | (87) ! [v0] : ( ~ v2_membered(v0) | v1_membered(v0)) % 6.04/2.00 | (88) ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ v2_membered(v0) | v1_xcmplx_0(v1)) % 6.04/2.00 | (89) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ element(v2, v1) | ~ v5_membered(v0) | v5_membered(v2)) % 6.04/2.00 | (90) ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ v4_membered(v0) | v1_rat_1(v1)) % 6.04/2.00 | (91) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cast_as_carrier_subset(v2) = v1) | ~ (cast_as_carrier_subset(v2) = v0)) % 6.04/2.00 | (92) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ empty(v2) | ~ in(v0, v1)) % 6.04/2.00 | (93) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_difference(v0, v1, v2) = v3) | ? [v4] : (powerset(v0) = v4 & ( ~ element(v2, v4) | ~ element(v1, v4) | element(v3, v4)))) % 6.04/2.00 | (94) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v5_membered(v0) | v3_membered(v2)) % 6.04/2.00 | (95) the_carrier(all_0_8_8) = all_0_7_7 % 6.04/2.00 | (96) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) % 6.04/2.00 | (97) ! [v0] : ! [v1] : ( ~ (cast_as_carrier_subset(v0) = v1) | ~ one_sorted_str(v0) | ? [v2] : ? [v3] : (the_carrier(v0) = v2 & powerset(v2) = v3 & element(v1, v3))) % 6.04/2.00 | (98) v1_membered(empty_set) % 6.04/2.00 | (99) ! [v0] : ( ~ empty(v0) | v2_membered(v0)) % 6.04/2.00 | (100) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ? [v3] : ? [v4] : (subset_complement(v0, v1) = v4 & powerset(v0) = v3 & (v4 = v2 | ~ element(v1, v3)))) % 6.04/2.00 | (101) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_complement(v0, v1) = v2) | ? [v3] : (powerset(v0) = v3 & ( ~ element(v1, v3) | element(v2, v3)))) % 6.04/2.00 | (102) ! [v0] : ( ~ empty(v0) | v1_membered(v0)) % 6.04/2.00 | (103) ! [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)))) % 6.04/2.00 | (104) v5_membered(all_0_0_0) % 6.04/2.00 | (105) element(all_0_4_4, all_0_6_6) % 6.04/2.00 | (106) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1)) % 6.04/2.00 | (107) ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ v5_membered(v0) | v1_rat_1(v1)) % 6.04/2.01 | (108) subset_difference(all_0_7_7, all_0_5_5, all_0_4_4) = all_0_2_2 % 6.04/2.01 | (109) ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ v3_membered(v0) | v1_rat_1(v1)) % 6.04/2.01 | (110) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_difference(v0, empty_set) = v1)) % 6.04/2.01 | % 6.04/2.01 | Instantiating formula (103) with all_0_2_2, 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_2_2, yields: % 6.04/2.01 | (111) ? [v0] : ? [v1] : (set_difference(all_0_5_5, all_0_4_4) = v1 & powerset(all_0_7_7) = v0 & (v1 = all_0_2_2 | ~ element(all_0_4_4, v0) | ~ element(all_0_5_5, v0))) % 6.04/2.01 | % 6.04/2.01 | Instantiating formula (93) with all_0_2_2, 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_2_2, yields: % 6.04/2.01 | (112) ? [v0] : (powerset(all_0_7_7) = v0 & ( ~ element(all_0_4_4, v0) | ~ element(all_0_5_5, v0) | element(all_0_2_2, v0))) % 6.04/2.01 | % 6.04/2.01 | Instantiating formula (80) with all_0_3_3, all_0_4_4, all_0_7_7 and discharging atoms subset_complement(all_0_7_7, all_0_4_4) = all_0_3_3, yields: % 6.04/2.01 | (113) ? [v0] : ? [v1] : (set_difference(all_0_7_7, all_0_4_4) = v1 & powerset(all_0_7_7) = v0 & (v1 = all_0_3_3 | ~ element(all_0_4_4, v0))) % 6.04/2.01 | % 6.04/2.01 | Instantiating formula (101) with all_0_3_3, all_0_4_4, all_0_7_7 and discharging atoms subset_complement(all_0_7_7, all_0_4_4) = all_0_3_3, yields: % 6.04/2.01 | (114) ? [v0] : (powerset(all_0_7_7) = v0 & ( ~ element(all_0_4_4, v0) | element(all_0_3_3, v0))) % 6.04/2.01 | % 6.04/2.01 | Instantiating formula (81) 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: % 6.04/2.01 | (115) cast_as_carrier_subset(all_0_8_8) = all_0_7_7 % 6.04/2.01 | % 6.04/2.01 | Instantiating formula (50) 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: % 6.04/2.01 | (116) ? [v0] : ? [v1] : (cast_as_carrier_subset(all_0_8_8) = v0 & powerset(all_0_7_7) = v1 & element(v0, v1)) % 6.04/2.01 | % 6.04/2.01 | Instantiating formula (61) 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: % 6.04/2.01 | (117) the_carrier(all_0_8_8) = all_0_5_5 % 6.04/2.01 | % 6.04/2.01 | Instantiating formula (97) 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: % 6.04/2.01 | (118) ? [v0] : ? [v1] : (the_carrier(all_0_8_8) = v0 & powerset(v0) = v1 & element(all_0_5_5, v1)) % 6.04/2.01 | % 6.04/2.01 | Instantiating (118) with all_15_0_13, all_15_1_14 yields: % 6.04/2.01 | (119) the_carrier(all_0_8_8) = all_15_1_14 & powerset(all_15_1_14) = all_15_0_13 & element(all_0_5_5, all_15_0_13) % 6.04/2.01 | % 6.04/2.01 | Applying alpha-rule on (119) yields: % 6.04/2.01 | (120) the_carrier(all_0_8_8) = all_15_1_14 % 6.04/2.01 | (121) powerset(all_15_1_14) = all_15_0_13 % 6.04/2.01 | (122) element(all_0_5_5, all_15_0_13) % 6.04/2.01 | % 6.04/2.01 | Instantiating (116) with all_17_0_15, all_17_1_16 yields: % 6.04/2.01 | (123) cast_as_carrier_subset(all_0_8_8) = all_17_1_16 & powerset(all_0_7_7) = all_17_0_15 & element(all_17_1_16, all_17_0_15) % 6.04/2.01 | % 6.04/2.01 | Applying alpha-rule on (123) yields: % 6.04/2.01 | (124) cast_as_carrier_subset(all_0_8_8) = all_17_1_16 % 6.04/2.01 | (125) powerset(all_0_7_7) = all_17_0_15 % 6.04/2.01 | (126) element(all_17_1_16, all_17_0_15) % 6.04/2.01 | % 6.04/2.01 | Instantiating (114) with all_19_0_17 yields: % 6.04/2.01 | (127) powerset(all_0_7_7) = all_19_0_17 & ( ~ element(all_0_4_4, all_19_0_17) | element(all_0_3_3, all_19_0_17)) % 6.04/2.01 | % 6.04/2.01 | Applying alpha-rule on (127) yields: % 6.04/2.01 | (128) powerset(all_0_7_7) = all_19_0_17 % 6.04/2.01 | (129) ~ element(all_0_4_4, all_19_0_17) | element(all_0_3_3, all_19_0_17) % 6.04/2.01 | % 6.04/2.01 | Instantiating (113) with all_21_0_18, all_21_1_19 yields: % 6.04/2.01 | (130) set_difference(all_0_7_7, all_0_4_4) = all_21_0_18 & powerset(all_0_7_7) = all_21_1_19 & (all_21_0_18 = all_0_3_3 | ~ element(all_0_4_4, all_21_1_19)) % 6.04/2.01 | % 6.04/2.01 | Applying alpha-rule on (130) yields: % 6.04/2.01 | (131) set_difference(all_0_7_7, all_0_4_4) = all_21_0_18 % 6.04/2.01 | (132) powerset(all_0_7_7) = all_21_1_19 % 6.04/2.01 | (133) all_21_0_18 = all_0_3_3 | ~ element(all_0_4_4, all_21_1_19) % 6.04/2.01 | % 6.04/2.01 | Instantiating (112) with all_23_0_20 yields: % 6.04/2.01 | (134) powerset(all_0_7_7) = all_23_0_20 & ( ~ element(all_0_4_4, all_23_0_20) | ~ element(all_0_5_5, all_23_0_20) | element(all_0_2_2, all_23_0_20)) % 6.04/2.01 | % 6.04/2.01 | Applying alpha-rule on (134) yields: % 6.04/2.01 | (135) powerset(all_0_7_7) = all_23_0_20 % 6.04/2.01 | (136) ~ element(all_0_4_4, all_23_0_20) | ~ element(all_0_5_5, all_23_0_20) | element(all_0_2_2, all_23_0_20) % 6.04/2.01 | % 6.04/2.01 | Instantiating (111) with all_25_0_21, all_25_1_22 yields: % 6.04/2.01 | (137) set_difference(all_0_5_5, all_0_4_4) = all_25_0_21 & powerset(all_0_7_7) = all_25_1_22 & (all_25_0_21 = all_0_2_2 | ~ element(all_0_4_4, all_25_1_22) | ~ element(all_0_5_5, all_25_1_22)) % 6.04/2.01 | % 6.04/2.01 | Applying alpha-rule on (137) yields: % 6.04/2.01 | (138) set_difference(all_0_5_5, all_0_4_4) = all_25_0_21 % 6.04/2.01 | (139) powerset(all_0_7_7) = all_25_1_22 % 6.04/2.01 | (140) all_25_0_21 = all_0_2_2 | ~ element(all_0_4_4, all_25_1_22) | ~ element(all_0_5_5, all_25_1_22) % 6.04/2.01 | % 6.04/2.01 | Instantiating formula (55) with all_0_8_8, all_15_1_14, all_0_7_7 and discharging atoms the_carrier(all_0_8_8) = all_15_1_14, the_carrier(all_0_8_8) = all_0_7_7, yields: % 6.04/2.01 | (141) all_15_1_14 = all_0_7_7 % 6.04/2.01 | % 6.04/2.01 | Instantiating formula (55) with all_0_8_8, all_0_5_5, all_15_1_14 and discharging atoms the_carrier(all_0_8_8) = all_15_1_14, the_carrier(all_0_8_8) = all_0_5_5, yields: % 6.04/2.01 | (142) all_15_1_14 = all_0_5_5 % 6.04/2.01 | % 6.04/2.01 | Instantiating formula (91) with all_0_8_8, all_0_7_7, all_17_1_16 and discharging atoms cast_as_carrier_subset(all_0_8_8) = all_17_1_16, cast_as_carrier_subset(all_0_8_8) = all_0_7_7, yields: % 6.04/2.01 | (143) all_17_1_16 = all_0_7_7 % 6.04/2.01 | % 6.04/2.01 | Instantiating formula (96) with all_0_7_7, all_23_0_20, all_25_1_22 and discharging atoms powerset(all_0_7_7) = all_25_1_22, powerset(all_0_7_7) = all_23_0_20, yields: % 6.04/2.01 | (144) all_25_1_22 = all_23_0_20 % 6.04/2.01 | % 6.04/2.01 | Instantiating formula (96) with all_0_7_7, all_21_1_19, all_0_6_6 and discharging atoms powerset(all_0_7_7) = all_21_1_19, powerset(all_0_7_7) = all_0_6_6, yields: % 6.04/2.01 | (145) all_21_1_19 = all_0_6_6 % 6.04/2.01 | % 6.04/2.01 | Instantiating formula (96) with all_0_7_7, all_21_1_19, all_23_0_20 and discharging atoms powerset(all_0_7_7) = all_23_0_20, powerset(all_0_7_7) = all_21_1_19, yields: % 6.04/2.01 | (146) all_23_0_20 = all_21_1_19 % 6.04/2.01 | % 6.04/2.01 | Instantiating formula (96) with all_0_7_7, all_19_0_17, all_25_1_22 and discharging atoms powerset(all_0_7_7) = all_25_1_22, powerset(all_0_7_7) = all_19_0_17, yields: % 6.04/2.01 | (147) all_25_1_22 = all_19_0_17 % 6.04/2.01 | % 6.04/2.01 | Instantiating formula (96) with all_0_7_7, all_17_0_15, all_21_1_19 and discharging atoms powerset(all_0_7_7) = all_21_1_19, powerset(all_0_7_7) = all_17_0_15, yields: % 6.04/2.01 | (148) all_21_1_19 = all_17_0_15 % 6.04/2.01 | % 6.04/2.01 | Combining equations (144,147) yields a new equation: % 6.04/2.02 | (149) all_23_0_20 = all_19_0_17 % 6.04/2.02 | % 6.04/2.02 | Simplifying 149 yields: % 6.04/2.02 | (150) all_23_0_20 = all_19_0_17 % 6.04/2.02 | % 6.04/2.02 | Combining equations (146,150) yields a new equation: % 6.04/2.02 | (151) all_21_1_19 = all_19_0_17 % 6.04/2.02 | % 6.04/2.02 | Simplifying 151 yields: % 6.04/2.02 | (152) all_21_1_19 = all_19_0_17 % 6.04/2.02 | % 6.04/2.02 | Combining equations (145,152) yields a new equation: % 6.04/2.02 | (153) all_19_0_17 = all_0_6_6 % 6.04/2.02 | % 6.04/2.02 | Combining equations (148,152) yields a new equation: % 6.04/2.02 | (154) all_19_0_17 = all_17_0_15 % 6.04/2.02 | % 6.04/2.02 | Combining equations (154,153) yields a new equation: % 6.04/2.02 | (155) all_17_0_15 = all_0_6_6 % 6.04/2.02 | % 6.04/2.02 | Simplifying 155 yields: % 6.04/2.02 | (156) all_17_0_15 = all_0_6_6 % 6.04/2.02 | % 6.04/2.02 | Combining equations (141,142) yields a new equation: % 6.04/2.02 | (157) all_0_5_5 = all_0_7_7 % 6.04/2.02 | % 6.04/2.02 | Combining equations (153,152) yields a new equation: % 6.04/2.02 | (145) all_21_1_19 = all_0_6_6 % 6.04/2.02 | % 6.04/2.02 | Combining equations (153,150) yields a new equation: % 6.04/2.02 | (159) all_23_0_20 = all_0_6_6 % 6.04/2.02 | % 6.04/2.02 | Combining equations (153,147) yields a new equation: % 6.04/2.02 | (160) all_25_1_22 = all_0_6_6 % 6.04/2.02 | % 6.04/2.02 | From (157) and (138) follows: % 6.04/2.02 | (161) set_difference(all_0_7_7, all_0_4_4) = all_25_0_21 % 6.04/2.02 | % 6.04/2.02 | From (143)(156) and (126) follows: % 6.04/2.02 | (162) element(all_0_7_7, all_0_6_6) % 6.04/2.02 | % 6.04/2.02 +-Applying beta-rule and splitting (140), into two cases. % 6.04/2.02 |-Branch one: % 6.04/2.02 | (163) ~ element(all_0_4_4, all_25_1_22) % 6.04/2.02 | % 6.04/2.02 | From (160) and (163) follows: % 6.04/2.02 | (164) ~ element(all_0_4_4, all_0_6_6) % 6.04/2.02 | % 6.04/2.02 | Using (105) and (164) yields: % 6.04/2.02 | (165) $false % 6.04/2.02 | % 6.04/2.02 |-The branch is then unsatisfiable % 6.04/2.02 |-Branch two: % 6.04/2.02 | (166) element(all_0_4_4, all_25_1_22) % 6.04/2.02 | (167) all_25_0_21 = all_0_2_2 | ~ element(all_0_5_5, all_25_1_22) % 6.04/2.02 | % 6.04/2.02 | From (160) and (166) follows: % 6.04/2.02 | (105) element(all_0_4_4, all_0_6_6) % 6.04/2.02 | % 6.04/2.02 +-Applying beta-rule and splitting (129), into two cases. % 6.04/2.02 |-Branch one: % 6.04/2.02 | (169) ~ element(all_0_4_4, all_19_0_17) % 6.04/2.02 | % 6.04/2.02 | From (153) and (169) follows: % 6.04/2.02 | (164) ~ element(all_0_4_4, all_0_6_6) % 6.04/2.02 | % 6.04/2.02 | Using (105) and (164) yields: % 6.04/2.02 | (165) $false % 6.04/2.02 | % 6.04/2.02 |-The branch is then unsatisfiable % 6.04/2.02 |-Branch two: % 6.04/2.02 | (172) element(all_0_4_4, all_19_0_17) % 6.04/2.02 | (173) element(all_0_3_3, all_19_0_17) % 6.04/2.02 | % 6.04/2.02 | From (153) and (172) follows: % 6.04/2.02 | (105) element(all_0_4_4, all_0_6_6) % 6.04/2.02 | % 6.04/2.02 +-Applying beta-rule and splitting (167), into two cases. % 6.04/2.02 |-Branch one: % 6.04/2.02 | (175) ~ element(all_0_5_5, all_25_1_22) % 6.04/2.02 | % 6.04/2.02 | From (157)(160) and (175) follows: % 6.04/2.02 | (176) ~ element(all_0_7_7, all_0_6_6) % 6.04/2.02 | % 6.04/2.02 | Using (162) and (176) yields: % 6.04/2.02 | (165) $false % 6.04/2.02 | % 6.04/2.02 |-The branch is then unsatisfiable % 6.04/2.02 |-Branch two: % 6.04/2.02 | (178) element(all_0_5_5, all_25_1_22) % 6.04/2.02 | (179) all_25_0_21 = all_0_2_2 % 6.04/2.02 | % 6.04/2.02 | From (179) and (161) follows: % 6.04/2.02 | (180) set_difference(all_0_7_7, all_0_4_4) = all_0_2_2 % 6.04/2.02 | % 6.04/2.02 +-Applying beta-rule and splitting (136), into two cases. % 6.04/2.02 |-Branch one: % 6.04/2.02 | (181) ~ element(all_0_4_4, all_23_0_20) % 6.04/2.02 | % 6.04/2.02 | From (159) and (181) follows: % 6.04/2.02 | (164) ~ element(all_0_4_4, all_0_6_6) % 6.04/2.02 | % 6.04/2.02 | Using (105) and (164) yields: % 6.04/2.02 | (165) $false % 6.04/2.02 | % 6.04/2.02 |-The branch is then unsatisfiable % 6.04/2.02 |-Branch two: % 6.04/2.02 | (184) element(all_0_4_4, all_23_0_20) % 6.04/2.02 | (185) ~ element(all_0_5_5, all_23_0_20) | element(all_0_2_2, all_23_0_20) % 6.04/2.02 | % 6.04/2.02 | From (159) and (184) follows: % 6.04/2.02 | (105) element(all_0_4_4, all_0_6_6) % 6.04/2.02 | % 6.04/2.02 +-Applying beta-rule and splitting (133), into two cases. % 6.04/2.02 |-Branch one: % 6.04/2.02 | (187) ~ element(all_0_4_4, all_21_1_19) % 6.04/2.02 | % 6.04/2.02 | From (145) and (187) follows: % 6.04/2.02 | (164) ~ element(all_0_4_4, all_0_6_6) % 6.04/2.02 | % 6.04/2.02 | Using (105) and (164) yields: % 6.04/2.02 | (165) $false % 6.04/2.02 | % 6.04/2.02 |-The branch is then unsatisfiable % 6.04/2.02 |-Branch two: % 6.04/2.02 | (190) element(all_0_4_4, all_21_1_19) % 6.04/2.02 | (191) all_21_0_18 = all_0_3_3 % 6.04/2.02 | % 6.04/2.02 | From (191) and (131) follows: % 6.04/2.02 | (192) set_difference(all_0_7_7, all_0_4_4) = all_0_3_3 % 6.04/2.02 | % 6.04/2.02 | Instantiating formula (60) with all_0_7_7, all_0_4_4, all_0_3_3, all_0_2_2 and discharging atoms set_difference(all_0_7_7, all_0_4_4) = all_0_2_2, set_difference(all_0_7_7, all_0_4_4) = all_0_3_3, yields: % 6.04/2.02 | (193) all_0_2_2 = all_0_3_3 % 6.04/2.02 | % 6.04/2.02 | Equations (193) can reduce 74 to: % 6.04/2.02 | (194) $false % 6.04/2.02 | % 6.04/2.02 |-The branch is then unsatisfiable % 6.04/2.02 % SZS output end Proof for theBenchmark % 6.04/2.02 % 6.04/2.02 1429ms %------------------------------------------------------------------------------