%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET594+3 : 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 00:20:33 EDT 2022 % Result : Theorem 3.35s 1.56s % Output : Proof 5.33s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SET594+3 : TPTP v8.1.0. Released v2.2.0. % 0.11/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n018.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 : Sat Jul 9 21:14:12 EDT 2022 % 0.12/0.34 % CPUTime : % 0.55/0.58 ____ _ % 0.55/0.58 ___ / __ \_____(_)___ ________ __________ % 0.55/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.55/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.55/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.55/0.58 % 0.55/0.58 A Theorem Prover for First-Order Logic % 0.55/0.58 (ePrincess v.1.0) % 0.55/0.58 % 0.55/0.58 (c) Philipp Rümmer, 2009-2015 % 0.55/0.58 (c) Peter Backeman, 2014-2015 % 0.55/0.58 (contributions by Angelo Brillout, Peter Baumgartner) % 0.55/0.58 Free software under GNU Lesser General Public License (LGPL). % 0.55/0.58 Bug reports to peter@backeman.se % 0.55/0.58 % 0.55/0.58 For more information, visit http://user.uu.se/~petba168/breu/ % 0.55/0.58 % 0.55/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.74/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.42/0.92 Prover 0: Preprocessing ... % 1.85/1.12 Prover 0: Warning: ignoring some quantifiers % 1.85/1.14 Prover 0: Constructing countermodel ... % 2.64/1.34 Prover 0: gave up % 2.64/1.34 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 2.64/1.36 Prover 1: Preprocessing ... % 2.92/1.44 Prover 1: Warning: ignoring some quantifiers % 2.92/1.45 Prover 1: Constructing countermodel ... % 3.35/1.56 Prover 1: proved (214ms) % 3.35/1.56 % 3.35/1.56 No countermodel exists, formula is valid % 3.35/1.56 % SZS status Theorem for theBenchmark % 3.35/1.56 % 3.35/1.56 Generating proof ... Warning: ignoring some quantifiers % 5.33/2.00 found it (size 71) % 5.33/2.00 % 5.33/2.00 % SZS output start Proof for theBenchmark % 5.33/2.00 Assumed formulas after preprocessing and simplification: % 5.33/2.00 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = 0) & intersection(v0, v2) = v4 & intersection(v0, v1) = v3 & union(v3, v4) = v0 & union(v1, v2) = v5 & subset(v0, v5) = v6 & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (intersection(v7, v8) = v10) | ~ (member(v9, v10) = v11) | ? [v12] : ? [v13] : (member(v9, v8) = v13 & member(v9, v7) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (union(v7, v8) = v10) | ~ (member(v9, v10) = v11) | ? [v12] : ? [v13] : ( ~ (v13 = 0) & ~ (v12 = 0) & member(v9, v8) = v13 & member(v9, v7) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (intersection(v10, v9) = v8) | ~ (intersection(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (union(v10, v9) = v8) | ~ (union(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] : ( ~ (intersection(v7, v8) = v10) | ~ (member(v9, v10) = 0) | (member(v9, v8) = 0 & member(v9, v7) = 0)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (union(v7, v8) = v10) | ~ (member(v9, v10) = 0) | ? [v11] : ? [v12] : (member(v9, v8) = v12 & member(v9, v7) = v11 & (v12 = 0 | v11 = 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] : ( ~ (intersection(v7, v8) = v9) | intersection(v8, v7) = v9) & ! [v7] : ! [v8] : ! [v9] : ( ~ (union(v7, v8) = v9) | union(v8, v7) = v9) & ! [v7] : ! [v8] : ! [v9] : ( ~ (subset(v7, v8) = 0) | ~ (member(v9, v7) = 0) | member(v9, v8) = 0) & ! [v7] : ! [v8] : (v8 = v7 | ~ (subset(v7, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & subset(v8, v7) = v9)) & ! [v7] : ! [v8] : (v8 = 0 | ~ (subset(v7, v7) = v8)) & ? [v7] : ? [v8] : (v8 = v7 | ? [v9] : ? [v10] : ? [v11] : (member(v9, v8) = v11 & member(v9, v7) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0)) & (v11 = 0 | v10 = 0)))) % 5.33/2.04 | 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: % 5.33/2.04 | (1) ~ (all_0_0_0 = 0) & intersection(all_0_6_6, all_0_4_4) = all_0_2_2 & intersection(all_0_6_6, all_0_5_5) = all_0_3_3 & union(all_0_3_3, all_0_2_2) = all_0_6_6 & union(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 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (intersection(v0, v1) = v3) | ~ (member(v2, v3) = v4) | ? [v5] : ? [v6] : (member(v2, v1) = v6 & member(v2, v0) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (union(v0, v1) = v3) | ~ (member(v2, v3) = v4) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & ~ (v5 = 0) & member(v2, v1) = v6 & member(v2, v0) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(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] : ( ~ (intersection(v0, v1) = v3) | ~ (member(v2, v3) = 0) | (member(v2, v1) = 0 & member(v2, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ? [v4] : ? [v5] : (member(v2, v1) = v5 & member(v2, v0) = v4 & (v5 = 0 | v4 = 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] : ( ~ (intersection(v0, v1) = v2) | intersection(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0, v1) = v2) | union(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0) & ! [v0] : ! [v1] : (v1 = v0 | ~ (subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v1, v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) & ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : ? [v3] : ? [v4] : (member(v2, v1) = v4 & member(v2, v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)) & (v4 = 0 | v3 = 0))) % 5.33/2.04 | % 5.33/2.04 | Applying alpha-rule on (1) yields: % 5.33/2.04 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) % 5.33/2.04 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (union(v0, v1) = v3) | ~ (member(v2, v3) = v4) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & ~ (v5 = 0) & member(v2, v1) = v6 & member(v2, v0) = v5)) % 5.33/2.04 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) % 5.33/2.04 | (5) intersection(all_0_6_6, all_0_4_4) = all_0_2_2 % 5.33/2.04 | (6) subset(all_0_6_6, all_0_1_1) = all_0_0_0 % 5.33/2.05 | (7) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0) % 5.33/2.05 | (8) intersection(all_0_6_6, all_0_5_5) = all_0_3_3 % 5.33/2.05 | (9) ! [v0] : ! [v1] : (v1 = v0 | ~ (subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v1, v0) = v2)) % 5.33/2.05 | (10) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) % 5.33/2.05 | (11) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0)) % 5.33/2.05 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection(v0, v1) = v2) | intersection(v1, v0) = v2) % 5.33/2.05 | (13) union(all_0_3_3, all_0_2_2) = all_0_6_6 % 5.33/2.05 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) % 5.33/2.05 | (15) union(all_0_5_5, all_0_4_4) = all_0_1_1 % 5.33/2.05 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ? [v4] : ? [v5] : (member(v2, v1) = v5 & member(v2, v0) = v4 & (v5 = 0 | v4 = 0))) % 5.33/2.05 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v0, v1) = v3) | ~ (member(v2, v3) = 0) | (member(v2, v1) = 0 & member(v2, v0) = 0)) % 5.33/2.05 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) % 5.33/2.05 | (19) ~ (all_0_0_0 = 0) % 5.33/2.05 | (20) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0, v1) = v2) | union(v1, v0) = v2) % 5.33/2.05 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (intersection(v0, v1) = v3) | ~ (member(v2, v3) = v4) | ? [v5] : ? [v6] : (member(v2, v1) = v6 & member(v2, v0) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) % 5.33/2.05 | (22) ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : ? [v3] : ? [v4] : (member(v2, v1) = v4 & member(v2, v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)) & (v4 = 0 | v3 = 0))) % 5.33/2.05 | % 5.33/2.05 | Instantiating formula (20) with all_0_6_6, all_0_2_2, all_0_3_3 and discharging atoms union(all_0_3_3, all_0_2_2) = all_0_6_6, yields: % 5.33/2.05 | (23) union(all_0_2_2, all_0_3_3) = all_0_6_6 % 5.33/2.05 | % 5.33/2.05 | Instantiating formula (20) with all_0_1_1, all_0_4_4, all_0_5_5 and discharging atoms union(all_0_5_5, all_0_4_4) = all_0_1_1, yields: % 5.33/2.05 | (24) union(all_0_4_4, all_0_5_5) = all_0_1_1 % 5.33/2.05 | % 5.33/2.05 | Instantiating formula (11) 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: % 5.33/2.05 | (25) all_0_0_0 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, all_0_6_6) = 0) % 5.33/2.05 | % 5.33/2.05 +-Applying beta-rule and splitting (25), into two cases. % 5.33/2.05 |-Branch one: % 5.33/2.05 | (26) all_0_0_0 = 0 % 5.33/2.05 | % 5.33/2.05 | Equations (26) can reduce 19 to: % 5.33/2.05 | (27) $false % 5.33/2.05 | % 5.33/2.05 |-The branch is then unsatisfiable % 5.33/2.05 |-Branch two: % 5.33/2.05 | (19) ~ (all_0_0_0 = 0) % 5.33/2.05 | (29) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, all_0_6_6) = 0) % 5.33/2.05 | % 5.33/2.05 | Instantiating (29) with all_18_0_9, all_18_1_10 yields: % 5.33/2.05 | (30) ~ (all_18_0_9 = 0) & member(all_18_1_10, all_0_1_1) = all_18_0_9 & member(all_18_1_10, all_0_6_6) = 0 % 5.33/2.05 | % 5.33/2.05 | Applying alpha-rule on (30) yields: % 5.33/2.05 | (31) ~ (all_18_0_9 = 0) % 5.33/2.05 | (32) member(all_18_1_10, all_0_1_1) = all_18_0_9 % 5.33/2.05 | (33) member(all_18_1_10, all_0_6_6) = 0 % 5.33/2.05 | % 5.33/2.05 | Instantiating formula (3) with all_18_0_9, all_0_1_1, all_18_1_10, all_0_4_4, all_0_5_5 and discharging atoms union(all_0_5_5, all_0_4_4) = all_0_1_1, member(all_18_1_10, all_0_1_1) = all_18_0_9, yields: % 5.33/2.05 | (34) all_18_0_9 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_18_1_10, all_0_4_4) = v1 & member(all_18_1_10, all_0_5_5) = v0) % 5.33/2.06 | % 5.33/2.06 | Instantiating formula (3) with all_18_0_9, all_0_1_1, all_18_1_10, all_0_5_5, all_0_4_4 and discharging atoms union(all_0_4_4, all_0_5_5) = all_0_1_1, member(all_18_1_10, all_0_1_1) = all_18_0_9, yields: % 5.33/2.06 | (35) all_18_0_9 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_18_1_10, all_0_4_4) = v0 & member(all_18_1_10, all_0_5_5) = v1) % 5.33/2.06 | % 5.33/2.06 | Instantiating formula (17) with all_0_6_6, all_18_1_10, all_0_4_4, all_0_6_6 and discharging atoms member(all_18_1_10, all_0_6_6) = 0, yields: % 5.33/2.06 | (36) ~ (intersection(all_0_6_6, all_0_4_4) = all_0_6_6) | member(all_18_1_10, all_0_4_4) = 0 % 5.33/2.06 | % 5.33/2.06 | Instantiating formula (17) with all_0_6_6, all_18_1_10, all_0_5_5, all_0_6_6 and discharging atoms member(all_18_1_10, all_0_6_6) = 0, yields: % 5.33/2.06 | (37) ~ (intersection(all_0_6_6, all_0_5_5) = all_0_6_6) | member(all_18_1_10, all_0_5_5) = 0 % 5.33/2.06 | % 5.33/2.06 | Instantiating formula (17) with all_0_6_6, all_18_1_10, all_0_6_6, all_0_4_4 and discharging atoms member(all_18_1_10, all_0_6_6) = 0, yields: % 5.33/2.06 | (38) ~ (intersection(all_0_4_4, all_0_6_6) = all_0_6_6) | member(all_18_1_10, all_0_4_4) = 0 % 5.33/2.06 | % 5.33/2.06 | Instantiating formula (17) with all_0_6_6, all_18_1_10, all_0_6_6, all_0_5_5 and discharging atoms member(all_18_1_10, all_0_6_6) = 0, yields: % 5.33/2.06 | (39) ~ (intersection(all_0_5_5, all_0_6_6) = all_0_6_6) | member(all_18_1_10, all_0_5_5) = 0 % 5.33/2.06 | % 5.33/2.06 | Instantiating formula (16) with all_0_6_6, all_18_1_10, all_0_2_2, all_0_3_3 and discharging atoms union(all_0_3_3, all_0_2_2) = all_0_6_6, member(all_18_1_10, all_0_6_6) = 0, yields: % 5.33/2.06 | (40) ? [v0] : ? [v1] : (member(all_18_1_10, all_0_2_2) = v1 & member(all_18_1_10, all_0_3_3) = v0 & (v1 = 0 | v0 = 0)) % 5.33/2.06 | % 5.33/2.06 | Instantiating formula (16) with all_0_6_6, all_18_1_10, all_0_3_3, all_0_2_2 and discharging atoms union(all_0_2_2, all_0_3_3) = all_0_6_6, member(all_18_1_10, all_0_6_6) = 0, yields: % 5.33/2.06 | (41) ? [v0] : ? [v1] : (member(all_18_1_10, all_0_2_2) = v0 & member(all_18_1_10, all_0_3_3) = v1 & (v1 = 0 | v0 = 0)) % 5.33/2.06 | % 5.33/2.06 | Instantiating (41) with all_29_0_11, all_29_1_12 yields: % 5.33/2.06 | (42) member(all_18_1_10, all_0_2_2) = all_29_1_12 & member(all_18_1_10, all_0_3_3) = all_29_0_11 & (all_29_0_11 = 0 | all_29_1_12 = 0) % 5.33/2.06 | % 5.33/2.06 | Applying alpha-rule on (42) yields: % 5.33/2.06 | (43) member(all_18_1_10, all_0_2_2) = all_29_1_12 % 5.33/2.06 | (44) member(all_18_1_10, all_0_3_3) = all_29_0_11 % 5.33/2.06 | (45) all_29_0_11 = 0 | all_29_1_12 = 0 % 5.33/2.06 | % 5.33/2.06 | Instantiating (40) with all_31_0_13, all_31_1_14 yields: % 5.33/2.06 | (46) member(all_18_1_10, all_0_2_2) = all_31_0_13 & member(all_18_1_10, all_0_3_3) = all_31_1_14 & (all_31_0_13 = 0 | all_31_1_14 = 0) % 5.33/2.06 | % 5.33/2.06 | Applying alpha-rule on (46) yields: % 5.33/2.06 | (47) member(all_18_1_10, all_0_2_2) = all_31_0_13 % 5.33/2.06 | (48) member(all_18_1_10, all_0_3_3) = all_31_1_14 % 5.33/2.06 | (49) all_31_0_13 = 0 | all_31_1_14 = 0 % 5.33/2.06 | % 5.33/2.06 +-Applying beta-rule and splitting (34), into two cases. % 5.33/2.06 |-Branch one: % 5.33/2.06 | (50) all_18_0_9 = 0 % 5.33/2.06 | % 5.33/2.06 | Equations (50) can reduce 31 to: % 5.33/2.06 | (27) $false % 5.33/2.06 | % 5.33/2.06 |-The branch is then unsatisfiable % 5.33/2.06 |-Branch two: % 5.33/2.06 | (31) ~ (all_18_0_9 = 0) % 5.33/2.06 | (53) ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_18_1_10, all_0_4_4) = v1 & member(all_18_1_10, all_0_5_5) = v0) % 5.33/2.06 | % 5.33/2.06 | Instantiating (53) with all_37_0_15, all_37_1_16 yields: % 5.33/2.06 | (54) ~ (all_37_0_15 = 0) & ~ (all_37_1_16 = 0) & member(all_18_1_10, all_0_4_4) = all_37_0_15 & member(all_18_1_10, all_0_5_5) = all_37_1_16 % 5.33/2.06 | % 5.33/2.06 | Applying alpha-rule on (54) yields: % 5.33/2.06 | (55) ~ (all_37_0_15 = 0) % 5.33/2.06 | (56) ~ (all_37_1_16 = 0) % 5.33/2.06 | (57) member(all_18_1_10, all_0_4_4) = all_37_0_15 % 5.33/2.06 | (58) member(all_18_1_10, all_0_5_5) = all_37_1_16 % 5.33/2.06 | % 5.33/2.06 +-Applying beta-rule and splitting (35), into two cases. % 5.33/2.06 |-Branch one: % 5.33/2.06 | (50) all_18_0_9 = 0 % 5.33/2.06 | % 5.33/2.06 | Equations (50) can reduce 31 to: % 5.33/2.06 | (27) $false % 5.33/2.06 | % 5.33/2.06 |-The branch is then unsatisfiable % 5.33/2.06 |-Branch two: % 5.33/2.06 | (31) ~ (all_18_0_9 = 0) % 5.33/2.06 | (62) ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_18_1_10, all_0_4_4) = v0 & member(all_18_1_10, all_0_5_5) = v1) % 5.33/2.06 | % 5.33/2.06 | Instantiating (62) with all_42_0_17, all_42_1_18 yields: % 5.33/2.06 | (63) ~ (all_42_0_17 = 0) & ~ (all_42_1_18 = 0) & member(all_18_1_10, all_0_4_4) = all_42_1_18 & member(all_18_1_10, all_0_5_5) = all_42_0_17 % 5.33/2.06 | % 5.33/2.06 | Applying alpha-rule on (63) yields: % 5.33/2.06 | (64) ~ (all_42_0_17 = 0) % 5.33/2.06 | (65) ~ (all_42_1_18 = 0) % 5.33/2.06 | (66) member(all_18_1_10, all_0_4_4) = all_42_1_18 % 5.33/2.06 | (67) member(all_18_1_10, all_0_5_5) = all_42_0_17 % 5.33/2.06 | % 5.33/2.06 +-Applying beta-rule and splitting (37), into two cases. % 5.33/2.06 |-Branch one: % 5.33/2.06 | (68) member(all_18_1_10, all_0_5_5) = 0 % 5.33/2.06 | % 5.33/2.06 | Instantiating formula (2) with all_18_1_10, all_0_5_5, all_42_0_17, 0 and discharging atoms member(all_18_1_10, all_0_5_5) = all_42_0_17, member(all_18_1_10, all_0_5_5) = 0, yields: % 5.33/2.06 | (69) all_42_0_17 = 0 % 5.33/2.06 | % 5.33/2.06 | Instantiating formula (2) with all_18_1_10, all_0_5_5, all_37_1_16, all_42_0_17 and discharging atoms member(all_18_1_10, all_0_5_5) = all_42_0_17, member(all_18_1_10, all_0_5_5) = all_37_1_16, yields: % 5.33/2.06 | (70) all_42_0_17 = all_37_1_16 % 5.33/2.06 | % 5.33/2.06 | Combining equations (69,70) yields a new equation: % 5.33/2.06 | (71) all_37_1_16 = 0 % 5.33/2.06 | % 5.33/2.07 | Equations (71) can reduce 56 to: % 5.33/2.07 | (27) $false % 5.33/2.07 | % 5.33/2.07 |-The branch is then unsatisfiable % 5.33/2.07 |-Branch two: % 5.33/2.07 | (73) ~ (member(all_18_1_10, all_0_5_5) = 0) % 5.33/2.07 | (74) ~ (intersection(all_0_6_6, all_0_5_5) = all_0_6_6) % 5.33/2.07 | % 5.33/2.07 +-Applying beta-rule and splitting (38), into two cases. % 5.33/2.07 |-Branch one: % 5.33/2.07 | (75) member(all_18_1_10, all_0_4_4) = 0 % 5.33/2.07 | % 5.33/2.07 | Instantiating formula (2) with all_18_1_10, all_0_4_4, all_37_0_15, all_42_1_18 and discharging atoms member(all_18_1_10, all_0_4_4) = all_42_1_18, member(all_18_1_10, all_0_4_4) = all_37_0_15, yields: % 5.33/2.07 | (76) all_42_1_18 = all_37_0_15 % 5.33/2.07 | % 5.33/2.07 | Instantiating formula (2) with all_18_1_10, all_0_4_4, 0, all_42_1_18 and discharging atoms member(all_18_1_10, all_0_4_4) = all_42_1_18, member(all_18_1_10, all_0_4_4) = 0, yields: % 5.33/2.07 | (77) all_42_1_18 = 0 % 5.33/2.07 | % 5.33/2.07 | Combining equations (77,76) yields a new equation: % 5.33/2.07 | (78) all_37_0_15 = 0 % 5.33/2.07 | % 5.33/2.07 | Equations (78) can reduce 55 to: % 5.33/2.07 | (27) $false % 5.33/2.07 | % 5.33/2.07 |-The branch is then unsatisfiable % 5.33/2.07 |-Branch two: % 5.33/2.07 | (80) ~ (member(all_18_1_10, all_0_4_4) = 0) % 5.33/2.07 | (81) ~ (intersection(all_0_4_4, all_0_6_6) = all_0_6_6) % 5.33/2.07 | % 5.33/2.07 +-Applying beta-rule and splitting (39), into two cases. % 5.33/2.07 |-Branch one: % 5.33/2.07 | (68) member(all_18_1_10, all_0_5_5) = 0 % 5.33/2.07 | % 5.33/2.07 | Using (68) and (73) yields: % 5.33/2.07 | (83) $false % 5.33/2.07 | % 5.33/2.07 |-The branch is then unsatisfiable % 5.33/2.07 |-Branch two: % 5.33/2.07 | (73) ~ (member(all_18_1_10, all_0_5_5) = 0) % 5.33/2.07 | (85) ~ (intersection(all_0_5_5, all_0_6_6) = all_0_6_6) % 5.33/2.07 | % 5.33/2.07 +-Applying beta-rule and splitting (36), into two cases. % 5.33/2.07 |-Branch one: % 5.33/2.07 | (75) member(all_18_1_10, all_0_4_4) = 0 % 5.33/2.07 | % 5.33/2.07 | Using (75) and (80) yields: % 5.33/2.07 | (83) $false % 5.33/2.07 | % 5.33/2.07 |-The branch is then unsatisfiable % 5.33/2.07 |-Branch two: % 5.33/2.07 | (80) ~ (member(all_18_1_10, all_0_4_4) = 0) % 5.33/2.07 | (89) ~ (intersection(all_0_6_6, all_0_4_4) = all_0_6_6) % 5.33/2.07 | % 5.33/2.07 | Instantiating formula (2) with all_18_1_10, all_0_2_2, all_29_1_12, all_31_0_13 and discharging atoms member(all_18_1_10, all_0_2_2) = all_31_0_13, member(all_18_1_10, all_0_2_2) = all_29_1_12, yields: % 5.33/2.07 | (90) all_31_0_13 = all_29_1_12 % 5.33/2.07 | % 5.33/2.07 | Instantiating formula (2) with all_18_1_10, all_0_3_3, all_29_0_11, all_31_1_14 and discharging atoms member(all_18_1_10, all_0_3_3) = all_31_1_14, member(all_18_1_10, all_0_3_3) = all_29_0_11, yields: % 5.33/2.07 | (91) all_31_1_14 = all_29_0_11 % 5.33/2.07 | % 5.33/2.07 | From (90) and (47) follows: % 5.33/2.07 | (43) member(all_18_1_10, all_0_2_2) = all_29_1_12 % 5.33/2.07 | % 5.33/2.07 | From (91) and (48) follows: % 5.33/2.07 | (44) member(all_18_1_10, all_0_3_3) = all_29_0_11 % 5.33/2.07 | % 5.33/2.07 | Instantiating formula (17) with all_0_2_2, all_18_1_10, all_0_4_4, all_0_6_6 and discharging atoms intersection(all_0_6_6, all_0_4_4) = all_0_2_2, yields: % 5.33/2.07 | (94) ~ (member(all_18_1_10, all_0_2_2) = 0) | (member(all_18_1_10, all_0_4_4) = 0 & member(all_18_1_10, all_0_6_6) = 0) % 5.33/2.07 | % 5.33/2.07 | Instantiating formula (17) with all_0_3_3, all_18_1_10, all_0_5_5, all_0_6_6 and discharging atoms intersection(all_0_6_6, all_0_5_5) = all_0_3_3, yields: % 5.33/2.07 | (95) ~ (member(all_18_1_10, all_0_3_3) = 0) | (member(all_18_1_10, all_0_5_5) = 0 & member(all_18_1_10, all_0_6_6) = 0) % 5.33/2.07 | % 5.33/2.07 +-Applying beta-rule and splitting (95), into two cases. % 5.33/2.07 |-Branch one: % 5.33/2.07 | (96) ~ (member(all_18_1_10, all_0_3_3) = 0) % 5.33/2.07 | % 5.33/2.07 +-Applying beta-rule and splitting (94), into two cases. % 5.33/2.07 |-Branch one: % 5.33/2.07 | (97) ~ (member(all_18_1_10, all_0_2_2) = 0) % 5.33/2.07 | % 5.33/2.07 | Using (43) and (97) yields: % 5.33/2.07 | (98) ~ (all_29_1_12 = 0) % 5.33/2.07 | % 5.33/2.07 | Using (44) and (96) yields: % 5.33/2.07 | (99) ~ (all_29_0_11 = 0) % 5.33/2.07 | % 5.33/2.07 +-Applying beta-rule and splitting (45), into two cases. % 5.33/2.07 |-Branch one: % 5.33/2.07 | (100) all_29_0_11 = 0 % 5.33/2.07 | % 5.33/2.07 | Equations (100) can reduce 99 to: % 5.33/2.07 | (27) $false % 5.33/2.07 | % 5.33/2.07 |-The branch is then unsatisfiable % 5.33/2.07 |-Branch two: % 5.33/2.07 | (99) ~ (all_29_0_11 = 0) % 5.33/2.07 | (103) all_29_1_12 = 0 % 5.33/2.07 | % 5.33/2.07 | Equations (103) can reduce 98 to: % 5.33/2.07 | (27) $false % 5.33/2.07 | % 5.33/2.07 |-The branch is then unsatisfiable % 5.33/2.07 |-Branch two: % 5.33/2.07 | (105) member(all_18_1_10, all_0_2_2) = 0 % 5.33/2.07 | (106) member(all_18_1_10, all_0_4_4) = 0 & member(all_18_1_10, all_0_6_6) = 0 % 5.33/2.07 | % 5.33/2.07 | Applying alpha-rule on (106) yields: % 5.33/2.07 | (75) member(all_18_1_10, all_0_4_4) = 0 % 5.33/2.07 | (33) member(all_18_1_10, all_0_6_6) = 0 % 5.33/2.07 | % 5.33/2.07 | Using (75) and (80) yields: % 5.33/2.07 | (83) $false % 5.33/2.07 | % 5.33/2.07 |-The branch is then unsatisfiable % 5.33/2.07 |-Branch two: % 5.33/2.08 | (110) member(all_18_1_10, all_0_3_3) = 0 % 5.33/2.08 | (111) member(all_18_1_10, all_0_5_5) = 0 & member(all_18_1_10, all_0_6_6) = 0 % 5.33/2.08 | % 5.33/2.08 | Applying alpha-rule on (111) yields: % 5.33/2.08 | (68) member(all_18_1_10, all_0_5_5) = 0 % 5.33/2.08 | (33) member(all_18_1_10, all_0_6_6) = 0 % 5.33/2.08 | % 5.33/2.08 | Using (68) and (73) yields: % 5.33/2.08 | (83) $false % 5.33/2.08 | % 5.33/2.08 |-The branch is then unsatisfiable % 5.33/2.08 % SZS output end Proof for theBenchmark % 5.33/2.08 % 5.33/2.08 1484ms %------------------------------------------------------------------------------