%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET793+4 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n021.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 00:22:07 EDT 2022 % Result : Theorem 4.82s 1.79s % Output : Proof 6.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SET793+4 : TPTP v8.1.0. Released v3.2.0. % 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.34 % Computer : n021.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 600 % 0.12/0.34 % DateTime : Sun Jul 10 02:05:07 EDT 2022 % 0.12/0.34 % CPUTime : % 0.59/0.59 ____ _ % 0.59/0.59 ___ / __ \_____(_)___ ________ __________ % 0.59/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.59/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.59/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.59/0.59 % 0.59/0.59 A Theorem Prover for First-Order Logic % 0.59/0.59 (ePrincess v.1.0) % 0.59/0.59 % 0.59/0.59 (c) Philipp Rümmer, 2009-2015 % 0.59/0.59 (c) Peter Backeman, 2014-2015 % 0.59/0.59 (contributions by Angelo Brillout, Peter Baumgartner) % 0.59/0.59 Free software under GNU Lesser General Public License (LGPL). % 0.59/0.59 Bug reports to peter@backeman.se % 0.59/0.59 % 0.59/0.59 For more information, visit http://user.uu.se/~petba168/breu/ % 0.59/0.59 % 0.59/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.70/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.63/0.98 Prover 0: Preprocessing ... % 1.98/1.17 Prover 0: Warning: ignoring some quantifiers % 2.28/1.19 Prover 0: Constructing countermodel ... % 3.69/1.56 Prover 0: gave up % 3.69/1.56 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 3.69/1.59 Prover 1: Preprocessing ... % 4.38/1.74 Prover 1: Constructing countermodel ... % 4.82/1.78 Prover 1: proved (225ms) % 4.82/1.78 % 4.82/1.78 No countermodel exists, formula is valid % 4.82/1.79 % SZS status Theorem for theBenchmark % 4.82/1.79 % 4.82/1.79 Generating proof ... found it (size 52) % 6.16/2.08 % 6.16/2.08 % SZS output start Proof for theBenchmark % 6.16/2.09 Assumed formulas after preprocessing and simplification: % 6.16/2.09 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = 0) & max(v2, v0, v1) = 0 & greatest(v2, v0, v1) = v3 & total_order(v0, 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] : (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] : (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 | ~ (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] : (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] : ( ~ (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] : ( ~ (total_order(v4, v5) = 0) | order(v4, v5) = 0)) % 6.38/2.14 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields: % 6.38/2.14 | (1) ~ (all_0_0_0 = 0) & max(all_0_1_1, all_0_3_3, all_0_2_2) = 0 & greatest(all_0_1_1, all_0_3_3, all_0_2_2) = all_0_0_0 & total_order(all_0_3_3, 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] : (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] : (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 | ~ (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] : (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] : ( ~ (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] : ( ~ (total_order(v0, v1) = 0) | order(v0, v1) = 0) % 6.38/2.16 | % 6.38/2.16 | Applying alpha-rule on (1) yields: % 6.38/2.16 | (2) greatest(all_0_1_1, all_0_3_3, all_0_2_2) = all_0_0_0 % 6.38/2.16 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (min(v4, v3, v2) = v1) | ~ (min(v4, v3, v2) = v0)) % 6.38/2.16 | (4) ! [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))) % 6.38/2.16 | (5) ! [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))))) % 6.38/2.16 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (max(v2, v0, v1) = 0) | ~ (apply(v0, v2, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4)) % 6.38/2.16 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (order(v3, v2) = v1) | ~ (order(v3, v2) = v0)) % 6.38/2.16 | (8) ! [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))) % 6.38/2.16 | (9) ! [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)) % 6.38/2.16 | (10) total_order(all_0_3_3, all_0_2_2) = 0 % 6.38/2.16 | (11) ! [v0] : ! [v1] : ! [v2] : ( ~ (max(v2, v0, v1) = 0) | member(v2, v1) = 0) % 6.38/2.16 | (12) ! [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))) % 6.38/2.16 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (least(v2, v0, v1) = 0) | ~ (apply(v0, v2, v3) = v4) | ? [v5] : ( ~ (v5 = 0) & member(v3, v1) = v5)) % 6.38/2.16 | (14) ! [v0] : ! [v1] : ! [v2] : ( ~ (greatest(v2, v0, v1) = 0) | member(v2, v1) = 0) % 6.38/2.16 | (15) ! [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)))) % 6.38/2.16 | (16) max(all_0_1_1, all_0_3_3, all_0_2_2) = 0 % 6.38/2.16 | (17) ! [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))) % 6.38/2.16 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (least_upper_bound(v0, v1, v2, v3) = 0) | (upper_bound(v0, v2, v1) = 0 & member(v0, v1) = 0)) % 6.38/2.17 | (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)) % 6.38/2.17 | (20) ! [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))))) % 6.38/2.17 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (greatest_lower_bound(v5, v4, v3, v2) = v1) | ~ (greatest_lower_bound(v5, v4, v3, v2) = v0)) % 6.38/2.17 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (order(v0, v1) = 0) | ~ (apply(v0, v2, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v1) = v4)) % 6.38/2.17 | (23) ! [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))) % 6.38/2.17 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | ~ (apply(v4, v3, v2) = v0)) % 6.38/2.17 | (25) ! [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)))) % 6.38/2.17 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (lower_bound(v4, v3, v2) = v1) | ~ (lower_bound(v4, v3, v2) = v0)) % 6.38/2.17 | (27) ! [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))) % 6.38/2.17 | (28) ! [v0] : ! [v1] : ! [v2] : ( ~ (least(v2, v0, v1) = 0) | member(v2, v1) = 0) % 6.38/2.17 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (least(v4, v3, v2) = v1) | ~ (least(v4, v3, v2) = v0)) % 6.38/2.17 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (total_order(v3, v2) = v1) | ~ (total_order(v3, v2) = v0)) % 6.38/2.17 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (greatest_lower_bound(v0, v1, v2, v3) = 0) | (lower_bound(v0, v2, v1) = 0 & member(v0, v1) = 0)) % 6.38/2.17 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (min(v2, v0, v1) = 0) | ~ (apply(v0, v3, v2) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4)) % 6.38/2.17 | (33) ! [v0] : ! [v1] : ( ~ (total_order(v0, v1) = 0) | order(v0, v1) = 0) % 6.38/2.17 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (greatest(v2, v0, v1) = 0) | ~ (apply(v0, v3, v2) = v4) | ? [v5] : ( ~ (v5 = 0) & member(v3, v1) = v5)) % 6.38/2.17 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) % 6.38/2.17 | (36) ! [v0] : ! [v1] : ! [v2] : ( ~ (min(v2, v0, v1) = 0) | member(v2, v1) = 0) % 6.38/2.17 | (37) ~ (all_0_0_0 = 0) % 6.38/2.17 | (38) ! [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)) % 6.38/2.17 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (upper_bound(v4, v3, v2) = v1) | ~ (upper_bound(v4, v3, v2) = v0)) % 6.38/2.18 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (greatest(v4, v3, v2) = v1) | ~ (greatest(v4, v3, v2) = v0)) % 6.38/2.18 | (41) ! [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))) % 6.38/2.18 | (42) ! [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)) % 6.38/2.18 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (max(v4, v3, v2) = v1) | ~ (max(v4, v3, v2) = v0)) % 6.38/2.18 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (least_upper_bound(v5, v4, v3, v2) = v1) | ~ (least_upper_bound(v5, v4, v3, v2) = v0)) % 6.38/2.18 | (45) ! [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))) % 6.38/2.18 | (46) ! [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))) % 6.38/2.18 | % 6.38/2.18 | Instantiating formula (11) with all_0_1_1, all_0_2_2, all_0_3_3 and discharging atoms max(all_0_1_1, all_0_3_3, all_0_2_2) = 0, yields: % 6.38/2.18 | (47) member(all_0_1_1, all_0_2_2) = 0 % 6.38/2.18 | % 6.38/2.18 | Instantiating formula (8) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 and discharging atoms greatest(all_0_1_1, all_0_3_3, all_0_2_2) = all_0_0_0, yields: % 6.38/2.18 | (48) all_0_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ((v1 = 0 & ~ (v2 = 0) & apply(all_0_3_3, v0, all_0_1_1) = v2 & member(v0, all_0_2_2) = 0) | ( ~ (v0 = 0) & member(all_0_1_1, all_0_2_2) = v0)) % 6.38/2.18 | % 6.38/2.18 | Instantiating formula (33) with all_0_2_2, all_0_3_3 and discharging atoms total_order(all_0_3_3, all_0_2_2) = 0, yields: % 6.38/2.18 | (49) order(all_0_3_3, all_0_2_2) = 0 % 6.38/2.18 | % 6.38/2.18 +-Applying beta-rule and splitting (48), into two cases. % 6.38/2.18 |-Branch one: % 6.38/2.18 | (50) all_0_0_0 = 0 % 6.38/2.18 | % 6.38/2.18 | Equations (50) can reduce 37 to: % 6.38/2.18 | (51) $false % 6.38/2.18 | % 6.38/2.18 |-The branch is then unsatisfiable % 6.38/2.18 |-Branch two: % 6.38/2.18 | (37) ~ (all_0_0_0 = 0) % 6.38/2.18 | (53) ? [v0] : ? [v1] : ? [v2] : ((v1 = 0 & ~ (v2 = 0) & apply(all_0_3_3, v0, all_0_1_1) = v2 & member(v0, all_0_2_2) = 0) | ( ~ (v0 = 0) & member(all_0_1_1, all_0_2_2) = v0)) % 6.38/2.18 | % 6.38/2.18 | Instantiating (53) with all_13_0_4, all_13_1_5, all_13_2_6 yields: % 6.38/2.18 | (54) (all_13_1_5 = 0 & ~ (all_13_0_4 = 0) & apply(all_0_3_3, all_13_2_6, all_0_1_1) = all_13_0_4 & member(all_13_2_6, all_0_2_2) = 0) | ( ~ (all_13_2_6 = 0) & member(all_0_1_1, all_0_2_2) = all_13_2_6) % 6.38/2.18 | % 6.38/2.18 +-Applying beta-rule and splitting (54), into two cases. % 6.38/2.18 |-Branch one: % 6.38/2.18 | (55) all_13_1_5 = 0 & ~ (all_13_0_4 = 0) & apply(all_0_3_3, all_13_2_6, all_0_1_1) = all_13_0_4 & member(all_13_2_6, all_0_2_2) = 0 % 6.38/2.18 | % 6.38/2.18 | Applying alpha-rule on (55) yields: % 6.38/2.18 | (56) all_13_1_5 = 0 % 6.38/2.18 | (57) ~ (all_13_0_4 = 0) % 6.38/2.19 | (58) apply(all_0_3_3, all_13_2_6, all_0_1_1) = all_13_0_4 % 6.38/2.19 | (59) member(all_13_2_6, all_0_2_2) = 0 % 6.38/2.19 | % 6.38/2.19 | Instantiating formula (41) with all_13_0_4, all_0_1_1, all_13_2_6, all_0_2_2, all_0_3_3 and discharging atoms total_order(all_0_3_3, all_0_2_2) = 0, apply(all_0_3_3, all_13_2_6, all_0_1_1) = all_13_0_4, yields: % 6.38/2.19 | (60) all_13_0_4 = 0 | ? [v0] : ? [v1] : ? [v2] : (apply(all_0_3_3, all_0_1_1, all_13_2_6) = v2 & member(all_13_2_6, all_0_2_2) = v0 & member(all_0_1_1, all_0_2_2) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 6.38/2.19 | % 6.38/2.19 | Instantiating formula (22) with all_13_0_4, all_0_1_1, all_0_2_2, all_0_3_3 and discharging atoms order(all_0_3_3, all_0_2_2) = 0, yields: % 6.38/2.19 | (61) all_13_0_4 = 0 | ~ (apply(all_0_3_3, all_0_1_1, all_0_1_1) = all_13_0_4) | ? [v0] : ( ~ (v0 = 0) & member(all_0_1_1, all_0_2_2) = v0) % 6.38/2.19 | % 6.38/2.19 +-Applying beta-rule and splitting (60), into two cases. % 6.38/2.19 |-Branch one: % 6.38/2.19 | (62) all_13_0_4 = 0 % 6.38/2.19 | % 6.38/2.19 | Equations (62) can reduce 57 to: % 6.38/2.19 | (51) $false % 6.38/2.19 | % 6.38/2.19 |-The branch is then unsatisfiable % 6.38/2.19 |-Branch two: % 6.38/2.19 | (57) ~ (all_13_0_4 = 0) % 6.38/2.19 | (65) ? [v0] : ? [v1] : ? [v2] : (apply(all_0_3_3, all_0_1_1, all_13_2_6) = v2 & member(all_13_2_6, all_0_2_2) = v0 & member(all_0_1_1, all_0_2_2) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 6.38/2.19 | % 6.38/2.19 | Instantiating (65) with all_25_0_7, all_25_1_8, all_25_2_9 yields: % 6.38/2.19 | (66) apply(all_0_3_3, all_0_1_1, all_13_2_6) = all_25_0_7 & member(all_13_2_6, all_0_2_2) = all_25_2_9 & member(all_0_1_1, all_0_2_2) = all_25_1_8 & ( ~ (all_25_1_8 = 0) | ~ (all_25_2_9 = 0) | all_25_0_7 = 0) % 6.38/2.19 | % 6.38/2.19 | Applying alpha-rule on (66) yields: % 6.38/2.19 | (67) apply(all_0_3_3, all_0_1_1, all_13_2_6) = all_25_0_7 % 6.38/2.19 | (68) member(all_13_2_6, all_0_2_2) = all_25_2_9 % 6.38/2.19 | (69) member(all_0_1_1, all_0_2_2) = all_25_1_8 % 6.38/2.19 | (70) ~ (all_25_1_8 = 0) | ~ (all_25_2_9 = 0) | all_25_0_7 = 0 % 6.38/2.19 | % 6.38/2.19 | Instantiating formula (35) with all_13_2_6, all_0_2_2, all_25_2_9, 0 and discharging atoms member(all_13_2_6, all_0_2_2) = all_25_2_9, member(all_13_2_6, all_0_2_2) = 0, yields: % 6.38/2.19 | (71) all_25_2_9 = 0 % 6.38/2.19 | % 6.38/2.19 | Instantiating formula (35) with all_0_1_1, all_0_2_2, all_25_1_8, 0 and discharging atoms member(all_0_1_1, all_0_2_2) = all_25_1_8, member(all_0_1_1, all_0_2_2) = 0, yields: % 6.38/2.19 | (72) all_25_1_8 = 0 % 6.38/2.19 | % 6.38/2.19 | From (71) and (68) follows: % 6.38/2.19 | (59) member(all_13_2_6, all_0_2_2) = 0 % 6.38/2.19 | % 6.38/2.19 | From (72) and (69) follows: % 6.38/2.19 | (47) member(all_0_1_1, all_0_2_2) = 0 % 6.38/2.19 | % 6.38/2.19 +-Applying beta-rule and splitting (61), into two cases. % 6.38/2.19 |-Branch one: % 6.38/2.19 | (75) ~ (apply(all_0_3_3, all_0_1_1, all_0_1_1) = all_13_0_4) % 6.38/2.19 | % 6.38/2.19 +-Applying beta-rule and splitting (70), into two cases. % 6.38/2.19 |-Branch one: % 6.38/2.19 | (76) ~ (all_25_1_8 = 0) % 6.38/2.19 | % 6.38/2.19 | Equations (72) can reduce 76 to: % 6.38/2.19 | (51) $false % 6.38/2.19 | % 6.38/2.19 |-The branch is then unsatisfiable % 6.38/2.19 |-Branch two: % 6.38/2.19 | (72) all_25_1_8 = 0 % 6.38/2.19 | (79) ~ (all_25_2_9 = 0) | all_25_0_7 = 0 % 6.38/2.19 | % 6.38/2.19 +-Applying beta-rule and splitting (79), into two cases. % 6.38/2.19 |-Branch one: % 6.38/2.19 | (80) ~ (all_25_2_9 = 0) % 6.38/2.19 | % 6.38/2.19 | Equations (71) can reduce 80 to: % 6.38/2.20 | (51) $false % 6.38/2.20 | % 6.38/2.20 |-The branch is then unsatisfiable % 6.38/2.20 |-Branch two: % 6.38/2.20 | (71) all_25_2_9 = 0 % 6.38/2.20 | (83) all_25_0_7 = 0 % 6.38/2.20 | % 6.38/2.20 | From (83) and (67) follows: % 6.38/2.20 | (84) apply(all_0_3_3, all_0_1_1, all_13_2_6) = 0 % 6.38/2.20 | % 6.38/2.20 | Using (58) and (75) yields: % 6.38/2.20 | (85) ~ (all_13_2_6 = all_0_1_1) % 6.38/2.20 | % 6.38/2.20 | Instantiating formula (6) with all_13_2_6, all_0_1_1, all_0_2_2, all_0_3_3 and discharging atoms max(all_0_1_1, all_0_3_3, all_0_2_2) = 0, apply(all_0_3_3, all_0_1_1, all_13_2_6) = 0, yields: % 6.38/2.20 | (86) all_13_2_6 = all_0_1_1 | ? [v0] : ( ~ (v0 = 0) & member(all_13_2_6, all_0_2_2) = v0) % 6.38/2.20 | % 6.38/2.20 +-Applying beta-rule and splitting (86), into two cases. % 6.38/2.20 |-Branch one: % 6.38/2.20 | (87) all_13_2_6 = all_0_1_1 % 6.38/2.20 | % 6.38/2.20 | Equations (87) can reduce 85 to: % 6.38/2.20 | (51) $false % 6.38/2.20 | % 6.38/2.20 |-The branch is then unsatisfiable % 6.38/2.20 |-Branch two: % 6.38/2.20 | (85) ~ (all_13_2_6 = all_0_1_1) % 6.38/2.20 | (90) ? [v0] : ( ~ (v0 = 0) & member(all_13_2_6, all_0_2_2) = v0) % 6.38/2.20 | % 6.38/2.20 | Instantiating (90) with all_58_0_10 yields: % 6.38/2.20 | (91) ~ (all_58_0_10 = 0) & member(all_13_2_6, all_0_2_2) = all_58_0_10 % 6.38/2.20 | % 6.38/2.20 | Applying alpha-rule on (91) yields: % 6.38/2.20 | (92) ~ (all_58_0_10 = 0) % 6.38/2.20 | (93) member(all_13_2_6, all_0_2_2) = all_58_0_10 % 6.38/2.20 | % 6.38/2.20 | Instantiating formula (35) with all_13_2_6, all_0_2_2, all_58_0_10, 0 and discharging atoms member(all_13_2_6, all_0_2_2) = all_58_0_10, member(all_13_2_6, all_0_2_2) = 0, yields: % 6.38/2.20 | (94) all_58_0_10 = 0 % 6.38/2.20 | % 6.38/2.20 | Equations (94) can reduce 92 to: % 6.38/2.20 | (51) $false % 6.38/2.20 | % 6.38/2.20 |-The branch is then unsatisfiable % 6.38/2.20 |-Branch two: % 6.38/2.20 | (96) apply(all_0_3_3, all_0_1_1, all_0_1_1) = all_13_0_4 % 6.38/2.20 | (97) all_13_0_4 = 0 | ? [v0] : ( ~ (v0 = 0) & member(all_0_1_1, all_0_2_2) = v0) % 6.38/2.20 | % 6.38/2.20 +-Applying beta-rule and splitting (97), into two cases. % 6.38/2.20 |-Branch one: % 6.38/2.20 | (62) all_13_0_4 = 0 % 6.38/2.20 | % 6.38/2.20 | Equations (62) can reduce 57 to: % 6.38/2.20 | (51) $false % 6.38/2.20 | % 6.38/2.20 |-The branch is then unsatisfiable % 6.38/2.20 |-Branch two: % 6.38/2.20 | (57) ~ (all_13_0_4 = 0) % 6.38/2.20 | (101) ? [v0] : ( ~ (v0 = 0) & member(all_0_1_1, all_0_2_2) = v0) % 6.38/2.20 | % 6.38/2.20 | Instantiating (101) with all_43_0_11 yields: % 6.38/2.20 | (102) ~ (all_43_0_11 = 0) & member(all_0_1_1, all_0_2_2) = all_43_0_11 % 6.38/2.20 | % 6.38/2.20 | Applying alpha-rule on (102) yields: % 6.38/2.20 | (103) ~ (all_43_0_11 = 0) % 6.38/2.20 | (104) member(all_0_1_1, all_0_2_2) = all_43_0_11 % 6.38/2.20 | % 6.38/2.20 | Instantiating formula (35) with all_0_1_1, all_0_2_2, all_43_0_11, 0 and discharging atoms member(all_0_1_1, all_0_2_2) = all_43_0_11, member(all_0_1_1, all_0_2_2) = 0, yields: % 6.38/2.20 | (105) all_43_0_11 = 0 % 6.38/2.20 | % 6.38/2.20 | Equations (105) can reduce 103 to: % 6.38/2.20 | (51) $false % 6.38/2.20 | % 6.38/2.20 |-The branch is then unsatisfiable % 6.38/2.20 |-Branch two: % 6.38/2.20 | (107) ~ (all_13_2_6 = 0) & member(all_0_1_1, all_0_2_2) = all_13_2_6 % 6.38/2.20 | % 6.38/2.20 | Applying alpha-rule on (107) yields: % 6.38/2.20 | (108) ~ (all_13_2_6 = 0) % 6.38/2.20 | (109) member(all_0_1_1, all_0_2_2) = all_13_2_6 % 6.38/2.20 | % 6.38/2.20 | Instantiating formula (35) with all_0_1_1, all_0_2_2, 0, all_13_2_6 and discharging atoms member(all_0_1_1, all_0_2_2) = all_13_2_6, member(all_0_1_1, all_0_2_2) = 0, yields: % 6.38/2.20 | (110) all_13_2_6 = 0 % 6.38/2.20 | % 6.38/2.20 | Equations (110) can reduce 108 to: % 6.38/2.20 | (51) $false % 6.38/2.20 | % 6.38/2.20 |-The branch is then unsatisfiable % 6.38/2.20 % SZS output end Proof for theBenchmark % 6.38/2.20 % 6.38/2.20 1596ms %------------------------------------------------------------------------------