%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET792+4 : TPTP v8.1.0. Released v3.2.0. % 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 00:22:07 EDT 2022 % Result : Theorem 4.71s 1.70s % Output : Proof 6.33s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SET792+4 : TPTP v8.1.0. Released v3.2.0. % 0.11/0.12 % 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 05:26:53 EDT 2022 % 0.12/0.33 % CPUTime : % 0.19/0.58 ____ _ % 0.19/0.58 ___ / __ \_____(_)___ ________ __________ % 0.19/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.19/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.19/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.19/0.58 % 0.19/0.58 A Theorem Prover for First-Order Logic % 0.19/0.58 (ePrincess v.1.0) % 0.19/0.58 % 0.19/0.58 (c) Philipp Rümmer, 2009-2015 % 0.19/0.58 (c) Peter Backeman, 2014-2015 % 0.19/0.58 (contributions by Angelo Brillout, Peter Baumgartner) % 0.19/0.58 Free software under GNU Lesser General Public License (LGPL). % 0.19/0.58 Bug reports to peter@backeman.se % 0.19/0.58 % 0.19/0.58 For more information, visit http://user.uu.se/~petba168/breu/ % 0.19/0.58 % 0.19/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.72/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.64/0.91 Prover 0: Preprocessing ... % 2.15/1.08 Prover 0: Warning: ignoring some quantifiers % 2.15/1.11 Prover 0: Constructing countermodel ... % 3.63/1.48 Prover 0: gave up % 3.63/1.48 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 3.78/1.51 Prover 1: Preprocessing ... % 4.39/1.66 Prover 1: Constructing countermodel ... % 4.71/1.70 Prover 1: proved (226ms) % 4.71/1.70 % 4.71/1.70 No countermodel exists, formula is valid % 4.71/1.70 % SZS status Theorem for theBenchmark % 4.71/1.70 % 4.71/1.70 Generating proof ... found it (size 38) % 5.65/1.97 % 5.65/1.97 % SZS output start Proof for theBenchmark % 5.65/1.97 Assumed formulas after preprocessing and simplification: % 5.65/1.97 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = 0) & min(v2, v0, v1) = v3 & least(v2, v0, v1) = 0 & 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)) % 5.93/2.02 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields: % 5.93/2.02 | (1) ~ (all_0_0_0 = 0) & min(all_0_1_1, all_0_3_3, all_0_2_2) = all_0_0_0 & least(all_0_1_1, all_0_3_3, all_0_2_2) = 0 & 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) % 5.93/2.03 | % 5.93/2.03 | Applying alpha-rule on (1) yields: % 5.93/2.03 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (min(v4, v3, v2) = v1) | ~ (min(v4, v3, v2) = v0)) % 5.93/2.03 | (3) ! [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))) % 5.93/2.04 | (4) ! [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))))) % 5.93/2.04 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (max(v2, v0, v1) = 0) | ~ (apply(v0, v2, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4)) % 5.93/2.04 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (order(v3, v2) = v1) | ~ (order(v3, v2) = v0)) % 5.93/2.04 | (7) ! [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))) % 5.93/2.04 | (8) ! [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)) % 5.93/2.04 | (9) ! [v0] : ! [v1] : ! [v2] : ( ~ (max(v2, v0, v1) = 0) | member(v2, v1) = 0) % 5.93/2.04 | (10) ! [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))) % 5.93/2.04 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (least(v2, v0, v1) = 0) | ~ (apply(v0, v2, v3) = v4) | ? [v5] : ( ~ (v5 = 0) & member(v3, v1) = v5)) % 5.93/2.04 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (greatest(v2, v0, v1) = 0) | member(v2, v1) = 0) % 5.93/2.04 | (13) ! [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)))) % 5.93/2.04 | (14) ! [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))) % 5.93/2.04 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (least_upper_bound(v0, v1, v2, v3) = 0) | (upper_bound(v0, v2, v1) = 0 & member(v0, v1) = 0)) % 5.93/2.04 | (16) min(all_0_1_1, all_0_3_3, all_0_2_2) = all_0_0_0 % 5.93/2.04 | (17) ! [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)) % 5.93/2.04 | (18) ! [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))))) % 5.93/2.04 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (greatest_lower_bound(v5, v4, v3, v2) = v1) | ~ (greatest_lower_bound(v5, v4, v3, v2) = v0)) % 5.93/2.04 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (order(v0, v1) = 0) | ~ (apply(v0, v2, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v1) = v4)) % 5.93/2.04 | (21) ! [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))) % 5.93/2.05 | (22) order(all_0_3_3, all_0_2_2) = 0 % 5.93/2.05 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | ~ (apply(v4, v3, v2) = v0)) % 5.93/2.05 | (24) ! [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)))) % 5.93/2.05 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (lower_bound(v4, v3, v2) = v1) | ~ (lower_bound(v4, v3, v2) = v0)) % 5.93/2.05 | (26) ! [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))) % 5.93/2.05 | (27) ! [v0] : ! [v1] : ! [v2] : ( ~ (least(v2, v0, v1) = 0) | member(v2, v1) = 0) % 5.93/2.05 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (least(v4, v3, v2) = v1) | ~ (least(v4, v3, v2) = v0)) % 5.93/2.05 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (total_order(v3, v2) = v1) | ~ (total_order(v3, v2) = v0)) % 5.93/2.05 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (greatest_lower_bound(v0, v1, v2, v3) = 0) | (lower_bound(v0, v2, v1) = 0 & member(v0, v1) = 0)) % 5.93/2.05 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (min(v2, v0, v1) = 0) | ~ (apply(v0, v3, v2) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4)) % 5.93/2.05 | (32) ! [v0] : ! [v1] : ( ~ (total_order(v0, v1) = 0) | order(v0, v1) = 0) % 5.93/2.05 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (greatest(v2, v0, v1) = 0) | ~ (apply(v0, v3, v2) = v4) | ? [v5] : ( ~ (v5 = 0) & member(v3, v1) = v5)) % 5.93/2.05 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) % 5.93/2.05 | (35) least(all_0_1_1, all_0_3_3, all_0_2_2) = 0 % 5.93/2.05 | (36) ! [v0] : ! [v1] : ! [v2] : ( ~ (min(v2, v0, v1) = 0) | member(v2, v1) = 0) % 5.93/2.05 | (37) ~ (all_0_0_0 = 0) % 5.93/2.05 | (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)) % 5.93/2.05 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (upper_bound(v4, v3, v2) = v1) | ~ (upper_bound(v4, v3, v2) = v0)) % 5.93/2.05 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (greatest(v4, v3, v2) = v1) | ~ (greatest(v4, v3, v2) = v0)) % 5.93/2.05 | (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))) % 5.93/2.05 | (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)) % 5.93/2.05 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (max(v4, v3, v2) = v1) | ~ (max(v4, v3, v2) = v0)) % 5.93/2.05 | (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)) % 5.93/2.05 | (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))) % 5.93/2.06 | (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))) % 5.93/2.06 | % 5.93/2.06 | Instantiating formula (21) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 and discharging atoms min(all_0_1_1, all_0_3_3, all_0_2_2) = all_0_0_0, yields: % 5.93/2.06 | (47) all_0_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ((v2 = 0 & v1 = 0 & ~ (v0 = all_0_1_1) & apply(all_0_3_3, v0, all_0_1_1) = 0 & member(v0, all_0_2_2) = 0) | ( ~ (v0 = 0) & member(all_0_1_1, all_0_2_2) = v0)) % 5.93/2.06 | % 5.93/2.06 | Instantiating formula (27) with all_0_1_1, all_0_2_2, all_0_3_3 and discharging atoms least(all_0_1_1, all_0_3_3, all_0_2_2) = 0, yields: % 5.93/2.06 | (48) member(all_0_1_1, all_0_2_2) = 0 % 5.93/2.06 | % 5.93/2.06 +-Applying beta-rule and splitting (47), into two cases. % 5.93/2.06 |-Branch one: % 5.93/2.06 | (49) all_0_0_0 = 0 % 5.93/2.06 | % 5.93/2.06 | Equations (49) can reduce 37 to: % 5.93/2.06 | (50) $false % 5.93/2.06 | % 5.93/2.06 |-The branch is then unsatisfiable % 5.93/2.06 |-Branch two: % 5.93/2.06 | (37) ~ (all_0_0_0 = 0) % 5.93/2.06 | (52) ? [v0] : ? [v1] : ? [v2] : ((v2 = 0 & v1 = 0 & ~ (v0 = all_0_1_1) & apply(all_0_3_3, v0, all_0_1_1) = 0 & member(v0, all_0_2_2) = 0) | ( ~ (v0 = 0) & member(all_0_1_1, all_0_2_2) = v0)) % 5.93/2.06 | % 5.93/2.06 | Instantiating (52) with all_13_0_4, all_13_1_5, all_13_2_6 yields: % 5.93/2.06 | (53) (all_13_0_4 = 0 & all_13_1_5 = 0 & ~ (all_13_2_6 = all_0_1_1) & apply(all_0_3_3, all_13_2_6, all_0_1_1) = 0 & 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) % 5.93/2.06 | % 5.93/2.06 +-Applying beta-rule and splitting (53), into two cases. % 5.93/2.06 |-Branch one: % 5.93/2.06 | (54) all_13_0_4 = 0 & all_13_1_5 = 0 & ~ (all_13_2_6 = all_0_1_1) & apply(all_0_3_3, all_13_2_6, all_0_1_1) = 0 & member(all_13_2_6, all_0_2_2) = 0 % 5.93/2.06 | % 5.93/2.06 | Applying alpha-rule on (54) yields: % 5.93/2.06 | (55) member(all_13_2_6, all_0_2_2) = 0 % 5.93/2.06 | (56) apply(all_0_3_3, all_13_2_6, all_0_1_1) = 0 % 5.93/2.06 | (57) ~ (all_13_2_6 = all_0_1_1) % 6.33/2.06 | (58) all_13_0_4 = 0 % 6.33/2.06 | (59) all_13_1_5 = 0 % 6.33/2.06 | % 6.33/2.06 | Instantiating formula (13) with all_0_1_1, all_13_2_6, 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_13_2_6, all_0_1_1) = 0, yields: % 6.33/2.06 | (60) all_13_2_6 = all_0_1_1 | ? [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 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))) % 6.33/2.07 | % 6.33/2.07 +-Applying beta-rule and splitting (60), into two cases. % 6.33/2.07 |-Branch one: % 6.33/2.07 | (61) all_13_2_6 = all_0_1_1 % 6.33/2.07 | % 6.33/2.07 | Equations (61) can reduce 57 to: % 6.33/2.07 | (50) $false % 6.33/2.07 | % 6.33/2.07 |-The branch is then unsatisfiable % 6.33/2.07 |-Branch two: % 6.33/2.07 | (57) ~ (all_13_2_6 = all_0_1_1) % 6.33/2.07 | (64) ? [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 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))) % 6.33/2.07 | % 6.33/2.07 | Instantiating (64) with all_25_0_7, all_25_1_8, all_25_2_9 yields: % 6.33/2.07 | (65) 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_0_7 = 0) | ~ (all_25_1_8 = 0) | ~ (all_25_2_9 = 0)) % 6.33/2.07 | % 6.33/2.07 | Applying alpha-rule on (65) yields: % 6.33/2.07 | (66) apply(all_0_3_3, all_0_1_1, all_13_2_6) = all_25_0_7 % 6.33/2.07 | (67) member(all_13_2_6, all_0_2_2) = all_25_2_9 % 6.33/2.07 | (68) member(all_0_1_1, all_0_2_2) = all_25_1_8 % 6.33/2.07 | (69) ~ (all_25_0_7 = 0) | ~ (all_25_1_8 = 0) | ~ (all_25_2_9 = 0) % 6.33/2.07 | % 6.33/2.07 | Instantiating formula (34) 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: % 6.33/2.07 | (70) all_25_2_9 = 0 % 6.33/2.07 | % 6.33/2.07 | Instantiating formula (34) 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: % 6.33/2.07 | (71) all_25_1_8 = 0 % 6.33/2.07 | % 6.33/2.07 | From (70) and (67) follows: % 6.33/2.07 | (55) member(all_13_2_6, all_0_2_2) = 0 % 6.33/2.07 | % 6.33/2.07 +-Applying beta-rule and splitting (69), into two cases. % 6.33/2.07 |-Branch one: % 6.33/2.07 | (73) ~ (all_25_0_7 = 0) % 6.33/2.07 | % 6.33/2.07 | Instantiating formula (11) with all_25_0_7, all_13_2_6, all_0_1_1, all_0_2_2, all_0_3_3 and discharging atoms least(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) = all_25_0_7, yields: % 6.33/2.07 | (74) all_25_0_7 = 0 | ? [v0] : ( ~ (v0 = 0) & member(all_13_2_6, all_0_2_2) = v0) % 6.33/2.07 | % 6.33/2.07 +-Applying beta-rule and splitting (74), into two cases. % 6.33/2.07 |-Branch one: % 6.33/2.07 | (75) all_25_0_7 = 0 % 6.33/2.07 | % 6.33/2.07 | Equations (75) can reduce 73 to: % 6.33/2.07 | (50) $false % 6.33/2.07 | % 6.33/2.07 |-The branch is then unsatisfiable % 6.33/2.07 |-Branch two: % 6.33/2.07 | (73) ~ (all_25_0_7 = 0) % 6.33/2.07 | (78) ? [v0] : ( ~ (v0 = 0) & member(all_13_2_6, all_0_2_2) = v0) % 6.33/2.07 | % 6.33/2.07 | Instantiating (78) with all_42_0_10 yields: % 6.33/2.07 | (79) ~ (all_42_0_10 = 0) & member(all_13_2_6, all_0_2_2) = all_42_0_10 % 6.33/2.07 | % 6.33/2.07 | Applying alpha-rule on (79) yields: % 6.33/2.07 | (80) ~ (all_42_0_10 = 0) % 6.33/2.07 | (81) member(all_13_2_6, all_0_2_2) = all_42_0_10 % 6.33/2.07 | % 6.33/2.07 | Instantiating formula (34) with all_13_2_6, all_0_2_2, all_42_0_10, 0 and discharging atoms member(all_13_2_6, all_0_2_2) = all_42_0_10, member(all_13_2_6, all_0_2_2) = 0, yields: % 6.33/2.07 | (82) all_42_0_10 = 0 % 6.33/2.07 | % 6.33/2.07 | Equations (82) can reduce 80 to: % 6.33/2.07 | (50) $false % 6.33/2.07 | % 6.33/2.07 |-The branch is then unsatisfiable % 6.33/2.07 |-Branch two: % 6.33/2.07 | (75) all_25_0_7 = 0 % 6.33/2.07 | (85) ~ (all_25_1_8 = 0) | ~ (all_25_2_9 = 0) % 6.33/2.07 | % 6.33/2.07 +-Applying beta-rule and splitting (85), into two cases. % 6.33/2.07 |-Branch one: % 6.33/2.07 | (86) ~ (all_25_1_8 = 0) % 6.33/2.07 | % 6.33/2.07 | Equations (71) can reduce 86 to: % 6.33/2.07 | (50) $false % 6.33/2.07 | % 6.33/2.07 |-The branch is then unsatisfiable % 6.33/2.07 |-Branch two: % 6.33/2.07 | (71) all_25_1_8 = 0 % 6.33/2.07 | (89) ~ (all_25_2_9 = 0) % 6.33/2.07 | % 6.33/2.07 | Equations (70) can reduce 89 to: % 6.33/2.07 | (50) $false % 6.33/2.07 | % 6.33/2.07 |-The branch is then unsatisfiable % 6.33/2.07 |-Branch two: % 6.33/2.07 | (91) ~ (all_13_2_6 = 0) & member(all_0_1_1, all_0_2_2) = all_13_2_6 % 6.33/2.07 | % 6.33/2.07 | Applying alpha-rule on (91) yields: % 6.33/2.07 | (92) ~ (all_13_2_6 = 0) % 6.33/2.07 | (93) member(all_0_1_1, all_0_2_2) = all_13_2_6 % 6.33/2.07 | % 6.33/2.07 | Instantiating formula (34) 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: % 6.33/2.07 | (94) all_13_2_6 = 0 % 6.33/2.07 | % 6.33/2.07 | Equations (94) can reduce 92 to: % 6.33/2.07 | (50) $false % 6.33/2.07 | % 6.33/2.07 |-The branch is then unsatisfiable % 6.33/2.07 % SZS output end Proof for theBenchmark % 6.33/2.07 % 6.33/2.07 1486ms %------------------------------------------------------------------------------