%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET702+4 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n011.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 600s % DateTime : Tue Jul 19 00:21:30 EDT 2022 % Result : Theorem 11.84s 3.55s % Output : Proof 13.28s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SET702+4 : TPTP v8.1.0. Released v2.2.0. % 0.06/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.34 % Computer : n011.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 : Sat Jul 9 16:03:25 EDT 2022 % 0.12/0.34 % CPUTime : % 0.48/0.59 ____ _ % 0.48/0.59 ___ / __ \_____(_)___ ________ __________ % 0.48/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.48/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.48/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.48/0.59 % 0.48/0.59 A Theorem Prover for First-Order Logic % 0.48/0.59 (ePrincess v.1.0) % 0.48/0.59 % 0.48/0.59 (c) Philipp Rümmer, 2009-2015 % 0.48/0.59 (c) Peter Backeman, 2014-2015 % 0.48/0.59 (contributions by Angelo Brillout, Peter Baumgartner) % 0.48/0.59 Free software under GNU Lesser General Public License (LGPL). % 0.48/0.59 Bug reports to peter@backeman.se % 0.48/0.59 % 0.48/0.59 For more information, visit http://user.uu.se/~petba168/breu/ % 0.48/0.59 % 0.48/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.72/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.37/0.93 Prover 0: Preprocessing ... % 2.15/1.13 Prover 0: Warning: ignoring some quantifiers % 2.15/1.15 Prover 0: Constructing countermodel ... % 10.97/3.39 Prover 0: gave up % 10.97/3.39 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 11.17/3.41 Prover 1: Preprocessing ... % 11.59/3.49 Prover 1: Constructing countermodel ... % 11.84/3.55 Prover 1: proved (160ms) % 11.84/3.55 % 11.84/3.55 No countermodel exists, formula is valid % 11.84/3.55 % SZS status Theorem for theBenchmark % 11.84/3.55 % 11.84/3.55 Generating proof ... found it (size 31) % 13.28/3.84 % 13.28/3.84 % SZS output start Proof for theBenchmark % 13.28/3.84 Assumed formulas after preprocessing and simplification: % 13.28/3.84 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ( ~ (v7 = 0) & product(v5) = v6 & product(v1) = v3 & product(v0) = v2 & intersection(v2, v3) = v4 & intersection(v0, v1) = v5 & subset(v4, v6) = v7 & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (product(v9) = v10) | ~ (member(v8, v11) = v12) | ~ (member(v8, v10) = 0) | ? [v13] : ( ~ (v13 = 0) & member(v11, v9) = v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (difference(v10, v9) = v11) | ~ (member(v8, v11) = v12) | ? [v13] : ? [v14] : (member(v8, v10) = v13 & member(v8, v9) = v14 & ( ~ (v13 = 0) | v14 = 0))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (union(v9, v10) = v11) | ~ (member(v8, v11) = v12) | ? [v13] : ? [v14] : ( ~ (v14 = 0) & ~ (v13 = 0) & member(v8, v10) = v14 & member(v8, v9) = v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (intersection(v9, v10) = v11) | ~ (member(v8, v11) = v12) | ? [v13] : ? [v14] : (member(v8, v10) = v14 & member(v8, v9) = v13 & ( ~ (v14 = 0) | ~ (v13 = 0)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v11 = 0 | ~ (sum(v9) = v10) | ~ (member(v8, v12) = 0) | ~ (member(v8, v10) = v11) | ? [v13] : ( ~ (v13 = 0) & member(v12, v9) = v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (product(v9) = v10) | ~ (member(v8, v10) = v11) | ? [v12] : ? [v13] : ( ~ (v13 = 0) & member(v12, v9) = 0 & member(v8, v12) = v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (unordered_pair(v9, v8) = v10) | ~ (member(v8, v10) = v11)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (unordered_pair(v8, v9) = v10) | ~ (member(v8, v10) = v11)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (power_set(v9) = v10) | ~ (member(v8, v10) = v11) | ? [v12] : ( ~ (v12 = 0) & subset(v8, v9) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v10 = v8 | v9 = v8 | ~ (unordered_pair(v9, v10) = v11) | ~ (member(v8, v11) = 0)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (unordered_pair(v11, v10) = v9) | ~ (unordered_pair(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (difference(v11, v10) = v9) | ~ (difference(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (union(v11, v10) = v9) | ~ (union(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (intersection(v11, v10) = v9) | ~ (intersection(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (equal_set(v11, v10) = v9) | ~ (equal_set(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (subset(v11, v10) = v9) | ~ (subset(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (member(v11, v10) = v9) | ~ (member(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (difference(v10, v9) = v11) | ~ (member(v8, v11) = 0) | ? [v12] : ( ~ (v12 = 0) & member(v8, v10) = 0 & member(v8, v9) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (union(v9, v10) = v11) | ~ (member(v8, v11) = 0) | ? [v12] : ? [v13] : (member(v8, v10) = v13 & member(v8, v9) = v12 & (v13 = 0 | v12 = 0))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (intersection(v9, v10) = v11) | ~ (member(v8, v11) = 0) | (member(v8, v10) = 0 & member(v8, v9) = 0)) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (singleton(v8) = v9) | ~ (member(v8, v9) = v10)) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (equal_set(v8, v9) = v10) | ? [v11] : ? [v12] : (subset(v9, v8) = v12 & subset(v8, v9) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0)))) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (subset(v8, v9) = v10) | ? [v11] : ? [v12] : ( ~ (v12 = 0) & member(v11, v9) = v12 & member(v11, v8) = 0)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (product(v10) = v9) | ~ (product(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (sum(v10) = v9) | ~ (sum(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (singleton(v10) = v9) | ~ (singleton(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (singleton(v9) = v10) | ~ (member(v8, v10) = 0)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (power_set(v10) = v9) | ~ (power_set(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (sum(v9) = v10) | ~ (member(v8, v10) = 0) | ? [v11] : (member(v11, v9) = 0 & member(v8, v11) = 0)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (power_set(v9) = v10) | ~ (member(v8, v10) = 0) | subset(v8, v9) = 0) & ! [v8] : ! [v9] : ! [v10] : ( ~ (subset(v8, v9) = 0) | ~ (member(v10, v8) = 0) | member(v10, v9) = 0) & ! [v8] : ! [v9] : ( ~ (equal_set(v8, v9) = 0) | (subset(v9, v8) = 0 & subset(v8, v9) = 0)) & ! [v8] : ~ (member(v8, empty_set) = 0)) % 13.28/3.88 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7 yields: % 13.28/3.88 | (1) ~ (all_0_0_0 = 0) & product(all_0_2_2) = all_0_1_1 & product(all_0_6_6) = all_0_4_4 & product(all_0_7_7) = all_0_5_5 & intersection(all_0_5_5, all_0_4_4) = all_0_3_3 & intersection(all_0_7_7, all_0_6_6) = all_0_2_2 & subset(all_0_3_3, all_0_1_1) = all_0_0_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] : (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 | ~ (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] : ( ~ (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 | ~ (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] : ( ~ (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] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0)) & ! [v0] : ~ (member(v0, empty_set) = 0) % 13.28/3.88 | % 13.28/3.88 | Applying alpha-rule on (1) yields: % 13.28/3.89 | (2) ! [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))) % 13.28/3.89 | (3) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 13.28/3.89 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0)) % 13.28/3.89 | (5) intersection(all_0_7_7, all_0_6_6) = all_0_2_2 % 13.28/3.89 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) % 13.28/3.89 | (7) ! [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)) % 13.28/3.89 | (8) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (member(v0, v1) = v2)) % 13.28/3.89 | (9) intersection(all_0_5_5, all_0_4_4) = all_0_3_3 % 13.28/3.89 | (10) ! [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)) % 13.28/3.89 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3)) % 13.28/3.89 | (12) subset(all_0_3_3, all_0_1_1) = all_0_0_0 % 13.28/3.89 | (13) ! [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)))) % 13.28/3.89 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) % 13.28/3.89 | (15) product(all_0_6_6) = all_0_4_4 % 13.28/3.89 | (16) ! [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)) % 13.28/3.89 | (17) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_set(v0, v1) = v2) | ? [v3] : ? [v4] : (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) % 13.28/3.89 | (18) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0)) % 13.28/3.89 | (19) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0)) % 13.28/3.89 | (20) product(all_0_7_7) = all_0_5_5 % 13.28/3.89 | (21) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0)) % 13.28/3.89 | (22) ~ (all_0_0_0 = 0) % 13.28/3.89 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0)) % 13.28/3.89 | (24) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | subset(v0, v1) = 0) % 13.28/3.89 | (25) ! [v0] : ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0)) % 13.28/3.89 | (26) ! [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)) % 13.28/3.89 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) % 13.28/3.89 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v0, v2) = 0 & member(v0, v1) = v4)) % 13.28/3.89 | (29) ! [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))) % 13.28/3.89 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) % 13.28/3.89 | (31) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0)) % 13.28/3.89 | (32) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ (member(v0, v2) = 0) | ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0)) % 13.28/3.89 | (33) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0)) % 13.28/3.89 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | (member(v0, v2) = 0 & member(v0, v1) = 0)) % 13.28/3.89 | (35) ! [v0] : ~ (member(v0, empty_set) = 0) % 13.28/3.89 | (36) product(all_0_2_2) = all_0_1_1 % 13.28/3.90 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) % 13.28/3.90 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) % 13.28/3.90 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) % 13.28/3.90 | (40) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0) % 13.28/3.90 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = v3)) % 13.28/3.90 | % 13.28/3.90 | Instantiating formula (21) with all_0_0_0, all_0_1_1, all_0_3_3 and discharging atoms subset(all_0_3_3, all_0_1_1) = all_0_0_0, yields: % 13.28/3.90 | (42) all_0_0_0 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, all_0_3_3) = 0) % 13.28/3.90 | % 13.28/3.90 +-Applying beta-rule and splitting (42), into two cases. % 13.28/3.90 |-Branch one: % 13.28/3.90 | (43) all_0_0_0 = 0 % 13.28/3.90 | % 13.28/3.90 | Equations (43) can reduce 22 to: % 13.28/3.90 | (44) $false % 13.28/3.90 | % 13.28/3.90 |-The branch is then unsatisfiable % 13.28/3.90 |-Branch two: % 13.28/3.90 | (22) ~ (all_0_0_0 = 0) % 13.28/3.90 | (46) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, all_0_3_3) = 0) % 13.28/3.90 | % 13.28/3.90 | Instantiating (46) with all_14_0_8, all_14_1_9 yields: % 13.28/3.90 | (47) ~ (all_14_0_8 = 0) & member(all_14_1_9, all_0_1_1) = all_14_0_8 & member(all_14_1_9, all_0_3_3) = 0 % 13.28/3.90 | % 13.28/3.90 | Applying alpha-rule on (47) yields: % 13.28/3.90 | (48) ~ (all_14_0_8 = 0) % 13.28/3.90 | (49) member(all_14_1_9, all_0_1_1) = all_14_0_8 % 13.28/3.90 | (50) member(all_14_1_9, all_0_3_3) = 0 % 13.28/3.90 | % 13.28/3.90 | Instantiating formula (7) with all_14_0_8, all_0_1_1, all_0_2_2, all_14_1_9 and discharging atoms product(all_0_2_2) = all_0_1_1, member(all_14_1_9, all_0_1_1) = all_14_0_8, yields: % 13.28/3.90 | (51) all_14_0_8 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_2_2) = 0 & member(all_14_1_9, v0) = v1) % 13.28/3.90 | % 13.28/3.90 | Instantiating formula (16) with all_14_0_8, all_0_1_1, all_0_5_5, all_0_7_7, all_14_1_9 and discharging atoms product(all_0_7_7) = all_0_5_5, member(all_14_1_9, all_0_1_1) = all_14_0_8, yields: % 13.28/3.90 | (52) all_14_0_8 = 0 | ~ (member(all_14_1_9, all_0_5_5) = 0) | ? [v0] : ( ~ (v0 = 0) & member(all_0_1_1, all_0_7_7) = v0) % 13.28/3.90 | % 13.28/3.90 | Instantiating formula (34) with all_0_3_3, all_0_4_4, all_0_5_5, all_14_1_9 and discharging atoms intersection(all_0_5_5, all_0_4_4) = all_0_3_3, member(all_14_1_9, all_0_3_3) = 0, yields: % 13.28/3.90 | (53) member(all_14_1_9, all_0_4_4) = 0 & member(all_14_1_9, all_0_5_5) = 0 % 13.28/3.90 | % 13.28/3.90 | Applying alpha-rule on (53) yields: % 13.28/3.90 | (54) member(all_14_1_9, all_0_4_4) = 0 % 13.28/3.90 | (55) member(all_14_1_9, all_0_5_5) = 0 % 13.28/3.90 | % 13.28/3.90 +-Applying beta-rule and splitting (52), into two cases. % 13.28/3.90 |-Branch one: % 13.28/3.90 | (56) ~ (member(all_14_1_9, all_0_5_5) = 0) % 13.28/3.90 | % 13.28/3.90 | Using (55) and (56) yields: % 13.28/3.90 | (57) $false % 13.28/3.90 | % 13.28/3.90 |-The branch is then unsatisfiable % 13.28/3.90 |-Branch two: % 13.28/3.90 | (55) member(all_14_1_9, all_0_5_5) = 0 % 13.28/3.90 | (59) all_14_0_8 = 0 | ? [v0] : ( ~ (v0 = 0) & member(all_0_1_1, all_0_7_7) = v0) % 13.28/3.90 | % 13.28/3.90 +-Applying beta-rule and splitting (51), into two cases. % 13.28/3.90 |-Branch one: % 13.28/3.90 | (60) all_14_0_8 = 0 % 13.28/3.90 | % 13.28/3.90 | Equations (60) can reduce 48 to: % 13.28/3.90 | (44) $false % 13.28/3.90 | % 13.28/3.90 |-The branch is then unsatisfiable % 13.28/3.90 |-Branch two: % 13.28/3.90 | (48) ~ (all_14_0_8 = 0) % 13.28/3.90 | (63) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_2_2) = 0 & member(all_14_1_9, v0) = v1) % 13.28/3.90 | % 13.28/3.90 | Instantiating (63) with all_40_0_10, all_40_1_11 yields: % 13.28/3.90 | (64) ~ (all_40_0_10 = 0) & member(all_40_1_11, all_0_2_2) = 0 & member(all_14_1_9, all_40_1_11) = all_40_0_10 % 13.28/3.90 | % 13.28/3.90 | Applying alpha-rule on (64) yields: % 13.28/3.90 | (65) ~ (all_40_0_10 = 0) % 13.28/3.90 | (66) member(all_40_1_11, all_0_2_2) = 0 % 13.28/3.90 | (67) member(all_14_1_9, all_40_1_11) = all_40_0_10 % 13.28/3.90 | % 13.28/3.90 | Instantiating formula (34) with all_0_2_2, all_0_6_6, all_0_7_7, all_40_1_11 and discharging atoms intersection(all_0_7_7, all_0_6_6) = all_0_2_2, member(all_40_1_11, all_0_2_2) = 0, yields: % 13.28/3.90 | (68) member(all_40_1_11, all_0_6_6) = 0 & member(all_40_1_11, all_0_7_7) = 0 % 13.28/3.90 | % 13.28/3.90 | Applying alpha-rule on (68) yields: % 13.28/3.91 | (69) member(all_40_1_11, all_0_6_6) = 0 % 13.28/3.91 | (70) member(all_40_1_11, all_0_7_7) = 0 % 13.28/3.91 | % 13.28/3.91 | Instantiating formula (16) with all_40_0_10, all_40_1_11, all_0_5_5, all_0_7_7, all_14_1_9 and discharging atoms product(all_0_7_7) = all_0_5_5, member(all_14_1_9, all_40_1_11) = all_40_0_10, member(all_14_1_9, all_0_5_5) = 0, yields: % 13.28/3.91 | (71) all_40_0_10 = 0 | ? [v0] : ( ~ (v0 = 0) & member(all_40_1_11, all_0_7_7) = v0) % 13.28/3.91 | % 13.28/3.91 +-Applying beta-rule and splitting (71), into two cases. % 13.28/3.91 |-Branch one: % 13.28/3.91 | (72) all_40_0_10 = 0 % 13.28/3.91 | % 13.28/3.91 | Equations (72) can reduce 65 to: % 13.28/3.91 | (44) $false % 13.28/3.91 | % 13.28/3.91 |-The branch is then unsatisfiable % 13.28/3.91 |-Branch two: % 13.28/3.91 | (65) ~ (all_40_0_10 = 0) % 13.28/3.91 | (75) ? [v0] : ( ~ (v0 = 0) & member(all_40_1_11, all_0_7_7) = v0) % 13.28/3.91 | % 13.28/3.91 | Instantiating (75) with all_71_0_14 yields: % 13.28/3.91 | (76) ~ (all_71_0_14 = 0) & member(all_40_1_11, all_0_7_7) = all_71_0_14 % 13.28/3.91 | % 13.28/3.91 | Applying alpha-rule on (76) yields: % 13.28/3.91 | (77) ~ (all_71_0_14 = 0) % 13.28/3.91 | (78) member(all_40_1_11, all_0_7_7) = all_71_0_14 % 13.28/3.91 | % 13.28/3.91 | Instantiating formula (38) with all_40_1_11, all_0_7_7, all_71_0_14, 0 and discharging atoms member(all_40_1_11, all_0_7_7) = all_71_0_14, member(all_40_1_11, all_0_7_7) = 0, yields: % 13.28/3.91 | (79) all_71_0_14 = 0 % 13.28/3.91 | % 13.28/3.91 | Equations (79) can reduce 77 to: % 13.28/3.91 | (44) $false % 13.28/3.91 | % 13.28/3.91 |-The branch is then unsatisfiable % 13.28/3.91 % SZS output end Proof for theBenchmark % 13.28/3.91 % 13.28/3.91 3304ms %------------------------------------------------------------------------------