%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU120+2 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n028.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 08:46:42 EDT 2022 % Result : Theorem 3.30s 1.54s % Output : Proof 4.78s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU120+2 : TPTP v8.1.0. Released v3.3.0. % 0.00/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.33 % Computer : n028.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 600 % 0.13/0.33 % DateTime : Sun Jun 19 13:34:00 EDT 2022 % 0.13/0.33 % CPUTime : % 0.56/0.60 ____ _ % 0.56/0.60 ___ / __ \_____(_)___ ________ __________ % 0.56/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.56/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.56/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.56/0.60 % 0.56/0.60 A Theorem Prover for First-Order Logic % 0.56/0.61 (ePrincess v.1.0) % 0.56/0.61 % 0.56/0.61 (c) Philipp Rümmer, 2009-2015 % 0.56/0.61 (c) Peter Backeman, 2014-2015 % 0.56/0.61 (contributions by Angelo Brillout, Peter Baumgartner) % 0.56/0.61 Free software under GNU Lesser General Public License (LGPL). % 0.56/0.61 Bug reports to peter@backeman.se % 0.56/0.61 % 0.56/0.61 For more information, visit http://user.uu.se/~petba168/breu/ % 0.56/0.61 % 0.56/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.71/0.68 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.49/0.97 Prover 0: Preprocessing ... % 1.83/1.13 Prover 0: Warning: ignoring some quantifiers % 1.83/1.15 Prover 0: Constructing countermodel ... % 2.56/1.35 Prover 0: gave up % 2.56/1.35 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 2.56/1.37 Prover 1: Preprocessing ... % 2.81/1.44 Prover 1: Warning: ignoring some quantifiers % 2.81/1.45 Prover 1: Constructing countermodel ... % 3.30/1.54 Prover 1: proved (189ms) % 3.30/1.54 % 3.30/1.54 No countermodel exists, formula is valid % 3.30/1.54 % SZS status Theorem for theBenchmark % 3.30/1.54 % 3.30/1.54 Generating proof ... Warning: ignoring some quantifiers % 4.43/1.83 found it (size 61) % 4.43/1.83 % 4.43/1.83 % SZS output start Proof for theBenchmark % 4.43/1.83 Assumed formulas after preprocessing and simplification: % 4.43/1.83 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ( ~ (v7 = 0) & empty(v8) = 0 & empty(v6) = v7 & empty(empty_set) = 0 & disjoint(v0, v1) = v2 & set_intersection2(v0, v1) = v3 & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (set_intersection2(v9, v10) = v11) | ~ (in(v12, v9) = v13) | ? [v14] : ? [v15] : (in(v12, v11) = v14 & in(v12, v10) = v15 & ( ~ (v14 = 0) | (v15 = 0 & v13 = 0)))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (disjoint(v12, v11) = v10) | ~ (disjoint(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (set_intersection2(v12, v11) = v10) | ~ (set_intersection2(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (in(v12, v11) = v10) | ~ (in(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (set_intersection2(v9, v10) = v11) | ~ (in(v12, v9) = 0) | ? [v13] : ? [v14] : (in(v12, v11) = v14 & in(v12, v10) = v13 & ( ~ (v13 = 0) | v14 = 0))) & ? [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v9 | ~ (set_intersection2(v10, v11) = v12) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : (in(v13, v11) = v16 & in(v13, v10) = v15 & in(v13, v9) = v14 & ( ~ (v16 = 0) | ~ (v15 = 0) | ~ (v14 = 0)) & (v14 = 0 | (v16 = 0 & v15 = 0)))) & ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (disjoint(v9, v10) = v11) | ? [v12] : ( ~ (v12 = empty_set) & set_intersection2(v9, v10) = v12)) & ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (disjoint(v9, v10) = v11) | ? [v12] : (in(v12, v10) = 0 & in(v12, v9) = 0)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (empty(v11) = v10) | ~ (empty(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (disjoint(v9, v10) = 0) | ~ (in(v11, v9) = 0) | ? [v12] : ( ~ (v12 = 0) & in(v11, v10) = v12)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_intersection2(v9, v10) = v11) | set_intersection2(v10, v9) = v11) & ! [v9] : ! [v10] : (v10 = v9 | ~ (set_intersection2(v9, v9) = v10)) & ! [v9] : ! [v10] : ( ~ (disjoint(v9, v10) = 0) | disjoint(v10, v9) = 0) & ! [v9] : ! [v10] : ( ~ (disjoint(v9, v10) = 0) | set_intersection2(v9, v10) = empty_set) & ! [v9] : ! [v10] : ( ~ (in(v9, v10) = 0) | ? [v11] : ( ~ (v11 = 0) & in(v10, v9) = v11)) & ! [v9] : ~ (in(v9, empty_set) = 0) & ? [v9] : (v9 = empty_set | ? [v10] : in(v10, v9) = 0) & ((v5 = 0 & v2 = 0 & in(v4, v3) = 0) | ( ~ (v2 = 0) & ! [v9] : ~ (in(v9, v3) = 0)))) % 4.43/1.86 | 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, all_0_8_8 yields: % 4.43/1.86 | (1) ~ (all_0_1_1 = 0) & empty(all_0_0_0) = 0 & empty(all_0_2_2) = all_0_1_1 & empty(empty_set) = 0 & disjoint(all_0_8_8, all_0_7_7) = all_0_6_6 & set_intersection2(all_0_8_8, all_0_7_7) = all_0_5_5 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v0) = 0) | ? [v4] : ? [v5] : (in(v3, v2) = v5 & in(v3, v1) = v4 & ( ~ (v4 = 0) | v5 = 0))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_intersection2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0)) & (v5 = 0 | (v7 = 0 & v6 = 0)))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ( ~ (v3 = empty_set) & set_intersection2(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : (in(v3, v1) = 0 & in(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v0, v1) = 0) | ~ (in(v2, v0) = 0) | ? [v3] : ( ~ (v3 = 0) & in(v2, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | disjoint(v1, v0) = 0) & ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | set_intersection2(v0, v1) = empty_set) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) & ! [v0] : ~ (in(v0, empty_set) = 0) & ? [v0] : (v0 = empty_set | ? [v1] : in(v1, v0) = 0) & ((all_0_3_3 = 0 & all_0_6_6 = 0 & in(all_0_4_4, all_0_5_5) = 0) | ( ~ (all_0_6_6 = 0) & ! [v0] : ~ (in(v0, all_0_5_5) = 0))) % 4.43/1.87 | % 4.43/1.87 | Applying alpha-rule on (1) yields: % 4.43/1.87 | (2) empty(all_0_2_2) = all_0_1_1 % 4.43/1.87 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 4.43/1.87 | (4) set_intersection2(all_0_8_8, all_0_7_7) = all_0_5_5 % 4.43/1.87 | (5) ? [v0] : (v0 = empty_set | ? [v1] : in(v1, v0) = 0) % 4.43/1.87 | (6) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_intersection2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0)) & (v5 = 0 | (v7 = 0 & v6 = 0)))) % 4.43/1.87 | (7) ~ (all_0_1_1 = 0) % 4.43/1.87 | (8) empty(all_0_0_0) = 0 % 4.43/1.87 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = 0)))) % 4.43/1.87 | (10) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | disjoint(v1, v0) = 0) % 4.43/1.87 | (11) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1)) % 4.43/1.87 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v0, v1) = 0) | ~ (in(v2, v0) = 0) | ? [v3] : ( ~ (v3 = 0) & in(v2, v1) = v3)) % 4.43/1.87 | (13) disjoint(all_0_8_8, all_0_7_7) = all_0_6_6 % 4.43/1.87 | (14) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ( ~ (v3 = empty_set) & set_intersection2(v0, v1) = v3)) % 4.43/1.88 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) % 4.43/1.88 | (16) (all_0_3_3 = 0 & all_0_6_6 = 0 & in(all_0_4_4, all_0_5_5) = 0) | ( ~ (all_0_6_6 = 0) & ! [v0] : ~ (in(v0, all_0_5_5) = 0)) % 4.43/1.88 | (17) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) % 4.43/1.88 | (18) ! [v0] : ~ (in(v0, empty_set) = 0) % 4.43/1.88 | (19) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : (in(v3, v1) = 0 & in(v3, v0) = 0)) % 4.43/1.88 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0)) % 4.43/1.88 | (21) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) % 4.43/1.88 | (22) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | set_intersection2(v0, v1) = empty_set) % 4.43/1.88 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v0) = 0) | ? [v4] : ? [v5] : (in(v3, v2) = v5 & in(v3, v1) = v4 & ( ~ (v4 = 0) | v5 = 0))) % 4.43/1.88 | (24) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) % 4.43/1.88 | (25) empty(empty_set) = 0 % 4.43/1.88 | % 4.43/1.88 | Instantiating formula (22) with all_0_7_7, all_0_8_8 yields: % 4.43/1.88 | (26) ~ (disjoint(all_0_8_8, all_0_7_7) = 0) | set_intersection2(all_0_8_8, all_0_7_7) = empty_set % 4.43/1.88 | % 4.43/1.88 | Instantiating formula (14) with all_0_6_6, all_0_7_7, all_0_8_8 and discharging atoms disjoint(all_0_8_8, all_0_7_7) = all_0_6_6, yields: % 4.43/1.88 | (27) all_0_6_6 = 0 | ? [v0] : ( ~ (v0 = empty_set) & set_intersection2(all_0_8_8, all_0_7_7) = v0) % 4.43/1.88 | % 4.43/1.88 | Instantiating formula (19) with all_0_6_6, all_0_7_7, all_0_8_8 and discharging atoms disjoint(all_0_8_8, all_0_7_7) = all_0_6_6, yields: % 4.43/1.88 | (28) all_0_6_6 = 0 | ? [v0] : (in(v0, all_0_7_7) = 0 & in(v0, all_0_8_8) = 0) % 4.43/1.88 | % 4.43/1.88 | Instantiating formula (17) with all_0_5_5, all_0_7_7, all_0_8_8 and discharging atoms set_intersection2(all_0_8_8, all_0_7_7) = all_0_5_5, yields: % 4.43/1.88 | (29) set_intersection2(all_0_7_7, all_0_8_8) = all_0_5_5 % 4.43/1.88 | % 4.43/1.88 +-Applying beta-rule and splitting (16), into two cases. % 4.43/1.88 |-Branch one: % 4.43/1.88 | (30) all_0_3_3 = 0 & all_0_6_6 = 0 & in(all_0_4_4, all_0_5_5) = 0 % 4.43/1.88 | % 4.43/1.88 | Applying alpha-rule on (30) yields: % 4.43/1.88 | (31) all_0_3_3 = 0 % 4.43/1.88 | (32) all_0_6_6 = 0 % 4.43/1.88 | (33) in(all_0_4_4, all_0_5_5) = 0 % 4.43/1.88 | % 4.43/1.88 | From (32) and (13) follows: % 4.43/1.88 | (34) disjoint(all_0_8_8, all_0_7_7) = 0 % 4.43/1.88 | % 4.43/1.88 +-Applying beta-rule and splitting (26), into two cases. % 4.43/1.88 |-Branch one: % 4.43/1.88 | (35) set_intersection2(all_0_8_8, all_0_7_7) = empty_set % 4.43/1.88 | % 4.43/1.88 | Instantiating formula (15) with all_0_8_8, all_0_7_7, empty_set, all_0_5_5 and discharging atoms set_intersection2(all_0_8_8, all_0_7_7) = all_0_5_5, set_intersection2(all_0_8_8, all_0_7_7) = empty_set, yields: % 4.43/1.88 | (36) all_0_5_5 = empty_set % 4.43/1.88 | % 4.43/1.88 | Instantiating formula (18) with all_0_4_4 yields: % 4.43/1.88 | (37) ~ (in(all_0_4_4, empty_set) = 0) % 4.43/1.88 | % 4.43/1.88 | From (36) and (33) follows: % 4.43/1.88 | (38) in(all_0_4_4, empty_set) = 0 % 4.43/1.89 | % 4.43/1.89 | Using (38) and (37) yields: % 4.43/1.89 | (39) $false % 4.43/1.89 | % 4.43/1.89 |-The branch is then unsatisfiable % 4.43/1.89 |-Branch two: % 4.43/1.89 | (40) ~ (set_intersection2(all_0_8_8, all_0_7_7) = empty_set) % 4.43/1.89 | (41) ~ (disjoint(all_0_8_8, all_0_7_7) = 0) % 4.43/1.89 | % 4.43/1.89 | Using (34) and (41) yields: % 4.43/1.89 | (39) $false % 4.43/1.89 | % 4.43/1.89 |-The branch is then unsatisfiable % 4.43/1.89 |-Branch two: % 4.43/1.89 | (43) ~ (all_0_6_6 = 0) & ! [v0] : ~ (in(v0, all_0_5_5) = 0) % 4.43/1.89 | % 4.43/1.89 | Applying alpha-rule on (43) yields: % 4.43/1.89 | (44) ~ (all_0_6_6 = 0) % 4.43/1.89 | (45) ! [v0] : ~ (in(v0, all_0_5_5) = 0) % 4.43/1.89 | % 4.43/1.89 +-Applying beta-rule and splitting (27), into two cases. % 4.43/1.89 |-Branch one: % 4.43/1.89 | (32) all_0_6_6 = 0 % 4.43/1.89 | % 4.43/1.89 | Equations (32) can reduce 44 to: % 4.43/1.89 | (47) $false % 4.43/1.89 | % 4.43/1.89 |-The branch is then unsatisfiable % 4.43/1.89 |-Branch two: % 4.43/1.89 | (44) ~ (all_0_6_6 = 0) % 4.43/1.89 | (49) ? [v0] : ( ~ (v0 = empty_set) & set_intersection2(all_0_8_8, all_0_7_7) = v0) % 4.43/1.89 | % 4.43/1.89 | Instantiating (49) with all_24_0_11 yields: % 4.43/1.89 | (50) ~ (all_24_0_11 = empty_set) & set_intersection2(all_0_8_8, all_0_7_7) = all_24_0_11 % 4.43/1.89 | % 4.43/1.89 | Applying alpha-rule on (50) yields: % 4.43/1.89 | (51) ~ (all_24_0_11 = empty_set) % 4.43/1.89 | (52) set_intersection2(all_0_8_8, all_0_7_7) = all_24_0_11 % 4.43/1.89 | % 4.43/1.89 +-Applying beta-rule and splitting (28), into two cases. % 4.43/1.89 |-Branch one: % 4.43/1.89 | (32) all_0_6_6 = 0 % 4.43/1.89 | % 4.43/1.89 | Equations (32) can reduce 44 to: % 4.43/1.89 | (47) $false % 4.43/1.89 | % 4.43/1.89 |-The branch is then unsatisfiable % 4.43/1.89 |-Branch two: % 4.43/1.89 | (44) ~ (all_0_6_6 = 0) % 4.43/1.89 | (56) ? [v0] : (in(v0, all_0_7_7) = 0 & in(v0, all_0_8_8) = 0) % 4.43/1.89 | % 4.43/1.89 | Instantiating (56) with all_30_0_12 yields: % 4.43/1.89 | (57) in(all_30_0_12, all_0_7_7) = 0 & in(all_30_0_12, all_0_8_8) = 0 % 4.43/1.89 | % 4.43/1.89 | Applying alpha-rule on (57) yields: % 4.43/1.89 | (58) in(all_30_0_12, all_0_7_7) = 0 % 4.43/1.89 | (59) in(all_30_0_12, all_0_8_8) = 0 % 4.43/1.89 | % 4.43/1.89 | Instantiating formula (15) with all_0_8_8, all_0_7_7, all_24_0_11, all_0_5_5 and discharging atoms set_intersection2(all_0_8_8, all_0_7_7) = all_24_0_11, set_intersection2(all_0_8_8, all_0_7_7) = all_0_5_5, yields: % 4.43/1.89 | (60) all_24_0_11 = all_0_5_5 % 4.43/1.89 | % 4.43/1.89 | Instantiating formula (45) with all_30_0_12 yields: % 4.43/1.89 | (61) ~ (in(all_30_0_12, all_0_5_5) = 0) % 4.43/1.89 | % 4.43/1.89 | From (60) and (52) follows: % 4.43/1.89 | (4) set_intersection2(all_0_8_8, all_0_7_7) = all_0_5_5 % 4.43/1.89 | % 4.43/1.89 | Instantiating formula (9) with 0, all_30_0_12, all_0_5_5, all_0_8_8, all_0_7_7 and discharging atoms set_intersection2(all_0_7_7, all_0_8_8) = all_0_5_5, in(all_30_0_12, all_0_7_7) = 0, yields: % 4.43/1.89 | (63) ? [v0] : ? [v1] : (in(all_30_0_12, all_0_5_5) = v0 & in(all_30_0_12, all_0_8_8) = v1 & ( ~ (v0 = 0) | v1 = 0)) % 4.43/1.89 | % 4.43/1.89 | Instantiating formula (23) with all_30_0_12, all_0_5_5, all_0_8_8, all_0_7_7 and discharging atoms set_intersection2(all_0_7_7, all_0_8_8) = all_0_5_5, in(all_30_0_12, all_0_7_7) = 0, yields: % 4.43/1.89 | (64) ? [v0] : ? [v1] : (in(all_30_0_12, all_0_5_5) = v1 & in(all_30_0_12, all_0_8_8) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 4.43/1.89 | % 4.43/1.89 | Instantiating formula (9) with 0, all_30_0_12, all_0_5_5, all_0_7_7, all_0_8_8 and discharging atoms set_intersection2(all_0_8_8, all_0_7_7) = all_0_5_5, in(all_30_0_12, all_0_8_8) = 0, yields: % 4.43/1.89 | (65) ? [v0] : ? [v1] : (in(all_30_0_12, all_0_5_5) = v0 & in(all_30_0_12, all_0_7_7) = v1 & ( ~ (v0 = 0) | v1 = 0)) % 4.43/1.89 | % 4.43/1.89 | Instantiating formula (23) with all_30_0_12, all_0_5_5, all_0_7_7, all_0_8_8 and discharging atoms set_intersection2(all_0_8_8, all_0_7_7) = all_0_5_5, in(all_30_0_12, all_0_8_8) = 0, yields: % 4.43/1.89 | (66) ? [v0] : ? [v1] : (in(all_30_0_12, all_0_5_5) = v1 & in(all_30_0_12, all_0_7_7) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 4.43/1.89 | % 4.43/1.89 | Instantiating (65) with all_55_0_14, all_55_1_15 yields: % 4.43/1.89 | (67) in(all_30_0_12, all_0_5_5) = all_55_1_15 & in(all_30_0_12, all_0_7_7) = all_55_0_14 & ( ~ (all_55_1_15 = 0) | all_55_0_14 = 0) % 4.43/1.89 | % 4.43/1.89 | Applying alpha-rule on (67) yields: % 4.43/1.89 | (68) in(all_30_0_12, all_0_5_5) = all_55_1_15 % 4.43/1.90 | (69) in(all_30_0_12, all_0_7_7) = all_55_0_14 % 4.43/1.90 | (70) ~ (all_55_1_15 = 0) | all_55_0_14 = 0 % 4.43/1.90 | % 4.43/1.90 | Instantiating (64) with all_57_0_16, all_57_1_17 yields: % 4.43/1.90 | (71) in(all_30_0_12, all_0_5_5) = all_57_0_16 & in(all_30_0_12, all_0_8_8) = all_57_1_17 & ( ~ (all_57_1_17 = 0) | all_57_0_16 = 0) % 4.43/1.90 | % 4.43/1.90 | Applying alpha-rule on (71) yields: % 4.43/1.90 | (72) in(all_30_0_12, all_0_5_5) = all_57_0_16 % 4.43/1.90 | (73) in(all_30_0_12, all_0_8_8) = all_57_1_17 % 4.43/1.90 | (74) ~ (all_57_1_17 = 0) | all_57_0_16 = 0 % 4.43/1.90 | % 4.43/1.90 | Instantiating (63) with all_59_0_18, all_59_1_19 yields: % 4.43/1.90 | (75) in(all_30_0_12, all_0_5_5) = all_59_1_19 & in(all_30_0_12, all_0_8_8) = all_59_0_18 & ( ~ (all_59_1_19 = 0) | all_59_0_18 = 0) % 4.78/1.90 | % 4.78/1.90 | Applying alpha-rule on (75) yields: % 4.78/1.90 | (76) in(all_30_0_12, all_0_5_5) = all_59_1_19 % 4.78/1.90 | (77) in(all_30_0_12, all_0_8_8) = all_59_0_18 % 4.78/1.90 | (78) ~ (all_59_1_19 = 0) | all_59_0_18 = 0 % 4.78/1.90 | % 4.78/1.90 | Instantiating (66) with all_63_0_21, all_63_1_22 yields: % 4.78/1.90 | (79) in(all_30_0_12, all_0_5_5) = all_63_0_21 & in(all_30_0_12, all_0_7_7) = all_63_1_22 & ( ~ (all_63_1_22 = 0) | all_63_0_21 = 0) % 4.78/1.90 | % 4.78/1.90 | Applying alpha-rule on (79) yields: % 4.78/1.90 | (80) in(all_30_0_12, all_0_5_5) = all_63_0_21 % 4.78/1.90 | (81) in(all_30_0_12, all_0_7_7) = all_63_1_22 % 4.78/1.90 | (82) ~ (all_63_1_22 = 0) | all_63_0_21 = 0 % 4.78/1.90 | % 4.78/1.90 | Instantiating formula (3) with all_30_0_12, all_0_5_5, all_59_1_19, all_63_0_21 and discharging atoms in(all_30_0_12, all_0_5_5) = all_63_0_21, in(all_30_0_12, all_0_5_5) = all_59_1_19, yields: % 4.78/1.90 | (83) all_63_0_21 = all_59_1_19 % 4.78/1.90 | % 4.78/1.90 | Instantiating formula (3) with all_30_0_12, all_0_5_5, all_57_0_16, all_59_1_19 and discharging atoms in(all_30_0_12, all_0_5_5) = all_59_1_19, in(all_30_0_12, all_0_5_5) = all_57_0_16, yields: % 4.78/1.90 | (84) all_59_1_19 = all_57_0_16 % 4.78/1.90 | % 4.78/1.90 | Using (72) and (61) yields: % 4.78/1.90 | (85) ~ (all_57_0_16 = 0) % 4.78/1.90 | % 4.78/1.90 | Instantiating formula (3) with all_30_0_12, all_0_5_5, all_55_1_15, all_63_0_21 and discharging atoms in(all_30_0_12, all_0_5_5) = all_63_0_21, in(all_30_0_12, all_0_5_5) = all_55_1_15, yields: % 4.78/1.90 | (86) all_63_0_21 = all_55_1_15 % 4.78/1.90 | % 4.78/1.90 | Instantiating formula (3) with all_30_0_12, all_0_8_8, all_59_0_18, 0 and discharging atoms in(all_30_0_12, all_0_8_8) = all_59_0_18, in(all_30_0_12, all_0_8_8) = 0, yields: % 4.78/1.90 | (87) all_59_0_18 = 0 % 4.78/1.90 | % 4.78/1.90 | Instantiating formula (3) with all_30_0_12, all_0_8_8, all_57_1_17, all_59_0_18 and discharging atoms in(all_30_0_12, all_0_8_8) = all_59_0_18, in(all_30_0_12, all_0_8_8) = all_57_1_17, yields: % 4.78/1.90 | (88) all_59_0_18 = all_57_1_17 % 4.78/1.90 | % 4.78/1.90 | Combining equations (83,86) yields a new equation: % 4.78/1.90 | (89) all_59_1_19 = all_55_1_15 % 4.78/1.90 | % 4.78/1.90 | Simplifying 89 yields: % 4.78/1.90 | (90) all_59_1_19 = all_55_1_15 % 4.78/1.90 | % 4.78/1.90 | Combining equations (87,88) yields a new equation: % 4.78/1.90 | (91) all_57_1_17 = 0 % 4.78/1.90 | % 4.78/1.90 | Combining equations (90,84) yields a new equation: % 4.78/1.90 | (92) all_57_0_16 = all_55_1_15 % 4.78/1.90 | % 4.78/1.90 | Equations (92) can reduce 85 to: % 4.78/1.90 | (93) ~ (all_55_1_15 = 0) % 4.78/1.90 | % 4.78/1.90 +-Applying beta-rule and splitting (74), into two cases. % 4.78/1.90 |-Branch one: % 4.78/1.90 | (94) ~ (all_57_1_17 = 0) % 4.78/1.90 | % 4.78/1.90 | Equations (91) can reduce 94 to: % 4.78/1.90 | (47) $false % 4.78/1.90 | % 4.78/1.90 |-The branch is then unsatisfiable % 4.78/1.90 |-Branch two: % 4.78/1.90 | (91) all_57_1_17 = 0 % 4.78/1.90 | (97) all_57_0_16 = 0 % 4.78/1.90 | % 4.78/1.90 | Combining equations (92,97) yields a new equation: % 4.78/1.90 | (98) all_55_1_15 = 0 % 4.78/1.90 | % 4.78/1.90 | Simplifying 98 yields: % 4.78/1.90 | (99) all_55_1_15 = 0 % 4.78/1.90 | % 4.78/1.91 | Equations (99) can reduce 93 to: % 4.78/1.91 | (47) $false % 4.78/1.91 | % 4.78/1.91 |-The branch is then unsatisfiable % 4.78/1.91 % SZS output end Proof for theBenchmark % 4.78/1.91 % 4.78/1.91 1282ms %------------------------------------------------------------------------------