%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET619+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 00:20:52 EDT 2022 % Result : Theorem 2.51s 1.32s % Output : Proof 4.29s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SET619+3 : TPTP v8.1.0. Released v2.2.0. % 0.06/0.12 % 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 : Sun Jul 10 20:55:28 EDT 2022 % 0.12/0.33 % CPUTime : % 0.18/0.58 ____ _ % 0.18/0.58 ___ / __ \_____(_)___ ________ __________ % 0.18/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.18/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.18/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.18/0.58 % 0.18/0.58 A Theorem Prover for First-Order Logic % 0.18/0.58 (ePrincess v.1.0) % 0.18/0.58 % 0.18/0.58 (c) Philipp Rümmer, 2009-2015 % 0.18/0.58 (c) Peter Backeman, 2014-2015 % 0.18/0.58 (contributions by Angelo Brillout, Peter Baumgartner) % 0.18/0.58 Free software under GNU Lesser General Public License (LGPL). % 0.18/0.58 Bug reports to peter@backeman.se % 0.18/0.58 % 0.18/0.58 For more information, visit http://user.uu.se/~petba168/breu/ % 0.18/0.58 % 0.18/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.66/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.42/0.91 Prover 0: Preprocessing ... % 1.87/1.12 Prover 0: Warning: ignoring some quantifiers % 1.87/1.14 Prover 0: Constructing countermodel ... % 2.51/1.32 Prover 0: proved (685ms) % 2.51/1.32 % 2.51/1.32 No countermodel exists, formula is valid % 2.51/1.32 % SZS status Theorem for theBenchmark % 2.51/1.32 % 2.51/1.32 Generating proof ... Warning: ignoring some quantifiers % 3.72/1.60 found it (size 41) % 3.72/1.60 % 3.72/1.60 % SZS output start Proof for theBenchmark % 3.72/1.60 Assumed formulas after preprocessing and simplification: % 3.72/1.60 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = v2) & intersection(v0, v1) = v4 & union(v3, v4) = v5 & union(v0, v1) = v2 & symmetric_difference(v0, v1) = v3 & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v6 | ~ (intersection(v6, v7) = v8) | ~ (difference(v6, v7) = v9) | ~ (union(v8, v9) = v10)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (difference(v7, v6) = v9) | ~ (difference(v6, v7) = v8) | ~ (union(v8, v9) = v10) | symmetric_difference(v6, v7) = v10) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (union(v9, v8) = v10) | ~ (union(v6, v7) = v9) | ? [v11] : (union(v7, v8) = v11 & union(v6, v11) = v10)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (union(v7, v8) = v9) | ~ (union(v6, v9) = v10) | ? [v11] : (union(v11, v8) = v10 & union(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = v6 | ~ (intersection(v6, v7) = v8) | ~ (union(v6, v8) = v9)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (intersection(v9, v8) = v7) | ~ (intersection(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (difference(v9, v8) = v7) | ~ (difference(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (union(v9, v8) = v7) | ~ (union(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (symmetric_difference(v9, v8) = v7) | ~ (symmetric_difference(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (intersection(v6, v7) = v9) | ~ member(v8, v9) | member(v8, v7)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (intersection(v6, v7) = v9) | ~ member(v8, v9) | member(v8, v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (intersection(v6, v7) = v9) | ~ member(v8, v7) | ~ member(v8, v6) | member(v8, v9)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (union(v6, v7) = v9) | ~ member(v8, v9) | member(v8, v7) | member(v8, v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (union(v6, v7) = v9) | ~ member(v8, v7) | member(v8, v9)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (union(v6, v7) = v9) | ~ member(v8, v6) | member(v8, v9)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (intersection(v7, v6) = v8) | intersection(v6, v7) = v8) & ! [v6] : ! [v7] : ! [v8] : ( ~ (intersection(v6, v7) = v8) | intersection(v7, v6) = v8) & ! [v6] : ! [v7] : ! [v8] : ( ~ (union(v7, v6) = v8) | union(v6, v7) = v8) & ! [v6] : ! [v7] : ! [v8] : ( ~ (union(v6, v7) = v8) | union(v7, v6) = v8) & ! [v6] : ! [v7] : ! [v8] : ( ~ (symmetric_difference(v7, v6) = v8) | symmetric_difference(v6, v7) = v8) & ! [v6] : ! [v7] : ! [v8] : ( ~ (symmetric_difference(v6, v7) = v8) | symmetric_difference(v7, v6) = v8) & ! [v6] : ! [v7] : ! [v8] : ( ~ (symmetric_difference(v6, v7) = v8) | ? [v9] : ? [v10] : (difference(v7, v6) = v10 & difference(v6, v7) = v9 & union(v9, v10) = v8)) & ! [v6] : ! [v7] : ! [v8] : ( ~ subset(v6, v7) | ~ member(v8, v6) | member(v8, v7)) & ! [v6] : ! [v7] : (v7 = v6 | ~ subset(v7, v6) | ~ subset(v6, v7)) & ? [v6] : ? [v7] : (v7 = v6 | ? [v8] : (( ~ member(v8, v7) | ~ member(v8, v6)) & (member(v8, v7) | member(v8, v6)))) & ? [v6] : ? [v7] : (subset(v6, v7) | ? [v8] : (member(v8, v6) & ~ member(v8, v7))) & ? [v6] : subset(v6, v6)) % 4.07/1.65 | 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 yields: % 4.07/1.65 | (1) ~ (all_0_0_0 = all_0_3_3) & intersection(all_0_5_5, all_0_4_4) = all_0_1_1 & union(all_0_2_2, all_0_1_1) = all_0_0_0 & union(all_0_5_5, all_0_4_4) = all_0_3_3 & symmetric_difference(all_0_5_5, all_0_4_4) = all_0_2_2 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v0 | ~ (intersection(v0, v1) = v2) | ~ (difference(v0, v1) = v3) | ~ (union(v2, v3) = 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] : ( ~ (union(v3, v2) = v4) | ~ (union(v0, v1) = v3) | ? [v5] : (union(v1, v2) = v5 & union(v0, v5) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (union(v1, v2) = v3) | ~ (union(v0, v3) = v4) | ? [v5] : (union(v5, v2) = v4 & union(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (intersection(v0, v1) = v2) | ~ (union(v0, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(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 | ~ (symmetric_difference(v3, v2) = v1) | ~ (symmetric_difference(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v0, v1) = v3) | ~ member(v2, v3) | member(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v0, v1) = v3) | ~ member(v2, v3) | member(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v0, v1) = v3) | ~ member(v2, v1) | ~ member(v2, v0) | member(v2, v3)) & ! [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] : ( ~ (intersection(v1, v0) = v2) | intersection(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection(v0, v1) = v2) | intersection(v1, v0) = v2) & ! [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) % 4.07/1.66 | % 4.07/1.66 | Applying alpha-rule on (1) yields: % 4.07/1.66 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0, v1) = v3) | ~ member(v2, v0) | member(v2, v3)) % 4.07/1.66 | (3) ! [v0] : ! [v1] : ! [v2] : ( ~ (symmetric_difference(v0, v1) = v2) | ? [v3] : ? [v4] : (difference(v1, v0) = v4 & difference(v0, v1) = v3 & union(v3, v4) = v2)) % 4.07/1.66 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) % 4.07/1.66 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (union(v1, v2) = v3) | ~ (union(v0, v3) = v4) | ? [v5] : (union(v5, v2) = v4 & union(v0, v1) = v5)) % 4.07/1.66 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (intersection(v0, v1) = v2) | ~ (union(v0, v2) = v3)) % 4.07/1.66 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) % 4.07/1.66 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ subset(v0, v1) | ~ member(v2, v0) | member(v2, v1)) % 4.07/1.66 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (union(v3, v2) = v4) | ~ (union(v0, v1) = v3) | ? [v5] : (union(v1, v2) = v5 & union(v0, v5) = v4)) % 4.07/1.66 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0, v1) = v2) | union(v1, v0) = v2) % 4.07/1.66 | (11) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v1, v0) = v2) | union(v0, v1) = v2) % 4.07/1.66 | (12) union(all_0_2_2, all_0_1_1) = all_0_0_0 % 4.07/1.66 | (13) symmetric_difference(all_0_5_5, all_0_4_4) = all_0_2_2 % 4.07/1.66 | (14) ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : (( ~ member(v2, v1) | ~ member(v2, v0)) & (member(v2, v1) | member(v2, v0)))) % 4.07/1.66 | (15) ? [v0] : ? [v1] : (subset(v0, v1) | ? [v2] : (member(v2, v0) & ~ member(v2, v1))) % 4.07/1.66 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0, v1) = v3) | ~ member(v2, v1) | member(v2, v3)) % 4.07/1.66 | (17) ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v1, v0) | ~ subset(v0, v1)) % 4.07/1.66 | (18) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection(v0, v1) = v2) | intersection(v1, v0) = v2) % 4.07/1.66 | (19) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection(v1, v0) = v2) | intersection(v0, v1) = v2) % 4.07/1.66 | (20) ! [v0] : ! [v1] : ! [v2] : ( ~ (symmetric_difference(v0, v1) = v2) | symmetric_difference(v1, v0) = v2) % 4.07/1.67 | (21) ! [v0] : ! [v1] : ! [v2] : ( ~ (symmetric_difference(v1, v0) = v2) | symmetric_difference(v0, v1) = v2) % 4.07/1.67 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) % 4.07/1.67 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v0, v1) = v3) | ~ member(v2, v3) | member(v2, v1)) % 4.07/1.67 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v0, v1) = v3) | ~ member(v2, v1) | ~ member(v2, v0) | member(v2, v3)) % 4.07/1.67 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0, v1) = v3) | ~ member(v2, v3) | member(v2, v1) | member(v2, v0)) % 4.07/1.67 | (26) ? [v0] : subset(v0, v0) % 4.07/1.67 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (difference(v1, v0) = v3) | ~ (difference(v0, v1) = v2) | ~ (union(v2, v3) = v4) | symmetric_difference(v0, v1) = v4) % 4.07/1.67 | (28) ~ (all_0_0_0 = all_0_3_3) % 4.07/1.67 | (29) union(all_0_5_5, all_0_4_4) = all_0_3_3 % 4.07/1.67 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v0 | ~ (intersection(v0, v1) = v2) | ~ (difference(v0, v1) = v3) | ~ (union(v2, v3) = v4)) % 4.07/1.67 | (31) intersection(all_0_5_5, all_0_4_4) = all_0_1_1 % 4.07/1.67 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v0, v1) = v3) | ~ member(v2, v3) | member(v2, v0)) % 4.07/1.67 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (symmetric_difference(v3, v2) = v1) | ~ (symmetric_difference(v3, v2) = v0)) % 4.07/1.67 | % 4.07/1.67 | Instantiating formula (19) with all_0_1_1, all_0_5_5, all_0_4_4 and discharging atoms intersection(all_0_5_5, all_0_4_4) = all_0_1_1, yields: % 4.07/1.67 | (34) intersection(all_0_4_4, all_0_5_5) = all_0_1_1 % 4.07/1.67 | % 4.07/1.67 | Instantiating formula (11) with all_0_0_0, all_0_2_2, all_0_1_1 and discharging atoms union(all_0_2_2, all_0_1_1) = all_0_0_0, yields: % 4.07/1.67 | (35) union(all_0_1_1, all_0_2_2) = all_0_0_0 % 4.07/1.67 | % 4.07/1.67 | Instantiating formula (11) with all_0_3_3, all_0_5_5, all_0_4_4 and discharging atoms union(all_0_5_5, all_0_4_4) = all_0_3_3, yields: % 4.07/1.67 | (36) union(all_0_4_4, all_0_5_5) = all_0_3_3 % 4.07/1.67 | % 4.07/1.67 | Instantiating formula (21) with all_0_2_2, all_0_5_5, all_0_4_4 and discharging atoms symmetric_difference(all_0_5_5, all_0_4_4) = all_0_2_2, yields: % 4.07/1.67 | (37) symmetric_difference(all_0_4_4, all_0_5_5) = all_0_2_2 % 4.07/1.67 | % 4.07/1.67 | Instantiating formula (3) with all_0_2_2, all_0_4_4, all_0_5_5 and discharging atoms symmetric_difference(all_0_5_5, all_0_4_4) = all_0_2_2, yields: % 4.07/1.67 | (38) ? [v0] : ? [v1] : (difference(all_0_4_4, all_0_5_5) = v1 & difference(all_0_5_5, all_0_4_4) = v0 & union(v0, v1) = all_0_2_2) % 4.07/1.67 | % 4.07/1.67 | Instantiating (38) with all_13_0_11, all_13_1_12 yields: % 4.07/1.67 | (39) difference(all_0_4_4, all_0_5_5) = all_13_0_11 & difference(all_0_5_5, all_0_4_4) = all_13_1_12 & union(all_13_1_12, all_13_0_11) = all_0_2_2 % 4.07/1.67 | % 4.07/1.67 | Applying alpha-rule on (39) yields: % 4.07/1.67 | (40) difference(all_0_4_4, all_0_5_5) = all_13_0_11 % 4.07/1.67 | (41) difference(all_0_5_5, all_0_4_4) = all_13_1_12 % 4.07/1.67 | (42) union(all_13_1_12, all_13_0_11) = all_0_2_2 % 4.07/1.67 | % 4.07/1.67 | Instantiating formula (9) with all_0_0_0, all_0_2_2, all_0_1_1, all_13_0_11, all_13_1_12 and discharging atoms union(all_13_1_12, all_13_0_11) = all_0_2_2, union(all_0_2_2, all_0_1_1) = all_0_0_0, yields: % 4.07/1.67 | (43) ? [v0] : (union(all_13_0_11, all_0_1_1) = v0 & union(all_13_1_12, v0) = all_0_0_0) % 4.07/1.67 | % 4.07/1.67 | Instantiating formula (5) with all_0_0_0, all_0_2_2, all_13_0_11, all_13_1_12, all_0_1_1 and discharging atoms union(all_13_1_12, all_13_0_11) = all_0_2_2, union(all_0_1_1, all_0_2_2) = all_0_0_0, yields: % 4.07/1.67 | (44) ? [v0] : (union(v0, all_13_0_11) = all_0_0_0 & union(all_0_1_1, all_13_1_12) = v0) % 4.07/1.67 | % 4.07/1.67 | Instantiating formula (3) with all_0_2_2, all_0_5_5, all_0_4_4 and discharging atoms symmetric_difference(all_0_4_4, all_0_5_5) = all_0_2_2, yields: % 4.07/1.67 | (45) ? [v0] : ? [v1] : (difference(all_0_4_4, all_0_5_5) = v0 & difference(all_0_5_5, all_0_4_4) = v1 & union(v0, v1) = all_0_2_2) % 4.07/1.67 | % 4.07/1.67 | Instantiating (45) with all_21_0_13, all_21_1_14 yields: % 4.07/1.67 | (46) difference(all_0_4_4, all_0_5_5) = all_21_1_14 & difference(all_0_5_5, all_0_4_4) = all_21_0_13 & union(all_21_1_14, all_21_0_13) = all_0_2_2 % 4.07/1.67 | % 4.07/1.67 | Applying alpha-rule on (46) yields: % 4.07/1.68 | (47) difference(all_0_4_4, all_0_5_5) = all_21_1_14 % 4.07/1.68 | (48) difference(all_0_5_5, all_0_4_4) = all_21_0_13 % 4.07/1.68 | (49) union(all_21_1_14, all_21_0_13) = all_0_2_2 % 4.07/1.68 | % 4.07/1.68 | Instantiating (43) with all_23_0_15 yields: % 4.07/1.68 | (50) union(all_13_0_11, all_0_1_1) = all_23_0_15 & union(all_13_1_12, all_23_0_15) = all_0_0_0 % 4.07/1.68 | % 4.07/1.68 | Applying alpha-rule on (50) yields: % 4.07/1.68 | (51) union(all_13_0_11, all_0_1_1) = all_23_0_15 % 4.07/1.68 | (52) union(all_13_1_12, all_23_0_15) = all_0_0_0 % 4.07/1.68 | % 4.07/1.68 | Instantiating (44) with all_25_0_16 yields: % 4.07/1.68 | (53) union(all_25_0_16, all_13_0_11) = all_0_0_0 & union(all_0_1_1, all_13_1_12) = all_25_0_16 % 4.07/1.68 | % 4.07/1.68 | Applying alpha-rule on (53) yields: % 4.07/1.68 | (54) union(all_25_0_16, all_13_0_11) = all_0_0_0 % 4.07/1.68 | (55) union(all_0_1_1, all_13_1_12) = all_25_0_16 % 4.07/1.68 | % 4.07/1.68 | Instantiating formula (7) with all_0_4_4, all_0_5_5, all_21_1_14, all_13_0_11 and discharging atoms difference(all_0_4_4, all_0_5_5) = all_21_1_14, difference(all_0_4_4, all_0_5_5) = all_13_0_11, yields: % 4.07/1.68 | (56) all_21_1_14 = all_13_0_11 % 4.07/1.68 | % 4.07/1.68 | Instantiating formula (7) with all_0_5_5, all_0_4_4, all_21_0_13, all_13_1_12 and discharging atoms difference(all_0_5_5, all_0_4_4) = all_21_0_13, difference(all_0_5_5, all_0_4_4) = all_13_1_12, yields: % 4.07/1.68 | (57) all_21_0_13 = all_13_1_12 % 4.07/1.68 | % 4.07/1.68 | Instantiating formula (30) with all_25_0_16, all_13_1_12, all_0_1_1, all_0_4_4, all_0_5_5 and discharging atoms intersection(all_0_5_5, all_0_4_4) = all_0_1_1, difference(all_0_5_5, all_0_4_4) = all_13_1_12, union(all_0_1_1, all_13_1_12) = all_25_0_16, yields: % 4.07/1.68 | (58) all_25_0_16 = all_0_5_5 % 4.07/1.68 | % 4.07/1.68 | From (56) and (47) follows: % 4.07/1.68 | (40) difference(all_0_4_4, all_0_5_5) = all_13_0_11 % 4.07/1.68 | % 4.07/1.68 | From (56)(57) and (49) follows: % 4.07/1.68 | (60) union(all_13_0_11, all_13_1_12) = all_0_2_2 % 4.07/1.68 | % 4.07/1.68 | From (58) and (55) follows: % 4.07/1.68 | (61) union(all_0_1_1, all_13_1_12) = all_0_5_5 % 4.07/1.68 | % 4.07/1.68 | Instantiating formula (5) with all_0_0_0, all_0_2_2, all_13_1_12, all_13_0_11, all_0_1_1 and discharging atoms union(all_13_0_11, all_13_1_12) = all_0_2_2, union(all_0_1_1, all_0_2_2) = all_0_0_0, yields: % 4.07/1.68 | (62) ? [v0] : (union(v0, all_13_1_12) = all_0_0_0 & union(all_0_1_1, all_13_0_11) = v0) % 4.07/1.68 | % 4.07/1.68 | Instantiating formula (11) with all_23_0_15, all_13_0_11, all_0_1_1 and discharging atoms union(all_13_0_11, all_0_1_1) = all_23_0_15, yields: % 4.07/1.68 | (63) union(all_0_1_1, all_13_0_11) = all_23_0_15 % 4.07/1.68 | % 4.07/1.68 | Instantiating formula (11) with all_0_0_0, all_13_1_12, all_23_0_15 and discharging atoms union(all_13_1_12, all_23_0_15) = all_0_0_0, yields: % 4.07/1.68 | (64) union(all_23_0_15, all_13_1_12) = all_0_0_0 % 4.29/1.68 | % 4.29/1.68 | Instantiating formula (5) with all_0_3_3, all_0_5_5, all_13_1_12, all_0_1_1, all_0_4_4 and discharging atoms union(all_0_1_1, all_13_1_12) = all_0_5_5, union(all_0_4_4, all_0_5_5) = all_0_3_3, yields: % 4.29/1.68 | (65) ? [v0] : (union(v0, all_13_1_12) = all_0_3_3 & union(all_0_4_4, all_0_1_1) = v0) % 4.29/1.68 | % 4.29/1.68 | Instantiating (62) with all_39_0_18 yields: % 4.29/1.68 | (66) union(all_39_0_18, all_13_1_12) = all_0_0_0 & union(all_0_1_1, all_13_0_11) = all_39_0_18 % 4.29/1.68 | % 4.29/1.68 | Applying alpha-rule on (66) yields: % 4.29/1.68 | (67) union(all_39_0_18, all_13_1_12) = all_0_0_0 % 4.29/1.68 | (68) union(all_0_1_1, all_13_0_11) = all_39_0_18 % 4.29/1.68 | % 4.29/1.68 | Instantiating (65) with all_43_0_20 yields: % 4.29/1.68 | (69) union(all_43_0_20, all_13_1_12) = all_0_3_3 & union(all_0_4_4, all_0_1_1) = all_43_0_20 % 4.29/1.68 | % 4.29/1.68 | Applying alpha-rule on (69) yields: % 4.29/1.68 | (70) union(all_43_0_20, all_13_1_12) = all_0_3_3 % 4.29/1.68 | (71) union(all_0_4_4, all_0_1_1) = all_43_0_20 % 4.29/1.68 | % 4.29/1.68 | Instantiating formula (30) with all_39_0_18, all_13_0_11, all_0_1_1, all_0_5_5, all_0_4_4 and discharging atoms intersection(all_0_4_4, all_0_5_5) = all_0_1_1, difference(all_0_4_4, all_0_5_5) = all_13_0_11, union(all_0_1_1, all_13_0_11) = all_39_0_18, yields: % 4.29/1.68 | (72) all_39_0_18 = all_0_4_4 % 4.29/1.68 | % 4.29/1.68 | Instantiating formula (22) with all_0_1_1, all_13_0_11, all_23_0_15, all_39_0_18 and discharging atoms union(all_0_1_1, all_13_0_11) = all_39_0_18, union(all_0_1_1, all_13_0_11) = all_23_0_15, yields: % 4.29/1.69 | (73) all_39_0_18 = all_23_0_15 % 4.29/1.69 | % 4.29/1.69 | Instantiating formula (6) with all_43_0_20, all_0_1_1, all_0_5_5, all_0_4_4 and discharging atoms intersection(all_0_4_4, all_0_5_5) = all_0_1_1, union(all_0_4_4, all_0_1_1) = all_43_0_20, yields: % 4.29/1.69 | (74) all_43_0_20 = all_0_4_4 % 4.29/1.69 | % 4.29/1.69 | Combining equations (72,73) yields a new equation: % 4.29/1.69 | (75) all_23_0_15 = all_0_4_4 % 4.29/1.69 | % 4.29/1.69 | From (74) and (70) follows: % 4.29/1.69 | (76) union(all_0_4_4, all_13_1_12) = all_0_3_3 % 4.29/1.69 | % 4.29/1.69 | From (75) and (64) follows: % 4.29/1.69 | (77) union(all_0_4_4, all_13_1_12) = all_0_0_0 % 4.29/1.69 | % 4.29/1.69 | Instantiating formula (22) with all_0_4_4, all_13_1_12, all_0_3_3, all_0_0_0 and discharging atoms union(all_0_4_4, all_13_1_12) = all_0_0_0, union(all_0_4_4, all_13_1_12) = all_0_3_3, yields: % 4.29/1.69 | (78) all_0_0_0 = all_0_3_3 % 4.29/1.69 | % 4.29/1.69 | Equations (78) can reduce 28 to: % 4.29/1.69 | (79) $false % 4.29/1.69 | % 4.29/1.69 |-The branch is then unsatisfiable % 4.29/1.69 % SZS output end Proof for theBenchmark % 4.29/1.69 % 4.29/1.69 1097ms %------------------------------------------------------------------------------