%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET665+3 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n019.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 00:21:16 EDT 2022 % Result : Theorem 4.46s 1.69s % Output : Proof 7.29s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SET665+3 : TPTP v8.1.0. Released v2.2.0. % 0.06/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n019.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Sun Jul 10 02:20:38 EDT 2022 % 0.12/0.33 % CPUTime : % 0.45/0.62 ____ _ % 0.45/0.62 ___ / __ \_____(_)___ ________ __________ % 0.45/0.62 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.45/0.62 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.45/0.62 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.45/0.62 % 0.45/0.62 A Theorem Prover for First-Order Logic % 0.66/0.62 (ePrincess v.1.0) % 0.66/0.62 % 0.66/0.62 (c) Philipp Rümmer, 2009-2015 % 0.66/0.62 (c) Peter Backeman, 2014-2015 % 0.66/0.62 (contributions by Angelo Brillout, Peter Baumgartner) % 0.66/0.62 Free software under GNU Lesser General Public License (LGPL). % 0.66/0.62 Bug reports to peter@backeman.se % 0.66/0.62 % 0.66/0.62 For more information, visit http://user.uu.se/~petba168/breu/ % 0.66/0.62 % 0.66/0.63 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.66/0.68 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.72/1.01 Prover 0: Preprocessing ... % 2.71/1.30 Prover 0: Warning: ignoring some quantifiers % 2.71/1.33 Prover 0: Constructing countermodel ... % 4.46/1.69 Prover 0: proved (1012ms) % 4.46/1.69 % 4.46/1.69 No countermodel exists, formula is valid % 4.46/1.69 % SZS status Theorem for theBenchmark % 4.46/1.69 % 4.46/1.69 Generating proof ... Warning: ignoring some quantifiers % 6.66/2.20 found it (size 43) % 6.66/2.20 % 6.66/2.20 % SZS output start Proof for theBenchmark % 6.66/2.20 Assumed formulas after preprocessing and simplification: % 6.66/2.20 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (cross_product(v0, v0) = v2 & identity_relation_of(v0) = v1 & ilf_type(v3, binary_relation_type) & ilf_type(v0, set_type) & ~ subset(v1, v2) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (cross_product(v7, v8) = v9) | ~ (ordered_pair(v4, v5) = v6) | ~ member(v6, v9) | ~ ilf_type(v8, set_type) | ~ ilf_type(v7, set_type) | ~ ilf_type(v5, set_type) | ~ ilf_type(v4, set_type) | member(v5, v8)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (cross_product(v7, v8) = v9) | ~ (ordered_pair(v4, v5) = v6) | ~ member(v6, v9) | ~ ilf_type(v8, set_type) | ~ ilf_type(v7, set_type) | ~ ilf_type(v5, set_type) | ~ ilf_type(v4, set_type) | member(v4, v7)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (cross_product(v7, v8) = v9) | ~ (ordered_pair(v4, v5) = v6) | ~ member(v5, v8) | ~ member(v4, v7) | ~ ilf_type(v8, set_type) | ~ ilf_type(v7, set_type) | ~ ilf_type(v5, set_type) | ~ ilf_type(v4, set_type) | member(v6, v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (cross_product(v4, v5) = v6) | ~ (ordered_pair(v8, v9) = v7) | ~ 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] : ! [v8] : (v7 = v6 | ~ (identity_relation_of(v4) = v5) | ~ (ordered_pair(v6, v7) = v8) | ~ member(v8, v5) | ~ ilf_type(v7, set_type) | ~ ilf_type(v6, set_type) | ~ ilf_type(v4, set_type)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (identity_relation_of(v4) = v5) | ~ (ordered_pair(v6, v7) = v8) | ~ member(v8, v5) | ~ ilf_type(v7, set_type) | ~ ilf_type(v6, set_type) | ~ ilf_type(v4, set_type) | member(v6, v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (ordered_pair(v6, v7) = v8) | ~ member(v8, v4) | ~ subset(v4, v5) | ~ ilf_type(v7, set_type) | ~ ilf_type(v6, set_type) | ~ ilf_type(v5, binary_relation_type) | ~ ilf_type(v4, binary_relation_type) | member(v8, v5)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (relation_type(v7, v6) = v5) | ~ (relation_type(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 | ~ (ordered_pair(v7, v6) = v5) | ~ (ordered_pair(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(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] : ( ~ (identity_relation_of(v4) = v5) | ~ (ordered_pair(v6, v6) = v7) | ~ member(v6, v4) | ~ ilf_type(v6, set_type) | ~ ilf_type(v4, set_type) | member(v7, v5)) & ! [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] : (v5 = v4 | ~ (identity_relation_of(v6) = v5) | ~ (identity_relation_of(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] : ( ~ (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] : ( ~ (relation_type(v4, v5) = v6) | ~ ilf_type(v5, set_type) | ~ ilf_type(v4, set_type) | ? [v7] : (cross_product(v4, v5) = v7 & ilf_type(v7, v6))) & ! [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] : ( ~ (cross_product(v4, v5) = v6) | ~ ilf_type(v5, set_type) | ~ ilf_type(v4, set_type) | ? [v7] : (relation_type(v4, v5) = v7 & ilf_type(v6, v7))) & ! [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] : ( ~ 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] : ( ~ (identity_relation_of(v4) = v5) | ~ ilf_type(v4, set_type) | ilf_type(v5, binary_relation_type)) & ! [v4] : ! [v5] : ( ~ empty(v4) | ~ member(v5, v4) | ~ ilf_type(v5, set_type) | ~ ilf_type(v4, set_type)) & ! [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] : ( ~ 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] : ! [v5] : ( ~ ilf_type(v5, binary_relation_type) | ~ ilf_type(v4, binary_relation_type) | subset(v4, v5) | ? [v6] : ? [v7] : ? [v8] : (ordered_pair(v6, v7) = v8 & member(v8, v4) & ilf_type(v7, set_type) & ilf_type(v6, set_type) & ~ member(v8, v5))) & ! [v4] : ( ~ empty(v4) | ~ ilf_type(v4, set_type) | relation_like(v4)) & ! [v4] : ( ~ relation_like(v4) | ~ ilf_type(v4, set_type) | ilf_type(v4, binary_relation_type)) & ! [v4] : ( ~ ilf_type(v4, set_type) | ~ ilf_type(v4, binary_relation_type) | relation_like(v4)) & ! [v4] : ( ~ ilf_type(v4, set_type) | empty(v4) | ? [v5] : (member(v5, v4) & ilf_type(v5, set_type))) & ! [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) | subset(v4, v4)) & ! [v4] : ( ~ ilf_type(v4, binary_relation_type) | subset(v4, v4)) & ? [v4] : ilf_type(v4, set_type)) % 6.66/2.25 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields: % 6.66/2.25 | (1) cross_product(all_0_3_3, all_0_3_3) = all_0_1_1 & identity_relation_of(all_0_3_3) = all_0_2_2 & ilf_type(all_0_0_0, binary_relation_type) & ilf_type(all_0_3_3, set_type) & ~ subset(all_0_2_2, all_0_1_1) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cross_product(v3, v4) = v5) | ~ (ordered_pair(v0, v1) = v2) | ~ member(v2, v5) | ~ ilf_type(v4, set_type) | ~ ilf_type(v3, set_type) | ~ ilf_type(v1, set_type) | ~ ilf_type(v0, set_type) | member(v1, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cross_product(v3, v4) = v5) | ~ (ordered_pair(v0, v1) = v2) | ~ member(v2, v5) | ~ ilf_type(v4, set_type) | ~ ilf_type(v3, set_type) | ~ ilf_type(v1, set_type) | ~ ilf_type(v0, set_type) | member(v0, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cross_product(v3, v4) = v5) | ~ (ordered_pair(v0, v1) = v2) | ~ member(v1, v4) | ~ member(v0, v3) | ~ ilf_type(v4, set_type) | ~ ilf_type(v3, set_type) | ~ ilf_type(v1, set_type) | ~ ilf_type(v0, set_type) | member(v2, v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cross_product(v0, v1) = v2) | ~ (ordered_pair(v4, v5) = v3) | ~ 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] : ! [v4] : (v3 = v2 | ~ (identity_relation_of(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ member(v4, v1) | ~ ilf_type(v3, set_type) | ~ ilf_type(v2, set_type) | ~ ilf_type(v0, set_type)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (identity_relation_of(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ member(v4, v1) | ~ ilf_type(v3, set_type) | ~ ilf_type(v2, set_type) | ~ ilf_type(v0, set_type) | member(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (ordered_pair(v2, v3) = v4) | ~ member(v4, v0) | ~ subset(v0, v1) | ~ ilf_type(v3, set_type) | ~ ilf_type(v2, set_type) | ~ ilf_type(v1, binary_relation_type) | ~ ilf_type(v0, binary_relation_type) | member(v4, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_type(v3, v2) = v1) | ~ (relation_type(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 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(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(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] : ( ~ (identity_relation_of(v0) = v1) | ~ (ordered_pair(v2, v2) = v3) | ~ member(v2, v0) | ~ ilf_type(v2, set_type) | ~ ilf_type(v0, set_type) | member(v3, v1)) & ! [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] : (v1 = v0 | ~ (identity_relation_of(v2) = v1) | ~ (identity_relation_of(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] : ( ~ (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] : ( ~ (relation_type(v0, v1) = v2) | ~ ilf_type(v1, set_type) | ~ ilf_type(v0, set_type) | ? [v3] : (cross_product(v0, v1) = v3 & ilf_type(v3, v2))) & ! [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] : ( ~ (cross_product(v0, v1) = v2) | ~ ilf_type(v1, set_type) | ~ ilf_type(v0, set_type) | ? [v3] : (relation_type(v0, v1) = v3 & ilf_type(v2, v3))) & ! [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] : ( ~ 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] : ( ~ (identity_relation_of(v0) = v1) | ~ ilf_type(v0, set_type) | ilf_type(v1, binary_relation_type)) & ! [v0] : ! [v1] : ( ~ empty(v0) | ~ member(v1, v0) | ~ ilf_type(v1, set_type) | ~ ilf_type(v0, set_type)) & ! [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] : ( ~ 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] : ! [v1] : ( ~ ilf_type(v1, binary_relation_type) | ~ ilf_type(v0, binary_relation_type) | subset(v0, v1) | ? [v2] : ? [v3] : ? [v4] : (ordered_pair(v2, v3) = v4 & member(v4, v0) & ilf_type(v3, set_type) & ilf_type(v2, set_type) & ~ member(v4, v1))) & ! [v0] : ( ~ empty(v0) | ~ ilf_type(v0, set_type) | relation_like(v0)) & ! [v0] : ( ~ relation_like(v0) | ~ ilf_type(v0, set_type) | ilf_type(v0, binary_relation_type)) & ! [v0] : ( ~ ilf_type(v0, set_type) | ~ ilf_type(v0, binary_relation_type) | relation_like(v0)) & ! [v0] : ( ~ ilf_type(v0, set_type) | empty(v0) | ? [v1] : (member(v1, v0) & ilf_type(v1, set_type))) & ! [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) | subset(v0, v0)) & ! [v0] : ( ~ ilf_type(v0, binary_relation_type) | subset(v0, v0)) & ? [v0] : ilf_type(v0, set_type) % 7.08/2.26 | % 7.08/2.26 | Applying alpha-rule on (1) yields: % 7.08/2.26 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cross_product(v3, v2) = v1) | ~ (cross_product(v3, v2) = v0)) % 7.08/2.26 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cross_product(v3, v4) = v5) | ~ (ordered_pair(v0, v1) = v2) | ~ member(v1, v4) | ~ member(v0, v3) | ~ ilf_type(v4, set_type) | ~ ilf_type(v3, set_type) | ~ ilf_type(v1, set_type) | ~ ilf_type(v0, set_type) | member(v2, v5)) % 7.08/2.26 | (4) ! [v0] : ( ~ empty(v0) | ~ ilf_type(v0, set_type) | relation_like(v0)) % 7.08/2.27 | (5) ! [v0] : ! [v1] : ( ~ (member_type(v0) = v1) | ~ ilf_type(v0, set_type) | empty(v0) | ? [v2] : ilf_type(v2, v1)) % 7.08/2.27 | (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)))) % 7.08/2.27 | (7) identity_relation_of(all_0_3_3) = all_0_2_2 % 7.08/2.27 | (8) ilf_type(all_0_3_3, set_type) % 7.08/2.27 | (9) ! [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)) % 7.08/2.27 | (10) ! [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)) % 7.08/2.27 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (identity_relation_of(v0) = v1) | ~ (ordered_pair(v2, v2) = v3) | ~ member(v2, v0) | ~ ilf_type(v2, set_type) | ~ ilf_type(v0, set_type) | member(v3, v1)) % 7.08/2.27 | (12) ! [v0] : ( ~ ilf_type(v0, set_type) | ~ ilf_type(v0, binary_relation_type) | relation_like(v0)) % 7.08/2.27 | (13) ! [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)))) % 7.08/2.27 | (14) ! [v0] : ! [v1] : ! [v2] : ( ~ (cross_product(v0, v1) = v2) | ~ ilf_type(v1, set_type) | ~ ilf_type(v0, set_type) | ? [v3] : (relation_type(v0, v1) = v3 & ilf_type(v2, v3))) % 7.08/2.27 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (ordered_pair(v2, v3) = v4) | ~ member(v4, v0) | ~ subset(v0, v1) | ~ ilf_type(v3, set_type) | ~ ilf_type(v2, set_type) | ~ ilf_type(v1, binary_relation_type) | ~ ilf_type(v0, binary_relation_type) | member(v4, v1)) % 7.08/2.27 | (16) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ ilf_type(v1, set_type) | ~ ilf_type(v0, set_type) | ilf_type(v2, set_type)) % 7.08/2.27 | (17) ! [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)))) % 7.08/2.27 | (18) ! [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))) % 7.08/2.27 | (19) ! [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)))) % 7.08/2.27 | (20) ~ subset(all_0_2_2, all_0_1_1) % 7.08/2.27 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (identity_relation_of(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ member(v4, v1) | ~ ilf_type(v3, set_type) | ~ ilf_type(v2, set_type) | ~ ilf_type(v0, set_type) | member(v2, v0)) % 7.08/2.27 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cross_product(v3, v4) = v5) | ~ (ordered_pair(v0, v1) = v2) | ~ member(v2, v5) | ~ ilf_type(v4, set_type) | ~ ilf_type(v3, set_type) | ~ ilf_type(v1, set_type) | ~ ilf_type(v0, set_type) | member(v0, v3)) % 7.08/2.27 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) % 7.08/2.27 | (24) ! [v0] : ! [v1] : ( ~ (power_set(v0) = v1) | ~ empty(v1) | ~ ilf_type(v0, set_type)) % 7.08/2.27 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (identity_relation_of(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ member(v4, v1) | ~ ilf_type(v3, set_type) | ~ ilf_type(v2, set_type) | ~ ilf_type(v0, set_type)) % 7.08/2.27 | (26) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (identity_relation_of(v2) = v1) | ~ (identity_relation_of(v2) = v0)) % 7.08/2.27 | (27) ! [v0] : ! [v1] : ( ~ (subset_type(v0) = v1) | ~ ilf_type(v0, set_type) | ? [v2] : ilf_type(v2, v1)) % 7.08/2.27 | (28) ! [v0] : ! [v1] : ! [v2] : ( ~ (cross_product(v0, v1) = v2) | ~ ilf_type(v1, set_type) | ~ ilf_type(v0, set_type) | ilf_type(v2, set_type)) % 7.08/2.27 | (29) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0)) % 7.08/2.27 | (30) ! [v0] : ( ~ ilf_type(v0, set_type) | subset(v0, v0)) % 7.08/2.27 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_type(v3, v2) = v1) | ~ (relation_type(v3, v2) = v0)) % 7.08/2.27 | (32) ! [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))) % 7.08/2.28 | (33) ! [v0] : ( ~ ilf_type(v0, binary_relation_type) | subset(v0, v0)) % 7.08/2.28 | (34) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (member_type(v2) = v1) | ~ (member_type(v2) = v0)) % 7.08/2.28 | (35) ! [v0] : ! [v1] : ( ~ (power_set(v0) = v1) | ~ ilf_type(v0, set_type) | ilf_type(v1, set_type)) % 7.08/2.28 | (36) ! [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)) % 7.08/2.28 | (37) cross_product(all_0_3_3, all_0_3_3) = all_0_1_1 % 7.08/2.28 | (38) ! [v0] : ! [v1] : ( ~ empty(v0) | ~ member(v1, v0) | ~ ilf_type(v1, set_type) | ~ ilf_type(v0, set_type)) % 7.08/2.28 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cross_product(v3, v4) = v5) | ~ (ordered_pair(v0, v1) = v2) | ~ member(v2, v5) | ~ ilf_type(v4, set_type) | ~ ilf_type(v3, set_type) | ~ ilf_type(v1, set_type) | ~ ilf_type(v0, set_type) | member(v1, v4)) % 7.08/2.28 | (40) ? [v0] : ilf_type(v0, set_type) % 7.08/2.28 | (41) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (subset_type(v2) = v1) | ~ (subset_type(v2) = v0)) % 7.08/2.28 | (42) ! [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)))) % 7.08/2.28 | (43) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_type(v0, v1) = v2) | ~ ilf_type(v1, set_type) | ~ ilf_type(v0, set_type) | ? [v3] : (cross_product(v0, v1) = v3 & ilf_type(v3, v2))) % 7.08/2.28 | (44) ! [v0] : ( ~ ilf_type(v0, set_type) | empty(v0) | ? [v1] : (member(v1, v0) & ilf_type(v1, set_type))) % 7.08/2.28 | (45) ! [v0] : ! [v1] : ( ~ (identity_relation_of(v0) = v1) | ~ ilf_type(v0, set_type) | ilf_type(v1, binary_relation_type)) % 7.08/2.28 | (46) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_type(v1, v0) = v2) | ~ ilf_type(v1, set_type) | ~ ilf_type(v0, set_type) | ? [v3] : ilf_type(v3, v2)) % 7.08/2.28 | (47) ! [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))) % 7.08/2.28 | (48) ! [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))) % 7.08/2.28 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cross_product(v0, v1) = v2) | ~ (ordered_pair(v4, v5) = v3) | ~ 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)) % 7.08/2.28 | (50) ! [v0] : ! [v1] : ( ~ ilf_type(v1, binary_relation_type) | ~ ilf_type(v0, binary_relation_type) | subset(v0, v1) | ? [v2] : ? [v3] : ? [v4] : (ordered_pair(v2, v3) = v4 & member(v4, v0) & ilf_type(v3, set_type) & ilf_type(v2, set_type) & ~ member(v4, v1))) % 7.08/2.28 | (51) ! [v0] : ( ~ relation_like(v0) | ~ ilf_type(v0, set_type) | ilf_type(v0, binary_relation_type)) % 7.08/2.28 | (52) ilf_type(all_0_0_0, binary_relation_type) % 7.08/2.28 | (53) ! [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)))) % 7.08/2.28 | (54) ! [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)) % 7.08/2.28 | % 7.08/2.28 | Instantiating formula (28) with all_0_1_1, all_0_3_3, all_0_3_3 and discharging atoms cross_product(all_0_3_3, all_0_3_3) = all_0_1_1, ilf_type(all_0_3_3, set_type), yields: % 7.08/2.28 | (55) ilf_type(all_0_1_1, set_type) % 7.08/2.28 | % 7.08/2.28 | Instantiating formula (42) with all_0_1_1, all_0_3_3, all_0_3_3 and discharging atoms cross_product(all_0_3_3, all_0_3_3) = all_0_1_1, ilf_type(all_0_3_3, set_type), yields: % 7.08/2.28 | (56) ? [v0] : ? [v1] : (subset_type(all_0_1_1) = v0 & relation_type(all_0_3_3, all_0_3_3) = v1 & ! [v2] : ( ~ ilf_type(v2, v1) | ilf_type(v2, v0)) & ! [v2] : ( ~ ilf_type(v2, v0) | ilf_type(v2, v1))) % 7.08/2.28 | % 7.08/2.28 | Instantiating formula (53) with all_0_1_1, all_0_3_3, all_0_3_3 and discharging atoms cross_product(all_0_3_3, all_0_3_3) = all_0_1_1, ilf_type(all_0_3_3, set_type), yields: % 7.08/2.29 | (57) ? [v0] : (subset_type(all_0_1_1) = v0 & ! [v1] : ( ~ ilf_type(v1, v0) | relation_like(v1))) % 7.08/2.29 | % 7.08/2.29 | Instantiating formula (14) with all_0_1_1, all_0_3_3, all_0_3_3 and discharging atoms cross_product(all_0_3_3, all_0_3_3) = all_0_1_1, ilf_type(all_0_3_3, set_type), yields: % 7.08/2.29 | (58) ? [v0] : (relation_type(all_0_3_3, all_0_3_3) = v0 & ilf_type(all_0_1_1, v0)) % 7.08/2.29 | % 7.08/2.29 | Instantiating formula (45) with all_0_2_2, all_0_3_3 and discharging atoms identity_relation_of(all_0_3_3) = all_0_2_2, ilf_type(all_0_3_3, set_type), yields: % 7.08/2.29 | (59) ilf_type(all_0_2_2, binary_relation_type) % 7.08/2.29 | % 7.08/2.29 | Instantiating (56) with all_11_0_5, all_11_1_6 yields: % 7.08/2.29 | (60) subset_type(all_0_1_1) = all_11_1_6 & relation_type(all_0_3_3, all_0_3_3) = all_11_0_5 & ! [v0] : ( ~ ilf_type(v0, all_11_0_5) | ilf_type(v0, all_11_1_6)) & ! [v0] : ( ~ ilf_type(v0, all_11_1_6) | ilf_type(v0, all_11_0_5)) % 7.08/2.29 | % 7.08/2.29 | Applying alpha-rule on (60) yields: % 7.08/2.29 | (61) subset_type(all_0_1_1) = all_11_1_6 % 7.08/2.29 | (62) relation_type(all_0_3_3, all_0_3_3) = all_11_0_5 % 7.08/2.29 | (63) ! [v0] : ( ~ ilf_type(v0, all_11_0_5) | ilf_type(v0, all_11_1_6)) % 7.08/2.29 | (64) ! [v0] : ( ~ ilf_type(v0, all_11_1_6) | ilf_type(v0, all_11_0_5)) % 7.08/2.29 | % 7.08/2.29 | Instantiating (58) with all_14_0_7 yields: % 7.08/2.29 | (65) relation_type(all_0_3_3, all_0_3_3) = all_14_0_7 & ilf_type(all_0_1_1, all_14_0_7) % 7.08/2.29 | % 7.08/2.29 | Applying alpha-rule on (65) yields: % 7.08/2.29 | (66) relation_type(all_0_3_3, all_0_3_3) = all_14_0_7 % 7.08/2.29 | (67) ilf_type(all_0_1_1, all_14_0_7) % 7.08/2.29 | % 7.08/2.29 | Instantiating (57) with all_16_0_8 yields: % 7.08/2.29 | (68) subset_type(all_0_1_1) = all_16_0_8 & ! [v0] : ( ~ ilf_type(v0, all_16_0_8) | relation_like(v0)) % 7.08/2.29 | % 7.08/2.29 | Applying alpha-rule on (68) yields: % 7.08/2.29 | (69) subset_type(all_0_1_1) = all_16_0_8 % 7.08/2.29 | (70) ! [v0] : ( ~ ilf_type(v0, all_16_0_8) | relation_like(v0)) % 7.08/2.29 | % 7.08/2.29 | Instantiating formula (41) with all_0_1_1, all_11_1_6, all_16_0_8 and discharging atoms subset_type(all_0_1_1) = all_16_0_8, subset_type(all_0_1_1) = all_11_1_6, yields: % 7.08/2.29 | (71) all_16_0_8 = all_11_1_6 % 7.08/2.29 | % 7.08/2.29 | Instantiating formula (31) with all_0_3_3, all_0_3_3, all_11_0_5, all_14_0_7 and discharging atoms relation_type(all_0_3_3, all_0_3_3) = all_14_0_7, relation_type(all_0_3_3, all_0_3_3) = all_11_0_5, yields: % 7.08/2.29 | (72) all_14_0_7 = all_11_0_5 % 7.08/2.29 | % 7.08/2.29 | From (71) and (69) follows: % 7.08/2.29 | (61) subset_type(all_0_1_1) = all_11_1_6 % 7.08/2.29 | % 7.08/2.29 | From (72) and (66) follows: % 7.08/2.29 | (62) relation_type(all_0_3_3, all_0_3_3) = all_11_0_5 % 7.08/2.29 | % 7.08/2.29 | From (72) and (67) follows: % 7.08/2.29 | (75) ilf_type(all_0_1_1, all_11_0_5) % 7.08/2.29 | % 7.08/2.29 | Instantiating formula (17) with all_11_0_5, all_0_3_3, all_0_3_3 and discharging atoms relation_type(all_0_3_3, all_0_3_3) = all_11_0_5, ilf_type(all_0_3_3, set_type), yields: % 7.08/2.29 | (76) ? [v0] : ? [v1] : (subset_type(v0) = v1 & cross_product(all_0_3_3, all_0_3_3) = v0 & ! [v2] : ( ~ ilf_type(v2, v1) | ilf_type(v2, all_11_0_5)) & ! [v2] : ( ~ ilf_type(v2, all_11_0_5) | ilf_type(v2, v1))) % 7.08/2.29 | % 7.08/2.29 | Instantiating (76) with all_36_0_13, all_36_1_14 yields: % 7.08/2.29 | (77) subset_type(all_36_1_14) = all_36_0_13 & cross_product(all_0_3_3, all_0_3_3) = all_36_1_14 & ! [v0] : ( ~ ilf_type(v0, all_36_0_13) | ilf_type(v0, all_11_0_5)) & ! [v0] : ( ~ ilf_type(v0, all_11_0_5) | ilf_type(v0, all_36_0_13)) % 7.08/2.29 | % 7.08/2.29 | Applying alpha-rule on (77) yields: % 7.08/2.29 | (78) subset_type(all_36_1_14) = all_36_0_13 % 7.08/2.29 | (79) cross_product(all_0_3_3, all_0_3_3) = all_36_1_14 % 7.08/2.29 | (80) ! [v0] : ( ~ ilf_type(v0, all_36_0_13) | ilf_type(v0, all_11_0_5)) % 7.08/2.29 | (81) ! [v0] : ( ~ ilf_type(v0, all_11_0_5) | ilf_type(v0, all_36_0_13)) % 7.08/2.29 | % 7.08/2.29 | Instantiating formula (81) with all_0_1_1 and discharging atoms ilf_type(all_0_1_1, all_11_0_5), yields: % 7.08/2.29 | (82) ilf_type(all_0_1_1, all_36_0_13) % 7.08/2.29 | % 7.08/2.29 | Instantiating formula (2) with all_0_3_3, all_0_3_3, all_36_1_14, all_0_1_1 and discharging atoms cross_product(all_0_3_3, all_0_3_3) = all_36_1_14, cross_product(all_0_3_3, all_0_3_3) = all_0_1_1, yields: % 7.08/2.29 | (83) all_36_1_14 = all_0_1_1 % 7.08/2.29 | % 7.08/2.29 | From (83) and (78) follows: % 7.08/2.29 | (84) subset_type(all_0_1_1) = all_36_0_13 % 7.08/2.30 | % 7.08/2.30 | From (83) and (79) follows: % 7.08/2.30 | (37) cross_product(all_0_3_3, all_0_3_3) = all_0_1_1 % 7.08/2.30 | % 7.08/2.30 | Instantiating formula (41) with all_0_1_1, all_36_0_13, all_11_1_6 and discharging atoms subset_type(all_0_1_1) = all_36_0_13, subset_type(all_0_1_1) = all_11_1_6, yields: % 7.08/2.30 | (86) all_36_0_13 = all_11_1_6 % 7.08/2.30 | % 7.08/2.30 | From (86) and (82) follows: % 7.08/2.30 | (87) ilf_type(all_0_1_1, all_11_1_6) % 7.08/2.30 | % 7.08/2.30 | Instantiating formula (70) with all_0_1_1 yields: % 7.08/2.30 | (88) ~ ilf_type(all_0_1_1, all_16_0_8) | relation_like(all_0_1_1) % 7.08/2.30 | % 7.08/2.30 +-Applying beta-rule and splitting (88), into two cases. % 7.08/2.30 |-Branch one: % 7.08/2.30 | (89) ~ ilf_type(all_0_1_1, all_16_0_8) % 7.08/2.30 | % 7.08/2.30 | From (71) and (89) follows: % 7.08/2.30 | (90) ~ ilf_type(all_0_1_1, all_11_1_6) % 7.08/2.30 | % 7.08/2.30 | Using (87) and (90) yields: % 7.08/2.30 | (91) $false % 7.08/2.30 | % 7.08/2.30 |-The branch is then unsatisfiable % 7.08/2.30 |-Branch two: % 7.08/2.30 | (92) ilf_type(all_0_1_1, all_16_0_8) % 7.08/2.30 | (93) relation_like(all_0_1_1) % 7.08/2.30 | % 7.08/2.30 | Instantiating formula (51) with all_0_1_1 and discharging atoms relation_like(all_0_1_1), ilf_type(all_0_1_1, set_type), yields: % 7.08/2.30 | (94) ilf_type(all_0_1_1, binary_relation_type) % 7.08/2.30 | % 7.08/2.30 | Instantiating formula (50) with all_0_1_1, all_0_2_2 and discharging atoms ilf_type(all_0_1_1, binary_relation_type), ilf_type(all_0_2_2, binary_relation_type), ~ subset(all_0_2_2, all_0_1_1), yields: % 7.08/2.30 | (95) ? [v0] : ? [v1] : ? [v2] : (ordered_pair(v0, v1) = v2 & member(v2, all_0_2_2) & ilf_type(v1, set_type) & ilf_type(v0, set_type) & ~ member(v2, all_0_1_1)) % 7.29/2.30 | % 7.29/2.30 | Instantiating (95) with all_84_0_17, all_84_1_18, all_84_2_19 yields: % 7.29/2.30 | (96) ordered_pair(all_84_2_19, all_84_1_18) = all_84_0_17 & member(all_84_0_17, all_0_2_2) & ilf_type(all_84_1_18, set_type) & ilf_type(all_84_2_19, set_type) & ~ member(all_84_0_17, all_0_1_1) % 7.29/2.30 | % 7.29/2.30 | Applying alpha-rule on (96) yields: % 7.29/2.30 | (97) member(all_84_0_17, all_0_2_2) % 7.29/2.30 | (98) ilf_type(all_84_2_19, set_type) % 7.29/2.30 | (99) ~ member(all_84_0_17, all_0_1_1) % 7.29/2.30 | (100) ordered_pair(all_84_2_19, all_84_1_18) = all_84_0_17 % 7.29/2.30 | (101) ilf_type(all_84_1_18, set_type) % 7.29/2.30 | % 7.29/2.30 | Instantiating formula (25) with all_84_0_17, all_84_1_18, all_84_2_19, all_0_2_2, all_0_3_3 and discharging atoms identity_relation_of(all_0_3_3) = all_0_2_2, ordered_pair(all_84_2_19, all_84_1_18) = all_84_0_17, member(all_84_0_17, all_0_2_2), ilf_type(all_84_1_18, set_type), ilf_type(all_84_2_19, set_type), ilf_type(all_0_3_3, set_type), yields: % 7.29/2.30 | (102) all_84_1_18 = all_84_2_19 % 7.29/2.30 | % 7.29/2.30 | From (102) and (100) follows: % 7.29/2.30 | (103) ordered_pair(all_84_2_19, all_84_2_19) = all_84_0_17 % 7.29/2.30 | % 7.29/2.30 | From (102) and (101) follows: % 7.29/2.30 | (98) ilf_type(all_84_2_19, set_type) % 7.29/2.30 | % 7.29/2.30 | Instantiating formula (21) with all_84_0_17, all_84_2_19, all_84_2_19, all_0_2_2, all_0_3_3 and discharging atoms identity_relation_of(all_0_3_3) = all_0_2_2, ordered_pair(all_84_2_19, all_84_2_19) = all_84_0_17, member(all_84_0_17, all_0_2_2), ilf_type(all_84_2_19, set_type), ilf_type(all_0_3_3, set_type), yields: % 7.29/2.30 | (105) member(all_84_2_19, all_0_3_3) % 7.29/2.30 | % 7.29/2.30 | Instantiating formula (16) with all_84_0_17, all_84_2_19, all_84_2_19 and discharging atoms ordered_pair(all_84_2_19, all_84_2_19) = all_84_0_17, ilf_type(all_84_2_19, set_type), yields: % 7.29/2.30 | (106) ilf_type(all_84_0_17, set_type) % 7.29/2.30 | % 7.29/2.31 | Instantiating formula (49) with all_84_2_19, all_84_2_19, all_84_0_17, all_0_1_1, all_0_3_3, all_0_3_3 and discharging atoms cross_product(all_0_3_3, all_0_3_3) = all_0_1_1, ordered_pair(all_84_2_19, all_84_2_19) = all_84_0_17, member(all_84_2_19, all_0_3_3), ilf_type(all_84_0_17, set_type), ilf_type(all_84_2_19, set_type), ilf_type(all_0_3_3, set_type), ~ member(all_84_0_17, all_0_1_1), yields: % 7.29/2.31 | (91) $false % 7.29/2.31 | % 7.29/2.31 |-The branch is then unsatisfiable % 7.29/2.31 % SZS output end Proof for theBenchmark % 7.29/2.31 % 7.29/2.31 1667ms %------------------------------------------------------------------------------