%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET968+1 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n014.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 00:23:30 EDT 2022 % Result : Theorem 2.55s 1.30s % Output : Proof 4.23s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SET968+1 : TPTP v8.1.0. Released v3.2.0. % 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n014.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 : Mon Jul 11 02:48:34 EDT 2022 % 0.12/0.33 % CPUTime : % 0.53/0.57 ____ _ % 0.53/0.57 ___ / __ \_____(_)___ ________ __________ % 0.53/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.53/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.53/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.53/0.57 % 0.53/0.57 A Theorem Prover for First-Order Logic % 0.53/0.58 (ePrincess v.1.0) % 0.53/0.58 % 0.53/0.58 (c) Philipp Rümmer, 2009-2015 % 0.53/0.58 (c) Peter Backeman, 2014-2015 % 0.53/0.58 (contributions by Angelo Brillout, Peter Baumgartner) % 0.53/0.58 Free software under GNU Lesser General Public License (LGPL). % 0.53/0.58 Bug reports to peter@backeman.se % 0.53/0.58 % 0.53/0.58 For more information, visit http://user.uu.se/~petba168/breu/ % 0.53/0.58 % 0.53/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.53/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.29/0.88 Prover 0: Preprocessing ... % 1.72/1.06 Prover 0: Constructing countermodel ... % 2.55/1.29 Prover 0: proved (670ms) % 2.55/1.30 % 2.55/1.30 No countermodel exists, formula is valid % 2.55/1.30 % SZS status Theorem for theBenchmark % 2.55/1.30 % 2.55/1.30 Generating proof ... found it (size 65) % 3.76/1.63 % 3.76/1.63 % SZS output start Proof for theBenchmark % 3.76/1.63 Assumed formulas after preprocessing and simplification: % 3.76/1.63 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ( ~ (v13 = v6) & cartesian_product2(v4, v5) = v6 & cartesian_product2(v1, v3) = v12 & cartesian_product2(v1, v2) = v10 & cartesian_product2(v0, v3) = v8 & cartesian_product2(v0, v2) = v7 & set_union2(v11, v12) = v13 & set_union2(v9, v10) = v11 & set_union2(v7, v8) = v9 & set_union2(v2, v3) = v5 & set_union2(v0, v1) = v4 & empty(v15) & ~ empty(v14) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (cartesian_product2(v18, v17) = v20) | ~ (cartesian_product2(v18, v16) = v19) | ~ (set_union2(v19, v20) = v21) | ? [v22] : (cartesian_product2(v18, v22) = v21 & set_union2(v16, v17) = v22)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (cartesian_product2(v17, v18) = v20) | ~ (cartesian_product2(v16, v18) = v19) | ~ (set_union2(v19, v20) = v21) | ? [v22] : (cartesian_product2(v22, v18) = v21 & set_union2(v16, v17) = v22)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (cartesian_product2(v19, v18) = v20) | ~ (set_union2(v16, v17) = v19) | ? [v21] : ? [v22] : (cartesian_product2(v17, v18) = v22 & cartesian_product2(v16, v18) = v21 & set_union2(v21, v22) = v20)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (cartesian_product2(v18, v19) = v20) | ~ (set_union2(v16, v17) = v19) | ? [v21] : ? [v22] : (cartesian_product2(v18, v17) = v22 & cartesian_product2(v18, v16) = v21 & set_union2(v21, v22) = v20)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (set_union2(v19, v18) = v20) | ~ (set_union2(v16, v17) = v19) | ? [v21] : (set_union2(v17, v18) = v21 & set_union2(v16, v21) = v20)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (set_union2(v17, v18) = v19) | ~ (set_union2(v16, v19) = v20) | ? [v21] : (set_union2(v21, v18) = v20 & set_union2(v16, v17) = v21)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v17 = v16 | ~ (cartesian_product2(v19, v18) = v17) | ~ (cartesian_product2(v19, v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v17 = v16 | ~ (set_union2(v19, v18) = v17) | ~ (set_union2(v19, v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (set_union2(v17, v16) = v18) | ~ empty(v18) | empty(v16)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (set_union2(v17, v16) = v18) | set_union2(v16, v17) = v18) & ! [v16] : ! [v17] : ! [v18] : ( ~ (set_union2(v16, v17) = v18) | ~ empty(v18) | empty(v16)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (set_union2(v16, v17) = v18) | set_union2(v17, v16) = v18) & ! [v16] : ! [v17] : (v17 = v16 | ~ (set_union2(v16, v16) = v17))) % 4.06/1.66 | 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, all_0_9_9, all_0_10_10, all_0_11_11, all_0_12_12, all_0_13_13, all_0_14_14, all_0_15_15 yields: % 4.06/1.66 | (1) ~ (all_0_2_2 = all_0_9_9) & cartesian_product2(all_0_11_11, all_0_10_10) = all_0_9_9 & cartesian_product2(all_0_14_14, all_0_12_12) = all_0_3_3 & cartesian_product2(all_0_14_14, all_0_13_13) = all_0_5_5 & cartesian_product2(all_0_15_15, all_0_12_12) = all_0_7_7 & cartesian_product2(all_0_15_15, all_0_13_13) = all_0_8_8 & set_union2(all_0_4_4, all_0_3_3) = all_0_2_2 & set_union2(all_0_6_6, all_0_5_5) = all_0_4_4 & set_union2(all_0_8_8, all_0_7_7) = all_0_6_6 & set_union2(all_0_13_13, all_0_12_12) = all_0_10_10 & set_union2(all_0_15_15, all_0_14_14) = all_0_11_11 & empty(all_0_0_0) & ~ empty(all_0_1_1) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v1) = v4) | ~ (cartesian_product2(v2, v0) = v3) | ~ (set_union2(v3, v4) = v5) | ? [v6] : (cartesian_product2(v2, v6) = v5 & set_union2(v0, v1) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v1, v2) = v4) | ~ (cartesian_product2(v0, v2) = v3) | ~ (set_union2(v3, v4) = v5) | ? [v6] : (cartesian_product2(v6, v2) = v5 & set_union2(v0, v1) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v3, v2) = v4) | ~ (set_union2(v0, v1) = v3) | ? [v5] : ? [v6] : (cartesian_product2(v1, v2) = v6 & cartesian_product2(v0, v2) = v5 & set_union2(v5, v6) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v2, v3) = v4) | ~ (set_union2(v0, v1) = v3) | ? [v5] : ? [v6] : (cartesian_product2(v2, v1) = v6 & cartesian_product2(v2, v0) = v5 & set_union2(v5, v6) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_union2(v3, v2) = v4) | ~ (set_union2(v0, v1) = v3) | ? [v5] : (set_union2(v1, v2) = v5 & set_union2(v0, v5) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_union2(v1, v2) = v3) | ~ (set_union2(v0, v3) = v4) | ? [v5] : (set_union2(v5, v2) = v4 & set_union2(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, 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)) % 4.06/1.67 | % 4.06/1.67 | Applying alpha-rule on (1) yields: % 4.06/1.67 | (2) cartesian_product2(all_0_11_11, all_0_10_10) = all_0_9_9 % 4.06/1.67 | (3) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) % 4.06/1.67 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2) % 4.06/1.67 | (5) empty(all_0_0_0) % 4.06/1.67 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_union2(v3, v2) = v4) | ~ (set_union2(v0, v1) = v3) | ? [v5] : (set_union2(v1, v2) = v5 & set_union2(v0, v5) = v4)) % 4.06/1.67 | (7) set_union2(all_0_6_6, all_0_5_5) = all_0_4_4 % 4.06/1.67 | (8) set_union2(all_0_15_15, all_0_14_14) = all_0_11_11 % 4.06/1.67 | (9) ~ empty(all_0_1_1) % 4.06/1.67 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) % 4.06/1.67 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v3, v2) = v4) | ~ (set_union2(v0, v1) = v3) | ? [v5] : ? [v6] : (cartesian_product2(v1, v2) = v6 & cartesian_product2(v0, v2) = v5 & set_union2(v5, v6) = v4)) % 4.06/1.67 | (12) ~ (all_0_2_2 = all_0_9_9) % 4.06/1.67 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v1, v2) = v4) | ~ (cartesian_product2(v0, v2) = v3) | ~ (set_union2(v3, v4) = v5) | ? [v6] : (cartesian_product2(v6, v2) = v5 & set_union2(v0, v1) = v6)) % 4.06/1.67 | (14) cartesian_product2(all_0_15_15, all_0_12_12) = all_0_7_7 % 4.06/1.67 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v1) = v4) | ~ (cartesian_product2(v2, v0) = v3) | ~ (set_union2(v3, v4) = v5) | ? [v6] : (cartesian_product2(v2, v6) = v5 & set_union2(v0, v1) = v6)) % 4.06/1.67 | (16) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ~ empty(v2) | empty(v0)) % 4.06/1.67 | (17) cartesian_product2(all_0_14_14, all_0_12_12) = all_0_3_3 % 4.06/1.67 | (18) set_union2(all_0_8_8, all_0_7_7) = all_0_6_6 % 4.23/1.67 | (19) set_union2(all_0_4_4, all_0_3_3) = all_0_2_2 % 4.23/1.67 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_union2(v1, v2) = v3) | ~ (set_union2(v0, v3) = v4) | ? [v5] : (set_union2(v5, v2) = v4 & set_union2(v0, v1) = v5)) % 4.23/1.67 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) % 4.23/1.67 | (22) cartesian_product2(all_0_14_14, all_0_13_13) = all_0_5_5 % 4.23/1.67 | (23) set_union2(all_0_13_13, all_0_12_12) = all_0_10_10 % 4.23/1.67 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v2, v3) = v4) | ~ (set_union2(v0, v1) = v3) | ? [v5] : ? [v6] : (cartesian_product2(v2, v1) = v6 & cartesian_product2(v2, v0) = v5 & set_union2(v5, v6) = v4)) % 4.23/1.67 | (25) cartesian_product2(all_0_15_15, all_0_13_13) = all_0_8_8 % 4.23/1.68 | (26) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) % 4.23/1.68 | (27) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ empty(v2) | empty(v0)) % 4.23/1.68 | % 4.23/1.68 | Instantiating formula (6) with all_0_2_2, all_0_4_4, all_0_3_3, all_0_5_5, all_0_6_6 and discharging atoms set_union2(all_0_4_4, all_0_3_3) = all_0_2_2, set_union2(all_0_6_6, all_0_5_5) = all_0_4_4, yields: % 4.23/1.68 | (28) ? [v0] : (set_union2(all_0_5_5, all_0_3_3) = v0 & set_union2(all_0_6_6, v0) = all_0_2_2) % 4.23/1.68 | % 4.23/1.68 | Instantiating formula (15) with all_0_6_6, all_0_7_7, all_0_8_8, all_0_15_15, all_0_12_12, all_0_13_13 and discharging atoms cartesian_product2(all_0_15_15, all_0_12_12) = all_0_7_7, cartesian_product2(all_0_15_15, all_0_13_13) = all_0_8_8, set_union2(all_0_8_8, all_0_7_7) = all_0_6_6, yields: % 4.23/1.68 | (29) ? [v0] : (cartesian_product2(all_0_15_15, v0) = all_0_6_6 & set_union2(all_0_13_13, all_0_12_12) = v0) % 4.23/1.68 | % 4.23/1.68 | Instantiating formula (24) with all_0_9_9, all_0_10_10, all_0_11_11, all_0_12_12, all_0_13_13 and discharging atoms cartesian_product2(all_0_11_11, all_0_10_10) = all_0_9_9, set_union2(all_0_13_13, all_0_12_12) = all_0_10_10, yields: % 4.23/1.68 | (30) ? [v0] : ? [v1] : (cartesian_product2(all_0_11_11, all_0_12_12) = v1 & cartesian_product2(all_0_11_11, all_0_13_13) = v0 & set_union2(v0, v1) = all_0_9_9) % 4.23/1.68 | % 4.23/1.68 | Instantiating formula (4) with all_0_10_10, all_0_13_13, all_0_12_12 and discharging atoms set_union2(all_0_13_13, all_0_12_12) = all_0_10_10, yields: % 4.23/1.68 | (31) set_union2(all_0_12_12, all_0_13_13) = all_0_10_10 % 4.23/1.68 | % 4.23/1.68 | Instantiating formula (11) with all_0_9_9, all_0_11_11, all_0_10_10, all_0_14_14, all_0_15_15 and discharging atoms cartesian_product2(all_0_11_11, all_0_10_10) = all_0_9_9, set_union2(all_0_15_15, all_0_14_14) = all_0_11_11, yields: % 4.23/1.68 | (32) ? [v0] : ? [v1] : (cartesian_product2(all_0_14_14, all_0_10_10) = v1 & cartesian_product2(all_0_15_15, all_0_10_10) = v0 & set_union2(v0, v1) = all_0_9_9) % 4.23/1.68 | % 4.23/1.68 | Instantiating formula (4) with all_0_11_11, all_0_15_15, all_0_14_14 and discharging atoms set_union2(all_0_15_15, all_0_14_14) = all_0_11_11, yields: % 4.23/1.68 | (33) set_union2(all_0_14_14, all_0_15_15) = all_0_11_11 % 4.23/1.68 | % 4.23/1.68 | Instantiating (30) with all_9_0_16, all_9_1_17 yields: % 4.23/1.68 | (34) cartesian_product2(all_0_11_11, all_0_12_12) = all_9_0_16 & cartesian_product2(all_0_11_11, all_0_13_13) = all_9_1_17 & set_union2(all_9_1_17, all_9_0_16) = all_0_9_9 % 4.23/1.68 | % 4.23/1.68 | Applying alpha-rule on (34) yields: % 4.23/1.68 | (35) cartesian_product2(all_0_11_11, all_0_12_12) = all_9_0_16 % 4.23/1.68 | (36) cartesian_product2(all_0_11_11, all_0_13_13) = all_9_1_17 % 4.23/1.68 | (37) set_union2(all_9_1_17, all_9_0_16) = all_0_9_9 % 4.23/1.68 | % 4.23/1.68 | Instantiating (29) with all_11_0_18 yields: % 4.23/1.68 | (38) cartesian_product2(all_0_15_15, all_11_0_18) = all_0_6_6 & set_union2(all_0_13_13, all_0_12_12) = all_11_0_18 % 4.23/1.68 | % 4.23/1.68 | Applying alpha-rule on (38) yields: % 4.23/1.68 | (39) cartesian_product2(all_0_15_15, all_11_0_18) = all_0_6_6 % 4.23/1.68 | (40) set_union2(all_0_13_13, all_0_12_12) = all_11_0_18 % 4.23/1.68 | % 4.23/1.68 | Instantiating (28) with all_13_0_19 yields: % 4.23/1.68 | (41) set_union2(all_0_5_5, all_0_3_3) = all_13_0_19 & set_union2(all_0_6_6, all_13_0_19) = all_0_2_2 % 4.23/1.68 | % 4.23/1.68 | Applying alpha-rule on (41) yields: % 4.23/1.68 | (42) set_union2(all_0_5_5, all_0_3_3) = all_13_0_19 % 4.23/1.68 | (43) set_union2(all_0_6_6, all_13_0_19) = all_0_2_2 % 4.23/1.68 | % 4.23/1.68 | Instantiating (32) with all_15_0_20, all_15_1_21 yields: % 4.23/1.68 | (44) cartesian_product2(all_0_14_14, all_0_10_10) = all_15_0_20 & cartesian_product2(all_0_15_15, all_0_10_10) = all_15_1_21 & set_union2(all_15_1_21, all_15_0_20) = all_0_9_9 % 4.23/1.68 | % 4.23/1.68 | Applying alpha-rule on (44) yields: % 4.23/1.68 | (45) cartesian_product2(all_0_14_14, all_0_10_10) = all_15_0_20 % 4.23/1.68 | (46) cartesian_product2(all_0_15_15, all_0_10_10) = all_15_1_21 % 4.23/1.68 | (47) set_union2(all_15_1_21, all_15_0_20) = all_0_9_9 % 4.23/1.68 | % 4.23/1.68 | Instantiating formula (10) with all_0_13_13, all_0_12_12, all_11_0_18, all_0_10_10 and discharging atoms set_union2(all_0_13_13, all_0_12_12) = all_11_0_18, set_union2(all_0_13_13, all_0_12_12) = all_0_10_10, yields: % 4.23/1.68 | (48) all_11_0_18 = all_0_10_10 % 4.23/1.68 | % 4.23/1.68 | From (48) and (39) follows: % 4.23/1.68 | (49) cartesian_product2(all_0_15_15, all_0_10_10) = all_0_6_6 % 4.23/1.68 | % 4.23/1.68 | From (48) and (40) follows: % 4.23/1.68 | (23) set_union2(all_0_13_13, all_0_12_12) = all_0_10_10 % 4.23/1.68 | % 4.23/1.68 | Instantiating formula (21) with all_0_15_15, all_0_10_10, all_0_6_6, all_15_1_21 and discharging atoms cartesian_product2(all_0_15_15, all_0_10_10) = all_15_1_21, cartesian_product2(all_0_15_15, all_0_10_10) = all_0_6_6, yields: % 4.23/1.69 | (51) all_15_1_21 = all_0_6_6 % 4.23/1.69 | % 4.23/1.69 | From (51) and (47) follows: % 4.23/1.69 | (52) set_union2(all_0_6_6, all_15_0_20) = all_0_9_9 % 4.23/1.69 | % 4.23/1.69 | Instantiating formula (11) with all_9_0_16, all_0_11_11, all_0_12_12, all_0_14_14, all_0_15_15 and discharging atoms cartesian_product2(all_0_11_11, all_0_12_12) = all_9_0_16, set_union2(all_0_15_15, all_0_14_14) = all_0_11_11, yields: % 4.23/1.69 | (53) ? [v0] : ? [v1] : (cartesian_product2(all_0_14_14, all_0_12_12) = v1 & cartesian_product2(all_0_15_15, all_0_12_12) = v0 & set_union2(v0, v1) = all_9_0_16) % 4.23/1.69 | % 4.23/1.69 | Instantiating formula (11) with all_9_1_17, all_0_11_11, all_0_13_13, all_0_14_14, all_0_15_15 and discharging atoms cartesian_product2(all_0_11_11, all_0_13_13) = all_9_1_17, set_union2(all_0_15_15, all_0_14_14) = all_0_11_11, yields: % 4.23/1.69 | (54) ? [v0] : ? [v1] : (cartesian_product2(all_0_14_14, all_0_13_13) = v1 & cartesian_product2(all_0_15_15, all_0_13_13) = v0 & set_union2(v0, v1) = all_9_1_17) % 4.23/1.69 | % 4.23/1.69 | Instantiating formula (24) with all_15_0_20, all_0_10_10, all_0_14_14, all_0_12_12, all_0_13_13 and discharging atoms cartesian_product2(all_0_14_14, all_0_10_10) = all_15_0_20, set_union2(all_0_13_13, all_0_12_12) = all_0_10_10, yields: % 4.23/1.69 | (55) ? [v0] : ? [v1] : (cartesian_product2(all_0_14_14, all_0_12_12) = v1 & cartesian_product2(all_0_14_14, all_0_13_13) = v0 & set_union2(v0, v1) = all_15_0_20) % 4.23/1.69 | % 4.23/1.69 | Instantiating formula (24) with all_15_0_20, all_0_10_10, all_0_14_14, all_0_13_13, all_0_12_12 and discharging atoms cartesian_product2(all_0_14_14, all_0_10_10) = all_15_0_20, set_union2(all_0_12_12, all_0_13_13) = all_0_10_10, yields: % 4.23/1.69 | (56) ? [v0] : ? [v1] : (cartesian_product2(all_0_14_14, all_0_12_12) = v0 & cartesian_product2(all_0_14_14, all_0_13_13) = v1 & set_union2(v0, v1) = all_15_0_20) % 4.23/1.69 | % 4.23/1.69 | Instantiating formula (11) with all_9_0_16, all_0_11_11, all_0_12_12, all_0_15_15, all_0_14_14 and discharging atoms cartesian_product2(all_0_11_11, all_0_12_12) = all_9_0_16, set_union2(all_0_14_14, all_0_15_15) = all_0_11_11, yields: % 4.23/1.69 | (57) ? [v0] : ? [v1] : (cartesian_product2(all_0_14_14, all_0_12_12) = v0 & cartesian_product2(all_0_15_15, all_0_12_12) = v1 & set_union2(v0, v1) = all_9_0_16) % 4.23/1.69 | % 4.23/1.69 | Instantiating formula (11) with all_9_1_17, all_0_11_11, all_0_13_13, all_0_15_15, all_0_14_14 and discharging atoms cartesian_product2(all_0_11_11, all_0_13_13) = all_9_1_17, set_union2(all_0_14_14, all_0_15_15) = all_0_11_11, yields: % 4.23/1.69 | (58) ? [v0] : ? [v1] : (cartesian_product2(all_0_14_14, all_0_13_13) = v0 & cartesian_product2(all_0_15_15, all_0_13_13) = v1 & set_union2(v0, v1) = all_9_1_17) % 4.23/1.69 | % 4.23/1.69 | Instantiating (55) with all_45_0_29, all_45_1_30 yields: % 4.23/1.69 | (59) cartesian_product2(all_0_14_14, all_0_12_12) = all_45_0_29 & cartesian_product2(all_0_14_14, all_0_13_13) = all_45_1_30 & set_union2(all_45_1_30, all_45_0_29) = all_15_0_20 % 4.23/1.69 | % 4.23/1.69 | Applying alpha-rule on (59) yields: % 4.23/1.69 | (60) cartesian_product2(all_0_14_14, all_0_12_12) = all_45_0_29 % 4.23/1.69 | (61) cartesian_product2(all_0_14_14, all_0_13_13) = all_45_1_30 % 4.23/1.69 | (62) set_union2(all_45_1_30, all_45_0_29) = all_15_0_20 % 4.23/1.69 | % 4.23/1.69 | Instantiating (54) with all_55_0_35, all_55_1_36 yields: % 4.23/1.69 | (63) cartesian_product2(all_0_14_14, all_0_13_13) = all_55_0_35 & cartesian_product2(all_0_15_15, all_0_13_13) = all_55_1_36 & set_union2(all_55_1_36, all_55_0_35) = all_9_1_17 % 4.23/1.69 | % 4.23/1.69 | Applying alpha-rule on (63) yields: % 4.23/1.69 | (64) cartesian_product2(all_0_14_14, all_0_13_13) = all_55_0_35 % 4.23/1.69 | (65) cartesian_product2(all_0_15_15, all_0_13_13) = all_55_1_36 % 4.23/1.69 | (66) set_union2(all_55_1_36, all_55_0_35) = all_9_1_17 % 4.23/1.69 | % 4.23/1.69 | Instantiating (58) with all_63_0_40, all_63_1_41 yields: % 4.23/1.69 | (67) cartesian_product2(all_0_14_14, all_0_13_13) = all_63_1_41 & cartesian_product2(all_0_15_15, all_0_13_13) = all_63_0_40 & set_union2(all_63_1_41, all_63_0_40) = all_9_1_17 % 4.23/1.69 | % 4.23/1.69 | Applying alpha-rule on (67) yields: % 4.23/1.69 | (68) cartesian_product2(all_0_14_14, all_0_13_13) = all_63_1_41 % 4.23/1.69 | (69) cartesian_product2(all_0_15_15, all_0_13_13) = all_63_0_40 % 4.23/1.69 | (70) set_union2(all_63_1_41, all_63_0_40) = all_9_1_17 % 4.23/1.69 | % 4.23/1.69 | Instantiating (57) with all_65_0_42, all_65_1_43 yields: % 4.23/1.69 | (71) cartesian_product2(all_0_14_14, all_0_12_12) = all_65_1_43 & cartesian_product2(all_0_15_15, all_0_12_12) = all_65_0_42 & set_union2(all_65_1_43, all_65_0_42) = all_9_0_16 % 4.23/1.69 | % 4.23/1.69 | Applying alpha-rule on (71) yields: % 4.23/1.69 | (72) cartesian_product2(all_0_14_14, all_0_12_12) = all_65_1_43 % 4.23/1.69 | (73) cartesian_product2(all_0_15_15, all_0_12_12) = all_65_0_42 % 4.23/1.69 | (74) set_union2(all_65_1_43, all_65_0_42) = all_9_0_16 % 4.23/1.69 | % 4.23/1.69 | Instantiating (53) with all_69_0_46, all_69_1_47 yields: % 4.23/1.69 | (75) cartesian_product2(all_0_14_14, all_0_12_12) = all_69_0_46 & cartesian_product2(all_0_15_15, all_0_12_12) = all_69_1_47 & set_union2(all_69_1_47, all_69_0_46) = all_9_0_16 % 4.23/1.69 | % 4.23/1.69 | Applying alpha-rule on (75) yields: % 4.23/1.69 | (76) cartesian_product2(all_0_14_14, all_0_12_12) = all_69_0_46 % 4.23/1.69 | (77) cartesian_product2(all_0_15_15, all_0_12_12) = all_69_1_47 % 4.23/1.69 | (78) set_union2(all_69_1_47, all_69_0_46) = all_9_0_16 % 4.23/1.69 | % 4.23/1.69 | Instantiating (56) with all_71_0_48, all_71_1_49 yields: % 4.23/1.69 | (79) cartesian_product2(all_0_14_14, all_0_12_12) = all_71_1_49 & cartesian_product2(all_0_14_14, all_0_13_13) = all_71_0_48 & set_union2(all_71_1_49, all_71_0_48) = all_15_0_20 % 4.23/1.69 | % 4.23/1.69 | Applying alpha-rule on (79) yields: % 4.23/1.69 | (80) cartesian_product2(all_0_14_14, all_0_12_12) = all_71_1_49 % 4.23/1.69 | (81) cartesian_product2(all_0_14_14, all_0_13_13) = all_71_0_48 % 4.23/1.69 | (82) set_union2(all_71_1_49, all_71_0_48) = all_15_0_20 % 4.23/1.69 | % 4.23/1.69 | Instantiating formula (21) with all_0_14_14, all_0_12_12, all_69_0_46, all_0_3_3 and discharging atoms cartesian_product2(all_0_14_14, all_0_12_12) = all_69_0_46, cartesian_product2(all_0_14_14, all_0_12_12) = all_0_3_3, yields: % 4.23/1.69 | (83) all_69_0_46 = all_0_3_3 % 4.23/1.69 | % 4.23/1.70 | Instantiating formula (21) with all_0_14_14, all_0_12_12, all_69_0_46, all_71_1_49 and discharging atoms cartesian_product2(all_0_14_14, all_0_12_12) = all_71_1_49, cartesian_product2(all_0_14_14, all_0_12_12) = all_69_0_46, yields: % 4.23/1.70 | (84) all_71_1_49 = all_69_0_46 % 4.23/1.70 | % 4.23/1.70 | Instantiating formula (21) with all_0_14_14, all_0_12_12, all_65_1_43, all_71_1_49 and discharging atoms cartesian_product2(all_0_14_14, all_0_12_12) = all_71_1_49, cartesian_product2(all_0_14_14, all_0_12_12) = all_65_1_43, yields: % 4.23/1.70 | (85) all_71_1_49 = all_65_1_43 % 4.23/1.70 | % 4.23/1.70 | Instantiating formula (21) with all_0_14_14, all_0_12_12, all_45_0_29, all_71_1_49 and discharging atoms cartesian_product2(all_0_14_14, all_0_12_12) = all_71_1_49, cartesian_product2(all_0_14_14, all_0_12_12) = all_45_0_29, yields: % 4.23/1.70 | (86) all_71_1_49 = all_45_0_29 % 4.23/1.70 | % 4.23/1.70 | Instantiating formula (21) with all_0_14_14, all_0_13_13, all_71_0_48, all_0_5_5 and discharging atoms cartesian_product2(all_0_14_14, all_0_13_13) = all_71_0_48, cartesian_product2(all_0_14_14, all_0_13_13) = all_0_5_5, yields: % 4.23/1.70 | (87) all_71_0_48 = all_0_5_5 % 4.23/1.70 | % 4.23/1.70 | Instantiating formula (21) with all_0_14_14, all_0_13_13, all_63_1_41, all_71_0_48 and discharging atoms cartesian_product2(all_0_14_14, all_0_13_13) = all_71_0_48, cartesian_product2(all_0_14_14, all_0_13_13) = all_63_1_41, yields: % 4.23/1.70 | (88) all_71_0_48 = all_63_1_41 % 4.23/1.70 | % 4.23/1.70 | Instantiating formula (21) with all_0_14_14, all_0_13_13, all_55_0_35, all_63_1_41 and discharging atoms cartesian_product2(all_0_14_14, all_0_13_13) = all_63_1_41, cartesian_product2(all_0_14_14, all_0_13_13) = all_55_0_35, yields: % 4.23/1.70 | (89) all_63_1_41 = all_55_0_35 % 4.23/1.70 | % 4.23/1.70 | Instantiating formula (21) with all_0_14_14, all_0_13_13, all_45_1_30, all_55_0_35 and discharging atoms cartesian_product2(all_0_14_14, all_0_13_13) = all_55_0_35, cartesian_product2(all_0_14_14, all_0_13_13) = all_45_1_30, yields: % 4.23/1.70 | (90) all_55_0_35 = all_45_1_30 % 4.23/1.70 | % 4.23/1.70 | Combining equations (88,87) yields a new equation: % 4.23/1.70 | (91) all_63_1_41 = all_0_5_5 % 4.23/1.70 | % 4.23/1.70 | Simplifying 91 yields: % 4.23/1.70 | (92) all_63_1_41 = all_0_5_5 % 4.23/1.70 | % 4.23/1.70 | Combining equations (84,85) yields a new equation: % 4.23/1.70 | (93) all_69_0_46 = all_65_1_43 % 4.23/1.70 | % 4.23/1.70 | Simplifying 93 yields: % 4.23/1.70 | (94) all_69_0_46 = all_65_1_43 % 4.23/1.70 | % 4.23/1.70 | Combining equations (86,85) yields a new equation: % 4.23/1.70 | (95) all_65_1_43 = all_45_0_29 % 4.23/1.70 | % 4.23/1.70 | Combining equations (94,83) yields a new equation: % 4.23/1.70 | (96) all_65_1_43 = all_0_3_3 % 4.23/1.70 | % 4.23/1.70 | Simplifying 96 yields: % 4.23/1.70 | (97) all_65_1_43 = all_0_3_3 % 4.23/1.70 | % 4.23/1.70 | Combining equations (97,95) yields a new equation: % 4.23/1.70 | (98) all_45_0_29 = all_0_3_3 % 4.23/1.70 | % 4.23/1.70 | Combining equations (89,92) yields a new equation: % 4.23/1.70 | (99) all_55_0_35 = all_0_5_5 % 4.23/1.70 | % 4.23/1.70 | Simplifying 99 yields: % 4.23/1.70 | (100) all_55_0_35 = all_0_5_5 % 4.23/1.70 | % 4.23/1.70 | Combining equations (90,100) yields a new equation: % 4.23/1.70 | (101) all_45_1_30 = all_0_5_5 % 4.23/1.70 | % 4.23/1.70 | Simplifying 101 yields: % 4.23/1.70 | (102) all_45_1_30 = all_0_5_5 % 4.23/1.70 | % 4.23/1.70 | From (102)(98) and (62) follows: % 4.23/1.70 | (103) set_union2(all_0_5_5, all_0_3_3) = all_15_0_20 % 4.23/1.70 | % 4.23/1.70 | Instantiating formula (10) with all_0_5_5, all_0_3_3, all_15_0_20, all_13_0_19 and discharging atoms set_union2(all_0_5_5, all_0_3_3) = all_15_0_20, set_union2(all_0_5_5, all_0_3_3) = all_13_0_19, yields: % 4.23/1.70 | (104) all_15_0_20 = all_13_0_19 % 4.23/1.70 | % 4.23/1.70 | From (104) and (52) follows: % 4.23/1.70 | (105) set_union2(all_0_6_6, all_13_0_19) = all_0_9_9 % 4.23/1.70 | % 4.23/1.70 | Instantiating formula (10) with all_0_6_6, all_13_0_19, all_0_9_9, all_0_2_2 and discharging atoms set_union2(all_0_6_6, all_13_0_19) = all_0_2_2, set_union2(all_0_6_6, all_13_0_19) = all_0_9_9, yields: % 4.23/1.70 | (106) all_0_2_2 = all_0_9_9 % 4.23/1.70 | % 4.23/1.70 | Equations (106) can reduce 12 to: % 4.23/1.70 | (107) $false % 4.23/1.70 | % 4.23/1.70 |-The branch is then unsatisfiable % 4.23/1.70 % SZS output end Proof for theBenchmark % 4.23/1.70 % 4.23/1.70 1118ms %------------------------------------------------------------------------------