%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET903+1 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n028.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 00:23:02 EDT 2022 % Result : Theorem 2.05s 1.20s % Output : Proof 2.89s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.13 % Problem : SET903+1 : TPTP v8.1.0. Released v3.2.0. % 0.08/0.14 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.35 % Computer : n028.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 600 % 0.13/0.35 % DateTime : Sat Jul 9 17:48:11 EDT 2022 % 0.13/0.35 % CPUTime : % 0.63/0.61 ____ _ % 0.63/0.61 ___ / __ \_____(_)___ ________ __________ % 0.63/0.61 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.63/0.61 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.63/0.61 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.63/0.61 % 0.63/0.61 A Theorem Prover for First-Order Logic % 0.63/0.61 (ePrincess v.1.0) % 0.63/0.61 % 0.63/0.61 (c) Philipp Rümmer, 2009-2015 % 0.63/0.61 (c) Peter Backeman, 2014-2015 % 0.63/0.61 (contributions by Angelo Brillout, Peter Baumgartner) % 0.63/0.61 Free software under GNU Lesser General Public License (LGPL). % 0.63/0.61 Bug reports to peter@backeman.se % 0.63/0.61 % 0.63/0.61 For more information, visit http://user.uu.se/~petba168/breu/ % 0.63/0.61 % 0.63/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.71/0.66 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.36/0.93 Prover 0: Preprocessing ... % 1.78/1.12 Prover 0: Constructing countermodel ... % 2.05/1.20 Prover 0: proved (541ms) % 2.05/1.20 % 2.05/1.20 No countermodel exists, formula is valid % 2.05/1.20 % SZS status Theorem for theBenchmark % 2.05/1.20 % 2.05/1.20 Generating proof ... found it (size 14) % 2.65/1.41 % 2.65/1.41 % SZS output start Proof for theBenchmark % 2.65/1.41 Assumed formulas after preprocessing and simplification: % 2.65/1.42 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v2 = v1) & ~ (v2 = empty_set) & ~ (v1 = empty_set) & singleton(v0) = v3 & set_union2(v1, v2) = v3 & empty(v5) & empty(empty_set) & ~ empty(v4) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = v8 | v9 = v7 | v8 = empty_set | ~ (singleton(v6) = v9) | ~ (set_union2(v7, v8) = v9)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = v8 | v9 = v7 | v7 = empty_set | ~ (singleton(v6) = v9) | ~ (set_union2(v7, v8) = v9)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = v8 | v9 = v7 | ~ (singleton(v6) = v9) | ~ (set_union2(v7, v8) = v9)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = v8 | v8 = empty_set | v7 = empty_set | ~ (singleton(v6) = v9) | ~ (set_union2(v7, v8) = v9)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = v8 | v8 = empty_set | ~ (singleton(v6) = v9) | ~ (set_union2(v7, v8) = v9)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = v7 | v8 = empty_set | v7 = empty_set | ~ (singleton(v6) = v9) | ~ (set_union2(v7, v8) = v9)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = v7 | v7 = empty_set | ~ (singleton(v6) = v9) | ~ (set_union2(v7, v8) = v9)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (set_union2(v9, v8) = v7) | ~ (set_union2(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (singleton(v8) = v7) | ~ (singleton(v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (set_union2(v7, v6) = v8) | ~ empty(v8) | empty(v6)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (set_union2(v7, v6) = v8) | set_union2(v6, v7) = v8) & ! [v6] : ! [v7] : ! [v8] : ( ~ (set_union2(v6, v7) = v8) | ~ empty(v8) | empty(v6)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (set_union2(v6, v7) = v8) | set_union2(v7, v6) = v8) & ! [v6] : ! [v7] : (v7 = v6 | ~ (set_union2(v6, v6) = v7))) % 2.65/1.45 | 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: % 2.65/1.45 | (1) ~ (all_0_3_3 = all_0_4_4) & ~ (all_0_3_3 = empty_set) & ~ (all_0_4_4 = empty_set) & singleton(all_0_5_5) = all_0_2_2 & set_union2(all_0_4_4, all_0_3_3) = all_0_2_2 & empty(all_0_0_0) & empty(empty_set) & ~ empty(all_0_1_1) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | v3 = v1 | v2 = empty_set | ~ (singleton(v0) = v3) | ~ (set_union2(v1, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | v3 = v1 | v1 = empty_set | ~ (singleton(v0) = v3) | ~ (set_union2(v1, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | v3 = v1 | ~ (singleton(v0) = v3) | ~ (set_union2(v1, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | v2 = empty_set | v1 = empty_set | ~ (singleton(v0) = v3) | ~ (set_union2(v1, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | v2 = empty_set | ~ (singleton(v0) = v3) | ~ (set_union2(v1, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v2 = empty_set | v1 = empty_set | ~ (singleton(v0) = v3) | ~ (set_union2(v1, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v1 = empty_set | ~ (singleton(v0) = v3) | ~ (set_union2(v1, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ~ empty(v2) | empty(v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ empty(v2) | empty(v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) % 2.89/1.46 | % 2.89/1.46 | Applying alpha-rule on (1) yields: % 2.89/1.46 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | v3 = v1 | ~ (singleton(v0) = v3) | ~ (set_union2(v1, v2) = v3)) % 2.89/1.46 | (3) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) % 2.89/1.46 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | v2 = empty_set | ~ (singleton(v0) = v3) | ~ (set_union2(v1, v2) = v3)) % 2.89/1.46 | (5) ~ empty(all_0_1_1) % 2.89/1.46 | (6) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) % 2.89/1.46 | (7) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2) % 2.89/1.46 | (8) ~ (all_0_3_3 = all_0_4_4) % 2.89/1.46 | (9) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ~ empty(v2) | empty(v0)) % 2.89/1.46 | (10) ~ (all_0_3_3 = empty_set) % 2.89/1.46 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | v3 = v1 | v1 = empty_set | ~ (singleton(v0) = v3) | ~ (set_union2(v1, v2) = v3)) % 2.89/1.46 | (12) set_union2(all_0_4_4, all_0_3_3) = all_0_2_2 % 2.89/1.46 | (13) ~ (all_0_4_4 = empty_set) % 2.89/1.46 | (14) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 2.89/1.46 | (15) empty(empty_set) % 2.89/1.46 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v2 = empty_set | v1 = empty_set | ~ (singleton(v0) = v3) | ~ (set_union2(v1, v2) = v3)) % 2.89/1.47 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | v2 = empty_set | v1 = empty_set | ~ (singleton(v0) = v3) | ~ (set_union2(v1, v2) = v3)) % 2.89/1.47 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | v3 = v1 | v2 = empty_set | ~ (singleton(v0) = v3) | ~ (set_union2(v1, v2) = v3)) % 2.89/1.47 | (19) singleton(all_0_5_5) = all_0_2_2 % 2.89/1.47 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v1 = empty_set | ~ (singleton(v0) = v3) | ~ (set_union2(v1, v2) = v3)) % 2.89/1.47 | (21) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ empty(v2) | empty(v0)) % 2.89/1.47 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) % 2.89/1.47 | (23) empty(all_0_0_0) % 2.89/1.47 | % 2.89/1.47 | Instantiating formula (4) with all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5 and discharging atoms singleton(all_0_5_5) = all_0_2_2, set_union2(all_0_4_4, all_0_3_3) = all_0_2_2, yields: % 2.89/1.47 | (24) all_0_2_2 = all_0_3_3 | all_0_3_3 = empty_set % 2.89/1.47 | % 2.89/1.47 | Instantiating formula (20) with all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5 and discharging atoms singleton(all_0_5_5) = all_0_2_2, set_union2(all_0_4_4, all_0_3_3) = all_0_2_2, yields: % 2.89/1.47 | (25) all_0_2_2 = all_0_4_4 | all_0_4_4 = empty_set % 2.89/1.47 | % 2.89/1.47 +-Applying beta-rule and splitting (25), into two cases. % 2.89/1.47 |-Branch one: % 2.89/1.47 | (26) all_0_4_4 = empty_set % 2.89/1.47 | % 2.89/1.47 | Equations (26) can reduce 13 to: % 2.89/1.47 | (27) $false % 2.89/1.47 | % 2.89/1.47 |-The branch is then unsatisfiable % 2.89/1.47 |-Branch two: % 2.89/1.47 | (13) ~ (all_0_4_4 = empty_set) % 2.89/1.47 | (29) all_0_2_2 = all_0_4_4 % 2.89/1.47 | % 2.89/1.47 +-Applying beta-rule and splitting (24), into two cases. % 2.89/1.47 |-Branch one: % 2.89/1.47 | (30) all_0_3_3 = empty_set % 2.89/1.47 | % 2.89/1.47 | Equations (30) can reduce 10 to: % 2.89/1.47 | (27) $false % 2.89/1.47 | % 2.89/1.47 |-The branch is then unsatisfiable % 2.89/1.47 |-Branch two: % 2.89/1.47 | (10) ~ (all_0_3_3 = empty_set) % 2.89/1.47 | (33) all_0_2_2 = all_0_3_3 % 2.89/1.47 | % 2.89/1.47 | Combining equations (33,29) yields a new equation: % 2.89/1.47 | (34) all_0_3_3 = all_0_4_4 % 2.89/1.47 | % 2.89/1.47 | Simplifying 34 yields: % 2.89/1.47 | (35) all_0_3_3 = all_0_4_4 % 2.89/1.47 | % 2.89/1.47 | Equations (35) can reduce 8 to: % 2.89/1.47 | (27) $false % 2.89/1.47 | % 2.89/1.47 |-The branch is then unsatisfiable % 2.89/1.47 % SZS output end Proof for theBenchmark % 2.89/1.47 % 2.89/1.47 854ms %------------------------------------------------------------------------------