%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET691+4 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n017.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 00:21:26 EDT 2022 % Result : Theorem 3.22s 1.41s % Output : Proof 4.52s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET691+4 : TPTP v8.1.0. Released v2.2.0. % 0.12/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n017.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 05:51:47 EDT 2022 % 0.12/0.33 % CPUTime : % 0.18/0.53 ____ _ % 0.18/0.53 ___ / __ \_____(_)___ ________ __________ % 0.18/0.53 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.18/0.53 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.18/0.53 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.18/0.53 % 0.18/0.53 A Theorem Prover for First-Order Logic % 0.18/0.53 (ePrincess v.1.0) % 0.18/0.53 % 0.18/0.53 (c) Philipp Rümmer, 2009-2015 % 0.18/0.53 (c) Peter Backeman, 2014-2015 % 0.18/0.53 (contributions by Angelo Brillout, Peter Baumgartner) % 0.18/0.53 Free software under GNU Lesser General Public License (LGPL). % 0.18/0.53 Bug reports to peter@backeman.se % 0.18/0.53 % 0.18/0.53 For more information, visit http://user.uu.se/~petba168/breu/ % 0.18/0.53 % 0.18/0.53 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.68/0.58 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.51/0.88 Prover 0: Preprocessing ... % 1.89/1.06 Prover 0: Warning: ignoring some quantifiers % 2.06/1.09 Prover 0: Constructing countermodel ... % 2.47/1.22 Prover 0: gave up % 2.47/1.22 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 2.56/1.24 Prover 1: Preprocessing ... % 2.89/1.35 Prover 1: Constructing countermodel ... % 3.22/1.41 Prover 1: proved (197ms) % 3.22/1.41 % 3.22/1.41 No countermodel exists, formula is valid % 3.22/1.41 % SZS status Theorem for theBenchmark % 3.22/1.42 % 3.22/1.42 Generating proof ... found it (size 39) % 4.26/1.65 % 4.26/1.65 % SZS output start Proof for theBenchmark % 4.26/1.65 Assumed formulas after preprocessing and simplification: % 4.26/1.65 | (0) ? [v0] : ? [v1] : ? [v2] : (equal_set(v0, empty_set) = v2 & subset(v0, empty_set) = v1 & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (product(v4) = v5) | ~ (member(v3, v6) = v7) | ~ (member(v3, v5) = 0) | ? [v8] : ( ~ (v8 = 0) & member(v6, v4) = v8)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (difference(v5, v4) = v6) | ~ (member(v3, v6) = v7) | ? [v8] : ? [v9] : (member(v3, v5) = v8 & member(v3, v4) = v9 & ( ~ (v8 = 0) | v9 = 0))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (union(v4, v5) = v6) | ~ (member(v3, v6) = v7) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & ~ (v8 = 0) & member(v3, v5) = v9 & member(v3, v4) = v8)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (intersection(v4, v5) = v6) | ~ (member(v3, v6) = v7) | ? [v8] : ? [v9] : (member(v3, v5) = v9 & member(v3, v4) = v8 & ( ~ (v9 = 0) | ~ (v8 = 0)))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v6 = 0 | ~ (sum(v4) = v5) | ~ (member(v3, v7) = 0) | ~ (member(v3, v5) = v6) | ? [v8] : ( ~ (v8 = 0) & member(v7, v4) = v8)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (product(v4) = v5) | ~ (member(v3, v5) = v6) | ? [v7] : ? [v8] : ( ~ (v8 = 0) & member(v7, v4) = 0 & member(v3, v7) = v8)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (unordered_pair(v4, v3) = v5) | ~ (member(v3, v5) = v6)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (unordered_pair(v3, v4) = v5) | ~ (member(v3, v5) = v6)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (power_set(v4) = v5) | ~ (member(v3, v5) = v6) | ? [v7] : ( ~ (v7 = 0) & subset(v3, v4) = v7)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v5 = v3 | v4 = v3 | ~ (unordered_pair(v4, v5) = v6) | ~ (member(v3, v6) = 0)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (unordered_pair(v6, v5) = v4) | ~ (unordered_pair(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (difference(v6, v5) = v4) | ~ (difference(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (union(v6, v5) = v4) | ~ (union(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (intersection(v6, v5) = v4) | ~ (intersection(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (equal_set(v6, v5) = v4) | ~ (equal_set(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (subset(v6, v5) = v4) | ~ (subset(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (member(v6, v5) = v4) | ~ (member(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (difference(v5, v4) = v6) | ~ (member(v3, v6) = 0) | ? [v7] : ( ~ (v7 = 0) & member(v3, v5) = 0 & member(v3, v4) = v7)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (union(v4, v5) = v6) | ~ (member(v3, v6) = 0) | ? [v7] : ? [v8] : (member(v3, v5) = v8 & member(v3, v4) = v7 & (v8 = 0 | v7 = 0))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (intersection(v4, v5) = v6) | ~ (member(v3, v6) = 0) | (member(v3, v5) = 0 & member(v3, v4) = 0)) & ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (singleton(v3) = v4) | ~ (member(v3, v4) = v5)) & ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (equal_set(v3, v4) = v5) | ? [v6] : ? [v7] : (subset(v4, v3) = v7 & subset(v3, v4) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (subset(v3, v4) = v5) | ? [v6] : ? [v7] : ( ~ (v7 = 0) & member(v6, v4) = v7 & member(v6, v3) = 0)) & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (product(v5) = v4) | ~ (product(v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (sum(v5) = v4) | ~ (sum(v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (singleton(v5) = v4) | ~ (singleton(v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (singleton(v4) = v5) | ~ (member(v3, v5) = 0)) & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (power_set(v5) = v4) | ~ (power_set(v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ( ~ (sum(v4) = v5) | ~ (member(v3, v5) = 0) | ? [v6] : (member(v6, v4) = 0 & member(v3, v6) = 0)) & ! [v3] : ! [v4] : ! [v5] : ( ~ (power_set(v4) = v5) | ~ (member(v3, v5) = 0) | subset(v3, v4) = 0) & ! [v3] : ! [v4] : ! [v5] : ( ~ (subset(v3, v4) = 0) | ~ (member(v5, v3) = 0) | member(v5, v4) = 0) & ! [v3] : ! [v4] : ( ~ (equal_set(v3, v4) = 0) | (subset(v4, v3) = 0 & subset(v3, v4) = 0)) & ! [v3] : ~ (member(v3, empty_set) = 0) & ((v2 = 0 & ~ (v1 = 0)) | (v1 = 0 & ~ (v2 = 0)))) % 4.52/1.69 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2 yields: % 4.52/1.69 | (1) equal_set(all_0_2_2, empty_set) = all_0_0_0 & subset(all_0_2_2, empty_set) = all_0_1_1 & ! [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_1_1 = 0)) | (all_0_1_1 = 0 & ~ (all_0_0_0 = 0))) % 4.52/1.71 | % 4.52/1.71 | Applying alpha-rule on (1) yields: % 4.52/1.71 | (2) ! [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)) % 4.52/1.71 | (3) ! [v0] : ~ (member(v0, empty_set) = 0) % 4.52/1.71 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) % 4.52/1.71 | (5) ! [v0] : ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0)) % 4.52/1.71 | (6) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (member(v0, v1) = v2)) % 4.52/1.71 | (7) (all_0_0_0 = 0 & ~ (all_0_1_1 = 0)) | (all_0_1_1 = 0 & ~ (all_0_0_0 = 0)) % 4.52/1.71 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ (member(v0, v2) = 0) | ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0)) % 4.52/1.71 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = v3)) % 4.52/1.71 | (10) ! [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))) % 4.52/1.71 | (11) ! [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)) % 4.52/1.71 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0)) % 4.52/1.71 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v0, v2) = 0 & member(v0, v1) = v4)) % 4.52/1.71 | (14) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0)) % 4.52/1.71 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) % 4.52/1.71 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3)) % 4.52/1.71 | (17) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 4.52/1.71 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) % 4.52/1.71 | (19) ! [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)) % 4.52/1.71 | (20) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0)) % 4.52/1.71 | (21) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0)) % 4.52/1.72 | (22) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | subset(v0, v1) = 0) % 4.52/1.72 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0)) % 4.52/1.72 | (24) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0)) % 4.52/1.72 | (25) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_set(v0, v1) = v2) | ? [v3] : ? [v4] : (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) % 4.52/1.72 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) % 4.52/1.72 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) % 4.52/1.72 | (28) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0)) % 4.52/1.72 | (29) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0) % 4.52/1.72 | (30) ! [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)))) % 4.52/1.72 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) % 4.52/1.72 | (32) equal_set(all_0_2_2, empty_set) = all_0_0_0 % 4.52/1.72 | (33) ! [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)) % 4.52/1.72 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) % 4.52/1.72 | (35) ! [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))) % 4.52/1.72 | (36) subset(all_0_2_2, empty_set) = all_0_1_1 % 4.52/1.72 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | (member(v0, v2) = 0 & member(v0, v1) = 0)) % 4.52/1.72 | % 4.52/1.72 | Instantiating formula (5) with empty_set, all_0_2_2 yields: % 4.52/1.72 | (38) ~ (equal_set(all_0_2_2, empty_set) = 0) | (subset(all_0_2_2, empty_set) = 0 & subset(empty_set, all_0_2_2) = 0) % 4.52/1.72 | % 4.52/1.72 | Instantiating formula (25) with all_0_0_0, empty_set, all_0_2_2 and discharging atoms equal_set(all_0_2_2, empty_set) = all_0_0_0, yields: % 4.52/1.73 | (39) all_0_0_0 = 0 | ? [v0] : ? [v1] : (subset(all_0_2_2, empty_set) = v0 & subset(empty_set, all_0_2_2) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 4.52/1.73 | % 4.52/1.73 +-Applying beta-rule and splitting (38), into two cases. % 4.52/1.73 |-Branch one: % 4.52/1.73 | (40) ~ (equal_set(all_0_2_2, empty_set) = 0) % 4.52/1.73 | % 4.52/1.73 | Using (32) and (40) yields: % 4.52/1.73 | (41) ~ (all_0_0_0 = 0) % 4.52/1.73 | % 4.52/1.73 +-Applying beta-rule and splitting (7), into two cases. % 4.52/1.73 |-Branch one: % 4.52/1.73 | (42) all_0_0_0 = 0 & ~ (all_0_1_1 = 0) % 4.52/1.73 | % 4.52/1.73 | Applying alpha-rule on (42) yields: % 4.52/1.73 | (43) all_0_0_0 = 0 % 4.52/1.73 | (44) ~ (all_0_1_1 = 0) % 4.52/1.73 | % 4.52/1.73 | Equations (43) can reduce 41 to: % 4.52/1.73 | (45) $false % 4.52/1.73 | % 4.52/1.73 |-The branch is then unsatisfiable % 4.52/1.73 |-Branch two: % 4.52/1.73 | (46) all_0_1_1 = 0 & ~ (all_0_0_0 = 0) % 4.52/1.73 | % 4.52/1.73 | Applying alpha-rule on (46) yields: % 4.52/1.73 | (47) all_0_1_1 = 0 % 4.52/1.73 | (41) ~ (all_0_0_0 = 0) % 4.52/1.73 | % 4.52/1.73 | From (47) and (36) follows: % 4.52/1.73 | (49) subset(all_0_2_2, empty_set) = 0 % 4.52/1.73 | % 4.52/1.73 +-Applying beta-rule and splitting (39), into two cases. % 4.52/1.73 |-Branch one: % 4.52/1.73 | (43) all_0_0_0 = 0 % 4.52/1.73 | % 4.52/1.73 | Equations (43) can reduce 41 to: % 4.52/1.73 | (45) $false % 4.52/1.73 | % 4.52/1.73 |-The branch is then unsatisfiable % 4.52/1.73 |-Branch two: % 4.52/1.73 | (41) ~ (all_0_0_0 = 0) % 4.52/1.73 | (53) ? [v0] : ? [v1] : (subset(all_0_2_2, empty_set) = v0 & subset(empty_set, all_0_2_2) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 4.52/1.73 | % 4.52/1.73 | Instantiating (53) with all_22_0_3, all_22_1_4 yields: % 4.52/1.73 | (54) subset(all_0_2_2, empty_set) = all_22_1_4 & subset(empty_set, all_0_2_2) = all_22_0_3 & ( ~ (all_22_0_3 = 0) | ~ (all_22_1_4 = 0)) % 4.52/1.73 | % 4.52/1.73 | Applying alpha-rule on (54) yields: % 4.52/1.73 | (55) subset(all_0_2_2, empty_set) = all_22_1_4 % 4.52/1.73 | (56) subset(empty_set, all_0_2_2) = all_22_0_3 % 4.52/1.73 | (57) ~ (all_22_0_3 = 0) | ~ (all_22_1_4 = 0) % 4.52/1.73 | % 4.52/1.73 | Instantiating formula (31) with all_0_2_2, empty_set, 0, all_22_1_4 and discharging atoms subset(all_0_2_2, empty_set) = all_22_1_4, subset(all_0_2_2, empty_set) = 0, yields: % 4.52/1.73 | (58) all_22_1_4 = 0 % 4.52/1.73 | % 4.52/1.73 +-Applying beta-rule and splitting (57), into two cases. % 4.52/1.73 |-Branch one: % 4.52/1.73 | (59) ~ (all_22_0_3 = 0) % 4.52/1.73 | % 4.52/1.73 | Instantiating formula (21) with all_22_0_3, all_0_2_2, empty_set and discharging atoms subset(empty_set, all_0_2_2) = all_22_0_3, yields: % 4.52/1.73 | (60) all_22_0_3 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_2_2) = v1 & member(v0, empty_set) = 0) % 4.52/1.73 | % 4.52/1.73 +-Applying beta-rule and splitting (60), into two cases. % 4.52/1.73 |-Branch one: % 4.52/1.73 | (61) all_22_0_3 = 0 % 4.52/1.73 | % 4.52/1.73 | Equations (61) can reduce 59 to: % 4.52/1.73 | (45) $false % 4.52/1.73 | % 4.52/1.73 |-The branch is then unsatisfiable % 4.52/1.73 |-Branch two: % 4.52/1.73 | (59) ~ (all_22_0_3 = 0) % 4.52/1.73 | (64) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_2_2) = v1 & member(v0, empty_set) = 0) % 4.52/1.73 | % 4.52/1.73 | Instantiating (64) with all_39_0_5, all_39_1_6 yields: % 4.52/1.73 | (65) ~ (all_39_0_5 = 0) & member(all_39_1_6, all_0_2_2) = all_39_0_5 & member(all_39_1_6, empty_set) = 0 % 4.52/1.74 | % 4.52/1.74 | Applying alpha-rule on (65) yields: % 4.52/1.74 | (66) ~ (all_39_0_5 = 0) % 4.52/1.74 | (67) member(all_39_1_6, all_0_2_2) = all_39_0_5 % 4.52/1.74 | (68) member(all_39_1_6, empty_set) = 0 % 4.52/1.74 | % 4.52/1.74 | Instantiating formula (3) with all_39_1_6 and discharging atoms member(all_39_1_6, empty_set) = 0, yields: % 4.52/1.74 | (69) $false % 4.52/1.74 | % 4.52/1.74 |-The branch is then unsatisfiable % 4.52/1.74 |-Branch two: % 4.52/1.74 | (61) all_22_0_3 = 0 % 4.52/1.74 | (71) ~ (all_22_1_4 = 0) % 4.52/1.74 | % 4.52/1.74 | Equations (58) can reduce 71 to: % 4.52/1.74 | (45) $false % 4.52/1.74 | % 4.52/1.74 |-The branch is then unsatisfiable % 4.52/1.74 |-Branch two: % 4.52/1.74 | (73) equal_set(all_0_2_2, empty_set) = 0 % 4.52/1.74 | (74) subset(all_0_2_2, empty_set) = 0 & subset(empty_set, all_0_2_2) = 0 % 4.52/1.74 | % 4.52/1.74 | Applying alpha-rule on (74) yields: % 4.52/1.74 | (49) subset(all_0_2_2, empty_set) = 0 % 4.52/1.74 | (76) subset(empty_set, all_0_2_2) = 0 % 4.52/1.74 | % 4.52/1.74 | Instantiating formula (12) with all_0_2_2, empty_set, 0, all_0_0_0 and discharging atoms equal_set(all_0_2_2, empty_set) = all_0_0_0, equal_set(all_0_2_2, empty_set) = 0, yields: % 4.52/1.74 | (43) all_0_0_0 = 0 % 4.52/1.74 | % 4.52/1.74 | Instantiating formula (31) with all_0_2_2, empty_set, 0, all_0_1_1 and discharging atoms subset(all_0_2_2, empty_set) = all_0_1_1, subset(all_0_2_2, empty_set) = 0, yields: % 4.52/1.74 | (47) all_0_1_1 = 0 % 4.52/1.74 | % 4.52/1.74 +-Applying beta-rule and splitting (7), into two cases. % 4.52/1.74 |-Branch one: % 4.52/1.74 | (42) all_0_0_0 = 0 & ~ (all_0_1_1 = 0) % 4.52/1.74 | % 4.52/1.74 | Applying alpha-rule on (42) yields: % 4.52/1.74 | (43) all_0_0_0 = 0 % 4.52/1.74 | (44) ~ (all_0_1_1 = 0) % 4.52/1.74 | % 4.52/1.74 | Equations (47) can reduce 44 to: % 4.52/1.74 | (45) $false % 4.52/1.74 | % 4.52/1.74 |-The branch is then unsatisfiable % 4.52/1.74 |-Branch two: % 4.52/1.74 | (46) all_0_1_1 = 0 & ~ (all_0_0_0 = 0) % 4.52/1.74 | % 4.52/1.74 | Applying alpha-rule on (46) yields: % 4.52/1.74 | (47) all_0_1_1 = 0 % 4.52/1.74 | (41) ~ (all_0_0_0 = 0) % 4.52/1.74 | % 4.52/1.74 | Equations (43) can reduce 41 to: % 4.52/1.74 | (45) $false % 4.52/1.74 | % 4.52/1.74 |-The branch is then unsatisfiable % 4.52/1.74 % SZS output end Proof for theBenchmark % 4.52/1.74 % 4.52/1.74 1200ms %------------------------------------------------------------------------------