%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET642+3 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n023.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 00:21:07 EDT 2022 % Result : Theorem 3.29s 1.58s % Output : Proof 5.79s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.02/0.08 % Problem : SET642+3 : TPTP v8.1.0. Released v2.2.0. % 0.02/0.09 % Command : ePrincess-casc -timeout=%d %s % 0.08/0.28 % Computer : n023.cluster.edu % 0.08/0.28 % Model : x86_64 x86_64 % 0.08/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.08/0.28 % Memory : 8042.1875MB % 0.08/0.28 % OS : Linux 3.10.0-693.el7.x86_64 % 0.08/0.28 % CPULimit : 300 % 0.08/0.28 % WCLimit : 600 % 0.08/0.28 % DateTime : Sun Jul 10 09:29:55 EDT 2022 % 0.08/0.28 % CPUTime : % 0.13/0.52 ____ _ % 0.13/0.52 ___ / __ \_____(_)___ ________ __________ % 0.13/0.52 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.13/0.52 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.13/0.52 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.13/0.52 % 0.13/0.52 A Theorem Prover for First-Order Logic % 0.13/0.52 (ePrincess v.1.0) % 0.13/0.52 % 0.13/0.52 (c) Philipp Rümmer, 2009-2015 % 0.13/0.52 (c) Peter Backeman, 2014-2015 % 0.13/0.52 (contributions by Angelo Brillout, Peter Baumgartner) % 0.13/0.52 Free software under GNU Lesser General Public License (LGPL). % 0.13/0.52 Bug reports to peter@backeman.se % 0.13/0.52 % 0.13/0.52 For more information, visit http://user.uu.se/~petba168/breu/ % 0.13/0.52 % 0.13/0.52 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.61/0.58 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.61/0.95 Prover 0: Preprocessing ... % 2.29/1.27 Prover 0: Warning: ignoring some quantifiers % 2.47/1.31 Prover 0: Constructing countermodel ... % 3.29/1.58 Prover 0: proved (1000ms) % 3.29/1.58 % 3.29/1.58 No countermodel exists, formula is valid % 3.29/1.58 % SZS status Theorem for theBenchmark % 3.29/1.58 % 3.29/1.58 Generating proof ... Warning: ignoring some quantifiers % 4.97/1.96 found it (size 38) % 4.97/1.96 % 4.97/1.96 % SZS output start Proof for theBenchmark % 4.97/1.96 Assumed formulas after preprocessing and simplification: % 4.97/1.96 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (relation_type(v1, v2) = v3 & subset(v0, v4) & ilf_type(v4, v3) & ilf_type(v2, set_type) & ilf_type(v1, set_type) & ilf_type(v0, set_type) & ~ ilf_type(v0, v3) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (ordered_pair(v8, v7) = v6) | ~ (ordered_pair(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (cross_product(v8, v7) = v6) | ~ (cross_product(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (relation_type(v8, v7) = v6) | ~ (relation_type(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (power_set(v6) = v7) | ~ member(v8, v5) | ~ member(v5, v7) | ~ ilf_type(v8, set_type) | ~ ilf_type(v6, set_type) | ~ ilf_type(v5, set_type) | member(v8, v6)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (cross_product(v6, v7) = v8) | ~ subset(v5, v8) | ~ ilf_type(v7, set_type) | ~ ilf_type(v6, set_type) | ~ ilf_type(v5, set_type) | ? [v9] : (relation_type(v6, v7) = v9 & ilf_type(v5, v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (cross_product(v6, v7) = v8) | ~ ilf_type(v7, set_type) | ~ ilf_type(v6, set_type) | ~ ilf_type(v5, set_type) | ? [v9] : (relation_type(v6, v7) = v9 & ! [v10] : ( ~ subset(v5, v10) | ~ ilf_type(v10, v9) | subset(v5, v8)))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (relation_type(v6, v7) = v8) | ~ ilf_type(v7, set_type) | ~ ilf_type(v6, set_type) | ~ ilf_type(v5, set_type) | ilf_type(v5, v8) | ? [v9] : (cross_product(v6, v7) = v9 & ~ subset(v5, v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (relation_type(v6, v7) = v8) | ~ ilf_type(v7, set_type) | ~ ilf_type(v6, set_type) | ~ ilf_type(v5, set_type) | ? [v9] : (cross_product(v6, v7) = v9 & ! [v10] : ( ~ subset(v5, v10) | ~ ilf_type(v10, v8) | subset(v5, v9)))) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (power_set(v7) = v6) | ~ (power_set(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (member_type(v7) = v6) | ~ (member_type(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (subset_type(v7) = v6) | ~ (subset_type(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (ordered_pair(v5, v6) = v7) | ~ ilf_type(v6, set_type) | ~ ilf_type(v5, set_type) | ilf_type(v7, set_type)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (power_set(v6) = v7) | ~ ilf_type(v6, set_type) | ~ ilf_type(v5, set_type) | member(v5, v7) | ? [v8] : (member(v8, v5) & ilf_type(v8, set_type) & ~ member(v8, v6))) & ! [v5] : ! [v6] : ! [v7] : ( ~ (member_type(v6) = v7) | ~ member(v5, v6) | ~ ilf_type(v6, set_type) | ~ ilf_type(v5, set_type) | empty(v6) | ilf_type(v5, v7)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (member_type(v6) = v7) | ~ ilf_type(v6, set_type) | ~ ilf_type(v5, v7) | ~ ilf_type(v5, set_type) | empty(v6) | member(v5, v6)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (cross_product(v5, v6) = v7) | ~ ilf_type(v6, set_type) | ~ ilf_type(v5, set_type) | ilf_type(v7, set_type)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (cross_product(v5, v6) = v7) | ~ ilf_type(v6, set_type) | ~ ilf_type(v5, set_type) | ? [v8] : ? [v9] : (subset_type(v7) = v8 & relation_type(v5, v6) = v9 & ! [v10] : ( ~ ilf_type(v10, v9) | ilf_type(v10, v8)) & ! [v10] : ( ~ ilf_type(v10, v8) | ilf_type(v10, v9)))) & ! [v5] : ! [v6] : ! [v7] : ( ~ (cross_product(v5, v6) = v7) | ~ ilf_type(v6, set_type) | ~ ilf_type(v5, set_type) | ? [v8] : (subset_type(v7) = v8 & ! [v9] : ( ~ ilf_type(v9, v8) | relation_like(v9)))) & ! [v5] : ! [v6] : ! [v7] : ( ~ (relation_type(v6, v5) = v7) | ~ ilf_type(v6, set_type) | ~ ilf_type(v5, set_type) | ? [v8] : ilf_type(v8, v7)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (relation_type(v5, v6) = v7) | ~ ilf_type(v6, set_type) | ~ ilf_type(v5, set_type) | ? [v8] : ? [v9] : (subset_type(v8) = v9 & cross_product(v5, v6) = v8 & ! [v10] : ( ~ ilf_type(v10, v9) | ilf_type(v10, v7)) & ! [v10] : ( ~ ilf_type(v10, v7) | ilf_type(v10, v9)))) & ! [v5] : ! [v6] : ! [v7] : ( ~ member(v7, v5) | ~ subset(v5, v6) | ~ ilf_type(v7, set_type) | ~ ilf_type(v6, set_type) | ~ ilf_type(v5, set_type) | member(v7, v6)) & ! [v5] : ! [v6] : ( ~ (power_set(v5) = v6) | ~ empty(v6) | ~ ilf_type(v5, set_type)) & ! [v5] : ! [v6] : ( ~ (power_set(v5) = v6) | ~ ilf_type(v5, set_type) | ilf_type(v6, set_type)) & ! [v5] : ! [v6] : ( ~ (power_set(v5) = v6) | ~ ilf_type(v5, set_type) | ? [v7] : ? [v8] : (member_type(v6) = v8 & subset_type(v5) = v7 & ! [v9] : ( ~ ilf_type(v9, v8) | ~ ilf_type(v9, set_type) | ilf_type(v9, v7)) & ! [v9] : ( ~ ilf_type(v9, v7) | ~ ilf_type(v9, set_type) | ilf_type(v9, v8)))) & ! [v5] : ! [v6] : ( ~ (member_type(v5) = v6) | ~ ilf_type(v5, set_type) | empty(v5) | ? [v7] : ilf_type(v7, v6)) & ! [v5] : ! [v6] : ( ~ (subset_type(v5) = v6) | ~ ilf_type(v5, set_type) | ? [v7] : ? [v8] : (power_set(v5) = v7 & member_type(v7) = v8 & ! [v9] : ( ~ ilf_type(v9, v8) | ~ ilf_type(v9, set_type) | ilf_type(v9, v6)) & ! [v9] : ( ~ ilf_type(v9, v6) | ~ ilf_type(v9, set_type) | ilf_type(v9, v8)))) & ! [v5] : ! [v6] : ( ~ (subset_type(v5) = v6) | ~ ilf_type(v5, set_type) | ? [v7] : ilf_type(v7, v6)) & ! [v5] : ! [v6] : ( ~ relation_like(v5) | ~ member(v6, v5) | ~ ilf_type(v6, set_type) | ~ ilf_type(v5, set_type) | ? [v7] : ? [v8] : (ordered_pair(v7, v8) = v6 & ilf_type(v8, set_type) & ilf_type(v7, set_type))) & ! [v5] : ! [v6] : ( ~ empty(v5) | ~ member(v6, v5) | ~ ilf_type(v6, set_type) | ~ ilf_type(v5, set_type)) & ! [v5] : ! [v6] : ( ~ ilf_type(v6, set_type) | ~ ilf_type(v5, set_type) | subset(v5, v6) | ? [v7] : (member(v7, v5) & ilf_type(v7, set_type) & ~ member(v7, v6))) & ! [v5] : ( ~ empty(v5) | ~ ilf_type(v5, set_type) | relation_like(v5)) & ! [v5] : ( ~ ilf_type(v5, set_type) | relation_like(v5) | ? [v6] : (member(v6, v5) & ilf_type(v6, set_type) & ! [v7] : ! [v8] : ( ~ (ordered_pair(v7, v8) = v6) | ~ ilf_type(v8, set_type) | ~ ilf_type(v7, set_type)))) & ! [v5] : ( ~ ilf_type(v5, set_type) | empty(v5) | ? [v6] : (member(v6, v5) & ilf_type(v6, set_type))) & ! [v5] : ( ~ ilf_type(v5, set_type) | subset(v5, v5)) & ? [v5] : ilf_type(v5, set_type)) % 5.35/2.03 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields: % 5.35/2.03 | (1) relation_type(all_0_3_3, all_0_2_2) = all_0_1_1 & subset(all_0_4_4, all_0_0_0) & ilf_type(all_0_0_0, all_0_1_1) & ilf_type(all_0_2_2, set_type) & ilf_type(all_0_3_3, set_type) & ilf_type(all_0_4_4, set_type) & ~ ilf_type(all_0_4_4, all_0_1_1) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cross_product(v3, v2) = v1) | ~ (cross_product(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_type(v3, v2) = v1) | ~ (relation_type(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (power_set(v1) = v2) | ~ member(v3, v0) | ~ member(v0, v2) | ~ ilf_type(v3, set_type) | ~ ilf_type(v1, set_type) | ~ ilf_type(v0, set_type) | member(v3, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cross_product(v1, v2) = v3) | ~ subset(v0, v3) | ~ ilf_type(v2, set_type) | ~ ilf_type(v1, set_type) | ~ ilf_type(v0, set_type) | ? [v4] : (relation_type(v1, v2) = v4 & ilf_type(v0, v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cross_product(v1, v2) = v3) | ~ ilf_type(v2, set_type) | ~ ilf_type(v1, set_type) | ~ ilf_type(v0, set_type) | ? [v4] : (relation_type(v1, v2) = v4 & ! [v5] : ( ~ subset(v0, v5) | ~ ilf_type(v5, v4) | subset(v0, v3)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_type(v1, v2) = v3) | ~ ilf_type(v2, set_type) | ~ ilf_type(v1, set_type) | ~ ilf_type(v0, set_type) | ilf_type(v0, v3) | ? [v4] : (cross_product(v1, v2) = v4 & ~ subset(v0, v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_type(v1, v2) = v3) | ~ ilf_type(v2, set_type) | ~ ilf_type(v1, set_type) | ~ ilf_type(v0, set_type) | ? [v4] : (cross_product(v1, v2) = v4 & ! [v5] : ( ~ subset(v0, v5) | ~ ilf_type(v5, v3) | subset(v0, v4)))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (member_type(v2) = v1) | ~ (member_type(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (subset_type(v2) = v1) | ~ (subset_type(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ ilf_type(v1, set_type) | ~ ilf_type(v0, set_type) | ilf_type(v2, set_type)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ ilf_type(v1, set_type) | ~ ilf_type(v0, set_type) | member(v0, v2) | ? [v3] : (member(v3, v0) & ilf_type(v3, set_type) & ~ member(v3, v1))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (member_type(v1) = v2) | ~ member(v0, v1) | ~ ilf_type(v1, set_type) | ~ ilf_type(v0, set_type) | empty(v1) | ilf_type(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (member_type(v1) = v2) | ~ ilf_type(v1, set_type) | ~ ilf_type(v0, v2) | ~ ilf_type(v0, set_type) | empty(v1) | member(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (cross_product(v0, v1) = v2) | ~ ilf_type(v1, set_type) | ~ ilf_type(v0, set_type) | ilf_type(v2, set_type)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (cross_product(v0, v1) = v2) | ~ ilf_type(v1, set_type) | ~ ilf_type(v0, set_type) | ? [v3] : ? [v4] : (subset_type(v2) = v3 & relation_type(v0, v1) = v4 & ! [v5] : ( ~ ilf_type(v5, v4) | ilf_type(v5, v3)) & ! [v5] : ( ~ ilf_type(v5, v3) | ilf_type(v5, v4)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (cross_product(v0, v1) = v2) | ~ ilf_type(v1, set_type) | ~ ilf_type(v0, set_type) | ? [v3] : (subset_type(v2) = v3 & ! [v4] : ( ~ ilf_type(v4, v3) | relation_like(v4)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_type(v1, v0) = v2) | ~ ilf_type(v1, set_type) | ~ ilf_type(v0, set_type) | ? [v3] : ilf_type(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_type(v0, v1) = v2) | ~ ilf_type(v1, set_type) | ~ ilf_type(v0, set_type) | ? [v3] : ? [v4] : (subset_type(v3) = v4 & cross_product(v0, v1) = v3 & ! [v5] : ( ~ ilf_type(v5, v4) | ilf_type(v5, v2)) & ! [v5] : ( ~ ilf_type(v5, v2) | ilf_type(v5, v4)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ member(v2, v0) | ~ subset(v0, v1) | ~ ilf_type(v2, set_type) | ~ ilf_type(v1, set_type) | ~ ilf_type(v0, set_type) | member(v2, v1)) & ! [v0] : ! [v1] : ( ~ (power_set(v0) = v1) | ~ empty(v1) | ~ ilf_type(v0, set_type)) & ! [v0] : ! [v1] : ( ~ (power_set(v0) = v1) | ~ ilf_type(v0, set_type) | ilf_type(v1, set_type)) & ! [v0] : ! [v1] : ( ~ (power_set(v0) = v1) | ~ ilf_type(v0, set_type) | ? [v2] : ? [v3] : (member_type(v1) = v3 & subset_type(v0) = v2 & ! [v4] : ( ~ ilf_type(v4, v3) | ~ ilf_type(v4, set_type) | ilf_type(v4, v2)) & ! [v4] : ( ~ ilf_type(v4, v2) | ~ ilf_type(v4, set_type) | ilf_type(v4, v3)))) & ! [v0] : ! [v1] : ( ~ (member_type(v0) = v1) | ~ ilf_type(v0, set_type) | empty(v0) | ? [v2] : ilf_type(v2, v1)) & ! [v0] : ! [v1] : ( ~ (subset_type(v0) = v1) | ~ ilf_type(v0, set_type) | ? [v2] : ? [v3] : (power_set(v0) = v2 & member_type(v2) = v3 & ! [v4] : ( ~ ilf_type(v4, v3) | ~ ilf_type(v4, set_type) | ilf_type(v4, v1)) & ! [v4] : ( ~ ilf_type(v4, v1) | ~ ilf_type(v4, set_type) | ilf_type(v4, v3)))) & ! [v0] : ! [v1] : ( ~ (subset_type(v0) = v1) | ~ ilf_type(v0, set_type) | ? [v2] : ilf_type(v2, v1)) & ! [v0] : ! [v1] : ( ~ relation_like(v0) | ~ member(v1, v0) | ~ ilf_type(v1, set_type) | ~ ilf_type(v0, set_type) | ? [v2] : ? [v3] : (ordered_pair(v2, v3) = v1 & ilf_type(v3, set_type) & ilf_type(v2, set_type))) & ! [v0] : ! [v1] : ( ~ empty(v0) | ~ member(v1, v0) | ~ ilf_type(v1, set_type) | ~ ilf_type(v0, set_type)) & ! [v0] : ! [v1] : ( ~ ilf_type(v1, set_type) | ~ ilf_type(v0, set_type) | subset(v0, v1) | ? [v2] : (member(v2, v0) & ilf_type(v2, set_type) & ~ member(v2, v1))) & ! [v0] : ( ~ empty(v0) | ~ ilf_type(v0, set_type) | relation_like(v0)) & ! [v0] : ( ~ ilf_type(v0, set_type) | relation_like(v0) | ? [v1] : (member(v1, v0) & ilf_type(v1, set_type) & ! [v2] : ! [v3] : ( ~ (ordered_pair(v2, v3) = v1) | ~ ilf_type(v3, set_type) | ~ ilf_type(v2, set_type)))) & ! [v0] : ( ~ ilf_type(v0, set_type) | empty(v0) | ? [v1] : (member(v1, v0) & ilf_type(v1, set_type))) & ! [v0] : ( ~ ilf_type(v0, set_type) | subset(v0, v0)) & ? [v0] : ilf_type(v0, set_type) % 5.35/2.04 | % 5.35/2.04 | Applying alpha-rule on (1) yields: % 5.35/2.05 | (2) ! [v0] : ! [v1] : ( ~ (power_set(v0) = v1) | ~ ilf_type(v0, set_type) | ilf_type(v1, set_type)) % 5.35/2.05 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cross_product(v1, v2) = v3) | ~ ilf_type(v2, set_type) | ~ ilf_type(v1, set_type) | ~ ilf_type(v0, set_type) | ? [v4] : (relation_type(v1, v2) = v4 & ! [v5] : ( ~ subset(v0, v5) | ~ ilf_type(v5, v4) | subset(v0, v3)))) % 5.35/2.05 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ ilf_type(v1, set_type) | ~ ilf_type(v0, set_type) | member(v0, v2) | ? [v3] : (member(v3, v0) & ilf_type(v3, set_type) & ~ member(v3, v1))) % 5.35/2.05 | (5) ! [v0] : ! [v1] : ! [v2] : ( ~ (member_type(v1) = v2) | ~ ilf_type(v1, set_type) | ~ ilf_type(v0, v2) | ~ ilf_type(v0, set_type) | empty(v1) | member(v0, v1)) % 5.35/2.05 | (6) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (subset_type(v2) = v1) | ~ (subset_type(v2) = v0)) % 5.35/2.05 | (7) ilf_type(all_0_4_4, set_type) % 5.35/2.05 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ ilf_type(v1, set_type) | ~ ilf_type(v0, set_type) | ilf_type(v2, set_type)) % 5.35/2.05 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_type(v3, v2) = v1) | ~ (relation_type(v3, v2) = v0)) % 5.35/2.05 | (10) ilf_type(all_0_0_0, all_0_1_1) % 5.35/2.05 | (11) relation_type(all_0_3_3, all_0_2_2) = all_0_1_1 % 5.35/2.05 | (12) ilf_type(all_0_3_3, set_type) % 5.35/2.05 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cross_product(v1, v2) = v3) | ~ subset(v0, v3) | ~ ilf_type(v2, set_type) | ~ ilf_type(v1, set_type) | ~ ilf_type(v0, set_type) | ? [v4] : (relation_type(v1, v2) = v4 & ilf_type(v0, v4))) % 5.35/2.05 | (14) ! [v0] : ( ~ empty(v0) | ~ ilf_type(v0, set_type) | relation_like(v0)) % 5.35/2.05 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_type(v1, v2) = v3) | ~ ilf_type(v2, set_type) | ~ ilf_type(v1, set_type) | ~ ilf_type(v0, set_type) | ilf_type(v0, v3) | ? [v4] : (cross_product(v1, v2) = v4 & ~ subset(v0, v4))) % 5.35/2.05 | (16) ! [v0] : ( ~ ilf_type(v0, set_type) | empty(v0) | ? [v1] : (member(v1, v0) & ilf_type(v1, set_type))) % 5.35/2.05 | (17) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (member_type(v2) = v1) | ~ (member_type(v2) = v0)) % 5.35/2.05 | (18) ! [v0] : ! [v1] : ( ~ (subset_type(v0) = v1) | ~ ilf_type(v0, set_type) | ? [v2] : ? [v3] : (power_set(v0) = v2 & member_type(v2) = v3 & ! [v4] : ( ~ ilf_type(v4, v3) | ~ ilf_type(v4, set_type) | ilf_type(v4, v1)) & ! [v4] : ( ~ ilf_type(v4, v1) | ~ ilf_type(v4, set_type) | ilf_type(v4, v3)))) % 5.35/2.05 | (19) ! [v0] : ! [v1] : ! [v2] : ( ~ member(v2, v0) | ~ subset(v0, v1) | ~ ilf_type(v2, set_type) | ~ ilf_type(v1, set_type) | ~ ilf_type(v0, set_type) | member(v2, v1)) % 5.35/2.05 | (20) ! [v0] : ! [v1] : ( ~ ilf_type(v1, set_type) | ~ ilf_type(v0, set_type) | subset(v0, v1) | ? [v2] : (member(v2, v0) & ilf_type(v2, set_type) & ~ member(v2, v1))) % 5.35/2.06 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) % 5.35/2.06 | (22) ! [v0] : ! [v1] : ( ~ (power_set(v0) = v1) | ~ ilf_type(v0, set_type) | ? [v2] : ? [v3] : (member_type(v1) = v3 & subset_type(v0) = v2 & ! [v4] : ( ~ ilf_type(v4, v3) | ~ ilf_type(v4, set_type) | ilf_type(v4, v2)) & ! [v4] : ( ~ ilf_type(v4, v2) | ~ ilf_type(v4, set_type) | ilf_type(v4, v3)))) % 5.35/2.06 | (23) ! [v0] : ! [v1] : ( ~ (subset_type(v0) = v1) | ~ ilf_type(v0, set_type) | ? [v2] : ilf_type(v2, v1)) % 5.35/2.06 | (24) ! [v0] : ! [v1] : ( ~ (member_type(v0) = v1) | ~ ilf_type(v0, set_type) | empty(v0) | ? [v2] : ilf_type(v2, v1)) % 5.35/2.06 | (25) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_type(v1, v0) = v2) | ~ ilf_type(v1, set_type) | ~ ilf_type(v0, set_type) | ? [v3] : ilf_type(v3, v2)) % 5.35/2.06 | (26) ! [v0] : ( ~ ilf_type(v0, set_type) | subset(v0, v0)) % 5.35/2.06 | (27) ! [v0] : ! [v1] : ( ~ empty(v0) | ~ member(v1, v0) | ~ ilf_type(v1, set_type) | ~ ilf_type(v0, set_type)) % 5.35/2.06 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (power_set(v1) = v2) | ~ member(v3, v0) | ~ member(v0, v2) | ~ ilf_type(v3, set_type) | ~ ilf_type(v1, set_type) | ~ ilf_type(v0, set_type) | member(v3, v1)) % 5.35/2.06 | (29) ! [v0] : ( ~ ilf_type(v0, set_type) | relation_like(v0) | ? [v1] : (member(v1, v0) & ilf_type(v1, set_type) & ! [v2] : ! [v3] : ( ~ (ordered_pair(v2, v3) = v1) | ~ ilf_type(v3, set_type) | ~ ilf_type(v2, set_type)))) % 5.35/2.06 | (30) ~ ilf_type(all_0_4_4, all_0_1_1) % 5.35/2.06 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cross_product(v3, v2) = v1) | ~ (cross_product(v3, v2) = v0)) % 5.35/2.06 | (32) ! [v0] : ! [v1] : ( ~ relation_like(v0) | ~ member(v1, v0) | ~ ilf_type(v1, set_type) | ~ ilf_type(v0, set_type) | ? [v2] : ? [v3] : (ordered_pair(v2, v3) = v1 & ilf_type(v3, set_type) & ilf_type(v2, set_type))) % 5.35/2.06 | (33) ! [v0] : ! [v1] : ! [v2] : ( ~ (cross_product(v0, v1) = v2) | ~ ilf_type(v1, set_type) | ~ ilf_type(v0, set_type) | ilf_type(v2, set_type)) % 5.35/2.06 | (34) ! [v0] : ! [v1] : ( ~ (power_set(v0) = v1) | ~ empty(v1) | ~ ilf_type(v0, set_type)) % 5.35/2.06 | (35) ? [v0] : ilf_type(v0, set_type) % 5.35/2.06 | (36) ! [v0] : ! [v1] : ! [v2] : ( ~ (cross_product(v0, v1) = v2) | ~ ilf_type(v1, set_type) | ~ ilf_type(v0, set_type) | ? [v3] : (subset_type(v2) = v3 & ! [v4] : ( ~ ilf_type(v4, v3) | relation_like(v4)))) % 5.35/2.06 | (37) subset(all_0_4_4, all_0_0_0) % 5.35/2.06 | (38) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_type(v0, v1) = v2) | ~ ilf_type(v1, set_type) | ~ ilf_type(v0, set_type) | ? [v3] : ? [v4] : (subset_type(v3) = v4 & cross_product(v0, v1) = v3 & ! [v5] : ( ~ ilf_type(v5, v4) | ilf_type(v5, v2)) & ! [v5] : ( ~ ilf_type(v5, v2) | ilf_type(v5, v4)))) % 5.35/2.07 | (39) ilf_type(all_0_2_2, set_type) % 5.35/2.07 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_type(v1, v2) = v3) | ~ ilf_type(v2, set_type) | ~ ilf_type(v1, set_type) | ~ ilf_type(v0, set_type) | ? [v4] : (cross_product(v1, v2) = v4 & ! [v5] : ( ~ subset(v0, v5) | ~ ilf_type(v5, v3) | subset(v0, v4)))) % 5.35/2.07 | (41) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0)) % 5.35/2.07 | (42) ! [v0] : ! [v1] : ! [v2] : ( ~ (member_type(v1) = v2) | ~ member(v0, v1) | ~ ilf_type(v1, set_type) | ~ ilf_type(v0, set_type) | empty(v1) | ilf_type(v0, v2)) % 5.35/2.07 | (43) ! [v0] : ! [v1] : ! [v2] : ( ~ (cross_product(v0, v1) = v2) | ~ ilf_type(v1, set_type) | ~ ilf_type(v0, set_type) | ? [v3] : ? [v4] : (subset_type(v2) = v3 & relation_type(v0, v1) = v4 & ! [v5] : ( ~ ilf_type(v5, v4) | ilf_type(v5, v3)) & ! [v5] : ( ~ ilf_type(v5, v3) | ilf_type(v5, v4)))) % 5.35/2.07 | % 5.35/2.07 | Instantiating (35) with all_3_0_5 yields: % 5.35/2.07 | (44) ilf_type(all_3_0_5, set_type) % 5.35/2.07 | % 5.35/2.07 | Instantiating formula (40) with all_0_1_1, all_0_2_2, all_0_3_3, all_0_3_3 and discharging atoms relation_type(all_0_3_3, all_0_2_2) = all_0_1_1, ilf_type(all_0_2_2, set_type), ilf_type(all_0_3_3, set_type), yields: % 5.35/2.07 | (45) ? [v0] : (cross_product(all_0_3_3, all_0_2_2) = v0 & ! [v1] : ( ~ subset(all_0_3_3, v1) | ~ ilf_type(v1, all_0_1_1) | subset(all_0_3_3, v0))) % 5.35/2.07 | % 5.35/2.07 | Instantiating formula (40) with all_0_1_1, all_0_2_2, all_0_3_3, all_3_0_5 and discharging atoms relation_type(all_0_3_3, all_0_2_2) = all_0_1_1, ilf_type(all_3_0_5, set_type), ilf_type(all_0_2_2, set_type), ilf_type(all_0_3_3, set_type), yields: % 5.35/2.07 | (46) ? [v0] : (cross_product(all_0_3_3, all_0_2_2) = v0 & ! [v1] : ( ~ subset(all_3_0_5, v1) | ~ ilf_type(v1, all_0_1_1) | subset(all_3_0_5, v0))) % 5.35/2.07 | % 5.35/2.07 | Instantiating formula (40) with all_0_1_1, all_0_2_2, all_0_3_3, all_0_2_2 and discharging atoms relation_type(all_0_3_3, all_0_2_2) = all_0_1_1, ilf_type(all_0_2_2, set_type), ilf_type(all_0_3_3, set_type), yields: % 5.35/2.07 | (47) ? [v0] : (cross_product(all_0_3_3, all_0_2_2) = v0 & ! [v1] : ( ~ subset(all_0_2_2, v1) | ~ ilf_type(v1, all_0_1_1) | subset(all_0_2_2, v0))) % 5.35/2.07 | % 5.35/2.07 | Instantiating formula (38) with all_0_1_1, all_0_2_2, all_0_3_3 and discharging atoms relation_type(all_0_3_3, all_0_2_2) = all_0_1_1, ilf_type(all_0_2_2, set_type), ilf_type(all_0_3_3, set_type), yields: % 5.35/2.07 | (48) ? [v0] : ? [v1] : (subset_type(v0) = v1 & cross_product(all_0_3_3, all_0_2_2) = v0 & ! [v2] : ( ~ ilf_type(v2, v1) | ilf_type(v2, all_0_1_1)) & ! [v2] : ( ~ ilf_type(v2, all_0_1_1) | ilf_type(v2, v1))) % 5.35/2.07 | % 5.35/2.07 | Instantiating formula (15) with all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms relation_type(all_0_3_3, all_0_2_2) = all_0_1_1, ilf_type(all_0_2_2, set_type), ilf_type(all_0_3_3, set_type), ilf_type(all_0_4_4, set_type), ~ ilf_type(all_0_4_4, all_0_1_1), yields: % 5.35/2.07 | (49) ? [v0] : (cross_product(all_0_3_3, all_0_2_2) = v0 & ~ subset(all_0_4_4, v0)) % 5.35/2.08 | % 5.35/2.08 | Instantiating formula (40) with all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms relation_type(all_0_3_3, all_0_2_2) = all_0_1_1, ilf_type(all_0_2_2, set_type), ilf_type(all_0_3_3, set_type), ilf_type(all_0_4_4, set_type), yields: % 5.35/2.08 | (50) ? [v0] : (cross_product(all_0_3_3, all_0_2_2) = v0 & ! [v1] : ( ~ subset(all_0_4_4, v1) | ~ ilf_type(v1, all_0_1_1) | subset(all_0_4_4, v0))) % 5.35/2.08 | % 5.35/2.08 | Instantiating (50) with all_11_0_6 yields: % 5.35/2.08 | (51) cross_product(all_0_3_3, all_0_2_2) = all_11_0_6 & ! [v0] : ( ~ subset(all_0_4_4, v0) | ~ ilf_type(v0, all_0_1_1) | subset(all_0_4_4, all_11_0_6)) % 5.35/2.08 | % 5.35/2.08 | Applying alpha-rule on (51) yields: % 5.35/2.08 | (52) cross_product(all_0_3_3, all_0_2_2) = all_11_0_6 % 5.35/2.08 | (53) ! [v0] : ( ~ subset(all_0_4_4, v0) | ~ ilf_type(v0, all_0_1_1) | subset(all_0_4_4, all_11_0_6)) % 5.35/2.08 | % 5.35/2.08 | Instantiating formula (53) with all_0_0_0 and discharging atoms subset(all_0_4_4, all_0_0_0), ilf_type(all_0_0_0, all_0_1_1), yields: % 5.35/2.08 | (54) subset(all_0_4_4, all_11_0_6) % 5.35/2.08 | % 5.35/2.08 | Instantiating (49) with all_15_0_7 yields: % 5.35/2.08 | (55) cross_product(all_0_3_3, all_0_2_2) = all_15_0_7 & ~ subset(all_0_4_4, all_15_0_7) % 5.35/2.08 | % 5.35/2.08 | Applying alpha-rule on (55) yields: % 5.35/2.08 | (56) cross_product(all_0_3_3, all_0_2_2) = all_15_0_7 % 5.35/2.08 | (57) ~ subset(all_0_4_4, all_15_0_7) % 5.35/2.08 | % 5.35/2.08 | Instantiating (48) with all_17_0_8, all_17_1_9 yields: % 5.35/2.08 | (58) subset_type(all_17_1_9) = all_17_0_8 & cross_product(all_0_3_3, all_0_2_2) = all_17_1_9 & ! [v0] : ( ~ ilf_type(v0, all_17_0_8) | ilf_type(v0, all_0_1_1)) & ! [v0] : ( ~ ilf_type(v0, all_0_1_1) | ilf_type(v0, all_17_0_8)) % 5.35/2.08 | % 5.35/2.08 | Applying alpha-rule on (58) yields: % 5.35/2.08 | (59) subset_type(all_17_1_9) = all_17_0_8 % 5.35/2.08 | (60) cross_product(all_0_3_3, all_0_2_2) = all_17_1_9 % 5.35/2.08 | (61) ! [v0] : ( ~ ilf_type(v0, all_17_0_8) | ilf_type(v0, all_0_1_1)) % 5.35/2.08 | (62) ! [v0] : ( ~ ilf_type(v0, all_0_1_1) | ilf_type(v0, all_17_0_8)) % 5.35/2.08 | % 5.35/2.08 | Instantiating (47) with all_21_0_10 yields: % 5.35/2.08 | (63) cross_product(all_0_3_3, all_0_2_2) = all_21_0_10 & ! [v0] : ( ~ subset(all_0_2_2, v0) | ~ ilf_type(v0, all_0_1_1) | subset(all_0_2_2, all_21_0_10)) % 5.79/2.08 | % 5.79/2.08 | Applying alpha-rule on (63) yields: % 5.79/2.08 | (64) cross_product(all_0_3_3, all_0_2_2) = all_21_0_10 % 5.79/2.08 | (65) ! [v0] : ( ~ subset(all_0_2_2, v0) | ~ ilf_type(v0, all_0_1_1) | subset(all_0_2_2, all_21_0_10)) % 5.79/2.08 | % 5.79/2.08 | Instantiating (46) with all_26_0_12 yields: % 5.79/2.08 | (66) cross_product(all_0_3_3, all_0_2_2) = all_26_0_12 & ! [v0] : ( ~ subset(all_3_0_5, v0) | ~ ilf_type(v0, all_0_1_1) | subset(all_3_0_5, all_26_0_12)) % 5.79/2.08 | % 5.79/2.08 | Applying alpha-rule on (66) yields: % 5.79/2.08 | (67) cross_product(all_0_3_3, all_0_2_2) = all_26_0_12 % 5.79/2.08 | (68) ! [v0] : ( ~ subset(all_3_0_5, v0) | ~ ilf_type(v0, all_0_1_1) | subset(all_3_0_5, all_26_0_12)) % 5.79/2.08 | % 5.79/2.08 | Instantiating (45) with all_29_0_13 yields: % 5.79/2.08 | (69) cross_product(all_0_3_3, all_0_2_2) = all_29_0_13 & ! [v0] : ( ~ subset(all_0_3_3, v0) | ~ ilf_type(v0, all_0_1_1) | subset(all_0_3_3, all_29_0_13)) % 5.79/2.08 | % 5.79/2.08 | Applying alpha-rule on (69) yields: % 5.79/2.08 | (70) cross_product(all_0_3_3, all_0_2_2) = all_29_0_13 % 5.79/2.08 | (71) ! [v0] : ( ~ subset(all_0_3_3, v0) | ~ ilf_type(v0, all_0_1_1) | subset(all_0_3_3, all_29_0_13)) % 5.79/2.08 | % 5.79/2.08 | Instantiating formula (31) with all_0_3_3, all_0_2_2, all_26_0_12, all_29_0_13 and discharging atoms cross_product(all_0_3_3, all_0_2_2) = all_29_0_13, cross_product(all_0_3_3, all_0_2_2) = all_26_0_12, yields: % 5.79/2.08 | (72) all_29_0_13 = all_26_0_12 % 5.79/2.09 | % 5.79/2.09 | Instantiating formula (31) with all_0_3_3, all_0_2_2, all_21_0_10, all_26_0_12 and discharging atoms cross_product(all_0_3_3, all_0_2_2) = all_26_0_12, cross_product(all_0_3_3, all_0_2_2) = all_21_0_10, yields: % 5.79/2.09 | (73) all_26_0_12 = all_21_0_10 % 5.79/2.09 | % 5.79/2.09 | Instantiating formula (31) with all_0_3_3, all_0_2_2, all_17_1_9, all_26_0_12 and discharging atoms cross_product(all_0_3_3, all_0_2_2) = all_26_0_12, cross_product(all_0_3_3, all_0_2_2) = all_17_1_9, yields: % 5.79/2.09 | (74) all_26_0_12 = all_17_1_9 % 5.79/2.09 | % 5.79/2.09 | Instantiating formula (31) with all_0_3_3, all_0_2_2, all_15_0_7, all_29_0_13 and discharging atoms cross_product(all_0_3_3, all_0_2_2) = all_29_0_13, cross_product(all_0_3_3, all_0_2_2) = all_15_0_7, yields: % 5.79/2.09 | (75) all_29_0_13 = all_15_0_7 % 5.79/2.09 | % 5.79/2.09 | Instantiating formula (31) with all_0_3_3, all_0_2_2, all_11_0_6, all_26_0_12 and discharging atoms cross_product(all_0_3_3, all_0_2_2) = all_26_0_12, cross_product(all_0_3_3, all_0_2_2) = all_11_0_6, yields: % 5.79/2.09 | (76) all_26_0_12 = all_11_0_6 % 5.79/2.09 | % 5.79/2.09 | Combining equations (72,75) yields a new equation: % 5.79/2.09 | (77) all_26_0_12 = all_15_0_7 % 5.79/2.09 | % 5.79/2.09 | Simplifying 77 yields: % 5.79/2.09 | (78) all_26_0_12 = all_15_0_7 % 5.79/2.09 | % 5.79/2.09 | Combining equations (76,73) yields a new equation: % 5.79/2.09 | (79) all_21_0_10 = all_11_0_6 % 5.79/2.09 | % 5.79/2.09 | Combining equations (74,73) yields a new equation: % 5.79/2.09 | (80) all_21_0_10 = all_17_1_9 % 5.79/2.09 | % 5.79/2.09 | Combining equations (78,73) yields a new equation: % 5.79/2.09 | (81) all_21_0_10 = all_15_0_7 % 5.79/2.09 | % 5.79/2.09 | Combining equations (79,80) yields a new equation: % 5.79/2.09 | (82) all_17_1_9 = all_11_0_6 % 5.79/2.09 | % 5.79/2.09 | Combining equations (81,80) yields a new equation: % 5.79/2.09 | (83) all_17_1_9 = all_15_0_7 % 5.79/2.09 | % 5.79/2.09 | Combining equations (82,83) yields a new equation: % 5.79/2.09 | (84) all_15_0_7 = all_11_0_6 % 5.79/2.09 | % 5.79/2.09 | From (84) and (57) follows: % 5.79/2.09 | (85) ~ subset(all_0_4_4, all_11_0_6) % 5.79/2.09 | % 5.79/2.09 | Using (54) and (85) yields: % 5.79/2.09 | (86) $false % 5.79/2.09 | % 5.79/2.09 |-The branch is then unsatisfiable % 5.79/2.09 % SZS output end Proof for theBenchmark % 5.79/2.09 % 5.79/2.09 1558ms %------------------------------------------------------------------------------