%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET987+1 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n017.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 00:23:38 EDT 2022 % Result : Theorem 2.05s 1.20s % Output : Proof 2.84s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET987+1 : TPTP v8.1.0. Released v3.2.0. % 0.13/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.34 % Computer : n017.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 11:19:32 EDT 2022 % 0.13/0.34 % CPUTime : % 0.58/0.60 ____ _ % 0.58/0.60 ___ / __ \_____(_)___ ________ __________ % 0.58/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.58/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.58/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.58/0.60 % 0.58/0.60 A Theorem Prover for First-Order Logic % 0.58/0.60 (ePrincess v.1.0) % 0.58/0.60 % 0.58/0.60 (c) Philipp Rümmer, 2009-2015 % 0.58/0.60 (c) Peter Backeman, 2014-2015 % 0.58/0.60 (contributions by Angelo Brillout, Peter Baumgartner) % 0.58/0.60 Free software under GNU Lesser General Public License (LGPL). % 0.58/0.60 Bug reports to peter@backeman.se % 0.58/0.60 % 0.58/0.60 For more information, visit http://user.uu.se/~petba168/breu/ % 0.58/0.60 % 0.58/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.76/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.34/0.92 Prover 0: Preprocessing ... % 1.75/1.08 Prover 0: Constructing countermodel ... % 2.05/1.20 Prover 0: proved (545ms) % 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 6) % 2.67/1.39 % 2.67/1.39 % SZS output start Proof for theBenchmark % 2.67/1.39 Assumed formulas after preprocessing and simplification: % 2.67/1.39 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ( ~ (v4 = v1) & singleton(v0) = v2 & set_difference(v3, v2) = v4 & set_union2(v1, v2) = v3 & empty(v6) & ~ empty(v5) & ~ in(v0, v1) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v7 | ~ (singleton(v8) = v9) | ~ (set_difference(v7, v9) = v10) | in(v8, v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (set_difference(v10, v9) = v8) | ~ (set_difference(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (set_union2(v10, v9) = v8) | ~ (set_union2(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (set_difference(v9, v8) = v10) | ~ (set_union2(v7, v8) = v9) | set_difference(v7, v8) = v10) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (singleton(v9) = v8) | ~ (singleton(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (singleton(v8) = v9) | ~ (set_difference(v7, v9) = v7) | ~ in(v8, v7)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (set_difference(v7, v8) = v9) | ? [v10] : (set_difference(v10, v8) = v9 & set_union2(v7, v8) = v10)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (set_union2(v8, v7) = v9) | ~ empty(v9) | empty(v7)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (set_union2(v8, v7) = v9) | set_union2(v7, v8) = v9) & ! [v7] : ! [v8] : ! [v9] : ( ~ (set_union2(v7, v8) = v9) | ~ empty(v9) | empty(v7)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (set_union2(v7, v8) = v9) | set_union2(v8, v7) = v9) & ! [v7] : ! [v8] : (v8 = v7 | ~ (set_union2(v7, v7) = v8)) & ! [v7] : ! [v8] : ( ~ in(v8, v7) | ~ in(v7, v8))) % 2.84/1.43 | 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: % 2.84/1.43 | (1) ~ (all_0_2_2 = all_0_5_5) & singleton(all_0_6_6) = all_0_4_4 & set_difference(all_0_3_3, all_0_4_4) = all_0_2_2 & set_union2(all_0_5_5, all_0_4_4) = all_0_3_3 & empty(all_0_0_0) & ~ empty(all_0_1_1) & ~ in(all_0_6_6, all_0_5_5) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (singleton(v1) = v2) | ~ (set_difference(v0, v2) = v3) | in(v1, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v2, v1) = v3) | ~ (set_union2(v0, v1) = v2) | set_difference(v0, v1) = v3) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v1) = v2) | ~ (set_difference(v0, v2) = v0) | ~ in(v1, v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ? [v3] : (set_difference(v3, v1) = v2 & set_union2(v0, v1) = v3)) & ! [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)) & ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) % 2.84/1.43 | % 2.84/1.43 | Applying alpha-rule on (1) yields: % 2.84/1.43 | (2) ~ (all_0_2_2 = all_0_5_5) % 2.84/1.43 | (3) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 2.84/1.43 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ empty(v2) | empty(v0)) % 2.84/1.43 | (5) empty(all_0_0_0) % 2.84/1.43 | (6) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ~ empty(v2) | empty(v0)) % 2.84/1.43 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) % 2.84/1.44 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (singleton(v1) = v2) | ~ (set_difference(v0, v2) = v3) | in(v1, v0)) % 2.84/1.44 | (9) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ? [v3] : (set_difference(v3, v1) = v2 & set_union2(v0, v1) = v3)) % 2.84/1.44 | (10) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) % 2.84/1.44 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v2, v1) = v3) | ~ (set_union2(v0, v1) = v2) | set_difference(v0, v1) = v3) % 2.84/1.44 | (12) ~ empty(all_0_1_1) % 2.84/1.44 | (13) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) % 2.84/1.44 | (14) singleton(all_0_6_6) = all_0_4_4 % 2.84/1.44 | (15) set_difference(all_0_3_3, all_0_4_4) = all_0_2_2 % 2.84/1.44 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) % 2.84/1.44 | (17) set_union2(all_0_5_5, all_0_4_4) = all_0_3_3 % 2.84/1.44 | (18) ~ in(all_0_6_6, all_0_5_5) % 2.84/1.44 | (19) ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v1) = v2) | ~ (set_difference(v0, v2) = v0) | ~ in(v1, v0)) % 2.84/1.44 | (20) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) % 2.84/1.44 | (21) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2) % 2.84/1.44 | % 2.84/1.44 | Instantiating formula (11) with all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5 and discharging atoms set_difference(all_0_3_3, all_0_4_4) = all_0_2_2, set_union2(all_0_5_5, all_0_4_4) = all_0_3_3, yields: % 2.84/1.44 | (22) set_difference(all_0_5_5, all_0_4_4) = all_0_2_2 % 2.84/1.44 | % 2.84/1.44 | Instantiating formula (8) with all_0_2_2, all_0_4_4, all_0_6_6, all_0_5_5 and discharging atoms singleton(all_0_6_6) = all_0_4_4, set_difference(all_0_5_5, all_0_4_4) = all_0_2_2, ~ in(all_0_6_6, all_0_5_5), yields: % 2.84/1.44 | (23) all_0_2_2 = all_0_5_5 % 2.84/1.44 | % 2.84/1.44 | Equations (23) can reduce 2 to: % 2.84/1.44 | (24) $false % 2.84/1.44 | % 2.84/1.44 |-The branch is then unsatisfiable % 2.84/1.44 % SZS output end Proof for theBenchmark % 2.84/1.44 % 2.84/1.44 833ms %------------------------------------------------------------------------------