%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU211+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n006.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 4.42s 1.69s % Output : Proof 6.24s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.11 % Problem : SEU211+1 : TPTP v8.1.0. Released v3.3.0. % 0.11/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.11/0.32 % Computer : n006.cluster.edu % 0.11/0.32 % Model : x86_64 x86_64 % 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.32 % Memory : 8042.1875MB % 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.32 % CPULimit : 300 % 0.11/0.32 % WCLimit : 600 % 0.11/0.32 % DateTime : Mon Jun 20 06:07:10 EDT 2022 % 0.11/0.32 % CPUTime : % 0.18/0.58 ____ _ % 0.18/0.58 ___ / __ \_____(_)___ ________ __________ % 0.18/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.18/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 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 ... % 0.67/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.57/0.93 Prover 0: Preprocessing ... % 2.06/1.14 Prover 0: Warning: ignoring some quantifiers % 2.06/1.16 Prover 0: Constructing countermodel ... % 3.43/1.47 Prover 0: gave up % 3.43/1.47 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 3.56/1.50 Prover 1: Preprocessing ... % 3.72/1.59 Prover 1: Warning: ignoring some quantifiers % 3.72/1.60 Prover 1: Constructing countermodel ... % 4.42/1.69 Prover 1: proved (220ms) % 4.42/1.69 % 4.42/1.69 No countermodel exists, formula is valid % 4.42/1.69 % SZS status Theorem for theBenchmark % 4.42/1.69 % 4.42/1.69 Generating proof ... Warning: ignoring some quantifiers % 5.77/2.02 found it (size 21) % 5.77/2.02 % 5.77/2.02 % SZS output start Proof for theBenchmark % 5.77/2.02 Assumed formulas after preprocessing and simplification: % 5.77/2.02 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ( ~ (v9 = 0) & ~ (v7 = 0) & ~ (v5 = 0) & subset(v3, v4) = v5 & subset(v0, v1) = 0 & relation_inverse_image(v2, v1) = v4 & relation_inverse_image(v2, v0) = v3 & relation(v11) = 0 & relation(v8) = 0 & relation(v2) = 0 & relation(empty_set) = 0 & empty(v11) = 0 & empty(v10) = 0 & empty(v8) = v9 & empty(v6) = v7 & empty(empty_set) = 0 & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = 0 | ~ (relation_inverse_image(v12, v13) = v14) | ~ (ordered_pair(v15, v17) = v18) | ~ (relation(v12) = 0) | ~ (in(v18, v12) = 0) | ~ (in(v15, v14) = v16) | ? [v19] : ( ~ (v19 = 0) & in(v17, v13) = v19)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (powerset(v14) = v15) | ~ (element(v13, v15) = 0) | ~ (element(v12, v14) = v16) | ? [v17] : ( ~ (v17 = 0) & in(v12, v13) = v17)) & ! [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] : (v15 = 0 | ~ (powerset(v13) = v14) | ~ (element(v12, v14) = v15) | ? [v16] : ( ~ (v16 = 0) & subset(v12, v13) = v16)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (element(v15, v14) = v13) | ~ (element(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (subset(v15, v14) = v13) | ~ (subset(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (relation_inverse_image(v15, v14) = v13) | ~ (relation_inverse_image(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 | ~ (unordered_pair(v15, v14) = v13) | ~ (unordered_pair(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (in(v15, v14) = v13) | ~ (in(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (powerset(v14) = v15) | ~ (element(v13, v15) = 0) | ~ (in(v12, v13) = 0) | ? [v16] : ( ~ (v16 = 0) & empty(v14) = v16)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (relation_inverse_image(v12, v13) = v14) | ~ (relation(v12) = 0) | ~ (in(v15, v14) = 0) | ? [v16] : ? [v17] : (ordered_pair(v15, v16) = v17 & in(v17, v12) = 0 & in(v16, v13) = 0)) & ? [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = v12 | ~ (relation_inverse_image(v13, v14) = v15) | ~ (relation(v13) = 0) | ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : (in(v16, v12) = v17 & ( ~ (v17 = 0) | ! [v22] : ! [v23] : ( ~ (ordered_pair(v16, v22) = v23) | ~ (in(v23, v13) = 0) | ? [v24] : ( ~ (v24 = 0) & in(v22, v14) = v24))) & (v17 = 0 | (v21 = 0 & v20 = 0 & ordered_pair(v16, v18) = v19 & in(v19, v13) = 0 & in(v18, v14) = 0)))) & ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (element(v12, v13) = v14) | ? [v15] : ( ~ (v15 = 0) & in(v12, v13) = v15)) & ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (subset(v12, v13) = v14) | ? [v15] : ? [v16] : ( ~ (v16 = 0) & in(v15, v13) = v16 & in(v15, v12) = 0)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (powerset(v14) = v13) | ~ (powerset(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (singleton(v14) = v13) | ~ (singleton(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (relation(v14) = v13) | ~ (relation(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (empty(v14) = v13) | ~ (empty(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (powerset(v13) = v14) | ~ (element(v12, v14) = 0) | subset(v12, v13) = 0) & ! [v12] : ! [v13] : ! [v14] : ( ~ (subset(v12, v13) = 0) | ~ (in(v14, v12) = 0) | in(v14, v13) = 0) & ! [v12] : ! [v13] : ! [v14] : ( ~ (ordered_pair(v12, v13) = v14) | ? [v15] : ( ~ (v15 = 0) & empty(v14) = v15)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (unordered_pair(v12, v13) = v14) | unordered_pair(v13, v12) = v14) & ! [v12] : ! [v13] : ! [v14] : ( ~ (unordered_pair(v12, v13) = v14) | ? [v15] : ( ~ (v15 = 0) & empty(v14) = v15)) & ! [v12] : ! [v13] : (v13 = v12 | ~ (empty(v13) = 0) | ~ (empty(v12) = 0)) & ! [v12] : ! [v13] : (v13 = 0 | ~ (subset(v12, v12) = v13)) & ! [v12] : ! [v13] : (v13 = 0 | ~ (relation(v12) = v13) | ? [v14] : ( ~ (v14 = 0) & empty(v12) = v14)) & ! [v12] : ! [v13] : ( ~ (powerset(v12) = v13) | ? [v14] : ? [v15] : ? [v16] : ((v15 = 0 & ~ (v16 = 0) & element(v14, v13) = 0 & empty(v14) = v16) | (v14 = 0 & empty(v12) = 0))) & ! [v12] : ! [v13] : ( ~ (powerset(v12) = v13) | ? [v14] : ( ~ (v14 = 0) & empty(v13) = v14)) & ! [v12] : ! [v13] : ( ~ (powerset(v12) = v13) | ? [v14] : (element(v14, v13) = 0 & empty(v14) = 0)) & ! [v12] : ! [v13] : ( ~ (element(v12, v13) = 0) | ? [v14] : ? [v15] : (empty(v13) = v14 & in(v12, v13) = v15 & (v15 = 0 | v14 = 0))) & ! [v12] : ! [v13] : ( ~ (singleton(v12) = v13) | ? [v14] : ( ~ (v14 = 0) & empty(v13) = v14)) & ! [v12] : ! [v13] : ( ~ (in(v12, v13) = 0) | ? [v14] : ( ~ (v14 = 0) & empty(v13) = v14)) & ! [v12] : ! [v13] : ( ~ (in(v12, v13) = 0) | ? [v14] : ( ~ (v14 = 0) & in(v13, v12) = v14)) & ! [v12] : (v12 = empty_set | ~ (empty(v12) = 0)) & ? [v12] : ? [v13] : element(v13, v12) = 0) % 5.77/2.06 | 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: % 5.77/2.06 | (1) ~ (all_0_2_2 = 0) & ~ (all_0_4_4 = 0) & ~ (all_0_6_6 = 0) & subset(all_0_8_8, all_0_7_7) = all_0_6_6 & subset(all_0_11_11, all_0_10_10) = 0 & relation_inverse_image(all_0_9_9, all_0_10_10) = all_0_7_7 & relation_inverse_image(all_0_9_9, all_0_11_11) = all_0_8_8 & relation(all_0_0_0) = 0 & relation(all_0_3_3) = 0 & relation(all_0_9_9) = 0 & relation(empty_set) = 0 & empty(all_0_0_0) = 0 & empty(all_0_1_1) = 0 & empty(all_0_3_3) = all_0_2_2 & empty(all_0_5_5) = all_0_4_4 & empty(empty_set) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = 0 | ~ (relation_inverse_image(v0, v1) = v2) | ~ (ordered_pair(v3, v5) = v6) | ~ (relation(v0) = 0) | ~ (in(v6, v0) = 0) | ~ (in(v3, v2) = v4) | ? [v7] : ( ~ (v7 = 0) & in(v5, v1) = v7)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (element(v0, v2) = v4) | ? [v5] : ( ~ (v5 = 0) & in(v0, v1) = v5)) & ! [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] : (v3 = 0 | ~ (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_inverse_image(v3, v2) = v1) | ~ (relation_inverse_image(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 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_inverse_image(v0, v1) = v2) | ~ (relation(v0) = 0) | ~ (in(v3, v2) = 0) | ? [v4] : ? [v5] : (ordered_pair(v3, v4) = v5 & in(v5, v0) = 0 & in(v4, v1) = 0)) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (relation_inverse_image(v1, v2) = v3) | ~ (relation(v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (in(v4, v0) = v5 & ( ~ (v5 = 0) | ! [v10] : ! [v11] : ( ~ (ordered_pair(v4, v10) = v11) | ~ (in(v11, v1) = 0) | ? [v12] : ( ~ (v12 = 0) & in(v10, v2) = v12))) & (v5 = 0 | (v9 = 0 & v8 = 0 & ordered_pair(v4, v6) = v7 & in(v7, v1) = 0 & in(v6, v2) = 0)))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | subset(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (relation(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v3 = 0 & ~ (v4 = 0) & element(v2, v1) = 0 & empty(v2) = v4) | (v2 = 0 & empty(v0) = 0))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) = 0 & empty(v2) = 0)) & ! [v0] : ! [v1] : ( ~ (element(v0, v1) = 0) | ? [v2] : ? [v3] : (empty(v1) = v2 & in(v0, v1) = v3 & (v3 = 0 | v2 = 0))) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) & ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0)) & ? [v0] : ? [v1] : element(v1, v0) = 0 % 6.18/2.07 | % 6.18/2.07 | Applying alpha-rule on (1) yields: % 6.18/2.07 | (2) relation(empty_set) = 0 % 6.18/2.07 | (3) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) % 6.18/2.07 | (4) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) % 6.18/2.07 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_inverse_image(v0, v1) = v2) | ~ (relation(v0) = 0) | ~ (in(v3, v2) = 0) | ? [v4] : ? [v5] : (ordered_pair(v3, v4) = v5 & in(v5, v0) = 0 & in(v4, v1) = 0)) % 6.18/2.07 | (6) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) % 6.18/2.07 | (7) relation(all_0_3_3) = 0 % 6.18/2.07 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) % 6.18/2.07 | (9) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0)) % 6.18/2.07 | (10) subset(all_0_8_8, all_0_7_7) = all_0_6_6 % 6.18/2.07 | (11) relation(all_0_9_9) = 0 % 6.18/2.07 | (12) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) % 6.18/2.07 | (13) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0)) % 6.18/2.07 | (14) empty(all_0_0_0) = 0 % 6.18/2.07 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4) % 6.18/2.07 | (16) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) % 6.18/2.07 | (17) relation_inverse_image(all_0_9_9, all_0_11_11) = all_0_8_8 % 6.18/2.07 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) % 6.18/2.08 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = 0 | ~ (relation_inverse_image(v0, v1) = v2) | ~ (ordered_pair(v3, v5) = v6) | ~ (relation(v0) = 0) | ~ (in(v6, v0) = 0) | ~ (in(v3, v2) = v4) | ? [v7] : ( ~ (v7 = 0) & in(v5, v1) = v7)) % 6.18/2.08 | (20) ~ (all_0_2_2 = 0) % 6.18/2.08 | (21) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3)) % 6.18/2.08 | (22) ! [v0] : ! [v1] : (v1 = 0 | ~ (relation(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2)) % 6.18/2.08 | (23) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) % 6.18/2.08 | (24) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 6.18/2.08 | (25) empty(all_0_3_3) = all_0_2_2 % 6.18/2.08 | (26) empty(empty_set) = 0 % 6.18/2.08 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) % 6.18/2.08 | (28) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (relation_inverse_image(v1, v2) = v3) | ~ (relation(v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (in(v4, v0) = v5 & ( ~ (v5 = 0) | ! [v10] : ! [v11] : ( ~ (ordered_pair(v4, v10) = v11) | ~ (in(v11, v1) = 0) | ? [v12] : ( ~ (v12 = 0) & in(v10, v2) = v12))) & (v5 = 0 | (v9 = 0 & v8 = 0 & ordered_pair(v4, v6) = v7 & in(v7, v1) = 0 & in(v6, v2) = 0)))) % 6.18/2.08 | (29) empty(all_0_1_1) = 0 % 6.18/2.08 | (30) ? [v0] : ? [v1] : element(v1, v0) = 0 % 6.18/2.08 | (31) relation_inverse_image(all_0_9_9, all_0_10_10) = all_0_7_7 % 6.24/2.08 | (32) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) % 6.24/2.08 | (33) relation(all_0_0_0) = 0 % 6.24/2.08 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_inverse_image(v3, v2) = v1) | ~ (relation_inverse_image(v3, v2) = v0)) % 6.24/2.08 | (35) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) % 6.24/2.08 | (36) empty(all_0_5_5) = all_0_4_4 % 6.24/2.08 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) % 6.24/2.08 | (38) subset(all_0_11_11, all_0_10_10) = 0 % 6.24/2.08 | (39) ~ (all_0_4_4 = 0) % 6.24/2.08 | (40) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) % 6.24/2.08 | (41) ~ (all_0_6_6 = 0) % 6.24/2.08 | (42) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | subset(v0, v1) = 0) % 6.24/2.08 | (43) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3)) % 6.24/2.08 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4)) % 6.24/2.08 | (45) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3)) % 6.24/2.08 | (46) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v3 = 0 & ~ (v4 = 0) & element(v2, v1) = 0 & empty(v2) = v4) | (v2 = 0 & empty(v0) = 0))) % 6.24/2.08 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (element(v0, v2) = v4) | ? [v5] : ( ~ (v5 = 0) & in(v0, v1) = v5)) % 6.24/2.09 | (48) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)) % 6.24/2.09 | (49) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0) % 6.24/2.09 | (50) ! [v0] : ! [v1] : ( ~ (element(v0, v1) = 0) | ? [v2] : ? [v3] : (empty(v1) = v2 & in(v0, v1) = v3 & (v3 = 0 | v2 = 0))) % 6.24/2.09 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 6.24/2.09 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) % 6.24/2.09 | (53) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) = 0 & empty(v2) = 0)) % 6.24/2.09 | % 6.24/2.09 | Instantiating formula (9) with all_0_6_6, all_0_7_7, all_0_8_8 and discharging atoms subset(all_0_8_8, all_0_7_7) = all_0_6_6, yields: % 6.24/2.09 | (54) all_0_6_6 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_7_7) = v1 & in(v0, all_0_8_8) = 0) % 6.24/2.09 | % 6.24/2.09 +-Applying beta-rule and splitting (54), into two cases. % 6.24/2.09 |-Branch one: % 6.24/2.09 | (55) all_0_6_6 = 0 % 6.24/2.09 | % 6.24/2.09 | Equations (55) can reduce 41 to: % 6.24/2.09 | (56) $false % 6.24/2.09 | % 6.24/2.09 |-The branch is then unsatisfiable % 6.24/2.09 |-Branch two: % 6.24/2.09 | (41) ~ (all_0_6_6 = 0) % 6.24/2.09 | (58) ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_7_7) = v1 & in(v0, all_0_8_8) = 0) % 6.24/2.09 | % 6.24/2.09 | Instantiating (58) with all_30_0_17, all_30_1_18 yields: % 6.24/2.09 | (59) ~ (all_30_0_17 = 0) & in(all_30_1_18, all_0_7_7) = all_30_0_17 & in(all_30_1_18, all_0_8_8) = 0 % 6.24/2.09 | % 6.24/2.09 | Applying alpha-rule on (59) yields: % 6.24/2.09 | (60) ~ (all_30_0_17 = 0) % 6.24/2.09 | (61) in(all_30_1_18, all_0_7_7) = all_30_0_17 % 6.24/2.09 | (62) in(all_30_1_18, all_0_8_8) = 0 % 6.24/2.09 | % 6.24/2.09 | Instantiating formula (5) with all_30_1_18, all_0_8_8, all_0_11_11, all_0_9_9 and discharging atoms relation_inverse_image(all_0_9_9, all_0_11_11) = all_0_8_8, relation(all_0_9_9) = 0, in(all_30_1_18, all_0_8_8) = 0, yields: % 6.24/2.09 | (63) ? [v0] : ? [v1] : (ordered_pair(all_30_1_18, v0) = v1 & in(v1, all_0_9_9) = 0 & in(v0, all_0_11_11) = 0) % 6.24/2.09 | % 6.24/2.09 | Instantiating (63) with all_41_0_21, all_41_1_22 yields: % 6.24/2.09 | (64) ordered_pair(all_30_1_18, all_41_1_22) = all_41_0_21 & in(all_41_0_21, all_0_9_9) = 0 & in(all_41_1_22, all_0_11_11) = 0 % 6.24/2.09 | % 6.24/2.09 | Applying alpha-rule on (64) yields: % 6.24/2.09 | (65) ordered_pair(all_30_1_18, all_41_1_22) = all_41_0_21 % 6.24/2.09 | (66) in(all_41_0_21, all_0_9_9) = 0 % 6.24/2.09 | (67) in(all_41_1_22, all_0_11_11) = 0 % 6.24/2.09 | % 6.24/2.09 | Instantiating formula (19) with all_41_0_21, all_41_1_22, all_30_0_17, all_30_1_18, all_0_7_7, all_0_10_10, all_0_9_9 and discharging atoms relation_inverse_image(all_0_9_9, all_0_10_10) = all_0_7_7, ordered_pair(all_30_1_18, all_41_1_22) = all_41_0_21, relation(all_0_9_9) = 0, in(all_41_0_21, all_0_9_9) = 0, in(all_30_1_18, all_0_7_7) = all_30_0_17, yields: % 6.24/2.09 | (68) all_30_0_17 = 0 | ? [v0] : ( ~ (v0 = 0) & in(all_41_1_22, all_0_10_10) = v0) % 6.24/2.09 | % 6.24/2.09 | Instantiating formula (49) with all_41_1_22, all_0_10_10, all_0_11_11 and discharging atoms subset(all_0_11_11, all_0_10_10) = 0, in(all_41_1_22, all_0_11_11) = 0, yields: % 6.24/2.09 | (69) in(all_41_1_22, all_0_10_10) = 0 % 6.24/2.09 | % 6.24/2.09 +-Applying beta-rule and splitting (68), into two cases. % 6.24/2.09 |-Branch one: % 6.24/2.09 | (70) all_30_0_17 = 0 % 6.24/2.09 | % 6.24/2.09 | Equations (70) can reduce 60 to: % 6.24/2.09 | (56) $false % 6.24/2.09 | % 6.24/2.09 |-The branch is then unsatisfiable % 6.24/2.09 |-Branch two: % 6.24/2.09 | (60) ~ (all_30_0_17 = 0) % 6.24/2.09 | (73) ? [v0] : ( ~ (v0 = 0) & in(all_41_1_22, all_0_10_10) = v0) % 6.24/2.10 | % 6.24/2.10 | Instantiating (73) with all_63_0_28 yields: % 6.24/2.10 | (74) ~ (all_63_0_28 = 0) & in(all_41_1_22, all_0_10_10) = all_63_0_28 % 6.24/2.10 | % 6.24/2.10 | Applying alpha-rule on (74) yields: % 6.24/2.10 | (75) ~ (all_63_0_28 = 0) % 6.24/2.10 | (76) in(all_41_1_22, all_0_10_10) = all_63_0_28 % 6.24/2.10 | % 6.24/2.10 | Instantiating formula (51) with all_41_1_22, all_0_10_10, 0, all_63_0_28 and discharging atoms in(all_41_1_22, all_0_10_10) = all_63_0_28, in(all_41_1_22, all_0_10_10) = 0, yields: % 6.24/2.10 | (77) all_63_0_28 = 0 % 6.24/2.10 | % 6.24/2.10 | Equations (77) can reduce 75 to: % 6.24/2.10 | (56) $false % 6.24/2.10 | % 6.24/2.10 |-The branch is then unsatisfiable % 6.24/2.10 % SZS output end Proof for theBenchmark % 6.24/2.10 % 6.24/2.10 1510ms %------------------------------------------------------------------------------