%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET908+1 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n005.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 00:23:04 EDT 2022 % Result : Theorem 2.10s 1.20s % Output : Proof 3.07s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SET908+1 : TPTP v8.1.0. Released v3.2.0. % 0.07/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n005.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 19:17:37 EDT 2022 % 0.12/0.33 % CPUTime : % 0.50/0.58 ____ _ % 0.50/0.58 ___ / __ \_____(_)___ ________ __________ % 0.50/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.50/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.50/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.50/0.58 % 0.50/0.58 A Theorem Prover for First-Order Logic % 0.50/0.58 (ePrincess v.1.0) % 0.50/0.58 % 0.50/0.58 (c) Philipp Rümmer, 2009-2015 % 0.50/0.58 (c) Peter Backeman, 2014-2015 % 0.50/0.58 (contributions by Angelo Brillout, Peter Baumgartner) % 0.50/0.58 Free software under GNU Lesser General Public License (LGPL). % 0.50/0.58 Bug reports to peter@backeman.se % 0.50/0.58 % 0.50/0.58 For more information, visit http://user.uu.se/~petba168/breu/ % 0.50/0.58 % 0.50/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.50/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.25/0.89 Prover 0: Preprocessing ... % 1.75/1.07 Prover 0: Warning: ignoring some quantifiers % 1.82/1.08 Prover 0: Constructing countermodel ... % 2.10/1.20 Prover 0: proved (571ms) % 2.10/1.20 % 2.10/1.20 No countermodel exists, formula is valid % 2.10/1.20 % SZS status Theorem for theBenchmark % 2.10/1.20 % 2.10/1.20 Generating proof ... Warning: ignoring some quantifiers % 2.79/1.40 found it (size 7) % 2.79/1.40 % 2.79/1.40 % SZS output start Proof for theBenchmark % 2.79/1.40 Assumed formulas after preprocessing and simplification: % 2.79/1.40 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (singleton(v0) = v2 & set_union2(v2, v1) = empty_set & empty(v4) & empty(empty_set) & ~ empty(v3) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (set_union2(v8, v7) = v6) | ~ (set_union2(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (set_union2(v5, v6) = v7) | ~ in(v8, v7) | in(v8, v6) | in(v8, v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (set_union2(v5, v6) = v7) | ~ in(v8, v6) | in(v8, v7)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (set_union2(v5, v6) = v7) | ~ in(v8, v5) | in(v8, v7)) & ? [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = v5 | ~ (set_union2(v6, v7) = v8) | ? [v9] : (( ~ in(v9, v5) | ( ~ in(v9, v7) & ~ in(v9, v6))) & (in(v9, v7) | in(v9, v6) | in(v9, v5)))) & ! [v5] : ! [v6] : ! [v7] : (v7 = v5 | ~ (singleton(v5) = v6) | ~ in(v7, v6)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (singleton(v7) = v6) | ~ (singleton(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (set_union2(v6, v5) = v7) | ~ empty(v7) | empty(v5)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (set_union2(v6, v5) = v7) | set_union2(v5, v6) = v7) & ! [v5] : ! [v6] : ! [v7] : ( ~ (set_union2(v5, v6) = v7) | ~ empty(v7) | empty(v5)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (set_union2(v5, v6) = v7) | set_union2(v6, v5) = v7) & ? [v5] : ! [v6] : ! [v7] : (v7 = v5 | ~ (singleton(v6) = v7) | ? [v8] : (( ~ (v8 = v6) | ~ in(v6, v5)) & (v8 = v6 | in(v8, v5)))) & ! [v5] : ! [v6] : (v6 = v5 | ~ (set_union2(v5, v5) = v6)) & ! [v5] : ! [v6] : ( ~ (singleton(v5) = v6) | in(v5, v6)) & ! [v5] : ! [v6] : ( ~ in(v6, v5) | ~ in(v5, v6)) & ! [v5] : ~ in(v5, empty_set) & ? [v5] : (v5 = empty_set | ? [v6] : in(v6, v5))) % 2.97/1.44 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields: % 2.97/1.44 | (1) singleton(all_0_4_4) = all_0_2_2 & set_union2(all_0_2_2, all_0_3_3) = empty_set & empty(all_0_0_0) & empty(empty_set) & ~ empty(all_0_1_1) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v1) | in(v3, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v1) | in(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v0) | in(v3, v2)) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_union2(v1, v2) = v3) | ? [v4] : (( ~ in(v4, v0) | ( ~ in(v4, v2) & ~ in(v4, v1))) & (in(v4, v2) | in(v4, v1) | in(v4, v0)))) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ in(v2, v1)) & ! [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] : ! [v2] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : (( ~ (v3 = v1) | ~ in(v1, v0)) & (v3 = v1 | in(v3, v0)))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | in(v0, v1)) & ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) & ! [v0] : ~ in(v0, empty_set) & ? [v0] : (v0 = empty_set | ? [v1] : in(v1, v0)) % 2.97/1.45 | % 2.97/1.45 | Applying alpha-rule on (1) yields: % 2.97/1.45 | (2) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) % 2.97/1.45 | (3) ! [v0] : ~ in(v0, empty_set) % 2.97/1.45 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ empty(v2) | empty(v0)) % 2.97/1.45 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v1) | in(v3, v2)) % 2.97/1.45 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) % 2.97/1.45 | (7) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) % 2.97/1.45 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2) % 2.97/1.45 | (9) ? [v0] : (v0 = empty_set | ? [v1] : in(v1, v0)) % 2.97/1.45 | (10) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ in(v2, v1)) % 2.97/1.45 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v1) | in(v3, v0)) % 2.97/1.46 | (12) set_union2(all_0_2_2, all_0_3_3) = empty_set % 2.97/1.46 | (13) singleton(all_0_4_4) = all_0_2_2 % 2.97/1.46 | (14) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) % 2.97/1.46 | (15) empty(all_0_0_0) % 2.97/1.46 | (16) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | in(v0, v1)) % 2.97/1.46 | (17) ~ empty(all_0_1_1) % 2.97/1.46 | (18) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : (( ~ (v3 = v1) | ~ in(v1, v0)) & (v3 = v1 | in(v3, v0)))) % 2.97/1.46 | (19) empty(empty_set) % 2.97/1.46 | (20) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_union2(v1, v2) = v3) | ? [v4] : (( ~ in(v4, v0) | ( ~ in(v4, v2) & ~ in(v4, v1))) & (in(v4, v2) | in(v4, v1) | in(v4, v0)))) % 2.97/1.46 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v0) | in(v3, v2)) % 2.97/1.46 | (22) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ~ empty(v2) | empty(v0)) % 2.97/1.46 | (23) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 2.97/1.46 | % 2.97/1.46 | Instantiating formula (16) with all_0_2_2, all_0_4_4 and discharging atoms singleton(all_0_4_4) = all_0_2_2, yields: % 2.97/1.46 | (24) in(all_0_4_4, all_0_2_2) % 2.97/1.46 | % 2.97/1.46 | Instantiating formula (8) with empty_set, all_0_2_2, all_0_3_3 and discharging atoms set_union2(all_0_2_2, all_0_3_3) = empty_set, yields: % 2.97/1.46 | (25) set_union2(all_0_3_3, all_0_2_2) = empty_set % 2.97/1.46 | % 2.97/1.46 | Instantiating formula (5) with all_0_4_4, empty_set, all_0_2_2, all_0_3_3 and discharging atoms set_union2(all_0_3_3, all_0_2_2) = empty_set, in(all_0_4_4, all_0_2_2), yields: % 3.07/1.46 | (26) in(all_0_4_4, empty_set) % 3.07/1.46 | % 3.07/1.46 | Instantiating formula (3) with all_0_4_4 and discharging atoms in(all_0_4_4, empty_set), yields: % 3.07/1.46 | (27) $false % 3.07/1.46 | % 3.07/1.46 |-The branch is then unsatisfiable % 3.07/1.46 % SZS output end Proof for theBenchmark % 3.07/1.46 % 3.07/1.46 875ms %------------------------------------------------------------------------------