%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET979+1 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n012.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 00:23:34 EDT 2022 % Result : Theorem 2.28s 1.21s % Output : Proof 3.33s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SET979+1 : TPTP v8.1.0. Released v3.2.0. % 0.11/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n012.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 : Sat Jul 9 21:07:43 EDT 2022 % 0.12/0.33 % CPUTime : % 0.18/0.57 ____ _ % 0.18/0.57 ___ / __ \_____(_)___ ________ __________ % 0.18/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.18/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.18/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.18/0.58 % 0.18/0.58 A Theorem Prover for First-Order Logic % 0.18/0.58 (ePrincess v.1.0) % 0.18/0.58 % 0.18/0.58 (c) Philipp Rümmer, 2009-2015 % 0.18/0.58 (c) Peter Backeman, 2014-2015 % 0.18/0.58 (contributions by Angelo Brillout, Peter Baumgartner) % 0.18/0.58 Free software under GNU Lesser General Public License (LGPL). % 0.18/0.58 Bug reports to peter@backeman.se % 0.18/0.58 % 0.18/0.58 For more information, visit http://user.uu.se/~petba168/breu/ % 0.18/0.58 % 0.18/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.64/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.32/0.89 Prover 0: Preprocessing ... % 1.71/1.09 Prover 0: Constructing countermodel ... % 2.28/1.21 Prover 0: proved (584ms) % 2.28/1.21 % 2.28/1.21 No countermodel exists, formula is valid % 2.28/1.21 % SZS status Theorem for theBenchmark % 2.28/1.21 % 2.28/1.21 Generating proof ... found it (size 27) % 3.09/1.45 % 3.09/1.45 % SZS output start Proof for theBenchmark % 3.09/1.45 Assumed formulas after preprocessing and simplification: % 3.09/1.45 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : (singleton(v1) = v7 & singleton(v0) = v5 & cartesian_product2(v7, v2) = v8 & cartesian_product2(v5, v2) = v6 & cartesian_product2(v3, v2) = v4 & cartesian_product2(v2, v7) = v12 & cartesian_product2(v2, v5) = v11 & cartesian_product2(v2, v3) = v10 & set_union2(v11, v12) = v13 & set_union2(v6, v8) = v9 & unordered_pair(v0, v1) = v3 & 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] : ( ~ (singleton(v17) = v19) | ~ (singleton(v16) = v18) | ~ (set_union2(v18, v19) = v20) | unordered_pair(v16, v17) = v20) & ! [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] : (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] : ! [v19] : (v17 = v16 | ~ (unordered_pair(v19, v18) = v17) | ~ (unordered_pair(v19, v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : (v17 = v16 | ~ (singleton(v18) = v17) | ~ (singleton(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] : ! [v18] : ( ~ (unordered_pair(v17, v16) = v18) | unordered_pair(v16, v17) = v18) & ! [v16] : ! [v17] : ! [v18] : ( ~ (unordered_pair(v16, v17) = v18) | unordered_pair(v17, v16) = v18) & ! [v16] : ! [v17] : ! [v18] : ( ~ (unordered_pair(v16, v17) = v18) | ? [v19] : ? [v20] : (singleton(v17) = v20 & singleton(v16) = v19 & set_union2(v19, v20) = v18)) & ! [v16] : ! [v17] : (v17 = v16 | ~ (set_union2(v16, v16) = v17)) & ( ~ (v13 = v10) | ~ (v9 = v4))) % 3.09/1.49 | 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: % 3.09/1.49 | (1) singleton(all_0_14_14) = all_0_8_8 & singleton(all_0_15_15) = all_0_10_10 & cartesian_product2(all_0_8_8, all_0_13_13) = all_0_7_7 & cartesian_product2(all_0_10_10, all_0_13_13) = all_0_9_9 & cartesian_product2(all_0_12_12, all_0_13_13) = all_0_11_11 & cartesian_product2(all_0_13_13, all_0_8_8) = all_0_3_3 & cartesian_product2(all_0_13_13, all_0_10_10) = all_0_4_4 & cartesian_product2(all_0_13_13, all_0_12_12) = all_0_5_5 & set_union2(all_0_4_4, all_0_3_3) = all_0_2_2 & set_union2(all_0_9_9, all_0_7_7) = all_0_6_6 & unordered_pair(all_0_15_15, all_0_14_14) = all_0_12_12 & 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] : ( ~ (singleton(v1) = v3) | ~ (singleton(v0) = v2) | ~ (set_union2(v2, v3) = v4) | unordered_pair(v0, v1) = v4) & ! [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] : (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] : ! [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] : ( ~ (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) | ? [v3] : ? [v4] : (singleton(v1) = v4 & singleton(v0) = v3 & set_union2(v3, v4) = v2)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) & ( ~ (all_0_2_2 = all_0_5_5) | ~ (all_0_6_6 = all_0_11_11)) % 3.09/1.50 | % 3.09/1.50 | Applying alpha-rule on (1) yields: % 3.09/1.50 | (2) cartesian_product2(all_0_10_10, all_0_13_13) = all_0_9_9 % 3.09/1.50 | (3) ! [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)) % 3.09/1.50 | (4) cartesian_product2(all_0_13_13, all_0_8_8) = all_0_3_3 % 3.09/1.50 | (5) set_union2(all_0_9_9, all_0_7_7) = all_0_6_6 % 3.09/1.50 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) % 3.09/1.50 | (7) cartesian_product2(all_0_12_12, all_0_13_13) = all_0_11_11 % 3.09/1.50 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v1) = v4 & singleton(v0) = v3 & set_union2(v3, v4) = v2)) % 3.09/1.50 | (9) ~ (all_0_2_2 = all_0_5_5) | ~ (all_0_6_6 = all_0_11_11) % 3.09/1.50 | (10) cartesian_product2(all_0_13_13, all_0_12_12) = all_0_5_5 % 3.09/1.50 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) % 3.09/1.50 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v1) = v3) | ~ (singleton(v0) = v2) | ~ (set_union2(v2, v3) = v4) | unordered_pair(v0, v1) = v4) % 3.09/1.50 | (13) unordered_pair(all_0_15_15, all_0_14_14) = all_0_12_12 % 3.09/1.50 | (14) ! [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)) % 3.09/1.50 | (15) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) % 3.09/1.50 | (16) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2) % 3.09/1.51 | (17) singleton(all_0_14_14) = all_0_8_8 % 3.09/1.51 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) % 3.09/1.51 | (19) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ~ empty(v2) | empty(v0)) % 3.09/1.51 | (20) empty(all_0_0_0) % 3.09/1.51 | (21) ~ empty(all_0_1_1) % 3.09/1.51 | (22) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ empty(v2) | empty(v0)) % 3.09/1.51 | (23) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) % 3.09/1.51 | (24) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2) % 3.09/1.51 | (25) ! [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)) % 3.09/1.51 | (26) cartesian_product2(all_0_8_8, all_0_13_13) = all_0_7_7 % 3.09/1.51 | (27) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 3.09/1.51 | (28) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) % 3.09/1.51 | (29) cartesian_product2(all_0_13_13, all_0_10_10) = all_0_4_4 % 3.09/1.51 | (30) set_union2(all_0_4_4, all_0_3_3) = all_0_2_2 % 3.09/1.51 | (31) singleton(all_0_15_15) = all_0_10_10 % 3.09/1.51 | (32) ! [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)) % 3.09/1.51 | % 3.09/1.51 | Instantiating formula (3) with all_0_2_2, all_0_3_3, all_0_4_4, all_0_13_13, all_0_8_8, all_0_10_10 and discharging atoms cartesian_product2(all_0_13_13, all_0_8_8) = all_0_3_3, cartesian_product2(all_0_13_13, all_0_10_10) = all_0_4_4, set_union2(all_0_4_4, all_0_3_3) = all_0_2_2, yields: % 3.09/1.51 | (33) ? [v0] : (cartesian_product2(all_0_13_13, v0) = all_0_2_2 & set_union2(all_0_10_10, all_0_8_8) = v0) % 3.09/1.51 | % 3.09/1.51 | Instantiating formula (32) with all_0_6_6, all_0_7_7, all_0_9_9, all_0_13_13, all_0_8_8, all_0_10_10 and discharging atoms cartesian_product2(all_0_8_8, all_0_13_13) = all_0_7_7, cartesian_product2(all_0_10_10, all_0_13_13) = all_0_9_9, set_union2(all_0_9_9, all_0_7_7) = all_0_6_6, yields: % 3.09/1.51 | (34) ? [v0] : (cartesian_product2(v0, all_0_13_13) = all_0_6_6 & set_union2(all_0_10_10, all_0_8_8) = v0) % 3.09/1.51 | % 3.09/1.51 | Instantiating formula (8) with all_0_12_12, all_0_14_14, all_0_15_15 and discharging atoms unordered_pair(all_0_15_15, all_0_14_14) = all_0_12_12, yields: % 3.09/1.51 | (35) ? [v0] : ? [v1] : (singleton(all_0_14_14) = v1 & singleton(all_0_15_15) = v0 & set_union2(v0, v1) = all_0_12_12) % 3.09/1.51 | % 3.09/1.51 | Instantiating (34) with all_9_0_16 yields: % 3.09/1.51 | (36) cartesian_product2(all_9_0_16, all_0_13_13) = all_0_6_6 & set_union2(all_0_10_10, all_0_8_8) = all_9_0_16 % 3.09/1.51 | % 3.09/1.51 | Applying alpha-rule on (36) yields: % 3.09/1.51 | (37) cartesian_product2(all_9_0_16, all_0_13_13) = all_0_6_6 % 3.09/1.51 | (38) set_union2(all_0_10_10, all_0_8_8) = all_9_0_16 % 3.09/1.51 | % 3.09/1.51 | Instantiating (35) with all_11_0_17, all_11_1_18 yields: % 3.09/1.51 | (39) singleton(all_0_14_14) = all_11_0_17 & singleton(all_0_15_15) = all_11_1_18 & set_union2(all_11_1_18, all_11_0_17) = all_0_12_12 % 3.09/1.51 | % 3.09/1.51 | Applying alpha-rule on (39) yields: % 3.09/1.51 | (40) singleton(all_0_14_14) = all_11_0_17 % 3.33/1.51 | (41) singleton(all_0_15_15) = all_11_1_18 % 3.33/1.51 | (42) set_union2(all_11_1_18, all_11_0_17) = all_0_12_12 % 3.33/1.51 | % 3.33/1.51 | Instantiating (33) with all_13_0_19 yields: % 3.33/1.51 | (43) cartesian_product2(all_0_13_13, all_13_0_19) = all_0_2_2 & set_union2(all_0_10_10, all_0_8_8) = all_13_0_19 % 3.33/1.51 | % 3.33/1.51 | Applying alpha-rule on (43) yields: % 3.33/1.51 | (44) cartesian_product2(all_0_13_13, all_13_0_19) = all_0_2_2 % 3.33/1.51 | (45) set_union2(all_0_10_10, all_0_8_8) = all_13_0_19 % 3.33/1.51 | % 3.33/1.52 | Instantiating formula (27) with all_0_14_14, all_11_0_17, all_0_8_8 and discharging atoms singleton(all_0_14_14) = all_11_0_17, singleton(all_0_14_14) = all_0_8_8, yields: % 3.33/1.52 | (46) all_11_0_17 = all_0_8_8 % 3.33/1.52 | % 3.33/1.52 | Instantiating formula (27) with all_0_15_15, all_11_1_18, all_0_10_10 and discharging atoms singleton(all_0_15_15) = all_11_1_18, singleton(all_0_15_15) = all_0_10_10, yields: % 3.33/1.52 | (47) all_11_1_18 = all_0_10_10 % 3.33/1.52 | % 3.33/1.52 | Instantiating formula (11) with all_0_10_10, all_0_8_8, all_9_0_16, all_13_0_19 and discharging atoms set_union2(all_0_10_10, all_0_8_8) = all_13_0_19, set_union2(all_0_10_10, all_0_8_8) = all_9_0_16, yields: % 3.33/1.52 | (48) all_13_0_19 = all_9_0_16 % 3.33/1.52 | % 3.33/1.52 | From (48) and (44) follows: % 3.33/1.52 | (49) cartesian_product2(all_0_13_13, all_9_0_16) = all_0_2_2 % 3.33/1.52 | % 3.33/1.52 | From (47)(46) and (42) follows: % 3.33/1.52 | (50) set_union2(all_0_10_10, all_0_8_8) = all_0_12_12 % 3.33/1.52 | % 3.33/1.52 | From (48) and (45) follows: % 3.33/1.52 | (38) set_union2(all_0_10_10, all_0_8_8) = all_9_0_16 % 3.33/1.52 | % 3.33/1.52 | Instantiating formula (11) with all_0_10_10, all_0_8_8, all_0_12_12, all_9_0_16 and discharging atoms set_union2(all_0_10_10, all_0_8_8) = all_9_0_16, set_union2(all_0_10_10, all_0_8_8) = all_0_12_12, yields: % 3.33/1.52 | (52) all_9_0_16 = all_0_12_12 % 3.33/1.52 | % 3.33/1.52 | From (52) and (37) follows: % 3.33/1.52 | (53) cartesian_product2(all_0_12_12, all_0_13_13) = all_0_6_6 % 3.33/1.52 | % 3.33/1.52 | From (52) and (49) follows: % 3.33/1.52 | (54) cartesian_product2(all_0_13_13, all_0_12_12) = all_0_2_2 % 3.33/1.52 | % 3.33/1.52 | Instantiating formula (6) with all_0_12_12, all_0_13_13, all_0_6_6, all_0_11_11 and discharging atoms cartesian_product2(all_0_12_12, all_0_13_13) = all_0_6_6, cartesian_product2(all_0_12_12, all_0_13_13) = all_0_11_11, yields: % 3.33/1.52 | (55) all_0_6_6 = all_0_11_11 % 3.33/1.52 | % 3.33/1.52 | Instantiating formula (6) with all_0_13_13, all_0_12_12, all_0_2_2, all_0_5_5 and discharging atoms cartesian_product2(all_0_13_13, all_0_12_12) = all_0_2_2, cartesian_product2(all_0_13_13, all_0_12_12) = all_0_5_5, yields: % 3.33/1.52 | (56) all_0_2_2 = all_0_5_5 % 3.33/1.52 | % 3.33/1.52 +-Applying beta-rule and splitting (9), into two cases. % 3.33/1.52 |-Branch one: % 3.33/1.52 | (57) ~ (all_0_2_2 = all_0_5_5) % 3.33/1.52 | % 3.33/1.52 | Equations (56) can reduce 57 to: % 3.33/1.52 | (58) $false % 3.33/1.52 | % 3.33/1.52 |-The branch is then unsatisfiable % 3.33/1.52 |-Branch two: % 3.33/1.52 | (56) all_0_2_2 = all_0_5_5 % 3.33/1.52 | (60) ~ (all_0_6_6 = all_0_11_11) % 3.33/1.52 | % 3.33/1.52 | Equations (55) can reduce 60 to: % 3.33/1.52 | (58) $false % 3.33/1.52 | % 3.33/1.52 |-The branch is then unsatisfiable % 3.33/1.52 % SZS output end Proof for theBenchmark % 3.33/1.52 % 3.33/1.52 935ms %------------------------------------------------------------------------------