%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET580+3 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n015.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 00:20:24 EDT 2022 % Result : Theorem 2.50s 1.30s % Output : Proof 3.52s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SET580+3 : TPTP v8.1.0. Released v2.2.0. % 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.33 % Computer : n015.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 Jul 10 02:18:37 EDT 2022 % 0.13/0.33 % CPUTime : % 0.66/0.63 ____ _ % 0.66/0.63 ___ / __ \_____(_)___ ________ __________ % 0.66/0.63 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.66/0.63 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.66/0.63 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.66/0.63 % 0.66/0.63 A Theorem Prover for First-Order Logic % 0.66/0.63 (ePrincess v.1.0) % 0.66/0.63 % 0.66/0.63 (c) Philipp Rümmer, 2009-2015 % 0.66/0.63 (c) Peter Backeman, 2014-2015 % 0.66/0.63 (contributions by Angelo Brillout, Peter Baumgartner) % 0.66/0.63 Free software under GNU Lesser General Public License (LGPL). % 0.66/0.63 Bug reports to peter@backeman.se % 0.66/0.63 % 0.66/0.63 For more information, visit http://user.uu.se/~petba168/breu/ % 0.66/0.63 % 0.66/0.63 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.75/0.68 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.33/0.92 Prover 0: Preprocessing ... % 1.75/1.09 Prover 0: Warning: ignoring some quantifiers % 1.86/1.10 Prover 0: Constructing countermodel ... % 2.50/1.30 Prover 0: proved (616ms) % 2.50/1.30 % 2.50/1.30 No countermodel exists, formula is valid % 2.50/1.30 % SZS status Theorem for theBenchmark % 2.50/1.30 % 2.50/1.30 Generating proof ... Warning: ignoring some quantifiers % 3.41/1.53 found it (size 43) % 3.41/1.53 % 3.41/1.53 % SZS output start Proof for theBenchmark % 3.41/1.53 Assumed formulas after preprocessing and simplification: % 3.41/1.53 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (symmetric_difference(v1, v2) = v3 & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (difference(v5, v4) = v7) | ~ (difference(v4, v5) = v6) | ~ (union(v6, v7) = v8) | symmetric_difference(v4, v5) = v8) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (symmetric_difference(v7, v6) = v5) | ~ (symmetric_difference(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (difference(v7, v6) = v5) | ~ (difference(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (union(v7, v6) = v5) | ~ (union(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (difference(v4, v5) = v7) | ~ member(v6, v7) | ~ member(v6, v5)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (difference(v4, v5) = v7) | ~ member(v6, v7) | member(v6, v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (difference(v4, v5) = v7) | ~ member(v6, v4) | member(v6, v7) | member(v6, v5)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (union(v4, v5) = v7) | ~ member(v6, v7) | member(v6, v5) | member(v6, v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (union(v4, v5) = v7) | ~ member(v6, v5) | member(v6, v7)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (union(v4, v5) = v7) | ~ member(v6, v4) | member(v6, v7)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (symmetric_difference(v5, v4) = v6) | symmetric_difference(v4, v5) = v6) & ! [v4] : ! [v5] : ! [v6] : ( ~ (symmetric_difference(v4, v5) = v6) | symmetric_difference(v5, v4) = v6) & ! [v4] : ! [v5] : ! [v6] : ( ~ (symmetric_difference(v4, v5) = v6) | ? [v7] : ? [v8] : (difference(v5, v4) = v8 & difference(v4, v5) = v7 & union(v7, v8) = v6)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (union(v5, v4) = v6) | union(v4, v5) = v6) & ! [v4] : ! [v5] : ! [v6] : ( ~ (union(v4, v5) = v6) | union(v5, v4) = v6) & ? [v4] : ? [v5] : (v5 = v4 | ? [v6] : (( ~ member(v6, v5) | ~ member(v6, v4)) & (member(v6, v5) | member(v6, v4)))) & ((member(v0, v3) & ((member(v0, v2) & member(v0, v1)) | ( ~ member(v0, v2) & ~ member(v0, v1)))) | ( ~ member(v0, v3) & ((member(v0, v2) & ~ member(v0, v1)) | (member(v0, v1) & ~ member(v0, v2)))))) % 3.52/1.57 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields: % 3.52/1.57 | (1) symmetric_difference(all_0_2_2, all_0_1_1) = all_0_0_0 & ! [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 | ~ (symmetric_difference(v3, v2) = v1) | ~ (symmetric_difference(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] : ( ~ (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] : ( ~ (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] : ( ~ (union(v1, v0) = v2) | union(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0, v1) = v2) | union(v1, v0) = v2) & ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : (( ~ member(v2, v1) | ~ member(v2, v0)) & (member(v2, v1) | member(v2, v0)))) & ((member(all_0_3_3, all_0_0_0) & ((member(all_0_3_3, all_0_1_1) & member(all_0_3_3, all_0_2_2)) | ( ~ member(all_0_3_3, all_0_1_1) & ~ member(all_0_3_3, all_0_2_2)))) | ( ~ member(all_0_3_3, all_0_0_0) & ((member(all_0_3_3, all_0_1_1) & ~ member(all_0_3_3, all_0_2_2)) | (member(all_0_3_3, all_0_2_2) & ~ member(all_0_3_3, all_0_1_1))))) % 3.52/1.58 | % 3.52/1.58 | Applying alpha-rule on (1) yields: % 3.52/1.58 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0, v1) = v3) | ~ member(v2, v1) | member(v2, v3)) % 3.52/1.58 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) % 3.52/1.58 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (symmetric_difference(v3, v2) = v1) | ~ (symmetric_difference(v3, v2) = v0)) % 3.52/1.58 | (5) ! [v0] : ! [v1] : ! [v2] : ( ~ (symmetric_difference(v0, v1) = v2) | symmetric_difference(v1, v0) = v2) % 3.52/1.58 | (6) ! [v0] : ! [v1] : ! [v2] : ( ~ (symmetric_difference(v1, v0) = v2) | symmetric_difference(v0, v1) = v2) % 3.52/1.58 | (7) (member(all_0_3_3, all_0_0_0) & ((member(all_0_3_3, all_0_1_1) & member(all_0_3_3, all_0_2_2)) | ( ~ member(all_0_3_3, all_0_1_1) & ~ member(all_0_3_3, all_0_2_2)))) | ( ~ member(all_0_3_3, all_0_0_0) & ((member(all_0_3_3, all_0_1_1) & ~ member(all_0_3_3, all_0_2_2)) | (member(all_0_3_3, all_0_2_2) & ~ member(all_0_3_3, all_0_1_1)))) % 3.52/1.58 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v0, v1) = v3) | ~ member(v2, v3) | member(v2, v0)) % 3.52/1.58 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0, v1) = v3) | ~ member(v2, v0) | member(v2, v3)) % 3.52/1.58 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0, v1) = v3) | ~ member(v2, v3) | member(v2, v1) | member(v2, v0)) % 3.52/1.58 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) % 3.52/1.58 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0, v1) = v2) | union(v1, v0) = v2) % 3.52/1.58 | (13) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v1, v0) = v2) | union(v0, v1) = v2) % 3.52/1.58 | (14) symmetric_difference(all_0_2_2, all_0_1_1) = all_0_0_0 % 3.52/1.58 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v0, v1) = v3) | ~ member(v2, v0) | member(v2, v3) | member(v2, v1)) % 3.52/1.58 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (difference(v1, v0) = v3) | ~ (difference(v0, v1) = v2) | ~ (union(v2, v3) = v4) | symmetric_difference(v0, v1) = v4) % 3.52/1.58 | (17) ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : (( ~ member(v2, v1) | ~ member(v2, v0)) & (member(v2, v1) | member(v2, v0)))) % 3.52/1.58 | (18) ! [v0] : ! [v1] : ! [v2] : ( ~ (symmetric_difference(v0, v1) = v2) | ? [v3] : ? [v4] : (difference(v1, v0) = v4 & difference(v0, v1) = v3 & union(v3, v4) = v2)) % 3.52/1.58 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v0, v1) = v3) | ~ member(v2, v3) | ~ member(v2, v1)) % 3.52/1.58 | % 3.52/1.58 | Instantiating formula (6) with all_0_0_0, all_0_2_2, all_0_1_1 and discharging atoms symmetric_difference(all_0_2_2, all_0_1_1) = all_0_0_0, yields: % 3.52/1.58 | (20) symmetric_difference(all_0_1_1, all_0_2_2) = all_0_0_0 % 3.52/1.58 | % 3.52/1.58 | Instantiating formula (18) with all_0_0_0, all_0_1_1, all_0_2_2 and discharging atoms symmetric_difference(all_0_2_2, all_0_1_1) = all_0_0_0, yields: % 3.52/1.59 | (21) ? [v0] : ? [v1] : (difference(all_0_1_1, all_0_2_2) = v1 & difference(all_0_2_2, all_0_1_1) = v0 & union(v0, v1) = all_0_0_0) % 3.52/1.59 | % 3.52/1.59 | Instantiating (21) with all_10_0_6, all_10_1_7 yields: % 3.52/1.59 | (22) difference(all_0_1_1, all_0_2_2) = all_10_0_6 & difference(all_0_2_2, all_0_1_1) = all_10_1_7 & union(all_10_1_7, all_10_0_6) = all_0_0_0 % 3.52/1.59 | % 3.52/1.59 | Applying alpha-rule on (22) yields: % 3.52/1.59 | (23) difference(all_0_1_1, all_0_2_2) = all_10_0_6 % 3.52/1.59 | (24) difference(all_0_2_2, all_0_1_1) = all_10_1_7 % 3.52/1.59 | (25) union(all_10_1_7, all_10_0_6) = all_0_0_0 % 3.52/1.59 | % 3.52/1.59 | Instantiating formula (18) with all_0_0_0, all_0_2_2, all_0_1_1 and discharging atoms symmetric_difference(all_0_1_1, all_0_2_2) = all_0_0_0, yields: % 3.52/1.59 | (26) ? [v0] : ? [v1] : (difference(all_0_1_1, all_0_2_2) = v0 & difference(all_0_2_2, all_0_1_1) = v1 & union(v0, v1) = all_0_0_0) % 3.52/1.59 | % 3.52/1.59 | Instantiating (26) with all_18_0_8, all_18_1_9 yields: % 3.52/1.59 | (27) difference(all_0_1_1, all_0_2_2) = all_18_1_9 & difference(all_0_2_2, all_0_1_1) = all_18_0_8 & union(all_18_1_9, all_18_0_8) = all_0_0_0 % 3.52/1.59 | % 3.52/1.59 | Applying alpha-rule on (27) yields: % 3.52/1.59 | (28) difference(all_0_1_1, all_0_2_2) = all_18_1_9 % 3.52/1.59 | (29) difference(all_0_2_2, all_0_1_1) = all_18_0_8 % 3.52/1.59 | (30) union(all_18_1_9, all_18_0_8) = all_0_0_0 % 3.52/1.59 | % 3.52/1.59 | Instantiating formula (11) with all_0_1_1, all_0_2_2, all_18_1_9, all_10_0_6 and discharging atoms difference(all_0_1_1, all_0_2_2) = all_18_1_9, difference(all_0_1_1, all_0_2_2) = all_10_0_6, yields: % 3.52/1.59 | (31) all_18_1_9 = all_10_0_6 % 3.52/1.59 | % 3.52/1.59 | Instantiating formula (11) with all_0_2_2, all_0_1_1, all_18_0_8, all_10_1_7 and discharging atoms difference(all_0_2_2, all_0_1_1) = all_18_0_8, difference(all_0_2_2, all_0_1_1) = all_10_1_7, yields: % 3.52/1.59 | (32) all_18_0_8 = all_10_1_7 % 3.52/1.59 | % 3.52/1.59 | From (31) and (28) follows: % 3.52/1.59 | (23) difference(all_0_1_1, all_0_2_2) = all_10_0_6 % 3.52/1.59 | % 3.52/1.59 | From (32) and (29) follows: % 3.52/1.59 | (24) difference(all_0_2_2, all_0_1_1) = all_10_1_7 % 3.52/1.59 | % 3.52/1.59 +-Applying beta-rule and splitting (7), into two cases. % 3.52/1.59 |-Branch one: % 3.52/1.59 | (35) member(all_0_3_3, all_0_0_0) & ((member(all_0_3_3, all_0_1_1) & member(all_0_3_3, all_0_2_2)) | ( ~ member(all_0_3_3, all_0_1_1) & ~ member(all_0_3_3, all_0_2_2))) % 3.52/1.59 | % 3.52/1.59 | Applying alpha-rule on (35) yields: % 3.52/1.59 | (36) member(all_0_3_3, all_0_0_0) % 3.52/1.59 | (37) (member(all_0_3_3, all_0_1_1) & member(all_0_3_3, all_0_2_2)) | ( ~ member(all_0_3_3, all_0_1_1) & ~ member(all_0_3_3, all_0_2_2)) % 3.52/1.59 | % 3.52/1.59 | Instantiating formula (10) with all_0_0_0, all_0_3_3, all_10_0_6, all_10_1_7 and discharging atoms union(all_10_1_7, all_10_0_6) = all_0_0_0, member(all_0_3_3, all_0_0_0), yields: % 3.52/1.59 | (38) member(all_0_3_3, all_10_0_6) | member(all_0_3_3, all_10_1_7) % 3.52/1.59 | % 3.52/1.59 +-Applying beta-rule and splitting (38), into two cases. % 3.52/1.59 |-Branch one: % 3.52/1.59 | (39) member(all_0_3_3, all_10_0_6) % 3.52/1.59 | % 3.52/1.59 | Instantiating formula (8) with all_10_0_6, all_0_3_3, all_0_2_2, all_0_1_1 and discharging atoms difference(all_0_1_1, all_0_2_2) = all_10_0_6, member(all_0_3_3, all_10_0_6), yields: % 3.52/1.59 | (40) member(all_0_3_3, all_0_1_1) % 3.52/1.59 | % 3.52/1.59 +-Applying beta-rule and splitting (37), into two cases. % 3.52/1.59 |-Branch one: % 3.52/1.59 | (41) member(all_0_3_3, all_0_1_1) & member(all_0_3_3, all_0_2_2) % 3.52/1.59 | % 3.52/1.59 | Applying alpha-rule on (41) yields: % 3.52/1.59 | (40) member(all_0_3_3, all_0_1_1) % 3.52/1.59 | (43) member(all_0_3_3, all_0_2_2) % 3.52/1.59 | % 3.52/1.59 | Instantiating formula (19) with all_10_0_6, all_0_3_3, all_0_2_2, all_0_1_1 and discharging atoms difference(all_0_1_1, all_0_2_2) = all_10_0_6, member(all_0_3_3, all_10_0_6), member(all_0_3_3, all_0_2_2), yields: % 3.52/1.59 | (44) $false % 3.52/1.59 | % 3.52/1.59 |-The branch is then unsatisfiable % 3.52/1.59 |-Branch two: % 3.52/1.59 | (45) ~ member(all_0_3_3, all_0_1_1) & ~ member(all_0_3_3, all_0_2_2) % 3.52/1.59 | % 3.52/1.59 | Applying alpha-rule on (45) yields: % 3.52/1.59 | (46) ~ member(all_0_3_3, all_0_1_1) % 3.52/1.60 | (47) ~ member(all_0_3_3, all_0_2_2) % 3.52/1.60 | % 3.52/1.60 | Using (40) and (46) yields: % 3.52/1.60 | (44) $false % 3.52/1.60 | % 3.52/1.60 |-The branch is then unsatisfiable % 3.52/1.60 |-Branch two: % 3.52/1.60 | (49) ~ member(all_0_3_3, all_10_0_6) % 3.52/1.60 | (50) member(all_0_3_3, all_10_1_7) % 3.52/1.60 | % 3.52/1.60 | Instantiating formula (8) with all_10_1_7, all_0_3_3, all_0_1_1, all_0_2_2 and discharging atoms difference(all_0_2_2, all_0_1_1) = all_10_1_7, member(all_0_3_3, all_10_1_7), yields: % 3.52/1.60 | (43) member(all_0_3_3, all_0_2_2) % 3.52/1.60 | % 3.52/1.60 +-Applying beta-rule and splitting (37), into two cases. % 3.52/1.60 |-Branch one: % 3.52/1.60 | (41) member(all_0_3_3, all_0_1_1) & member(all_0_3_3, all_0_2_2) % 3.52/1.60 | % 3.52/1.60 | Applying alpha-rule on (41) yields: % 3.52/1.60 | (40) member(all_0_3_3, all_0_1_1) % 3.52/1.60 | (43) member(all_0_3_3, all_0_2_2) % 3.52/1.60 | % 3.52/1.60 | Instantiating formula (19) with all_10_1_7, all_0_3_3, all_0_1_1, all_0_2_2 and discharging atoms difference(all_0_2_2, all_0_1_1) = all_10_1_7, member(all_0_3_3, all_10_1_7), member(all_0_3_3, all_0_1_1), yields: % 3.52/1.60 | (44) $false % 3.52/1.60 | % 3.52/1.60 |-The branch is then unsatisfiable % 3.52/1.60 |-Branch two: % 3.52/1.60 | (45) ~ member(all_0_3_3, all_0_1_1) & ~ member(all_0_3_3, all_0_2_2) % 3.52/1.60 | % 3.52/1.60 | Applying alpha-rule on (45) yields: % 3.52/1.60 | (46) ~ member(all_0_3_3, all_0_1_1) % 3.52/1.60 | (47) ~ member(all_0_3_3, all_0_2_2) % 3.52/1.60 | % 3.52/1.60 | Using (43) and (47) yields: % 3.52/1.60 | (44) $false % 3.52/1.60 | % 3.52/1.60 |-The branch is then unsatisfiable % 3.52/1.60 |-Branch two: % 3.52/1.60 | (60) ~ member(all_0_3_3, all_0_0_0) & ((member(all_0_3_3, all_0_1_1) & ~ member(all_0_3_3, all_0_2_2)) | (member(all_0_3_3, all_0_2_2) & ~ member(all_0_3_3, all_0_1_1))) % 3.52/1.60 | % 3.52/1.60 | Applying alpha-rule on (60) yields: % 3.52/1.60 | (61) ~ member(all_0_3_3, all_0_0_0) % 3.52/1.60 | (62) (member(all_0_3_3, all_0_1_1) & ~ member(all_0_3_3, all_0_2_2)) | (member(all_0_3_3, all_0_2_2) & ~ member(all_0_3_3, all_0_1_1)) % 3.52/1.60 | % 3.52/1.60 +-Applying beta-rule and splitting (62), into two cases. % 3.52/1.60 |-Branch one: % 3.52/1.60 | (63) member(all_0_3_3, all_0_1_1) & ~ member(all_0_3_3, all_0_2_2) % 3.52/1.60 | % 3.52/1.60 | Applying alpha-rule on (63) yields: % 3.52/1.60 | (40) member(all_0_3_3, all_0_1_1) % 3.52/1.60 | (47) ~ member(all_0_3_3, all_0_2_2) % 3.52/1.60 | % 3.52/1.60 | Instantiating formula (15) with all_10_0_6, all_0_3_3, all_0_2_2, all_0_1_1 and discharging atoms difference(all_0_1_1, all_0_2_2) = all_10_0_6, member(all_0_3_3, all_0_1_1), ~ member(all_0_3_3, all_0_2_2), yields: % 3.52/1.60 | (39) member(all_0_3_3, all_10_0_6) % 3.52/1.60 | % 3.52/1.60 | Instantiating formula (2) with all_0_0_0, all_0_3_3, all_10_0_6, all_10_1_7 and discharging atoms union(all_10_1_7, all_10_0_6) = all_0_0_0, member(all_0_3_3, all_10_0_6), ~ member(all_0_3_3, all_0_0_0), yields: % 3.52/1.60 | (44) $false % 3.52/1.60 | % 3.52/1.60 |-The branch is then unsatisfiable % 3.52/1.60 |-Branch two: % 3.52/1.60 | (68) member(all_0_3_3, all_0_2_2) & ~ member(all_0_3_3, all_0_1_1) % 3.52/1.60 | % 3.52/1.60 | Applying alpha-rule on (68) yields: % 3.52/1.60 | (43) member(all_0_3_3, all_0_2_2) % 3.52/1.60 | (46) ~ member(all_0_3_3, all_0_1_1) % 3.52/1.60 | % 3.52/1.60 | Instantiating formula (15) with all_10_1_7, all_0_3_3, all_0_1_1, all_0_2_2 and discharging atoms difference(all_0_2_2, all_0_1_1) = all_10_1_7, member(all_0_3_3, all_0_2_2), ~ member(all_0_3_3, all_0_1_1), yields: % 3.52/1.60 | (50) member(all_0_3_3, all_10_1_7) % 3.52/1.60 | % 3.52/1.60 | Instantiating formula (9) with all_0_0_0, all_0_3_3, all_10_0_6, all_10_1_7 and discharging atoms union(all_10_1_7, all_10_0_6) = all_0_0_0, member(all_0_3_3, all_10_1_7), ~ member(all_0_3_3, all_0_0_0), yields: % 3.52/1.60 | (44) $false % 3.52/1.60 | % 3.52/1.60 |-The branch is then unsatisfiable % 3.52/1.60 % SZS output end Proof for theBenchmark % 3.52/1.60 % 3.52/1.60 960ms %------------------------------------------------------------------------------