%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET148+4 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n018.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 00:17:56 EDT 2022 % Result : Theorem 3.54s 1.47s % Output : Proof 4.88s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SET148+4 : TPTP v8.1.0. Released v2.2.0. % 0.11/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.34 % Computer : n018.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Sun Jul 10 04:27:12 EDT 2022 % 0.13/0.34 % CPUTime : % 0.20/0.59 ____ _ % 0.20/0.59 ___ / __ \_____(_)___ ________ __________ % 0.20/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.20/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.20/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.20/0.59 % 0.20/0.59 A Theorem Prover for First-Order Logic % 0.20/0.59 (ePrincess v.1.0) % 0.20/0.59 % 0.20/0.59 (c) Philipp Rümmer, 2009-2015 % 0.20/0.59 (c) Peter Backeman, 2014-2015 % 0.20/0.59 (contributions by Angelo Brillout, Peter Baumgartner) % 0.20/0.59 Free software under GNU Lesser General Public License (LGPL). % 0.20/0.59 Bug reports to peter@backeman.se % 0.20/0.59 % 0.20/0.59 For more information, visit http://user.uu.se/~petba168/breu/ % 0.20/0.59 % 0.20/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.74/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.58/0.92 Prover 0: Preprocessing ... % 2.02/1.12 Prover 0: Warning: ignoring some quantifiers % 2.02/1.15 Prover 0: Constructing countermodel ... % 2.54/1.27 Prover 0: gave up % 2.54/1.27 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 2.54/1.29 Prover 1: Preprocessing ... % 3.21/1.40 Prover 1: Constructing countermodel ... % 3.54/1.47 Prover 1: proved (199ms) % 3.54/1.47 % 3.54/1.47 No countermodel exists, formula is valid % 3.54/1.47 % SZS status Theorem for theBenchmark % 3.54/1.47 % 3.54/1.47 Generating proof ... found it (size 43) % 4.53/1.73 % 4.53/1.73 % SZS output start Proof for theBenchmark % 4.53/1.73 Assumed formulas after preprocessing and simplification: % 4.53/1.73 | (0) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = 0) & intersection(v0, v0) = v1 & equal_set(v1, v0) = v2 & ! [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)) % 4.53/1.77 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2 yields: % 4.53/1.77 | (1) ~ (all_0_0_0 = 0) & intersection(all_0_2_2, all_0_2_2) = all_0_1_1 & equal_set(all_0_1_1, all_0_2_2) = 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) % 4.88/1.78 | % 4.88/1.78 | Applying alpha-rule on (1) yields: % 4.88/1.78 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = v3)) % 4.88/1.78 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) % 4.88/1.78 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) % 4.88/1.78 | (5) intersection(all_0_2_2, all_0_2_2) = all_0_1_1 % 4.88/1.78 | (6) ! [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)))) % 4.88/1.79 | (7) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0)) % 4.88/1.79 | (8) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (member(v0, v1) = v2)) % 4.88/1.79 | (9) ! [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)) % 4.88/1.79 | (10) ! [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)) % 4.88/1.79 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) % 4.88/1.79 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) % 4.88/1.79 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3)) % 4.88/1.79 | (14) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0)) % 4.88/1.79 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | (member(v0, v2) = 0 & member(v0, v1) = 0)) % 4.88/1.79 | (16) ! [v0] : ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0)) % 4.88/1.79 | (17) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ (member(v0, v2) = 0) | ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0)) % 4.88/1.79 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) % 4.88/1.79 | (19) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 4.88/1.79 | (20) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0)) % 4.88/1.79 | (21) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | subset(v0, v1) = 0) % 4.88/1.79 | (22) ! [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))) % 4.88/1.79 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v0, v2) = 0 & member(v0, v1) = v4)) % 4.88/1.79 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0)) % 4.88/1.79 | (25) ~ (all_0_0_0 = 0) % 4.88/1.79 | (26) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0)) % 4.88/1.79 | (27) ! [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)) % 4.88/1.79 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) % 4.88/1.79 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0)) % 4.88/1.79 | (30) ! [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))) % 4.88/1.80 | (31) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0) % 4.88/1.80 | (32) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0)) % 4.88/1.80 | (33) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_set(v0, v1) = v2) | ? [v3] : ? [v4] : (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) % 4.88/1.80 | (34) equal_set(all_0_1_1, all_0_2_2) = all_0_0_0 % 4.88/1.80 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) % 4.88/1.80 | (36) ! [v0] : ~ (member(v0, empty_set) = 0) % 4.88/1.80 | (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)) % 4.88/1.80 | % 4.88/1.80 | Instantiating formula (33) with all_0_0_0, all_0_2_2, all_0_1_1 and discharging atoms equal_set(all_0_1_1, all_0_2_2) = all_0_0_0, yields: % 4.88/1.80 | (38) all_0_0_0 = 0 | ? [v0] : ? [v1] : (subset(all_0_1_1, all_0_2_2) = v0 & subset(all_0_2_2, all_0_1_1) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 4.88/1.80 | % 4.88/1.80 +-Applying beta-rule and splitting (38), into two cases. % 4.88/1.80 |-Branch one: % 4.88/1.80 | (39) all_0_0_0 = 0 % 4.88/1.80 | % 4.88/1.80 | Equations (39) can reduce 25 to: % 4.88/1.80 | (40) $false % 4.88/1.80 | % 4.88/1.80 |-The branch is then unsatisfiable % 4.88/1.80 |-Branch two: % 4.88/1.80 | (25) ~ (all_0_0_0 = 0) % 4.88/1.80 | (42) ? [v0] : ? [v1] : (subset(all_0_1_1, all_0_2_2) = v0 & subset(all_0_2_2, all_0_1_1) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 4.88/1.80 | % 4.88/1.80 | Instantiating (42) with all_10_0_3, all_10_1_4 yields: % 4.88/1.80 | (43) subset(all_0_1_1, all_0_2_2) = all_10_1_4 & subset(all_0_2_2, all_0_1_1) = all_10_0_3 & ( ~ (all_10_0_3 = 0) | ~ (all_10_1_4 = 0)) % 4.88/1.80 | % 4.88/1.80 | Applying alpha-rule on (43) yields: % 4.88/1.80 | (44) subset(all_0_1_1, all_0_2_2) = all_10_1_4 % 4.88/1.80 | (45) subset(all_0_2_2, all_0_1_1) = all_10_0_3 % 4.88/1.80 | (46) ~ (all_10_0_3 = 0) | ~ (all_10_1_4 = 0) % 4.88/1.80 | % 4.88/1.80 | Instantiating formula (20) with all_10_1_4, all_0_2_2, all_0_1_1 and discharging atoms subset(all_0_1_1, all_0_2_2) = all_10_1_4, yields: % 4.88/1.80 | (47) all_10_1_4 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = 0 & member(v0, all_0_2_2) = v1) % 4.88/1.80 | % 4.88/1.80 | Instantiating formula (20) with all_10_0_3, all_0_1_1, all_0_2_2 and discharging atoms subset(all_0_2_2, all_0_1_1) = all_10_0_3, yields: % 4.88/1.80 | (48) all_10_0_3 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, all_0_2_2) = 0) % 4.88/1.80 | % 4.88/1.80 +-Applying beta-rule and splitting (46), into two cases. % 4.88/1.80 |-Branch one: % 4.88/1.80 | (49) ~ (all_10_0_3 = 0) % 4.88/1.80 | % 4.88/1.80 +-Applying beta-rule and splitting (48), into two cases. % 4.88/1.80 |-Branch one: % 4.88/1.80 | (50) all_10_0_3 = 0 % 4.88/1.80 | % 4.88/1.80 | Equations (50) can reduce 49 to: % 4.88/1.80 | (40) $false % 4.88/1.80 | % 4.88/1.80 |-The branch is then unsatisfiable % 4.88/1.80 |-Branch two: % 4.88/1.80 | (49) ~ (all_10_0_3 = 0) % 4.88/1.80 | (53) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, all_0_2_2) = 0) % 4.88/1.80 | % 4.88/1.80 | Instantiating (53) with all_23_0_5, all_23_1_6 yields: % 4.88/1.80 | (54) ~ (all_23_0_5 = 0) & member(all_23_1_6, all_0_1_1) = all_23_0_5 & member(all_23_1_6, all_0_2_2) = 0 % 4.88/1.80 | % 4.88/1.80 | Applying alpha-rule on (54) yields: % 4.88/1.80 | (55) ~ (all_23_0_5 = 0) % 4.88/1.80 | (56) member(all_23_1_6, all_0_1_1) = all_23_0_5 % 4.88/1.80 | (57) member(all_23_1_6, all_0_2_2) = 0 % 4.88/1.80 | % 4.88/1.80 | Instantiating formula (6) with all_23_0_5, all_0_1_1, all_0_2_2, all_0_2_2, all_23_1_6 and discharging atoms intersection(all_0_2_2, all_0_2_2) = all_0_1_1, member(all_23_1_6, all_0_1_1) = all_23_0_5, yields: % 4.88/1.80 | (58) all_23_0_5 = 0 | ? [v0] : ? [v1] : (member(all_23_1_6, all_0_2_2) = v1 & member(all_23_1_6, all_0_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 4.88/1.81 | % 4.88/1.81 +-Applying beta-rule and splitting (58), into two cases. % 4.88/1.81 |-Branch one: % 4.88/1.81 | (59) all_23_0_5 = 0 % 4.88/1.81 | % 4.88/1.81 | Equations (59) can reduce 55 to: % 4.88/1.81 | (40) $false % 4.88/1.81 | % 4.88/1.81 |-The branch is then unsatisfiable % 4.88/1.81 |-Branch two: % 4.88/1.81 | (55) ~ (all_23_0_5 = 0) % 4.88/1.81 | (62) ? [v0] : ? [v1] : (member(all_23_1_6, all_0_2_2) = v1 & member(all_23_1_6, all_0_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 4.88/1.81 | % 4.88/1.81 | Instantiating (62) with all_44_0_7, all_44_1_8 yields: % 4.88/1.81 | (63) member(all_23_1_6, all_0_2_2) = all_44_0_7 & member(all_23_1_6, all_0_2_2) = all_44_1_8 & ( ~ (all_44_0_7 = 0) | ~ (all_44_1_8 = 0)) % 4.88/1.81 | % 4.88/1.81 | Applying alpha-rule on (63) yields: % 4.88/1.81 | (64) member(all_23_1_6, all_0_2_2) = all_44_0_7 % 4.88/1.81 | (65) member(all_23_1_6, all_0_2_2) = all_44_1_8 % 4.88/1.81 | (66) ~ (all_44_0_7 = 0) | ~ (all_44_1_8 = 0) % 4.88/1.81 | % 4.88/1.81 | Instantiating formula (3) with all_23_1_6, all_0_2_2, all_44_0_7, 0 and discharging atoms member(all_23_1_6, all_0_2_2) = all_44_0_7, member(all_23_1_6, all_0_2_2) = 0, yields: % 4.88/1.81 | (67) all_44_0_7 = 0 % 4.88/1.81 | % 4.88/1.81 | Instantiating formula (3) with all_23_1_6, all_0_2_2, all_44_1_8, all_44_0_7 and discharging atoms member(all_23_1_6, all_0_2_2) = all_44_0_7, member(all_23_1_6, all_0_2_2) = all_44_1_8, yields: % 4.88/1.81 | (68) all_44_0_7 = all_44_1_8 % 4.88/1.81 | % 4.88/1.81 | Combining equations (67,68) yields a new equation: % 4.88/1.81 | (69) all_44_1_8 = 0 % 4.88/1.81 | % 4.88/1.81 | Combining equations (69,68) yields a new equation: % 4.88/1.81 | (67) all_44_0_7 = 0 % 4.88/1.81 | % 4.88/1.81 +-Applying beta-rule and splitting (66), into two cases. % 4.88/1.81 |-Branch one: % 4.88/1.81 | (71) ~ (all_44_0_7 = 0) % 4.88/1.81 | % 4.88/1.81 | Equations (67) can reduce 71 to: % 4.88/1.81 | (40) $false % 4.88/1.81 | % 4.88/1.81 |-The branch is then unsatisfiable % 4.88/1.81 |-Branch two: % 4.88/1.81 | (67) all_44_0_7 = 0 % 4.88/1.81 | (74) ~ (all_44_1_8 = 0) % 4.88/1.81 | % 4.88/1.81 | Equations (69) can reduce 74 to: % 4.88/1.81 | (40) $false % 4.88/1.81 | % 4.88/1.81 |-The branch is then unsatisfiable % 4.88/1.81 |-Branch two: % 4.88/1.81 | (50) all_10_0_3 = 0 % 4.88/1.81 | (77) ~ (all_10_1_4 = 0) % 4.88/1.81 | % 4.88/1.81 +-Applying beta-rule and splitting (47), into two cases. % 4.88/1.81 |-Branch one: % 4.88/1.81 | (78) all_10_1_4 = 0 % 4.88/1.81 | % 4.88/1.81 | Equations (78) can reduce 77 to: % 4.88/1.81 | (40) $false % 4.88/1.81 | % 4.88/1.81 |-The branch is then unsatisfiable % 4.88/1.81 |-Branch two: % 4.88/1.81 | (77) ~ (all_10_1_4 = 0) % 4.88/1.81 | (81) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = 0 & member(v0, all_0_2_2) = v1) % 4.88/1.81 | % 4.88/1.81 | Instantiating (81) with all_23_0_9, all_23_1_10 yields: % 4.88/1.81 | (82) ~ (all_23_0_9 = 0) & member(all_23_1_10, all_0_1_1) = 0 & member(all_23_1_10, all_0_2_2) = all_23_0_9 % 4.88/1.81 | % 4.88/1.81 | Applying alpha-rule on (82) yields: % 4.88/1.81 | (83) ~ (all_23_0_9 = 0) % 4.88/1.81 | (84) member(all_23_1_10, all_0_1_1) = 0 % 4.88/1.81 | (85) member(all_23_1_10, all_0_2_2) = all_23_0_9 % 4.88/1.81 | % 4.88/1.81 | Instantiating formula (3) with all_23_1_10, all_0_2_2, all_23_0_9, 0 and discharging atoms member(all_23_1_10, all_0_2_2) = all_23_0_9, yields: % 4.88/1.81 | (86) all_23_0_9 = 0 | ~ (member(all_23_1_10, all_0_2_2) = 0) % 4.88/1.81 | % 4.88/1.81 | Instantiating formula (15) with all_0_1_1, all_0_2_2, all_0_2_2, all_23_1_10 and discharging atoms intersection(all_0_2_2, all_0_2_2) = all_0_1_1, member(all_23_1_10, all_0_1_1) = 0, yields: % 4.88/1.81 | (87) member(all_23_1_10, all_0_2_2) = 0 % 4.88/1.81 | % 4.88/1.81 +-Applying beta-rule and splitting (86), into two cases. % 4.88/1.81 |-Branch one: % 4.88/1.81 | (88) ~ (member(all_23_1_10, all_0_2_2) = 0) % 4.88/1.81 | % 4.88/1.81 | Using (87) and (88) yields: % 4.88/1.81 | (89) $false % 4.88/1.81 | % 4.88/1.81 |-The branch is then unsatisfiable % 4.88/1.81 |-Branch two: % 4.88/1.81 | (87) member(all_23_1_10, all_0_2_2) = 0 % 4.88/1.81 | (91) all_23_0_9 = 0 % 4.88/1.81 | % 4.88/1.81 | Equations (91) can reduce 83 to: % 4.88/1.81 | (40) $false % 4.88/1.81 | % 4.88/1.81 |-The branch is then unsatisfiable % 4.88/1.81 % SZS output end Proof for theBenchmark % 4.88/1.81 % 4.88/1.81 1216ms %------------------------------------------------------------------------------