%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU321+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n014.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 600s % DateTime : Tue Jul 19 08:48:50 EDT 2022 % Result : Theorem 3.38s 1.47s % Output : Proof 5.51s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SEU321+1 : TPTP v8.1.0. Released v3.3.0. % 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.34 % Computer : n014.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Mon Jun 20 06:31:18 EDT 2022 % 0.13/0.34 % CPUTime : % 0.19/0.59 ____ _ % 0.19/0.59 ___ / __ \_____(_)___ ________ __________ % 0.19/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.19/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.19/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.19/0.59 % 0.19/0.59 A Theorem Prover for First-Order Logic % 0.19/0.60 (ePrincess v.1.0) % 0.19/0.60 % 0.19/0.60 (c) Philipp Rümmer, 2009-2015 % 0.19/0.60 (c) Peter Backeman, 2014-2015 % 0.19/0.60 (contributions by Angelo Brillout, Peter Baumgartner) % 0.19/0.60 Free software under GNU Lesser General Public License (LGPL). % 0.19/0.60 Bug reports to peter@backeman.se % 0.19/0.60 % 0.19/0.60 For more information, visit http://user.uu.se/~petba168/breu/ % 0.19/0.60 % 0.19/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.71/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.59/0.99 Prover 0: Preprocessing ... % 2.35/1.23 Prover 0: Warning: ignoring some quantifiers % 2.44/1.26 Prover 0: Constructing countermodel ... % 3.38/1.47 Prover 0: proved (821ms) % 3.38/1.47 % 3.38/1.47 No countermodel exists, formula is valid % 3.38/1.47 % SZS status Theorem for theBenchmark % 3.38/1.47 % 3.38/1.47 Generating proof ... Warning: ignoring some quantifiers % 5.09/1.83 found it (size 37) % 5.09/1.83 % 5.09/1.83 % SZS output start Proof for theBenchmark % 5.09/1.83 Assumed formulas after preprocessing and simplification: % 5.09/1.83 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (subset_complement(v1, v3) = v4 & the_carrier(v0) = v1 & powerset(v1) = v2 & 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(empty_set) & element(v5, v1) & element(v3, v2) & one_sorted_str(v7) & one_sorted_str(v6) & one_sorted_str(v0) & ~ empty(v8) & ~ empty_carrier(v6) & ~ empty_carrier(v0) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v9 = empty_set | ~ (subset_complement(v9, v11) = v12) | ~ (powerset(v9) = v10) | ~ element(v13, v9) | ~ element(v11, v10) | in(v13, v12) | in(v13, v11)) & ! [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] : ( ~ (subset_complement(v9, v11) = v12) | ~ in(v10, v12) | ~ in(v10, v11) | ? [v13] : (powerset(v9) = v13 & ~ element(v11, v13))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (powerset(v11) = v12) | ~ in(v9, v10) | ~ empty(v11) | ~ element(v10, v12)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (powerset(v11) = v12) | ~ in(v9, v10) | ~ element(v10, v12) | element(v9, v11)) & ! [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] : ( ~ (subset_complement(v9, v10) = v11) | ? [v12] : (powerset(v9) = v12 & ( ~ element(v10, v12) | element(v11, v12)))) & ! [v9] : ! [v10] : ! [v11] : ( ~ (powerset(v10) = v11) | ~ element(v9, v11) | subset(v9, v10)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (powerset(v10) = v11) | ~ subset(v9, v10) | element(v9, v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (powerset(v9) = v10) | ~ v1_membered(v9) | ~ element(v11, v10) | v1_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (powerset(v9) = v10) | ~ v2_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) | ~ v3_membered(v9) | ~ element(v11, v10) | v1_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) | v3_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (powerset(v9) = v10) | ~ v4_membered(v9) | ~ element(v11, v10) | v1_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) | v3_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (powerset(v9) = v10) | ~ v4_membered(v9) | ~ element(v11, v10) | v4_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (powerset(v9) = v10) | ~ v5_membered(v9) | ~ element(v11, v10) | v1_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) | v3_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) | v5_membered(v11)) & ! [v9] : ! [v10] : (v10 = v9 | ~ empty(v10) | ~ empty(v9)) & ! [v9] : ! [v10] : ( ~ (the_carrier(v9) = v10) | ~ empty(v10) | ~ one_sorted_str(v9) | empty_carrier(v9)) & ! [v9] : ! [v10] : ( ~ (the_carrier(v9) = v10) | ~ one_sorted_str(v9) | empty_carrier(v9) | ? [v11] : ? [v12] : (powerset(v10) = v11 & element(v12, v11) & ~ empty(v12))) & ! [v9] : ! [v10] : ( ~ in(v10, v9) | ~ in(v9, v10)) & ! [v9] : ! [v10] : ( ~ in(v9, v10) | ~ empty(v10)) & ! [v9] : ! [v10] : ( ~ in(v9, v10) | element(v9, v10)) & ! [v9] : ! [v10] : ( ~ v1_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] : ( ~ 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] : ( ~ 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] : ( ~ 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] : ( ~ element(v9, v10) | in(v9, v10) | empty(v10)) & ! [v9] : (v9 = empty_set | ~ empty(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] : ( ~ 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] : ? [v10] : element(v10, v9) & ? [v9] : subset(v9, v9) & ((in(v5, v4) & in(v5, v3)) | ( ~ in(v5, v4) & ~ in(v5, v3)))) % 5.17/1.88 | 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: % 5.17/1.88 | (1) subset_complement(all_0_7_7, all_0_5_5) = all_0_4_4 & the_carrier(all_0_8_8) = all_0_7_7 & powerset(all_0_7_7) = all_0_6_6 & 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(empty_set) & element(all_0_3_3, all_0_7_7) & element(all_0_5_5, all_0_6_6) & one_sorted_str(all_0_1_1) & one_sorted_str(all_0_2_2) & one_sorted_str(all_0_8_8) & ~ empty(all_0_0_0) & ~ empty_carrier(all_0_2_2) & ~ empty_carrier(all_0_8_8) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v0 = empty_set | ~ (subset_complement(v0, v2) = v3) | ~ (powerset(v0) = v1) | ~ element(v4, v0) | ~ element(v2, v1) | in(v4, v3) | in(v4, v2)) & ! [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] : ( ~ (subset_complement(v0, v2) = v3) | ~ in(v1, v3) | ~ in(v1, v2) | ? [v4] : (powerset(v0) = v4 & ~ element(v2, v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ in(v0, v1) | ~ empty(v2) | ~ element(v1, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ in(v0, v1) | ~ element(v1, v3) | element(v0, v2)) & ! [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] : ( ~ (subset_complement(v0, v1) = v2) | ? [v3] : (powerset(v0) = v3 & ( ~ element(v1, v3) | element(v2, v3)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ element(v0, v2) | subset(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v1_membered(v0) | ~ element(v2, v1) | v1_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v2_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) | ~ v3_membered(v0) | ~ element(v2, v1) | v1_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) | v3_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v4_membered(v0) | ~ element(v2, v1) | v1_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) | v3_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v4_membered(v0) | ~ element(v2, v1) | v4_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v5_membered(v0) | ~ element(v2, v1) | v1_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) | v3_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) | v5_membered(v2)) & ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) & ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ empty(v1) | ~ one_sorted_str(v0) | empty_carrier(v0)) & ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ one_sorted_str(v0) | empty_carrier(v0) | ? [v2] : ? [v3] : (powerset(v1) = v2 & element(v3, v2) & ~ empty(v3))) & ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ( ~ in(v0, v1) | ~ empty(v1)) & ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1)) & ! [v0] : ! [v1] : ( ~ v1_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] : ( ~ 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] : ( ~ 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] : ( ~ 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] : ( ~ element(v0, v1) | in(v0, v1) | empty(v1)) & ! [v0] : (v0 = empty_set | ~ empty(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] : ( ~ 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] : ? [v1] : element(v1, v0) & ? [v0] : subset(v0, v0) & ((in(all_0_3_3, all_0_4_4) & in(all_0_3_3, all_0_5_5)) | ( ~ in(all_0_3_3, all_0_4_4) & ~ in(all_0_3_3, all_0_5_5))) % 5.17/1.89 | % 5.17/1.89 | Applying alpha-rule on (1) yields: % 5.17/1.89 | (2) ! [v0] : ! [v1] : ( ~ v4_membered(v0) | ~ element(v1, v0) | v1_xcmplx_0(v1)) % 5.17/1.90 | (3) ! [v0] : ! [v1] : ( ~ v5_membered(v0) | ~ element(v1, v0) | v1_rat_1(v1)) % 5.17/1.90 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v4_membered(v0) | ~ element(v2, v1) | v2_membered(v2)) % 5.17/1.90 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset_complement(v3, v2) = v1) | ~ (subset_complement(v3, v2) = v0)) % 5.17/1.90 | (6) ? [v0] : subset(v0, v0) % 5.17/1.90 | (7) ! [v0] : ! [v1] : ( ~ element(v0, v1) | in(v0, v1) | empty(v1)) % 5.17/1.90 | (8) v2_membered(empty_set) % 5.17/1.90 | (9) ! [v0] : ( ~ v2_membered(v0) | v1_membered(v0)) % 5.17/1.90 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v3_membered(v0) | ~ element(v2, v1) | v3_membered(v2)) % 5.17/1.90 | (11) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_complement(v0, v1) = v2) | ? [v3] : (powerset(v0) = v3 & ( ~ element(v1, v3) | element(v2, v3)))) % 5.17/1.90 | (12) ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ empty(v1) | ~ one_sorted_str(v0) | empty_carrier(v0)) % 5.17/1.90 | (13) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v3_membered(v0) | ~ element(v2, v1) | v1_membered(v2)) % 5.17/1.90 | (14) ! [v0] : ! [v1] : ( ~ v2_membered(v0) | ~ element(v1, v0) | v1_xreal_0(v1)) % 5.17/1.90 | (15) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v4_membered(v0) | ~ element(v2, v1) | v4_membered(v2)) % 5.17/1.90 | (16) ! [v0] : ! [v1] : ( ~ v4_membered(v0) | ~ element(v1, v0) | v1_int_1(v1)) % 5.17/1.90 | (17) one_sorted_str(all_0_2_2) % 5.17/1.90 | (18) ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ one_sorted_str(v0) | empty_carrier(v0) | ? [v2] : ? [v3] : (powerset(v1) = v2 & element(v3, v2) & ~ empty(v3))) % 5.17/1.90 | (19) ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1)) % 5.17/1.90 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (subset_complement(v0, v2) = v3) | ~ (subset_complement(v0, v1) = v2) | ? [v4] : (powerset(v0) = v4 & ~ element(v1, v4))) % 5.17/1.90 | (21) ! [v0] : ! [v1] : ( ~ v4_membered(v0) | ~ element(v1, v0) | v1_rat_1(v1)) % 5.17/1.90 | (22) v2_membered(all_0_0_0) % 5.17/1.90 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ in(v0, v1) | ~ element(v1, v3) | element(v0, v2)) % 5.17/1.90 | (24) ~ empty_carrier(all_0_2_2) % 5.17/1.90 | (25) ! [v0] : ! [v1] : ( ~ v5_membered(v0) | ~ element(v1, v0) | v1_xcmplx_0(v1)) % 5.17/1.90 | (26) ! [v0] : ! [v1] : ( ~ v3_membered(v0) | ~ element(v1, v0) | v1_xreal_0(v1)) % 5.17/1.90 | (27) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v5_membered(v0) | ~ element(v2, v1) | v3_membered(v2)) % 5.17/1.90 | (28) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) % 5.17/1.90 | (29) ! [v0] : (v0 = empty_set | ~ empty(v0)) % 5.17/1.90 | (30) ! [v0] : ! [v1] : ( ~ v2_membered(v0) | ~ element(v1, v0) | v1_xcmplx_0(v1)) % 5.17/1.90 | (31) v1_membered(all_0_0_0) % 5.17/1.90 | (32) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v5_membered(v0) | ~ element(v2, v1) | v1_membered(v2)) % 5.17/1.90 | (33) the_carrier(all_0_8_8) = all_0_7_7 % 5.17/1.90 | (34) ! [v0] : ( ~ empty(v0) | v4_membered(v0)) % 5.17/1.90 | (35) (in(all_0_3_3, all_0_4_4) & in(all_0_3_3, all_0_5_5)) | ( ~ in(all_0_3_3, all_0_4_4) & ~ in(all_0_3_3, all_0_5_5)) % 5.17/1.90 | (36) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v3_membered(v0) | ~ element(v2, v1) | v2_membered(v2)) % 5.17/1.90 | (37) ~ empty_carrier(all_0_8_8) % 5.17/1.90 | (38) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) % 5.17/1.90 | (39) ! [v0] : ! [v1] : ( ~ v5_membered(v0) | ~ element(v1, v0) | v1_xreal_0(v1)) % 5.17/1.90 | (40) ! [v0] : ( ~ empty(v0) | v5_membered(v0)) % 5.17/1.90 | (41) v4_membered(empty_set) % 5.17/1.91 | (42) ! [v0] : ! [v1] : ( ~ v5_membered(v0) | ~ element(v1, v0) | natural(v1)) % 5.17/1.91 | (43) ! [v0] : ! [v1] : ( ~ in(v0, v1) | ~ empty(v1)) % 5.17/1.91 | (44) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v4_membered(v0) | ~ element(v2, v1) | v3_membered(v2)) % 5.17/1.91 | (45) ! [v0] : ! [v1] : ( ~ v3_membered(v0) | ~ element(v1, v0) | v1_xcmplx_0(v1)) % 5.17/1.91 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_complement(v0, v2) = v3) | ~ in(v1, v3) | ~ in(v1, v2) | ? [v4] : (powerset(v0) = v4 & ~ element(v2, v4))) % 5.17/1.91 | (47) ! [v0] : ! [v1] : ( ~ v1_membered(v0) | ~ element(v1, v0) | v1_xcmplx_0(v1)) % 5.17/1.91 | (48) v4_membered(all_0_0_0) % 5.17/1.91 | (49) one_sorted_str(all_0_8_8) % 5.17/1.91 | (50) element(all_0_5_5, all_0_6_6) % 5.17/1.91 | (51) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2)) % 5.17/1.91 | (52) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ element(v0, v2) | subset(v0, v1)) % 5.17/1.91 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v0 = empty_set | ~ (subset_complement(v0, v2) = v3) | ~ (powerset(v0) = v1) | ~ element(v4, v0) | ~ element(v2, v1) | in(v4, v3) | in(v4, v2)) % 5.17/1.91 | (54) powerset(all_0_7_7) = all_0_6_6 % 5.17/1.91 | (55) ! [v0] : ( ~ v3_membered(v0) | v2_membered(v0)) % 5.17/1.91 | (56) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) % 5.17/1.91 | (57) ! [v0] : ( ~ v5_membered(v0) | v4_membered(v0)) % 5.17/1.91 | (58) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v5_membered(v0) | ~ element(v2, v1) | v4_membered(v2)) % 5.17/1.91 | (59) one_sorted_str(all_0_1_1) % 5.17/1.91 | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ in(v0, v1) | ~ empty(v2) | ~ element(v1, v3)) % 5.17/1.91 | (61) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v2_membered(v0) | ~ element(v2, v1) | v1_membered(v2)) % 5.17/1.91 | (62) ! [v0] : ( ~ v4_membered(v0) | v3_membered(v0)) % 5.17/1.91 | (63) ~ empty(all_0_0_0) % 5.17/1.91 | (64) ! [v0] : ( ~ empty(v0) | v1_membered(v0)) % 5.17/1.91 | (65) ! [v0] : ( ~ empty(v0) | v2_membered(v0)) % 5.17/1.91 | (66) ! [v0] : ( ~ empty(v0) | v3_membered(v0)) % 5.17/1.91 | (67) v3_membered(all_0_0_0) % 5.17/1.91 | (68) empty(empty_set) % 5.17/1.91 | (69) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v5_membered(v0) | ~ element(v2, v1) | v5_membered(v2)) % 5.17/1.91 | (70) v5_membered(empty_set) % 5.17/1.91 | (71) v5_membered(all_0_0_0) % 5.17/1.91 | (72) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (the_carrier(v2) = v1) | ~ (the_carrier(v2) = v0)) % 5.17/1.91 | (73) subset_complement(all_0_7_7, all_0_5_5) = all_0_4_4 % 5.17/1.91 | (74) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v1_membered(v0) | ~ element(v2, v1) | v1_membered(v2)) % 5.17/1.91 | (75) ? [v0] : ? [v1] : element(v1, v0) % 5.17/1.91 | (76) v1_membered(empty_set) % 5.17/1.91 | (77) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v2_membered(v0) | ~ element(v2, v1) | v2_membered(v2)) % 5.17/1.91 | (78) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v5_membered(v0) | ~ element(v2, v1) | v2_membered(v2)) % 5.17/1.91 | (79) element(all_0_3_3, all_0_7_7) % 5.17/1.91 | (80) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v4_membered(v0) | ~ element(v2, v1) | v1_membered(v2)) % 5.17/1.91 | (81) v3_membered(empty_set) % 5.17/1.91 | (82) ! [v0] : ! [v1] : ( ~ v5_membered(v0) | ~ element(v1, v0) | v1_int_1(v1)) % 5.17/1.91 | (83) ! [v0] : ! [v1] : ( ~ v3_membered(v0) | ~ element(v1, v0) | v1_rat_1(v1)) % 5.17/1.91 | (84) ! [v0] : ! [v1] : ( ~ v4_membered(v0) | ~ element(v1, v0) | v1_xreal_0(v1)) % 5.17/1.92 | % 5.17/1.92 | Instantiating formula (11) with all_0_4_4, all_0_5_5, all_0_7_7 and discharging atoms subset_complement(all_0_7_7, all_0_5_5) = all_0_4_4, yields: % 5.51/1.92 | (85) ? [v0] : (powerset(all_0_7_7) = v0 & ( ~ element(all_0_5_5, v0) | element(all_0_4_4, v0))) % 5.51/1.92 | % 5.51/1.92 | Instantiating formula (53) with all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7 and discharging atoms subset_complement(all_0_7_7, all_0_5_5) = all_0_4_4, powerset(all_0_7_7) = all_0_6_6, element(all_0_3_3, all_0_7_7), element(all_0_5_5, all_0_6_6), yields: % 5.51/1.92 | (86) all_0_7_7 = empty_set | in(all_0_3_3, all_0_4_4) | in(all_0_3_3, all_0_5_5) % 5.51/1.92 | % 5.51/1.92 | Instantiating formula (18) 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), ~ empty_carrier(all_0_8_8), yields: % 5.51/1.92 | (87) ? [v0] : ? [v1] : (powerset(all_0_7_7) = v0 & element(v1, v0) & ~ empty(v1)) % 5.51/1.92 | % 5.51/1.92 | Instantiating (85) with all_13_0_12 yields: % 5.51/1.92 | (88) powerset(all_0_7_7) = all_13_0_12 & ( ~ element(all_0_5_5, all_13_0_12) | element(all_0_4_4, all_13_0_12)) % 5.51/1.92 | % 5.51/1.92 | Applying alpha-rule on (88) yields: % 5.51/1.92 | (89) powerset(all_0_7_7) = all_13_0_12 % 5.51/1.92 | (90) ~ element(all_0_5_5, all_13_0_12) | element(all_0_4_4, all_13_0_12) % 5.51/1.92 | % 5.51/1.92 | Instantiating (87) with all_15_0_13, all_15_1_14 yields: % 5.51/1.92 | (91) powerset(all_0_7_7) = all_15_1_14 & element(all_15_0_13, all_15_1_14) & ~ empty(all_15_0_13) % 5.51/1.92 | % 5.51/1.92 | Applying alpha-rule on (91) yields: % 5.51/1.92 | (92) powerset(all_0_7_7) = all_15_1_14 % 5.51/1.92 | (93) element(all_15_0_13, all_15_1_14) % 5.51/1.92 | (94) ~ empty(all_15_0_13) % 5.51/1.92 | % 5.51/1.92 | Instantiating formula (56) with all_0_7_7, all_15_1_14, all_0_6_6 and discharging atoms powerset(all_0_7_7) = all_15_1_14, powerset(all_0_7_7) = all_0_6_6, yields: % 5.51/1.92 | (95) all_15_1_14 = all_0_6_6 % 5.51/1.92 | % 5.51/1.92 | Instantiating formula (56) with all_0_7_7, all_13_0_12, all_15_1_14 and discharging atoms powerset(all_0_7_7) = all_15_1_14, powerset(all_0_7_7) = all_13_0_12, yields: % 5.51/1.92 | (96) all_15_1_14 = all_13_0_12 % 5.51/1.92 | % 5.51/1.92 | Combining equations (95,96) yields a new equation: % 5.51/1.92 | (97) all_13_0_12 = all_0_6_6 % 5.51/1.92 | % 5.51/1.92 | From (97) and (89) follows: % 5.51/1.92 | (54) powerset(all_0_7_7) = all_0_6_6 % 5.51/1.92 | % 5.51/1.92 +-Applying beta-rule and splitting (90), into two cases. % 5.51/1.92 |-Branch one: % 5.51/1.92 | (99) ~ element(all_0_5_5, all_13_0_12) % 5.51/1.92 | % 5.51/1.92 | From (97) and (99) follows: % 5.51/1.92 | (100) ~ element(all_0_5_5, all_0_6_6) % 5.51/1.92 | % 5.51/1.92 | Using (50) and (100) yields: % 5.51/1.92 | (101) $false % 5.51/1.92 | % 5.51/1.92 |-The branch is then unsatisfiable % 5.51/1.92 |-Branch two: % 5.51/1.92 | (102) element(all_0_5_5, all_13_0_12) % 5.51/1.92 | (103) element(all_0_4_4, all_13_0_12) % 5.51/1.92 | % 5.51/1.92 | From (97) and (102) follows: % 5.51/1.92 | (50) element(all_0_5_5, all_0_6_6) % 5.51/1.92 | % 5.51/1.92 +-Applying beta-rule and splitting (35), into two cases. % 5.51/1.92 |-Branch one: % 5.51/1.92 | (105) in(all_0_3_3, all_0_4_4) & in(all_0_3_3, all_0_5_5) % 5.51/1.92 | % 5.51/1.92 | Applying alpha-rule on (105) yields: % 5.51/1.92 | (106) in(all_0_3_3, all_0_4_4) % 5.51/1.93 | (107) in(all_0_3_3, all_0_5_5) % 5.51/1.93 | % 5.51/1.93 | Instantiating formula (46) with all_0_4_4, all_0_5_5, all_0_3_3, all_0_7_7 and discharging atoms subset_complement(all_0_7_7, all_0_5_5) = all_0_4_4, in(all_0_3_3, all_0_4_4), in(all_0_3_3, all_0_5_5), yields: % 5.51/1.93 | (108) ? [v0] : (powerset(all_0_7_7) = v0 & ~ element(all_0_5_5, v0)) % 5.51/1.93 | % 5.51/1.93 | Instantiating (108) with all_44_0_15 yields: % 5.51/1.93 | (109) powerset(all_0_7_7) = all_44_0_15 & ~ element(all_0_5_5, all_44_0_15) % 5.51/1.93 | % 5.51/1.93 | Applying alpha-rule on (109) yields: % 5.51/1.93 | (110) powerset(all_0_7_7) = all_44_0_15 % 5.51/1.93 | (111) ~ element(all_0_5_5, all_44_0_15) % 5.51/1.93 | % 5.51/1.93 | Instantiating formula (56) with all_0_7_7, all_44_0_15, all_0_6_6 and discharging atoms powerset(all_0_7_7) = all_44_0_15, powerset(all_0_7_7) = all_0_6_6, yields: % 5.51/1.93 | (112) all_44_0_15 = all_0_6_6 % 5.51/1.93 | % 5.51/1.93 | From (112) and (111) follows: % 5.51/1.93 | (100) ~ element(all_0_5_5, all_0_6_6) % 5.51/1.93 | % 5.51/1.93 | Using (50) and (100) yields: % 5.51/1.93 | (101) $false % 5.51/1.93 | % 5.51/1.93 |-The branch is then unsatisfiable % 5.51/1.93 |-Branch two: % 5.51/1.93 | (115) ~ in(all_0_3_3, all_0_4_4) & ~ in(all_0_3_3, all_0_5_5) % 5.51/1.93 | % 5.51/1.93 | Applying alpha-rule on (115) yields: % 5.51/1.93 | (116) ~ in(all_0_3_3, all_0_4_4) % 5.51/1.93 | (117) ~ in(all_0_3_3, all_0_5_5) % 5.51/1.93 | % 5.51/1.93 +-Applying beta-rule and splitting (86), into two cases. % 5.51/1.93 |-Branch one: % 5.51/1.93 | (106) in(all_0_3_3, all_0_4_4) % 5.51/1.93 | % 5.51/1.93 | Using (106) and (116) yields: % 5.51/1.93 | (101) $false % 5.51/1.93 | % 5.51/1.93 |-The branch is then unsatisfiable % 5.51/1.93 |-Branch two: % 5.51/1.93 | (116) ~ in(all_0_3_3, all_0_4_4) % 5.51/1.93 | (121) all_0_7_7 = empty_set | in(all_0_3_3, all_0_5_5) % 5.51/1.93 | % 5.51/1.93 +-Applying beta-rule and splitting (121), into two cases. % 5.51/1.93 |-Branch one: % 5.51/1.93 | (107) in(all_0_3_3, all_0_5_5) % 5.51/1.93 | % 5.51/1.93 | Using (107) and (117) yields: % 5.51/1.93 | (101) $false % 5.51/1.93 | % 5.51/1.93 |-The branch is then unsatisfiable % 5.51/1.93 |-Branch two: % 5.51/1.93 | (117) ~ in(all_0_3_3, all_0_5_5) % 5.51/1.93 | (125) all_0_7_7 = empty_set % 5.51/1.93 | % 5.51/1.93 | From (125) and (33) follows: % 5.51/1.93 | (126) the_carrier(all_0_8_8) = empty_set % 5.51/1.93 | % 5.51/1.93 | Instantiating formula (12) with empty_set, all_0_8_8 and discharging atoms the_carrier(all_0_8_8) = empty_set, empty(empty_set), one_sorted_str(all_0_8_8), ~ empty_carrier(all_0_8_8), yields: % 5.51/1.93 | (101) $false % 5.51/1.93 | % 5.51/1.93 |-The branch is then unsatisfiable % 5.51/1.93 % SZS output end Proof for theBenchmark % 5.51/1.93 % 5.51/1.93 1328ms %------------------------------------------------------------------------------