%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET621+3 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n005.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 00:20:54 EDT 2022 % Result : Theorem 2.44s 1.25s % Output : Proof 3.78s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SET621+3 : TPTP v8.1.0. Released v2.2.0. % 0.06/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.33 % Computer : n005.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 : Sat Jul 9 18:51:22 EDT 2022 % 0.13/0.33 % CPUTime : % 0.51/0.57 ____ _ % 0.51/0.57 ___ / __ \_____(_)___ ________ __________ % 0.51/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.51/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.51/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.51/0.57 % 0.51/0.57 A Theorem Prover for First-Order Logic % 0.51/0.57 (ePrincess v.1.0) % 0.51/0.57 % 0.51/0.57 (c) Philipp Rümmer, 2009-2015 % 0.51/0.57 (c) Peter Backeman, 2014-2015 % 0.51/0.57 (contributions by Angelo Brillout, Peter Baumgartner) % 0.51/0.57 Free software under GNU Lesser General Public License (LGPL). % 0.51/0.57 Bug reports to peter@backeman.se % 0.51/0.57 % 0.51/0.57 For more information, visit http://user.uu.se/~petba168/breu/ % 0.51/0.57 % 0.51/0.57 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.51/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.32/0.89 Prover 0: Preprocessing ... % 1.89/1.09 Prover 0: Warning: ignoring some quantifiers % 1.89/1.11 Prover 0: Constructing countermodel ... % 2.44/1.25 Prover 0: proved (632ms) % 2.44/1.25 % 2.44/1.25 No countermodel exists, formula is valid % 2.44/1.25 % SZS status Theorem for theBenchmark % 2.44/1.25 % 2.44/1.25 Generating proof ... Warning: ignoring some quantifiers % 3.62/1.54 found it (size 23) % 3.62/1.54 % 3.62/1.54 % SZS output start Proof for theBenchmark % 3.62/1.54 Assumed formulas after preprocessing and simplification: % 3.62/1.54 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ( ~ (v9 = v4) & difference(v3, v2) = v4 & difference(v1, v7) = v8 & difference(v0, v5) = v6 & union(v6, v8) = v9 & union(v1, v2) = v5 & union(v0, v2) = v7 & symmetric_difference(v0, v1) = v3 & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (difference(v11, v12) = v14) | ~ (difference(v10, v12) = v13) | ~ (union(v13, v14) = v15) | ? [v16] : (difference(v16, v12) = v15 & union(v10, v11) = v16)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (difference(v13, v12) = v14) | ~ (difference(v10, v11) = v13) | ? [v15] : (difference(v10, v15) = v14 & union(v11, v12) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (difference(v13, v12) = v14) | ~ (union(v10, v11) = v13) | ? [v15] : ? [v16] : (difference(v11, v12) = v16 & difference(v10, v12) = v15 & union(v15, v16) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (difference(v11, v10) = v13) | ~ (difference(v10, v11) = v12) | ~ (union(v12, v13) = v14) | symmetric_difference(v10, v11) = v14) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (difference(v10, v13) = v14) | ~ (union(v11, v12) = v13) | ? [v15] : (difference(v15, v12) = v14 & difference(v10, v11) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (difference(v13, v12) = v11) | ~ (difference(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (union(v13, v12) = v11) | ~ (union(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (symmetric_difference(v13, v12) = v11) | ~ (symmetric_difference(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (difference(v10, v11) = v13) | ~ member(v12, v13) | ~ member(v12, v11)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (difference(v10, v11) = v13) | ~ member(v12, v13) | member(v12, v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (difference(v10, v11) = v13) | ~ member(v12, v10) | member(v12, v13) | member(v12, v11)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (union(v10, v11) = v13) | ~ member(v12, v13) | member(v12, v11) | member(v12, v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (union(v10, v11) = v13) | ~ member(v12, v11) | member(v12, v13)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (union(v10, v11) = v13) | ~ member(v12, v10) | member(v12, v13)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (union(v11, v10) = v12) | union(v10, v11) = v12) & ! [v10] : ! [v11] : ! [v12] : ( ~ (union(v10, v11) = v12) | union(v11, v10) = v12) & ! [v10] : ! [v11] : ! [v12] : ( ~ (symmetric_difference(v11, v10) = v12) | symmetric_difference(v10, v11) = v12) & ! [v10] : ! [v11] : ! [v12] : ( ~ (symmetric_difference(v10, v11) = v12) | symmetric_difference(v11, v10) = v12) & ! [v10] : ! [v11] : ! [v12] : ( ~ (symmetric_difference(v10, v11) = v12) | ? [v13] : ? [v14] : (difference(v11, v10) = v14 & difference(v10, v11) = v13 & union(v13, v14) = v12)) & ! [v10] : ! [v11] : ! [v12] : ( ~ subset(v10, v11) | ~ member(v12, v10) | member(v12, v11)) & ! [v10] : ! [v11] : (v11 = v10 | ~ subset(v11, v10) | ~ subset(v10, v11)) & ? [v10] : ? [v11] : (v11 = v10 | ? [v12] : (( ~ member(v12, v11) | ~ member(v12, v10)) & (member(v12, v11) | member(v12, v10)))) & ? [v10] : ? [v11] : (subset(v10, v11) | ? [v12] : (member(v12, v10) & ~ member(v12, v11))) & ? [v10] : subset(v10, v10)) % 3.78/1.59 | 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, all_0_9_9 yields: % 3.78/1.59 | (1) ~ (all_0_0_0 = all_0_5_5) & difference(all_0_6_6, all_0_7_7) = all_0_5_5 & difference(all_0_8_8, all_0_2_2) = all_0_1_1 & difference(all_0_9_9, all_0_4_4) = all_0_3_3 & union(all_0_3_3, all_0_1_1) = all_0_0_0 & union(all_0_8_8, all_0_7_7) = all_0_4_4 & union(all_0_9_9, all_0_7_7) = all_0_2_2 & symmetric_difference(all_0_9_9, all_0_8_8) = all_0_6_6 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (difference(v1, v2) = v4) | ~ (difference(v0, v2) = v3) | ~ (union(v3, v4) = v5) | ? [v6] : (difference(v6, v2) = v5 & union(v0, v1) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (difference(v3, v2) = v4) | ~ (difference(v0, v1) = v3) | ? [v5] : (difference(v0, v5) = v4 & union(v1, v2) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (difference(v3, v2) = v4) | ~ (union(v0, v1) = v3) | ? [v5] : ? [v6] : (difference(v1, v2) = v6 & difference(v0, v2) = v5 & union(v5, v6) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (difference(v1, v0) = v3) | ~ (difference(v0, v1) = v2) | ~ (union(v2, v3) = v4) | symmetric_difference(v0, v1) = v4) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (difference(v0, v3) = v4) | ~ (union(v1, v2) = v3) | ? [v5] : (difference(v5, v2) = v4 & difference(v0, v1) = v5)) & ! [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 | ~ (symmetric_difference(v3, v2) = v1) | ~ (symmetric_difference(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v0, v1) = v3) | ~ member(v2, v3) | ~ member(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v0, v1) = v3) | ~ member(v2, v3) | member(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v0, v1) = v3) | ~ member(v2, v0) | member(v2, v3) | member(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0, v1) = v3) | ~ member(v2, v3) | member(v2, v1) | member(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0, v1) = v3) | ~ member(v2, v1) | member(v2, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0, v1) = v3) | ~ member(v2, v0) | member(v2, v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v1, v0) = v2) | union(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0, v1) = v2) | union(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (symmetric_difference(v1, v0) = v2) | symmetric_difference(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (symmetric_difference(v0, v1) = v2) | symmetric_difference(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (symmetric_difference(v0, v1) = v2) | ? [v3] : ? [v4] : (difference(v1, v0) = v4 & difference(v0, v1) = v3 & union(v3, v4) = v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ subset(v0, v1) | ~ member(v2, v0) | member(v2, v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v1, v0) | ~ subset(v0, v1)) & ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : (( ~ member(v2, v1) | ~ member(v2, v0)) & (member(v2, v1) | member(v2, v0)))) & ? [v0] : ? [v1] : (subset(v0, v1) | ? [v2] : (member(v2, v0) & ~ member(v2, v1))) & ? [v0] : subset(v0, v0) % 3.78/1.59 | % 3.78/1.59 | Applying alpha-rule on (1) yields: % 3.78/1.59 | (2) ? [v0] : subset(v0, v0) % 3.78/1.59 | (3) ! [v0] : ! [v1] : ! [v2] : ( ~ subset(v0, v1) | ~ member(v2, v0) | member(v2, v1)) % 3.78/1.59 | (4) difference(all_0_6_6, all_0_7_7) = all_0_5_5 % 3.78/1.59 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (difference(v3, v2) = v4) | ~ (difference(v0, v1) = v3) | ? [v5] : (difference(v0, v5) = v4 & union(v1, v2) = v5)) % 3.78/1.60 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) % 3.78/1.60 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (difference(v1, v0) = v3) | ~ (difference(v0, v1) = v2) | ~ (union(v2, v3) = v4) | symmetric_difference(v0, v1) = v4) % 3.78/1.60 | (8) difference(all_0_8_8, all_0_2_2) = all_0_1_1 % 3.78/1.60 | (9) union(all_0_3_3, all_0_1_1) = all_0_0_0 % 3.78/1.60 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v0, v1) = v3) | ~ member(v2, v0) | member(v2, v3) | member(v2, v1)) % 3.78/1.60 | (11) union(all_0_9_9, all_0_7_7) = all_0_2_2 % 3.78/1.60 | (12) symmetric_difference(all_0_9_9, all_0_8_8) = all_0_6_6 % 3.78/1.60 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (difference(v1, v2) = v4) | ~ (difference(v0, v2) = v3) | ~ (union(v3, v4) = v5) | ? [v6] : (difference(v6, v2) = v5 & union(v0, v1) = v6)) % 3.78/1.60 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0, v1) = v3) | ~ member(v2, v3) | member(v2, v1) | member(v2, v0)) % 3.78/1.60 | (15) difference(all_0_9_9, all_0_4_4) = all_0_3_3 % 3.78/1.60 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0, v1) = v3) | ~ member(v2, v1) | member(v2, v3)) % 3.78/1.60 | (17) ! [v0] : ! [v1] : ! [v2] : ( ~ (symmetric_difference(v0, v1) = v2) | symmetric_difference(v1, v0) = v2) % 3.78/1.60 | (18) ! [v0] : ! [v1] : ! [v2] : ( ~ (symmetric_difference(v1, v0) = v2) | symmetric_difference(v0, v1) = v2) % 3.78/1.60 | (19) ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : (( ~ member(v2, v1) | ~ member(v2, v0)) & (member(v2, v1) | member(v2, v0)))) % 3.78/1.60 | (20) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0, v1) = v2) | union(v1, v0) = v2) % 3.78/1.60 | (21) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v1, v0) = v2) | union(v0, v1) = v2) % 3.78/1.60 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v0, v1) = v3) | ~ member(v2, v3) | member(v2, v0)) % 3.78/1.60 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (symmetric_difference(v3, v2) = v1) | ~ (symmetric_difference(v3, v2) = v0)) % 3.78/1.60 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0, v1) = v3) | ~ member(v2, v0) | member(v2, v3)) % 3.78/1.60 | (25) ~ (all_0_0_0 = all_0_5_5) % 3.78/1.60 | (26) ! [v0] : ! [v1] : ! [v2] : ( ~ (symmetric_difference(v0, v1) = v2) | ? [v3] : ? [v4] : (difference(v1, v0) = v4 & difference(v0, v1) = v3 & union(v3, v4) = v2)) % 3.78/1.60 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (difference(v0, v3) = v4) | ~ (union(v1, v2) = v3) | ? [v5] : (difference(v5, v2) = v4 & difference(v0, v1) = v5)) % 3.78/1.60 | (28) ? [v0] : ? [v1] : (subset(v0, v1) | ? [v2] : (member(v2, v0) & ~ member(v2, v1))) % 3.78/1.60 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v0, v1) = v3) | ~ member(v2, v3) | ~ member(v2, v1)) % 3.78/1.60 | (30) union(all_0_8_8, all_0_7_7) = all_0_4_4 % 3.78/1.60 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (difference(v3, v2) = v4) | ~ (union(v0, v1) = v3) | ? [v5] : ? [v6] : (difference(v1, v2) = v6 & difference(v0, v2) = v5 & union(v5, v6) = v4)) % 3.78/1.60 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) % 3.78/1.61 | (33) ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v1, v0) | ~ subset(v0, v1)) % 3.78/1.61 | % 3.78/1.61 | Instantiating formula (27) with all_0_3_3, all_0_4_4, all_0_7_7, all_0_8_8, all_0_9_9 and discharging atoms difference(all_0_9_9, all_0_4_4) = all_0_3_3, union(all_0_8_8, all_0_7_7) = all_0_4_4, yields: % 3.78/1.61 | (34) ? [v0] : (difference(v0, all_0_7_7) = all_0_3_3 & difference(all_0_9_9, all_0_8_8) = v0) % 3.78/1.61 | % 3.78/1.61 | Instantiating formula (27) with all_0_1_1, all_0_2_2, all_0_7_7, all_0_9_9, all_0_8_8 and discharging atoms difference(all_0_8_8, all_0_2_2) = all_0_1_1, union(all_0_9_9, all_0_7_7) = all_0_2_2, yields: % 3.78/1.61 | (35) ? [v0] : (difference(v0, all_0_7_7) = all_0_1_1 & difference(all_0_8_8, all_0_9_9) = v0) % 3.78/1.61 | % 3.78/1.61 | Instantiating formula (26) with all_0_6_6, all_0_8_8, all_0_9_9 and discharging atoms symmetric_difference(all_0_9_9, all_0_8_8) = all_0_6_6, yields: % 3.78/1.61 | (36) ? [v0] : ? [v1] : (difference(all_0_8_8, all_0_9_9) = v1 & difference(all_0_9_9, all_0_8_8) = v0 & union(v0, v1) = all_0_6_6) % 3.78/1.61 | % 3.78/1.61 | Instantiating (34) with all_13_0_15 yields: % 3.78/1.61 | (37) difference(all_13_0_15, all_0_7_7) = all_0_3_3 & difference(all_0_9_9, all_0_8_8) = all_13_0_15 % 3.78/1.61 | % 3.78/1.61 | Applying alpha-rule on (37) yields: % 3.78/1.61 | (38) difference(all_13_0_15, all_0_7_7) = all_0_3_3 % 3.78/1.61 | (39) difference(all_0_9_9, all_0_8_8) = all_13_0_15 % 3.78/1.61 | % 3.78/1.61 | Instantiating (35) with all_15_0_16 yields: % 3.78/1.61 | (40) difference(all_15_0_16, all_0_7_7) = all_0_1_1 & difference(all_0_8_8, all_0_9_9) = all_15_0_16 % 3.78/1.61 | % 3.78/1.61 | Applying alpha-rule on (40) yields: % 3.78/1.61 | (41) difference(all_15_0_16, all_0_7_7) = all_0_1_1 % 3.78/1.61 | (42) difference(all_0_8_8, all_0_9_9) = all_15_0_16 % 3.78/1.61 | % 3.78/1.61 | Instantiating (36) with all_17_0_17, all_17_1_18 yields: % 3.78/1.61 | (43) difference(all_0_8_8, all_0_9_9) = all_17_0_17 & difference(all_0_9_9, all_0_8_8) = all_17_1_18 & union(all_17_1_18, all_17_0_17) = all_0_6_6 % 3.78/1.61 | % 3.78/1.61 | Applying alpha-rule on (43) yields: % 3.78/1.61 | (44) difference(all_0_8_8, all_0_9_9) = all_17_0_17 % 3.78/1.61 | (45) difference(all_0_9_9, all_0_8_8) = all_17_1_18 % 3.78/1.61 | (46) union(all_17_1_18, all_17_0_17) = all_0_6_6 % 3.78/1.61 | % 3.78/1.61 | Instantiating formula (6) with all_0_8_8, all_0_9_9, all_15_0_16, all_17_0_17 and discharging atoms difference(all_0_8_8, all_0_9_9) = all_17_0_17, difference(all_0_8_8, all_0_9_9) = all_15_0_16, yields: % 3.78/1.61 | (47) all_17_0_17 = all_15_0_16 % 3.78/1.61 | % 3.78/1.61 | Instantiating formula (6) with all_0_9_9, all_0_8_8, all_13_0_15, all_17_1_18 and discharging atoms difference(all_0_9_9, all_0_8_8) = all_17_1_18, difference(all_0_9_9, all_0_8_8) = all_13_0_15, yields: % 3.78/1.61 | (48) all_17_1_18 = all_13_0_15 % 3.78/1.61 | % 3.78/1.61 | From (48)(47) and (46) follows: % 3.78/1.61 | (49) union(all_13_0_15, all_15_0_16) = all_0_6_6 % 3.78/1.61 | % 3.78/1.61 | Instantiating formula (31) with all_0_5_5, all_0_6_6, all_0_7_7, all_15_0_16, all_13_0_15 and discharging atoms difference(all_0_6_6, all_0_7_7) = all_0_5_5, union(all_13_0_15, all_15_0_16) = all_0_6_6, yields: % 3.78/1.61 | (50) ? [v0] : ? [v1] : (difference(all_15_0_16, all_0_7_7) = v1 & difference(all_13_0_15, all_0_7_7) = v0 & union(v0, v1) = all_0_5_5) % 3.78/1.61 | % 3.78/1.61 | Instantiating (50) with all_37_0_24, all_37_1_25 yields: % 3.78/1.61 | (51) difference(all_15_0_16, all_0_7_7) = all_37_0_24 & difference(all_13_0_15, all_0_7_7) = all_37_1_25 & union(all_37_1_25, all_37_0_24) = all_0_5_5 % 3.78/1.61 | % 3.78/1.61 | Applying alpha-rule on (51) yields: % 3.78/1.61 | (52) difference(all_15_0_16, all_0_7_7) = all_37_0_24 % 3.78/1.61 | (53) difference(all_13_0_15, all_0_7_7) = all_37_1_25 % 3.78/1.61 | (54) union(all_37_1_25, all_37_0_24) = all_0_5_5 % 3.78/1.61 | % 3.78/1.61 | Instantiating formula (6) with all_15_0_16, all_0_7_7, all_37_0_24, all_0_1_1 and discharging atoms difference(all_15_0_16, all_0_7_7) = all_37_0_24, difference(all_15_0_16, all_0_7_7) = all_0_1_1, yields: % 3.78/1.61 | (55) all_37_0_24 = all_0_1_1 % 3.78/1.61 | % 3.78/1.61 | Instantiating formula (6) with all_13_0_15, all_0_7_7, all_37_1_25, all_0_3_3 and discharging atoms difference(all_13_0_15, all_0_7_7) = all_37_1_25, difference(all_13_0_15, all_0_7_7) = all_0_3_3, yields: % 3.78/1.62 | (56) all_37_1_25 = all_0_3_3 % 3.78/1.62 | % 3.78/1.62 | From (56)(55) and (54) follows: % 3.78/1.62 | (57) union(all_0_3_3, all_0_1_1) = all_0_5_5 % 3.78/1.62 | % 3.78/1.62 | Instantiating formula (32) with all_0_3_3, all_0_1_1, all_0_5_5, all_0_0_0 and discharging atoms union(all_0_3_3, all_0_1_1) = all_0_0_0, union(all_0_3_3, all_0_1_1) = all_0_5_5, yields: % 3.78/1.62 | (58) all_0_0_0 = all_0_5_5 % 3.78/1.62 | % 3.78/1.62 | Equations (58) can reduce 25 to: % 3.78/1.62 | (59) $false % 3.78/1.62 | % 3.78/1.62 |-The branch is then unsatisfiable % 3.78/1.62 % SZS output end Proof for theBenchmark % 3.78/1.62 % 3.78/1.62 1036ms %------------------------------------------------------------------------------