TSTP Solution File: SEU293+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU293+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n032.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 08:48:33 EDT 2022
% Result : Theorem 9.42s 2.84s
% Output : Proof 149.50s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU293+1 : TPTP v8.1.0. Released v3.3.0.
% 0.00/0.10 % Command : ePrincess-casc -timeout=%d %s
% 0.09/0.29 % Computer : n032.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 600
% 0.09/0.29 % DateTime : Mon Jun 20 13:02:19 EDT 2022
% 0.09/0.29 % CPUTime :
% 0.14/0.48 ____ _
% 0.14/0.48 ___ / __ \_____(_)___ ________ __________
% 0.14/0.48 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.14/0.48 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.14/0.48 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.14/0.48
% 0.14/0.48 A Theorem Prover for First-Order Logic
% 0.14/0.48 (ePrincess v.1.0)
% 0.14/0.48
% 0.14/0.48 (c) Philipp Rümmer, 2009-2015
% 0.14/0.48 (c) Peter Backeman, 2014-2015
% 0.14/0.48 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.14/0.48 Free software under GNU Lesser General Public License (LGPL).
% 0.14/0.48 Bug reports to peter@backeman.se
% 0.14/0.48
% 0.14/0.48 For more information, visit http://user.uu.se/~petba168/breu/
% 0.14/0.48
% 0.14/0.48 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.14/0.53 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.34/0.82 Prover 0: Preprocessing ...
% 1.94/1.09 Prover 0: Warning: ignoring some quantifiers
% 2.14/1.11 Prover 0: Constructing countermodel ...
% 2.99/1.38 Prover 0: gave up
% 2.99/1.38 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 3.33/1.42 Prover 1: Preprocessing ...
% 3.69/1.55 Prover 1: Warning: ignoring some quantifiers
% 3.69/1.55 Prover 1: Constructing countermodel ...
% 5.16/1.82 Prover 1: gave up
% 5.16/1.82 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 5.16/1.85 Prover 2: Preprocessing ...
% 6.11/2.01 Prover 2: Warning: ignoring some quantifiers
% 6.11/2.02 Prover 2: Constructing countermodel ...
% 9.42/2.84 Prover 2: proved (1023ms)
% 9.42/2.84
% 9.42/2.84 No countermodel exists, formula is valid
% 9.42/2.84 % SZS status Theorem for theBenchmark
% 9.42/2.84
% 9.42/2.84 Generating proof ... Warning: ignoring some quantifiers
% 148.79/119.37 found it (size 121)
% 148.79/119.37
% 148.79/119.37 % SZS output start Proof for theBenchmark
% 148.79/119.37 Assumed formulas after preprocessing and simplification:
% 148.79/119.37 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ( ~ (v16 = 0) & ~ (v14 = 0) & ~ (v1 = empty_set) & relation_empty_yielding(v11) = 0 & relation_empty_yielding(v10) = 0 & relation_empty_yielding(empty_set) = 0 & relation_of2_as_subset(v3, v0, v1) = 0 & quasi_total(v3, v0, v1) = 0 & relation_inverse_image(v3, v2) = v4 & one_to_one(v20) = 0 & one_to_one(v12) = 0 & relation(v21) = 0 & relation(v20) = 0 & relation(v19) = 0 & relation(v17) = 0 & relation(v15) = 0 & relation(v12) = 0 & relation(v11) = 0 & relation(v10) = 0 & relation(empty_set) = 0 & function(v21) = 0 & function(v20) = 0 & function(v17) = 0 & function(v12) = 0 & function(v10) = 0 & function(v3) = 0 & empty(v20) = 0 & empty(v19) = 0 & empty(v18) = 0 & empty(v17) = 0 & empty(v15) = v16 & empty(v13) = v14 & empty(empty_set) = 0 & in(v5, v4) = v6 & ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : ! [v27] : (v27 = 0 | ~ (relation_dom(v22) = v23) | ~ (relation_inverse_image(v22, v24) = v25) | ~ (in(v26, v25) = v27) | ? [v28] : ? [v29] : (( ~ (v29 = 0) & apply(v22, v26) = v28 & in(v28, v24) = v29) | ( ~ (v28 = 0) & relation(v22) = v28) | ( ~ (v28 = 0) & function(v22) = v28) | ( ~ (v28 = 0) & in(v26, v23) = v28))) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : ! [v27] : (v27 = 0 | ~ (cartesian_product2(v22, v23) = v25) | ~ (powerset(v25) = v26) | ~ (element(v24, v26) = v27) | ? [v28] : ( ~ (v28 = 0) & relation_of2_as_subset(v24, v22, v23) = v28)) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : ! [v27] : ( ~ (relation_dom(v22) = v23) | ~ (relation_inverse_image(v22, v24) = v25) | ~ (apply(v22, v26) = v27) | ? [v28] : ? [v29] : ((v29 = 0 & v28 = 0 & in(v27, v24) = 0 & in(v26, v23) = 0) | ( ~ (v28 = 0) & relation(v22) = v28) | ( ~ (v28 = 0) & function(v22) = v28) | ( ~ (v28 = 0) & in(v26, v25) = v28))) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : ! [v27] : ( ~ (relation_dom(v22) = v23) | ~ (relation_inverse_image(v22, v24) = v25) | ~ (apply(v22, v26) = v27) | ? [v28] : ((v28 = 0 & in(v26, v25) = 0) | ( ~ (v28 = 0) & relation(v22) = v28) | ( ~ (v28 = 0) & function(v22) = v28) | ( ~ (v28 = 0) & in(v27, v24) = v28) | ( ~ (v28 = 0) & in(v26, v23) = v28))) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : ! [v27] : ( ~ (relation_dom(v22) = v23) | ~ (relation_inverse_image(v22, v24) = v25) | ~ (in(v26, v23) = v27) | ? [v28] : ? [v29] : ((v29 = 0 & v27 = 0 & apply(v22, v26) = v28 & in(v28, v24) = 0) | ( ~ (v28 = 0) & relation(v22) = v28) | ( ~ (v28 = 0) & function(v22) = v28) | ( ~ (v28 = 0) & in(v26, v25) = v28))) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : (v26 = 0 | ~ (powerset(v24) = v25) | ~ (element(v23, v25) = 0) | ~ (element(v22, v24) = v26) | ? [v27] : ( ~ (v27 = 0) & in(v22, v23) = v27)) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : (v23 = v22 | ~ (relation_of2(v26, v25, v24) = v23) | ~ (relation_of2(v26, v25, v24) = v22)) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : (v23 = v22 | ~ (relation_dom_as_subset(v26, v25, v24) = v23) | ~ (relation_dom_as_subset(v26, v25, v24) = v22)) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : (v23 = v22 | ~ (relation_of2_as_subset(v26, v25, v24) = v23) | ~ (relation_of2_as_subset(v26, v25, v24) = v22)) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : (v23 = v22 | ~ (quasi_total(v26, v25, v24) = v23) | ~ (quasi_total(v26, v25, v24) = v22)) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : ( ~ (relation_dom(v22) = v23) | ~ (relation_inverse_image(v22, v24) = v25) | ~ (in(v26, v25) = 0) | ? [v27] : ? [v28] : ? [v29] : ((v29 = 0 & v27 = 0 & apply(v22, v26) = v28 & in(v28, v24) = 0 & in(v26, v23) = 0) | ( ~ (v27 = 0) & relation(v22) = v27) | ( ~ (v27 = 0) & function(v22) = v27))) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : ( ~ (relation_dom(v22) = v23) | ~ (relation_inverse_image(v22, v24) = v25) | ~ (in(v26, v23) = 0) | ? [v27] : ? [v28] : ((v27 = 0 & in(v26, v25) = 0) | ( ~ (v28 = 0) & apply(v22, v26) = v27 & in(v27, v24) = v28) | ( ~ (v27 = 0) & relation(v22) = v27) | ( ~ (v27 = 0) & function(v22) = v27))) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : ( ~ (cartesian_product2(v22, v23) = v25) | ~ (powerset(v25) = v26) | ~ (element(v24, v26) = 0) | relation(v24) = 0) & ? [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : (v26 = v22 | ~ (relation_dom(v23) = v24) | ~ (relation_inverse_image(v23, v25) = v26) | ? [v27] : ? [v28] : ? [v29] : ? [v30] : ? [v31] : (( ~ (v27 = 0) & relation(v23) = v27) | ( ~ (v27 = 0) & function(v23) = v27) | (((v31 = 0 & v29 = 0 & apply(v23, v27) = v30 & in(v30, v25) = 0 & in(v27, v24) = 0) | (v28 = 0 & in(v27, v22) = 0)) & (( ~ (v31 = 0) & apply(v23, v27) = v30 & in(v30, v25) = v31) | ( ~ (v29 = 0) & in(v27, v24) = v29) | ( ~ (v28 = 0) & in(v27, v22) = v28))))) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : (v25 = 0 | ~ (relation_of2(v24, v22, v23) = v25) | ? [v26] : ( ~ (v26 = 0) & relation_of2_as_subset(v24, v22, v23) = v26)) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : (v25 = 0 | ~ (relation_of2_as_subset(v24, v22, v23) = v25) | ? [v26] : ( ~ (v26 = 0) & relation_of2(v24, v22, v23) = v26)) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : (v25 = 0 | ~ (powerset(v23) = v24) | ~ (element(v22, v24) = v25) | ? [v26] : ( ~ (v26 = 0) & subset(v22, v23) = v26)) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : (v25 = 0 | ~ (element(v22, v24) = v25) | ~ (in(v22, v23) = 0) | ? [v26] : ? [v27] : ( ~ (v27 = 0) & powerset(v24) = v26 & element(v23, v26) = v27)) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : (v23 = v22 | ~ (subset(v25, v24) = v23) | ~ (subset(v25, v24) = v22)) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : (v23 = v22 | ~ (relation_inverse_image(v25, v24) = v23) | ~ (relation_inverse_image(v25, v24) = v22)) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : (v23 = v22 | ~ (apply(v25, v24) = v23) | ~ (apply(v25, v24) = v22)) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : (v23 = v22 | ~ (cartesian_product2(v25, v24) = v23) | ~ (cartesian_product2(v25, v24) = v22)) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : (v23 = v22 | ~ (element(v25, v24) = v23) | ~ (element(v25, v24) = v22)) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : (v23 = v22 | ~ (in(v25, v24) = v23) | ~ (in(v25, v24) = v22)) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : (v23 = empty_set | ~ (quasi_total(v24, v22, v23) = v25) | ? [v26] : (( ~ (v26 = 0) & relation_of2_as_subset(v24, v22, v23) = v26) | (( ~ (v25 = 0) | (v26 = v22 & relation_dom_as_subset(v22, v23, v24) = v22)) & (v25 = 0 | ( ~ (v26 = v22) & relation_dom_as_subset(v22, v23, v24) = v26))))) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : ( ~ (relation_dom_as_subset(v22, v23, v24) = v25) | ? [v26] : ? [v27] : ((v27 = 0 & powerset(v22) = v26 & element(v25, v26) = 0) | ( ~ (v26 = 0) & relation_of2(v24, v22, v23) = v26))) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : ( ~ (relation_dom_as_subset(v22, v23, v24) = v25) | ? [v26] : ((v26 = v25 & relation_dom(v24) = v25) | ( ~ (v26 = 0) & relation_of2(v24, v22, v23) = v26))) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : ( ~ (relation_dom_as_subset(v22, v23, v24) = v25) | ? [v26] : (( ~ (v26 = 0) & relation_of2_as_subset(v24, v22, v23) = v26) | (( ~ (v23 = empty_set) | v22 = empty_set | (( ~ (v24 = empty_set) | (v26 = 0 & quasi_total(empty_set, v22, empty_set) = 0)) & (v24 = empty_set | ( ~ (v26 = 0) & quasi_total(v24, v22, empty_set) = v26)))) & ((v23 = empty_set & ~ (v22 = empty_set)) | (( ~ (v25 = v22) | (v26 = 0 & quasi_total(v24, v22, v23) = 0)) & (v25 = v22 | ( ~ (v26 = 0) & quasi_total(v24, v22, v23) = v26))))))) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : ( ~ (powerset(v24) = v25) | ~ (element(v23, v25) = 0) | ~ (in(v22, v23) = 0) | element(v22, v24) = 0) & ! [v22] : ! [v23] : ! [v24] : ! [v25] : ( ~ (powerset(v24) = v25) | ~ (element(v23, v25) = 0) | ~ (in(v22, v23) = 0) | ? [v26] : ( ~ (v26 = 0) & empty(v24) = v26)) & ! [v22] : ! [v23] : ! [v24] : (v24 = 0 | ~ (subset(v22, v23) = v24) | ? [v25] : ? [v26] : ( ~ (v26 = 0) & powerset(v23) = v25 & element(v22, v25) = v26)) & ! [v22] : ! [v23] : ! [v24] : (v24 = 0 | ~ (element(v22, v23) = v24) | ? [v25] : ( ~ (v25 = 0) & in(v22, v23) = v25)) & ! [v22] : ! [v23] : ! [v24] : (v24 = 0 | ~ (in(v22, v23) = v24) | ? [v25] : ((v25 = 0 & empty(v23) = 0) | ( ~ (v25 = 0) & element(v22, v23) = v25))) & ! [v22] : ! [v23] : ! [v24] : (v23 = v22 | ~ (relation_empty_yielding(v24) = v23) | ~ (relation_empty_yielding(v24) = v22)) & ! [v22] : ! [v23] : ! [v24] : (v23 = v22 | ~ (relation_dom(v24) = v23) | ~ (relation_dom(v24) = v22)) & ! [v22] : ! [v23] : ! [v24] : (v23 = v22 | ~ (one_to_one(v24) = v23) | ~ (one_to_one(v24) = v22)) & ! [v22] : ! [v23] : ! [v24] : (v23 = v22 | ~ (powerset(v24) = v23) | ~ (powerset(v24) = v22)) & ! [v22] : ! [v23] : ! [v24] : (v23 = v22 | ~ (relation(v24) = v23) | ~ (relation(v24) = v22)) & ! [v22] : ! [v23] : ! [v24] : (v23 = v22 | ~ (function(v24) = v23) | ~ (function(v24) = v22)) & ! [v22] : ! [v23] : ! [v24] : (v23 = v22 | ~ (empty(v24) = v23) | ~ (empty(v24) = v22)) & ! [v22] : ! [v23] : ! [v24] : ( ~ (relation_of2(v24, v22, v23) = 0) | relation_of2_as_subset(v24, v22, v23) = 0) & ! [v22] : ! [v23] : ! [v24] : ( ~ (relation_of2(v24, v22, v23) = 0) | ? [v25] : ? [v26] : (relation_dom_as_subset(v22, v23, v24) = v25 & powerset(v22) = v26 & element(v25, v26) = 0)) & ! [v22] : ! [v23] : ! [v24] : ( ~ (relation_of2(v24, v22, v23) = 0) | ? [v25] : (relation_dom_as_subset(v22, v23, v24) = v25 & relation_dom(v24) = v25)) & ! [v22] : ! [v23] : ! [v24] : ( ~ (relation_of2_as_subset(v24, v22, v23) = 0) | relation_of2(v24, v22, v23) = 0) & ! [v22] : ! [v23] : ! [v24] : ( ~ (relation_of2_as_subset(v24, v22, v23) = 0) | ? [v25] : ? [v26] : (cartesian_product2(v22, v23) = v25 & powerset(v25) = v26 & element(v24, v26) = 0)) & ! [v22] : ! [v23] : ! [v24] : ( ~ (relation_of2_as_subset(v24, v22, v23) = 0) | ? [v25] : ? [v26] : (( ~ (v23 = empty_set) | v22 = empty_set | (( ~ (v24 = empty_set) | (v25 = 0 & quasi_total(empty_set, v22, empty_set) = 0)) & (v24 = empty_set | ( ~ (v25 = 0) & quasi_total(v24, v22, empty_set) = v25)))) & ((v23 = empty_set & ~ (v22 = empty_set)) | (((v26 = v22 & relation_dom_as_subset(v22, v23, v24) = v22) | ( ~ (v25 = 0) & quasi_total(v24, v22, v23) = v25)) & ((v25 = 0 & quasi_total(v24, v22, v23) = 0) | ( ~ (v26 = v22) & relation_dom_as_subset(v22, v23, v24) = v26)))))) & ! [v22] : ! [v23] : ! [v24] : ( ~ (quasi_total(v23, empty_set, v22) = v24) | ? [v25] : (( ~ (v25 = 0) & relation_of2_as_subset(v23, empty_set, v22) = v25) | (( ~ (v24 = 0) | (v25 = empty_set & relation_dom_as_subset(empty_set, v22, v23) = empty_set)) & (v24 = 0 | ( ~ (v25 = empty_set) & relation_dom_as_subset(empty_set, v22, v23) = v25))))) & ! [v22] : ! [v23] : ! [v24] : ( ~ (cartesian_product2(v22, v23) = v24) | ? [v25] : ((v25 = 0 & empty(v23) = 0) | (v25 = 0 & empty(v22) = 0) | ( ~ (v25 = 0) & empty(v24) = v25))) & ! [v22] : ! [v23] : ! [v24] : ( ~ (powerset(v23) = v24) | ~ (element(v22, v24) = 0) | subset(v22, v23) = 0) & ! [v22] : ! [v23] : ! [v24] : ( ~ (empty(v24) = 0) | ~ (in(v22, v23) = 0) | ? [v25] : ? [v26] : ( ~ (v26 = 0) & powerset(v24) = v25 & element(v23, v25) = v26)) & ! [v22] : ! [v23] : (v23 = v22 | ~ (empty(v23) = 0) | ~ (empty(v22) = 0)) & ! [v22] : ! [v23] : (v23 = empty_set | v22 = empty_set | ~ (quasi_total(v23, v22, empty_set) = 0) | ? [v24] : ( ~ (v24 = 0) & relation_of2_as_subset(v23, v22, empty_set) = v24)) & ! [v22] : ! [v23] : (v23 = 0 | v22 = empty_set | ~ (quasi_total(empty_set, v22, empty_set) = v23) | ? [v24] : ( ~ (v24 = 0) & relation_of2_as_subset(empty_set, v22, empty_set) = v24)) & ! [v22] : ! [v23] : (v23 = 0 | ~ (subset(v22, v22) = v23)) & ! [v22] : ! [v23] : (v23 = 0 | ~ (relation(v22) = v23) | ? [v24] : ( ~ (v24 = 0) & empty(v22) = v24)) & ! [v22] : ! [v23] : (v23 = 0 | ~ (function(v22) = v23) | ? [v24] : ( ~ (v24 = 0) & empty(v22) = v24)) & ! [v22] : ! [v23] : (v23 = 0 | ~ (empty(v22) = v23) | ? [v24] : ? [v25] : ? [v26] : ( ~ (v26 = 0) & powerset(v22) = v24 & element(v25, v24) = 0 & empty(v25) = v26)) & ! [v22] : ! [v23] : (v23 = 0 | ~ (empty(v22) = v23) | ? [v24] : ? [v25] : (( ~ (v25 = 0) & relation_dom(v22) = v24 & empty(v24) = v25) | ( ~ (v24 = 0) & relation(v22) = v24))) & ! [v22] : ! [v23] : ( ~ (subset(v22, v23) = 0) | ? [v24] : (powerset(v23) = v24 & element(v22, v24) = 0)) & ! [v22] : ! [v23] : ( ~ (relation_dom(v22) = v23) | ? [v24] : ? [v25] : ((v25 = 0 & v24 = 0 & relation(v23) = 0 & empty(v23) = 0) | ( ~ (v24 = 0) & empty(v22) = v24))) & ! [v22] : ! [v23] : ( ~ (relation_dom(v22) = v23) | ? [v24] : ((v24 = 0 & empty(v22) = 0) | ( ~ (v24 = 0) & relation(v22) = v24) | ( ~ (v24 = 0) & empty(v23) = v24))) & ! [v22] : ! [v23] : ( ~ (one_to_one(v22) = v23) | ? [v24] : ? [v25] : ((v25 = 0 & v24 = 0 & v23 = 0 & relation(v22) = 0 & function(v22) = 0) | ( ~ (v24 = 0) & relation(v22) = v24) | ( ~ (v24 = 0) & function(v22) = v24) | ( ~ (v24 = 0) & empty(v22) = v24))) & ! [v22] : ! [v23] : ( ~ (powerset(v22) = v23) | ? [v24] : ? [v25] : ? [v26] : ((v25 = 0 & ~ (v26 = 0) & element(v24, v23) = 0 & empty(v24) = v26) | (v24 = 0 & empty(v22) = 0))) & ! [v22] : ! [v23] : ( ~ (powerset(v22) = v23) | ? [v24] : ( ~ (v24 = 0) & empty(v23) = v24)) & ! [v22] : ! [v23] : ( ~ (powerset(v22) = v23) | ? [v24] : (element(v24, v23) = 0 & empty(v24) = 0)) & ! [v22] : ! [v23] : ( ~ (element(v22, v23) = 0) | ? [v24] : ((v24 = 0 & empty(v23) = 0) | (v24 = 0 & in(v22, v23) = 0))) & ! [v22] : ! [v23] : ( ~ (in(v23, v22) = 0) | ? [v24] : ( ~ (v24 = 0) & in(v22, v23) = v24)) & ! [v22] : ! [v23] : ( ~ (in(v22, v23) = 0) | element(v22, v23) = 0) & ! [v22] : ! [v23] : ( ~ (in(v22, v23) = 0) | ? [v24] : ( ~ (v24 = 0) & empty(v23) = v24)) & ! [v22] : ! [v23] : ( ~ (in(v22, v23) = 0) | ? [v24] : ( ~ (v24 = 0) & in(v23, v22) = v24)) & ! [v22] : (v22 = empty_set | ~ (empty(v22) = 0)) & ! [v22] : ( ~ (relation(v22) = 0) | ? [v23] : ? [v24] : ((v24 = 0 & v23 = 0 & one_to_one(v22) = 0 & function(v22) = 0) | ( ~ (v23 = 0) & function(v22) = v23) | ( ~ (v23 = 0) & empty(v22) = v23))) & ! [v22] : ( ~ (relation(v22) = 0) | ? [v23] : ? [v24] : ((v23 = 0 & empty(v22) = 0) | ( ~ (v24 = 0) & relation_dom(v22) = v23 & empty(v23) = v24))) & ! [v22] : ( ~ (relation(v22) = 0) | ? [v23] : (( ~ (v23 = 0) & function(v22) = v23) | (relation_dom(v22) = v23 & ! [v24] : ! [v25] : ! [v26] : ! [v27] : (v27 = 0 | ~ (relation_inverse_image(v22, v24) = v25) | ~ (in(v26, v25) = v27) | ? [v28] : ? [v29] : (( ~ (v29 = 0) & apply(v22, v26) = v28 & in(v28, v24) = v29) | ( ~ (v28 = 0) & in(v26, v23) = v28))) & ! [v24] : ! [v25] : ! [v26] : ! [v27] : ( ~ (relation_inverse_image(v22, v24) = v25) | ~ (apply(v22, v26) = v27) | ? [v28] : ? [v29] : ((v29 = 0 & v28 = 0 & in(v27, v24) = 0 & in(v26, v23) = 0) | ( ~ (v28 = 0) & in(v26, v25) = v28))) & ! [v24] : ! [v25] : ! [v26] : ! [v27] : ( ~ (relation_inverse_image(v22, v24) = v25) | ~ (apply(v22, v26) = v27) | ? [v28] : ((v28 = 0 & in(v26, v25) = 0) | ( ~ (v28 = 0) & in(v27, v24) = v28) | ( ~ (v28 = 0) & in(v26, v23) = v28))) & ! [v24] : ! [v25] : ! [v26] : ! [v27] : ( ~ (relation_inverse_image(v22, v24) = v25) | ~ (in(v26, v23) = v27) | ? [v28] : ? [v29] : ((v29 = 0 & v27 = 0 & apply(v22, v26) = v28 & in(v28, v24) = 0) | ( ~ (v28 = 0) & in(v26, v25) = v28))) & ! [v24] : ! [v25] : ! [v26] : ( ~ (relation_inverse_image(v22, v24) = v25) | ~ (in(v26, v25) = 0) | ? [v27] : (apply(v22, v26) = v27 & in(v27, v24) = 0 & in(v26, v23) = 0)) & ! [v24] : ! [v25] : ! [v26] : ( ~ (relation_inverse_image(v22, v24) = v25) | ~ (in(v26, v23) = 0) | ? [v27] : ? [v28] : ((v27 = 0 & in(v26, v25) = 0) | ( ~ (v28 = 0) & apply(v22, v26) = v27 & in(v27, v24) = v28))) & ? [v24] : ! [v25] : ! [v26] : (v26 = v24 | ~ (relation_inverse_image(v22, v25) = v26) | ? [v27] : ? [v28] : ? [v29] : ? [v30] : ? [v31] : (((v31 = 0 & v29 = 0 & apply(v22, v27) = v30 & in(v30, v25) = 0 & in(v27, v23) = 0) | (v28 = 0 & in(v27, v24) = 0)) & (( ~ (v31 = 0) & apply(v22, v27) = v30 & in(v30, v25) = v31) | ( ~ (v29 = 0) & in(v27, v23) = v29) | ( ~ (v28 = 0) & in(v27, v24) = v28))))))) & ! [v22] : ( ~ (function(v22) = 0) | ? [v23] : ? [v24] : ((v24 = 0 & v23 = 0 & one_to_one(v22) = 0 & relation(v22) = 0) | ( ~ (v23 = 0) & relation(v22) = v23) | ( ~ (v23 = 0) & empty(v22) = v23))) & ! [v22] : ( ~ (function(v22) = 0) | ? [v23] : (( ~ (v23 = 0) & relation(v22) = v23) | (relation_dom(v22) = v23 & ! [v24] : ! [v25] : ! [v26] : ! [v27] : (v27 = 0 | ~ (relation_inverse_image(v22, v24) = v25) | ~ (in(v26, v25) = v27) | ? [v28] : ? [v29] : (( ~ (v29 = 0) & apply(v22, v26) = v28 & in(v28, v24) = v29) | ( ~ (v28 = 0) & in(v26, v23) = v28))) & ! [v24] : ! [v25] : ! [v26] : ! [v27] : ( ~ (relation_inverse_image(v22, v24) = v25) | ~ (apply(v22, v26) = v27) | ? [v28] : ? [v29] : ((v29 = 0 & v28 = 0 & in(v27, v24) = 0 & in(v26, v23) = 0) | ( ~ (v28 = 0) & in(v26, v25) = v28))) & ! [v24] : ! [v25] : ! [v26] : ! [v27] : ( ~ (relation_inverse_image(v22, v24) = v25) | ~ (apply(v22, v26) = v27) | ? [v28] : ((v28 = 0 & in(v26, v25) = 0) | ( ~ (v28 = 0) & in(v27, v24) = v28) | ( ~ (v28 = 0) & in(v26, v23) = v28))) & ! [v24] : ! [v25] : ! [v26] : ! [v27] : ( ~ (relation_inverse_image(v22, v24) = v25) | ~ (in(v26, v23) = v27) | ? [v28] : ? [v29] : ((v29 = 0 & v27 = 0 & apply(v22, v26) = v28 & in(v28, v24) = 0) | ( ~ (v28 = 0) & in(v26, v25) = v28))) & ! [v24] : ! [v25] : ! [v26] : ( ~ (relation_inverse_image(v22, v24) = v25) | ~ (in(v26, v25) = 0) | ? [v27] : (apply(v22, v26) = v27 & in(v27, v24) = 0 & in(v26, v23) = 0)) & ! [v24] : ! [v25] : ! [v26] : ( ~ (relation_inverse_image(v22, v24) = v25) | ~ (in(v26, v23) = 0) | ? [v27] : ? [v28] : ((v27 = 0 & in(v26, v25) = 0) | ( ~ (v28 = 0) & apply(v22, v26) = v27 & in(v27, v24) = v28))) & ? [v24] : ! [v25] : ! [v26] : (v26 = v24 | ~ (relation_inverse_image(v22, v25) = v26) | ? [v27] : ? [v28] : ? [v29] : ? [v30] : ? [v31] : (((v31 = 0 & v29 = 0 & apply(v22, v27) = v30 & in(v30, v25) = 0 & in(v27, v23) = 0) | (v28 = 0 & in(v27, v24) = 0)) & (( ~ (v31 = 0) & apply(v22, v27) = v30 & in(v30, v25) = v31) | ( ~ (v29 = 0) & in(v27, v23) = v29) | ( ~ (v28 = 0) & in(v27, v24) = v28))))))) & ! [v22] : ( ~ (empty(v22) = 0) | relation(v22) = 0) & ! [v22] : ( ~ (empty(v22) = 0) | function(v22) = 0) & ! [v22] : ( ~ (empty(v22) = 0) | ? [v23] : ? [v24] : ? [v25] : ((v25 = 0 & v24 = 0 & v23 = 0 & one_to_one(v22) = 0 & relation(v22) = 0 & function(v22) = 0) | ( ~ (v23 = 0) & relation(v22) = v23) | ( ~ (v23 = 0) & function(v22) = v23))) & ! [v22] : ( ~ (empty(v22) = 0) | ? [v23] : (relation_dom(v22) = v23 & relation(v23) = 0 & empty(v23) = 0)) & ? [v22] : ? [v23] : ? [v24] : ? [v25] : relation_of2(v24, v23, v22) = v25 & ? [v22] : ? [v23] : ? [v24] : ? [v25] : relation_dom_as_subset(v24, v23, v22) = v25 & ? [v22] : ? [v23] : ? [v24] : ? [v25] : relation_of2_as_subset(v24, v23, v22) = v25 & ? [v22] : ? [v23] : ? [v24] : ? [v25] : quasi_total(v24, v23, v22) = v25 & ? [v22] : ? [v23] : ? [v24] : subset(v23, v22) = v24 & ? [v22] : ? [v23] : ? [v24] : relation_of2(v24, v22, v23) = 0 & ? [v22] : ? [v23] : ? [v24] : relation_of2_as_subset(v24, v22, v23) = 0 & ? [v22] : ? [v23] : ? [v24] : relation_inverse_image(v23, v22) = v24 & ? [v22] : ? [v23] : ? [v24] : apply(v23, v22) = v24 & ? [v22] : ? [v23] : ? [v24] : cartesian_product2(v23, v22) = v24 & ? [v22] : ? [v23] : ? [v24] : element(v23, v22) = v24 & ? [v22] : ? [v23] : ? [v24] : in(v23, v22) = v24 & ? [v22] : ? [v23] : ? [v24] : (relation_of2(v24, v22, v23) = 0 & quasi_total(v24, v22, v23) = 0 & relation(v24) = 0 & function(v24) = 0) & ? [v22] : ? [v23] : ? [v24] : (relation_of2(v24, v22, v23) = 0 & relation(v24) = 0 & function(v24) = 0) & ? [v22] : ? [v23] : relation_empty_yielding(v22) = v23 & ? [v22] : ? [v23] : relation_dom(v22) = v23 & ? [v22] : ? [v23] : one_to_one(v22) = v23 & ? [v22] : ? [v23] : powerset(v22) = v23 & ? [v22] : ? [v23] : element(v23, v22) = 0 & ? [v22] : ? [v23] : relation(v22) = v23 & ? [v22] : ? [v23] : function(v22) = v23 & ? [v22] : ? [v23] : empty(v22) = v23 & ((v9 = 0 & v7 = 0 & ~ (v6 = 0) & apply(v3, v5) = v8 & in(v8, v2) = 0 & in(v5, v0) = 0) | (v6 = 0 & (( ~ (v9 = 0) & apply(v3, v5) = v8 & in(v8, v2) = v9) | ( ~ (v7 = 0) & in(v5, v0) = v7)))))
% 148.98/119.44 | 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, all_0_21_21 yields:
% 148.98/119.44 | (1) ~ (all_0_5_5 = 0) & ~ (all_0_7_7 = 0) & ~ (all_0_20_20 = empty_set) & relation_empty_yielding(all_0_10_10) = 0 & relation_empty_yielding(all_0_11_11) = 0 & relation_empty_yielding(empty_set) = 0 & relation_of2_as_subset(all_0_18_18, all_0_21_21, all_0_20_20) = 0 & quasi_total(all_0_18_18, all_0_21_21, all_0_20_20) = 0 & relation_inverse_image(all_0_18_18, all_0_19_19) = all_0_17_17 & 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(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_18_18) = 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_16_16, all_0_17_17) = all_0_15_15 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (relation_dom(v0) = v1) | ~ (relation_inverse_image(v0, v2) = v3) | ~ (in(v4, v3) = v5) | ? [v6] : ? [v7] : (( ~ (v7 = 0) & apply(v0, v4) = v6 & in(v6, v2) = v7) | ( ~ (v6 = 0) & relation(v0) = v6) | ( ~ (v6 = 0) & function(v0) = v6) | ( ~ (v6 = 0) & in(v4, v1) = v6))) & ! [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] : ! [v5] : ( ~ (relation_dom(v0) = v1) | ~ (relation_inverse_image(v0, v2) = v3) | ~ (apply(v0, v4) = v5) | ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & in(v5, v2) = 0 & in(v4, v1) = 0) | ( ~ (v6 = 0) & relation(v0) = v6) | ( ~ (v6 = 0) & function(v0) = v6) | ( ~ (v6 = 0) & in(v4, v3) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_dom(v0) = v1) | ~ (relation_inverse_image(v0, v2) = v3) | ~ (apply(v0, v4) = v5) | ? [v6] : ((v6 = 0 & in(v4, v3) = 0) | ( ~ (v6 = 0) & relation(v0) = v6) | ( ~ (v6 = 0) & function(v0) = v6) | ( ~ (v6 = 0) & in(v5, v2) = v6) | ( ~ (v6 = 0) & in(v4, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_dom(v0) = v1) | ~ (relation_inverse_image(v0, v2) = v3) | ~ (in(v4, v1) = v5) | ? [v6] : ? [v7] : ((v7 = 0 & v5 = 0 & apply(v0, v4) = v6 & in(v6, v2) = 0) | ( ~ (v6 = 0) & relation(v0) = v6) | ( ~ (v6 = 0) & function(v0) = v6) | ( ~ (v6 = 0) & in(v4, v3) = 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] : ( ~ (relation_dom(v0) = v1) | ~ (relation_inverse_image(v0, v2) = v3) | ~ (in(v4, v3) = 0) | ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v5 = 0 & apply(v0, v4) = v6 & in(v6, v2) = 0 & in(v4, v1) = 0) | ( ~ (v5 = 0) & relation(v0) = v5) | ( ~ (v5 = 0) & function(v0) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v0) = v1) | ~ (relation_inverse_image(v0, v2) = v3) | ~ (in(v4, v1) = 0) | ? [v5] : ? [v6] : ((v5 = 0 & in(v4, v3) = 0) | ( ~ (v6 = 0) & apply(v0, v4) = v5 & in(v5, v2) = v6) | ( ~ (v5 = 0) & relation(v0) = v5) | ( ~ (v5 = 0) & function(v0) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v0, v1) = v3) | ~ (powerset(v3) = v4) | ~ (element(v2, v4) = 0) | relation(v2) = 0) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v0 | ~ (relation_dom(v1) = v2) | ~ (relation_inverse_image(v1, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (( ~ (v5 = 0) & relation(v1) = v5) | ( ~ (v5 = 0) & function(v1) = v5) | (((v9 = 0 & v7 = 0 & apply(v1, v5) = v8 & in(v8, v3) = 0 & in(v5, v2) = 0) | (v6 = 0 & in(v5, v0) = 0)) & (( ~ (v9 = 0) & apply(v1, v5) = v8 & in(v8, v3) = v9) | ( ~ (v7 = 0) & in(v5, v2) = v7) | ( ~ (v6 = 0) & in(v5, v0) = v6))))) & ! [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 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_inverse_image(v3, v2) = v1) | ~ (relation_inverse_image(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apply(v3, v2) = v1) | ~ (apply(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_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] : ( ~ (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_as_subset(v0, v1, v2) = v3 & relation_dom(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] : ( ~ (relation(v0) = 0) | ? [v1] : (( ~ (v1 = 0) & function(v0) = v1) | (relation_dom(v0) = v1 & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (relation_inverse_image(v0, v2) = v3) | ~ (in(v4, v3) = v5) | ? [v6] : ? [v7] : (( ~ (v7 = 0) & apply(v0, v4) = v6 & in(v6, v2) = v7) | ( ~ (v6 = 0) & in(v4, v1) = v6))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_inverse_image(v0, v2) = v3) | ~ (apply(v0, v4) = v5) | ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & in(v5, v2) = 0 & in(v4, v1) = 0) | ( ~ (v6 = 0) & in(v4, v3) = v6))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_inverse_image(v0, v2) = v3) | ~ (apply(v0, v4) = v5) | ? [v6] : ((v6 = 0 & in(v4, v3) = 0) | ( ~ (v6 = 0) & in(v5, v2) = v6) | ( ~ (v6 = 0) & in(v4, v1) = v6))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_inverse_image(v0, v2) = v3) | ~ (in(v4, v1) = v5) | ? [v6] : ? [v7] : ((v7 = 0 & v5 = 0 & apply(v0, v4) = v6 & in(v6, v2) = 0) | ( ~ (v6 = 0) & in(v4, v3) = v6))) & ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_inverse_image(v0, v2) = v3) | ~ (in(v4, v3) = 0) | ? [v5] : (apply(v0, v4) = v5 & in(v5, v2) = 0 & in(v4, v1) = 0)) & ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_inverse_image(v0, v2) = v3) | ~ (in(v4, v1) = 0) | ? [v5] : ? [v6] : ((v5 = 0 & in(v4, v3) = 0) | ( ~ (v6 = 0) & apply(v0, v4) = v5 & in(v5, v2) = v6))) & ? [v2] : ! [v3] : ! [v4] : (v4 = v2 | ~ (relation_inverse_image(v0, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (((v9 = 0 & v7 = 0 & apply(v0, v5) = v8 & in(v8, v3) = 0 & in(v5, v1) = 0) | (v6 = 0 & in(v5, v2) = 0)) & (( ~ (v9 = 0) & apply(v0, v5) = v8 & in(v8, v3) = v9) | ( ~ (v7 = 0) & in(v5, v1) = v7) | ( ~ (v6 = 0) & in(v5, v2) = v6))))))) & ! [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] : ( ~ (function(v0) = 0) | ? [v1] : (( ~ (v1 = 0) & relation(v0) = v1) | (relation_dom(v0) = v1 & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (relation_inverse_image(v0, v2) = v3) | ~ (in(v4, v3) = v5) | ? [v6] : ? [v7] : (( ~ (v7 = 0) & apply(v0, v4) = v6 & in(v6, v2) = v7) | ( ~ (v6 = 0) & in(v4, v1) = v6))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_inverse_image(v0, v2) = v3) | ~ (apply(v0, v4) = v5) | ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & in(v5, v2) = 0 & in(v4, v1) = 0) | ( ~ (v6 = 0) & in(v4, v3) = v6))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_inverse_image(v0, v2) = v3) | ~ (apply(v0, v4) = v5) | ? [v6] : ((v6 = 0 & in(v4, v3) = 0) | ( ~ (v6 = 0) & in(v5, v2) = v6) | ( ~ (v6 = 0) & in(v4, v1) = v6))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_inverse_image(v0, v2) = v3) | ~ (in(v4, v1) = v5) | ? [v6] : ? [v7] : ((v7 = 0 & v5 = 0 & apply(v0, v4) = v6 & in(v6, v2) = 0) | ( ~ (v6 = 0) & in(v4, v3) = v6))) & ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_inverse_image(v0, v2) = v3) | ~ (in(v4, v3) = 0) | ? [v5] : (apply(v0, v4) = v5 & in(v5, v2) = 0 & in(v4, v1) = 0)) & ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_inverse_image(v0, v2) = v3) | ~ (in(v4, v1) = 0) | ? [v5] : ? [v6] : ((v5 = 0 & in(v4, v3) = 0) | ( ~ (v6 = 0) & apply(v0, v4) = v5 & in(v5, v2) = v6))) & ? [v2] : ! [v3] : ! [v4] : (v4 = v2 | ~ (relation_inverse_image(v0, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (((v9 = 0 & v7 = 0 & apply(v0, v5) = v8 & in(v8, v3) = 0 & in(v5, v1) = 0) | (v6 = 0 & in(v5, v2) = 0)) & (( ~ (v9 = 0) & apply(v0, v5) = v8 & in(v8, v3) = v9) | ( ~ (v7 = 0) & in(v5, v1) = v7) | ( ~ (v6 = 0) & in(v5, v2) = v6))))))) & ! [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] : subset(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] : relation_inverse_image(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : apply(v1, v0) = v2 & ? [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 & ((all_0_12_12 = 0 & all_0_14_14 = 0 & ~ (all_0_15_15 = 0) & apply(all_0_18_18, all_0_16_16) = all_0_13_13 & in(all_0_13_13, all_0_19_19) = 0 & in(all_0_16_16, all_0_21_21) = 0) | (all_0_15_15 = 0 & (( ~ (all_0_12_12 = 0) & apply(all_0_18_18, all_0_16_16) = all_0_13_13 & in(all_0_13_13, all_0_19_19) = all_0_12_12) | ( ~ (all_0_14_14 = 0) & in(all_0_16_16, all_0_21_21) = all_0_14_14))))
% 148.98/119.47 |
% 148.98/119.47 | Applying alpha-rule on (1) yields:
% 148.98/119.47 | (2) function(all_0_1_1) = 0
% 148.98/119.47 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (relation_of2(v4, v3, v2) = v1) | ~ (relation_of2(v4, v3, v2) = v0))
% 148.98/119.47 | (4) ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2
% 148.98/119.47 | (5) ? [v0] : ? [v1] : one_to_one(v0) = v1
% 148.98/119.47 | (6) ! [v0] : ! [v1] : ! [v2] : ( ~ (empty(v2) = 0) | ~ (in(v0, v1) = 0) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v2) = v3 & element(v1, v3) = v4))
% 148.98/119.47 | (7) ! [v0] : ( ~ (empty(v0) = 0) | ? [v1] : (relation_dom(v0) = v1 & relation(v1) = 0 & empty(v1) = 0))
% 148.98/119.47 | (8) ? [v0] : ? [v1] : ? [v2] : ? [v3] : quasi_total(v2, v1, v0) = v3
% 148.98/119.47 | (9) ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2
% 148.98/119.47 | (10) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ((v2 = 0 & empty(v0) = 0) | ( ~ (v2 = 0) & relation(v0) = v2) | ( ~ (v2 = 0) & empty(v1) = v2)))
% 148.98/119.47 | (11) ? [v0] : ? [v1] : ? [v2] : relation_of2_as_subset(v2, v0, v1) = 0
% 148.98/119.47 | (12) empty(all_0_1_1) = 0
% 148.98/119.47 | (13) function(all_0_11_11) = 0
% 148.98/119.47 | (14) relation(all_0_0_0) = 0
% 148.98/119.47 | (15) ! [v0] : ( ~ (empty(v0) = 0) | relation(v0) = 0)
% 148.98/119.47 | (16) relation(empty_set) = 0
% 148.98/119.47 | (17) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0))
% 148.98/119.47 | (18) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0))
% 148.98/119.47 | (19) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0))
% 148.98/119.47 | (20) ! [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)))))))
% 148.98/119.47 | (21) ? [v0] : ? [v1] : ? [v2] : element(v1, v0) = v2
% 148.98/119.47 | (22) empty(all_0_4_4) = 0
% 148.98/119.47 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | element(v0, v2) = 0)
% 148.98/119.47 | (24) (all_0_12_12 = 0 & all_0_14_14 = 0 & ~ (all_0_15_15 = 0) & apply(all_0_18_18, all_0_16_16) = all_0_13_13 & in(all_0_13_13, all_0_19_19) = 0 & in(all_0_16_16, all_0_21_21) = 0) | (all_0_15_15 = 0 & (( ~ (all_0_12_12 = 0) & apply(all_0_18_18, all_0_16_16) = all_0_13_13 & in(all_0_13_13, all_0_19_19) = all_0_12_12) | ( ~ (all_0_14_14 = 0) & in(all_0_16_16, all_0_21_21) = all_0_14_14)))
% 148.98/119.47 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 148.98/119.47 | (26) ! [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))
% 148.98/119.47 | (27) ? [v0] : ? [v1] : ? [v2] : cartesian_product2(v1, v0) = v2
% 148.98/119.47 | (28) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0))
% 148.98/119.47 | (29) ! [v0] : ! [v1] : ! [v2] : ( ~ (cartesian_product2(v0, v1) = v2) | ? [v3] : ((v3 = 0 & empty(v1) = 0) | (v3 = 0 & empty(v0) = 0) | ( ~ (v3 = 0) & empty(v2) = v3)))
% 148.98/119.47 | (30) ! [v0] : ( ~ (empty(v0) = 0) | function(v0) = 0)
% 148.98/119.47 | (31) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (powerset(v1) = v2 & element(v0, v2) = 0))
% 148.98/119.47 | (32) empty(all_0_6_6) = all_0_5_5
% 148.98/119.47 | (33) ! [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))
% 148.98/119.47 | (34) ? [v0] : ? [v1] : ? [v2] : relation_inverse_image(v1, v0) = v2
% 148.98/119.47 | (35) ? [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v0 | ~ (relation_dom(v1) = v2) | ~ (relation_inverse_image(v1, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (( ~ (v5 = 0) & relation(v1) = v5) | ( ~ (v5 = 0) & function(v1) = v5) | (((v9 = 0 & v7 = 0 & apply(v1, v5) = v8 & in(v8, v3) = 0 & in(v5, v2) = 0) | (v6 = 0 & in(v5, v0) = 0)) & (( ~ (v9 = 0) & apply(v1, v5) = v8 & in(v8, v3) = v9) | ( ~ (v7 = 0) & in(v5, v2) = v7) | ( ~ (v6 = 0) & in(v5, v0) = v6)))))
% 148.98/119.47 | (36) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v0, v1) = v2) | ? [v3] : ((v3 = 0 & empty(v1) = 0) | ( ~ (v3 = 0) & element(v0, v1) = v3)))
% 148.98/119.48 | (37) relation(all_0_2_2) = 0
% 148.98/119.48 | (38) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_of2(v2, v0, v1) = 0) | ? [v3] : (relation_dom_as_subset(v0, v1, v2) = v3 & relation_dom(v2) = v3))
% 148.98/119.48 | (39) relation(all_0_11_11) = 0
% 148.98/119.48 | (40) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1))
% 148.98/119.48 | (41) function(all_0_9_9) = 0
% 148.98/119.48 | (42) ! [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)))
% 148.98/119.48 | (43) ! [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)))))
% 148.98/119.48 | (44) relation(all_0_9_9) = 0
% 148.98/119.48 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v0) = v1) | ~ (relation_inverse_image(v0, v2) = v3) | ~ (in(v4, v1) = 0) | ? [v5] : ? [v6] : ((v5 = 0 & in(v4, v3) = 0) | ( ~ (v6 = 0) & apply(v0, v4) = v5 & in(v5, v2) = v6) | ( ~ (v5 = 0) & relation(v0) = v5) | ( ~ (v5 = 0) & function(v0) = v5)))
% 148.98/119.48 | (46) ! [v0] : ! [v1] : (v1 = 0 | ~ (function(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2))
% 148.98/119.48 | (47) ? [v0] : ? [v1] : element(v1, v0) = 0
% 148.98/119.48 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (relation_dom(v0) = v1) | ~ (relation_inverse_image(v0, v2) = v3) | ~ (in(v4, v3) = v5) | ? [v6] : ? [v7] : (( ~ (v7 = 0) & apply(v0, v4) = v6 & in(v6, v2) = v7) | ( ~ (v6 = 0) & relation(v0) = v6) | ( ~ (v6 = 0) & function(v0) = v6) | ( ~ (v6 = 0) & in(v4, v1) = v6)))
% 148.98/119.48 | (49) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) = 0 & empty(v2) = 0))
% 148.98/119.48 | (50) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ((v1 = 0 & empty(v0) = 0) | ( ~ (v2 = 0) & relation_dom(v0) = v1 & empty(v1) = v2)))
% 148.98/119.48 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (relation_dom_as_subset(v4, v3, v2) = v1) | ~ (relation_dom_as_subset(v4, v3, v2) = v0))
% 148.98/119.48 | (52) ! [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))
% 148.98/119.48 | (53) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | element(v0, v1) = 0)
% 148.98/119.48 | (54) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | subset(v0, v1) = 0)
% 148.98/119.48 | (55) ? [v0] : ? [v1] : ? [v2] : (relation_of2(v2, v0, v1) = 0 & quasi_total(v2, v0, v1) = 0 & relation(v2) = 0 & function(v2) = 0)
% 148.98/119.48 | (56) ! [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))
% 148.98/119.48 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 148.98/119.48 | (58) ! [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))
% 148.98/119.48 | (59) function(all_0_0_0) = 0
% 148.98/119.48 | (60) ? [v0] : ? [v1] : ? [v2] : relation_of2(v2, v0, v1) = 0
% 148.98/119.48 | (61) relation(all_0_10_10) = 0
% 148.98/119.48 | (62) ? [v0] : ? [v1] : ? [v2] : apply(v1, v0) = v2
% 148.98/119.48 | (63) function(all_0_4_4) = 0
% 148.98/119.48 | (64) ! [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)))
% 148.98/119.48 | (65) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4))
% 148.98/119.48 | (66) ? [v0] : ? [v1] : function(v0) = v1
% 148.98/119.48 | (67) ~ (all_0_20_20 = empty_set)
% 148.98/119.48 | (68) ! [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))))))
% 148.98/119.48 | (69) ! [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))
% 148.98/119.48 | (70) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & relation(v1) = 0 & empty(v1) = 0) | ( ~ (v2 = 0) & empty(v0) = v2)))
% 148.98/119.48 | (71) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0))
% 148.98/119.48 | (72) ! [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)))))
% 149.38/119.48 | (73) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_dom(v0) = v1) | ~ (relation_inverse_image(v0, v2) = v3) | ~ (apply(v0, v4) = v5) | ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & in(v5, v2) = 0 & in(v4, v1) = 0) | ( ~ (v6 = 0) & relation(v0) = v6) | ( ~ (v6 = 0) & function(v0) = v6) | ( ~ (v6 = 0) & in(v4, v3) = v6)))
% 149.38/119.48 | (74) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (relation_of2_as_subset(v2, v0, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & relation_of2(v2, v0, v1) = v4))
% 149.38/119.49 | (75) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (relation_of2(v2, v0, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & relation_of2_as_subset(v2, v0, v1) = v4))
% 149.38/119.49 | (76) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0))
% 149.38/119.49 | (77) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 149.38/119.49 | (78) in(all_0_16_16, all_0_17_17) = all_0_15_15
% 149.38/119.49 | (79) ! [v0] : ( ~ (function(v0) = 0) | ? [v1] : (( ~ (v1 = 0) & relation(v0) = v1) | (relation_dom(v0) = v1 & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (relation_inverse_image(v0, v2) = v3) | ~ (in(v4, v3) = v5) | ? [v6] : ? [v7] : (( ~ (v7 = 0) & apply(v0, v4) = v6 & in(v6, v2) = v7) | ( ~ (v6 = 0) & in(v4, v1) = v6))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_inverse_image(v0, v2) = v3) | ~ (apply(v0, v4) = v5) | ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & in(v5, v2) = 0 & in(v4, v1) = 0) | ( ~ (v6 = 0) & in(v4, v3) = v6))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_inverse_image(v0, v2) = v3) | ~ (apply(v0, v4) = v5) | ? [v6] : ((v6 = 0 & in(v4, v3) = 0) | ( ~ (v6 = 0) & in(v5, v2) = v6) | ( ~ (v6 = 0) & in(v4, v1) = v6))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_inverse_image(v0, v2) = v3) | ~ (in(v4, v1) = v5) | ? [v6] : ? [v7] : ((v7 = 0 & v5 = 0 & apply(v0, v4) = v6 & in(v6, v2) = 0) | ( ~ (v6 = 0) & in(v4, v3) = v6))) & ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_inverse_image(v0, v2) = v3) | ~ (in(v4, v3) = 0) | ? [v5] : (apply(v0, v4) = v5 & in(v5, v2) = 0 & in(v4, v1) = 0)) & ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_inverse_image(v0, v2) = v3) | ~ (in(v4, v1) = 0) | ? [v5] : ? [v6] : ((v5 = 0 & in(v4, v3) = 0) | ( ~ (v6 = 0) & apply(v0, v4) = v5 & in(v5, v2) = v6))) & ? [v2] : ! [v3] : ! [v4] : (v4 = v2 | ~ (relation_inverse_image(v0, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (((v9 = 0 & v7 = 0 & apply(v0, v5) = v8 & in(v8, v3) = 0 & in(v5, v1) = 0) | (v6 = 0 & in(v5, v2) = 0)) & (( ~ (v9 = 0) & apply(v0, v5) = v8 & in(v8, v3) = v9) | ( ~ (v7 = 0) & in(v5, v1) = v7) | ( ~ (v6 = 0) & in(v5, v2) = v6)))))))
% 149.38/119.49 | (80) relation_empty_yielding(empty_set) = 0
% 149.38/119.49 | (81) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 149.38/119.49 | (82) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (relation_of2_as_subset(v4, v3, v2) = v1) | ~ (relation_of2_as_subset(v4, v3, v2) = v0))
% 149.38/119.49 | (83) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0))
% 149.38/119.49 | (84) ! [v0] : ! [v1] : (v1 = 0 | ~ (relation(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2))
% 149.38/119.49 | (85) ! [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)))
% 149.38/119.49 | (86) relation(all_0_1_1) = 0
% 149.38/119.49 | (87) ! [v0] : ! [v1] : (v1 = 0 | ~ (empty(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v0) = v2 & element(v3, v2) = 0 & empty(v3) = v4))
% 149.38/119.49 | (88) quasi_total(all_0_18_18, all_0_21_21, all_0_20_20) = 0
% 149.38/119.49 | (89) ? [v0] : ? [v1] : ? [v2] : ? [v3] : relation_of2(v2, v1, v0) = v3
% 149.38/119.49 | (90) ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2))
% 149.38/119.49 | (91) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_empty_yielding(v2) = v1) | ~ (relation_empty_yielding(v2) = v0))
% 149.38/119.49 | (92) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_of2_as_subset(v2, v0, v1) = 0) | relation_of2(v2, v0, v1) = 0)
% 149.41/119.49 | (93) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_of2(v2, v0, v1) = 0) | relation_of2_as_subset(v2, v0, v1) = 0)
% 149.41/119.49 | (94) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v0, v1) = v3) | ~ (powerset(v3) = v4) | ~ (element(v2, v4) = 0) | relation(v2) = 0)
% 149.41/119.49 | (95) ! [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))
% 149.41/119.49 | (96) ! [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)))
% 149.41/119.49 | (97) ? [v0] : ? [v1] : powerset(v0) = v1
% 149.41/119.49 | (98) empty(empty_set) = 0
% 149.41/119.49 | (99) empty(all_0_3_3) = 0
% 149.41/119.49 | (100) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v3 = 0 & ~ (v4 = 0) & element(v2, v1) = 0 & empty(v2) = v4) | (v2 = 0 & empty(v0) = 0)))
% 149.41/119.49 | (101) one_to_one(all_0_9_9) = 0
% 149.41/119.49 | (102) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 149.41/119.49 | (103) ? [v0] : ? [v1] : relation_empty_yielding(v0) = v1
% 149.41/119.49 | (104) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0))
% 149.41/119.49 | (105) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_dom(v0) = v1) | ~ (relation_inverse_image(v0, v2) = v3) | ~ (in(v4, v1) = v5) | ? [v6] : ? [v7] : ((v7 = 0 & v5 = 0 & apply(v0, v4) = v6 & in(v6, v2) = 0) | ( ~ (v6 = 0) & relation(v0) = v6) | ( ~ (v6 = 0) & function(v0) = v6) | ( ~ (v6 = 0) & in(v4, v3) = v6)))
% 149.41/119.49 | (106) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3))
% 149.41/119.49 | (107) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v1) = v3 & element(v0, v3) = v4))
% 149.41/119.49 | (108) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_dom(v0) = v1) | ~ (relation_inverse_image(v0, v2) = v3) | ~ (apply(v0, v4) = v5) | ? [v6] : ((v6 = 0 & in(v4, v3) = 0) | ( ~ (v6 = 0) & relation(v0) = v6) | ( ~ (v6 = 0) & function(v0) = v6) | ( ~ (v6 = 0) & in(v5, v2) = v6) | ( ~ (v6 = 0) & in(v4, v1) = v6)))
% 149.41/119.50 | (109) function(all_0_18_18) = 0
% 149.41/119.50 | (110) ~ (all_0_5_5 = 0)
% 149.41/119.50 | (111) relation_inverse_image(all_0_18_18, all_0_19_19) = all_0_17_17
% 149.41/119.50 | (112) ~ (all_0_7_7 = 0)
% 149.41/119.50 | (113) relation(all_0_6_6) = 0
% 149.41/119.50 | (114) relation_of2_as_subset(all_0_18_18, all_0_21_21, all_0_20_20) = 0
% 149.41/119.50 | (115) ! [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)))
% 149.41/119.50 | (116) empty(all_0_2_2) = 0
% 149.41/119.50 | (117) ? [v0] : ? [v1] : ? [v2] : (relation_of2(v2, v0, v1) = 0 & relation(v2) = 0 & function(v2) = 0)
% 149.41/119.50 | (118) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (quasi_total(v4, v3, v2) = v1) | ~ (quasi_total(v4, v3, v2) = v0))
% 149.41/119.50 | (119) relation_empty_yielding(all_0_11_11) = 0
% 149.41/119.50 | (120) ? [v0] : ? [v1] : relation(v0) = v1
% 149.41/119.50 | (121) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0))
% 149.41/119.50 | (122) ? [v0] : ? [v1] : ? [v2] : ? [v3] : relation_of2_as_subset(v2, v1, v0) = v3
% 149.41/119.50 | (123) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_inverse_image(v3, v2) = v1) | ~ (relation_inverse_image(v3, v2) = v0))
% 149.41/119.50 | (124) ! [v0] : ! [v1] : ( ~ (element(v0, v1) = 0) | ? [v2] : ((v2 = 0 & empty(v1) = 0) | (v2 = 0 & in(v0, v1) = 0)))
% 149.41/119.50 | (125) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v0) = v1) | ~ (relation_inverse_image(v0, v2) = v3) | ~ (in(v4, v3) = 0) | ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v5 = 0 & apply(v0, v4) = v6 & in(v6, v2) = 0 & in(v4, v1) = 0) | ( ~ (v5 = 0) & relation(v0) = v5) | ( ~ (v5 = 0) & function(v0) = v5)))
% 149.41/119.50 | (126) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 149.41/119.50 | (127) ? [v0] : ? [v1] : empty(v0) = v1
% 149.41/119.50 | (128) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0))
% 149.41/119.50 | (129) one_to_one(all_0_1_1) = 0
% 149.41/119.50 | (130) empty(all_0_8_8) = all_0_7_7
% 149.41/119.50 | (131) relation(all_0_4_4) = 0
% 149.41/119.50 | (132) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : (( ~ (v1 = 0) & function(v0) = v1) | (relation_dom(v0) = v1 & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (relation_inverse_image(v0, v2) = v3) | ~ (in(v4, v3) = v5) | ? [v6] : ? [v7] : (( ~ (v7 = 0) & apply(v0, v4) = v6 & in(v6, v2) = v7) | ( ~ (v6 = 0) & in(v4, v1) = v6))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_inverse_image(v0, v2) = v3) | ~ (apply(v0, v4) = v5) | ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & in(v5, v2) = 0 & in(v4, v1) = 0) | ( ~ (v6 = 0) & in(v4, v3) = v6))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_inverse_image(v0, v2) = v3) | ~ (apply(v0, v4) = v5) | ? [v6] : ((v6 = 0 & in(v4, v3) = 0) | ( ~ (v6 = 0) & in(v5, v2) = v6) | ( ~ (v6 = 0) & in(v4, v1) = v6))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_inverse_image(v0, v2) = v3) | ~ (in(v4, v1) = v5) | ? [v6] : ? [v7] : ((v7 = 0 & v5 = 0 & apply(v0, v4) = v6 & in(v6, v2) = 0) | ( ~ (v6 = 0) & in(v4, v3) = v6))) & ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_inverse_image(v0, v2) = v3) | ~ (in(v4, v3) = 0) | ? [v5] : (apply(v0, v4) = v5 & in(v5, v2) = 0 & in(v4, v1) = 0)) & ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_inverse_image(v0, v2) = v3) | ~ (in(v4, v1) = 0) | ? [v5] : ? [v6] : ((v5 = 0 & in(v4, v3) = 0) | ( ~ (v6 = 0) & apply(v0, v4) = v5 & in(v5, v2) = v6))) & ? [v2] : ! [v3] : ! [v4] : (v4 = v2 | ~ (relation_inverse_image(v0, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (((v9 = 0 & v7 = 0 & apply(v0, v5) = v8 & in(v8, v3) = 0 & in(v5, v1) = 0) | (v6 = 0 & in(v5, v2) = 0)) & (( ~ (v9 = 0) & apply(v0, v5) = v8 & in(v8, v3) = v9) | ( ~ (v7 = 0) & in(v5, v1) = v7) | ( ~ (v6 = 0) & in(v5, v2) = v6)))))))
% 149.41/119.50 | (133) ! [v0] : ! [v1] : (v1 = 0 | ~ (empty(v0) = v1) | ? [v2] : ? [v3] : (( ~ (v3 = 0) & relation_dom(v0) = v2 & empty(v2) = v3) | ( ~ (v2 = 0) & relation(v0) = v2)))
% 149.41/119.50 | (134) relation_empty_yielding(all_0_10_10) = 0
% 149.41/119.50 | (135) ! [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)))
% 149.41/119.50 | (136) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 149.41/119.50 | (137) ? [v0] : ? [v1] : ? [v2] : ? [v3] : relation_dom_as_subset(v2, v1, v0) = v3
% 149.47/119.50 | (138) ? [v0] : ? [v1] : relation_dom(v0) = v1
% 149.47/119.50 |
% 149.47/119.50 | Instantiating formula (92) with all_0_18_18, all_0_20_20, all_0_21_21 and discharging atoms relation_of2_as_subset(all_0_18_18, all_0_21_21, all_0_20_20) = 0, yields:
% 149.47/119.50 | (139) relation_of2(all_0_18_18, all_0_21_21, all_0_20_20) = 0
% 149.47/119.50 |
% 149.47/119.50 | Instantiating formula (95) with all_0_18_18, all_0_20_20, all_0_21_21 and discharging atoms relation_of2_as_subset(all_0_18_18, all_0_21_21, all_0_20_20) = 0, yields:
% 149.47/119.50 | (140) ? [v0] : ? [v1] : (cartesian_product2(all_0_21_21, all_0_20_20) = v0 & powerset(v0) = v1 & element(all_0_18_18, v1) = 0)
% 149.47/119.50 |
% 149.47/119.50 | Instantiating formula (68) with all_0_18_18, all_0_20_20, all_0_21_21 and discharging atoms relation_of2_as_subset(all_0_18_18, all_0_21_21, all_0_20_20) = 0, yields:
% 149.47/119.50 | (141) ? [v0] : ? [v1] : (( ~ (all_0_20_20 = empty_set) | all_0_21_21 = empty_set | (( ~ (all_0_18_18 = empty_set) | (v0 = 0 & quasi_total(empty_set, all_0_21_21, empty_set) = 0)) & (all_0_18_18 = empty_set | ( ~ (v0 = 0) & quasi_total(all_0_18_18, all_0_21_21, empty_set) = v0)))) & ((all_0_20_20 = empty_set & ~ (all_0_21_21 = empty_set)) | (((v1 = all_0_21_21 & relation_dom_as_subset(all_0_21_21, all_0_20_20, all_0_18_18) = all_0_21_21) | ( ~ (v0 = 0) & quasi_total(all_0_18_18, all_0_21_21, all_0_20_20) = v0)) & ((v0 = 0 & quasi_total(all_0_18_18, all_0_21_21, all_0_20_20) = 0) | ( ~ (v1 = all_0_21_21) & relation_dom_as_subset(all_0_21_21, all_0_20_20, all_0_18_18) = v1)))))
% 149.47/119.51 |
% 149.47/119.51 | Instantiating formula (43) with 0, all_0_18_18, all_0_20_20, all_0_21_21 and discharging atoms quasi_total(all_0_18_18, all_0_21_21, all_0_20_20) = 0, yields:
% 149.47/119.51 | (142) all_0_20_20 = empty_set | ? [v0] : ((v0 = all_0_21_21 & relation_dom_as_subset(all_0_21_21, all_0_20_20, all_0_18_18) = all_0_21_21) | ( ~ (v0 = 0) & relation_of2_as_subset(all_0_18_18, all_0_21_21, all_0_20_20) = v0))
% 149.47/119.51 |
% 149.47/119.51 | Instantiating formula (79) with all_0_18_18 and discharging atoms function(all_0_18_18) = 0, yields:
% 149.47/119.51 | (143) ? [v0] : (( ~ (v0 = 0) & relation(all_0_18_18) = v0) | (relation_dom(all_0_18_18) = v0 & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (relation_inverse_image(all_0_18_18, v1) = v2) | ~ (in(v3, v2) = v4) | ? [v5] : ? [v6] : (( ~ (v6 = 0) & apply(all_0_18_18, v3) = v5 & in(v5, v1) = v6) | ( ~ (v5 = 0) & in(v3, v0) = v5))) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_inverse_image(all_0_18_18, v1) = v2) | ~ (apply(all_0_18_18, v3) = v4) | ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & in(v4, v1) = 0 & in(v3, v0) = 0) | ( ~ (v5 = 0) & in(v3, v2) = v5))) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_inverse_image(all_0_18_18, v1) = v2) | ~ (apply(all_0_18_18, v3) = v4) | ? [v5] : ((v5 = 0 & in(v3, v2) = 0) | ( ~ (v5 = 0) & in(v4, v1) = v5) | ( ~ (v5 = 0) & in(v3, v0) = v5))) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_inverse_image(all_0_18_18, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : ((v6 = 0 & v4 = 0 & apply(all_0_18_18, v3) = v5 & in(v5, v1) = 0) | ( ~ (v5 = 0) & in(v3, v2) = v5))) & ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_inverse_image(all_0_18_18, v1) = v2) | ~ (in(v3, v2) = 0) | ? [v4] : (apply(all_0_18_18, v3) = v4 & in(v4, v1) = 0 & in(v3, v0) = 0)) & ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_inverse_image(all_0_18_18, v1) = v2) | ~ (in(v3, v0) = 0) | ? [v4] : ? [v5] : ((v4 = 0 & in(v3, v2) = 0) | ( ~ (v5 = 0) & apply(all_0_18_18, v3) = v4 & in(v4, v1) = v5))) & ? [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (relation_inverse_image(all_0_18_18, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (((v8 = 0 & v6 = 0 & apply(all_0_18_18, v4) = v7 & in(v7, v2) = 0 & in(v4, v0) = 0) | (v5 = 0 & in(v4, v1) = 0)) & (( ~ (v8 = 0) & apply(all_0_18_18, v4) = v7 & in(v7, v2) = v8) | ( ~ (v6 = 0) & in(v4, v0) = v6) | ( ~ (v5 = 0) & in(v4, v1) = v5))))))
% 149.47/119.51 |
% 149.47/119.51 | Instantiating (141) with all_96_0_139, all_96_1_140 yields:
% 149.47/119.51 | (144) ( ~ (all_0_20_20 = empty_set) | all_0_21_21 = empty_set | (( ~ (all_0_18_18 = empty_set) | (all_96_1_140 = 0 & quasi_total(empty_set, all_0_21_21, empty_set) = 0)) & (all_0_18_18 = empty_set | ( ~ (all_96_1_140 = 0) & quasi_total(all_0_18_18, all_0_21_21, empty_set) = all_96_1_140)))) & ((all_0_20_20 = empty_set & ~ (all_0_21_21 = empty_set)) | (((all_96_0_139 = all_0_21_21 & relation_dom_as_subset(all_0_21_21, all_0_20_20, all_0_18_18) = all_0_21_21) | ( ~ (all_96_1_140 = 0) & quasi_total(all_0_18_18, all_0_21_21, all_0_20_20) = all_96_1_140)) & ((all_96_1_140 = 0 & quasi_total(all_0_18_18, all_0_21_21, all_0_20_20) = 0) | ( ~ (all_96_0_139 = all_0_21_21) & relation_dom_as_subset(all_0_21_21, all_0_20_20, all_0_18_18) = all_96_0_139))))
% 149.47/119.51 |
% 149.47/119.51 | Applying alpha-rule on (144) yields:
% 149.47/119.51 | (145) ~ (all_0_20_20 = empty_set) | all_0_21_21 = empty_set | (( ~ (all_0_18_18 = empty_set) | (all_96_1_140 = 0 & quasi_total(empty_set, all_0_21_21, empty_set) = 0)) & (all_0_18_18 = empty_set | ( ~ (all_96_1_140 = 0) & quasi_total(all_0_18_18, all_0_21_21, empty_set) = all_96_1_140)))
% 149.50/119.51 | (146) (all_0_20_20 = empty_set & ~ (all_0_21_21 = empty_set)) | (((all_96_0_139 = all_0_21_21 & relation_dom_as_subset(all_0_21_21, all_0_20_20, all_0_18_18) = all_0_21_21) | ( ~ (all_96_1_140 = 0) & quasi_total(all_0_18_18, all_0_21_21, all_0_20_20) = all_96_1_140)) & ((all_96_1_140 = 0 & quasi_total(all_0_18_18, all_0_21_21, all_0_20_20) = 0) | ( ~ (all_96_0_139 = all_0_21_21) & relation_dom_as_subset(all_0_21_21, all_0_20_20, all_0_18_18) = all_96_0_139)))
% 149.50/119.51 |
% 149.50/119.51 | Instantiating (140) with all_99_0_142, all_99_1_143 yields:
% 149.50/119.51 | (147) cartesian_product2(all_0_21_21, all_0_20_20) = all_99_1_143 & powerset(all_99_1_143) = all_99_0_142 & element(all_0_18_18, all_99_0_142) = 0
% 149.50/119.51 |
% 149.50/119.51 | Applying alpha-rule on (147) yields:
% 149.50/119.51 | (148) cartesian_product2(all_0_21_21, all_0_20_20) = all_99_1_143
% 149.50/119.51 | (149) powerset(all_99_1_143) = all_99_0_142
% 149.50/119.51 | (150) element(all_0_18_18, all_99_0_142) = 0
% 149.50/119.51 |
% 149.50/119.51 | Instantiating (143) with all_101_0_144 yields:
% 149.50/119.51 | (151) ( ~ (all_101_0_144 = 0) & relation(all_0_18_18) = all_101_0_144) | (relation_dom(all_0_18_18) = all_101_0_144 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (relation_inverse_image(all_0_18_18, v0) = v1) | ~ (in(v2, v1) = v3) | ? [v4] : ? [v5] : (( ~ (v5 = 0) & apply(all_0_18_18, v2) = v4 & in(v4, v0) = v5) | ( ~ (v4 = 0) & in(v2, all_101_0_144) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_inverse_image(all_0_18_18, v0) = v1) | ~ (apply(all_0_18_18, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & in(v3, v0) = 0 & in(v2, all_101_0_144) = 0) | ( ~ (v4 = 0) & in(v2, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_inverse_image(all_0_18_18, v0) = v1) | ~ (apply(all_0_18_18, v2) = v3) | ? [v4] : ((v4 = 0 & in(v2, v1) = 0) | ( ~ (v4 = 0) & in(v3, v0) = v4) | ( ~ (v4 = 0) & in(v2, all_101_0_144) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_inverse_image(all_0_18_18, v0) = v1) | ~ (in(v2, all_101_0_144) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v3 = 0 & apply(all_0_18_18, v2) = v4 & in(v4, v0) = 0) | ( ~ (v4 = 0) & in(v2, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_inverse_image(all_0_18_18, v0) = v1) | ~ (in(v2, v1) = 0) | ? [v3] : (apply(all_0_18_18, v2) = v3 & in(v3, v0) = 0 & in(v2, all_101_0_144) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_inverse_image(all_0_18_18, v0) = v1) | ~ (in(v2, all_101_0_144) = 0) | ? [v3] : ? [v4] : ((v3 = 0 & in(v2, v1) = 0) | ( ~ (v4 = 0) & apply(all_0_18_18, v2) = v3 & in(v3, v0) = v4))) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_inverse_image(all_0_18_18, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (((v7 = 0 & v5 = 0 & apply(all_0_18_18, v3) = v6 & in(v6, v1) = 0 & in(v3, all_101_0_144) = 0) | (v4 = 0 & in(v3, v0) = 0)) & (( ~ (v7 = 0) & apply(all_0_18_18, v3) = v6 & in(v6, v1) = v7) | ( ~ (v5 = 0) & in(v3, all_101_0_144) = v5) | ( ~ (v4 = 0) & in(v3, v0) = v4)))))
% 149.50/119.51 |
% 149.50/119.51 +-Applying beta-rule and splitting (142), into two cases.
% 149.50/119.51 |-Branch one:
% 149.50/119.51 | (152) all_0_20_20 = empty_set
% 149.50/119.51 |
% 149.50/119.51 | Equations (152) can reduce 67 to:
% 149.50/119.51 | (153) $false
% 149.50/119.51 |
% 149.50/119.51 |-The branch is then unsatisfiable
% 149.50/119.51 |-Branch two:
% 149.50/119.51 | (67) ~ (all_0_20_20 = empty_set)
% 149.50/119.51 | (155) ? [v0] : ((v0 = all_0_21_21 & relation_dom_as_subset(all_0_21_21, all_0_20_20, all_0_18_18) = all_0_21_21) | ( ~ (v0 = 0) & relation_of2_as_subset(all_0_18_18, all_0_21_21, all_0_20_20) = v0))
% 149.50/119.51 |
% 149.50/119.51 +-Applying beta-rule and splitting (146), into two cases.
% 149.50/119.51 |-Branch one:
% 149.50/119.51 | (156) all_0_20_20 = empty_set & ~ (all_0_21_21 = empty_set)
% 149.50/119.51 |
% 149.50/119.51 | Applying alpha-rule on (156) yields:
% 149.50/119.51 | (152) all_0_20_20 = empty_set
% 149.50/119.51 | (158) ~ (all_0_21_21 = empty_set)
% 149.50/119.51 |
% 149.50/119.51 | Equations (152) can reduce 67 to:
% 149.50/119.51 | (153) $false
% 149.50/119.51 |
% 149.50/119.51 |-The branch is then unsatisfiable
% 149.50/119.51 |-Branch two:
% 149.50/119.51 | (160) ((all_96_0_139 = all_0_21_21 & relation_dom_as_subset(all_0_21_21, all_0_20_20, all_0_18_18) = all_0_21_21) | ( ~ (all_96_1_140 = 0) & quasi_total(all_0_18_18, all_0_21_21, all_0_20_20) = all_96_1_140)) & ((all_96_1_140 = 0 & quasi_total(all_0_18_18, all_0_21_21, all_0_20_20) = 0) | ( ~ (all_96_0_139 = all_0_21_21) & relation_dom_as_subset(all_0_21_21, all_0_20_20, all_0_18_18) = all_96_0_139))
% 149.50/119.51 |
% 149.50/119.51 | Applying alpha-rule on (160) yields:
% 149.50/119.51 | (161) (all_96_0_139 = all_0_21_21 & relation_dom_as_subset(all_0_21_21, all_0_20_20, all_0_18_18) = all_0_21_21) | ( ~ (all_96_1_140 = 0) & quasi_total(all_0_18_18, all_0_21_21, all_0_20_20) = all_96_1_140)
% 149.50/119.51 | (162) (all_96_1_140 = 0 & quasi_total(all_0_18_18, all_0_21_21, all_0_20_20) = 0) | ( ~ (all_96_0_139 = all_0_21_21) & relation_dom_as_subset(all_0_21_21, all_0_20_20, all_0_18_18) = all_96_0_139)
% 149.50/119.51 |
% 149.50/119.51 +-Applying beta-rule and splitting (162), into two cases.
% 149.50/119.51 |-Branch one:
% 149.50/119.51 | (163) all_96_1_140 = 0 & quasi_total(all_0_18_18, all_0_21_21, all_0_20_20) = 0
% 149.50/119.51 |
% 149.50/119.51 | Applying alpha-rule on (163) yields:
% 149.50/119.51 | (164) all_96_1_140 = 0
% 149.50/119.51 | (88) quasi_total(all_0_18_18, all_0_21_21, all_0_20_20) = 0
% 149.50/119.51 |
% 149.50/119.51 +-Applying beta-rule and splitting (161), into two cases.
% 149.50/119.51 |-Branch one:
% 149.50/119.51 | (166) all_96_0_139 = all_0_21_21 & relation_dom_as_subset(all_0_21_21, all_0_20_20, all_0_18_18) = all_0_21_21
% 149.50/119.51 |
% 149.50/119.51 | Applying alpha-rule on (166) yields:
% 149.50/119.51 | (167) all_96_0_139 = all_0_21_21
% 149.50/119.51 | (168) relation_dom_as_subset(all_0_21_21, all_0_20_20, all_0_18_18) = all_0_21_21
% 149.50/119.51 |
% 149.50/119.51 | Instantiating formula (26) with all_0_18_18, all_0_20_20, all_0_21_21 and discharging atoms relation_of2(all_0_18_18, all_0_21_21, all_0_20_20) = 0, yields:
% 149.50/119.51 | (169) ? [v0] : ? [v1] : (relation_dom_as_subset(all_0_21_21, all_0_20_20, all_0_18_18) = v0 & powerset(all_0_21_21) = v1 & element(v0, v1) = 0)
% 149.50/119.51 |
% 149.50/119.51 | Instantiating formula (38) with all_0_18_18, all_0_20_20, all_0_21_21 and discharging atoms relation_of2(all_0_18_18, all_0_21_21, all_0_20_20) = 0, yields:
% 149.50/119.51 | (170) ? [v0] : (relation_dom_as_subset(all_0_21_21, all_0_20_20, all_0_18_18) = v0 & relation_dom(all_0_18_18) = v0)
% 149.50/119.51 |
% 149.50/119.51 | Instantiating formula (94) with all_99_0_142, all_99_1_143, all_0_18_18, all_0_20_20, all_0_21_21 and discharging atoms cartesian_product2(all_0_21_21, all_0_20_20) = all_99_1_143, powerset(all_99_1_143) = all_99_0_142, element(all_0_18_18, all_99_0_142) = 0, yields:
% 149.50/119.51 | (171) relation(all_0_18_18) = 0
% 149.50/119.51 |
% 149.50/119.52 | Instantiating (170) with all_288_0_508 yields:
% 149.50/119.52 | (172) relation_dom_as_subset(all_0_21_21, all_0_20_20, all_0_18_18) = all_288_0_508 & relation_dom(all_0_18_18) = all_288_0_508
% 149.50/119.52 |
% 149.50/119.52 | Applying alpha-rule on (172) yields:
% 149.50/119.52 | (173) relation_dom_as_subset(all_0_21_21, all_0_20_20, all_0_18_18) = all_288_0_508
% 149.50/119.52 | (174) relation_dom(all_0_18_18) = all_288_0_508
% 149.50/119.52 |
% 149.50/119.52 | Instantiating (169) with all_290_0_509, all_290_1_510 yields:
% 149.50/119.52 | (175) relation_dom_as_subset(all_0_21_21, all_0_20_20, all_0_18_18) = all_290_1_510 & powerset(all_0_21_21) = all_290_0_509 & element(all_290_1_510, all_290_0_509) = 0
% 149.50/119.52 |
% 149.50/119.52 | Applying alpha-rule on (175) yields:
% 149.50/119.52 | (176) relation_dom_as_subset(all_0_21_21, all_0_20_20, all_0_18_18) = all_290_1_510
% 149.50/119.52 | (177) powerset(all_0_21_21) = all_290_0_509
% 149.50/119.52 | (178) element(all_290_1_510, all_290_0_509) = 0
% 149.50/119.52 |
% 149.50/119.52 +-Applying beta-rule and splitting (151), into two cases.
% 149.50/119.52 |-Branch one:
% 149.50/119.52 | (179) ~ (all_101_0_144 = 0) & relation(all_0_18_18) = all_101_0_144
% 149.50/119.52 |
% 149.50/119.52 | Applying alpha-rule on (179) yields:
% 149.50/119.52 | (180) ~ (all_101_0_144 = 0)
% 149.50/119.52 | (181) relation(all_0_18_18) = all_101_0_144
% 149.50/119.52 |
% 149.50/119.52 | Instantiating formula (76) with all_0_18_18, 0, all_101_0_144 and discharging atoms relation(all_0_18_18) = all_101_0_144, relation(all_0_18_18) = 0, yields:
% 149.50/119.52 | (182) all_101_0_144 = 0
% 149.50/119.52 |
% 149.50/119.52 | Equations (182) can reduce 180 to:
% 149.50/119.52 | (153) $false
% 149.50/119.52 |
% 149.50/119.52 |-The branch is then unsatisfiable
% 149.50/119.52 |-Branch two:
% 149.50/119.52 | (184) relation_dom(all_0_18_18) = all_101_0_144 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (relation_inverse_image(all_0_18_18, v0) = v1) | ~ (in(v2, v1) = v3) | ? [v4] : ? [v5] : (( ~ (v5 = 0) & apply(all_0_18_18, v2) = v4 & in(v4, v0) = v5) | ( ~ (v4 = 0) & in(v2, all_101_0_144) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_inverse_image(all_0_18_18, v0) = v1) | ~ (apply(all_0_18_18, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & in(v3, v0) = 0 & in(v2, all_101_0_144) = 0) | ( ~ (v4 = 0) & in(v2, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_inverse_image(all_0_18_18, v0) = v1) | ~ (apply(all_0_18_18, v2) = v3) | ? [v4] : ((v4 = 0 & in(v2, v1) = 0) | ( ~ (v4 = 0) & in(v3, v0) = v4) | ( ~ (v4 = 0) & in(v2, all_101_0_144) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_inverse_image(all_0_18_18, v0) = v1) | ~ (in(v2, all_101_0_144) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v3 = 0 & apply(all_0_18_18, v2) = v4 & in(v4, v0) = 0) | ( ~ (v4 = 0) & in(v2, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_inverse_image(all_0_18_18, v0) = v1) | ~ (in(v2, v1) = 0) | ? [v3] : (apply(all_0_18_18, v2) = v3 & in(v3, v0) = 0 & in(v2, all_101_0_144) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_inverse_image(all_0_18_18, v0) = v1) | ~ (in(v2, all_101_0_144) = 0) | ? [v3] : ? [v4] : ((v3 = 0 & in(v2, v1) = 0) | ( ~ (v4 = 0) & apply(all_0_18_18, v2) = v3 & in(v3, v0) = v4))) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_inverse_image(all_0_18_18, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (((v7 = 0 & v5 = 0 & apply(all_0_18_18, v3) = v6 & in(v6, v1) = 0 & in(v3, all_101_0_144) = 0) | (v4 = 0 & in(v3, v0) = 0)) & (( ~ (v7 = 0) & apply(all_0_18_18, v3) = v6 & in(v6, v1) = v7) | ( ~ (v5 = 0) & in(v3, all_101_0_144) = v5) | ( ~ (v4 = 0) & in(v3, v0) = v4))))
% 149.50/119.52 |
% 149.50/119.52 | Applying alpha-rule on (184) yields:
% 149.50/119.52 | (185) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_inverse_image(all_0_18_18, v0) = v1) | ~ (in(v2, all_101_0_144) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v3 = 0 & apply(all_0_18_18, v2) = v4 & in(v4, v0) = 0) | ( ~ (v4 = 0) & in(v2, v1) = v4)))
% 149.50/119.52 | (186) relation_dom(all_0_18_18) = all_101_0_144
% 149.50/119.52 | (187) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_inverse_image(all_0_18_18, v0) = v1) | ~ (in(v2, v1) = 0) | ? [v3] : (apply(all_0_18_18, v2) = v3 & in(v3, v0) = 0 & in(v2, all_101_0_144) = 0))
% 149.50/119.52 | (188) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_inverse_image(all_0_18_18, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (((v7 = 0 & v5 = 0 & apply(all_0_18_18, v3) = v6 & in(v6, v1) = 0 & in(v3, all_101_0_144) = 0) | (v4 = 0 & in(v3, v0) = 0)) & (( ~ (v7 = 0) & apply(all_0_18_18, v3) = v6 & in(v6, v1) = v7) | ( ~ (v5 = 0) & in(v3, all_101_0_144) = v5) | ( ~ (v4 = 0) & in(v3, v0) = v4))))
% 149.50/119.52 | (189) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_inverse_image(all_0_18_18, v0) = v1) | ~ (apply(all_0_18_18, v2) = v3) | ? [v4] : ((v4 = 0 & in(v2, v1) = 0) | ( ~ (v4 = 0) & in(v3, v0) = v4) | ( ~ (v4 = 0) & in(v2, all_101_0_144) = v4)))
% 149.50/119.52 | (190) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_inverse_image(all_0_18_18, v0) = v1) | ~ (in(v2, all_101_0_144) = 0) | ? [v3] : ? [v4] : ((v3 = 0 & in(v2, v1) = 0) | ( ~ (v4 = 0) & apply(all_0_18_18, v2) = v3 & in(v3, v0) = v4)))
% 149.50/119.52 | (191) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_inverse_image(all_0_18_18, v0) = v1) | ~ (apply(all_0_18_18, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & in(v3, v0) = 0 & in(v2, all_101_0_144) = 0) | ( ~ (v4 = 0) & in(v2, v1) = v4)))
% 149.50/119.52 | (192) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (relation_inverse_image(all_0_18_18, v0) = v1) | ~ (in(v2, v1) = v3) | ? [v4] : ? [v5] : (( ~ (v5 = 0) & apply(all_0_18_18, v2) = v4 & in(v4, v0) = v5) | ( ~ (v4 = 0) & in(v2, all_101_0_144) = v4)))
% 149.50/119.52 |
% 149.50/119.52 | Instantiating formula (192) with all_0_15_15, all_0_16_16, all_0_17_17, all_0_19_19 and discharging atoms relation_inverse_image(all_0_18_18, all_0_19_19) = all_0_17_17, in(all_0_16_16, all_0_17_17) = all_0_15_15, yields:
% 149.50/119.52 | (193) all_0_15_15 = 0 | ? [v0] : ? [v1] : (( ~ (v1 = 0) & apply(all_0_18_18, all_0_16_16) = v0 & in(v0, all_0_19_19) = v1) | ( ~ (v0 = 0) & in(all_0_16_16, all_101_0_144) = v0))
% 149.50/119.52 |
% 149.50/119.52 | Instantiating formula (51) with all_0_21_21, all_0_20_20, all_0_18_18, all_290_1_510, all_0_21_21 and discharging atoms relation_dom_as_subset(all_0_21_21, all_0_20_20, all_0_18_18) = all_290_1_510, relation_dom_as_subset(all_0_21_21, all_0_20_20, all_0_18_18) = all_0_21_21, yields:
% 149.50/119.52 | (194) all_290_1_510 = all_0_21_21
% 149.50/119.52 |
% 149.50/119.52 | Instantiating formula (51) with all_0_21_21, all_0_20_20, all_0_18_18, all_288_0_508, all_290_1_510 and discharging atoms relation_dom_as_subset(all_0_21_21, all_0_20_20, all_0_18_18) = all_290_1_510, relation_dom_as_subset(all_0_21_21, all_0_20_20, all_0_18_18) = all_288_0_508, yields:
% 149.50/119.52 | (195) all_290_1_510 = all_288_0_508
% 149.50/119.52 |
% 149.50/119.52 | Instantiating formula (71) with all_0_18_18, all_101_0_144, all_288_0_508 and discharging atoms relation_dom(all_0_18_18) = all_288_0_508, relation_dom(all_0_18_18) = all_101_0_144, yields:
% 149.50/119.52 | (196) all_288_0_508 = all_101_0_144
% 149.50/119.52 |
% 149.50/119.52 | Combining equations (195,194) yields a new equation:
% 149.50/119.52 | (197) all_288_0_508 = all_0_21_21
% 149.50/119.52 |
% 149.50/119.52 | Simplifying 197 yields:
% 149.50/119.52 | (198) all_288_0_508 = all_0_21_21
% 149.50/119.52 |
% 149.50/119.52 | Combining equations (198,196) yields a new equation:
% 149.50/119.52 | (199) all_101_0_144 = all_0_21_21
% 149.50/119.52 |
% 149.50/119.52 | From (199) and (186) follows:
% 149.50/119.52 | (200) relation_dom(all_0_18_18) = all_0_21_21
% 149.50/119.52 |
% 149.50/119.52 +-Applying beta-rule and splitting (24), into two cases.
% 149.50/119.52 |-Branch one:
% 149.50/119.52 | (201) all_0_12_12 = 0 & all_0_14_14 = 0 & ~ (all_0_15_15 = 0) & apply(all_0_18_18, all_0_16_16) = all_0_13_13 & in(all_0_13_13, all_0_19_19) = 0 & in(all_0_16_16, all_0_21_21) = 0
% 149.50/119.52 |
% 149.50/119.52 | Applying alpha-rule on (201) yields:
% 149.50/119.52 | (202) in(all_0_13_13, all_0_19_19) = 0
% 149.50/119.52 | (203) ~ (all_0_15_15 = 0)
% 149.50/119.52 | (204) apply(all_0_18_18, all_0_16_16) = all_0_13_13
% 149.50/119.52 | (205) all_0_12_12 = 0
% 149.50/119.52 | (206) all_0_14_14 = 0
% 149.50/119.52 | (207) in(all_0_16_16, all_0_21_21) = 0
% 149.50/119.52 |
% 149.50/119.52 +-Applying beta-rule and splitting (193), into two cases.
% 149.50/119.52 |-Branch one:
% 149.50/119.52 | (208) all_0_15_15 = 0
% 149.50/119.52 |
% 149.50/119.52 | Equations (208) can reduce 203 to:
% 149.50/119.52 | (153) $false
% 149.50/119.52 |
% 149.50/119.52 |-The branch is then unsatisfiable
% 149.50/119.52 |-Branch two:
% 149.50/119.52 | (203) ~ (all_0_15_15 = 0)
% 149.50/119.52 | (211) ? [v0] : ? [v1] : (( ~ (v1 = 0) & apply(all_0_18_18, all_0_16_16) = v0 & in(v0, all_0_19_19) = v1) | ( ~ (v0 = 0) & in(all_0_16_16, all_101_0_144) = v0))
% 149.50/119.52 |
% 149.50/119.52 | Instantiating (211) with all_422_0_656, all_422_1_657 yields:
% 149.50/119.52 | (212) ( ~ (all_422_0_656 = 0) & apply(all_0_18_18, all_0_16_16) = all_422_1_657 & in(all_422_1_657, all_0_19_19) = all_422_0_656) | ( ~ (all_422_1_657 = 0) & in(all_0_16_16, all_101_0_144) = all_422_1_657)
% 149.50/119.52 |
% 149.50/119.52 +-Applying beta-rule and splitting (212), into two cases.
% 149.50/119.52 |-Branch one:
% 149.50/119.52 | (213) ~ (all_422_0_656 = 0) & apply(all_0_18_18, all_0_16_16) = all_422_1_657 & in(all_422_1_657, all_0_19_19) = all_422_0_656
% 149.50/119.52 |
% 149.50/119.52 | Applying alpha-rule on (213) yields:
% 149.50/119.53 | (214) ~ (all_422_0_656 = 0)
% 149.50/119.53 | (215) apply(all_0_18_18, all_0_16_16) = all_422_1_657
% 149.50/119.53 | (216) in(all_422_1_657, all_0_19_19) = all_422_0_656
% 149.50/119.53 |
% 149.50/119.53 | Instantiating formula (121) with all_0_18_18, all_0_16_16, all_0_13_13, all_422_1_657 and discharging atoms apply(all_0_18_18, all_0_16_16) = all_422_1_657, apply(all_0_18_18, all_0_16_16) = all_0_13_13, yields:
% 149.50/119.53 | (217) all_422_1_657 = all_0_13_13
% 149.50/119.53 |
% 149.50/119.53 | From (217) and (216) follows:
% 149.50/119.53 | (218) in(all_0_13_13, all_0_19_19) = all_422_0_656
% 149.50/119.53 |
% 149.50/119.53 | Instantiating formula (77) with all_0_13_13, all_0_19_19, all_422_0_656, 0 and discharging atoms in(all_0_13_13, all_0_19_19) = all_422_0_656, in(all_0_13_13, all_0_19_19) = 0, yields:
% 149.50/119.53 | (219) all_422_0_656 = 0
% 149.50/119.53 |
% 149.50/119.53 | Equations (219) can reduce 214 to:
% 149.50/119.53 | (153) $false
% 149.50/119.53 |
% 149.50/119.53 |-The branch is then unsatisfiable
% 149.50/119.53 |-Branch two:
% 149.50/119.53 | (221) ~ (all_422_1_657 = 0) & in(all_0_16_16, all_101_0_144) = all_422_1_657
% 149.50/119.53 |
% 149.50/119.53 | Applying alpha-rule on (221) yields:
% 149.50/119.53 | (222) ~ (all_422_1_657 = 0)
% 149.50/119.53 | (223) in(all_0_16_16, all_101_0_144) = all_422_1_657
% 149.50/119.53 |
% 149.50/119.53 | From (199) and (223) follows:
% 149.50/119.53 | (224) in(all_0_16_16, all_0_21_21) = all_422_1_657
% 149.50/119.53 |
% 149.50/119.53 | Instantiating formula (77) with all_0_16_16, all_0_21_21, 0, all_422_1_657 and discharging atoms in(all_0_16_16, all_0_21_21) = all_422_1_657, in(all_0_16_16, all_0_21_21) = 0, yields:
% 149.50/119.53 | (225) all_422_1_657 = 0
% 149.50/119.53 |
% 149.50/119.53 | Equations (225) can reduce 222 to:
% 149.50/119.53 | (153) $false
% 149.50/119.53 |
% 149.50/119.53 |-The branch is then unsatisfiable
% 149.50/119.53 |-Branch two:
% 149.50/119.53 | (227) all_0_15_15 = 0 & (( ~ (all_0_12_12 = 0) & apply(all_0_18_18, all_0_16_16) = all_0_13_13 & in(all_0_13_13, all_0_19_19) = all_0_12_12) | ( ~ (all_0_14_14 = 0) & in(all_0_16_16, all_0_21_21) = all_0_14_14))
% 149.50/119.53 |
% 149.50/119.53 | Applying alpha-rule on (227) yields:
% 149.50/119.53 | (208) all_0_15_15 = 0
% 149.50/119.53 | (229) ( ~ (all_0_12_12 = 0) & apply(all_0_18_18, all_0_16_16) = all_0_13_13 & in(all_0_13_13, all_0_19_19) = all_0_12_12) | ( ~ (all_0_14_14 = 0) & in(all_0_16_16, all_0_21_21) = all_0_14_14)
% 149.50/119.53 |
% 149.50/119.53 | From (208) and (78) follows:
% 149.50/119.53 | (230) in(all_0_16_16, all_0_17_17) = 0
% 149.50/119.53 |
% 149.50/119.53 | Instantiating formula (132) with all_0_18_18 and discharging atoms relation(all_0_18_18) = 0, yields:
% 149.50/119.53 | (231) ? [v0] : (( ~ (v0 = 0) & function(all_0_18_18) = v0) | (relation_dom(all_0_18_18) = v0 & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (relation_inverse_image(all_0_18_18, v1) = v2) | ~ (in(v3, v2) = v4) | ? [v5] : ? [v6] : (( ~ (v6 = 0) & apply(all_0_18_18, v3) = v5 & in(v5, v1) = v6) | ( ~ (v5 = 0) & in(v3, v0) = v5))) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_inverse_image(all_0_18_18, v1) = v2) | ~ (apply(all_0_18_18, v3) = v4) | ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & in(v4, v1) = 0 & in(v3, v0) = 0) | ( ~ (v5 = 0) & in(v3, v2) = v5))) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_inverse_image(all_0_18_18, v1) = v2) | ~ (apply(all_0_18_18, v3) = v4) | ? [v5] : ((v5 = 0 & in(v3, v2) = 0) | ( ~ (v5 = 0) & in(v4, v1) = v5) | ( ~ (v5 = 0) & in(v3, v0) = v5))) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_inverse_image(all_0_18_18, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : ((v6 = 0 & v4 = 0 & apply(all_0_18_18, v3) = v5 & in(v5, v1) = 0) | ( ~ (v5 = 0) & in(v3, v2) = v5))) & ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_inverse_image(all_0_18_18, v1) = v2) | ~ (in(v3, v2) = 0) | ? [v4] : (apply(all_0_18_18, v3) = v4 & in(v4, v1) = 0 & in(v3, v0) = 0)) & ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_inverse_image(all_0_18_18, v1) = v2) | ~ (in(v3, v0) = 0) | ? [v4] : ? [v5] : ((v4 = 0 & in(v3, v2) = 0) | ( ~ (v5 = 0) & apply(all_0_18_18, v3) = v4 & in(v4, v1) = v5))) & ? [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (relation_inverse_image(all_0_18_18, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (((v8 = 0 & v6 = 0 & apply(all_0_18_18, v4) = v7 & in(v7, v2) = 0 & in(v4, v0) = 0) | (v5 = 0 & in(v4, v1) = 0)) & (( ~ (v8 = 0) & apply(all_0_18_18, v4) = v7 & in(v7, v2) = v8) | ( ~ (v6 = 0) & in(v4, v0) = v6) | ( ~ (v5 = 0) & in(v4, v1) = v5))))))
% 149.50/119.53 |
% 149.50/119.53 | Instantiating formula (125) with all_0_16_16, all_0_17_17, all_0_19_19, all_0_21_21, all_0_18_18 and discharging atoms relation_dom(all_0_18_18) = all_0_21_21, relation_inverse_image(all_0_18_18, all_0_19_19) = all_0_17_17, in(all_0_16_16, all_0_17_17) = 0, yields:
% 149.50/119.53 | (232) ? [v0] : ? [v1] : ? [v2] : ((v2 = 0 & v0 = 0 & apply(all_0_18_18, all_0_16_16) = v1 & in(v1, all_0_19_19) = 0 & in(all_0_16_16, all_0_21_21) = 0) | ( ~ (v0 = 0) & relation(all_0_18_18) = v0) | ( ~ (v0 = 0) & function(all_0_18_18) = v0))
% 149.50/119.53 |
% 149.50/119.53 | Instantiating formula (187) with all_0_16_16, all_0_17_17, all_0_19_19 and discharging atoms relation_inverse_image(all_0_18_18, all_0_19_19) = all_0_17_17, in(all_0_16_16, all_0_17_17) = 0, yields:
% 149.50/119.53 | (233) ? [v0] : (apply(all_0_18_18, all_0_16_16) = v0 & in(v0, all_0_19_19) = 0 & in(all_0_16_16, all_101_0_144) = 0)
% 149.50/119.53 |
% 149.50/119.53 | Instantiating (231) with all_652_0_1241 yields:
% 149.50/119.53 | (234) ( ~ (all_652_0_1241 = 0) & function(all_0_18_18) = all_652_0_1241) | (relation_dom(all_0_18_18) = all_652_0_1241 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (relation_inverse_image(all_0_18_18, v0) = v1) | ~ (in(v2, v1) = v3) | ? [v4] : ? [v5] : (( ~ (v5 = 0) & apply(all_0_18_18, v2) = v4 & in(v4, v0) = v5) | ( ~ (v4 = 0) & in(v2, all_652_0_1241) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_inverse_image(all_0_18_18, v0) = v1) | ~ (apply(all_0_18_18, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & in(v3, v0) = 0 & in(v2, all_652_0_1241) = 0) | ( ~ (v4 = 0) & in(v2, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_inverse_image(all_0_18_18, v0) = v1) | ~ (apply(all_0_18_18, v2) = v3) | ? [v4] : ((v4 = 0 & in(v2, v1) = 0) | ( ~ (v4 = 0) & in(v3, v0) = v4) | ( ~ (v4 = 0) & in(v2, all_652_0_1241) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_inverse_image(all_0_18_18, v0) = v1) | ~ (in(v2, all_652_0_1241) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v3 = 0 & apply(all_0_18_18, v2) = v4 & in(v4, v0) = 0) | ( ~ (v4 = 0) & in(v2, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_inverse_image(all_0_18_18, v0) = v1) | ~ (in(v2, v1) = 0) | ? [v3] : (apply(all_0_18_18, v2) = v3 & in(v3, v0) = 0 & in(v2, all_652_0_1241) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_inverse_image(all_0_18_18, v0) = v1) | ~ (in(v2, all_652_0_1241) = 0) | ? [v3] : ? [v4] : ((v3 = 0 & in(v2, v1) = 0) | ( ~ (v4 = 0) & apply(all_0_18_18, v2) = v3 & in(v3, v0) = v4))) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_inverse_image(all_0_18_18, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (((v7 = 0 & v5 = 0 & apply(all_0_18_18, v3) = v6 & in(v6, v1) = 0 & in(v3, all_652_0_1241) = 0) | (v4 = 0 & in(v3, v0) = 0)) & (( ~ (v7 = 0) & apply(all_0_18_18, v3) = v6 & in(v6, v1) = v7) | ( ~ (v5 = 0) & in(v3, all_652_0_1241) = v5) | ( ~ (v4 = 0) & in(v3, v0) = v4)))))
% 149.50/119.53 |
% 149.50/119.53 | Instantiating (233) with all_719_0_1313 yields:
% 149.50/119.53 | (235) apply(all_0_18_18, all_0_16_16) = all_719_0_1313 & in(all_719_0_1313, all_0_19_19) = 0 & in(all_0_16_16, all_101_0_144) = 0
% 149.50/119.53 |
% 149.50/119.53 | Applying alpha-rule on (235) yields:
% 149.50/119.53 | (236) apply(all_0_18_18, all_0_16_16) = all_719_0_1313
% 149.50/119.53 | (237) in(all_719_0_1313, all_0_19_19) = 0
% 149.50/119.53 | (238) in(all_0_16_16, all_101_0_144) = 0
% 149.50/119.53 |
% 149.50/119.53 | Instantiating (232) with all_729_0_1320, all_729_1_1321, all_729_2_1322 yields:
% 149.50/119.53 | (239) (all_729_0_1320 = 0 & all_729_2_1322 = 0 & apply(all_0_18_18, all_0_16_16) = all_729_1_1321 & in(all_729_1_1321, all_0_19_19) = 0 & in(all_0_16_16, all_0_21_21) = 0) | ( ~ (all_729_2_1322 = 0) & relation(all_0_18_18) = all_729_2_1322) | ( ~ (all_729_2_1322 = 0) & function(all_0_18_18) = all_729_2_1322)
% 149.50/119.53 |
% 149.50/119.53 | From (199) and (238) follows:
% 149.50/119.53 | (207) in(all_0_16_16, all_0_21_21) = 0
% 149.50/119.53 |
% 149.50/119.53 +-Applying beta-rule and splitting (229), into two cases.
% 149.50/119.53 |-Branch one:
% 149.50/119.53 | (241) ~ (all_0_12_12 = 0) & apply(all_0_18_18, all_0_16_16) = all_0_13_13 & in(all_0_13_13, all_0_19_19) = all_0_12_12
% 149.50/119.53 |
% 149.50/119.53 | Applying alpha-rule on (241) yields:
% 149.50/119.53 | (242) ~ (all_0_12_12 = 0)
% 149.50/119.53 | (204) apply(all_0_18_18, all_0_16_16) = all_0_13_13
% 149.50/119.53 | (244) in(all_0_13_13, all_0_19_19) = all_0_12_12
% 149.50/119.53 |
% 149.50/119.53 +-Applying beta-rule and splitting (239), into two cases.
% 149.50/119.53 |-Branch one:
% 149.50/119.53 | (245) (all_729_0_1320 = 0 & all_729_2_1322 = 0 & apply(all_0_18_18, all_0_16_16) = all_729_1_1321 & in(all_729_1_1321, all_0_19_19) = 0 & in(all_0_16_16, all_0_21_21) = 0) | ( ~ (all_729_2_1322 = 0) & relation(all_0_18_18) = all_729_2_1322)
% 149.50/119.53 |
% 149.50/119.53 +-Applying beta-rule and splitting (245), into two cases.
% 149.50/119.53 |-Branch one:
% 149.50/119.53 | (246) all_729_0_1320 = 0 & all_729_2_1322 = 0 & apply(all_0_18_18, all_0_16_16) = all_729_1_1321 & in(all_729_1_1321, all_0_19_19) = 0 & in(all_0_16_16, all_0_21_21) = 0
% 149.50/119.53 |
% 149.50/119.53 | Applying alpha-rule on (246) yields:
% 149.50/119.53 | (247) in(all_729_1_1321, all_0_19_19) = 0
% 149.50/119.53 | (248) apply(all_0_18_18, all_0_16_16) = all_729_1_1321
% 149.50/119.53 | (207) in(all_0_16_16, all_0_21_21) = 0
% 149.50/119.53 | (250) all_729_2_1322 = 0
% 149.50/119.53 | (251) all_729_0_1320 = 0
% 149.50/119.53 |
% 149.50/119.53 +-Applying beta-rule and splitting (234), into two cases.
% 149.50/119.53 |-Branch one:
% 149.50/119.53 | (252) ~ (all_652_0_1241 = 0) & function(all_0_18_18) = all_652_0_1241
% 149.50/119.53 |
% 149.50/119.53 | Applying alpha-rule on (252) yields:
% 149.50/119.53 | (253) ~ (all_652_0_1241 = 0)
% 149.50/119.53 | (254) function(all_0_18_18) = all_652_0_1241
% 149.50/119.53 |
% 149.50/119.53 | Instantiating formula (17) with all_0_18_18, all_652_0_1241, 0 and discharging atoms function(all_0_18_18) = all_652_0_1241, function(all_0_18_18) = 0, yields:
% 149.50/119.53 | (255) all_652_0_1241 = 0
% 149.50/119.53 |
% 149.50/119.53 | Equations (255) can reduce 253 to:
% 149.50/119.53 | (153) $false
% 149.50/119.53 |
% 149.50/119.53 |-The branch is then unsatisfiable
% 149.50/119.53 |-Branch two:
% 149.50/119.53 | (257) relation_dom(all_0_18_18) = all_652_0_1241 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (relation_inverse_image(all_0_18_18, v0) = v1) | ~ (in(v2, v1) = v3) | ? [v4] : ? [v5] : (( ~ (v5 = 0) & apply(all_0_18_18, v2) = v4 & in(v4, v0) = v5) | ( ~ (v4 = 0) & in(v2, all_652_0_1241) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_inverse_image(all_0_18_18, v0) = v1) | ~ (apply(all_0_18_18, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & in(v3, v0) = 0 & in(v2, all_652_0_1241) = 0) | ( ~ (v4 = 0) & in(v2, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_inverse_image(all_0_18_18, v0) = v1) | ~ (apply(all_0_18_18, v2) = v3) | ? [v4] : ((v4 = 0 & in(v2, v1) = 0) | ( ~ (v4 = 0) & in(v3, v0) = v4) | ( ~ (v4 = 0) & in(v2, all_652_0_1241) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_inverse_image(all_0_18_18, v0) = v1) | ~ (in(v2, all_652_0_1241) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v3 = 0 & apply(all_0_18_18, v2) = v4 & in(v4, v0) = 0) | ( ~ (v4 = 0) & in(v2, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_inverse_image(all_0_18_18, v0) = v1) | ~ (in(v2, v1) = 0) | ? [v3] : (apply(all_0_18_18, v2) = v3 & in(v3, v0) = 0 & in(v2, all_652_0_1241) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_inverse_image(all_0_18_18, v0) = v1) | ~ (in(v2, all_652_0_1241) = 0) | ? [v3] : ? [v4] : ((v3 = 0 & in(v2, v1) = 0) | ( ~ (v4 = 0) & apply(all_0_18_18, v2) = v3 & in(v3, v0) = v4))) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_inverse_image(all_0_18_18, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (((v7 = 0 & v5 = 0 & apply(all_0_18_18, v3) = v6 & in(v6, v1) = 0 & in(v3, all_652_0_1241) = 0) | (v4 = 0 & in(v3, v0) = 0)) & (( ~ (v7 = 0) & apply(all_0_18_18, v3) = v6 & in(v6, v1) = v7) | ( ~ (v5 = 0) & in(v3, all_652_0_1241) = v5) | ( ~ (v4 = 0) & in(v3, v0) = v4))))
% 149.50/119.53 |
% 149.50/119.53 | Applying alpha-rule on (257) yields:
% 149.50/119.53 | (258) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_inverse_image(all_0_18_18, v0) = v1) | ~ (in(v2, all_652_0_1241) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v3 = 0 & apply(all_0_18_18, v2) = v4 & in(v4, v0) = 0) | ( ~ (v4 = 0) & in(v2, v1) = v4)))
% 149.50/119.53 | (259) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_inverse_image(all_0_18_18, v0) = v1) | ~ (apply(all_0_18_18, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & in(v3, v0) = 0 & in(v2, all_652_0_1241) = 0) | ( ~ (v4 = 0) & in(v2, v1) = v4)))
% 149.50/119.53 | (260) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_inverse_image(all_0_18_18, v0) = v1) | ~ (apply(all_0_18_18, v2) = v3) | ? [v4] : ((v4 = 0 & in(v2, v1) = 0) | ( ~ (v4 = 0) & in(v3, v0) = v4) | ( ~ (v4 = 0) & in(v2, all_652_0_1241) = v4)))
% 149.50/119.53 | (261) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_inverse_image(all_0_18_18, v0) = v1) | ~ (in(v2, all_652_0_1241) = 0) | ? [v3] : ? [v4] : ((v3 = 0 & in(v2, v1) = 0) | ( ~ (v4 = 0) & apply(all_0_18_18, v2) = v3 & in(v3, v0) = v4)))
% 149.50/119.54 | (262) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (relation_inverse_image(all_0_18_18, v0) = v1) | ~ (in(v2, v1) = v3) | ? [v4] : ? [v5] : (( ~ (v5 = 0) & apply(all_0_18_18, v2) = v4 & in(v4, v0) = v5) | ( ~ (v4 = 0) & in(v2, all_652_0_1241) = v4)))
% 149.50/119.54 | (263) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_inverse_image(all_0_18_18, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (((v7 = 0 & v5 = 0 & apply(all_0_18_18, v3) = v6 & in(v6, v1) = 0 & in(v3, all_652_0_1241) = 0) | (v4 = 0 & in(v3, v0) = 0)) & (( ~ (v7 = 0) & apply(all_0_18_18, v3) = v6 & in(v6, v1) = v7) | ( ~ (v5 = 0) & in(v3, all_652_0_1241) = v5) | ( ~ (v4 = 0) & in(v3, v0) = v4))))
% 149.50/119.54 | (264) relation_dom(all_0_18_18) = all_652_0_1241
% 149.50/119.54 | (265) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_inverse_image(all_0_18_18, v0) = v1) | ~ (in(v2, v1) = 0) | ? [v3] : (apply(all_0_18_18, v2) = v3 & in(v3, v0) = 0 & in(v2, all_652_0_1241) = 0))
% 149.50/119.54 |
% 149.50/119.54 | Instantiating formula (265) with all_0_16_16, all_0_17_17, all_0_19_19 and discharging atoms relation_inverse_image(all_0_18_18, all_0_19_19) = all_0_17_17, in(all_0_16_16, all_0_17_17) = 0, yields:
% 149.50/119.54 | (266) ? [v0] : (apply(all_0_18_18, all_0_16_16) = v0 & in(v0, all_0_19_19) = 0 & in(all_0_16_16, all_652_0_1241) = 0)
% 149.50/119.54 |
% 149.50/119.54 | Instantiating (266) with all_931_0_2562 yields:
% 149.50/119.54 | (267) apply(all_0_18_18, all_0_16_16) = all_931_0_2562 & in(all_931_0_2562, all_0_19_19) = 0 & in(all_0_16_16, all_652_0_1241) = 0
% 149.50/119.54 |
% 149.50/119.54 | Applying alpha-rule on (267) yields:
% 149.50/119.54 | (268) apply(all_0_18_18, all_0_16_16) = all_931_0_2562
% 149.50/119.54 | (269) in(all_931_0_2562, all_0_19_19) = 0
% 149.50/119.54 | (270) in(all_0_16_16, all_652_0_1241) = 0
% 149.50/119.54 |
% 149.50/119.54 | Instantiating formula (121) with all_0_18_18, all_0_16_16, all_729_1_1321, all_931_0_2562 and discharging atoms apply(all_0_18_18, all_0_16_16) = all_931_0_2562, apply(all_0_18_18, all_0_16_16) = all_729_1_1321, yields:
% 149.50/119.54 | (271) all_931_0_2562 = all_729_1_1321
% 149.50/119.54 |
% 149.50/119.54 | Instantiating formula (121) with all_0_18_18, all_0_16_16, all_719_0_1313, all_931_0_2562 and discharging atoms apply(all_0_18_18, all_0_16_16) = all_931_0_2562, apply(all_0_18_18, all_0_16_16) = all_719_0_1313, yields:
% 149.50/119.54 | (272) all_931_0_2562 = all_719_0_1313
% 149.50/119.54 |
% 149.50/119.54 | Instantiating formula (121) with all_0_18_18, all_0_16_16, all_0_13_13, all_729_1_1321 and discharging atoms apply(all_0_18_18, all_0_16_16) = all_729_1_1321, apply(all_0_18_18, all_0_16_16) = all_0_13_13, yields:
% 149.50/119.54 | (273) all_729_1_1321 = all_0_13_13
% 149.50/119.54 |
% 149.50/119.54 | Combining equations (271,272) yields a new equation:
% 149.50/119.54 | (274) all_729_1_1321 = all_719_0_1313
% 149.50/119.54 |
% 149.50/119.54 | Simplifying 274 yields:
% 149.50/119.54 | (275) all_729_1_1321 = all_719_0_1313
% 149.50/119.54 |
% 149.50/119.54 | Combining equations (273,275) yields a new equation:
% 149.50/119.54 | (276) all_719_0_1313 = all_0_13_13
% 149.50/119.54 |
% 149.50/119.54 | From (276) and (237) follows:
% 149.50/119.54 | (202) in(all_0_13_13, all_0_19_19) = 0
% 149.50/119.54 |
% 149.50/119.54 | Instantiating formula (77) with all_0_13_13, all_0_19_19, 0, all_0_12_12 and discharging atoms in(all_0_13_13, all_0_19_19) = all_0_12_12, in(all_0_13_13, all_0_19_19) = 0, yields:
% 149.50/119.54 | (205) all_0_12_12 = 0
% 149.50/119.54 |
% 149.50/119.54 | Equations (205) can reduce 242 to:
% 149.50/119.54 | (153) $false
% 149.50/119.54 |
% 149.50/119.54 |-The branch is then unsatisfiable
% 149.50/119.54 |-Branch two:
% 149.50/119.54 | (280) ~ (all_729_2_1322 = 0) & relation(all_0_18_18) = all_729_2_1322
% 149.50/119.54 |
% 149.50/119.54 | Applying alpha-rule on (280) yields:
% 149.50/119.54 | (281) ~ (all_729_2_1322 = 0)
% 149.50/119.54 | (282) relation(all_0_18_18) = all_729_2_1322
% 149.50/119.54 |
% 149.50/119.54 | Instantiating formula (76) with all_0_18_18, all_729_2_1322, 0 and discharging atoms relation(all_0_18_18) = all_729_2_1322, relation(all_0_18_18) = 0, yields:
% 149.50/119.54 | (250) all_729_2_1322 = 0
% 149.50/119.54 |
% 149.50/119.54 | Equations (250) can reduce 281 to:
% 149.50/119.54 | (153) $false
% 149.50/119.54 |
% 149.50/119.54 |-The branch is then unsatisfiable
% 149.50/119.54 |-Branch two:
% 149.50/119.54 | (285) ~ (all_729_2_1322 = 0) & function(all_0_18_18) = all_729_2_1322
% 149.50/119.54 |
% 149.50/119.54 | Applying alpha-rule on (285) yields:
% 149.50/119.54 | (281) ~ (all_729_2_1322 = 0)
% 149.50/119.54 | (287) function(all_0_18_18) = all_729_2_1322
% 149.50/119.54 |
% 149.50/119.54 | Instantiating formula (17) with all_0_18_18, all_729_2_1322, 0 and discharging atoms function(all_0_18_18) = all_729_2_1322, function(all_0_18_18) = 0, yields:
% 149.50/119.54 | (250) all_729_2_1322 = 0
% 149.50/119.54 |
% 149.50/119.54 | Equations (250) can reduce 281 to:
% 149.50/119.54 | (153) $false
% 149.50/119.54 |
% 149.50/119.54 |-The branch is then unsatisfiable
% 149.50/119.54 |-Branch two:
% 149.50/119.54 | (290) ~ (all_0_14_14 = 0) & in(all_0_16_16, all_0_21_21) = all_0_14_14
% 149.50/119.54 |
% 149.50/119.54 | Applying alpha-rule on (290) yields:
% 149.50/119.54 | (291) ~ (all_0_14_14 = 0)
% 149.50/119.54 | (292) in(all_0_16_16, all_0_21_21) = all_0_14_14
% 149.50/119.54 |
% 149.50/119.54 | Instantiating formula (77) with all_0_16_16, all_0_21_21, 0, all_0_14_14 and discharging atoms in(all_0_16_16, all_0_21_21) = all_0_14_14, in(all_0_16_16, all_0_21_21) = 0, yields:
% 149.50/119.54 | (206) all_0_14_14 = 0
% 149.50/119.54 |
% 149.50/119.54 | Equations (206) can reduce 291 to:
% 149.50/119.54 | (153) $false
% 149.50/119.54 |
% 149.50/119.54 |-The branch is then unsatisfiable
% 149.50/119.54 |-Branch two:
% 149.50/119.54 | (295) ~ (all_96_1_140 = 0) & quasi_total(all_0_18_18, all_0_21_21, all_0_20_20) = all_96_1_140
% 149.50/119.54 |
% 149.50/119.54 | Applying alpha-rule on (295) yields:
% 149.50/119.54 | (296) ~ (all_96_1_140 = 0)
% 149.50/119.54 | (297) quasi_total(all_0_18_18, all_0_21_21, all_0_20_20) = all_96_1_140
% 149.50/119.54 |
% 149.50/119.54 | Equations (164) can reduce 296 to:
% 149.50/119.54 | (153) $false
% 149.50/119.54 |
% 149.50/119.54 |-The branch is then unsatisfiable
% 149.50/119.54 |-Branch two:
% 149.50/119.54 | (299) ~ (all_96_0_139 = all_0_21_21) & relation_dom_as_subset(all_0_21_21, all_0_20_20, all_0_18_18) = all_96_0_139
% 149.50/119.54 |
% 149.50/119.54 | Applying alpha-rule on (299) yields:
% 149.50/119.54 | (300) ~ (all_96_0_139 = all_0_21_21)
% 149.50/119.54 | (301) relation_dom_as_subset(all_0_21_21, all_0_20_20, all_0_18_18) = all_96_0_139
% 149.50/119.54 |
% 149.50/119.54 +-Applying beta-rule and splitting (161), into two cases.
% 149.50/119.54 |-Branch one:
% 149.50/119.54 | (166) all_96_0_139 = all_0_21_21 & relation_dom_as_subset(all_0_21_21, all_0_20_20, all_0_18_18) = all_0_21_21
% 149.50/119.54 |
% 149.50/119.54 | Applying alpha-rule on (166) yields:
% 149.50/119.54 | (167) all_96_0_139 = all_0_21_21
% 149.50/119.54 | (168) relation_dom_as_subset(all_0_21_21, all_0_20_20, all_0_18_18) = all_0_21_21
% 149.50/119.54 |
% 149.50/119.54 | Equations (167) can reduce 300 to:
% 149.50/119.54 | (153) $false
% 149.50/119.54 |
% 149.50/119.54 |-The branch is then unsatisfiable
% 149.50/119.54 |-Branch two:
% 149.50/119.54 | (295) ~ (all_96_1_140 = 0) & quasi_total(all_0_18_18, all_0_21_21, all_0_20_20) = all_96_1_140
% 149.50/119.54 |
% 149.50/119.54 | Applying alpha-rule on (295) yields:
% 149.50/119.54 | (296) ~ (all_96_1_140 = 0)
% 149.50/119.54 | (297) quasi_total(all_0_18_18, all_0_21_21, all_0_20_20) = all_96_1_140
% 149.50/119.54 |
% 149.50/119.54 | Instantiating formula (118) with all_0_18_18, all_0_21_21, all_0_20_20, all_96_1_140, 0 and discharging atoms quasi_total(all_0_18_18, all_0_21_21, all_0_20_20) = all_96_1_140, quasi_total(all_0_18_18, all_0_21_21, all_0_20_20) = 0, yields:
% 149.50/119.54 | (164) all_96_1_140 = 0
% 149.50/119.54 |
% 149.50/119.54 | Equations (164) can reduce 296 to:
% 149.50/119.54 | (153) $false
% 149.50/119.54 |
% 149.50/119.54 |-The branch is then unsatisfiable
% 149.50/119.54 % SZS output end Proof for theBenchmark
% 149.50/119.54
% 149.50/119.54 119051ms
%------------------------------------------------------------------------------