%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET951+1 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n005.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 00:23:24 EDT 2022 % Result : Theorem 2.81s 1.36s % Output : Proof 4.34s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SET951+1 : TPTP v8.1.0. Released v3.2.0. % 0.03/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.34 % Computer : n005.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 : Sat Jul 9 23:50:22 EDT 2022 % 0.13/0.34 % CPUTime : % 0.55/0.60 ____ _ % 0.55/0.60 ___ / __ \_____(_)___ ________ __________ % 0.55/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.55/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.55/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.55/0.60 % 0.55/0.60 A Theorem Prover for First-Order Logic % 0.55/0.60 (ePrincess v.1.0) % 0.55/0.60 % 0.55/0.60 (c) Philipp Rümmer, 2009-2015 % 0.55/0.60 (c) Peter Backeman, 2014-2015 % 0.55/0.60 (contributions by Angelo Brillout, Peter Baumgartner) % 0.55/0.60 Free software under GNU Lesser General Public License (LGPL). % 0.55/0.60 Bug reports to peter@backeman.se % 0.55/0.60 % 0.55/0.60 For more information, visit http://user.uu.se/~petba168/breu/ % 0.55/0.60 % 0.55/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.70/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.47/0.91 Prover 0: Preprocessing ... % 1.95/1.13 Prover 0: Warning: ignoring some quantifiers % 2.15/1.15 Prover 0: Constructing countermodel ... % 2.81/1.36 Prover 0: proved (709ms) % 2.81/1.36 % 2.81/1.36 No countermodel exists, formula is valid % 2.81/1.36 % SZS status Theorem for theBenchmark % 2.81/1.36 % 2.81/1.36 Generating proof ... Warning: ignoring some quantifiers % 4.08/1.66 found it (size 23) % 4.08/1.66 % 4.08/1.66 % SZS output start Proof for theBenchmark % 4.08/1.66 Assumed formulas after preprocessing and simplification: % 4.08/1.66 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : (cartesian_product2(v3, v4) = v6 & cartesian_product2(v1, v2) = v5 & set_intersection2(v5, v6) = v7 & set_intersection2(v2, v4) = v9 & set_intersection2(v1, v3) = v8 & empty(v11) & in(v0, v7) & ~ empty(v10) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (cartesian_product2(v12, v13) = v14) | ~ (ordered_pair(v16, v17) = v15) | ~ in(v17, v13) | ~ in(v16, v12) | in(v15, v14)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v15 = v13 | ~ (ordered_pair(v14, v15) = v16) | ~ (ordered_pair(v12, v13) = v16)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v14 = v12 | ~ (ordered_pair(v14, v15) = v16) | ~ (ordered_pair(v12, v13) = v16)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (singleton(v12) = v15) | ~ (unordered_pair(v14, v15) = v16) | ~ (unordered_pair(v12, v13) = v14) | ordered_pair(v12, v13) = v16) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (cartesian_product2(v15, v14) = v13) | ~ (cartesian_product2(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (ordered_pair(v15, v14) = v13) | ~ (ordered_pair(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (set_intersection2(v15, v14) = v13) | ~ (set_intersection2(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (unordered_pair(v15, v14) = v13) | ~ (unordered_pair(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (cartesian_product2(v12, v13) = v14) | ~ in(v15, v14) | ? [v16] : ? [v17] : (ordered_pair(v16, v17) = v15 & in(v17, v13) & in(v16, v12))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (set_intersection2(v12, v13) = v14) | ~ in(v15, v14) | in(v15, v13)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (set_intersection2(v12, v13) = v14) | ~ in(v15, v14) | in(v15, v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (set_intersection2(v12, v13) = v14) | ~ in(v15, v13) | ~ in(v15, v12) | in(v15, v14)) & ? [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = v12 | ~ (cartesian_product2(v13, v14) = v15) | ? [v16] : ? [v17] : ? [v18] : ? [v19] : (( ~ in(v16, v12) | ! [v20] : ! [v21] : ( ~ (ordered_pair(v20, v21) = v16) | ~ in(v21, v14) | ~ in(v20, v13))) & (in(v16, v12) | (v19 = v16 & ordered_pair(v17, v18) = v16 & in(v18, v14) & in(v17, v13))))) & ? [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = v12 | ~ (set_intersection2(v13, v14) = v15) | ? [v16] : (( ~ in(v16, v14) | ~ in(v16, v13) | ~ in(v16, v12)) & (in(v16, v12) | (in(v16, v14) & in(v16, v13))))) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (singleton(v14) = v13) | ~ (singleton(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (ordered_pair(v12, v13) = v14) | ~ empty(v14)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (ordered_pair(v12, v13) = v14) | ? [v15] : ? [v16] : (singleton(v12) = v16 & unordered_pair(v15, v16) = v14 & unordered_pair(v12, v13) = v15)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (set_intersection2(v13, v12) = v14) | set_intersection2(v12, v13) = v14) & ! [v12] : ! [v13] : ! [v14] : ( ~ (set_intersection2(v12, v13) = v14) | set_intersection2(v13, v12) = v14) & ! [v12] : ! [v13] : ! [v14] : ( ~ (unordered_pair(v13, v12) = v14) | unordered_pair(v12, v13) = v14) & ! [v12] : ! [v13] : ! [v14] : ( ~ (unordered_pair(v12, v13) = v14) | unordered_pair(v13, v12) = v14) & ! [v12] : ! [v13] : (v13 = v12 | ~ (set_intersection2(v12, v12) = v13)) & ! [v12] : ! [v13] : ( ~ in(v13, v12) | ~ in(v12, v13)) & ! [v12] : ! [v13] : ( ~ in(v13, v9) | ~ in(v12, v8) | ? [v14] : ( ~ (v14 = v0) & ordered_pair(v12, v13) = v14))) % 4.34/1.70 | 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 yields: % 4.34/1.70 | (1) cartesian_product2(all_0_8_8, all_0_7_7) = all_0_5_5 & cartesian_product2(all_0_10_10, all_0_9_9) = all_0_6_6 & set_intersection2(all_0_6_6, all_0_5_5) = all_0_4_4 & set_intersection2(all_0_9_9, all_0_7_7) = all_0_2_2 & set_intersection2(all_0_10_10, all_0_8_8) = all_0_3_3 & empty(all_0_0_0) & in(all_0_11_11, all_0_4_4) & ~ empty(all_0_1_1) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v0, v1) = v2) | ~ (ordered_pair(v4, v5) = v3) | ~ in(v5, v1) | ~ in(v4, v0) | in(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v1 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v0 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cartesian_product2(v0, v1) = v2) | ~ in(v3, v2) | ? [v4] : ? [v5] : (ordered_pair(v4, v5) = v3 & in(v5, v1) & in(v4, v0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v1) | ~ in(v3, v0) | in(v3, v2)) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (cartesian_product2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (( ~ in(v4, v0) | ! [v8] : ! [v9] : ( ~ (ordered_pair(v8, v9) = v4) | ~ in(v9, v2) | ~ in(v8, v1))) & (in(v4, v0) | (v7 = v4 & ordered_pair(v5, v6) = v4 & in(v6, v2) & in(v5, v1))))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_intersection2(v1, v2) = v3) | ? [v4] : (( ~ in(v4, v2) | ~ in(v4, v1) | ~ in(v4, v0)) & (in(v4, v0) | (in(v4, v2) & in(v4, v1))))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ empty(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(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] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1)) & ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ( ~ in(v1, all_0_2_2) | ~ in(v0, all_0_3_3) | ? [v2] : ( ~ (v2 = all_0_11_11) & ordered_pair(v0, v1) = v2)) % 4.34/1.71 | % 4.34/1.71 | Applying alpha-rule on (1) yields: % 4.34/1.71 | (2) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 4.34/1.71 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) % 4.34/1.71 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v1 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4)) % 4.34/1.71 | (5) cartesian_product2(all_0_10_10, all_0_9_9) = all_0_6_6 % 4.34/1.71 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v1)) % 4.34/1.71 | (7) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) % 4.34/1.71 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2) % 4.34/1.71 | (9) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) % 4.34/1.71 | (10) ! [v0] : ! [v1] : ( ~ in(v1, all_0_2_2) | ~ in(v0, all_0_3_3) | ? [v2] : ( ~ (v2 = all_0_11_11) & ordered_pair(v0, v1) = v2)) % 4.34/1.71 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cartesian_product2(v0, v1) = v2) | ~ in(v3, v2) | ? [v4] : ? [v5] : (ordered_pair(v4, v5) = v3 & in(v5, v1) & in(v4, v0))) % 4.34/1.71 | (12) set_intersection2(all_0_6_6, all_0_5_5) = all_0_4_4 % 4.34/1.71 | (13) set_intersection2(all_0_10_10, all_0_8_8) = all_0_3_3 % 4.34/1.71 | (14) empty(all_0_0_0) % 4.34/1.71 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v0 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4)) % 4.34/1.72 | (16) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) % 4.34/1.72 | (17) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2) % 4.34/1.72 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v1) | ~ in(v3, v0) | in(v3, v2)) % 4.34/1.72 | (19) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3)) % 4.34/1.72 | (20) cartesian_product2(all_0_8_8, all_0_7_7) = all_0_5_5 % 4.34/1.72 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) % 4.34/1.72 | (22) set_intersection2(all_0_9_9, all_0_7_7) = all_0_2_2 % 4.34/1.72 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v0, v1) = v2) | ~ (ordered_pair(v4, v5) = v3) | ~ in(v5, v1) | ~ in(v4, v0) | in(v3, v2)) % 4.34/1.72 | (24) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1)) % 4.34/1.72 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4) % 4.34/1.72 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v0)) % 4.34/1.72 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) % 4.34/1.72 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) % 4.34/1.72 | (29) ~ empty(all_0_1_1) % 4.34/1.72 | (30) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (cartesian_product2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (( ~ in(v4, v0) | ! [v8] : ! [v9] : ( ~ (ordered_pair(v8, v9) = v4) | ~ in(v9, v2) | ~ in(v8, v1))) & (in(v4, v0) | (v7 = v4 & ordered_pair(v5, v6) = v4 & in(v6, v2) & in(v5, v1))))) % 4.34/1.72 | (31) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_intersection2(v1, v2) = v3) | ? [v4] : (( ~ in(v4, v2) | ~ in(v4, v1) | ~ in(v4, v0)) & (in(v4, v0) | (in(v4, v2) & in(v4, v1))))) % 4.34/1.72 | (32) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ empty(v2)) % 4.34/1.72 | (33) in(all_0_11_11, all_0_4_4) % 4.34/1.72 | % 4.34/1.72 | Instantiating formula (6) with all_0_11_11, all_0_4_4, all_0_5_5, all_0_6_6 and discharging atoms set_intersection2(all_0_6_6, all_0_5_5) = all_0_4_4, in(all_0_11_11, all_0_4_4), yields: % 4.34/1.72 | (34) in(all_0_11_11, all_0_5_5) % 4.34/1.72 | % 4.34/1.72 | Instantiating formula (26) with all_0_11_11, all_0_4_4, all_0_5_5, all_0_6_6 and discharging atoms set_intersection2(all_0_6_6, all_0_5_5) = all_0_4_4, in(all_0_11_11, all_0_4_4), yields: % 4.34/1.72 | (35) in(all_0_11_11, all_0_6_6) % 4.34/1.72 | % 4.34/1.72 | Instantiating formula (11) with all_0_11_11, all_0_5_5, all_0_7_7, all_0_8_8 and discharging atoms cartesian_product2(all_0_8_8, all_0_7_7) = all_0_5_5, in(all_0_11_11, all_0_5_5), yields: % 4.34/1.72 | (36) ? [v0] : ? [v1] : (ordered_pair(v0, v1) = all_0_11_11 & in(v1, all_0_7_7) & in(v0, all_0_8_8)) % 4.34/1.72 | % 4.34/1.72 | Instantiating formula (11) with all_0_11_11, all_0_6_6, all_0_9_9, all_0_10_10 and discharging atoms cartesian_product2(all_0_10_10, all_0_9_9) = all_0_6_6, in(all_0_11_11, all_0_6_6), yields: % 4.34/1.72 | (37) ? [v0] : ? [v1] : (ordered_pair(v0, v1) = all_0_11_11 & in(v1, all_0_9_9) & in(v0, all_0_10_10)) % 4.34/1.73 | % 4.34/1.73 | Instantiating (37) with all_18_0_14, all_18_1_15 yields: % 4.34/1.73 | (38) ordered_pair(all_18_1_15, all_18_0_14) = all_0_11_11 & in(all_18_0_14, all_0_9_9) & in(all_18_1_15, all_0_10_10) % 4.34/1.73 | % 4.34/1.73 | Applying alpha-rule on (38) yields: % 4.34/1.73 | (39) ordered_pair(all_18_1_15, all_18_0_14) = all_0_11_11 % 4.34/1.73 | (40) in(all_18_0_14, all_0_9_9) % 4.34/1.73 | (41) in(all_18_1_15, all_0_10_10) % 4.34/1.73 | % 4.34/1.73 | Instantiating (36) with all_20_0_16, all_20_1_17 yields: % 4.34/1.73 | (42) ordered_pair(all_20_1_17, all_20_0_16) = all_0_11_11 & in(all_20_0_16, all_0_7_7) & in(all_20_1_17, all_0_8_8) % 4.34/1.73 | % 4.34/1.73 | Applying alpha-rule on (42) yields: % 4.34/1.73 | (43) ordered_pair(all_20_1_17, all_20_0_16) = all_0_11_11 % 4.34/1.73 | (44) in(all_20_0_16, all_0_7_7) % 4.34/1.73 | (45) in(all_20_1_17, all_0_8_8) % 4.34/1.73 | % 4.34/1.73 | Instantiating formula (4) with all_0_11_11, all_18_0_14, all_18_1_15, all_20_0_16, all_20_1_17 and discharging atoms ordered_pair(all_20_1_17, all_20_0_16) = all_0_11_11, ordered_pair(all_18_1_15, all_18_0_14) = all_0_11_11, yields: % 4.34/1.73 | (46) all_20_0_16 = all_18_0_14 % 4.34/1.73 | % 4.34/1.73 | Instantiating formula (15) with all_0_11_11, all_18_0_14, all_18_1_15, all_20_0_16, all_20_1_17 and discharging atoms ordered_pair(all_20_1_17, all_20_0_16) = all_0_11_11, ordered_pair(all_18_1_15, all_18_0_14) = all_0_11_11, yields: % 4.34/1.73 | (47) all_20_1_17 = all_18_1_15 % 4.34/1.73 | % 4.34/1.73 | From (47)(46) and (43) follows: % 4.34/1.73 | (39) ordered_pair(all_18_1_15, all_18_0_14) = all_0_11_11 % 4.34/1.73 | % 4.34/1.73 | From (46) and (44) follows: % 4.34/1.73 | (49) in(all_18_0_14, all_0_7_7) % 4.34/1.73 | % 4.34/1.73 | From (47) and (45) follows: % 4.34/1.73 | (50) in(all_18_1_15, all_0_8_8) % 4.34/1.73 | % 4.34/1.73 | Instantiating formula (18) with all_18_0_14, all_0_2_2, all_0_7_7, all_0_9_9 and discharging atoms set_intersection2(all_0_9_9, all_0_7_7) = all_0_2_2, in(all_18_0_14, all_0_7_7), in(all_18_0_14, all_0_9_9), yields: % 4.34/1.73 | (51) in(all_18_0_14, all_0_2_2) % 4.34/1.73 | % 4.34/1.73 | Instantiating formula (18) with all_18_1_15, all_0_3_3, all_0_8_8, all_0_10_10 and discharging atoms set_intersection2(all_0_10_10, all_0_8_8) = all_0_3_3, in(all_18_1_15, all_0_8_8), in(all_18_1_15, all_0_10_10), yields: % 4.34/1.73 | (52) in(all_18_1_15, all_0_3_3) % 4.34/1.73 | % 4.34/1.73 | Instantiating formula (10) with all_18_0_14, all_18_1_15 and discharging atoms in(all_18_0_14, all_0_2_2), in(all_18_1_15, all_0_3_3), yields: % 4.34/1.73 | (53) ? [v0] : ( ~ (v0 = all_0_11_11) & ordered_pair(all_18_1_15, all_18_0_14) = v0) % 4.34/1.73 | % 4.34/1.73 | Instantiating (53) with all_40_0_20 yields: % 4.34/1.73 | (54) ~ (all_40_0_20 = all_0_11_11) & ordered_pair(all_18_1_15, all_18_0_14) = all_40_0_20 % 4.34/1.73 | % 4.34/1.73 | Applying alpha-rule on (54) yields: % 4.34/1.73 | (55) ~ (all_40_0_20 = all_0_11_11) % 4.34/1.73 | (56) ordered_pair(all_18_1_15, all_18_0_14) = all_40_0_20 % 4.34/1.73 | % 4.34/1.73 | Instantiating formula (21) with all_18_1_15, all_18_0_14, all_40_0_20, all_0_11_11 and discharging atoms ordered_pair(all_18_1_15, all_18_0_14) = all_40_0_20, ordered_pair(all_18_1_15, all_18_0_14) = all_0_11_11, yields: % 4.34/1.73 | (57) all_40_0_20 = all_0_11_11 % 4.34/1.73 | % 4.34/1.73 | Equations (57) can reduce 55 to: % 4.34/1.73 | (58) $false % 4.34/1.73 | % 4.34/1.73 |-The branch is then unsatisfiable % 4.34/1.73 % SZS output end Proof for theBenchmark % 4.34/1.73 % 4.34/1.73 1122ms %------------------------------------------------------------------------------