TSTP Solution File: SEU075+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU075+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 08:46:29 EDT 2022
% Result : Theorem 4.06s 1.67s
% Output : Proof 11.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SEU075+1 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.14/0.34 % Computer : n025.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Mon Jun 20 08:17:59 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.59/0.60 ____ _
% 0.59/0.60 ___ / __ \_____(_)___ ________ __________
% 0.59/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.59/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.59/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.59/0.61
% 0.59/0.61 A Theorem Prover for First-Order Logic
% 0.59/0.61 (ePrincess v.1.0)
% 0.59/0.61
% 0.59/0.61 (c) Philipp Rümmer, 2009-2015
% 0.59/0.61 (c) Peter Backeman, 2014-2015
% 0.59/0.61 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.59/0.61 Free software under GNU Lesser General Public License (LGPL).
% 0.59/0.61 Bug reports to peter@backeman.se
% 0.59/0.61
% 0.59/0.61 For more information, visit http://user.uu.se/~petba168/breu/
% 0.59/0.61
% 0.59/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.69/0.69 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.77/1.02 Prover 0: Preprocessing ...
% 2.79/1.33 Prover 0: Warning: ignoring some quantifiers
% 2.79/1.36 Prover 0: Constructing countermodel ...
% 4.06/1.67 Prover 0: proved (983ms)
% 4.06/1.67
% 4.06/1.67 No countermodel exists, formula is valid
% 4.06/1.67 % SZS status Theorem for theBenchmark
% 4.06/1.67
% 4.06/1.67 Generating proof ... Warning: ignoring some quantifiers
% 10.11/3.01 found it (size 505)
% 10.11/3.01
% 10.11/3.01 % SZS output start Proof for theBenchmark
% 10.11/3.01 Assumed formulas after preprocessing and simplification:
% 10.11/3.01 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ( ~ (v4 = v2) & relation_composition(v1, v4) = v3 & relation_composition(v1, v2) = v3 & relation_rng(v1) = v0 & relation_dom(v4) = v0 & relation_dom(v2) = v0 & relation_empty_yielding(v5) & relation_empty_yielding(empty_set) & one_to_one(v6) & relation(v12) & relation(v11) & relation(v9) & relation(v8) & relation(v6) & relation(v5) & relation(v4) & relation(v2) & relation(v1) & relation(empty_set) & function(v12) & function(v9) & function(v6) & function(v4) & function(v2) & function(v1) & empty(v11) & empty(v10) & empty(v9) & empty(empty_set) & ~ empty(v8) & ~ empty(v7) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v14 = v13 | ~ (relation_composition(v16, v15) = v14) | ~ (relation_composition(v16, v15) = v13)) & ! [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 | ~ (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] : ! [v15] : ( ~ (relation_composition(v14, v13) = v15) | ~ relation(v14) | ~ empty(v13) | relation(v15)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (relation_composition(v14, v13) = v15) | ~ relation(v14) | ~ empty(v13) | empty(v15)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (relation_composition(v13, v14) = v15) | ~ relation(v14) | ~ relation(v13) | ~ function(v14) | ~ function(v13) | relation(v15)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (relation_composition(v13, v14) = v15) | ~ relation(v14) | ~ relation(v13) | ~ function(v14) | ~ function(v13) | function(v15)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (relation_composition(v13, v14) = v15) | ~ relation(v14) | ~ relation(v13) | relation(v15)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (relation_composition(v13, v14) = v15) | ~ relation(v14) | ~ empty(v13) | relation(v15)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (relation_composition(v13, v14) = v15) | ~ relation(v14) | ~ empty(v13) | empty(v15)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (apply(v14, v13) = v15) | ~ relation(v14) | ~ function(v14) | ? [v16] : (relation_dom(v14) = v16 & ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_composition(v14, v17) = v18) | ~ (apply(v18, v13) = v19) | ~ relation(v17) | ~ function(v17) | ~ in(v13, v16) | apply(v17, v15) = v19) & ! [v17] : ! [v18] : ( ~ (apply(v17, v15) = v18) | ~ relation(v17) | ~ function(v17) | ~ in(v13, v16) | ? [v19] : (relation_composition(v14, v17) = v19 & apply(v19, v13) = v18)))) & ! [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] : ( ~ (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) | ~ 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(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))
% 10.11/3.06 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9, all_0_10_10, all_0_11_11, all_0_12_12 yields:
% 10.11/3.06 | (1) ~ (all_0_8_8 = all_0_10_10) & relation_composition(all_0_11_11, all_0_8_8) = all_0_9_9 & relation_composition(all_0_11_11, all_0_10_10) = all_0_9_9 & relation_rng(all_0_11_11) = all_0_12_12 & relation_dom(all_0_8_8) = all_0_12_12 & relation_dom(all_0_10_10) = all_0_12_12 & relation_empty_yielding(all_0_7_7) & relation_empty_yielding(empty_set) & one_to_one(all_0_6_6) & 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_10_10) & relation(all_0_11_11) & 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_10_10) & function(all_0_11_11) & 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 | ~ (relation_composition(v3, v2) = v1) | ~ (relation_composition(v3, v2) = v0)) & ! [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 | ~ (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] : ! [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) | ~ 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] : ! [v2] : ( ~ (apply(v1, v0) = v2) | ~ relation(v1) | ~ function(v1) | ? [v3] : (relation_dom(v1) = v3 & ! [v4] : ! [v5] : ! [v6] : ( ~ (relation_composition(v1, v4) = v5) | ~ (apply(v5, v0) = v6) | ~ relation(v4) | ~ function(v4) | ~ in(v0, v3) | apply(v4, v2) = v6) & ! [v4] : ! [v5] : ( ~ (apply(v4, v2) = v5) | ~ relation(v4) | ~ function(v4) | ~ in(v0, v3) | ? [v6] : (relation_composition(v1, v4) = v6 & apply(v6, v0) = v5)))) & ! [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] : ( ~ (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) | ~ 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(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)
% 10.11/3.07 |
% 10.11/3.07 | Applying alpha-rule on (1) yields:
% 10.11/3.07 | (2) empty(all_0_1_1)
% 10.11/3.07 | (3) ~ empty(all_0_5_5)
% 10.11/3.07 | (4) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0))
% 10.11/3.07 | (5) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | relation(v1))
% 10.11/3.07 | (6) ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1))
% 10.11/3.07 | (7) ~ empty(all_0_4_4)
% 10.11/3.07 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ empty(v2) | ~ in(v0, v1))
% 10.11/3.07 | (9) empty(all_0_3_3)
% 10.11/3.07 | (10) relation_empty_yielding(empty_set)
% 10.11/3.07 | (11) function(all_0_6_6)
% 10.11/3.07 | (12) relation_dom(all_0_8_8) = all_0_12_12
% 10.11/3.07 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_composition(v3, v2) = v1) | ~ (relation_composition(v3, v2) = v0))
% 10.11/3.07 | (14) ! [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)))))))
% 10.11/3.07 | (15) relation(all_0_6_6)
% 10.11/3.07 | (16) ! [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)))
% 10.11/3.07 | (17) ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1))
% 10.11/3.07 | (18) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ empty(v0) | empty(v2))
% 10.11/3.07 | (19) ! [v0] : ( ~ empty(v0) | function(v0))
% 10.46/3.07 | (20) ! [v0] : ( ~ relation(v0) | ~ function(v0) | ~ empty(v0) | one_to_one(v0))
% 10.46/3.07 | (21) relation(all_0_4_4)
% 10.46/3.07 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0))
% 10.46/3.07 | (23) empty(all_0_2_2)
% 10.46/3.07 | (24) relation_composition(all_0_11_11, all_0_8_8) = all_0_9_9
% 10.46/3.07 | (25) relation(all_0_11_11)
% 10.46/3.07 | (26) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2))
% 10.46/3.07 | (27) ! [v0] : ( ~ empty(v0) | relation(v0))
% 10.46/3.07 | (28) function(all_0_8_8)
% 10.46/3.07 | (29) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | empty(v1))
% 10.46/3.07 | (30) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (element(v2, v1) & ~ empty(v2)))
% 10.46/3.07 | (31) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0))
% 10.46/3.07 | (32) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | empty(v1))
% 10.46/3.07 | (33) ? [v0] : subset(v0, v0)
% 10.46/3.07 | (34) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0))
% 10.46/3.07 | (35) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v1) | ~ function(v0) | function(v2))
% 10.46/3.07 | (36) function(all_0_0_0)
% 10.46/3.08 | (37) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v1, v0) = v2) | ~ relation(v1) | ~ empty(v0) | empty(v2))
% 10.46/3.08 | (38) relation(all_0_3_3)
% 10.46/3.08 | (39) relation(all_0_7_7)
% 10.46/3.08 | (40) relation(all_0_8_8)
% 10.46/3.08 | (41) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1))
% 10.46/3.08 | (42) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ empty(v0) | relation(v2))
% 10.46/3.08 | (43) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1))
% 10.46/3.08 | (44) ! [v0] : ! [v1] : ! [v2] : ( ~ (apply(v1, v0) = v2) | ~ relation(v1) | ~ function(v1) | ? [v3] : (relation_dom(v1) = v3 & ! [v4] : ! [v5] : ! [v6] : ( ~ (relation_composition(v1, v4) = v5) | ~ (apply(v5, v0) = v6) | ~ relation(v4) | ~ function(v4) | ~ in(v0, v3) | apply(v4, v2) = v6) & ! [v4] : ! [v5] : ( ~ (apply(v4, v2) = v5) | ~ relation(v4) | ~ function(v4) | ~ in(v0, v3) | ? [v6] : (relation_composition(v1, v4) = v6 & apply(v6, v0) = v5))))
% 10.46/3.08 | (45) ! [v0] : (v0 = empty_set | ~ empty(v0))
% 10.46/3.08 | (46) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ element(v0, v2) | subset(v0, v1))
% 10.46/3.08 | (47) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2))
% 10.46/3.08 | (48) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v1) | ~ function(v0) | relation(v2))
% 10.46/3.08 | (49) relation_dom(all_0_10_10) = all_0_12_12
% 10.46/3.08 | (50) one_to_one(all_0_6_6)
% 10.46/3.08 | (51) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v1, v0) = v2) | ~ relation(v1) | ~ empty(v0) | relation(v2))
% 10.46/3.08 | (52) empty(empty_set)
% 10.46/3.08 | (53) relation_rng(all_0_11_11) = all_0_12_12
% 10.46/3.08 | (54) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0))
% 10.46/3.08 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ in(v0, v1) | element(v0, v2))
% 10.46/3.08 | (56) ? [v0] : ? [v1] : element(v1, v0)
% 10.46/3.08 | (57) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ empty(v1))
% 10.46/3.08 | (58) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | relation(v1))
% 10.46/3.08 | (59) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0))
% 10.46/3.08 | (60) ! [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)))))))
% 10.46/3.08 | (61) ~ (all_0_8_8 = all_0_10_10)
% 10.46/3.08 | (62) relation_empty_yielding(all_0_7_7)
% 10.46/3.08 | (63) relation_composition(all_0_11_11, all_0_10_10) = all_0_9_9
% 10.46/3.08 | (64) relation(all_0_10_10)
% 10.46/3.08 | (65) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) & empty(v2)))
% 10.46/3.08 | (66) relation(all_0_0_0)
% 10.46/3.08 | (67) function(all_0_10_10)
% 10.46/3.08 | (68) function(all_0_11_11)
% 10.46/3.08 | (69) relation(all_0_1_1)
% 10.46/3.08 | (70) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0))
% 10.46/3.08 | (71) function(all_0_3_3)
% 10.46/3.08 | (72) relation(empty_set)
% 10.46/3.08 |
% 10.46/3.08 | Instantiating formula (14) with all_0_12_12, all_0_8_8 and discharging atoms relation_dom(all_0_8_8) = all_0_12_12, relation(all_0_8_8), function(all_0_8_8), yields:
% 10.46/3.08 | (73) ? [v0] : (relation_rng(all_0_8_8) = v0 & ! [v1] : ! [v2] : ( ~ (apply(all_0_8_8, v2) = v1) | ~ in(v2, all_0_12_12) | in(v1, v0)) & ! [v1] : ( ~ in(v1, v0) | ? [v2] : (apply(all_0_8_8, v2) = v1 & in(v2, all_0_12_12))) & ? [v1] : (v1 = v0 | ? [v2] : ? [v3] : ? [v4] : (( ~ in(v2, v1) | ! [v5] : ( ~ (apply(all_0_8_8, v5) = v2) | ~ in(v5, all_0_12_12))) & (in(v2, v1) | (v4 = v2 & apply(all_0_8_8, v3) = v2 & in(v3, all_0_12_12))))))
% 10.46/3.09 |
% 10.46/3.09 | Instantiating formula (16) with all_0_8_8, all_0_12_12, all_0_10_10 and discharging atoms relation_dom(all_0_8_8) = all_0_12_12, relation_dom(all_0_10_10) = all_0_12_12, relation(all_0_8_8), relation(all_0_10_10), function(all_0_8_8), function(all_0_10_10), yields:
% 10.46/3.09 | (74) all_0_8_8 = all_0_10_10 | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = v1) & apply(all_0_8_8, v0) = v2 & apply(all_0_10_10, v0) = v1 & in(v0, all_0_12_12))
% 10.46/3.09 |
% 10.46/3.09 | Instantiating formula (16) with all_0_10_10, all_0_12_12, all_0_8_8 and discharging atoms relation_dom(all_0_8_8) = all_0_12_12, relation_dom(all_0_10_10) = all_0_12_12, relation(all_0_8_8), relation(all_0_10_10), function(all_0_8_8), function(all_0_10_10), yields:
% 10.46/3.09 | (75) all_0_8_8 = all_0_10_10 | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = v1) & apply(all_0_8_8, v0) = v1 & apply(all_0_10_10, v0) = v2 & in(v0, all_0_12_12))
% 10.46/3.09 |
% 10.46/3.09 | Instantiating formula (14) with all_0_12_12, all_0_10_10 and discharging atoms relation_dom(all_0_10_10) = all_0_12_12, relation(all_0_10_10), function(all_0_10_10), yields:
% 10.46/3.09 | (76) ? [v0] : (relation_rng(all_0_10_10) = v0 & ! [v1] : ! [v2] : ( ~ (apply(all_0_10_10, v2) = v1) | ~ in(v2, all_0_12_12) | in(v1, v0)) & ! [v1] : ( ~ in(v1, v0) | ? [v2] : (apply(all_0_10_10, v2) = v1 & in(v2, all_0_12_12))) & ? [v1] : (v1 = v0 | ? [v2] : ? [v3] : ? [v4] : (( ~ in(v2, v1) | ! [v5] : ( ~ (apply(all_0_10_10, v5) = v2) | ~ in(v5, all_0_12_12))) & (in(v2, v1) | (v4 = v2 & apply(all_0_10_10, v3) = v2 & in(v3, all_0_12_12))))))
% 10.46/3.09 |
% 10.46/3.09 | Instantiating formula (60) with all_0_12_12, all_0_11_11 and discharging atoms relation_rng(all_0_11_11) = all_0_12_12, relation(all_0_11_11), function(all_0_11_11), yields:
% 10.46/3.09 | (77) ? [v0] : (relation_dom(all_0_11_11) = v0 & ! [v1] : ! [v2] : ( ~ (apply(all_0_11_11, v2) = v1) | ~ in(v2, v0) | in(v1, all_0_12_12)) & ! [v1] : ( ~ in(v1, all_0_12_12) | ? [v2] : (apply(all_0_11_11, v2) = v1 & in(v2, v0))) & ? [v1] : (v1 = all_0_12_12 | ? [v2] : ? [v3] : ? [v4] : (( ~ in(v2, v1) | ! [v5] : ( ~ (apply(all_0_11_11, v5) = v2) | ~ in(v5, v0))) & (in(v2, v1) | (v4 = v2 & apply(all_0_11_11, v3) = v2 & in(v3, v0))))))
% 10.46/3.09 |
% 10.46/3.09 | Instantiating (73) with all_17_0_16 yields:
% 10.46/3.09 | (78) relation_rng(all_0_8_8) = all_17_0_16 & ! [v0] : ! [v1] : ( ~ (apply(all_0_8_8, v1) = v0) | ~ in(v1, all_0_12_12) | in(v0, all_17_0_16)) & ! [v0] : ( ~ in(v0, all_17_0_16) | ? [v1] : (apply(all_0_8_8, v1) = v0 & in(v1, all_0_12_12))) & ? [v0] : (v0 = all_17_0_16 | ? [v1] : ? [v2] : ? [v3] : (( ~ in(v1, v0) | ! [v4] : ( ~ (apply(all_0_8_8, v4) = v1) | ~ in(v4, all_0_12_12))) & (in(v1, v0) | (v3 = v1 & apply(all_0_8_8, v2) = v1 & in(v2, all_0_12_12)))))
% 10.46/3.09 |
% 10.46/3.09 | Applying alpha-rule on (78) yields:
% 10.46/3.09 | (79) relation_rng(all_0_8_8) = all_17_0_16
% 10.46/3.09 | (80) ! [v0] : ! [v1] : ( ~ (apply(all_0_8_8, v1) = v0) | ~ in(v1, all_0_12_12) | in(v0, all_17_0_16))
% 10.46/3.09 | (81) ! [v0] : ( ~ in(v0, all_17_0_16) | ? [v1] : (apply(all_0_8_8, v1) = v0 & in(v1, all_0_12_12)))
% 10.46/3.09 | (82) ? [v0] : (v0 = all_17_0_16 | ? [v1] : ? [v2] : ? [v3] : (( ~ in(v1, v0) | ! [v4] : ( ~ (apply(all_0_8_8, v4) = v1) | ~ in(v4, all_0_12_12))) & (in(v1, v0) | (v3 = v1 & apply(all_0_8_8, v2) = v1 & in(v2, all_0_12_12)))))
% 10.46/3.09 |
% 10.46/3.09 | Instantiating (76) with all_20_0_17 yields:
% 10.46/3.09 | (83) relation_rng(all_0_10_10) = all_20_0_17 & ! [v0] : ! [v1] : ( ~ (apply(all_0_10_10, v1) = v0) | ~ in(v1, all_0_12_12) | in(v0, all_20_0_17)) & ! [v0] : ( ~ in(v0, all_20_0_17) | ? [v1] : (apply(all_0_10_10, v1) = v0 & in(v1, all_0_12_12))) & ? [v0] : (v0 = all_20_0_17 | ? [v1] : ? [v2] : ? [v3] : (( ~ in(v1, v0) | ! [v4] : ( ~ (apply(all_0_10_10, v4) = v1) | ~ in(v4, all_0_12_12))) & (in(v1, v0) | (v3 = v1 & apply(all_0_10_10, v2) = v1 & in(v2, all_0_12_12)))))
% 10.46/3.09 |
% 10.46/3.09 | Applying alpha-rule on (83) yields:
% 10.46/3.09 | (84) relation_rng(all_0_10_10) = all_20_0_17
% 10.46/3.09 | (85) ! [v0] : ! [v1] : ( ~ (apply(all_0_10_10, v1) = v0) | ~ in(v1, all_0_12_12) | in(v0, all_20_0_17))
% 10.46/3.09 | (86) ! [v0] : ( ~ in(v0, all_20_0_17) | ? [v1] : (apply(all_0_10_10, v1) = v0 & in(v1, all_0_12_12)))
% 10.46/3.09 | (87) ? [v0] : (v0 = all_20_0_17 | ? [v1] : ? [v2] : ? [v3] : (( ~ in(v1, v0) | ! [v4] : ( ~ (apply(all_0_10_10, v4) = v1) | ~ in(v4, all_0_12_12))) & (in(v1, v0) | (v3 = v1 & apply(all_0_10_10, v2) = v1 & in(v2, all_0_12_12)))))
% 10.46/3.09 |
% 10.46/3.09 | Instantiating (77) with all_23_0_18 yields:
% 10.46/3.09 | (88) relation_dom(all_0_11_11) = all_23_0_18 & ! [v0] : ! [v1] : ( ~ (apply(all_0_11_11, v1) = v0) | ~ in(v1, all_23_0_18) | in(v0, all_0_12_12)) & ! [v0] : ( ~ in(v0, all_0_12_12) | ? [v1] : (apply(all_0_11_11, v1) = v0 & in(v1, all_23_0_18))) & ? [v0] : (v0 = all_0_12_12 | ? [v1] : ? [v2] : ? [v3] : (( ~ in(v1, v0) | ! [v4] : ( ~ (apply(all_0_11_11, v4) = v1) | ~ in(v4, all_23_0_18))) & (in(v1, v0) | (v3 = v1 & apply(all_0_11_11, v2) = v1 & in(v2, all_23_0_18)))))
% 10.46/3.09 |
% 10.46/3.09 | Applying alpha-rule on (88) yields:
% 10.46/3.09 | (89) relation_dom(all_0_11_11) = all_23_0_18
% 10.46/3.09 | (90) ! [v0] : ! [v1] : ( ~ (apply(all_0_11_11, v1) = v0) | ~ in(v1, all_23_0_18) | in(v0, all_0_12_12))
% 10.46/3.09 | (91) ! [v0] : ( ~ in(v0, all_0_12_12) | ? [v1] : (apply(all_0_11_11, v1) = v0 & in(v1, all_23_0_18)))
% 10.46/3.10 | (92) ? [v0] : (v0 = all_0_12_12 | ? [v1] : ? [v2] : ? [v3] : (( ~ in(v1, v0) | ! [v4] : ( ~ (apply(all_0_11_11, v4) = v1) | ~ in(v4, all_23_0_18))) & (in(v1, v0) | (v3 = v1 & apply(all_0_11_11, v2) = v1 & in(v2, all_23_0_18)))))
% 10.46/3.10 |
% 10.46/3.10 +-Applying beta-rule and splitting (75), into two cases.
% 10.46/3.10 |-Branch one:
% 10.46/3.10 | (93) all_0_8_8 = all_0_10_10
% 10.46/3.10 |
% 10.46/3.10 | Equations (93) can reduce 61 to:
% 10.46/3.10 | (94) $false
% 10.46/3.10 |
% 10.46/3.10 |-The branch is then unsatisfiable
% 10.46/3.10 |-Branch two:
% 10.46/3.10 | (61) ~ (all_0_8_8 = all_0_10_10)
% 10.46/3.10 | (96) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = v1) & apply(all_0_8_8, v0) = v1 & apply(all_0_10_10, v0) = v2 & in(v0, all_0_12_12))
% 10.46/3.10 |
% 10.46/3.10 | Instantiating (96) with all_33_0_22, all_33_1_23, all_33_2_24 yields:
% 10.46/3.10 | (97) ~ (all_33_0_22 = all_33_1_23) & apply(all_0_8_8, all_33_2_24) = all_33_1_23 & apply(all_0_10_10, all_33_2_24) = all_33_0_22 & in(all_33_2_24, all_0_12_12)
% 10.46/3.10 |
% 10.46/3.10 | Applying alpha-rule on (97) yields:
% 10.46/3.10 | (98) ~ (all_33_0_22 = all_33_1_23)
% 10.46/3.10 | (99) apply(all_0_8_8, all_33_2_24) = all_33_1_23
% 10.46/3.10 | (100) apply(all_0_10_10, all_33_2_24) = all_33_0_22
% 10.46/3.10 | (101) in(all_33_2_24, all_0_12_12)
% 10.46/3.10 |
% 10.46/3.10 +-Applying beta-rule and splitting (74), into two cases.
% 10.46/3.10 |-Branch one:
% 10.46/3.10 | (93) all_0_8_8 = all_0_10_10
% 10.46/3.10 |
% 10.46/3.10 | Equations (93) can reduce 61 to:
% 10.46/3.10 | (94) $false
% 10.46/3.10 |
% 10.46/3.10 |-The branch is then unsatisfiable
% 10.46/3.10 |-Branch two:
% 10.46/3.10 | (61) ~ (all_0_8_8 = all_0_10_10)
% 10.46/3.10 | (105) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = v1) & apply(all_0_8_8, v0) = v2 & apply(all_0_10_10, v0) = v1 & in(v0, all_0_12_12))
% 10.46/3.10 |
% 10.46/3.10 | Instantiating (105) with all_38_0_25, all_38_1_26, all_38_2_27 yields:
% 10.46/3.10 | (106) ~ (all_38_0_25 = all_38_1_26) & apply(all_0_8_8, all_38_2_27) = all_38_0_25 & apply(all_0_10_10, all_38_2_27) = all_38_1_26 & in(all_38_2_27, all_0_12_12)
% 10.46/3.10 |
% 10.46/3.10 | Applying alpha-rule on (106) yields:
% 10.46/3.10 | (107) ~ (all_38_0_25 = all_38_1_26)
% 10.46/3.10 | (108) apply(all_0_8_8, all_38_2_27) = all_38_0_25
% 10.46/3.10 | (109) apply(all_0_10_10, all_38_2_27) = all_38_1_26
% 10.46/3.10 | (110) in(all_38_2_27, all_0_12_12)
% 10.46/3.10 |
% 10.46/3.10 | Instantiating formula (60) with all_17_0_16, all_0_8_8 and discharging atoms relation_rng(all_0_8_8) = all_17_0_16, relation(all_0_8_8), function(all_0_8_8), yields:
% 10.46/3.10 | (111) ? [v0] : (relation_dom(all_0_8_8) = v0 & ! [v1] : ! [v2] : ( ~ (apply(all_0_8_8, v2) = v1) | ~ in(v2, v0) | in(v1, all_17_0_16)) & ! [v1] : ( ~ in(v1, all_17_0_16) | ? [v2] : (apply(all_0_8_8, v2) = v1 & in(v2, v0))) & ? [v1] : (v1 = all_17_0_16 | ? [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))))))
% 10.46/3.10 |
% 10.46/3.10 | Instantiating formula (60) with all_20_0_17, all_0_10_10 and discharging atoms relation_rng(all_0_10_10) = all_20_0_17, relation(all_0_10_10), function(all_0_10_10), yields:
% 10.46/3.10 | (112) ? [v0] : (relation_dom(all_0_10_10) = v0 & ! [v1] : ! [v2] : ( ~ (apply(all_0_10_10, v2) = v1) | ~ in(v2, v0) | in(v1, all_20_0_17)) & ! [v1] : ( ~ in(v1, all_20_0_17) | ? [v2] : (apply(all_0_10_10, v2) = v1 & in(v2, v0))) & ? [v1] : (v1 = all_20_0_17 | ? [v2] : ? [v3] : ? [v4] : (( ~ in(v2, v1) | ! [v5] : ( ~ (apply(all_0_10_10, v5) = v2) | ~ in(v5, v0))) & (in(v2, v1) | (v4 = v2 & apply(all_0_10_10, v3) = v2 & in(v3, v0))))))
% 10.46/3.10 |
% 10.46/3.10 | Instantiating formula (14) with all_23_0_18, all_0_11_11 and discharging atoms relation_dom(all_0_11_11) = all_23_0_18, relation(all_0_11_11), function(all_0_11_11), yields:
% 10.46/3.10 | (113) ? [v0] : (relation_rng(all_0_11_11) = v0 & ! [v1] : ! [v2] : ( ~ (apply(all_0_11_11, v2) = v1) | ~ in(v2, all_23_0_18) | in(v1, v0)) & ! [v1] : ( ~ in(v1, v0) | ? [v2] : (apply(all_0_11_11, v2) = v1 & in(v2, all_23_0_18))) & ? [v1] : (v1 = v0 | ? [v2] : ? [v3] : ? [v4] : (( ~ in(v2, v1) | ! [v5] : ( ~ (apply(all_0_11_11, v5) = v2) | ~ in(v5, all_23_0_18))) & (in(v2, v1) | (v4 = v2 & apply(all_0_11_11, v3) = v2 & in(v3, all_23_0_18))))))
% 10.46/3.10 |
% 10.46/3.10 | Instantiating formula (44) with all_38_0_25, all_0_8_8, all_38_2_27 and discharging atoms apply(all_0_8_8, all_38_2_27) = all_38_0_25, relation(all_0_8_8), function(all_0_8_8), yields:
% 10.46/3.10 | (114) ? [v0] : (relation_dom(all_0_8_8) = v0 & ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_composition(all_0_8_8, v1) = v2) | ~ (apply(v2, all_38_2_27) = v3) | ~ relation(v1) | ~ function(v1) | ~ in(all_38_2_27, v0) | apply(v1, all_38_0_25) = v3) & ! [v1] : ! [v2] : ( ~ (apply(v1, all_38_0_25) = v2) | ~ relation(v1) | ~ function(v1) | ~ in(all_38_2_27, v0) | ? [v3] : (relation_composition(all_0_8_8, v1) = v3 & apply(v3, all_38_2_27) = v2)))
% 10.46/3.11 |
% 10.46/3.11 | Instantiating formula (44) with all_33_1_23, all_0_8_8, all_33_2_24 and discharging atoms apply(all_0_8_8, all_33_2_24) = all_33_1_23, relation(all_0_8_8), function(all_0_8_8), yields:
% 10.46/3.11 | (115) ? [v0] : (relation_dom(all_0_8_8) = v0 & ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_composition(all_0_8_8, v1) = v2) | ~ (apply(v2, all_33_2_24) = v3) | ~ relation(v1) | ~ function(v1) | ~ in(all_33_2_24, v0) | apply(v1, all_33_1_23) = v3) & ! [v1] : ! [v2] : ( ~ (apply(v1, all_33_1_23) = v2) | ~ relation(v1) | ~ function(v1) | ~ in(all_33_2_24, v0) | ? [v3] : (relation_composition(all_0_8_8, v1) = v3 & apply(v3, all_33_2_24) = v2)))
% 10.46/3.11 |
% 10.46/3.11 | Instantiating formula (44) with all_38_1_26, all_0_10_10, all_38_2_27 and discharging atoms apply(all_0_10_10, all_38_2_27) = all_38_1_26, relation(all_0_10_10), function(all_0_10_10), yields:
% 10.46/3.11 | (116) ? [v0] : (relation_dom(all_0_10_10) = v0 & ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_composition(all_0_10_10, v1) = v2) | ~ (apply(v2, all_38_2_27) = v3) | ~ relation(v1) | ~ function(v1) | ~ in(all_38_2_27, v0) | apply(v1, all_38_1_26) = v3) & ! [v1] : ! [v2] : ( ~ (apply(v1, all_38_1_26) = v2) | ~ relation(v1) | ~ function(v1) | ~ in(all_38_2_27, v0) | ? [v3] : (relation_composition(all_0_10_10, v1) = v3 & apply(v3, all_38_2_27) = v2)))
% 10.46/3.11 |
% 10.46/3.11 | Instantiating formula (44) with all_33_0_22, all_0_10_10, all_33_2_24 and discharging atoms apply(all_0_10_10, all_33_2_24) = all_33_0_22, relation(all_0_10_10), function(all_0_10_10), yields:
% 10.46/3.11 | (117) ? [v0] : (relation_dom(all_0_10_10) = v0 & ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_composition(all_0_10_10, v1) = v2) | ~ (apply(v2, all_33_2_24) = v3) | ~ relation(v1) | ~ function(v1) | ~ in(all_33_2_24, v0) | apply(v1, all_33_0_22) = v3) & ! [v1] : ! [v2] : ( ~ (apply(v1, all_33_0_22) = v2) | ~ relation(v1) | ~ function(v1) | ~ in(all_33_2_24, v0) | ? [v3] : (relation_composition(all_0_10_10, v1) = v3 & apply(v3, all_33_2_24) = v2)))
% 10.46/3.11 |
% 10.46/3.11 | Instantiating formula (80) with all_38_2_27, all_38_0_25 and discharging atoms apply(all_0_8_8, all_38_2_27) = all_38_0_25, in(all_38_2_27, all_0_12_12), yields:
% 10.46/3.11 | (118) in(all_38_0_25, all_17_0_16)
% 10.46/3.11 |
% 10.46/3.11 | Instantiating formula (85) with all_38_2_27, all_38_1_26 and discharging atoms apply(all_0_10_10, all_38_2_27) = all_38_1_26, in(all_38_2_27, all_0_12_12), yields:
% 10.46/3.11 | (119) in(all_38_1_26, all_20_0_17)
% 10.46/3.11 |
% 10.46/3.11 | Instantiating formula (91) with all_38_2_27 and discharging atoms in(all_38_2_27, all_0_12_12), yields:
% 10.46/3.11 | (120) ? [v0] : (apply(all_0_11_11, v0) = all_38_2_27 & in(v0, all_23_0_18))
% 10.46/3.11 |
% 10.46/3.11 | Instantiating formula (80) with all_33_2_24, all_33_1_23 and discharging atoms apply(all_0_8_8, all_33_2_24) = all_33_1_23, in(all_33_2_24, all_0_12_12), yields:
% 10.46/3.11 | (121) in(all_33_1_23, all_17_0_16)
% 10.46/3.11 |
% 10.46/3.11 | Instantiating formula (85) with all_33_2_24, all_33_0_22 and discharging atoms apply(all_0_10_10, all_33_2_24) = all_33_0_22, in(all_33_2_24, all_0_12_12), yields:
% 10.46/3.11 | (122) in(all_33_0_22, all_20_0_17)
% 10.46/3.11 |
% 10.46/3.11 | Instantiating formula (91) with all_33_2_24 and discharging atoms in(all_33_2_24, all_0_12_12), yields:
% 10.46/3.11 | (123) ? [v0] : (apply(all_0_11_11, v0) = all_33_2_24 & in(v0, all_23_0_18))
% 10.46/3.11 |
% 10.46/3.11 | Instantiating (114) with all_46_0_28 yields:
% 10.46/3.11 | (124) relation_dom(all_0_8_8) = all_46_0_28 & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(all_0_8_8, v0) = v1) | ~ (apply(v1, all_38_2_27) = v2) | ~ relation(v0) | ~ function(v0) | ~ in(all_38_2_27, all_46_0_28) | apply(v0, all_38_0_25) = v2) & ! [v0] : ! [v1] : ( ~ (apply(v0, all_38_0_25) = v1) | ~ relation(v0) | ~ function(v0) | ~ in(all_38_2_27, all_46_0_28) | ? [v2] : (relation_composition(all_0_8_8, v0) = v2 & apply(v2, all_38_2_27) = v1))
% 10.46/3.11 |
% 10.46/3.11 | Applying alpha-rule on (124) yields:
% 10.46/3.11 | (125) relation_dom(all_0_8_8) = all_46_0_28
% 10.46/3.11 | (126) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(all_0_8_8, v0) = v1) | ~ (apply(v1, all_38_2_27) = v2) | ~ relation(v0) | ~ function(v0) | ~ in(all_38_2_27, all_46_0_28) | apply(v0, all_38_0_25) = v2)
% 10.46/3.11 | (127) ! [v0] : ! [v1] : ( ~ (apply(v0, all_38_0_25) = v1) | ~ relation(v0) | ~ function(v0) | ~ in(all_38_2_27, all_46_0_28) | ? [v2] : (relation_composition(all_0_8_8, v0) = v2 & apply(v2, all_38_2_27) = v1))
% 10.46/3.11 |
% 10.46/3.11 | Instantiating (113) with all_49_0_29 yields:
% 10.46/3.11 | (128) relation_rng(all_0_11_11) = all_49_0_29 & ! [v0] : ! [v1] : ( ~ (apply(all_0_11_11, v1) = v0) | ~ in(v1, all_23_0_18) | in(v0, all_49_0_29)) & ! [v0] : ( ~ in(v0, all_49_0_29) | ? [v1] : (apply(all_0_11_11, v1) = v0 & in(v1, all_23_0_18))) & ? [v0] : (v0 = all_49_0_29 | ? [v1] : ? [v2] : ? [v3] : (( ~ in(v1, v0) | ! [v4] : ( ~ (apply(all_0_11_11, v4) = v1) | ~ in(v4, all_23_0_18))) & (in(v1, v0) | (v3 = v1 & apply(all_0_11_11, v2) = v1 & in(v2, all_23_0_18)))))
% 10.46/3.11 |
% 10.46/3.11 | Applying alpha-rule on (128) yields:
% 10.46/3.11 | (129) relation_rng(all_0_11_11) = all_49_0_29
% 10.46/3.11 | (130) ! [v0] : ! [v1] : ( ~ (apply(all_0_11_11, v1) = v0) | ~ in(v1, all_23_0_18) | in(v0, all_49_0_29))
% 10.46/3.11 | (131) ! [v0] : ( ~ in(v0, all_49_0_29) | ? [v1] : (apply(all_0_11_11, v1) = v0 & in(v1, all_23_0_18)))
% 10.46/3.11 | (132) ? [v0] : (v0 = all_49_0_29 | ? [v1] : ? [v2] : ? [v3] : (( ~ in(v1, v0) | ! [v4] : ( ~ (apply(all_0_11_11, v4) = v1) | ~ in(v4, all_23_0_18))) & (in(v1, v0) | (v3 = v1 & apply(all_0_11_11, v2) = v1 & in(v2, all_23_0_18)))))
% 10.46/3.11 |
% 10.46/3.11 | Instantiating (112) with all_52_0_30 yields:
% 10.46/3.11 | (133) relation_dom(all_0_10_10) = all_52_0_30 & ! [v0] : ! [v1] : ( ~ (apply(all_0_10_10, v1) = v0) | ~ in(v1, all_52_0_30) | in(v0, all_20_0_17)) & ! [v0] : ( ~ in(v0, all_20_0_17) | ? [v1] : (apply(all_0_10_10, v1) = v0 & in(v1, all_52_0_30))) & ? [v0] : (v0 = all_20_0_17 | ? [v1] : ? [v2] : ? [v3] : (( ~ in(v1, v0) | ! [v4] : ( ~ (apply(all_0_10_10, v4) = v1) | ~ in(v4, all_52_0_30))) & (in(v1, v0) | (v3 = v1 & apply(all_0_10_10, v2) = v1 & in(v2, all_52_0_30)))))
% 10.46/3.12 |
% 10.46/3.12 | Applying alpha-rule on (133) yields:
% 10.46/3.12 | (134) relation_dom(all_0_10_10) = all_52_0_30
% 10.46/3.12 | (135) ! [v0] : ! [v1] : ( ~ (apply(all_0_10_10, v1) = v0) | ~ in(v1, all_52_0_30) | in(v0, all_20_0_17))
% 10.46/3.12 | (136) ! [v0] : ( ~ in(v0, all_20_0_17) | ? [v1] : (apply(all_0_10_10, v1) = v0 & in(v1, all_52_0_30)))
% 10.46/3.12 | (137) ? [v0] : (v0 = all_20_0_17 | ? [v1] : ? [v2] : ? [v3] : (( ~ in(v1, v0) | ! [v4] : ( ~ (apply(all_0_10_10, v4) = v1) | ~ in(v4, all_52_0_30))) & (in(v1, v0) | (v3 = v1 & apply(all_0_10_10, v2) = v1 & in(v2, all_52_0_30)))))
% 10.46/3.12 |
% 10.46/3.12 | Instantiating (123) with all_55_0_31 yields:
% 10.46/3.12 | (138) apply(all_0_11_11, all_55_0_31) = all_33_2_24 & in(all_55_0_31, all_23_0_18)
% 10.46/3.12 |
% 10.46/3.12 | Applying alpha-rule on (138) yields:
% 10.46/3.12 | (139) apply(all_0_11_11, all_55_0_31) = all_33_2_24
% 10.46/3.12 | (140) in(all_55_0_31, all_23_0_18)
% 10.46/3.12 |
% 10.46/3.12 | Instantiating (117) with all_57_0_32 yields:
% 10.46/3.12 | (141) relation_dom(all_0_10_10) = all_57_0_32 & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(all_0_10_10, v0) = v1) | ~ (apply(v1, all_33_2_24) = v2) | ~ relation(v0) | ~ function(v0) | ~ in(all_33_2_24, all_57_0_32) | apply(v0, all_33_0_22) = v2) & ! [v0] : ! [v1] : ( ~ (apply(v0, all_33_0_22) = v1) | ~ relation(v0) | ~ function(v0) | ~ in(all_33_2_24, all_57_0_32) | ? [v2] : (relation_composition(all_0_10_10, v0) = v2 & apply(v2, all_33_2_24) = v1))
% 10.46/3.12 |
% 10.46/3.12 | Applying alpha-rule on (141) yields:
% 10.46/3.12 | (142) relation_dom(all_0_10_10) = all_57_0_32
% 10.46/3.12 | (143) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(all_0_10_10, v0) = v1) | ~ (apply(v1, all_33_2_24) = v2) | ~ relation(v0) | ~ function(v0) | ~ in(all_33_2_24, all_57_0_32) | apply(v0, all_33_0_22) = v2)
% 10.46/3.12 | (144) ! [v0] : ! [v1] : ( ~ (apply(v0, all_33_0_22) = v1) | ~ relation(v0) | ~ function(v0) | ~ in(all_33_2_24, all_57_0_32) | ? [v2] : (relation_composition(all_0_10_10, v0) = v2 & apply(v2, all_33_2_24) = v1))
% 10.46/3.12 |
% 10.46/3.12 | Instantiating (111) with all_60_0_33 yields:
% 10.46/3.12 | (145) relation_dom(all_0_8_8) = all_60_0_33 & ! [v0] : ! [v1] : ( ~ (apply(all_0_8_8, v1) = v0) | ~ in(v1, all_60_0_33) | in(v0, all_17_0_16)) & ! [v0] : ( ~ in(v0, all_17_0_16) | ? [v1] : (apply(all_0_8_8, v1) = v0 & in(v1, all_60_0_33))) & ? [v0] : (v0 = all_17_0_16 | ? [v1] : ? [v2] : ? [v3] : (( ~ in(v1, v0) | ! [v4] : ( ~ (apply(all_0_8_8, v4) = v1) | ~ in(v4, all_60_0_33))) & (in(v1, v0) | (v3 = v1 & apply(all_0_8_8, v2) = v1 & in(v2, all_60_0_33)))))
% 10.46/3.12 |
% 10.46/3.12 | Applying alpha-rule on (145) yields:
% 10.46/3.12 | (146) relation_dom(all_0_8_8) = all_60_0_33
% 10.46/3.12 | (147) ! [v0] : ! [v1] : ( ~ (apply(all_0_8_8, v1) = v0) | ~ in(v1, all_60_0_33) | in(v0, all_17_0_16))
% 10.46/3.12 | (148) ! [v0] : ( ~ in(v0, all_17_0_16) | ? [v1] : (apply(all_0_8_8, v1) = v0 & in(v1, all_60_0_33)))
% 10.46/3.12 | (149) ? [v0] : (v0 = all_17_0_16 | ? [v1] : ? [v2] : ? [v3] : (( ~ in(v1, v0) | ! [v4] : ( ~ (apply(all_0_8_8, v4) = v1) | ~ in(v4, all_60_0_33))) & (in(v1, v0) | (v3 = v1 & apply(all_0_8_8, v2) = v1 & in(v2, all_60_0_33)))))
% 10.46/3.12 |
% 10.46/3.12 | Instantiating (116) with all_63_0_34 yields:
% 10.46/3.12 | (150) relation_dom(all_0_10_10) = all_63_0_34 & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(all_0_10_10, v0) = v1) | ~ (apply(v1, all_38_2_27) = v2) | ~ relation(v0) | ~ function(v0) | ~ in(all_38_2_27, all_63_0_34) | apply(v0, all_38_1_26) = v2) & ! [v0] : ! [v1] : ( ~ (apply(v0, all_38_1_26) = v1) | ~ relation(v0) | ~ function(v0) | ~ in(all_38_2_27, all_63_0_34) | ? [v2] : (relation_composition(all_0_10_10, v0) = v2 & apply(v2, all_38_2_27) = v1))
% 10.46/3.12 |
% 10.46/3.12 | Applying alpha-rule on (150) yields:
% 10.46/3.12 | (151) relation_dom(all_0_10_10) = all_63_0_34
% 10.46/3.12 | (152) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(all_0_10_10, v0) = v1) | ~ (apply(v1, all_38_2_27) = v2) | ~ relation(v0) | ~ function(v0) | ~ in(all_38_2_27, all_63_0_34) | apply(v0, all_38_1_26) = v2)
% 10.46/3.12 | (153) ! [v0] : ! [v1] : ( ~ (apply(v0, all_38_1_26) = v1) | ~ relation(v0) | ~ function(v0) | ~ in(all_38_2_27, all_63_0_34) | ? [v2] : (relation_composition(all_0_10_10, v0) = v2 & apply(v2, all_38_2_27) = v1))
% 10.46/3.12 |
% 10.46/3.12 | Instantiating (120) with all_66_0_35 yields:
% 10.46/3.12 | (154) apply(all_0_11_11, all_66_0_35) = all_38_2_27 & in(all_66_0_35, all_23_0_18)
% 10.46/3.12 |
% 10.46/3.12 | Applying alpha-rule on (154) yields:
% 10.46/3.12 | (155) apply(all_0_11_11, all_66_0_35) = all_38_2_27
% 10.46/3.12 | (156) in(all_66_0_35, all_23_0_18)
% 10.46/3.12 |
% 10.46/3.12 | Instantiating (115) with all_68_0_36 yields:
% 10.46/3.12 | (157) relation_dom(all_0_8_8) = all_68_0_36 & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(all_0_8_8, v0) = v1) | ~ (apply(v1, all_33_2_24) = v2) | ~ relation(v0) | ~ function(v0) | ~ in(all_33_2_24, all_68_0_36) | apply(v0, all_33_1_23) = v2) & ! [v0] : ! [v1] : ( ~ (apply(v0, all_33_1_23) = v1) | ~ relation(v0) | ~ function(v0) | ~ in(all_33_2_24, all_68_0_36) | ? [v2] : (relation_composition(all_0_8_8, v0) = v2 & apply(v2, all_33_2_24) = v1))
% 10.46/3.13 |
% 10.46/3.13 | Applying alpha-rule on (157) yields:
% 10.46/3.13 | (158) relation_dom(all_0_8_8) = all_68_0_36
% 10.46/3.13 | (159) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(all_0_8_8, v0) = v1) | ~ (apply(v1, all_33_2_24) = v2) | ~ relation(v0) | ~ function(v0) | ~ in(all_33_2_24, all_68_0_36) | apply(v0, all_33_1_23) = v2)
% 10.46/3.13 | (160) ! [v0] : ! [v1] : ( ~ (apply(v0, all_33_1_23) = v1) | ~ relation(v0) | ~ function(v0) | ~ in(all_33_2_24, all_68_0_36) | ? [v2] : (relation_composition(all_0_8_8, v0) = v2 & apply(v2, all_33_2_24) = v1))
% 10.46/3.13 |
% 10.46/3.13 | Instantiating formula (54) with all_0_11_11, all_49_0_29, all_0_12_12 and discharging atoms relation_rng(all_0_11_11) = all_49_0_29, relation_rng(all_0_11_11) = all_0_12_12, yields:
% 10.46/3.13 | (161) all_49_0_29 = all_0_12_12
% 10.46/3.13 |
% 10.46/3.13 | Instantiating formula (31) with all_0_8_8, all_68_0_36, all_0_12_12 and discharging atoms relation_dom(all_0_8_8) = all_68_0_36, relation_dom(all_0_8_8) = all_0_12_12, yields:
% 10.46/3.13 | (162) all_68_0_36 = all_0_12_12
% 10.46/3.13 |
% 10.46/3.13 | Instantiating formula (31) with all_0_8_8, all_60_0_33, all_68_0_36 and discharging atoms relation_dom(all_0_8_8) = all_68_0_36, relation_dom(all_0_8_8) = all_60_0_33, yields:
% 10.46/3.13 | (163) all_68_0_36 = all_60_0_33
% 10.46/3.13 |
% 10.46/3.13 | Instantiating formula (31) with all_0_8_8, all_46_0_28, all_68_0_36 and discharging atoms relation_dom(all_0_8_8) = all_68_0_36, relation_dom(all_0_8_8) = all_46_0_28, yields:
% 10.46/3.13 | (164) all_68_0_36 = all_46_0_28
% 10.46/3.13 |
% 10.46/3.13 | Instantiating formula (31) with all_0_10_10, all_63_0_34, all_0_12_12 and discharging atoms relation_dom(all_0_10_10) = all_63_0_34, relation_dom(all_0_10_10) = all_0_12_12, yields:
% 10.46/3.13 | (165) all_63_0_34 = all_0_12_12
% 10.46/3.13 |
% 10.46/3.13 | Instantiating formula (31) with all_0_10_10, all_57_0_32, all_63_0_34 and discharging atoms relation_dom(all_0_10_10) = all_63_0_34, relation_dom(all_0_10_10) = all_57_0_32, yields:
% 10.46/3.13 | (166) all_63_0_34 = all_57_0_32
% 10.46/3.13 |
% 10.46/3.13 | Instantiating formula (31) with all_0_10_10, all_52_0_30, all_63_0_34 and discharging atoms relation_dom(all_0_10_10) = all_63_0_34, relation_dom(all_0_10_10) = all_52_0_30, yields:
% 10.46/3.13 | (167) all_63_0_34 = all_52_0_30
% 10.46/3.13 |
% 10.46/3.13 | Combining equations (162,163) yields a new equation:
% 10.46/3.13 | (168) all_60_0_33 = all_0_12_12
% 10.46/3.13 |
% 10.46/3.13 | Combining equations (164,163) yields a new equation:
% 10.46/3.13 | (169) all_60_0_33 = all_46_0_28
% 10.46/3.13 |
% 10.46/3.13 | Combining equations (165,166) yields a new equation:
% 10.46/3.13 | (170) all_57_0_32 = all_0_12_12
% 10.46/3.13 |
% 10.46/3.13 | Combining equations (167,166) yields a new equation:
% 10.46/3.13 | (171) all_57_0_32 = all_52_0_30
% 10.46/3.13 |
% 10.46/3.13 | Combining equations (168,169) yields a new equation:
% 10.46/3.13 | (172) all_46_0_28 = all_0_12_12
% 10.46/3.13 |
% 10.46/3.13 | Combining equations (170,171) yields a new equation:
% 10.46/3.13 | (173) all_52_0_30 = all_0_12_12
% 10.46/3.13 |
% 10.46/3.13 | Combining equations (172,169) yields a new equation:
% 10.46/3.13 | (168) all_60_0_33 = all_0_12_12
% 10.46/3.13 |
% 10.46/3.13 | Instantiating formula (44) with all_38_2_27, all_0_11_11, all_66_0_35 and discharging atoms apply(all_0_11_11, all_66_0_35) = all_38_2_27, relation(all_0_11_11), function(all_0_11_11), yields:
% 10.46/3.13 | (175) ? [v0] : (relation_dom(all_0_11_11) = v0 & ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_composition(all_0_11_11, v1) = v2) | ~ (apply(v2, all_66_0_35) = v3) | ~ relation(v1) | ~ function(v1) | ~ in(all_66_0_35, v0) | apply(v1, all_38_2_27) = v3) & ! [v1] : ! [v2] : ( ~ (apply(v1, all_38_2_27) = v2) | ~ relation(v1) | ~ function(v1) | ~ in(all_66_0_35, v0) | ? [v3] : (relation_composition(all_0_11_11, v1) = v3 & apply(v3, all_66_0_35) = v2)))
% 10.46/3.13 |
% 10.46/3.13 | Instantiating formula (44) with all_33_2_24, all_0_11_11, all_55_0_31 and discharging atoms apply(all_0_11_11, all_55_0_31) = all_33_2_24, relation(all_0_11_11), function(all_0_11_11), yields:
% 10.46/3.13 | (176) ? [v0] : (relation_dom(all_0_11_11) = v0 & ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_composition(all_0_11_11, v1) = v2) | ~ (apply(v2, all_55_0_31) = v3) | ~ relation(v1) | ~ function(v1) | ~ in(all_55_0_31, v0) | apply(v1, all_33_2_24) = v3) & ! [v1] : ! [v2] : ( ~ (apply(v1, all_33_2_24) = v2) | ~ relation(v1) | ~ function(v1) | ~ in(all_55_0_31, v0) | ? [v3] : (relation_composition(all_0_11_11, v1) = v3 & apply(v3, all_55_0_31) = v2)))
% 10.46/3.14 |
% 10.46/3.14 | Instantiating formula (148) with all_38_0_25 and discharging atoms in(all_38_0_25, all_17_0_16), yields:
% 10.46/3.14 | (177) ? [v0] : (apply(all_0_8_8, v0) = all_38_0_25 & in(v0, all_60_0_33))
% 10.46/3.14 |
% 10.46/3.14 | Instantiating formula (81) with all_38_0_25 and discharging atoms in(all_38_0_25, all_17_0_16), yields:
% 10.46/3.14 | (178) ? [v0] : (apply(all_0_8_8, v0) = all_38_0_25 & in(v0, all_0_12_12))
% 10.46/3.14 |
% 10.46/3.14 | Instantiating formula (136) with all_38_1_26 and discharging atoms in(all_38_1_26, all_20_0_17), yields:
% 10.46/3.14 | (179) ? [v0] : (apply(all_0_10_10, v0) = all_38_1_26 & in(v0, all_52_0_30))
% 10.46/3.14 |
% 10.46/3.14 | Instantiating formula (86) with all_38_1_26 and discharging atoms in(all_38_1_26, all_20_0_17), yields:
% 10.46/3.14 | (180) ? [v0] : (apply(all_0_10_10, v0) = all_38_1_26 & in(v0, all_0_12_12))
% 10.46/3.14 |
% 10.46/3.14 | Instantiating formula (136) with all_33_0_22 and discharging atoms in(all_33_0_22, all_20_0_17), yields:
% 10.46/3.14 | (181) ? [v0] : (apply(all_0_10_10, v0) = all_33_0_22 & in(v0, all_52_0_30))
% 10.46/3.14 |
% 10.46/3.14 | Instantiating formula (86) with all_33_0_22 and discharging atoms in(all_33_0_22, all_20_0_17), yields:
% 10.46/3.14 | (182) ? [v0] : (apply(all_0_10_10, v0) = all_33_0_22 & in(v0, all_0_12_12))
% 10.46/3.14 |
% 10.46/3.14 | Instantiating formula (148) with all_33_1_23 and discharging atoms in(all_33_1_23, all_17_0_16), yields:
% 10.46/3.14 | (183) ? [v0] : (apply(all_0_8_8, v0) = all_33_1_23 & in(v0, all_60_0_33))
% 10.46/3.14 |
% 10.46/3.14 | Instantiating formula (81) with all_33_1_23 and discharging atoms in(all_33_1_23, all_17_0_16), yields:
% 10.46/3.14 | (184) ? [v0] : (apply(all_0_8_8, v0) = all_33_1_23 & in(v0, all_0_12_12))
% 10.46/3.14 |
% 10.46/3.14 | Instantiating (179) with all_84_0_40 yields:
% 10.46/3.14 | (185) apply(all_0_10_10, all_84_0_40) = all_38_1_26 & in(all_84_0_40, all_52_0_30)
% 10.46/3.14 |
% 10.46/3.14 | Applying alpha-rule on (185) yields:
% 10.46/3.14 | (186) apply(all_0_10_10, all_84_0_40) = all_38_1_26
% 10.46/3.14 | (187) in(all_84_0_40, all_52_0_30)
% 10.46/3.14 |
% 10.46/3.14 | Instantiating (178) with all_86_0_41 yields:
% 10.46/3.14 | (188) apply(all_0_8_8, all_86_0_41) = all_38_0_25 & in(all_86_0_41, all_0_12_12)
% 10.46/3.14 |
% 10.46/3.14 | Applying alpha-rule on (188) yields:
% 10.46/3.14 | (189) apply(all_0_8_8, all_86_0_41) = all_38_0_25
% 10.46/3.14 | (190) in(all_86_0_41, all_0_12_12)
% 10.46/3.14 |
% 10.46/3.14 | Instantiating (177) with all_88_0_42 yields:
% 10.46/3.14 | (191) apply(all_0_8_8, all_88_0_42) = all_38_0_25 & in(all_88_0_42, all_60_0_33)
% 10.46/3.14 |
% 10.46/3.14 | Applying alpha-rule on (191) yields:
% 10.46/3.14 | (192) apply(all_0_8_8, all_88_0_42) = all_38_0_25
% 10.46/3.14 | (193) in(all_88_0_42, all_60_0_33)
% 10.46/3.14 |
% 10.46/3.14 | Instantiating (183) with all_90_0_43 yields:
% 10.46/3.14 | (194) apply(all_0_8_8, all_90_0_43) = all_33_1_23 & in(all_90_0_43, all_60_0_33)
% 10.46/3.14 |
% 10.46/3.14 | Applying alpha-rule on (194) yields:
% 10.46/3.14 | (195) apply(all_0_8_8, all_90_0_43) = all_33_1_23
% 10.46/3.14 | (196) in(all_90_0_43, all_60_0_33)
% 10.46/3.14 |
% 10.46/3.14 | Instantiating (182) with all_92_0_44 yields:
% 10.46/3.14 | (197) apply(all_0_10_10, all_92_0_44) = all_33_0_22 & in(all_92_0_44, all_0_12_12)
% 10.46/3.14 |
% 10.46/3.14 | Applying alpha-rule on (197) yields:
% 10.46/3.14 | (198) apply(all_0_10_10, all_92_0_44) = all_33_0_22
% 10.46/3.14 | (199) in(all_92_0_44, all_0_12_12)
% 10.46/3.14 |
% 10.46/3.14 | Instantiating (181) with all_94_0_45 yields:
% 10.46/3.14 | (200) apply(all_0_10_10, all_94_0_45) = all_33_0_22 & in(all_94_0_45, all_52_0_30)
% 10.46/3.14 |
% 10.46/3.14 | Applying alpha-rule on (200) yields:
% 10.46/3.14 | (201) apply(all_0_10_10, all_94_0_45) = all_33_0_22
% 10.46/3.14 | (202) in(all_94_0_45, all_52_0_30)
% 10.46/3.14 |
% 10.46/3.14 | Instantiating (176) with all_96_0_46 yields:
% 10.46/3.14 | (203) relation_dom(all_0_11_11) = all_96_0_46 & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(all_0_11_11, v0) = v1) | ~ (apply(v1, all_55_0_31) = v2) | ~ relation(v0) | ~ function(v0) | ~ in(all_55_0_31, all_96_0_46) | apply(v0, all_33_2_24) = v2) & ! [v0] : ! [v1] : ( ~ (apply(v0, all_33_2_24) = v1) | ~ relation(v0) | ~ function(v0) | ~ in(all_55_0_31, all_96_0_46) | ? [v2] : (relation_composition(all_0_11_11, v0) = v2 & apply(v2, all_55_0_31) = v1))
% 10.46/3.14 |
% 10.46/3.14 | Applying alpha-rule on (203) yields:
% 10.46/3.14 | (204) relation_dom(all_0_11_11) = all_96_0_46
% 10.46/3.14 | (205) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(all_0_11_11, v0) = v1) | ~ (apply(v1, all_55_0_31) = v2) | ~ relation(v0) | ~ function(v0) | ~ in(all_55_0_31, all_96_0_46) | apply(v0, all_33_2_24) = v2)
% 10.46/3.14 | (206) ! [v0] : ! [v1] : ( ~ (apply(v0, all_33_2_24) = v1) | ~ relation(v0) | ~ function(v0) | ~ in(all_55_0_31, all_96_0_46) | ? [v2] : (relation_composition(all_0_11_11, v0) = v2 & apply(v2, all_55_0_31) = v1))
% 10.46/3.14 |
% 10.46/3.14 | Instantiating (175) with all_99_0_47 yields:
% 10.46/3.14 | (207) relation_dom(all_0_11_11) = all_99_0_47 & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(all_0_11_11, v0) = v1) | ~ (apply(v1, all_66_0_35) = v2) | ~ relation(v0) | ~ function(v0) | ~ in(all_66_0_35, all_99_0_47) | apply(v0, all_38_2_27) = v2) & ! [v0] : ! [v1] : ( ~ (apply(v0, all_38_2_27) = v1) | ~ relation(v0) | ~ function(v0) | ~ in(all_66_0_35, all_99_0_47) | ? [v2] : (relation_composition(all_0_11_11, v0) = v2 & apply(v2, all_66_0_35) = v1))
% 10.46/3.15 |
% 10.46/3.15 | Applying alpha-rule on (207) yields:
% 10.46/3.15 | (208) relation_dom(all_0_11_11) = all_99_0_47
% 10.46/3.15 | (209) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(all_0_11_11, v0) = v1) | ~ (apply(v1, all_66_0_35) = v2) | ~ relation(v0) | ~ function(v0) | ~ in(all_66_0_35, all_99_0_47) | apply(v0, all_38_2_27) = v2)
% 10.46/3.15 | (210) ! [v0] : ! [v1] : ( ~ (apply(v0, all_38_2_27) = v1) | ~ relation(v0) | ~ function(v0) | ~ in(all_66_0_35, all_99_0_47) | ? [v2] : (relation_composition(all_0_11_11, v0) = v2 & apply(v2, all_66_0_35) = v1))
% 10.46/3.15 |
% 10.46/3.15 | Instantiating (184) with all_102_0_48 yields:
% 10.46/3.15 | (211) apply(all_0_8_8, all_102_0_48) = all_33_1_23 & in(all_102_0_48, all_0_12_12)
% 10.46/3.15 |
% 10.46/3.15 | Applying alpha-rule on (211) yields:
% 10.46/3.15 | (212) apply(all_0_8_8, all_102_0_48) = all_33_1_23
% 10.46/3.15 | (213) in(all_102_0_48, all_0_12_12)
% 10.46/3.15 |
% 10.46/3.15 | Instantiating (180) with all_104_0_49 yields:
% 10.46/3.15 | (214) apply(all_0_10_10, all_104_0_49) = all_38_1_26 & in(all_104_0_49, all_0_12_12)
% 10.46/3.15 |
% 10.46/3.15 | Applying alpha-rule on (214) yields:
% 10.46/3.15 | (215) apply(all_0_10_10, all_104_0_49) = all_38_1_26
% 10.46/3.15 | (216) in(all_104_0_49, all_0_12_12)
% 10.46/3.15 |
% 10.46/3.15 | From (173) and (202) follows:
% 10.46/3.15 | (217) in(all_94_0_45, all_0_12_12)
% 10.46/3.15 |
% 10.46/3.15 | From (168) and (196) follows:
% 10.46/3.15 | (218) in(all_90_0_43, all_0_12_12)
% 10.46/3.15 |
% 10.46/3.15 | From (168) and (193) follows:
% 10.46/3.15 | (219) in(all_88_0_42, all_0_12_12)
% 10.46/3.15 |
% 10.46/3.15 | From (173) and (187) follows:
% 10.46/3.15 | (220) in(all_84_0_40, all_0_12_12)
% 10.46/3.15 |
% 10.46/3.15 | Instantiating formula (31) with all_0_11_11, all_99_0_47, all_23_0_18 and discharging atoms relation_dom(all_0_11_11) = all_99_0_47, relation_dom(all_0_11_11) = all_23_0_18, yields:
% 10.46/3.15 | (221) all_99_0_47 = all_23_0_18
% 10.46/3.15 |
% 10.46/3.15 | Instantiating formula (31) with all_0_11_11, all_96_0_46, all_99_0_47 and discharging atoms relation_dom(all_0_11_11) = all_99_0_47, relation_dom(all_0_11_11) = all_96_0_46, yields:
% 10.46/3.15 | (222) all_99_0_47 = all_96_0_46
% 10.46/3.15 |
% 10.46/3.15 | Combining equations (221,222) yields a new equation:
% 10.46/3.15 | (223) all_96_0_46 = all_23_0_18
% 10.46/3.15 |
% 10.46/3.15 | Combining equations (223,222) yields a new equation:
% 10.46/3.15 | (221) all_99_0_47 = all_23_0_18
% 10.46/3.15 |
% 10.46/3.15 | From (223) and (204) follows:
% 10.46/3.15 | (89) relation_dom(all_0_11_11) = all_23_0_18
% 10.46/3.15 |
% 10.46/3.15 | Instantiating formula (91) with all_104_0_49 and discharging atoms in(all_104_0_49, all_0_12_12), yields:
% 10.46/3.15 | (226) ? [v0] : (apply(all_0_11_11, v0) = all_104_0_49 & in(v0, all_23_0_18))
% 10.46/3.15 |
% 10.46/3.15 | Instantiating formula (131) with all_104_0_49 yields:
% 10.46/3.15 | (227) ~ in(all_104_0_49, all_49_0_29) | ? [v0] : (apply(all_0_11_11, v0) = all_104_0_49 & in(v0, all_23_0_18))
% 10.46/3.15 |
% 10.46/3.15 | Instantiating formula (91) with all_102_0_48 and discharging atoms in(all_102_0_48, all_0_12_12), yields:
% 10.46/3.15 | (228) ? [v0] : (apply(all_0_11_11, v0) = all_102_0_48 & in(v0, all_23_0_18))
% 10.46/3.15 |
% 10.46/3.15 | Instantiating formula (131) with all_102_0_48 yields:
% 10.46/3.15 | (229) ~ in(all_102_0_48, all_49_0_29) | ? [v0] : (apply(all_0_11_11, v0) = all_102_0_48 & in(v0, all_23_0_18))
% 10.46/3.15 |
% 10.46/3.15 | Instantiating formula (91) with all_94_0_45 and discharging atoms in(all_94_0_45, all_0_12_12), yields:
% 10.46/3.15 | (230) ? [v0] : (apply(all_0_11_11, v0) = all_94_0_45 & in(v0, all_23_0_18))
% 10.46/3.15 |
% 10.46/3.15 | Instantiating formula (131) with all_94_0_45 yields:
% 10.46/3.15 | (231) ~ in(all_94_0_45, all_49_0_29) | ? [v0] : (apply(all_0_11_11, v0) = all_94_0_45 & in(v0, all_23_0_18))
% 10.46/3.15 |
% 10.46/3.15 | Instantiating formula (91) with all_92_0_44 and discharging atoms in(all_92_0_44, all_0_12_12), yields:
% 10.46/3.15 | (232) ? [v0] : (apply(all_0_11_11, v0) = all_92_0_44 & in(v0, all_23_0_18))
% 10.46/3.15 |
% 10.46/3.15 | Instantiating formula (131) with all_92_0_44 yields:
% 10.46/3.15 | (233) ~ in(all_92_0_44, all_49_0_29) | ? [v0] : (apply(all_0_11_11, v0) = all_92_0_44 & in(v0, all_23_0_18))
% 10.46/3.15 |
% 10.46/3.15 | Instantiating formula (91) with all_90_0_43 and discharging atoms in(all_90_0_43, all_0_12_12), yields:
% 10.46/3.15 | (234) ? [v0] : (apply(all_0_11_11, v0) = all_90_0_43 & in(v0, all_23_0_18))
% 10.46/3.15 |
% 10.46/3.15 | Instantiating formula (131) with all_90_0_43 yields:
% 10.46/3.15 | (235) ~ in(all_90_0_43, all_49_0_29) | ? [v0] : (apply(all_0_11_11, v0) = all_90_0_43 & in(v0, all_23_0_18))
% 10.46/3.15 |
% 10.46/3.15 | Instantiating formula (91) with all_88_0_42 and discharging atoms in(all_88_0_42, all_0_12_12), yields:
% 10.46/3.15 | (236) ? [v0] : (apply(all_0_11_11, v0) = all_88_0_42 & in(v0, all_23_0_18))
% 10.46/3.15 |
% 10.46/3.15 | Instantiating formula (131) with all_88_0_42 yields:
% 10.46/3.15 | (237) ~ in(all_88_0_42, all_49_0_29) | ? [v0] : (apply(all_0_11_11, v0) = all_88_0_42 & in(v0, all_23_0_18))
% 10.46/3.15 |
% 10.46/3.15 | Instantiating formula (91) with all_86_0_41 and discharging atoms in(all_86_0_41, all_0_12_12), yields:
% 10.46/3.15 | (238) ? [v0] : (apply(all_0_11_11, v0) = all_86_0_41 & in(v0, all_23_0_18))
% 10.46/3.15 |
% 10.46/3.15 | Instantiating formula (131) with all_86_0_41 yields:
% 10.46/3.15 | (239) ~ in(all_86_0_41, all_49_0_29) | ? [v0] : (apply(all_0_11_11, v0) = all_86_0_41 & in(v0, all_23_0_18))
% 10.46/3.15 |
% 10.46/3.15 | Instantiating formula (91) with all_84_0_40 and discharging atoms in(all_84_0_40, all_0_12_12), yields:
% 10.46/3.15 | (240) ? [v0] : (apply(all_0_11_11, v0) = all_84_0_40 & in(v0, all_23_0_18))
% 10.46/3.15 |
% 10.46/3.15 | Instantiating formula (131) with all_84_0_40 yields:
% 10.46/3.15 | (241) ~ in(all_84_0_40, all_49_0_29) | ? [v0] : (apply(all_0_11_11, v0) = all_84_0_40 & in(v0, all_23_0_18))
% 10.46/3.15 |
% 10.46/3.15 | Instantiating (232) with all_116_0_50 yields:
% 10.46/3.15 | (242) apply(all_0_11_11, all_116_0_50) = all_92_0_44 & in(all_116_0_50, all_23_0_18)
% 10.46/3.15 |
% 10.46/3.15 | Applying alpha-rule on (242) yields:
% 10.46/3.15 | (243) apply(all_0_11_11, all_116_0_50) = all_92_0_44
% 10.46/3.15 | (244) in(all_116_0_50, all_23_0_18)
% 10.46/3.15 |
% 10.46/3.15 | Instantiating (236) with all_118_0_51 yields:
% 10.46/3.15 | (245) apply(all_0_11_11, all_118_0_51) = all_88_0_42 & in(all_118_0_51, all_23_0_18)
% 10.46/3.15 |
% 10.46/3.15 | Applying alpha-rule on (245) yields:
% 10.46/3.15 | (246) apply(all_0_11_11, all_118_0_51) = all_88_0_42
% 10.46/3.15 | (247) in(all_118_0_51, all_23_0_18)
% 10.46/3.15 |
% 10.46/3.15 | Instantiating (226) with all_120_0_52 yields:
% 10.46/3.15 | (248) apply(all_0_11_11, all_120_0_52) = all_104_0_49 & in(all_120_0_52, all_23_0_18)
% 10.46/3.15 |
% 10.46/3.15 | Applying alpha-rule on (248) yields:
% 10.46/3.15 | (249) apply(all_0_11_11, all_120_0_52) = all_104_0_49
% 10.46/3.16 | (250) in(all_120_0_52, all_23_0_18)
% 10.46/3.16 |
% 10.46/3.16 | Instantiating (228) with all_122_0_53 yields:
% 10.46/3.16 | (251) apply(all_0_11_11, all_122_0_53) = all_102_0_48 & in(all_122_0_53, all_23_0_18)
% 10.46/3.16 |
% 10.46/3.16 | Applying alpha-rule on (251) yields:
% 10.46/3.16 | (252) apply(all_0_11_11, all_122_0_53) = all_102_0_48
% 10.46/3.16 | (253) in(all_122_0_53, all_23_0_18)
% 10.46/3.16 |
% 10.46/3.16 | Instantiating (234) with all_124_0_54 yields:
% 10.46/3.16 | (254) apply(all_0_11_11, all_124_0_54) = all_90_0_43 & in(all_124_0_54, all_23_0_18)
% 10.46/3.16 |
% 10.46/3.16 | Applying alpha-rule on (254) yields:
% 10.46/3.16 | (255) apply(all_0_11_11, all_124_0_54) = all_90_0_43
% 10.46/3.16 | (256) in(all_124_0_54, all_23_0_18)
% 10.46/3.16 |
% 10.46/3.16 | Instantiating (230) with all_126_0_55 yields:
% 10.46/3.16 | (257) apply(all_0_11_11, all_126_0_55) = all_94_0_45 & in(all_126_0_55, all_23_0_18)
% 10.46/3.16 |
% 10.46/3.16 | Applying alpha-rule on (257) yields:
% 10.46/3.16 | (258) apply(all_0_11_11, all_126_0_55) = all_94_0_45
% 10.46/3.16 | (259) in(all_126_0_55, all_23_0_18)
% 10.46/3.16 |
% 10.46/3.16 | Instantiating (240) with all_140_0_60 yields:
% 10.46/3.16 | (260) apply(all_0_11_11, all_140_0_60) = all_84_0_40 & in(all_140_0_60, all_23_0_18)
% 10.46/3.16 |
% 10.46/3.16 | Applying alpha-rule on (260) yields:
% 10.46/3.16 | (261) apply(all_0_11_11, all_140_0_60) = all_84_0_40
% 10.46/3.16 | (262) in(all_140_0_60, all_23_0_18)
% 10.46/3.16 |
% 10.46/3.16 | Instantiating (238) with all_142_0_61 yields:
% 10.46/3.16 | (263) apply(all_0_11_11, all_142_0_61) = all_86_0_41 & in(all_142_0_61, all_23_0_18)
% 10.46/3.16 |
% 10.46/3.16 | Applying alpha-rule on (263) yields:
% 10.46/3.16 | (264) apply(all_0_11_11, all_142_0_61) = all_86_0_41
% 10.46/3.16 | (265) in(all_142_0_61, all_23_0_18)
% 10.46/3.16 |
% 10.46/3.16 +-Applying beta-rule and splitting (227), into two cases.
% 10.46/3.16 |-Branch one:
% 10.46/3.16 | (266) ~ in(all_104_0_49, all_49_0_29)
% 10.46/3.16 |
% 10.46/3.16 | From (161) and (266) follows:
% 10.46/3.16 | (267) ~ in(all_104_0_49, all_0_12_12)
% 10.46/3.16 |
% 10.46/3.16 | Using (216) and (267) yields:
% 10.46/3.16 | (268) $false
% 10.46/3.16 |
% 10.46/3.16 |-The branch is then unsatisfiable
% 10.46/3.16 |-Branch two:
% 10.46/3.16 | (269) in(all_104_0_49, all_49_0_29)
% 10.46/3.16 | (226) ? [v0] : (apply(all_0_11_11, v0) = all_104_0_49 & in(v0, all_23_0_18))
% 10.46/3.16 |
% 10.46/3.16 | Instantiating (226) with all_160_0_66 yields:
% 10.46/3.16 | (271) apply(all_0_11_11, all_160_0_66) = all_104_0_49 & in(all_160_0_66, all_23_0_18)
% 10.46/3.16 |
% 10.46/3.16 | Applying alpha-rule on (271) yields:
% 10.46/3.16 | (272) apply(all_0_11_11, all_160_0_66) = all_104_0_49
% 10.46/3.16 | (273) in(all_160_0_66, all_23_0_18)
% 10.46/3.16 |
% 10.46/3.16 +-Applying beta-rule and splitting (229), into two cases.
% 10.46/3.16 |-Branch one:
% 10.46/3.16 | (274) ~ in(all_102_0_48, all_49_0_29)
% 10.46/3.16 |
% 10.46/3.16 | From (161) and (274) follows:
% 10.46/3.16 | (275) ~ in(all_102_0_48, all_0_12_12)
% 10.46/3.16 |
% 10.46/3.16 | Using (213) and (275) yields:
% 10.46/3.16 | (268) $false
% 10.46/3.16 |
% 10.46/3.16 |-The branch is then unsatisfiable
% 10.46/3.16 |-Branch two:
% 10.46/3.16 | (277) in(all_102_0_48, all_49_0_29)
% 10.46/3.16 | (228) ? [v0] : (apply(all_0_11_11, v0) = all_102_0_48 & in(v0, all_23_0_18))
% 10.46/3.16 |
% 10.46/3.16 | Instantiating (228) with all_165_0_67 yields:
% 10.46/3.16 | (279) apply(all_0_11_11, all_165_0_67) = all_102_0_48 & in(all_165_0_67, all_23_0_18)
% 10.46/3.16 |
% 10.46/3.16 | Applying alpha-rule on (279) yields:
% 10.46/3.16 | (280) apply(all_0_11_11, all_165_0_67) = all_102_0_48
% 10.46/3.16 | (281) in(all_165_0_67, all_23_0_18)
% 10.46/3.16 |
% 10.46/3.16 +-Applying beta-rule and splitting (239), into two cases.
% 10.46/3.16 |-Branch one:
% 10.46/3.16 | (282) ~ in(all_86_0_41, all_49_0_29)
% 10.46/3.16 |
% 10.46/3.16 | From (161) and (282) follows:
% 10.46/3.16 | (283) ~ in(all_86_0_41, all_0_12_12)
% 10.46/3.16 |
% 10.46/3.16 | Using (190) and (283) yields:
% 10.46/3.16 | (268) $false
% 10.46/3.16 |
% 10.46/3.16 |-The branch is then unsatisfiable
% 10.46/3.16 |-Branch two:
% 10.46/3.16 | (285) in(all_86_0_41, all_49_0_29)
% 10.46/3.16 | (238) ? [v0] : (apply(all_0_11_11, v0) = all_86_0_41 & in(v0, all_23_0_18))
% 10.46/3.16 |
% 10.46/3.16 | Instantiating (238) with all_170_0_68 yields:
% 10.46/3.16 | (287) apply(all_0_11_11, all_170_0_68) = all_86_0_41 & in(all_170_0_68, all_23_0_18)
% 10.46/3.16 |
% 10.46/3.16 | Applying alpha-rule on (287) yields:
% 10.46/3.16 | (288) apply(all_0_11_11, all_170_0_68) = all_86_0_41
% 10.46/3.16 | (289) in(all_170_0_68, all_23_0_18)
% 10.46/3.16 |
% 10.46/3.16 +-Applying beta-rule and splitting (231), into two cases.
% 10.46/3.16 |-Branch one:
% 10.46/3.16 | (290) ~ in(all_94_0_45, all_49_0_29)
% 10.46/3.16 |
% 10.46/3.16 | From (161) and (290) follows:
% 10.46/3.16 | (291) ~ in(all_94_0_45, all_0_12_12)
% 10.46/3.16 |
% 10.46/3.16 | Using (217) and (291) yields:
% 10.46/3.16 | (268) $false
% 10.46/3.16 |
% 10.46/3.16 |-The branch is then unsatisfiable
% 10.46/3.16 |-Branch two:
% 10.46/3.16 | (293) in(all_94_0_45, all_49_0_29)
% 10.46/3.16 | (230) ? [v0] : (apply(all_0_11_11, v0) = all_94_0_45 & in(v0, all_23_0_18))
% 10.46/3.16 |
% 10.46/3.16 | Instantiating (230) with all_175_0_69 yields:
% 10.46/3.16 | (295) apply(all_0_11_11, all_175_0_69) = all_94_0_45 & in(all_175_0_69, all_23_0_18)
% 10.46/3.16 |
% 10.46/3.16 | Applying alpha-rule on (295) yields:
% 10.46/3.16 | (296) apply(all_0_11_11, all_175_0_69) = all_94_0_45
% 10.46/3.16 | (297) in(all_175_0_69, all_23_0_18)
% 10.46/3.16 |
% 10.46/3.16 +-Applying beta-rule and splitting (237), into two cases.
% 10.46/3.16 |-Branch one:
% 10.46/3.16 | (298) ~ in(all_88_0_42, all_49_0_29)
% 10.46/3.16 |
% 10.46/3.16 | From (161) and (298) follows:
% 10.46/3.16 | (299) ~ in(all_88_0_42, all_0_12_12)
% 10.46/3.16 |
% 10.46/3.16 | Using (219) and (299) yields:
% 10.46/3.16 | (268) $false
% 10.46/3.16 |
% 10.46/3.16 |-The branch is then unsatisfiable
% 10.46/3.16 |-Branch two:
% 10.46/3.16 | (301) in(all_88_0_42, all_49_0_29)
% 10.46/3.16 | (236) ? [v0] : (apply(all_0_11_11, v0) = all_88_0_42 & in(v0, all_23_0_18))
% 10.46/3.16 |
% 10.46/3.16 | Instantiating (236) with all_180_0_70 yields:
% 10.46/3.16 | (303) apply(all_0_11_11, all_180_0_70) = all_88_0_42 & in(all_180_0_70, all_23_0_18)
% 10.46/3.16 |
% 10.46/3.16 | Applying alpha-rule on (303) yields:
% 10.46/3.16 | (304) apply(all_0_11_11, all_180_0_70) = all_88_0_42
% 10.46/3.16 | (305) in(all_180_0_70, all_23_0_18)
% 10.46/3.16 |
% 10.46/3.16 +-Applying beta-rule and splitting (241), into two cases.
% 10.46/3.16 |-Branch one:
% 10.46/3.16 | (306) ~ in(all_84_0_40, all_49_0_29)
% 10.46/3.16 |
% 10.46/3.16 | From (161) and (306) follows:
% 10.46/3.16 | (307) ~ in(all_84_0_40, all_0_12_12)
% 10.46/3.16 |
% 10.46/3.16 | Using (220) and (307) yields:
% 10.46/3.16 | (268) $false
% 10.46/3.16 |
% 10.46/3.16 |-The branch is then unsatisfiable
% 10.46/3.16 |-Branch two:
% 10.46/3.16 | (309) in(all_84_0_40, all_49_0_29)
% 10.46/3.16 | (240) ? [v0] : (apply(all_0_11_11, v0) = all_84_0_40 & in(v0, all_23_0_18))
% 10.46/3.16 |
% 10.46/3.16 | Instantiating (240) with all_185_0_71 yields:
% 10.46/3.16 | (311) apply(all_0_11_11, all_185_0_71) = all_84_0_40 & in(all_185_0_71, all_23_0_18)
% 10.46/3.16 |
% 10.46/3.16 | Applying alpha-rule on (311) yields:
% 10.46/3.16 | (312) apply(all_0_11_11, all_185_0_71) = all_84_0_40
% 10.46/3.16 | (313) in(all_185_0_71, all_23_0_18)
% 10.46/3.16 |
% 10.46/3.16 +-Applying beta-rule and splitting (235), into two cases.
% 10.46/3.16 |-Branch one:
% 10.46/3.16 | (314) ~ in(all_90_0_43, all_49_0_29)
% 10.46/3.16 |
% 10.46/3.16 | From (161) and (314) follows:
% 10.46/3.16 | (315) ~ in(all_90_0_43, all_0_12_12)
% 10.46/3.16 |
% 10.46/3.16 | Using (218) and (315) yields:
% 10.46/3.16 | (268) $false
% 10.46/3.16 |
% 10.46/3.16 |-The branch is then unsatisfiable
% 10.46/3.16 |-Branch two:
% 10.46/3.16 | (317) in(all_90_0_43, all_49_0_29)
% 10.46/3.16 | (234) ? [v0] : (apply(all_0_11_11, v0) = all_90_0_43 & in(v0, all_23_0_18))
% 10.46/3.16 |
% 10.46/3.16 | Instantiating (234) with all_190_0_72 yields:
% 10.46/3.16 | (319) apply(all_0_11_11, all_190_0_72) = all_90_0_43 & in(all_190_0_72, all_23_0_18)
% 10.46/3.16 |
% 10.46/3.16 | Applying alpha-rule on (319) yields:
% 10.46/3.16 | (320) apply(all_0_11_11, all_190_0_72) = all_90_0_43
% 10.46/3.16 | (321) in(all_190_0_72, all_23_0_18)
% 10.46/3.16 |
% 10.46/3.16 +-Applying beta-rule and splitting (233), into two cases.
% 10.46/3.16 |-Branch one:
% 10.46/3.16 | (322) ~ in(all_92_0_44, all_49_0_29)
% 10.46/3.16 |
% 10.46/3.16 | From (161) and (322) follows:
% 10.46/3.16 | (323) ~ in(all_92_0_44, all_0_12_12)
% 10.46/3.16 |
% 10.46/3.16 | Using (199) and (323) yields:
% 10.46/3.17 | (268) $false
% 10.46/3.17 |
% 10.46/3.17 |-The branch is then unsatisfiable
% 10.46/3.17 |-Branch two:
% 10.46/3.17 | (325) in(all_92_0_44, all_49_0_29)
% 10.46/3.17 | (232) ? [v0] : (apply(all_0_11_11, v0) = all_92_0_44 & in(v0, all_23_0_18))
% 10.46/3.17 |
% 10.46/3.17 | Instantiating (232) with all_195_0_73 yields:
% 10.46/3.17 | (327) apply(all_0_11_11, all_195_0_73) = all_92_0_44 & in(all_195_0_73, all_23_0_18)
% 10.46/3.17 |
% 10.46/3.17 | Applying alpha-rule on (327) yields:
% 10.46/3.17 | (328) apply(all_0_11_11, all_195_0_73) = all_92_0_44
% 10.46/3.17 | (329) in(all_195_0_73, all_23_0_18)
% 10.46/3.17 |
% 10.46/3.17 | Instantiating formula (44) with all_92_0_44, all_0_11_11, all_195_0_73 and discharging atoms apply(all_0_11_11, all_195_0_73) = all_92_0_44, relation(all_0_11_11), function(all_0_11_11), yields:
% 10.46/3.17 | (330) ? [v0] : (relation_dom(all_0_11_11) = v0 & ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_composition(all_0_11_11, v1) = v2) | ~ (apply(v2, all_195_0_73) = v3) | ~ relation(v1) | ~ function(v1) | ~ in(all_195_0_73, v0) | apply(v1, all_92_0_44) = v3) & ! [v1] : ! [v2] : ( ~ (apply(v1, all_92_0_44) = v2) | ~ relation(v1) | ~ function(v1) | ~ in(all_195_0_73, v0) | ? [v3] : (relation_composition(all_0_11_11, v1) = v3 & apply(v3, all_195_0_73) = v2)))
% 10.46/3.17 |
% 10.46/3.17 | Instantiating formula (44) with all_90_0_43, all_0_11_11, all_190_0_72 and discharging atoms apply(all_0_11_11, all_190_0_72) = all_90_0_43, relation(all_0_11_11), function(all_0_11_11), yields:
% 10.46/3.17 | (331) ? [v0] : (relation_dom(all_0_11_11) = v0 & ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_composition(all_0_11_11, v1) = v2) | ~ (apply(v2, all_190_0_72) = v3) | ~ relation(v1) | ~ function(v1) | ~ in(all_190_0_72, v0) | apply(v1, all_90_0_43) = v3) & ! [v1] : ! [v2] : ( ~ (apply(v1, all_90_0_43) = v2) | ~ relation(v1) | ~ function(v1) | ~ in(all_190_0_72, v0) | ? [v3] : (relation_composition(all_0_11_11, v1) = v3 & apply(v3, all_190_0_72) = v2)))
% 10.46/3.17 |
% 10.46/3.17 | Instantiating formula (44) with all_84_0_40, all_0_11_11, all_185_0_71 and discharging atoms apply(all_0_11_11, all_185_0_71) = all_84_0_40, relation(all_0_11_11), function(all_0_11_11), yields:
% 10.46/3.17 | (332) ? [v0] : (relation_dom(all_0_11_11) = v0 & ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_composition(all_0_11_11, v1) = v2) | ~ (apply(v2, all_185_0_71) = v3) | ~ relation(v1) | ~ function(v1) | ~ in(all_185_0_71, v0) | apply(v1, all_84_0_40) = v3) & ! [v1] : ! [v2] : ( ~ (apply(v1, all_84_0_40) = v2) | ~ relation(v1) | ~ function(v1) | ~ in(all_185_0_71, v0) | ? [v3] : (relation_composition(all_0_11_11, v1) = v3 & apply(v3, all_185_0_71) = v2)))
% 10.46/3.17 |
% 10.46/3.17 | Instantiating formula (44) with all_88_0_42, all_0_11_11, all_180_0_70 and discharging atoms apply(all_0_11_11, all_180_0_70) = all_88_0_42, relation(all_0_11_11), function(all_0_11_11), yields:
% 10.46/3.17 | (333) ? [v0] : (relation_dom(all_0_11_11) = v0 & ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_composition(all_0_11_11, v1) = v2) | ~ (apply(v2, all_180_0_70) = v3) | ~ relation(v1) | ~ function(v1) | ~ in(all_180_0_70, v0) | apply(v1, all_88_0_42) = v3) & ! [v1] : ! [v2] : ( ~ (apply(v1, all_88_0_42) = v2) | ~ relation(v1) | ~ function(v1) | ~ in(all_180_0_70, v0) | ? [v3] : (relation_composition(all_0_11_11, v1) = v3 & apply(v3, all_180_0_70) = v2)))
% 10.46/3.17 |
% 10.46/3.17 | Instantiating formula (44) with all_94_0_45, all_0_11_11, all_175_0_69 and discharging atoms apply(all_0_11_11, all_175_0_69) = all_94_0_45, relation(all_0_11_11), function(all_0_11_11), yields:
% 10.46/3.17 | (334) ? [v0] : (relation_dom(all_0_11_11) = v0 & ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_composition(all_0_11_11, v1) = v2) | ~ (apply(v2, all_175_0_69) = v3) | ~ relation(v1) | ~ function(v1) | ~ in(all_175_0_69, v0) | apply(v1, all_94_0_45) = v3) & ! [v1] : ! [v2] : ( ~ (apply(v1, all_94_0_45) = v2) | ~ relation(v1) | ~ function(v1) | ~ in(all_175_0_69, v0) | ? [v3] : (relation_composition(all_0_11_11, v1) = v3 & apply(v3, all_175_0_69) = v2)))
% 10.46/3.17 |
% 10.46/3.17 | Instantiating formula (44) with all_86_0_41, all_0_11_11, all_170_0_68 and discharging atoms apply(all_0_11_11, all_170_0_68) = all_86_0_41, relation(all_0_11_11), function(all_0_11_11), yields:
% 10.46/3.17 | (335) ? [v0] : (relation_dom(all_0_11_11) = v0 & ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_composition(all_0_11_11, v1) = v2) | ~ (apply(v2, all_170_0_68) = v3) | ~ relation(v1) | ~ function(v1) | ~ in(all_170_0_68, v0) | apply(v1, all_86_0_41) = v3) & ! [v1] : ! [v2] : ( ~ (apply(v1, all_86_0_41) = v2) | ~ relation(v1) | ~ function(v1) | ~ in(all_170_0_68, v0) | ? [v3] : (relation_composition(all_0_11_11, v1) = v3 & apply(v3, all_170_0_68) = v2)))
% 10.94/3.17 |
% 10.94/3.17 | Instantiating formula (44) with all_102_0_48, all_0_11_11, all_165_0_67 and discharging atoms apply(all_0_11_11, all_165_0_67) = all_102_0_48, relation(all_0_11_11), function(all_0_11_11), yields:
% 10.94/3.17 | (336) ? [v0] : (relation_dom(all_0_11_11) = v0 & ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_composition(all_0_11_11, v1) = v2) | ~ (apply(v2, all_165_0_67) = v3) | ~ relation(v1) | ~ function(v1) | ~ in(all_165_0_67, v0) | apply(v1, all_102_0_48) = v3) & ! [v1] : ! [v2] : ( ~ (apply(v1, all_102_0_48) = v2) | ~ relation(v1) | ~ function(v1) | ~ in(all_165_0_67, v0) | ? [v3] : (relation_composition(all_0_11_11, v1) = v3 & apply(v3, all_165_0_67) = v2)))
% 10.94/3.17 |
% 10.94/3.17 | Instantiating formula (44) with all_104_0_49, all_0_11_11, all_160_0_66 and discharging atoms apply(all_0_11_11, all_160_0_66) = all_104_0_49, relation(all_0_11_11), function(all_0_11_11), yields:
% 10.94/3.17 | (337) ? [v0] : (relation_dom(all_0_11_11) = v0 & ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_composition(all_0_11_11, v1) = v2) | ~ (apply(v2, all_160_0_66) = v3) | ~ relation(v1) | ~ function(v1) | ~ in(all_160_0_66, v0) | apply(v1, all_104_0_49) = v3) & ! [v1] : ! [v2] : ( ~ (apply(v1, all_104_0_49) = v2) | ~ relation(v1) | ~ function(v1) | ~ in(all_160_0_66, v0) | ? [v3] : (relation_composition(all_0_11_11, v1) = v3 & apply(v3, all_160_0_66) = v2)))
% 10.94/3.17 |
% 10.94/3.17 | Instantiating formula (44) with all_86_0_41, all_0_11_11, all_142_0_61 and discharging atoms apply(all_0_11_11, all_142_0_61) = all_86_0_41, relation(all_0_11_11), function(all_0_11_11), yields:
% 10.94/3.17 | (338) ? [v0] : (relation_dom(all_0_11_11) = v0 & ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_composition(all_0_11_11, v1) = v2) | ~ (apply(v2, all_142_0_61) = v3) | ~ relation(v1) | ~ function(v1) | ~ in(all_142_0_61, v0) | apply(v1, all_86_0_41) = v3) & ! [v1] : ! [v2] : ( ~ (apply(v1, all_86_0_41) = v2) | ~ relation(v1) | ~ function(v1) | ~ in(all_142_0_61, v0) | ? [v3] : (relation_composition(all_0_11_11, v1) = v3 & apply(v3, all_142_0_61) = v2)))
% 10.94/3.17 |
% 10.94/3.17 | Instantiating formula (44) with all_84_0_40, all_0_11_11, all_140_0_60 and discharging atoms apply(all_0_11_11, all_140_0_60) = all_84_0_40, relation(all_0_11_11), function(all_0_11_11), yields:
% 10.94/3.17 | (339) ? [v0] : (relation_dom(all_0_11_11) = v0 & ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_composition(all_0_11_11, v1) = v2) | ~ (apply(v2, all_140_0_60) = v3) | ~ relation(v1) | ~ function(v1) | ~ in(all_140_0_60, v0) | apply(v1, all_84_0_40) = v3) & ! [v1] : ! [v2] : ( ~ (apply(v1, all_84_0_40) = v2) | ~ relation(v1) | ~ function(v1) | ~ in(all_140_0_60, v0) | ? [v3] : (relation_composition(all_0_11_11, v1) = v3 & apply(v3, all_140_0_60) = v2)))
% 10.94/3.17 |
% 10.94/3.17 | Instantiating formula (44) with all_94_0_45, all_0_11_11, all_126_0_55 and discharging atoms apply(all_0_11_11, all_126_0_55) = all_94_0_45, relation(all_0_11_11), function(all_0_11_11), yields:
% 10.94/3.17 | (340) ? [v0] : (relation_dom(all_0_11_11) = v0 & ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_composition(all_0_11_11, v1) = v2) | ~ (apply(v2, all_126_0_55) = v3) | ~ relation(v1) | ~ function(v1) | ~ in(all_126_0_55, v0) | apply(v1, all_94_0_45) = v3) & ! [v1] : ! [v2] : ( ~ (apply(v1, all_94_0_45) = v2) | ~ relation(v1) | ~ function(v1) | ~ in(all_126_0_55, v0) | ? [v3] : (relation_composition(all_0_11_11, v1) = v3 & apply(v3, all_126_0_55) = v2)))
% 10.94/3.17 |
% 10.94/3.17 | Instantiating formula (44) with all_90_0_43, all_0_11_11, all_124_0_54 and discharging atoms apply(all_0_11_11, all_124_0_54) = all_90_0_43, relation(all_0_11_11), function(all_0_11_11), yields:
% 10.94/3.17 | (341) ? [v0] : (relation_dom(all_0_11_11) = v0 & ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_composition(all_0_11_11, v1) = v2) | ~ (apply(v2, all_124_0_54) = v3) | ~ relation(v1) | ~ function(v1) | ~ in(all_124_0_54, v0) | apply(v1, all_90_0_43) = v3) & ! [v1] : ! [v2] : ( ~ (apply(v1, all_90_0_43) = v2) | ~ relation(v1) | ~ function(v1) | ~ in(all_124_0_54, v0) | ? [v3] : (relation_composition(all_0_11_11, v1) = v3 & apply(v3, all_124_0_54) = v2)))
% 10.94/3.17 |
% 10.94/3.17 | Instantiating formula (44) with all_102_0_48, all_0_11_11, all_122_0_53 and discharging atoms apply(all_0_11_11, all_122_0_53) = all_102_0_48, relation(all_0_11_11), function(all_0_11_11), yields:
% 10.94/3.17 | (342) ? [v0] : (relation_dom(all_0_11_11) = v0 & ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_composition(all_0_11_11, v1) = v2) | ~ (apply(v2, all_122_0_53) = v3) | ~ relation(v1) | ~ function(v1) | ~ in(all_122_0_53, v0) | apply(v1, all_102_0_48) = v3) & ! [v1] : ! [v2] : ( ~ (apply(v1, all_102_0_48) = v2) | ~ relation(v1) | ~ function(v1) | ~ in(all_122_0_53, v0) | ? [v3] : (relation_composition(all_0_11_11, v1) = v3 & apply(v3, all_122_0_53) = v2)))
% 10.94/3.17 |
% 10.94/3.17 | Instantiating formula (44) with all_104_0_49, all_0_11_11, all_120_0_52 and discharging atoms apply(all_0_11_11, all_120_0_52) = all_104_0_49, relation(all_0_11_11), function(all_0_11_11), yields:
% 10.94/3.17 | (343) ? [v0] : (relation_dom(all_0_11_11) = v0 & ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_composition(all_0_11_11, v1) = v2) | ~ (apply(v2, all_120_0_52) = v3) | ~ relation(v1) | ~ function(v1) | ~ in(all_120_0_52, v0) | apply(v1, all_104_0_49) = v3) & ! [v1] : ! [v2] : ( ~ (apply(v1, all_104_0_49) = v2) | ~ relation(v1) | ~ function(v1) | ~ in(all_120_0_52, v0) | ? [v3] : (relation_composition(all_0_11_11, v1) = v3 & apply(v3, all_120_0_52) = v2)))
% 10.94/3.17 |
% 10.94/3.17 | Instantiating formula (44) with all_88_0_42, all_0_11_11, all_118_0_51 and discharging atoms apply(all_0_11_11, all_118_0_51) = all_88_0_42, relation(all_0_11_11), function(all_0_11_11), yields:
% 10.94/3.17 | (344) ? [v0] : (relation_dom(all_0_11_11) = v0 & ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_composition(all_0_11_11, v1) = v2) | ~ (apply(v2, all_118_0_51) = v3) | ~ relation(v1) | ~ function(v1) | ~ in(all_118_0_51, v0) | apply(v1, all_88_0_42) = v3) & ! [v1] : ! [v2] : ( ~ (apply(v1, all_88_0_42) = v2) | ~ relation(v1) | ~ function(v1) | ~ in(all_118_0_51, v0) | ? [v3] : (relation_composition(all_0_11_11, v1) = v3 & apply(v3, all_118_0_51) = v2)))
% 10.94/3.17 |
% 10.94/3.17 | Instantiating formula (44) with all_92_0_44, all_0_11_11, all_116_0_50 and discharging atoms apply(all_0_11_11, all_116_0_50) = all_92_0_44, relation(all_0_11_11), function(all_0_11_11), yields:
% 10.94/3.18 | (345) ? [v0] : (relation_dom(all_0_11_11) = v0 & ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_composition(all_0_11_11, v1) = v2) | ~ (apply(v2, all_116_0_50) = v3) | ~ relation(v1) | ~ function(v1) | ~ in(all_116_0_50, v0) | apply(v1, all_92_0_44) = v3) & ! [v1] : ! [v2] : ( ~ (apply(v1, all_92_0_44) = v2) | ~ relation(v1) | ~ function(v1) | ~ in(all_116_0_50, v0) | ? [v3] : (relation_composition(all_0_11_11, v1) = v3 & apply(v3, all_116_0_50) = v2)))
% 10.94/3.18 |
% 10.94/3.18 | Instantiating (337) with all_217_0_74 yields:
% 10.94/3.18 | (346) relation_dom(all_0_11_11) = all_217_0_74 & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(all_0_11_11, v0) = v1) | ~ (apply(v1, all_160_0_66) = v2) | ~ relation(v0) | ~ function(v0) | ~ in(all_160_0_66, all_217_0_74) | apply(v0, all_104_0_49) = v2) & ! [v0] : ! [v1] : ( ~ (apply(v0, all_104_0_49) = v1) | ~ relation(v0) | ~ function(v0) | ~ in(all_160_0_66, all_217_0_74) | ? [v2] : (relation_composition(all_0_11_11, v0) = v2 & apply(v2, all_160_0_66) = v1))
% 10.94/3.18 |
% 10.94/3.18 | Applying alpha-rule on (346) yields:
% 10.94/3.18 | (347) relation_dom(all_0_11_11) = all_217_0_74
% 10.94/3.18 | (348) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(all_0_11_11, v0) = v1) | ~ (apply(v1, all_160_0_66) = v2) | ~ relation(v0) | ~ function(v0) | ~ in(all_160_0_66, all_217_0_74) | apply(v0, all_104_0_49) = v2)
% 10.94/3.18 | (349) ! [v0] : ! [v1] : ( ~ (apply(v0, all_104_0_49) = v1) | ~ relation(v0) | ~ function(v0) | ~ in(all_160_0_66, all_217_0_74) | ? [v2] : (relation_composition(all_0_11_11, v0) = v2 & apply(v2, all_160_0_66) = v1))
% 10.94/3.18 |
% 10.94/3.18 | Instantiating (336) with all_220_0_75 yields:
% 10.94/3.18 | (350) relation_dom(all_0_11_11) = all_220_0_75 & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(all_0_11_11, v0) = v1) | ~ (apply(v1, all_165_0_67) = v2) | ~ relation(v0) | ~ function(v0) | ~ in(all_165_0_67, all_220_0_75) | apply(v0, all_102_0_48) = v2) & ! [v0] : ! [v1] : ( ~ (apply(v0, all_102_0_48) = v1) | ~ relation(v0) | ~ function(v0) | ~ in(all_165_0_67, all_220_0_75) | ? [v2] : (relation_composition(all_0_11_11, v0) = v2 & apply(v2, all_165_0_67) = v1))
% 10.94/3.18 |
% 10.94/3.18 | Applying alpha-rule on (350) yields:
% 10.94/3.18 | (351) relation_dom(all_0_11_11) = all_220_0_75
% 10.94/3.18 | (352) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(all_0_11_11, v0) = v1) | ~ (apply(v1, all_165_0_67) = v2) | ~ relation(v0) | ~ function(v0) | ~ in(all_165_0_67, all_220_0_75) | apply(v0, all_102_0_48) = v2)
% 10.94/3.18 | (353) ! [v0] : ! [v1] : ( ~ (apply(v0, all_102_0_48) = v1) | ~ relation(v0) | ~ function(v0) | ~ in(all_165_0_67, all_220_0_75) | ? [v2] : (relation_composition(all_0_11_11, v0) = v2 & apply(v2, all_165_0_67) = v1))
% 10.94/3.18 |
% 10.94/3.18 | Instantiating (333) with all_223_0_76 yields:
% 10.94/3.18 | (354) relation_dom(all_0_11_11) = all_223_0_76 & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(all_0_11_11, v0) = v1) | ~ (apply(v1, all_180_0_70) = v2) | ~ relation(v0) | ~ function(v0) | ~ in(all_180_0_70, all_223_0_76) | apply(v0, all_88_0_42) = v2) & ! [v0] : ! [v1] : ( ~ (apply(v0, all_88_0_42) = v1) | ~ relation(v0) | ~ function(v0) | ~ in(all_180_0_70, all_223_0_76) | ? [v2] : (relation_composition(all_0_11_11, v0) = v2 & apply(v2, all_180_0_70) = v1))
% 10.94/3.18 |
% 10.94/3.18 | Applying alpha-rule on (354) yields:
% 10.94/3.18 | (355) relation_dom(all_0_11_11) = all_223_0_76
% 10.94/3.18 | (356) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(all_0_11_11, v0) = v1) | ~ (apply(v1, all_180_0_70) = v2) | ~ relation(v0) | ~ function(v0) | ~ in(all_180_0_70, all_223_0_76) | apply(v0, all_88_0_42) = v2)
% 10.94/3.18 | (357) ! [v0] : ! [v1] : ( ~ (apply(v0, all_88_0_42) = v1) | ~ relation(v0) | ~ function(v0) | ~ in(all_180_0_70, all_223_0_76) | ? [v2] : (relation_composition(all_0_11_11, v0) = v2 & apply(v2, all_180_0_70) = v1))
% 10.94/3.18 |
% 10.94/3.18 | Instantiating (331) with all_226_0_77 yields:
% 10.94/3.18 | (358) relation_dom(all_0_11_11) = all_226_0_77 & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(all_0_11_11, v0) = v1) | ~ (apply(v1, all_190_0_72) = v2) | ~ relation(v0) | ~ function(v0) | ~ in(all_190_0_72, all_226_0_77) | apply(v0, all_90_0_43) = v2) & ! [v0] : ! [v1] : ( ~ (apply(v0, all_90_0_43) = v1) | ~ relation(v0) | ~ function(v0) | ~ in(all_190_0_72, all_226_0_77) | ? [v2] : (relation_composition(all_0_11_11, v0) = v2 & apply(v2, all_190_0_72) = v1))
% 10.94/3.18 |
% 10.94/3.18 | Applying alpha-rule on (358) yields:
% 10.94/3.18 | (359) relation_dom(all_0_11_11) = all_226_0_77
% 10.94/3.18 | (360) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(all_0_11_11, v0) = v1) | ~ (apply(v1, all_190_0_72) = v2) | ~ relation(v0) | ~ function(v0) | ~ in(all_190_0_72, all_226_0_77) | apply(v0, all_90_0_43) = v2)
% 10.94/3.18 | (361) ! [v0] : ! [v1] : ( ~ (apply(v0, all_90_0_43) = v1) | ~ relation(v0) | ~ function(v0) | ~ in(all_190_0_72, all_226_0_77) | ? [v2] : (relation_composition(all_0_11_11, v0) = v2 & apply(v2, all_190_0_72) = v1))
% 10.94/3.18 |
% 10.94/3.18 | Instantiating (345) with all_229_0_78 yields:
% 10.94/3.18 | (362) relation_dom(all_0_11_11) = all_229_0_78 & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(all_0_11_11, v0) = v1) | ~ (apply(v1, all_116_0_50) = v2) | ~ relation(v0) | ~ function(v0) | ~ in(all_116_0_50, all_229_0_78) | apply(v0, all_92_0_44) = v2) & ! [v0] : ! [v1] : ( ~ (apply(v0, all_92_0_44) = v1) | ~ relation(v0) | ~ function(v0) | ~ in(all_116_0_50, all_229_0_78) | ? [v2] : (relation_composition(all_0_11_11, v0) = v2 & apply(v2, all_116_0_50) = v1))
% 10.94/3.18 |
% 10.94/3.18 | Applying alpha-rule on (362) yields:
% 10.94/3.18 | (363) relation_dom(all_0_11_11) = all_229_0_78
% 10.94/3.18 | (364) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(all_0_11_11, v0) = v1) | ~ (apply(v1, all_116_0_50) = v2) | ~ relation(v0) | ~ function(v0) | ~ in(all_116_0_50, all_229_0_78) | apply(v0, all_92_0_44) = v2)
% 10.94/3.18 | (365) ! [v0] : ! [v1] : ( ~ (apply(v0, all_92_0_44) = v1) | ~ relation(v0) | ~ function(v0) | ~ in(all_116_0_50, all_229_0_78) | ? [v2] : (relation_composition(all_0_11_11, v0) = v2 & apply(v2, all_116_0_50) = v1))
% 10.94/3.18 |
% 10.94/3.18 | Instantiating (343) with all_232_0_79 yields:
% 10.94/3.18 | (366) relation_dom(all_0_11_11) = all_232_0_79 & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(all_0_11_11, v0) = v1) | ~ (apply(v1, all_120_0_52) = v2) | ~ relation(v0) | ~ function(v0) | ~ in(all_120_0_52, all_232_0_79) | apply(v0, all_104_0_49) = v2) & ! [v0] : ! [v1] : ( ~ (apply(v0, all_104_0_49) = v1) | ~ relation(v0) | ~ function(v0) | ~ in(all_120_0_52, all_232_0_79) | ? [v2] : (relation_composition(all_0_11_11, v0) = v2 & apply(v2, all_120_0_52) = v1))
% 10.94/3.18 |
% 10.94/3.18 | Applying alpha-rule on (366) yields:
% 10.94/3.18 | (367) relation_dom(all_0_11_11) = all_232_0_79
% 10.94/3.18 | (368) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(all_0_11_11, v0) = v1) | ~ (apply(v1, all_120_0_52) = v2) | ~ relation(v0) | ~ function(v0) | ~ in(all_120_0_52, all_232_0_79) | apply(v0, all_104_0_49) = v2)
% 10.94/3.18 | (369) ! [v0] : ! [v1] : ( ~ (apply(v0, all_104_0_49) = v1) | ~ relation(v0) | ~ function(v0) | ~ in(all_120_0_52, all_232_0_79) | ? [v2] : (relation_composition(all_0_11_11, v0) = v2 & apply(v2, all_120_0_52) = v1))
% 10.94/3.18 |
% 10.94/3.18 | Instantiating (342) with all_235_0_80 yields:
% 10.94/3.18 | (370) relation_dom(all_0_11_11) = all_235_0_80 & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(all_0_11_11, v0) = v1) | ~ (apply(v1, all_122_0_53) = v2) | ~ relation(v0) | ~ function(v0) | ~ in(all_122_0_53, all_235_0_80) | apply(v0, all_102_0_48) = v2) & ! [v0] : ! [v1] : ( ~ (apply(v0, all_102_0_48) = v1) | ~ relation(v0) | ~ function(v0) | ~ in(all_122_0_53, all_235_0_80) | ? [v2] : (relation_composition(all_0_11_11, v0) = v2 & apply(v2, all_122_0_53) = v1))
% 10.94/3.18 |
% 10.94/3.18 | Applying alpha-rule on (370) yields:
% 10.94/3.18 | (371) relation_dom(all_0_11_11) = all_235_0_80
% 10.94/3.18 | (372) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(all_0_11_11, v0) = v1) | ~ (apply(v1, all_122_0_53) = v2) | ~ relation(v0) | ~ function(v0) | ~ in(all_122_0_53, all_235_0_80) | apply(v0, all_102_0_48) = v2)
% 10.94/3.18 | (373) ! [v0] : ! [v1] : ( ~ (apply(v0, all_102_0_48) = v1) | ~ relation(v0) | ~ function(v0) | ~ in(all_122_0_53, all_235_0_80) | ? [v2] : (relation_composition(all_0_11_11, v0) = v2 & apply(v2, all_122_0_53) = v1))
% 10.94/3.18 |
% 10.94/3.18 | Instantiating (330) with all_238_0_81 yields:
% 10.94/3.18 | (374) relation_dom(all_0_11_11) = all_238_0_81 & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(all_0_11_11, v0) = v1) | ~ (apply(v1, all_195_0_73) = v2) | ~ relation(v0) | ~ function(v0) | ~ in(all_195_0_73, all_238_0_81) | apply(v0, all_92_0_44) = v2) & ! [v0] : ! [v1] : ( ~ (apply(v0, all_92_0_44) = v1) | ~ relation(v0) | ~ function(v0) | ~ in(all_195_0_73, all_238_0_81) | ? [v2] : (relation_composition(all_0_11_11, v0) = v2 & apply(v2, all_195_0_73) = v1))
% 10.94/3.18 |
% 10.94/3.18 | Applying alpha-rule on (374) yields:
% 10.94/3.18 | (375) relation_dom(all_0_11_11) = all_238_0_81
% 10.94/3.18 | (376) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(all_0_11_11, v0) = v1) | ~ (apply(v1, all_195_0_73) = v2) | ~ relation(v0) | ~ function(v0) | ~ in(all_195_0_73, all_238_0_81) | apply(v0, all_92_0_44) = v2)
% 10.94/3.18 | (377) ! [v0] : ! [v1] : ( ~ (apply(v0, all_92_0_44) = v1) | ~ relation(v0) | ~ function(v0) | ~ in(all_195_0_73, all_238_0_81) | ? [v2] : (relation_composition(all_0_11_11, v0) = v2 & apply(v2, all_195_0_73) = v1))
% 10.94/3.18 |
% 10.94/3.18 | Instantiating (344) with all_241_0_82 yields:
% 10.94/3.18 | (378) relation_dom(all_0_11_11) = all_241_0_82 & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(all_0_11_11, v0) = v1) | ~ (apply(v1, all_118_0_51) = v2) | ~ relation(v0) | ~ function(v0) | ~ in(all_118_0_51, all_241_0_82) | apply(v0, all_88_0_42) = v2) & ! [v0] : ! [v1] : ( ~ (apply(v0, all_88_0_42) = v1) | ~ relation(v0) | ~ function(v0) | ~ in(all_118_0_51, all_241_0_82) | ? [v2] : (relation_composition(all_0_11_11, v0) = v2 & apply(v2, all_118_0_51) = v1))
% 10.94/3.18 |
% 10.94/3.18 | Applying alpha-rule on (378) yields:
% 10.94/3.18 | (379) relation_dom(all_0_11_11) = all_241_0_82
% 10.94/3.18 | (380) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(all_0_11_11, v0) = v1) | ~ (apply(v1, all_118_0_51) = v2) | ~ relation(v0) | ~ function(v0) | ~ in(all_118_0_51, all_241_0_82) | apply(v0, all_88_0_42) = v2)
% 10.94/3.18 | (381) ! [v0] : ! [v1] : ( ~ (apply(v0, all_88_0_42) = v1) | ~ relation(v0) | ~ function(v0) | ~ in(all_118_0_51, all_241_0_82) | ? [v2] : (relation_composition(all_0_11_11, v0) = v2 & apply(v2, all_118_0_51) = v1))
% 10.94/3.19 |
% 10.94/3.19 | Instantiating (341) with all_244_0_83 yields:
% 10.94/3.19 | (382) relation_dom(all_0_11_11) = all_244_0_83 & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(all_0_11_11, v0) = v1) | ~ (apply(v1, all_124_0_54) = v2) | ~ relation(v0) | ~ function(v0) | ~ in(all_124_0_54, all_244_0_83) | apply(v0, all_90_0_43) = v2) & ! [v0] : ! [v1] : ( ~ (apply(v0, all_90_0_43) = v1) | ~ relation(v0) | ~ function(v0) | ~ in(all_124_0_54, all_244_0_83) | ? [v2] : (relation_composition(all_0_11_11, v0) = v2 & apply(v2, all_124_0_54) = v1))
% 10.94/3.19 |
% 10.94/3.19 | Applying alpha-rule on (382) yields:
% 10.94/3.19 | (383) relation_dom(all_0_11_11) = all_244_0_83
% 10.94/3.19 | (384) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(all_0_11_11, v0) = v1) | ~ (apply(v1, all_124_0_54) = v2) | ~ relation(v0) | ~ function(v0) | ~ in(all_124_0_54, all_244_0_83) | apply(v0, all_90_0_43) = v2)
% 10.94/3.19 | (385) ! [v0] : ! [v1] : ( ~ (apply(v0, all_90_0_43) = v1) | ~ relation(v0) | ~ function(v0) | ~ in(all_124_0_54, all_244_0_83) | ? [v2] : (relation_composition(all_0_11_11, v0) = v2 & apply(v2, all_124_0_54) = v1))
% 10.94/3.19 |
% 10.94/3.19 | Instantiating (340) with all_247_0_84 yields:
% 10.94/3.19 | (386) relation_dom(all_0_11_11) = all_247_0_84 & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(all_0_11_11, v0) = v1) | ~ (apply(v1, all_126_0_55) = v2) | ~ relation(v0) | ~ function(v0) | ~ in(all_126_0_55, all_247_0_84) | apply(v0, all_94_0_45) = v2) & ! [v0] : ! [v1] : ( ~ (apply(v0, all_94_0_45) = v1) | ~ relation(v0) | ~ function(v0) | ~ in(all_126_0_55, all_247_0_84) | ? [v2] : (relation_composition(all_0_11_11, v0) = v2 & apply(v2, all_126_0_55) = v1))
% 10.94/3.19 |
% 10.94/3.19 | Applying alpha-rule on (386) yields:
% 10.94/3.19 | (387) relation_dom(all_0_11_11) = all_247_0_84
% 10.94/3.19 | (388) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(all_0_11_11, v0) = v1) | ~ (apply(v1, all_126_0_55) = v2) | ~ relation(v0) | ~ function(v0) | ~ in(all_126_0_55, all_247_0_84) | apply(v0, all_94_0_45) = v2)
% 10.94/3.19 | (389) ! [v0] : ! [v1] : ( ~ (apply(v0, all_94_0_45) = v1) | ~ relation(v0) | ~ function(v0) | ~ in(all_126_0_55, all_247_0_84) | ? [v2] : (relation_composition(all_0_11_11, v0) = v2 & apply(v2, all_126_0_55) = v1))
% 10.94/3.19 |
% 10.94/3.19 | Instantiating (339) with all_250_0_85 yields:
% 10.94/3.19 | (390) relation_dom(all_0_11_11) = all_250_0_85 & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(all_0_11_11, v0) = v1) | ~ (apply(v1, all_140_0_60) = v2) | ~ relation(v0) | ~ function(v0) | ~ in(all_140_0_60, all_250_0_85) | apply(v0, all_84_0_40) = v2) & ! [v0] : ! [v1] : ( ~ (apply(v0, all_84_0_40) = v1) | ~ relation(v0) | ~ function(v0) | ~ in(all_140_0_60, all_250_0_85) | ? [v2] : (relation_composition(all_0_11_11, v0) = v2 & apply(v2, all_140_0_60) = v1))
% 10.94/3.19 |
% 10.94/3.19 | Applying alpha-rule on (390) yields:
% 10.94/3.19 | (391) relation_dom(all_0_11_11) = all_250_0_85
% 10.94/3.19 | (392) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(all_0_11_11, v0) = v1) | ~ (apply(v1, all_140_0_60) = v2) | ~ relation(v0) | ~ function(v0) | ~ in(all_140_0_60, all_250_0_85) | apply(v0, all_84_0_40) = v2)
% 10.94/3.19 | (393) ! [v0] : ! [v1] : ( ~ (apply(v0, all_84_0_40) = v1) | ~ relation(v0) | ~ function(v0) | ~ in(all_140_0_60, all_250_0_85) | ? [v2] : (relation_composition(all_0_11_11, v0) = v2 & apply(v2, all_140_0_60) = v1))
% 10.94/3.19 |
% 10.94/3.19 | Instantiating (332) with all_253_0_86 yields:
% 10.94/3.19 | (394) relation_dom(all_0_11_11) = all_253_0_86 & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(all_0_11_11, v0) = v1) | ~ (apply(v1, all_185_0_71) = v2) | ~ relation(v0) | ~ function(v0) | ~ in(all_185_0_71, all_253_0_86) | apply(v0, all_84_0_40) = v2) & ! [v0] : ! [v1] : ( ~ (apply(v0, all_84_0_40) = v1) | ~ relation(v0) | ~ function(v0) | ~ in(all_185_0_71, all_253_0_86) | ? [v2] : (relation_composition(all_0_11_11, v0) = v2 & apply(v2, all_185_0_71) = v1))
% 10.94/3.19 |
% 10.94/3.19 | Applying alpha-rule on (394) yields:
% 10.94/3.19 | (395) relation_dom(all_0_11_11) = all_253_0_86
% 10.94/3.19 | (396) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(all_0_11_11, v0) = v1) | ~ (apply(v1, all_185_0_71) = v2) | ~ relation(v0) | ~ function(v0) | ~ in(all_185_0_71, all_253_0_86) | apply(v0, all_84_0_40) = v2)
% 10.94/3.19 | (397) ! [v0] : ! [v1] : ( ~ (apply(v0, all_84_0_40) = v1) | ~ relation(v0) | ~ function(v0) | ~ in(all_185_0_71, all_253_0_86) | ? [v2] : (relation_composition(all_0_11_11, v0) = v2 & apply(v2, all_185_0_71) = v1))
% 10.94/3.19 |
% 10.94/3.19 | Instantiating (335) with all_256_0_87 yields:
% 10.94/3.19 | (398) relation_dom(all_0_11_11) = all_256_0_87 & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(all_0_11_11, v0) = v1) | ~ (apply(v1, all_170_0_68) = v2) | ~ relation(v0) | ~ function(v0) | ~ in(all_170_0_68, all_256_0_87) | apply(v0, all_86_0_41) = v2) & ! [v0] : ! [v1] : ( ~ (apply(v0, all_86_0_41) = v1) | ~ relation(v0) | ~ function(v0) | ~ in(all_170_0_68, all_256_0_87) | ? [v2] : (relation_composition(all_0_11_11, v0) = v2 & apply(v2, all_170_0_68) = v1))
% 10.94/3.19 |
% 10.94/3.19 | Applying alpha-rule on (398) yields:
% 10.94/3.19 | (399) relation_dom(all_0_11_11) = all_256_0_87
% 10.94/3.19 | (400) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(all_0_11_11, v0) = v1) | ~ (apply(v1, all_170_0_68) = v2) | ~ relation(v0) | ~ function(v0) | ~ in(all_170_0_68, all_256_0_87) | apply(v0, all_86_0_41) = v2)
% 10.94/3.19 | (401) ! [v0] : ! [v1] : ( ~ (apply(v0, all_86_0_41) = v1) | ~ relation(v0) | ~ function(v0) | ~ in(all_170_0_68, all_256_0_87) | ? [v2] : (relation_composition(all_0_11_11, v0) = v2 & apply(v2, all_170_0_68) = v1))
% 10.94/3.19 |
% 10.94/3.19 | Instantiating (334) with all_259_0_88 yields:
% 10.94/3.19 | (402) relation_dom(all_0_11_11) = all_259_0_88 & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(all_0_11_11, v0) = v1) | ~ (apply(v1, all_175_0_69) = v2) | ~ relation(v0) | ~ function(v0) | ~ in(all_175_0_69, all_259_0_88) | apply(v0, all_94_0_45) = v2) & ! [v0] : ! [v1] : ( ~ (apply(v0, all_94_0_45) = v1) | ~ relation(v0) | ~ function(v0) | ~ in(all_175_0_69, all_259_0_88) | ? [v2] : (relation_composition(all_0_11_11, v0) = v2 & apply(v2, all_175_0_69) = v1))
% 10.94/3.19 |
% 10.94/3.19 | Applying alpha-rule on (402) yields:
% 10.94/3.19 | (403) relation_dom(all_0_11_11) = all_259_0_88
% 10.94/3.19 | (404) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(all_0_11_11, v0) = v1) | ~ (apply(v1, all_175_0_69) = v2) | ~ relation(v0) | ~ function(v0) | ~ in(all_175_0_69, all_259_0_88) | apply(v0, all_94_0_45) = v2)
% 10.94/3.19 | (405) ! [v0] : ! [v1] : ( ~ (apply(v0, all_94_0_45) = v1) | ~ relation(v0) | ~ function(v0) | ~ in(all_175_0_69, all_259_0_88) | ? [v2] : (relation_composition(all_0_11_11, v0) = v2 & apply(v2, all_175_0_69) = v1))
% 10.94/3.19 |
% 10.94/3.19 | Instantiating (338) with all_262_0_89 yields:
% 10.94/3.19 | (406) relation_dom(all_0_11_11) = all_262_0_89 & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(all_0_11_11, v0) = v1) | ~ (apply(v1, all_142_0_61) = v2) | ~ relation(v0) | ~ function(v0) | ~ in(all_142_0_61, all_262_0_89) | apply(v0, all_86_0_41) = v2) & ! [v0] : ! [v1] : ( ~ (apply(v0, all_86_0_41) = v1) | ~ relation(v0) | ~ function(v0) | ~ in(all_142_0_61, all_262_0_89) | ? [v2] : (relation_composition(all_0_11_11, v0) = v2 & apply(v2, all_142_0_61) = v1))
% 10.94/3.19 |
% 10.94/3.19 | Applying alpha-rule on (406) yields:
% 10.94/3.19 | (407) relation_dom(all_0_11_11) = all_262_0_89
% 10.94/3.19 | (408) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(all_0_11_11, v0) = v1) | ~ (apply(v1, all_142_0_61) = v2) | ~ relation(v0) | ~ function(v0) | ~ in(all_142_0_61, all_262_0_89) | apply(v0, all_86_0_41) = v2)
% 10.94/3.19 | (409) ! [v0] : ! [v1] : ( ~ (apply(v0, all_86_0_41) = v1) | ~ relation(v0) | ~ function(v0) | ~ in(all_142_0_61, all_262_0_89) | ? [v2] : (relation_composition(all_0_11_11, v0) = v2 & apply(v2, all_142_0_61) = v1))
% 10.94/3.19 |
% 10.94/3.19 | Instantiating formula (31) with all_0_11_11, all_259_0_88, all_23_0_18 and discharging atoms relation_dom(all_0_11_11) = all_259_0_88, relation_dom(all_0_11_11) = all_23_0_18, yields:
% 10.94/3.19 | (410) all_259_0_88 = all_23_0_18
% 10.94/3.19 |
% 10.94/3.19 | Instantiating formula (31) with all_0_11_11, all_253_0_86, all_262_0_89 and discharging atoms relation_dom(all_0_11_11) = all_262_0_89, relation_dom(all_0_11_11) = all_253_0_86, yields:
% 10.94/3.19 | (411) all_262_0_89 = all_253_0_86
% 10.94/3.19 |
% 10.94/3.19 | Instantiating formula (31) with all_0_11_11, all_253_0_86, all_256_0_87 and discharging atoms relation_dom(all_0_11_11) = all_256_0_87, relation_dom(all_0_11_11) = all_253_0_86, yields:
% 10.94/3.19 | (412) all_256_0_87 = all_253_0_86
% 10.94/3.19 |
% 10.94/3.19 | Instantiating formula (31) with all_0_11_11, all_247_0_84, all_256_0_87 and discharging atoms relation_dom(all_0_11_11) = all_256_0_87, relation_dom(all_0_11_11) = all_247_0_84, yields:
% 10.94/3.19 | (413) all_256_0_87 = all_247_0_84
% 10.94/3.19 |
% 10.94/3.19 | Instantiating formula (31) with all_0_11_11, all_244_0_83, all_259_0_88 and discharging atoms relation_dom(all_0_11_11) = all_259_0_88, relation_dom(all_0_11_11) = all_244_0_83, yields:
% 10.94/3.19 | (414) all_259_0_88 = all_244_0_83
% 10.94/3.19 |
% 10.94/3.19 | Instantiating formula (31) with all_0_11_11, all_241_0_82, all_250_0_85 and discharging atoms relation_dom(all_0_11_11) = all_250_0_85, relation_dom(all_0_11_11) = all_241_0_82, yields:
% 10.94/3.19 | (415) all_250_0_85 = all_241_0_82
% 10.94/3.19 |
% 10.94/3.19 | Instantiating formula (31) with all_0_11_11, all_238_0_81, all_259_0_88 and discharging atoms relation_dom(all_0_11_11) = all_259_0_88, relation_dom(all_0_11_11) = all_238_0_81, yields:
% 10.94/3.19 | (416) all_259_0_88 = all_238_0_81
% 10.94/3.19 |
% 10.94/3.19 | Instantiating formula (31) with all_0_11_11, all_235_0_80, all_262_0_89 and discharging atoms relation_dom(all_0_11_11) = all_262_0_89, relation_dom(all_0_11_11) = all_235_0_80, yields:
% 10.94/3.19 | (417) all_262_0_89 = all_235_0_80
% 10.94/3.19 |
% 10.94/3.19 | Instantiating formula (31) with all_0_11_11, all_235_0_80, all_241_0_82 and discharging atoms relation_dom(all_0_11_11) = all_241_0_82, relation_dom(all_0_11_11) = all_235_0_80, yields:
% 10.94/3.19 | (418) all_241_0_82 = all_235_0_80
% 10.94/3.19 |
% 10.94/3.19 | Instantiating formula (31) with all_0_11_11, all_232_0_79, all_235_0_80 and discharging atoms relation_dom(all_0_11_11) = all_235_0_80, relation_dom(all_0_11_11) = all_232_0_79, yields:
% 11.05/3.19 | (419) all_235_0_80 = all_232_0_79
% 11.05/3.19 |
% 11.05/3.19 | Instantiating formula (31) with all_0_11_11, all_229_0_78, all_262_0_89 and discharging atoms relation_dom(all_0_11_11) = all_262_0_89, relation_dom(all_0_11_11) = all_229_0_78, yields:
% 11.05/3.19 | (420) all_262_0_89 = all_229_0_78
% 11.05/3.19 |
% 11.05/3.19 | Instantiating formula (31) with all_0_11_11, all_229_0_78, all_259_0_88 and discharging atoms relation_dom(all_0_11_11) = all_259_0_88, relation_dom(all_0_11_11) = all_229_0_78, yields:
% 11.05/3.19 | (421) all_259_0_88 = all_229_0_78
% 11.05/3.19 |
% 11.05/3.19 | Instantiating formula (31) with all_0_11_11, all_226_0_77, all_262_0_89 and discharging atoms relation_dom(all_0_11_11) = all_262_0_89, relation_dom(all_0_11_11) = all_226_0_77, yields:
% 11.05/3.19 | (422) all_262_0_89 = all_226_0_77
% 11.05/3.19 |
% 11.05/3.19 | Instantiating formula (31) with all_0_11_11, all_223_0_76, all_250_0_85 and discharging atoms relation_dom(all_0_11_11) = all_250_0_85, relation_dom(all_0_11_11) = all_223_0_76, yields:
% 11.05/3.19 | (423) all_250_0_85 = all_223_0_76
% 11.05/3.19 |
% 11.05/3.19 | Instantiating formula (31) with all_0_11_11, all_220_0_75, all_253_0_86 and discharging atoms relation_dom(all_0_11_11) = all_253_0_86, relation_dom(all_0_11_11) = all_220_0_75, yields:
% 11.05/3.20 | (424) all_253_0_86 = all_220_0_75
% 11.05/3.20 |
% 11.05/3.20 | Instantiating formula (31) with all_0_11_11, all_217_0_74, all_262_0_89 and discharging atoms relation_dom(all_0_11_11) = all_262_0_89, relation_dom(all_0_11_11) = all_217_0_74, yields:
% 11.05/3.20 | (425) all_262_0_89 = all_217_0_74
% 11.05/3.20 |
% 11.05/3.20 | Combining equations (417,422) yields a new equation:
% 11.05/3.20 | (426) all_235_0_80 = all_226_0_77
% 11.05/3.20 |
% 11.05/3.20 | Simplifying 426 yields:
% 11.05/3.20 | (427) all_235_0_80 = all_226_0_77
% 11.05/3.20 |
% 11.05/3.20 | Combining equations (411,422) yields a new equation:
% 11.05/3.20 | (428) all_253_0_86 = all_226_0_77
% 11.05/3.20 |
% 11.05/3.20 | Simplifying 428 yields:
% 11.05/3.20 | (429) all_253_0_86 = all_226_0_77
% 11.05/3.20 |
% 11.05/3.20 | Combining equations (425,422) yields a new equation:
% 11.05/3.20 | (430) all_226_0_77 = all_217_0_74
% 11.05/3.20 |
% 11.05/3.20 | Combining equations (420,422) yields a new equation:
% 11.05/3.20 | (431) all_229_0_78 = all_226_0_77
% 11.05/3.20 |
% 11.05/3.20 | Simplifying 431 yields:
% 11.05/3.20 | (432) all_229_0_78 = all_226_0_77
% 11.05/3.20 |
% 11.05/3.20 | Combining equations (410,414) yields a new equation:
% 11.05/3.20 | (433) all_244_0_83 = all_23_0_18
% 11.05/3.20 |
% 11.05/3.20 | Combining equations (416,414) yields a new equation:
% 11.05/3.20 | (434) all_244_0_83 = all_238_0_81
% 11.05/3.20 |
% 11.05/3.20 | Combining equations (421,414) yields a new equation:
% 11.05/3.20 | (435) all_244_0_83 = all_229_0_78
% 11.05/3.20 |
% 11.05/3.20 | Combining equations (412,413) yields a new equation:
% 11.05/3.20 | (436) all_253_0_86 = all_247_0_84
% 11.05/3.20 |
% 11.05/3.20 | Simplifying 436 yields:
% 11.05/3.20 | (437) all_253_0_86 = all_247_0_84
% 11.05/3.20 |
% 11.05/3.20 | Combining equations (429,437) yields a new equation:
% 11.05/3.20 | (438) all_247_0_84 = all_226_0_77
% 11.05/3.20 |
% 11.05/3.20 | Combining equations (424,437) yields a new equation:
% 11.05/3.20 | (439) all_247_0_84 = all_220_0_75
% 11.05/3.20 |
% 11.05/3.20 | Combining equations (415,423) yields a new equation:
% 11.05/3.20 | (440) all_241_0_82 = all_223_0_76
% 11.05/3.20 |
% 11.05/3.20 | Simplifying 440 yields:
% 11.05/3.20 | (441) all_241_0_82 = all_223_0_76
% 11.05/3.20 |
% 11.05/3.20 | Combining equations (438,439) yields a new equation:
% 11.05/3.20 | (442) all_226_0_77 = all_220_0_75
% 11.05/3.20 |
% 11.05/3.20 | Simplifying 442 yields:
% 11.05/3.20 | (443) all_226_0_77 = all_220_0_75
% 11.05/3.20 |
% 11.05/3.20 | Combining equations (433,434) yields a new equation:
% 11.05/3.20 | (444) all_238_0_81 = all_23_0_18
% 11.05/3.20 |
% 11.05/3.20 | Combining equations (435,434) yields a new equation:
% 11.05/3.20 | (445) all_238_0_81 = all_229_0_78
% 11.05/3.20 |
% 11.05/3.20 | Combining equations (418,441) yields a new equation:
% 11.05/3.20 | (446) all_235_0_80 = all_223_0_76
% 11.05/3.20 |
% 11.05/3.20 | Simplifying 446 yields:
% 11.05/3.20 | (447) all_235_0_80 = all_223_0_76
% 11.05/3.20 |
% 11.05/3.20 | Combining equations (445,444) yields a new equation:
% 11.05/3.20 | (448) all_229_0_78 = all_23_0_18
% 11.05/3.20 |
% 11.05/3.20 | Simplifying 448 yields:
% 11.05/3.20 | (449) all_229_0_78 = all_23_0_18
% 11.05/3.20 |
% 11.05/3.20 | Combining equations (447,419) yields a new equation:
% 11.05/3.20 | (450) all_232_0_79 = all_223_0_76
% 11.05/3.20 |
% 11.05/3.20 | Combining equations (427,419) yields a new equation:
% 11.05/3.20 | (451) all_232_0_79 = all_226_0_77
% 11.05/3.20 |
% 11.05/3.20 | Combining equations (451,450) yields a new equation:
% 11.05/3.20 | (452) all_226_0_77 = all_223_0_76
% 11.05/3.20 |
% 11.05/3.20 | Simplifying 452 yields:
% 11.05/3.20 | (453) all_226_0_77 = all_223_0_76
% 11.05/3.20 |
% 11.05/3.20 | Combining equations (432,449) yields a new equation:
% 11.05/3.20 | (454) all_226_0_77 = all_23_0_18
% 11.05/3.20 |
% 11.05/3.20 | Simplifying 454 yields:
% 11.05/3.20 | (455) all_226_0_77 = all_23_0_18
% 11.05/3.20 |
% 11.05/3.20 | Combining equations (430,453) yields a new equation:
% 11.05/3.20 | (456) all_223_0_76 = all_217_0_74
% 11.05/3.20 |
% 11.05/3.20 | Combining equations (443,453) yields a new equation:
% 11.05/3.20 | (457) all_223_0_76 = all_220_0_75
% 11.05/3.20 |
% 11.05/3.20 | Combining equations (455,453) yields a new equation:
% 11.05/3.20 | (458) all_223_0_76 = all_23_0_18
% 11.05/3.20 |
% 11.05/3.20 | Combining equations (458,457) yields a new equation:
% 11.05/3.20 | (459) all_220_0_75 = all_23_0_18
% 11.05/3.20 |
% 11.05/3.20 | Combining equations (456,457) yields a new equation:
% 11.05/3.20 | (460) all_220_0_75 = all_217_0_74
% 11.05/3.20 |
% 11.05/3.20 | Combining equations (460,459) yields a new equation:
% 11.05/3.20 | (461) all_217_0_74 = all_23_0_18
% 11.05/3.20 |
% 11.05/3.20 | Simplifying 461 yields:
% 11.05/3.20 | (462) all_217_0_74 = all_23_0_18
% 11.05/3.20 |
% 11.05/3.20 | Combining equations (459,457) yields a new equation:
% 11.05/3.20 | (458) all_223_0_76 = all_23_0_18
% 11.05/3.20 |
% 11.05/3.20 | Combining equations (458,453) yields a new equation:
% 11.05/3.20 | (455) all_226_0_77 = all_23_0_18
% 11.05/3.20 |
% 11.05/3.20 | Combining equations (458,450) yields a new equation:
% 11.05/3.20 | (465) all_232_0_79 = all_23_0_18
% 11.05/3.20 |
% 11.05/3.20 | Combining equations (465,419) yields a new equation:
% 11.05/3.20 | (466) all_235_0_80 = all_23_0_18
% 11.05/3.20 |
% 11.05/3.20 | Combining equations (458,441) yields a new equation:
% 11.05/3.20 | (467) all_241_0_82 = all_23_0_18
% 11.05/3.20 |
% 11.05/3.20 | Combining equations (444,434) yields a new equation:
% 11.05/3.20 | (433) all_244_0_83 = all_23_0_18
% 11.05/3.20 |
% 11.05/3.20 | Combining equations (459,439) yields a new equation:
% 11.05/3.20 | (469) all_247_0_84 = all_23_0_18
% 11.05/3.20 |
% 11.05/3.20 | Combining equations (458,423) yields a new equation:
% 11.05/3.20 | (470) all_250_0_85 = all_23_0_18
% 11.05/3.20 |
% 11.05/3.20 | Combining equations (469,437) yields a new equation:
% 11.05/3.20 | (471) all_253_0_86 = all_23_0_18
% 11.05/3.20 |
% 11.05/3.20 | Combining equations (469,413) yields a new equation:
% 11.05/3.20 | (472) all_256_0_87 = all_23_0_18
% 11.05/3.20 |
% 11.05/3.20 | Combining equations (433,414) yields a new equation:
% 11.05/3.20 | (410) all_259_0_88 = all_23_0_18
% 11.05/3.20 |
% 11.05/3.20 | Combining equations (455,422) yields a new equation:
% 11.05/3.20 | (474) all_262_0_89 = all_23_0_18
% 11.05/3.20 |
% 11.05/3.20 | Instantiating formula (377) with all_33_0_22, all_0_10_10 and discharging atoms apply(all_0_10_10, all_92_0_44) = all_33_0_22, relation(all_0_10_10), function(all_0_10_10), yields:
% 11.05/3.20 | (475) ~ in(all_195_0_73, all_238_0_81) | ? [v0] : (relation_composition(all_0_11_11, all_0_10_10) = v0 & apply(v0, all_195_0_73) = all_33_0_22)
% 11.05/3.20 |
% 11.05/3.20 | Instantiating formula (361) with all_33_1_23, all_0_8_8 and discharging atoms apply(all_0_8_8, all_90_0_43) = all_33_1_23, relation(all_0_8_8), function(all_0_8_8), yields:
% 11.05/3.20 | (476) ~ in(all_190_0_72, all_226_0_77) | ? [v0] : (relation_composition(all_0_11_11, all_0_8_8) = v0 & apply(v0, all_190_0_72) = all_33_1_23)
% 11.05/3.20 |
% 11.05/3.20 | Instantiating formula (397) with all_38_1_26, all_0_10_10 and discharging atoms apply(all_0_10_10, all_84_0_40) = all_38_1_26, relation(all_0_10_10), function(all_0_10_10), yields:
% 11.05/3.20 | (477) ~ in(all_185_0_71, all_253_0_86) | ? [v0] : (relation_composition(all_0_11_11, all_0_10_10) = v0 & apply(v0, all_185_0_71) = all_38_1_26)
% 11.05/3.20 |
% 11.05/3.20 | Instantiating formula (357) with all_38_0_25, all_0_8_8 and discharging atoms apply(all_0_8_8, all_88_0_42) = all_38_0_25, relation(all_0_8_8), function(all_0_8_8), yields:
% 11.05/3.20 | (478) ~ in(all_180_0_70, all_223_0_76) | ? [v0] : (relation_composition(all_0_11_11, all_0_8_8) = v0 & apply(v0, all_180_0_70) = all_38_0_25)
% 11.05/3.20 |
% 11.05/3.20 | Instantiating formula (405) with all_33_0_22, all_0_10_10 and discharging atoms apply(all_0_10_10, all_94_0_45) = all_33_0_22, relation(all_0_10_10), function(all_0_10_10), yields:
% 11.05/3.20 | (479) ~ in(all_175_0_69, all_259_0_88) | ? [v0] : (relation_composition(all_0_11_11, all_0_10_10) = v0 & apply(v0, all_175_0_69) = all_33_0_22)
% 11.05/3.20 |
% 11.05/3.20 | Instantiating formula (401) with all_38_0_25, all_0_8_8 and discharging atoms apply(all_0_8_8, all_86_0_41) = all_38_0_25, relation(all_0_8_8), function(all_0_8_8), yields:
% 11.05/3.20 | (480) ~ in(all_170_0_68, all_256_0_87) | ? [v0] : (relation_composition(all_0_11_11, all_0_8_8) = v0 & apply(v0, all_170_0_68) = all_38_0_25)
% 11.05/3.20 |
% 11.05/3.20 | Instantiating formula (353) with all_33_1_23, all_0_8_8 and discharging atoms apply(all_0_8_8, all_102_0_48) = all_33_1_23, relation(all_0_8_8), function(all_0_8_8), yields:
% 11.05/3.20 | (481) ~ in(all_165_0_67, all_220_0_75) | ? [v0] : (relation_composition(all_0_11_11, all_0_8_8) = v0 & apply(v0, all_165_0_67) = all_33_1_23)
% 11.05/3.20 |
% 11.05/3.20 | Instantiating formula (349) with all_38_1_26, all_0_10_10 and discharging atoms apply(all_0_10_10, all_104_0_49) = all_38_1_26, relation(all_0_10_10), function(all_0_10_10), yields:
% 11.05/3.20 | (482) ~ in(all_160_0_66, all_217_0_74) | ? [v0] : (relation_composition(all_0_11_11, all_0_10_10) = v0 & apply(v0, all_160_0_66) = all_38_1_26)
% 11.05/3.20 |
% 11.05/3.20 | Instantiating formula (409) with all_38_0_25, all_0_8_8 and discharging atoms apply(all_0_8_8, all_86_0_41) = all_38_0_25, relation(all_0_8_8), function(all_0_8_8), yields:
% 11.05/3.20 | (483) ~ in(all_142_0_61, all_262_0_89) | ? [v0] : (relation_composition(all_0_11_11, all_0_8_8) = v0 & apply(v0, all_142_0_61) = all_38_0_25)
% 11.05/3.20 |
% 11.05/3.20 | Instantiating formula (393) with all_38_1_26, all_0_10_10 and discharging atoms apply(all_0_10_10, all_84_0_40) = all_38_1_26, relation(all_0_10_10), function(all_0_10_10), yields:
% 11.05/3.20 | (484) ~ in(all_140_0_60, all_250_0_85) | ? [v0] : (relation_composition(all_0_11_11, all_0_10_10) = v0 & apply(v0, all_140_0_60) = all_38_1_26)
% 11.05/3.20 |
% 11.05/3.20 | Instantiating formula (389) with all_33_0_22, all_0_10_10 and discharging atoms apply(all_0_10_10, all_94_0_45) = all_33_0_22, relation(all_0_10_10), function(all_0_10_10), yields:
% 11.05/3.20 | (485) ~ in(all_126_0_55, all_247_0_84) | ? [v0] : (relation_composition(all_0_11_11, all_0_10_10) = v0 & apply(v0, all_126_0_55) = all_33_0_22)
% 11.05/3.20 |
% 11.05/3.20 | Instantiating formula (385) with all_33_1_23, all_0_8_8 and discharging atoms apply(all_0_8_8, all_90_0_43) = all_33_1_23, relation(all_0_8_8), function(all_0_8_8), yields:
% 11.05/3.20 | (486) ~ in(all_124_0_54, all_244_0_83) | ? [v0] : (relation_composition(all_0_11_11, all_0_8_8) = v0 & apply(v0, all_124_0_54) = all_33_1_23)
% 11.05/3.20 |
% 11.05/3.20 | Instantiating formula (373) with all_33_1_23, all_0_8_8 and discharging atoms apply(all_0_8_8, all_102_0_48) = all_33_1_23, relation(all_0_8_8), function(all_0_8_8), yields:
% 11.05/3.20 | (487) ~ in(all_122_0_53, all_235_0_80) | ? [v0] : (relation_composition(all_0_11_11, all_0_8_8) = v0 & apply(v0, all_122_0_53) = all_33_1_23)
% 11.05/3.20 |
% 11.05/3.20 | Instantiating formula (369) with all_38_1_26, all_0_10_10 and discharging atoms apply(all_0_10_10, all_104_0_49) = all_38_1_26, relation(all_0_10_10), function(all_0_10_10), yields:
% 11.05/3.20 | (488) ~ in(all_120_0_52, all_232_0_79) | ? [v0] : (relation_composition(all_0_11_11, all_0_10_10) = v0 & apply(v0, all_120_0_52) = all_38_1_26)
% 11.05/3.20 |
% 11.05/3.20 | Instantiating formula (381) with all_38_0_25, all_0_8_8 and discharging atoms apply(all_0_8_8, all_88_0_42) = all_38_0_25, relation(all_0_8_8), function(all_0_8_8), yields:
% 11.05/3.20 | (489) ~ in(all_118_0_51, all_241_0_82) | ? [v0] : (relation_composition(all_0_11_11, all_0_8_8) = v0 & apply(v0, all_118_0_51) = all_38_0_25)
% 11.05/3.20 |
% 11.05/3.20 | Instantiating formula (365) with all_33_0_22, all_0_10_10 and discharging atoms apply(all_0_10_10, all_92_0_44) = all_33_0_22, relation(all_0_10_10), function(all_0_10_10), yields:
% 11.05/3.20 | (490) ~ in(all_116_0_50, all_229_0_78) | ? [v0] : (relation_composition(all_0_11_11, all_0_10_10) = v0 & apply(v0, all_116_0_50) = all_33_0_22)
% 11.05/3.20 |
% 11.05/3.20 | Instantiating formula (210) with all_38_0_25, all_0_8_8 and discharging atoms apply(all_0_8_8, all_38_2_27) = all_38_0_25, relation(all_0_8_8), function(all_0_8_8), yields:
% 11.05/3.20 | (491) ~ in(all_66_0_35, all_99_0_47) | ? [v0] : (relation_composition(all_0_11_11, all_0_8_8) = v0 & apply(v0, all_66_0_35) = all_38_0_25)
% 11.05/3.20 |
% 11.05/3.20 | Instantiating formula (210) with all_38_1_26, all_0_10_10 and discharging atoms apply(all_0_10_10, all_38_2_27) = all_38_1_26, relation(all_0_10_10), function(all_0_10_10), yields:
% 11.05/3.20 | (492) ~ in(all_66_0_35, all_99_0_47) | ? [v0] : (relation_composition(all_0_11_11, all_0_10_10) = v0 & apply(v0, all_66_0_35) = all_38_1_26)
% 11.05/3.20 |
% 11.05/3.20 | Instantiating formula (206) with all_33_1_23, all_0_8_8 and discharging atoms apply(all_0_8_8, all_33_2_24) = all_33_1_23, relation(all_0_8_8), function(all_0_8_8), yields:
% 11.05/3.20 | (493) ~ in(all_55_0_31, all_96_0_46) | ? [v0] : (relation_composition(all_0_11_11, all_0_8_8) = v0 & apply(v0, all_55_0_31) = all_33_1_23)
% 11.05/3.20 |
% 11.05/3.20 | Instantiating formula (206) with all_33_0_22, all_0_10_10 and discharging atoms apply(all_0_10_10, all_33_2_24) = all_33_0_22, relation(all_0_10_10), function(all_0_10_10), yields:
% 11.05/3.20 | (494) ~ in(all_55_0_31, all_96_0_46) | ? [v0] : (relation_composition(all_0_11_11, all_0_10_10) = v0 & apply(v0, all_55_0_31) = all_33_0_22)
% 11.05/3.20 |
% 11.05/3.20 +-Applying beta-rule and splitting (494), into two cases.
% 11.05/3.20 |-Branch one:
% 11.05/3.20 | (495) ~ in(all_55_0_31, all_96_0_46)
% 11.05/3.20 |
% 11.05/3.20 | From (223) and (495) follows:
% 11.05/3.20 | (496) ~ in(all_55_0_31, all_23_0_18)
% 11.05/3.21 |
% 11.05/3.21 | Using (140) and (496) yields:
% 11.05/3.21 | (268) $false
% 11.05/3.21 |
% 11.05/3.21 |-The branch is then unsatisfiable
% 11.05/3.21 |-Branch two:
% 11.05/3.21 | (498) in(all_55_0_31, all_96_0_46)
% 11.05/3.21 | (499) ? [v0] : (relation_composition(all_0_11_11, all_0_10_10) = v0 & apply(v0, all_55_0_31) = all_33_0_22)
% 11.05/3.21 |
% 11.05/3.21 | Instantiating (499) with all_401_0_94 yields:
% 11.05/3.21 | (500) relation_composition(all_0_11_11, all_0_10_10) = all_401_0_94 & apply(all_401_0_94, all_55_0_31) = all_33_0_22
% 11.05/3.21 |
% 11.05/3.21 | Applying alpha-rule on (500) yields:
% 11.05/3.21 | (501) relation_composition(all_0_11_11, all_0_10_10) = all_401_0_94
% 11.05/3.21 | (502) apply(all_401_0_94, all_55_0_31) = all_33_0_22
% 11.05/3.21 |
% 11.05/3.21 | From (223) and (498) follows:
% 11.05/3.21 | (140) in(all_55_0_31, all_23_0_18)
% 11.05/3.21 |
% 11.05/3.21 +-Applying beta-rule and splitting (493), into two cases.
% 11.05/3.21 |-Branch one:
% 11.05/3.21 | (495) ~ in(all_55_0_31, all_96_0_46)
% 11.05/3.21 |
% 11.05/3.21 | From (223) and (495) follows:
% 11.05/3.21 | (496) ~ in(all_55_0_31, all_23_0_18)
% 11.05/3.21 |
% 11.05/3.21 | Using (140) and (496) yields:
% 11.05/3.21 | (268) $false
% 11.05/3.21 |
% 11.05/3.21 |-The branch is then unsatisfiable
% 11.05/3.21 |-Branch two:
% 11.05/3.21 | (498) in(all_55_0_31, all_96_0_46)
% 11.05/3.21 | (508) ? [v0] : (relation_composition(all_0_11_11, all_0_8_8) = v0 & apply(v0, all_55_0_31) = all_33_1_23)
% 11.05/3.21 |
% 11.05/3.21 | Instantiating (508) with all_412_0_96 yields:
% 11.05/3.21 | (509) relation_composition(all_0_11_11, all_0_8_8) = all_412_0_96 & apply(all_412_0_96, all_55_0_31) = all_33_1_23
% 11.05/3.21 |
% 11.05/3.21 | Applying alpha-rule on (509) yields:
% 11.05/3.21 | (510) relation_composition(all_0_11_11, all_0_8_8) = all_412_0_96
% 11.05/3.21 | (511) apply(all_412_0_96, all_55_0_31) = all_33_1_23
% 11.05/3.21 |
% 11.05/3.21 +-Applying beta-rule and splitting (491), into two cases.
% 11.05/3.21 |-Branch one:
% 11.05/3.21 | (512) ~ in(all_66_0_35, all_99_0_47)
% 11.05/3.21 |
% 11.05/3.21 | From (221) and (512) follows:
% 11.05/3.21 | (513) ~ in(all_66_0_35, all_23_0_18)
% 11.05/3.21 |
% 11.05/3.21 | Using (156) and (513) yields:
% 11.05/3.21 | (268) $false
% 11.05/3.21 |
% 11.05/3.21 |-The branch is then unsatisfiable
% 11.05/3.21 |-Branch two:
% 11.05/3.21 | (515) in(all_66_0_35, all_99_0_47)
% 11.05/3.21 | (516) ? [v0] : (relation_composition(all_0_11_11, all_0_8_8) = v0 & apply(v0, all_66_0_35) = all_38_0_25)
% 11.05/3.21 |
% 11.05/3.21 | Instantiating (516) with all_418_0_97 yields:
% 11.05/3.21 | (517) relation_composition(all_0_11_11, all_0_8_8) = all_418_0_97 & apply(all_418_0_97, all_66_0_35) = all_38_0_25
% 11.05/3.21 |
% 11.05/3.21 | Applying alpha-rule on (517) yields:
% 11.05/3.21 | (518) relation_composition(all_0_11_11, all_0_8_8) = all_418_0_97
% 11.05/3.21 | (519) apply(all_418_0_97, all_66_0_35) = all_38_0_25
% 11.05/3.21 |
% 11.05/3.21 | From (221) and (515) follows:
% 11.05/3.21 | (156) in(all_66_0_35, all_23_0_18)
% 11.05/3.21 |
% 11.05/3.21 +-Applying beta-rule and splitting (490), into two cases.
% 11.05/3.21 |-Branch one:
% 11.05/3.21 | (521) ~ in(all_116_0_50, all_229_0_78)
% 11.05/3.21 |
% 11.05/3.21 | From (449) and (521) follows:
% 11.05/3.21 | (522) ~ in(all_116_0_50, all_23_0_18)
% 11.05/3.21 |
% 11.05/3.21 | Using (244) and (522) yields:
% 11.05/3.21 | (268) $false
% 11.05/3.21 |
% 11.05/3.21 |-The branch is then unsatisfiable
% 11.05/3.21 |-Branch two:
% 11.05/3.21 | (524) in(all_116_0_50, all_229_0_78)
% 11.05/3.21 | (525) ? [v0] : (relation_composition(all_0_11_11, all_0_10_10) = v0 & apply(v0, all_116_0_50) = all_33_0_22)
% 11.05/3.21 |
% 11.05/3.21 | Instantiating (525) with all_429_0_99 yields:
% 11.05/3.21 | (526) relation_composition(all_0_11_11, all_0_10_10) = all_429_0_99 & apply(all_429_0_99, all_116_0_50) = all_33_0_22
% 11.05/3.21 |
% 11.05/3.21 | Applying alpha-rule on (526) yields:
% 11.05/3.21 | (527) relation_composition(all_0_11_11, all_0_10_10) = all_429_0_99
% 11.05/3.21 | (528) apply(all_429_0_99, all_116_0_50) = all_33_0_22
% 11.05/3.21 |
% 11.05/3.21 +-Applying beta-rule and splitting (483), into two cases.
% 11.05/3.21 |-Branch one:
% 11.05/3.21 | (529) ~ in(all_142_0_61, all_262_0_89)
% 11.05/3.21 |
% 11.05/3.21 | From (474) and (529) follows:
% 11.05/3.21 | (530) ~ in(all_142_0_61, all_23_0_18)
% 11.05/3.21 |
% 11.05/3.21 | Using (265) and (530) yields:
% 11.05/3.21 | (268) $false
% 11.05/3.21 |
% 11.05/3.21 |-The branch is then unsatisfiable
% 11.05/3.21 |-Branch two:
% 11.05/3.21 | (532) in(all_142_0_61, all_262_0_89)
% 11.05/3.21 | (533) ? [v0] : (relation_composition(all_0_11_11, all_0_8_8) = v0 & apply(v0, all_142_0_61) = all_38_0_25)
% 11.05/3.21 |
% 11.05/3.21 | Instantiating (533) with all_455_0_104 yields:
% 11.05/3.21 | (534) relation_composition(all_0_11_11, all_0_8_8) = all_455_0_104 & apply(all_455_0_104, all_142_0_61) = all_38_0_25
% 11.05/3.21 |
% 11.05/3.21 | Applying alpha-rule on (534) yields:
% 11.05/3.21 | (535) relation_composition(all_0_11_11, all_0_8_8) = all_455_0_104
% 11.05/3.21 | (536) apply(all_455_0_104, all_142_0_61) = all_38_0_25
% 11.05/3.21 |
% 11.05/3.21 +-Applying beta-rule and splitting (492), into two cases.
% 11.05/3.21 |-Branch one:
% 11.05/3.21 | (512) ~ in(all_66_0_35, all_99_0_47)
% 11.05/3.21 |
% 11.05/3.21 | From (221) and (512) follows:
% 11.05/3.21 | (513) ~ in(all_66_0_35, all_23_0_18)
% 11.05/3.21 |
% 11.05/3.21 | Using (156) and (513) yields:
% 11.05/3.21 | (268) $false
% 11.05/3.21 |
% 11.05/3.21 |-The branch is then unsatisfiable
% 11.05/3.21 |-Branch two:
% 11.05/3.21 | (515) in(all_66_0_35, all_99_0_47)
% 11.05/3.21 | (541) ? [v0] : (relation_composition(all_0_11_11, all_0_10_10) = v0 & apply(v0, all_66_0_35) = all_38_1_26)
% 11.05/3.21 |
% 11.05/3.21 | Instantiating (541) with all_461_0_105 yields:
% 11.05/3.21 | (542) relation_composition(all_0_11_11, all_0_10_10) = all_461_0_105 & apply(all_461_0_105, all_66_0_35) = all_38_1_26
% 11.05/3.21 |
% 11.05/3.21 | Applying alpha-rule on (542) yields:
% 11.05/3.21 | (543) relation_composition(all_0_11_11, all_0_10_10) = all_461_0_105
% 11.05/3.21 | (544) apply(all_461_0_105, all_66_0_35) = all_38_1_26
% 11.05/3.21 |
% 11.05/3.21 +-Applying beta-rule and splitting (489), into two cases.
% 11.05/3.21 |-Branch one:
% 11.05/3.21 | (545) ~ in(all_118_0_51, all_241_0_82)
% 11.05/3.21 |
% 11.05/3.21 | From (467) and (545) follows:
% 11.05/3.21 | (546) ~ in(all_118_0_51, all_23_0_18)
% 11.05/3.21 |
% 11.05/3.21 | Using (247) and (546) yields:
% 11.05/3.21 | (268) $false
% 11.05/3.21 |
% 11.05/3.21 |-The branch is then unsatisfiable
% 11.05/3.21 |-Branch two:
% 11.05/3.21 | (548) in(all_118_0_51, all_241_0_82)
% 11.05/3.21 | (549) ? [v0] : (relation_composition(all_0_11_11, all_0_8_8) = v0 & apply(v0, all_118_0_51) = all_38_0_25)
% 11.05/3.21 |
% 11.05/3.21 | Instantiating (549) with all_467_0_106 yields:
% 11.05/3.21 | (550) relation_composition(all_0_11_11, all_0_8_8) = all_467_0_106 & apply(all_467_0_106, all_118_0_51) = all_38_0_25
% 11.05/3.21 |
% 11.05/3.21 | Applying alpha-rule on (550) yields:
% 11.05/3.21 | (551) relation_composition(all_0_11_11, all_0_8_8) = all_467_0_106
% 11.05/3.21 | (552) apply(all_467_0_106, all_118_0_51) = all_38_0_25
% 11.05/3.21 |
% 11.05/3.21 +-Applying beta-rule and splitting (487), into two cases.
% 11.05/3.21 |-Branch one:
% 11.05/3.21 | (553) ~ in(all_122_0_53, all_235_0_80)
% 11.05/3.21 |
% 11.05/3.21 | From (466) and (553) follows:
% 11.05/3.21 | (554) ~ in(all_122_0_53, all_23_0_18)
% 11.05/3.21 |
% 11.05/3.21 | Using (253) and (554) yields:
% 11.05/3.21 | (268) $false
% 11.05/3.21 |
% 11.05/3.21 |-The branch is then unsatisfiable
% 11.05/3.21 |-Branch two:
% 11.05/3.21 | (556) in(all_122_0_53, all_235_0_80)
% 11.05/3.21 | (557) ? [v0] : (relation_composition(all_0_11_11, all_0_8_8) = v0 & apply(v0, all_122_0_53) = all_33_1_23)
% 11.05/3.21 |
% 11.05/3.21 | Instantiating (557) with all_473_0_107 yields:
% 11.05/3.21 | (558) relation_composition(all_0_11_11, all_0_8_8) = all_473_0_107 & apply(all_473_0_107, all_122_0_53) = all_33_1_23
% 11.05/3.21 |
% 11.05/3.21 | Applying alpha-rule on (558) yields:
% 11.05/3.21 | (559) relation_composition(all_0_11_11, all_0_8_8) = all_473_0_107
% 11.05/3.21 | (560) apply(all_473_0_107, all_122_0_53) = all_33_1_23
% 11.05/3.21 |
% 11.05/3.21 +-Applying beta-rule and splitting (486), into two cases.
% 11.05/3.21 |-Branch one:
% 11.05/3.21 | (561) ~ in(all_124_0_54, all_244_0_83)
% 11.05/3.21 |
% 11.05/3.21 | From (433) and (561) follows:
% 11.05/3.21 | (562) ~ in(all_124_0_54, all_23_0_18)
% 11.05/3.21 |
% 11.05/3.21 | Using (256) and (562) yields:
% 11.05/3.21 | (268) $false
% 11.05/3.21 |
% 11.05/3.21 |-The branch is then unsatisfiable
% 11.05/3.21 |-Branch two:
% 11.05/3.21 | (564) in(all_124_0_54, all_244_0_83)
% 11.05/3.21 | (565) ? [v0] : (relation_composition(all_0_11_11, all_0_8_8) = v0 & apply(v0, all_124_0_54) = all_33_1_23)
% 11.05/3.21 |
% 11.05/3.21 | Instantiating (565) with all_479_0_108 yields:
% 11.05/3.21 | (566) relation_composition(all_0_11_11, all_0_8_8) = all_479_0_108 & apply(all_479_0_108, all_124_0_54) = all_33_1_23
% 11.05/3.21 |
% 11.05/3.21 | Applying alpha-rule on (566) yields:
% 11.05/3.21 | (567) relation_composition(all_0_11_11, all_0_8_8) = all_479_0_108
% 11.05/3.21 | (568) apply(all_479_0_108, all_124_0_54) = all_33_1_23
% 11.05/3.21 |
% 11.05/3.21 +-Applying beta-rule and splitting (488), into two cases.
% 11.05/3.21 |-Branch one:
% 11.05/3.21 | (569) ~ in(all_120_0_52, all_232_0_79)
% 11.05/3.21 |
% 11.05/3.21 | From (465) and (569) follows:
% 11.05/3.21 | (570) ~ in(all_120_0_52, all_23_0_18)
% 11.05/3.21 |
% 11.05/3.21 | Using (250) and (570) yields:
% 11.05/3.21 | (268) $false
% 11.05/3.21 |
% 11.05/3.21 |-The branch is then unsatisfiable
% 11.05/3.21 |-Branch two:
% 11.05/3.21 | (572) in(all_120_0_52, all_232_0_79)
% 11.05/3.21 | (573) ? [v0] : (relation_composition(all_0_11_11, all_0_10_10) = v0 & apply(v0, all_120_0_52) = all_38_1_26)
% 11.05/3.21 |
% 11.05/3.21 | Instantiating (573) with all_485_0_109 yields:
% 11.05/3.21 | (574) relation_composition(all_0_11_11, all_0_10_10) = all_485_0_109 & apply(all_485_0_109, all_120_0_52) = all_38_1_26
% 11.05/3.21 |
% 11.05/3.21 | Applying alpha-rule on (574) yields:
% 11.05/3.21 | (575) relation_composition(all_0_11_11, all_0_10_10) = all_485_0_109
% 11.05/3.21 | (576) apply(all_485_0_109, all_120_0_52) = all_38_1_26
% 11.05/3.21 |
% 11.05/3.21 +-Applying beta-rule and splitting (481), into two cases.
% 11.05/3.21 |-Branch one:
% 11.05/3.21 | (577) ~ in(all_165_0_67, all_220_0_75)
% 11.05/3.21 |
% 11.05/3.21 | From (459) and (577) follows:
% 11.05/3.21 | (578) ~ in(all_165_0_67, all_23_0_18)
% 11.05/3.21 |
% 11.05/3.21 | Using (281) and (578) yields:
% 11.05/3.21 | (268) $false
% 11.05/3.21 |
% 11.05/3.21 |-The branch is then unsatisfiable
% 11.05/3.21 |-Branch two:
% 11.05/3.21 | (580) in(all_165_0_67, all_220_0_75)
% 11.05/3.21 | (581) ? [v0] : (relation_composition(all_0_11_11, all_0_8_8) = v0 & apply(v0, all_165_0_67) = all_33_1_23)
% 11.05/3.21 |
% 11.05/3.21 | Instantiating (581) with all_491_0_110 yields:
% 11.05/3.21 | (582) relation_composition(all_0_11_11, all_0_8_8) = all_491_0_110 & apply(all_491_0_110, all_165_0_67) = all_33_1_23
% 11.05/3.21 |
% 11.05/3.21 | Applying alpha-rule on (582) yields:
% 11.05/3.21 | (583) relation_composition(all_0_11_11, all_0_8_8) = all_491_0_110
% 11.05/3.21 | (584) apply(all_491_0_110, all_165_0_67) = all_33_1_23
% 11.05/3.21 |
% 11.05/3.21 +-Applying beta-rule and splitting (482), into two cases.
% 11.05/3.21 |-Branch one:
% 11.05/3.21 | (585) ~ in(all_160_0_66, all_217_0_74)
% 11.05/3.21 |
% 11.05/3.21 | From (462) and (585) follows:
% 11.05/3.21 | (586) ~ in(all_160_0_66, all_23_0_18)
% 11.05/3.21 |
% 11.05/3.21 | Using (273) and (586) yields:
% 11.05/3.21 | (268) $false
% 11.05/3.21 |
% 11.05/3.21 |-The branch is then unsatisfiable
% 11.05/3.21 |-Branch two:
% 11.05/3.21 | (588) in(all_160_0_66, all_217_0_74)
% 11.05/3.21 | (589) ? [v0] : (relation_composition(all_0_11_11, all_0_10_10) = v0 & apply(v0, all_160_0_66) = all_38_1_26)
% 11.05/3.21 |
% 11.05/3.21 | Instantiating (589) with all_512_0_114 yields:
% 11.05/3.21 | (590) relation_composition(all_0_11_11, all_0_10_10) = all_512_0_114 & apply(all_512_0_114, all_160_0_66) = all_38_1_26
% 11.05/3.21 |
% 11.05/3.21 | Applying alpha-rule on (590) yields:
% 11.05/3.21 | (591) relation_composition(all_0_11_11, all_0_10_10) = all_512_0_114
% 11.05/3.21 | (592) apply(all_512_0_114, all_160_0_66) = all_38_1_26
% 11.05/3.21 |
% 11.05/3.21 +-Applying beta-rule and splitting (480), into two cases.
% 11.05/3.21 |-Branch one:
% 11.05/3.21 | (593) ~ in(all_170_0_68, all_256_0_87)
% 11.05/3.21 |
% 11.05/3.21 | From (472) and (593) follows:
% 11.05/3.21 | (594) ~ in(all_170_0_68, all_23_0_18)
% 11.05/3.21 |
% 11.05/3.21 | Using (289) and (594) yields:
% 11.05/3.21 | (268) $false
% 11.05/3.21 |
% 11.05/3.21 |-The branch is then unsatisfiable
% 11.05/3.21 |-Branch two:
% 11.05/3.21 | (596) in(all_170_0_68, all_256_0_87)
% 11.05/3.21 | (597) ? [v0] : (relation_composition(all_0_11_11, all_0_8_8) = v0 & apply(v0, all_170_0_68) = all_38_0_25)
% 11.05/3.21 |
% 11.05/3.21 | Instantiating (597) with all_518_0_115 yields:
% 11.05/3.21 | (598) relation_composition(all_0_11_11, all_0_8_8) = all_518_0_115 & apply(all_518_0_115, all_170_0_68) = all_38_0_25
% 11.05/3.21 |
% 11.05/3.21 | Applying alpha-rule on (598) yields:
% 11.05/3.21 | (599) relation_composition(all_0_11_11, all_0_8_8) = all_518_0_115
% 11.05/3.21 | (600) apply(all_518_0_115, all_170_0_68) = all_38_0_25
% 11.05/3.21 |
% 11.05/3.21 +-Applying beta-rule and splitting (485), into two cases.
% 11.05/3.21 |-Branch one:
% 11.05/3.21 | (601) ~ in(all_126_0_55, all_247_0_84)
% 11.05/3.21 |
% 11.05/3.21 | From (469) and (601) follows:
% 11.05/3.21 | (602) ~ in(all_126_0_55, all_23_0_18)
% 11.05/3.21 |
% 11.05/3.21 | Using (259) and (602) yields:
% 11.05/3.21 | (268) $false
% 11.05/3.21 |
% 11.05/3.21 |-The branch is then unsatisfiable
% 11.05/3.21 |-Branch two:
% 11.05/3.21 | (604) in(all_126_0_55, all_247_0_84)
% 11.05/3.21 | (605) ? [v0] : (relation_composition(all_0_11_11, all_0_10_10) = v0 & apply(v0, all_126_0_55) = all_33_0_22)
% 11.05/3.21 |
% 11.05/3.21 | Instantiating (605) with all_524_0_116 yields:
% 11.05/3.21 | (606) relation_composition(all_0_11_11, all_0_10_10) = all_524_0_116 & apply(all_524_0_116, all_126_0_55) = all_33_0_22
% 11.05/3.21 |
% 11.05/3.21 | Applying alpha-rule on (606) yields:
% 11.05/3.21 | (607) relation_composition(all_0_11_11, all_0_10_10) = all_524_0_116
% 11.05/3.21 | (608) apply(all_524_0_116, all_126_0_55) = all_33_0_22
% 11.05/3.22 |
% 11.05/3.22 +-Applying beta-rule and splitting (475), into two cases.
% 11.05/3.22 |-Branch one:
% 11.05/3.22 | (609) ~ in(all_195_0_73, all_238_0_81)
% 11.05/3.22 |
% 11.05/3.22 | From (444) and (609) follows:
% 11.05/3.22 | (610) ~ in(all_195_0_73, all_23_0_18)
% 11.05/3.22 |
% 11.05/3.22 | Using (329) and (610) yields:
% 11.05/3.22 | (268) $false
% 11.05/3.22 |
% 11.05/3.22 |-The branch is then unsatisfiable
% 11.05/3.22 |-Branch two:
% 11.05/3.22 | (612) in(all_195_0_73, all_238_0_81)
% 11.05/3.22 | (613) ? [v0] : (relation_composition(all_0_11_11, all_0_10_10) = v0 & apply(v0, all_195_0_73) = all_33_0_22)
% 11.05/3.22 |
% 11.05/3.22 | Instantiating (613) with all_535_0_118 yields:
% 11.05/3.22 | (614) relation_composition(all_0_11_11, all_0_10_10) = all_535_0_118 & apply(all_535_0_118, all_195_0_73) = all_33_0_22
% 11.05/3.22 |
% 11.05/3.22 | Applying alpha-rule on (614) yields:
% 11.05/3.22 | (615) relation_composition(all_0_11_11, all_0_10_10) = all_535_0_118
% 11.05/3.22 | (616) apply(all_535_0_118, all_195_0_73) = all_33_0_22
% 11.05/3.22 |
% 11.05/3.22 +-Applying beta-rule and splitting (484), into two cases.
% 11.05/3.22 |-Branch one:
% 11.05/3.22 | (617) ~ in(all_140_0_60, all_250_0_85)
% 11.05/3.22 |
% 11.05/3.22 | From (470) and (617) follows:
% 11.05/3.22 | (618) ~ in(all_140_0_60, all_23_0_18)
% 11.05/3.22 |
% 11.05/3.22 | Using (262) and (618) yields:
% 11.05/3.22 | (268) $false
% 11.05/3.22 |
% 11.05/3.22 |-The branch is then unsatisfiable
% 11.05/3.22 |-Branch two:
% 11.05/3.22 | (620) in(all_140_0_60, all_250_0_85)
% 11.05/3.22 | (621) ? [v0] : (relation_composition(all_0_11_11, all_0_10_10) = v0 & apply(v0, all_140_0_60) = all_38_1_26)
% 11.05/3.22 |
% 11.05/3.22 | Instantiating (621) with all_541_0_119 yields:
% 11.05/3.22 | (622) relation_composition(all_0_11_11, all_0_10_10) = all_541_0_119 & apply(all_541_0_119, all_140_0_60) = all_38_1_26
% 11.05/3.22 |
% 11.05/3.22 | Applying alpha-rule on (622) yields:
% 11.05/3.22 | (623) relation_composition(all_0_11_11, all_0_10_10) = all_541_0_119
% 11.05/3.22 | (624) apply(all_541_0_119, all_140_0_60) = all_38_1_26
% 11.05/3.22 |
% 11.05/3.22 +-Applying beta-rule and splitting (479), into two cases.
% 11.05/3.22 |-Branch one:
% 11.05/3.22 | (625) ~ in(all_175_0_69, all_259_0_88)
% 11.05/3.22 |
% 11.05/3.22 | From (410) and (625) follows:
% 11.05/3.22 | (626) ~ in(all_175_0_69, all_23_0_18)
% 11.05/3.22 |
% 11.05/3.22 | Using (297) and (626) yields:
% 11.05/3.22 | (268) $false
% 11.05/3.22 |
% 11.05/3.22 |-The branch is then unsatisfiable
% 11.05/3.22 |-Branch two:
% 11.05/3.22 | (628) in(all_175_0_69, all_259_0_88)
% 11.05/3.22 | (629) ? [v0] : (relation_composition(all_0_11_11, all_0_10_10) = v0 & apply(v0, all_175_0_69) = all_33_0_22)
% 11.05/3.22 |
% 11.05/3.22 | Instantiating (629) with all_547_0_120 yields:
% 11.05/3.22 | (630) relation_composition(all_0_11_11, all_0_10_10) = all_547_0_120 & apply(all_547_0_120, all_175_0_69) = all_33_0_22
% 11.05/3.22 |
% 11.05/3.22 | Applying alpha-rule on (630) yields:
% 11.05/3.22 | (631) relation_composition(all_0_11_11, all_0_10_10) = all_547_0_120
% 11.05/3.22 | (632) apply(all_547_0_120, all_175_0_69) = all_33_0_22
% 11.05/3.22 |
% 11.05/3.22 +-Applying beta-rule and splitting (478), into two cases.
% 11.05/3.22 |-Branch one:
% 11.05/3.22 | (633) ~ in(all_180_0_70, all_223_0_76)
% 11.05/3.22 |
% 11.05/3.22 | From (458) and (633) follows:
% 11.05/3.22 | (634) ~ in(all_180_0_70, all_23_0_18)
% 11.05/3.22 |
% 11.05/3.22 | Using (305) and (634) yields:
% 11.05/3.22 | (268) $false
% 11.05/3.22 |
% 11.05/3.22 |-The branch is then unsatisfiable
% 11.05/3.22 |-Branch two:
% 11.05/3.22 | (636) in(all_180_0_70, all_223_0_76)
% 11.05/3.22 | (637) ? [v0] : (relation_composition(all_0_11_11, all_0_8_8) = v0 & apply(v0, all_180_0_70) = all_38_0_25)
% 11.05/3.22 |
% 11.05/3.22 | Instantiating (637) with all_553_0_121 yields:
% 11.05/3.22 | (638) relation_composition(all_0_11_11, all_0_8_8) = all_553_0_121 & apply(all_553_0_121, all_180_0_70) = all_38_0_25
% 11.05/3.22 |
% 11.05/3.22 | Applying alpha-rule on (638) yields:
% 11.05/3.22 | (639) relation_composition(all_0_11_11, all_0_8_8) = all_553_0_121
% 11.05/3.22 | (640) apply(all_553_0_121, all_180_0_70) = all_38_0_25
% 11.05/3.22 |
% 11.05/3.22 +-Applying beta-rule and splitting (477), into two cases.
% 11.05/3.22 |-Branch one:
% 11.05/3.22 | (641) ~ in(all_185_0_71, all_253_0_86)
% 11.05/3.22 |
% 11.05/3.22 | From (471) and (641) follows:
% 11.05/3.22 | (642) ~ in(all_185_0_71, all_23_0_18)
% 11.05/3.22 |
% 11.05/3.22 | Using (313) and (642) yields:
% 11.05/3.22 | (268) $false
% 11.05/3.22 |
% 11.05/3.22 |-The branch is then unsatisfiable
% 11.05/3.22 |-Branch two:
% 11.05/3.22 | (644) in(all_185_0_71, all_253_0_86)
% 11.05/3.22 | (645) ? [v0] : (relation_composition(all_0_11_11, all_0_10_10) = v0 & apply(v0, all_185_0_71) = all_38_1_26)
% 11.05/3.22 |
% 11.05/3.22 | Instantiating (645) with all_559_0_122 yields:
% 11.05/3.22 | (646) relation_composition(all_0_11_11, all_0_10_10) = all_559_0_122 & apply(all_559_0_122, all_185_0_71) = all_38_1_26
% 11.05/3.22 |
% 11.05/3.22 | Applying alpha-rule on (646) yields:
% 11.05/3.22 | (647) relation_composition(all_0_11_11, all_0_10_10) = all_559_0_122
% 11.05/3.22 | (648) apply(all_559_0_122, all_185_0_71) = all_38_1_26
% 11.05/3.22 |
% 11.05/3.22 +-Applying beta-rule and splitting (476), into two cases.
% 11.05/3.22 |-Branch one:
% 11.05/3.22 | (649) ~ in(all_190_0_72, all_226_0_77)
% 11.05/3.22 |
% 11.05/3.22 | From (455) and (649) follows:
% 11.05/3.22 | (650) ~ in(all_190_0_72, all_23_0_18)
% 11.05/3.22 |
% 11.05/3.22 | Using (321) and (650) yields:
% 11.05/3.22 | (268) $false
% 11.05/3.22 |
% 11.05/3.22 |-The branch is then unsatisfiable
% 11.05/3.22 |-Branch two:
% 11.05/3.22 | (652) in(all_190_0_72, all_226_0_77)
% 11.05/3.22 | (653) ? [v0] : (relation_composition(all_0_11_11, all_0_8_8) = v0 & apply(v0, all_190_0_72) = all_33_1_23)
% 11.05/3.22 |
% 11.05/3.22 | Instantiating (653) with all_565_0_123 yields:
% 11.05/3.22 | (654) relation_composition(all_0_11_11, all_0_8_8) = all_565_0_123 & apply(all_565_0_123, all_190_0_72) = all_33_1_23
% 11.05/3.22 |
% 11.05/3.22 | Applying alpha-rule on (654) yields:
% 11.05/3.22 | (655) relation_composition(all_0_11_11, all_0_8_8) = all_565_0_123
% 11.05/3.22 | (656) apply(all_565_0_123, all_190_0_72) = all_33_1_23
% 11.05/3.22 |
% 11.05/3.22 | Instantiating formula (13) with all_0_11_11, all_0_8_8, all_553_0_121, all_0_9_9 and discharging atoms relation_composition(all_0_11_11, all_0_8_8) = all_553_0_121, relation_composition(all_0_11_11, all_0_8_8) = all_0_9_9, yields:
% 11.05/3.22 | (657) all_553_0_121 = all_0_9_9
% 11.05/3.22 |
% 11.05/3.22 | Instantiating formula (13) with all_0_11_11, all_0_8_8, all_491_0_110, all_553_0_121 and discharging atoms relation_composition(all_0_11_11, all_0_8_8) = all_553_0_121, relation_composition(all_0_11_11, all_0_8_8) = all_491_0_110, yields:
% 11.05/3.22 | (658) all_553_0_121 = all_491_0_110
% 11.05/3.22 |
% 11.05/3.22 | Instantiating formula (13) with all_0_11_11, all_0_8_8, all_479_0_108, all_518_0_115 and discharging atoms relation_composition(all_0_11_11, all_0_8_8) = all_518_0_115, relation_composition(all_0_11_11, all_0_8_8) = all_479_0_108, yields:
% 11.05/3.22 | (659) all_518_0_115 = all_479_0_108
% 11.05/3.22 |
% 11.05/3.22 | Instantiating formula (13) with all_0_11_11, all_0_8_8, all_473_0_107, all_491_0_110 and discharging atoms relation_composition(all_0_11_11, all_0_8_8) = all_491_0_110, relation_composition(all_0_11_11, all_0_8_8) = all_473_0_107, yields:
% 11.05/3.22 | (660) all_491_0_110 = all_473_0_107
% 11.05/3.22 |
% 11.05/3.22 | Instantiating formula (13) with all_0_11_11, all_0_8_8, all_473_0_107, all_479_0_108 and discharging atoms relation_composition(all_0_11_11, all_0_8_8) = all_479_0_108, relation_composition(all_0_11_11, all_0_8_8) = all_473_0_107, yields:
% 11.05/3.22 | (661) all_479_0_108 = all_473_0_107
% 11.05/3.22 |
% 11.05/3.22 | Instantiating formula (13) with all_0_11_11, all_0_8_8, all_467_0_106, all_473_0_107 and discharging atoms relation_composition(all_0_11_11, all_0_8_8) = all_473_0_107, relation_composition(all_0_11_11, all_0_8_8) = all_467_0_106, yields:
% 11.05/3.22 | (662) all_473_0_107 = all_467_0_106
% 11.05/3.22 |
% 11.05/3.22 | Instantiating formula (13) with all_0_11_11, all_0_8_8, all_455_0_104, all_518_0_115 and discharging atoms relation_composition(all_0_11_11, all_0_8_8) = all_518_0_115, relation_composition(all_0_11_11, all_0_8_8) = all_455_0_104, yields:
% 11.05/3.22 | (663) all_518_0_115 = all_455_0_104
% 11.05/3.22 |
% 11.05/3.22 | Instantiating formula (13) with all_0_11_11, all_0_8_8, all_418_0_97, all_565_0_123 and discharging atoms relation_composition(all_0_11_11, all_0_8_8) = all_565_0_123, relation_composition(all_0_11_11, all_0_8_8) = all_418_0_97, yields:
% 11.05/3.22 | (664) all_565_0_123 = all_418_0_97
% 11.05/3.22 |
% 11.05/3.22 | Instantiating formula (13) with all_0_11_11, all_0_8_8, all_418_0_97, all_479_0_108 and discharging atoms relation_composition(all_0_11_11, all_0_8_8) = all_479_0_108, relation_composition(all_0_11_11, all_0_8_8) = all_418_0_97, yields:
% 11.05/3.22 | (665) all_479_0_108 = all_418_0_97
% 11.05/3.22 |
% 11.05/3.22 | Instantiating formula (13) with all_0_11_11, all_0_8_8, all_412_0_96, all_565_0_123 and discharging atoms relation_composition(all_0_11_11, all_0_8_8) = all_565_0_123, relation_composition(all_0_11_11, all_0_8_8) = all_412_0_96, yields:
% 11.05/3.22 | (666) all_565_0_123 = all_412_0_96
% 11.05/3.22 |
% 11.05/3.22 | Instantiating formula (13) with all_0_11_11, all_0_10_10, all_559_0_122, all_0_9_9 and discharging atoms relation_composition(all_0_11_11, all_0_10_10) = all_559_0_122, relation_composition(all_0_11_11, all_0_10_10) = all_0_9_9, yields:
% 11.05/3.22 | (667) all_559_0_122 = all_0_9_9
% 11.05/3.22 |
% 11.05/3.22 | Instantiating formula (13) with all_0_11_11, all_0_10_10, all_541_0_119, all_559_0_122 and discharging atoms relation_composition(all_0_11_11, all_0_10_10) = all_559_0_122, relation_composition(all_0_11_11, all_0_10_10) = all_541_0_119, yields:
% 11.05/3.22 | (668) all_559_0_122 = all_541_0_119
% 11.05/3.22 |
% 11.05/3.22 | Instantiating formula (13) with all_0_11_11, all_0_10_10, all_535_0_118, all_541_0_119 and discharging atoms relation_composition(all_0_11_11, all_0_10_10) = all_541_0_119, relation_composition(all_0_11_11, all_0_10_10) = all_535_0_118, yields:
% 11.05/3.22 | (669) all_541_0_119 = all_535_0_118
% 11.05/3.22 |
% 11.05/3.22 | Instantiating formula (13) with all_0_11_11, all_0_10_10, all_524_0_116, all_547_0_120 and discharging atoms relation_composition(all_0_11_11, all_0_10_10) = all_547_0_120, relation_composition(all_0_11_11, all_0_10_10) = all_524_0_116, yields:
% 11.05/3.22 | (670) all_547_0_120 = all_524_0_116
% 11.05/3.22 |
% 11.05/3.22 | Instantiating formula (13) with all_0_11_11, all_0_10_10, all_512_0_114, all_535_0_118 and discharging atoms relation_composition(all_0_11_11, all_0_10_10) = all_535_0_118, relation_composition(all_0_11_11, all_0_10_10) = all_512_0_114, yields:
% 11.18/3.22 | (671) all_535_0_118 = all_512_0_114
% 11.18/3.22 |
% 11.18/3.22 | Instantiating formula (13) with all_0_11_11, all_0_10_10, all_512_0_114, all_524_0_116 and discharging atoms relation_composition(all_0_11_11, all_0_10_10) = all_524_0_116, relation_composition(all_0_11_11, all_0_10_10) = all_512_0_114, yields:
% 11.18/3.22 | (672) all_524_0_116 = all_512_0_114
% 11.18/3.22 |
% 11.18/3.22 | Instantiating formula (13) with all_0_11_11, all_0_10_10, all_485_0_109, all_547_0_120 and discharging atoms relation_composition(all_0_11_11, all_0_10_10) = all_547_0_120, relation_composition(all_0_11_11, all_0_10_10) = all_485_0_109, yields:
% 11.18/3.22 | (673) all_547_0_120 = all_485_0_109
% 11.18/3.22 |
% 11.18/3.22 | Instantiating formula (13) with all_0_11_11, all_0_10_10, all_461_0_105, all_524_0_116 and discharging atoms relation_composition(all_0_11_11, all_0_10_10) = all_524_0_116, relation_composition(all_0_11_11, all_0_10_10) = all_461_0_105, yields:
% 11.18/3.22 | (674) all_524_0_116 = all_461_0_105
% 11.18/3.22 |
% 11.18/3.22 | Instantiating formula (13) with all_0_11_11, all_0_10_10, all_429_0_99, all_461_0_105 and discharging atoms relation_composition(all_0_11_11, all_0_10_10) = all_461_0_105, relation_composition(all_0_11_11, all_0_10_10) = all_429_0_99, yields:
% 11.18/3.22 | (675) all_461_0_105 = all_429_0_99
% 11.18/3.22 |
% 11.18/3.22 | Instantiating formula (13) with all_0_11_11, all_0_10_10, all_401_0_94, all_429_0_99 and discharging atoms relation_composition(all_0_11_11, all_0_10_10) = all_429_0_99, relation_composition(all_0_11_11, all_0_10_10) = all_401_0_94, yields:
% 11.18/3.22 | (676) all_429_0_99 = all_401_0_94
% 11.18/3.22 |
% 11.18/3.22 | Combining equations (664,666) yields a new equation:
% 11.18/3.22 | (677) all_418_0_97 = all_412_0_96
% 11.18/3.22 |
% 11.18/3.22 | Simplifying 677 yields:
% 11.18/3.22 | (678) all_418_0_97 = all_412_0_96
% 11.18/3.22 |
% 11.18/3.22 | Combining equations (668,667) yields a new equation:
% 11.18/3.22 | (679) all_541_0_119 = all_0_9_9
% 11.18/3.22 |
% 11.18/3.22 | Simplifying 679 yields:
% 11.18/3.22 | (680) all_541_0_119 = all_0_9_9
% 11.18/3.22 |
% 11.18/3.22 | Combining equations (658,657) yields a new equation:
% 11.18/3.22 | (681) all_491_0_110 = all_0_9_9
% 11.18/3.22 |
% 11.18/3.22 | Simplifying 681 yields:
% 11.18/3.22 | (682) all_491_0_110 = all_0_9_9
% 11.18/3.22 |
% 11.18/3.22 | Combining equations (670,673) yields a new equation:
% 11.18/3.22 | (683) all_524_0_116 = all_485_0_109
% 11.18/3.22 |
% 11.18/3.22 | Simplifying 683 yields:
% 11.18/3.22 | (684) all_524_0_116 = all_485_0_109
% 11.18/3.22 |
% 11.18/3.22 | Combining equations (669,680) yields a new equation:
% 11.18/3.22 | (685) all_535_0_118 = all_0_9_9
% 11.18/3.22 |
% 11.18/3.22 | Simplifying 685 yields:
% 11.18/3.22 | (686) all_535_0_118 = all_0_9_9
% 11.18/3.22 |
% 11.18/3.22 | Combining equations (671,686) yields a new equation:
% 11.18/3.22 | (687) all_512_0_114 = all_0_9_9
% 11.18/3.22 |
% 11.18/3.22 | Simplifying 687 yields:
% 11.18/3.22 | (688) all_512_0_114 = all_0_9_9
% 11.18/3.22 |
% 11.18/3.22 | Combining equations (674,684) yields a new equation:
% 11.18/3.22 | (689) all_485_0_109 = all_461_0_105
% 11.18/3.22 |
% 11.18/3.22 | Combining equations (672,684) yields a new equation:
% 11.18/3.22 | (690) all_512_0_114 = all_485_0_109
% 11.18/3.22 |
% 11.18/3.22 | Simplifying 690 yields:
% 11.18/3.22 | (691) all_512_0_114 = all_485_0_109
% 11.18/3.22 |
% 11.18/3.22 | Combining equations (659,663) yields a new equation:
% 11.18/3.22 | (692) all_479_0_108 = all_455_0_104
% 11.18/3.22 |
% 11.18/3.22 | Simplifying 692 yields:
% 11.18/3.22 | (693) all_479_0_108 = all_455_0_104
% 11.18/3.22 |
% 11.18/3.22 | Combining equations (691,688) yields a new equation:
% 11.18/3.22 | (694) all_485_0_109 = all_0_9_9
% 11.18/3.22 |
% 11.18/3.22 | Simplifying 694 yields:
% 11.18/3.22 | (695) all_485_0_109 = all_0_9_9
% 11.18/3.22 |
% 11.18/3.22 | Combining equations (660,682) yields a new equation:
% 11.18/3.22 | (696) all_473_0_107 = all_0_9_9
% 11.18/3.22 |
% 11.18/3.22 | Simplifying 696 yields:
% 11.18/3.22 | (697) all_473_0_107 = all_0_9_9
% 11.18/3.22 |
% 11.18/3.22 | Combining equations (689,695) yields a new equation:
% 11.18/3.22 | (698) all_461_0_105 = all_0_9_9
% 11.18/3.22 |
% 11.18/3.22 | Simplifying 698 yields:
% 11.18/3.22 | (699) all_461_0_105 = all_0_9_9
% 11.18/3.22 |
% 11.18/3.22 | Combining equations (661,693) yields a new equation:
% 11.18/3.22 | (700) all_473_0_107 = all_455_0_104
% 11.18/3.22 |
% 11.18/3.22 | Simplifying 700 yields:
% 11.18/3.22 | (701) all_473_0_107 = all_455_0_104
% 11.18/3.22 |
% 11.18/3.22 | Combining equations (665,693) yields a new equation:
% 11.18/3.22 | (702) all_455_0_104 = all_418_0_97
% 11.18/3.22 |
% 11.19/3.22 | Combining equations (697,662) yields a new equation:
% 11.19/3.22 | (703) all_467_0_106 = all_0_9_9
% 11.19/3.22 |
% 11.19/3.22 | Combining equations (701,662) yields a new equation:
% 11.19/3.22 | (704) all_467_0_106 = all_455_0_104
% 11.19/3.22 |
% 11.19/3.22 | Combining equations (704,703) yields a new equation:
% 11.19/3.22 | (705) all_455_0_104 = all_0_9_9
% 11.19/3.22 |
% 11.19/3.22 | Simplifying 705 yields:
% 11.19/3.22 | (706) all_455_0_104 = all_0_9_9
% 11.19/3.22 |
% 11.19/3.23 | Combining equations (675,699) yields a new equation:
% 11.19/3.23 | (707) all_429_0_99 = all_0_9_9
% 11.19/3.23 |
% 11.19/3.23 | Simplifying 707 yields:
% 11.19/3.23 | (708) all_429_0_99 = all_0_9_9
% 11.19/3.23 |
% 11.19/3.23 | Combining equations (702,706) yields a new equation:
% 11.19/3.23 | (709) all_418_0_97 = all_0_9_9
% 11.19/3.23 |
% 11.19/3.23 | Simplifying 709 yields:
% 11.19/3.23 | (710) all_418_0_97 = all_0_9_9
% 11.19/3.23 |
% 11.19/3.23 | Combining equations (676,708) yields a new equation:
% 11.19/3.23 | (711) all_401_0_94 = all_0_9_9
% 11.19/3.23 |
% 11.19/3.23 | Simplifying 711 yields:
% 11.19/3.23 | (712) all_401_0_94 = all_0_9_9
% 11.19/3.23 |
% 11.19/3.23 | Combining equations (678,710) yields a new equation:
% 11.19/3.23 | (713) all_412_0_96 = all_0_9_9
% 11.19/3.23 |
% 11.19/3.23 | Simplifying 713 yields:
% 11.19/3.23 | (714) all_412_0_96 = all_0_9_9
% 11.19/3.23 |
% 11.19/3.23 | From (714) and (511) follows:
% 11.19/3.23 | (715) apply(all_0_9_9, all_55_0_31) = all_33_1_23
% 11.19/3.23 |
% 11.19/3.23 | From (712) and (502) follows:
% 11.19/3.23 | (716) apply(all_0_9_9, all_55_0_31) = all_33_0_22
% 11.19/3.23 |
% 11.19/3.23 | Instantiating formula (22) with all_0_9_9, all_55_0_31, all_33_1_23, all_33_0_22 and discharging atoms apply(all_0_9_9, all_55_0_31) = all_33_0_22, apply(all_0_9_9, all_55_0_31) = all_33_1_23, yields:
% 11.19/3.23 | (717) all_33_0_22 = all_33_1_23
% 11.19/3.23 |
% 11.19/3.23 | Equations (717) can reduce 98 to:
% 11.19/3.23 | (94) $false
% 11.19/3.23 |
% 11.19/3.23 |-The branch is then unsatisfiable
% 11.19/3.23 % SZS output end Proof for theBenchmark
% 11.19/3.23
% 11.19/3.23 2603ms
%------------------------------------------------------------------------------