%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU212+1 : TPTP v8.1.0. Released v3.3.0. % 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 08:47:40 EDT 2022 % Result : Theorem 2.87s 1.39s % Output : Proof 4.50s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.05/0.12 % Problem : SEU212+1 : TPTP v8.1.0. Released v3.3.0. % 0.05/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.14/0.34 % Computer : n025.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 600 % 0.14/0.34 % DateTime : Sun Jun 19 19:03:44 EDT 2022 % 0.14/0.34 % CPUTime : % 0.54/0.59 ____ _ % 0.54/0.59 ___ / __ \_____(_)___ ________ __________ % 0.54/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.54/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.54/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.54/0.59 % 0.54/0.59 A Theorem Prover for First-Order Logic % 0.54/0.59 (ePrincess v.1.0) % 0.54/0.59 % 0.54/0.59 (c) Philipp Rümmer, 2009-2015 % 0.54/0.59 (c) Peter Backeman, 2014-2015 % 0.54/0.59 (contributions by Angelo Brillout, Peter Baumgartner) % 0.54/0.59 Free software under GNU Lesser General Public License (LGPL). % 0.54/0.59 Bug reports to peter@backeman.se % 0.54/0.59 % 0.54/0.59 For more information, visit http://user.uu.se/~petba168/breu/ % 0.54/0.59 % 0.54/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.71/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.57/0.96 Prover 0: Preprocessing ... % 2.19/1.19 Prover 0: Warning: ignoring some quantifiers % 2.19/1.21 Prover 0: Constructing countermodel ... % 2.87/1.39 Prover 0: proved (746ms) % 2.87/1.39 % 2.87/1.39 No countermodel exists, formula is valid % 2.87/1.39 % SZS status Theorem for theBenchmark % 2.87/1.39 % 2.87/1.39 Generating proof ... Warning: ignoring some quantifiers % 4.16/1.69 found it (size 29) % 4.16/1.69 % 4.16/1.69 % SZS output start Proof for theBenchmark % 4.16/1.69 Assumed formulas after preprocessing and simplification: % 4.16/1.69 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : (relation_dom(v2) = v4 & ordered_pair(v0, v1) = v3 & apply(v2, v0) = v5 & relation_empty_yielding(v6) & relation_empty_yielding(empty_set) & relation(v11) & relation(v10) & relation(v8) & relation(v6) & relation(v2) & relation(empty_set) & function(v11) & function(v2) & empty(v10) & empty(v9) & empty(empty_set) & ~ empty(v8) & ~ empty(v7) & ! [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] : ! [v16] : ( ~ (relation_dom(v12) = v13) | ~ (ordered_pair(v14, v15) = v16) | ~ relation(v12) | ~ function(v12) | ~ in(v14, v13) | ? [v17] : (apply(v12, v14) = v17 & ( ~ (v17 = v15) | in(v16, v12)) & (v17 = v15 | ~ in(v16, v12)))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (relation_dom(v12) = v13) | ~ (ordered_pair(v14, v15) = v16) | ~ relation(v12) | ~ in(v16, v12) | in(v14, v13)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = empty_set | ~ (relation_dom(v12) = v13) | ~ (apply(v12, v14) = v15) | ~ relation(v12) | ~ function(v12) | in(v14, v13)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (ordered_pair(v15, v14) = v13) | ~ (ordered_pair(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (apply(v15, v14) = v13) | ~ (apply(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (unordered_pair(v15, v14) = v13) | ~ (unordered_pair(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (singleton(v14) = v13) | ~ (singleton(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (relation_dom(v14) = v13) | ~ (relation_dom(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (relation_dom(v12) = v13) | ~ relation(v12) | ~ in(v14, v13) | ? [v15] : ? [v16] : (ordered_pair(v14, v15) = v16 & in(v16, 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] : ( ~ (unordered_pair(v13, v12) = v14) | unordered_pair(v12, v13) = v14) & ! [v12] : ! [v13] : ! [v14] : ( ~ (unordered_pair(v12, v13) = v14) | ~ empty(v14)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (unordered_pair(v12, v13) = v14) | unordered_pair(v13, v12) = v14) & ? [v12] : ! [v13] : ! [v14] : (v14 = v12 | ~ (relation_dom(v13) = v14) | ~ relation(v13) | ? [v15] : ? [v16] : ? [v17] : (( ~ in(v15, v12) | ! [v18] : ! [v19] : ( ~ (ordered_pair(v15, v18) = v19) | ~ in(v19, v13))) & (in(v15, v12) | (ordered_pair(v15, v16) = v17 & in(v17, v13))))) & ! [v12] : ! [v13] : (v13 = v12 | ~ empty(v13) | ~ empty(v12)) & ! [v12] : ! [v13] : ( ~ (singleton(v12) = v13) | ~ empty(v13)) & ! [v12] : ! [v13] : ( ~ (relation_dom(v12) = v13) | ~ relation(v12) | ~ empty(v13) | empty(v12)) & ! [v12] : ! [v13] : ( ~ (relation_dom(v12) = v13) | ~ empty(v12) | relation(v13)) & ! [v12] : ! [v13] : ( ~ (relation_dom(v12) = v13) | ~ empty(v12) | empty(v13)) & ! [v12] : ! [v13] : ( ~ element(v12, v13) | empty(v13) | in(v12, v13)) & ! [v12] : ! [v13] : ( ~ empty(v13) | ~ in(v12, v13)) & ! [v12] : ! [v13] : ( ~ in(v13, v12) | ~ in(v12, v13)) & ! [v12] : ! [v13] : ( ~ in(v12, v13) | element(v12, v13)) & ! [v12] : (v12 = empty_set | ~ empty(v12)) & ! [v12] : ( ~ empty(v12) | relation(v12)) & ! [v12] : ( ~ empty(v12) | function(v12)) & ? [v12] : ? [v13] : element(v13, v12) & ((v5 = v1 & in(v0, v4) & ~ in(v3, v2)) | (in(v3, v2) & ( ~ (v5 = v1) | ~ in(v0, v4))))) % 4.16/1.73 | 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: % 4.16/1.73 | (1) relation_dom(all_0_9_9) = all_0_7_7 & ordered_pair(all_0_11_11, all_0_10_10) = all_0_8_8 & apply(all_0_9_9, all_0_11_11) = all_0_6_6 & relation_empty_yielding(all_0_5_5) & relation_empty_yielding(empty_set) & relation(all_0_0_0) & relation(all_0_1_1) & relation(all_0_3_3) & relation(all_0_5_5) & relation(all_0_9_9) & relation(empty_set) & function(all_0_0_0) & function(all_0_9_9) & empty(all_0_1_1) & empty(all_0_2_2) & empty(empty_set) & ~ empty(all_0_3_3) & ~ empty(all_0_4_4) & ! [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] : ! [v4] : ( ~ (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v0) | ~ function(v0) | ~ in(v2, v1) | ? [v5] : (apply(v0, v2) = v5 & ( ~ (v5 = v3) | in(v4, v0)) & (v5 = v3 | ~ in(v4, v0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v0) | ~ in(v4, v0) | in(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = empty_set | ~ (relation_dom(v0) = v1) | ~ (apply(v0, v2) = v3) | ~ relation(v0) | ~ function(v0) | in(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apply(v3, v2) = v1) | ~ (apply(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 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ in(v2, v1) | ? [v3] : ? [v4] : (ordered_pair(v2, v3) = v4 & in(v4, 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] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ~ empty(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_dom(v1) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : ? [v5] : (( ~ in(v3, v0) | ! [v6] : ! [v7] : ( ~ (ordered_pair(v3, v6) = v7) | ~ in(v7, v1))) & (in(v3, v0) | (ordered_pair(v3, v4) = v5 & in(v5, v1))))) & ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ~ empty(v1)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | relation(v1)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | empty(v1)) & ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1)) & ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1)) & ! [v0] : (v0 = empty_set | ~ empty(v0)) & ! [v0] : ( ~ empty(v0) | relation(v0)) & ! [v0] : ( ~ empty(v0) | function(v0)) & ? [v0] : ? [v1] : element(v1, v0) & ((all_0_6_6 = all_0_10_10 & in(all_0_11_11, all_0_7_7) & ~ in(all_0_8_8, all_0_9_9)) | (in(all_0_8_8, all_0_9_9) & ( ~ (all_0_6_6 = all_0_10_10) | ~ in(all_0_11_11, all_0_7_7)))) % 4.16/1.74 | % 4.16/1.74 | Applying alpha-rule on (1) yields: % 4.16/1.74 | (2) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) % 4.16/1.74 | (3) relation(all_0_1_1) % 4.16/1.74 | (4) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1)) % 4.16/1.74 | (5) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ~ empty(v1)) % 4.16/1.74 | (6) relation(all_0_5_5) % 4.16/1.74 | (7) relation_empty_yielding(all_0_5_5) % 4.16/1.74 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) % 4.16/1.74 | (9) relation(all_0_9_9) % 4.16/1.74 | (10) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) % 4.16/1.74 | (11) function(all_0_0_0) % 4.16/1.74 | (12) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0)) % 4.16/1.74 | (13) ! [v0] : ( ~ empty(v0) | function(v0)) % 4.16/1.74 | (14) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ~ empty(v2)) % 4.16/1.74 | (15) relation(all_0_0_0) % 4.16/1.74 | (16) function(all_0_9_9) % 4.16/1.74 | (17) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 4.16/1.74 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = empty_set | ~ (relation_dom(v0) = v1) | ~ (apply(v0, v2) = v3) | ~ relation(v0) | ~ function(v0) | in(v2, v1)) % 4.16/1.74 | (19) relation_dom(all_0_9_9) = all_0_7_7 % 4.16/1.74 | (20) ~ empty(all_0_4_4) % 4.16/1.74 | (21) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) % 4.16/1.74 | (22) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3)) % 4.16/1.74 | (23) relation(empty_set) % 4.16/1.74 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v0) | ~ in(v4, v0) | in(v2, v1)) % 4.16/1.75 | (25) ! [v0] : ( ~ empty(v0) | relation(v0)) % 4.16/1.75 | (26) ? [v0] : ? [v1] : element(v1, v0) % 4.16/1.75 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) % 4.16/1.75 | (28) apply(all_0_9_9, all_0_11_11) = all_0_6_6 % 4.16/1.75 | (29) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | relation(v1)) % 4.16/1.75 | (30) relation(all_0_3_3) % 4.16/1.75 | (31) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) % 4.16/1.75 | (32) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2) % 4.16/1.75 | (33) ! [v0] : (v0 = empty_set | ~ empty(v0)) % 4.16/1.75 | (34) ~ empty(all_0_3_3) % 4.16/1.75 | (35) ordered_pair(all_0_11_11, all_0_10_10) = all_0_8_8 % 4.16/1.75 | (36) ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1)) % 4.16/1.75 | (37) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ in(v2, v1) | ? [v3] : ? [v4] : (ordered_pair(v2, v3) = v4 & in(v4, v0))) % 4.16/1.75 | (38) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_dom(v1) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : ? [v5] : (( ~ in(v3, v0) | ! [v6] : ! [v7] : ( ~ (ordered_pair(v3, v6) = v7) | ~ in(v7, v1))) & (in(v3, v0) | (ordered_pair(v3, v4) = v5 & in(v5, v1))))) % 4.16/1.75 | (39) empty(all_0_2_2) % 4.16/1.75 | (40) relation_empty_yielding(empty_set) % 4.16/1.75 | (41) empty(empty_set) % 4.16/1.75 | (42) ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1)) % 4.16/1.75 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4) % 4.16/1.75 | (44) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | empty(v1)) % 4.16/1.75 | (45) empty(all_0_1_1) % 4.16/1.75 | (46) (all_0_6_6 = all_0_10_10 & in(all_0_11_11, all_0_7_7) & ~ in(all_0_8_8, all_0_9_9)) | (in(all_0_8_8, all_0_9_9) & ( ~ (all_0_6_6 = all_0_10_10) | ~ in(all_0_11_11, all_0_7_7))) % 4.16/1.75 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) % 4.16/1.75 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v0) | ~ function(v0) | ~ in(v2, v1) | ? [v5] : (apply(v0, v2) = v5 & ( ~ (v5 = v3) | in(v4, v0)) & (v5 = v3 | ~ in(v4, v0)))) % 4.16/1.75 | (49) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ empty(v2)) % 4.16/1.75 | % 4.16/1.75 +-Applying beta-rule and splitting (46), into two cases. % 4.16/1.75 |-Branch one: % 4.16/1.75 | (50) all_0_6_6 = all_0_10_10 & in(all_0_11_11, all_0_7_7) & ~ in(all_0_8_8, all_0_9_9) % 4.16/1.75 | % 4.16/1.75 | Applying alpha-rule on (50) yields: % 4.16/1.75 | (51) all_0_6_6 = all_0_10_10 % 4.16/1.75 | (52) in(all_0_11_11, all_0_7_7) % 4.16/1.75 | (53) ~ in(all_0_8_8, all_0_9_9) % 4.16/1.75 | % 4.16/1.76 | From (51) and (28) follows: % 4.50/1.76 | (54) apply(all_0_9_9, all_0_11_11) = all_0_10_10 % 4.50/1.76 | % 4.50/1.76 | Instantiating formula (48) with all_0_8_8, all_0_10_10, all_0_11_11, all_0_7_7, all_0_9_9 and discharging atoms relation_dom(all_0_9_9) = all_0_7_7, ordered_pair(all_0_11_11, all_0_10_10) = all_0_8_8, relation(all_0_9_9), function(all_0_9_9), in(all_0_11_11, all_0_7_7), yields: % 4.50/1.76 | (55) ? [v0] : (apply(all_0_9_9, all_0_11_11) = v0 & ( ~ (v0 = all_0_10_10) | in(all_0_8_8, all_0_9_9)) & (v0 = all_0_10_10 | ~ in(all_0_8_8, all_0_9_9))) % 4.50/1.76 | % 4.50/1.76 | Instantiating (55) with all_40_0_19 yields: % 4.50/1.76 | (56) apply(all_0_9_9, all_0_11_11) = all_40_0_19 & ( ~ (all_40_0_19 = all_0_10_10) | in(all_0_8_8, all_0_9_9)) & (all_40_0_19 = all_0_10_10 | ~ in(all_0_8_8, all_0_9_9)) % 4.50/1.76 | % 4.50/1.76 | Applying alpha-rule on (56) yields: % 4.50/1.76 | (57) apply(all_0_9_9, all_0_11_11) = all_40_0_19 % 4.50/1.76 | (58) ~ (all_40_0_19 = all_0_10_10) | in(all_0_8_8, all_0_9_9) % 4.50/1.76 | (59) all_40_0_19 = all_0_10_10 | ~ in(all_0_8_8, all_0_9_9) % 4.50/1.76 | % 4.50/1.76 +-Applying beta-rule and splitting (58), into two cases. % 4.50/1.76 |-Branch one: % 4.50/1.76 | (60) in(all_0_8_8, all_0_9_9) % 4.50/1.76 | % 4.50/1.76 | Using (60) and (53) yields: % 4.50/1.76 | (61) $false % 4.50/1.76 | % 4.50/1.76 |-The branch is then unsatisfiable % 4.50/1.76 |-Branch two: % 4.50/1.76 | (53) ~ in(all_0_8_8, all_0_9_9) % 4.50/1.76 | (63) ~ (all_40_0_19 = all_0_10_10) % 4.50/1.76 | % 4.50/1.76 | Instantiating formula (8) with all_0_9_9, all_0_11_11, all_40_0_19, all_0_10_10 and discharging atoms apply(all_0_9_9, all_0_11_11) = all_40_0_19, apply(all_0_9_9, all_0_11_11) = all_0_10_10, yields: % 4.50/1.76 | (64) all_40_0_19 = all_0_10_10 % 4.50/1.76 | % 4.50/1.76 | Equations (64) can reduce 63 to: % 4.50/1.76 | (65) $false % 4.50/1.76 | % 4.50/1.76 |-The branch is then unsatisfiable % 4.50/1.76 |-Branch two: % 4.50/1.76 | (66) in(all_0_8_8, all_0_9_9) & ( ~ (all_0_6_6 = all_0_10_10) | ~ in(all_0_11_11, all_0_7_7)) % 4.50/1.76 | % 4.50/1.76 | Applying alpha-rule on (66) yields: % 4.50/1.76 | (60) in(all_0_8_8, all_0_9_9) % 4.50/1.76 | (68) ~ (all_0_6_6 = all_0_10_10) | ~ in(all_0_11_11, all_0_7_7) % 4.50/1.76 | % 4.50/1.76 | Instantiating formula (24) with all_0_8_8, all_0_10_10, all_0_11_11, all_0_7_7, all_0_9_9 and discharging atoms relation_dom(all_0_9_9) = all_0_7_7, ordered_pair(all_0_11_11, all_0_10_10) = all_0_8_8, relation(all_0_9_9), in(all_0_8_8, all_0_9_9), yields: % 4.50/1.76 | (52) in(all_0_11_11, all_0_7_7) % 4.50/1.76 | % 4.50/1.76 +-Applying beta-rule and splitting (68), into two cases. % 4.50/1.76 |-Branch one: % 4.50/1.76 | (70) ~ in(all_0_11_11, all_0_7_7) % 4.50/1.76 | % 4.50/1.76 | Using (52) and (70) yields: % 4.50/1.76 | (61) $false % 4.50/1.76 | % 4.50/1.76 |-The branch is then unsatisfiable % 4.50/1.76 |-Branch two: % 4.50/1.76 | (52) in(all_0_11_11, all_0_7_7) % 4.50/1.76 | (73) ~ (all_0_6_6 = all_0_10_10) % 4.50/1.76 | % 4.50/1.76 | Instantiating formula (48) with all_0_8_8, all_0_10_10, all_0_11_11, all_0_7_7, all_0_9_9 and discharging atoms relation_dom(all_0_9_9) = all_0_7_7, ordered_pair(all_0_11_11, all_0_10_10) = all_0_8_8, relation(all_0_9_9), function(all_0_9_9), in(all_0_11_11, all_0_7_7), yields: % 4.50/1.76 | (55) ? [v0] : (apply(all_0_9_9, all_0_11_11) = v0 & ( ~ (v0 = all_0_10_10) | in(all_0_8_8, all_0_9_9)) & (v0 = all_0_10_10 | ~ in(all_0_8_8, all_0_9_9))) % 4.50/1.76 | % 4.50/1.76 | Instantiating (55) with all_50_0_22 yields: % 4.50/1.76 | (75) apply(all_0_9_9, all_0_11_11) = all_50_0_22 & ( ~ (all_50_0_22 = all_0_10_10) | in(all_0_8_8, all_0_9_9)) & (all_50_0_22 = all_0_10_10 | ~ in(all_0_8_8, all_0_9_9)) % 4.50/1.77 | % 4.50/1.77 | Applying alpha-rule on (75) yields: % 4.50/1.77 | (76) apply(all_0_9_9, all_0_11_11) = all_50_0_22 % 4.50/1.77 | (77) ~ (all_50_0_22 = all_0_10_10) | in(all_0_8_8, all_0_9_9) % 4.50/1.77 | (78) all_50_0_22 = all_0_10_10 | ~ in(all_0_8_8, all_0_9_9) % 4.50/1.77 | % 4.50/1.77 +-Applying beta-rule and splitting (78), into two cases. % 4.50/1.77 |-Branch one: % 4.50/1.77 | (53) ~ in(all_0_8_8, all_0_9_9) % 4.50/1.77 | % 4.50/1.77 | Using (60) and (53) yields: % 4.50/1.77 | (61) $false % 4.50/1.77 | % 4.50/1.77 |-The branch is then unsatisfiable % 4.50/1.77 |-Branch two: % 4.50/1.77 | (60) in(all_0_8_8, all_0_9_9) % 4.50/1.77 | (82) all_50_0_22 = all_0_10_10 % 4.50/1.77 | % 4.50/1.77 | From (82) and (76) follows: % 4.50/1.77 | (54) apply(all_0_9_9, all_0_11_11) = all_0_10_10 % 4.50/1.77 | % 4.50/1.77 | Instantiating formula (8) with all_0_9_9, all_0_11_11, all_0_10_10, all_0_6_6 and discharging atoms apply(all_0_9_9, all_0_11_11) = all_0_6_6, apply(all_0_9_9, all_0_11_11) = all_0_10_10, yields: % 4.50/1.77 | (51) all_0_6_6 = all_0_10_10 % 4.50/1.77 | % 4.50/1.77 | Equations (51) can reduce 73 to: % 4.50/1.77 | (65) $false % 4.50/1.77 | % 4.50/1.77 |-The branch is then unsatisfiable % 4.50/1.77 % SZS output end Proof for theBenchmark % 4.50/1.77 % 4.50/1.77 1166ms %------------------------------------------------------------------------------