%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET620+3 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n026.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 00:20:53 EDT 2022 % Result : Theorem 2.74s 1.44s % Output : Proof 4.62s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.08 % Problem : SET620+3 : TPTP v8.1.0. Released v2.2.0. % 0.07/0.08 % Command : ePrincess-casc -timeout=%d %s % 0.07/0.28 % Computer : n026.cluster.edu % 0.07/0.28 % Model : x86_64 x86_64 % 0.07/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.07/0.28 % Memory : 8042.1875MB % 0.07/0.28 % OS : Linux 3.10.0-693.el7.x86_64 % 0.07/0.28 % CPULimit : 300 % 0.07/0.28 % WCLimit : 600 % 0.07/0.28 % DateTime : Mon Jul 11 06:03:42 EDT 2022 % 0.07/0.28 % CPUTime : % 0.48/0.53 ____ _ % 0.48/0.53 ___ / __ \_____(_)___ ________ __________ % 0.48/0.53 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.48/0.53 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.48/0.53 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.48/0.53 % 0.48/0.53 A Theorem Prover for First-Order Logic % 0.48/0.53 (ePrincess v.1.0) % 0.48/0.53 % 0.48/0.53 (c) Philipp Rümmer, 2009-2015 % 0.48/0.53 (c) Peter Backeman, 2014-2015 % 0.48/0.53 (contributions by Angelo Brillout, Peter Baumgartner) % 0.48/0.53 Free software under GNU Lesser General Public License (LGPL). % 0.48/0.53 Bug reports to peter@backeman.se % 0.48/0.53 % 0.48/0.53 For more information, visit http://user.uu.se/~petba168/breu/ % 0.48/0.53 % 0.48/0.53 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.50/0.59 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.21/0.90 Prover 0: Preprocessing ... % 1.89/1.18 Prover 0: Warning: ignoring some quantifiers % 1.89/1.21 Prover 0: Constructing countermodel ... % 2.74/1.44 Prover 0: proved (846ms) % 2.74/1.44 % 2.74/1.44 No countermodel exists, formula is valid % 2.74/1.44 % SZS status Theorem for theBenchmark % 2.74/1.44 % 2.74/1.44 Generating proof ... Warning: ignoring some quantifiers % 4.18/1.78 found it (size 27) % 4.18/1.78 % 4.18/1.78 % SZS output start Proof for theBenchmark % 4.18/1.78 Assumed formulas after preprocessing and simplification: % 4.18/1.78 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = v2) & intersection(v0, v1) = v4 & difference(v3, v4) = v5 & union(v0, v1) = v3 & symmetric_difference(v0, v1) = v2 & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (difference(v7, v8) = v10) | ~ (difference(v6, v8) = v9) | ~ (union(v9, v10) = v11) | ? [v12] : (difference(v12, v8) = v11 & union(v6, v7) = v12)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (difference(v9, v8) = v10) | ~ (union(v6, v7) = v9) | ? [v11] : ? [v12] : (difference(v7, v8) = v12 & difference(v6, v8) = v11 & union(v11, v12) = 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] : (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] : ( ~ (intersection(v6, v7) = v8) | ~ (difference(v6, v8) = v9) | difference(v6, v7) = v9) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (difference(v6, v7) = v9) | ~ member(v8, v9) | ~ member(v8, v7)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (difference(v6, v7) = v9) | ~ member(v8, v9) | member(v8, v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (difference(v6, v7) = v9) | ~ member(v8, v6) | member(v8, v9) | member(v8, v7)) & ! [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] : ( ~ (difference(v6, v7) = v8) | ? [v9] : (intersection(v6, v7) = v9 & difference(v6, v9) = 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)) % 4.40/1.85 | 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: % 4.40/1.85 | (1) ~ (all_0_0_0 = all_0_3_3) & intersection(all_0_5_5, all_0_4_4) = all_0_1_1 & difference(all_0_2_2, all_0_1_1) = all_0_0_0 & union(all_0_5_5, all_0_4_4) = all_0_2_2 & symmetric_difference(all_0_5_5, all_0_4_4) = all_0_3_3 & ! [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) | ~ (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] : (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] : ( ~ (intersection(v0, v1) = v2) | ~ (difference(v0, v2) = v3) | difference(v0, v1) = v3) & ! [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] : ( ~ (intersection(v1, v0) = v2) | intersection(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection(v0, v1) = v2) | intersection(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (difference(v0, v1) = v2) | ? [v3] : (intersection(v0, v1) = v3 & difference(v0, v3) = 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) % 4.62/1.86 | % 4.62/1.86 | Applying alpha-rule on (1) yields: % 4.62/1.86 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v0, v1) = v3) | ~ member(v2, v3) | member(v2, v0)) % 4.62/1.86 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) % 4.62/1.87 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0, v1) = v2) | union(v1, v0) = v2) % 4.62/1.87 | (5) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v1, v0) = v2) | union(v0, v1) = v2) % 4.62/1.87 | (6) ! [v0] : ! [v1] : ! [v2] : ( ~ (symmetric_difference(v0, v1) = v2) | ? [v3] : ? [v4] : (difference(v1, v0) = v4 & difference(v0, v1) = v3 & union(v3, v4) = v2)) % 4.62/1.87 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v0, v1) = v3) | ~ member(v2, v3) | member(v2, v1)) % 4.62/1.87 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0, v1) = v3) | ~ member(v2, v1) | member(v2, v3)) % 4.62/1.87 | (9) ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v1, v0) | ~ subset(v0, v1)) % 4.62/1.87 | (10) difference(all_0_2_2, all_0_1_1) = all_0_0_0 % 4.62/1.87 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v0, v1) = v3) | ~ member(v2, v3) | ~ member(v2, v1)) % 4.62/1.87 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ subset(v0, v1) | ~ member(v2, v0) | member(v2, v1)) % 4.62/1.87 | (13) intersection(all_0_5_5, all_0_4_4) = all_0_1_1 % 4.62/1.87 | (14) ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : (( ~ member(v2, v1) | ~ member(v2, v0)) & (member(v2, v1) | member(v2, v0)))) % 4.62/1.87 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) % 4.62/1.87 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (symmetric_difference(v3, v2) = v1) | ~ (symmetric_difference(v3, v2) = v0)) % 4.62/1.87 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v0, v1) = v2) | ~ (difference(v0, v2) = v3) | difference(v0, v1) = v3) % 4.62/1.87 | (18) union(all_0_5_5, all_0_4_4) = all_0_2_2 % 4.62/1.87 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0, v1) = v3) | ~ member(v2, v3) | member(v2, v1) | member(v2, v0)) % 4.62/1.87 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v0, v1) = v3) | ~ member(v2, v0) | member(v2, v3) | member(v2, v1)) % 4.62/1.88 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) % 4.62/1.88 | (22) ? [v0] : subset(v0, v0) % 4.62/1.88 | (23) ! [v0] : ! [v1] : ! [v2] : ( ~ (symmetric_difference(v0, v1) = v2) | symmetric_difference(v1, v0) = v2) % 4.62/1.88 | (24) ! [v0] : ! [v1] : ! [v2] : ( ~ (symmetric_difference(v1, v0) = v2) | symmetric_difference(v0, v1) = v2) % 4.62/1.88 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (difference(v1, v0) = v3) | ~ (difference(v0, v1) = v2) | ~ (union(v2, v3) = v4) | symmetric_difference(v0, v1) = v4) % 4.62/1.88 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0, v1) = v3) | ~ member(v2, v0) | member(v2, v3)) % 4.62/1.88 | (27) ~ (all_0_0_0 = all_0_3_3) % 4.62/1.88 | (28) ? [v0] : ? [v1] : (subset(v0, v1) | ? [v2] : (member(v2, v0) & ~ member(v2, v1))) % 4.62/1.88 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v0, v1) = v3) | ~ member(v2, v3) | member(v2, v0)) % 4.62/1.88 | (30) symmetric_difference(all_0_5_5, all_0_4_4) = all_0_3_3 % 4.62/1.88 | (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)) % 4.62/1.88 | (32) ! [v0] : ! [v1] : ! [v2] : ( ~ (difference(v0, v1) = v2) | ? [v3] : (intersection(v0, v1) = v3 & difference(v0, v3) = v2)) % 4.62/1.88 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v0, v1) = v3) | ~ member(v2, v1) | ~ member(v2, v0) | member(v2, v3)) % 4.62/1.88 | (34) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection(v0, v1) = v2) | intersection(v1, v0) = v2) % 4.62/1.88 | (35) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection(v1, v0) = v2) | intersection(v0, v1) = v2) % 4.62/1.89 | (36) ! [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)) % 4.62/1.89 | % 4.62/1.89 | Instantiating formula (35) 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: % 4.62/1.89 | (37) intersection(all_0_4_4, all_0_5_5) = all_0_1_1 % 4.62/1.89 | % 4.62/1.89 | Instantiating formula (31) with all_0_0_0, all_0_2_2, all_0_1_1, all_0_4_4, all_0_5_5 and discharging atoms difference(all_0_2_2, all_0_1_1) = all_0_0_0, union(all_0_5_5, all_0_4_4) = all_0_2_2, yields: % 4.62/1.89 | (38) ? [v0] : ? [v1] : (difference(all_0_4_4, all_0_1_1) = v1 & difference(all_0_5_5, all_0_1_1) = v0 & union(v0, v1) = all_0_0_0) % 4.62/1.89 | % 4.62/1.89 | Instantiating formula (24) with all_0_3_3, all_0_5_5, all_0_4_4 and discharging atoms symmetric_difference(all_0_5_5, all_0_4_4) = all_0_3_3, yields: % 4.62/1.89 | (39) symmetric_difference(all_0_4_4, all_0_5_5) = all_0_3_3 % 4.62/1.89 | % 4.62/1.89 | Instantiating formula (6) with all_0_3_3, all_0_4_4, all_0_5_5 and discharging atoms symmetric_difference(all_0_5_5, all_0_4_4) = all_0_3_3, yields: % 4.62/1.89 | (40) ? [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_3_3) % 4.62/1.89 | % 4.62/1.89 | Instantiating (38) with all_13_0_11, all_13_1_12 yields: % 4.62/1.89 | (41) difference(all_0_4_4, all_0_1_1) = all_13_0_11 & difference(all_0_5_5, all_0_1_1) = all_13_1_12 & union(all_13_1_12, all_13_0_11) = all_0_0_0 % 4.62/1.89 | % 4.62/1.89 | Applying alpha-rule on (41) yields: % 4.62/1.89 | (42) difference(all_0_4_4, all_0_1_1) = all_13_0_11 % 4.62/1.89 | (43) difference(all_0_5_5, all_0_1_1) = all_13_1_12 % 4.62/1.89 | (44) union(all_13_1_12, all_13_0_11) = all_0_0_0 % 4.62/1.89 | % 4.62/1.89 | Instantiating (40) with all_15_0_13, all_15_1_14 yields: % 4.62/1.89 | (45) difference(all_0_4_4, all_0_5_5) = all_15_0_13 & difference(all_0_5_5, all_0_4_4) = all_15_1_14 & union(all_15_1_14, all_15_0_13) = all_0_3_3 % 4.62/1.89 | % 4.62/1.89 | Applying alpha-rule on (45) yields: % 4.62/1.89 | (46) difference(all_0_4_4, all_0_5_5) = all_15_0_13 % 4.62/1.89 | (47) difference(all_0_5_5, all_0_4_4) = all_15_1_14 % 4.62/1.89 | (48) union(all_15_1_14, all_15_0_13) = all_0_3_3 % 4.62/1.89 | % 4.62/1.89 | Instantiating formula (17) with 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_1_1) = all_13_0_11, yields: % 4.62/1.90 | (49) difference(all_0_4_4, all_0_5_5) = all_13_0_11 % 4.62/1.90 | % 4.62/1.90 | Instantiating formula (17) with 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_1_1) = all_13_1_12, yields: % 4.62/1.90 | (50) difference(all_0_5_5, all_0_4_4) = all_13_1_12 % 4.62/1.90 | % 4.62/1.90 | Instantiating formula (6) with all_0_3_3, all_0_5_5, all_0_4_4 and discharging atoms symmetric_difference(all_0_4_4, all_0_5_5) = all_0_3_3, yields: % 4.62/1.90 | (51) ? [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_3_3) % 4.62/1.90 | % 4.62/1.90 | Instantiating (51) with all_35_0_23, all_35_1_24 yields: % 4.62/1.90 | (52) difference(all_0_4_4, all_0_5_5) = all_35_1_24 & difference(all_0_5_5, all_0_4_4) = all_35_0_23 & union(all_35_1_24, all_35_0_23) = all_0_3_3 % 4.62/1.90 | % 4.62/1.90 | Applying alpha-rule on (52) yields: % 4.62/1.90 | (53) difference(all_0_4_4, all_0_5_5) = all_35_1_24 % 4.62/1.90 | (54) difference(all_0_5_5, all_0_4_4) = all_35_0_23 % 4.62/1.90 | (55) union(all_35_1_24, all_35_0_23) = all_0_3_3 % 4.62/1.90 | % 4.62/1.90 | Instantiating formula (15) with all_0_4_4, all_0_5_5, all_35_1_24, all_15_0_13 and discharging atoms difference(all_0_4_4, all_0_5_5) = all_35_1_24, difference(all_0_4_4, all_0_5_5) = all_15_0_13, yields: % 4.62/1.90 | (56) all_35_1_24 = all_15_0_13 % 4.62/1.90 | % 4.62/1.90 | Instantiating formula (15) with all_0_4_4, all_0_5_5, all_13_0_11, all_35_1_24 and discharging atoms difference(all_0_4_4, all_0_5_5) = all_35_1_24, difference(all_0_4_4, all_0_5_5) = all_13_0_11, yields: % 4.62/1.90 | (57) all_35_1_24 = all_13_0_11 % 4.62/1.90 | % 4.62/1.90 | Instantiating formula (15) with all_0_5_5, all_0_4_4, all_35_0_23, all_15_1_14 and discharging atoms difference(all_0_5_5, all_0_4_4) = all_35_0_23, difference(all_0_5_5, all_0_4_4) = all_15_1_14, yields: % 4.62/1.90 | (58) all_35_0_23 = all_15_1_14 % 4.62/1.90 | % 4.62/1.90 | Instantiating formula (15) with all_0_5_5, all_0_4_4, all_13_1_12, all_35_0_23 and discharging atoms difference(all_0_5_5, all_0_4_4) = all_35_0_23, difference(all_0_5_5, all_0_4_4) = all_13_1_12, yields: % 4.62/1.90 | (59) all_35_0_23 = all_13_1_12 % 4.62/1.90 | % 4.62/1.90 | Combining equations (58,59) yields a new equation: % 4.62/1.90 | (60) all_15_1_14 = all_13_1_12 % 4.62/1.90 | % 4.62/1.90 | Simplifying 60 yields: % 4.62/1.90 | (61) all_15_1_14 = all_13_1_12 % 4.62/1.90 | % 4.62/1.90 | Combining equations (56,57) yields a new equation: % 4.62/1.90 | (62) all_15_0_13 = all_13_0_11 % 4.62/1.90 | % 4.62/1.90 | Simplifying 62 yields: % 4.62/1.90 | (63) all_15_0_13 = all_13_0_11 % 4.62/1.90 | % 4.62/1.90 | From (61)(63) and (48) follows: % 4.62/1.90 | (64) union(all_13_1_12, all_13_0_11) = all_0_3_3 % 4.62/1.90 | % 4.62/1.90 | Instantiating formula (21) with all_13_1_12, all_13_0_11, all_0_3_3, all_0_0_0 and discharging atoms union(all_13_1_12, all_13_0_11) = all_0_0_0, union(all_13_1_12, all_13_0_11) = all_0_3_3, yields: % 4.62/1.91 | (65) all_0_0_0 = all_0_3_3 % 4.62/1.91 | % 4.62/1.91 | Equations (65) can reduce 27 to: % 4.62/1.91 | (66) $false % 4.62/1.91 | % 4.62/1.91 |-The branch is then unsatisfiable % 4.62/1.91 % SZS output end Proof for theBenchmark % 4.62/1.91 % 4.62/1.91 1364ms %------------------------------------------------------------------------------