%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET906+1 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n020.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 00:23:03 EDT 2022 % Result : Theorem 2.47s 1.19s % Output : Proof 3.17s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.10 % Problem : SET906+1 : TPTP v8.1.0. Released v3.2.0. % 0.00/0.11 % Command : ePrincess-casc -timeout=%d %s % 0.10/0.30 % Computer : n020.cluster.edu % 0.10/0.30 % Model : x86_64 x86_64 % 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.30 % Memory : 8042.1875MB % 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64 % 0.10/0.30 % CPULimit : 300 % 0.10/0.30 % WCLimit : 600 % 0.10/0.30 % DateTime : Sun Jul 10 22:44:43 EDT 2022 % 0.10/0.30 % CPUTime : % 0.15/0.55 ____ _ % 0.15/0.55 ___ / __ \_____(_)___ ________ __________ % 0.15/0.55 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.15/0.55 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.15/0.55 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.15/0.55 % 0.15/0.55 A Theorem Prover for First-Order Logic % 0.15/0.56 (ePrincess v.1.0) % 0.15/0.56 % 0.15/0.56 (c) Philipp Rümmer, 2009-2015 % 0.15/0.56 (c) Peter Backeman, 2014-2015 % 0.15/0.56 (contributions by Angelo Brillout, Peter Baumgartner) % 0.15/0.56 Free software under GNU Lesser General Public License (LGPL). % 0.15/0.56 Bug reports to peter@backeman.se % 0.15/0.56 % 0.15/0.56 For more information, visit http://user.uu.se/~petba168/breu/ % 0.15/0.56 % 0.15/0.56 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.70/0.60 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.45/0.87 Prover 0: Preprocessing ... % 1.82/1.04 Prover 0: Warning: ignoring some quantifiers % 1.82/1.06 Prover 0: Constructing countermodel ... % 2.47/1.18 Prover 0: proved (580ms) % 2.47/1.19 % 2.47/1.19 No countermodel exists, formula is valid % 2.47/1.19 % SZS status Theorem for theBenchmark % 2.47/1.19 % 2.47/1.19 Generating proof ... Warning: ignoring some quantifiers % 2.97/1.39 found it (size 7) % 2.97/1.39 % 2.97/1.39 % SZS output start Proof for theBenchmark % 2.97/1.39 Assumed formulas after preprocessing and simplification: % 2.97/1.39 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (set_union2(v3, v2) = v4 & unordered_pair(v0, v1) = v3 & empty(v6) & subset(v4, v2) & ~ empty(v5) & ~ in(v0, v2) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v8 | v10 = v7 | ~ (unordered_pair(v7, v8) = v9) | ~ in(v10, v9)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (set_union2(v10, v9) = v8) | ~ (set_union2(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (unordered_pair(v10, v9) = v8) | ~ (unordered_pair(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (set_union2(v7, v8) = v9) | ~ in(v10, v9) | in(v10, v8) | in(v10, v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (set_union2(v7, v8) = v9) | ~ in(v10, v8) | in(v10, v9)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (set_union2(v7, v8) = v9) | ~ in(v10, v7) | in(v10, v9)) & ? [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v7 | ~ (set_union2(v8, v9) = v10) | ? [v11] : (( ~ in(v11, v7) | ( ~ in(v11, v9) & ~ in(v11, v8))) & (in(v11, v9) | in(v11, v8) | in(v11, v7)))) & ? [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v7 | ~ (unordered_pair(v8, v9) = v10) | ? [v11] : ((v11 = v9 | v11 = v8 | in(v11, v7)) & ( ~ in(v11, v7) | ( ~ (v11 = v9) & ~ (v11 = v8))))) & ! [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] : ! [v9] : ( ~ (unordered_pair(v8, v7) = v9) | unordered_pair(v7, v8) = v9) & ! [v7] : ! [v8] : ! [v9] : ( ~ (unordered_pair(v7, v8) = v9) | unordered_pair(v8, v7) = v9) & ! [v7] : ! [v8] : ! [v9] : ( ~ (unordered_pair(v7, v8) = v9) | in(v8, v9)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (unordered_pair(v7, v8) = v9) | in(v7, v9)) & ! [v7] : ! [v8] : ! [v9] : ( ~ subset(v7, v8) | ~ in(v9, v7) | in(v9, v8)) & ! [v7] : ! [v8] : (v8 = v7 | ~ (set_union2(v7, v7) = v8)) & ! [v7] : ! [v8] : ( ~ in(v8, v7) | ~ in(v7, v8)) & ? [v7] : ? [v8] : (subset(v7, v8) | ? [v9] : (in(v9, v7) & ~ in(v9, v8))) & ? [v7] : subset(v7, v7)) % 3.17/1.43 | 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: % 3.17/1.43 | (1) set_union2(all_0_3_3, all_0_4_4) = all_0_2_2 & unordered_pair(all_0_6_6, all_0_5_5) = all_0_3_3 & empty(all_0_0_0) & subset(all_0_2_2, all_0_4_4) & ~ empty(all_0_1_1) & ~ in(all_0_6_6, all_0_4_4) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v3 = v0 | ~ (unordered_pair(v0, v1) = v2) | ~ in(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(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] : ! [v3] : (v3 = v0 | ~ (unordered_pair(v1, v2) = v3) | ? [v4] : ((v4 = v2 | v4 = v1 | in(v4, v0)) & ( ~ in(v4, v0) | ( ~ (v4 = v2) & ~ (v4 = v1))))) & ! [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] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | in(v1, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | in(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ subset(v0, v1) | ~ in(v2, v0) | in(v2, v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) & ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) & ? [v0] : ? [v1] : (subset(v0, v1) | ? [v2] : (in(v2, v0) & ~ in(v2, v1))) & ? [v0] : subset(v0, v0) % 3.17/1.44 | % 3.17/1.44 | Applying alpha-rule on (1) yields: % 3.17/1.44 | (2) ~ empty(all_0_1_1) % 3.17/1.44 | (3) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ empty(v2) | empty(v0)) % 3.17/1.44 | (4) ~ in(all_0_6_6, all_0_4_4) % 3.17/1.44 | (5) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) % 3.17/1.44 | (6) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2) % 3.17/1.44 | (7) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (unordered_pair(v1, v2) = v3) | ? [v4] : ((v4 = v2 | v4 = v1 | in(v4, v0)) & ( ~ in(v4, v0) | ( ~ (v4 = v2) & ~ (v4 = v1))))) % 3.17/1.45 | (8) empty(all_0_0_0) % 3.17/1.45 | (9) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) % 3.17/1.45 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) % 3.17/1.45 | (11) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) % 3.17/1.45 | (12) unordered_pair(all_0_6_6, all_0_5_5) = all_0_3_3 % 3.17/1.45 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v3 = v0 | ~ (unordered_pair(v0, v1) = v2) | ~ in(v3, v2)) % 3.17/1.45 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v1) | in(v3, v0)) % 3.17/1.45 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v1) | in(v3, v2)) % 3.17/1.45 | (16) set_union2(all_0_3_3, all_0_4_4) = all_0_2_2 % 3.17/1.45 | (17) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ~ empty(v2) | empty(v0)) % 3.17/1.45 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) % 3.17/1.45 | (19) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | in(v0, v2)) % 3.17/1.45 | (20) ! [v0] : ! [v1] : ! [v2] : ( ~ subset(v0, v1) | ~ in(v2, v0) | in(v2, v1)) % 3.17/1.45 | (21) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) % 3.17/1.45 | (22) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2) % 3.17/1.45 | (23) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | in(v1, v2)) % 3.17/1.45 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v0) | in(v3, v2)) % 3.17/1.45 | (25) ? [v0] : subset(v0, v0) % 3.17/1.45 | (26) subset(all_0_2_2, all_0_4_4) % 3.17/1.45 | (27) ? [v0] : ? [v1] : (subset(v0, v1) | ? [v2] : (in(v2, v0) & ~ in(v2, v1))) % 3.17/1.45 | (28) ? [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)))) % 3.17/1.46 | % 3.17/1.46 | Instantiating formula (6) with all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms set_union2(all_0_3_3, all_0_4_4) = all_0_2_2, yields: % 3.17/1.46 | (29) set_union2(all_0_4_4, all_0_3_3) = all_0_2_2 % 3.17/1.46 | % 3.17/1.46 | Instantiating formula (19) with all_0_3_3, all_0_5_5, all_0_6_6 and discharging atoms unordered_pair(all_0_6_6, all_0_5_5) = all_0_3_3, yields: % 3.17/1.46 | (30) in(all_0_6_6, all_0_3_3) % 3.17/1.46 | % 3.17/1.46 | Instantiating formula (15) with all_0_6_6, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms set_union2(all_0_4_4, all_0_3_3) = all_0_2_2, in(all_0_6_6, all_0_3_3), yields: % 3.17/1.46 | (31) in(all_0_6_6, all_0_2_2) % 3.17/1.46 | % 3.17/1.46 | Instantiating formula (20) with all_0_6_6, all_0_4_4, all_0_2_2 and discharging atoms subset(all_0_2_2, all_0_4_4), in(all_0_6_6, all_0_2_2), ~ in(all_0_6_6, all_0_4_4), yields: % 3.17/1.46 | (32) $false % 3.17/1.46 | % 3.17/1.46 |-The branch is then unsatisfiable % 3.17/1.46 % SZS output end Proof for theBenchmark % 3.17/1.46 % 3.17/1.46 894ms %------------------------------------------------------------------------------