%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET593+3 : 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 00:20:33 EDT 2022 % Result : Theorem 3.44s 1.53s % Output : Proof 5.33s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SET593+3 : TPTP v8.1.0. Released v2.2.0. % 0.03/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.34 % Computer : n017.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 11:02:17 EDT 2022 % 0.13/0.34 % CPUTime : % 0.52/0.59 ____ _ % 0.52/0.59 ___ / __ \_____(_)___ ________ __________ % 0.52/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.52/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.52/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.52/0.59 % 0.52/0.59 A Theorem Prover for First-Order Logic % 0.52/0.59 (ePrincess v.1.0) % 0.52/0.59 % 0.52/0.59 (c) Philipp Rümmer, 2009-2015 % 0.52/0.59 (c) Peter Backeman, 2014-2015 % 0.52/0.59 (contributions by Angelo Brillout, Peter Baumgartner) % 0.52/0.59 Free software under GNU Lesser General Public License (LGPL). % 0.52/0.59 Bug reports to peter@backeman.se % 0.52/0.59 % 0.52/0.59 For more information, visit http://user.uu.se/~petba168/breu/ % 0.52/0.59 % 0.52/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.52/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.40/0.89 Prover 0: Preprocessing ... % 1.78/1.03 Prover 0: Warning: ignoring some quantifiers % 1.78/1.05 Prover 0: Constructing countermodel ... % 2.14/1.18 Prover 0: gave up % 2.14/1.18 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 2.28/1.20 Prover 1: Preprocessing ... % 2.54/1.28 Prover 1: Warning: ignoring some quantifiers % 2.54/1.28 Prover 1: Constructing countermodel ... % 3.44/1.52 Prover 1: proved (338ms) % 3.44/1.52 % 3.44/1.53 No countermodel exists, formula is valid % 3.44/1.53 % SZS status Theorem for theBenchmark % 3.44/1.53 % 3.44/1.53 Generating proof ... Warning: ignoring some quantifiers % 4.98/1.85 found it (size 79) % 4.98/1.85 % 4.98/1.85 % SZS output start Proof for theBenchmark % 4.98/1.85 Assumed formulas after preprocessing and simplification: % 4.98/1.85 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (subset(v6, v1) = v7 & subset(v4, v2) = v5 & subset(v0, v3) = 0 & difference(v0, v2) = v6 & difference(v0, v1) = v4 & union(v1, v2) = v3 & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (difference(v8, v9) = v11) | ~ (member(v10, v11) = v12) | ? [v13] : ? [v14] : (member(v10, v9) = v14 & member(v10, v8) = v13 & ( ~ (v13 = 0) | v14 = 0))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (union(v8, v9) = v11) | ~ (member(v10, v11) = v12) | ? [v13] : ? [v14] : ( ~ (v14 = 0) & ~ (v13 = 0) & member(v10, v9) = v14 & member(v10, v8) = v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (subset(v11, v10) = v9) | ~ (subset(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (difference(v11, v10) = v9) | ~ (difference(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (union(v11, v10) = v9) | ~ (union(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (member(v11, v10) = v9) | ~ (member(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (difference(v8, v9) = v11) | ~ (member(v10, v11) = 0) | ? [v12] : ( ~ (v12 = 0) & member(v10, v9) = v12 & member(v10, v8) = 0)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (union(v8, v9) = v11) | ~ (member(v10, v11) = 0) | ? [v12] : ? [v13] : (member(v10, v9) = v13 & member(v10, v8) = v12 & (v13 = 0 | v12 = 0))) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (subset(v8, v9) = v10) | ? [v11] : ? [v12] : ( ~ (v12 = 0) & member(v11, v9) = v12 & member(v11, v8) = 0)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (subset(v8, v9) = 0) | ~ (member(v10, v8) = 0) | member(v10, v9) = 0) & ! [v8] : ! [v9] : ! [v10] : ( ~ (union(v8, v9) = v10) | union(v9, v8) = v10) & ! [v8] : ! [v9] : (v9 = 0 | ~ (subset(v8, v8) = v9)) & ? [v8] : ? [v9] : (v9 = v8 | ? [v10] : ? [v11] : ? [v12] : (member(v10, v9) = v12 & member(v10, v8) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0)) & (v12 = 0 | v11 = 0))) & ( ~ (v7 = 0) | ~ (v5 = 0))) % 4.98/1.88 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7 yields: % 4.98/1.88 | (1) subset(all_0_1_1, all_0_6_6) = all_0_0_0 & subset(all_0_3_3, all_0_5_5) = all_0_2_2 & subset(all_0_7_7, all_0_4_4) = 0 & difference(all_0_7_7, all_0_5_5) = all_0_1_1 & difference(all_0_7_7, all_0_6_6) = all_0_3_3 & union(all_0_6_6, all_0_5_5) = all_0_4_4 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (difference(v0, v1) = v3) | ~ (member(v2, v3) = v4) | ? [v5] : ? [v6] : (member(v2, v1) = v6 & member(v2, v0) = v5 & ( ~ (v5 = 0) | v6 = 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 | ~ (subset(v3, v2) = v1) | ~ (subset(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 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v2, v1) = v4 & 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] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0, v1) = v2) | union(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))) & ( ~ (all_0_0_0 = 0) | ~ (all_0_2_2 = 0)) % 4.98/1.89 | % 4.98/1.89 | Applying alpha-rule on (1) yields: % 4.98/1.89 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (difference(v0, v1) = v3) | ~ (member(v2, v3) = v4) | ? [v5] : ? [v6] : (member(v2, v1) = v6 & member(v2, v0) = v5 & ( ~ (v5 = 0) | v6 = 0))) % 4.98/1.89 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) % 4.98/1.89 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0, v1) = v2) | union(v1, v0) = v2) % 4.98/1.89 | (5) ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : ? [v3] : ? [v4] : (member(v2, v1) = v4 & member(v2, v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)) & (v4 = 0 | v3 = 0))) % 4.98/1.89 | (6) difference(all_0_7_7, all_0_5_5) = all_0_1_1 % 4.98/1.89 | (7) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0) % 4.98/1.89 | (8) subset(all_0_3_3, all_0_5_5) = all_0_2_2 % 4.98/1.89 | (9) ~ (all_0_0_0 = 0) | ~ (all_0_2_2 = 0) % 4.98/1.89 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) % 4.98/1.89 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v2, v1) = v4 & member(v2, v0) = 0)) % 4.98/1.89 | (12) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) % 4.98/1.89 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) % 4.98/1.89 | (14) difference(all_0_7_7, all_0_6_6) = all_0_3_3 % 4.98/1.89 | (15) subset(all_0_7_7, all_0_4_4) = 0 % 4.98/1.89 | (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))) % 4.98/1.89 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) % 4.98/1.90 | (18) ! [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)) % 4.98/1.90 | (19) union(all_0_6_6, all_0_5_5) = all_0_4_4 % 4.98/1.90 | (20) subset(all_0_1_1, all_0_6_6) = all_0_0_0 % 4.98/1.90 | (21) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0)) % 4.98/1.90 | % 4.98/1.90 | Instantiating formula (21) with all_0_0_0, all_0_6_6, all_0_1_1 and discharging atoms subset(all_0_1_1, all_0_6_6) = all_0_0_0, yields: % 4.98/1.90 | (22) all_0_0_0 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = 0 & member(v0, all_0_6_6) = v1) % 4.98/1.90 | % 4.98/1.90 | Instantiating formula (21) with all_0_2_2, all_0_5_5, all_0_3_3 and discharging atoms subset(all_0_3_3, all_0_5_5) = all_0_2_2, yields: % 4.98/1.90 | (23) all_0_2_2 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_3_3) = 0 & member(v0, all_0_5_5) = v1) % 4.98/1.90 | % 4.98/1.90 +-Applying beta-rule and splitting (9), into two cases. % 4.98/1.90 |-Branch one: % 4.98/1.90 | (24) ~ (all_0_0_0 = 0) % 4.98/1.90 | % 4.98/1.90 +-Applying beta-rule and splitting (22), into two cases. % 4.98/1.90 |-Branch one: % 4.98/1.90 | (25) all_0_0_0 = 0 % 4.98/1.90 | % 4.98/1.90 | Equations (25) can reduce 24 to: % 4.98/1.90 | (26) $false % 4.98/1.90 | % 4.98/1.90 |-The branch is then unsatisfiable % 4.98/1.90 |-Branch two: % 4.98/1.90 | (24) ~ (all_0_0_0 = 0) % 4.98/1.90 | (28) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = 0 & member(v0, all_0_6_6) = v1) % 4.98/1.90 | % 4.98/1.90 | Instantiating (28) with all_32_0_10, all_32_1_11 yields: % 4.98/1.90 | (29) ~ (all_32_0_10 = 0) & member(all_32_1_11, all_0_1_1) = 0 & member(all_32_1_11, all_0_6_6) = all_32_0_10 % 4.98/1.90 | % 4.98/1.90 | Applying alpha-rule on (29) yields: % 4.98/1.90 | (30) ~ (all_32_0_10 = 0) % 4.98/1.90 | (31) member(all_32_1_11, all_0_1_1) = 0 % 4.98/1.90 | (32) member(all_32_1_11, all_0_6_6) = all_32_0_10 % 4.98/1.90 | % 4.98/1.90 | Instantiating formula (11) with all_0_1_1, all_32_1_11, all_0_5_5, all_0_7_7 and discharging atoms difference(all_0_7_7, all_0_5_5) = all_0_1_1, member(all_32_1_11, all_0_1_1) = 0, yields: % 4.98/1.90 | (33) ? [v0] : ( ~ (v0 = 0) & member(all_32_1_11, all_0_5_5) = v0 & member(all_32_1_11, all_0_7_7) = 0) % 4.98/1.90 | % 4.98/1.90 | Instantiating formula (16) with all_0_4_4, all_32_1_11, all_0_5_5, all_0_6_6 and discharging atoms union(all_0_6_6, all_0_5_5) = all_0_4_4, yields: % 4.98/1.90 | (34) ~ (member(all_32_1_11, all_0_4_4) = 0) | ? [v0] : ? [v1] : (member(all_32_1_11, all_0_5_5) = v1 & member(all_32_1_11, all_0_6_6) = v0 & (v1 = 0 | v0 = 0)) % 4.98/1.90 | % 4.98/1.90 | Instantiating formula (7) with all_32_1_11, all_0_4_4, all_0_7_7 and discharging atoms subset(all_0_7_7, all_0_4_4) = 0, yields: % 4.98/1.90 | (35) ~ (member(all_32_1_11, all_0_7_7) = 0) | member(all_32_1_11, all_0_4_4) = 0 % 4.98/1.90 | % 4.98/1.90 | Instantiating (33) with all_43_0_12 yields: % 4.98/1.90 | (36) ~ (all_43_0_12 = 0) & member(all_32_1_11, all_0_5_5) = all_43_0_12 & member(all_32_1_11, all_0_7_7) = 0 % 4.98/1.90 | % 4.98/1.90 | Applying alpha-rule on (36) yields: % 4.98/1.90 | (37) ~ (all_43_0_12 = 0) % 4.98/1.90 | (38) member(all_32_1_11, all_0_5_5) = all_43_0_12 % 4.98/1.90 | (39) member(all_32_1_11, all_0_7_7) = 0 % 4.98/1.90 | % 4.98/1.90 +-Applying beta-rule and splitting (35), into two cases. % 4.98/1.90 |-Branch one: % 4.98/1.90 | (40) ~ (member(all_32_1_11, all_0_7_7) = 0) % 4.98/1.90 | % 4.98/1.90 | Using (39) and (40) yields: % 4.98/1.90 | (41) $false % 4.98/1.90 | % 4.98/1.91 |-The branch is then unsatisfiable % 4.98/1.91 |-Branch two: % 4.98/1.91 | (39) member(all_32_1_11, all_0_7_7) = 0 % 4.98/1.91 | (43) member(all_32_1_11, all_0_4_4) = 0 % 4.98/1.91 | % 4.98/1.91 +-Applying beta-rule and splitting (34), into two cases. % 4.98/1.91 |-Branch one: % 4.98/1.91 | (44) ~ (member(all_32_1_11, all_0_4_4) = 0) % 4.98/1.91 | % 4.98/1.91 | Using (43) and (44) yields: % 4.98/1.91 | (41) $false % 4.98/1.91 | % 4.98/1.91 |-The branch is then unsatisfiable % 4.98/1.91 |-Branch two: % 4.98/1.91 | (43) member(all_32_1_11, all_0_4_4) = 0 % 4.98/1.91 | (47) ? [v0] : ? [v1] : (member(all_32_1_11, all_0_5_5) = v1 & member(all_32_1_11, all_0_6_6) = v0 & (v1 = 0 | v0 = 0)) % 4.98/1.91 | % 4.98/1.91 | Instantiating (47) with all_53_0_13, all_53_1_14 yields: % 4.98/1.91 | (48) member(all_32_1_11, all_0_5_5) = all_53_0_13 & member(all_32_1_11, all_0_6_6) = all_53_1_14 & (all_53_0_13 = 0 | all_53_1_14 = 0) % 4.98/1.91 | % 4.98/1.91 | Applying alpha-rule on (48) yields: % 4.98/1.91 | (49) member(all_32_1_11, all_0_5_5) = all_53_0_13 % 4.98/1.91 | (50) member(all_32_1_11, all_0_6_6) = all_53_1_14 % 5.33/1.91 | (51) all_53_0_13 = 0 | all_53_1_14 = 0 % 5.33/1.91 | % 5.33/1.91 | Instantiating formula (13) with all_32_1_11, all_0_5_5, all_43_0_12, all_53_0_13 and discharging atoms member(all_32_1_11, all_0_5_5) = all_53_0_13, member(all_32_1_11, all_0_5_5) = all_43_0_12, yields: % 5.33/1.91 | (52) all_53_0_13 = all_43_0_12 % 5.33/1.91 | % 5.33/1.91 | Instantiating formula (13) with all_32_1_11, all_0_6_6, all_53_1_14, all_32_0_10 and discharging atoms member(all_32_1_11, all_0_6_6) = all_53_1_14, member(all_32_1_11, all_0_6_6) = all_32_0_10, yields: % 5.33/1.91 | (53) all_53_1_14 = all_32_0_10 % 5.33/1.91 | % 5.33/1.91 +-Applying beta-rule and splitting (51), into two cases. % 5.33/1.91 |-Branch one: % 5.33/1.91 | (54) all_53_0_13 = 0 % 5.33/1.91 | % 5.33/1.91 | Combining equations (54,52) yields a new equation: % 5.33/1.91 | (55) all_43_0_12 = 0 % 5.33/1.91 | % 5.33/1.91 | Equations (55) can reduce 37 to: % 5.33/1.91 | (26) $false % 5.33/1.91 | % 5.33/1.91 |-The branch is then unsatisfiable % 5.33/1.91 |-Branch two: % 5.33/1.91 | (57) ~ (all_53_0_13 = 0) % 5.33/1.91 | (58) all_53_1_14 = 0 % 5.33/1.91 | % 5.33/1.91 | Combining equations (53,58) yields a new equation: % 5.33/1.91 | (59) all_32_0_10 = 0 % 5.33/1.91 | % 5.33/1.91 | Simplifying 59 yields: % 5.33/1.91 | (60) all_32_0_10 = 0 % 5.33/1.91 | % 5.33/1.91 | Equations (60) can reduce 30 to: % 5.33/1.91 | (26) $false % 5.33/1.91 | % 5.33/1.91 |-The branch is then unsatisfiable % 5.33/1.91 |-Branch two: % 5.33/1.91 | (25) all_0_0_0 = 0 % 5.33/1.91 | (63) ~ (all_0_2_2 = 0) % 5.33/1.91 | % 5.33/1.91 +-Applying beta-rule and splitting (23), into two cases. % 5.33/1.91 |-Branch one: % 5.33/1.91 | (64) all_0_2_2 = 0 % 5.33/1.91 | % 5.33/1.91 | Equations (64) can reduce 63 to: % 5.33/1.91 | (26) $false % 5.33/1.91 | % 5.33/1.91 |-The branch is then unsatisfiable % 5.33/1.91 |-Branch two: % 5.33/1.91 | (63) ~ (all_0_2_2 = 0) % 5.33/1.91 | (67) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_3_3) = 0 & member(v0, all_0_5_5) = v1) % 5.33/1.91 | % 5.33/1.91 | Instantiating (67) with all_32_0_17, all_32_1_18 yields: % 5.33/1.91 | (68) ~ (all_32_0_17 = 0) & member(all_32_1_18, all_0_3_3) = 0 & member(all_32_1_18, all_0_5_5) = all_32_0_17 % 5.33/1.91 | % 5.33/1.91 | Applying alpha-rule on (68) yields: % 5.33/1.91 | (69) ~ (all_32_0_17 = 0) % 5.33/1.91 | (70) member(all_32_1_18, all_0_3_3) = 0 % 5.33/1.91 | (71) member(all_32_1_18, all_0_5_5) = all_32_0_17 % 5.33/1.91 | % 5.33/1.91 | Instantiating formula (11) with all_0_3_3, all_32_1_18, all_0_6_6, all_0_7_7 and discharging atoms difference(all_0_7_7, all_0_6_6) = all_0_3_3, member(all_32_1_18, all_0_3_3) = 0, yields: % 5.33/1.91 | (72) ? [v0] : ( ~ (v0 = 0) & member(all_32_1_18, all_0_6_6) = v0 & member(all_32_1_18, all_0_7_7) = 0) % 5.33/1.91 | % 5.33/1.91 | Instantiating formula (16) with all_0_4_4, all_32_1_18, all_0_5_5, all_0_6_6 and discharging atoms union(all_0_6_6, all_0_5_5) = all_0_4_4, yields: % 5.33/1.91 | (73) ~ (member(all_32_1_18, all_0_4_4) = 0) | ? [v0] : ? [v1] : (member(all_32_1_18, all_0_5_5) = v1 & member(all_32_1_18, all_0_6_6) = v0 & (v1 = 0 | v0 = 0)) % 5.33/1.91 | % 5.33/1.91 | Instantiating formula (7) with all_32_1_18, all_0_4_4, all_0_7_7 and discharging atoms subset(all_0_7_7, all_0_4_4) = 0, yields: % 5.33/1.91 | (74) ~ (member(all_32_1_18, all_0_7_7) = 0) | member(all_32_1_18, all_0_4_4) = 0 % 5.33/1.91 | % 5.33/1.91 | Instantiating formula (7) with all_32_1_18, all_0_6_6, all_0_3_3 and discharging atoms member(all_32_1_18, all_0_3_3) = 0, yields: % 5.33/1.92 | (75) ~ (subset(all_0_3_3, all_0_6_6) = 0) | member(all_32_1_18, all_0_6_6) = 0 % 5.33/1.92 | % 5.33/1.92 | Instantiating (72) with all_43_0_19 yields: % 5.33/1.92 | (76) ~ (all_43_0_19 = 0) & member(all_32_1_18, all_0_6_6) = all_43_0_19 & member(all_32_1_18, all_0_7_7) = 0 % 5.33/1.92 | % 5.33/1.92 | Applying alpha-rule on (76) yields: % 5.33/1.92 | (77) ~ (all_43_0_19 = 0) % 5.33/1.92 | (78) member(all_32_1_18, all_0_6_6) = all_43_0_19 % 5.33/1.92 | (79) member(all_32_1_18, all_0_7_7) = 0 % 5.33/1.92 | % 5.33/1.92 +-Applying beta-rule and splitting (75), into two cases. % 5.33/1.92 |-Branch one: % 5.33/1.92 | (80) member(all_32_1_18, all_0_6_6) = 0 % 5.33/1.92 | % 5.33/1.92 +-Applying beta-rule and splitting (74), into two cases. % 5.33/1.92 |-Branch one: % 5.33/1.92 | (81) ~ (member(all_32_1_18, all_0_7_7) = 0) % 5.33/1.92 | % 5.33/1.92 | Using (79) and (81) yields: % 5.33/1.92 | (41) $false % 5.33/1.92 | % 5.33/1.92 |-The branch is then unsatisfiable % 5.33/1.92 |-Branch two: % 5.33/1.92 | (79) member(all_32_1_18, all_0_7_7) = 0 % 5.33/1.92 | (84) member(all_32_1_18, all_0_4_4) = 0 % 5.33/1.92 | % 5.33/1.92 +-Applying beta-rule and splitting (73), into two cases. % 5.33/1.92 |-Branch one: % 5.33/1.92 | (85) ~ (member(all_32_1_18, all_0_4_4) = 0) % 5.33/1.92 | % 5.33/1.92 | Using (84) and (85) yields: % 5.33/1.92 | (41) $false % 5.33/1.92 | % 5.33/1.92 |-The branch is then unsatisfiable % 5.33/1.92 |-Branch two: % 5.33/1.92 | (84) member(all_32_1_18, all_0_4_4) = 0 % 5.33/1.92 | (88) ? [v0] : ? [v1] : (member(all_32_1_18, all_0_5_5) = v1 & member(all_32_1_18, all_0_6_6) = v0 & (v1 = 0 | v0 = 0)) % 5.33/1.92 | % 5.33/1.92 | Instantiating (88) with all_57_0_20, all_57_1_21 yields: % 5.33/1.92 | (89) member(all_32_1_18, all_0_5_5) = all_57_0_20 & member(all_32_1_18, all_0_6_6) = all_57_1_21 & (all_57_0_20 = 0 | all_57_1_21 = 0) % 5.33/1.92 | % 5.33/1.92 | Applying alpha-rule on (89) yields: % 5.33/1.92 | (90) member(all_32_1_18, all_0_5_5) = all_57_0_20 % 5.33/1.92 | (91) member(all_32_1_18, all_0_6_6) = all_57_1_21 % 5.33/1.92 | (92) all_57_0_20 = 0 | all_57_1_21 = 0 % 5.33/1.92 | % 5.33/1.92 | Instantiating formula (13) with all_32_1_18, all_0_6_6, all_57_1_21, 0 and discharging atoms member(all_32_1_18, all_0_6_6) = all_57_1_21, member(all_32_1_18, all_0_6_6) = 0, yields: % 5.33/1.92 | (93) all_57_1_21 = 0 % 5.33/1.92 | % 5.33/1.92 | Instantiating formula (13) with all_32_1_18, all_0_6_6, all_43_0_19, all_57_1_21 and discharging atoms member(all_32_1_18, all_0_6_6) = all_57_1_21, member(all_32_1_18, all_0_6_6) = all_43_0_19, yields: % 5.33/1.92 | (94) all_57_1_21 = all_43_0_19 % 5.33/1.92 | % 5.33/1.92 | Combining equations (94,93) yields a new equation: % 5.33/1.92 | (95) all_43_0_19 = 0 % 5.33/1.92 | % 5.33/1.92 | Simplifying 95 yields: % 5.33/1.92 | (96) all_43_0_19 = 0 % 5.33/1.92 | % 5.33/1.92 | Equations (96) can reduce 77 to: % 5.33/1.92 | (26) $false % 5.33/1.92 | % 5.33/1.92 |-The branch is then unsatisfiable % 5.33/1.92 |-Branch two: % 5.33/1.92 | (98) ~ (member(all_32_1_18, all_0_6_6) = 0) % 5.33/1.92 | (99) ~ (subset(all_0_3_3, all_0_6_6) = 0) % 5.33/1.92 | % 5.33/1.92 +-Applying beta-rule and splitting (74), into two cases. % 5.33/1.92 |-Branch one: % 5.33/1.92 | (81) ~ (member(all_32_1_18, all_0_7_7) = 0) % 5.33/1.92 | % 5.33/1.92 | Using (79) and (81) yields: % 5.33/1.92 | (41) $false % 5.33/1.92 | % 5.33/1.92 |-The branch is then unsatisfiable % 5.33/1.92 |-Branch two: % 5.33/1.92 | (79) member(all_32_1_18, all_0_7_7) = 0 % 5.33/1.92 | (84) member(all_32_1_18, all_0_4_4) = 0 % 5.33/1.92 | % 5.33/1.92 +-Applying beta-rule and splitting (73), into two cases. % 5.33/1.92 |-Branch one: % 5.33/1.92 | (85) ~ (member(all_32_1_18, all_0_4_4) = 0) % 5.33/1.92 | % 5.33/1.92 | Using (84) and (85) yields: % 5.33/1.92 | (41) $false % 5.33/1.92 | % 5.33/1.92 |-The branch is then unsatisfiable % 5.33/1.92 |-Branch two: % 5.33/1.92 | (84) member(all_32_1_18, all_0_4_4) = 0 % 5.33/1.92 | (88) ? [v0] : ? [v1] : (member(all_32_1_18, all_0_5_5) = v1 & member(all_32_1_18, all_0_6_6) = v0 & (v1 = 0 | v0 = 0)) % 5.33/1.93 | % 5.33/1.93 | Instantiating (88) with all_57_0_22, all_57_1_23 yields: % 5.33/1.93 | (108) member(all_32_1_18, all_0_5_5) = all_57_0_22 & member(all_32_1_18, all_0_6_6) = all_57_1_23 & (all_57_0_22 = 0 | all_57_1_23 = 0) % 5.33/1.93 | % 5.33/1.93 | Applying alpha-rule on (108) yields: % 5.33/1.93 | (109) member(all_32_1_18, all_0_5_5) = all_57_0_22 % 5.33/1.93 | (110) member(all_32_1_18, all_0_6_6) = all_57_1_23 % 5.33/1.93 | (111) all_57_0_22 = 0 | all_57_1_23 = 0 % 5.33/1.93 | % 5.33/1.93 | Instantiating formula (13) with all_32_1_18, all_0_5_5, all_57_0_22, all_32_0_17 and discharging atoms member(all_32_1_18, all_0_5_5) = all_57_0_22, member(all_32_1_18, all_0_5_5) = all_32_0_17, yields: % 5.33/1.93 | (112) all_57_0_22 = all_32_0_17 % 5.33/1.93 | % 5.33/1.93 | Instantiating formula (13) with all_32_1_18, all_0_6_6, all_43_0_19, all_57_1_23 and discharging atoms member(all_32_1_18, all_0_6_6) = all_57_1_23, member(all_32_1_18, all_0_6_6) = all_43_0_19, yields: % 5.33/1.93 | (113) all_57_1_23 = all_43_0_19 % 5.33/1.93 | % 5.33/1.93 | Using (110) and (98) yields: % 5.33/1.93 | (114) ~ (all_57_1_23 = 0) % 5.33/1.93 | % 5.33/1.93 | Equations (113) can reduce 114 to: % 5.33/1.93 | (77) ~ (all_43_0_19 = 0) % 5.33/1.93 | % 5.33/1.93 +-Applying beta-rule and splitting (111), into two cases. % 5.33/1.93 |-Branch one: % 5.33/1.93 | (116) all_57_0_22 = 0 % 5.33/1.93 | % 5.33/1.93 | Combining equations (116,112) yields a new equation: % 5.33/1.93 | (117) all_32_0_17 = 0 % 5.33/1.93 | % 5.33/1.93 | Equations (117) can reduce 69 to: % 5.33/1.93 | (26) $false % 5.33/1.93 | % 5.33/1.93 |-The branch is then unsatisfiable % 5.33/1.93 |-Branch two: % 5.33/1.93 | (119) ~ (all_57_0_22 = 0) % 5.33/1.93 | (120) all_57_1_23 = 0 % 5.33/1.93 | % 5.33/1.93 | Combining equations (113,120) yields a new equation: % 5.33/1.93 | (95) all_43_0_19 = 0 % 5.33/1.93 | % 5.33/1.93 | Simplifying 95 yields: % 5.33/1.93 | (96) all_43_0_19 = 0 % 5.33/1.93 | % 5.33/1.93 | Equations (96) can reduce 77 to: % 5.33/1.93 | (26) $false % 5.33/1.93 | % 5.33/1.93 |-The branch is then unsatisfiable % 5.33/1.93 % SZS output end Proof for theBenchmark % 5.33/1.93 % 5.33/1.93 1327ms %------------------------------------------------------------------------------