%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU317+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n015.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 08:48:47 EDT 2022 % Result : Theorem 6.99s 2.33s % Output : Proof 12.97s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.14 % Problem : SEU317+1 : TPTP v8.1.0. Released v3.3.0. % 0.04/0.14 % Command : ePrincess-casc -timeout=%d %s % 0.15/0.36 % Computer : n015.cluster.edu % 0.15/0.36 % Model : x86_64 x86_64 % 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.36 % Memory : 8042.1875MB % 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.36 % CPULimit : 300 % 0.15/0.36 % WCLimit : 600 % 0.15/0.36 % DateTime : Sat Jun 18 19:22:13 EDT 2022 % 0.15/0.36 % CPUTime : % 0.48/0.62 ____ _ % 0.48/0.62 ___ / __ \_____(_)___ ________ __________ % 0.48/0.62 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.48/0.62 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.48/0.62 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.48/0.62 % 0.48/0.62 A Theorem Prover for First-Order Logic % 0.48/0.62 (ePrincess v.1.0) % 0.48/0.62 % 0.48/0.62 (c) Philipp Rümmer, 2009-2015 % 0.48/0.62 (c) Peter Backeman, 2014-2015 % 0.48/0.62 (contributions by Angelo Brillout, Peter Baumgartner) % 0.48/0.62 Free software under GNU Lesser General Public License (LGPL). % 0.48/0.62 Bug reports to peter@backeman.se % 0.48/0.62 % 0.48/0.62 For more information, visit http://user.uu.se/~petba168/breu/ % 0.48/0.62 % 0.48/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.68/0.67 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.68/0.99 Prover 0: Preprocessing ... % 2.40/1.25 Prover 0: Warning: ignoring some quantifiers % 2.47/1.28 Prover 0: Constructing countermodel ... % 4.97/1.86 Prover 0: gave up % 4.97/1.86 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 4.97/1.90 Prover 1: Preprocessing ... % 5.59/2.03 Prover 1: Warning: ignoring some quantifiers % 5.59/2.04 Prover 1: Constructing countermodel ... % 6.99/2.33 Prover 1: proved (472ms) % 6.99/2.33 % 6.99/2.33 No countermodel exists, formula is valid % 6.99/2.33 % SZS status Theorem for theBenchmark % 6.99/2.33 % 6.99/2.33 Generating proof ... Warning: ignoring some quantifiers % 12.35/3.60 found it (size 55) % 12.35/3.60 % 12.35/3.60 % SZS output start Proof for theBenchmark % 12.35/3.60 Assumed formulas after preprocessing and simplification: % 12.35/3.60 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ( ~ (v7 = 0) & ~ (v5 = 0) & one_sorted_str(v8) = 0 & the_carrier(v0) = v1 & topstr_closure(v0, v3) = v4 & top_str(v9) = 0 & top_str(v0) = 0 & subset(v3, v4) = v5 & powerset(v1) = v2 & empty(v6) = v7 & empty(empty_set) = 0 & v5_membered(v6) = 0 & v5_membered(empty_set) = 0 & v4_membered(v6) = 0 & v4_membered(empty_set) = 0 & v3_membered(v6) = 0 & v3_membered(empty_set) = 0 & v2_membered(v6) = 0 & v2_membered(empty_set) = 0 & v1_membered(v6) = 0 & v1_membered(empty_set) = 0 & element(v3, v2) = 0 & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (the_carrier(v10) = v12) | ~ (topstr_closure(v10, v11) = v14) | ~ (powerset(v12) = v13) | ~ (element(v14, v13) = v15) | ? [v16] : ? [v17] : (top_str(v10) = v16 & element(v11, v13) = v17 & ( ~ (v17 = 0) | ~ (v16 = 0)))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (powerset(v11) = v12) | ~ (element(v10, v12) = v13) | ? [v14] : ( ~ (v14 = 0) & subset(v10, v11) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (closed_subset(v13, v12) = v11) | ~ (closed_subset(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (topstr_closure(v13, v12) = v11) | ~ (topstr_closure(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (subset(v13, v12) = v11) | ~ (subset(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (element(v13, v12) = v11) | ~ (element(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (in(v13, v12) = v11) | ~ (in(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (powerset(v12) = v13) | ~ (element(v11, v13) = 0) | ~ (in(v10, v11) = 0) | element(v10, v12) = 0) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (powerset(v12) = v13) | ~ (element(v11, v13) = 0) | ~ (in(v10, v11) = 0) | ? [v14] : ( ~ (v14 = 0) & empty(v12) = v14)) & ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (subset(v10, v11) = v12) | ? [v13] : ? [v14] : ( ~ (v14 = 0) & in(v13, v11) = v14 & in(v13, v10) = 0)) & ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (v1_membered(v10) = 0) | ~ (v1_xcmplx_0(v11) = v12) | ? [v13] : ( ~ (v13 = 0) & element(v11, v10) = v13)) & ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (in(v10, v11) = v12) | ? [v13] : ? [v14] : (empty(v11) = v14 & element(v10, v11) = v13 & ( ~ (v13 = 0) | v14 = 0))) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (one_sorted_str(v12) = v11) | ~ (one_sorted_str(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (the_carrier(v12) = v11) | ~ (the_carrier(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (top_str(v12) = v11) | ~ (top_str(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (powerset(v12) = v11) | ~ (powerset(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (empty(v12) = v11) | ~ (empty(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (v5_membered(v12) = v11) | ~ (v5_membered(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (natural(v12) = v11) | ~ (natural(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (v4_membered(v12) = v11) | ~ (v4_membered(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (v1_int_1(v12) = v11) | ~ (v1_int_1(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (v3_membered(v12) = v11) | ~ (v3_membered(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (v1_rat_1(v12) = v11) | ~ (v1_rat_1(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (v2_membered(v12) = v11) | ~ (v2_membered(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (v1_xreal_0(v12) = v11) | ~ (v1_xreal_0(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (v1_membered(v12) = v11) | ~ (v1_membered(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (v1_xcmplx_0(v12) = v11) | ~ (v1_xcmplx_0(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (subset(v10, v11) = 0) | ~ (in(v12, v10) = 0) | in(v12, v11) = 0) & ! [v10] : ! [v11] : ! [v12] : ( ~ (powerset(v11) = v12) | ~ (element(v10, v12) = 0) | subset(v10, v11) = 0) & ! [v10] : ! [v11] : ! [v12] : ( ~ (v5_membered(v10) = 0) | ~ (natural(v11) = v12) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : (v1_int_1(v11) = v16 & v1_rat_1(v11) = v17 & v1_xreal_0(v11) = v15 & v1_xcmplx_0(v11) = v14 & element(v11, v10) = v13 & ( ~ (v13 = 0) | (v17 = 0 & v16 = 0 & v15 = 0 & v14 = 0 & v12 = 0)))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (v4_membered(v10) = 0) | ~ (v1_int_1(v11) = v12) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : (v1_rat_1(v11) = v16 & v1_xreal_0(v11) = v15 & v1_xcmplx_0(v11) = v14 & element(v11, v10) = v13 & ( ~ (v13 = 0) | (v16 = 0 & v15 = 0 & v14 = 0 & v12 = 0)))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (v3_membered(v10) = 0) | ~ (v1_rat_1(v11) = v12) | ? [v13] : ? [v14] : ? [v15] : (v1_xreal_0(v11) = v15 & v1_xcmplx_0(v11) = v14 & element(v11, v10) = v13 & ( ~ (v13 = 0) | (v15 = 0 & v14 = 0 & v12 = 0)))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (v2_membered(v10) = 0) | ~ (v1_xreal_0(v11) = v12) | ? [v13] : ? [v14] : (v1_xcmplx_0(v11) = v14 & element(v11, v10) = v13 & ( ~ (v13 = 0) | (v14 = 0 & v12 = 0)))) & ! [v10] : ! [v11] : (v11 = v10 | ~ (empty(v11) = 0) | ~ (empty(v10) = 0)) & ! [v10] : ! [v11] : (v11 = 0 | ~ (one_sorted_str(v10) = v11) | ? [v12] : ( ~ (v12 = 0) & top_str(v10) = v12)) & ! [v10] : ! [v11] : (v11 = 0 | ~ (subset(v10, v10) = v11)) & ! [v10] : ! [v11] : (v11 = 0 | ~ (empty(v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ( ~ (v14 = 0) & powerset(v10) = v12 & empty(v13) = v14 & element(v13, v12) = 0)) & ! [v10] : ! [v11] : ( ~ (powerset(v10) = v11) | ? [v12] : ( ~ (v12 = 0) & empty(v11) = v12)) & ! [v10] : ! [v11] : ( ~ (powerset(v10) = v11) | ? [v12] : (empty(v12) = 0 & element(v12, v11) = 0)) & ! [v10] : ! [v11] : ( ~ (v5_membered(v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : (empty(v10) = v12 & v4_membered(v10) = v16 & v3_membered(v10) = v15 & v2_membered(v10) = v14 & v1_membered(v10) = v13 & ( ~ (v12 = 0) | (v16 = 0 & v15 = 0 & v14 = 0 & v13 = 0 & v11 = 0)))) & ! [v10] : ! [v11] : ( ~ (in(v10, v11) = 0) | element(v10, v11) = 0) & ! [v10] : ! [v11] : ( ~ (in(v10, v11) = 0) | ? [v12] : ( ~ (v12 = 0) & empty(v11) = v12)) & ! [v10] : ! [v11] : ( ~ (in(v10, v11) = 0) | ? [v12] : ( ~ (v12 = 0) & in(v11, v10) = v12)) & ! [v10] : (v10 = empty_set | ~ (empty(v10) = 0)) & ! [v10] : ( ~ (top_str(v10) = 0) | ? [v11] : ? [v12] : (the_carrier(v10) = v11 & powerset(v11) = v12 & ! [v13] : ( ~ (element(v13, v12) = 0) | ? [v14] : (topstr_closure(v10, v13) = v14 & ! [v15] : ! [v16] : (v16 = 0 | ~ (in(v15, v14) = v16) | ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ((v20 = 0 & v19 = 0 & v18 = 0 & ~ (v21 = 0) & closed_subset(v17, v10) = 0 & subset(v13, v17) = 0 & element(v17, v12) = 0 & in(v15, v17) = v21) | ( ~ (v17 = 0) & in(v15, v11) = v17))) & ! [v15] : ! [v16] : ( ~ (element(v16, v12) = 0) | ~ (in(v15, v14) = 0) | ? [v17] : ? [v18] : ? [v19] : (( ~ (v17 = 0) & in(v15, v11) = v17) | (closed_subset(v16, v10) = v17 & subset(v13, v16) = v18 & in(v15, v16) = v19 & ( ~ (v18 = 0) | ~ (v17 = 0) | v19 = 0)))))))) & ! [v10] : ( ~ (v5_membered(v10) = 0) | v4_membered(v10) = 0) & ! [v10] : ( ~ (v5_membered(v10) = 0) | ? [v11] : (powerset(v10) = v11 & ! [v12] : ( ~ (element(v12, v11) = 0) | (v5_membered(v12) = 0 & v4_membered(v12) = 0 & v3_membered(v12) = 0 & v2_membered(v12) = 0 & v1_membered(v12) = 0)))) & ! [v10] : ( ~ (v4_membered(v10) = 0) | v3_membered(v10) = 0) & ! [v10] : ( ~ (v4_membered(v10) = 0) | ? [v11] : (powerset(v10) = v11 & ! [v12] : ( ~ (element(v12, v11) = 0) | (v4_membered(v12) = 0 & v3_membered(v12) = 0 & v2_membered(v12) = 0 & v1_membered(v12) = 0)))) & ! [v10] : ( ~ (v3_membered(v10) = 0) | v2_membered(v10) = 0) & ! [v10] : ( ~ (v3_membered(v10) = 0) | ? [v11] : (powerset(v10) = v11 & ! [v12] : ( ~ (element(v12, v11) = 0) | (v3_membered(v12) = 0 & v2_membered(v12) = 0 & v1_membered(v12) = 0)))) & ! [v10] : ( ~ (v2_membered(v10) = 0) | v1_membered(v10) = 0) & ! [v10] : ( ~ (v2_membered(v10) = 0) | ? [v11] : (powerset(v10) = v11 & ! [v12] : ( ~ (element(v12, v11) = 0) | (v2_membered(v12) = 0 & v1_membered(v12) = 0)))) & ! [v10] : ( ~ (v1_membered(v10) = 0) | ? [v11] : (powerset(v10) = v11 & ! [v12] : ( ~ (element(v12, v11) = 0) | v1_membered(v12) = 0))) & ? [v10] : ? [v11] : element(v11, v10) = 0) % 12.68/3.66 | 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, all_0_9_9 yields: % 12.68/3.66 | (1) ~ (all_0_2_2 = 0) & ~ (all_0_4_4 = 0) & one_sorted_str(all_0_1_1) = 0 & the_carrier(all_0_9_9) = all_0_8_8 & topstr_closure(all_0_9_9, all_0_6_6) = all_0_5_5 & top_str(all_0_0_0) = 0 & top_str(all_0_9_9) = 0 & subset(all_0_6_6, all_0_5_5) = all_0_4_4 & powerset(all_0_8_8) = all_0_7_7 & empty(all_0_3_3) = all_0_2_2 & empty(empty_set) = 0 & v5_membered(all_0_3_3) = 0 & v5_membered(empty_set) = 0 & v4_membered(all_0_3_3) = 0 & v4_membered(empty_set) = 0 & v3_membered(all_0_3_3) = 0 & v3_membered(empty_set) = 0 & v2_membered(all_0_3_3) = 0 & v2_membered(empty_set) = 0 & v1_membered(all_0_3_3) = 0 & v1_membered(empty_set) = 0 & element(all_0_6_6, all_0_7_7) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (the_carrier(v0) = v2) | ~ (topstr_closure(v0, v1) = v4) | ~ (powerset(v2) = v3) | ~ (element(v4, v3) = v5) | ? [v6] : ? [v7] : (top_str(v0) = v6 & element(v1, v3) = v7 & ( ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (closed_subset(v3, v2) = v1) | ~ (closed_subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (topstr_closure(v3, v2) = v1) | ~ (topstr_closure(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | element(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (v1_membered(v0) = 0) | ~ (v1_xcmplx_0(v1) = v2) | ? [v3] : ( ~ (v3 = 0) & element(v1, v0) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v0, v1) = v2) | ? [v3] : ? [v4] : (empty(v1) = v4 & element(v0, v1) = v3 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (one_sorted_str(v2) = v1) | ~ (one_sorted_str(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (the_carrier(v2) = v1) | ~ (the_carrier(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (top_str(v2) = v1) | ~ (top_str(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (v5_membered(v2) = v1) | ~ (v5_membered(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (natural(v2) = v1) | ~ (natural(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (v4_membered(v2) = v1) | ~ (v4_membered(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (v1_int_1(v2) = v1) | ~ (v1_int_1(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (v3_membered(v2) = v1) | ~ (v3_membered(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (v1_rat_1(v2) = v1) | ~ (v1_rat_1(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (v2_membered(v2) = v1) | ~ (v2_membered(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (v1_xreal_0(v2) = v1) | ~ (v1_xreal_0(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (v1_membered(v2) = v1) | ~ (v1_membered(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (v1_xcmplx_0(v2) = v1) | ~ (v1_xcmplx_0(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | subset(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (v5_membered(v0) = 0) | ~ (natural(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (v1_int_1(v1) = v6 & v1_rat_1(v1) = v7 & v1_xreal_0(v1) = v5 & v1_xcmplx_0(v1) = v4 & element(v1, v0) = v3 & ( ~ (v3 = 0) | (v7 = 0 & v6 = 0 & v5 = 0 & v4 = 0 & v2 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (v4_membered(v0) = 0) | ~ (v1_int_1(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (v1_rat_1(v1) = v6 & v1_xreal_0(v1) = v5 & v1_xcmplx_0(v1) = v4 & element(v1, v0) = v3 & ( ~ (v3 = 0) | (v6 = 0 & v5 = 0 & v4 = 0 & v2 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (v3_membered(v0) = 0) | ~ (v1_rat_1(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (v1_xreal_0(v1) = v5 & v1_xcmplx_0(v1) = v4 & element(v1, v0) = v3 & ( ~ (v3 = 0) | (v5 = 0 & v4 = 0 & v2 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (v2_membered(v0) = 0) | ~ (v1_xreal_0(v1) = v2) | ? [v3] : ? [v4] : (v1_xcmplx_0(v1) = v4 & element(v1, v0) = v3 & ( ~ (v3 = 0) | (v4 = 0 & v2 = 0)))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (one_sorted_str(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & top_str(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (empty(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v0) = v2 & empty(v3) = v4 & element(v3, v2) = 0)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (empty(v2) = 0 & element(v2, v1) = 0)) & ! [v0] : ! [v1] : ( ~ (v5_membered(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (empty(v0) = v2 & v4_membered(v0) = v6 & v3_membered(v0) = v5 & v2_membered(v0) = v4 & v1_membered(v0) = v3 & ( ~ (v2 = 0) | (v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & v1 = 0)))) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | element(v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) & ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0)) & ! [v0] : ( ~ (top_str(v0) = 0) | ? [v1] : ? [v2] : (the_carrier(v0) = v1 & powerset(v1) = v2 & ! [v3] : ( ~ (element(v3, v2) = 0) | ? [v4] : (topstr_closure(v0, v3) = v4 & ! [v5] : ! [v6] : (v6 = 0 | ~ (in(v5, v4) = v6) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ((v10 = 0 & v9 = 0 & v8 = 0 & ~ (v11 = 0) & closed_subset(v7, v0) = 0 & subset(v3, v7) = 0 & element(v7, v2) = 0 & in(v5, v7) = v11) | ( ~ (v7 = 0) & in(v5, v1) = v7))) & ! [v5] : ! [v6] : ( ~ (element(v6, v2) = 0) | ~ (in(v5, v4) = 0) | ? [v7] : ? [v8] : ? [v9] : (( ~ (v7 = 0) & in(v5, v1) = v7) | (closed_subset(v6, v0) = v7 & subset(v3, v6) = v8 & in(v5, v6) = v9 & ( ~ (v8 = 0) | ~ (v7 = 0) | v9 = 0)))))))) & ! [v0] : ( ~ (v5_membered(v0) = 0) | v4_membered(v0) = 0) & ! [v0] : ( ~ (v5_membered(v0) = 0) | ? [v1] : (powerset(v0) = v1 & ! [v2] : ( ~ (element(v2, v1) = 0) | (v5_membered(v2) = 0 & v4_membered(v2) = 0 & v3_membered(v2) = 0 & v2_membered(v2) = 0 & v1_membered(v2) = 0)))) & ! [v0] : ( ~ (v4_membered(v0) = 0) | v3_membered(v0) = 0) & ! [v0] : ( ~ (v4_membered(v0) = 0) | ? [v1] : (powerset(v0) = v1 & ! [v2] : ( ~ (element(v2, v1) = 0) | (v4_membered(v2) = 0 & v3_membered(v2) = 0 & v2_membered(v2) = 0 & v1_membered(v2) = 0)))) & ! [v0] : ( ~ (v3_membered(v0) = 0) | v2_membered(v0) = 0) & ! [v0] : ( ~ (v3_membered(v0) = 0) | ? [v1] : (powerset(v0) = v1 & ! [v2] : ( ~ (element(v2, v1) = 0) | (v3_membered(v2) = 0 & v2_membered(v2) = 0 & v1_membered(v2) = 0)))) & ! [v0] : ( ~ (v2_membered(v0) = 0) | v1_membered(v0) = 0) & ! [v0] : ( ~ (v2_membered(v0) = 0) | ? [v1] : (powerset(v0) = v1 & ! [v2] : ( ~ (element(v2, v1) = 0) | (v2_membered(v2) = 0 & v1_membered(v2) = 0)))) & ! [v0] : ( ~ (v1_membered(v0) = 0) | ? [v1] : (powerset(v0) = v1 & ! [v2] : ( ~ (element(v2, v1) = 0) | v1_membered(v2) = 0))) & ? [v0] : ? [v1] : element(v1, v0) = 0 % 12.68/3.67 | % 12.68/3.67 | Applying alpha-rule on (1) yields: % 12.68/3.67 | (2) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v0, v1) = v2) | ? [v3] : ? [v4] : (empty(v1) = v4 & element(v0, v1) = v3 & ( ~ (v3 = 0) | v4 = 0))) % 12.68/3.67 | (3) element(all_0_6_6, all_0_7_7) = 0 % 12.68/3.67 | (4) ! [v0] : ! [v1] : (v1 = 0 | ~ (empty(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v0) = v2 & empty(v3) = v4 & element(v3, v2) = 0)) % 12.68/3.67 | (5) v2_membered(empty_set) = 0 % 12.68/3.67 | (6) top_str(all_0_9_9) = 0 % 12.68/3.67 | (7) subset(all_0_6_6, all_0_5_5) = all_0_4_4 % 12.68/3.67 | (8) empty(empty_set) = 0 % 12.68/3.67 | (9) ! [v0] : ! [v1] : ! [v2] : ( ~ (v5_membered(v0) = 0) | ~ (natural(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (v1_int_1(v1) = v6 & v1_rat_1(v1) = v7 & v1_xreal_0(v1) = v5 & v1_xcmplx_0(v1) = v4 & element(v1, v0) = v3 & ( ~ (v3 = 0) | (v7 = 0 & v6 = 0 & v5 = 0 & v4 = 0 & v2 = 0)))) % 12.68/3.67 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) % 12.68/3.67 | (11) ! [v0] : ( ~ (v3_membered(v0) = 0) | v2_membered(v0) = 0) % 12.68/3.67 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | element(v0, v2) = 0) % 12.68/3.67 | (13) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) % 12.68/3.67 | (14) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (v2_membered(v2) = v1) | ~ (v2_membered(v2) = v0)) % 12.68/3.67 | (15) v1_membered(empty_set) = 0 % 12.68/3.67 | (16) ! [v0] : ( ~ (v5_membered(v0) = 0) | v4_membered(v0) = 0) % 12.68/3.68 | (17) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (top_str(v2) = v1) | ~ (top_str(v2) = v0)) % 12.68/3.68 | (18) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | element(v0, v1) = 0) % 12.68/3.68 | (19) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (v1_xreal_0(v2) = v1) | ~ (v1_xreal_0(v2) = v0)) % 12.68/3.68 | (20) powerset(all_0_8_8) = all_0_7_7 % 12.97/3.68 | (21) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)) % 12.97/3.68 | (22) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0) % 12.97/3.68 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 12.97/3.68 | (24) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0)) % 12.97/3.68 | (25) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (natural(v2) = v1) | ~ (natural(v2) = v0)) % 12.97/3.68 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) % 12.97/3.68 | (27) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (v1_membered(v0) = 0) | ~ (v1_xcmplx_0(v1) = v2) | ? [v3] : ( ~ (v3 = 0) & element(v1, v0) = v3)) % 12.97/3.68 | (28) empty(all_0_3_3) = all_0_2_2 % 12.97/3.68 | (29) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (v5_membered(v2) = v1) | ~ (v5_membered(v2) = v0)) % 12.97/3.68 | (30) v3_membered(empty_set) = 0 % 12.97/3.68 | (31) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) % 12.97/3.68 | (32) v4_membered(empty_set) = 0 % 12.97/3.68 | (33) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (v1_membered(v2) = v1) | ~ (v1_membered(v2) = v0)) % 12.97/3.68 | (34) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0)) % 12.97/3.68 | (35) v2_membered(all_0_3_3) = 0 % 12.97/3.68 | (36) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (v1_xcmplx_0(v2) = v1) | ~ (v1_xcmplx_0(v2) = v0)) % 12.97/3.68 | (37) ! [v0] : ! [v1] : ! [v2] : ( ~ (v3_membered(v0) = 0) | ~ (v1_rat_1(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (v1_xreal_0(v1) = v5 & v1_xcmplx_0(v1) = v4 & element(v1, v0) = v3 & ( ~ (v3 = 0) | (v5 = 0 & v4 = 0 & v2 = 0)))) % 12.97/3.68 | (38) topstr_closure(all_0_9_9, all_0_6_6) = all_0_5_5 % 12.97/3.68 | (39) ! [v0] : ! [v1] : ! [v2] : ( ~ (v4_membered(v0) = 0) | ~ (v1_int_1(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (v1_rat_1(v1) = v6 & v1_xreal_0(v1) = v5 & v1_xcmplx_0(v1) = v4 & element(v1, v0) = v3 & ( ~ (v3 = 0) | (v6 = 0 & v5 = 0 & v4 = 0 & v2 = 0)))) % 12.97/3.68 | (40) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | subset(v0, v1) = 0) % 12.97/3.68 | (41) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) % 12.97/3.68 | (42) v5_membered(all_0_3_3) = 0 % 12.97/3.68 | (43) v5_membered(empty_set) = 0 % 12.97/3.68 | (44) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (v3_membered(v2) = v1) | ~ (v3_membered(v2) = v0)) % 12.97/3.68 | (45) ~ (all_0_2_2 = 0) % 12.97/3.68 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) % 12.97/3.68 | (47) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) % 12.97/3.68 | (48) ! [v0] : ( ~ (v2_membered(v0) = 0) | ? [v1] : (powerset(v0) = v1 & ! [v2] : ( ~ (element(v2, v1) = 0) | (v2_membered(v2) = 0 & v1_membered(v2) = 0)))) % 12.97/3.68 | (49) v1_membered(all_0_3_3) = 0 % 12.97/3.68 | (50) ! [v0] : ( ~ (v1_membered(v0) = 0) | ? [v1] : (powerset(v0) = v1 & ! [v2] : ( ~ (element(v2, v1) = 0) | v1_membered(v2) = 0))) % 12.97/3.68 | (51) v3_membered(all_0_3_3) = 0 % 12.97/3.68 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (topstr_closure(v3, v2) = v1) | ~ (topstr_closure(v3, v2) = v0)) % 12.97/3.68 | (53) the_carrier(all_0_9_9) = all_0_8_8 % 12.97/3.68 | (54) top_str(all_0_0_0) = 0 % 12.97/3.68 | (55) ! [v0] : ( ~ (v4_membered(v0) = 0) | v3_membered(v0) = 0) % 12.97/3.69 | (56) ~ (all_0_4_4 = 0) % 12.97/3.69 | (57) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (the_carrier(v2) = v1) | ~ (the_carrier(v2) = v0)) % 12.97/3.69 | (58) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (v1_rat_1(v2) = v1) | ~ (v1_rat_1(v2) = v0)) % 12.97/3.69 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4)) % 12.97/3.69 | (60) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (v1_int_1(v2) = v1) | ~ (v1_int_1(v2) = v0)) % 12.97/3.69 | (61) ? [v0] : ? [v1] : element(v1, v0) = 0 % 12.97/3.69 | (62) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (empty(v2) = 0 & element(v2, v1) = 0)) % 12.97/3.69 | (63) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (v4_membered(v2) = v1) | ~ (v4_membered(v2) = v0)) % 12.97/3.69 | (64) ! [v0] : ( ~ (top_str(v0) = 0) | ? [v1] : ? [v2] : (the_carrier(v0) = v1 & powerset(v1) = v2 & ! [v3] : ( ~ (element(v3, v2) = 0) | ? [v4] : (topstr_closure(v0, v3) = v4 & ! [v5] : ! [v6] : (v6 = 0 | ~ (in(v5, v4) = v6) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ((v10 = 0 & v9 = 0 & v8 = 0 & ~ (v11 = 0) & closed_subset(v7, v0) = 0 & subset(v3, v7) = 0 & element(v7, v2) = 0 & in(v5, v7) = v11) | ( ~ (v7 = 0) & in(v5, v1) = v7))) & ! [v5] : ! [v6] : ( ~ (element(v6, v2) = 0) | ~ (in(v5, v4) = 0) | ? [v7] : ? [v8] : ? [v9] : (( ~ (v7 = 0) & in(v5, v1) = v7) | (closed_subset(v6, v0) = v7 & subset(v3, v6) = v8 & in(v5, v6) = v9 & ( ~ (v8 = 0) | ~ (v7 = 0) | v9 = 0)))))))) % 12.97/3.69 | (65) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) % 12.97/3.69 | (66) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (closed_subset(v3, v2) = v1) | ~ (closed_subset(v3, v2) = v0)) % 12.97/3.69 | (67) ! [v0] : ! [v1] : ! [v2] : ( ~ (v2_membered(v0) = 0) | ~ (v1_xreal_0(v1) = v2) | ? [v3] : ? [v4] : (v1_xcmplx_0(v1) = v4 & element(v1, v0) = v3 & ( ~ (v3 = 0) | (v4 = 0 & v2 = 0)))) % 12.97/3.69 | (68) ! [v0] : ( ~ (v4_membered(v0) = 0) | ? [v1] : (powerset(v0) = v1 & ! [v2] : ( ~ (element(v2, v1) = 0) | (v4_membered(v2) = 0 & v3_membered(v2) = 0 & v2_membered(v2) = 0 & v1_membered(v2) = 0)))) % 12.97/3.69 | (69) ! [v0] : ( ~ (v5_membered(v0) = 0) | ? [v1] : (powerset(v0) = v1 & ! [v2] : ( ~ (element(v2, v1) = 0) | (v5_membered(v2) = 0 & v4_membered(v2) = 0 & v3_membered(v2) = 0 & v2_membered(v2) = 0 & v1_membered(v2) = 0)))) % 12.97/3.69 | (70) v4_membered(all_0_3_3) = 0 % 12.97/3.69 | (71) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) % 12.97/3.69 | (72) ! [v0] : ! [v1] : ( ~ (v5_membered(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (empty(v0) = v2 & v4_membered(v0) = v6 & v3_membered(v0) = v5 & v2_membered(v0) = v4 & v1_membered(v0) = v3 & ( ~ (v2 = 0) | (v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & v1 = 0)))) % 12.97/3.69 | (73) ! [v0] : ( ~ (v2_membered(v0) = 0) | v1_membered(v0) = 0) % 12.97/3.69 | (74) one_sorted_str(all_0_1_1) = 0 % 12.97/3.69 | (75) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (the_carrier(v0) = v2) | ~ (topstr_closure(v0, v1) = v4) | ~ (powerset(v2) = v3) | ~ (element(v4, v3) = v5) | ? [v6] : ? [v7] : (top_str(v0) = v6 & element(v1, v3) = v7 & ( ~ (v7 = 0) | ~ (v6 = 0)))) % 12.97/3.69 | (76) ! [v0] : ( ~ (v3_membered(v0) = 0) | ? [v1] : (powerset(v0) = v1 & ! [v2] : ( ~ (element(v2, v1) = 0) | (v3_membered(v2) = 0 & v2_membered(v2) = 0 & v1_membered(v2) = 0)))) % 12.97/3.69 | (77) ! [v0] : ! [v1] : (v1 = 0 | ~ (one_sorted_str(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & top_str(v0) = v2)) % 12.97/3.69 | (78) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (one_sorted_str(v2) = v1) | ~ (one_sorted_str(v2) = v0)) % 12.97/3.69 | % 12.97/3.70 | Instantiating formula (64) with all_0_9_9 and discharging atoms top_str(all_0_9_9) = 0, yields: % 12.97/3.70 | (79) ? [v0] : ? [v1] : (the_carrier(all_0_9_9) = v0 & powerset(v0) = v1 & ! [v2] : ( ~ (element(v2, v1) = 0) | ? [v3] : (topstr_closure(all_0_9_9, v2) = v3 & ! [v4] : ! [v5] : (v5 = 0 | ~ (in(v4, v3) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ((v9 = 0 & v8 = 0 & v7 = 0 & ~ (v10 = 0) & closed_subset(v6, all_0_9_9) = 0 & subset(v2, v6) = 0 & element(v6, v1) = 0 & in(v4, v6) = v10) | ( ~ (v6 = 0) & in(v4, v0) = v6))) & ! [v4] : ! [v5] : ( ~ (element(v5, v1) = 0) | ~ (in(v4, v3) = 0) | ? [v6] : ? [v7] : ? [v8] : (( ~ (v6 = 0) & in(v4, v0) = v6) | (closed_subset(v5, all_0_9_9) = v6 & subset(v2, v5) = v7 & in(v4, v5) = v8 & ( ~ (v7 = 0) | ~ (v6 = 0) | v8 = 0))))))) % 12.97/3.70 | % 12.97/3.70 | Instantiating formula (34) with all_0_4_4, all_0_5_5, all_0_6_6 and discharging atoms subset(all_0_6_6, all_0_5_5) = all_0_4_4, yields: % 12.97/3.70 | (80) all_0_4_4 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_5_5) = v1 & in(v0, all_0_6_6) = 0) % 12.97/3.70 | % 12.97/3.70 | Instantiating formula (40) with all_0_7_7, all_0_8_8, all_0_6_6 and discharging atoms powerset(all_0_8_8) = all_0_7_7, element(all_0_6_6, all_0_7_7) = 0, yields: % 12.97/3.70 | (81) subset(all_0_6_6, all_0_8_8) = 0 % 12.97/3.70 | % 12.97/3.70 | Instantiating (79) with all_24_0_17, all_24_1_18 yields: % 12.97/3.70 | (82) the_carrier(all_0_9_9) = all_24_1_18 & powerset(all_24_1_18) = all_24_0_17 & ! [v0] : ( ~ (element(v0, all_24_0_17) = 0) | ? [v1] : (topstr_closure(all_0_9_9, v0) = v1 & ! [v2] : ! [v3] : (v3 = 0 | ~ (in(v2, v1) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ((v7 = 0 & v6 = 0 & v5 = 0 & ~ (v8 = 0) & closed_subset(v4, all_0_9_9) = 0 & subset(v0, v4) = 0 & element(v4, all_24_0_17) = 0 & in(v2, v4) = v8) | ( ~ (v4 = 0) & in(v2, all_24_1_18) = v4))) & ! [v2] : ! [v3] : ( ~ (element(v3, all_24_0_17) = 0) | ~ (in(v2, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : (( ~ (v4 = 0) & in(v2, all_24_1_18) = v4) | (closed_subset(v3, all_0_9_9) = v4 & subset(v0, v3) = v5 & in(v2, v3) = v6 & ( ~ (v5 = 0) | ~ (v4 = 0) | v6 = 0)))))) % 12.97/3.70 | % 12.97/3.70 | Applying alpha-rule on (82) yields: % 12.97/3.70 | (83) the_carrier(all_0_9_9) = all_24_1_18 % 12.97/3.70 | (84) powerset(all_24_1_18) = all_24_0_17 % 12.97/3.70 | (85) ! [v0] : ( ~ (element(v0, all_24_0_17) = 0) | ? [v1] : (topstr_closure(all_0_9_9, v0) = v1 & ! [v2] : ! [v3] : (v3 = 0 | ~ (in(v2, v1) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ((v7 = 0 & v6 = 0 & v5 = 0 & ~ (v8 = 0) & closed_subset(v4, all_0_9_9) = 0 & subset(v0, v4) = 0 & element(v4, all_24_0_17) = 0 & in(v2, v4) = v8) | ( ~ (v4 = 0) & in(v2, all_24_1_18) = v4))) & ! [v2] : ! [v3] : ( ~ (element(v3, all_24_0_17) = 0) | ~ (in(v2, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : (( ~ (v4 = 0) & in(v2, all_24_1_18) = v4) | (closed_subset(v3, all_0_9_9) = v4 & subset(v0, v3) = v5 & in(v2, v3) = v6 & ( ~ (v5 = 0) | ~ (v4 = 0) | v6 = 0)))))) % 12.97/3.70 | % 12.97/3.70 | Instantiating formula (85) with all_0_6_6 yields: % 12.97/3.70 | (86) ~ (element(all_0_6_6, all_24_0_17) = 0) | ? [v0] : (topstr_closure(all_0_9_9, all_0_6_6) = v0 & ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v1, v0) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v6 = 0 & v5 = 0 & v4 = 0 & ~ (v7 = 0) & closed_subset(v3, all_0_9_9) = 0 & subset(all_0_6_6, v3) = 0 & element(v3, all_24_0_17) = 0 & in(v1, v3) = v7) | ( ~ (v3 = 0) & in(v1, all_24_1_18) = v3))) & ! [v1] : ! [v2] : ( ~ (element(v2, all_24_0_17) = 0) | ~ (in(v1, v0) = 0) | ? [v3] : ? [v4] : ? [v5] : (( ~ (v3 = 0) & in(v1, all_24_1_18) = v3) | (closed_subset(v2, all_0_9_9) = v3 & subset(all_0_6_6, v2) = v4 & in(v1, v2) = v5 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0))))) % 12.97/3.70 | % 12.97/3.70 +-Applying beta-rule and splitting (80), into two cases. % 12.97/3.70 |-Branch one: % 12.97/3.70 | (87) all_0_4_4 = 0 % 12.97/3.70 | % 12.97/3.71 | Equations (87) can reduce 56 to: % 12.97/3.71 | (88) $false % 12.97/3.71 | % 12.97/3.71 |-The branch is then unsatisfiable % 12.97/3.71 |-Branch two: % 12.97/3.71 | (56) ~ (all_0_4_4 = 0) % 12.97/3.71 | (90) ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_5_5) = v1 & in(v0, all_0_6_6) = 0) % 12.97/3.71 | % 12.97/3.71 | Instantiating (90) with all_64_0_31, all_64_1_32 yields: % 12.97/3.71 | (91) ~ (all_64_0_31 = 0) & in(all_64_1_32, all_0_5_5) = all_64_0_31 & in(all_64_1_32, all_0_6_6) = 0 % 12.97/3.71 | % 12.97/3.71 | Applying alpha-rule on (91) yields: % 12.97/3.71 | (92) ~ (all_64_0_31 = 0) % 12.97/3.71 | (93) in(all_64_1_32, all_0_5_5) = all_64_0_31 % 12.97/3.71 | (94) in(all_64_1_32, all_0_6_6) = 0 % 12.97/3.71 | % 12.97/3.71 | Instantiating formula (57) with all_0_9_9, all_24_1_18, all_0_8_8 and discharging atoms the_carrier(all_0_9_9) = all_24_1_18, the_carrier(all_0_9_9) = all_0_8_8, yields: % 12.97/3.71 | (95) all_24_1_18 = all_0_8_8 % 12.97/3.71 | % 12.97/3.71 | Instantiating formula (71) with all_0_8_8, all_24_0_17, all_0_7_7 and discharging atoms powerset(all_0_8_8) = all_0_7_7, yields: % 12.97/3.71 | (96) all_24_0_17 = all_0_7_7 | ~ (powerset(all_0_8_8) = all_24_0_17) % 12.97/3.71 | % 12.97/3.71 | From (95) and (84) follows: % 12.97/3.71 | (97) powerset(all_0_8_8) = all_24_0_17 % 12.97/3.71 | % 12.97/3.71 +-Applying beta-rule and splitting (96), into two cases. % 12.97/3.71 |-Branch one: % 12.97/3.71 | (98) ~ (powerset(all_0_8_8) = all_24_0_17) % 12.97/3.71 | % 12.97/3.71 | Using (97) and (98) yields: % 12.97/3.71 | (99) $false % 12.97/3.71 | % 12.97/3.71 |-The branch is then unsatisfiable % 12.97/3.71 |-Branch two: % 12.97/3.71 | (97) powerset(all_0_8_8) = all_24_0_17 % 12.97/3.71 | (101) all_24_0_17 = all_0_7_7 % 12.97/3.71 | % 12.97/3.71 +-Applying beta-rule and splitting (86), into two cases. % 12.97/3.71 |-Branch one: % 12.97/3.71 | (102) ~ (element(all_0_6_6, all_24_0_17) = 0) % 12.97/3.71 | % 12.97/3.71 | From (101) and (102) follows: % 12.97/3.71 | (103) ~ (element(all_0_6_6, all_0_7_7) = 0) % 12.97/3.71 | % 12.97/3.71 | Using (3) and (103) yields: % 12.97/3.71 | (99) $false % 12.97/3.71 | % 12.97/3.71 |-The branch is then unsatisfiable % 12.97/3.71 |-Branch two: % 12.97/3.71 | (105) element(all_0_6_6, all_24_0_17) = 0 % 12.97/3.71 | (106) ? [v0] : (topstr_closure(all_0_9_9, all_0_6_6) = v0 & ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v1, v0) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v6 = 0 & v5 = 0 & v4 = 0 & ~ (v7 = 0) & closed_subset(v3, all_0_9_9) = 0 & subset(all_0_6_6, v3) = 0 & element(v3, all_24_0_17) = 0 & in(v1, v3) = v7) | ( ~ (v3 = 0) & in(v1, all_24_1_18) = v3))) & ! [v1] : ! [v2] : ( ~ (element(v2, all_24_0_17) = 0) | ~ (in(v1, v0) = 0) | ? [v3] : ? [v4] : ? [v5] : (( ~ (v3 = 0) & in(v1, all_24_1_18) = v3) | (closed_subset(v2, all_0_9_9) = v3 & subset(all_0_6_6, v2) = v4 & in(v1, v2) = v5 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0))))) % 12.97/3.71 | % 12.97/3.71 | Instantiating (106) with all_78_0_33 yields: % 12.97/3.71 | (107) topstr_closure(all_0_9_9, all_0_6_6) = all_78_0_33 & ! [v0] : ! [v1] : (v1 = 0 | ~ (in(v0, all_78_0_33) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ((v5 = 0 & v4 = 0 & v3 = 0 & ~ (v6 = 0) & closed_subset(v2, all_0_9_9) = 0 & subset(all_0_6_6, v2) = 0 & element(v2, all_24_0_17) = 0 & in(v0, v2) = v6) | ( ~ (v2 = 0) & in(v0, all_24_1_18) = v2))) & ! [v0] : ! [v1] : ( ~ (element(v1, all_24_0_17) = 0) | ~ (in(v0, all_78_0_33) = 0) | ? [v2] : ? [v3] : ? [v4] : (( ~ (v2 = 0) & in(v0, all_24_1_18) = v2) | (closed_subset(v1, all_0_9_9) = v2 & subset(all_0_6_6, v1) = v3 & in(v0, v1) = v4 & ( ~ (v3 = 0) | ~ (v2 = 0) | v4 = 0)))) % 12.97/3.71 | % 12.97/3.71 | Applying alpha-rule on (107) yields: % 12.97/3.71 | (108) topstr_closure(all_0_9_9, all_0_6_6) = all_78_0_33 % 12.97/3.71 | (109) ! [v0] : ! [v1] : (v1 = 0 | ~ (in(v0, all_78_0_33) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ((v5 = 0 & v4 = 0 & v3 = 0 & ~ (v6 = 0) & closed_subset(v2, all_0_9_9) = 0 & subset(all_0_6_6, v2) = 0 & element(v2, all_24_0_17) = 0 & in(v0, v2) = v6) | ( ~ (v2 = 0) & in(v0, all_24_1_18) = v2))) % 12.97/3.71 | (110) ! [v0] : ! [v1] : ( ~ (element(v1, all_24_0_17) = 0) | ~ (in(v0, all_78_0_33) = 0) | ? [v2] : ? [v3] : ? [v4] : (( ~ (v2 = 0) & in(v0, all_24_1_18) = v2) | (closed_subset(v1, all_0_9_9) = v2 & subset(all_0_6_6, v1) = v3 & in(v0, v1) = v4 & ( ~ (v3 = 0) | ~ (v2 = 0) | v4 = 0)))) % 12.97/3.72 | % 12.97/3.72 | Instantiating formula (52) with all_0_9_9, all_0_6_6, all_78_0_33, all_0_5_5 and discharging atoms topstr_closure(all_0_9_9, all_0_6_6) = all_78_0_33, topstr_closure(all_0_9_9, all_0_6_6) = all_0_5_5, yields: % 12.97/3.72 | (111) all_78_0_33 = all_0_5_5 % 12.97/3.72 | % 12.97/3.72 | Instantiating formula (109) with all_64_0_31, all_64_1_32 yields: % 12.97/3.72 | (112) all_64_0_31 = 0 | ~ (in(all_64_1_32, all_78_0_33) = all_64_0_31) | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ((v3 = 0 & v2 = 0 & v1 = 0 & ~ (v4 = 0) & closed_subset(v0, all_0_9_9) = 0 & subset(all_0_6_6, v0) = 0 & element(v0, all_24_0_17) = 0 & in(all_64_1_32, v0) = v4) | ( ~ (v0 = 0) & in(all_64_1_32, all_24_1_18) = v0)) % 12.97/3.72 | % 12.97/3.72 | Instantiating formula (2) with all_64_0_31, all_0_5_5, all_64_1_32 and discharging atoms in(all_64_1_32, all_0_5_5) = all_64_0_31, yields: % 12.97/3.72 | (113) all_64_0_31 = 0 | ? [v0] : ? [v1] : (empty(all_0_5_5) = v1 & element(all_64_1_32, all_0_5_5) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 12.97/3.72 | % 12.97/3.72 | Instantiating formula (22) with all_64_1_32, all_0_8_8, all_0_6_6 and discharging atoms subset(all_0_6_6, all_0_8_8) = 0, in(all_64_1_32, all_0_6_6) = 0, yields: % 12.97/3.72 | (114) in(all_64_1_32, all_0_8_8) = 0 % 12.97/3.72 | % 12.97/3.72 +-Applying beta-rule and splitting (112), into two cases. % 12.97/3.72 |-Branch one: % 12.97/3.72 | (115) ~ (in(all_64_1_32, all_78_0_33) = all_64_0_31) % 12.97/3.72 | % 12.97/3.72 | From (111) and (115) follows: % 12.97/3.72 | (116) ~ (in(all_64_1_32, all_0_5_5) = all_64_0_31) % 12.97/3.72 | % 12.97/3.72 | Using (93) and (116) yields: % 12.97/3.72 | (99) $false % 12.97/3.72 | % 12.97/3.72 |-The branch is then unsatisfiable % 12.97/3.72 |-Branch two: % 12.97/3.72 | (118) in(all_64_1_32, all_78_0_33) = all_64_0_31 % 12.97/3.72 | (119) all_64_0_31 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ((v3 = 0 & v2 = 0 & v1 = 0 & ~ (v4 = 0) & closed_subset(v0, all_0_9_9) = 0 & subset(all_0_6_6, v0) = 0 & element(v0, all_24_0_17) = 0 & in(all_64_1_32, v0) = v4) | ( ~ (v0 = 0) & in(all_64_1_32, all_24_1_18) = v0)) % 12.97/3.72 | % 12.97/3.72 +-Applying beta-rule and splitting (113), into two cases. % 12.97/3.72 |-Branch one: % 12.97/3.72 | (120) all_64_0_31 = 0 % 12.97/3.72 | % 12.97/3.72 | Equations (120) can reduce 92 to: % 12.97/3.72 | (88) $false % 12.97/3.72 | % 12.97/3.72 |-The branch is then unsatisfiable % 12.97/3.72 |-Branch two: % 12.97/3.72 | (92) ~ (all_64_0_31 = 0) % 12.97/3.72 | (123) ? [v0] : ? [v1] : (empty(all_0_5_5) = v1 & element(all_64_1_32, all_0_5_5) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 12.97/3.72 | % 12.97/3.72 +-Applying beta-rule and splitting (119), into two cases. % 12.97/3.72 |-Branch one: % 12.97/3.72 | (120) all_64_0_31 = 0 % 12.97/3.72 | % 12.97/3.72 | Equations (120) can reduce 92 to: % 12.97/3.72 | (88) $false % 12.97/3.72 | % 12.97/3.72 |-The branch is then unsatisfiable % 12.97/3.72 |-Branch two: % 12.97/3.72 | (92) ~ (all_64_0_31 = 0) % 12.97/3.72 | (127) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ((v3 = 0 & v2 = 0 & v1 = 0 & ~ (v4 = 0) & closed_subset(v0, all_0_9_9) = 0 & subset(all_0_6_6, v0) = 0 & element(v0, all_24_0_17) = 0 & in(all_64_1_32, v0) = v4) | ( ~ (v0 = 0) & in(all_64_1_32, all_24_1_18) = v0)) % 12.97/3.72 | % 12.97/3.72 | Instantiating (127) with all_150_0_52, all_150_1_53, all_150_2_54, all_150_3_55, all_150_4_56 yields: % 12.97/3.72 | (128) (all_150_1_53 = 0 & all_150_2_54 = 0 & all_150_3_55 = 0 & ~ (all_150_0_52 = 0) & closed_subset(all_150_4_56, all_0_9_9) = 0 & subset(all_0_6_6, all_150_4_56) = 0 & element(all_150_4_56, all_24_0_17) = 0 & in(all_64_1_32, all_150_4_56) = all_150_0_52) | ( ~ (all_150_4_56 = 0) & in(all_64_1_32, all_24_1_18) = all_150_4_56) % 12.97/3.72 | % 12.97/3.72 +-Applying beta-rule and splitting (128), into two cases. % 12.97/3.72 |-Branch one: % 12.97/3.72 | (129) all_150_1_53 = 0 & all_150_2_54 = 0 & all_150_3_55 = 0 & ~ (all_150_0_52 = 0) & closed_subset(all_150_4_56, all_0_9_9) = 0 & subset(all_0_6_6, all_150_4_56) = 0 & element(all_150_4_56, all_24_0_17) = 0 & in(all_64_1_32, all_150_4_56) = all_150_0_52 % 12.97/3.72 | % 12.97/3.72 | Applying alpha-rule on (129) yields: % 12.97/3.72 | (130) all_150_3_55 = 0 % 12.97/3.72 | (131) in(all_64_1_32, all_150_4_56) = all_150_0_52 % 12.97/3.72 | (132) element(all_150_4_56, all_24_0_17) = 0 % 12.97/3.72 | (133) subset(all_0_6_6, all_150_4_56) = 0 % 12.97/3.72 | (134) all_150_1_53 = 0 % 12.97/3.72 | (135) ~ (all_150_0_52 = 0) % 12.97/3.72 | (136) all_150_2_54 = 0 % 12.97/3.72 | (137) closed_subset(all_150_4_56, all_0_9_9) = 0 % 12.97/3.72 | % 12.97/3.72 | Instantiating formula (22) with all_64_1_32, all_150_4_56, all_0_6_6 and discharging atoms subset(all_0_6_6, all_150_4_56) = 0, in(all_64_1_32, all_0_6_6) = 0, yields: % 12.97/3.72 | (138) in(all_64_1_32, all_150_4_56) = 0 % 12.97/3.72 | % 12.97/3.72 | Instantiating formula (2) with all_150_0_52, all_150_4_56, all_64_1_32 and discharging atoms in(all_64_1_32, all_150_4_56) = all_150_0_52, yields: % 12.97/3.72 | (139) all_150_0_52 = 0 | ? [v0] : ? [v1] : (empty(all_150_4_56) = v1 & element(all_64_1_32, all_150_4_56) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 12.97/3.72 | % 12.97/3.72 +-Applying beta-rule and splitting (139), into two cases. % 12.97/3.72 |-Branch one: % 12.97/3.72 | (140) all_150_0_52 = 0 % 12.97/3.72 | % 12.97/3.72 | Equations (140) can reduce 135 to: % 12.97/3.72 | (88) $false % 12.97/3.72 | % 12.97/3.72 |-The branch is then unsatisfiable % 12.97/3.72 |-Branch two: % 12.97/3.72 | (135) ~ (all_150_0_52 = 0) % 12.97/3.72 | (143) ? [v0] : ? [v1] : (empty(all_150_4_56) = v1 & element(all_64_1_32, all_150_4_56) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 12.97/3.72 | % 12.97/3.72 | Instantiating formula (23) with all_64_1_32, all_150_4_56, 0, all_150_0_52 and discharging atoms in(all_64_1_32, all_150_4_56) = all_150_0_52, in(all_64_1_32, all_150_4_56) = 0, yields: % 12.97/3.73 | (140) all_150_0_52 = 0 % 12.97/3.73 | % 12.97/3.73 | Equations (140) can reduce 135 to: % 12.97/3.73 | (88) $false % 12.97/3.73 | % 12.97/3.73 |-The branch is then unsatisfiable % 12.97/3.73 |-Branch two: % 12.97/3.73 | (146) ~ (all_150_4_56 = 0) & in(all_64_1_32, all_24_1_18) = all_150_4_56 % 12.97/3.73 | % 12.97/3.73 | Applying alpha-rule on (146) yields: % 12.97/3.73 | (147) ~ (all_150_4_56 = 0) % 12.97/3.73 | (148) in(all_64_1_32, all_24_1_18) = all_150_4_56 % 12.97/3.73 | % 12.97/3.73 | From (95) and (148) follows: % 12.97/3.73 | (149) in(all_64_1_32, all_0_8_8) = all_150_4_56 % 12.97/3.73 | % 12.97/3.73 | Instantiating formula (23) with all_64_1_32, all_0_8_8, all_150_4_56, 0 and discharging atoms in(all_64_1_32, all_0_8_8) = all_150_4_56, in(all_64_1_32, all_0_8_8) = 0, yields: % 12.97/3.73 | (150) all_150_4_56 = 0 % 12.97/3.73 | % 12.97/3.73 | Equations (150) can reduce 147 to: % 12.97/3.73 | (88) $false % 12.97/3.73 | % 12.97/3.73 |-The branch is then unsatisfiable % 12.97/3.73 % SZS output end Proof for theBenchmark % 12.97/3.73 % 12.97/3.73 3098ms %------------------------------------------------------------------------------