%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU198+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n028.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 08:47:33 EDT 2022 % Result : Theorem 3.76s 1.62s % Output : Proof 5.90s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SEU198+1 : TPTP v8.1.0. Released v3.3.0. % 0.07/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n028.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 : Sun Jun 19 21:30:46 EDT 2022 % 0.12/0.33 % CPUTime : % 0.50/0.59 ____ _ % 0.50/0.59 ___ / __ \_____(_)___ ________ __________ % 0.50/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.50/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.50/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.50/0.59 % 0.50/0.59 A Theorem Prover for First-Order Logic % 0.50/0.59 (ePrincess v.1.0) % 0.50/0.59 % 0.50/0.59 (c) Philipp Rümmer, 2009-2015 % 0.50/0.59 (c) Peter Backeman, 2014-2015 % 0.50/0.59 (contributions by Angelo Brillout, Peter Baumgartner) % 0.50/0.59 Free software under GNU Lesser General Public License (LGPL). % 0.50/0.59 Bug reports to peter@backeman.se % 0.50/0.59 % 0.50/0.59 For more information, visit http://user.uu.se/~petba168/breu/ % 0.50/0.59 % 0.50/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.74/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.55/0.94 Prover 0: Preprocessing ... % 1.92/1.11 Prover 0: Warning: ignoring some quantifiers % 2.03/1.13 Prover 0: Constructing countermodel ... % 2.84/1.39 Prover 0: gave up % 2.84/1.39 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 2.84/1.42 Prover 1: Preprocessing ... % 3.24/1.52 Prover 1: Warning: ignoring some quantifiers % 3.24/1.53 Prover 1: Constructing countermodel ... % 3.76/1.62 Prover 1: proved (231ms) % 3.76/1.62 % 3.76/1.62 No countermodel exists, formula is valid % 3.76/1.62 % SZS status Theorem for theBenchmark % 3.76/1.62 % 3.76/1.62 Generating proof ... Warning: ignoring some quantifiers % 5.57/1.98 found it (size 26) % 5.57/1.98 % 5.57/1.98 % SZS output start Proof for theBenchmark % 5.57/1.98 Assumed formulas after preprocessing and simplification: % 5.57/1.98 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ( ~ (v8 = 0) & ~ (v6 = 0) & ~ (v4 = 0) & relation_rng(v2) = v3 & relation_rng_restriction(v0, v1) = v2 & subset(v3, v0) = v4 & relation(v10) = 0 & relation(v7) = 0 & relation(v1) = 0 & relation(empty_set) = 0 & empty(v10) = 0 & empty(v9) = 0 & empty(v7) = v8 & empty(v5) = v6 & empty(empty_set) = 0 & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (relation_rng(v14) = v15) | ~ (relation_rng_restriction(v12, v13) = v14) | ~ (in(v11, v15) = v16) | ? [v17] : ? [v18] : ? [v19] : ? [v20] : (relation_rng(v13) = v19 & relation(v13) = v17 & in(v11, v19) = v20 & in(v11, v12) = v18 & ( ~ (v17 = 0) | (( ~ (v20 = 0) | ~ (v18 = 0) | v16 = 0) & ( ~ (v16 = 0) | (v20 = 0 & v18 = 0)))))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (powerset(v13) = v14) | ~ (element(v12, v14) = 0) | ~ (element(v11, v13) = v15) | ? [v16] : ( ~ (v16 = 0) & in(v11, v12) = v16)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (powerset(v12) = v13) | ~ (element(v11, v13) = v14) | ? [v15] : ( ~ (v15 = 0) & subset(v11, v12) = v15)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (element(v14, v13) = v12) | ~ (element(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (relation_rng_restriction(v14, v13) = v12) | ~ (relation_rng_restriction(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (subset(v14, v13) = v12) | ~ (subset(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (in(v14, v13) = v12) | ~ (in(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (powerset(v13) = v14) | ~ (element(v12, v14) = 0) | ~ (in(v11, v12) = 0) | ? [v15] : ( ~ (v15 = 0) & empty(v13) = v15)) & ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (element(v11, v12) = v13) | ? [v14] : ( ~ (v14 = 0) & in(v11, v12) = v14)) & ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (subset(v11, v12) = v13) | ? [v14] : ? [v15] : ( ~ (v15 = 0) & in(v14, v12) = v15 & in(v14, v11) = 0)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (relation_rng(v13) = v12) | ~ (relation_rng(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (powerset(v13) = v12) | ~ (powerset(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (relation(v13) = v12) | ~ (relation(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (empty(v13) = v12) | ~ (empty(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (powerset(v12) = v13) | ~ (element(v11, v13) = 0) | subset(v11, v12) = 0) & ! [v11] : ! [v12] : ! [v13] : ( ~ (relation_rng_restriction(v11, v12) = v13) | ? [v14] : ? [v15] : (relation(v13) = v15 & relation(v12) = v14 & ( ~ (v14 = 0) | v15 = 0))) & ! [v11] : ! [v12] : ! [v13] : ( ~ (subset(v11, v12) = 0) | ~ (in(v13, v11) = 0) | in(v13, v12) = 0) & ! [v11] : ! [v12] : (v12 = v11 | ~ (empty(v12) = 0) | ~ (empty(v11) = 0)) & ! [v11] : ! [v12] : (v12 = 0 | ~ (subset(v11, v11) = v12)) & ! [v11] : ! [v12] : (v12 = 0 | ~ (relation(v11) = v12) | ? [v13] : ( ~ (v13 = 0) & empty(v11) = v13)) & ! [v11] : ! [v12] : ( ~ (relation_rng(v11) = v12) | ? [v13] : ? [v14] : ? [v15] : (relation(v12) = v15 & empty(v12) = v14 & empty(v11) = v13 & ( ~ (v13 = 0) | (v15 = 0 & v14 = 0)))) & ! [v11] : ! [v12] : ( ~ (relation_rng(v11) = v12) | ? [v13] : ? [v14] : ? [v15] : (relation(v11) = v14 & empty(v12) = v15 & empty(v11) = v13 & ( ~ (v15 = 0) | ~ (v14 = 0) | v13 = 0))) & ! [v11] : ! [v12] : ( ~ (powerset(v11) = v12) | ? [v13] : ? [v14] : ? [v15] : ((v14 = 0 & ~ (v15 = 0) & element(v13, v12) = 0 & empty(v13) = v15) | (v13 = 0 & empty(v11) = 0))) & ! [v11] : ! [v12] : ( ~ (powerset(v11) = v12) | ? [v13] : ( ~ (v13 = 0) & empty(v12) = v13)) & ! [v11] : ! [v12] : ( ~ (powerset(v11) = v12) | ? [v13] : (element(v13, v12) = 0 & empty(v13) = 0)) & ! [v11] : ! [v12] : ( ~ (element(v11, v12) = 0) | ? [v13] : ? [v14] : (empty(v12) = v13 & in(v11, v12) = v14 & (v14 = 0 | v13 = 0))) & ! [v11] : ! [v12] : ( ~ (in(v11, v12) = 0) | ? [v13] : ( ~ (v13 = 0) & empty(v12) = v13)) & ! [v11] : ! [v12] : ( ~ (in(v11, v12) = 0) | ? [v13] : ( ~ (v13 = 0) & in(v12, v11) = v13)) & ! [v11] : (v11 = empty_set | ~ (empty(v11) = 0)) & ? [v11] : ? [v12] : element(v12, v11) = 0) % 5.57/2.02 | 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 yields: % 5.57/2.02 | (1) ~ (all_0_2_2 = 0) & ~ (all_0_4_4 = 0) & ~ (all_0_6_6 = 0) & relation_rng(all_0_8_8) = all_0_7_7 & relation_rng_restriction(all_0_10_10, all_0_9_9) = all_0_8_8 & subset(all_0_7_7, all_0_10_10) = all_0_6_6 & 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] : ( ~ (relation_rng(v3) = v4) | ~ (relation_rng_restriction(v1, v2) = v3) | ~ (in(v0, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (relation_rng(v2) = v8 & relation(v2) = v6 & in(v0, v8) = v9 & in(v0, v1) = v7 & ( ~ (v6 = 0) | (( ~ (v9 = 0) | ~ (v7 = 0) | v5 = 0) & ( ~ (v5 = 0) | (v9 = 0 & v7 = 0)))))) & ! [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] : (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 | ~ (relation_rng_restriction(v3, v2) = v1) | ~ (relation_rng_restriction(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(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] : (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 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(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] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ? [v3] : ? [v4] : (relation(v2) = v4 & relation(v1) = v3 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0) & ! [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] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation(v1) = v4 & empty(v1) = v3 & empty(v0) = v2 & ( ~ (v2 = 0) | (v4 = 0 & v3 = 0)))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation(v0) = v3 & empty(v1) = v4 & empty(v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2 = 0))) & ! [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] : ( ~ (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 % 5.57/2.03 | % 5.57/2.03 | Applying alpha-rule on (1) yields: % 5.57/2.03 | (2) empty(all_0_3_3) = all_0_2_2 % 5.57/2.03 | (3) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) % 5.57/2.03 | (4) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0)) % 5.57/2.04 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_rng(v3) = v4) | ~ (relation_rng_restriction(v1, v2) = v3) | ~ (in(v0, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (relation_rng(v2) = v8 & relation(v2) = v6 & in(v0, v8) = v9 & in(v0, v1) = v7 & ( ~ (v6 = 0) | (( ~ (v9 = 0) | ~ (v7 = 0) | v5 = 0) & ( ~ (v5 = 0) | (v9 = 0 & v7 = 0)))))) % 5.57/2.04 | (6) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | subset(v0, v1) = 0) % 5.57/2.04 | (7) ~ (all_0_6_6 = 0) % 5.57/2.04 | (8) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) % 5.57/2.04 | (9) relation(all_0_3_3) = 0 % 5.57/2.04 | (10) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)) % 5.57/2.04 | (11) ~ (all_0_4_4 = 0) % 5.57/2.04 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ? [v3] : ? [v4] : (relation(v2) = v4 & relation(v1) = v3 & ( ~ (v3 = 0) | v4 = 0))) % 5.57/2.04 | (13) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v3 = 0 & ~ (v4 = 0) & element(v2, v1) = 0 & empty(v2) = v4) | (v2 = 0 & empty(v0) = 0))) % 5.57/2.04 | (14) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation(v1) = v4 & empty(v1) = v3 & empty(v0) = v2 & ( ~ (v2 = 0) | (v4 = 0 & v3 = 0)))) % 5.82/2.04 | (15) ! [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)) % 5.82/2.04 | (16) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0)) % 5.82/2.04 | (17) ! [v0] : ! [v1] : ( ~ (element(v0, v1) = 0) | ? [v2] : ? [v3] : (empty(v1) = v2 & in(v0, v1) = v3 & (v3 = 0 | v2 = 0))) % 5.82/2.04 | (18) ~ (all_0_2_2 = 0) % 5.82/2.04 | (19) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation(v0) = v3 & empty(v1) = v4 & empty(v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2 = 0))) % 5.82/2.04 | (20) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) % 5.82/2.04 | (21) empty(all_0_1_1) = 0 % 5.82/2.04 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) % 5.82/2.04 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) % 5.82/2.04 | (24) relation(all_0_9_9) = 0 % 5.82/2.04 | (25) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) % 5.82/2.04 | (26) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0) % 5.82/2.04 | (27) relation(all_0_0_0) = 0 % 5.82/2.04 | (28) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) % 5.82/2.04 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 5.82/2.05 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) % 5.82/2.05 | (31) ! [v0] : ! [v1] : (v1 = 0 | ~ (relation(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2)) % 5.82/2.05 | (32) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) % 5.82/2.05 | (33) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) % 5.82/2.05 | (34) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) % 5.82/2.05 | (35) relation_rng_restriction(all_0_10_10, all_0_9_9) = all_0_8_8 % 5.82/2.05 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_rng_restriction(v3, v2) = v1) | ~ (relation_rng_restriction(v3, v2) = v0)) % 5.82/2.05 | (37) empty(all_0_0_0) = 0 % 5.82/2.05 | (38) relation_rng(all_0_8_8) = all_0_7_7 % 5.82/2.05 | (39) relation(empty_set) = 0 % 5.82/2.05 | (40) ? [v0] : ? [v1] : element(v1, v0) = 0 % 5.82/2.05 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4)) % 5.82/2.05 | (42) subset(all_0_7_7, all_0_10_10) = all_0_6_6 % 5.82/2.05 | (43) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) = 0 & empty(v2) = 0)) % 5.82/2.05 | (44) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3)) % 5.82/2.05 | (45) empty(empty_set) = 0 % 5.82/2.05 | (46) empty(all_0_5_5) = all_0_4_4 % 5.82/2.05 | % 5.82/2.05 | Instantiating formula (12) with all_0_8_8, all_0_9_9, all_0_10_10 and discharging atoms relation_rng_restriction(all_0_10_10, all_0_9_9) = all_0_8_8, yields: % 5.82/2.05 | (47) ? [v0] : ? [v1] : (relation(all_0_8_8) = v1 & relation(all_0_9_9) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 5.82/2.05 | % 5.82/2.05 | Instantiating formula (4) with all_0_6_6, all_0_10_10, all_0_7_7 and discharging atoms subset(all_0_7_7, all_0_10_10) = all_0_6_6, yields: % 5.82/2.05 | (48) all_0_6_6 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_7_7) = 0 & in(v0, all_0_10_10) = v1) % 5.82/2.05 | % 5.82/2.05 | Instantiating (47) with all_22_0_13, all_22_1_14 yields: % 5.82/2.05 | (49) relation(all_0_8_8) = all_22_0_13 & relation(all_0_9_9) = all_22_1_14 & ( ~ (all_22_1_14 = 0) | all_22_0_13 = 0) % 5.82/2.05 | % 5.82/2.05 | Applying alpha-rule on (49) yields: % 5.82/2.05 | (50) relation(all_0_8_8) = all_22_0_13 % 5.82/2.05 | (51) relation(all_0_9_9) = all_22_1_14 % 5.82/2.05 | (52) ~ (all_22_1_14 = 0) | all_22_0_13 = 0 % 5.82/2.05 | % 5.82/2.05 +-Applying beta-rule and splitting (48), into two cases. % 5.82/2.05 |-Branch one: % 5.82/2.05 | (53) all_0_6_6 = 0 % 5.82/2.05 | % 5.82/2.05 | Equations (53) can reduce 7 to: % 5.82/2.05 | (54) $false % 5.82/2.05 | % 5.82/2.05 |-The branch is then unsatisfiable % 5.82/2.05 |-Branch two: % 5.82/2.05 | (7) ~ (all_0_6_6 = 0) % 5.82/2.05 | (56) ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_7_7) = 0 & in(v0, all_0_10_10) = v1) % 5.82/2.06 | % 5.82/2.06 | Instantiating (56) with all_34_0_23, all_34_1_24 yields: % 5.82/2.06 | (57) ~ (all_34_0_23 = 0) & in(all_34_1_24, all_0_7_7) = 0 & in(all_34_1_24, all_0_10_10) = all_34_0_23 % 5.82/2.06 | % 5.82/2.06 | Applying alpha-rule on (57) yields: % 5.82/2.06 | (58) ~ (all_34_0_23 = 0) % 5.82/2.06 | (59) in(all_34_1_24, all_0_7_7) = 0 % 5.82/2.06 | (60) in(all_34_1_24, all_0_10_10) = all_34_0_23 % 5.82/2.06 | % 5.90/2.06 | Instantiating formula (33) with all_0_9_9, all_22_1_14, 0 and discharging atoms relation(all_0_9_9) = all_22_1_14, relation(all_0_9_9) = 0, yields: % 5.90/2.06 | (61) all_22_1_14 = 0 % 5.90/2.06 | % 5.90/2.06 | From (61) and (51) follows: % 5.90/2.06 | (24) relation(all_0_9_9) = 0 % 5.90/2.06 | % 5.90/2.06 | Instantiating formula (5) with 0, all_0_7_7, all_0_8_8, all_0_9_9, all_0_10_10, all_34_1_24 and discharging atoms relation_rng(all_0_8_8) = all_0_7_7, relation_rng_restriction(all_0_10_10, all_0_9_9) = all_0_8_8, in(all_34_1_24, all_0_7_7) = 0, yields: % 5.90/2.06 | (63) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (relation_rng(all_0_9_9) = v2 & relation(all_0_9_9) = v0 & in(all_34_1_24, v2) = v3 & in(all_34_1_24, all_0_10_10) = v1 & ( ~ (v0 = 0) | (v3 = 0 & v1 = 0))) % 5.90/2.06 | % 5.90/2.06 | Instantiating (63) with all_51_0_26, all_51_1_27, all_51_2_28, all_51_3_29 yields: % 5.90/2.06 | (64) relation_rng(all_0_9_9) = all_51_1_27 & relation(all_0_9_9) = all_51_3_29 & in(all_34_1_24, all_51_1_27) = all_51_0_26 & in(all_34_1_24, all_0_10_10) = all_51_2_28 & ( ~ (all_51_3_29 = 0) | (all_51_0_26 = 0 & all_51_2_28 = 0)) % 5.90/2.06 | % 5.90/2.06 | Applying alpha-rule on (64) yields: % 5.90/2.06 | (65) in(all_34_1_24, all_51_1_27) = all_51_0_26 % 5.90/2.06 | (66) relation(all_0_9_9) = all_51_3_29 % 5.90/2.06 | (67) in(all_34_1_24, all_0_10_10) = all_51_2_28 % 5.90/2.06 | (68) ~ (all_51_3_29 = 0) | (all_51_0_26 = 0 & all_51_2_28 = 0) % 5.90/2.06 | (69) relation_rng(all_0_9_9) = all_51_1_27 % 5.90/2.06 | % 5.90/2.06 | Instantiating formula (33) with all_0_9_9, all_51_3_29, 0 and discharging atoms relation(all_0_9_9) = all_51_3_29, relation(all_0_9_9) = 0, yields: % 5.90/2.06 | (70) all_51_3_29 = 0 % 5.90/2.06 | % 5.90/2.06 | Instantiating formula (29) with all_34_1_24, all_0_10_10, all_51_2_28, all_34_0_23 and discharging atoms in(all_34_1_24, all_0_10_10) = all_51_2_28, in(all_34_1_24, all_0_10_10) = all_34_0_23, yields: % 5.90/2.06 | (71) all_51_2_28 = all_34_0_23 % 5.90/2.06 | % 5.90/2.06 +-Applying beta-rule and splitting (68), into two cases. % 5.90/2.06 |-Branch one: % 5.90/2.06 | (72) ~ (all_51_3_29 = 0) % 5.90/2.06 | % 5.90/2.06 | Equations (70) can reduce 72 to: % 5.90/2.06 | (54) $false % 5.90/2.06 | % 5.90/2.06 |-The branch is then unsatisfiable % 5.90/2.06 |-Branch two: % 5.90/2.06 | (70) all_51_3_29 = 0 % 5.90/2.06 | (75) all_51_0_26 = 0 & all_51_2_28 = 0 % 5.90/2.06 | % 5.90/2.06 | Applying alpha-rule on (75) yields: % 5.90/2.06 | (76) all_51_0_26 = 0 % 5.90/2.06 | (77) all_51_2_28 = 0 % 5.90/2.06 | % 5.90/2.06 | Combining equations (71,77) yields a new equation: % 5.90/2.06 | (78) all_34_0_23 = 0 % 5.90/2.06 | % 5.90/2.06 | Simplifying 78 yields: % 5.90/2.06 | (79) all_34_0_23 = 0 % 5.90/2.06 | % 5.90/2.06 | Equations (79) can reduce 58 to: % 5.90/2.06 | (54) $false % 5.90/2.06 | % 5.90/2.06 |-The branch is then unsatisfiable % 5.90/2.06 % SZS output end Proof for theBenchmark % 5.90/2.06 % 5.90/2.06 1465ms %------------------------------------------------------------------------------