%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET891+1 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n025.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 00:22:57 EDT 2022 % Result : Theorem 1.91s 1.13s % Output : Proof 2.79s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.11 % Problem : SET891+1 : TPTP v8.1.0. Released v3.2.0. % 0.07/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n025.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 16:04:31 EDT 2022 % 0.12/0.33 % CPUTime : % 0.18/0.57 ____ _ % 0.18/0.57 ___ / __ \_____(_)___ ________ __________ % 0.18/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.18/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.18/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.18/0.57 % 0.18/0.57 A Theorem Prover for First-Order Logic % 0.18/0.57 (ePrincess v.1.0) % 0.18/0.57 % 0.18/0.57 (c) Philipp Rümmer, 2009-2015 % 0.18/0.57 (c) Peter Backeman, 2014-2015 % 0.18/0.57 (contributions by Angelo Brillout, Peter Baumgartner) % 0.18/0.57 Free software under GNU Lesser General Public License (LGPL). % 0.18/0.57 Bug reports to peter@backeman.se % 0.18/0.57 % 0.18/0.57 For more information, visit http://user.uu.se/~petba168/breu/ % 0.18/0.57 % 0.18/0.57 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.69/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.36/0.88 Prover 0: Preprocessing ... % 1.68/1.04 Prover 0: Constructing countermodel ... % 1.91/1.13 Prover 0: proved (482ms) % 1.91/1.13 % 1.91/1.13 No countermodel exists, formula is valid % 1.91/1.13 % SZS status Theorem for theBenchmark % 1.91/1.13 % 1.91/1.13 Generating proof ... found it (size 16) % 2.60/1.34 % 2.60/1.34 % SZS output start Proof for theBenchmark % 2.60/1.34 Assumed formulas after preprocessing and simplification: % 2.60/1.34 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ( ~ (v6 = v5) & singleton(v1) = v3 & singleton(v0) = v2 & union(v4) = v5 & unordered_pair(v2, v3) = v4 & unordered_pair(v0, v1) = v6 & empty(v8) & ~ empty(v7) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (singleton(v10) = v12) | ~ (singleton(v9) = v11) | ~ (set_union2(v11, v12) = v13) | unordered_pair(v9, v10) = v13) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (set_union2(v12, v11) = v10) | ~ (set_union2(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (unordered_pair(v12, v11) = v10) | ~ (unordered_pair(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (singleton(v11) = v10) | ~ (singleton(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (union(v11) = v10) | ~ (union(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_union2(v10, v9) = v11) | ~ empty(v11) | empty(v9)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_union2(v10, v9) = v11) | set_union2(v9, v10) = v11) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_union2(v9, v10) = v11) | ~ empty(v11) | empty(v9)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_union2(v9, v10) = v11) | set_union2(v10, v9) = v11) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_union2(v9, v10) = v11) | ? [v12] : (union(v12) = v11 & unordered_pair(v9, v10) = v12)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (unordered_pair(v10, v9) = v11) | unordered_pair(v9, v10) = v11) & ! [v9] : ! [v10] : ! [v11] : ( ~ (unordered_pair(v9, v10) = v11) | unordered_pair(v10, v9) = v11) & ! [v9] : ! [v10] : ! [v11] : ( ~ (unordered_pair(v9, v10) = v11) | ? [v12] : ? [v13] : (singleton(v10) = v13 & singleton(v9) = v12 & set_union2(v12, v13) = v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (unordered_pair(v9, v10) = v11) | ? [v12] : (union(v11) = v12 & set_union2(v9, v10) = v12)) & ! [v9] : ! [v10] : (v10 = v9 | ~ (set_union2(v9, v9) = v10))) % 2.79/1.38 | 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, all_0_7_7, all_0_8_8 yields: % 2.79/1.38 | (1) ~ (all_0_2_2 = all_0_3_3) & singleton(all_0_7_7) = all_0_5_5 & singleton(all_0_8_8) = all_0_6_6 & union(all_0_4_4) = all_0_3_3 & unordered_pair(all_0_6_6, all_0_5_5) = all_0_4_4 & unordered_pair(all_0_8_8, all_0_7_7) = all_0_2_2 & empty(all_0_0_0) & ~ empty(all_0_1_1) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v1) = v3) | ~ (singleton(v0) = v2) | ~ (set_union2(v2, v3) = v4) | unordered_pair(v0, v1) = v4) & ! [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] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(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] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : (union(v3) = v2 & unordered_pair(v0, v1) = v3)) & ! [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) | ? [v3] : ? [v4] : (singleton(v1) = v4 & singleton(v0) = v3 & set_union2(v3, v4) = v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ? [v3] : (union(v2) = v3 & set_union2(v0, v1) = v3)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) % 2.79/1.39 | % 2.79/1.39 | Applying alpha-rule on (1) yields: % 2.79/1.39 | (2) singleton(all_0_8_8) = all_0_6_6 % 2.79/1.39 | (3) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ? [v3] : (union(v2) = v3 & set_union2(v0, v1) = v3)) % 2.79/1.39 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) % 2.79/1.39 | (5) unordered_pair(all_0_8_8, all_0_7_7) = all_0_2_2 % 2.79/1.39 | (6) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = v0)) % 2.79/1.39 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v1) = v3) | ~ (singleton(v0) = v2) | ~ (set_union2(v2, v3) = v4) | unordered_pair(v0, v1) = v4) % 2.79/1.39 | (8) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) % 2.79/1.39 | (9) union(all_0_4_4) = all_0_3_3 % 2.79/1.39 | (10) empty(all_0_0_0) % 2.79/1.39 | (11) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ~ empty(v2) | empty(v0)) % 2.79/1.39 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) % 2.79/1.39 | (13) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2) % 2.79/1.39 | (14) singleton(all_0_7_7) = all_0_5_5 % 2.79/1.39 | (15) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v1) = v4 & singleton(v0) = v3 & set_union2(v3, v4) = v2)) % 2.79/1.39 | (16) ~ empty(all_0_1_1) % 2.79/1.39 | (17) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 2.79/1.39 | (18) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ empty(v2) | empty(v0)) % 2.79/1.39 | (19) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) % 2.79/1.39 | (20) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2) % 2.79/1.39 | (21) unordered_pair(all_0_6_6, all_0_5_5) = all_0_4_4 % 2.79/1.39 | (22) ~ (all_0_2_2 = all_0_3_3) % 2.79/1.39 | (23) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : (union(v3) = v2 & unordered_pair(v0, v1) = v3)) % 2.79/1.39 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) % 2.79/1.39 | % 2.79/1.39 | Instantiating formula (3) with all_0_4_4, all_0_5_5, all_0_6_6 and discharging atoms unordered_pair(all_0_6_6, all_0_5_5) = all_0_4_4, yields: % 2.79/1.39 | (25) ? [v0] : (union(all_0_4_4) = v0 & set_union2(all_0_6_6, all_0_5_5) = v0) % 2.79/1.39 | % 2.79/1.39 | Instantiating formula (15) with all_0_2_2, all_0_7_7, all_0_8_8 and discharging atoms unordered_pair(all_0_8_8, all_0_7_7) = all_0_2_2, yields: % 2.79/1.39 | (26) ? [v0] : ? [v1] : (singleton(all_0_7_7) = v1 & singleton(all_0_8_8) = v0 & set_union2(v0, v1) = all_0_2_2) % 2.79/1.39 | % 2.79/1.39 | Instantiating (25) with all_11_0_10 yields: % 2.79/1.39 | (27) union(all_0_4_4) = all_11_0_10 & set_union2(all_0_6_6, all_0_5_5) = all_11_0_10 % 2.79/1.39 | % 2.79/1.40 | Applying alpha-rule on (27) yields: % 2.79/1.40 | (28) union(all_0_4_4) = all_11_0_10 % 2.79/1.40 | (29) set_union2(all_0_6_6, all_0_5_5) = all_11_0_10 % 2.79/1.40 | % 2.79/1.40 | Instantiating (26) with all_13_0_11, all_13_1_12 yields: % 2.79/1.40 | (30) singleton(all_0_7_7) = all_13_0_11 & singleton(all_0_8_8) = all_13_1_12 & set_union2(all_13_1_12, all_13_0_11) = all_0_2_2 % 2.79/1.40 | % 2.79/1.40 | Applying alpha-rule on (30) yields: % 2.79/1.40 | (31) singleton(all_0_7_7) = all_13_0_11 % 2.79/1.40 | (32) singleton(all_0_8_8) = all_13_1_12 % 2.79/1.40 | (33) set_union2(all_13_1_12, all_13_0_11) = all_0_2_2 % 2.79/1.40 | % 2.79/1.40 | Instantiating formula (17) with all_0_7_7, all_13_0_11, all_0_5_5 and discharging atoms singleton(all_0_7_7) = all_13_0_11, singleton(all_0_7_7) = all_0_5_5, yields: % 2.79/1.40 | (34) all_13_0_11 = all_0_5_5 % 2.79/1.40 | % 2.79/1.40 | Instantiating formula (17) with all_0_8_8, all_13_1_12, all_0_6_6 and discharging atoms singleton(all_0_8_8) = all_13_1_12, singleton(all_0_8_8) = all_0_6_6, yields: % 2.79/1.40 | (35) all_13_1_12 = all_0_6_6 % 2.79/1.40 | % 2.79/1.40 | Instantiating formula (6) with all_0_4_4, all_11_0_10, all_0_3_3 and discharging atoms union(all_0_4_4) = all_11_0_10, union(all_0_4_4) = all_0_3_3, yields: % 2.79/1.40 | (36) all_11_0_10 = all_0_3_3 % 2.79/1.40 | % 2.79/1.40 | From (35)(34) and (33) follows: % 2.79/1.40 | (37) set_union2(all_0_6_6, all_0_5_5) = all_0_2_2 % 2.79/1.40 | % 2.79/1.40 | From (36) and (29) follows: % 2.79/1.40 | (38) set_union2(all_0_6_6, all_0_5_5) = all_0_3_3 % 2.79/1.40 | % 2.79/1.40 | Instantiating formula (24) with all_0_6_6, all_0_5_5, all_0_3_3, all_0_2_2 and discharging atoms set_union2(all_0_6_6, all_0_5_5) = all_0_2_2, set_union2(all_0_6_6, all_0_5_5) = all_0_3_3, yields: % 2.79/1.40 | (39) all_0_2_2 = all_0_3_3 % 2.79/1.40 | % 2.79/1.40 | Equations (39) can reduce 22 to: % 2.79/1.40 | (40) $false % 2.79/1.40 | % 2.79/1.40 |-The branch is then unsatisfiable % 2.79/1.40 % SZS output end Proof for theBenchmark % 2.79/1.40 % 2.79/1.40 813ms %------------------------------------------------------------------------------