TSTP Solution File: SEU220+3 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU220+3 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 08:47:48 EDT 2022
% Result : Theorem 3.93s 1.60s
% Output : Proof 7.06s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU220+3 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n013.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jun 19 03:07:44 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.58 ____ _
% 0.19/0.58 ___ / __ \_____(_)___ ________ __________
% 0.19/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.19/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.19/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.19/0.58
% 0.19/0.58 A Theorem Prover for First-Order Logic
% 0.19/0.58 (ePrincess v.1.0)
% 0.19/0.58
% 0.19/0.58 (c) Philipp Rümmer, 2009-2015
% 0.19/0.58 (c) Peter Backeman, 2014-2015
% 0.19/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.19/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.19/0.58 Bug reports to peter@backeman.se
% 0.19/0.58
% 0.19/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.19/0.58
% 0.19/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.68/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.61/0.95 Prover 0: Preprocessing ...
% 2.65/1.29 Prover 0: Warning: ignoring some quantifiers
% 2.88/1.32 Prover 0: Constructing countermodel ...
% 3.93/1.59 Prover 0: proved (967ms)
% 3.93/1.60
% 3.93/1.60 No countermodel exists, formula is valid
% 3.93/1.60 % SZS status Theorem for theBenchmark
% 3.93/1.60
% 3.93/1.60 Generating proof ... Warning: ignoring some quantifiers
% 6.68/2.15 found it (size 58)
% 6.68/2.15
% 6.68/2.15 % SZS output start Proof for theBenchmark
% 6.68/2.15 Assumed formulas after preprocessing and simplification:
% 6.68/2.15 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : (apply(v6, v0) = v7 & apply(v3, v0) = v4 & apply(v1, v4) = v5 & relation_rng(v1) = v2 & relation_composition(v3, v1) = v6 & function_inverse(v1) = v3 & relation_empty_yielding(v8) & relation_empty_yielding(empty_set) & one_to_one(v9) & one_to_one(v1) & relation(v15) & relation(v14) & relation(v12) & relation(v11) & relation(v9) & relation(v8) & relation(v1) & relation(empty_set) & function(v15) & function(v12) & function(v9) & function(v1) & empty(v14) & empty(v13) & empty(v12) & empty(empty_set) & in(v0, v2) & ~ empty(v11) & ~ empty(v10) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v17 = v16 | ~ (apply(v19, v18) = v17) | ~ (apply(v19, v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v17 = v16 | ~ (relation_composition(v19, v18) = v17) | ~ (relation_composition(v19, v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (powerset(v18) = v19) | ~ element(v17, v19) | ~ empty(v18) | ~ in(v16, v17)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (powerset(v18) = v19) | ~ element(v17, v19) | ~ in(v16, v17) | element(v16, v18)) & ! [v16] : ! [v17] : ! [v18] : (v17 = v16 | ~ (relation_rng(v18) = v17) | ~ (relation_rng(v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : (v17 = v16 | ~ (relation_dom(v18) = v17) | ~ (relation_dom(v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : (v17 = v16 | ~ (powerset(v18) = v17) | ~ (powerset(v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : (v17 = v16 | ~ (function_inverse(v18) = v17) | ~ (function_inverse(v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (apply(v17, v16) = v18) | ~ relation(v17) | ~ function(v17) | ? [v19] : (relation_dom(v17) = v19 & ! [v20] : ! [v21] : ! [v22] : ( ~ (apply(v21, v16) = v22) | ~ (relation_composition(v17, v20) = v21) | ~ relation(v20) | ~ function(v20) | ~ in(v16, v19) | apply(v20, v18) = v22) & ! [v20] : ! [v21] : ( ~ (apply(v20, v18) = v21) | ~ relation(v20) | ~ function(v20) | ~ in(v16, v19) | ? [v22] : (apply(v22, v16) = v21 & relation_composition(v17, v20) = v22)))) & ! [v16] : ! [v17] : ! [v18] : ( ~ (powerset(v17) = v18) | ~ subset(v16, v17) | element(v16, v18)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (powerset(v17) = v18) | ~ element(v16, v18) | subset(v16, v17)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_composition(v17, v16) = v18) | ~ relation(v17) | ~ empty(v16) | relation(v18)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_composition(v17, v16) = v18) | ~ relation(v17) | ~ empty(v16) | empty(v18)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_composition(v16, v17) = v18) | ~ relation(v17) | ~ relation(v16) | ~ function(v17) | ~ function(v16) | relation(v18)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_composition(v16, v17) = v18) | ~ relation(v17) | ~ relation(v16) | ~ function(v17) | ~ function(v16) | function(v18)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_composition(v16, v17) = v18) | ~ relation(v17) | ~ relation(v16) | relation(v18)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_composition(v16, v17) = v18) | ~ relation(v17) | ~ empty(v16) | relation(v18)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_composition(v16, v17) = v18) | ~ relation(v17) | ~ empty(v16) | empty(v18)) & ! [v16] : ! [v17] : (v17 = v16 | ~ empty(v17) | ~ empty(v16)) & ! [v16] : ! [v17] : ( ~ (relation_rng(v16) = v17) | ~ one_to_one(v16) | ~ relation(v16) | ~ function(v16) | ? [v18] : ? [v19] : (relation_rng(v18) = v19 & relation_dom(v18) = v17 & relation_dom(v16) = v19 & function_inverse(v16) = v18)) & ! [v16] : ! [v17] : ( ~ (relation_rng(v16) = v17) | ~ one_to_one(v16) | ~ relation(v16) | ~ function(v16) | ? [v18] : ? [v19] : (relation_dom(v16) = v19 & function_inverse(v16) = v18 & ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v23 = v22 | ~ (apply(v18, v21) = v23) | ~ (apply(v16, v22) = v21) | ~ (relation_dom(v18) = v20) | ~ relation(v18) | ~ function(v18) | ~ in(v22, v19)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v23 = v21 | ~ (apply(v18, v21) = v22) | ~ (apply(v16, v22) = v23) | ~ (relation_dom(v18) = v20) | ~ relation(v18) | ~ function(v18) | ~ in(v21, v17)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ( ~ (apply(v18, v21) = v23) | ~ (apply(v16, v22) = v21) | ~ (relation_dom(v18) = v20) | ~ relation(v18) | ~ function(v18) | ~ in(v22, v19) | in(v21, v17)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ( ~ (apply(v18, v21) = v22) | ~ (apply(v16, v22) = v23) | ~ (relation_dom(v18) = v20) | ~ relation(v18) | ~ function(v18) | ~ in(v21, v17) | in(v22, v19)) & ! [v20] : (v20 = v18 | ~ (relation_dom(v20) = v17) | ~ relation(v20) | ~ function(v20) | ? [v21] : ? [v22] : ? [v23] : ? [v24] : (apply(v20, v21) = v23 & apply(v16, v22) = v24 & ((v24 = v21 & in(v22, v19) & ( ~ (v23 = v22) | ~ in(v21, v17))) | (v23 = v22 & in(v21, v17) & ( ~ (v24 = v21) | ~ in(v22, v19)))))) & ! [v20] : (v20 = v17 | ~ (relation_dom(v18) = v20) | ~ relation(v18) | ~ function(v18)))) & ! [v16] : ! [v17] : ( ~ (relation_rng(v16) = v17) | ~ relation(v16) | ~ empty(v17) | empty(v16)) & ! [v16] : ! [v17] : ( ~ (relation_rng(v16) = v17) | ~ empty(v16) | relation(v17)) & ! [v16] : ! [v17] : ( ~ (relation_rng(v16) = v17) | ~ empty(v16) | empty(v17)) & ! [v16] : ! [v17] : ( ~ (relation_dom(v16) = v17) | ~ one_to_one(v16) | ~ relation(v16) | ~ function(v16) | ? [v18] : ? [v19] : (relation_rng(v19) = v17 & relation_rng(v16) = v18 & relation_dom(v19) = v18 & function_inverse(v16) = v19)) & ! [v16] : ! [v17] : ( ~ (relation_dom(v16) = v17) | ~ one_to_one(v16) | ~ relation(v16) | ~ function(v16) | ? [v18] : ? [v19] : (relation_rng(v16) = v19 & function_inverse(v16) = v18 & ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v23 = v22 | ~ (apply(v18, v21) = v23) | ~ (apply(v16, v22) = v21) | ~ (relation_dom(v18) = v20) | ~ relation(v18) | ~ function(v18) | ~ in(v22, v17)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v23 = v21 | ~ (apply(v18, v21) = v22) | ~ (apply(v16, v22) = v23) | ~ (relation_dom(v18) = v20) | ~ relation(v18) | ~ function(v18) | ~ in(v21, v19)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ( ~ (apply(v18, v21) = v23) | ~ (apply(v16, v22) = v21) | ~ (relation_dom(v18) = v20) | ~ relation(v18) | ~ function(v18) | ~ in(v22, v17) | in(v21, v19)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ( ~ (apply(v18, v21) = v22) | ~ (apply(v16, v22) = v23) | ~ (relation_dom(v18) = v20) | ~ relation(v18) | ~ function(v18) | ~ in(v21, v19) | in(v22, v17)) & ! [v20] : (v20 = v19 | ~ (relation_dom(v18) = v20) | ~ relation(v18) | ~ function(v18)) & ! [v20] : (v20 = v18 | ~ (relation_dom(v20) = v19) | ~ relation(v20) | ~ function(v20) | ? [v21] : ? [v22] : ? [v23] : ? [v24] : (apply(v20, v21) = v23 & apply(v16, v22) = v24 & ((v24 = v21 & in(v22, v17) & ( ~ (v23 = v22) | ~ in(v21, v19))) | (v23 = v22 & in(v21, v19) & ( ~ (v24 = v21) | ~ in(v22, v17)))))))) & ! [v16] : ! [v17] : ( ~ (relation_dom(v16) = v17) | ~ relation(v16) | ~ empty(v17) | empty(v16)) & ! [v16] : ! [v17] : ( ~ (relation_dom(v16) = v17) | ~ empty(v16) | relation(v17)) & ! [v16] : ! [v17] : ( ~ (relation_dom(v16) = v17) | ~ empty(v16) | empty(v17)) & ! [v16] : ! [v17] : ( ~ (powerset(v16) = v17) | ~ empty(v17)) & ! [v16] : ! [v17] : ( ~ (powerset(v16) = v17) | empty(v16) | ? [v18] : (element(v18, v17) & ~ empty(v18))) & ! [v16] : ! [v17] : ( ~ (powerset(v16) = v17) | ? [v18] : (element(v18, v17) & empty(v18))) & ! [v16] : ! [v17] : ( ~ (function_inverse(v16) = v17) | ~ one_to_one(v16) | ~ relation(v16) | ~ function(v16) | ? [v18] : ? [v19] : (relation_rng(v17) = v19 & relation_rng(v16) = v18 & relation_dom(v17) = v18 & relation_dom(v16) = v19)) & ! [v16] : ! [v17] : ( ~ (function_inverse(v16) = v17) | ~ one_to_one(v16) | ~ relation(v16) | ~ function(v16) | ? [v18] : ? [v19] : (relation_rng(v16) = v18 & relation_dom(v16) = v19 & ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v23 = v22 | ~ (apply(v17, v21) = v23) | ~ (apply(v16, v22) = v21) | ~ (relation_dom(v17) = v20) | ~ relation(v17) | ~ function(v17) | ~ in(v22, v19)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v23 = v21 | ~ (apply(v17, v21) = v22) | ~ (apply(v16, v22) = v23) | ~ (relation_dom(v17) = v20) | ~ relation(v17) | ~ function(v17) | ~ in(v21, v18)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ( ~ (apply(v17, v21) = v23) | ~ (apply(v16, v22) = v21) | ~ (relation_dom(v17) = v20) | ~ relation(v17) | ~ function(v17) | ~ in(v22, v19) | in(v21, v18)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ( ~ (apply(v17, v21) = v22) | ~ (apply(v16, v22) = v23) | ~ (relation_dom(v17) = v20) | ~ relation(v17) | ~ function(v17) | ~ in(v21, v18) | in(v22, v19)) & ! [v20] : (v20 = v18 | ~ (relation_dom(v17) = v20) | ~ relation(v17) | ~ function(v17)) & ! [v20] : (v20 = v17 | ~ (relation_dom(v20) = v18) | ~ relation(v20) | ~ function(v20) | ? [v21] : ? [v22] : ? [v23] : ? [v24] : (apply(v20, v21) = v23 & apply(v16, v22) = v24 & ((v24 = v21 & in(v22, v19) & ( ~ (v23 = v22) | ~ in(v21, v18))) | (v23 = v22 & in(v21, v18) & ( ~ (v24 = v21) | ~ in(v22, v19)))))))) & ! [v16] : ! [v17] : ( ~ (function_inverse(v16) = v17) | ~ relation(v16) | ~ function(v16) | relation(v17)) & ! [v16] : ! [v17] : ( ~ (function_inverse(v16) = v17) | ~ relation(v16) | ~ function(v16) | function(v17)) & ! [v16] : ! [v17] : ( ~ element(v16, v17) | empty(v17) | in(v16, v17)) & ! [v16] : ! [v17] : ( ~ empty(v17) | ~ in(v16, v17)) & ! [v16] : ! [v17] : ( ~ in(v17, v16) | ~ in(v16, v17)) & ! [v16] : ! [v17] : ( ~ in(v16, v17) | element(v16, v17)) & ! [v16] : (v16 = empty_set | ~ empty(v16)) & ! [v16] : ( ~ relation(v16) | ~ function(v16) | ~ empty(v16) | one_to_one(v16)) & ! [v16] : ( ~ empty(v16) | relation(v16)) & ! [v16] : ( ~ empty(v16) | function(v16)) & ? [v16] : ? [v17] : element(v17, v16) & ? [v16] : subset(v16, v16) & ( ~ (v7 = v0) | ~ (v5 = v0)))
% 6.68/2.20 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9, all_0_10_10, all_0_11_11, all_0_12_12, all_0_13_13, all_0_14_14, all_0_15_15 yields:
% 6.68/2.20 | (1) apply(all_0_9_9, all_0_15_15) = all_0_8_8 & apply(all_0_12_12, all_0_15_15) = all_0_11_11 & apply(all_0_14_14, all_0_11_11) = all_0_10_10 & relation_rng(all_0_14_14) = all_0_13_13 & relation_composition(all_0_12_12, all_0_14_14) = all_0_9_9 & function_inverse(all_0_14_14) = all_0_12_12 & relation_empty_yielding(all_0_7_7) & relation_empty_yielding(empty_set) & one_to_one(all_0_6_6) & one_to_one(all_0_14_14) & 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_14_14) & relation(empty_set) & function(all_0_0_0) & function(all_0_3_3) & function(all_0_6_6) & function(all_0_14_14) & empty(all_0_1_1) & empty(all_0_2_2) & empty(all_0_3_3) & empty(empty_set) & in(all_0_15_15, all_0_13_13) & ~ empty(all_0_4_4) & ~ empty(all_0_5_5) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_composition(v3, v2) = v1) | ~ (relation_composition(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ empty(v2) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ in(v0, v1) | element(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function_inverse(v2) = v1) | ~ (function_inverse(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (apply(v1, v0) = v2) | ~ relation(v1) | ~ function(v1) | ? [v3] : (relation_dom(v1) = v3 & ! [v4] : ! [v5] : ! [v6] : ( ~ (apply(v5, v0) = v6) | ~ (relation_composition(v1, v4) = v5) | ~ 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] : (apply(v6, v0) = v5 & relation_composition(v1, v4) = v6)))) & ! [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] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : (relation_rng(v2) = v3 & relation_dom(v2) = v1 & relation_dom(v0) = v3 & function_inverse(v0) = v2)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : (relation_dom(v0) = v3 & function_inverse(v0) = v2 & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v6 | ~ (apply(v2, v5) = v7) | ~ (apply(v0, v6) = v5) | ~ (relation_dom(v2) = v4) | ~ relation(v2) | ~ function(v2) | ~ in(v6, v3)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v5 | ~ (apply(v2, v5) = v6) | ~ (apply(v0, v6) = v7) | ~ (relation_dom(v2) = v4) | ~ relation(v2) | ~ function(v2) | ~ in(v5, v1)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (apply(v2, v5) = v7) | ~ (apply(v0, v6) = v5) | ~ (relation_dom(v2) = v4) | ~ relation(v2) | ~ function(v2) | ~ in(v6, v3) | in(v5, v1)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (apply(v2, v5) = v6) | ~ (apply(v0, v6) = v7) | ~ (relation_dom(v2) = v4) | ~ relation(v2) | ~ function(v2) | ~ in(v5, v1) | in(v6, v3)) & ! [v4] : (v4 = v2 | ~ (relation_dom(v4) = v1) | ~ relation(v4) | ~ function(v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (apply(v4, v5) = v7 & apply(v0, v6) = v8 & ((v8 = v5 & in(v6, v3) & ( ~ (v7 = v6) | ~ in(v5, v1))) | (v7 = v6 & in(v5, v1) & ( ~ (v8 = v5) | ~ in(v6, v3)))))) & ! [v4] : (v4 = v1 | ~ (relation_dom(v2) = v4) | ~ relation(v2) | ~ function(v2)))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | relation(v1)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | empty(v1)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : (relation_rng(v3) = v1 & relation_rng(v0) = v2 & relation_dom(v3) = v2 & function_inverse(v0) = v3)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : (relation_rng(v0) = v3 & function_inverse(v0) = v2 & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v6 | ~ (apply(v2, v5) = v7) | ~ (apply(v0, v6) = v5) | ~ (relation_dom(v2) = v4) | ~ relation(v2) | ~ function(v2) | ~ in(v6, v1)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v5 | ~ (apply(v2, v5) = v6) | ~ (apply(v0, v6) = v7) | ~ (relation_dom(v2) = v4) | ~ relation(v2) | ~ function(v2) | ~ in(v5, v3)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (apply(v2, v5) = v7) | ~ (apply(v0, v6) = v5) | ~ (relation_dom(v2) = v4) | ~ relation(v2) | ~ function(v2) | ~ in(v6, v1) | in(v5, v3)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (apply(v2, v5) = v6) | ~ (apply(v0, v6) = v7) | ~ (relation_dom(v2) = v4) | ~ relation(v2) | ~ function(v2) | ~ in(v5, v3) | in(v6, v1)) & ! [v4] : (v4 = v3 | ~ (relation_dom(v2) = v4) | ~ relation(v2) | ~ function(v2)) & ! [v4] : (v4 = v2 | ~ (relation_dom(v4) = v3) | ~ relation(v4) | ~ function(v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (apply(v4, v5) = v7 & apply(v0, v6) = v8 & ((v8 = v5 & in(v6, v1) & ( ~ (v7 = v6) | ~ in(v5, v3))) | (v7 = v6 & in(v5, v3) & ( ~ (v8 = v5) | ~ in(v6, v1)))))))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | relation(v1)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | empty(v1)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ empty(v1)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (element(v2, v1) & ~ empty(v2))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) & empty(v2))) & ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : (relation_rng(v1) = v3 & relation_rng(v0) = v2 & relation_dom(v1) = v2 & relation_dom(v0) = v3)) & ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : (relation_rng(v0) = v2 & relation_dom(v0) = v3 & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v6 | ~ (apply(v1, v5) = v7) | ~ (apply(v0, v6) = v5) | ~ (relation_dom(v1) = v4) | ~ relation(v1) | ~ function(v1) | ~ in(v6, v3)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v5 | ~ (apply(v1, v5) = v6) | ~ (apply(v0, v6) = v7) | ~ (relation_dom(v1) = v4) | ~ relation(v1) | ~ function(v1) | ~ in(v5, v2)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (apply(v1, v5) = v7) | ~ (apply(v0, v6) = v5) | ~ (relation_dom(v1) = v4) | ~ relation(v1) | ~ function(v1) | ~ in(v6, v3) | in(v5, v2)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (apply(v1, v5) = v6) | ~ (apply(v0, v6) = v7) | ~ (relation_dom(v1) = v4) | ~ relation(v1) | ~ function(v1) | ~ in(v5, v2) | in(v6, v3)) & ! [v4] : (v4 = v2 | ~ (relation_dom(v1) = v4) | ~ relation(v1) | ~ function(v1)) & ! [v4] : (v4 = v1 | ~ (relation_dom(v4) = v2) | ~ relation(v4) | ~ function(v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (apply(v4, v5) = v7 & apply(v0, v6) = v8 & ((v8 = v5 & in(v6, v3) & ( ~ (v7 = v6) | ~ in(v5, v2))) | (v7 = v6 & in(v5, v2) & ( ~ (v8 = v5) | ~ in(v6, v3)))))))) & ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ relation(v0) | ~ function(v0) | relation(v1)) & ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ relation(v0) | ~ function(v0) | function(v1)) & ! [v0] : ! [v1] : ( ~ 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) & ( ~ (all_0_8_8 = all_0_15_15) | ~ (all_0_10_10 = all_0_15_15))
% 7.06/2.22 |
% 7.06/2.22 | Applying alpha-rule on (1) yields:
% 7.06/2.22 | (2) relation(empty_set)
% 7.06/2.22 | (3) ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : (relation_rng(v0) = v2 & relation_dom(v0) = v3 & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v6 | ~ (apply(v1, v5) = v7) | ~ (apply(v0, v6) = v5) | ~ (relation_dom(v1) = v4) | ~ relation(v1) | ~ function(v1) | ~ in(v6, v3)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v5 | ~ (apply(v1, v5) = v6) | ~ (apply(v0, v6) = v7) | ~ (relation_dom(v1) = v4) | ~ relation(v1) | ~ function(v1) | ~ in(v5, v2)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (apply(v1, v5) = v7) | ~ (apply(v0, v6) = v5) | ~ (relation_dom(v1) = v4) | ~ relation(v1) | ~ function(v1) | ~ in(v6, v3) | in(v5, v2)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (apply(v1, v5) = v6) | ~ (apply(v0, v6) = v7) | ~ (relation_dom(v1) = v4) | ~ relation(v1) | ~ function(v1) | ~ in(v5, v2) | in(v6, v3)) & ! [v4] : (v4 = v2 | ~ (relation_dom(v1) = v4) | ~ relation(v1) | ~ function(v1)) & ! [v4] : (v4 = v1 | ~ (relation_dom(v4) = v2) | ~ relation(v4) | ~ function(v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (apply(v4, v5) = v7 & apply(v0, v6) = v8 & ((v8 = v5 & in(v6, v3) & ( ~ (v7 = v6) | ~ in(v5, v2))) | (v7 = v6 & in(v5, v2) & ( ~ (v8 = v5) | ~ in(v6, v3))))))))
% 7.06/2.22 | (4) relation(all_0_4_4)
% 7.06/2.22 | (5) relation(all_0_0_0)
% 7.06/2.22 | (6) relation(all_0_7_7)
% 7.06/2.22 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_composition(v3, v2) = v1) | ~ (relation_composition(v3, v2) = v0))
% 7.06/2.22 | (8) ! [v0] : ( ~ relation(v0) | ~ function(v0) | ~ empty(v0) | one_to_one(v0))
% 7.06/2.22 | (9) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : (relation_rng(v0) = v3 & function_inverse(v0) = v2 & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v6 | ~ (apply(v2, v5) = v7) | ~ (apply(v0, v6) = v5) | ~ (relation_dom(v2) = v4) | ~ relation(v2) | ~ function(v2) | ~ in(v6, v1)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v5 | ~ (apply(v2, v5) = v6) | ~ (apply(v0, v6) = v7) | ~ (relation_dom(v2) = v4) | ~ relation(v2) | ~ function(v2) | ~ in(v5, v3)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (apply(v2, v5) = v7) | ~ (apply(v0, v6) = v5) | ~ (relation_dom(v2) = v4) | ~ relation(v2) | ~ function(v2) | ~ in(v6, v1) | in(v5, v3)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (apply(v2, v5) = v6) | ~ (apply(v0, v6) = v7) | ~ (relation_dom(v2) = v4) | ~ relation(v2) | ~ function(v2) | ~ in(v5, v3) | in(v6, v1)) & ! [v4] : (v4 = v3 | ~ (relation_dom(v2) = v4) | ~ relation(v2) | ~ function(v2)) & ! [v4] : (v4 = v2 | ~ (relation_dom(v4) = v3) | ~ relation(v4) | ~ function(v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (apply(v4, v5) = v7 & apply(v0, v6) = v8 & ((v8 = v5 & in(v6, v1) & ( ~ (v7 = v6) | ~ in(v5, v3))) | (v7 = v6 & in(v5, v3) & ( ~ (v8 = v5) | ~ in(v6, v1))))))))
% 7.06/2.22 | (10) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : (relation_rng(v2) = v3 & relation_dom(v2) = v1 & relation_dom(v0) = v3 & function_inverse(v0) = v2))
% 7.06/2.22 | (11) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | empty(v1))
% 7.06/2.23 | (12) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0))
% 7.06/2.23 | (13) in(all_0_15_15, all_0_13_13)
% 7.06/2.23 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ in(v0, v1) | element(v0, v2))
% 7.06/2.23 | (15) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function_inverse(v2) = v1) | ~ (function_inverse(v2) = v0))
% 7.06/2.23 | (16) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : (relation_rng(v3) = v1 & relation_rng(v0) = v2 & relation_dom(v3) = v2 & function_inverse(v0) = v3))
% 7.06/2.23 | (17) empty(all_0_3_3)
% 7.06/2.23 | (18) apply(all_0_12_12, all_0_15_15) = all_0_11_11
% 7.06/2.23 | (19) ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : (relation_rng(v1) = v3 & relation_rng(v0) = v2 & relation_dom(v1) = v2 & relation_dom(v0) = v3))
% 7.06/2.23 | (20) ? [v0] : subset(v0, v0)
% 7.06/2.23 | (21) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0))
% 7.06/2.23 | (22) ! [v0] : ( ~ empty(v0) | function(v0))
% 7.06/2.23 | (23) ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ relation(v0) | ~ function(v0) | function(v1))
% 7.06/2.23 | (24) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ empty(v1))
% 7.06/2.23 | (25) empty(all_0_1_1)
% 7.06/2.23 | (26) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v1) | ~ function(v0) | relation(v2))
% 7.06/2.23 | (27) function_inverse(all_0_14_14) = all_0_12_12
% 7.06/2.23 | (28) relation_empty_yielding(all_0_7_7)
% 7.06/2.23 | (29) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0))
% 7.06/2.23 | (30) function(all_0_3_3)
% 7.06/2.23 | (31) relation_empty_yielding(empty_set)
% 7.06/2.23 | (32) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) & empty(v2)))
% 7.06/2.23 | (33) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ element(v0, v2) | subset(v0, v1))
% 7.06/2.23 | (34) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2))
% 7.06/2.23 | (35) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v1) | ~ function(v0) | function(v2))
% 7.06/2.23 | (36) one_to_one(all_0_14_14)
% 7.06/2.23 | (37) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ empty(v0) | relation(v2))
% 7.06/2.23 | (38) ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1))
% 7.06/2.23 | (39) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1))
% 7.06/2.23 | (40) function(all_0_14_14)
% 7.06/2.23 | (41) relation_composition(all_0_12_12, all_0_14_14) = all_0_9_9
% 7.06/2.23 | (42) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v1, v0) = v2) | ~ relation(v1) | ~ empty(v0) | relation(v2))
% 7.06/2.23 | (43) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1))
% 7.06/2.23 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ empty(v2) | ~ in(v0, v1))
% 7.06/2.23 | (45) ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ relation(v0) | ~ function(v0) | relation(v1))
% 7.06/2.23 | (46) apply(all_0_14_14, all_0_11_11) = all_0_10_10
% 7.06/2.23 | (47) ~ empty(all_0_5_5)
% 7.06/2.23 | (48) ! [v0] : (v0 = empty_set | ~ empty(v0))
% 7.06/2.23 | (49) empty(empty_set)
% 7.06/2.23 | (50) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v1, v0) = v2) | ~ relation(v1) | ~ empty(v0) | empty(v2))
% 7.06/2.23 | (51) apply(all_0_9_9, all_0_15_15) = all_0_8_8
% 7.06/2.23 | (52) ! [v0] : ! [v1] : ! [v2] : ( ~ (apply(v1, v0) = v2) | ~ relation(v1) | ~ function(v1) | ? [v3] : (relation_dom(v1) = v3 & ! [v4] : ! [v5] : ! [v6] : ( ~ (apply(v5, v0) = v6) | ~ (relation_composition(v1, v4) = v5) | ~ 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] : (apply(v6, v0) = v5 & relation_composition(v1, v4) = v6))))
% 7.06/2.23 | (53) ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1))
% 7.06/2.23 | (54) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | relation(v1))
% 7.06/2.24 | (55) relation(all_0_6_6)
% 7.06/2.24 | (56) empty(all_0_2_2)
% 7.06/2.24 | (57) ! [v0] : ( ~ empty(v0) | relation(v0))
% 7.06/2.24 | (58) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (element(v2, v1) & ~ empty(v2)))
% 7.06/2.24 | (59) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ empty(v0) | empty(v2))
% 7.06/2.24 | (60) ? [v0] : ? [v1] : element(v1, v0)
% 7.06/2.24 | (61) relation(all_0_14_14)
% 7.06/2.24 | (62) relation(all_0_3_3)
% 7.06/2.24 | (63) relation_rng(all_0_14_14) = all_0_13_13
% 7.06/2.24 | (64) ~ empty(all_0_4_4)
% 7.06/2.24 | (65) relation(all_0_1_1)
% 7.06/2.24 | (66) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0))
% 7.06/2.24 | (67) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2))
% 7.06/2.24 | (68) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0))
% 7.06/2.24 | (69) function(all_0_0_0)
% 7.06/2.24 | (70) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | empty(v1))
% 7.06/2.24 | (71) one_to_one(all_0_6_6)
% 7.06/2.24 | (72) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0))
% 7.06/2.24 | (73) function(all_0_6_6)
% 7.06/2.24 | (74) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : (relation_dom(v0) = v3 & function_inverse(v0) = v2 & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v6 | ~ (apply(v2, v5) = v7) | ~ (apply(v0, v6) = v5) | ~ (relation_dom(v2) = v4) | ~ relation(v2) | ~ function(v2) | ~ in(v6, v3)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v5 | ~ (apply(v2, v5) = v6) | ~ (apply(v0, v6) = v7) | ~ (relation_dom(v2) = v4) | ~ relation(v2) | ~ function(v2) | ~ in(v5, v1)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (apply(v2, v5) = v7) | ~ (apply(v0, v6) = v5) | ~ (relation_dom(v2) = v4) | ~ relation(v2) | ~ function(v2) | ~ in(v6, v3) | in(v5, v1)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (apply(v2, v5) = v6) | ~ (apply(v0, v6) = v7) | ~ (relation_dom(v2) = v4) | ~ relation(v2) | ~ function(v2) | ~ in(v5, v1) | in(v6, v3)) & ! [v4] : (v4 = v2 | ~ (relation_dom(v4) = v1) | ~ relation(v4) | ~ function(v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (apply(v4, v5) = v7 & apply(v0, v6) = v8 & ((v8 = v5 & in(v6, v3) & ( ~ (v7 = v6) | ~ in(v5, v1))) | (v7 = v6 & in(v5, v1) & ( ~ (v8 = v5) | ~ in(v6, v3)))))) & ! [v4] : (v4 = v1 | ~ (relation_dom(v2) = v4) | ~ relation(v2) | ~ function(v2))))
% 7.06/2.24 | (75) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0))
% 7.06/2.24 | (76) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | relation(v1))
% 7.06/2.24 | (77) ~ (all_0_8_8 = all_0_15_15) | ~ (all_0_10_10 = all_0_15_15)
% 7.06/2.24 |
% 7.06/2.24 | Instantiating formula (52) with all_0_10_10, all_0_14_14, all_0_11_11 and discharging atoms apply(all_0_14_14, all_0_11_11) = all_0_10_10, relation(all_0_14_14), function(all_0_14_14), yields:
% 7.06/2.24 | (78) ? [v0] : (relation_dom(all_0_14_14) = v0 & ! [v1] : ! [v2] : ! [v3] : ( ~ (apply(v2, all_0_11_11) = v3) | ~ (relation_composition(all_0_14_14, v1) = v2) | ~ relation(v1) | ~ function(v1) | ~ in(all_0_11_11, v0) | apply(v1, all_0_10_10) = v3) & ! [v1] : ! [v2] : ( ~ (apply(v1, all_0_10_10) = v2) | ~ relation(v1) | ~ function(v1) | ~ in(all_0_11_11, v0) | ? [v3] : (apply(v3, all_0_11_11) = v2 & relation_composition(all_0_14_14, v1) = v3)))
% 7.06/2.24 |
% 7.06/2.24 | Instantiating formula (19) with all_0_12_12, all_0_14_14 and discharging atoms function_inverse(all_0_14_14) = all_0_12_12, one_to_one(all_0_14_14), relation(all_0_14_14), function(all_0_14_14), yields:
% 7.06/2.24 | (79) ? [v0] : ? [v1] : (relation_rng(all_0_12_12) = v1 & relation_rng(all_0_14_14) = v0 & relation_dom(all_0_12_12) = v0 & relation_dom(all_0_14_14) = v1)
% 7.06/2.24 |
% 7.06/2.24 | Instantiating formula (3) with all_0_12_12, all_0_14_14 and discharging atoms function_inverse(all_0_14_14) = all_0_12_12, one_to_one(all_0_14_14), relation(all_0_14_14), function(all_0_14_14), yields:
% 7.06/2.25 | (80) ? [v0] : ? [v1] : (relation_rng(all_0_14_14) = v0 & relation_dom(all_0_14_14) = v1 & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v4 | ~ (apply(all_0_12_12, v3) = v5) | ~ (apply(all_0_14_14, v4) = v3) | ~ (relation_dom(all_0_12_12) = v2) | ~ relation(all_0_12_12) | ~ function(all_0_12_12) | ~ in(v4, v1)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v3 | ~ (apply(all_0_12_12, v3) = v4) | ~ (apply(all_0_14_14, v4) = v5) | ~ (relation_dom(all_0_12_12) = v2) | ~ relation(all_0_12_12) | ~ function(all_0_12_12) | ~ in(v3, v0)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (apply(all_0_12_12, v3) = v5) | ~ (apply(all_0_14_14, v4) = v3) | ~ (relation_dom(all_0_12_12) = v2) | ~ relation(all_0_12_12) | ~ function(all_0_12_12) | ~ in(v4, v1) | in(v3, v0)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (apply(all_0_12_12, v3) = v4) | ~ (apply(all_0_14_14, v4) = v5) | ~ (relation_dom(all_0_12_12) = v2) | ~ relation(all_0_12_12) | ~ function(all_0_12_12) | ~ in(v3, v0) | in(v4, v1)) & ! [v2] : (v2 = v0 | ~ (relation_dom(all_0_12_12) = v2) | ~ relation(all_0_12_12) | ~ function(all_0_12_12)) & ! [v2] : (v2 = all_0_12_12 | ~ (relation_dom(v2) = v0) | ~ relation(v2) | ~ function(v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (apply(v2, v3) = v5 & apply(all_0_14_14, v4) = v6 & ((v6 = v3 & in(v4, v1) & ( ~ (v5 = v4) | ~ in(v3, v0))) | (v5 = v4 & in(v3, v0) & ( ~ (v6 = v3) | ~ in(v4, v1)))))))
% 7.06/2.25 |
% 7.06/2.25 | Instantiating formula (45) with all_0_12_12, all_0_14_14 and discharging atoms function_inverse(all_0_14_14) = all_0_12_12, relation(all_0_14_14), function(all_0_14_14), yields:
% 7.06/2.25 | (81) relation(all_0_12_12)
% 7.06/2.25 |
% 7.06/2.25 | Instantiating formula (23) with all_0_12_12, all_0_14_14 and discharging atoms function_inverse(all_0_14_14) = all_0_12_12, relation(all_0_14_14), function(all_0_14_14), yields:
% 7.06/2.25 | (82) function(all_0_12_12)
% 7.06/2.25 |
% 7.06/2.25 | Instantiating (79) with all_17_0_19, all_17_1_20 yields:
% 7.06/2.25 | (83) relation_rng(all_0_12_12) = all_17_0_19 & relation_rng(all_0_14_14) = all_17_1_20 & relation_dom(all_0_12_12) = all_17_1_20 & relation_dom(all_0_14_14) = all_17_0_19
% 7.06/2.25 |
% 7.06/2.25 | Applying alpha-rule on (83) yields:
% 7.06/2.25 | (84) relation_rng(all_0_12_12) = all_17_0_19
% 7.06/2.25 | (85) relation_rng(all_0_14_14) = all_17_1_20
% 7.06/2.25 | (86) relation_dom(all_0_12_12) = all_17_1_20
% 7.06/2.25 | (87) relation_dom(all_0_14_14) = all_17_0_19
% 7.06/2.25 |
% 7.06/2.25 | Instantiating (80) with all_22_0_23, all_22_1_24 yields:
% 7.06/2.25 | (88) relation_rng(all_0_14_14) = all_22_1_24 & relation_dom(all_0_14_14) = all_22_0_23 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (apply(all_0_12_12, v1) = v3) | ~ (apply(all_0_14_14, v2) = v1) | ~ (relation_dom(all_0_12_12) = v0) | ~ relation(all_0_12_12) | ~ function(all_0_12_12) | ~ in(v2, all_22_0_23)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (apply(all_0_12_12, v1) = v2) | ~ (apply(all_0_14_14, v2) = v3) | ~ (relation_dom(all_0_12_12) = v0) | ~ relation(all_0_12_12) | ~ function(all_0_12_12) | ~ in(v1, all_22_1_24)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (apply(all_0_12_12, v1) = v3) | ~ (apply(all_0_14_14, v2) = v1) | ~ (relation_dom(all_0_12_12) = v0) | ~ relation(all_0_12_12) | ~ function(all_0_12_12) | ~ in(v2, all_22_0_23) | in(v1, all_22_1_24)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (apply(all_0_12_12, v1) = v2) | ~ (apply(all_0_14_14, v2) = v3) | ~ (relation_dom(all_0_12_12) = v0) | ~ relation(all_0_12_12) | ~ function(all_0_12_12) | ~ in(v1, all_22_1_24) | in(v2, all_22_0_23)) & ! [v0] : (v0 = all_22_1_24 | ~ (relation_dom(all_0_12_12) = v0) | ~ relation(all_0_12_12) | ~ function(all_0_12_12)) & ! [v0] : (v0 = all_0_12_12 | ~ (relation_dom(v0) = all_22_1_24) | ~ relation(v0) | ~ function(v0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : (apply(v0, v1) = v3 & apply(all_0_14_14, v2) = v4 & ((v4 = v1 & in(v2, all_22_0_23) & ( ~ (v3 = v2) | ~ in(v1, all_22_1_24))) | (v3 = v2 & in(v1, all_22_1_24) & ( ~ (v4 = v1) | ~ in(v2, all_22_0_23))))))
% 7.06/2.25 |
% 7.06/2.25 | Applying alpha-rule on (88) yields:
% 7.06/2.25 | (89) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (apply(all_0_12_12, v1) = v2) | ~ (apply(all_0_14_14, v2) = v3) | ~ (relation_dom(all_0_12_12) = v0) | ~ relation(all_0_12_12) | ~ function(all_0_12_12) | ~ in(v1, all_22_1_24))
% 7.06/2.25 | (90) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (apply(all_0_12_12, v1) = v3) | ~ (apply(all_0_14_14, v2) = v1) | ~ (relation_dom(all_0_12_12) = v0) | ~ relation(all_0_12_12) | ~ function(all_0_12_12) | ~ in(v2, all_22_0_23))
% 7.06/2.25 | (91) relation_dom(all_0_14_14) = all_22_0_23
% 7.06/2.25 | (92) ! [v0] : (v0 = all_0_12_12 | ~ (relation_dom(v0) = all_22_1_24) | ~ relation(v0) | ~ function(v0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : (apply(v0, v1) = v3 & apply(all_0_14_14, v2) = v4 & ((v4 = v1 & in(v2, all_22_0_23) & ( ~ (v3 = v2) | ~ in(v1, all_22_1_24))) | (v3 = v2 & in(v1, all_22_1_24) & ( ~ (v4 = v1) | ~ in(v2, all_22_0_23))))))
% 7.06/2.25 | (93) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (apply(all_0_12_12, v1) = v3) | ~ (apply(all_0_14_14, v2) = v1) | ~ (relation_dom(all_0_12_12) = v0) | ~ relation(all_0_12_12) | ~ function(all_0_12_12) | ~ in(v2, all_22_0_23) | in(v1, all_22_1_24))
% 7.06/2.25 | (94) ! [v0] : (v0 = all_22_1_24 | ~ (relation_dom(all_0_12_12) = v0) | ~ relation(all_0_12_12) | ~ function(all_0_12_12))
% 7.06/2.25 | (95) relation_rng(all_0_14_14) = all_22_1_24
% 7.06/2.25 | (96) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (apply(all_0_12_12, v1) = v2) | ~ (apply(all_0_14_14, v2) = v3) | ~ (relation_dom(all_0_12_12) = v0) | ~ relation(all_0_12_12) | ~ function(all_0_12_12) | ~ in(v1, all_22_1_24) | in(v2, all_22_0_23))
% 7.06/2.25 |
% 7.06/2.25 | Instantiating (78) with all_27_0_27 yields:
% 7.06/2.25 | (97) relation_dom(all_0_14_14) = all_27_0_27 & ! [v0] : ! [v1] : ! [v2] : ( ~ (apply(v1, all_0_11_11) = v2) | ~ (relation_composition(all_0_14_14, v0) = v1) | ~ relation(v0) | ~ function(v0) | ~ in(all_0_11_11, all_27_0_27) | apply(v0, all_0_10_10) = v2) & ! [v0] : ! [v1] : ( ~ (apply(v0, all_0_10_10) = v1) | ~ relation(v0) | ~ function(v0) | ~ in(all_0_11_11, all_27_0_27) | ? [v2] : (apply(v2, all_0_11_11) = v1 & relation_composition(all_0_14_14, v0) = v2))
% 7.06/2.25 |
% 7.06/2.25 | Applying alpha-rule on (97) yields:
% 7.06/2.25 | (98) relation_dom(all_0_14_14) = all_27_0_27
% 7.06/2.25 | (99) ! [v0] : ! [v1] : ! [v2] : ( ~ (apply(v1, all_0_11_11) = v2) | ~ (relation_composition(all_0_14_14, v0) = v1) | ~ relation(v0) | ~ function(v0) | ~ in(all_0_11_11, all_27_0_27) | apply(v0, all_0_10_10) = v2)
% 7.06/2.25 | (100) ! [v0] : ! [v1] : ( ~ (apply(v0, all_0_10_10) = v1) | ~ relation(v0) | ~ function(v0) | ~ in(all_0_11_11, all_27_0_27) | ? [v2] : (apply(v2, all_0_11_11) = v1 & relation_composition(all_0_14_14, v0) = v2))
% 7.06/2.25 |
% 7.06/2.25 | Instantiating formula (72) with all_0_14_14, all_22_1_24, all_0_13_13 and discharging atoms relation_rng(all_0_14_14) = all_22_1_24, relation_rng(all_0_14_14) = all_0_13_13, yields:
% 7.06/2.25 | (101) all_22_1_24 = all_0_13_13
% 7.06/2.25 |
% 7.06/2.25 | Instantiating formula (94) with all_17_1_20 and discharging atoms relation_dom(all_0_12_12) = all_17_1_20, relation(all_0_12_12), function(all_0_12_12), yields:
% 7.06/2.25 | (102) all_22_1_24 = all_17_1_20
% 7.06/2.25 |
% 7.06/2.26 | Combining equations (102,101) yields a new equation:
% 7.06/2.26 | (103) all_17_1_20 = all_0_13_13
% 7.06/2.26 |
% 7.06/2.26 | Simplifying 103 yields:
% 7.06/2.26 | (104) all_17_1_20 = all_0_13_13
% 7.06/2.26 |
% 7.06/2.26 | From (104) and (86) follows:
% 7.06/2.26 | (105) relation_dom(all_0_12_12) = all_0_13_13
% 7.06/2.26 |
% 7.06/2.26 | Instantiating formula (89) with all_0_10_10, all_0_11_11, all_0_15_15, all_0_13_13 and discharging atoms apply(all_0_12_12, all_0_15_15) = all_0_11_11, apply(all_0_14_14, all_0_11_11) = all_0_10_10, relation_dom(all_0_12_12) = all_0_13_13, relation(all_0_12_12), function(all_0_12_12), yields:
% 7.06/2.26 | (106) all_0_10_10 = all_0_15_15 | ~ in(all_0_15_15, all_22_1_24)
% 7.06/2.26 |
% 7.06/2.26 | Instantiating formula (52) with all_0_11_11, all_0_12_12, all_0_15_15 and discharging atoms apply(all_0_12_12, all_0_15_15) = all_0_11_11, relation(all_0_12_12), function(all_0_12_12), yields:
% 7.06/2.26 | (107) ? [v0] : (relation_dom(all_0_12_12) = v0 & ! [v1] : ! [v2] : ! [v3] : ( ~ (apply(v2, all_0_15_15) = v3) | ~ (relation_composition(all_0_12_12, v1) = v2) | ~ relation(v1) | ~ function(v1) | ~ in(all_0_15_15, v0) | apply(v1, all_0_11_11) = v3) & ! [v1] : ! [v2] : ( ~ (apply(v1, all_0_11_11) = v2) | ~ relation(v1) | ~ function(v1) | ~ in(all_0_15_15, v0) | ? [v3] : (apply(v3, all_0_15_15) = v2 & relation_composition(all_0_12_12, v1) = v3)))
% 7.06/2.26 |
% 7.06/2.26 | Instantiating formula (26) with all_0_9_9, all_0_14_14, all_0_12_12 and discharging atoms relation_composition(all_0_12_12, all_0_14_14) = all_0_9_9, relation(all_0_12_12), relation(all_0_14_14), function(all_0_12_12), function(all_0_14_14), yields:
% 7.06/2.26 | (108) relation(all_0_9_9)
% 7.06/2.26 |
% 7.06/2.26 | Instantiating formula (35) with all_0_9_9, all_0_14_14, all_0_12_12 and discharging atoms relation_composition(all_0_12_12, all_0_14_14) = all_0_9_9, relation(all_0_12_12), relation(all_0_14_14), function(all_0_12_12), function(all_0_14_14), yields:
% 7.06/2.26 | (109) function(all_0_9_9)
% 7.06/2.26 |
% 7.06/2.26 | Instantiating formula (96) with all_0_10_10, all_0_11_11, all_0_15_15, all_0_13_13 and discharging atoms apply(all_0_12_12, all_0_15_15) = all_0_11_11, apply(all_0_14_14, all_0_11_11) = all_0_10_10, relation_dom(all_0_12_12) = all_0_13_13, relation(all_0_12_12), function(all_0_12_12), yields:
% 7.06/2.26 | (110) ~ in(all_0_15_15, all_22_1_24) | in(all_0_11_11, all_22_0_23)
% 7.06/2.26 |
% 7.06/2.26 | Instantiating (107) with all_43_0_30 yields:
% 7.06/2.26 | (111) relation_dom(all_0_12_12) = all_43_0_30 & ! [v0] : ! [v1] : ! [v2] : ( ~ (apply(v1, all_0_15_15) = v2) | ~ (relation_composition(all_0_12_12, v0) = v1) | ~ relation(v0) | ~ function(v0) | ~ in(all_0_15_15, all_43_0_30) | apply(v0, all_0_11_11) = v2) & ! [v0] : ! [v1] : ( ~ (apply(v0, all_0_11_11) = v1) | ~ relation(v0) | ~ function(v0) | ~ in(all_0_15_15, all_43_0_30) | ? [v2] : (apply(v2, all_0_15_15) = v1 & relation_composition(all_0_12_12, v0) = v2))
% 7.06/2.26 |
% 7.06/2.26 | Applying alpha-rule on (111) yields:
% 7.06/2.26 | (112) relation_dom(all_0_12_12) = all_43_0_30
% 7.06/2.26 | (113) ! [v0] : ! [v1] : ! [v2] : ( ~ (apply(v1, all_0_15_15) = v2) | ~ (relation_composition(all_0_12_12, v0) = v1) | ~ relation(v0) | ~ function(v0) | ~ in(all_0_15_15, all_43_0_30) | apply(v0, all_0_11_11) = v2)
% 7.06/2.26 | (114) ! [v0] : ! [v1] : ( ~ (apply(v0, all_0_11_11) = v1) | ~ relation(v0) | ~ function(v0) | ~ in(all_0_15_15, all_43_0_30) | ? [v2] : (apply(v2, all_0_15_15) = v1 & relation_composition(all_0_12_12, v0) = v2))
% 7.06/2.26 |
% 7.06/2.26 +-Applying beta-rule and splitting (110), into two cases.
% 7.06/2.26 |-Branch one:
% 7.06/2.26 | (115) ~ in(all_0_15_15, all_22_1_24)
% 7.06/2.26 |
% 7.06/2.26 | From (101) and (115) follows:
% 7.06/2.26 | (116) ~ in(all_0_15_15, all_0_13_13)
% 7.06/2.26 |
% 7.06/2.26 | Using (13) and (116) yields:
% 7.06/2.26 | (117) $false
% 7.06/2.26 |
% 7.06/2.26 |-The branch is then unsatisfiable
% 7.06/2.26 |-Branch two:
% 7.06/2.26 | (118) in(all_0_15_15, all_22_1_24)
% 7.06/2.26 | (119) in(all_0_11_11, all_22_0_23)
% 7.06/2.26 |
% 7.06/2.26 | From (101) and (118) follows:
% 7.06/2.26 | (13) in(all_0_15_15, all_0_13_13)
% 7.06/2.26 |
% 7.06/2.26 +-Applying beta-rule and splitting (106), into two cases.
% 7.06/2.26 |-Branch one:
% 7.06/2.26 | (115) ~ in(all_0_15_15, all_22_1_24)
% 7.06/2.26 |
% 7.06/2.26 | From (101) and (115) follows:
% 7.06/2.26 | (116) ~ in(all_0_15_15, all_0_13_13)
% 7.06/2.26 |
% 7.06/2.26 | Using (13) and (116) yields:
% 7.06/2.26 | (117) $false
% 7.06/2.26 |
% 7.06/2.26 |-The branch is then unsatisfiable
% 7.06/2.26 |-Branch two:
% 7.06/2.26 | (118) in(all_0_15_15, all_22_1_24)
% 7.06/2.26 | (125) all_0_10_10 = all_0_15_15
% 7.06/2.26 |
% 7.06/2.26 | From (125) and (46) follows:
% 7.06/2.26 | (126) apply(all_0_14_14, all_0_11_11) = all_0_15_15
% 7.06/2.26 |
% 7.06/2.26 | From (101) and (118) follows:
% 7.06/2.26 | (13) in(all_0_15_15, all_0_13_13)
% 7.06/2.26 |
% 7.06/2.26 +-Applying beta-rule and splitting (77), into two cases.
% 7.06/2.26 |-Branch one:
% 7.06/2.26 | (128) ~ (all_0_8_8 = all_0_15_15)
% 7.06/2.26 |
% 7.06/2.26 | Instantiating formula (68) with all_0_12_12, all_43_0_30, all_0_13_13 and discharging atoms relation_dom(all_0_12_12) = all_43_0_30, relation_dom(all_0_12_12) = all_0_13_13, yields:
% 7.06/2.26 | (129) all_43_0_30 = all_0_13_13
% 7.06/2.26 |
% 7.06/2.26 | Instantiating formula (114) with all_0_15_15, all_0_14_14 and discharging atoms apply(all_0_14_14, all_0_11_11) = all_0_15_15, relation(all_0_14_14), function(all_0_14_14), yields:
% 7.06/2.26 | (130) ~ in(all_0_15_15, all_43_0_30) | ? [v0] : (apply(v0, all_0_15_15) = all_0_15_15 & relation_composition(all_0_12_12, all_0_14_14) = v0)
% 7.06/2.26 |
% 7.06/2.26 | Instantiating formula (100) with all_0_8_8, all_0_9_9 and discharging atoms relation(all_0_9_9), function(all_0_9_9), yields:
% 7.06/2.26 | (131) ~ (apply(all_0_9_9, all_0_10_10) = all_0_8_8) | ~ in(all_0_11_11, all_27_0_27) | ? [v0] : (apply(v0, all_0_11_11) = all_0_8_8 & relation_composition(all_0_14_14, all_0_9_9) = v0)
% 7.06/2.26 |
% 7.06/2.26 +-Applying beta-rule and splitting (130), into two cases.
% 7.06/2.26 |-Branch one:
% 7.06/2.26 | (132) ~ in(all_0_15_15, all_43_0_30)
% 7.06/2.26 |
% 7.06/2.26 | From (129) and (132) follows:
% 7.06/2.26 | (116) ~ in(all_0_15_15, all_0_13_13)
% 7.06/2.26 |
% 7.06/2.26 | Using (13) and (116) yields:
% 7.06/2.26 | (117) $false
% 7.06/2.26 |
% 7.06/2.26 |-The branch is then unsatisfiable
% 7.06/2.26 |-Branch two:
% 7.06/2.26 | (135) in(all_0_15_15, all_43_0_30)
% 7.06/2.26 | (136) ? [v0] : (apply(v0, all_0_15_15) = all_0_15_15 & relation_composition(all_0_12_12, all_0_14_14) = v0)
% 7.06/2.26 |
% 7.06/2.26 | Instantiating (136) with all_83_0_32 yields:
% 7.06/2.26 | (137) apply(all_83_0_32, all_0_15_15) = all_0_15_15 & relation_composition(all_0_12_12, all_0_14_14) = all_83_0_32
% 7.06/2.26 |
% 7.06/2.26 | Applying alpha-rule on (137) yields:
% 7.06/2.26 | (138) apply(all_83_0_32, all_0_15_15) = all_0_15_15
% 7.06/2.26 | (139) relation_composition(all_0_12_12, all_0_14_14) = all_83_0_32
% 7.06/2.26 |
% 7.06/2.26 +-Applying beta-rule and splitting (131), into two cases.
% 7.06/2.26 |-Branch one:
% 7.06/2.26 | (140) ~ (apply(all_0_9_9, all_0_10_10) = all_0_8_8)
% 7.06/2.26 |
% 7.06/2.26 | From (125) and (140) follows:
% 7.06/2.26 | (141) ~ (apply(all_0_9_9, all_0_15_15) = all_0_8_8)
% 7.06/2.26 |
% 7.06/2.26 | Using (51) and (141) yields:
% 7.06/2.26 | (117) $false
% 7.06/2.26 |
% 7.06/2.26 |-The branch is then unsatisfiable
% 7.06/2.26 |-Branch two:
% 7.06/2.26 | (143) apply(all_0_9_9, all_0_10_10) = all_0_8_8
% 7.06/2.26 | (144) ~ in(all_0_11_11, all_27_0_27) | ? [v0] : (apply(v0, all_0_11_11) = all_0_8_8 & relation_composition(all_0_14_14, all_0_9_9) = v0)
% 7.06/2.26 |
% 7.06/2.26 | From (125) and (143) follows:
% 7.06/2.26 | (51) apply(all_0_9_9, all_0_15_15) = all_0_8_8
% 7.06/2.27 |
% 7.06/2.27 | Instantiating formula (7) with all_0_12_12, all_0_14_14, all_83_0_32, all_0_9_9 and discharging atoms relation_composition(all_0_12_12, all_0_14_14) = all_83_0_32, relation_composition(all_0_12_12, all_0_14_14) = all_0_9_9, yields:
% 7.06/2.27 | (146) all_83_0_32 = all_0_9_9
% 7.06/2.27 |
% 7.06/2.27 | From (146) and (138) follows:
% 7.06/2.27 | (147) apply(all_0_9_9, all_0_15_15) = all_0_15_15
% 7.06/2.27 |
% 7.06/2.27 | Instantiating formula (66) with all_0_9_9, all_0_15_15, all_0_15_15, all_0_8_8 and discharging atoms apply(all_0_9_9, all_0_15_15) = all_0_8_8, apply(all_0_9_9, all_0_15_15) = all_0_15_15, yields:
% 7.06/2.27 | (148) all_0_8_8 = all_0_15_15
% 7.06/2.27 |
% 7.06/2.27 | Equations (148) can reduce 128 to:
% 7.06/2.27 | (149) $false
% 7.06/2.27 |
% 7.06/2.27 |-The branch is then unsatisfiable
% 7.06/2.27 |-Branch two:
% 7.06/2.27 | (148) all_0_8_8 = all_0_15_15
% 7.06/2.27 | (151) ~ (all_0_10_10 = all_0_15_15)
% 7.06/2.27 |
% 7.06/2.27 | Equations (125) can reduce 151 to:
% 7.06/2.27 | (149) $false
% 7.06/2.27 |
% 7.06/2.27 |-The branch is then unsatisfiable
% 7.06/2.27 % SZS output end Proof for theBenchmark
% 7.06/2.27
% 7.06/2.27 1678ms
%------------------------------------------------------------------------------