%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET199+4 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n008.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 00:18:21 EDT 2022 % Result : Theorem 3.74s 1.56s % Output : Proof 5.42s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SET199+4 : TPTP v8.1.0. Released v2.2.0. % 0.07/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n008.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 01:59:08 EDT 2022 % 0.12/0.34 % 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 ... % 0.76/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.54/0.93 Prover 0: Preprocessing ... % 1.95/1.13 Prover 0: Warning: ignoring some quantifiers % 1.95/1.16 Prover 0: Constructing countermodel ... % 2.50/1.33 Prover 0: gave up % 2.50/1.33 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 2.80/1.35 Prover 1: Preprocessing ... % 3.36/1.46 Prover 1: Constructing countermodel ... % 3.74/1.56 Prover 1: proved (233ms) % 3.74/1.56 % 3.74/1.56 No countermodel exists, formula is valid % 3.74/1.56 % SZS status Theorem for theBenchmark % 3.74/1.56 % 3.74/1.56 Generating proof ... found it (size 65) % 4.87/1.89 % 4.87/1.89 % SZS output start Proof for theBenchmark % 4.87/1.89 Assumed formulas after preprocessing and simplification: % 4.87/1.89 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (intersection(v1, v2) = v5 & subset(v0, v5) = v6 & subset(v0, v2) = v4 & subset(v0, v1) = v3 & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (product(v8) = v9) | ~ (member(v7, v10) = v11) | ~ (member(v7, v9) = 0) | ? [v12] : ( ~ (v12 = 0) & member(v10, v8) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (difference(v9, v8) = v10) | ~ (member(v7, v10) = v11) | ? [v12] : ? [v13] : (member(v7, v9) = v12 & member(v7, v8) = v13 & ( ~ (v12 = 0) | v13 = 0))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (union(v8, v9) = v10) | ~ (member(v7, v10) = v11) | ? [v12] : ? [v13] : ( ~ (v13 = 0) & ~ (v12 = 0) & member(v7, v9) = v13 & member(v7, v8) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (intersection(v8, v9) = v10) | ~ (member(v7, v10) = v11) | ? [v12] : ? [v13] : (member(v7, v9) = v13 & member(v7, v8) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v10 = 0 | ~ (sum(v8) = v9) | ~ (member(v7, v11) = 0) | ~ (member(v7, v9) = v10) | ? [v12] : ( ~ (v12 = 0) & member(v11, v8) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (product(v8) = v9) | ~ (member(v7, v9) = v10) | ? [v11] : ? [v12] : ( ~ (v12 = 0) & member(v11, v8) = 0 & member(v7, v11) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (unordered_pair(v8, v7) = v9) | ~ (member(v7, v9) = v10)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (unordered_pair(v7, v8) = v9) | ~ (member(v7, v9) = v10)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (power_set(v8) = v9) | ~ (member(v7, v9) = v10) | ? [v11] : ( ~ (v11 = 0) & subset(v7, v8) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v9 = v7 | v8 = v7 | ~ (unordered_pair(v8, v9) = v10) | ~ (member(v7, v10) = 0)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (unordered_pair(v10, v9) = v8) | ~ (unordered_pair(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (difference(v10, v9) = v8) | ~ (difference(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (union(v10, v9) = v8) | ~ (union(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (intersection(v10, v9) = v8) | ~ (intersection(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (equal_set(v10, v9) = v8) | ~ (equal_set(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (subset(v10, v9) = v8) | ~ (subset(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (member(v10, v9) = v8) | ~ (member(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (difference(v9, v8) = v10) | ~ (member(v7, v10) = 0) | ? [v11] : ( ~ (v11 = 0) & member(v7, v9) = 0 & member(v7, v8) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (union(v8, v9) = v10) | ~ (member(v7, v10) = 0) | ? [v11] : ? [v12] : (member(v7, v9) = v12 & member(v7, v8) = v11 & (v12 = 0 | v11 = 0))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (intersection(v8, v9) = v10) | ~ (member(v7, v10) = 0) | (member(v7, v9) = 0 & member(v7, v8) = 0)) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (singleton(v7) = v8) | ~ (member(v7, v8) = v9)) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (equal_set(v7, v8) = v9) | ? [v10] : ? [v11] : (subset(v8, v7) = v11 & subset(v7, v8) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0)))) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (subset(v7, v8) = v9) | ? [v10] : ? [v11] : ( ~ (v11 = 0) & member(v10, v8) = v11 & member(v10, v7) = 0)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (product(v9) = v8) | ~ (product(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (sum(v9) = v8) | ~ (sum(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (singleton(v9) = v8) | ~ (singleton(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (singleton(v8) = v9) | ~ (member(v7, v9) = 0)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (power_set(v9) = v8) | ~ (power_set(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (sum(v8) = v9) | ~ (member(v7, v9) = 0) | ? [v10] : (member(v10, v8) = 0 & member(v7, v10) = 0)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (power_set(v8) = v9) | ~ (member(v7, v9) = 0) | subset(v7, v8) = 0) & ! [v7] : ! [v8] : ! [v9] : ( ~ (subset(v7, v8) = 0) | ~ (member(v9, v7) = 0) | member(v9, v8) = 0) & ! [v7] : ! [v8] : ( ~ (equal_set(v7, v8) = 0) | (subset(v8, v7) = 0 & subset(v7, v8) = 0)) & ! [v7] : ~ (member(v7, empty_set) = 0) & ((v6 = 0 & ( ~ (v4 = 0) | ~ (v3 = 0))) | (v4 = 0 & v3 = 0 & ~ (v6 = 0)))) % 5.17/1.93 | 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 yields: % 5.17/1.93 | (1) intersection(all_0_5_5, all_0_4_4) = all_0_1_1 & subset(all_0_6_6, all_0_1_1) = all_0_0_0 & subset(all_0_6_6, all_0_4_4) = all_0_2_2 & subset(all_0_6_6, all_0_5_5) = all_0_3_3 & ! [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) & ((all_0_0_0 = 0 & ( ~ (all_0_2_2 = 0) | ~ (all_0_3_3 = 0))) | (all_0_2_2 = 0 & all_0_3_3 = 0 & ~ (all_0_0_0 = 0))) % 5.17/1.95 | % 5.17/1.95 | Applying alpha-rule on (1) yields: % 5.17/1.95 | (2) ! [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)))) % 5.17/1.95 | (3) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_set(v0, v1) = v2) | ? [v3] : ? [v4] : (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) % 5.17/1.95 | (4) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0)) % 5.17/1.95 | (5) ! [v0] : ~ (member(v0, empty_set) = 0) % 5.17/1.95 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) % 5.17/1.95 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) % 5.17/1.95 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3)) % 5.17/1.95 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = v3)) % 5.17/1.95 | (10) ! [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))) % 5.17/1.95 | (11) ! [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)) % 5.17/1.95 | (12) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0)) % 5.17/1.95 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0)) % 5.17/1.95 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) % 5.17/1.95 | (15) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0)) % 5.17/1.95 | (16) ! [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)) % 5.17/1.95 | (17) intersection(all_0_5_5, all_0_4_4) = all_0_1_1 % 5.17/1.95 | (18) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0)) % 5.17/1.95 | (19) (all_0_0_0 = 0 & ( ~ (all_0_2_2 = 0) | ~ (all_0_3_3 = 0))) | (all_0_2_2 = 0 & all_0_3_3 = 0 & ~ (all_0_0_0 = 0)) % 5.17/1.95 | (20) subset(all_0_6_6, all_0_4_4) = all_0_2_2 % 5.17/1.95 | (21) ! [v0] : ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0)) % 5.17/1.96 | (22) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0) % 5.17/1.96 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) % 5.17/1.96 | (24) ! [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))) % 5.17/1.96 | (25) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 5.17/1.96 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) % 5.17/1.96 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) % 5.17/1.96 | (28) subset(all_0_6_6, all_0_5_5) = all_0_3_3 % 5.17/1.96 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0)) % 5.17/1.96 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) % 5.17/1.96 | (31) ! [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)) % 5.17/1.96 | (32) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ (member(v0, v2) = 0) | ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0)) % 5.17/1.96 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | (member(v0, v2) = 0 & member(v0, v1) = 0)) % 5.17/1.96 | (34) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | subset(v0, v1) = 0) % 5.17/1.96 | (35) subset(all_0_6_6, all_0_1_1) = all_0_0_0 % 5.17/1.96 | (36) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0)) % 5.17/1.96 | (37) ! [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)) % 5.17/1.96 | (38) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (member(v0, v1) = v2)) % 5.17/1.96 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v0, v2) = 0 & member(v0, v1) = v4)) % 5.17/1.96 | % 5.17/1.96 | Instantiating formula (7) with all_0_6_6, all_0_5_5, all_0_3_3, all_0_0_0 and discharging atoms subset(all_0_6_6, all_0_5_5) = all_0_3_3, yields: % 5.17/1.96 | (40) all_0_0_0 = all_0_3_3 | ~ (subset(all_0_6_6, all_0_5_5) = all_0_0_0) % 5.17/1.96 | % 5.17/1.96 | Instantiating formula (18) with all_0_0_0, all_0_1_1, all_0_6_6 and discharging atoms subset(all_0_6_6, all_0_1_1) = all_0_0_0, yields: % 5.17/1.96 | (41) all_0_0_0 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, all_0_6_6) = 0) % 5.17/1.97 | % 5.17/1.97 | Instantiating formula (18) with all_0_2_2, all_0_4_4, all_0_6_6 and discharging atoms subset(all_0_6_6, all_0_4_4) = all_0_2_2, yields: % 5.17/1.97 | (42) all_0_2_2 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_4_4) = v1 & member(v0, all_0_6_6) = 0) % 5.17/1.97 | % 5.17/1.97 | Instantiating formula (18) with all_0_3_3, all_0_5_5, all_0_6_6 and discharging atoms subset(all_0_6_6, all_0_5_5) = all_0_3_3, yields: % 5.17/1.97 | (43) all_0_3_3 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_5_5) = v1 & member(v0, all_0_6_6) = 0) % 5.17/1.97 | % 5.17/1.97 +-Applying beta-rule and splitting (19), into two cases. % 5.17/1.97 |-Branch one: % 5.17/1.97 | (44) all_0_0_0 = 0 & ( ~ (all_0_2_2 = 0) | ~ (all_0_3_3 = 0)) % 5.17/1.97 | % 5.17/1.97 | Applying alpha-rule on (44) yields: % 5.17/1.97 | (45) all_0_0_0 = 0 % 5.17/1.97 | (46) ~ (all_0_2_2 = 0) | ~ (all_0_3_3 = 0) % 5.17/1.97 | % 5.17/1.97 | From (45) and (35) follows: % 5.42/1.97 | (47) subset(all_0_6_6, all_0_1_1) = 0 % 5.42/1.97 | % 5.42/1.97 +-Applying beta-rule and splitting (40), into two cases. % 5.42/1.97 |-Branch one: % 5.42/1.97 | (48) ~ (subset(all_0_6_6, all_0_5_5) = all_0_0_0) % 5.42/1.97 | % 5.42/1.97 | From (45) and (48) follows: % 5.42/1.97 | (49) ~ (subset(all_0_6_6, all_0_5_5) = 0) % 5.42/1.97 | % 5.42/1.97 | Using (28) and (49) yields: % 5.42/1.97 | (50) ~ (all_0_3_3 = 0) % 5.42/1.97 | % 5.42/1.97 +-Applying beta-rule and splitting (43), into two cases. % 5.42/1.97 |-Branch one: % 5.42/1.97 | (51) all_0_3_3 = 0 % 5.42/1.97 | % 5.42/1.97 | Equations (51) can reduce 50 to: % 5.42/1.97 | (52) $false % 5.42/1.97 | % 5.42/1.97 |-The branch is then unsatisfiable % 5.42/1.97 |-Branch two: % 5.42/1.97 | (50) ~ (all_0_3_3 = 0) % 5.42/1.97 | (54) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_5_5) = v1 & member(v0, all_0_6_6) = 0) % 5.42/1.97 | % 5.42/1.97 | Instantiating (54) with all_25_0_7, all_25_1_8 yields: % 5.42/1.97 | (55) ~ (all_25_0_7 = 0) & member(all_25_1_8, all_0_5_5) = all_25_0_7 & member(all_25_1_8, all_0_6_6) = 0 % 5.42/1.97 | % 5.42/1.97 | Applying alpha-rule on (55) yields: % 5.42/1.97 | (56) ~ (all_25_0_7 = 0) % 5.42/1.97 | (57) member(all_25_1_8, all_0_5_5) = all_25_0_7 % 5.42/1.97 | (58) member(all_25_1_8, all_0_6_6) = 0 % 5.42/1.97 | % 5.42/1.97 | Instantiating formula (22) with all_25_1_8, all_0_1_1, all_0_6_6 and discharging atoms subset(all_0_6_6, all_0_1_1) = 0, member(all_25_1_8, all_0_6_6) = 0, yields: % 5.42/1.97 | (59) member(all_25_1_8, all_0_1_1) = 0 % 5.42/1.97 | % 5.42/1.97 | Instantiating formula (33) with all_0_1_1, all_0_4_4, all_0_5_5, all_25_1_8 and discharging atoms intersection(all_0_5_5, all_0_4_4) = all_0_1_1, member(all_25_1_8, all_0_1_1) = 0, yields: % 5.42/1.97 | (60) member(all_25_1_8, all_0_4_4) = 0 & member(all_25_1_8, all_0_5_5) = 0 % 5.42/1.97 | % 5.42/1.97 | Applying alpha-rule on (60) yields: % 5.42/1.97 | (61) member(all_25_1_8, all_0_4_4) = 0 % 5.42/1.97 | (62) member(all_25_1_8, all_0_5_5) = 0 % 5.42/1.97 | % 5.42/1.97 | Instantiating formula (14) with all_25_1_8, all_0_5_5, 0, all_25_0_7 and discharging atoms member(all_25_1_8, all_0_5_5) = all_25_0_7, member(all_25_1_8, all_0_5_5) = 0, yields: % 5.42/1.97 | (63) all_25_0_7 = 0 % 5.42/1.97 | % 5.42/1.97 | Equations (63) can reduce 56 to: % 5.42/1.97 | (52) $false % 5.42/1.97 | % 5.42/1.97 |-The branch is then unsatisfiable % 5.42/1.97 |-Branch two: % 5.42/1.97 | (65) subset(all_0_6_6, all_0_5_5) = all_0_0_0 % 5.42/1.97 | (66) all_0_0_0 = all_0_3_3 % 5.42/1.97 | % 5.42/1.97 | Combining equations (66,45) yields a new equation: % 5.42/1.97 | (67) all_0_3_3 = 0 % 5.42/1.97 | % 5.42/1.97 | Simplifying 67 yields: % 5.42/1.97 | (51) all_0_3_3 = 0 % 5.42/1.97 | % 5.42/1.97 +-Applying beta-rule and splitting (46), into two cases. % 5.42/1.97 |-Branch one: % 5.42/1.97 | (69) ~ (all_0_2_2 = 0) % 5.42/1.97 | % 5.42/1.97 +-Applying beta-rule and splitting (42), into two cases. % 5.42/1.97 |-Branch one: % 5.42/1.97 | (70) all_0_2_2 = 0 % 5.42/1.97 | % 5.42/1.97 | Equations (70) can reduce 69 to: % 5.42/1.97 | (52) $false % 5.42/1.97 | % 5.42/1.97 |-The branch is then unsatisfiable % 5.42/1.97 |-Branch two: % 5.42/1.97 | (69) ~ (all_0_2_2 = 0) % 5.42/1.97 | (73) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_4_4) = v1 & member(v0, all_0_6_6) = 0) % 5.42/1.98 | % 5.42/1.98 | Instantiating (73) with all_25_0_9, all_25_1_10 yields: % 5.42/1.98 | (74) ~ (all_25_0_9 = 0) & member(all_25_1_10, all_0_4_4) = all_25_0_9 & member(all_25_1_10, all_0_6_6) = 0 % 5.42/1.98 | % 5.42/1.98 | Applying alpha-rule on (74) yields: % 5.42/1.98 | (75) ~ (all_25_0_9 = 0) % 5.42/1.98 | (76) member(all_25_1_10, all_0_4_4) = all_25_0_9 % 5.42/1.98 | (77) member(all_25_1_10, all_0_6_6) = 0 % 5.42/1.98 | % 5.42/1.98 | Instantiating formula (22) with all_25_1_10, all_0_1_1, all_0_6_6 and discharging atoms subset(all_0_6_6, all_0_1_1) = 0, member(all_25_1_10, all_0_6_6) = 0, yields: % 5.42/1.98 | (78) member(all_25_1_10, all_0_1_1) = 0 % 5.42/1.98 | % 5.42/1.98 | Instantiating formula (14) with all_25_1_10, all_0_4_4, 0, all_25_0_9 and discharging atoms member(all_25_1_10, all_0_4_4) = all_25_0_9, yields: % 5.42/1.98 | (79) all_25_0_9 = 0 | ~ (member(all_25_1_10, all_0_4_4) = 0) % 5.42/1.98 | % 5.42/1.98 | Instantiating formula (33) with all_0_1_1, all_0_4_4, all_0_5_5, all_25_1_10 and discharging atoms intersection(all_0_5_5, all_0_4_4) = all_0_1_1, member(all_25_1_10, all_0_1_1) = 0, yields: % 5.42/1.98 | (80) member(all_25_1_10, all_0_4_4) = 0 & member(all_25_1_10, all_0_5_5) = 0 % 5.42/1.98 | % 5.42/1.98 | Applying alpha-rule on (80) yields: % 5.42/1.98 | (81) member(all_25_1_10, all_0_4_4) = 0 % 5.42/1.98 | (82) member(all_25_1_10, all_0_5_5) = 0 % 5.42/1.98 | % 5.42/1.98 +-Applying beta-rule and splitting (79), into two cases. % 5.42/1.98 |-Branch one: % 5.42/1.98 | (83) ~ (member(all_25_1_10, all_0_4_4) = 0) % 5.42/1.98 | % 5.42/1.98 | Using (81) and (83) yields: % 5.42/1.98 | (84) $false % 5.42/1.98 | % 5.42/1.98 |-The branch is then unsatisfiable % 5.42/1.98 |-Branch two: % 5.42/1.98 | (81) member(all_25_1_10, all_0_4_4) = 0 % 5.42/1.98 | (86) all_25_0_9 = 0 % 5.42/1.98 | % 5.42/1.98 | Equations (86) can reduce 75 to: % 5.42/1.98 | (52) $false % 5.42/1.98 | % 5.42/1.98 |-The branch is then unsatisfiable % 5.42/1.98 |-Branch two: % 5.42/1.98 | (70) all_0_2_2 = 0 % 5.42/1.98 | (50) ~ (all_0_3_3 = 0) % 5.42/1.98 | % 5.42/1.98 | Equations (51) can reduce 50 to: % 5.42/1.98 | (52) $false % 5.42/1.98 | % 5.42/1.98 |-The branch is then unsatisfiable % 5.42/1.98 |-Branch two: % 5.42/1.98 | (91) all_0_2_2 = 0 & all_0_3_3 = 0 & ~ (all_0_0_0 = 0) % 5.42/1.98 | % 5.42/1.98 | Applying alpha-rule on (91) yields: % 5.42/1.98 | (70) all_0_2_2 = 0 % 5.42/1.98 | (51) all_0_3_3 = 0 % 5.42/1.98 | (94) ~ (all_0_0_0 = 0) % 5.42/1.98 | % 5.42/1.98 | From (70) and (20) follows: % 5.42/1.98 | (95) subset(all_0_6_6, all_0_4_4) = 0 % 5.42/1.98 | % 5.42/1.98 | From (51) and (28) follows: % 5.42/1.98 | (96) subset(all_0_6_6, all_0_5_5) = 0 % 5.42/1.98 | % 5.42/1.98 +-Applying beta-rule and splitting (41), into two cases. % 5.42/1.98 |-Branch one: % 5.42/1.98 | (45) all_0_0_0 = 0 % 5.42/1.98 | % 5.42/1.98 | Equations (45) can reduce 94 to: % 5.42/1.98 | (52) $false % 5.42/1.98 | % 5.42/1.98 |-The branch is then unsatisfiable % 5.42/1.98 |-Branch two: % 5.42/1.98 | (94) ~ (all_0_0_0 = 0) % 5.42/1.98 | (100) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, all_0_6_6) = 0) % 5.42/1.98 | % 5.42/1.98 | Instantiating (100) with all_14_0_11, all_14_1_12 yields: % 5.42/1.98 | (101) ~ (all_14_0_11 = 0) & member(all_14_1_12, all_0_1_1) = all_14_0_11 & member(all_14_1_12, all_0_6_6) = 0 % 5.42/1.98 | % 5.42/1.98 | Applying alpha-rule on (101) yields: % 5.42/1.98 | (102) ~ (all_14_0_11 = 0) % 5.42/1.98 | (103) member(all_14_1_12, all_0_1_1) = all_14_0_11 % 5.42/1.98 | (104) member(all_14_1_12, all_0_6_6) = 0 % 5.42/1.98 | % 5.42/1.98 | Instantiating formula (2) with all_14_0_11, all_0_1_1, all_0_4_4, all_0_5_5, all_14_1_12 and discharging atoms intersection(all_0_5_5, all_0_4_4) = all_0_1_1, member(all_14_1_12, all_0_1_1) = all_14_0_11, yields: % 5.42/1.98 | (105) all_14_0_11 = 0 | ? [v0] : ? [v1] : (member(all_14_1_12, all_0_4_4) = v1 & member(all_14_1_12, all_0_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 5.42/1.98 | % 5.42/1.98 | Instantiating formula (22) with all_14_1_12, all_0_4_4, all_0_6_6 and discharging atoms subset(all_0_6_6, all_0_4_4) = 0, member(all_14_1_12, all_0_6_6) = 0, yields: % 5.42/1.98 | (106) member(all_14_1_12, all_0_4_4) = 0 % 5.42/1.98 | % 5.42/1.98 | Instantiating formula (22) with all_14_1_12, all_0_5_5, all_0_6_6 and discharging atoms subset(all_0_6_6, all_0_5_5) = 0, member(all_14_1_12, all_0_6_6) = 0, yields: % 5.42/1.98 | (107) member(all_14_1_12, all_0_5_5) = 0 % 5.42/1.98 | % 5.42/1.98 +-Applying beta-rule and splitting (105), into two cases. % 5.42/1.98 |-Branch one: % 5.42/1.98 | (108) all_14_0_11 = 0 % 5.42/1.98 | % 5.42/1.98 | Equations (108) can reduce 102 to: % 5.42/1.98 | (52) $false % 5.42/1.98 | % 5.42/1.98 |-The branch is then unsatisfiable % 5.42/1.98 |-Branch two: % 5.42/1.98 | (102) ~ (all_14_0_11 = 0) % 5.42/1.99 | (111) ? [v0] : ? [v1] : (member(all_14_1_12, all_0_4_4) = v1 & member(all_14_1_12, all_0_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 5.42/1.99 | % 5.42/1.99 | Instantiating (111) with all_34_0_13, all_34_1_14 yields: % 5.42/1.99 | (112) member(all_14_1_12, all_0_4_4) = all_34_0_13 & member(all_14_1_12, all_0_5_5) = all_34_1_14 & ( ~ (all_34_0_13 = 0) | ~ (all_34_1_14 = 0)) % 5.42/1.99 | % 5.42/1.99 | Applying alpha-rule on (112) yields: % 5.42/1.99 | (113) member(all_14_1_12, all_0_4_4) = all_34_0_13 % 5.42/1.99 | (114) member(all_14_1_12, all_0_5_5) = all_34_1_14 % 5.42/1.99 | (115) ~ (all_34_0_13 = 0) | ~ (all_34_1_14 = 0) % 5.42/1.99 | % 5.42/1.99 | Instantiating formula (14) with all_14_1_12, all_0_4_4, 0, all_34_0_13 and discharging atoms member(all_14_1_12, all_0_4_4) = all_34_0_13, member(all_14_1_12, all_0_4_4) = 0, yields: % 5.42/1.99 | (116) all_34_0_13 = 0 % 5.42/1.99 | % 5.42/1.99 | Instantiating formula (14) with all_14_1_12, all_0_5_5, all_34_1_14, 0 and discharging atoms member(all_14_1_12, all_0_5_5) = all_34_1_14, member(all_14_1_12, all_0_5_5) = 0, yields: % 5.42/1.99 | (117) all_34_1_14 = 0 % 5.42/1.99 | % 5.42/1.99 +-Applying beta-rule and splitting (115), into two cases. % 5.42/1.99 |-Branch one: % 5.42/1.99 | (118) ~ (all_34_0_13 = 0) % 5.42/1.99 | % 5.42/1.99 | Equations (116) can reduce 118 to: % 5.42/1.99 | (52) $false % 5.42/1.99 | % 5.42/1.99 |-The branch is then unsatisfiable % 5.42/1.99 |-Branch two: % 5.42/1.99 | (116) all_34_0_13 = 0 % 5.42/1.99 | (121) ~ (all_34_1_14 = 0) % 5.42/1.99 | % 5.42/1.99 | Equations (117) can reduce 121 to: % 5.42/1.99 | (52) $false % 5.42/1.99 | % 5.42/1.99 |-The branch is then unsatisfiable % 5.42/1.99 % SZS output end Proof for theBenchmark % 5.42/1.99 % 5.42/1.99 1398ms %------------------------------------------------------------------------------