TSTP Solution File: SEU292+1 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU292+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n011.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 08:48:32 EDT 2022
% Result : Theorem 19.15s 5.32s
% Output : Proof 49.36s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SEU292+1 : TPTP v8.1.0. Released v3.3.0.
% 0.10/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n011.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 : Mon Jun 20 01:35:54 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.58 ____ _
% 0.18/0.58 ___ / __ \_____(_)___ ________ __________
% 0.18/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.18/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.18/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.18/0.58
% 0.18/0.58 A Theorem Prover for First-Order Logic
% 0.18/0.58 (ePrincess v.1.0)
% 0.18/0.58
% 0.18/0.58 (c) Philipp Rümmer, 2009-2015
% 0.18/0.58 (c) Peter Backeman, 2014-2015
% 0.18/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.18/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.18/0.58 Bug reports to peter@backeman.se
% 0.18/0.58
% 0.18/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.18/0.58
% 0.18/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.69/0.66 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.53/1.02 Prover 0: Preprocessing ...
% 2.37/1.29 Prover 0: Warning: ignoring some quantifiers
% 2.63/1.32 Prover 0: Constructing countermodel ...
% 15.98/4.58 Prover 0: gave up
% 15.98/4.58 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 16.37/4.62 Prover 1: Preprocessing ...
% 16.74/4.73 Prover 1: Warning: ignoring some quantifiers
% 16.74/4.74 Prover 1: Constructing countermodel ...
% 17.82/4.96 Prover 1: gave up
% 17.82/4.96 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 17.82/4.99 Prover 2: Preprocessing ...
% 18.51/5.11 Prover 2: Warning: ignoring some quantifiers
% 18.51/5.12 Prover 2: Constructing countermodel ...
% 19.15/5.32 Prover 2: proved (360ms)
% 19.15/5.32
% 19.15/5.32 No countermodel exists, formula is valid
% 19.15/5.32 % SZS status Theorem for theBenchmark
% 19.15/5.32
% 19.15/5.32 Generating proof ... Warning: ignoring some quantifiers
% 48.35/17.68 found it (size 116)
% 48.35/17.68
% 48.35/17.68 % SZS output start Proof for theBenchmark
% 48.35/17.68 Assumed formulas after preprocessing and simplification:
% 48.35/17.68 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ( ~ (v15 = 0) & ~ (v13 = 0) & ~ (v8 = v7) & ~ (v1 = empty_set) & apply(v6, v2) = v7 & apply(v5, v4) = v8 & apply(v3, v2) = v4 & relation_empty_yielding(v10) = 0 & relation_empty_yielding(v9) = 0 & relation_empty_yielding(empty_set) = 0 & relation_composition(v3, v5) = v6 & relation_of2_as_subset(v3, v0, v1) = 0 & quasi_total(v3, v0, v1) = 0 & one_to_one(v19) = 0 & one_to_one(v11) = 0 & relation(v20) = 0 & relation(v19) = 0 & relation(v18) = 0 & relation(v16) = 0 & relation(v14) = 0 & relation(v11) = 0 & relation(v10) = 0 & relation(v9) = 0 & relation(v5) = 0 & relation(empty_set) = 0 & function(v20) = 0 & function(v19) = 0 & function(v16) = 0 & function(v11) = 0 & function(v9) = 0 & function(v5) = 0 & function(v3) = 0 & empty(v19) = 0 & empty(v18) = 0 & empty(v17) = 0 & empty(v16) = 0 & empty(v14) = v15 & empty(v12) = v13 & empty(empty_set) = 0 & in(v2, v0) = 0 & ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : (v26 = 0 | ~ (cartesian_product2(v21, v22) = v24) | ~ (powerset(v24) = v25) | ~ (element(v23, v25) = v26) | ? [v27] : ( ~ (v27 = 0) & relation_of2_as_subset(v23, v21, v22) = v27)) & ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : (v25 = 0 | ~ (powerset(v23) = v24) | ~ (element(v22, v24) = 0) | ~ (element(v21, v23) = v25) | ? [v26] : ( ~ (v26 = 0) & in(v21, v22) = v26)) & ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : (v22 = v21 | ~ (relation_of2(v25, v24, v23) = v22) | ~ (relation_of2(v25, v24, v23) = v21)) & ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : (v22 = v21 | ~ (relation_dom_as_subset(v25, v24, v23) = v22) | ~ (relation_dom_as_subset(v25, v24, v23) = v21)) & ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : (v22 = v21 | ~ (relation_of2_as_subset(v25, v24, v23) = v22) | ~ (relation_of2_as_subset(v25, v24, v23) = v21)) & ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : (v22 = v21 | ~ (quasi_total(v25, v24, v23) = v22) | ~ (quasi_total(v25, v24, v23) = v21)) & ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : ( ~ (cartesian_product2(v21, v22) = v24) | ~ (powerset(v24) = v25) | ~ (element(v23, v25) = 0) | relation(v23) = 0) & ! [v21] : ! [v22] : ! [v23] : ! [v24] : (v24 = 0 | ~ (relation_of2(v23, v21, v22) = v24) | ? [v25] : ( ~ (v25 = 0) & relation_of2_as_subset(v23, v21, v22) = v25)) & ! [v21] : ! [v22] : ! [v23] : ! [v24] : (v24 = 0 | ~ (relation_of2_as_subset(v23, v21, v22) = v24) | ? [v25] : ( ~ (v25 = 0) & relation_of2(v23, v21, v22) = v25)) & ! [v21] : ! [v22] : ! [v23] : ! [v24] : (v24 = 0 | ~ (powerset(v22) = v23) | ~ (element(v21, v23) = v24) | ? [v25] : ( ~ (v25 = 0) & subset(v21, v22) = v25)) & ! [v21] : ! [v22] : ! [v23] : ! [v24] : (v24 = 0 | ~ (element(v21, v23) = v24) | ~ (in(v21, v22) = 0) | ? [v25] : ? [v26] : ( ~ (v26 = 0) & powerset(v23) = v25 & element(v22, v25) = v26)) & ! [v21] : ! [v22] : ! [v23] : ! [v24] : (v22 = v21 | ~ (apply(v24, v23) = v22) | ~ (apply(v24, v23) = v21)) & ! [v21] : ! [v22] : ! [v23] : ! [v24] : (v22 = v21 | ~ (subset(v24, v23) = v22) | ~ (subset(v24, v23) = v21)) & ! [v21] : ! [v22] : ! [v23] : ! [v24] : (v22 = v21 | ~ (relation_composition(v24, v23) = v22) | ~ (relation_composition(v24, v23) = v21)) & ! [v21] : ! [v22] : ! [v23] : ! [v24] : (v22 = v21 | ~ (cartesian_product2(v24, v23) = v22) | ~ (cartesian_product2(v24, v23) = v21)) & ! [v21] : ! [v22] : ! [v23] : ! [v24] : (v22 = v21 | ~ (element(v24, v23) = v22) | ~ (element(v24, v23) = v21)) & ! [v21] : ! [v22] : ! [v23] : ! [v24] : (v22 = v21 | ~ (in(v24, v23) = v22) | ~ (in(v24, v23) = v21)) & ! [v21] : ! [v22] : ! [v23] : ! [v24] : (v22 = empty_set | ~ (quasi_total(v23, v21, v22) = v24) | ? [v25] : (( ~ (v25 = 0) & relation_of2_as_subset(v23, v21, v22) = v25) | (( ~ (v24 = 0) | (v25 = v21 & relation_dom_as_subset(v21, v22, v23) = v21)) & (v24 = 0 | ( ~ (v25 = v21) & relation_dom_as_subset(v21, v22, v23) = v25))))) & ! [v21] : ! [v22] : ! [v23] : ! [v24] : ( ~ (relation_dom(v22) = v23) | ~ (in(v21, v23) = v24) | ? [v25] : (( ~ (v25 = 0) & relation(v22) = v25) | ( ~ (v25 = 0) & function(v22) = v25) | (apply(v22, v21) = v25 & ! [v26] : ! [v27] : ( ~ (v24 = 0) | ~ (apply(v26, v25) = v27) | ? [v28] : ? [v29] : ((v29 = v27 & apply(v28, v21) = v27 & relation_composition(v22, v26) = v28) | ( ~ (v28 = 0) & relation(v26) = v28) | ( ~ (v28 = 0) & function(v26) = v28))) & ! [v26] : ! [v27] : ( ~ (v24 = 0) | ~ (relation_composition(v22, v26) = v27) | ? [v28] : ? [v29] : ((v29 = v28 & apply(v27, v21) = v28 & apply(v26, v25) = v28) | ( ~ (v28 = 0) & relation(v26) = v28) | ( ~ (v28 = 0) & function(v26) = v28))) & ! [v26] : ( ~ (v24 = 0) | ~ (relation(v26) = 0) | ? [v27] : ? [v28] : ? [v29] : ((v29 = v28 & apply(v27, v21) = v28 & apply(v26, v25) = v28 & relation_composition(v22, v26) = v27) | ( ~ (v27 = 0) & function(v26) = v27))) & ! [v26] : ( ~ (v24 = 0) | ~ (function(v26) = 0) | ? [v27] : ? [v28] : ? [v29] : ((v29 = v28 & apply(v27, v21) = v28 & apply(v26, v25) = v28 & relation_composition(v22, v26) = v27) | ( ~ (v27 = 0) & relation(v26) = v27)))))) & ! [v21] : ! [v22] : ! [v23] : ! [v24] : ( ~ (relation_dom_as_subset(v21, v22, v23) = v24) | ? [v25] : ? [v26] : ((v26 = 0 & powerset(v21) = v25 & element(v24, v25) = 0) | ( ~ (v25 = 0) & relation_of2(v23, v21, v22) = v25))) & ! [v21] : ! [v22] : ! [v23] : ! [v24] : ( ~ (relation_dom_as_subset(v21, v22, v23) = v24) | ? [v25] : ((v25 = v24 & relation_dom(v23) = v24) | ( ~ (v25 = 0) & relation_of2(v23, v21, v22) = v25))) & ! [v21] : ! [v22] : ! [v23] : ! [v24] : ( ~ (relation_dom_as_subset(v21, v22, v23) = v24) | ? [v25] : (( ~ (v25 = 0) & relation_of2_as_subset(v23, v21, v22) = v25) | (( ~ (v22 = empty_set) | v21 = empty_set | (( ~ (v23 = empty_set) | (v25 = 0 & quasi_total(empty_set, v21, empty_set) = 0)) & (v23 = empty_set | ( ~ (v25 = 0) & quasi_total(v23, v21, empty_set) = v25)))) & ((v22 = empty_set & ~ (v21 = empty_set)) | (( ~ (v24 = v21) | (v25 = 0 & quasi_total(v23, v21, v22) = 0)) & (v24 = v21 | ( ~ (v25 = 0) & quasi_total(v23, v21, v22) = v25))))))) & ! [v21] : ! [v22] : ! [v23] : ! [v24] : ( ~ (powerset(v23) = v24) | ~ (element(v22, v24) = 0) | ~ (in(v21, v22) = 0) | element(v21, v23) = 0) & ! [v21] : ! [v22] : ! [v23] : ! [v24] : ( ~ (powerset(v23) = v24) | ~ (element(v22, v24) = 0) | ~ (in(v21, v22) = 0) | ? [v25] : ( ~ (v25 = 0) & empty(v23) = v25)) & ! [v21] : ! [v22] : ! [v23] : (v23 = 0 | ~ (subset(v21, v22) = v23) | ? [v24] : ? [v25] : ( ~ (v25 = 0) & powerset(v22) = v24 & element(v21, v24) = v25)) & ! [v21] : ! [v22] : ! [v23] : (v23 = 0 | ~ (element(v21, v22) = v23) | ? [v24] : ( ~ (v24 = 0) & in(v21, v22) = v24)) & ! [v21] : ! [v22] : ! [v23] : (v23 = 0 | ~ (in(v21, v22) = v23) | ? [v24] : ((v24 = 0 & empty(v22) = 0) | ( ~ (v24 = 0) & element(v21, v22) = v24))) & ! [v21] : ! [v22] : ! [v23] : (v22 = v21 | ~ (relation_empty_yielding(v23) = v22) | ~ (relation_empty_yielding(v23) = v21)) & ! [v21] : ! [v22] : ! [v23] : (v22 = v21 | ~ (relation_dom(v23) = v22) | ~ (relation_dom(v23) = v21)) & ! [v21] : ! [v22] : ! [v23] : (v22 = v21 | ~ (one_to_one(v23) = v22) | ~ (one_to_one(v23) = v21)) & ! [v21] : ! [v22] : ! [v23] : (v22 = v21 | ~ (powerset(v23) = v22) | ~ (powerset(v23) = v21)) & ! [v21] : ! [v22] : ! [v23] : (v22 = v21 | ~ (relation(v23) = v22) | ~ (relation(v23) = v21)) & ! [v21] : ! [v22] : ! [v23] : (v22 = v21 | ~ (function(v23) = v22) | ~ (function(v23) = v21)) & ! [v21] : ! [v22] : ! [v23] : (v22 = v21 | ~ (empty(v23) = v22) | ~ (empty(v23) = v21)) & ! [v21] : ! [v22] : ! [v23] : ( ~ (apply(v22, v21) = v23) | ? [v24] : ? [v25] : (( ~ (v24 = 0) & relation(v22) = v24) | ( ~ (v24 = 0) & function(v22) = v24) | (relation_dom(v22) = v24 & in(v21, v24) = v25 & ! [v26] : ! [v27] : ( ~ (v25 = 0) | ~ (apply(v26, v23) = v27) | ? [v28] : ? [v29] : ((v29 = v27 & apply(v28, v21) = v27 & relation_composition(v22, v26) = v28) | ( ~ (v28 = 0) & relation(v26) = v28) | ( ~ (v28 = 0) & function(v26) = v28))) & ! [v26] : ! [v27] : ( ~ (v25 = 0) | ~ (relation_composition(v22, v26) = v27) | ? [v28] : ? [v29] : ((v29 = v28 & apply(v27, v21) = v28 & apply(v26, v23) = v28) | ( ~ (v28 = 0) & relation(v26) = v28) | ( ~ (v28 = 0) & function(v26) = v28))) & ! [v26] : ( ~ (v25 = 0) | ~ (relation(v26) = 0) | ? [v27] : ? [v28] : ? [v29] : ((v29 = v28 & apply(v27, v21) = v28 & apply(v26, v23) = v28 & relation_composition(v22, v26) = v27) | ( ~ (v27 = 0) & function(v26) = v27))) & ! [v26] : ( ~ (v25 = 0) | ~ (function(v26) = 0) | ? [v27] : ? [v28] : ? [v29] : ((v29 = v28 & apply(v27, v21) = v28 & apply(v26, v23) = v28 & relation_composition(v22, v26) = v27) | ( ~ (v27 = 0) & relation(v26) = v27)))))) & ! [v21] : ! [v22] : ! [v23] : ( ~ (relation_composition(v22, v21) = v23) | ? [v24] : ? [v25] : ((v25 = 0 & v24 = 0 & relation(v23) = 0 & empty(v23) = 0) | ( ~ (v24 = 0) & relation(v22) = v24) | ( ~ (v24 = 0) & empty(v21) = v24))) & ! [v21] : ! [v22] : ! [v23] : ( ~ (relation_composition(v21, v22) = v23) | ? [v24] : ? [v25] : ((v25 = 0 & v24 = 0 & relation(v23) = 0 & function(v23) = 0) | ( ~ (v24 = 0) & relation(v22) = v24) | ( ~ (v24 = 0) & relation(v21) = v24) | ( ~ (v24 = 0) & function(v22) = v24) | ( ~ (v24 = 0) & function(v21) = v24))) & ! [v21] : ! [v22] : ! [v23] : ( ~ (relation_composition(v21, v22) = v23) | ? [v24] : ? [v25] : ((v25 = 0 & v24 = 0 & relation(v23) = 0 & empty(v23) = 0) | ( ~ (v24 = 0) & relation(v22) = v24) | ( ~ (v24 = 0) & empty(v21) = v24))) & ! [v21] : ! [v22] : ! [v23] : ( ~ (relation_composition(v21, v22) = v23) | ? [v24] : ((v24 = 0 & relation(v23) = 0) | ( ~ (v24 = 0) & relation(v22) = v24) | ( ~ (v24 = 0) & relation(v21) = v24))) & ! [v21] : ! [v22] : ! [v23] : ( ~ (relation_of2(v23, v21, v22) = 0) | relation_of2_as_subset(v23, v21, v22) = 0) & ! [v21] : ! [v22] : ! [v23] : ( ~ (relation_of2(v23, v21, v22) = 0) | ? [v24] : ? [v25] : (relation_dom_as_subset(v21, v22, v23) = v24 & powerset(v21) = v25 & element(v24, v25) = 0)) & ! [v21] : ! [v22] : ! [v23] : ( ~ (relation_of2(v23, v21, v22) = 0) | ? [v24] : (relation_dom(v23) = v24 & relation_dom_as_subset(v21, v22, v23) = v24)) & ! [v21] : ! [v22] : ! [v23] : ( ~ (relation_of2_as_subset(v23, v21, v22) = 0) | relation_of2(v23, v21, v22) = 0) & ! [v21] : ! [v22] : ! [v23] : ( ~ (relation_of2_as_subset(v23, v21, v22) = 0) | ? [v24] : ? [v25] : (cartesian_product2(v21, v22) = v24 & powerset(v24) = v25 & element(v23, v25) = 0)) & ! [v21] : ! [v22] : ! [v23] : ( ~ (relation_of2_as_subset(v23, v21, v22) = 0) | ? [v24] : ? [v25] : (( ~ (v22 = empty_set) | v21 = empty_set | (( ~ (v23 = empty_set) | (v24 = 0 & quasi_total(empty_set, v21, empty_set) = 0)) & (v23 = empty_set | ( ~ (v24 = 0) & quasi_total(v23, v21, empty_set) = v24)))) & ((v22 = empty_set & ~ (v21 = empty_set)) | (((v25 = v21 & relation_dom_as_subset(v21, v22, v23) = v21) | ( ~ (v24 = 0) & quasi_total(v23, v21, v22) = v24)) & ((v24 = 0 & quasi_total(v23, v21, v22) = 0) | ( ~ (v25 = v21) & relation_dom_as_subset(v21, v22, v23) = v25)))))) & ! [v21] : ! [v22] : ! [v23] : ( ~ (quasi_total(v22, empty_set, v21) = v23) | ? [v24] : (( ~ (v24 = 0) & relation_of2_as_subset(v22, empty_set, v21) = v24) | (( ~ (v23 = 0) | (v24 = empty_set & relation_dom_as_subset(empty_set, v21, v22) = empty_set)) & (v23 = 0 | ( ~ (v24 = empty_set) & relation_dom_as_subset(empty_set, v21, v22) = v24))))) & ! [v21] : ! [v22] : ! [v23] : ( ~ (cartesian_product2(v21, v22) = v23) | ? [v24] : ((v24 = 0 & empty(v22) = 0) | (v24 = 0 & empty(v21) = 0) | ( ~ (v24 = 0) & empty(v23) = v24))) & ! [v21] : ! [v22] : ! [v23] : ( ~ (powerset(v22) = v23) | ~ (element(v21, v23) = 0) | subset(v21, v22) = 0) & ! [v21] : ! [v22] : ! [v23] : ( ~ (empty(v23) = 0) | ~ (in(v21, v22) = 0) | ? [v24] : ? [v25] : ( ~ (v25 = 0) & powerset(v23) = v24 & element(v22, v24) = v25)) & ! [v21] : ! [v22] : (v22 = v21 | ~ (empty(v22) = 0) | ~ (empty(v21) = 0)) & ! [v21] : ! [v22] : (v22 = empty_set | v21 = empty_set | ~ (quasi_total(v22, v21, empty_set) = 0) | ? [v23] : ( ~ (v23 = 0) & relation_of2_as_subset(v22, v21, empty_set) = v23)) & ! [v21] : ! [v22] : (v22 = 0 | v21 = empty_set | ~ (quasi_total(empty_set, v21, empty_set) = v22) | ? [v23] : ( ~ (v23 = 0) & relation_of2_as_subset(empty_set, v21, empty_set) = v23)) & ! [v21] : ! [v22] : (v22 = 0 | ~ (subset(v21, v21) = v22)) & ! [v21] : ! [v22] : (v22 = 0 | ~ (relation(v21) = v22) | ? [v23] : ( ~ (v23 = 0) & empty(v21) = v23)) & ! [v21] : ! [v22] : (v22 = 0 | ~ (function(v21) = v22) | ? [v23] : ( ~ (v23 = 0) & empty(v21) = v23)) & ! [v21] : ! [v22] : (v22 = 0 | ~ (empty(v21) = v22) | ? [v23] : ? [v24] : ? [v25] : ( ~ (v25 = 0) & powerset(v21) = v23 & element(v24, v23) = 0 & empty(v24) = v25)) & ! [v21] : ! [v22] : (v22 = 0 | ~ (empty(v21) = v22) | ? [v23] : ? [v24] : (( ~ (v24 = 0) & relation_dom(v21) = v23 & empty(v23) = v24) | ( ~ (v23 = 0) & relation(v21) = v23))) & ! [v21] : ! [v22] : ( ~ (subset(v21, v22) = 0) | ? [v23] : (powerset(v22) = v23 & element(v21, v23) = 0)) & ! [v21] : ! [v22] : ( ~ (relation_dom(v21) = v22) | ? [v23] : ? [v24] : ((v24 = 0 & v23 = 0 & relation(v22) = 0 & empty(v22) = 0) | ( ~ (v23 = 0) & empty(v21) = v23))) & ! [v21] : ! [v22] : ( ~ (relation_dom(v21) = v22) | ? [v23] : ((v23 = 0 & empty(v21) = 0) | ( ~ (v23 = 0) & relation(v21) = v23) | ( ~ (v23 = 0) & empty(v22) = v23))) & ! [v21] : ! [v22] : ( ~ (one_to_one(v21) = v22) | ? [v23] : ? [v24] : ((v24 = 0 & v23 = 0 & v22 = 0 & relation(v21) = 0 & function(v21) = 0) | ( ~ (v23 = 0) & relation(v21) = v23) | ( ~ (v23 = 0) & function(v21) = v23) | ( ~ (v23 = 0) & empty(v21) = v23))) & ! [v21] : ! [v22] : ( ~ (powerset(v21) = v22) | ? [v23] : ? [v24] : ? [v25] : ((v24 = 0 & ~ (v25 = 0) & element(v23, v22) = 0 & empty(v23) = v25) | (v23 = 0 & empty(v21) = 0))) & ! [v21] : ! [v22] : ( ~ (powerset(v21) = v22) | ? [v23] : ( ~ (v23 = 0) & empty(v22) = v23)) & ! [v21] : ! [v22] : ( ~ (powerset(v21) = v22) | ? [v23] : (element(v23, v22) = 0 & empty(v23) = 0)) & ! [v21] : ! [v22] : ( ~ (element(v21, v22) = 0) | ? [v23] : ((v23 = 0 & empty(v22) = 0) | (v23 = 0 & in(v21, v22) = 0))) & ! [v21] : ! [v22] : ( ~ (in(v22, v21) = 0) | ? [v23] : ( ~ (v23 = 0) & in(v21, v22) = v23)) & ! [v21] : ! [v22] : ( ~ (in(v21, v22) = 0) | element(v21, v22) = 0) & ! [v21] : ! [v22] : ( ~ (in(v21, v22) = 0) | ? [v23] : ( ~ (v23 = 0) & empty(v22) = v23)) & ! [v21] : ! [v22] : ( ~ (in(v21, v22) = 0) | ? [v23] : ( ~ (v23 = 0) & in(v22, v21) = v23)) & ! [v21] : (v21 = empty_set | ~ (empty(v21) = 0)) & ! [v21] : ( ~ (relation(v21) = 0) | ? [v22] : ? [v23] : ((v23 = 0 & v22 = 0 & one_to_one(v21) = 0 & function(v21) = 0) | ( ~ (v22 = 0) & function(v21) = v22) | ( ~ (v22 = 0) & empty(v21) = v22))) & ! [v21] : ( ~ (relation(v21) = 0) | ? [v22] : ? [v23] : ((v22 = 0 & empty(v21) = 0) | ( ~ (v23 = 0) & relation_dom(v21) = v22 & empty(v22) = v23))) & ! [v21] : ( ~ (function(v21) = 0) | ? [v22] : ? [v23] : ((v23 = 0 & v22 = 0 & one_to_one(v21) = 0 & relation(v21) = 0) | ( ~ (v22 = 0) & relation(v21) = v22) | ( ~ (v22 = 0) & empty(v21) = v22))) & ! [v21] : ( ~ (empty(v21) = 0) | relation(v21) = 0) & ! [v21] : ( ~ (empty(v21) = 0) | function(v21) = 0) & ! [v21] : ( ~ (empty(v21) = 0) | ? [v22] : ? [v23] : ? [v24] : ((v24 = 0 & v23 = 0 & v22 = 0 & one_to_one(v21) = 0 & relation(v21) = 0 & function(v21) = 0) | ( ~ (v22 = 0) & relation(v21) = v22) | ( ~ (v22 = 0) & function(v21) = v22))) & ! [v21] : ( ~ (empty(v21) = 0) | ? [v22] : (relation_dom(v21) = v22 & relation(v22) = 0 & empty(v22) = 0)) & ? [v21] : ? [v22] : ? [v23] : ? [v24] : relation_of2(v23, v22, v21) = v24 & ? [v21] : ? [v22] : ? [v23] : ? [v24] : relation_dom_as_subset(v23, v22, v21) = v24 & ? [v21] : ? [v22] : ? [v23] : ? [v24] : relation_of2_as_subset(v23, v22, v21) = v24 & ? [v21] : ? [v22] : ? [v23] : ? [v24] : quasi_total(v23, v22, v21) = v24 & ? [v21] : ? [v22] : ? [v23] : apply(v22, v21) = v23 & ? [v21] : ? [v22] : ? [v23] : subset(v22, v21) = v23 & ? [v21] : ? [v22] : ? [v23] : relation_composition(v22, v21) = v23 & ? [v21] : ? [v22] : ? [v23] : relation_of2(v23, v21, v22) = 0 & ? [v21] : ? [v22] : ? [v23] : relation_of2_as_subset(v23, v21, v22) = 0 & ? [v21] : ? [v22] : ? [v23] : cartesian_product2(v22, v21) = v23 & ? [v21] : ? [v22] : ? [v23] : element(v22, v21) = v23 & ? [v21] : ? [v22] : ? [v23] : in(v22, v21) = v23 & ? [v21] : ? [v22] : ? [v23] : (relation_of2(v23, v21, v22) = 0 & quasi_total(v23, v21, v22) = 0 & relation(v23) = 0 & function(v23) = 0) & ? [v21] : ? [v22] : ? [v23] : (relation_of2(v23, v21, v22) = 0 & relation(v23) = 0 & function(v23) = 0) & ? [v21] : ? [v22] : relation_empty_yielding(v21) = v22 & ? [v21] : ? [v22] : relation_dom(v21) = v22 & ? [v21] : ? [v22] : one_to_one(v21) = v22 & ? [v21] : ? [v22] : powerset(v21) = v22 & ? [v21] : ? [v22] : element(v22, v21) = 0 & ? [v21] : ? [v22] : relation(v21) = v22 & ? [v21] : ? [v22] : function(v21) = v22 & ? [v21] : ? [v22] : empty(v21) = v22)
% 48.61/17.76 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9, all_0_10_10, all_0_11_11, all_0_12_12, all_0_13_13, all_0_14_14, all_0_15_15, all_0_16_16, all_0_17_17, all_0_18_18, all_0_19_19, all_0_20_20 yields:
% 48.61/17.76 | (1) ~ (all_0_5_5 = 0) & ~ (all_0_7_7 = 0) & ~ (all_0_12_12 = all_0_13_13) & ~ (all_0_19_19 = empty_set) & apply(all_0_14_14, all_0_18_18) = all_0_13_13 & apply(all_0_15_15, all_0_16_16) = all_0_12_12 & apply(all_0_17_17, all_0_18_18) = all_0_16_16 & relation_empty_yielding(all_0_10_10) = 0 & relation_empty_yielding(all_0_11_11) = 0 & relation_empty_yielding(empty_set) = 0 & relation_composition(all_0_17_17, all_0_15_15) = all_0_14_14 & relation_of2_as_subset(all_0_17_17, all_0_20_20, all_0_19_19) = 0 & quasi_total(all_0_17_17, all_0_20_20, all_0_19_19) = 0 & one_to_one(all_0_1_1) = 0 & one_to_one(all_0_9_9) = 0 & relation(all_0_0_0) = 0 & relation(all_0_1_1) = 0 & relation(all_0_2_2) = 0 & relation(all_0_4_4) = 0 & relation(all_0_6_6) = 0 & relation(all_0_9_9) = 0 & relation(all_0_10_10) = 0 & relation(all_0_11_11) = 0 & relation(all_0_15_15) = 0 & relation(empty_set) = 0 & function(all_0_0_0) = 0 & function(all_0_1_1) = 0 & function(all_0_4_4) = 0 & function(all_0_9_9) = 0 & function(all_0_11_11) = 0 & function(all_0_15_15) = 0 & function(all_0_17_17) = 0 & empty(all_0_1_1) = 0 & empty(all_0_2_2) = 0 & empty(all_0_3_3) = 0 & empty(all_0_4_4) = 0 & empty(all_0_6_6) = all_0_5_5 & empty(all_0_8_8) = all_0_7_7 & empty(empty_set) = 0 & in(all_0_18_18, all_0_20_20) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (cartesian_product2(v0, v1) = v3) | ~ (powerset(v3) = v4) | ~ (element(v2, v4) = v5) | ? [v6] : ( ~ (v6 = 0) & relation_of2_as_subset(v2, v0, v1) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (element(v0, v2) = v4) | ? [v5] : ( ~ (v5 = 0) & in(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (relation_of2(v4, v3, v2) = v1) | ~ (relation_of2(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (relation_dom_as_subset(v4, v3, v2) = v1) | ~ (relation_dom_as_subset(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (relation_of2_as_subset(v4, v3, v2) = v1) | ~ (relation_of2_as_subset(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (quasi_total(v4, v3, v2) = v1) | ~ (quasi_total(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v0, v1) = v3) | ~ (powerset(v3) = v4) | ~ (element(v2, v4) = 0) | relation(v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (relation_of2(v2, v0, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & relation_of2_as_subset(v2, v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (relation_of2_as_subset(v2, v0, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & relation_of2(v2, v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (element(v0, v2) = v3) | ~ (in(v0, v1) = 0) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & powerset(v2) = v4 & element(v1, v4) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_composition(v3, v2) = v1) | ~ (relation_composition(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = empty_set | ~ (quasi_total(v2, v0, v1) = v3) | ? [v4] : (( ~ (v4 = 0) & relation_of2_as_subset(v2, v0, v1) = v4) | (( ~ (v3 = 0) | (v4 = v0 & relation_dom_as_subset(v0, v1, v2) = v0)) & (v3 = 0 | ( ~ (v4 = v0) & relation_dom_as_subset(v0, v1, v2) = v4))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom(v1) = v2) | ~ (in(v0, v2) = v3) | ? [v4] : (( ~ (v4 = 0) & relation(v1) = v4) | ( ~ (v4 = 0) & function(v1) = v4) | (apply(v1, v0) = v4 & ! [v5] : ! [v6] : ( ~ (v3 = 0) | ~ (apply(v5, v4) = v6) | ? [v7] : ? [v8] : ((v8 = v6 & apply(v7, v0) = v6 & relation_composition(v1, v5) = v7) | ( ~ (v7 = 0) & relation(v5) = v7) | ( ~ (v7 = 0) & function(v5) = v7))) & ! [v5] : ! [v6] : ( ~ (v3 = 0) | ~ (relation_composition(v1, v5) = v6) | ? [v7] : ? [v8] : ((v8 = v7 & apply(v6, v0) = v7 & apply(v5, v4) = v7) | ( ~ (v7 = 0) & relation(v5) = v7) | ( ~ (v7 = 0) & function(v5) = v7))) & ! [v5] : ( ~ (v3 = 0) | ~ (relation(v5) = 0) | ? [v6] : ? [v7] : ? [v8] : ((v8 = v7 & apply(v6, v0) = v7 & apply(v5, v4) = v7 & relation_composition(v1, v5) = v6) | ( ~ (v6 = 0) & function(v5) = v6))) & ! [v5] : ( ~ (v3 = 0) | ~ (function(v5) = 0) | ? [v6] : ? [v7] : ? [v8] : ((v8 = v7 & apply(v6, v0) = v7 & apply(v5, v4) = v7 & relation_composition(v1, v5) = v6) | ( ~ (v6 = 0) & relation(v5) = v6)))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom_as_subset(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & powerset(v0) = v4 & element(v3, v4) = 0) | ( ~ (v4 = 0) & relation_of2(v2, v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom_as_subset(v0, v1, v2) = v3) | ? [v4] : ((v4 = v3 & relation_dom(v2) = v3) | ( ~ (v4 = 0) & relation_of2(v2, v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom_as_subset(v0, v1, v2) = v3) | ? [v4] : (( ~ (v4 = 0) & relation_of2_as_subset(v2, v0, v1) = v4) | (( ~ (v1 = empty_set) | v0 = empty_set | (( ~ (v2 = empty_set) | (v4 = 0 & quasi_total(empty_set, v0, empty_set) = 0)) & (v2 = empty_set | ( ~ (v4 = 0) & quasi_total(v2, v0, empty_set) = v4)))) & ((v1 = empty_set & ~ (v0 = empty_set)) | (( ~ (v3 = v0) | (v4 = 0 & quasi_total(v2, v0, v1) = 0)) & (v3 = v0 | ( ~ (v4 = 0) & quasi_total(v2, v0, v1) = v4))))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | element(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v1) = v3 & element(v0, v3) = v4)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v0, v1) = v2) | ? [v3] : ((v3 = 0 & empty(v1) = 0) | ( ~ (v3 = 0) & element(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_empty_yielding(v2) = v1) | ~ (relation_empty_yielding(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (apply(v1, v0) = v2) | ? [v3] : ? [v4] : (( ~ (v3 = 0) & relation(v1) = v3) | ( ~ (v3 = 0) & function(v1) = v3) | (relation_dom(v1) = v3 & in(v0, v3) = v4 & ! [v5] : ! [v6] : ( ~ (v4 = 0) | ~ (apply(v5, v2) = v6) | ? [v7] : ? [v8] : ((v8 = v6 & apply(v7, v0) = v6 & relation_composition(v1, v5) = v7) | ( ~ (v7 = 0) & relation(v5) = v7) | ( ~ (v7 = 0) & function(v5) = v7))) & ! [v5] : ! [v6] : ( ~ (v4 = 0) | ~ (relation_composition(v1, v5) = v6) | ? [v7] : ? [v8] : ((v8 = v7 & apply(v6, v0) = v7 & apply(v5, v2) = v7) | ( ~ (v7 = 0) & relation(v5) = v7) | ( ~ (v7 = 0) & function(v5) = v7))) & ! [v5] : ( ~ (v4 = 0) | ~ (relation(v5) = 0) | ? [v6] : ? [v7] : ? [v8] : ((v8 = v7 & apply(v6, v0) = v7 & apply(v5, v2) = v7 & relation_composition(v1, v5) = v6) | ( ~ (v6 = 0) & function(v5) = v6))) & ! [v5] : ( ~ (v4 = 0) | ~ (function(v5) = 0) | ? [v6] : ? [v7] : ? [v8] : ((v8 = v7 & apply(v6, v0) = v7 & apply(v5, v2) = v7 & relation_composition(v1, v5) = v6) | ( ~ (v6 = 0) & relation(v5) = v6)))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v1, v0) = v2) | ? [v3] : ? [v4] : ((v4 = 0 & v3 = 0 & relation(v2) = 0 & empty(v2) = 0) | ( ~ (v3 = 0) & relation(v1) = v3) | ( ~ (v3 = 0) & empty(v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ? [v3] : ? [v4] : ((v4 = 0 & v3 = 0 & relation(v2) = 0 & function(v2) = 0) | ( ~ (v3 = 0) & relation(v1) = v3) | ( ~ (v3 = 0) & relation(v0) = v3) | ( ~ (v3 = 0) & function(v1) = v3) | ( ~ (v3 = 0) & function(v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ? [v3] : ? [v4] : ((v4 = 0 & v3 = 0 & relation(v2) = 0 & empty(v2) = 0) | ( ~ (v3 = 0) & relation(v1) = v3) | ( ~ (v3 = 0) & empty(v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ? [v3] : ((v3 = 0 & relation(v2) = 0) | ( ~ (v3 = 0) & relation(v1) = v3) | ( ~ (v3 = 0) & relation(v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_of2(v2, v0, v1) = 0) | relation_of2_as_subset(v2, v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_of2(v2, v0, v1) = 0) | ? [v3] : ? [v4] : (relation_dom_as_subset(v0, v1, v2) = v3 & powerset(v0) = v4 & element(v3, v4) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_of2(v2, v0, v1) = 0) | ? [v3] : (relation_dom(v2) = v3 & relation_dom_as_subset(v0, v1, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_of2_as_subset(v2, v0, v1) = 0) | relation_of2(v2, v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_of2_as_subset(v2, v0, v1) = 0) | ? [v3] : ? [v4] : (cartesian_product2(v0, v1) = v3 & powerset(v3) = v4 & element(v2, v4) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_of2_as_subset(v2, v0, v1) = 0) | ? [v3] : ? [v4] : (( ~ (v1 = empty_set) | v0 = empty_set | (( ~ (v2 = empty_set) | (v3 = 0 & quasi_total(empty_set, v0, empty_set) = 0)) & (v2 = empty_set | ( ~ (v3 = 0) & quasi_total(v2, v0, empty_set) = v3)))) & ((v1 = empty_set & ~ (v0 = empty_set)) | (((v4 = v0 & relation_dom_as_subset(v0, v1, v2) = v0) | ( ~ (v3 = 0) & quasi_total(v2, v0, v1) = v3)) & ((v3 = 0 & quasi_total(v2, v0, v1) = 0) | ( ~ (v4 = v0) & relation_dom_as_subset(v0, v1, v2) = v4)))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (quasi_total(v1, empty_set, v0) = v2) | ? [v3] : (( ~ (v3 = 0) & relation_of2_as_subset(v1, empty_set, v0) = v3) | (( ~ (v2 = 0) | (v3 = empty_set & relation_dom_as_subset(empty_set, v0, v1) = empty_set)) & (v2 = 0 | ( ~ (v3 = empty_set) & relation_dom_as_subset(empty_set, v0, v1) = v3))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (cartesian_product2(v0, v1) = v2) | ? [v3] : ((v3 = 0 & empty(v1) = 0) | (v3 = 0 & empty(v0) = 0) | ( ~ (v3 = 0) & empty(v2) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | subset(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (empty(v2) = 0) | ~ (in(v0, v1) = 0) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v2) = v3 & element(v1, v3) = v4)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)) & ! [v0] : ! [v1] : (v1 = empty_set | v0 = empty_set | ~ (quasi_total(v1, v0, empty_set) = 0) | ? [v2] : ( ~ (v2 = 0) & relation_of2_as_subset(v1, v0, empty_set) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | v0 = empty_set | ~ (quasi_total(empty_set, v0, empty_set) = v1) | ? [v2] : ( ~ (v2 = 0) & relation_of2_as_subset(empty_set, v0, empty_set) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (relation(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (function(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (empty(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v0) = v2 & element(v3, v2) = 0 & empty(v3) = v4)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (empty(v0) = v1) | ? [v2] : ? [v3] : (( ~ (v3 = 0) & relation_dom(v0) = v2 & empty(v2) = v3) | ( ~ (v2 = 0) & relation(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (powerset(v1) = v2 & element(v0, v2) = 0)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & relation(v1) = 0 & empty(v1) = 0) | ( ~ (v2 = 0) & empty(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ((v2 = 0 & empty(v0) = 0) | ( ~ (v2 = 0) & relation(v0) = v2) | ( ~ (v2 = 0) & empty(v1) = v2))) & ! [v0] : ! [v1] : ( ~ (one_to_one(v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & relation(v0) = 0 & function(v0) = 0) | ( ~ (v2 = 0) & relation(v0) = v2) | ( ~ (v2 = 0) & function(v0) = v2) | ( ~ (v2 = 0) & empty(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v3 = 0 & ~ (v4 = 0) & element(v2, v1) = 0 & empty(v2) = v4) | (v2 = 0 & empty(v0) = 0))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) = 0 & empty(v2) = 0)) & ! [v0] : ! [v1] : ( ~ (element(v0, v1) = 0) | ? [v2] : ((v2 = 0 & empty(v1) = 0) | (v2 = 0 & in(v0, v1) = 0))) & ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | element(v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) & ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0)) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ((v2 = 0 & v1 = 0 & one_to_one(v0) = 0 & function(v0) = 0) | ( ~ (v1 = 0) & function(v0) = v1) | ( ~ (v1 = 0) & empty(v0) = v1))) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ((v1 = 0 & empty(v0) = 0) | ( ~ (v2 = 0) & relation_dom(v0) = v1 & empty(v1) = v2))) & ! [v0] : ( ~ (function(v0) = 0) | ? [v1] : ? [v2] : ((v2 = 0 & v1 = 0 & one_to_one(v0) = 0 & relation(v0) = 0) | ( ~ (v1 = 0) & relation(v0) = v1) | ( ~ (v1 = 0) & empty(v0) = v1))) & ! [v0] : ( ~ (empty(v0) = 0) | relation(v0) = 0) & ! [v0] : ( ~ (empty(v0) = 0) | function(v0) = 0) & ! [v0] : ( ~ (empty(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & one_to_one(v0) = 0 & relation(v0) = 0 & function(v0) = 0) | ( ~ (v1 = 0) & relation(v0) = v1) | ( ~ (v1 = 0) & function(v0) = v1))) & ! [v0] : ( ~ (empty(v0) = 0) | ? [v1] : (relation_dom(v0) = v1 & relation(v1) = 0 & empty(v1) = 0)) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : relation_of2(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : relation_dom_as_subset(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : relation_of2_as_subset(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : quasi_total(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : apply(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : relation_composition(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : relation_of2(v2, v0, v1) = 0 & ? [v0] : ? [v1] : ? [v2] : relation_of2_as_subset(v2, v0, v1) = 0 & ? [v0] : ? [v1] : ? [v2] : cartesian_product2(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : element(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : (relation_of2(v2, v0, v1) = 0 & quasi_total(v2, v0, v1) = 0 & relation(v2) = 0 & function(v2) = 0) & ? [v0] : ? [v1] : ? [v2] : (relation_of2(v2, v0, v1) = 0 & relation(v2) = 0 & function(v2) = 0) & ? [v0] : ? [v1] : relation_empty_yielding(v0) = v1 & ? [v0] : ? [v1] : relation_dom(v0) = v1 & ? [v0] : ? [v1] : one_to_one(v0) = v1 & ? [v0] : ? [v1] : powerset(v0) = v1 & ? [v0] : ? [v1] : element(v1, v0) = 0 & ? [v0] : ? [v1] : relation(v0) = v1 & ? [v0] : ? [v1] : function(v0) = v1 & ? [v0] : ? [v1] : empty(v0) = v1
% 48.96/17.79 |
% 48.96/17.79 | Applying alpha-rule on (1) yields:
% 48.96/17.79 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (element(v0, v2) = v4) | ? [v5] : ( ~ (v5 = 0) & in(v0, v1) = v5))
% 48.96/17.79 | (3) ! [v0] : ( ~ (empty(v0) = 0) | ? [v1] : (relation_dom(v0) = v1 & relation(v1) = 0 & empty(v1) = 0))
% 48.96/17.79 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_composition(v3, v2) = v1) | ~ (relation_composition(v3, v2) = v0))
% 48.96/17.79 | (5) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v3 = 0 & ~ (v4 = 0) & element(v2, v1) = 0 & empty(v2) = v4) | (v2 = 0 & empty(v0) = 0)))
% 48.96/17.79 | (6) one_to_one(all_0_1_1) = 0
% 48.96/17.79 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = empty_set | ~ (quasi_total(v2, v0, v1) = v3) | ? [v4] : (( ~ (v4 = 0) & relation_of2_as_subset(v2, v0, v1) = v4) | (( ~ (v3 = 0) | (v4 = v0 & relation_dom_as_subset(v0, v1, v2) = v0)) & (v3 = 0 | ( ~ (v4 = v0) & relation_dom_as_subset(v0, v1, v2) = v4)))))
% 48.96/17.79 | (8) ! [v0] : ! [v1] : ( ~ (element(v0, v1) = 0) | ? [v2] : ((v2 = 0 & empty(v1) = 0) | (v2 = 0 & in(v0, v1) = 0)))
% 48.96/17.79 | (9) relation_empty_yielding(all_0_11_11) = 0
% 48.96/17.79 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom_as_subset(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & powerset(v0) = v4 & element(v3, v4) = 0) | ( ~ (v4 = 0) & relation_of2(v2, v0, v1) = v4)))
% 48.96/17.79 | (11) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v1, v0) = v2) | ? [v3] : ? [v4] : ((v4 = 0 & v3 = 0 & relation(v2) = 0 & empty(v2) = 0) | ( ~ (v3 = 0) & relation(v1) = v3) | ( ~ (v3 = 0) & empty(v0) = v3)))
% 48.96/17.79 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ? [v3] : ? [v4] : ((v4 = 0 & v3 = 0 & relation(v2) = 0 & function(v2) = 0) | ( ~ (v3 = 0) & relation(v1) = v3) | ( ~ (v3 = 0) & relation(v0) = v3) | ( ~ (v3 = 0) & function(v1) = v3) | ( ~ (v3 = 0) & function(v0) = v3)))
% 48.96/17.79 | (13) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0))
% 48.96/17.79 | (14) ? [v0] : ? [v1] : ? [v2] : ? [v3] : relation_dom_as_subset(v2, v1, v0) = v3
% 48.96/17.79 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom(v1) = v2) | ~ (in(v0, v2) = v3) | ? [v4] : (( ~ (v4 = 0) & relation(v1) = v4) | ( ~ (v4 = 0) & function(v1) = v4) | (apply(v1, v0) = v4 & ! [v5] : ! [v6] : ( ~ (v3 = 0) | ~ (apply(v5, v4) = v6) | ? [v7] : ? [v8] : ((v8 = v6 & apply(v7, v0) = v6 & relation_composition(v1, v5) = v7) | ( ~ (v7 = 0) & relation(v5) = v7) | ( ~ (v7 = 0) & function(v5) = v7))) & ! [v5] : ! [v6] : ( ~ (v3 = 0) | ~ (relation_composition(v1, v5) = v6) | ? [v7] : ? [v8] : ((v8 = v7 & apply(v6, v0) = v7 & apply(v5, v4) = v7) | ( ~ (v7 = 0) & relation(v5) = v7) | ( ~ (v7 = 0) & function(v5) = v7))) & ! [v5] : ( ~ (v3 = 0) | ~ (relation(v5) = 0) | ? [v6] : ? [v7] : ? [v8] : ((v8 = v7 & apply(v6, v0) = v7 & apply(v5, v4) = v7 & relation_composition(v1, v5) = v6) | ( ~ (v6 = 0) & function(v5) = v6))) & ! [v5] : ( ~ (v3 = 0) | ~ (function(v5) = 0) | ? [v6] : ? [v7] : ? [v8] : ((v8 = v7 & apply(v6, v0) = v7 & apply(v5, v4) = v7 & relation_composition(v1, v5) = v6) | ( ~ (v6 = 0) & relation(v5) = v6))))))
% 48.96/17.79 | (16) relation(all_0_15_15) = 0
% 48.96/17.79 | (17) ? [v0] : ? [v1] : relation(v0) = v1
% 48.96/17.79 | (18) relation_empty_yielding(all_0_10_10) = 0
% 48.96/17.79 | (19) ~ (all_0_19_19 = empty_set)
% 48.96/17.79 | (20) ! [v0] : ! [v1] : (v1 = 0 | v0 = empty_set | ~ (quasi_total(empty_set, v0, empty_set) = v1) | ? [v2] : ( ~ (v2 = 0) & relation_of2_as_subset(empty_set, v0, empty_set) = v2))
% 48.96/17.79 | (21) function(all_0_9_9) = 0
% 48.96/17.79 | (22) relation(all_0_2_2) = 0
% 48.96/17.79 | (23) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3))
% 48.96/17.79 | (24) relation(all_0_10_10) = 0
% 48.96/17.79 | (25) ~ (all_0_5_5 = 0)
% 48.96/17.79 | (26) in(all_0_18_18, all_0_20_20) = 0
% 48.96/17.79 | (27) ? [v0] : ? [v1] : ? [v2] : (relation_of2(v2, v0, v1) = 0 & relation(v2) = 0 & function(v2) = 0)
% 48.96/17.80 | (28) ? [v0] : ? [v1] : ? [v2] : cartesian_product2(v1, v0) = v2
% 48.96/17.80 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 48.96/17.80 | (30) ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2
% 48.96/17.80 | (31) empty(all_0_2_2) = 0
% 48.96/17.80 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4))
% 48.96/17.80 | (33) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ((v1 = 0 & empty(v0) = 0) | ( ~ (v2 = 0) & relation_dom(v0) = v1 & empty(v1) = v2)))
% 48.96/17.80 | (34) function(all_0_4_4) = 0
% 48.96/17.80 | (35) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_of2_as_subset(v2, v0, v1) = 0) | ? [v3] : ? [v4] : (( ~ (v1 = empty_set) | v0 = empty_set | (( ~ (v2 = empty_set) | (v3 = 0 & quasi_total(empty_set, v0, empty_set) = 0)) & (v2 = empty_set | ( ~ (v3 = 0) & quasi_total(v2, v0, empty_set) = v3)))) & ((v1 = empty_set & ~ (v0 = empty_set)) | (((v4 = v0 & relation_dom_as_subset(v0, v1, v2) = v0) | ( ~ (v3 = 0) & quasi_total(v2, v0, v1) = v3)) & ((v3 = 0 & quasi_total(v2, v0, v1) = 0) | ( ~ (v4 = v0) & relation_dom_as_subset(v0, v1, v2) = v4))))))
% 48.96/17.80 | (36) ? [v0] : ? [v1] : relation_empty_yielding(v0) = v1
% 48.96/17.80 | (37) ! [v0] : ! [v1] : ! [v2] : ( ~ (cartesian_product2(v0, v1) = v2) | ? [v3] : ((v3 = 0 & empty(v1) = 0) | (v3 = 0 & empty(v0) = 0) | ( ~ (v3 = 0) & empty(v2) = v3)))
% 48.96/17.80 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0))
% 48.96/17.80 | (39) function(all_0_15_15) = 0
% 48.96/17.80 | (40) relation(all_0_4_4) = 0
% 48.96/17.80 | (41) ! [v0] : ( ~ (empty(v0) = 0) | relation(v0) = 0)
% 48.96/17.80 | (42) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_of2_as_subset(v2, v0, v1) = 0) | relation_of2(v2, v0, v1) = 0)
% 48.96/17.80 | (43) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_of2(v2, v0, v1) = 0) | relation_of2_as_subset(v2, v0, v1) = 0)
% 48.96/17.80 | (44) empty(all_0_8_8) = all_0_7_7
% 48.96/17.80 | (45) function(all_0_17_17) = 0
% 48.96/17.80 | (46) ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2
% 48.96/17.80 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (relation_of2_as_subset(v2, v0, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & relation_of2(v2, v0, v1) = v4))
% 48.96/17.80 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (relation_of2(v2, v0, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & relation_of2_as_subset(v2, v0, v1) = v4))
% 48.96/17.80 | (49) ? [v0] : ? [v1] : element(v1, v0) = 0
% 48.96/17.80 | (50) relation(all_0_1_1) = 0
% 48.96/17.80 | (51) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ? [v3] : ((v3 = 0 & relation(v2) = 0) | ( ~ (v3 = 0) & relation(v1) = v3) | ( ~ (v3 = 0) & relation(v0) = v3)))
% 48.96/17.80 | (52) relation_composition(all_0_17_17, all_0_15_15) = all_0_14_14
% 48.96/17.80 | (53) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1))
% 48.96/17.80 | (54) ! [v0] : ! [v1] : (v1 = 0 | ~ (function(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2))
% 48.96/17.80 | (55) one_to_one(all_0_9_9) = 0
% 48.96/17.80 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (relation_dom_as_subset(v4, v3, v2) = v1) | ~ (relation_dom_as_subset(v4, v3, v2) = v0))
% 48.96/17.80 | (57) relation(all_0_0_0) = 0
% 48.96/17.80 | (58) ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2))
% 48.96/17.80 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v0, v1) = v3) | ~ (powerset(v3) = v4) | ~ (element(v2, v4) = 0) | relation(v2) = 0)
% 48.96/17.80 | (60) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0))
% 48.96/17.80 | (61) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ((v2 = 0 & v1 = 0 & one_to_one(v0) = 0 & function(v0) = 0) | ( ~ (v1 = 0) & function(v0) = v1) | ( ~ (v1 = 0) & empty(v0) = v1)))
% 48.96/17.80 | (62) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0))
% 48.96/17.80 | (63) quasi_total(all_0_17_17, all_0_20_20, all_0_19_19) = 0
% 48.96/17.80 | (64) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_of2(v2, v0, v1) = 0) | ? [v3] : (relation_dom(v2) = v3 & relation_dom_as_subset(v0, v1, v2) = v3))
% 48.96/17.80 | (65) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 48.96/17.80 | (66) ! [v0] : ( ~ (function(v0) = 0) | ? [v1] : ? [v2] : ((v2 = 0 & v1 = 0 & one_to_one(v0) = 0 & relation(v0) = 0) | ( ~ (v1 = 0) & relation(v0) = v1) | ( ~ (v1 = 0) & empty(v0) = v1)))
% 48.96/17.80 | (67) ! [v0] : ! [v1] : ! [v2] : ( ~ (quasi_total(v1, empty_set, v0) = v2) | ? [v3] : (( ~ (v3 = 0) & relation_of2_as_subset(v1, empty_set, v0) = v3) | (( ~ (v2 = 0) | (v3 = empty_set & relation_dom_as_subset(empty_set, v0, v1) = empty_set)) & (v2 = 0 | ( ~ (v3 = empty_set) & relation_dom_as_subset(empty_set, v0, v1) = v3)))))
% 48.96/17.81 | (68) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 48.96/17.81 | (69) ~ (all_0_12_12 = all_0_13_13)
% 48.96/17.81 | (70) ! [v0] : ( ~ (empty(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & one_to_one(v0) = 0 & relation(v0) = 0 & function(v0) = 0) | ( ~ (v1 = 0) & relation(v0) = v1) | ( ~ (v1 = 0) & function(v0) = v1)))
% 48.96/17.81 | (71) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 48.96/17.81 | (72) ? [v0] : ? [v1] : ? [v2] : relation_of2_as_subset(v2, v0, v1) = 0
% 48.96/17.81 | (73) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | element(v0, v1) = 0)
% 48.96/17.81 | (74) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 48.96/17.81 | (75) ? [v0] : ? [v1] : ? [v2] : ? [v3] : relation_of2_as_subset(v2, v1, v0) = v3
% 48.96/17.81 | (76) ! [v0] : ! [v1] : ! [v2] : ( ~ (apply(v1, v0) = v2) | ? [v3] : ? [v4] : (( ~ (v3 = 0) & relation(v1) = v3) | ( ~ (v3 = 0) & function(v1) = v3) | (relation_dom(v1) = v3 & in(v0, v3) = v4 & ! [v5] : ! [v6] : ( ~ (v4 = 0) | ~ (apply(v5, v2) = v6) | ? [v7] : ? [v8] : ((v8 = v6 & apply(v7, v0) = v6 & relation_composition(v1, v5) = v7) | ( ~ (v7 = 0) & relation(v5) = v7) | ( ~ (v7 = 0) & function(v5) = v7))) & ! [v5] : ! [v6] : ( ~ (v4 = 0) | ~ (relation_composition(v1, v5) = v6) | ? [v7] : ? [v8] : ((v8 = v7 & apply(v6, v0) = v7 & apply(v5, v2) = v7) | ( ~ (v7 = 0) & relation(v5) = v7) | ( ~ (v7 = 0) & function(v5) = v7))) & ! [v5] : ( ~ (v4 = 0) | ~ (relation(v5) = 0) | ? [v6] : ? [v7] : ? [v8] : ((v8 = v7 & apply(v6, v0) = v7 & apply(v5, v2) = v7 & relation_composition(v1, v5) = v6) | ( ~ (v6 = 0) & function(v5) = v6))) & ! [v5] : ( ~ (v4 = 0) | ~ (function(v5) = 0) | ? [v6] : ? [v7] : ? [v8] : ((v8 = v7 & apply(v6, v0) = v7 & apply(v5, v2) = v7 & relation_composition(v1, v5) = v6) | ( ~ (v6 = 0) & relation(v5) = v6))))))
% 48.96/17.81 | (77) empty(empty_set) = 0
% 48.96/17.81 | (78) relation(all_0_11_11) = 0
% 48.96/17.81 | (79) apply(all_0_17_17, all_0_18_18) = all_0_16_16
% 48.96/17.81 | (80) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (powerset(v1) = v2 & element(v0, v2) = 0))
% 48.96/17.81 | (81) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom_as_subset(v0, v1, v2) = v3) | ? [v4] : ((v4 = v3 & relation_dom(v2) = v3) | ( ~ (v4 = 0) & relation_of2(v2, v0, v1) = v4)))
% 48.96/17.81 | (82) ! [v0] : ! [v1] : (v1 = empty_set | v0 = empty_set | ~ (quasi_total(v1, v0, empty_set) = 0) | ? [v2] : ( ~ (v2 = 0) & relation_of2_as_subset(v1, v0, empty_set) = v2))
% 48.96/17.81 | (83) ? [v0] : ? [v1] : one_to_one(v0) = v1
% 48.96/17.81 | (84) ? [v0] : ? [v1] : empty(v0) = v1
% 48.96/17.81 | (85) ! [v0] : ! [v1] : ! [v2] : ( ~ (empty(v2) = 0) | ~ (in(v0, v1) = 0) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v2) = v3 & element(v1, v3) = v4))
% 48.96/17.81 | (86) ! [v0] : ( ~ (empty(v0) = 0) | function(v0) = 0)
% 48.96/17.81 | (87) ? [v0] : ? [v1] : powerset(v0) = v1
% 48.96/17.81 | (88) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (quasi_total(v4, v3, v2) = v1) | ~ (quasi_total(v4, v3, v2) = v0))
% 48.96/17.81 | (89) ? [v0] : ? [v1] : ? [v2] : element(v1, v0) = v2
% 48.96/17.81 | (90) apply(all_0_15_15, all_0_16_16) = all_0_12_12
% 48.96/17.81 | (91) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | element(v0, v2) = 0)
% 48.96/17.81 | (92) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0))
% 48.96/17.81 | (93) ? [v0] : ? [v1] : relation_dom(v0) = v1
% 48.96/17.81 | (94) ? [v0] : ? [v1] : ? [v2] : relation_of2(v2, v0, v1) = 0
% 48.96/17.81 | (95) ? [v0] : ? [v1] : function(v0) = v1
% 48.96/17.81 | (96) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_of2(v2, v0, v1) = 0) | ? [v3] : ? [v4] : (relation_dom_as_subset(v0, v1, v2) = v3 & powerset(v0) = v4 & element(v3, v4) = 0))
% 48.96/17.81 | (97) ! [v0] : ! [v1] : (v1 = 0 | ~ (relation(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2))
% 48.96/17.81 | (98) ~ (all_0_7_7 = 0)
% 48.96/17.81 | (99) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0))
% 48.96/17.81 | (100) relation(all_0_6_6) = 0
% 48.96/17.81 | (101) empty(all_0_4_4) = 0
% 48.96/17.81 | (102) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) = 0 & empty(v2) = 0))
% 48.96/17.81 | (103) relation(all_0_9_9) = 0
% 48.96/17.81 | (104) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 48.96/17.82 | (105) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0))
% 48.96/17.82 | (106) apply(all_0_14_14, all_0_18_18) = all_0_13_13
% 48.96/17.82 | (107) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (relation_of2(v4, v3, v2) = v1) | ~ (relation_of2(v4, v3, v2) = v0))
% 48.96/17.82 | (108) relation(empty_set) = 0
% 48.96/17.82 | (109) empty(all_0_3_3) = 0
% 48.96/17.82 | (110) ? [v0] : ? [v1] : ? [v2] : apply(v1, v0) = v2
% 48.96/17.82 | (111) function(all_0_11_11) = 0
% 48.96/17.82 | (112) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (element(v0, v2) = v3) | ~ (in(v0, v1) = 0) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & powerset(v2) = v4 & element(v1, v4) = v5))
% 48.96/17.82 | (113) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (relation_of2_as_subset(v4, v3, v2) = v1) | ~ (relation_of2_as_subset(v4, v3, v2) = v0))
% 48.96/17.82 | (114) function(all_0_0_0) = 0
% 48.96/17.82 | (115) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | subset(v0, v1) = 0)
% 48.96/17.82 | (116) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ? [v3] : ? [v4] : ((v4 = 0 & v3 = 0 & relation(v2) = 0 & empty(v2) = 0) | ( ~ (v3 = 0) & relation(v1) = v3) | ( ~ (v3 = 0) & empty(v0) = v3)))
% 48.96/17.82 | (117) function(all_0_1_1) = 0
% 48.96/17.82 | (118) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v1) = v3 & element(v0, v3) = v4))
% 48.96/17.82 | (119) ? [v0] : ? [v1] : ? [v2] : (relation_of2(v2, v0, v1) = 0 & quasi_total(v2, v0, v1) = 0 & relation(v2) = 0 & function(v2) = 0)
% 48.96/17.82 | (120) empty(all_0_6_6) = all_0_5_5
% 48.96/17.82 | (121) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_of2_as_subset(v2, v0, v1) = 0) | ? [v3] : ? [v4] : (cartesian_product2(v0, v1) = v3 & powerset(v3) = v4 & element(v2, v4) = 0))
% 48.96/17.82 | (122) ! [v0] : ! [v1] : (v1 = 0 | ~ (empty(v0) = v1) | ? [v2] : ? [v3] : (( ~ (v3 = 0) & relation_dom(v0) = v2 & empty(v2) = v3) | ( ~ (v2 = 0) & relation(v0) = v2)))
% 48.96/17.82 | (123) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0))
% 48.96/17.82 | (124) empty(all_0_1_1) = 0
% 48.96/17.82 | (125) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom_as_subset(v0, v1, v2) = v3) | ? [v4] : (( ~ (v4 = 0) & relation_of2_as_subset(v2, v0, v1) = v4) | (( ~ (v1 = empty_set) | v0 = empty_set | (( ~ (v2 = empty_set) | (v4 = 0 & quasi_total(empty_set, v0, empty_set) = 0)) & (v2 = empty_set | ( ~ (v4 = 0) & quasi_total(v2, v0, empty_set) = v4)))) & ((v1 = empty_set & ~ (v0 = empty_set)) | (( ~ (v3 = v0) | (v4 = 0 & quasi_total(v2, v0, v1) = 0)) & (v3 = v0 | ( ~ (v4 = 0) & quasi_total(v2, v0, v1) = v4)))))))
% 48.96/17.82 | (126) relation_of2_as_subset(all_0_17_17, all_0_20_20, all_0_19_19) = 0
% 48.96/17.82 | (127) relation_empty_yielding(empty_set) = 0
% 48.96/17.82 | (128) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_empty_yielding(v2) = v1) | ~ (relation_empty_yielding(v2) = v0))
% 48.96/17.82 | (129) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (cartesian_product2(v0, v1) = v3) | ~ (powerset(v3) = v4) | ~ (element(v2, v4) = v5) | ? [v6] : ( ~ (v6 = 0) & relation_of2_as_subset(v2, v0, v1) = v6))
% 48.96/17.82 | (130) ! [v0] : ! [v1] : (v1 = 0 | ~ (empty(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v0) = v2 & element(v3, v2) = 0 & empty(v3) = v4))
% 48.96/17.82 | (131) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & relation(v1) = 0 & empty(v1) = 0) | ( ~ (v2 = 0) & empty(v0) = v2)))
% 48.96/17.82 | (132) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ((v2 = 0 & empty(v0) = 0) | ( ~ (v2 = 0) & relation(v0) = v2) | ( ~ (v2 = 0) & empty(v1) = v2)))
% 48.96/17.82 | (133) ? [v0] : ? [v1] : ? [v2] : ? [v3] : quasi_total(v2, v1, v0) = v3
% 48.96/17.82 | (134) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0))
% 48.96/17.82 | (135) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v0, v1) = v2) | ? [v3] : ((v3 = 0 & empty(v1) = 0) | ( ~ (v3 = 0) & element(v0, v1) = v3)))
% 48.96/17.82 | (136) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 48.96/17.82 | (137) ? [v0] : ? [v1] : ? [v2] : relation_composition(v1, v0) = v2
% 48.96/17.82 | (138) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0))
% 48.96/17.82 | (139) ? [v0] : ? [v1] : ? [v2] : ? [v3] : relation_of2(v2, v1, v0) = v3
% 48.96/17.82 | (140) ! [v0] : ! [v1] : ( ~ (one_to_one(v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & relation(v0) = 0 & function(v0) = 0) | ( ~ (v2 = 0) & relation(v0) = v2) | ( ~ (v2 = 0) & function(v0) = v2) | ( ~ (v2 = 0) & empty(v0) = v2)))
% 48.96/17.82 |
% 48.96/17.83 | Instantiating formula (76) with all_0_12_12, all_0_15_15, all_0_16_16 and discharging atoms apply(all_0_15_15, all_0_16_16) = all_0_12_12, yields:
% 48.96/17.83 | (141) ? [v0] : ? [v1] : (( ~ (v0 = 0) & relation(all_0_15_15) = v0) | ( ~ (v0 = 0) & function(all_0_15_15) = v0) | (relation_dom(all_0_15_15) = v0 & in(all_0_16_16, v0) = v1 & ! [v2] : ! [v3] : ( ~ (v1 = 0) | ~ (apply(v2, all_0_12_12) = v3) | ? [v4] : ? [v5] : ((v5 = v3 & apply(v4, all_0_16_16) = v3 & relation_composition(all_0_15_15, v2) = v4) | ( ~ (v4 = 0) & relation(v2) = v4) | ( ~ (v4 = 0) & function(v2) = v4))) & ! [v2] : ! [v3] : ( ~ (v1 = 0) | ~ (relation_composition(all_0_15_15, v2) = v3) | ? [v4] : ? [v5] : ((v5 = v4 & apply(v3, all_0_16_16) = v4 & apply(v2, all_0_12_12) = v4) | ( ~ (v4 = 0) & relation(v2) = v4) | ( ~ (v4 = 0) & function(v2) = v4))) & ! [v2] : ( ~ (v1 = 0) | ~ (relation(v2) = 0) | ? [v3] : ? [v4] : ? [v5] : ((v5 = v4 & apply(v3, all_0_16_16) = v4 & apply(v2, all_0_12_12) = v4 & relation_composition(all_0_15_15, v2) = v3) | ( ~ (v3 = 0) & function(v2) = v3))) & ! [v2] : ( ~ (v1 = 0) | ~ (function(v2) = 0) | ? [v3] : ? [v4] : ? [v5] : ((v5 = v4 & apply(v3, all_0_16_16) = v4 & apply(v2, all_0_12_12) = v4 & relation_composition(all_0_15_15, v2) = v3) | ( ~ (v3 = 0) & relation(v2) = v3)))))
% 48.96/17.83 |
% 48.96/17.83 | Instantiating formula (76) with all_0_16_16, all_0_17_17, all_0_18_18 and discharging atoms apply(all_0_17_17, all_0_18_18) = all_0_16_16, yields:
% 48.96/17.83 | (142) ? [v0] : ? [v1] : (( ~ (v0 = 0) & relation(all_0_17_17) = v0) | ( ~ (v0 = 0) & function(all_0_17_17) = v0) | (relation_dom(all_0_17_17) = v0 & in(all_0_18_18, v0) = v1 & ! [v2] : ! [v3] : ( ~ (v1 = 0) | ~ (apply(v2, all_0_16_16) = v3) | ? [v4] : ? [v5] : ((v5 = v3 & apply(v4, all_0_18_18) = v3 & relation_composition(all_0_17_17, v2) = v4) | ( ~ (v4 = 0) & relation(v2) = v4) | ( ~ (v4 = 0) & function(v2) = v4))) & ! [v2] : ! [v3] : ( ~ (v1 = 0) | ~ (relation_composition(all_0_17_17, v2) = v3) | ? [v4] : ? [v5] : ((v5 = v4 & apply(v3, all_0_18_18) = v4 & apply(v2, all_0_16_16) = v4) | ( ~ (v4 = 0) & relation(v2) = v4) | ( ~ (v4 = 0) & function(v2) = v4))) & ! [v2] : ( ~ (v1 = 0) | ~ (relation(v2) = 0) | ? [v3] : ? [v4] : ? [v5] : ((v5 = v4 & apply(v3, all_0_18_18) = v4 & apply(v2, all_0_16_16) = v4 & relation_composition(all_0_17_17, v2) = v3) | ( ~ (v3 = 0) & function(v2) = v3))) & ! [v2] : ( ~ (v1 = 0) | ~ (function(v2) = 0) | ? [v3] : ? [v4] : ? [v5] : ((v5 = v4 & apply(v3, all_0_18_18) = v4 & apply(v2, all_0_16_16) = v4 & relation_composition(all_0_17_17, v2) = v3) | ( ~ (v3 = 0) & relation(v2) = v3)))))
% 48.96/17.83 |
% 48.96/17.83 | Instantiating formula (42) with all_0_17_17, all_0_19_19, all_0_20_20 and discharging atoms relation_of2_as_subset(all_0_17_17, all_0_20_20, all_0_19_19) = 0, yields:
% 48.96/17.83 | (143) relation_of2(all_0_17_17, all_0_20_20, all_0_19_19) = 0
% 48.96/17.83 |
% 48.96/17.83 | Instantiating formula (121) with all_0_17_17, all_0_19_19, all_0_20_20 and discharging atoms relation_of2_as_subset(all_0_17_17, all_0_20_20, all_0_19_19) = 0, yields:
% 48.96/17.83 | (144) ? [v0] : ? [v1] : (cartesian_product2(all_0_20_20, all_0_19_19) = v0 & powerset(v0) = v1 & element(all_0_17_17, v1) = 0)
% 48.96/17.83 |
% 48.96/17.83 | Instantiating formula (35) with all_0_17_17, all_0_19_19, all_0_20_20 and discharging atoms relation_of2_as_subset(all_0_17_17, all_0_20_20, all_0_19_19) = 0, yields:
% 48.96/17.83 | (145) ? [v0] : ? [v1] : (( ~ (all_0_19_19 = empty_set) | all_0_20_20 = empty_set | (( ~ (all_0_17_17 = empty_set) | (v0 = 0 & quasi_total(empty_set, all_0_20_20, empty_set) = 0)) & (all_0_17_17 = empty_set | ( ~ (v0 = 0) & quasi_total(all_0_17_17, all_0_20_20, empty_set) = v0)))) & ((all_0_19_19 = empty_set & ~ (all_0_20_20 = empty_set)) | (((v1 = all_0_20_20 & relation_dom_as_subset(all_0_20_20, all_0_19_19, all_0_17_17) = all_0_20_20) | ( ~ (v0 = 0) & quasi_total(all_0_17_17, all_0_20_20, all_0_19_19) = v0)) & ((v0 = 0 & quasi_total(all_0_17_17, all_0_20_20, all_0_19_19) = 0) | ( ~ (v1 = all_0_20_20) & relation_dom_as_subset(all_0_20_20, all_0_19_19, all_0_17_17) = v1)))))
% 48.96/17.83 |
% 48.96/17.83 | Instantiating formula (7) with 0, all_0_17_17, all_0_19_19, all_0_20_20 and discharging atoms quasi_total(all_0_17_17, all_0_20_20, all_0_19_19) = 0, yields:
% 48.96/17.83 | (146) all_0_19_19 = empty_set | ? [v0] : ((v0 = all_0_20_20 & relation_dom_as_subset(all_0_20_20, all_0_19_19, all_0_17_17) = all_0_20_20) | ( ~ (v0 = 0) & relation_of2_as_subset(all_0_17_17, all_0_20_20, all_0_19_19) = v0))
% 48.96/17.83 |
% 48.96/17.83 | Instantiating (142) with all_63_0_91, all_63_1_92 yields:
% 48.96/17.83 | (147) ( ~ (all_63_1_92 = 0) & relation(all_0_17_17) = all_63_1_92) | ( ~ (all_63_1_92 = 0) & function(all_0_17_17) = all_63_1_92) | (relation_dom(all_0_17_17) = all_63_1_92 & in(all_0_18_18, all_63_1_92) = all_63_0_91 & ! [v0] : ! [v1] : ( ~ (all_63_0_91 = 0) | ~ (apply(v0, all_0_16_16) = v1) | ? [v2] : ? [v3] : ((v3 = v1 & apply(v2, all_0_18_18) = v1 & relation_composition(all_0_17_17, v0) = v2) | ( ~ (v2 = 0) & relation(v0) = v2) | ( ~ (v2 = 0) & function(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (all_63_0_91 = 0) | ~ (relation_composition(all_0_17_17, v0) = v1) | ? [v2] : ? [v3] : ((v3 = v2 & apply(v1, all_0_18_18) = v2 & apply(v0, all_0_16_16) = v2) | ( ~ (v2 = 0) & relation(v0) = v2) | ( ~ (v2 = 0) & function(v0) = v2))) & ! [v0] : ( ~ (all_63_0_91 = 0) | ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ((v3 = v2 & apply(v1, all_0_18_18) = v2 & apply(v0, all_0_16_16) = v2 & relation_composition(all_0_17_17, v0) = v1) | ( ~ (v1 = 0) & function(v0) = v1))) & ! [v0] : ( ~ (all_63_0_91 = 0) | ~ (function(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ((v3 = v2 & apply(v1, all_0_18_18) = v2 & apply(v0, all_0_16_16) = v2 & relation_composition(all_0_17_17, v0) = v1) | ( ~ (v1 = 0) & relation(v0) = v1))))
% 48.96/17.83 |
% 48.96/17.83 | Instantiating (145) with all_71_0_102, all_71_1_103 yields:
% 48.96/17.83 | (148) ( ~ (all_0_19_19 = empty_set) | all_0_20_20 = empty_set | (( ~ (all_0_17_17 = empty_set) | (all_71_1_103 = 0 & quasi_total(empty_set, all_0_20_20, empty_set) = 0)) & (all_0_17_17 = empty_set | ( ~ (all_71_1_103 = 0) & quasi_total(all_0_17_17, all_0_20_20, empty_set) = all_71_1_103)))) & ((all_0_19_19 = empty_set & ~ (all_0_20_20 = empty_set)) | (((all_71_0_102 = all_0_20_20 & relation_dom_as_subset(all_0_20_20, all_0_19_19, all_0_17_17) = all_0_20_20) | ( ~ (all_71_1_103 = 0) & quasi_total(all_0_17_17, all_0_20_20, all_0_19_19) = all_71_1_103)) & ((all_71_1_103 = 0 & quasi_total(all_0_17_17, all_0_20_20, all_0_19_19) = 0) | ( ~ (all_71_0_102 = all_0_20_20) & relation_dom_as_subset(all_0_20_20, all_0_19_19, all_0_17_17) = all_71_0_102))))
% 48.96/17.83 |
% 48.96/17.83 | Applying alpha-rule on (148) yields:
% 48.96/17.83 | (149) ~ (all_0_19_19 = empty_set) | all_0_20_20 = empty_set | (( ~ (all_0_17_17 = empty_set) | (all_71_1_103 = 0 & quasi_total(empty_set, all_0_20_20, empty_set) = 0)) & (all_0_17_17 = empty_set | ( ~ (all_71_1_103 = 0) & quasi_total(all_0_17_17, all_0_20_20, empty_set) = all_71_1_103)))
% 48.96/17.83 | (150) (all_0_19_19 = empty_set & ~ (all_0_20_20 = empty_set)) | (((all_71_0_102 = all_0_20_20 & relation_dom_as_subset(all_0_20_20, all_0_19_19, all_0_17_17) = all_0_20_20) | ( ~ (all_71_1_103 = 0) & quasi_total(all_0_17_17, all_0_20_20, all_0_19_19) = all_71_1_103)) & ((all_71_1_103 = 0 & quasi_total(all_0_17_17, all_0_20_20, all_0_19_19) = 0) | ( ~ (all_71_0_102 = all_0_20_20) & relation_dom_as_subset(all_0_20_20, all_0_19_19, all_0_17_17) = all_71_0_102)))
% 48.96/17.83 |
% 48.96/17.83 | Instantiating (144) with all_76_0_107, all_76_1_108 yields:
% 48.96/17.83 | (151) cartesian_product2(all_0_20_20, all_0_19_19) = all_76_1_108 & powerset(all_76_1_108) = all_76_0_107 & element(all_0_17_17, all_76_0_107) = 0
% 48.96/17.83 |
% 48.96/17.83 | Applying alpha-rule on (151) yields:
% 48.96/17.83 | (152) cartesian_product2(all_0_20_20, all_0_19_19) = all_76_1_108
% 48.96/17.84 | (153) powerset(all_76_1_108) = all_76_0_107
% 48.96/17.84 | (154) element(all_0_17_17, all_76_0_107) = 0
% 48.96/17.84 |
% 48.96/17.84 | Instantiating (141) with all_80_0_113, all_80_1_114 yields:
% 48.96/17.84 | (155) ( ~ (all_80_1_114 = 0) & relation(all_0_15_15) = all_80_1_114) | ( ~ (all_80_1_114 = 0) & function(all_0_15_15) = all_80_1_114) | (relation_dom(all_0_15_15) = all_80_1_114 & in(all_0_16_16, all_80_1_114) = all_80_0_113 & ! [v0] : ! [v1] : ( ~ (all_80_0_113 = 0) | ~ (apply(v0, all_0_12_12) = v1) | ? [v2] : ? [v3] : ((v3 = v1 & apply(v2, all_0_16_16) = v1 & relation_composition(all_0_15_15, v0) = v2) | ( ~ (v2 = 0) & relation(v0) = v2) | ( ~ (v2 = 0) & function(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (all_80_0_113 = 0) | ~ (relation_composition(all_0_15_15, v0) = v1) | ? [v2] : ? [v3] : ((v3 = v2 & apply(v1, all_0_16_16) = v2 & apply(v0, all_0_12_12) = v2) | ( ~ (v2 = 0) & relation(v0) = v2) | ( ~ (v2 = 0) & function(v0) = v2))) & ! [v0] : ( ~ (all_80_0_113 = 0) | ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ((v3 = v2 & apply(v1, all_0_16_16) = v2 & apply(v0, all_0_12_12) = v2 & relation_composition(all_0_15_15, v0) = v1) | ( ~ (v1 = 0) & function(v0) = v1))) & ! [v0] : ( ~ (all_80_0_113 = 0) | ~ (function(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ((v3 = v2 & apply(v1, all_0_16_16) = v2 & apply(v0, all_0_12_12) = v2 & relation_composition(all_0_15_15, v0) = v1) | ( ~ (v1 = 0) & relation(v0) = v1))))
% 48.96/17.84 |
% 48.96/17.84 +-Applying beta-rule and splitting (155), into two cases.
% 48.96/17.84 |-Branch one:
% 48.96/17.84 | (156) ( ~ (all_80_1_114 = 0) & relation(all_0_15_15) = all_80_1_114) | ( ~ (all_80_1_114 = 0) & function(all_0_15_15) = all_80_1_114)
% 48.96/17.84 |
% 48.96/17.84 +-Applying beta-rule and splitting (156), into two cases.
% 48.96/17.84 |-Branch one:
% 48.96/17.84 | (157) ~ (all_80_1_114 = 0) & relation(all_0_15_15) = all_80_1_114
% 48.96/17.84 |
% 48.96/17.84 | Applying alpha-rule on (157) yields:
% 48.96/17.84 | (158) ~ (all_80_1_114 = 0)
% 48.96/17.84 | (159) relation(all_0_15_15) = all_80_1_114
% 48.96/17.84 |
% 48.96/17.84 | Instantiating formula (60) with all_0_15_15, all_80_1_114, 0 and discharging atoms relation(all_0_15_15) = all_80_1_114, relation(all_0_15_15) = 0, yields:
% 48.96/17.84 | (160) all_80_1_114 = 0
% 48.96/17.84 |
% 48.96/17.84 | Equations (160) can reduce 158 to:
% 48.96/17.84 | (161) $false
% 48.96/17.84 |
% 48.96/17.84 |-The branch is then unsatisfiable
% 48.96/17.84 |-Branch two:
% 48.96/17.84 | (162) ~ (all_80_1_114 = 0) & function(all_0_15_15) = all_80_1_114
% 48.96/17.84 |
% 48.96/17.84 | Applying alpha-rule on (162) yields:
% 48.96/17.84 | (158) ~ (all_80_1_114 = 0)
% 48.96/17.84 | (164) function(all_0_15_15) = all_80_1_114
% 48.96/17.84 |
% 48.96/17.84 | Instantiating formula (13) with all_0_15_15, all_80_1_114, 0 and discharging atoms function(all_0_15_15) = all_80_1_114, function(all_0_15_15) = 0, yields:
% 48.96/17.84 | (160) all_80_1_114 = 0
% 48.96/17.84 |
% 48.96/17.84 | Equations (160) can reduce 158 to:
% 48.96/17.84 | (161) $false
% 48.96/17.84 |
% 48.96/17.84 |-The branch is then unsatisfiable
% 48.96/17.84 |-Branch two:
% 48.96/17.84 | (167) relation_dom(all_0_15_15) = all_80_1_114 & in(all_0_16_16, all_80_1_114) = all_80_0_113 & ! [v0] : ! [v1] : ( ~ (all_80_0_113 = 0) | ~ (apply(v0, all_0_12_12) = v1) | ? [v2] : ? [v3] : ((v3 = v1 & apply(v2, all_0_16_16) = v1 & relation_composition(all_0_15_15, v0) = v2) | ( ~ (v2 = 0) & relation(v0) = v2) | ( ~ (v2 = 0) & function(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (all_80_0_113 = 0) | ~ (relation_composition(all_0_15_15, v0) = v1) | ? [v2] : ? [v3] : ((v3 = v2 & apply(v1, all_0_16_16) = v2 & apply(v0, all_0_12_12) = v2) | ( ~ (v2 = 0) & relation(v0) = v2) | ( ~ (v2 = 0) & function(v0) = v2))) & ! [v0] : ( ~ (all_80_0_113 = 0) | ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ((v3 = v2 & apply(v1, all_0_16_16) = v2 & apply(v0, all_0_12_12) = v2 & relation_composition(all_0_15_15, v0) = v1) | ( ~ (v1 = 0) & function(v0) = v1))) & ! [v0] : ( ~ (all_80_0_113 = 0) | ~ (function(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ((v3 = v2 & apply(v1, all_0_16_16) = v2 & apply(v0, all_0_12_12) = v2 & relation_composition(all_0_15_15, v0) = v1) | ( ~ (v1 = 0) & relation(v0) = v1)))
% 48.96/17.84 |
% 48.96/17.84 | Applying alpha-rule on (167) yields:
% 48.96/17.84 | (168) ! [v0] : ! [v1] : ( ~ (all_80_0_113 = 0) | ~ (relation_composition(all_0_15_15, v0) = v1) | ? [v2] : ? [v3] : ((v3 = v2 & apply(v1, all_0_16_16) = v2 & apply(v0, all_0_12_12) = v2) | ( ~ (v2 = 0) & relation(v0) = v2) | ( ~ (v2 = 0) & function(v0) = v2)))
% 48.96/17.84 | (169) relation_dom(all_0_15_15) = all_80_1_114
% 48.96/17.84 | (170) in(all_0_16_16, all_80_1_114) = all_80_0_113
% 48.96/17.84 | (171) ! [v0] : ! [v1] : ( ~ (all_80_0_113 = 0) | ~ (apply(v0, all_0_12_12) = v1) | ? [v2] : ? [v3] : ((v3 = v1 & apply(v2, all_0_16_16) = v1 & relation_composition(all_0_15_15, v0) = v2) | ( ~ (v2 = 0) & relation(v0) = v2) | ( ~ (v2 = 0) & function(v0) = v2)))
% 48.96/17.84 | (172) ! [v0] : ( ~ (all_80_0_113 = 0) | ~ (function(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ((v3 = v2 & apply(v1, all_0_16_16) = v2 & apply(v0, all_0_12_12) = v2 & relation_composition(all_0_15_15, v0) = v1) | ( ~ (v1 = 0) & relation(v0) = v1)))
% 48.96/17.84 | (173) ! [v0] : ( ~ (all_80_0_113 = 0) | ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ((v3 = v2 & apply(v1, all_0_16_16) = v2 & apply(v0, all_0_12_12) = v2 & relation_composition(all_0_15_15, v0) = v1) | ( ~ (v1 = 0) & function(v0) = v1)))
% 48.96/17.84 |
% 48.96/17.84 +-Applying beta-rule and splitting (146), into two cases.
% 48.96/17.84 |-Branch one:
% 48.96/17.84 | (174) all_0_19_19 = empty_set
% 48.96/17.84 |
% 48.96/17.84 | Equations (174) can reduce 19 to:
% 48.96/17.84 | (161) $false
% 48.96/17.84 |
% 48.96/17.84 |-The branch is then unsatisfiable
% 48.96/17.84 |-Branch two:
% 48.96/17.84 | (19) ~ (all_0_19_19 = empty_set)
% 48.96/17.84 | (177) ? [v0] : ((v0 = all_0_20_20 & relation_dom_as_subset(all_0_20_20, all_0_19_19, all_0_17_17) = all_0_20_20) | ( ~ (v0 = 0) & relation_of2_as_subset(all_0_17_17, all_0_20_20, all_0_19_19) = v0))
% 48.96/17.84 |
% 48.96/17.84 +-Applying beta-rule and splitting (150), into two cases.
% 48.96/17.84 |-Branch one:
% 48.96/17.84 | (178) all_0_19_19 = empty_set & ~ (all_0_20_20 = empty_set)
% 48.96/17.84 |
% 48.96/17.84 | Applying alpha-rule on (178) yields:
% 48.96/17.84 | (174) all_0_19_19 = empty_set
% 48.96/17.84 | (180) ~ (all_0_20_20 = empty_set)
% 48.96/17.84 |
% 48.96/17.84 | Equations (174) can reduce 19 to:
% 48.96/17.84 | (161) $false
% 48.96/17.84 |
% 48.96/17.84 |-The branch is then unsatisfiable
% 48.96/17.84 |-Branch two:
% 48.96/17.84 | (182) ((all_71_0_102 = all_0_20_20 & relation_dom_as_subset(all_0_20_20, all_0_19_19, all_0_17_17) = all_0_20_20) | ( ~ (all_71_1_103 = 0) & quasi_total(all_0_17_17, all_0_20_20, all_0_19_19) = all_71_1_103)) & ((all_71_1_103 = 0 & quasi_total(all_0_17_17, all_0_20_20, all_0_19_19) = 0) | ( ~ (all_71_0_102 = all_0_20_20) & relation_dom_as_subset(all_0_20_20, all_0_19_19, all_0_17_17) = all_71_0_102))
% 48.96/17.84 |
% 48.96/17.84 | Applying alpha-rule on (182) yields:
% 48.96/17.85 | (183) (all_71_0_102 = all_0_20_20 & relation_dom_as_subset(all_0_20_20, all_0_19_19, all_0_17_17) = all_0_20_20) | ( ~ (all_71_1_103 = 0) & quasi_total(all_0_17_17, all_0_20_20, all_0_19_19) = all_71_1_103)
% 48.96/17.85 | (184) (all_71_1_103 = 0 & quasi_total(all_0_17_17, all_0_20_20, all_0_19_19) = 0) | ( ~ (all_71_0_102 = all_0_20_20) & relation_dom_as_subset(all_0_20_20, all_0_19_19, all_0_17_17) = all_71_0_102)
% 48.96/17.85 |
% 48.96/17.85 +-Applying beta-rule and splitting (184), into two cases.
% 48.96/17.85 |-Branch one:
% 48.96/17.85 | (185) all_71_1_103 = 0 & quasi_total(all_0_17_17, all_0_20_20, all_0_19_19) = 0
% 48.96/17.85 |
% 48.96/17.85 | Applying alpha-rule on (185) yields:
% 48.96/17.85 | (186) all_71_1_103 = 0
% 48.96/17.85 | (63) quasi_total(all_0_17_17, all_0_20_20, all_0_19_19) = 0
% 48.96/17.85 |
% 48.96/17.85 +-Applying beta-rule and splitting (183), into two cases.
% 48.96/17.85 |-Branch one:
% 48.96/17.85 | (188) all_71_0_102 = all_0_20_20 & relation_dom_as_subset(all_0_20_20, all_0_19_19, all_0_17_17) = all_0_20_20
% 48.96/17.85 |
% 48.96/17.85 | Applying alpha-rule on (188) yields:
% 48.96/17.85 | (189) all_71_0_102 = all_0_20_20
% 48.96/17.85 | (190) relation_dom_as_subset(all_0_20_20, all_0_19_19, all_0_17_17) = all_0_20_20
% 48.96/17.85 |
% 48.96/17.85 | Instantiating formula (96) with all_0_17_17, all_0_19_19, all_0_20_20 and discharging atoms relation_of2(all_0_17_17, all_0_20_20, all_0_19_19) = 0, yields:
% 48.96/17.85 | (191) ? [v0] : ? [v1] : (relation_dom_as_subset(all_0_20_20, all_0_19_19, all_0_17_17) = v0 & powerset(all_0_20_20) = v1 & element(v0, v1) = 0)
% 48.96/17.85 |
% 48.96/17.85 | Instantiating formula (64) with all_0_17_17, all_0_19_19, all_0_20_20 and discharging atoms relation_of2(all_0_17_17, all_0_20_20, all_0_19_19) = 0, yields:
% 48.96/17.85 | (192) ? [v0] : (relation_dom(all_0_17_17) = v0 & relation_dom_as_subset(all_0_20_20, all_0_19_19, all_0_17_17) = v0)
% 48.96/17.85 |
% 48.96/17.85 | Instantiating formula (59) with all_76_0_107, all_76_1_108, all_0_17_17, all_0_19_19, all_0_20_20 and discharging atoms cartesian_product2(all_0_20_20, all_0_19_19) = all_76_1_108, powerset(all_76_1_108) = all_76_0_107, element(all_0_17_17, all_76_0_107) = 0, yields:
% 48.96/17.85 | (193) relation(all_0_17_17) = 0
% 48.96/17.85 |
% 48.96/17.85 | Instantiating formula (15) with all_80_0_113, all_80_1_114, all_0_15_15, all_0_16_16 and discharging atoms relation_dom(all_0_15_15) = all_80_1_114, in(all_0_16_16, all_80_1_114) = all_80_0_113, yields:
% 48.96/17.85 | (194) ? [v0] : (( ~ (v0 = 0) & relation(all_0_15_15) = v0) | ( ~ (v0 = 0) & function(all_0_15_15) = v0) | (apply(all_0_15_15, all_0_16_16) = v0 & ! [v1] : ! [v2] : ( ~ (all_80_0_113 = 0) | ~ (apply(v1, v0) = v2) | ? [v3] : ? [v4] : ((v4 = v2 & apply(v3, all_0_16_16) = v2 & relation_composition(all_0_15_15, v1) = v3) | ( ~ (v3 = 0) & relation(v1) = v3) | ( ~ (v3 = 0) & function(v1) = v3))) & ! [v1] : ! [v2] : ( ~ (all_80_0_113 = 0) | ~ (relation_composition(all_0_15_15, v1) = v2) | ? [v3] : ? [v4] : ((v4 = v3 & apply(v2, all_0_16_16) = v3 & apply(v1, v0) = v3) | ( ~ (v3 = 0) & relation(v1) = v3) | ( ~ (v3 = 0) & function(v1) = v3))) & ! [v1] : ( ~ (all_80_0_113 = 0) | ~ (relation(v1) = 0) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v3 & apply(v2, all_0_16_16) = v3 & apply(v1, v0) = v3 & relation_composition(all_0_15_15, v1) = v2) | ( ~ (v2 = 0) & function(v1) = v2))) & ! [v1] : ( ~ (all_80_0_113 = 0) | ~ (function(v1) = 0) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v3 & apply(v2, all_0_16_16) = v3 & apply(v1, v0) = v3 & relation_composition(all_0_15_15, v1) = v2) | ( ~ (v2 = 0) & relation(v1) = v2)))))
% 48.96/17.85 |
% 48.96/17.85 | Instantiating (192) with all_206_0_252 yields:
% 48.96/17.85 | (195) relation_dom(all_0_17_17) = all_206_0_252 & relation_dom_as_subset(all_0_20_20, all_0_19_19, all_0_17_17) = all_206_0_252
% 48.96/17.85 |
% 48.96/17.85 | Applying alpha-rule on (195) yields:
% 48.96/17.85 | (196) relation_dom(all_0_17_17) = all_206_0_252
% 48.96/17.85 | (197) relation_dom_as_subset(all_0_20_20, all_0_19_19, all_0_17_17) = all_206_0_252
% 48.96/17.85 |
% 48.96/17.85 | Instantiating (191) with all_208_0_253, all_208_1_254 yields:
% 48.96/17.85 | (198) relation_dom_as_subset(all_0_20_20, all_0_19_19, all_0_17_17) = all_208_1_254 & powerset(all_0_20_20) = all_208_0_253 & element(all_208_1_254, all_208_0_253) = 0
% 48.96/17.85 |
% 48.96/17.85 | Applying alpha-rule on (198) yields:
% 48.96/17.85 | (199) relation_dom_as_subset(all_0_20_20, all_0_19_19, all_0_17_17) = all_208_1_254
% 48.96/17.85 | (200) powerset(all_0_20_20) = all_208_0_253
% 48.96/17.85 | (201) element(all_208_1_254, all_208_0_253) = 0
% 48.96/17.85 |
% 48.96/17.85 | Instantiating (194) with all_214_0_258 yields:
% 48.96/17.85 | (202) ( ~ (all_214_0_258 = 0) & relation(all_0_15_15) = all_214_0_258) | ( ~ (all_214_0_258 = 0) & function(all_0_15_15) = all_214_0_258) | (apply(all_0_15_15, all_0_16_16) = all_214_0_258 & ! [v0] : ! [v1] : ( ~ (all_80_0_113 = 0) | ~ (apply(v0, all_214_0_258) = v1) | ? [v2] : ? [v3] : ((v3 = v1 & apply(v2, all_0_16_16) = v1 & relation_composition(all_0_15_15, v0) = v2) | ( ~ (v2 = 0) & relation(v0) = v2) | ( ~ (v2 = 0) & function(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (all_80_0_113 = 0) | ~ (relation_composition(all_0_15_15, v0) = v1) | ? [v2] : ? [v3] : ((v3 = v2 & apply(v1, all_0_16_16) = v2 & apply(v0, all_214_0_258) = v2) | ( ~ (v2 = 0) & relation(v0) = v2) | ( ~ (v2 = 0) & function(v0) = v2))) & ! [v0] : ( ~ (all_80_0_113 = 0) | ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ((v3 = v2 & apply(v1, all_0_16_16) = v2 & apply(v0, all_214_0_258) = v2 & relation_composition(all_0_15_15, v0) = v1) | ( ~ (v1 = 0) & function(v0) = v1))) & ! [v0] : ( ~ (all_80_0_113 = 0) | ~ (function(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ((v3 = v2 & apply(v1, all_0_16_16) = v2 & apply(v0, all_214_0_258) = v2 & relation_composition(all_0_15_15, v0) = v1) | ( ~ (v1 = 0) & relation(v0) = v1))))
% 48.96/17.85 |
% 48.96/17.85 +-Applying beta-rule and splitting (202), into two cases.
% 48.96/17.85 |-Branch one:
% 48.96/17.85 | (203) ( ~ (all_214_0_258 = 0) & relation(all_0_15_15) = all_214_0_258) | ( ~ (all_214_0_258 = 0) & function(all_0_15_15) = all_214_0_258)
% 48.96/17.85 |
% 48.96/17.85 +-Applying beta-rule and splitting (203), into two cases.
% 48.96/17.85 |-Branch one:
% 48.96/17.85 | (204) ~ (all_214_0_258 = 0) & relation(all_0_15_15) = all_214_0_258
% 48.96/17.85 |
% 48.96/17.85 | Applying alpha-rule on (204) yields:
% 48.96/17.85 | (205) ~ (all_214_0_258 = 0)
% 48.96/17.85 | (206) relation(all_0_15_15) = all_214_0_258
% 48.96/17.85 |
% 48.96/17.85 | Instantiating formula (60) with all_0_15_15, all_214_0_258, 0 and discharging atoms relation(all_0_15_15) = all_214_0_258, relation(all_0_15_15) = 0, yields:
% 48.96/17.85 | (207) all_214_0_258 = 0
% 48.96/17.85 |
% 48.96/17.85 | Equations (207) can reduce 205 to:
% 48.96/17.85 | (161) $false
% 48.96/17.85 |
% 48.96/17.85 |-The branch is then unsatisfiable
% 48.96/17.85 |-Branch two:
% 48.96/17.85 | (209) ~ (all_214_0_258 = 0) & function(all_0_15_15) = all_214_0_258
% 48.96/17.85 |
% 48.96/17.85 | Applying alpha-rule on (209) yields:
% 48.96/17.85 | (205) ~ (all_214_0_258 = 0)
% 48.96/17.85 | (211) function(all_0_15_15) = all_214_0_258
% 48.96/17.85 |
% 48.96/17.85 | Instantiating formula (13) with all_0_15_15, all_214_0_258, 0 and discharging atoms function(all_0_15_15) = all_214_0_258, function(all_0_15_15) = 0, yields:
% 48.96/17.85 | (207) all_214_0_258 = 0
% 48.96/17.85 |
% 48.96/17.85 | Equations (207) can reduce 205 to:
% 48.96/17.85 | (161) $false
% 48.96/17.85 |
% 48.96/17.85 |-The branch is then unsatisfiable
% 48.96/17.85 |-Branch two:
% 48.96/17.85 | (214) apply(all_0_15_15, all_0_16_16) = all_214_0_258 & ! [v0] : ! [v1] : ( ~ (all_80_0_113 = 0) | ~ (apply(v0, all_214_0_258) = v1) | ? [v2] : ? [v3] : ((v3 = v1 & apply(v2, all_0_16_16) = v1 & relation_composition(all_0_15_15, v0) = v2) | ( ~ (v2 = 0) & relation(v0) = v2) | ( ~ (v2 = 0) & function(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (all_80_0_113 = 0) | ~ (relation_composition(all_0_15_15, v0) = v1) | ? [v2] : ? [v3] : ((v3 = v2 & apply(v1, all_0_16_16) = v2 & apply(v0, all_214_0_258) = v2) | ( ~ (v2 = 0) & relation(v0) = v2) | ( ~ (v2 = 0) & function(v0) = v2))) & ! [v0] : ( ~ (all_80_0_113 = 0) | ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ((v3 = v2 & apply(v1, all_0_16_16) = v2 & apply(v0, all_214_0_258) = v2 & relation_composition(all_0_15_15, v0) = v1) | ( ~ (v1 = 0) & function(v0) = v1))) & ! [v0] : ( ~ (all_80_0_113 = 0) | ~ (function(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ((v3 = v2 & apply(v1, all_0_16_16) = v2 & apply(v0, all_214_0_258) = v2 & relation_composition(all_0_15_15, v0) = v1) | ( ~ (v1 = 0) & relation(v0) = v1)))
% 48.96/17.86 |
% 48.96/17.86 | Applying alpha-rule on (214) yields:
% 48.96/17.86 | (215) apply(all_0_15_15, all_0_16_16) = all_214_0_258
% 48.96/17.86 | (216) ! [v0] : ( ~ (all_80_0_113 = 0) | ~ (function(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ((v3 = v2 & apply(v1, all_0_16_16) = v2 & apply(v0, all_214_0_258) = v2 & relation_composition(all_0_15_15, v0) = v1) | ( ~ (v1 = 0) & relation(v0) = v1)))
% 48.96/17.86 | (217) ! [v0] : ( ~ (all_80_0_113 = 0) | ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ((v3 = v2 & apply(v1, all_0_16_16) = v2 & apply(v0, all_214_0_258) = v2 & relation_composition(all_0_15_15, v0) = v1) | ( ~ (v1 = 0) & function(v0) = v1)))
% 48.96/17.86 | (218) ! [v0] : ! [v1] : ( ~ (all_80_0_113 = 0) | ~ (apply(v0, all_214_0_258) = v1) | ? [v2] : ? [v3] : ((v3 = v1 & apply(v2, all_0_16_16) = v1 & relation_composition(all_0_15_15, v0) = v2) | ( ~ (v2 = 0) & relation(v0) = v2) | ( ~ (v2 = 0) & function(v0) = v2)))
% 48.96/17.86 | (219) ! [v0] : ! [v1] : ( ~ (all_80_0_113 = 0) | ~ (relation_composition(all_0_15_15, v0) = v1) | ? [v2] : ? [v3] : ((v3 = v2 & apply(v1, all_0_16_16) = v2 & apply(v0, all_214_0_258) = v2) | ( ~ (v2 = 0) & relation(v0) = v2) | ( ~ (v2 = 0) & function(v0) = v2)))
% 48.96/17.86 |
% 48.96/17.86 +-Applying beta-rule and splitting (147), into two cases.
% 48.96/17.86 |-Branch one:
% 48.96/17.86 | (220) ( ~ (all_63_1_92 = 0) & relation(all_0_17_17) = all_63_1_92) | ( ~ (all_63_1_92 = 0) & function(all_0_17_17) = all_63_1_92)
% 48.96/17.86 |
% 48.96/17.86 +-Applying beta-rule and splitting (220), into two cases.
% 48.96/17.86 |-Branch one:
% 48.96/17.86 | (221) ~ (all_63_1_92 = 0) & relation(all_0_17_17) = all_63_1_92
% 48.96/17.86 |
% 48.96/17.86 | Applying alpha-rule on (221) yields:
% 48.96/17.86 | (222) ~ (all_63_1_92 = 0)
% 48.96/17.86 | (223) relation(all_0_17_17) = all_63_1_92
% 48.96/17.86 |
% 48.96/17.86 | Instantiating formula (60) with all_0_17_17, 0, all_63_1_92 and discharging atoms relation(all_0_17_17) = all_63_1_92, relation(all_0_17_17) = 0, yields:
% 48.96/17.86 | (224) all_63_1_92 = 0
% 48.96/17.86 |
% 48.96/17.86 | Equations (224) can reduce 222 to:
% 48.96/17.86 | (161) $false
% 48.96/17.86 |
% 48.96/17.86 |-The branch is then unsatisfiable
% 48.96/17.86 |-Branch two:
% 48.96/17.86 | (226) ~ (all_63_1_92 = 0) & function(all_0_17_17) = all_63_1_92
% 48.96/17.86 |
% 48.96/17.86 | Applying alpha-rule on (226) yields:
% 48.96/17.86 | (222) ~ (all_63_1_92 = 0)
% 48.96/17.86 | (228) function(all_0_17_17) = all_63_1_92
% 48.96/17.86 |
% 48.96/17.86 | Instantiating formula (13) with all_0_17_17, all_63_1_92, 0 and discharging atoms function(all_0_17_17) = all_63_1_92, function(all_0_17_17) = 0, yields:
% 48.96/17.86 | (224) all_63_1_92 = 0
% 48.96/17.86 |
% 48.96/17.86 | Equations (224) can reduce 222 to:
% 48.96/17.86 | (161) $false
% 48.96/17.86 |
% 48.96/17.86 |-The branch is then unsatisfiable
% 48.96/17.86 |-Branch two:
% 48.96/17.86 | (231) relation_dom(all_0_17_17) = all_63_1_92 & in(all_0_18_18, all_63_1_92) = all_63_0_91 & ! [v0] : ! [v1] : ( ~ (all_63_0_91 = 0) | ~ (apply(v0, all_0_16_16) = v1) | ? [v2] : ? [v3] : ((v3 = v1 & apply(v2, all_0_18_18) = v1 & relation_composition(all_0_17_17, v0) = v2) | ( ~ (v2 = 0) & relation(v0) = v2) | ( ~ (v2 = 0) & function(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (all_63_0_91 = 0) | ~ (relation_composition(all_0_17_17, v0) = v1) | ? [v2] : ? [v3] : ((v3 = v2 & apply(v1, all_0_18_18) = v2 & apply(v0, all_0_16_16) = v2) | ( ~ (v2 = 0) & relation(v0) = v2) | ( ~ (v2 = 0) & function(v0) = v2))) & ! [v0] : ( ~ (all_63_0_91 = 0) | ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ((v3 = v2 & apply(v1, all_0_18_18) = v2 & apply(v0, all_0_16_16) = v2 & relation_composition(all_0_17_17, v0) = v1) | ( ~ (v1 = 0) & function(v0) = v1))) & ! [v0] : ( ~ (all_63_0_91 = 0) | ~ (function(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ((v3 = v2 & apply(v1, all_0_18_18) = v2 & apply(v0, all_0_16_16) = v2 & relation_composition(all_0_17_17, v0) = v1) | ( ~ (v1 = 0) & relation(v0) = v1)))
% 48.96/17.86 |
% 48.96/17.86 | Applying alpha-rule on (231) yields:
% 48.96/17.86 | (232) ! [v0] : ! [v1] : ( ~ (all_63_0_91 = 0) | ~ (relation_composition(all_0_17_17, v0) = v1) | ? [v2] : ? [v3] : ((v3 = v2 & apply(v1, all_0_18_18) = v2 & apply(v0, all_0_16_16) = v2) | ( ~ (v2 = 0) & relation(v0) = v2) | ( ~ (v2 = 0) & function(v0) = v2)))
% 48.96/17.86 | (233) ! [v0] : ! [v1] : ( ~ (all_63_0_91 = 0) | ~ (apply(v0, all_0_16_16) = v1) | ? [v2] : ? [v3] : ((v3 = v1 & apply(v2, all_0_18_18) = v1 & relation_composition(all_0_17_17, v0) = v2) | ( ~ (v2 = 0) & relation(v0) = v2) | ( ~ (v2 = 0) & function(v0) = v2)))
% 48.96/17.86 | (234) relation_dom(all_0_17_17) = all_63_1_92
% 48.96/17.86 | (235) in(all_0_18_18, all_63_1_92) = all_63_0_91
% 48.96/17.86 | (236) ! [v0] : ( ~ (all_63_0_91 = 0) | ~ (function(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ((v3 = v2 & apply(v1, all_0_18_18) = v2 & apply(v0, all_0_16_16) = v2 & relation_composition(all_0_17_17, v0) = v1) | ( ~ (v1 = 0) & relation(v0) = v1)))
% 48.96/17.86 | (237) ! [v0] : ( ~ (all_63_0_91 = 0) | ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ((v3 = v2 & apply(v1, all_0_18_18) = v2 & apply(v0, all_0_16_16) = v2 & relation_composition(all_0_17_17, v0) = v1) | ( ~ (v1 = 0) & function(v0) = v1)))
% 48.96/17.86 |
% 48.96/17.86 | Instantiating formula (233) with all_0_12_12, all_0_15_15 and discharging atoms apply(all_0_15_15, all_0_16_16) = all_0_12_12, yields:
% 48.96/17.86 | (238) ~ (all_63_0_91 = 0) | ? [v0] : ? [v1] : ((v1 = all_0_12_12 & apply(v0, all_0_18_18) = all_0_12_12 & relation_composition(all_0_17_17, all_0_15_15) = v0) | ( ~ (v0 = 0) & relation(all_0_15_15) = v0) | ( ~ (v0 = 0) & function(all_0_15_15) = v0))
% 48.96/17.86 |
% 48.96/17.86 | Instantiating formula (232) with all_0_14_14, all_0_15_15 and discharging atoms relation_composition(all_0_17_17, all_0_15_15) = all_0_14_14, yields:
% 48.96/17.86 | (239) ~ (all_63_0_91 = 0) | ? [v0] : ? [v1] : ((v1 = v0 & apply(all_0_14_14, all_0_18_18) = v0 & apply(all_0_15_15, all_0_16_16) = v0) | ( ~ (v0 = 0) & relation(all_0_15_15) = v0) | ( ~ (v0 = 0) & function(all_0_15_15) = v0))
% 48.96/17.86 |
% 48.96/17.86 +-Applying beta-rule and splitting (238), into two cases.
% 48.96/17.86 |-Branch one:
% 48.96/17.86 | (240) ~ (all_63_0_91 = 0)
% 48.96/17.86 |
% 48.96/17.86 | Instantiating formula (62) with all_0_17_17, all_63_1_92, all_206_0_252 and discharging atoms relation_dom(all_0_17_17) = all_206_0_252, relation_dom(all_0_17_17) = all_63_1_92, yields:
% 48.96/17.86 | (241) all_206_0_252 = all_63_1_92
% 48.96/17.86 |
% 48.96/17.86 | Instantiating formula (56) with all_0_20_20, all_0_19_19, all_0_17_17, all_208_1_254, all_0_20_20 and discharging atoms relation_dom_as_subset(all_0_20_20, all_0_19_19, all_0_17_17) = all_208_1_254, relation_dom_as_subset(all_0_20_20, all_0_19_19, all_0_17_17) = all_0_20_20, yields:
% 48.96/17.86 | (242) all_208_1_254 = all_0_20_20
% 48.96/17.86 |
% 48.96/17.86 | Instantiating formula (56) with all_0_20_20, all_0_19_19, all_0_17_17, all_206_0_252, all_208_1_254 and discharging atoms relation_dom_as_subset(all_0_20_20, all_0_19_19, all_0_17_17) = all_208_1_254, relation_dom_as_subset(all_0_20_20, all_0_19_19, all_0_17_17) = all_206_0_252, yields:
% 48.96/17.86 | (243) all_208_1_254 = all_206_0_252
% 48.96/17.87 |
% 48.96/17.87 | Combining equations (242,243) yields a new equation:
% 48.96/17.87 | (244) all_206_0_252 = all_0_20_20
% 48.96/17.87 |
% 48.96/17.87 | Combining equations (241,244) yields a new equation:
% 48.96/17.87 | (245) all_63_1_92 = all_0_20_20
% 48.96/17.87 |
% 48.96/17.87 | Simplifying 245 yields:
% 48.96/17.87 | (246) all_63_1_92 = all_0_20_20
% 48.96/17.87 |
% 48.96/17.87 | From (246) and (235) follows:
% 48.96/17.87 | (247) in(all_0_18_18, all_0_20_20) = all_63_0_91
% 48.96/17.87 |
% 48.96/17.87 | Instantiating formula (29) with all_0_18_18, all_0_20_20, all_63_0_91, 0 and discharging atoms in(all_0_18_18, all_0_20_20) = all_63_0_91, in(all_0_18_18, all_0_20_20) = 0, yields:
% 48.96/17.87 | (248) all_63_0_91 = 0
% 48.96/17.87 |
% 48.96/17.87 | Equations (248) can reduce 240 to:
% 48.96/17.87 | (161) $false
% 48.96/17.87 |
% 48.96/17.87 |-The branch is then unsatisfiable
% 48.96/17.87 |-Branch two:
% 48.96/17.87 | (248) all_63_0_91 = 0
% 48.96/17.87 | (251) ? [v0] : ? [v1] : ((v1 = all_0_12_12 & apply(v0, all_0_18_18) = all_0_12_12 & relation_composition(all_0_17_17, all_0_15_15) = v0) | ( ~ (v0 = 0) & relation(all_0_15_15) = v0) | ( ~ (v0 = 0) & function(all_0_15_15) = v0))
% 49.36/17.87 |
% 49.36/17.87 +-Applying beta-rule and splitting (239), into two cases.
% 49.36/17.87 |-Branch one:
% 49.36/17.87 | (240) ~ (all_63_0_91 = 0)
% 49.36/17.87 |
% 49.36/17.87 | Equations (248) can reduce 240 to:
% 49.36/17.87 | (161) $false
% 49.36/17.87 |
% 49.36/17.87 |-The branch is then unsatisfiable
% 49.36/17.87 |-Branch two:
% 49.36/17.87 | (248) all_63_0_91 = 0
% 49.36/17.87 | (255) ? [v0] : ? [v1] : ((v1 = v0 & apply(all_0_14_14, all_0_18_18) = v0 & apply(all_0_15_15, all_0_16_16) = v0) | ( ~ (v0 = 0) & relation(all_0_15_15) = v0) | ( ~ (v0 = 0) & function(all_0_15_15) = v0))
% 49.36/17.87 |
% 49.36/17.87 | Instantiating (255) with all_299_0_567, all_299_1_568 yields:
% 49.36/17.87 | (256) (all_299_0_567 = all_299_1_568 & apply(all_0_14_14, all_0_18_18) = all_299_1_568 & apply(all_0_15_15, all_0_16_16) = all_299_1_568) | ( ~ (all_299_1_568 = 0) & relation(all_0_15_15) = all_299_1_568) | ( ~ (all_299_1_568 = 0) & function(all_0_15_15) = all_299_1_568)
% 49.36/17.87 |
% 49.36/17.87 +-Applying beta-rule and splitting (256), into two cases.
% 49.36/17.87 |-Branch one:
% 49.36/17.87 | (257) (all_299_0_567 = all_299_1_568 & apply(all_0_14_14, all_0_18_18) = all_299_1_568 & apply(all_0_15_15, all_0_16_16) = all_299_1_568) | ( ~ (all_299_1_568 = 0) & relation(all_0_15_15) = all_299_1_568)
% 49.36/17.87 |
% 49.36/17.87 +-Applying beta-rule and splitting (257), into two cases.
% 49.36/17.87 |-Branch one:
% 49.36/17.87 | (258) all_299_0_567 = all_299_1_568 & apply(all_0_14_14, all_0_18_18) = all_299_1_568 & apply(all_0_15_15, all_0_16_16) = all_299_1_568
% 49.36/17.87 |
% 49.36/17.87 | Applying alpha-rule on (258) yields:
% 49.36/17.87 | (259) all_299_0_567 = all_299_1_568
% 49.36/17.87 | (260) apply(all_0_14_14, all_0_18_18) = all_299_1_568
% 49.36/17.87 | (261) apply(all_0_15_15, all_0_16_16) = all_299_1_568
% 49.36/17.87 |
% 49.36/17.87 | Instantiating formula (123) with all_0_14_14, all_0_18_18, all_299_1_568, all_0_13_13 and discharging atoms apply(all_0_14_14, all_0_18_18) = all_299_1_568, apply(all_0_14_14, all_0_18_18) = all_0_13_13, yields:
% 49.36/17.87 | (262) all_299_1_568 = all_0_13_13
% 49.36/17.87 |
% 49.36/17.87 | Instantiating formula (123) with all_0_15_15, all_0_16_16, all_299_1_568, all_0_12_12 and discharging atoms apply(all_0_15_15, all_0_16_16) = all_299_1_568, apply(all_0_15_15, all_0_16_16) = all_0_12_12, yields:
% 49.36/17.87 | (263) all_299_1_568 = all_0_12_12
% 49.36/17.87 |
% 49.36/17.87 | Instantiating formula (123) with all_0_15_15, all_0_16_16, all_214_0_258, all_299_1_568 and discharging atoms apply(all_0_15_15, all_0_16_16) = all_299_1_568, apply(all_0_15_15, all_0_16_16) = all_214_0_258, yields:
% 49.36/17.87 | (264) all_299_1_568 = all_214_0_258
% 49.36/17.87 |
% 49.36/17.87 | Combining equations (263,264) yields a new equation:
% 49.36/17.87 | (265) all_214_0_258 = all_0_12_12
% 49.36/17.87 |
% 49.36/17.87 | Combining equations (262,264) yields a new equation:
% 49.36/17.87 | (266) all_214_0_258 = all_0_13_13
% 49.36/17.87 |
% 49.36/17.87 | Combining equations (266,265) yields a new equation:
% 49.36/17.87 | (267) all_0_12_12 = all_0_13_13
% 49.36/17.87 |
% 49.36/17.87 | Equations (267) can reduce 69 to:
% 49.36/17.87 | (161) $false
% 49.36/17.87 |
% 49.36/17.87 |-The branch is then unsatisfiable
% 49.36/17.87 |-Branch two:
% 49.36/17.87 | (269) ~ (all_299_1_568 = 0) & relation(all_0_15_15) = all_299_1_568
% 49.36/17.87 |
% 49.36/17.87 | Applying alpha-rule on (269) yields:
% 49.36/17.87 | (270) ~ (all_299_1_568 = 0)
% 49.36/17.87 | (271) relation(all_0_15_15) = all_299_1_568
% 49.36/17.87 |
% 49.36/17.87 | Instantiating formula (60) with all_0_15_15, all_299_1_568, 0 and discharging atoms relation(all_0_15_15) = all_299_1_568, relation(all_0_15_15) = 0, yields:
% 49.36/17.87 | (272) all_299_1_568 = 0
% 49.36/17.87 |
% 49.36/17.87 | Equations (272) can reduce 270 to:
% 49.36/17.87 | (161) $false
% 49.36/17.87 |
% 49.36/17.87 |-The branch is then unsatisfiable
% 49.36/17.87 |-Branch two:
% 49.36/17.87 | (274) ~ (all_299_1_568 = 0) & function(all_0_15_15) = all_299_1_568
% 49.36/17.87 |
% 49.36/17.87 | Applying alpha-rule on (274) yields:
% 49.36/17.87 | (270) ~ (all_299_1_568 = 0)
% 49.36/17.87 | (276) function(all_0_15_15) = all_299_1_568
% 49.36/17.87 |
% 49.36/17.87 | Instantiating formula (13) with all_0_15_15, all_299_1_568, 0 and discharging atoms function(all_0_15_15) = all_299_1_568, function(all_0_15_15) = 0, yields:
% 49.36/17.87 | (272) all_299_1_568 = 0
% 49.36/17.87 |
% 49.36/17.87 | Equations (272) can reduce 270 to:
% 49.36/17.87 | (161) $false
% 49.36/17.87 |
% 49.36/17.87 |-The branch is then unsatisfiable
% 49.36/17.87 |-Branch two:
% 49.36/17.87 | (279) ~ (all_71_1_103 = 0) & quasi_total(all_0_17_17, all_0_20_20, all_0_19_19) = all_71_1_103
% 49.36/17.87 |
% 49.36/17.87 | Applying alpha-rule on (279) yields:
% 49.36/17.87 | (280) ~ (all_71_1_103 = 0)
% 49.36/17.87 | (281) quasi_total(all_0_17_17, all_0_20_20, all_0_19_19) = all_71_1_103
% 49.36/17.87 |
% 49.36/17.87 | Equations (186) can reduce 280 to:
% 49.36/17.87 | (161) $false
% 49.36/17.87 |
% 49.36/17.87 |-The branch is then unsatisfiable
% 49.36/17.87 |-Branch two:
% 49.36/17.87 | (283) ~ (all_71_0_102 = all_0_20_20) & relation_dom_as_subset(all_0_20_20, all_0_19_19, all_0_17_17) = all_71_0_102
% 49.36/17.87 |
% 49.36/17.87 | Applying alpha-rule on (283) yields:
% 49.36/17.87 | (284) ~ (all_71_0_102 = all_0_20_20)
% 49.36/17.87 | (285) relation_dom_as_subset(all_0_20_20, all_0_19_19, all_0_17_17) = all_71_0_102
% 49.36/17.87 |
% 49.36/17.87 +-Applying beta-rule and splitting (183), into two cases.
% 49.36/17.87 |-Branch one:
% 49.36/17.87 | (188) all_71_0_102 = all_0_20_20 & relation_dom_as_subset(all_0_20_20, all_0_19_19, all_0_17_17) = all_0_20_20
% 49.36/17.87 |
% 49.36/17.87 | Applying alpha-rule on (188) yields:
% 49.36/17.87 | (189) all_71_0_102 = all_0_20_20
% 49.36/17.87 | (190) relation_dom_as_subset(all_0_20_20, all_0_19_19, all_0_17_17) = all_0_20_20
% 49.36/17.87 |
% 49.36/17.87 | Equations (189) can reduce 284 to:
% 49.36/17.87 | (161) $false
% 49.36/17.87 |
% 49.36/17.87 |-The branch is then unsatisfiable
% 49.36/17.87 |-Branch two:
% 49.36/17.87 | (279) ~ (all_71_1_103 = 0) & quasi_total(all_0_17_17, all_0_20_20, all_0_19_19) = all_71_1_103
% 49.36/17.87 |
% 49.36/17.87 | Applying alpha-rule on (279) yields:
% 49.36/17.87 | (280) ~ (all_71_1_103 = 0)
% 49.36/17.87 | (281) quasi_total(all_0_17_17, all_0_20_20, all_0_19_19) = all_71_1_103
% 49.36/17.87 |
% 49.36/17.87 | Instantiating formula (88) with all_0_17_17, all_0_20_20, all_0_19_19, all_71_1_103, 0 and discharging atoms quasi_total(all_0_17_17, all_0_20_20, all_0_19_19) = all_71_1_103, quasi_total(all_0_17_17, all_0_20_20, all_0_19_19) = 0, yields:
% 49.36/17.87 | (186) all_71_1_103 = 0
% 49.36/17.87 |
% 49.36/17.87 | Equations (186) can reduce 280 to:
% 49.36/17.87 | (161) $false
% 49.36/17.87 |
% 49.36/17.87 |-The branch is then unsatisfiable
% 49.36/17.87 % SZS output end Proof for theBenchmark
% 49.36/17.87
% 49.36/17.87 17275ms
%------------------------------------------------------------------------------