%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET589+3 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n003.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 00:20:30 EDT 2022 % Result : Theorem 6.46s 2.19s % Output : Proof 7.77s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.12 % Problem : SET589+3 : TPTP v8.1.0. Released v2.2.0. % 0.08/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.34 % Computer : n003.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Sun Jul 10 12:48:44 EDT 2022 % 0.13/0.34 % CPUTime : % 0.49/0.59 ____ _ % 0.49/0.59 ___ / __ \_____(_)___ ________ __________ % 0.49/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.49/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.49/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.49/0.59 % 0.49/0.59 A Theorem Prover for First-Order Logic % 0.49/0.59 (ePrincess v.1.0) % 0.49/0.59 % 0.49/0.59 (c) Philipp Rümmer, 2009-2015 % 0.49/0.59 (c) Peter Backeman, 2014-2015 % 0.49/0.59 (contributions by Angelo Brillout, Peter Baumgartner) % 0.49/0.59 Free software under GNU Lesser General Public License (LGPL). % 0.49/0.59 Bug reports to peter@backeman.se % 0.49/0.59 % 0.49/0.59 For more information, visit http://user.uu.se/~petba168/breu/ % 0.49/0.59 % 0.49/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.73/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.25/0.90 Prover 0: Preprocessing ... % 1.57/1.02 Prover 0: Warning: ignoring some quantifiers % 1.57/1.04 Prover 0: Constructing countermodel ... % 5.90/2.08 Prover 0: gave up % 5.90/2.08 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 5.90/2.09 Prover 1: Preprocessing ... % 6.19/2.14 Prover 1: Constructing countermodel ... % 6.46/2.19 Prover 1: proved (111ms) % 6.46/2.19 % 6.46/2.19 No countermodel exists, formula is valid % 6.46/2.19 % SZS status Theorem for theBenchmark % 6.46/2.19 % 6.46/2.19 Generating proof ... found it (size 33) % 7.50/2.41 % 7.50/2.41 % SZS output start Proof for theBenchmark % 7.50/2.41 Assumed formulas after preprocessing and simplification: % 7.50/2.41 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = 0) & difference(v1, v2) = v5 & difference(v0, v3) = v4 & subset(v4, v5) = v6 & subset(v2, v3) = 0 & subset(v0, v1) = 0 & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (difference(v9, v8) = v10) | ~ (difference(v9, v7) = v11) | ~ (subset(v10, v11) = v12) | ? [v13] : ( ~ (v13 = 0) & subset(v7, v8) = v13)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (difference(v8, v9) = v11) | ~ (difference(v7, v9) = v10) | ~ (subset(v10, v11) = v12) | ? [v13] : ( ~ (v13 = 0) & subset(v7, v8) = v13)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (member(v9, v10) = v11) | ~ (difference(v7, v8) = v10) | ? [v12] : ? [v13] : (member(v9, v8) = v13 & member(v9, v7) = v12 & ( ~ (v12 = 0) | v13 = 0))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (subset(v7, v9) = v10) | ~ (subset(v7, v8) = 0) | ? [v11] : ( ~ (v11 = 0) & subset(v8, v9) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (member(v10, v9) = v8) | ~ (member(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (difference(v10, v9) = v8) | ~ (difference(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (subset(v10, v9) = v8) | ~ (subset(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (member(v9, v10) = 0) | ~ (difference(v7, v8) = v10) | ? [v11] : ( ~ (v11 = 0) & member(v9, v8) = v11 & member(v9, v7) = 0)) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (subset(v7, v8) = v9) | ? [v10] : ? [v11] : ( ~ (v11 = 0) & member(v10, v8) = v11 & member(v10, v7) = 0)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (member(v9, v7) = 0) | ~ (subset(v7, v8) = 0) | member(v9, v8) = 0) & ! [v7] : ! [v8] : (v8 = 0 | ~ (subset(v7, v7) = v8))) % 7.50/2.44 | 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 yields: % 7.50/2.44 | (1) ~ (all_0_0_0 = 0) & difference(all_0_5_5, all_0_4_4) = all_0_1_1 & difference(all_0_6_6, all_0_3_3) = all_0_2_2 & subset(all_0_2_2, all_0_1_1) = all_0_0_0 & subset(all_0_4_4, all_0_3_3) = 0 & subset(all_0_6_6, all_0_5_5) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (difference(v2, v1) = v3) | ~ (difference(v2, v0) = v4) | ~ (subset(v3, v4) = v5) | ? [v6] : ( ~ (v6 = 0) & subset(v0, v1) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (difference(v1, v2) = v4) | ~ (difference(v0, v2) = v3) | ~ (subset(v3, v4) = v5) | ? [v6] : ( ~ (v6 = 0) & subset(v0, v1) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (member(v2, v3) = v4) | ~ (difference(v0, v1) = v3) | ? [v5] : ? [v6] : (member(v2, v1) = v6 & member(v2, v0) = v5 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v2) = v3) | ~ (subset(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & subset(v1, v2) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (member(v2, v3) = 0) | ~ (difference(v0, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v1) = v4 & member(v2, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (member(v2, v0) = 0) | ~ (subset(v0, v1) = 0) | member(v2, v1) = 0) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) % 7.50/2.44 | % 7.50/2.44 | Applying alpha-rule on (1) yields: % 7.50/2.44 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) % 7.50/2.44 | (3) subset(all_0_4_4, all_0_3_3) = 0 % 7.50/2.44 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v2) = v3) | ~ (subset(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & subset(v1, v2) = v4)) % 7.50/2.45 | (5) ! [v0] : ! [v1] : ! [v2] : ( ~ (member(v2, v0) = 0) | ~ (subset(v0, v1) = 0) | member(v2, v1) = 0) % 7.50/2.45 | (6) difference(all_0_5_5, all_0_4_4) = all_0_1_1 % 7.50/2.45 | (7) ~ (all_0_0_0 = 0) % 7.50/2.45 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (difference(v1, v2) = v4) | ~ (difference(v0, v2) = v3) | ~ (subset(v3, v4) = v5) | ? [v6] : ( ~ (v6 = 0) & subset(v0, v1) = v6)) % 7.50/2.45 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (member(v2, v3) = 0) | ~ (difference(v0, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v1) = v4 & member(v2, v0) = 0)) % 7.50/2.45 | (10) difference(all_0_6_6, all_0_3_3) = all_0_2_2 % 7.50/2.45 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) % 7.50/2.45 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) % 7.50/2.45 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (difference(v2, v1) = v3) | ~ (difference(v2, v0) = v4) | ~ (subset(v3, v4) = v5) | ? [v6] : ( ~ (v6 = 0) & subset(v0, v1) = v6)) % 7.50/2.45 | (14) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0)) % 7.50/2.45 | (15) subset(all_0_2_2, all_0_1_1) = all_0_0_0 % 7.50/2.45 | (16) subset(all_0_6_6, all_0_5_5) = 0 % 7.50/2.45 | (17) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) % 7.50/2.45 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (member(v2, v3) = v4) | ~ (difference(v0, v1) = v3) | ? [v5] : ? [v6] : (member(v2, v1) = v6 & member(v2, v0) = v5 & ( ~ (v5 = 0) | v6 = 0))) % 7.50/2.45 | % 7.50/2.45 | Instantiating formula (14) with all_0_0_0, all_0_1_1, all_0_2_2 and discharging atoms subset(all_0_2_2, all_0_1_1) = all_0_0_0, yields: % 7.50/2.45 | (19) all_0_0_0 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, all_0_2_2) = 0) % 7.50/2.45 | % 7.50/2.45 +-Applying beta-rule and splitting (19), into two cases. % 7.50/2.45 |-Branch one: % 7.50/2.45 | (20) all_0_0_0 = 0 % 7.50/2.45 | % 7.50/2.45 | Equations (20) can reduce 7 to: % 7.50/2.45 | (21) $false % 7.50/2.45 | % 7.50/2.45 |-The branch is then unsatisfiable % 7.50/2.45 |-Branch two: % 7.50/2.45 | (7) ~ (all_0_0_0 = 0) % 7.50/2.45 | (23) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, all_0_2_2) = 0) % 7.50/2.45 | % 7.50/2.45 | Instantiating (23) with all_22_0_7, all_22_1_8 yields: % 7.50/2.45 | (24) ~ (all_22_0_7 = 0) & member(all_22_1_8, all_0_1_1) = all_22_0_7 & member(all_22_1_8, all_0_2_2) = 0 % 7.50/2.45 | % 7.50/2.45 | Applying alpha-rule on (24) yields: % 7.50/2.45 | (25) ~ (all_22_0_7 = 0) % 7.50/2.45 | (26) member(all_22_1_8, all_0_1_1) = all_22_0_7 % 7.50/2.45 | (27) member(all_22_1_8, all_0_2_2) = 0 % 7.50/2.45 | % 7.50/2.45 | Instantiating formula (18) with all_22_0_7, all_0_1_1, all_22_1_8, all_0_4_4, all_0_5_5 and discharging atoms member(all_22_1_8, all_0_1_1) = all_22_0_7, difference(all_0_5_5, all_0_4_4) = all_0_1_1, yields: % 7.50/2.45 | (28) all_22_0_7 = 0 | ? [v0] : ? [v1] : (member(all_22_1_8, all_0_4_4) = v1 & member(all_22_1_8, all_0_5_5) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 7.50/2.45 | % 7.50/2.45 | Instantiating formula (9) with all_0_2_2, all_22_1_8, all_0_3_3, all_0_6_6 and discharging atoms member(all_22_1_8, all_0_2_2) = 0, difference(all_0_6_6, all_0_3_3) = all_0_2_2, yields: % 7.50/2.45 | (29) ? [v0] : ( ~ (v0 = 0) & member(all_22_1_8, all_0_3_3) = v0 & member(all_22_1_8, all_0_6_6) = 0) % 7.50/2.45 | % 7.50/2.45 | Instantiating formula (5) with all_22_1_8, all_0_3_3, all_0_4_4 and discharging atoms subset(all_0_4_4, all_0_3_3) = 0, yields: % 7.50/2.45 | (30) ~ (member(all_22_1_8, all_0_4_4) = 0) | member(all_22_1_8, all_0_3_3) = 0 % 7.50/2.45 | % 7.50/2.45 | Instantiating formula (5) with all_22_1_8, all_0_5_5, all_0_6_6 and discharging atoms subset(all_0_6_6, all_0_5_5) = 0, yields: % 7.50/2.45 | (31) ~ (member(all_22_1_8, all_0_6_6) = 0) | member(all_22_1_8, all_0_5_5) = 0 % 7.50/2.45 | % 7.50/2.45 | Instantiating (29) with all_33_0_9 yields: % 7.50/2.45 | (32) ~ (all_33_0_9 = 0) & member(all_22_1_8, all_0_3_3) = all_33_0_9 & member(all_22_1_8, all_0_6_6) = 0 % 7.50/2.46 | % 7.50/2.46 | Applying alpha-rule on (32) yields: % 7.50/2.46 | (33) ~ (all_33_0_9 = 0) % 7.77/2.46 | (34) member(all_22_1_8, all_0_3_3) = all_33_0_9 % 7.77/2.46 | (35) member(all_22_1_8, all_0_6_6) = 0 % 7.77/2.46 | % 7.77/2.46 +-Applying beta-rule and splitting (31), into two cases. % 7.77/2.46 |-Branch one: % 7.77/2.46 | (36) ~ (member(all_22_1_8, all_0_6_6) = 0) % 7.77/2.46 | % 7.77/2.46 | Using (35) and (36) yields: % 7.77/2.46 | (37) $false % 7.77/2.46 | % 7.77/2.46 |-The branch is then unsatisfiable % 7.77/2.46 |-Branch two: % 7.77/2.46 | (35) member(all_22_1_8, all_0_6_6) = 0 % 7.77/2.46 | (39) member(all_22_1_8, all_0_5_5) = 0 % 7.77/2.46 | % 7.77/2.46 +-Applying beta-rule and splitting (28), into two cases. % 7.77/2.46 |-Branch one: % 7.77/2.46 | (40) all_22_0_7 = 0 % 7.77/2.46 | % 7.77/2.46 | Equations (40) can reduce 25 to: % 7.77/2.46 | (21) $false % 7.77/2.46 | % 7.77/2.46 |-The branch is then unsatisfiable % 7.77/2.46 |-Branch two: % 7.77/2.46 | (25) ~ (all_22_0_7 = 0) % 7.77/2.46 | (43) ? [v0] : ? [v1] : (member(all_22_1_8, all_0_4_4) = v1 & member(all_22_1_8, all_0_5_5) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 7.77/2.46 | % 7.77/2.46 | Instantiating (43) with all_42_0_10, all_42_1_11 yields: % 7.77/2.46 | (44) member(all_22_1_8, all_0_4_4) = all_42_0_10 & member(all_22_1_8, all_0_5_5) = all_42_1_11 & ( ~ (all_42_1_11 = 0) | all_42_0_10 = 0) % 7.77/2.46 | % 7.77/2.46 | Applying alpha-rule on (44) yields: % 7.77/2.46 | (45) member(all_22_1_8, all_0_4_4) = all_42_0_10 % 7.77/2.46 | (46) member(all_22_1_8, all_0_5_5) = all_42_1_11 % 7.77/2.46 | (47) ~ (all_42_1_11 = 0) | all_42_0_10 = 0 % 7.77/2.46 | % 7.77/2.46 +-Applying beta-rule and splitting (30), into two cases. % 7.77/2.46 |-Branch one: % 7.77/2.46 | (48) ~ (member(all_22_1_8, all_0_4_4) = 0) % 7.77/2.46 | % 7.77/2.46 | Instantiating formula (12) with all_22_1_8, all_0_5_5, all_42_1_11, 0 and discharging atoms member(all_22_1_8, all_0_5_5) = all_42_1_11, member(all_22_1_8, all_0_5_5) = 0, yields: % 7.77/2.46 | (49) all_42_1_11 = 0 % 7.77/2.46 | % 7.77/2.46 | Using (45) and (48) yields: % 7.77/2.46 | (50) ~ (all_42_0_10 = 0) % 7.77/2.46 | % 7.77/2.46 +-Applying beta-rule and splitting (47), into two cases. % 7.77/2.46 |-Branch one: % 7.77/2.46 | (51) ~ (all_42_1_11 = 0) % 7.77/2.46 | % 7.77/2.46 | Equations (49) can reduce 51 to: % 7.77/2.46 | (21) $false % 7.77/2.46 | % 7.77/2.46 |-The branch is then unsatisfiable % 7.77/2.46 |-Branch two: % 7.77/2.46 | (49) all_42_1_11 = 0 % 7.77/2.46 | (54) all_42_0_10 = 0 % 7.77/2.46 | % 7.77/2.46 | Equations (54) can reduce 50 to: % 7.77/2.46 | (21) $false % 7.77/2.46 | % 7.77/2.46 |-The branch is then unsatisfiable % 7.77/2.46 |-Branch two: % 7.77/2.46 | (56) member(all_22_1_8, all_0_4_4) = 0 % 7.77/2.46 | (57) member(all_22_1_8, all_0_3_3) = 0 % 7.77/2.46 | % 7.77/2.46 | Instantiating formula (12) with all_22_1_8, all_0_3_3, all_33_0_9, 0 and discharging atoms member(all_22_1_8, all_0_3_3) = all_33_0_9, member(all_22_1_8, all_0_3_3) = 0, yields: % 7.77/2.46 | (58) all_33_0_9 = 0 % 7.77/2.46 | % 7.77/2.46 | Equations (58) can reduce 33 to: % 7.77/2.46 | (21) $false % 7.77/2.46 | % 7.77/2.46 |-The branch is then unsatisfiable % 7.77/2.46 % SZS output end Proof for theBenchmark % 7.77/2.46 % 7.77/2.46 1859ms %------------------------------------------------------------------------------