%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET643+3 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n028.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 3.26s 1.53s % Output : Proof 4.87s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.14 % Problem : SET643+3 : TPTP v8.1.0. Released v2.2.0. % 0.04/0.14 % Command : ePrincess-casc -timeout=%d %s % 0.14/0.36 % Computer : n028.cluster.edu % 0.14/0.36 % Model : x86_64 x86_64 % 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.36 % Memory : 8042.1875MB % 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 600 % 0.14/0.36 % DateTime : Sun Jul 10 04:17:42 EDT 2022 % 0.14/0.36 % CPUTime : % 0.51/0.61 ____ _ % 0.51/0.61 ___ / __ \_____(_)___ ________ __________ % 0.51/0.62 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.51/0.62 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.51/0.62 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.51/0.62 % 0.51/0.62 A Theorem Prover for First-Order Logic % 0.51/0.62 (ePrincess v.1.0) % 0.51/0.62 % 0.51/0.62 (c) Philipp Rümmer, 2009-2015 % 0.51/0.62 (c) Peter Backeman, 2014-2015 % 0.51/0.62 (contributions by Angelo Brillout, Peter Baumgartner) % 0.51/0.62 Free software under GNU Lesser General Public License (LGPL). % 0.51/0.62 Bug reports to peter@backeman.se % 0.51/0.62 % 0.51/0.62 For more information, visit http://user.uu.se/~petba168/breu/ % 0.51/0.62 % 0.51/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.81/0.67 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.69/1.02 Prover 0: Preprocessing ... % 2.43/1.28 Prover 0: Warning: ignoring some quantifiers % 2.60/1.31 Prover 0: Constructing countermodel ... % 3.26/1.53 Prover 0: proved (866ms) % 3.26/1.53 % 3.26/1.53 No countermodel exists, formula is valid % 3.26/1.53 % SZS status Theorem for theBenchmark % 3.26/1.53 % 3.26/1.53 Generating proof ... Warning: ignoring some quantifiers % 4.82/1.82 found it (size 21) % 4.82/1.82 % 4.82/1.82 % SZS output start Proof for theBenchmark % 4.82/1.82 Assumed formulas after preprocessing and simplification: % 4.82/1.82 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (cross_product(v0, v1) = v2 & relation_type(v0, v1) = v3 & ilf_type(v1, set_type) & ilf_type(v0, set_type) & ~ ilf_type(v2, v3) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (ordered_pair(v8, v9) = v7) | ~ (cross_product(v4, v5) = v6) | ~ member(v9, v5) | ~ member(v8, v4) | ~ ilf_type(v9, set_type) | ~ ilf_type(v8, set_type) | ~ ilf_type(v7, set_type) | ~ ilf_type(v5, set_type) | ~ ilf_type(v4, set_type) | member(v7, v6)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (ordered_pair(v7, v6) = v5) | ~ (ordered_pair(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (cross_product(v7, v6) = v5) | ~ (cross_product(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (relation_type(v7, v6) = v5) | ~ (relation_type(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (power_set(v5) = v6) | ~ member(v7, v4) | ~ member(v4, v6) | ~ ilf_type(v7, set_type) | ~ ilf_type(v5, set_type) | ~ ilf_type(v4, set_type) | member(v7, v5)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (cross_product(v5, v6) = v7) | ~ subset(v4, v7) | ~ ilf_type(v6, set_type) | ~ ilf_type(v5, set_type) | ~ ilf_type(v4, set_type) | ? [v8] : (relation_type(v5, v6) = v8 & ilf_type(v4, v8))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (cross_product(v4, v5) = v6) | ~ member(v7, v6) | ~ ilf_type(v7, set_type) | ~ ilf_type(v5, set_type) | ~ ilf_type(v4, set_type) | ? [v8] : ? [v9] : (ordered_pair(v8, v9) = v7 & member(v9, v5) & member(v8, v4) & ilf_type(v9, set_type) & ilf_type(v8, set_type))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (relation_type(v5, v6) = v7) | ~ ilf_type(v6, set_type) | ~ ilf_type(v5, set_type) | ~ ilf_type(v4, set_type) | ilf_type(v4, v7) | ? [v8] : (cross_product(v5, v6) = v8 & ~ subset(v4, v8))) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (power_set(v6) = v5) | ~ (power_set(v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (member_type(v6) = v5) | ~ (member_type(v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (subset_type(v6) = v5) | ~ (subset_type(v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (power_set(v5) = v6) | ~ ilf_type(v5, set_type) | ~ ilf_type(v4, set_type) | member(v4, v6) | ? [v7] : (member(v7, v4) & ilf_type(v7, set_type) & ~ member(v7, v5))) & ! [v4] : ! [v5] : ! [v6] : ( ~ (member_type(v5) = v6) | ~ member(v4, v5) | ~ ilf_type(v5, set_type) | ~ ilf_type(v4, set_type) | empty(v5) | ilf_type(v4, v6)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (member_type(v5) = v6) | ~ ilf_type(v5, set_type) | ~ ilf_type(v4, v6) | ~ ilf_type(v4, set_type) | empty(v5) | member(v4, v5)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (ordered_pair(v4, v5) = v6) | ~ ilf_type(v5, set_type) | ~ ilf_type(v4, set_type) | ilf_type(v6, set_type)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (cross_product(v4, v5) = v6) | ~ ilf_type(v5, set_type) | ~ ilf_type(v4, set_type) | ilf_type(v6, set_type)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (cross_product(v4, v5) = v6) | ~ ilf_type(v5, set_type) | ~ ilf_type(v4, set_type) | ? [v7] : ? [v8] : (subset_type(v6) = v7 & relation_type(v4, v5) = v8 & ! [v9] : ( ~ ilf_type(v9, v8) | ilf_type(v9, v7)) & ! [v9] : ( ~ ilf_type(v9, v7) | ilf_type(v9, v8)))) & ! [v4] : ! [v5] : ! [v6] : ( ~ (cross_product(v4, v5) = v6) | ~ ilf_type(v5, set_type) | ~ ilf_type(v4, set_type) | ? [v7] : (subset_type(v6) = v7 & ! [v8] : ( ~ ilf_type(v8, v7) | relation_like(v8)))) & ! [v4] : ! [v5] : ! [v6] : ( ~ (relation_type(v5, v4) = v6) | ~ ilf_type(v5, set_type) | ~ ilf_type(v4, set_type) | ? [v7] : ilf_type(v7, v6)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (relation_type(v4, v5) = v6) | ~ ilf_type(v5, set_type) | ~ ilf_type(v4, set_type) | ? [v7] : ? [v8] : (subset_type(v7) = v8 & cross_product(v4, v5) = v7 & ! [v9] : ( ~ ilf_type(v9, v8) | ilf_type(v9, v6)) & ! [v9] : ( ~ ilf_type(v9, v6) | ilf_type(v9, v8)))) & ! [v4] : ! [v5] : ! [v6] : ( ~ member(v6, v4) | ~ subset(v4, v5) | ~ ilf_type(v6, set_type) | ~ ilf_type(v5, set_type) | ~ ilf_type(v4, set_type) | member(v6, v5)) & ! [v4] : ! [v5] : ( ~ (power_set(v4) = v5) | ~ empty(v5) | ~ ilf_type(v4, set_type)) & ! [v4] : ! [v5] : ( ~ (power_set(v4) = v5) | ~ ilf_type(v4, set_type) | ilf_type(v5, set_type)) & ! [v4] : ! [v5] : ( ~ (power_set(v4) = v5) | ~ ilf_type(v4, set_type) | ? [v6] : ? [v7] : (member_type(v5) = v7 & subset_type(v4) = v6 & ! [v8] : ( ~ ilf_type(v8, v7) | ~ ilf_type(v8, set_type) | ilf_type(v8, v6)) & ! [v8] : ( ~ ilf_type(v8, v6) | ~ ilf_type(v8, set_type) | ilf_type(v8, v7)))) & ! [v4] : ! [v5] : ( ~ (member_type(v4) = v5) | ~ ilf_type(v4, set_type) | empty(v4) | ? [v6] : ilf_type(v6, v5)) & ! [v4] : ! [v5] : ( ~ (subset_type(v4) = v5) | ~ ilf_type(v4, set_type) | ? [v6] : ? [v7] : (power_set(v4) = v6 & member_type(v6) = v7 & ! [v8] : ( ~ ilf_type(v8, v7) | ~ ilf_type(v8, set_type) | ilf_type(v8, v5)) & ! [v8] : ( ~ ilf_type(v8, v5) | ~ ilf_type(v8, set_type) | ilf_type(v8, v7)))) & ! [v4] : ! [v5] : ( ~ (subset_type(v4) = v5) | ~ ilf_type(v4, set_type) | ? [v6] : ilf_type(v6, v5)) & ! [v4] : ! [v5] : ( ~ relation_like(v4) | ~ member(v5, v4) | ~ ilf_type(v5, set_type) | ~ ilf_type(v4, set_type) | ? [v6] : ? [v7] : (ordered_pair(v6, v7) = v5 & ilf_type(v7, set_type) & ilf_type(v6, set_type))) & ! [v4] : ! [v5] : ( ~ empty(v4) | ~ member(v5, v4) | ~ ilf_type(v5, set_type) | ~ ilf_type(v4, set_type)) & ! [v4] : ! [v5] : ( ~ ilf_type(v5, set_type) | ~ ilf_type(v4, set_type) | subset(v4, v5) | ? [v6] : (member(v6, v4) & ilf_type(v6, set_type) & ~ member(v6, v5))) & ! [v4] : ( ~ empty(v4) | ~ ilf_type(v4, set_type) | relation_like(v4)) & ! [v4] : ( ~ ilf_type(v4, set_type) | relation_like(v4) | ? [v5] : (member(v5, v4) & ilf_type(v5, set_type) & ! [v6] : ! [v7] : ( ~ (ordered_pair(v6, v7) = v5) | ~ ilf_type(v7, set_type) | ~ ilf_type(v6, set_type)))) & ! [v4] : ( ~ ilf_type(v4, set_type) | empty(v4) | ? [v5] : (member(v5, v4) & ilf_type(v5, set_type))) & ! [v4] : ( ~ ilf_type(v4, set_type) | subset(v4, v4)) & ? [v4] : ilf_type(v4, set_type)) % 4.87/1.86 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields: % 4.87/1.86 | (1) cross_product(all_0_3_3, all_0_2_2) = all_0_1_1 & relation_type(all_0_3_3, all_0_2_2) = all_0_0_0 & ilf_type(all_0_2_2, set_type) & ilf_type(all_0_3_3, set_type) & ~ ilf_type(all_0_1_1, all_0_0_0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (ordered_pair(v4, v5) = v3) | ~ (cross_product(v0, v1) = v2) | ~ member(v5, v1) | ~ member(v4, v0) | ~ ilf_type(v5, set_type) | ~ ilf_type(v4, set_type) | ~ ilf_type(v3, set_type) | ~ ilf_type(v1, set_type) | ~ ilf_type(v0, set_type) | member(v3, v2)) & ! [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(v0, v1) = v2) | ~ member(v3, v2) | ~ ilf_type(v3, set_type) | ~ ilf_type(v1, set_type) | ~ ilf_type(v0, set_type) | ? [v4] : ? [v5] : (ordered_pair(v4, v5) = v3 & member(v5, v1) & member(v4, v0) & ilf_type(v5, set_type) & ilf_type(v4, set_type))) & ! [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] : (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] : ( ~ (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] : ( ~ (ordered_pair(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) | 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) % 4.87/1.88 | % 4.87/1.88 | Applying alpha-rule on (1) yields: % 4.87/1.88 | (2) ! [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)) % 4.87/1.88 | (3) ! [v0] : ! [v1] : ( ~ (member_type(v0) = v1) | ~ ilf_type(v0, set_type) | empty(v0) | ? [v2] : ilf_type(v2, v1)) % 4.87/1.88 | (4) ! [v0] : ! [v1] : ( ~ empty(v0) | ~ member(v1, v0) | ~ ilf_type(v1, set_type) | ~ ilf_type(v0, set_type)) % 4.87/1.88 | (5) ! [v0] : ( ~ ilf_type(v0, set_type) | subset(v0, v0)) % 4.87/1.88 | (6) ! [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)))) % 4.87/1.88 | (7) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (subset_type(v2) = v1) | ~ (subset_type(v2) = v0)) % 4.87/1.88 | (8) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0)) % 4.87/1.88 | (9) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_type(v1, v0) = v2) | ~ ilf_type(v1, set_type) | ~ ilf_type(v0, set_type) | ? [v3] : ilf_type(v3, v2)) % 4.87/1.88 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ (cross_product(v0, v1) = v2) | ~ ilf_type(v1, set_type) | ~ ilf_type(v0, set_type) | ilf_type(v2, set_type)) % 4.87/1.88 | (11) ! [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)))) % 4.87/1.88 | (12) relation_type(all_0_3_3, all_0_2_2) = all_0_0_0 % 4.87/1.88 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cross_product(v0, v1) = v2) | ~ member(v3, v2) | ~ ilf_type(v3, set_type) | ~ ilf_type(v1, set_type) | ~ ilf_type(v0, set_type) | ? [v4] : ? [v5] : (ordered_pair(v4, v5) = v3 & member(v5, v1) & member(v4, v0) & ilf_type(v5, set_type) & ilf_type(v4, set_type))) % 4.87/1.88 | (14) ! [v0] : ( ~ ilf_type(v0, set_type) | empty(v0) | ? [v1] : (member(v1, v0) & ilf_type(v1, set_type))) % 4.87/1.88 | (15) ! [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))) % 4.87/1.88 | (16) ! [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))) % 4.87/1.88 | (17) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ ilf_type(v1, set_type) | ~ ilf_type(v0, set_type) | ilf_type(v2, set_type)) % 4.87/1.88 | (18) ! [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)))) % 4.87/1.88 | (19) ilf_type(all_0_3_3, set_type) % 4.87/1.88 | (20) ! [v0] : ! [v1] : ( ~ (subset_type(v0) = v1) | ~ ilf_type(v0, set_type) | ? [v2] : ilf_type(v2, v1)) % 4.87/1.88 | (21) ? [v0] : ilf_type(v0, set_type) % 4.87/1.89 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (ordered_pair(v4, v5) = v3) | ~ (cross_product(v0, v1) = v2) | ~ member(v5, v1) | ~ member(v4, v0) | ~ ilf_type(v5, set_type) | ~ ilf_type(v4, set_type) | ~ ilf_type(v3, set_type) | ~ ilf_type(v1, set_type) | ~ ilf_type(v0, set_type) | member(v3, v2)) % 4.87/1.89 | (23) ! [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)))) % 4.87/1.89 | (24) ! [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)))) % 4.87/1.89 | (25) cross_product(all_0_3_3, all_0_2_2) = all_0_1_1 % 4.87/1.89 | (26) ! [v0] : ( ~ empty(v0) | ~ ilf_type(v0, set_type) | relation_like(v0)) % 4.87/1.89 | (27) ! [v0] : ! [v1] : ( ~ (power_set(v0) = v1) | ~ ilf_type(v0, set_type) | ilf_type(v1, set_type)) % 4.87/1.89 | (28) ! [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)))) % 4.87/1.89 | (29) ilf_type(all_0_2_2, set_type) % 4.87/1.89 | (30) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (member_type(v2) = v1) | ~ (member_type(v2) = v0)) % 4.87/1.89 | (31) ! [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))) % 4.87/1.89 | (32) ~ ilf_type(all_0_1_1, all_0_0_0) % 4.87/1.89 | (33) ! [v0] : ! [v1] : ( ~ (power_set(v0) = v1) | ~ empty(v1) | ~ ilf_type(v0, set_type)) % 4.87/1.89 | (34) ! [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)) % 4.87/1.89 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_type(v3, v2) = v1) | ~ (relation_type(v3, v2) = v0)) % 4.87/1.89 | (36) ! [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))) % 4.87/1.89 | (37) ! [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)) % 4.87/1.89 | (38) ! [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))) % 4.87/1.89 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cross_product(v3, v2) = v1) | ~ (cross_product(v3, v2) = v0)) % 4.87/1.89 | (40) ! [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)) % 4.87/1.89 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) % 4.87/1.89 | % 4.87/1.89 | Instantiating formula (10) with all_0_1_1, all_0_2_2, all_0_3_3 and discharging atoms cross_product(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: % 4.87/1.89 | (42) ilf_type(all_0_1_1, set_type) % 4.87/1.89 | % 4.87/1.89 | Instantiating formula (23) with all_0_1_1, all_0_2_2, all_0_3_3 and discharging atoms cross_product(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: % 4.87/1.89 | (43) ? [v0] : ? [v1] : (subset_type(all_0_1_1) = v0 & relation_type(all_0_3_3, all_0_2_2) = v1 & ! [v2] : ( ~ ilf_type(v2, v1) | ilf_type(v2, v0)) & ! [v2] : ( ~ ilf_type(v2, v0) | ilf_type(v2, v1))) % 4.87/1.89 | % 4.87/1.89 | Instantiating formula (18) with all_0_0_0, all_0_2_2, all_0_3_3 and discharging atoms relation_type(all_0_3_3, all_0_2_2) = all_0_0_0, ilf_type(all_0_2_2, set_type), ilf_type(all_0_3_3, set_type), yields: % 4.87/1.90 | (44) ? [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_0_0)) & ! [v2] : ( ~ ilf_type(v2, all_0_0_0) | ilf_type(v2, v1))) % 4.87/1.90 | % 4.87/1.90 | Instantiating (44) with all_11_0_5, all_11_1_6 yields: % 4.87/1.90 | (45) subset_type(all_11_1_6) = all_11_0_5 & cross_product(all_0_3_3, all_0_2_2) = all_11_1_6 & ! [v0] : ( ~ ilf_type(v0, all_11_0_5) | ilf_type(v0, all_0_0_0)) & ! [v0] : ( ~ ilf_type(v0, all_0_0_0) | ilf_type(v0, all_11_0_5)) % 4.87/1.90 | % 4.87/1.90 | Applying alpha-rule on (45) yields: % 4.87/1.90 | (46) subset_type(all_11_1_6) = all_11_0_5 % 4.87/1.90 | (47) cross_product(all_0_3_3, all_0_2_2) = all_11_1_6 % 4.87/1.90 | (48) ! [v0] : ( ~ ilf_type(v0, all_11_0_5) | ilf_type(v0, all_0_0_0)) % 4.87/1.90 | (49) ! [v0] : ( ~ ilf_type(v0, all_0_0_0) | ilf_type(v0, all_11_0_5)) % 4.87/1.90 | % 4.87/1.90 | Instantiating (43) with all_16_0_8, all_16_1_9 yields: % 4.87/1.90 | (50) subset_type(all_0_1_1) = all_16_1_9 & relation_type(all_0_3_3, all_0_2_2) = all_16_0_8 & ! [v0] : ( ~ ilf_type(v0, all_16_0_8) | ilf_type(v0, all_16_1_9)) & ! [v0] : ( ~ ilf_type(v0, all_16_1_9) | ilf_type(v0, all_16_0_8)) % 4.87/1.90 | % 4.87/1.90 | Applying alpha-rule on (50) yields: % 4.87/1.90 | (51) subset_type(all_0_1_1) = all_16_1_9 % 4.87/1.90 | (52) relation_type(all_0_3_3, all_0_2_2) = all_16_0_8 % 4.87/1.90 | (53) ! [v0] : ( ~ ilf_type(v0, all_16_0_8) | ilf_type(v0, all_16_1_9)) % 4.87/1.90 | (54) ! [v0] : ( ~ ilf_type(v0, all_16_1_9) | ilf_type(v0, all_16_0_8)) % 4.87/1.90 | % 4.87/1.90 | Instantiating formula (39) with all_0_3_3, all_0_2_2, all_11_1_6, all_0_1_1 and discharging atoms cross_product(all_0_3_3, all_0_2_2) = all_11_1_6, cross_product(all_0_3_3, all_0_2_2) = all_0_1_1, yields: % 4.87/1.90 | (55) all_11_1_6 = all_0_1_1 % 4.87/1.90 | % 4.87/1.90 | Instantiating formula (35) with all_0_3_3, all_0_2_2, all_16_0_8, all_0_0_0 and discharging atoms relation_type(all_0_3_3, all_0_2_2) = all_16_0_8, relation_type(all_0_3_3, all_0_2_2) = all_0_0_0, yields: % 4.87/1.90 | (56) all_16_0_8 = all_0_0_0 % 4.87/1.90 | % 4.87/1.90 | From (55) and (47) follows: % 4.87/1.90 | (25) cross_product(all_0_3_3, all_0_2_2) = all_0_1_1 % 4.87/1.90 | % 4.87/1.90 | From (56) and (52) follows: % 4.87/1.90 | (12) relation_type(all_0_3_3, all_0_2_2) = all_0_0_0 % 4.87/1.90 | % 4.87/1.90 | Instantiating formula (16) with all_0_0_0, all_0_2_2, all_0_3_3, all_0_1_1 and discharging atoms relation_type(all_0_3_3, all_0_2_2) = all_0_0_0, ilf_type(all_0_1_1, set_type), ilf_type(all_0_2_2, set_type), ilf_type(all_0_3_3, set_type), ~ ilf_type(all_0_1_1, all_0_0_0), yields: % 4.87/1.90 | (59) ? [v0] : (cross_product(all_0_3_3, all_0_2_2) = v0 & ~ subset(all_0_1_1, v0)) % 4.87/1.90 | % 4.87/1.90 | Instantiating formula (31) with all_0_1_1, all_0_1_1 and discharging atoms ilf_type(all_0_1_1, set_type), yields: % 4.87/1.90 | (60) subset(all_0_1_1, all_0_1_1) % 4.87/1.90 | % 4.87/1.90 | Instantiating (59) with all_41_0_14 yields: % 4.87/1.90 | (61) cross_product(all_0_3_3, all_0_2_2) = all_41_0_14 & ~ subset(all_0_1_1, all_41_0_14) % 4.87/1.90 | % 4.87/1.90 | Applying alpha-rule on (61) yields: % 4.87/1.90 | (62) cross_product(all_0_3_3, all_0_2_2) = all_41_0_14 % 4.87/1.90 | (63) ~ subset(all_0_1_1, all_41_0_14) % 4.87/1.90 | % 4.87/1.90 | Instantiating formula (39) with all_0_3_3, all_0_2_2, all_41_0_14, all_0_1_1 and discharging atoms cross_product(all_0_3_3, all_0_2_2) = all_41_0_14, cross_product(all_0_3_3, all_0_2_2) = all_0_1_1, yields: % 4.87/1.90 | (64) all_41_0_14 = all_0_1_1 % 4.87/1.90 | % 4.87/1.90 | From (64) and (63) follows: % 4.87/1.90 | (65) ~ subset(all_0_1_1, all_0_1_1) % 4.87/1.90 | % 4.87/1.90 | Using (60) and (65) yields: % 4.87/1.90 | (66) $false % 4.87/1.90 | % 4.87/1.90 |-The branch is then unsatisfiable % 4.87/1.90 % SZS output end Proof for theBenchmark % 4.87/1.90 % 4.87/1.90 1276ms %------------------------------------------------------------------------------