TSTP Solution File: SEU027+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU027+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n022.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 5.38s 2.09s
% Output : Proof 8.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU027+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.34 % Computer : n022.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 20 13:23:31 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.69/0.66 ____ _
% 0.69/0.66 ___ / __ \_____(_)___ ________ __________
% 0.69/0.66 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.69/0.66 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.69/0.66 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.69/0.66
% 0.69/0.66 A Theorem Prover for First-Order Logic
% 0.69/0.66 (ePrincess v.1.0)
% 0.69/0.66
% 0.69/0.66 (c) Philipp Rümmer, 2009-2015
% 0.69/0.66 (c) Peter Backeman, 2014-2015
% 0.69/0.66 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.69/0.66 Free software under GNU Lesser General Public License (LGPL).
% 0.69/0.66 Bug reports to peter@backeman.se
% 0.69/0.66
% 0.69/0.66 For more information, visit http://user.uu.se/~petba168/breu/
% 0.69/0.66
% 0.69/0.66 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.85/0.71 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.86/1.12 Prover 0: Preprocessing ...
% 3.43/1.59 Prover 0: Warning: ignoring some quantifiers
% 3.56/1.62 Prover 0: Constructing countermodel ...
% 5.38/2.09 Prover 0: proved (1379ms)
% 5.38/2.09
% 5.38/2.09 No countermodel exists, formula is valid
% 5.38/2.09 % SZS status Theorem for theBenchmark
% 5.38/2.09
% 5.38/2.09 Generating proof ... Warning: ignoring some quantifiers
% 7.90/2.62 found it (size 118)
% 7.90/2.62
% 7.90/2.62 % SZS output start Proof for theBenchmark
% 7.90/2.62 Assumed formulas after preprocessing and simplification:
% 7.90/2.62 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ( ~ (v4 = v3) & function_inverse(v0) = v3 & relation_rng(v4) = v1 & relation_rng(v0) = v2 & relation_dom(v4) = v2 & relation_dom(v0) = v1 & relation_empty_yielding(v5) & relation_empty_yielding(empty_set) & one_to_one(v6) & one_to_one(v0) & relation(v12) & relation(v11) & relation(v9) & relation(v8) & relation(v6) & relation(v5) & relation(v4) & relation(v0) & relation(empty_set) & function(v12) & function(v9) & function(v6) & function(v4) & function(v0) & empty(v11) & empty(v10) & empty(v9) & empty(empty_set) & ~ empty(v8) & ~ empty(v7) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v14 = v13 | ~ (apply(v16, v15) = v14) | ~ (apply(v16, v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (powerset(v15) = v16) | ~ element(v14, v16) | ~ empty(v15) | ~ in(v13, v14)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (powerset(v15) = v16) | ~ element(v14, v16) | ~ in(v13, v14) | element(v13, v15)) & ! [v13] : ! [v14] : ! [v15] : (v15 = v13 | ~ (relation_dom(v15) = v14) | ~ (relation_dom(v13) = v14) | ~ relation(v15) | ~ relation(v13) | ~ function(v15) | ~ function(v13) | ? [v16] : ? [v17] : ? [v18] : ( ~ (v18 = v17) & apply(v15, v16) = v18 & apply(v13, v16) = v17 & in(v16, v14))) & ! [v13] : ! [v14] : ! [v15] : (v14 = v13 | ~ (powerset(v15) = v14) | ~ (powerset(v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : (v14 = v13 | ~ (function_inverse(v15) = v14) | ~ (function_inverse(v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : (v14 = v13 | ~ (relation_rng(v15) = v14) | ~ (relation_rng(v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : (v14 = v13 | ~ (relation_dom(v15) = v14) | ~ (relation_dom(v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (powerset(v14) = v15) | ~ subset(v13, v14) | element(v13, v15)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (powerset(v14) = v15) | ~ element(v13, v15) | subset(v13, v14)) & ! [v13] : ! [v14] : (v14 = v13 | ~ empty(v14) | ~ empty(v13)) & ! [v13] : ! [v14] : ( ~ (powerset(v13) = v14) | ~ empty(v14)) & ! [v13] : ! [v14] : ( ~ (powerset(v13) = v14) | empty(v13) | ? [v15] : (element(v15, v14) & ~ empty(v15))) & ! [v13] : ! [v14] : ( ~ (powerset(v13) = v14) | ? [v15] : (element(v15, v14) & empty(v15))) & ! [v13] : ! [v14] : ( ~ (function_inverse(v13) = v14) | ~ one_to_one(v13) | ~ relation(v13) | ~ function(v13) | ? [v15] : ? [v16] : (relation_rng(v13) = v15 & relation_dom(v13) = v16 & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v20 = v19 | ~ (relation_dom(v14) = v17) | ~ (apply(v14, v18) = v20) | ~ (apply(v13, v19) = v18) | ~ relation(v14) | ~ function(v14) | ~ in(v19, v16)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v20 = v18 | ~ (relation_dom(v14) = v17) | ~ (apply(v14, v18) = v19) | ~ (apply(v13, v19) = v20) | ~ relation(v14) | ~ function(v14) | ~ in(v18, v15)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_dom(v14) = v17) | ~ (apply(v14, v18) = v20) | ~ (apply(v13, v19) = v18) | ~ relation(v14) | ~ function(v14) | ~ in(v19, v16) | in(v18, v15)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_dom(v14) = v17) | ~ (apply(v14, v18) = v19) | ~ (apply(v13, v19) = v20) | ~ relation(v14) | ~ function(v14) | ~ in(v18, v15) | in(v19, v16)) & ! [v17] : (v17 = v15 | ~ (relation_dom(v14) = v17) | ~ relation(v14) | ~ function(v14)) & ! [v17] : (v17 = v14 | ~ (relation_dom(v17) = v15) | ~ relation(v17) | ~ function(v17) | ? [v18] : ? [v19] : ? [v20] : ? [v21] : (apply(v17, v18) = v20 & apply(v13, v19) = v21 & ((v21 = v18 & in(v19, v16) & ( ~ (v20 = v19) | ~ in(v18, v15))) | (v20 = v19 & in(v18, v15) & ( ~ (v21 = v18) | ~ in(v19, v16)))))))) & ! [v13] : ! [v14] : ( ~ (function_inverse(v13) = v14) | ~ relation(v13) | ~ function(v13) | relation(v14)) & ! [v13] : ! [v14] : ( ~ (function_inverse(v13) = v14) | ~ relation(v13) | ~ function(v13) | function(v14)) & ! [v13] : ! [v14] : ( ~ (relation_rng(v13) = v14) | ~ one_to_one(v13) | ~ relation(v13) | ~ function(v13) | ? [v15] : ? [v16] : (function_inverse(v13) = v15 & relation_dom(v13) = v16 & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v20 = v19 | ~ (relation_dom(v15) = v17) | ~ (apply(v15, v18) = v20) | ~ (apply(v13, v19) = v18) | ~ relation(v15) | ~ function(v15) | ~ in(v19, v16)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v20 = v18 | ~ (relation_dom(v15) = v17) | ~ (apply(v15, v18) = v19) | ~ (apply(v13, v19) = v20) | ~ relation(v15) | ~ function(v15) | ~ in(v18, v14)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_dom(v15) = v17) | ~ (apply(v15, v18) = v20) | ~ (apply(v13, v19) = v18) | ~ relation(v15) | ~ function(v15) | ~ in(v19, v16) | in(v18, v14)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_dom(v15) = v17) | ~ (apply(v15, v18) = v19) | ~ (apply(v13, v19) = v20) | ~ relation(v15) | ~ function(v15) | ~ in(v18, v14) | in(v19, v16)) & ! [v17] : (v17 = v15 | ~ (relation_dom(v17) = v14) | ~ relation(v17) | ~ function(v17) | ? [v18] : ? [v19] : ? [v20] : ? [v21] : (apply(v17, v18) = v20 & apply(v13, v19) = v21 & ((v21 = v18 & in(v19, v16) & ( ~ (v20 = v19) | ~ in(v18, v14))) | (v20 = v19 & in(v18, v14) & ( ~ (v21 = v18) | ~ in(v19, v16)))))) & ! [v17] : (v17 = v14 | ~ (relation_dom(v15) = v17) | ~ relation(v15) | ~ function(v15)))) & ! [v13] : ! [v14] : ( ~ (relation_rng(v13) = v14) | ~ relation(v13) | ~ function(v13) | ? [v15] : (relation_dom(v13) = v15 & ! [v16] : ! [v17] : ( ~ (apply(v13, v17) = v16) | ~ in(v17, v15) | in(v16, v14)) & ! [v16] : ( ~ in(v16, v14) | ? [v17] : (apply(v13, v17) = v16 & in(v17, v15))) & ? [v16] : (v16 = v14 | ? [v17] : ? [v18] : ? [v19] : (( ~ in(v17, v16) | ! [v20] : ( ~ (apply(v13, v20) = v17) | ~ in(v20, v15))) & (in(v17, v16) | (v19 = v17 & apply(v13, v18) = v17 & in(v18, v15))))))) & ! [v13] : ! [v14] : ( ~ (relation_rng(v13) = v14) | ~ relation(v13) | ~ empty(v14) | empty(v13)) & ! [v13] : ! [v14] : ( ~ (relation_rng(v13) = v14) | ~ empty(v13) | relation(v14)) & ! [v13] : ! [v14] : ( ~ (relation_rng(v13) = v14) | ~ empty(v13) | empty(v14)) & ! [v13] : ! [v14] : ( ~ (relation_dom(v13) = v14) | ~ one_to_one(v13) | ~ relation(v13) | ~ function(v13) | ? [v15] : ? [v16] : (function_inverse(v13) = v15 & relation_rng(v13) = v16 & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v20 = v19 | ~ (relation_dom(v15) = v17) | ~ (apply(v15, v18) = v20) | ~ (apply(v13, v19) = v18) | ~ relation(v15) | ~ function(v15) | ~ in(v19, v14)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v20 = v18 | ~ (relation_dom(v15) = v17) | ~ (apply(v15, v18) = v19) | ~ (apply(v13, v19) = v20) | ~ relation(v15) | ~ function(v15) | ~ in(v18, v16)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_dom(v15) = v17) | ~ (apply(v15, v18) = v20) | ~ (apply(v13, v19) = v18) | ~ relation(v15) | ~ function(v15) | ~ in(v19, v14) | in(v18, v16)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_dom(v15) = v17) | ~ (apply(v15, v18) = v19) | ~ (apply(v13, v19) = v20) | ~ relation(v15) | ~ function(v15) | ~ in(v18, v16) | in(v19, v14)) & ! [v17] : (v17 = v16 | ~ (relation_dom(v15) = v17) | ~ relation(v15) | ~ function(v15)) & ! [v17] : (v17 = v15 | ~ (relation_dom(v17) = v16) | ~ relation(v17) | ~ function(v17) | ? [v18] : ? [v19] : ? [v20] : ? [v21] : (apply(v17, v18) = v20 & apply(v13, v19) = v21 & ((v21 = v18 & in(v19, v14) & ( ~ (v20 = v19) | ~ in(v18, v16))) | (v20 = v19 & in(v18, v16) & ( ~ (v21 = v18) | ~ in(v19, v14)))))))) & ! [v13] : ! [v14] : ( ~ (relation_dom(v13) = v14) | ~ relation(v13) | ~ function(v13) | ? [v15] : (relation_rng(v13) = v15 & ! [v16] : ! [v17] : ( ~ (apply(v13, v17) = v16) | ~ in(v17, v14) | in(v16, v15)) & ! [v16] : ( ~ in(v16, v15) | ? [v17] : (apply(v13, v17) = v16 & in(v17, v14))) & ? [v16] : (v16 = v15 | ? [v17] : ? [v18] : ? [v19] : (( ~ in(v17, v16) | ! [v20] : ( ~ (apply(v13, v20) = v17) | ~ in(v20, v14))) & (in(v17, v16) | (v19 = v17 & apply(v13, v18) = v17 & in(v18, v14))))))) & ! [v13] : ! [v14] : ( ~ (relation_dom(v13) = v14) | ~ relation(v13) | ~ empty(v14) | empty(v13)) & ! [v13] : ! [v14] : ( ~ (relation_dom(v13) = v14) | ~ empty(v13) | relation(v14)) & ! [v13] : ! [v14] : ( ~ (relation_dom(v13) = v14) | ~ empty(v13) | empty(v14)) & ! [v13] : ! [v14] : ( ~ element(v13, v14) | empty(v14) | in(v13, v14)) & ! [v13] : ! [v14] : ( ~ empty(v14) | ~ in(v13, v14)) & ! [v13] : ! [v14] : ( ~ in(v14, v13) | ~ in(v13, v14)) & ! [v13] : ! [v14] : ( ~ in(v14, v2) | ~ in(v13, v1) | ? [v15] : ? [v16] : (apply(v4, v14) = v16 & apply(v0, v13) = v15 & ( ~ (v16 = v13) | v15 = v14) & ( ~ (v15 = v14) | v16 = v13))) & ! [v13] : ! [v14] : ( ~ in(v13, v14) | element(v13, v14)) & ! [v13] : (v13 = empty_set | ~ empty(v13)) & ! [v13] : ( ~ relation(v13) | ~ function(v13) | ~ empty(v13) | one_to_one(v13)) & ! [v13] : ( ~ empty(v13) | relation(v13)) & ! [v13] : ( ~ empty(v13) | function(v13)) & ? [v13] : ? [v14] : element(v14, v13) & ? [v13] : subset(v13, v13))
% 7.90/2.67 | 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 yields:
% 7.90/2.67 | (1) ~ (all_0_8_8 = all_0_9_9) & function_inverse(all_0_12_12) = all_0_9_9 & relation_rng(all_0_8_8) = all_0_11_11 & relation_rng(all_0_12_12) = all_0_10_10 & relation_dom(all_0_8_8) = all_0_10_10 & relation_dom(all_0_12_12) = all_0_11_11 & relation_empty_yielding(all_0_7_7) & relation_empty_yielding(empty_set) & one_to_one(all_0_6_6) & one_to_one(all_0_12_12) & 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_12_12) & 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_12_12) & 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] : (v1 = v0 | ~ (apply(v3, v2) = v1) | ~ (apply(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] : (v2 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v0) = v1) | ~ relation(v2) | ~ relation(v0) | ~ function(v2) | ~ function(v0) | ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = v4) & apply(v2, v3) = v5 & apply(v0, v3) = v4 & in(v3, v1))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function_inverse(v2) = v1) | ~ (function_inverse(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] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ element(v0, v2) | subset(v0, v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) & ! [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] : ( ~ (function_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : (relation_rng(v0) = v2 & relation_dom(v0) = v3 & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v6 | ~ (relation_dom(v1) = v4) | ~ (apply(v1, v5) = v7) | ~ (apply(v0, v6) = v5) | ~ relation(v1) | ~ function(v1) | ~ in(v6, v3)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v5 | ~ (relation_dom(v1) = v4) | ~ (apply(v1, v5) = v6) | ~ (apply(v0, v6) = v7) | ~ relation(v1) | ~ function(v1) | ~ in(v5, v2)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (relation_dom(v1) = v4) | ~ (apply(v1, v5) = v7) | ~ (apply(v0, v6) = v5) | ~ relation(v1) | ~ function(v1) | ~ in(v6, v3) | in(v5, v2)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (relation_dom(v1) = v4) | ~ (apply(v1, v5) = v6) | ~ (apply(v0, v6) = v7) | ~ relation(v1) | ~ function(v1) | ~ in(v5, v2) | in(v6, v3)) & ! [v4] : (v4 = v2 | ~ (relation_dom(v1) = v4) | ~ relation(v1) | ~ function(v1)) & ! [v4] : (v4 = v1 | ~ (relation_dom(v4) = v2) | ~ relation(v4) | ~ function(v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (apply(v4, v5) = v7 & apply(v0, v6) = v8 & ((v8 = v5 & in(v6, v3) & ( ~ (v7 = v6) | ~ in(v5, v2))) | (v7 = v6 & in(v5, v2) & ( ~ (v8 = v5) | ~ in(v6, 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] : ( ~ (relation_rng(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : (function_inverse(v0) = v2 & relation_dom(v0) = v3 & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v6 | ~ (relation_dom(v2) = v4) | ~ (apply(v2, v5) = v7) | ~ (apply(v0, v6) = v5) | ~ relation(v2) | ~ function(v2) | ~ in(v6, v3)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v5 | ~ (relation_dom(v2) = v4) | ~ (apply(v2, v5) = v6) | ~ (apply(v0, v6) = v7) | ~ relation(v2) | ~ function(v2) | ~ in(v5, v1)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (relation_dom(v2) = v4) | ~ (apply(v2, v5) = v7) | ~ (apply(v0, v6) = v5) | ~ relation(v2) | ~ function(v2) | ~ in(v6, v3) | in(v5, v1)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (relation_dom(v2) = v4) | ~ (apply(v2, v5) = v6) | ~ (apply(v0, v6) = v7) | ~ relation(v2) | ~ function(v2) | ~ in(v5, v1) | in(v6, v3)) & ! [v4] : (v4 = v2 | ~ (relation_dom(v4) = v1) | ~ relation(v4) | ~ function(v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (apply(v4, v5) = v7 & apply(v0, v6) = v8 & ((v8 = v5 & in(v6, v3) & ( ~ (v7 = v6) | ~ in(v5, v1))) | (v7 = v6 & in(v5, v1) & ( ~ (v8 = v5) | ~ in(v6, v3)))))) & ! [v4] : (v4 = v1 | ~ (relation_dom(v2) = v4) | ~ relation(v2) | ~ function(v2)))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ function(v0) | ? [v2] : (relation_dom(v0) = v2 & ! [v3] : ! [v4] : ( ~ (apply(v0, v4) = v3) | ~ in(v4, v2) | in(v3, v1)) & ! [v3] : ( ~ in(v3, v1) | ? [v4] : (apply(v0, v4) = v3 & in(v4, v2))) & ? [v3] : (v3 = v1 | ? [v4] : ? [v5] : ? [v6] : (( ~ in(v4, v3) | ! [v7] : ( ~ (apply(v0, v7) = v4) | ~ in(v7, v2))) & (in(v4, v3) | (v6 = v4 & apply(v0, v5) = v4 & in(v5, 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] : (function_inverse(v0) = v2 & relation_rng(v0) = v3 & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v6 | ~ (relation_dom(v2) = v4) | ~ (apply(v2, v5) = v7) | ~ (apply(v0, v6) = v5) | ~ relation(v2) | ~ function(v2) | ~ in(v6, v1)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v5 | ~ (relation_dom(v2) = v4) | ~ (apply(v2, v5) = v6) | ~ (apply(v0, v6) = v7) | ~ relation(v2) | ~ function(v2) | ~ in(v5, v3)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (relation_dom(v2) = v4) | ~ (apply(v2, v5) = v7) | ~ (apply(v0, v6) = v5) | ~ relation(v2) | ~ function(v2) | ~ in(v6, v1) | in(v5, v3)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (relation_dom(v2) = v4) | ~ (apply(v2, v5) = v6) | ~ (apply(v0, v6) = v7) | ~ relation(v2) | ~ function(v2) | ~ in(v5, v3) | in(v6, v1)) & ! [v4] : (v4 = v3 | ~ (relation_dom(v2) = v4) | ~ relation(v2) | ~ function(v2)) & ! [v4] : (v4 = v2 | ~ (relation_dom(v4) = v3) | ~ relation(v4) | ~ function(v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (apply(v4, v5) = v7 & apply(v0, v6) = v8 & ((v8 = v5 & in(v6, v1) & ( ~ (v7 = v6) | ~ in(v5, v3))) | (v7 = v6 & in(v5, v3) & ( ~ (v8 = v5) | ~ in(v6, v1)))))))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ function(v0) | ? [v2] : (relation_rng(v0) = v2 & ! [v3] : ! [v4] : ( ~ (apply(v0, v4) = v3) | ~ in(v4, v1) | in(v3, v2)) & ! [v3] : ( ~ in(v3, v2) | ? [v4] : (apply(v0, v4) = v3 & in(v4, v1))) & ? [v3] : (v3 = v2 | ? [v4] : ? [v5] : ? [v6] : (( ~ in(v4, v3) | ! [v7] : ( ~ (apply(v0, v7) = v4) | ~ in(v7, v1))) & (in(v4, v3) | (v6 = v4 & apply(v0, v5) = v4 & in(v5, v1))))))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | relation(v1)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | empty(v1)) & ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1)) & ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ( ~ in(v1, all_0_10_10) | ~ in(v0, all_0_11_11) | ? [v2] : ? [v3] : (apply(all_0_8_8, v1) = v3 & apply(all_0_12_12, v0) = v2 & ( ~ (v3 = v0) | v2 = v1) & ( ~ (v2 = v1) | v3 = v0))) & ! [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)
% 8.33/2.68 |
% 8.33/2.68 | Applying alpha-rule on (1) yields:
% 8.33/2.68 | (2) relation_dom(all_0_8_8) = all_0_10_10
% 8.33/2.68 | (3) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0))
% 8.33/2.68 | (4) function(all_0_8_8)
% 8.33/2.68 | (5) ? [v0] : ? [v1] : element(v1, v0)
% 8.33/2.68 | (6) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ element(v0, v2) | subset(v0, v1))
% 8.33/2.68 | (7) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2))
% 8.33/2.68 | (8) ! [v0] : ( ~ relation(v0) | ~ function(v0) | ~ empty(v0) | one_to_one(v0))
% 8.33/2.68 | (9) function_inverse(all_0_12_12) = all_0_9_9
% 8.33/2.68 | (10) relation(all_0_6_6)
% 8.33/2.68 | (11) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ function(v0) | ? [v2] : (relation_dom(v0) = v2 & ! [v3] : ! [v4] : ( ~ (apply(v0, v4) = v3) | ~ in(v4, v2) | in(v3, v1)) & ! [v3] : ( ~ in(v3, v1) | ? [v4] : (apply(v0, v4) = v3 & in(v4, v2))) & ? [v3] : (v3 = v1 | ? [v4] : ? [v5] : ? [v6] : (( ~ in(v4, v3) | ! [v7] : ( ~ (apply(v0, v7) = v4) | ~ in(v7, v2))) & (in(v4, v3) | (v6 = v4 & apply(v0, v5) = v4 & in(v5, v2)))))))
% 8.33/2.68 | (12) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0))
% 8.33/2.68 | (13) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | relation(v1))
% 8.33/2.68 | (14) ~ (all_0_8_8 = all_0_9_9)
% 8.33/2.68 | (15) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v0) = v1) | ~ relation(v2) | ~ relation(v0) | ~ function(v2) | ~ function(v0) | ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = v4) & apply(v2, v3) = v5 & apply(v0, v3) = v4 & in(v3, v1)))
% 8.33/2.69 | (16) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : (function_inverse(v0) = v2 & relation_dom(v0) = v3 & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v6 | ~ (relation_dom(v2) = v4) | ~ (apply(v2, v5) = v7) | ~ (apply(v0, v6) = v5) | ~ relation(v2) | ~ function(v2) | ~ in(v6, v3)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v5 | ~ (relation_dom(v2) = v4) | ~ (apply(v2, v5) = v6) | ~ (apply(v0, v6) = v7) | ~ relation(v2) | ~ function(v2) | ~ in(v5, v1)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (relation_dom(v2) = v4) | ~ (apply(v2, v5) = v7) | ~ (apply(v0, v6) = v5) | ~ relation(v2) | ~ function(v2) | ~ in(v6, v3) | in(v5, v1)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (relation_dom(v2) = v4) | ~ (apply(v2, v5) = v6) | ~ (apply(v0, v6) = v7) | ~ relation(v2) | ~ function(v2) | ~ in(v5, v1) | in(v6, v3)) & ! [v4] : (v4 = v2 | ~ (relation_dom(v4) = v1) | ~ relation(v4) | ~ function(v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (apply(v4, v5) = v7 & apply(v0, v6) = v8 & ((v8 = v5 & in(v6, v3) & ( ~ (v7 = v6) | ~ in(v5, v1))) | (v7 = v6 & in(v5, v1) & ( ~ (v8 = v5) | ~ in(v6, v3)))))) & ! [v4] : (v4 = v1 | ~ (relation_dom(v2) = v4) | ~ relation(v2) | ~ function(v2))))
% 8.33/2.69 | (17) ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1))
% 8.33/2.69 | (18) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | relation(v1))
% 8.33/2.69 | (19) ! [v0] : ( ~ empty(v0) | function(v0))
% 8.33/2.69 | (20) ~ empty(all_0_4_4)
% 8.33/2.69 | (21) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : (function_inverse(v0) = v2 & relation_rng(v0) = v3 & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v6 | ~ (relation_dom(v2) = v4) | ~ (apply(v2, v5) = v7) | ~ (apply(v0, v6) = v5) | ~ relation(v2) | ~ function(v2) | ~ in(v6, v1)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v5 | ~ (relation_dom(v2) = v4) | ~ (apply(v2, v5) = v6) | ~ (apply(v0, v6) = v7) | ~ relation(v2) | ~ function(v2) | ~ in(v5, v3)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (relation_dom(v2) = v4) | ~ (apply(v2, v5) = v7) | ~ (apply(v0, v6) = v5) | ~ relation(v2) | ~ function(v2) | ~ in(v6, v1) | in(v5, v3)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (relation_dom(v2) = v4) | ~ (apply(v2, v5) = v6) | ~ (apply(v0, v6) = v7) | ~ relation(v2) | ~ function(v2) | ~ in(v5, v3) | in(v6, v1)) & ! [v4] : (v4 = v3 | ~ (relation_dom(v2) = v4) | ~ relation(v2) | ~ function(v2)) & ! [v4] : (v4 = v2 | ~ (relation_dom(v4) = v3) | ~ relation(v4) | ~ function(v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (apply(v4, v5) = v7 & apply(v0, v6) = v8 & ((v8 = v5 & in(v6, v1) & ( ~ (v7 = v6) | ~ in(v5, v3))) | (v7 = v6 & in(v5, v3) & ( ~ (v8 = v5) | ~ in(v6, v1))))))))
% 8.41/2.69 | (22) one_to_one(all_0_6_6)
% 8.41/2.69 | (23) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ empty(v1))
% 8.41/2.69 | (24) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) & empty(v2)))
% 8.41/2.69 | (25) relation_empty_yielding(all_0_7_7)
% 8.41/2.69 | (26) ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : (relation_rng(v0) = v2 & relation_dom(v0) = v3 & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v6 | ~ (relation_dom(v1) = v4) | ~ (apply(v1, v5) = v7) | ~ (apply(v0, v6) = v5) | ~ relation(v1) | ~ function(v1) | ~ in(v6, v3)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v5 | ~ (relation_dom(v1) = v4) | ~ (apply(v1, v5) = v6) | ~ (apply(v0, v6) = v7) | ~ relation(v1) | ~ function(v1) | ~ in(v5, v2)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (relation_dom(v1) = v4) | ~ (apply(v1, v5) = v7) | ~ (apply(v0, v6) = v5) | ~ relation(v1) | ~ function(v1) | ~ in(v6, v3) | in(v5, v2)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (relation_dom(v1) = v4) | ~ (apply(v1, v5) = v6) | ~ (apply(v0, v6) = v7) | ~ relation(v1) | ~ function(v1) | ~ in(v5, v2) | in(v6, v3)) & ! [v4] : (v4 = v2 | ~ (relation_dom(v1) = v4) | ~ relation(v1) | ~ function(v1)) & ! [v4] : (v4 = v1 | ~ (relation_dom(v4) = v2) | ~ relation(v4) | ~ function(v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (apply(v4, v5) = v7 & apply(v0, v6) = v8 & ((v8 = v5 & in(v6, v3) & ( ~ (v7 = v6) | ~ in(v5, v2))) | (v7 = v6 & in(v5, v2) & ( ~ (v8 = v5) | ~ in(v6, v3))))))))
% 8.41/2.69 | (27) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ function(v0) | ? [v2] : (relation_rng(v0) = v2 & ! [v3] : ! [v4] : ( ~ (apply(v0, v4) = v3) | ~ in(v4, v1) | in(v3, v2)) & ! [v3] : ( ~ in(v3, v2) | ? [v4] : (apply(v0, v4) = v3 & in(v4, v1))) & ? [v3] : (v3 = v2 | ? [v4] : ? [v5] : ? [v6] : (( ~ in(v4, v3) | ! [v7] : ( ~ (apply(v0, v7) = v4) | ~ in(v7, v1))) & (in(v4, v3) | (v6 = v4 & apply(v0, v5) = v4 & in(v5, v1)))))))
% 8.41/2.70 | (28) relation(empty_set)
% 8.41/2.70 | (29) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0))
% 8.41/2.70 | (30) empty(all_0_1_1)
% 8.41/2.70 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ empty(v2) | ~ in(v0, v1))
% 8.41/2.70 | (32) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1))
% 8.41/2.70 | (33) relation(all_0_8_8)
% 8.41/2.70 | (34) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function_inverse(v2) = v1) | ~ (function_inverse(v2) = v0))
% 8.41/2.70 | (35) ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ relation(v0) | ~ function(v0) | function(v1))
% 8.41/2.70 | (36) relation(all_0_7_7)
% 8.41/2.70 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ in(v0, v1) | element(v0, v2))
% 8.41/2.70 | (38) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0))
% 8.41/2.70 | (39) relation_empty_yielding(empty_set)
% 8.41/2.70 | (40) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1))
% 8.41/2.70 | (41) ~ empty(all_0_5_5)
% 8.41/2.70 | (42) relation(all_0_4_4)
% 8.41/2.70 | (43) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0))
% 8.41/2.70 | (44) empty(empty_set)
% 8.41/2.70 | (45) function(all_0_12_12)
% 8.41/2.70 | (46) one_to_one(all_0_12_12)
% 8.41/2.70 | (47) relation_rng(all_0_12_12) = all_0_10_10
% 8.41/2.70 | (48) empty(all_0_2_2)
% 8.41/2.70 | (49) function(all_0_3_3)
% 8.41/2.70 | (50) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | empty(v1))
% 8.41/2.70 | (51) relation(all_0_12_12)
% 8.41/2.70 | (52) function(all_0_0_0)
% 8.41/2.70 | (53) ! [v0] : ! [v1] : ( ~ in(v1, all_0_10_10) | ~ in(v0, all_0_11_11) | ? [v2] : ? [v3] : (apply(all_0_8_8, v1) = v3 & apply(all_0_12_12, v0) = v2 & ( ~ (v3 = v0) | v2 = v1) & ( ~ (v2 = v1) | v3 = v0)))
% 8.41/2.70 | (54) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | empty(v1))
% 8.41/2.70 | (55) ! [v0] : ( ~ empty(v0) | relation(v0))
% 8.41/2.70 | (56) relation(all_0_0_0)
% 8.41/2.70 | (57) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (element(v2, v1) & ~ empty(v2)))
% 8.41/2.70 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0))
% 8.41/2.70 | (59) relation(all_0_3_3)
% 8.41/2.70 | (60) function(all_0_6_6)
% 8.41/2.70 | (61) relation_rng(all_0_8_8) = all_0_11_11
% 8.41/2.70 | (62) relation_dom(all_0_12_12) = all_0_11_11
% 8.41/2.70 | (63) ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ relation(v0) | ~ function(v0) | relation(v1))
% 8.41/2.70 | (64) empty(all_0_3_3)
% 8.41/2.70 | (65) relation(all_0_1_1)
% 8.41/2.70 | (66) ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1))
% 8.41/2.70 | (67) ! [v0] : (v0 = empty_set | ~ empty(v0))
% 8.41/2.70 | (68) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0))
% 8.41/2.70 | (69) ? [v0] : subset(v0, v0)
% 8.41/2.70 |
% 8.41/2.70 | Instantiating formula (27) with all_0_10_10, all_0_8_8 and discharging atoms relation_dom(all_0_8_8) = all_0_10_10, relation(all_0_8_8), function(all_0_8_8), yields:
% 8.41/2.70 | (70) ? [v0] : (relation_rng(all_0_8_8) = v0 & ! [v1] : ! [v2] : ( ~ (apply(all_0_8_8, v2) = v1) | ~ in(v2, all_0_10_10) | in(v1, v0)) & ! [v1] : ( ~ in(v1, v0) | ? [v2] : (apply(all_0_8_8, v2) = v1 & in(v2, all_0_10_10))) & ? [v1] : (v1 = v0 | ? [v2] : ? [v3] : ? [v4] : (( ~ in(v2, v1) | ! [v5] : ( ~ (apply(all_0_8_8, v5) = v2) | ~ in(v5, all_0_10_10))) & (in(v2, v1) | (v4 = v2 & apply(all_0_8_8, v3) = v2 & in(v3, all_0_10_10))))))
% 8.41/2.70 |
% 8.41/2.70 | Instantiating formula (11) with all_0_11_11, all_0_8_8 and discharging atoms relation_rng(all_0_8_8) = all_0_11_11, relation(all_0_8_8), function(all_0_8_8), yields:
% 8.41/2.70 | (71) ? [v0] : (relation_dom(all_0_8_8) = v0 & ! [v1] : ! [v2] : ( ~ (apply(all_0_8_8, v2) = v1) | ~ in(v2, v0) | in(v1, all_0_11_11)) & ! [v1] : ( ~ in(v1, all_0_11_11) | ? [v2] : (apply(all_0_8_8, v2) = v1 & in(v2, v0))) & ? [v1] : (v1 = all_0_11_11 | ? [v2] : ? [v3] : ? [v4] : (( ~ in(v2, v1) | ! [v5] : ( ~ (apply(all_0_8_8, v5) = v2) | ~ in(v5, v0))) & (in(v2, v1) | (v4 = v2 & apply(all_0_8_8, v3) = v2 & in(v3, v0))))))
% 8.41/2.70 |
% 8.41/2.70 | Instantiating formula (21) with all_0_11_11, all_0_12_12 and discharging atoms relation_dom(all_0_12_12) = all_0_11_11, one_to_one(all_0_12_12), relation(all_0_12_12), function(all_0_12_12), yields:
% 8.41/2.70 | (72) ? [v0] : ? [v1] : (function_inverse(all_0_12_12) = v0 & relation_rng(all_0_12_12) = v1 & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v4 | ~ (relation_dom(v0) = v2) | ~ (apply(v0, v3) = v5) | ~ (apply(all_0_12_12, v4) = v3) | ~ relation(v0) | ~ function(v0) | ~ in(v4, all_0_11_11)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v3 | ~ (relation_dom(v0) = v2) | ~ (apply(v0, v3) = v4) | ~ (apply(all_0_12_12, v4) = v5) | ~ relation(v0) | ~ function(v0) | ~ in(v3, v1)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_dom(v0) = v2) | ~ (apply(v0, v3) = v5) | ~ (apply(all_0_12_12, v4) = v3) | ~ relation(v0) | ~ function(v0) | ~ in(v4, all_0_11_11) | in(v3, v1)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_dom(v0) = v2) | ~ (apply(v0, v3) = v4) | ~ (apply(all_0_12_12, v4) = v5) | ~ relation(v0) | ~ function(v0) | ~ in(v3, v1) | in(v4, all_0_11_11)) & ! [v2] : (v2 = v1 | ~ (relation_dom(v0) = v2) | ~ relation(v0) | ~ function(v0)) & ! [v2] : (v2 = v0 | ~ (relation_dom(v2) = v1) | ~ relation(v2) | ~ function(v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (apply(v2, v3) = v5 & apply(all_0_12_12, v4) = v6 & ((v6 = v3 & in(v4, all_0_11_11) & ( ~ (v5 = v4) | ~ in(v3, v1))) | (v5 = v4 & in(v3, v1) & ( ~ (v6 = v3) | ~ in(v4, all_0_11_11)))))))
% 8.41/2.71 |
% 8.41/2.71 | Instantiating formula (27) with all_0_11_11, all_0_12_12 and discharging atoms relation_dom(all_0_12_12) = all_0_11_11, relation(all_0_12_12), function(all_0_12_12), yields:
% 8.41/2.71 | (73) ? [v0] : (relation_rng(all_0_12_12) = v0 & ! [v1] : ! [v2] : ( ~ (apply(all_0_12_12, v2) = v1) | ~ in(v2, all_0_11_11) | in(v1, v0)) & ! [v1] : ( ~ in(v1, v0) | ? [v2] : (apply(all_0_12_12, v2) = v1 & in(v2, all_0_11_11))) & ? [v1] : (v1 = v0 | ? [v2] : ? [v3] : ? [v4] : (( ~ in(v2, v1) | ! [v5] : ( ~ (apply(all_0_12_12, v5) = v2) | ~ in(v5, all_0_11_11))) & (in(v2, v1) | (v4 = v2 & apply(all_0_12_12, v3) = v2 & in(v3, all_0_11_11))))))
% 8.41/2.71 |
% 8.41/2.71 | Instantiating formula (26) with all_0_9_9, all_0_12_12 and discharging atoms function_inverse(all_0_12_12) = all_0_9_9, one_to_one(all_0_12_12), relation(all_0_12_12), function(all_0_12_12), yields:
% 8.41/2.71 | (74) ? [v0] : ? [v1] : (relation_rng(all_0_12_12) = v0 & relation_dom(all_0_12_12) = v1 & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v4 | ~ (relation_dom(all_0_9_9) = v2) | ~ (apply(all_0_9_9, v3) = v5) | ~ (apply(all_0_12_12, v4) = v3) | ~ relation(all_0_9_9) | ~ function(all_0_9_9) | ~ in(v4, v1)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v3 | ~ (relation_dom(all_0_9_9) = v2) | ~ (apply(all_0_9_9, v3) = v4) | ~ (apply(all_0_12_12, v4) = v5) | ~ relation(all_0_9_9) | ~ function(all_0_9_9) | ~ in(v3, v0)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_dom(all_0_9_9) = v2) | ~ (apply(all_0_9_9, v3) = v5) | ~ (apply(all_0_12_12, v4) = v3) | ~ relation(all_0_9_9) | ~ function(all_0_9_9) | ~ in(v4, v1) | in(v3, v0)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_dom(all_0_9_9) = v2) | ~ (apply(all_0_9_9, v3) = v4) | ~ (apply(all_0_12_12, v4) = v5) | ~ relation(all_0_9_9) | ~ function(all_0_9_9) | ~ in(v3, v0) | in(v4, v1)) & ! [v2] : (v2 = v0 | ~ (relation_dom(all_0_9_9) = v2) | ~ relation(all_0_9_9) | ~ function(all_0_9_9)) & ! [v2] : (v2 = all_0_9_9 | ~ (relation_dom(v2) = v0) | ~ relation(v2) | ~ function(v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (apply(v2, v3) = v5 & apply(all_0_12_12, v4) = v6 & ((v6 = v3 & in(v4, v1) & ( ~ (v5 = v4) | ~ in(v3, v0))) | (v5 = v4 & in(v3, v0) & ( ~ (v6 = v3) | ~ in(v4, v1)))))))
% 8.41/2.71 |
% 8.41/2.71 | Instantiating formula (16) with all_0_10_10, all_0_12_12 and discharging atoms relation_rng(all_0_12_12) = all_0_10_10, one_to_one(all_0_12_12), relation(all_0_12_12), function(all_0_12_12), yields:
% 8.41/2.71 | (75) ? [v0] : ? [v1] : (function_inverse(all_0_12_12) = v0 & relation_dom(all_0_12_12) = v1 & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v4 | ~ (relation_dom(v0) = v2) | ~ (apply(v0, v3) = v5) | ~ (apply(all_0_12_12, v4) = v3) | ~ relation(v0) | ~ function(v0) | ~ in(v4, v1)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v3 | ~ (relation_dom(v0) = v2) | ~ (apply(v0, v3) = v4) | ~ (apply(all_0_12_12, v4) = v5) | ~ relation(v0) | ~ function(v0) | ~ in(v3, all_0_10_10)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_dom(v0) = v2) | ~ (apply(v0, v3) = v5) | ~ (apply(all_0_12_12, v4) = v3) | ~ relation(v0) | ~ function(v0) | ~ in(v4, v1) | in(v3, all_0_10_10)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_dom(v0) = v2) | ~ (apply(v0, v3) = v4) | ~ (apply(all_0_12_12, v4) = v5) | ~ relation(v0) | ~ function(v0) | ~ in(v3, all_0_10_10) | in(v4, v1)) & ! [v2] : (v2 = v0 | ~ (relation_dom(v2) = all_0_10_10) | ~ relation(v2) | ~ function(v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (apply(v2, v3) = v5 & apply(all_0_12_12, v4) = v6 & ((v6 = v3 & in(v4, v1) & ( ~ (v5 = v4) | ~ in(v3, all_0_10_10))) | (v5 = v4 & in(v3, all_0_10_10) & ( ~ (v6 = v3) | ~ in(v4, v1)))))) & ! [v2] : (v2 = all_0_10_10 | ~ (relation_dom(v0) = v2) | ~ relation(v0) | ~ function(v0)))
% 8.41/2.71 |
% 8.41/2.71 | Instantiating formula (11) with all_0_10_10, all_0_12_12 and discharging atoms relation_rng(all_0_12_12) = all_0_10_10, relation(all_0_12_12), function(all_0_12_12), yields:
% 8.41/2.71 | (76) ? [v0] : (relation_dom(all_0_12_12) = v0 & ! [v1] : ! [v2] : ( ~ (apply(all_0_12_12, v2) = v1) | ~ in(v2, v0) | in(v1, all_0_10_10)) & ! [v1] : ( ~ in(v1, all_0_10_10) | ? [v2] : (apply(all_0_12_12, v2) = v1 & in(v2, v0))) & ? [v1] : (v1 = all_0_10_10 | ? [v2] : ? [v3] : ? [v4] : (( ~ in(v2, v1) | ! [v5] : ( ~ (apply(all_0_12_12, v5) = v2) | ~ in(v5, v0))) & (in(v2, v1) | (v4 = v2 & apply(all_0_12_12, v3) = v2 & in(v3, v0))))))
% 8.41/2.71 |
% 8.41/2.71 | Instantiating (74) with all_17_0_16, all_17_1_17 yields:
% 8.41/2.71 | (77) relation_rng(all_0_12_12) = all_17_1_17 & relation_dom(all_0_12_12) = all_17_0_16 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (relation_dom(all_0_9_9) = v0) | ~ (apply(all_0_9_9, v1) = v3) | ~ (apply(all_0_12_12, v2) = v1) | ~ relation(all_0_9_9) | ~ function(all_0_9_9) | ~ in(v2, all_17_0_16)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (relation_dom(all_0_9_9) = v0) | ~ (apply(all_0_9_9, v1) = v2) | ~ (apply(all_0_12_12, v2) = v3) | ~ relation(all_0_9_9) | ~ function(all_0_9_9) | ~ in(v1, all_17_1_17)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom(all_0_9_9) = v0) | ~ (apply(all_0_9_9, v1) = v3) | ~ (apply(all_0_12_12, v2) = v1) | ~ relation(all_0_9_9) | ~ function(all_0_9_9) | ~ in(v2, all_17_0_16) | in(v1, all_17_1_17)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom(all_0_9_9) = v0) | ~ (apply(all_0_9_9, v1) = v2) | ~ (apply(all_0_12_12, v2) = v3) | ~ relation(all_0_9_9) | ~ function(all_0_9_9) | ~ in(v1, all_17_1_17) | in(v2, all_17_0_16)) & ! [v0] : (v0 = all_17_1_17 | ~ (relation_dom(all_0_9_9) = v0) | ~ relation(all_0_9_9) | ~ function(all_0_9_9)) & ! [v0] : (v0 = all_0_9_9 | ~ (relation_dom(v0) = all_17_1_17) | ~ relation(v0) | ~ function(v0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : (apply(v0, v1) = v3 & apply(all_0_12_12, v2) = v4 & ((v4 = v1 & in(v2, all_17_0_16) & ( ~ (v3 = v2) | ~ in(v1, all_17_1_17))) | (v3 = v2 & in(v1, all_17_1_17) & ( ~ (v4 = v1) | ~ in(v2, all_17_0_16))))))
% 8.41/2.71 |
% 8.41/2.71 | Applying alpha-rule on (77) yields:
% 8.41/2.71 | (78) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom(all_0_9_9) = v0) | ~ (apply(all_0_9_9, v1) = v2) | ~ (apply(all_0_12_12, v2) = v3) | ~ relation(all_0_9_9) | ~ function(all_0_9_9) | ~ in(v1, all_17_1_17) | in(v2, all_17_0_16))
% 8.41/2.71 | (79) ! [v0] : (v0 = all_17_1_17 | ~ (relation_dom(all_0_9_9) = v0) | ~ relation(all_0_9_9) | ~ function(all_0_9_9))
% 8.52/2.71 | (80) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (relation_dom(all_0_9_9) = v0) | ~ (apply(all_0_9_9, v1) = v2) | ~ (apply(all_0_12_12, v2) = v3) | ~ relation(all_0_9_9) | ~ function(all_0_9_9) | ~ in(v1, all_17_1_17))
% 8.52/2.71 | (81) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (relation_dom(all_0_9_9) = v0) | ~ (apply(all_0_9_9, v1) = v3) | ~ (apply(all_0_12_12, v2) = v1) | ~ relation(all_0_9_9) | ~ function(all_0_9_9) | ~ in(v2, all_17_0_16))
% 8.52/2.71 | (82) relation_dom(all_0_12_12) = all_17_0_16
% 8.52/2.71 | (83) ! [v0] : (v0 = all_0_9_9 | ~ (relation_dom(v0) = all_17_1_17) | ~ relation(v0) | ~ function(v0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : (apply(v0, v1) = v3 & apply(all_0_12_12, v2) = v4 & ((v4 = v1 & in(v2, all_17_0_16) & ( ~ (v3 = v2) | ~ in(v1, all_17_1_17))) | (v3 = v2 & in(v1, all_17_1_17) & ( ~ (v4 = v1) | ~ in(v2, all_17_0_16))))))
% 8.52/2.71 | (84) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom(all_0_9_9) = v0) | ~ (apply(all_0_9_9, v1) = v3) | ~ (apply(all_0_12_12, v2) = v1) | ~ relation(all_0_9_9) | ~ function(all_0_9_9) | ~ in(v2, all_17_0_16) | in(v1, all_17_1_17))
% 8.52/2.71 | (85) relation_rng(all_0_12_12) = all_17_1_17
% 8.52/2.71 |
% 8.52/2.71 | Instantiating (76) with all_20_0_18 yields:
% 8.52/2.71 | (86) relation_dom(all_0_12_12) = all_20_0_18 & ! [v0] : ! [v1] : ( ~ (apply(all_0_12_12, v1) = v0) | ~ in(v1, all_20_0_18) | in(v0, all_0_10_10)) & ! [v0] : ( ~ in(v0, all_0_10_10) | ? [v1] : (apply(all_0_12_12, v1) = v0 & in(v1, all_20_0_18))) & ? [v0] : (v0 = all_0_10_10 | ? [v1] : ? [v2] : ? [v3] : (( ~ in(v1, v0) | ! [v4] : ( ~ (apply(all_0_12_12, v4) = v1) | ~ in(v4, all_20_0_18))) & (in(v1, v0) | (v3 = v1 & apply(all_0_12_12, v2) = v1 & in(v2, all_20_0_18)))))
% 8.52/2.71 |
% 8.52/2.71 | Applying alpha-rule on (86) yields:
% 8.52/2.71 | (87) relation_dom(all_0_12_12) = all_20_0_18
% 8.52/2.71 | (88) ! [v0] : ! [v1] : ( ~ (apply(all_0_12_12, v1) = v0) | ~ in(v1, all_20_0_18) | in(v0, all_0_10_10))
% 8.52/2.71 | (89) ! [v0] : ( ~ in(v0, all_0_10_10) | ? [v1] : (apply(all_0_12_12, v1) = v0 & in(v1, all_20_0_18)))
% 8.52/2.71 | (90) ? [v0] : (v0 = all_0_10_10 | ? [v1] : ? [v2] : ? [v3] : (( ~ in(v1, v0) | ! [v4] : ( ~ (apply(all_0_12_12, v4) = v1) | ~ in(v4, all_20_0_18))) & (in(v1, v0) | (v3 = v1 & apply(all_0_12_12, v2) = v1 & in(v2, all_20_0_18)))))
% 8.52/2.71 |
% 8.52/2.71 | Instantiating (75) with all_23_0_19, all_23_1_20 yields:
% 8.52/2.71 | (91) function_inverse(all_0_12_12) = all_23_1_20 & relation_dom(all_0_12_12) = all_23_0_19 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (relation_dom(all_23_1_20) = v0) | ~ (apply(all_23_1_20, v1) = v3) | ~ (apply(all_0_12_12, v2) = v1) | ~ relation(all_23_1_20) | ~ function(all_23_1_20) | ~ in(v2, all_23_0_19)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (relation_dom(all_23_1_20) = v0) | ~ (apply(all_23_1_20, v1) = v2) | ~ (apply(all_0_12_12, v2) = v3) | ~ relation(all_23_1_20) | ~ function(all_23_1_20) | ~ in(v1, all_0_10_10)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom(all_23_1_20) = v0) | ~ (apply(all_23_1_20, v1) = v3) | ~ (apply(all_0_12_12, v2) = v1) | ~ relation(all_23_1_20) | ~ function(all_23_1_20) | ~ in(v2, all_23_0_19) | in(v1, all_0_10_10)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom(all_23_1_20) = v0) | ~ (apply(all_23_1_20, v1) = v2) | ~ (apply(all_0_12_12, v2) = v3) | ~ relation(all_23_1_20) | ~ function(all_23_1_20) | ~ in(v1, all_0_10_10) | in(v2, all_23_0_19)) & ! [v0] : (v0 = all_23_1_20 | ~ (relation_dom(v0) = all_0_10_10) | ~ relation(v0) | ~ function(v0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : (apply(v0, v1) = v3 & apply(all_0_12_12, v2) = v4 & ((v4 = v1 & in(v2, all_23_0_19) & ( ~ (v3 = v2) | ~ in(v1, all_0_10_10))) | (v3 = v2 & in(v1, all_0_10_10) & ( ~ (v4 = v1) | ~ in(v2, all_23_0_19)))))) & ! [v0] : (v0 = all_0_10_10 | ~ (relation_dom(all_23_1_20) = v0) | ~ relation(all_23_1_20) | ~ function(all_23_1_20))
% 8.52/2.72 |
% 8.52/2.72 | Applying alpha-rule on (91) yields:
% 8.52/2.72 | (92) function_inverse(all_0_12_12) = all_23_1_20
% 8.52/2.72 | (93) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (relation_dom(all_23_1_20) = v0) | ~ (apply(all_23_1_20, v1) = v3) | ~ (apply(all_0_12_12, v2) = v1) | ~ relation(all_23_1_20) | ~ function(all_23_1_20) | ~ in(v2, all_23_0_19))
% 8.52/2.72 | (94) ! [v0] : (v0 = all_0_10_10 | ~ (relation_dom(all_23_1_20) = v0) | ~ relation(all_23_1_20) | ~ function(all_23_1_20))
% 8.52/2.72 | (95) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom(all_23_1_20) = v0) | ~ (apply(all_23_1_20, v1) = v2) | ~ (apply(all_0_12_12, v2) = v3) | ~ relation(all_23_1_20) | ~ function(all_23_1_20) | ~ in(v1, all_0_10_10) | in(v2, all_23_0_19))
% 8.52/2.72 | (96) ! [v0] : (v0 = all_23_1_20 | ~ (relation_dom(v0) = all_0_10_10) | ~ relation(v0) | ~ function(v0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : (apply(v0, v1) = v3 & apply(all_0_12_12, v2) = v4 & ((v4 = v1 & in(v2, all_23_0_19) & ( ~ (v3 = v2) | ~ in(v1, all_0_10_10))) | (v3 = v2 & in(v1, all_0_10_10) & ( ~ (v4 = v1) | ~ in(v2, all_23_0_19))))))
% 8.52/2.72 | (97) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (relation_dom(all_23_1_20) = v0) | ~ (apply(all_23_1_20, v1) = v2) | ~ (apply(all_0_12_12, v2) = v3) | ~ relation(all_23_1_20) | ~ function(all_23_1_20) | ~ in(v1, all_0_10_10))
% 8.52/2.72 | (98) relation_dom(all_0_12_12) = all_23_0_19
% 8.52/2.72 | (99) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom(all_23_1_20) = v0) | ~ (apply(all_23_1_20, v1) = v3) | ~ (apply(all_0_12_12, v2) = v1) | ~ relation(all_23_1_20) | ~ function(all_23_1_20) | ~ in(v2, all_23_0_19) | in(v1, all_0_10_10))
% 8.52/2.72 |
% 8.52/2.72 | Instantiating formula (96) with all_0_8_8 and discharging atoms relation_dom(all_0_8_8) = all_0_10_10, relation(all_0_8_8), function(all_0_8_8), yields:
% 8.52/2.72 | (100) all_23_1_20 = all_0_8_8 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apply(all_0_8_8, v0) = v2 & apply(all_0_12_12, v1) = v3 & ((v3 = v0 & in(v1, all_23_0_19) & ( ~ (v2 = v1) | ~ in(v0, all_0_10_10))) | (v2 = v1 & in(v0, all_0_10_10) & ( ~ (v3 = v0) | ~ in(v1, all_23_0_19)))))
% 8.52/2.72 |
% 8.52/2.72 | Instantiating (73) with all_26_0_21 yields:
% 8.52/2.72 | (101) relation_rng(all_0_12_12) = all_26_0_21 & ! [v0] : ! [v1] : ( ~ (apply(all_0_12_12, v1) = v0) | ~ in(v1, all_0_11_11) | in(v0, all_26_0_21)) & ! [v0] : ( ~ in(v0, all_26_0_21) | ? [v1] : (apply(all_0_12_12, v1) = v0 & in(v1, all_0_11_11))) & ? [v0] : (v0 = all_26_0_21 | ? [v1] : ? [v2] : ? [v3] : (( ~ in(v1, v0) | ! [v4] : ( ~ (apply(all_0_12_12, v4) = v1) | ~ in(v4, all_0_11_11))) & (in(v1, v0) | (v3 = v1 & apply(all_0_12_12, v2) = v1 & in(v2, all_0_11_11)))))
% 8.52/2.72 |
% 8.52/2.72 | Applying alpha-rule on (101) yields:
% 8.52/2.72 | (102) relation_rng(all_0_12_12) = all_26_0_21
% 8.52/2.72 | (103) ! [v0] : ! [v1] : ( ~ (apply(all_0_12_12, v1) = v0) | ~ in(v1, all_0_11_11) | in(v0, all_26_0_21))
% 8.52/2.72 | (104) ! [v0] : ( ~ in(v0, all_26_0_21) | ? [v1] : (apply(all_0_12_12, v1) = v0 & in(v1, all_0_11_11)))
% 8.52/2.72 | (105) ? [v0] : (v0 = all_26_0_21 | ? [v1] : ? [v2] : ? [v3] : (( ~ in(v1, v0) | ! [v4] : ( ~ (apply(all_0_12_12, v4) = v1) | ~ in(v4, all_0_11_11))) & (in(v1, v0) | (v3 = v1 & apply(all_0_12_12, v2) = v1 & in(v2, all_0_11_11)))))
% 8.56/2.72 |
% 8.56/2.72 | Instantiating (72) with all_29_0_22, all_29_1_23 yields:
% 8.56/2.72 | (106) function_inverse(all_0_12_12) = all_29_1_23 & relation_rng(all_0_12_12) = all_29_0_22 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (relation_dom(all_29_1_23) = v0) | ~ (apply(all_29_1_23, v1) = v3) | ~ (apply(all_0_12_12, v2) = v1) | ~ relation(all_29_1_23) | ~ function(all_29_1_23) | ~ in(v2, all_0_11_11)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (relation_dom(all_29_1_23) = v0) | ~ (apply(all_29_1_23, v1) = v2) | ~ (apply(all_0_12_12, v2) = v3) | ~ relation(all_29_1_23) | ~ function(all_29_1_23) | ~ in(v1, all_29_0_22)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom(all_29_1_23) = v0) | ~ (apply(all_29_1_23, v1) = v3) | ~ (apply(all_0_12_12, v2) = v1) | ~ relation(all_29_1_23) | ~ function(all_29_1_23) | ~ in(v2, all_0_11_11) | in(v1, all_29_0_22)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom(all_29_1_23) = v0) | ~ (apply(all_29_1_23, v1) = v2) | ~ (apply(all_0_12_12, v2) = v3) | ~ relation(all_29_1_23) | ~ function(all_29_1_23) | ~ in(v1, all_29_0_22) | in(v2, all_0_11_11)) & ! [v0] : (v0 = all_29_0_22 | ~ (relation_dom(all_29_1_23) = v0) | ~ relation(all_29_1_23) | ~ function(all_29_1_23)) & ! [v0] : (v0 = all_29_1_23 | ~ (relation_dom(v0) = all_29_0_22) | ~ relation(v0) | ~ function(v0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : (apply(v0, v1) = v3 & apply(all_0_12_12, v2) = v4 & ((v4 = v1 & in(v2, all_0_11_11) & ( ~ (v3 = v2) | ~ in(v1, all_29_0_22))) | (v3 = v2 & in(v1, all_29_0_22) & ( ~ (v4 = v1) | ~ in(v2, all_0_11_11))))))
% 8.56/2.72 |
% 8.56/2.72 | Applying alpha-rule on (106) yields:
% 8.56/2.72 | (107) ! [v0] : (v0 = all_29_0_22 | ~ (relation_dom(all_29_1_23) = v0) | ~ relation(all_29_1_23) | ~ function(all_29_1_23))
% 8.56/2.72 | (108) ! [v0] : (v0 = all_29_1_23 | ~ (relation_dom(v0) = all_29_0_22) | ~ relation(v0) | ~ function(v0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : (apply(v0, v1) = v3 & apply(all_0_12_12, v2) = v4 & ((v4 = v1 & in(v2, all_0_11_11) & ( ~ (v3 = v2) | ~ in(v1, all_29_0_22))) | (v3 = v2 & in(v1, all_29_0_22) & ( ~ (v4 = v1) | ~ in(v2, all_0_11_11))))))
% 8.56/2.72 | (109) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom(all_29_1_23) = v0) | ~ (apply(all_29_1_23, v1) = v3) | ~ (apply(all_0_12_12, v2) = v1) | ~ relation(all_29_1_23) | ~ function(all_29_1_23) | ~ in(v2, all_0_11_11) | in(v1, all_29_0_22))
% 8.56/2.72 | (110) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom(all_29_1_23) = v0) | ~ (apply(all_29_1_23, v1) = v2) | ~ (apply(all_0_12_12, v2) = v3) | ~ relation(all_29_1_23) | ~ function(all_29_1_23) | ~ in(v1, all_29_0_22) | in(v2, all_0_11_11))
% 8.56/2.72 | (111) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (relation_dom(all_29_1_23) = v0) | ~ (apply(all_29_1_23, v1) = v3) | ~ (apply(all_0_12_12, v2) = v1) | ~ relation(all_29_1_23) | ~ function(all_29_1_23) | ~ in(v2, all_0_11_11))
% 8.56/2.72 | (112) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (relation_dom(all_29_1_23) = v0) | ~ (apply(all_29_1_23, v1) = v2) | ~ (apply(all_0_12_12, v2) = v3) | ~ relation(all_29_1_23) | ~ function(all_29_1_23) | ~ in(v1, all_29_0_22))
% 8.56/2.72 | (113) function_inverse(all_0_12_12) = all_29_1_23
% 8.56/2.72 | (114) relation_rng(all_0_12_12) = all_29_0_22
% 8.56/2.72 |
% 8.56/2.72 | Instantiating (70) with all_32_0_24 yields:
% 8.56/2.72 | (115) relation_rng(all_0_8_8) = all_32_0_24 & ! [v0] : ! [v1] : ( ~ (apply(all_0_8_8, v1) = v0) | ~ in(v1, all_0_10_10) | in(v0, all_32_0_24)) & ! [v0] : ( ~ in(v0, all_32_0_24) | ? [v1] : (apply(all_0_8_8, v1) = v0 & in(v1, all_0_10_10))) & ? [v0] : (v0 = all_32_0_24 | ? [v1] : ? [v2] : ? [v3] : (( ~ in(v1, v0) | ! [v4] : ( ~ (apply(all_0_8_8, v4) = v1) | ~ in(v4, all_0_10_10))) & (in(v1, v0) | (v3 = v1 & apply(all_0_8_8, v2) = v1 & in(v2, all_0_10_10)))))
% 8.56/2.72 |
% 8.56/2.72 | Applying alpha-rule on (115) yields:
% 8.56/2.72 | (116) relation_rng(all_0_8_8) = all_32_0_24
% 8.56/2.72 | (117) ! [v0] : ! [v1] : ( ~ (apply(all_0_8_8, v1) = v0) | ~ in(v1, all_0_10_10) | in(v0, all_32_0_24))
% 8.56/2.72 | (118) ! [v0] : ( ~ in(v0, all_32_0_24) | ? [v1] : (apply(all_0_8_8, v1) = v0 & in(v1, all_0_10_10)))
% 8.56/2.72 | (119) ? [v0] : (v0 = all_32_0_24 | ? [v1] : ? [v2] : ? [v3] : (( ~ in(v1, v0) | ! [v4] : ( ~ (apply(all_0_8_8, v4) = v1) | ~ in(v4, all_0_10_10))) & (in(v1, v0) | (v3 = v1 & apply(all_0_8_8, v2) = v1 & in(v2, all_0_10_10)))))
% 8.56/2.72 |
% 8.56/2.72 | Instantiating (71) with all_35_0_25 yields:
% 8.56/2.72 | (120) relation_dom(all_0_8_8) = all_35_0_25 & ! [v0] : ! [v1] : ( ~ (apply(all_0_8_8, v1) = v0) | ~ in(v1, all_35_0_25) | in(v0, all_0_11_11)) & ! [v0] : ( ~ in(v0, all_0_11_11) | ? [v1] : (apply(all_0_8_8, v1) = v0 & in(v1, all_35_0_25))) & ? [v0] : (v0 = all_0_11_11 | ? [v1] : ? [v2] : ? [v3] : (( ~ in(v1, v0) | ! [v4] : ( ~ (apply(all_0_8_8, v4) = v1) | ~ in(v4, all_35_0_25))) & (in(v1, v0) | (v3 = v1 & apply(all_0_8_8, v2) = v1 & in(v2, all_35_0_25)))))
% 8.56/2.72 |
% 8.56/2.72 | Applying alpha-rule on (120) yields:
% 8.56/2.72 | (121) relation_dom(all_0_8_8) = all_35_0_25
% 8.56/2.72 | (122) ! [v0] : ! [v1] : ( ~ (apply(all_0_8_8, v1) = v0) | ~ in(v1, all_35_0_25) | in(v0, all_0_11_11))
% 8.56/2.72 | (123) ! [v0] : ( ~ in(v0, all_0_11_11) | ? [v1] : (apply(all_0_8_8, v1) = v0 & in(v1, all_35_0_25)))
% 8.56/2.72 | (124) ? [v0] : (v0 = all_0_11_11 | ? [v1] : ? [v2] : ? [v3] : (( ~ in(v1, v0) | ! [v4] : ( ~ (apply(all_0_8_8, v4) = v1) | ~ in(v4, all_35_0_25))) & (in(v1, v0) | (v3 = v1 & apply(all_0_8_8, v2) = v1 & in(v2, all_35_0_25)))))
% 8.56/2.73 |
% 8.56/2.73 | Instantiating formula (34) with all_0_12_12, all_29_1_23, all_0_9_9 and discharging atoms function_inverse(all_0_12_12) = all_29_1_23, function_inverse(all_0_12_12) = all_0_9_9, yields:
% 8.56/2.73 | (125) all_29_1_23 = all_0_9_9
% 8.56/2.73 |
% 8.56/2.73 | Instantiating formula (34) with all_0_12_12, all_23_1_20, all_29_1_23 and discharging atoms function_inverse(all_0_12_12) = all_29_1_23, function_inverse(all_0_12_12) = all_23_1_20, yields:
% 8.56/2.73 | (126) all_29_1_23 = all_23_1_20
% 8.56/2.73 |
% 8.56/2.73 | Instantiating formula (43) with all_0_8_8, all_32_0_24, all_0_11_11 and discharging atoms relation_rng(all_0_8_8) = all_32_0_24, relation_rng(all_0_8_8) = all_0_11_11, yields:
% 8.56/2.73 | (127) all_32_0_24 = all_0_11_11
% 8.56/2.73 |
% 8.56/2.73 | Instantiating formula (43) with all_0_12_12, all_29_0_22, all_0_10_10 and discharging atoms relation_rng(all_0_12_12) = all_29_0_22, relation_rng(all_0_12_12) = all_0_10_10, yields:
% 8.56/2.73 | (128) all_29_0_22 = all_0_10_10
% 8.56/2.73 |
% 8.56/2.73 | Instantiating formula (43) with all_0_12_12, all_26_0_21, all_29_0_22 and discharging atoms relation_rng(all_0_12_12) = all_29_0_22, relation_rng(all_0_12_12) = all_26_0_21, yields:
% 8.56/2.73 | (129) all_29_0_22 = all_26_0_21
% 8.56/2.73 |
% 8.56/2.73 | Instantiating formula (68) with all_0_8_8, all_35_0_25, all_0_10_10 and discharging atoms relation_dom(all_0_8_8) = all_35_0_25, relation_dom(all_0_8_8) = all_0_10_10, yields:
% 8.56/2.73 | (130) all_35_0_25 = all_0_10_10
% 8.56/2.73 |
% 8.56/2.73 | Instantiating formula (68) with all_0_12_12, all_20_0_18, all_0_11_11 and discharging atoms relation_dom(all_0_12_12) = all_20_0_18, relation_dom(all_0_12_12) = all_0_11_11, yields:
% 8.56/2.73 | (131) all_20_0_18 = all_0_11_11
% 8.56/2.73 |
% 8.56/2.73 | Instantiating formula (68) with all_0_12_12, all_20_0_18, all_23_0_19 and discharging atoms relation_dom(all_0_12_12) = all_23_0_19, relation_dom(all_0_12_12) = all_20_0_18, yields:
% 8.56/2.73 | (132) all_23_0_19 = all_20_0_18
% 8.56/2.73 |
% 8.56/2.73 | Instantiating formula (68) with all_0_12_12, all_17_0_16, all_23_0_19 and discharging atoms relation_dom(all_0_12_12) = all_23_0_19, relation_dom(all_0_12_12) = all_17_0_16, yields:
% 8.56/2.73 | (133) all_23_0_19 = all_17_0_16
% 8.56/2.73 |
% 8.56/2.73 | Combining equations (128,129) yields a new equation:
% 8.56/2.73 | (134) all_26_0_21 = all_0_10_10
% 8.56/2.73 |
% 8.56/2.73 | Combining equations (126,125) yields a new equation:
% 8.56/2.73 | (135) all_23_1_20 = all_0_9_9
% 8.56/2.73 |
% 8.56/2.73 | Simplifying 135 yields:
% 8.56/2.73 | (136) all_23_1_20 = all_0_9_9
% 8.56/2.73 |
% 8.56/2.73 | Combining equations (132,133) yields a new equation:
% 8.56/2.73 | (137) all_20_0_18 = all_17_0_16
% 8.56/2.73 |
% 8.56/2.73 | Simplifying 137 yields:
% 8.56/2.73 | (138) all_20_0_18 = all_17_0_16
% 8.56/2.73 |
% 8.56/2.73 | Combining equations (138,131) yields a new equation:
% 8.56/2.73 | (139) all_17_0_16 = all_0_11_11
% 8.56/2.73 |
% 8.56/2.73 | Simplifying 139 yields:
% 8.56/2.73 | (140) all_17_0_16 = all_0_11_11
% 8.56/2.73 |
% 8.56/2.73 | Combining equations (140,133) yields a new equation:
% 8.56/2.73 | (141) all_23_0_19 = all_0_11_11
% 8.56/2.73 |
% 8.56/2.73 +-Applying beta-rule and splitting (100), into two cases.
% 8.56/2.73 |-Branch one:
% 8.56/2.73 | (142) all_23_1_20 = all_0_8_8
% 8.56/2.73 |
% 8.56/2.73 | Combining equations (136,142) yields a new equation:
% 8.56/2.73 | (143) all_0_8_8 = all_0_9_9
% 8.56/2.73 |
% 8.56/2.73 | Equations (143) can reduce 14 to:
% 8.56/2.73 | (144) $false
% 8.56/2.73 |
% 8.56/2.73 |-The branch is then unsatisfiable
% 8.56/2.73 |-Branch two:
% 8.56/2.73 | (145) ~ (all_23_1_20 = all_0_8_8)
% 8.56/2.73 | (146) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apply(all_0_8_8, v0) = v2 & apply(all_0_12_12, v1) = v3 & ((v3 = v0 & in(v1, all_23_0_19) & ( ~ (v2 = v1) | ~ in(v0, all_0_10_10))) | (v2 = v1 & in(v0, all_0_10_10) & ( ~ (v3 = v0) | ~ in(v1, all_23_0_19)))))
% 8.56/2.73 |
% 8.56/2.73 | Instantiating (146) with all_50_0_30, all_50_1_31, all_50_2_32, all_50_3_33 yields:
% 8.56/2.73 | (147) apply(all_0_8_8, all_50_3_33) = all_50_1_31 & apply(all_0_12_12, all_50_2_32) = all_50_0_30 & ((all_50_0_30 = all_50_3_33 & in(all_50_2_32, all_23_0_19) & ( ~ (all_50_1_31 = all_50_2_32) | ~ in(all_50_3_33, all_0_10_10))) | (all_50_1_31 = all_50_2_32 & in(all_50_3_33, all_0_10_10) & ( ~ (all_50_0_30 = all_50_3_33) | ~ in(all_50_2_32, all_23_0_19))))
% 8.56/2.73 |
% 8.56/2.73 | Applying alpha-rule on (147) yields:
% 8.56/2.73 | (148) apply(all_0_8_8, all_50_3_33) = all_50_1_31
% 8.56/2.73 | (149) apply(all_0_12_12, all_50_2_32) = all_50_0_30
% 8.56/2.73 | (150) (all_50_0_30 = all_50_3_33 & in(all_50_2_32, all_23_0_19) & ( ~ (all_50_1_31 = all_50_2_32) | ~ in(all_50_3_33, all_0_10_10))) | (all_50_1_31 = all_50_2_32 & in(all_50_3_33, all_0_10_10) & ( ~ (all_50_0_30 = all_50_3_33) | ~ in(all_50_2_32, all_23_0_19)))
% 8.56/2.73 |
% 8.56/2.73 +-Applying beta-rule and splitting (150), into two cases.
% 8.56/2.73 |-Branch one:
% 8.56/2.73 | (151) all_50_0_30 = all_50_3_33 & in(all_50_2_32, all_23_0_19) & ( ~ (all_50_1_31 = all_50_2_32) | ~ in(all_50_3_33, all_0_10_10))
% 8.56/2.73 |
% 8.56/2.73 | Applying alpha-rule on (151) yields:
% 8.56/2.73 | (152) all_50_0_30 = all_50_3_33
% 8.56/2.73 | (153) in(all_50_2_32, all_23_0_19)
% 8.56/2.73 | (154) ~ (all_50_1_31 = all_50_2_32) | ~ in(all_50_3_33, all_0_10_10)
% 8.56/2.73 |
% 8.56/2.73 | From (152) and (149) follows:
% 8.56/2.73 | (155) apply(all_0_12_12, all_50_2_32) = all_50_3_33
% 8.56/2.73 |
% 8.56/2.73 | From (141) and (153) follows:
% 8.56/2.73 | (156) in(all_50_2_32, all_0_11_11)
% 8.56/2.73 |
% 8.56/2.73 | Instantiating formula (103) with all_50_2_32, all_50_3_33 and discharging atoms apply(all_0_12_12, all_50_2_32) = all_50_3_33, in(all_50_2_32, all_0_11_11), yields:
% 8.56/2.73 | (157) in(all_50_3_33, all_26_0_21)
% 8.56/2.73 |
% 8.56/2.73 | Instantiating formula (123) with all_50_2_32 and discharging atoms in(all_50_2_32, all_0_11_11), yields:
% 8.56/2.73 | (158) ? [v0] : (apply(all_0_8_8, v0) = all_50_2_32 & in(v0, all_35_0_25))
% 8.56/2.73 |
% 8.56/2.73 | Instantiating formula (118) with all_50_2_32 yields:
% 8.56/2.73 | (159) ~ in(all_50_2_32, all_32_0_24) | ? [v0] : (apply(all_0_8_8, v0) = all_50_2_32 & in(v0, all_0_10_10))
% 8.56/2.73 |
% 8.56/2.73 | Instantiating (158) with all_100_0_34 yields:
% 8.56/2.73 | (160) apply(all_0_8_8, all_100_0_34) = all_50_2_32 & in(all_100_0_34, all_35_0_25)
% 8.56/2.73 |
% 8.56/2.73 | Applying alpha-rule on (160) yields:
% 8.56/2.73 | (161) apply(all_0_8_8, all_100_0_34) = all_50_2_32
% 8.56/2.73 | (162) in(all_100_0_34, all_35_0_25)
% 8.56/2.73 |
% 8.56/2.73 | From (130) and (162) follows:
% 8.56/2.73 | (163) in(all_100_0_34, all_0_10_10)
% 8.56/2.73 |
% 8.56/2.73 | From (134) and (157) follows:
% 8.56/2.73 | (164) in(all_50_3_33, all_0_10_10)
% 8.56/2.73 |
% 8.56/2.73 +-Applying beta-rule and splitting (154), into two cases.
% 8.56/2.73 |-Branch one:
% 8.56/2.73 | (165) ~ in(all_50_3_33, all_0_10_10)
% 8.56/2.73 |
% 8.56/2.73 | Using (164) and (165) yields:
% 8.56/2.73 | (166) $false
% 8.56/2.73 |
% 8.56/2.73 |-The branch is then unsatisfiable
% 8.56/2.73 |-Branch two:
% 8.56/2.73 | (164) in(all_50_3_33, all_0_10_10)
% 8.56/2.73 | (168) ~ (all_50_1_31 = all_50_2_32)
% 8.56/2.73 |
% 8.56/2.73 +-Applying beta-rule and splitting (159), into two cases.
% 8.56/2.73 |-Branch one:
% 8.56/2.73 | (169) ~ in(all_50_2_32, all_32_0_24)
% 8.56/2.73 |
% 8.56/2.73 | From (127) and (169) follows:
% 8.56/2.73 | (170) ~ in(all_50_2_32, all_0_11_11)
% 8.56/2.73 |
% 8.56/2.73 | Using (156) and (170) yields:
% 8.56/2.73 | (166) $false
% 8.56/2.73 |
% 8.56/2.73 |-The branch is then unsatisfiable
% 8.56/2.73 |-Branch two:
% 8.56/2.73 | (172) in(all_50_2_32, all_32_0_24)
% 8.56/2.73 | (173) ? [v0] : (apply(all_0_8_8, v0) = all_50_2_32 & in(v0, all_0_10_10))
% 8.56/2.73 |
% 8.56/2.73 | Instantiating (173) with all_110_0_35 yields:
% 8.56/2.73 | (174) apply(all_0_8_8, all_110_0_35) = all_50_2_32 & in(all_110_0_35, all_0_10_10)
% 8.56/2.73 |
% 8.56/2.73 | Applying alpha-rule on (174) yields:
% 8.56/2.73 | (175) apply(all_0_8_8, all_110_0_35) = all_50_2_32
% 8.56/2.73 | (176) in(all_110_0_35, all_0_10_10)
% 8.56/2.73 |
% 8.56/2.73 | From (127) and (172) follows:
% 8.56/2.73 | (156) in(all_50_2_32, all_0_11_11)
% 8.56/2.73 |
% 8.56/2.73 | Instantiating formula (53) with all_110_0_35, all_50_2_32 and discharging atoms in(all_110_0_35, all_0_10_10), in(all_50_2_32, all_0_11_11), yields:
% 8.56/2.73 | (178) ? [v0] : ? [v1] : (apply(all_0_8_8, all_110_0_35) = v1 & apply(all_0_12_12, all_50_2_32) = v0 & ( ~ (v1 = all_50_2_32) | v0 = all_110_0_35) & ( ~ (v0 = all_110_0_35) | v1 = all_50_2_32))
% 8.56/2.73 |
% 8.56/2.73 | Instantiating formula (53) with all_100_0_34, all_50_2_32 and discharging atoms in(all_100_0_34, all_0_10_10), in(all_50_2_32, all_0_11_11), yields:
% 8.56/2.73 | (179) ? [v0] : ? [v1] : (apply(all_0_8_8, all_100_0_34) = v1 & apply(all_0_12_12, all_50_2_32) = v0 & ( ~ (v1 = all_50_2_32) | v0 = all_100_0_34) & ( ~ (v0 = all_100_0_34) | v1 = all_50_2_32))
% 8.56/2.73 |
% 8.56/2.73 | Instantiating formula (53) with all_50_3_33, all_50_2_32 and discharging atoms in(all_50_2_32, all_0_11_11), in(all_50_3_33, all_0_10_10), yields:
% 8.56/2.73 | (180) ? [v0] : ? [v1] : (apply(all_0_8_8, all_50_3_33) = v1 & apply(all_0_12_12, all_50_2_32) = v0 & ( ~ (v1 = all_50_2_32) | v0 = all_50_3_33) & ( ~ (v0 = all_50_3_33) | v1 = all_50_2_32))
% 8.56/2.73 |
% 8.56/2.73 | Instantiating (179) with all_122_0_38, all_122_1_39 yields:
% 8.56/2.73 | (181) apply(all_0_8_8, all_100_0_34) = all_122_0_38 & apply(all_0_12_12, all_50_2_32) = all_122_1_39 & ( ~ (all_122_0_38 = all_50_2_32) | all_122_1_39 = all_100_0_34) & ( ~ (all_122_1_39 = all_100_0_34) | all_122_0_38 = all_50_2_32)
% 8.56/2.73 |
% 8.56/2.73 | Applying alpha-rule on (181) yields:
% 8.56/2.73 | (182) apply(all_0_8_8, all_100_0_34) = all_122_0_38
% 8.56/2.73 | (183) apply(all_0_12_12, all_50_2_32) = all_122_1_39
% 8.56/2.73 | (184) ~ (all_122_0_38 = all_50_2_32) | all_122_1_39 = all_100_0_34
% 8.56/2.73 | (185) ~ (all_122_1_39 = all_100_0_34) | all_122_0_38 = all_50_2_32
% 8.56/2.73 |
% 8.56/2.73 | Instantiating (180) with all_126_0_41, all_126_1_42 yields:
% 8.56/2.73 | (186) apply(all_0_8_8, all_50_3_33) = all_126_0_41 & apply(all_0_12_12, all_50_2_32) = all_126_1_42 & ( ~ (all_126_0_41 = all_50_2_32) | all_126_1_42 = all_50_3_33) & ( ~ (all_126_1_42 = all_50_3_33) | all_126_0_41 = all_50_2_32)
% 8.56/2.73 |
% 8.56/2.73 | Applying alpha-rule on (186) yields:
% 8.56/2.73 | (187) apply(all_0_8_8, all_50_3_33) = all_126_0_41
% 8.56/2.73 | (188) apply(all_0_12_12, all_50_2_32) = all_126_1_42
% 8.56/2.73 | (189) ~ (all_126_0_41 = all_50_2_32) | all_126_1_42 = all_50_3_33
% 8.56/2.73 | (190) ~ (all_126_1_42 = all_50_3_33) | all_126_0_41 = all_50_2_32
% 8.56/2.73 |
% 8.56/2.73 | Instantiating (178) with all_128_0_43, all_128_1_44 yields:
% 8.56/2.73 | (191) apply(all_0_8_8, all_110_0_35) = all_128_0_43 & apply(all_0_12_12, all_50_2_32) = all_128_1_44 & ( ~ (all_128_0_43 = all_50_2_32) | all_128_1_44 = all_110_0_35) & ( ~ (all_128_1_44 = all_110_0_35) | all_128_0_43 = all_50_2_32)
% 8.56/2.73 |
% 8.56/2.73 | Applying alpha-rule on (191) yields:
% 8.56/2.73 | (192) apply(all_0_8_8, all_110_0_35) = all_128_0_43
% 8.56/2.73 | (193) apply(all_0_12_12, all_50_2_32) = all_128_1_44
% 8.56/2.73 | (194) ~ (all_128_0_43 = all_50_2_32) | all_128_1_44 = all_110_0_35
% 8.56/2.74 | (195) ~ (all_128_1_44 = all_110_0_35) | all_128_0_43 = all_50_2_32
% 8.56/2.74 |
% 8.56/2.74 | Instantiating formula (58) with all_0_8_8, all_50_3_33, all_126_0_41, all_50_1_31 and discharging atoms apply(all_0_8_8, all_50_3_33) = all_126_0_41, apply(all_0_8_8, all_50_3_33) = all_50_1_31, yields:
% 8.56/2.74 | (196) all_126_0_41 = all_50_1_31
% 8.56/2.74 |
% 8.56/2.74 | Instantiating formula (58) with all_0_12_12, all_50_2_32, all_126_1_42, all_50_3_33 and discharging atoms apply(all_0_12_12, all_50_2_32) = all_126_1_42, apply(all_0_12_12, all_50_2_32) = all_50_3_33, yields:
% 8.56/2.74 | (197) all_126_1_42 = all_50_3_33
% 8.56/2.74 |
% 8.56/2.74 | Instantiating formula (58) with all_0_12_12, all_50_2_32, all_126_1_42, all_128_1_44 and discharging atoms apply(all_0_12_12, all_50_2_32) = all_128_1_44, apply(all_0_12_12, all_50_2_32) = all_126_1_42, yields:
% 8.56/2.74 | (198) all_128_1_44 = all_126_1_42
% 8.56/2.74 |
% 8.56/2.74 | Instantiating formula (58) with all_0_12_12, all_50_2_32, all_122_1_39, all_128_1_44 and discharging atoms apply(all_0_12_12, all_50_2_32) = all_128_1_44, apply(all_0_12_12, all_50_2_32) = all_122_1_39, yields:
% 8.56/2.74 | (199) all_128_1_44 = all_122_1_39
% 8.56/2.74 |
% 8.56/2.74 | Combining equations (198,199) yields a new equation:
% 8.56/2.74 | (200) all_126_1_42 = all_122_1_39
% 8.56/2.74 |
% 8.56/2.74 | Simplifying 200 yields:
% 8.56/2.74 | (201) all_126_1_42 = all_122_1_39
% 8.56/2.74 |
% 8.56/2.74 | Combining equations (197,201) yields a new equation:
% 8.56/2.74 | (202) all_122_1_39 = all_50_3_33
% 8.56/2.74 |
% 8.56/2.74 | Combining equations (202,201) yields a new equation:
% 8.56/2.74 | (197) all_126_1_42 = all_50_3_33
% 8.56/2.74 |
% 8.56/2.74 +-Applying beta-rule and splitting (190), into two cases.
% 8.56/2.74 |-Branch one:
% 8.56/2.74 | (204) ~ (all_126_1_42 = all_50_3_33)
% 8.56/2.74 |
% 8.56/2.74 | Equations (197) can reduce 204 to:
% 8.56/2.74 | (144) $false
% 8.56/2.74 |
% 8.56/2.74 |-The branch is then unsatisfiable
% 8.56/2.74 |-Branch two:
% 8.56/2.74 | (197) all_126_1_42 = all_50_3_33
% 8.56/2.74 | (207) all_126_0_41 = all_50_2_32
% 8.56/2.74 |
% 8.56/2.74 | Combining equations (196,207) yields a new equation:
% 8.56/2.74 | (208) all_50_1_31 = all_50_2_32
% 8.56/2.74 |
% 8.56/2.74 | Simplifying 208 yields:
% 8.56/2.74 | (209) all_50_1_31 = all_50_2_32
% 8.56/2.74 |
% 8.56/2.74 | Equations (209) can reduce 168 to:
% 8.56/2.74 | (144) $false
% 8.56/2.74 |
% 8.56/2.74 |-The branch is then unsatisfiable
% 8.56/2.74 |-Branch two:
% 8.56/2.74 | (211) all_50_1_31 = all_50_2_32 & in(all_50_3_33, all_0_10_10) & ( ~ (all_50_0_30 = all_50_3_33) | ~ in(all_50_2_32, all_23_0_19))
% 8.56/2.74 |
% 8.56/2.74 | Applying alpha-rule on (211) yields:
% 8.56/2.74 | (209) all_50_1_31 = all_50_2_32
% 8.56/2.74 | (164) in(all_50_3_33, all_0_10_10)
% 8.56/2.74 | (214) ~ (all_50_0_30 = all_50_3_33) | ~ in(all_50_2_32, all_23_0_19)
% 8.56/2.74 |
% 8.56/2.74 | From (209) and (148) follows:
% 8.56/2.74 | (215) apply(all_0_8_8, all_50_3_33) = all_50_2_32
% 8.56/2.74 |
% 8.56/2.74 | Instantiating formula (117) with all_50_3_33, all_50_2_32 and discharging atoms apply(all_0_8_8, all_50_3_33) = all_50_2_32, in(all_50_3_33, all_0_10_10), yields:
% 8.56/2.74 | (172) in(all_50_2_32, all_32_0_24)
% 8.56/2.74 |
% 8.56/2.74 | Instantiating formula (104) with all_50_3_33 yields:
% 8.56/2.74 | (217) ~ in(all_50_3_33, all_26_0_21) | ? [v0] : (apply(all_0_12_12, v0) = all_50_3_33 & in(v0, all_0_11_11))
% 8.56/2.74 |
% 8.56/2.74 | From (127) and (172) follows:
% 8.56/2.74 | (156) in(all_50_2_32, all_0_11_11)
% 8.56/2.74 |
% 8.56/2.74 +-Applying beta-rule and splitting (214), into two cases.
% 8.56/2.74 |-Branch one:
% 8.56/2.74 | (219) ~ in(all_50_2_32, all_23_0_19)
% 8.56/2.74 |
% 8.56/2.74 | From (141) and (219) follows:
% 8.56/2.74 | (170) ~ in(all_50_2_32, all_0_11_11)
% 8.56/2.74 |
% 8.56/2.74 | Using (156) and (170) yields:
% 8.56/2.74 | (166) $false
% 8.56/2.74 |
% 8.56/2.74 |-The branch is then unsatisfiable
% 8.56/2.74 |-Branch two:
% 8.56/2.74 | (153) in(all_50_2_32, all_23_0_19)
% 8.56/2.74 | (223) ~ (all_50_0_30 = all_50_3_33)
% 8.56/2.74 |
% 8.56/2.74 | From (141) and (153) follows:
% 8.56/2.74 | (156) in(all_50_2_32, all_0_11_11)
% 8.56/2.74 |
% 8.56/2.74 +-Applying beta-rule and splitting (217), into two cases.
% 8.56/2.74 |-Branch one:
% 8.56/2.74 | (225) ~ in(all_50_3_33, all_26_0_21)
% 8.56/2.74 |
% 8.56/2.74 | From (134) and (225) follows:
% 8.56/2.74 | (165) ~ in(all_50_3_33, all_0_10_10)
% 8.56/2.74 |
% 8.56/2.74 | Using (164) and (165) yields:
% 8.56/2.74 | (166) $false
% 8.56/2.74 |
% 8.56/2.74 |-The branch is then unsatisfiable
% 8.56/2.74 |-Branch two:
% 8.56/2.74 | (157) in(all_50_3_33, all_26_0_21)
% 8.56/2.74 | (229) ? [v0] : (apply(all_0_12_12, v0) = all_50_3_33 & in(v0, all_0_11_11))
% 8.56/2.74 |
% 8.56/2.74 | From (134) and (157) follows:
% 8.56/2.74 | (164) in(all_50_3_33, all_0_10_10)
% 8.56/2.74 |
% 8.56/2.74 | Instantiating formula (53) with all_50_3_33, all_50_2_32 and discharging atoms in(all_50_2_32, all_0_11_11), in(all_50_3_33, all_0_10_10), yields:
% 8.56/2.74 | (180) ? [v0] : ? [v1] : (apply(all_0_8_8, all_50_3_33) = v1 & apply(all_0_12_12, all_50_2_32) = v0 & ( ~ (v1 = all_50_2_32) | v0 = all_50_3_33) & ( ~ (v0 = all_50_3_33) | v1 = all_50_2_32))
% 8.56/2.74 |
% 8.56/2.74 | Instantiating (180) with all_126_0_55, all_126_1_56 yields:
% 8.56/2.74 | (232) apply(all_0_8_8, all_50_3_33) = all_126_0_55 & apply(all_0_12_12, all_50_2_32) = all_126_1_56 & ( ~ (all_126_0_55 = all_50_2_32) | all_126_1_56 = all_50_3_33) & ( ~ (all_126_1_56 = all_50_3_33) | all_126_0_55 = all_50_2_32)
% 8.56/2.74 |
% 8.56/2.74 | Applying alpha-rule on (232) yields:
% 8.56/2.74 | (233) apply(all_0_8_8, all_50_3_33) = all_126_0_55
% 8.56/2.74 | (234) apply(all_0_12_12, all_50_2_32) = all_126_1_56
% 8.56/2.74 | (235) ~ (all_126_0_55 = all_50_2_32) | all_126_1_56 = all_50_3_33
% 8.56/2.74 | (236) ~ (all_126_1_56 = all_50_3_33) | all_126_0_55 = all_50_2_32
% 8.56/2.74 |
% 8.56/2.74 | Instantiating formula (58) with all_0_8_8, all_50_3_33, all_126_0_55, all_50_2_32 and discharging atoms apply(all_0_8_8, all_50_3_33) = all_126_0_55, apply(all_0_8_8, all_50_3_33) = all_50_2_32, yields:
% 8.56/2.74 | (237) all_126_0_55 = all_50_2_32
% 8.56/2.74 |
% 8.56/2.74 | Instantiating formula (58) with all_0_12_12, all_50_2_32, all_126_1_56, all_50_0_30 and discharging atoms apply(all_0_12_12, all_50_2_32) = all_126_1_56, apply(all_0_12_12, all_50_2_32) = all_50_0_30, yields:
% 8.56/2.74 | (238) all_126_1_56 = all_50_0_30
% 8.56/2.74 |
% 8.56/2.74 +-Applying beta-rule and splitting (235), into two cases.
% 8.56/2.74 |-Branch one:
% 8.56/2.74 | (239) ~ (all_126_0_55 = all_50_2_32)
% 8.56/2.74 |
% 8.56/2.74 | Equations (237) can reduce 239 to:
% 8.56/2.74 | (144) $false
% 8.56/2.74 |
% 8.56/2.74 |-The branch is then unsatisfiable
% 8.56/2.74 |-Branch two:
% 8.56/2.74 | (237) all_126_0_55 = all_50_2_32
% 8.56/2.74 | (242) all_126_1_56 = all_50_3_33
% 8.56/2.74 |
% 8.56/2.74 | Combining equations (242,238) yields a new equation:
% 8.56/2.74 | (152) all_50_0_30 = all_50_3_33
% 8.56/2.74 |
% 8.56/2.74 | Equations (152) can reduce 223 to:
% 8.56/2.74 | (144) $false
% 8.56/2.74 |
% 8.56/2.74 |-The branch is then unsatisfiable
% 8.56/2.74 % SZS output end Proof for theBenchmark
% 8.56/2.74
% 8.56/2.74 2067ms
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