%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU354+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n029.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 08:49:07 EDT 2022 % Result : Theorem 3.04s 1.44s % Output : Proof 5.11s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.11 % Problem : SEU354+1 : TPTP v8.1.0. Released v3.3.0. % 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.11/0.33 % Computer : n029.cluster.edu % 0.11/0.33 % Model : x86_64 x86_64 % 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.33 % Memory : 8042.1875MB % 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.33 % CPULimit : 300 % 0.11/0.33 % WCLimit : 600 % 0.11/0.33 % DateTime : Sat Jun 18 21:33:44 EDT 2022 % 0.11/0.33 % CPUTime : % 0.19/0.56 ____ _ % 0.19/0.56 ___ / __ \_____(_)___ ________ __________ % 0.19/0.56 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.19/0.56 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.19/0.56 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.19/0.56 % 0.19/0.56 A Theorem Prover for First-Order Logic % 0.19/0.56 (ePrincess v.1.0) % 0.19/0.56 % 0.19/0.56 (c) Philipp Rümmer, 2009-2015 % 0.19/0.56 (c) Peter Backeman, 2014-2015 % 0.19/0.56 (contributions by Angelo Brillout, Peter Baumgartner) % 0.57/0.56 Free software under GNU Lesser General Public License (LGPL). % 0.57/0.56 Bug reports to peter@backeman.se % 0.57/0.56 % 0.57/0.56 For more information, visit http://user.uu.se/~petba168/breu/ % 0.57/0.56 % 0.57/0.56 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.63/0.61 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.74/0.96 Prover 0: Preprocessing ... % 2.41/1.22 Prover 0: Warning: ignoring some quantifiers % 2.51/1.25 Prover 0: Constructing countermodel ... % 3.04/1.43 Prover 0: proved (823ms) % 3.04/1.44 % 3.04/1.44 No countermodel exists, formula is valid % 3.04/1.44 % SZS status Theorem for theBenchmark % 3.04/1.44 % 3.04/1.44 Generating proof ... Warning: ignoring some quantifiers % 4.49/1.77 found it (size 19) % 4.49/1.77 % 4.49/1.77 % SZS output start Proof for theBenchmark % 4.49/1.77 Assumed formulas after preprocessing and simplification: % 4.49/1.77 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (powerset(v0) = v2 & empty(empty_set) & v5_membered(v3) & v5_membered(empty_set) & v4_membered(v3) & v4_membered(empty_set) & v3_membered(v3) & v3_membered(empty_set) & v2_membered(v3) & v2_membered(empty_set) & element(v1, v2) & v1_membered(v3) & v1_membered(empty_set) & ~ empty(v3) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (union_of_subsets(v7, v6) = v5) | ~ (union_of_subsets(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (union(v5) = v7) | ~ (powerset(v4) = v6) | ? [v8] : ? [v9] : (union_of_subsets(v4, v5) = v9 & powerset(v6) = v8 & (v9 = v7 | ~ element(v5, v8)))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (powerset(v6) = v7) | ~ empty(v6) | ~ element(v5, v7) | ~ in(v4, v5)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (powerset(v6) = v7) | ~ element(v5, v7) | ~ in(v4, v5) | element(v4, v6)) & ! [v4] : ! [v5] : ! [v6] : (v6 = v5 | ~ (union(v4) = v6) | ~ element(v5, v4) | proper_element(v5, v4)) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (k1_pcomps_1(v6) = v5) | ~ (k1_pcomps_1(v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (union(v6) = v5) | ~ (union(v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (powerset(v6) = v5) | ~ (powerset(v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (union_of_subsets(v4, v5) = v6) | ? [v7] : ? [v8] : ? [v9] : (union(v5) = v9 & powerset(v7) = v8 & powerset(v4) = v7 & (v9 = v6 | ~ element(v5, v8)))) & ! [v4] : ! [v5] : ! [v6] : ( ~ (union_of_subsets(v4, v5) = v6) | ? [v7] : ? [v8] : (powerset(v7) = v8 & powerset(v4) = v7 & ( ~ element(v5, v8) | element(v6, v7)))) & ! [v4] : ! [v5] : ! [v6] : ( ~ (powerset(v5) = v6) | ~ subset(v4, v5) | element(v4, v6)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (powerset(v5) = v6) | ~ element(v4, v6) | subset(v4, v5)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (powerset(v4) = v5) | ~ v5_membered(v4) | ~ element(v6, v5) | v5_membered(v6)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (powerset(v4) = v5) | ~ v5_membered(v4) | ~ element(v6, v5) | v4_membered(v6)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (powerset(v4) = v5) | ~ v5_membered(v4) | ~ element(v6, v5) | v3_membered(v6)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (powerset(v4) = v5) | ~ v5_membered(v4) | ~ element(v6, v5) | v2_membered(v6)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (powerset(v4) = v5) | ~ v5_membered(v4) | ~ element(v6, v5) | v1_membered(v6)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (powerset(v4) = v5) | ~ v4_membered(v4) | ~ element(v6, v5) | v4_membered(v6)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (powerset(v4) = v5) | ~ v4_membered(v4) | ~ element(v6, v5) | v3_membered(v6)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (powerset(v4) = v5) | ~ v4_membered(v4) | ~ element(v6, v5) | v2_membered(v6)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (powerset(v4) = v5) | ~ v4_membered(v4) | ~ element(v6, v5) | v1_membered(v6)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (powerset(v4) = v5) | ~ v3_membered(v4) | ~ element(v6, v5) | v3_membered(v6)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (powerset(v4) = v5) | ~ v3_membered(v4) | ~ element(v6, v5) | v2_membered(v6)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (powerset(v4) = v5) | ~ v3_membered(v4) | ~ element(v6, v5) | v1_membered(v6)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (powerset(v4) = v5) | ~ v2_membered(v4) | ~ element(v6, v5) | v2_membered(v6)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (powerset(v4) = v5) | ~ v2_membered(v4) | ~ element(v6, v5) | v1_membered(v6)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (powerset(v4) = v5) | ~ element(v6, v5) | ~ v1_membered(v4) | v1_membered(v6)) & ! [v4] : ! [v5] : (v5 = v4 | ~ empty(v5) | ~ empty(v4)) & ! [v4] : ! [v5] : ( ~ (k1_pcomps_1(v4) = v5) | powerset(v4) = v5) & ! [v4] : ! [v5] : ( ~ (k1_pcomps_1(v4) = v5) | ? [v6] : ? [v7] : (powerset(v6) = v7 & powerset(v4) = v6 & element(v5, v7))) & ! [v4] : ! [v5] : ( ~ (union(v4) = v5) | ~ proper_element(v5, v4) | ~ element(v5, v4)) & ! [v4] : ! [v5] : ( ~ (powerset(v4) = v5) | ~ empty(v5)) & ! [v4] : ! [v5] : ( ~ (powerset(v4) = v5) | k1_pcomps_1(v4) = v5) & ! [v4] : ! [v5] : ( ~ (powerset(v4) = v5) | union(v5) = v4) & ! [v4] : ! [v5] : ( ~ (powerset(v4) = v5) | empty(v4) | ? [v6] : (element(v6, v5) & ~ empty(v6))) & ! [v4] : ! [v5] : ( ~ (powerset(v4) = v5) | ? [v6] : ? [v7] : (k1_pcomps_1(v4) = v6 & powerset(v5) = v7 & element(v6, v7))) & ! [v4] : ! [v5] : ( ~ (powerset(v4) = v5) | ? [v6] : (empty(v6) & element(v6, v5))) & ! [v4] : ! [v5] : ( ~ (powerset(v4) = v5) | ? [v6] : (element(v6, v5) & ~ proper_element(v6, v5))) & ! [v4] : ! [v5] : ( ~ empty(v5) | ~ in(v4, v5)) & ! [v4] : ! [v5] : ( ~ v5_membered(v4) | ~ element(v5, v4) | natural(v5)) & ! [v4] : ! [v5] : ( ~ v5_membered(v4) | ~ element(v5, v4) | v1_int_1(v5)) & ! [v4] : ! [v5] : ( ~ v5_membered(v4) | ~ element(v5, v4) | v1_rat_1(v5)) & ! [v4] : ! [v5] : ( ~ v5_membered(v4) | ~ element(v5, v4) | v1_xreal_0(v5)) & ! [v4] : ! [v5] : ( ~ v5_membered(v4) | ~ element(v5, v4) | v1_xcmplx_0(v5)) & ! [v4] : ! [v5] : ( ~ v4_membered(v4) | ~ element(v5, v4) | v1_int_1(v5)) & ! [v4] : ! [v5] : ( ~ v4_membered(v4) | ~ element(v5, v4) | v1_rat_1(v5)) & ! [v4] : ! [v5] : ( ~ v4_membered(v4) | ~ element(v5, v4) | v1_xreal_0(v5)) & ! [v4] : ! [v5] : ( ~ v4_membered(v4) | ~ element(v5, v4) | v1_xcmplx_0(v5)) & ! [v4] : ! [v5] : ( ~ v3_membered(v4) | ~ element(v5, v4) | v1_rat_1(v5)) & ! [v4] : ! [v5] : ( ~ v3_membered(v4) | ~ element(v5, v4) | v1_xreal_0(v5)) & ! [v4] : ! [v5] : ( ~ v3_membered(v4) | ~ element(v5, v4) | v1_xcmplx_0(v5)) & ! [v4] : ! [v5] : ( ~ v2_membered(v4) | ~ element(v5, v4) | v1_xreal_0(v5)) & ! [v4] : ! [v5] : ( ~ v2_membered(v4) | ~ element(v5, v4) | v1_xcmplx_0(v5)) & ! [v4] : ! [v5] : ( ~ element(v5, v4) | ~ v1_membered(v4) | v1_xcmplx_0(v5)) & ! [v4] : ! [v5] : ( ~ element(v4, v5) | empty(v5) | in(v4, v5)) & ! [v4] : ! [v5] : ( ~ in(v5, v4) | ~ in(v4, v5)) & ! [v4] : ! [v5] : ( ~ in(v4, v5) | element(v4, v5)) & ! [v4] : (v4 = empty_set | ~ empty(v4)) & ! [v4] : ( ~ empty(v4) | v5_membered(v4)) & ! [v4] : ( ~ empty(v4) | v4_membered(v4)) & ! [v4] : ( ~ empty(v4) | v3_membered(v4)) & ! [v4] : ( ~ empty(v4) | v2_membered(v4)) & ! [v4] : ( ~ empty(v4) | v1_membered(v4)) & ! [v4] : ( ~ v5_membered(v4) | v4_membered(v4)) & ! [v4] : ( ~ v4_membered(v4) | v3_membered(v4)) & ! [v4] : ( ~ v3_membered(v4) | v2_membered(v4)) & ! [v4] : ( ~ v2_membered(v4) | v1_membered(v4)) & ? [v4] : ? [v5] : element(v5, v4) & ? [v4] : subset(v4, v4) & ((v1 = v0 & proper_element(v0, v2)) | ( ~ (v1 = v0) & ~ proper_element(v1, v2)))) % 5.11/1.81 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields: % 5.11/1.81 | (1) powerset(all_0_3_3) = all_0_1_1 & empty(empty_set) & v5_membered(all_0_0_0) & v5_membered(empty_set) & v4_membered(all_0_0_0) & v4_membered(empty_set) & v3_membered(all_0_0_0) & v3_membered(empty_set) & v2_membered(all_0_0_0) & v2_membered(empty_set) & element(all_0_2_2, all_0_1_1) & v1_membered(all_0_0_0) & v1_membered(empty_set) & ~ empty(all_0_0_0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union_of_subsets(v3, v2) = v1) | ~ (union_of_subsets(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v1) = v3) | ~ (powerset(v0) = v2) | ? [v4] : ? [v5] : (union_of_subsets(v0, v1) = v5 & powerset(v2) = v4 & (v5 = v3 | ~ element(v1, 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] : (v2 = v1 | ~ (union(v0) = v2) | ~ element(v1, v0) | proper_element(v1, v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (k1_pcomps_1(v2) = v1) | ~ (k1_pcomps_1(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (union_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (union(v1) = v5 & powerset(v3) = v4 & powerset(v0) = v3 & (v5 = v2 | ~ element(v1, v4)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (union_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : (powerset(v3) = v4 & powerset(v0) = v3 & ( ~ element(v1, v4) | element(v2, 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 | ~ empty(v1) | ~ empty(v0)) & ! [v0] : ! [v1] : ( ~ (k1_pcomps_1(v0) = v1) | powerset(v0) = v1) & ! [v0] : ! [v1] : ( ~ (k1_pcomps_1(v0) = v1) | ? [v2] : ? [v3] : (powerset(v2) = v3 & powerset(v0) = v2 & element(v1, v3))) & ! [v0] : ! [v1] : ( ~ (union(v0) = v1) | ~ proper_element(v1, v0) | ~ element(v1, v0)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ empty(v1)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | k1_pcomps_1(v0) = v1) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | union(v1) = v0) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (element(v2, v1) & ~ empty(v2))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ? [v3] : (k1_pcomps_1(v0) = v2 & powerset(v1) = v3 & element(v2, v3))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (empty(v2) & element(v2, v1))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) & ~ proper_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) & ((all_0_2_2 = all_0_3_3 & proper_element(all_0_3_3, all_0_1_1)) | ( ~ (all_0_2_2 = all_0_3_3) & ~ proper_element(all_0_2_2, all_0_1_1))) % 5.11/1.83 | % 5.11/1.83 | Applying alpha-rule on (1) yields: % 5.11/1.83 | (2) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (union(v0) = v2) | ~ element(v1, v0) | proper_element(v1, v0)) % 5.11/1.83 | (3) ! [v0] : ! [v1] : ( ~ (union(v0) = v1) | ~ proper_element(v1, v0) | ~ element(v1, v0)) % 5.11/1.83 | (4) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ empty(v1)) % 5.11/1.83 | (5) element(all_0_2_2, all_0_1_1) % 5.11/1.83 | (6) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ element(v0, v2) | subset(v0, v1)) % 5.11/1.83 | (7) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2)) % 5.11/1.83 | (8) ! [v0] : ! [v1] : ( ~ v5_membered(v0) | ~ element(v1, v0) | v1_xcmplx_0(v1)) % 5.11/1.83 | (9) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v3_membered(v0) | ~ element(v2, v1) | v1_membered(v2)) % 5.11/1.83 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v5_membered(v0) | ~ element(v2, v1) | v1_membered(v2)) % 5.11/1.83 | (11) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v5_membered(v0) | ~ element(v2, v1) | v2_membered(v2)) % 5.11/1.83 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (union_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : (powerset(v3) = v4 & powerset(v0) = v3 & ( ~ element(v1, v4) | element(v2, v3)))) % 5.11/1.83 | (13) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v4_membered(v0) | ~ element(v2, v1) | v3_membered(v2)) % 5.11/1.83 | (14) ! [v0] : ! [v1] : ( ~ v5_membered(v0) | ~ element(v1, v0) | v1_int_1(v1)) % 5.11/1.83 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v1) = v3) | ~ (powerset(v0) = v2) | ? [v4] : ? [v5] : (union_of_subsets(v0, v1) = v5 & powerset(v2) = v4 & (v5 = v3 | ~ element(v1, v4)))) % 5.11/1.84 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union_of_subsets(v3, v2) = v1) | ~ (union_of_subsets(v3, v2) = v0)) % 5.11/1.84 | (17) v3_membered(all_0_0_0) % 5.11/1.84 | (18) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1)) % 5.11/1.84 | (19) ! [v0] : ! [v1] : ( ~ v3_membered(v0) | ~ element(v1, v0) | v1_xcmplx_0(v1)) % 5.11/1.84 | (20) ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1)) % 5.11/1.84 | (21) ! [v0] : ( ~ v2_membered(v0) | v1_membered(v0)) % 5.11/1.84 | (22) ! [v0] : (v0 = empty_set | ~ empty(v0)) % 5.11/1.84 | (23) ! [v0] : ! [v1] : ( ~ v5_membered(v0) | ~ element(v1, v0) | v1_rat_1(v1)) % 5.11/1.84 | (24) ! [v0] : ! [v1] : ( ~ v3_membered(v0) | ~ element(v1, v0) | v1_xreal_0(v1)) % 5.11/1.84 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ empty(v2) | ~ element(v1, v3) | ~ in(v0, v1)) % 5.11/1.84 | (26) ! [v0] : ( ~ empty(v0) | v1_membered(v0)) % 5.11/1.84 | (27) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v3_membered(v0) | ~ element(v2, v1) | v2_membered(v2)) % 5.11/1.84 | (28) ! [v0] : ! [v1] : ( ~ v2_membered(v0) | ~ element(v1, v0) | v1_xcmplx_0(v1)) % 5.11/1.84 | (29) ! [v0] : ! [v1] : ( ~ v5_membered(v0) | ~ element(v1, v0) | v1_xreal_0(v1)) % 5.11/1.84 | (30) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v5_membered(v0) | ~ element(v2, v1) | v4_membered(v2)) % 5.11/1.84 | (31) ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1)) % 5.11/1.84 | (32) ! [v0] : ( ~ v5_membered(v0) | v4_membered(v0)) % 5.11/1.84 | (33) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ? [v3] : (k1_pcomps_1(v0) = v2 & powerset(v1) = v3 & element(v2, v3))) % 5.11/1.84 | (34) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v4_membered(v0) | ~ element(v2, v1) | v2_membered(v2)) % 5.11/1.84 | (35) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v4_membered(v0) | ~ element(v2, v1) | v1_membered(v2)) % 5.11/1.84 | (36) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) % 5.11/1.84 | (37) ! [v0] : ! [v1] : ( ~ v3_membered(v0) | ~ element(v1, v0) | v1_rat_1(v1)) % 5.11/1.84 | (38) ! [v0] : ! [v1] : ( ~ v4_membered(v0) | ~ element(v1, v0) | v1_xreal_0(v1)) % 5.11/1.84 | (39) v2_membered(empty_set) % 5.11/1.84 | (40) ! [v0] : ! [v1] : ( ~ v4_membered(v0) | ~ element(v1, v0) | v1_rat_1(v1)) % 5.11/1.84 | (41) v5_membered(all_0_0_0) % 5.11/1.84 | (42) ! [v0] : ( ~ empty(v0) | v2_membered(v0)) % 5.11/1.84 | (43) v1_membered(all_0_0_0) % 5.11/1.84 | (44) ! [v0] : ! [v1] : ! [v2] : ( ~ (union_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (union(v1) = v5 & powerset(v3) = v4 & powerset(v0) = v3 & (v5 = v2 | ~ element(v1, v4)))) % 5.11/1.84 | (45) ! [v0] : ! [v1] : ( ~ v2_membered(v0) | ~ element(v1, v0) | v1_xreal_0(v1)) % 5.11/1.84 | (46) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (empty(v2) & element(v2, v1))) % 5.11/1.84 | (47) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v3_membered(v0) | ~ element(v2, v1) | v3_membered(v2)) % 5.11/1.84 | (48) ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ v1_membered(v0) | v1_xcmplx_0(v1)) % 5.11/1.84 | (49) v3_membered(empty_set) % 5.11/1.84 | (50) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (k1_pcomps_1(v2) = v1) | ~ (k1_pcomps_1(v2) = v0)) % 5.11/1.85 | (51) ! [v0] : ! [v1] : ( ~ v4_membered(v0) | ~ element(v1, v0) | v1_xcmplx_0(v1)) % 5.11/1.85 | (52) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v4_membered(v0) | ~ element(v2, v1) | v4_membered(v2)) % 5.11/1.85 | (53) v4_membered(empty_set) % 5.11/1.85 | (54) empty(empty_set) % 5.11/1.85 | (55) ~ empty(all_0_0_0) % 5.11/1.85 | (56) (all_0_2_2 = all_0_3_3 & proper_element(all_0_3_3, all_0_1_1)) | ( ~ (all_0_2_2 = all_0_3_3) & ~ proper_element(all_0_2_2, all_0_1_1)) % 5.11/1.85 | (57) ! [v0] : ! [v1] : ( ~ (k1_pcomps_1(v0) = v1) | ? [v2] : ? [v3] : (powerset(v2) = v3 & powerset(v0) = v2 & element(v1, v3))) % 5.11/1.85 | (58) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | union(v1) = v0) % 5.11/1.85 | (59) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) % 5.11/1.85 | (60) ? [v0] : subset(v0, v0) % 5.11/1.85 | (61) ! [v0] : ( ~ empty(v0) | v4_membered(v0)) % 5.11/1.85 | (62) ! [v0] : ( ~ v4_membered(v0) | v3_membered(v0)) % 5.11/1.85 | (63) powerset(all_0_3_3) = all_0_1_1 % 5.11/1.85 | (64) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = v0)) % 5.11/1.85 | (65) ! [v0] : ! [v1] : ( ~ v4_membered(v0) | ~ element(v1, v0) | v1_int_1(v1)) % 5.11/1.85 | (66) v5_membered(empty_set) % 5.11/1.85 | (67) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ element(v2, v1) | ~ v1_membered(v0) | v1_membered(v2)) % 5.11/1.85 | (68) ! [v0] : ( ~ v3_membered(v0) | v2_membered(v0)) % 5.11/1.85 | (69) ! [v0] : ( ~ empty(v0) | v5_membered(v0)) % 5.11/1.85 | (70) ! [v0] : ( ~ empty(v0) | v3_membered(v0)) % 5.11/1.85 | (71) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v5_membered(v0) | ~ element(v2, v1) | v3_membered(v2)) % 5.11/1.85 | (72) ? [v0] : ? [v1] : element(v1, v0) % 5.11/1.85 | (73) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v5_membered(v0) | ~ element(v2, v1) | v5_membered(v2)) % 5.11/1.85 | (74) ! [v0] : ! [v1] : ( ~ v5_membered(v0) | ~ element(v1, v0) | natural(v1)) % 5.11/1.85 | (75) v1_membered(empty_set) % 5.11/1.85 | (76) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v2_membered(v0) | ~ element(v2, v1) | v1_membered(v2)) % 5.11/1.85 | (77) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v2_membered(v0) | ~ element(v2, v1) | v2_membered(v2)) % 5.11/1.85 | (78) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) & ~ proper_element(v2, v1))) % 5.11/1.85 | (79) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | k1_pcomps_1(v0) = v1) % 5.11/1.85 | (80) ! [v0] : ! [v1] : ( ~ (k1_pcomps_1(v0) = v1) | powerset(v0) = v1) % 5.11/1.85 | (81) v4_membered(all_0_0_0) % 5.11/1.85 | (82) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (element(v2, v1) & ~ empty(v2))) % 5.11/1.85 | (83) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ in(v0, v1) | element(v0, v2)) % 5.11/1.85 | (84) v2_membered(all_0_0_0) % 5.11/1.85 | (85) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) % 5.11/1.85 | % 5.11/1.86 | Instantiating formula (58) with all_0_1_1, all_0_3_3 and discharging atoms powerset(all_0_3_3) = all_0_1_1, yields: % 5.11/1.86 | (86) union(all_0_1_1) = all_0_3_3 % 5.11/1.86 | % 5.11/1.86 | Instantiating formula (78) with all_0_1_1, all_0_3_3 and discharging atoms powerset(all_0_3_3) = all_0_1_1, yields: % 5.11/1.86 | (87) ? [v0] : (element(v0, all_0_1_1) & ~ proper_element(v0, all_0_1_1)) % 5.11/1.86 | % 5.11/1.86 | Instantiating (87) with all_13_0_7 yields: % 5.11/1.86 | (88) element(all_13_0_7, all_0_1_1) & ~ proper_element(all_13_0_7, all_0_1_1) % 5.11/1.86 | % 5.11/1.86 | Applying alpha-rule on (88) yields: % 5.11/1.86 | (89) element(all_13_0_7, all_0_1_1) % 5.11/1.86 | (90) ~ proper_element(all_13_0_7, all_0_1_1) % 5.11/1.86 | % 5.11/1.86 | Instantiating formula (2) with all_0_3_3, all_0_2_2, all_0_1_1 and discharging atoms union(all_0_1_1) = all_0_3_3, element(all_0_2_2, all_0_1_1), yields: % 5.11/1.86 | (91) all_0_2_2 = all_0_3_3 | proper_element(all_0_2_2, all_0_1_1) % 5.11/1.86 | % 5.11/1.86 | Instantiating formula (2) with all_0_3_3, all_13_0_7, all_0_1_1 and discharging atoms union(all_0_1_1) = all_0_3_3, element(all_13_0_7, all_0_1_1), ~ proper_element(all_13_0_7, all_0_1_1), yields: % 5.11/1.86 | (92) all_13_0_7 = all_0_3_3 % 5.11/1.86 | % 5.11/1.86 | From (92) and (90) follows: % 5.11/1.86 | (93) ~ proper_element(all_0_3_3, all_0_1_1) % 5.11/1.86 | % 5.11/1.86 +-Applying beta-rule and splitting (56), into two cases. % 5.11/1.86 |-Branch one: % 5.11/1.86 | (94) all_0_2_2 = all_0_3_3 & proper_element(all_0_3_3, all_0_1_1) % 5.11/1.86 | % 5.11/1.86 | Applying alpha-rule on (94) yields: % 5.11/1.86 | (95) all_0_2_2 = all_0_3_3 % 5.11/1.86 | (96) proper_element(all_0_3_3, all_0_1_1) % 5.11/1.86 | % 5.11/1.86 | Using (96) and (93) yields: % 5.11/1.86 | (97) $false % 5.11/1.86 | % 5.11/1.86 |-The branch is then unsatisfiable % 5.11/1.86 |-Branch two: % 5.11/1.86 | (98) ~ (all_0_2_2 = all_0_3_3) & ~ proper_element(all_0_2_2, all_0_1_1) % 5.11/1.86 | % 5.11/1.86 | Applying alpha-rule on (98) yields: % 5.11/1.86 | (99) ~ (all_0_2_2 = all_0_3_3) % 5.11/1.86 | (100) ~ proper_element(all_0_2_2, all_0_1_1) % 5.11/1.86 | % 5.11/1.86 +-Applying beta-rule and splitting (91), into two cases. % 5.11/1.86 |-Branch one: % 5.11/1.86 | (101) proper_element(all_0_2_2, all_0_1_1) % 5.11/1.86 | % 5.11/1.86 | Using (101) and (100) yields: % 5.11/1.86 | (97) $false % 5.11/1.86 | % 5.11/1.86 |-The branch is then unsatisfiable % 5.11/1.86 |-Branch two: % 5.11/1.86 | (100) ~ proper_element(all_0_2_2, all_0_1_1) % 5.11/1.86 | (95) all_0_2_2 = all_0_3_3 % 5.11/1.86 | % 5.11/1.86 | Equations (95) can reduce 99 to: % 5.11/1.86 | (105) $false % 5.11/1.86 | % 5.11/1.86 |-The branch is then unsatisfiable % 5.11/1.86 % SZS output end Proof for theBenchmark % 5.11/1.86 % 5.11/1.86 1291ms %------------------------------------------------------------------------------