%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU077+1 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n008.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 08:46:29 EDT 2022 % Result : Theorem 6.93s 2.32s % Output : Proof 11.81s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : SEU077+1 : TPTP v8.1.0. Released v3.2.0. % 0.12/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.14/0.34 % Computer : n008.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 19:35:52 EDT 2022 % 0.14/0.34 % CPUTime : % 0.56/0.59 ____ _ % 0.56/0.59 ___ / __ \_____(_)___ ________ __________ % 0.56/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.56/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.56/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.56/0.59 % 0.56/0.59 A Theorem Prover for First-Order Logic % 0.62/0.59 (ePrincess v.1.0) % 0.62/0.59 % 0.62/0.59 (c) Philipp Rümmer, 2009-2015 % 0.62/0.59 (c) Peter Backeman, 2014-2015 % 0.62/0.59 (contributions by Angelo Brillout, Peter Baumgartner) % 0.62/0.59 Free software under GNU Lesser General Public License (LGPL). % 0.62/0.59 Bug reports to peter@backeman.se % 0.62/0.59 % 0.62/0.59 For more information, visit http://user.uu.se/~petba168/breu/ % 0.62/0.59 % 0.62/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.76/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.63/0.97 Prover 0: Preprocessing ... % 2.42/1.26 Prover 0: Warning: ignoring some quantifiers % 2.42/1.28 Prover 0: Constructing countermodel ... % 5.16/1.94 Prover 0: gave up % 5.16/1.94 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 5.16/1.98 Prover 1: Preprocessing ... % 5.94/2.08 Prover 1: Warning: ignoring some quantifiers % 5.98/2.09 Prover 1: Constructing countermodel ... % 6.93/2.32 Prover 1: proved (377ms) % 6.93/2.32 % 6.93/2.32 No countermodel exists, formula is valid % 6.93/2.32 % SZS status Theorem for theBenchmark % 6.93/2.32 % 6.93/2.32 Generating proof ... Warning: ignoring some quantifiers % 11.21/3.31 found it (size 75) % 11.21/3.31 % 11.21/3.31 % SZS output start Proof for theBenchmark % 11.21/3.31 Assumed formulas after preprocessing and simplification: % 11.21/3.31 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ( ~ (v12 = 0) & ~ (v10 = 0) & ~ (v6 = 0) & relation_empty_yielding(v7) = 0 & relation_empty_yielding(empty_set) = 0 & relation_rng(v2) = v5 & subset(v3, v4) = 0 & subset(v0, v5) = 0 & subset(v0, v1) = v6 & relation_inverse_image(v2, v1) = v4 & relation_inverse_image(v2, v0) = v3 & one_to_one(v8) = 0 & relation(v16) = 0 & relation(v15) = 0 & relation(v13) = 0 & relation(v11) = 0 & relation(v8) = 0 & relation(v7) = 0 & relation(v2) = 0 & relation(empty_set) = 0 & function(v16) = 0 & function(v13) = 0 & function(v8) = 0 & function(v2) = 0 & empty(v15) = 0 & empty(v14) = 0 & empty(v13) = 0 & empty(v11) = v12 & empty(v9) = v10 & empty(empty_set) = 0 & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v21 = 0 | ~ (powerset(v19) = v20) | ~ (element(v18, v20) = 0) | ~ (element(v17, v19) = v21) | ? [v22] : ( ~ (v22 = 0) & in(v17, v18) = v22)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v20 = 0 | ~ (powerset(v18) = v19) | ~ (element(v17, v19) = v20) | ? [v21] : ( ~ (v21 = 0) & subset(v17, v18) = v21)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (element(v20, v19) = v18) | ~ (element(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (subset(v20, v19) = v18) | ~ (subset(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (relation_inverse_image(v20, v19) = v18) | ~ (relation_inverse_image(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (apply(v20, v19) = v18) | ~ (apply(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (in(v20, v19) = v18) | ~ (in(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (powerset(v19) = v20) | ~ (element(v18, v20) = 0) | ~ (in(v17, v18) = 0) | ? [v21] : ( ~ (v21 = 0) & empty(v19) = v21)) & ! [v17] : ! [v18] : ! [v19] : (v19 = 0 | ~ (element(v17, v18) = v19) | ? [v20] : ( ~ (v20 = 0) & in(v17, v18) = v20)) & ! [v17] : ! [v18] : ! [v19] : (v19 = 0 | ~ (subset(v17, v18) = v19) | ? [v20] : ? [v21] : ( ~ (v21 = 0) & in(v20, v18) = v21 & in(v20, v17) = 0)) & ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (relation_empty_yielding(v19) = v18) | ~ (relation_empty_yielding(v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (powerset(v19) = v18) | ~ (powerset(v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (relation_rng(v19) = v18) | ~ (relation_rng(v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (relation_dom(v19) = v18) | ~ (relation_dom(v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (one_to_one(v19) = v18) | ~ (one_to_one(v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (relation(v19) = v18) | ~ (relation(v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (function(v19) = v18) | ~ (function(v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (empty(v19) = v18) | ~ (empty(v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (powerset(v18) = v19) | ~ (element(v17, v19) = 0) | subset(v17, v18) = 0) & ! [v17] : ! [v18] : ! [v19] : ( ~ (subset(v17, v18) = 0) | ~ (in(v19, v17) = 0) | in(v19, v18) = 0) & ! [v17] : ! [v18] : (v18 = v17 | ~ (empty(v18) = 0) | ~ (empty(v17) = 0)) & ! [v17] : ! [v18] : (v18 = 0 | ~ (subset(v17, v17) = v18)) & ! [v17] : ! [v18] : (v18 = 0 | ~ (relation(v17) = v18) | ? [v19] : ( ~ (v19 = 0) & empty(v17) = v19)) & ! [v17] : ! [v18] : (v18 = 0 | ~ (function(v17) = v18) | ? [v19] : ( ~ (v19 = 0) & empty(v17) = v19)) & ! [v17] : ! [v18] : ( ~ (powerset(v17) = v18) | ? [v19] : ? [v20] : ? [v21] : ((v20 = 0 & ~ (v21 = 0) & element(v19, v18) = 0 & empty(v19) = v21) | (v19 = 0 & empty(v17) = 0))) & ! [v17] : ! [v18] : ( ~ (powerset(v17) = v18) | ? [v19] : ( ~ (v19 = 0) & empty(v18) = v19)) & ! [v17] : ! [v18] : ( ~ (powerset(v17) = v18) | ? [v19] : (element(v19, v18) = 0 & empty(v19) = 0)) & ! [v17] : ! [v18] : ( ~ (element(v17, v18) = 0) | ? [v19] : ? [v20] : (empty(v18) = v19 & in(v17, v18) = v20 & (v20 = 0 | v19 = 0))) & ! [v17] : ! [v18] : ( ~ (relation_rng(v17) = v18) | ? [v19] : ? [v20] : ? [v21] : (relation_dom(v17) = v21 & relation(v17) = v19 & function(v17) = v20 & ( ~ (v20 = 0) | ~ (v19 = 0) | ( ! [v22] : ! [v23] : ! [v24] : (v23 = 0 | ~ (in(v24, v21) = 0) | ~ (in(v22, v18) = v23) | ? [v25] : ( ~ (v25 = v22) & apply(v17, v24) = v25)) & ! [v22] : ( ~ (in(v22, v18) = 0) | ? [v23] : (apply(v17, v23) = v22 & in(v23, v21) = 0)) & ? [v22] : (v22 = v18 | ? [v23] : ? [v24] : ? [v25] : ? [v26] : ? [v27] : (in(v23, v22) = v24 & ( ~ (v24 = 0) | ! [v28] : ( ~ (in(v28, v21) = 0) | ? [v29] : ( ~ (v29 = v23) & apply(v17, v28) = v29))) & (v24 = 0 | (v27 = v23 & v26 = 0 & apply(v17, v25) = v23 & in(v25, v21) = 0)))))))) & ! [v17] : ! [v18] : ( ~ (relation_rng(v17) = v18) | ? [v19] : ? [v20] : ? [v21] : (relation(v18) = v21 & empty(v18) = v20 & empty(v17) = v19 & ( ~ (v19 = 0) | (v21 = 0 & v20 = 0)))) & ! [v17] : ! [v18] : ( ~ (relation_rng(v17) = v18) | ? [v19] : ? [v20] : ? [v21] : (relation(v17) = v20 & empty(v18) = v21 & empty(v17) = v19 & ( ~ (v21 = 0) | ~ (v20 = 0) | v19 = 0))) & ! [v17] : ! [v18] : ( ~ (relation_dom(v17) = v18) | ? [v19] : ? [v20] : ? [v21] : (relation(v18) = v21 & empty(v18) = v20 & empty(v17) = v19 & ( ~ (v19 = 0) | (v21 = 0 & v20 = 0)))) & ! [v17] : ! [v18] : ( ~ (relation_dom(v17) = v18) | ? [v19] : ? [v20] : ? [v21] : (relation(v17) = v20 & empty(v18) = v21 & empty(v17) = v19 & ( ~ (v21 = 0) | ~ (v20 = 0) | v19 = 0))) & ! [v17] : ! [v18] : ( ~ (one_to_one(v17) = v18) | ? [v19] : ? [v20] : ? [v21] : (relation(v17) = v19 & function(v17) = v21 & empty(v17) = v20 & ( ~ (v21 = 0) | ~ (v20 = 0) | ~ (v19 = 0) | v18 = 0))) & ! [v17] : ! [v18] : ( ~ (in(v17, v18) = 0) | ? [v19] : ( ~ (v19 = 0) & empty(v18) = v19)) & ! [v17] : ! [v18] : ( ~ (in(v17, v18) = 0) | ? [v19] : ( ~ (v19 = 0) & in(v18, v17) = v19)) & ! [v17] : (v17 = empty_set | ~ (empty(v17) = 0)) & ! [v17] : ( ~ (function(v17) = 0) | ? [v18] : ? [v19] : (relation_dom(v17) = v19 & relation(v17) = v18 & ( ~ (v18 = 0) | ( ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ( ~ (relation_inverse_image(v17, v20) = v21) | ~ (apply(v17, v22) = v23) | ~ (in(v23, v20) = v24) | ? [v25] : ? [v26] : (in(v22, v21) = v25 & in(v22, v19) = v26 & ( ~ (v25 = 0) | (v26 = 0 & v24 = 0)))) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ( ~ (relation_inverse_image(v17, v20) = v21) | ~ (apply(v17, v22) = v23) | ~ (in(v23, v20) = 0) | ? [v24] : ? [v25] : (in(v22, v21) = v25 & in(v22, v19) = v24 & ( ~ (v24 = 0) | v25 = 0))) & ? [v20] : ! [v21] : ! [v22] : (v22 = v20 | ~ (relation_inverse_image(v17, v21) = v22) | ? [v23] : ? [v24] : ? [v25] : ? [v26] : ? [v27] : (apply(v17, v23) = v26 & in(v26, v21) = v27 & in(v23, v20) = v24 & in(v23, v19) = v25 & ( ~ (v27 = 0) | ~ (v25 = 0) | ~ (v24 = 0)) & (v24 = 0 | (v27 = 0 & v25 = 0)))))))) & ? [v17] : ? [v18] : element(v18, v17) = 0) % 11.21/3.36 | 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, all_0_16_16 yields: % 11.21/3.36 | (1) ~ (all_0_4_4 = 0) & ~ (all_0_6_6 = 0) & ~ (all_0_10_10 = 0) & relation_empty_yielding(all_0_9_9) = 0 & relation_empty_yielding(empty_set) = 0 & relation_rng(all_0_14_14) = all_0_11_11 & subset(all_0_13_13, all_0_12_12) = 0 & subset(all_0_16_16, all_0_11_11) = 0 & subset(all_0_16_16, all_0_15_15) = all_0_10_10 & relation_inverse_image(all_0_14_14, all_0_15_15) = all_0_12_12 & relation_inverse_image(all_0_14_14, all_0_16_16) = all_0_13_13 & one_to_one(all_0_8_8) = 0 & relation(all_0_0_0) = 0 & relation(all_0_1_1) = 0 & relation(all_0_3_3) = 0 & relation(all_0_5_5) = 0 & relation(all_0_8_8) = 0 & relation(all_0_9_9) = 0 & relation(all_0_14_14) = 0 & relation(empty_set) = 0 & function(all_0_0_0) = 0 & function(all_0_3_3) = 0 & function(all_0_8_8) = 0 & function(all_0_14_14) = 0 & empty(all_0_1_1) = 0 & empty(all_0_2_2) = 0 & empty(all_0_3_3) = 0 & empty(all_0_5_5) = all_0_4_4 & empty(all_0_7_7) = all_0_6_6 & empty(empty_set) = 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 | ~ (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 | ~ (apply(v3, v2) = v1) | ~ (apply(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_empty_yielding(v2) = v1) | ~ (relation_empty_yielding(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(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] : (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] : (v1 = 0 | ~ (function(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] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation_dom(v0) = v4 & relation(v0) = v2 & function(v0) = v3 & ( ~ (v3 = 0) | ~ (v2 = 0) | ( ! [v5] : ! [v6] : ! [v7] : (v6 = 0 | ~ (in(v7, v4) = 0) | ~ (in(v5, v1) = v6) | ? [v8] : ( ~ (v8 = v5) & apply(v0, v7) = v8)) & ! [v5] : ( ~ (in(v5, v1) = 0) | ? [v6] : (apply(v0, v6) = v5 & in(v6, v4) = 0)) & ? [v5] : (v5 = v1 | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (in(v6, v5) = v7 & ( ~ (v7 = 0) | ! [v11] : ( ~ (in(v11, v4) = 0) | ? [v12] : ( ~ (v12 = v6) & apply(v0, v11) = v12))) & (v7 = 0 | (v10 = v6 & v9 = 0 & apply(v0, v8) = v6 & in(v8, v4) = 0)))))))) & ! [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] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation(v1) = v4 & empty(v1) = v3 & empty(v0) = v2 & ( ~ (v2 = 0) | (v4 = 0 & v3 = 0)))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation(v0) = v3 & empty(v1) = v4 & empty(v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2 = 0))) & ! [v0] : ! [v1] : ( ~ (one_to_one(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation(v0) = v2 & function(v0) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | v1 = 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] : ( ~ (function(v0) = 0) | ? [v1] : ? [v2] : (relation_dom(v0) = v2 & relation(v0) = v1 & ( ~ (v1 = 0) | ( ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (relation_inverse_image(v0, v3) = v4) | ~ (apply(v0, v5) = v6) | ~ (in(v6, v3) = v7) | ? [v8] : ? [v9] : (in(v5, v4) = v8 & in(v5, v2) = v9 & ( ~ (v8 = 0) | (v9 = 0 & v7 = 0)))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (relation_inverse_image(v0, v3) = v4) | ~ (apply(v0, v5) = v6) | ~ (in(v6, v3) = 0) | ? [v7] : ? [v8] : (in(v5, v4) = v8 & in(v5, v2) = v7 & ( ~ (v7 = 0) | v8 = 0))) & ? [v3] : ! [v4] : ! [v5] : (v5 = v3 | ~ (relation_inverse_image(v0, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (apply(v0, v6) = v9 & in(v9, v4) = v10 & in(v6, v3) = v7 & in(v6, v2) = v8 & ( ~ (v10 = 0) | ~ (v8 = 0) | ~ (v7 = 0)) & (v7 = 0 | (v10 = 0 & v8 = 0)))))))) & ? [v0] : ? [v1] : element(v1, v0) = 0 % 11.57/3.37 | % 11.57/3.37 | Applying alpha-rule on (1) yields: % 11.57/3.37 | (2) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) % 11.57/3.37 | (3) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0)) % 11.57/3.37 | (4) ! [v0] : ! [v1] : ( ~ (element(v0, v1) = 0) | ? [v2] : ? [v3] : (empty(v1) = v2 & in(v0, v1) = v3 & (v3 = 0 | v2 = 0))) % 11.57/3.37 | (5) empty(empty_set) = 0 % 11.57/3.37 | (6) empty(all_0_7_7) = all_0_6_6 % 11.57/3.37 | (7) relation(all_0_1_1) = 0 % 11.57/3.37 | (8) relation_inverse_image(all_0_14_14, all_0_15_15) = all_0_12_12 % 11.57/3.37 | (9) relation(all_0_9_9) = 0 % 11.57/3.37 | (10) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0)) % 11.57/3.37 | (11) empty(all_0_1_1) = 0 % 11.57/3.37 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_inverse_image(v3, v2) = v1) | ~ (relation_inverse_image(v3, v2) = v0)) % 11.57/3.37 | (13) ? [v0] : ? [v1] : element(v1, v0) = 0 % 11.57/3.37 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) % 11.57/3.37 | (15) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) % 11.57/3.37 | (16) function(all_0_8_8) = 0 % 11.57/3.37 | (17) subset(all_0_13_13, all_0_12_12) = 0 % 11.57/3.37 | (18) relation(all_0_3_3) = 0 % 11.57/3.37 | (19) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0) % 11.57/3.37 | (20) relation_empty_yielding(empty_set) = 0 % 11.57/3.37 | (21) ! [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)) % 11.57/3.37 | (22) relation(all_0_8_8) = 0 % 11.57/3.37 | (23) relation_rng(all_0_14_14) = all_0_11_11 % 11.57/3.37 | (24) ~ (all_0_6_6 = 0) % 11.57/3.38 | (25) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3)) % 11.57/3.38 | (26) ! [v0] : ! [v1] : (v1 = 0 | ~ (relation(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2)) % 11.57/3.38 | (27) subset(all_0_16_16, all_0_15_15) = all_0_10_10 % 11.57/3.38 | (28) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation(v1) = v4 & empty(v1) = v3 & empty(v0) = v2 & ( ~ (v2 = 0) | (v4 = 0 & v3 = 0)))) % 11.57/3.38 | (29) ~ (all_0_4_4 = 0) % 11.57/3.38 | (30) empty(all_0_2_2) = 0 % 11.57/3.38 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) % 11.57/3.38 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4)) % 11.57/3.38 | (33) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0)) % 11.57/3.38 | (34) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) % 11.57/3.38 | (35) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) % 11.57/3.38 | (36) empty(all_0_3_3) = 0 % 11.57/3.38 | (37) relation_empty_yielding(all_0_9_9) = 0 % 11.57/3.38 | (38) ! [v0] : ! [v1] : (v1 = 0 | ~ (function(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2)) % 11.57/3.38 | (39) empty(all_0_5_5) = all_0_4_4 % 11.57/3.38 | (40) relation(all_0_0_0) = 0 % 11.57/3.38 | (41) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) % 11.57/3.38 | (42) ! [v0] : ! [v1] : ( ~ (one_to_one(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation(v0) = v2 & function(v0) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | v1 = 0))) % 11.57/3.38 | (43) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) % 11.57/3.38 | (44) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)) % 11.57/3.38 | (45) ! [v0] : ( ~ (function(v0) = 0) | ? [v1] : ? [v2] : (relation_dom(v0) = v2 & relation(v0) = v1 & ( ~ (v1 = 0) | ( ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (relation_inverse_image(v0, v3) = v4) | ~ (apply(v0, v5) = v6) | ~ (in(v6, v3) = v7) | ? [v8] : ? [v9] : (in(v5, v4) = v8 & in(v5, v2) = v9 & ( ~ (v8 = 0) | (v9 = 0 & v7 = 0)))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (relation_inverse_image(v0, v3) = v4) | ~ (apply(v0, v5) = v6) | ~ (in(v6, v3) = 0) | ? [v7] : ? [v8] : (in(v5, v4) = v8 & in(v5, v2) = v7 & ( ~ (v7 = 0) | v8 = 0))) & ? [v3] : ! [v4] : ! [v5] : (v5 = v3 | ~ (relation_inverse_image(v0, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (apply(v0, v6) = v9 & in(v9, v4) = v10 & in(v6, v3) = v7 & in(v6, v2) = v8 & ( ~ (v10 = 0) | ~ (v8 = 0) | ~ (v7 = 0)) & (v7 = 0 | (v10 = 0 & v8 = 0)))))))) % 11.57/3.38 | (46) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation(v0) = v3 & empty(v1) = v4 & empty(v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2 = 0))) % 11.57/3.38 | (47) one_to_one(all_0_8_8) = 0 % 11.57/3.38 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 11.57/3.38 | (49) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) % 11.57/3.38 | (50) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | subset(v0, v1) = 0) % 11.57/3.38 | (51) relation(empty_set) = 0 % 11.57/3.38 | (52) relation(all_0_14_14) = 0 % 11.57/3.38 | (53) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0)) % 11.57/3.38 | (54) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) % 11.57/3.38 | (55) subset(all_0_16_16, all_0_11_11) = 0 % 11.57/3.38 | (56) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation_dom(v0) = v4 & relation(v0) = v2 & function(v0) = v3 & ( ~ (v3 = 0) | ~ (v2 = 0) | ( ! [v5] : ! [v6] : ! [v7] : (v6 = 0 | ~ (in(v7, v4) = 0) | ~ (in(v5, v1) = v6) | ? [v8] : ( ~ (v8 = v5) & apply(v0, v7) = v8)) & ! [v5] : ( ~ (in(v5, v1) = 0) | ? [v6] : (apply(v0, v6) = v5 & in(v6, v4) = 0)) & ? [v5] : (v5 = v1 | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (in(v6, v5) = v7 & ( ~ (v7 = 0) | ! [v11] : ( ~ (in(v11, v4) = 0) | ? [v12] : ( ~ (v12 = v6) & apply(v0, v11) = v12))) & (v7 = 0 | (v10 = v6 & v9 = 0 & apply(v0, v8) = v6 & in(v8, v4) = 0)))))))) % 11.57/3.39 | (57) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation(v0) = v3 & empty(v1) = v4 & empty(v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2 = 0))) % 11.57/3.39 | (58) relation_inverse_image(all_0_14_14, all_0_16_16) = all_0_13_13 % 11.57/3.39 | (59) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) = 0 & empty(v2) = 0)) % 11.57/3.39 | (60) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) % 11.57/3.39 | (61) function(all_0_0_0) = 0 % 11.57/3.39 | (62) function(all_0_14_14) = 0 % 11.57/3.39 | (63) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v3 = 0 & ~ (v4 = 0) & element(v2, v1) = 0 & empty(v2) = v4) | (v2 = 0 & empty(v0) = 0))) % 11.57/3.39 | (64) function(all_0_3_3) = 0 % 11.57/3.39 | (65) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) % 11.57/3.39 | (66) ~ (all_0_10_10 = 0) % 11.57/3.39 | (67) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_empty_yielding(v2) = v1) | ~ (relation_empty_yielding(v2) = v0)) % 11.57/3.39 | (68) relation(all_0_5_5) = 0 % 11.57/3.39 | (69) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation(v1) = v4 & empty(v1) = v3 & empty(v0) = v2 & ( ~ (v2 = 0) | (v4 = 0 & v3 = 0)))) % 11.57/3.39 | (70) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) % 11.57/3.39 | % 11.57/3.39 | Instantiating formula (56) with all_0_11_11, all_0_14_14 and discharging atoms relation_rng(all_0_14_14) = all_0_11_11, yields: % 11.68/3.39 | (71) ? [v0] : ? [v1] : ? [v2] : (relation_dom(all_0_14_14) = v2 & relation(all_0_14_14) = v0 & function(all_0_14_14) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | ( ! [v3] : ! [v4] : ! [v5] : (v4 = 0 | ~ (in(v5, v2) = 0) | ~ (in(v3, all_0_11_11) = v4) | ? [v6] : ( ~ (v6 = v3) & apply(all_0_14_14, v5) = v6)) & ! [v3] : ( ~ (in(v3, all_0_11_11) = 0) | ? [v4] : (apply(all_0_14_14, v4) = v3 & in(v4, v2) = 0)) & ? [v3] : (v3 = all_0_11_11 | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (in(v4, v3) = v5 & ( ~ (v5 = 0) | ! [v9] : ( ~ (in(v9, v2) = 0) | ? [v10] : ( ~ (v10 = v4) & apply(all_0_14_14, v9) = v10))) & (v5 = 0 | (v8 = v4 & v7 = 0 & apply(all_0_14_14, v6) = v4 & in(v6, v2) = 0))))))) % 11.68/3.39 | % 11.68/3.39 | Instantiating formula (33) with all_0_10_10, all_0_15_15, all_0_16_16 and discharging atoms subset(all_0_16_16, all_0_15_15) = all_0_10_10, yields: % 11.68/3.39 | (72) all_0_10_10 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_15_15) = v1 & in(v0, all_0_16_16) = 0) % 11.68/3.39 | % 11.68/3.39 | Instantiating formula (45) with all_0_14_14 and discharging atoms function(all_0_14_14) = 0, yields: % 11.68/3.39 | (73) ? [v0] : ? [v1] : (relation_dom(all_0_14_14) = v1 & relation(all_0_14_14) = v0 & ( ~ (v0 = 0) | ( ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (relation_inverse_image(all_0_14_14, v2) = v3) | ~ (apply(all_0_14_14, v4) = v5) | ~ (in(v5, v2) = v6) | ? [v7] : ? [v8] : (in(v4, v3) = v7 & in(v4, v1) = v8 & ( ~ (v7 = 0) | (v8 = 0 & v6 = 0)))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_inverse_image(all_0_14_14, v2) = v3) | ~ (apply(all_0_14_14, v4) = v5) | ~ (in(v5, v2) = 0) | ? [v6] : ? [v7] : (in(v4, v3) = v7 & in(v4, v1) = v6 & ( ~ (v6 = 0) | v7 = 0))) & ? [v2] : ! [v3] : ! [v4] : (v4 = v2 | ~ (relation_inverse_image(all_0_14_14, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (apply(all_0_14_14, v5) = v8 & in(v8, v3) = v9 & in(v5, v2) = v6 & in(v5, v1) = v7 & ( ~ (v9 = 0) | ~ (v7 = 0) | ~ (v6 = 0)) & (v6 = 0 | (v9 = 0 & v7 = 0))))))) % 11.68/3.40 | % 11.68/3.40 | Instantiating (71) with all_32_0_31, all_32_1_32, all_32_2_33 yields: % 11.68/3.40 | (74) relation_dom(all_0_14_14) = all_32_0_31 & relation(all_0_14_14) = all_32_2_33 & function(all_0_14_14) = all_32_1_32 & ( ~ (all_32_1_32 = 0) | ~ (all_32_2_33 = 0) | ( ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (in(v2, all_32_0_31) = 0) | ~ (in(v0, all_0_11_11) = v1) | ? [v3] : ( ~ (v3 = v0) & apply(all_0_14_14, v2) = v3)) & ! [v0] : ( ~ (in(v0, all_0_11_11) = 0) | ? [v1] : (apply(all_0_14_14, v1) = v0 & in(v1, all_32_0_31) = 0)) & ? [v0] : (v0 = all_0_11_11 | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (in(v1, v0) = v2 & ( ~ (v2 = 0) | ! [v6] : ( ~ (in(v6, all_32_0_31) = 0) | ? [v7] : ( ~ (v7 = v1) & apply(all_0_14_14, v6) = v7))) & (v2 = 0 | (v5 = v1 & v4 = 0 & apply(all_0_14_14, v3) = v1 & in(v3, all_32_0_31) = 0)))))) % 11.68/3.40 | % 11.68/3.40 | Applying alpha-rule on (74) yields: % 11.68/3.40 | (75) relation_dom(all_0_14_14) = all_32_0_31 % 11.68/3.40 | (76) relation(all_0_14_14) = all_32_2_33 % 11.68/3.40 | (77) function(all_0_14_14) = all_32_1_32 % 11.68/3.40 | (78) ~ (all_32_1_32 = 0) | ~ (all_32_2_33 = 0) | ( ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (in(v2, all_32_0_31) = 0) | ~ (in(v0, all_0_11_11) = v1) | ? [v3] : ( ~ (v3 = v0) & apply(all_0_14_14, v2) = v3)) & ! [v0] : ( ~ (in(v0, all_0_11_11) = 0) | ? [v1] : (apply(all_0_14_14, v1) = v0 & in(v1, all_32_0_31) = 0)) & ? [v0] : (v0 = all_0_11_11 | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (in(v1, v0) = v2 & ( ~ (v2 = 0) | ! [v6] : ( ~ (in(v6, all_32_0_31) = 0) | ? [v7] : ( ~ (v7 = v1) & apply(all_0_14_14, v6) = v7))) & (v2 = 0 | (v5 = v1 & v4 = 0 & apply(all_0_14_14, v3) = v1 & in(v3, all_32_0_31) = 0))))) % 11.68/3.40 | % 11.68/3.40 | Instantiating (73) with all_34_0_34, all_34_1_35 yields: % 11.68/3.40 | (79) relation_dom(all_0_14_14) = all_34_0_34 & relation(all_0_14_14) = all_34_1_35 & ( ~ (all_34_1_35 = 0) | ( ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_inverse_image(all_0_14_14, v0) = v1) | ~ (apply(all_0_14_14, v2) = v3) | ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v2, v1) = v5 & in(v2, all_34_0_34) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_inverse_image(all_0_14_14, v0) = v1) | ~ (apply(all_0_14_14, v2) = v3) | ~ (in(v3, v0) = 0) | ? [v4] : ? [v5] : (in(v2, v1) = v5 & in(v2, all_34_0_34) = v4 & ( ~ (v4 = 0) | v5 = 0))) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_inverse_image(all_0_14_14, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (apply(all_0_14_14, v3) = v6 & in(v6, v1) = v7 & in(v3, v0) = v4 & in(v3, all_34_0_34) = v5 & ( ~ (v7 = 0) | ~ (v5 = 0) | ~ (v4 = 0)) & (v4 = 0 | (v7 = 0 & v5 = 0)))))) % 11.68/3.40 | % 11.68/3.40 | Applying alpha-rule on (79) yields: % 11.68/3.40 | (80) relation_dom(all_0_14_14) = all_34_0_34 % 11.68/3.40 | (81) relation(all_0_14_14) = all_34_1_35 % 11.68/3.40 | (82) ~ (all_34_1_35 = 0) | ( ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_inverse_image(all_0_14_14, v0) = v1) | ~ (apply(all_0_14_14, v2) = v3) | ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v2, v1) = v5 & in(v2, all_34_0_34) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_inverse_image(all_0_14_14, v0) = v1) | ~ (apply(all_0_14_14, v2) = v3) | ~ (in(v3, v0) = 0) | ? [v4] : ? [v5] : (in(v2, v1) = v5 & in(v2, all_34_0_34) = v4 & ( ~ (v4 = 0) | v5 = 0))) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_inverse_image(all_0_14_14, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (apply(all_0_14_14, v3) = v6 & in(v6, v1) = v7 & in(v3, v0) = v4 & in(v3, all_34_0_34) = v5 & ( ~ (v7 = 0) | ~ (v5 = 0) | ~ (v4 = 0)) & (v4 = 0 | (v7 = 0 & v5 = 0))))) % 11.68/3.40 | % 11.68/3.40 +-Applying beta-rule and splitting (72), into two cases. % 11.68/3.40 |-Branch one: % 11.68/3.40 | (83) all_0_10_10 = 0 % 11.68/3.40 | % 11.68/3.40 | Equations (83) can reduce 66 to: % 11.68/3.40 | (84) $false % 11.68/3.41 | % 11.68/3.41 |-The branch is then unsatisfiable % 11.68/3.41 |-Branch two: % 11.68/3.41 | (66) ~ (all_0_10_10 = 0) % 11.68/3.41 | (86) ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_15_15) = v1 & in(v0, all_0_16_16) = 0) % 11.68/3.41 | % 11.68/3.41 | Instantiating (86) with all_44_0_41, all_44_1_42 yields: % 11.68/3.41 | (87) ~ (all_44_0_41 = 0) & in(all_44_1_42, all_0_15_15) = all_44_0_41 & in(all_44_1_42, all_0_16_16) = 0 % 11.68/3.41 | % 11.68/3.41 | Applying alpha-rule on (87) yields: % 11.68/3.41 | (88) ~ (all_44_0_41 = 0) % 11.68/3.41 | (89) in(all_44_1_42, all_0_15_15) = all_44_0_41 % 11.68/3.41 | (90) in(all_44_1_42, all_0_16_16) = 0 % 11.68/3.41 | % 11.68/3.41 | Instantiating formula (41) with all_0_14_14, all_32_0_31, all_34_0_34 and discharging atoms relation_dom(all_0_14_14) = all_34_0_34, relation_dom(all_0_14_14) = all_32_0_31, yields: % 11.68/3.41 | (91) all_34_0_34 = all_32_0_31 % 11.68/3.41 | % 11.68/3.41 | Instantiating formula (2) with all_0_14_14, all_34_1_35, 0 and discharging atoms relation(all_0_14_14) = all_34_1_35, relation(all_0_14_14) = 0, yields: % 11.68/3.41 | (92) all_34_1_35 = 0 % 11.68/3.41 | % 11.68/3.41 | Instantiating formula (2) with all_0_14_14, all_32_2_33, all_34_1_35 and discharging atoms relation(all_0_14_14) = all_34_1_35, relation(all_0_14_14) = all_32_2_33, yields: % 11.68/3.41 | (93) all_34_1_35 = all_32_2_33 % 11.68/3.41 | % 11.68/3.41 | Instantiating formula (3) with all_0_14_14, all_32_1_32, 0 and discharging atoms function(all_0_14_14) = all_32_1_32, function(all_0_14_14) = 0, yields: % 11.68/3.41 | (94) all_32_1_32 = 0 % 11.68/3.41 | % 11.68/3.41 | Combining equations (93,92) yields a new equation: % 11.68/3.41 | (95) all_32_2_33 = 0 % 11.68/3.41 | % 11.68/3.41 | Simplifying 95 yields: % 11.68/3.41 | (96) all_32_2_33 = 0 % 11.68/3.41 | % 11.68/3.41 +-Applying beta-rule and splitting (82), into two cases. % 11.68/3.41 |-Branch one: % 11.68/3.41 | (97) ~ (all_34_1_35 = 0) % 11.68/3.41 | % 11.68/3.41 | Equations (92) can reduce 97 to: % 11.68/3.41 | (84) $false % 11.68/3.41 | % 11.68/3.41 |-The branch is then unsatisfiable % 11.68/3.41 |-Branch two: % 11.68/3.41 | (92) all_34_1_35 = 0 % 11.68/3.41 | (100) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_inverse_image(all_0_14_14, v0) = v1) | ~ (apply(all_0_14_14, v2) = v3) | ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v2, v1) = v5 & in(v2, all_34_0_34) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_inverse_image(all_0_14_14, v0) = v1) | ~ (apply(all_0_14_14, v2) = v3) | ~ (in(v3, v0) = 0) | ? [v4] : ? [v5] : (in(v2, v1) = v5 & in(v2, all_34_0_34) = v4 & ( ~ (v4 = 0) | v5 = 0))) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_inverse_image(all_0_14_14, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (apply(all_0_14_14, v3) = v6 & in(v6, v1) = v7 & in(v3, v0) = v4 & in(v3, all_34_0_34) = v5 & ( ~ (v7 = 0) | ~ (v5 = 0) | ~ (v4 = 0)) & (v4 = 0 | (v7 = 0 & v5 = 0)))) % 11.68/3.41 | % 11.68/3.41 | Applying alpha-rule on (100) yields: % 11.68/3.41 | (101) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_inverse_image(all_0_14_14, v0) = v1) | ~ (apply(all_0_14_14, v2) = v3) | ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v2, v1) = v5 & in(v2, all_34_0_34) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = 0)))) % 11.68/3.41 | (102) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_inverse_image(all_0_14_14, v0) = v1) | ~ (apply(all_0_14_14, v2) = v3) | ~ (in(v3, v0) = 0) | ? [v4] : ? [v5] : (in(v2, v1) = v5 & in(v2, all_34_0_34) = v4 & ( ~ (v4 = 0) | v5 = 0))) % 11.68/3.41 | (103) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_inverse_image(all_0_14_14, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (apply(all_0_14_14, v3) = v6 & in(v6, v1) = v7 & in(v3, v0) = v4 & in(v3, all_34_0_34) = v5 & ( ~ (v7 = 0) | ~ (v5 = 0) | ~ (v4 = 0)) & (v4 = 0 | (v7 = 0 & v5 = 0)))) % 11.68/3.41 | % 11.68/3.41 +-Applying beta-rule and splitting (78), into two cases. % 11.68/3.41 |-Branch one: % 11.68/3.41 | (104) ~ (all_32_1_32 = 0) % 11.68/3.41 | % 11.68/3.41 | Equations (94) can reduce 104 to: % 11.68/3.41 | (84) $false % 11.68/3.41 | % 11.68/3.41 |-The branch is then unsatisfiable % 11.68/3.41 |-Branch two: % 11.68/3.41 | (94) all_32_1_32 = 0 % 11.68/3.41 | (107) ~ (all_32_2_33 = 0) | ( ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (in(v2, all_32_0_31) = 0) | ~ (in(v0, all_0_11_11) = v1) | ? [v3] : ( ~ (v3 = v0) & apply(all_0_14_14, v2) = v3)) & ! [v0] : ( ~ (in(v0, all_0_11_11) = 0) | ? [v1] : (apply(all_0_14_14, v1) = v0 & in(v1, all_32_0_31) = 0)) & ? [v0] : (v0 = all_0_11_11 | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (in(v1, v0) = v2 & ( ~ (v2 = 0) | ! [v6] : ( ~ (in(v6, all_32_0_31) = 0) | ? [v7] : ( ~ (v7 = v1) & apply(all_0_14_14, v6) = v7))) & (v2 = 0 | (v5 = v1 & v4 = 0 & apply(all_0_14_14, v3) = v1 & in(v3, all_32_0_31) = 0))))) % 11.68/3.41 | % 11.68/3.41 +-Applying beta-rule and splitting (107), into two cases. % 11.68/3.41 |-Branch one: % 11.68/3.41 | (108) ~ (all_32_2_33 = 0) % 11.68/3.42 | % 11.68/3.42 | Equations (96) can reduce 108 to: % 11.68/3.42 | (84) $false % 11.68/3.42 | % 11.68/3.42 |-The branch is then unsatisfiable % 11.68/3.42 |-Branch two: % 11.68/3.42 | (96) all_32_2_33 = 0 % 11.68/3.42 | (111) ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (in(v2, all_32_0_31) = 0) | ~ (in(v0, all_0_11_11) = v1) | ? [v3] : ( ~ (v3 = v0) & apply(all_0_14_14, v2) = v3)) & ! [v0] : ( ~ (in(v0, all_0_11_11) = 0) | ? [v1] : (apply(all_0_14_14, v1) = v0 & in(v1, all_32_0_31) = 0)) & ? [v0] : (v0 = all_0_11_11 | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (in(v1, v0) = v2 & ( ~ (v2 = 0) | ! [v6] : ( ~ (in(v6, all_32_0_31) = 0) | ? [v7] : ( ~ (v7 = v1) & apply(all_0_14_14, v6) = v7))) & (v2 = 0 | (v5 = v1 & v4 = 0 & apply(all_0_14_14, v3) = v1 & in(v3, all_32_0_31) = 0)))) % 11.68/3.42 | % 11.68/3.42 | Applying alpha-rule on (111) yields: % 11.68/3.42 | (112) ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (in(v2, all_32_0_31) = 0) | ~ (in(v0, all_0_11_11) = v1) | ? [v3] : ( ~ (v3 = v0) & apply(all_0_14_14, v2) = v3)) % 11.68/3.42 | (113) ! [v0] : ( ~ (in(v0, all_0_11_11) = 0) | ? [v1] : (apply(all_0_14_14, v1) = v0 & in(v1, all_32_0_31) = 0)) % 11.68/3.42 | (114) ? [v0] : (v0 = all_0_11_11 | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (in(v1, v0) = v2 & ( ~ (v2 = 0) | ! [v6] : ( ~ (in(v6, all_32_0_31) = 0) | ? [v7] : ( ~ (v7 = v1) & apply(all_0_14_14, v6) = v7))) & (v2 = 0 | (v5 = v1 & v4 = 0 & apply(all_0_14_14, v3) = v1 & in(v3, all_32_0_31) = 0)))) % 11.81/3.42 | % 11.81/3.42 | Instantiating formula (19) with all_44_1_42, all_0_11_11, all_0_16_16 and discharging atoms subset(all_0_16_16, all_0_11_11) = 0, in(all_44_1_42, all_0_16_16) = 0, yields: % 11.81/3.42 | (115) in(all_44_1_42, all_0_11_11) = 0 % 11.81/3.42 | % 11.81/3.42 | Instantiating formula (113) with all_44_1_42 yields: % 11.81/3.42 | (116) ~ (in(all_44_1_42, all_0_11_11) = 0) | ? [v0] : (apply(all_0_14_14, v0) = all_44_1_42 & in(v0, all_32_0_31) = 0) % 11.81/3.42 | % 11.81/3.42 +-Applying beta-rule and splitting (116), into two cases. % 11.81/3.42 |-Branch one: % 11.81/3.42 | (117) ~ (in(all_44_1_42, all_0_11_11) = 0) % 11.81/3.42 | % 11.81/3.42 | Using (115) and (117) yields: % 11.81/3.42 | (118) $false % 11.81/3.42 | % 11.81/3.42 |-The branch is then unsatisfiable % 11.81/3.42 |-Branch two: % 11.81/3.42 | (115) in(all_44_1_42, all_0_11_11) = 0 % 11.81/3.42 | (120) ? [v0] : (apply(all_0_14_14, v0) = all_44_1_42 & in(v0, all_32_0_31) = 0) % 11.81/3.42 | % 11.81/3.42 | Instantiating (120) with all_117_0_78 yields: % 11.81/3.42 | (121) apply(all_0_14_14, all_117_0_78) = all_44_1_42 & in(all_117_0_78, all_32_0_31) = 0 % 11.81/3.42 | % 11.81/3.42 | Applying alpha-rule on (121) yields: % 11.81/3.42 | (122) apply(all_0_14_14, all_117_0_78) = all_44_1_42 % 11.81/3.42 | (123) in(all_117_0_78, all_32_0_31) = 0 % 11.81/3.42 | % 11.81/3.42 | Instantiating formula (101) with all_44_0_41, all_44_1_42, all_117_0_78, all_0_12_12, all_0_15_15 and discharging atoms relation_inverse_image(all_0_14_14, all_0_15_15) = all_0_12_12, apply(all_0_14_14, all_117_0_78) = all_44_1_42, in(all_44_1_42, all_0_15_15) = all_44_0_41, yields: % 11.81/3.42 | (124) ? [v0] : ? [v1] : (in(all_117_0_78, all_34_0_34) = v1 & in(all_117_0_78, all_0_12_12) = v0 & ( ~ (v0 = 0) | (v1 = 0 & all_44_0_41 = 0))) % 11.81/3.42 | % 11.81/3.42 | Instantiating formula (102) with all_44_1_42, all_117_0_78, all_0_13_13, all_0_16_16 and discharging atoms relation_inverse_image(all_0_14_14, all_0_16_16) = all_0_13_13, apply(all_0_14_14, all_117_0_78) = all_44_1_42, in(all_44_1_42, all_0_16_16) = 0, yields: % 11.81/3.42 | (125) ? [v0] : ? [v1] : (in(all_117_0_78, all_34_0_34) = v0 & in(all_117_0_78, all_0_13_13) = v1 & ( ~ (v0 = 0) | v1 = 0)) % 11.81/3.42 | % 11.81/3.42 | Instantiating formula (101) with 0, all_44_1_42, all_117_0_78, all_0_13_13, all_0_16_16 and discharging atoms relation_inverse_image(all_0_14_14, all_0_16_16) = all_0_13_13, apply(all_0_14_14, all_117_0_78) = all_44_1_42, in(all_44_1_42, all_0_16_16) = 0, yields: % 11.81/3.42 | (126) ? [v0] : ? [v1] : (in(all_117_0_78, all_34_0_34) = v1 & in(all_117_0_78, all_0_13_13) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 11.81/3.42 | % 11.81/3.42 | Instantiating formula (19) with all_117_0_78, all_0_12_12, all_0_13_13 and discharging atoms subset(all_0_13_13, all_0_12_12) = 0, yields: % 11.81/3.42 | (127) ~ (in(all_117_0_78, all_0_13_13) = 0) | in(all_117_0_78, all_0_12_12) = 0 % 11.81/3.42 | % 11.81/3.42 | Instantiating (126) with all_146_0_82, all_146_1_83 yields: % 11.81/3.42 | (128) in(all_117_0_78, all_34_0_34) = all_146_0_82 & in(all_117_0_78, all_0_13_13) = all_146_1_83 & ( ~ (all_146_1_83 = 0) | all_146_0_82 = 0) % 11.81/3.42 | % 11.81/3.42 | Applying alpha-rule on (128) yields: % 11.81/3.42 | (129) in(all_117_0_78, all_34_0_34) = all_146_0_82 % 11.81/3.42 | (130) in(all_117_0_78, all_0_13_13) = all_146_1_83 % 11.81/3.42 | (131) ~ (all_146_1_83 = 0) | all_146_0_82 = 0 % 11.81/3.42 | % 11.81/3.42 | Instantiating (125) with all_150_0_85, all_150_1_86 yields: % 11.81/3.42 | (132) in(all_117_0_78, all_34_0_34) = all_150_1_86 & in(all_117_0_78, all_0_13_13) = all_150_0_85 & ( ~ (all_150_1_86 = 0) | all_150_0_85 = 0) % 11.81/3.42 | % 11.81/3.42 | Applying alpha-rule on (132) yields: % 11.81/3.43 | (133) in(all_117_0_78, all_34_0_34) = all_150_1_86 % 11.81/3.43 | (134) in(all_117_0_78, all_0_13_13) = all_150_0_85 % 11.81/3.43 | (135) ~ (all_150_1_86 = 0) | all_150_0_85 = 0 % 11.81/3.43 | % 11.81/3.43 | Instantiating (124) with all_152_0_87, all_152_1_88 yields: % 11.81/3.43 | (136) in(all_117_0_78, all_34_0_34) = all_152_0_87 & in(all_117_0_78, all_0_12_12) = all_152_1_88 & ( ~ (all_152_1_88 = 0) | (all_152_0_87 = 0 & all_44_0_41 = 0)) % 11.81/3.43 | % 11.81/3.43 | Applying alpha-rule on (136) yields: % 11.81/3.43 | (137) in(all_117_0_78, all_34_0_34) = all_152_0_87 % 11.81/3.43 | (138) in(all_117_0_78, all_0_12_12) = all_152_1_88 % 11.81/3.43 | (139) ~ (all_152_1_88 = 0) | (all_152_0_87 = 0 & all_44_0_41 = 0) % 11.81/3.43 | % 11.81/3.43 | From (91) and (137) follows: % 11.81/3.43 | (140) in(all_117_0_78, all_32_0_31) = all_152_0_87 % 11.81/3.43 | % 11.81/3.43 | From (91) and (133) follows: % 11.81/3.43 | (141) in(all_117_0_78, all_32_0_31) = all_150_1_86 % 11.81/3.43 | % 11.81/3.43 | From (91) and (129) follows: % 11.81/3.43 | (142) in(all_117_0_78, all_32_0_31) = all_146_0_82 % 11.81/3.43 | % 11.81/3.43 +-Applying beta-rule and splitting (139), into two cases. % 11.81/3.43 |-Branch one: % 11.81/3.43 | (143) ~ (all_152_1_88 = 0) % 11.81/3.43 | % 11.81/3.43 +-Applying beta-rule and splitting (127), into two cases. % 11.81/3.43 |-Branch one: % 11.81/3.43 | (144) ~ (in(all_117_0_78, all_0_13_13) = 0) % 11.81/3.43 | % 11.81/3.43 | Instantiating formula (48) with all_117_0_78, all_32_0_31, all_152_0_87, 0 and discharging atoms in(all_117_0_78, all_32_0_31) = all_152_0_87, in(all_117_0_78, all_32_0_31) = 0, yields: % 11.81/3.43 | (145) all_152_0_87 = 0 % 11.81/3.43 | % 11.81/3.43 | Instantiating formula (48) with all_117_0_78, all_32_0_31, all_150_1_86, all_152_0_87 and discharging atoms in(all_117_0_78, all_32_0_31) = all_152_0_87, in(all_117_0_78, all_32_0_31) = all_150_1_86, yields: % 11.81/3.43 | (146) all_152_0_87 = all_150_1_86 % 11.81/3.43 | % 11.81/3.43 | Instantiating formula (48) with all_117_0_78, all_32_0_31, all_146_0_82, all_152_0_87 and discharging atoms in(all_117_0_78, all_32_0_31) = all_152_0_87, in(all_117_0_78, all_32_0_31) = all_146_0_82, yields: % 11.81/3.43 | (147) all_152_0_87 = all_146_0_82 % 11.81/3.43 | % 11.81/3.43 | Instantiating formula (48) with all_117_0_78, all_0_13_13, all_146_1_83, all_150_0_85 and discharging atoms in(all_117_0_78, all_0_13_13) = all_150_0_85, in(all_117_0_78, all_0_13_13) = all_146_1_83, yields: % 11.81/3.43 | (148) all_150_0_85 = all_146_1_83 % 11.81/3.43 | % 11.81/3.43 | Using (134) and (144) yields: % 11.81/3.43 | (149) ~ (all_150_0_85 = 0) % 11.81/3.43 | % 11.81/3.43 | Combining equations (145,146) yields a new equation: % 11.81/3.43 | (150) all_150_1_86 = 0 % 11.81/3.43 | % 11.81/3.43 | Combining equations (147,146) yields a new equation: % 11.81/3.43 | (151) all_150_1_86 = all_146_0_82 % 11.81/3.43 | % 11.81/3.43 | Combining equations (150,151) yields a new equation: % 11.81/3.43 | (152) all_146_0_82 = 0 % 11.81/3.43 | % 11.81/3.43 | Combining equations (152,151) yields a new equation: % 11.81/3.43 | (150) all_150_1_86 = 0 % 11.81/3.43 | % 11.81/3.43 | Equations (148) can reduce 149 to: % 11.81/3.43 | (154) ~ (all_146_1_83 = 0) % 11.81/3.43 | % 11.81/3.43 +-Applying beta-rule and splitting (135), into two cases. % 11.81/3.43 |-Branch one: % 11.81/3.43 | (155) ~ (all_150_1_86 = 0) % 11.81/3.43 | % 11.81/3.43 | Equations (150) can reduce 155 to: % 11.81/3.43 | (84) $false % 11.81/3.43 | % 11.81/3.43 |-The branch is then unsatisfiable % 11.81/3.43 |-Branch two: % 11.81/3.43 | (150) all_150_1_86 = 0 % 11.81/3.43 | (158) all_150_0_85 = 0 % 11.81/3.43 | % 11.81/3.43 | Combining equations (158,148) yields a new equation: % 11.81/3.43 | (159) all_146_1_83 = 0 % 11.81/3.43 | % 11.81/3.43 | Equations (159) can reduce 154 to: % 11.81/3.43 | (84) $false % 11.81/3.43 | % 11.81/3.43 |-The branch is then unsatisfiable % 11.81/3.43 |-Branch two: % 11.81/3.43 | (161) in(all_117_0_78, all_0_13_13) = 0 % 11.81/3.43 | (162) in(all_117_0_78, all_0_12_12) = 0 % 11.81/3.43 | % 11.81/3.43 | Instantiating formula (48) with all_117_0_78, all_0_12_12, all_152_1_88, 0 and discharging atoms in(all_117_0_78, all_0_12_12) = all_152_1_88, in(all_117_0_78, all_0_12_12) = 0, yields: % 11.81/3.43 | (163) all_152_1_88 = 0 % 11.81/3.43 | % 11.81/3.43 | Equations (163) can reduce 143 to: % 11.81/3.43 | (84) $false % 11.81/3.43 | % 11.81/3.43 |-The branch is then unsatisfiable % 11.81/3.43 |-Branch two: % 11.81/3.43 | (163) all_152_1_88 = 0 % 11.81/3.43 | (166) all_152_0_87 = 0 & all_44_0_41 = 0 % 11.81/3.43 | % 11.81/3.43 | Applying alpha-rule on (166) yields: % 11.81/3.43 | (145) all_152_0_87 = 0 % 11.81/3.43 | (168) all_44_0_41 = 0 % 11.81/3.43 | % 11.81/3.43 | Equations (168) can reduce 88 to: % 11.81/3.43 | (84) $false % 11.81/3.43 | % 11.81/3.43 |-The branch is then unsatisfiable % 11.81/3.43 % SZS output end Proof for theBenchmark % 11.81/3.43 % 11.81/3.43 2832ms %------------------------------------------------------------------------------