%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET805+4 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n020.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 00:22:11 EDT 2022 % Result : Theorem 5.15s 1.77s % Output : Proof 7.54s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : SET805+4 : TPTP v8.1.0. Released v3.2.0. % 0.04/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n020.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 : Sat Jul 9 23:42:13 EDT 2022 % 0.12/0.34 % CPUTime : % 0.55/0.58 ____ _ % 0.55/0.58 ___ / __ \_____(_)___ ________ __________ % 0.55/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.55/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.55/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.55/0.58 % 0.55/0.58 A Theorem Prover for First-Order Logic % 0.55/0.58 (ePrincess v.1.0) % 0.55/0.58 % 0.55/0.58 (c) Philipp Rümmer, 2009-2015 % 0.55/0.58 (c) Peter Backeman, 2014-2015 % 0.55/0.58 (contributions by Angelo Brillout, Peter Baumgartner) % 0.55/0.58 Free software under GNU Lesser General Public License (LGPL). % 0.55/0.58 Bug reports to peter@backeman.se % 0.55/0.58 % 0.55/0.58 For more information, visit http://user.uu.se/~petba168/breu/ % 0.55/0.58 % 0.55/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.76/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.74/0.95 Prover 0: Preprocessing ... % 2.58/1.23 Prover 0: Warning: ignoring some quantifiers % 2.80/1.26 Prover 0: Constructing countermodel ... % 3.29/1.44 Prover 0: gave up % 3.29/1.44 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 3.67/1.48 Prover 1: Preprocessing ... % 4.75/1.68 Prover 1: Constructing countermodel ... % 4.75/1.77 Prover 1: proved (329ms) % 5.15/1.77 % 5.15/1.77 No countermodel exists, formula is valid % 5.15/1.77 % SZS status Theorem for theBenchmark % 5.15/1.77 % 5.15/1.77 Generating proof ... found it (size 65) % 6.81/2.17 % 6.81/2.17 % SZS output start Proof for theBenchmark % 6.81/2.17 Assumed formulas after preprocessing and simplification: % 6.81/2.17 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = 0) & order(v0, v2) = v3 & order(v0, v1) = 0 & subset(v2, v1) = 0 & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (order(v4, v5) = 0) | ~ (apply(v4, v6, v8) = v9) | ~ (apply(v4, v6, v7) = 0) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : (apply(v4, v7, v8) = v13 & member(v8, v5) = v12 & member(v7, v5) = v11 & member(v6, v5) = v10 & ( ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0) | ~ (v10 = 0)))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v5 = v4 | ~ (greatest_lower_bound(v9, v8, v7, v6) = v5) | ~ (greatest_lower_bound(v9, v8, v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v5 = v4 | ~ (least_upper_bound(v9, v8, v7, v6) = v5) | ~ (least_upper_bound(v9, v8, v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (greatest_lower_bound(v4, v5, v6, v7) = v8) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : ((v11 = 0 & v10 = 0 & ~ (v12 = 0) & lower_bound(v9, v6, v5) = 0 & apply(v6, v9, v4) = v12 & member(v9, v7) = 0) | (lower_bound(v4, v6, v5) = v10 & member(v4, v5) = v9 & ( ~ (v10 = 0) | ~ (v9 = 0))))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (least_upper_bound(v4, v5, v6, v7) = v8) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : ((v11 = 0 & v10 = 0 & ~ (v12 = 0) & upper_bound(v9, v6, v5) = 0 & apply(v6, v4, v9) = v12 & member(v9, v7) = 0) | (upper_bound(v4, v6, v5) = v10 & member(v4, v5) = v9 & ( ~ (v10 = 0) | ~ (v9 = 0))))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (least(v6, v4, v5) = 0) | ~ (apply(v4, v6, v7) = v8) | ? [v9] : ( ~ (v9 = 0) & member(v7, v5) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (greatest(v6, v4, v5) = 0) | ~ (apply(v4, v7, v6) = v8) | ? [v9] : ( ~ (v9 = 0) & member(v7, v5) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (lower_bound(v6, v4, v5) = 0) | ~ (apply(v4, v6, v7) = v8) | ? [v9] : ( ~ (v9 = 0) & member(v7, v5) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (upper_bound(v6, v4, v5) = 0) | ~ (apply(v4, v7, v6) = v8) | ? [v9] : ( ~ (v9 = 0) & member(v7, v5) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (total_order(v4, v5) = 0) | ~ (apply(v4, v6, v7) = v8) | ? [v9] : ? [v10] : ? [v11] : (apply(v4, v7, v6) = v11 & member(v7, v5) = v10 & member(v6, v5) = v9 & ( ~ (v10 = 0) | ~ (v9 = 0) | v11 = 0))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (product(v5) = v6) | ~ (member(v4, v7) = v8) | ~ (member(v4, v6) = 0) | ? [v9] : ( ~ (v9 = 0) & member(v7, v5) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (difference(v6, v5) = v7) | ~ (member(v4, v7) = v8) | ? [v9] : ? [v10] : (member(v4, v6) = v9 & member(v4, v5) = v10 & ( ~ (v9 = 0) | v10 = 0))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (union(v5, v6) = v7) | ~ (member(v4, v7) = v8) | ? [v9] : ? [v10] : ( ~ (v10 = 0) & ~ (v9 = 0) & member(v4, v6) = v10 & member(v4, v5) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (intersection(v5, v6) = v7) | ~ (member(v4, v7) = v8) | ? [v9] : ? [v10] : (member(v4, v6) = v10 & member(v4, v5) = v9 & ( ~ (v10 = 0) | ~ (v9 = 0)))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v7 = 0 | ~ (sum(v5) = v6) | ~ (member(v4, v8) = 0) | ~ (member(v4, v6) = v7) | ? [v9] : ( ~ (v9 = 0) & member(v8, v5) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v5 = v4 | ~ (min(v8, v7, v6) = v5) | ~ (min(v8, v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v5 = v4 | ~ (max(v8, v7, v6) = v5) | ~ (max(v8, v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v5 = v4 | ~ (least(v8, v7, v6) = v5) | ~ (least(v8, v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v5 = v4 | ~ (greatest(v8, v7, v6) = v5) | ~ (greatest(v8, v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v5 = v4 | ~ (lower_bound(v8, v7, v6) = v5) | ~ (lower_bound(v8, v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v5 = v4 | ~ (upper_bound(v8, v7, v6) = v5) | ~ (upper_bound(v8, v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v5 = v4 | ~ (apply(v8, v7, v6) = v5) | ~ (apply(v8, v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (greatest_lower_bound(v4, v5, v6, v7) = 0) | ~ (lower_bound(v8, v6, v5) = 0) | ? [v9] : ? [v10] : (apply(v6, v8, v4) = v10 & member(v8, v7) = v9 & ( ~ (v9 = 0) | v10 = 0))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (least_upper_bound(v4, v5, v6, v7) = 0) | ~ (upper_bound(v8, v6, v5) = 0) | ? [v9] : ? [v10] : (apply(v6, v4, v8) = v10 & member(v8, v7) = v9 & ( ~ (v9 = 0) | v10 = 0))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v6 | ~ (min(v6, v4, v5) = 0) | ~ (apply(v4, v7, v6) = 0) | ? [v8] : ( ~ (v8 = 0) & member(v7, v5) = v8)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v6 | ~ (max(v6, v4, v5) = 0) | ~ (apply(v4, v6, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & member(v7, v5) = v8)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v6 | ~ (order(v4, v5) = 0) | ~ (apply(v4, v6, v7) = 0) | ? [v8] : ? [v9] : ? [v10] : (apply(v4, v7, v6) = v10 & member(v7, v5) = v9 & member(v6, v5) = v8 & ( ~ (v10 = 0) | ~ (v9 = 0) | ~ (v8 = 0)))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (min(v6, v4, v5) = v7) | ? [v8] : ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & ~ (v8 = v6) & apply(v4, v8, v6) = 0 & member(v8, v5) = 0) | ( ~ (v8 = 0) & member(v6, v5) = v8))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (max(v6, v4, v5) = v7) | ? [v8] : ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & ~ (v8 = v6) & apply(v4, v6, v8) = 0 & member(v8, v5) = 0) | ( ~ (v8 = 0) & member(v6, v5) = v8))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (least(v6, v4, v5) = v7) | ? [v8] : ? [v9] : ? [v10] : ((v9 = 0 & ~ (v10 = 0) & apply(v4, v6, v8) = v10 & member(v8, v5) = 0) | ( ~ (v8 = 0) & member(v6, v5) = v8))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (greatest(v6, v4, v5) = v7) | ? [v8] : ? [v9] : ? [v10] : ((v9 = 0 & ~ (v10 = 0) & apply(v4, v8, v6) = v10 & member(v8, v5) = 0) | ( ~ (v8 = 0) & member(v6, v5) = v8))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (lower_bound(v6, v4, v5) = v7) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & apply(v4, v6, v8) = v9 & member(v8, v5) = 0)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (upper_bound(v6, v4, v5) = v7) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & apply(v4, v8, v6) = v9 & member(v8, v5) = 0)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (order(v4, v5) = 0) | ~ (apply(v4, v6, v6) = v7) | ? [v8] : ( ~ (v8 = 0) & member(v6, v5) = v8)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (product(v5) = v6) | ~ (member(v4, v6) = v7) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & member(v8, v5) = 0 & member(v4, v8) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (unordered_pair(v5, v4) = v6) | ~ (member(v4, v6) = v7)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (unordered_pair(v4, v5) = v6) | ~ (member(v4, v6) = v7)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (power_set(v5) = v6) | ~ (member(v4, v6) = v7) | ? [v8] : ( ~ (v8 = 0) & subset(v4, v5) = v8)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v6 = v4 | v5 = v4 | ~ (unordered_pair(v5, v6) = v7) | ~ (member(v4, v7) = 0)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (total_order(v7, v6) = v5) | ~ (total_order(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (order(v7, v6) = v5) | ~ (order(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (unordered_pair(v7, v6) = v5) | ~ (unordered_pair(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (difference(v7, v6) = v5) | ~ (difference(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (union(v7, v6) = v5) | ~ (union(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (intersection(v7, v6) = v5) | ~ (intersection(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (equal_set(v7, v6) = v5) | ~ (equal_set(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (subset(v7, v6) = v5) | ~ (subset(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (member(v7, v6) = v5) | ~ (member(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (greatest_lower_bound(v4, v5, v6, v7) = 0) | (lower_bound(v4, v6, v5) = 0 & member(v4, v5) = 0)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (least_upper_bound(v4, v5, v6, v7) = 0) | (upper_bound(v4, v6, v5) = 0 & member(v4, v5) = 0)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (difference(v6, v5) = v7) | ~ (member(v4, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & member(v4, v6) = 0 & member(v4, v5) = v8)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (union(v5, v6) = v7) | ~ (member(v4, v7) = 0) | ? [v8] : ? [v9] : (member(v4, v6) = v9 & member(v4, v5) = v8 & (v9 = 0 | v8 = 0))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (intersection(v5, v6) = v7) | ~ (member(v4, v7) = 0) | (member(v4, v6) = 0 & member(v4, v5) = 0)) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (total_order(v4, v5) = v6) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ((v10 = 0 & v9 = 0 & ~ (v12 = 0) & ~ (v11 = 0) & apply(v4, v8, v7) = v12 & apply(v4, v7, v8) = v11 & member(v8, v5) = 0 & member(v7, v5) = 0) | ( ~ (v7 = 0) & order(v4, v5) = v7))) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (order(v4, v5) = v6) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ((v14 = 0 & v13 = 0 & v12 = 0 & v11 = 0 & v10 = 0 & ~ (v15 = 0) & apply(v4, v8, v9) = 0 & apply(v4, v7, v9) = v15 & apply(v4, v7, v8) = 0 & member(v9, v5) = 0 & member(v8, v5) = 0 & member(v7, v5) = 0) | (v12 = 0 & v11 = 0 & v10 = 0 & v9 = 0 & ~ (v8 = v7) & apply(v4, v8, v7) = 0 & apply(v4, v7, v8) = 0 & member(v8, v5) = 0 & member(v7, v5) = 0) | (v8 = 0 & ~ (v9 = 0) & apply(v4, v7, v7) = v9 & member(v7, v5) = 0))) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (singleton(v4) = v5) | ~ (member(v4, v5) = v6)) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (equal_set(v4, v5) = v6) | ? [v7] : ? [v8] : (subset(v5, v4) = v8 & subset(v4, v5) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0)))) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (subset(v4, v5) = v6) | ? [v7] : ? [v8] : ( ~ (v8 = 0) & member(v7, v5) = v8 & member(v7, v4) = 0)) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (product(v6) = v5) | ~ (product(v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (sum(v6) = v5) | ~ (sum(v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (singleton(v6) = v5) | ~ (singleton(v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (singleton(v5) = v6) | ~ (member(v4, v6) = 0)) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (power_set(v6) = v5) | ~ (power_set(v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (min(v6, v4, v5) = 0) | member(v6, v5) = 0) & ! [v4] : ! [v5] : ! [v6] : ( ~ (max(v6, v4, v5) = 0) | member(v6, v5) = 0) & ! [v4] : ! [v5] : ! [v6] : ( ~ (least(v6, v4, v5) = 0) | member(v6, v5) = 0) & ! [v4] : ! [v5] : ! [v6] : ( ~ (greatest(v6, v4, v5) = 0) | member(v6, v5) = 0) & ! [v4] : ! [v5] : ! [v6] : ( ~ (sum(v5) = v6) | ~ (member(v4, v6) = 0) | ? [v7] : (member(v7, v5) = 0 & member(v4, v7) = 0)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (power_set(v5) = v6) | ~ (member(v4, v6) = 0) | subset(v4, v5) = 0) & ! [v4] : ! [v5] : ! [v6] : ( ~ (subset(v4, v5) = 0) | ~ (member(v6, v4) = 0) | member(v6, v5) = 0) & ! [v4] : ! [v5] : ( ~ (total_order(v4, v5) = 0) | order(v4, v5) = 0) & ! [v4] : ! [v5] : ( ~ (equal_set(v4, v5) = 0) | (subset(v5, v4) = 0 & subset(v4, v5) = 0)) & ! [v4] : ~ (member(v4, empty_set) = 0)) % 7.20/2.23 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields: % 7.20/2.23 | (1) ~ (all_0_0_0 = 0) & order(all_0_3_3, all_0_1_1) = all_0_0_0 & order(all_0_3_3, all_0_2_2) = 0 & subset(all_0_1_1, all_0_2_2) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (order(v0, v1) = 0) | ~ (apply(v0, v2, v4) = v5) | ~ (apply(v0, v2, v3) = 0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (apply(v0, v3, v4) = v9 & member(v4, v1) = v8 & member(v3, v1) = v7 & member(v2, v1) = v6 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (greatest_lower_bound(v5, v4, v3, v2) = v1) | ~ (greatest_lower_bound(v5, v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (least_upper_bound(v5, v4, v3, v2) = v1) | ~ (least_upper_bound(v5, v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (greatest_lower_bound(v0, v1, v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ((v7 = 0 & v6 = 0 & ~ (v8 = 0) & lower_bound(v5, v2, v1) = 0 & apply(v2, v5, v0) = v8 & member(v5, v3) = 0) | (lower_bound(v0, v2, v1) = v6 & member(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (least_upper_bound(v0, v1, v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ((v7 = 0 & v6 = 0 & ~ (v8 = 0) & upper_bound(v5, v2, v1) = 0 & apply(v2, v0, v5) = v8 & member(v5, v3) = 0) | (upper_bound(v0, v2, v1) = v6 & member(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (least(v2, v0, v1) = 0) | ~ (apply(v0, v2, v3) = v4) | ? [v5] : ( ~ (v5 = 0) & member(v3, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (greatest(v2, v0, v1) = 0) | ~ (apply(v0, v3, v2) = v4) | ? [v5] : ( ~ (v5 = 0) & member(v3, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (lower_bound(v2, v0, v1) = 0) | ~ (apply(v0, v2, v3) = v4) | ? [v5] : ( ~ (v5 = 0) & member(v3, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (upper_bound(v2, v0, v1) = 0) | ~ (apply(v0, v3, v2) = v4) | ? [v5] : ( ~ (v5 = 0) & member(v3, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (total_order(v0, v1) = 0) | ~ (apply(v0, v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : (apply(v0, v3, v2) = v7 & member(v3, v1) = v6 & member(v2, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | v7 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (product(v1) = v2) | ~ (member(v0, v3) = v4) | ~ (member(v0, v2) = 0) | ? [v5] : ( ~ (v5 = 0) & member(v3, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : ? [v6] : (member(v0, v2) = v5 & member(v0, v1) = v6 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & ~ (v5 = 0) & member(v0, v2) = v6 & member(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : ? [v6] : (member(v0, v2) = v6 & member(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (sum(v1) = v2) | ~ (member(v0, v4) = 0) | ~ (member(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & member(v4, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (min(v4, v3, v2) = v1) | ~ (min(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (max(v4, v3, v2) = v1) | ~ (max(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (least(v4, v3, v2) = v1) | ~ (least(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (greatest(v4, v3, v2) = v1) | ~ (greatest(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (lower_bound(v4, v3, v2) = v1) | ~ (lower_bound(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (upper_bound(v4, v3, v2) = v1) | ~ (upper_bound(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | ~ (apply(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (greatest_lower_bound(v0, v1, v2, v3) = 0) | ~ (lower_bound(v4, v2, v1) = 0) | ? [v5] : ? [v6] : (apply(v2, v4, v0) = v6 & member(v4, v3) = v5 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (least_upper_bound(v0, v1, v2, v3) = 0) | ~ (upper_bound(v4, v2, v1) = 0) | ? [v5] : ? [v6] : (apply(v2, v0, v4) = v6 & member(v4, v3) = v5 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (min(v2, v0, v1) = 0) | ~ (apply(v0, v3, v2) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (max(v2, v0, v1) = 0) | ~ (apply(v0, v2, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (order(v0, v1) = 0) | ~ (apply(v0, v2, v3) = 0) | ? [v4] : ? [v5] : ? [v6] : (apply(v0, v3, v2) = v6 & member(v3, v1) = v5 & member(v2, v1) = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (min(v2, v0, v1) = v3) | ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & ~ (v4 = v2) & apply(v0, v4, v2) = 0 & member(v4, v1) = 0) | ( ~ (v4 = 0) & member(v2, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (max(v2, v0, v1) = v3) | ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & ~ (v4 = v2) & apply(v0, v2, v4) = 0 & member(v4, v1) = 0) | ( ~ (v4 = 0) & member(v2, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (least(v2, v0, v1) = v3) | ? [v4] : ? [v5] : ? [v6] : ((v5 = 0 & ~ (v6 = 0) & apply(v0, v2, v4) = v6 & member(v4, v1) = 0) | ( ~ (v4 = 0) & member(v2, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (greatest(v2, v0, v1) = v3) | ? [v4] : ? [v5] : ? [v6] : ((v5 = 0 & ~ (v6 = 0) & apply(v0, v4, v2) = v6 & member(v4, v1) = 0) | ( ~ (v4 = 0) & member(v2, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (lower_bound(v2, v0, v1) = v3) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & apply(v0, v2, v4) = v5 & member(v4, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (upper_bound(v2, v0, v1) = v3) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & apply(v0, v4, v2) = v5 & member(v4, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (order(v0, v1) = 0) | ~ (apply(v0, v2, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (product(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & member(v4, v1) = 0 & member(v0, v4) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (total_order(v3, v2) = v1) | ~ (total_order(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (order(v3, v2) = v1) | ~ (order(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (greatest_lower_bound(v0, v1, v2, v3) = 0) | (lower_bound(v0, v2, v1) = 0 & member(v0, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (least_upper_bound(v0, v1, v2, v3) = 0) | (upper_bound(v0, v2, v1) = 0 & member(v0, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v0, v2) = 0 & member(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ? [v5] : (member(v0, v2) = v5 & member(v0, v1) = v4 & (v5 = 0 | v4 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | (member(v0, v2) = 0 & member(v0, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (total_order(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ((v6 = 0 & v5 = 0 & ~ (v8 = 0) & ~ (v7 = 0) & apply(v0, v4, v3) = v8 & apply(v0, v3, v4) = v7 & member(v4, v1) = 0 & member(v3, v1) = 0) | ( ~ (v3 = 0) & order(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (order(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ((v10 = 0 & v9 = 0 & v8 = 0 & v7 = 0 & v6 = 0 & ~ (v11 = 0) & apply(v0, v4, v5) = 0 & apply(v0, v3, v5) = v11 & apply(v0, v3, v4) = 0 & member(v5, v1) = 0 & member(v4, v1) = 0 & member(v3, v1) = 0) | (v8 = 0 & v7 = 0 & v6 = 0 & v5 = 0 & ~ (v4 = v3) & apply(v0, v4, v3) = 0 & apply(v0, v3, v4) = 0 & member(v4, v1) = 0 & member(v3, v1) = 0) | (v4 = 0 & ~ (v5 = 0) & apply(v0, v3, v3) = v5 & member(v3, v1) = 0))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (member(v0, v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_set(v0, v1) = v2) | ? [v3] : ? [v4] : (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (min(v2, v0, v1) = 0) | member(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (max(v2, v0, v1) = 0) | member(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (least(v2, v0, v1) = 0) | member(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (greatest(v2, v0, v1) = 0) | member(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ (member(v0, v2) = 0) | ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | subset(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0) & ! [v0] : ! [v1] : ( ~ (total_order(v0, v1) = 0) | order(v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0)) & ! [v0] : ~ (member(v0, empty_set) = 0) % 7.20/2.26 | % 7.20/2.26 | Applying alpha-rule on (1) yields: % 7.20/2.26 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3)) % 7.20/2.26 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (greatest(v2, v0, v1) = v3) | ? [v4] : ? [v5] : ? [v6] : ((v5 = 0 & ~ (v6 = 0) & apply(v0, v4, v2) = v6 & member(v4, v1) = 0) | ( ~ (v4 = 0) & member(v2, v1) = v4))) % 7.20/2.26 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ? [v5] : (member(v0, v2) = v5 & member(v0, v1) = v4 & (v5 = 0 | v4 = 0))) % 7.20/2.26 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (least_upper_bound(v0, v1, v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ((v7 = 0 & v6 = 0 & ~ (v8 = 0) & upper_bound(v5, v2, v1) = 0 & apply(v2, v0, v5) = v8 & member(v5, v3) = 0) | (upper_bound(v0, v2, v1) = v6 & member(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0))))) % 7.20/2.26 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (max(v4, v3, v2) = v1) | ~ (max(v4, v3, v2) = v0)) % 7.20/2.26 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (min(v2, v0, v1) = v3) | ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & ~ (v4 = v2) & apply(v0, v4, v2) = 0 & member(v4, v1) = 0) | ( ~ (v4 = 0) & member(v2, v1) = v4))) % 7.20/2.26 | (8) ! [v0] : ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0)) % 7.20/2.27 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (order(v0, v1) = 0) | ~ (apply(v0, v2, v3) = 0) | ? [v4] : ? [v5] : ? [v6] : (apply(v0, v3, v2) = v6 & member(v3, v1) = v5 & member(v2, v1) = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0)))) % 7.20/2.27 | (10) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0)) % 7.20/2.27 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (order(v0, v1) = 0) | ~ (apply(v0, v2, v4) = v5) | ~ (apply(v0, v2, v3) = 0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (apply(v0, v3, v4) = v9 & member(v4, v1) = v8 & member(v3, v1) = v7 & member(v2, v1) = v6 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0)))) % 7.20/2.27 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (upper_bound(v2, v0, v1) = v3) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & apply(v0, v4, v2) = v5 & member(v4, v1) = 0)) % 7.20/2.27 | (13) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (member(v0, v1) = v2)) % 7.20/2.27 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (lower_bound(v4, v3, v2) = v1) | ~ (lower_bound(v4, v3, v2) = v0)) % 7.20/2.27 | (15) ! [v0] : ! [v1] : ! [v2] : ( ~ (max(v2, v0, v1) = 0) | member(v2, v1) = 0) % 7.20/2.27 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | ~ (apply(v4, v3, v2) = v0)) % 7.20/2.27 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (least_upper_bound(v5, v4, v3, v2) = v1) | ~ (least_upper_bound(v5, v4, v3, v2) = v0)) % 7.20/2.27 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & ~ (v5 = 0) & member(v0, v2) = v6 & member(v0, v1) = v5)) % 7.20/2.27 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (lower_bound(v2, v0, v1) = 0) | ~ (apply(v0, v2, v3) = v4) | ? [v5] : ( ~ (v5 = 0) & member(v3, v1) = v5)) % 7.20/2.27 | (20) order(all_0_3_3, all_0_1_1) = all_0_0_0 % 7.20/2.27 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (min(v4, v3, v2) = v1) | ~ (min(v4, v3, v2) = v0)) % 7.20/2.27 | (22) ! [v0] : ! [v1] : ! [v2] : ( ~ (min(v2, v0, v1) = 0) | member(v2, v1) = 0) % 7.20/2.27 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (total_order(v0, v1) = 0) | ~ (apply(v0, v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : (apply(v0, v3, v2) = v7 & member(v3, v1) = v6 & member(v2, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | v7 = 0))) % 7.20/2.27 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : ? [v6] : (member(v0, v2) = v5 & member(v0, v1) = v6 & ( ~ (v5 = 0) | v6 = 0))) % 7.20/2.27 | (25) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0)) % 7.20/2.27 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (least(v2, v0, v1) = v3) | ? [v4] : ? [v5] : ? [v6] : ((v5 = 0 & ~ (v6 = 0) & apply(v0, v2, v4) = v6 & member(v4, v1) = 0) | ( ~ (v4 = 0) & member(v2, v1) = v4))) % 7.20/2.27 | (27) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_set(v0, v1) = v2) | ? [v3] : ? [v4] : (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) % 7.20/2.27 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) % 7.20/2.27 | (29) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0) % 7.20/2.27 | (30) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0)) % 7.20/2.27 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) % 7.20/2.28 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (greatest_lower_bound(v5, v4, v3, v2) = v1) | ~ (greatest_lower_bound(v5, v4, v3, v2) = v0)) % 7.20/2.28 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (greatest(v4, v3, v2) = v1) | ~ (greatest(v4, v3, v2) = v0)) % 7.20/2.28 | (34) ! [v0] : ! [v1] : ! [v2] : ( ~ (greatest(v2, v0, v1) = 0) | member(v2, v1) = 0) % 7.20/2.28 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (product(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & member(v4, v1) = 0 & member(v0, v4) = v5)) % 7.20/2.28 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (upper_bound(v4, v3, v2) = v1) | ~ (upper_bound(v4, v3, v2) = v0)) % 7.20/2.28 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) % 7.20/2.28 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (greatest_lower_bound(v0, v1, v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ((v7 = 0 & v6 = 0 & ~ (v8 = 0) & lower_bound(v5, v2, v1) = 0 & apply(v2, v5, v0) = v8 & member(v5, v3) = 0) | (lower_bound(v0, v2, v1) = v6 & member(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0))))) % 7.20/2.28 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (max(v2, v0, v1) = v3) | ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & ~ (v4 = v2) & apply(v0, v2, v4) = 0 & member(v4, v1) = 0) | ( ~ (v4 = 0) & member(v2, v1) = v4))) % 7.20/2.28 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) % 7.20/2.28 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (order(v0, v1) = 0) | ~ (apply(v0, v2, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v1) = v4)) % 7.20/2.28 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (greatest(v2, v0, v1) = 0) | ~ (apply(v0, v3, v2) = v4) | ? [v5] : ( ~ (v5 = 0) & member(v3, v1) = v5)) % 7.20/2.28 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (least(v4, v3, v2) = v1) | ~ (least(v4, v3, v2) = v0)) % 7.20/2.28 | (44) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (total_order(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ((v6 = 0 & v5 = 0 & ~ (v8 = 0) & ~ (v7 = 0) & apply(v0, v4, v3) = v8 & apply(v0, v3, v4) = v7 & member(v4, v1) = 0 & member(v3, v1) = 0) | ( ~ (v3 = 0) & order(v0, v1) = v3))) % 7.20/2.28 | (45) ! [v0] : ! [v1] : ! [v2] : ( ~ (least(v2, v0, v1) = 0) | member(v2, v1) = 0) % 7.20/2.28 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (total_order(v3, v2) = v1) | ~ (total_order(v3, v2) = v0)) % 7.20/2.28 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) % 7.20/2.28 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (upper_bound(v2, v0, v1) = 0) | ~ (apply(v0, v3, v2) = v4) | ? [v5] : ( ~ (v5 = 0) & member(v3, v1) = v5)) % 7.20/2.28 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) % 7.20/2.28 | (50) ~ (all_0_0_0 = 0) % 7.20/2.28 | (51) ! [v0] : ~ (member(v0, empty_set) = 0) % 7.20/2.28 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (product(v1) = v2) | ~ (member(v0, v3) = v4) | ~ (member(v0, v2) = 0) | ? [v5] : ( ~ (v5 = 0) & member(v3, v1) = v5)) % 7.20/2.28 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (greatest_lower_bound(v0, v1, v2, v3) = 0) | ~ (lower_bound(v4, v2, v1) = 0) | ? [v5] : ? [v6] : (apply(v2, v4, v0) = v6 & member(v4, v3) = v5 & ( ~ (v5 = 0) | v6 = 0))) % 7.20/2.28 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0)) % 7.20/2.28 | (55) order(all_0_3_3, all_0_2_2) = 0 % 7.20/2.28 | (56) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0)) % 7.20/2.28 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (order(v3, v2) = v1) | ~ (order(v3, v2) = v0)) % 7.20/2.28 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (greatest_lower_bound(v0, v1, v2, v3) = 0) | (lower_bound(v0, v2, v1) = 0 & member(v0, v1) = 0)) % 7.20/2.28 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = v3)) % 7.20/2.28 | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (lower_bound(v2, v0, v1) = v3) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & apply(v0, v2, v4) = v5 & member(v4, v1) = 0)) % 7.20/2.28 | (61) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (order(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ((v10 = 0 & v9 = 0 & v8 = 0 & v7 = 0 & v6 = 0 & ~ (v11 = 0) & apply(v0, v4, v5) = 0 & apply(v0, v3, v5) = v11 & apply(v0, v3, v4) = 0 & member(v5, v1) = 0 & member(v4, v1) = 0 & member(v3, v1) = 0) | (v8 = 0 & v7 = 0 & v6 = 0 & v5 = 0 & ~ (v4 = v3) & apply(v0, v4, v3) = 0 & apply(v0, v3, v4) = 0 & member(v4, v1) = 0 & member(v3, v1) = 0) | (v4 = 0 & ~ (v5 = 0) & apply(v0, v3, v3) = v5 & member(v3, v1) = 0))) % 7.20/2.29 | (62) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0)) % 7.20/2.29 | (63) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (least_upper_bound(v0, v1, v2, v3) = 0) | (upper_bound(v0, v2, v1) = 0 & member(v0, v1) = 0)) % 7.20/2.29 | (64) ! [v0] : ! [v1] : ( ~ (total_order(v0, v1) = 0) | order(v0, v1) = 0) % 7.20/2.29 | (65) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : ? [v6] : (member(v0, v2) = v6 & member(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) % 7.20/2.29 | (66) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (least(v2, v0, v1) = 0) | ~ (apply(v0, v2, v3) = v4) | ? [v5] : ( ~ (v5 = 0) & member(v3, v1) = v5)) % 7.20/2.29 | (67) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | (member(v0, v2) = 0 & member(v0, v1) = 0)) % 7.20/2.29 | (68) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v0, v2) = 0 & member(v0, v1) = v4)) % 7.20/2.29 | (69) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (max(v2, v0, v1) = 0) | ~ (apply(v0, v2, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4)) % 7.54/2.29 | (70) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (least_upper_bound(v0, v1, v2, v3) = 0) | ~ (upper_bound(v4, v2, v1) = 0) | ? [v5] : ? [v6] : (apply(v2, v0, v4) = v6 & member(v4, v3) = v5 & ( ~ (v5 = 0) | v6 = 0))) % 7.54/2.29 | (71) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (min(v2, v0, v1) = 0) | ~ (apply(v0, v3, v2) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4)) % 7.54/2.29 | (72) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 7.54/2.29 | (73) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | subset(v0, v1) = 0) % 7.54/2.29 | (74) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ (member(v0, v2) = 0) | ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0)) % 7.54/2.29 | (75) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0)) % 7.54/2.29 | (76) subset(all_0_1_1, all_0_2_2) = 0 % 7.54/2.29 | (77) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) % 7.54/2.29 | (78) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (sum(v1) = v2) | ~ (member(v0, v4) = 0) | ~ (member(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & member(v4, v1) = v5)) % 7.54/2.29 | % 7.54/2.29 | Instantiating formula (61) with all_0_0_0, all_0_1_1, all_0_3_3 and discharging atoms order(all_0_3_3, all_0_1_1) = all_0_0_0, yields: % 7.54/2.29 | (79) all_0_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ((v7 = 0 & v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & ~ (v8 = 0) & apply(all_0_3_3, v1, v2) = 0 & apply(all_0_3_3, v0, v2) = v8 & apply(all_0_3_3, v0, v1) = 0 & member(v2, all_0_1_1) = 0 & member(v1, all_0_1_1) = 0 & member(v0, all_0_1_1) = 0) | (v5 = 0 & v4 = 0 & v3 = 0 & v2 = 0 & ~ (v1 = v0) & apply(all_0_3_3, v1, v0) = 0 & apply(all_0_3_3, v0, v1) = 0 & member(v1, all_0_1_1) = 0 & member(v0, all_0_1_1) = 0) | (v1 = 0 & ~ (v2 = 0) & apply(all_0_3_3, v0, v0) = v2 & member(v0, all_0_1_1) = 0)) % 7.54/2.29 | % 7.54/2.29 +-Applying beta-rule and splitting (79), into two cases. % 7.54/2.29 |-Branch one: % 7.54/2.29 | (80) all_0_0_0 = 0 % 7.54/2.29 | % 7.54/2.29 | Equations (80) can reduce 50 to: % 7.54/2.29 | (81) $false % 7.54/2.29 | % 7.54/2.29 |-The branch is then unsatisfiable % 7.54/2.29 |-Branch two: % 7.54/2.29 | (50) ~ (all_0_0_0 = 0) % 7.54/2.29 | (83) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ((v7 = 0 & v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & ~ (v8 = 0) & apply(all_0_3_3, v1, v2) = 0 & apply(all_0_3_3, v0, v2) = v8 & apply(all_0_3_3, v0, v1) = 0 & member(v2, all_0_1_1) = 0 & member(v1, all_0_1_1) = 0 & member(v0, all_0_1_1) = 0) | (v5 = 0 & v4 = 0 & v3 = 0 & v2 = 0 & ~ (v1 = v0) & apply(all_0_3_3, v1, v0) = 0 & apply(all_0_3_3, v0, v1) = 0 & member(v1, all_0_1_1) = 0 & member(v0, all_0_1_1) = 0) | (v1 = 0 & ~ (v2 = 0) & apply(all_0_3_3, v0, v0) = v2 & member(v0, all_0_1_1) = 0)) % 7.54/2.29 | % 7.54/2.29 | Instantiating (83) with all_14_0_4, all_14_1_5, all_14_2_6, all_14_3_7, all_14_4_8, all_14_5_9, all_14_6_10, all_14_7_11, all_14_8_12 yields: % 7.54/2.29 | (84) (all_14_1_5 = 0 & all_14_2_6 = 0 & all_14_3_7 = 0 & all_14_4_8 = 0 & all_14_5_9 = 0 & ~ (all_14_0_4 = 0) & apply(all_0_3_3, all_14_7_11, all_14_6_10) = 0 & apply(all_0_3_3, all_14_8_12, all_14_6_10) = all_14_0_4 & apply(all_0_3_3, all_14_8_12, all_14_7_11) = 0 & member(all_14_6_10, all_0_1_1) = 0 & member(all_14_7_11, all_0_1_1) = 0 & member(all_14_8_12, all_0_1_1) = 0) | (all_14_3_7 = 0 & all_14_4_8 = 0 & all_14_5_9 = 0 & all_14_6_10 = 0 & ~ (all_14_7_11 = all_14_8_12) & apply(all_0_3_3, all_14_7_11, all_14_8_12) = 0 & apply(all_0_3_3, all_14_8_12, all_14_7_11) = 0 & member(all_14_7_11, all_0_1_1) = 0 & member(all_14_8_12, all_0_1_1) = 0) | (all_14_7_11 = 0 & ~ (all_14_6_10 = 0) & apply(all_0_3_3, all_14_8_12, all_14_8_12) = all_14_6_10 & member(all_14_8_12, all_0_1_1) = 0) % 7.54/2.30 | % 7.54/2.30 +-Applying beta-rule and splitting (84), into two cases. % 7.54/2.30 |-Branch one: % 7.54/2.30 | (85) (all_14_1_5 = 0 & all_14_2_6 = 0 & all_14_3_7 = 0 & all_14_4_8 = 0 & all_14_5_9 = 0 & ~ (all_14_0_4 = 0) & apply(all_0_3_3, all_14_7_11, all_14_6_10) = 0 & apply(all_0_3_3, all_14_8_12, all_14_6_10) = all_14_0_4 & apply(all_0_3_3, all_14_8_12, all_14_7_11) = 0 & member(all_14_6_10, all_0_1_1) = 0 & member(all_14_7_11, all_0_1_1) = 0 & member(all_14_8_12, all_0_1_1) = 0) | (all_14_3_7 = 0 & all_14_4_8 = 0 & all_14_5_9 = 0 & all_14_6_10 = 0 & ~ (all_14_7_11 = all_14_8_12) & apply(all_0_3_3, all_14_7_11, all_14_8_12) = 0 & apply(all_0_3_3, all_14_8_12, all_14_7_11) = 0 & member(all_14_7_11, all_0_1_1) = 0 & member(all_14_8_12, all_0_1_1) = 0) % 7.54/2.30 | % 7.54/2.30 +-Applying beta-rule and splitting (85), into two cases. % 7.54/2.30 |-Branch one: % 7.54/2.30 | (86) all_14_1_5 = 0 & all_14_2_6 = 0 & all_14_3_7 = 0 & all_14_4_8 = 0 & all_14_5_9 = 0 & ~ (all_14_0_4 = 0) & apply(all_0_3_3, all_14_7_11, all_14_6_10) = 0 & apply(all_0_3_3, all_14_8_12, all_14_6_10) = all_14_0_4 & apply(all_0_3_3, all_14_8_12, all_14_7_11) = 0 & member(all_14_6_10, all_0_1_1) = 0 & member(all_14_7_11, all_0_1_1) = 0 & member(all_14_8_12, all_0_1_1) = 0 % 7.54/2.30 | % 7.54/2.30 | Applying alpha-rule on (86) yields: % 7.54/2.30 | (87) all_14_5_9 = 0 % 7.54/2.30 | (88) apply(all_0_3_3, all_14_8_12, all_14_6_10) = all_14_0_4 % 7.54/2.30 | (89) ~ (all_14_0_4 = 0) % 7.54/2.30 | (90) apply(all_0_3_3, all_14_8_12, all_14_7_11) = 0 % 7.54/2.30 | (91) all_14_3_7 = 0 % 7.54/2.30 | (92) all_14_4_8 = 0 % 7.54/2.30 | (93) member(all_14_8_12, all_0_1_1) = 0 % 7.54/2.30 | (94) apply(all_0_3_3, all_14_7_11, all_14_6_10) = 0 % 7.54/2.30 | (95) member(all_14_7_11, all_0_1_1) = 0 % 7.54/2.30 | (96) member(all_14_6_10, all_0_1_1) = 0 % 7.54/2.30 | (97) all_14_2_6 = 0 % 7.54/2.30 | (98) all_14_1_5 = 0 % 7.54/2.30 | % 7.54/2.30 | Instantiating formula (11) with all_14_0_4, all_14_6_10, all_14_7_11, all_14_8_12, all_0_2_2, all_0_3_3 and discharging atoms order(all_0_3_3, all_0_2_2) = 0, apply(all_0_3_3, all_14_8_12, all_14_6_10) = all_14_0_4, apply(all_0_3_3, all_14_8_12, all_14_7_11) = 0, yields: % 7.54/2.30 | (99) all_14_0_4 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apply(all_0_3_3, all_14_7_11, all_14_6_10) = v3 & member(all_14_6_10, all_0_2_2) = v2 & member(all_14_7_11, all_0_2_2) = v1 & member(all_14_8_12, all_0_2_2) = v0 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))) % 7.54/2.30 | % 7.54/2.30 | Instantiating formula (29) with all_14_6_10, all_0_2_2, all_0_1_1 and discharging atoms subset(all_0_1_1, all_0_2_2) = 0, member(all_14_6_10, all_0_1_1) = 0, yields: % 7.54/2.30 | (100) member(all_14_6_10, all_0_2_2) = 0 % 7.54/2.30 | % 7.54/2.30 | Instantiating formula (29) with all_14_7_11, all_0_2_2, all_0_1_1 and discharging atoms subset(all_0_1_1, all_0_2_2) = 0, member(all_14_7_11, all_0_1_1) = 0, yields: % 7.54/2.30 | (101) member(all_14_7_11, all_0_2_2) = 0 % 7.54/2.30 | % 7.54/2.30 | Instantiating formula (29) with all_14_8_12, all_0_2_2, all_0_1_1 and discharging atoms subset(all_0_1_1, all_0_2_2) = 0, member(all_14_8_12, all_0_1_1) = 0, yields: % 7.54/2.30 | (102) member(all_14_8_12, all_0_2_2) = 0 % 7.54/2.30 | % 7.54/2.30 +-Applying beta-rule and splitting (99), into two cases. % 7.54/2.30 |-Branch one: % 7.54/2.30 | (103) all_14_0_4 = 0 % 7.54/2.30 | % 7.54/2.30 | Equations (103) can reduce 89 to: % 7.54/2.30 | (81) $false % 7.54/2.30 | % 7.54/2.30 |-The branch is then unsatisfiable % 7.54/2.30 |-Branch two: % 7.54/2.30 | (89) ~ (all_14_0_4 = 0) % 7.54/2.30 | (106) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apply(all_0_3_3, all_14_7_11, all_14_6_10) = v3 & member(all_14_6_10, all_0_2_2) = v2 & member(all_14_7_11, all_0_2_2) = v1 & member(all_14_8_12, all_0_2_2) = v0 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))) % 7.54/2.30 | % 7.54/2.30 | Instantiating (106) with all_44_0_13, all_44_1_14, all_44_2_15, all_44_3_16 yields: % 7.54/2.30 | (107) apply(all_0_3_3, all_14_7_11, all_14_6_10) = all_44_0_13 & member(all_14_6_10, all_0_2_2) = all_44_1_14 & member(all_14_7_11, all_0_2_2) = all_44_2_15 & member(all_14_8_12, all_0_2_2) = all_44_3_16 & ( ~ (all_44_0_13 = 0) | ~ (all_44_1_14 = 0) | ~ (all_44_2_15 = 0) | ~ (all_44_3_16 = 0)) % 7.54/2.30 | % 7.54/2.30 | Applying alpha-rule on (107) yields: % 7.54/2.30 | (108) ~ (all_44_0_13 = 0) | ~ (all_44_1_14 = 0) | ~ (all_44_2_15 = 0) | ~ (all_44_3_16 = 0) % 7.54/2.30 | (109) member(all_14_8_12, all_0_2_2) = all_44_3_16 % 7.54/2.30 | (110) apply(all_0_3_3, all_14_7_11, all_14_6_10) = all_44_0_13 % 7.54/2.30 | (111) member(all_14_6_10, all_0_2_2) = all_44_1_14 % 7.54/2.30 | (112) member(all_14_7_11, all_0_2_2) = all_44_2_15 % 7.54/2.30 | % 7.54/2.30 | Instantiating formula (16) with all_0_3_3, all_14_7_11, all_14_6_10, all_44_0_13, 0 and discharging atoms apply(all_0_3_3, all_14_7_11, all_14_6_10) = all_44_0_13, apply(all_0_3_3, all_14_7_11, all_14_6_10) = 0, yields: % 7.54/2.30 | (113) all_44_0_13 = 0 % 7.54/2.30 | % 7.54/2.30 | Instantiating formula (31) with all_14_6_10, all_0_2_2, 0, all_44_1_14 and discharging atoms member(all_14_6_10, all_0_2_2) = all_44_1_14, member(all_14_6_10, all_0_2_2) = 0, yields: % 7.54/2.30 | (114) all_44_1_14 = 0 % 7.54/2.30 | % 7.54/2.30 | Instantiating formula (31) with all_14_7_11, all_0_2_2, all_44_2_15, 0 and discharging atoms member(all_14_7_11, all_0_2_2) = all_44_2_15, member(all_14_7_11, all_0_2_2) = 0, yields: % 7.54/2.30 | (115) all_44_2_15 = 0 % 7.54/2.30 | % 7.54/2.30 | Instantiating formula (31) with all_14_8_12, all_0_2_2, all_44_3_16, 0 and discharging atoms member(all_14_8_12, all_0_2_2) = all_44_3_16, member(all_14_8_12, all_0_2_2) = 0, yields: % 7.54/2.30 | (116) all_44_3_16 = 0 % 7.54/2.30 | % 7.54/2.30 +-Applying beta-rule and splitting (108), into two cases. % 7.54/2.30 |-Branch one: % 7.54/2.30 | (117) ~ (all_44_0_13 = 0) % 7.54/2.30 | % 7.54/2.30 | Equations (113) can reduce 117 to: % 7.54/2.30 | (81) $false % 7.54/2.30 | % 7.54/2.30 |-The branch is then unsatisfiable % 7.54/2.30 |-Branch two: % 7.54/2.30 | (113) all_44_0_13 = 0 % 7.54/2.30 | (120) ~ (all_44_1_14 = 0) | ~ (all_44_2_15 = 0) | ~ (all_44_3_16 = 0) % 7.54/2.30 | % 7.54/2.30 +-Applying beta-rule and splitting (120), into two cases. % 7.54/2.30 |-Branch one: % 7.54/2.30 | (121) ~ (all_44_1_14 = 0) % 7.54/2.30 | % 7.54/2.30 | Equations (114) can reduce 121 to: % 7.54/2.30 | (81) $false % 7.54/2.30 | % 7.54/2.30 |-The branch is then unsatisfiable % 7.54/2.30 |-Branch two: % 7.54/2.30 | (114) all_44_1_14 = 0 % 7.54/2.30 | (124) ~ (all_44_2_15 = 0) | ~ (all_44_3_16 = 0) % 7.54/2.30 | % 7.54/2.30 +-Applying beta-rule and splitting (124), into two cases. % 7.54/2.30 |-Branch one: % 7.54/2.30 | (125) ~ (all_44_2_15 = 0) % 7.54/2.30 | % 7.54/2.30 | Equations (115) can reduce 125 to: % 7.54/2.30 | (81) $false % 7.54/2.30 | % 7.54/2.30 |-The branch is then unsatisfiable % 7.54/2.30 |-Branch two: % 7.54/2.30 | (115) all_44_2_15 = 0 % 7.54/2.30 | (128) ~ (all_44_3_16 = 0) % 7.54/2.30 | % 7.54/2.30 | Equations (116) can reduce 128 to: % 7.54/2.30 | (81) $false % 7.54/2.30 | % 7.54/2.30 |-The branch is then unsatisfiable % 7.54/2.30 |-Branch two: % 7.54/2.30 | (130) all_14_3_7 = 0 & all_14_4_8 = 0 & all_14_5_9 = 0 & all_14_6_10 = 0 & ~ (all_14_7_11 = all_14_8_12) & apply(all_0_3_3, all_14_7_11, all_14_8_12) = 0 & apply(all_0_3_3, all_14_8_12, all_14_7_11) = 0 & member(all_14_7_11, all_0_1_1) = 0 & member(all_14_8_12, all_0_1_1) = 0 % 7.54/2.30 | % 7.54/2.30 | Applying alpha-rule on (130) yields: % 7.54/2.30 | (87) all_14_5_9 = 0 % 7.54/2.30 | (132) ~ (all_14_7_11 = all_14_8_12) % 7.54/2.30 | (90) apply(all_0_3_3, all_14_8_12, all_14_7_11) = 0 % 7.54/2.30 | (91) all_14_3_7 = 0 % 7.54/2.31 | (92) all_14_4_8 = 0 % 7.54/2.31 | (93) member(all_14_8_12, all_0_1_1) = 0 % 7.54/2.31 | (95) member(all_14_7_11, all_0_1_1) = 0 % 7.54/2.31 | (138) apply(all_0_3_3, all_14_7_11, all_14_8_12) = 0 % 7.54/2.31 | (139) all_14_6_10 = 0 % 7.54/2.31 | % 7.54/2.31 | Instantiating formula (9) with all_14_7_11, all_14_8_12, all_0_2_2, all_0_3_3 and discharging atoms order(all_0_3_3, all_0_2_2) = 0, apply(all_0_3_3, all_14_8_12, all_14_7_11) = 0, yields: % 7.54/2.31 | (140) all_14_7_11 = all_14_8_12 | ? [v0] : ? [v1] : ? [v2] : (apply(all_0_3_3, all_14_7_11, all_14_8_12) = v2 & member(all_14_7_11, all_0_2_2) = v1 & member(all_14_8_12, all_0_2_2) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))) % 7.54/2.31 | % 7.54/2.31 | Instantiating formula (29) with all_14_7_11, all_0_2_2, all_0_1_1 and discharging atoms subset(all_0_1_1, all_0_2_2) = 0, member(all_14_7_11, all_0_1_1) = 0, yields: % 7.54/2.31 | (101) member(all_14_7_11, all_0_2_2) = 0 % 7.54/2.31 | % 7.54/2.31 | Instantiating formula (29) with all_14_8_12, all_0_2_2, all_0_1_1 and discharging atoms subset(all_0_1_1, all_0_2_2) = 0, member(all_14_8_12, all_0_1_1) = 0, yields: % 7.54/2.31 | (102) member(all_14_8_12, all_0_2_2) = 0 % 7.54/2.31 | % 7.54/2.31 +-Applying beta-rule and splitting (140), into two cases. % 7.54/2.31 |-Branch one: % 7.54/2.31 | (143) all_14_7_11 = all_14_8_12 % 7.54/2.31 | % 7.54/2.31 | Equations (143) can reduce 132 to: % 7.54/2.31 | (81) $false % 7.54/2.31 | % 7.54/2.31 |-The branch is then unsatisfiable % 7.54/2.31 |-Branch two: % 7.54/2.31 | (132) ~ (all_14_7_11 = all_14_8_12) % 7.54/2.31 | (146) ? [v0] : ? [v1] : ? [v2] : (apply(all_0_3_3, all_14_7_11, all_14_8_12) = v2 & member(all_14_7_11, all_0_2_2) = v1 & member(all_14_8_12, all_0_2_2) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))) % 7.54/2.31 | % 7.54/2.31 | Instantiating (146) with all_44_0_17, all_44_1_18, all_44_2_19 yields: % 7.54/2.31 | (147) apply(all_0_3_3, all_14_7_11, all_14_8_12) = all_44_0_17 & member(all_14_7_11, all_0_2_2) = all_44_1_18 & member(all_14_8_12, all_0_2_2) = all_44_2_19 & ( ~ (all_44_0_17 = 0) | ~ (all_44_1_18 = 0) | ~ (all_44_2_19 = 0)) % 7.54/2.31 | % 7.54/2.31 | Applying alpha-rule on (147) yields: % 7.54/2.31 | (148) apply(all_0_3_3, all_14_7_11, all_14_8_12) = all_44_0_17 % 7.54/2.31 | (149) member(all_14_7_11, all_0_2_2) = all_44_1_18 % 7.54/2.31 | (150) member(all_14_8_12, all_0_2_2) = all_44_2_19 % 7.54/2.31 | (151) ~ (all_44_0_17 = 0) | ~ (all_44_1_18 = 0) | ~ (all_44_2_19 = 0) % 7.54/2.31 | % 7.54/2.31 | Instantiating formula (16) with all_0_3_3, all_14_7_11, all_14_8_12, all_44_0_17, 0 and discharging atoms apply(all_0_3_3, all_14_7_11, all_14_8_12) = all_44_0_17, apply(all_0_3_3, all_14_7_11, all_14_8_12) = 0, yields: % 7.54/2.31 | (152) all_44_0_17 = 0 % 7.54/2.31 | % 7.54/2.31 | Instantiating formula (31) with all_14_7_11, all_0_2_2, 0, all_44_1_18 and discharging atoms member(all_14_7_11, all_0_2_2) = all_44_1_18, member(all_14_7_11, all_0_2_2) = 0, yields: % 7.54/2.31 | (153) all_44_1_18 = 0 % 7.54/2.31 | % 7.54/2.31 | Instantiating formula (31) with all_14_8_12, all_0_2_2, 0, all_44_2_19 and discharging atoms member(all_14_8_12, all_0_2_2) = all_44_2_19, member(all_14_8_12, all_0_2_2) = 0, yields: % 7.54/2.31 | (154) all_44_2_19 = 0 % 7.54/2.31 | % 7.54/2.31 +-Applying beta-rule and splitting (151), into two cases. % 7.54/2.31 |-Branch one: % 7.54/2.31 | (155) ~ (all_44_0_17 = 0) % 7.54/2.31 | % 7.54/2.31 | Equations (152) can reduce 155 to: % 7.54/2.31 | (81) $false % 7.54/2.31 | % 7.54/2.31 |-The branch is then unsatisfiable % 7.54/2.31 |-Branch two: % 7.54/2.31 | (152) all_44_0_17 = 0 % 7.54/2.31 | (158) ~ (all_44_1_18 = 0) | ~ (all_44_2_19 = 0) % 7.54/2.31 | % 7.54/2.31 +-Applying beta-rule and splitting (158), into two cases. % 7.54/2.31 |-Branch one: % 7.54/2.31 | (159) ~ (all_44_1_18 = 0) % 7.54/2.31 | % 7.54/2.31 | Equations (153) can reduce 159 to: % 7.54/2.31 | (81) $false % 7.54/2.31 | % 7.54/2.31 |-The branch is then unsatisfiable % 7.54/2.31 |-Branch two: % 7.54/2.31 | (153) all_44_1_18 = 0 % 7.54/2.31 | (162) ~ (all_44_2_19 = 0) % 7.54/2.31 | % 7.54/2.31 | Equations (154) can reduce 162 to: % 7.54/2.31 | (81) $false % 7.54/2.31 | % 7.54/2.31 |-The branch is then unsatisfiable % 7.54/2.31 |-Branch two: % 7.54/2.31 | (164) all_14_7_11 = 0 & ~ (all_14_6_10 = 0) & apply(all_0_3_3, all_14_8_12, all_14_8_12) = all_14_6_10 & member(all_14_8_12, all_0_1_1) = 0 % 7.54/2.31 | % 7.54/2.31 | Applying alpha-rule on (164) yields: % 7.54/2.31 | (165) all_14_7_11 = 0 % 7.54/2.31 | (166) ~ (all_14_6_10 = 0) % 7.54/2.31 | (167) apply(all_0_3_3, all_14_8_12, all_14_8_12) = all_14_6_10 % 7.54/2.31 | (93) member(all_14_8_12, all_0_1_1) = 0 % 7.54/2.31 | % 7.54/2.31 | Instantiating formula (41) with all_14_6_10, all_14_8_12, all_0_2_2, all_0_3_3 and discharging atoms order(all_0_3_3, all_0_2_2) = 0, apply(all_0_3_3, all_14_8_12, all_14_8_12) = all_14_6_10, yields: % 7.54/2.31 | (169) all_14_6_10 = 0 | ? [v0] : ( ~ (v0 = 0) & member(all_14_8_12, all_0_2_2) = v0) % 7.54/2.31 | % 7.54/2.31 | Instantiating formula (29) with all_14_8_12, all_0_2_2, all_0_1_1 and discharging atoms subset(all_0_1_1, all_0_2_2) = 0, member(all_14_8_12, all_0_1_1) = 0, yields: % 7.54/2.31 | (102) member(all_14_8_12, all_0_2_2) = 0 % 7.54/2.31 | % 7.54/2.31 +-Applying beta-rule and splitting (169), into two cases. % 7.54/2.31 |-Branch one: % 7.54/2.31 | (139) all_14_6_10 = 0 % 7.54/2.31 | % 7.54/2.31 | Equations (139) can reduce 166 to: % 7.54/2.31 | (81) $false % 7.54/2.31 | % 7.54/2.31 |-The branch is then unsatisfiable % 7.54/2.31 |-Branch two: % 7.54/2.31 | (166) ~ (all_14_6_10 = 0) % 7.54/2.31 | (174) ? [v0] : ( ~ (v0 = 0) & member(all_14_8_12, all_0_2_2) = v0) % 7.54/2.31 | % 7.54/2.31 | Instantiating (174) with all_44_0_23 yields: % 7.54/2.31 | (175) ~ (all_44_0_23 = 0) & member(all_14_8_12, all_0_2_2) = all_44_0_23 % 7.54/2.31 | % 7.54/2.31 | Applying alpha-rule on (175) yields: % 7.54/2.31 | (176) ~ (all_44_0_23 = 0) % 7.54/2.31 | (177) member(all_14_8_12, all_0_2_2) = all_44_0_23 % 7.54/2.31 | % 7.54/2.31 | Instantiating formula (31) with all_14_8_12, all_0_2_2, 0, all_44_0_23 and discharging atoms member(all_14_8_12, all_0_2_2) = all_44_0_23, member(all_14_8_12, all_0_2_2) = 0, yields: % 7.54/2.31 | (178) all_44_0_23 = 0 % 7.54/2.31 | % 7.54/2.31 | Equations (178) can reduce 176 to: % 7.54/2.31 | (81) $false % 7.54/2.31 | % 7.54/2.31 |-The branch is then unsatisfiable % 7.54/2.31 % SZS output end Proof for theBenchmark % 7.54/2.31 % 7.54/2.31 1719ms %------------------------------------------------------------------------------