TSTP Solution File: SEU030+1 by ePrincess---1.0
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- Process Solution
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% File : ePrincess---1.0
% Problem : SEU030+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n003.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 08:46:16 EDT 2022
% Result : Theorem 3.83s 1.60s
% Output : Proof 6.12s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU030+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.33 % Computer : n003.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sat Jun 18 23:28:28 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.67/0.63 ____ _
% 0.67/0.63 ___ / __ \_____(_)___ ________ __________
% 0.67/0.63 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.67/0.63 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.67/0.63 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.67/0.63
% 0.67/0.63 A Theorem Prover for First-Order Logic
% 0.67/0.63 (ePrincess v.1.0)
% 0.67/0.63
% 0.67/0.63 (c) Philipp Rümmer, 2009-2015
% 0.67/0.63 (c) Peter Backeman, 2014-2015
% 0.67/0.63 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.67/0.63 Free software under GNU Lesser General Public License (LGPL).
% 0.67/0.63 Bug reports to peter@backeman.se
% 0.67/0.63
% 0.67/0.63 For more information, visit http://user.uu.se/~petba168/breu/
% 0.67/0.63
% 0.67/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.81/0.69 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.70/1.05 Prover 0: Preprocessing ...
% 2.83/1.36 Prover 0: Warning: ignoring some quantifiers
% 2.93/1.38 Prover 0: Constructing countermodel ...
% 3.83/1.60 Prover 0: proved (905ms)
% 3.83/1.60
% 3.83/1.60 No countermodel exists, formula is valid
% 3.83/1.60 % SZS status Theorem for theBenchmark
% 3.83/1.60
% 3.83/1.60 Generating proof ... Warning: ignoring some quantifiers
% 5.60/1.96 found it (size 65)
% 5.60/1.96
% 5.60/1.96 % SZS output start Proof for theBenchmark
% 5.60/1.96 Assumed formulas after preprocessing and simplification:
% 5.60/1.96 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ( ~ (v5 = v4) & relation_rng(v0) = v1 & relation_dom(v5) = v1 & relation_dom(v0) = v2 & identity_relation(v2) = v3 & relation_composition(v0, v5) = v3 & function_inverse(v0) = v4 & relation_empty_yielding(v6) & relation_empty_yielding(empty_set) & one_to_one(v7) & one_to_one(v0) & relation(v13) & relation(v12) & relation(v10) & relation(v9) & relation(v7) & relation(v6) & relation(v5) & relation(v0) & relation(empty_set) & function(v13) & function(v10) & function(v7) & function(v5) & function(v0) & empty(v12) & empty(v11) & empty(v10) & empty(empty_set) & ~ empty(v9) & ~ empty(v8) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v19 = v15 | ~ (relation_rng(v15) = v14) | ~ (relation_dom(v19) = v20) | ~ (identity_relation(v14) = v16) | ~ (relation_composition(v15, v17) = v18) | ~ relation(v19) | ~ relation(v17) | ~ relation(v15) | ~ function(v19) | ~ function(v17) | ~ function(v15) | ? [v21] : ? [v22] : (identity_relation(v20) = v21 & relation_composition(v17, v19) = v22 & ( ~ (v22 = v16) | ~ (v21 = v18)))) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v19 = v15 | ~ (relation_rng(v15) = v14) | ~ (identity_relation(v14) = v16) | ~ (relation_composition(v17, v19) = v16) | ~ (relation_composition(v15, v17) = v18) | ~ relation(v19) | ~ relation(v17) | ~ relation(v15) | ~ function(v19) | ~ function(v17) | ~ function(v15) | ? [v20] : ? [v21] : ( ~ (v21 = v18) & relation_dom(v19) = v20 & identity_relation(v20) = v21)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v15 = v14 | ~ (relation_composition(v17, v16) = v15) | ~ (relation_composition(v17, v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (powerset(v16) = v17) | ~ element(v15, v17) | ~ empty(v16) | ~ in(v14, v15)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (powerset(v16) = v17) | ~ element(v15, v17) | ~ in(v14, v15) | element(v14, v16)) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (relation_rng(v16) = v15) | ~ (relation_rng(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (relation_dom(v16) = v15) | ~ (relation_dom(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (powerset(v16) = v15) | ~ (powerset(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (identity_relation(v16) = v15) | ~ (identity_relation(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (function_inverse(v16) = v15) | ~ (function_inverse(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : ( ~ (powerset(v15) = v16) | ~ subset(v14, v15) | element(v14, v16)) & ! [v14] : ! [v15] : ! [v16] : ( ~ (powerset(v15) = v16) | ~ element(v14, v16) | subset(v14, v15)) & ! [v14] : ! [v15] : ! [v16] : ( ~ (relation_composition(v15, v14) = v16) | ~ (function_inverse(v14) = v15) | ~ one_to_one(v14) | ~ relation(v14) | ~ function(v14) | ? [v17] : ? [v18] : ? [v19] : (relation_rng(v14) = v19 & relation_dom(v14) = v18 & identity_relation(v19) = v16 & identity_relation(v18) = v17 & relation_composition(v14, v15) = v17)) & ! [v14] : ! [v15] : ! [v16] : ( ~ (relation_composition(v15, v14) = v16) | ~ relation(v15) | ~ empty(v14) | relation(v16)) & ! [v14] : ! [v15] : ! [v16] : ( ~ (relation_composition(v15, v14) = v16) | ~ relation(v15) | ~ empty(v14) | empty(v16)) & ! [v14] : ! [v15] : ! [v16] : ( ~ (relation_composition(v14, v15) = v16) | ~ (function_inverse(v14) = v15) | ~ one_to_one(v14) | ~ relation(v14) | ~ function(v14) | ? [v17] : ? [v18] : ? [v19] : (relation_rng(v14) = v19 & relation_dom(v14) = v17 & identity_relation(v19) = v18 & identity_relation(v17) = v16 & relation_composition(v15, v14) = v18)) & ! [v14] : ! [v15] : ! [v16] : ( ~ (relation_composition(v14, v15) = v16) | ~ relation(v15) | ~ relation(v14) | ~ function(v15) | ~ function(v14) | relation(v16)) & ! [v14] : ! [v15] : ! [v16] : ( ~ (relation_composition(v14, v15) = v16) | ~ relation(v15) | ~ relation(v14) | ~ function(v15) | ~ function(v14) | function(v16)) & ! [v14] : ! [v15] : ! [v16] : ( ~ (relation_composition(v14, v15) = v16) | ~ relation(v15) | ~ relation(v14) | relation(v16)) & ! [v14] : ! [v15] : ! [v16] : ( ~ (relation_composition(v14, v15) = v16) | ~ relation(v15) | ~ empty(v14) | relation(v16)) & ! [v14] : ! [v15] : ! [v16] : ( ~ (relation_composition(v14, v15) = v16) | ~ relation(v15) | ~ empty(v14) | empty(v16)) & ! [v14] : ! [v15] : (v15 = v14 | ~ empty(v15) | ~ empty(v14)) & ! [v14] : ! [v15] : ( ~ (relation_rng(v14) = v15) | ~ one_to_one(v14) | ~ relation(v14) | ~ function(v14) | ? [v16] : ? [v17] : ? [v18] : ? [v19] : (relation_dom(v14) = v18 & identity_relation(v18) = v17 & identity_relation(v15) = v19 & relation_composition(v16, v14) = v19 & relation_composition(v14, v16) = v17 & function_inverse(v14) = v16)) & ! [v14] : ! [v15] : ( ~ (relation_rng(v14) = v15) | ~ one_to_one(v14) | ~ relation(v14) | ~ function(v14) | ? [v16] : ? [v17] : (relation_rng(v16) = v17 & relation_dom(v16) = v15 & relation_dom(v14) = v17 & function_inverse(v14) = v16)) & ! [v14] : ! [v15] : ( ~ (relation_rng(v14) = v15) | ~ relation(v14) | ~ empty(v15) | empty(v14)) & ! [v14] : ! [v15] : ( ~ (relation_rng(v14) = v15) | ~ empty(v14) | relation(v15)) & ! [v14] : ! [v15] : ( ~ (relation_rng(v14) = v15) | ~ empty(v14) | empty(v15)) & ! [v14] : ! [v15] : ( ~ (relation_dom(v14) = v15) | ~ one_to_one(v14) | ~ relation(v14) | ~ function(v14) | ? [v16] : ? [v17] : ? [v18] : ? [v19] : (relation_rng(v14) = v19 & identity_relation(v19) = v18 & identity_relation(v15) = v17 & relation_composition(v16, v14) = v18 & relation_composition(v14, v16) = v17 & function_inverse(v14) = v16)) & ! [v14] : ! [v15] : ( ~ (relation_dom(v14) = v15) | ~ one_to_one(v14) | ~ relation(v14) | ~ function(v14) | ? [v16] : ? [v17] : (relation_rng(v17) = v15 & relation_rng(v14) = v16 & relation_dom(v17) = v16 & function_inverse(v14) = v17)) & ! [v14] : ! [v15] : ( ~ (relation_dom(v14) = v15) | ~ relation(v14) | ~ empty(v15) | empty(v14)) & ! [v14] : ! [v15] : ( ~ (relation_dom(v14) = v15) | ~ empty(v14) | relation(v15)) & ! [v14] : ! [v15] : ( ~ (relation_dom(v14) = v15) | ~ empty(v14) | empty(v15)) & ! [v14] : ! [v15] : ( ~ (powerset(v14) = v15) | ~ empty(v15)) & ! [v14] : ! [v15] : ( ~ (powerset(v14) = v15) | empty(v14) | ? [v16] : (element(v16, v15) & ~ empty(v16))) & ! [v14] : ! [v15] : ( ~ (powerset(v14) = v15) | ? [v16] : (element(v16, v15) & empty(v16))) & ! [v14] : ! [v15] : ( ~ (identity_relation(v14) = v15) | relation(v15)) & ! [v14] : ! [v15] : ( ~ (identity_relation(v14) = v15) | function(v15)) & ! [v14] : ! [v15] : ( ~ (function_inverse(v14) = v15) | ~ one_to_one(v14) | ~ relation(v14) | ~ function(v14) | ? [v16] : ? [v17] : (relation_rng(v15) = v17 & relation_rng(v14) = v16 & relation_dom(v15) = v16 & relation_dom(v14) = v17)) & ! [v14] : ! [v15] : ( ~ (function_inverse(v14) = v15) | ~ relation(v14) | ~ function(v14) | relation(v15)) & ! [v14] : ! [v15] : ( ~ (function_inverse(v14) = v15) | ~ relation(v14) | ~ function(v14) | function(v15)) & ! [v14] : ! [v15] : ( ~ element(v14, v15) | empty(v15) | in(v14, v15)) & ! [v14] : ! [v15] : ( ~ empty(v15) | ~ in(v14, v15)) & ! [v14] : ! [v15] : ( ~ in(v15, v14) | ~ in(v14, v15)) & ! [v14] : ! [v15] : ( ~ in(v14, v15) | element(v14, v15)) & ! [v14] : (v14 = empty_set | ~ empty(v14)) & ! [v14] : ( ~ relation(v14) | ~ function(v14) | ~ empty(v14) | one_to_one(v14)) & ! [v14] : ( ~ empty(v14) | relation(v14)) & ! [v14] : ( ~ empty(v14) | function(v14)) & ? [v14] : ? [v15] : element(v15, v14) & ? [v14] : subset(v14, v14))
% 5.79/2.00 | 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 yields:
% 5.79/2.00 | (1) ~ (all_0_8_8 = all_0_9_9) & relation_rng(all_0_13_13) = all_0_12_12 & relation_dom(all_0_8_8) = all_0_12_12 & relation_dom(all_0_13_13) = all_0_11_11 & identity_relation(all_0_11_11) = all_0_10_10 & relation_composition(all_0_13_13, all_0_8_8) = all_0_10_10 & function_inverse(all_0_13_13) = all_0_9_9 & relation_empty_yielding(all_0_7_7) & relation_empty_yielding(empty_set) & one_to_one(all_0_6_6) & one_to_one(all_0_13_13) & relation(all_0_0_0) & relation(all_0_1_1) & relation(all_0_3_3) & relation(all_0_4_4) & relation(all_0_6_6) & relation(all_0_7_7) & relation(all_0_8_8) & relation(all_0_13_13) & relation(empty_set) & function(all_0_0_0) & function(all_0_3_3) & function(all_0_6_6) & function(all_0_8_8) & function(all_0_13_13) & empty(all_0_1_1) & empty(all_0_2_2) & empty(all_0_3_3) & empty(empty_set) & ~ empty(all_0_4_4) & ~ empty(all_0_5_5) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v5 = v1 | ~ (relation_rng(v1) = v0) | ~ (relation_dom(v5) = v6) | ~ (identity_relation(v0) = v2) | ~ (relation_composition(v1, v3) = v4) | ~ relation(v5) | ~ relation(v3) | ~ relation(v1) | ~ function(v5) | ~ function(v3) | ~ function(v1) | ? [v7] : ? [v8] : (identity_relation(v6) = v7 & relation_composition(v3, v5) = v8 & ( ~ (v8 = v2) | ~ (v7 = v4)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v1 | ~ (relation_rng(v1) = v0) | ~ (identity_relation(v0) = v2) | ~ (relation_composition(v3, v5) = v2) | ~ (relation_composition(v1, v3) = v4) | ~ relation(v5) | ~ relation(v3) | ~ relation(v1) | ~ function(v5) | ~ function(v3) | ~ function(v1) | ? [v6] : ? [v7] : ( ~ (v7 = v4) & relation_dom(v5) = v6 & identity_relation(v6) = v7)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_composition(v3, v2) = v1) | ~ (relation_composition(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ empty(v2) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ in(v0, v1) | element(v0, v2)) & ! [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 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (identity_relation(v2) = v1) | ~ (identity_relation(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function_inverse(v2) = v1) | ~ (function_inverse(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ element(v0, v2) | subset(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v1, v0) = v2) | ~ (function_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v3] : ? [v4] : ? [v5] : (relation_rng(v0) = v5 & relation_dom(v0) = v4 & identity_relation(v5) = v2 & identity_relation(v4) = v3 & relation_composition(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v1, v0) = v2) | ~ relation(v1) | ~ empty(v0) | relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v1, v0) = v2) | ~ relation(v1) | ~ empty(v0) | empty(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ (function_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v3] : ? [v4] : ? [v5] : (relation_rng(v0) = v5 & relation_dom(v0) = v3 & identity_relation(v5) = v4 & identity_relation(v3) = v2 & relation_composition(v1, v0) = v4)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v1) | ~ function(v0) | relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v1) | ~ function(v0) | function(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ empty(v0) | relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ empty(v0) | empty(v2)) & ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_dom(v0) = v4 & identity_relation(v4) = v3 & identity_relation(v1) = v5 & relation_composition(v2, v0) = v5 & relation_composition(v0, v2) = v3 & function_inverse(v0) = v2)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : (relation_rng(v2) = v3 & relation_dom(v2) = v1 & relation_dom(v0) = v3 & function_inverse(v0) = v2)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | relation(v1)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | empty(v1)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_rng(v0) = v5 & identity_relation(v5) = v4 & identity_relation(v1) = v3 & relation_composition(v2, v0) = v4 & relation_composition(v0, v2) = v3 & function_inverse(v0) = v2)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : (relation_rng(v3) = v1 & relation_rng(v0) = v2 & relation_dom(v3) = v2 & function_inverse(v0) = v3)) & ! [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] : ( ~ (powerset(v0) = v1) | ~ empty(v1)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (element(v2, v1) & ~ empty(v2))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) & empty(v2))) & ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation(v1)) & ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | function(v1)) & ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : (relation_rng(v1) = v3 & relation_rng(v0) = v2 & relation_dom(v1) = v2 & relation_dom(v0) = v3)) & ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ relation(v0) | ~ function(v0) | relation(v1)) & ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ relation(v0) | ~ function(v0) | function(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] : ( ~ relation(v0) | ~ function(v0) | ~ empty(v0) | one_to_one(v0)) & ! [v0] : ( ~ empty(v0) | relation(v0)) & ! [v0] : ( ~ empty(v0) | function(v0)) & ? [v0] : ? [v1] : element(v1, v0) & ? [v0] : subset(v0, v0)
% 5.79/2.02 |
% 5.79/2.02 | Applying alpha-rule on (1) yields:
% 5.79/2.02 | (2) ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ relation(v0) | ~ function(v0) | relation(v1))
% 5.79/2.02 | (3) one_to_one(all_0_6_6)
% 5.79/2.02 | (4) function(all_0_3_3)
% 5.79/2.02 | (5) identity_relation(all_0_11_11) = all_0_10_10
% 5.79/2.02 | (6) empty(all_0_3_3)
% 5.79/2.02 | (7) ! [v0] : ( ~ relation(v0) | ~ function(v0) | ~ empty(v0) | one_to_one(v0))
% 5.79/2.02 | (8) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : (relation_rng(v3) = v1 & relation_rng(v0) = v2 & relation_dom(v3) = v2 & function_inverse(v0) = v3))
% 5.79/2.02 | (9) ~ empty(all_0_4_4)
% 5.79/2.02 | (10) empty(all_0_1_1)
% 5.79/2.02 | (11) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | empty(v1))
% 5.79/2.02 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v5 = v1 | ~ (relation_rng(v1) = v0) | ~ (relation_dom(v5) = v6) | ~ (identity_relation(v0) = v2) | ~ (relation_composition(v1, v3) = v4) | ~ relation(v5) | ~ relation(v3) | ~ relation(v1) | ~ function(v5) | ~ function(v3) | ~ function(v1) | ? [v7] : ? [v8] : (identity_relation(v6) = v7 & relation_composition(v3, v5) = v8 & ( ~ (v8 = v2) | ~ (v7 = v4))))
% 5.79/2.02 | (13) function(all_0_6_6)
% 5.79/2.02 | (14) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ empty(v0) | relation(v2))
% 5.79/2.02 | (15) function(all_0_8_8)
% 5.79/2.02 | (16) relation(all_0_4_4)
% 5.79/2.02 | (17) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0))
% 5.79/2.02 | (18) function(all_0_0_0)
% 5.79/2.02 | (19) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0))
% 5.79/2.02 | (20) relation_dom(all_0_8_8) = all_0_12_12
% 5.79/2.02 | (21) relation(all_0_6_6)
% 5.79/2.02 | (22) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v1) | ~ function(v0) | function(v2))
% 5.79/2.02 | (23) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v1, v0) = v2) | ~ relation(v1) | ~ empty(v0) | empty(v2))
% 5.79/2.02 | (24) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ element(v0, v2) | subset(v0, v1))
% 5.79/2.02 | (25) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2))
% 5.79/2.02 | (26) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v1, v0) = v2) | ~ (function_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v3] : ? [v4] : ? [v5] : (relation_rng(v0) = v5 & relation_dom(v0) = v4 & identity_relation(v5) = v2 & identity_relation(v4) = v3 & relation_composition(v0, v1) = v3))
% 5.79/2.02 | (27) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) & empty(v2)))
% 5.79/2.03 | (28) ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ relation(v0) | ~ function(v0) | function(v1))
% 5.79/2.03 | (29) ! [v0] : ( ~ empty(v0) | function(v0))
% 5.79/2.03 | (30) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | relation(v1))
% 5.79/2.03 | (31) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0))
% 5.79/2.03 | (32) relation(all_0_13_13)
% 5.79/2.03 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_composition(v3, v2) = v1) | ~ (relation_composition(v3, v2) = v0))
% 5.79/2.03 | (34) ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1))
% 5.79/2.03 | (35) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ empty(v1))
% 5.79/2.03 | (36) relation(all_0_7_7)
% 5.79/2.03 | (37) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2))
% 5.79/2.03 | (38) empty(empty_set)
% 5.79/2.03 | (39) relation_composition(all_0_13_13, all_0_8_8) = all_0_10_10
% 5.79/2.03 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v1 | ~ (relation_rng(v1) = v0) | ~ (identity_relation(v0) = v2) | ~ (relation_composition(v3, v5) = v2) | ~ (relation_composition(v1, v3) = v4) | ~ relation(v5) | ~ relation(v3) | ~ relation(v1) | ~ function(v5) | ~ function(v3) | ~ function(v1) | ? [v6] : ? [v7] : ( ~ (v7 = v4) & relation_dom(v5) = v6 & identity_relation(v6) = v7))
% 5.79/2.03 | (41) relation(all_0_0_0)
% 5.79/2.03 | (42) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v1, v0) = v2) | ~ relation(v1) | ~ empty(v0) | relation(v2))
% 5.79/2.03 | (43) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : (relation_rng(v2) = v3 & relation_dom(v2) = v1 & relation_dom(v0) = v3 & function_inverse(v0) = v2))
% 5.79/2.03 | (44) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0))
% 5.79/2.03 | (45) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1))
% 5.79/2.03 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ in(v0, v1) | element(v0, v2))
% 5.79/2.03 | (47) relation(all_0_1_1)
% 5.79/2.03 | (48) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (identity_relation(v2) = v1) | ~ (identity_relation(v2) = v0))
% 5.79/2.03 | (49) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1))
% 5.79/2.03 | (50) ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : (relation_rng(v1) = v3 & relation_rng(v0) = v2 & relation_dom(v1) = v2 & relation_dom(v0) = v3))
% 5.79/2.03 | (51) function(all_0_13_13)
% 5.79/2.03 | (52) relation(empty_set)
% 5.79/2.03 | (53) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0))
% 5.79/2.03 | (54) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | relation(v1))
% 5.79/2.03 | (55) ? [v0] : subset(v0, v0)
% 5.79/2.03 | (56) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_dom(v0) = v4 & identity_relation(v4) = v3 & identity_relation(v1) = v5 & relation_composition(v2, v0) = v5 & relation_composition(v0, v2) = v3 & function_inverse(v0) = v2))
% 5.79/2.03 | (57) function_inverse(all_0_13_13) = all_0_9_9
% 5.79/2.03 | (58) relation_empty_yielding(empty_set)
% 5.79/2.03 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ empty(v2) | ~ in(v0, v1))
% 5.79/2.03 | (60) relation_empty_yielding(all_0_7_7)
% 5.79/2.03 | (61) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function_inverse(v2) = v1) | ~ (function_inverse(v2) = v0))
% 5.79/2.03 | (62) relation_dom(all_0_13_13) = all_0_11_11
% 5.79/2.03 | (63) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (element(v2, v1) & ~ empty(v2)))
% 5.79/2.03 | (64) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | function(v1))
% 5.79/2.03 | (65) ! [v0] : ( ~ empty(v0) | relation(v0))
% 5.79/2.03 | (66) one_to_one(all_0_13_13)
% 5.79/2.03 | (67) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0))
% 5.79/2.04 | (68) ~ (all_0_8_8 = all_0_9_9)
% 5.79/2.04 | (69) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v1) | ~ function(v0) | relation(v2))
% 5.79/2.04 | (70) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ (function_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v3] : ? [v4] : ? [v5] : (relation_rng(v0) = v5 & relation_dom(v0) = v3 & identity_relation(v5) = v4 & identity_relation(v3) = v2 & relation_composition(v1, v0) = v4))
% 5.79/2.04 | (71) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation(v1))
% 5.79/2.04 | (72) ~ empty(all_0_5_5)
% 5.79/2.04 | (73) ! [v0] : (v0 = empty_set | ~ empty(v0))
% 5.79/2.04 | (74) relation(all_0_3_3)
% 5.79/2.04 | (75) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_rng(v0) = v5 & identity_relation(v5) = v4 & identity_relation(v1) = v3 & relation_composition(v2, v0) = v4 & relation_composition(v0, v2) = v3 & function_inverse(v0) = v2))
% 5.79/2.04 | (76) empty(all_0_2_2)
% 5.79/2.04 | (77) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ empty(v0) | empty(v2))
% 5.79/2.04 | (78) relation_rng(all_0_13_13) = all_0_12_12
% 5.79/2.04 | (79) ? [v0] : ? [v1] : element(v1, v0)
% 5.79/2.04 | (80) ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1))
% 5.79/2.04 | (81) relation(all_0_8_8)
% 5.79/2.04 | (82) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | empty(v1))
% 5.79/2.04 |
% 5.79/2.04 | Instantiating formula (56) with all_0_12_12, all_0_13_13 and discharging atoms relation_rng(all_0_13_13) = all_0_12_12, one_to_one(all_0_13_13), relation(all_0_13_13), function(all_0_13_13), yields:
% 5.79/2.04 | (83) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (relation_dom(all_0_13_13) = v2 & identity_relation(v2) = v1 & identity_relation(all_0_12_12) = v3 & relation_composition(v0, all_0_13_13) = v3 & relation_composition(all_0_13_13, v0) = v1 & function_inverse(all_0_13_13) = v0)
% 5.79/2.04 |
% 5.79/2.04 | Instantiating formula (43) with all_0_12_12, all_0_13_13 and discharging atoms relation_rng(all_0_13_13) = all_0_12_12, one_to_one(all_0_13_13), relation(all_0_13_13), function(all_0_13_13), yields:
% 5.79/2.04 | (84) ? [v0] : ? [v1] : (relation_rng(v0) = v1 & relation_dom(v0) = all_0_12_12 & relation_dom(all_0_13_13) = v1 & function_inverse(all_0_13_13) = v0)
% 5.79/2.04 |
% 5.79/2.04 | Instantiating formula (75) with all_0_11_11, all_0_13_13 and discharging atoms relation_dom(all_0_13_13) = all_0_11_11, one_to_one(all_0_13_13), relation(all_0_13_13), function(all_0_13_13), yields:
% 6.06/2.04 | (85) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (relation_rng(all_0_13_13) = v3 & identity_relation(v3) = v2 & identity_relation(all_0_11_11) = v1 & relation_composition(v0, all_0_13_13) = v2 & relation_composition(all_0_13_13, v0) = v1 & function_inverse(all_0_13_13) = v0)
% 6.06/2.04 |
% 6.06/2.04 | Instantiating formula (8) with all_0_11_11, all_0_13_13 and discharging atoms relation_dom(all_0_13_13) = all_0_11_11, one_to_one(all_0_13_13), relation(all_0_13_13), function(all_0_13_13), yields:
% 6.06/2.04 | (86) ? [v0] : ? [v1] : (relation_rng(v1) = all_0_11_11 & relation_rng(all_0_13_13) = v0 & relation_dom(v1) = v0 & function_inverse(all_0_13_13) = v1)
% 6.06/2.04 |
% 6.06/2.04 | Instantiating formula (50) with all_0_9_9, all_0_13_13 and discharging atoms function_inverse(all_0_13_13) = all_0_9_9, one_to_one(all_0_13_13), relation(all_0_13_13), function(all_0_13_13), yields:
% 6.06/2.04 | (87) ? [v0] : ? [v1] : (relation_rng(all_0_9_9) = v1 & relation_rng(all_0_13_13) = v0 & relation_dom(all_0_9_9) = v0 & relation_dom(all_0_13_13) = v1)
% 6.06/2.04 |
% 6.06/2.04 | Instantiating formula (2) with all_0_9_9, all_0_13_13 and discharging atoms function_inverse(all_0_13_13) = all_0_9_9, relation(all_0_13_13), function(all_0_13_13), yields:
% 6.06/2.04 | (88) relation(all_0_9_9)
% 6.06/2.04 |
% 6.06/2.04 | Instantiating formula (28) with all_0_9_9, all_0_13_13 and discharging atoms function_inverse(all_0_13_13) = all_0_9_9, relation(all_0_13_13), function(all_0_13_13), yields:
% 6.06/2.04 | (89) function(all_0_9_9)
% 6.06/2.04 |
% 6.06/2.04 | Instantiating (87) with all_17_0_17, all_17_1_18 yields:
% 6.06/2.04 | (90) relation_rng(all_0_9_9) = all_17_0_17 & relation_rng(all_0_13_13) = all_17_1_18 & relation_dom(all_0_9_9) = all_17_1_18 & relation_dom(all_0_13_13) = all_17_0_17
% 6.06/2.04 |
% 6.06/2.04 | Applying alpha-rule on (90) yields:
% 6.06/2.04 | (91) relation_rng(all_0_9_9) = all_17_0_17
% 6.06/2.04 | (92) relation_rng(all_0_13_13) = all_17_1_18
% 6.06/2.04 | (93) relation_dom(all_0_9_9) = all_17_1_18
% 6.06/2.04 | (94) relation_dom(all_0_13_13) = all_17_0_17
% 6.06/2.04 |
% 6.06/2.04 | Instantiating (85) with all_19_0_19, all_19_1_20, all_19_2_21, all_19_3_22 yields:
% 6.06/2.04 | (95) relation_rng(all_0_13_13) = all_19_0_19 & identity_relation(all_19_0_19) = all_19_1_20 & identity_relation(all_0_11_11) = all_19_2_21 & relation_composition(all_19_3_22, all_0_13_13) = all_19_1_20 & relation_composition(all_0_13_13, all_19_3_22) = all_19_2_21 & function_inverse(all_0_13_13) = all_19_3_22
% 6.06/2.05 |
% 6.06/2.05 | Applying alpha-rule on (95) yields:
% 6.06/2.05 | (96) identity_relation(all_19_0_19) = all_19_1_20
% 6.06/2.05 | (97) relation_rng(all_0_13_13) = all_19_0_19
% 6.06/2.05 | (98) function_inverse(all_0_13_13) = all_19_3_22
% 6.06/2.05 | (99) relation_composition(all_0_13_13, all_19_3_22) = all_19_2_21
% 6.06/2.05 | (100) relation_composition(all_19_3_22, all_0_13_13) = all_19_1_20
% 6.06/2.05 | (101) identity_relation(all_0_11_11) = all_19_2_21
% 6.06/2.05 |
% 6.06/2.05 | Instantiating (84) with all_21_0_23, all_21_1_24 yields:
% 6.06/2.05 | (102) relation_rng(all_21_1_24) = all_21_0_23 & relation_dom(all_21_1_24) = all_0_12_12 & relation_dom(all_0_13_13) = all_21_0_23 & function_inverse(all_0_13_13) = all_21_1_24
% 6.06/2.05 |
% 6.06/2.05 | Applying alpha-rule on (102) yields:
% 6.06/2.05 | (103) relation_rng(all_21_1_24) = all_21_0_23
% 6.06/2.05 | (104) relation_dom(all_21_1_24) = all_0_12_12
% 6.06/2.05 | (105) relation_dom(all_0_13_13) = all_21_0_23
% 6.06/2.05 | (106) function_inverse(all_0_13_13) = all_21_1_24
% 6.06/2.05 |
% 6.06/2.05 | Instantiating (86) with all_23_0_25, all_23_1_26 yields:
% 6.06/2.05 | (107) relation_rng(all_23_0_25) = all_0_11_11 & relation_rng(all_0_13_13) = all_23_1_26 & relation_dom(all_23_0_25) = all_23_1_26 & function_inverse(all_0_13_13) = all_23_0_25
% 6.06/2.05 |
% 6.06/2.05 | Applying alpha-rule on (107) yields:
% 6.06/2.05 | (108) relation_rng(all_23_0_25) = all_0_11_11
% 6.06/2.05 | (109) relation_rng(all_0_13_13) = all_23_1_26
% 6.06/2.05 | (110) relation_dom(all_23_0_25) = all_23_1_26
% 6.06/2.05 | (111) function_inverse(all_0_13_13) = all_23_0_25
% 6.06/2.05 |
% 6.06/2.05 | Instantiating (83) with all_25_0_27, all_25_1_28, all_25_2_29, all_25_3_30 yields:
% 6.06/2.05 | (112) relation_dom(all_0_13_13) = all_25_1_28 & identity_relation(all_25_1_28) = all_25_2_29 & identity_relation(all_0_12_12) = all_25_0_27 & relation_composition(all_25_3_30, all_0_13_13) = all_25_0_27 & relation_composition(all_0_13_13, all_25_3_30) = all_25_2_29 & function_inverse(all_0_13_13) = all_25_3_30
% 6.06/2.05 |
% 6.06/2.05 | Applying alpha-rule on (112) yields:
% 6.06/2.05 | (113) function_inverse(all_0_13_13) = all_25_3_30
% 6.06/2.05 | (114) identity_relation(all_0_12_12) = all_25_0_27
% 6.06/2.05 | (115) relation_composition(all_25_3_30, all_0_13_13) = all_25_0_27
% 6.06/2.05 | (116) relation_dom(all_0_13_13) = all_25_1_28
% 6.06/2.05 | (117) relation_composition(all_0_13_13, all_25_3_30) = all_25_2_29
% 6.06/2.05 | (118) identity_relation(all_25_1_28) = all_25_2_29
% 6.06/2.05 |
% 6.06/2.05 | Instantiating formula (31) with all_0_13_13, all_25_1_28, all_0_11_11 and discharging atoms relation_dom(all_0_13_13) = all_25_1_28, relation_dom(all_0_13_13) = all_0_11_11, yields:
% 6.06/2.05 | (119) all_25_1_28 = all_0_11_11
% 6.06/2.05 |
% 6.06/2.05 | Instantiating formula (31) with all_0_13_13, all_21_0_23, all_25_1_28 and discharging atoms relation_dom(all_0_13_13) = all_25_1_28, relation_dom(all_0_13_13) = all_21_0_23, yields:
% 6.06/2.05 | (120) all_25_1_28 = all_21_0_23
% 6.06/2.05 |
% 6.06/2.05 | Instantiating formula (31) with all_0_13_13, all_17_0_17, all_21_0_23 and discharging atoms relation_dom(all_0_13_13) = all_21_0_23, relation_dom(all_0_13_13) = all_17_0_17, yields:
% 6.06/2.05 | (121) all_21_0_23 = all_17_0_17
% 6.06/2.05 |
% 6.06/2.05 | Instantiating formula (48) with all_0_11_11, all_19_2_21, all_0_10_10 and discharging atoms identity_relation(all_0_11_11) = all_19_2_21, identity_relation(all_0_11_11) = all_0_10_10, yields:
% 6.06/2.05 | (122) all_19_2_21 = all_0_10_10
% 6.06/2.05 |
% 6.06/2.05 | Instantiating formula (61) with all_0_13_13, all_25_3_30, all_0_9_9 and discharging atoms function_inverse(all_0_13_13) = all_25_3_30, function_inverse(all_0_13_13) = all_0_9_9, yields:
% 6.06/2.05 | (123) all_25_3_30 = all_0_9_9
% 6.06/2.05 |
% 6.06/2.05 | Instantiating formula (61) with all_0_13_13, all_23_0_25, all_25_3_30 and discharging atoms function_inverse(all_0_13_13) = all_25_3_30, function_inverse(all_0_13_13) = all_23_0_25, yields:
% 6.06/2.05 | (124) all_25_3_30 = all_23_0_25
% 6.06/2.05 |
% 6.06/2.05 | Instantiating formula (61) with all_0_13_13, all_21_1_24, all_23_0_25 and discharging atoms function_inverse(all_0_13_13) = all_23_0_25, function_inverse(all_0_13_13) = all_21_1_24, yields:
% 6.06/2.05 | (125) all_23_0_25 = all_21_1_24
% 6.06/2.05 |
% 6.12/2.05 | Instantiating formula (61) with all_0_13_13, all_19_3_22, all_21_1_24 and discharging atoms function_inverse(all_0_13_13) = all_21_1_24, function_inverse(all_0_13_13) = all_19_3_22, yields:
% 6.12/2.05 | (126) all_21_1_24 = all_19_3_22
% 6.12/2.05 |
% 6.12/2.05 | Combining equations (120,119) yields a new equation:
% 6.12/2.05 | (127) all_21_0_23 = all_0_11_11
% 6.12/2.05 |
% 6.12/2.05 | Simplifying 127 yields:
% 6.12/2.05 | (128) all_21_0_23 = all_0_11_11
% 6.12/2.05 |
% 6.12/2.05 | Combining equations (124,123) yields a new equation:
% 6.12/2.05 | (129) all_23_0_25 = all_0_9_9
% 6.12/2.05 |
% 6.12/2.05 | Simplifying 129 yields:
% 6.12/2.06 | (130) all_23_0_25 = all_0_9_9
% 6.12/2.06 |
% 6.12/2.06 | Combining equations (125,130) yields a new equation:
% 6.12/2.06 | (131) all_21_1_24 = all_0_9_9
% 6.12/2.06 |
% 6.12/2.06 | Simplifying 131 yields:
% 6.12/2.06 | (132) all_21_1_24 = all_0_9_9
% 6.12/2.06 |
% 6.12/2.06 | Combining equations (121,128) yields a new equation:
% 6.12/2.06 | (133) all_17_0_17 = all_0_11_11
% 6.12/2.06 |
% 6.12/2.06 | Simplifying 133 yields:
% 6.12/2.06 | (134) all_17_0_17 = all_0_11_11
% 6.12/2.06 |
% 6.12/2.06 | Combining equations (126,132) yields a new equation:
% 6.12/2.06 | (135) all_19_3_22 = all_0_9_9
% 6.12/2.06 |
% 6.12/2.06 | Simplifying 135 yields:
% 6.12/2.06 | (136) all_19_3_22 = all_0_9_9
% 6.12/2.06 |
% 6.12/2.06 | From (134) and (91) follows:
% 6.12/2.06 | (137) relation_rng(all_0_9_9) = all_0_11_11
% 6.12/2.06 |
% 6.12/2.06 | From (119) and (118) follows:
% 6.12/2.06 | (138) identity_relation(all_0_11_11) = all_25_2_29
% 6.12/2.06 |
% 6.12/2.06 | From (123) and (115) follows:
% 6.12/2.06 | (139) relation_composition(all_0_9_9, all_0_13_13) = all_25_0_27
% 6.12/2.06 |
% 6.12/2.06 | From (136) and (100) follows:
% 6.12/2.06 | (140) relation_composition(all_0_9_9, all_0_13_13) = all_19_1_20
% 6.12/2.06 |
% 6.12/2.06 | From (123) and (117) follows:
% 6.12/2.06 | (141) relation_composition(all_0_13_13, all_0_9_9) = all_25_2_29
% 6.12/2.06 |
% 6.12/2.06 | From (136)(122) and (99) follows:
% 6.12/2.06 | (142) relation_composition(all_0_13_13, all_0_9_9) = all_0_10_10
% 6.12/2.06 |
% 6.12/2.06 | Instantiating formula (33) with all_0_9_9, all_0_13_13, all_19_1_20, all_25_0_27 and discharging atoms relation_composition(all_0_9_9, all_0_13_13) = all_25_0_27, relation_composition(all_0_9_9, all_0_13_13) = all_19_1_20, yields:
% 6.12/2.06 | (143) all_25_0_27 = all_19_1_20
% 6.12/2.06 |
% 6.12/2.06 | Instantiating formula (33) with all_0_13_13, all_0_9_9, all_0_10_10, all_25_2_29 and discharging atoms relation_composition(all_0_13_13, all_0_9_9) = all_25_2_29, relation_composition(all_0_13_13, all_0_9_9) = all_0_10_10, yields:
% 6.12/2.06 | (144) all_25_2_29 = all_0_10_10
% 6.12/2.06 |
% 6.12/2.06 | From (144) and (138) follows:
% 6.12/2.06 | (5) identity_relation(all_0_11_11) = all_0_10_10
% 6.12/2.06 |
% 6.12/2.06 | From (143) and (114) follows:
% 6.12/2.06 | (146) identity_relation(all_0_12_12) = all_19_1_20
% 6.12/2.06 |
% 6.12/2.06 | From (143) and (139) follows:
% 6.12/2.06 | (140) relation_composition(all_0_9_9, all_0_13_13) = all_19_1_20
% 6.12/2.06 |
% 6.12/2.06 | Instantiating formula (12) with all_0_12_12, all_0_8_8, all_19_1_20, all_0_13_13, all_0_10_10, all_0_9_9, all_0_11_11 and discharging atoms relation_rng(all_0_9_9) = all_0_11_11, relation_dom(all_0_8_8) = all_0_12_12, identity_relation(all_0_11_11) = all_0_10_10, relation_composition(all_0_9_9, all_0_13_13) = all_19_1_20, relation(all_0_8_8), relation(all_0_9_9), relation(all_0_13_13), function(all_0_8_8), function(all_0_9_9), function(all_0_13_13), yields:
% 6.12/2.06 | (148) all_0_8_8 = all_0_9_9 | ? [v0] : ? [v1] : (identity_relation(all_0_12_12) = v0 & relation_composition(all_0_13_13, all_0_8_8) = v1 & ( ~ (v1 = all_0_10_10) | ~ (v0 = all_19_1_20)))
% 6.12/2.06 |
% 6.12/2.06 | Instantiating formula (40) with all_0_8_8, all_19_1_20, all_0_13_13, all_0_10_10, all_0_9_9, all_0_11_11 and discharging atoms relation_rng(all_0_9_9) = all_0_11_11, identity_relation(all_0_11_11) = all_0_10_10, relation_composition(all_0_9_9, all_0_13_13) = all_19_1_20, relation_composition(all_0_13_13, all_0_8_8) = all_0_10_10, relation(all_0_8_8), relation(all_0_9_9), relation(all_0_13_13), function(all_0_8_8), function(all_0_9_9), function(all_0_13_13), yields:
% 6.12/2.06 | (149) all_0_8_8 = all_0_9_9 | ? [v0] : ? [v1] : ( ~ (v1 = all_19_1_20) & relation_dom(all_0_8_8) = v0 & identity_relation(v0) = v1)
% 6.12/2.06 |
% 6.12/2.06 +-Applying beta-rule and splitting (149), into two cases.
% 6.12/2.06 |-Branch one:
% 6.12/2.06 | (150) all_0_8_8 = all_0_9_9
% 6.12/2.06 |
% 6.12/2.06 | Equations (150) can reduce 68 to:
% 6.12/2.06 | (151) $false
% 6.12/2.06 |
% 6.12/2.06 |-The branch is then unsatisfiable
% 6.12/2.06 |-Branch two:
% 6.12/2.06 | (68) ~ (all_0_8_8 = all_0_9_9)
% 6.12/2.06 | (153) ? [v0] : ? [v1] : ( ~ (v1 = all_19_1_20) & relation_dom(all_0_8_8) = v0 & identity_relation(v0) = v1)
% 6.12/2.06 |
% 6.12/2.06 +-Applying beta-rule and splitting (148), into two cases.
% 6.12/2.06 |-Branch one:
% 6.12/2.06 | (150) all_0_8_8 = all_0_9_9
% 6.12/2.06 |
% 6.12/2.06 | Equations (150) can reduce 68 to:
% 6.12/2.06 | (151) $false
% 6.12/2.06 |
% 6.12/2.06 |-The branch is then unsatisfiable
% 6.12/2.06 |-Branch two:
% 6.12/2.06 | (68) ~ (all_0_8_8 = all_0_9_9)
% 6.12/2.06 | (157) ? [v0] : ? [v1] : (identity_relation(all_0_12_12) = v0 & relation_composition(all_0_13_13, all_0_8_8) = v1 & ( ~ (v1 = all_0_10_10) | ~ (v0 = all_19_1_20)))
% 6.12/2.07 |
% 6.12/2.07 | Instantiating (157) with all_51_0_33, all_51_1_34 yields:
% 6.12/2.07 | (158) identity_relation(all_0_12_12) = all_51_1_34 & relation_composition(all_0_13_13, all_0_8_8) = all_51_0_33 & ( ~ (all_51_0_33 = all_0_10_10) | ~ (all_51_1_34 = all_19_1_20))
% 6.12/2.07 |
% 6.12/2.07 | Applying alpha-rule on (158) yields:
% 6.12/2.07 | (159) identity_relation(all_0_12_12) = all_51_1_34
% 6.12/2.07 | (160) relation_composition(all_0_13_13, all_0_8_8) = all_51_0_33
% 6.12/2.07 | (161) ~ (all_51_0_33 = all_0_10_10) | ~ (all_51_1_34 = all_19_1_20)
% 6.12/2.07 |
% 6.12/2.07 | Instantiating formula (48) with all_0_12_12, all_51_1_34, all_19_1_20 and discharging atoms identity_relation(all_0_12_12) = all_51_1_34, identity_relation(all_0_12_12) = all_19_1_20, yields:
% 6.12/2.07 | (162) all_51_1_34 = all_19_1_20
% 6.12/2.07 |
% 6.12/2.07 | Instantiating formula (33) with all_0_13_13, all_0_8_8, all_51_0_33, all_0_10_10 and discharging atoms relation_composition(all_0_13_13, all_0_8_8) = all_51_0_33, relation_composition(all_0_13_13, all_0_8_8) = all_0_10_10, yields:
% 6.12/2.07 | (163) all_51_0_33 = all_0_10_10
% 6.12/2.07 |
% 6.12/2.07 +-Applying beta-rule and splitting (161), into two cases.
% 6.12/2.07 |-Branch one:
% 6.12/2.07 | (164) ~ (all_51_0_33 = all_0_10_10)
% 6.12/2.07 |
% 6.12/2.07 | Equations (163) can reduce 164 to:
% 6.12/2.07 | (151) $false
% 6.12/2.07 |
% 6.12/2.07 |-The branch is then unsatisfiable
% 6.12/2.07 |-Branch two:
% 6.12/2.07 | (163) all_51_0_33 = all_0_10_10
% 6.12/2.07 | (167) ~ (all_51_1_34 = all_19_1_20)
% 6.12/2.07 |
% 6.12/2.07 | Equations (162) can reduce 167 to:
% 6.12/2.07 | (151) $false
% 6.12/2.07 |
% 6.12/2.07 |-The branch is then unsatisfiable
% 6.12/2.07 % SZS output end Proof for theBenchmark
% 6.12/2.07
% 6.12/2.07 1423ms
%------------------------------------------------------------------------------