%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU145+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n025.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 08:46:57 EDT 2022 % Result : Theorem 3.25s 1.47s % Output : Proof 4.26s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.12 % Problem : SEU145+1 : TPTP v8.1.0. Released v3.3.0. % 0.08/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.34 % Computer : n025.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 Jun 19 08:07:59 EDT 2022 % 0.13/0.34 % CPUTime : % 0.19/0.58 ____ _ % 0.19/0.58 ___ / __ \_____(_)___ ________ __________ % 0.19/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.19/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.19/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.19/0.58 % 0.19/0.58 A Theorem Prover for First-Order Logic % 0.19/0.58 (ePrincess v.1.0) % 0.19/0.58 % 0.19/0.58 (c) Philipp Rümmer, 2009-2015 % 0.19/0.58 (c) Peter Backeman, 2014-2015 % 0.19/0.58 (contributions by Angelo Brillout, Peter Baumgartner) % 0.19/0.58 Free software under GNU Lesser General Public License (LGPL). % 0.19/0.58 Bug reports to peter@backeman.se % 0.19/0.58 % 0.19/0.58 For more information, visit http://user.uu.se/~petba168/breu/ % 0.19/0.58 % 0.19/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.76/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.40/0.91 Prover 0: Preprocessing ... % 1.67/1.07 Prover 0: Warning: ignoring some quantifiers % 1.81/1.08 Prover 0: Constructing countermodel ... % 2.42/1.31 Prover 0: gave up % 2.42/1.31 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 2.42/1.33 Prover 1: Preprocessing ... % 2.99/1.39 Prover 1: Warning: ignoring some quantifiers % 2.99/1.39 Prover 1: Constructing countermodel ... % 3.25/1.46 Prover 1: proved (153ms) % 3.25/1.47 % 3.25/1.47 No countermodel exists, formula is valid % 3.25/1.47 % SZS status Theorem for theBenchmark % 3.25/1.47 % 3.25/1.47 Generating proof ... Warning: ignoring some quantifiers % 3.91/1.73 found it (size 37) % 3.91/1.73 % 3.91/1.73 % SZS output start Proof for theBenchmark % 3.91/1.73 Assumed formulas after preprocessing and simplification: % 3.91/1.73 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = 0) & ~ (v3 = 0) & set_difference(v1, v4) = v5 & subset(v0, v5) = v6 & subset(v0, v1) = 0 & singleton(v2) = v4 & in(v2, v0) = v3 & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (set_difference(v7, v8) = v9) | ~ (in(v10, v7) = v11) | ? [v12] : ? [v13] : (in(v10, v9) = v12 & in(v10, v8) = v13 & ( ~ (v12 = 0) | (v11 = 0 & ~ (v13 = 0))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (set_difference(v10, v9) = v8) | ~ (set_difference(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (subset(v10, v9) = v8) | ~ (subset(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (in(v10, v9) = v8) | ~ (in(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (set_difference(v7, v8) = v9) | ~ (in(v10, v7) = 0) | ? [v11] : ? [v12] : (in(v10, v9) = v12 & in(v10, v8) = v11 & (v12 = 0 | v11 = 0))) & ? [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v7 | ~ (set_difference(v8, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : (in(v11, v9) = v14 & in(v11, v8) = v13 & in(v11, v7) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0) | v14 = 0) & (v12 = 0 | (v13 = 0 & ~ (v14 = 0))))) & ! [v7] : ! [v8] : ! [v9] : (v9 = v7 | ~ (singleton(v7) = v8) | ~ (in(v9, v8) = 0)) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (subset(v7, v8) = v9) | ? [v10] : ? [v11] : ( ~ (v11 = 0) & in(v10, v8) = v11 & in(v10, v7) = 0)) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (singleton(v7) = v8) | ~ (in(v7, v8) = v9)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (singleton(v9) = v8) | ~ (singleton(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (subset(v7, v8) = 0) | ~ (in(v9, v7) = 0) | in(v9, v8) = 0) & ? [v7] : ! [v8] : ! [v9] : (v9 = v7 | ~ (singleton(v8) = v9) | ? [v10] : ? [v11] : (in(v10, v7) = v11 & ( ~ (v11 = 0) | ~ (v10 = v8)) & (v11 = 0 | v10 = v8))) & ! [v7] : ! [v8] : (v8 = 0 | ~ (subset(v7, v7) = v8)) & ! [v7] : ! [v8] : ( ~ (in(v7, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & in(v8, v7) = v9))) % 3.91/1.77 | 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: % 3.91/1.77 | (1) ~ (all_0_0_0 = 0) & ~ (all_0_3_3 = 0) & set_difference(all_0_5_5, all_0_2_2) = all_0_1_1 & subset(all_0_6_6, all_0_1_1) = all_0_0_0 & subset(all_0_6_6, all_0_5_5) = 0 & singleton(all_0_4_4) = all_0_2_2 & in(all_0_4_4, all_0_6_6) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | (v4 = 0 & ~ (v6 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v0) = 0) | ? [v4] : ? [v5] : (in(v3, v2) = v5 & in(v3, v1) = v4 & (v5 = 0 | v4 = 0))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_difference(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | v7 = 0) & (v5 = 0 | (v6 = 0 & ~ (v7 = 0))))) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ (in(v2, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (in(v0, v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : ? [v4] : (in(v3, v0) = v4 & ( ~ (v4 = 0) | ~ (v3 = v1)) & (v4 = 0 | v3 = v1))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) % 4.21/1.77 | % 4.21/1.77 | Applying alpha-rule on (1) yields: % 4.21/1.77 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | (v4 = 0 & ~ (v6 = 0))))) % 4.21/1.78 | (3) in(all_0_4_4, all_0_6_6) = all_0_3_3 % 4.21/1.78 | (4) subset(all_0_6_6, all_0_5_5) = 0 % 4.21/1.78 | (5) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) % 4.21/1.78 | (6) ~ (all_0_3_3 = 0) % 4.21/1.78 | (7) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0)) % 4.21/1.78 | (8) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : ? [v4] : (in(v3, v0) = v4 & ( ~ (v4 = 0) | ~ (v3 = v1)) & (v4 = 0 | v3 = v1))) % 4.21/1.78 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v0) = 0) | ? [v4] : ? [v5] : (in(v3, v2) = v5 & in(v3, v1) = v4 & (v5 = 0 | v4 = 0))) % 4.21/1.78 | (10) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 4.21/1.78 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) % 4.21/1.78 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 4.21/1.78 | (13) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0) % 4.21/1.78 | (14) set_difference(all_0_5_5, all_0_2_2) = all_0_1_1 % 4.21/1.78 | (15) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) % 4.21/1.78 | (16) subset(all_0_6_6, all_0_1_1) = all_0_0_0 % 4.21/1.78 | (17) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ (in(v2, v1) = 0)) % 4.21/1.78 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) % 4.21/1.78 | (19) singleton(all_0_4_4) = all_0_2_2 % 4.21/1.78 | (20) ~ (all_0_0_0 = 0) % 4.21/1.78 | (21) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (in(v0, v1) = v2)) % 4.21/1.78 | (22) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_difference(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | v7 = 0) & (v5 = 0 | (v6 = 0 & ~ (v7 = 0))))) % 4.26/1.78 | % 4.26/1.78 | Instantiating formula (7) 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: % 4.26/1.78 | (23) all_0_0_0 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_1_1) = v1 & in(v0, all_0_6_6) = 0) % 4.26/1.78 | % 4.26/1.78 +-Applying beta-rule and splitting (23), into two cases. % 4.26/1.78 |-Branch one: % 4.26/1.78 | (24) all_0_0_0 = 0 % 4.26/1.78 | % 4.26/1.78 | Equations (24) can reduce 20 to: % 4.26/1.78 | (25) $false % 4.26/1.78 | % 4.26/1.78 |-The branch is then unsatisfiable % 4.26/1.78 |-Branch two: % 4.26/1.78 | (20) ~ (all_0_0_0 = 0) % 4.26/1.78 | (27) ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_1_1) = v1 & in(v0, all_0_6_6) = 0) % 4.26/1.78 | % 4.26/1.78 | Instantiating (27) with all_26_0_9, all_26_1_10 yields: % 4.26/1.78 | (28) ~ (all_26_0_9 = 0) & in(all_26_1_10, all_0_1_1) = all_26_0_9 & in(all_26_1_10, all_0_6_6) = 0 % 4.26/1.78 | % 4.26/1.78 | Applying alpha-rule on (28) yields: % 4.26/1.78 | (29) ~ (all_26_0_9 = 0) % 4.26/1.78 | (30) in(all_26_1_10, all_0_1_1) = all_26_0_9 % 4.26/1.79 | (31) in(all_26_1_10, all_0_6_6) = 0 % 4.26/1.79 | % 4.26/1.79 | Instantiating formula (12) with all_0_4_4, all_0_6_6, 0, all_0_3_3 and discharging atoms in(all_0_4_4, all_0_6_6) = all_0_3_3, yields: % 4.26/1.79 | (32) all_0_3_3 = 0 | ~ (in(all_0_4_4, all_0_6_6) = 0) % 4.26/1.79 | % 4.26/1.79 | Instantiating formula (13) with all_26_1_10, all_0_5_5, all_0_6_6 and discharging atoms subset(all_0_6_6, all_0_5_5) = 0, in(all_26_1_10, all_0_6_6) = 0, yields: % 4.26/1.79 | (33) in(all_26_1_10, all_0_5_5) = 0 % 4.26/1.79 | % 4.26/1.79 | Instantiating formula (2) with 0, all_26_1_10, all_0_1_1, all_0_2_2, all_0_5_5 and discharging atoms set_difference(all_0_5_5, all_0_2_2) = all_0_1_1, in(all_26_1_10, all_0_5_5) = 0, yields: % 4.26/1.79 | (34) ? [v0] : ? [v1] : (in(all_26_1_10, all_0_1_1) = v0 & in(all_26_1_10, all_0_2_2) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 4.26/1.79 | % 4.26/1.79 | Instantiating formula (9) with all_26_1_10, all_0_1_1, all_0_2_2, all_0_5_5 and discharging atoms set_difference(all_0_5_5, all_0_2_2) = all_0_1_1, in(all_26_1_10, all_0_5_5) = 0, yields: % 4.26/1.79 | (35) ? [v0] : ? [v1] : (in(all_26_1_10, all_0_1_1) = v1 & in(all_26_1_10, all_0_2_2) = v0 & (v1 = 0 | v0 = 0)) % 4.26/1.79 | % 4.26/1.79 | Instantiating (35) with all_47_0_13, all_47_1_14 yields: % 4.26/1.79 | (36) in(all_26_1_10, all_0_1_1) = all_47_0_13 & in(all_26_1_10, all_0_2_2) = all_47_1_14 & (all_47_0_13 = 0 | all_47_1_14 = 0) % 4.26/1.79 | % 4.26/1.79 | Applying alpha-rule on (36) yields: % 4.26/1.79 | (37) in(all_26_1_10, all_0_1_1) = all_47_0_13 % 4.26/1.79 | (38) in(all_26_1_10, all_0_2_2) = all_47_1_14 % 4.26/1.79 | (39) all_47_0_13 = 0 | all_47_1_14 = 0 % 4.26/1.79 | % 4.26/1.79 | Instantiating (34) with all_49_0_15, all_49_1_16 yields: % 4.26/1.79 | (40) in(all_26_1_10, all_0_1_1) = all_49_1_16 & in(all_26_1_10, all_0_2_2) = all_49_0_15 & ( ~ (all_49_0_15 = 0) | ~ (all_49_1_16 = 0)) % 4.26/1.79 | % 4.26/1.79 | Applying alpha-rule on (40) yields: % 4.26/1.79 | (41) in(all_26_1_10, all_0_1_1) = all_49_1_16 % 4.26/1.79 | (42) in(all_26_1_10, all_0_2_2) = all_49_0_15 % 4.26/1.79 | (43) ~ (all_49_0_15 = 0) | ~ (all_49_1_16 = 0) % 4.26/1.79 | % 4.26/1.79 | Instantiating formula (12) with all_26_1_10, all_0_1_1, all_49_1_16, all_26_0_9 and discharging atoms in(all_26_1_10, all_0_1_1) = all_49_1_16, in(all_26_1_10, all_0_1_1) = all_26_0_9, yields: % 4.26/1.79 | (44) all_49_1_16 = all_26_0_9 % 4.26/1.79 | % 4.26/1.79 | Instantiating formula (12) with all_26_1_10, all_0_1_1, all_47_0_13, all_49_1_16 and discharging atoms in(all_26_1_10, all_0_1_1) = all_49_1_16, in(all_26_1_10, all_0_1_1) = all_47_0_13, yields: % 4.26/1.79 | (45) all_49_1_16 = all_47_0_13 % 4.26/1.79 | % 4.26/1.79 | Instantiating formula (17) with all_26_1_10, all_0_2_2, all_0_4_4 and discharging atoms singleton(all_0_4_4) = all_0_2_2, yields: % 4.26/1.79 | (46) all_26_1_10 = all_0_4_4 | ~ (in(all_26_1_10, all_0_2_2) = 0) % 4.26/1.79 | % 4.26/1.79 | Instantiating formula (12) with all_26_1_10, all_0_2_2, all_47_1_14, all_49_0_15 and discharging atoms in(all_26_1_10, all_0_2_2) = all_49_0_15, in(all_26_1_10, all_0_2_2) = all_47_1_14, yields: % 4.26/1.79 | (47) all_49_0_15 = all_47_1_14 % 4.26/1.79 | % 4.26/1.79 | Combining equations (45,44) yields a new equation: % 4.26/1.79 | (48) all_47_0_13 = all_26_0_9 % 4.26/1.79 | % 4.26/1.79 | Simplifying 48 yields: % 4.26/1.79 | (49) all_47_0_13 = all_26_0_9 % 4.26/1.79 | % 4.26/1.79 | From (47) and (42) follows: % 4.26/1.79 | (38) in(all_26_1_10, all_0_2_2) = all_47_1_14 % 4.26/1.79 | % 4.26/1.79 +-Applying beta-rule and splitting (39), into two cases. % 4.26/1.79 |-Branch one: % 4.26/1.79 | (51) all_47_0_13 = 0 % 4.26/1.79 | % 4.26/1.79 | Combining equations (51,49) yields a new equation: % 4.26/1.79 | (52) all_26_0_9 = 0 % 4.26/1.79 | % 4.26/1.79 | Equations (52) can reduce 29 to: % 4.26/1.79 | (25) $false % 4.26/1.79 | % 4.26/1.79 |-The branch is then unsatisfiable % 4.26/1.79 |-Branch two: % 4.26/1.79 | (54) ~ (all_47_0_13 = 0) % 4.26/1.79 | (55) all_47_1_14 = 0 % 4.26/1.79 | % 4.26/1.79 | From (55) and (38) follows: % 4.26/1.79 | (56) in(all_26_1_10, all_0_2_2) = 0 % 4.26/1.79 | % 4.26/1.79 +-Applying beta-rule and splitting (46), into two cases. % 4.26/1.79 |-Branch one: % 4.26/1.79 | (57) ~ (in(all_26_1_10, all_0_2_2) = 0) % 4.26/1.79 | % 4.26/1.79 | Using (56) and (57) yields: % 4.26/1.79 | (58) $false % 4.26/1.79 | % 4.26/1.79 |-The branch is then unsatisfiable % 4.26/1.79 |-Branch two: % 4.26/1.79 | (56) in(all_26_1_10, all_0_2_2) = 0 % 4.26/1.79 | (60) all_26_1_10 = all_0_4_4 % 4.26/1.79 | % 4.26/1.79 | From (60) and (31) follows: % 4.26/1.79 | (61) in(all_0_4_4, all_0_6_6) = 0 % 4.26/1.79 | % 4.26/1.79 +-Applying beta-rule and splitting (32), into two cases. % 4.26/1.79 |-Branch one: % 4.26/1.79 | (62) ~ (in(all_0_4_4, all_0_6_6) = 0) % 4.26/1.80 | % 4.26/1.80 | Using (61) and (62) yields: % 4.26/1.80 | (58) $false % 4.26/1.80 | % 4.26/1.80 |-The branch is then unsatisfiable % 4.26/1.80 |-Branch two: % 4.26/1.80 | (61) in(all_0_4_4, all_0_6_6) = 0 % 4.26/1.80 | (65) all_0_3_3 = 0 % 4.26/1.80 | % 4.26/1.80 | Equations (65) can reduce 6 to: % 4.26/1.80 | (25) $false % 4.26/1.80 | % 4.26/1.80 |-The branch is then unsatisfiable % 4.26/1.80 % SZS output end Proof for theBenchmark % 4.26/1.80 % 4.26/1.80 1204ms %------------------------------------------------------------------------------