TSTP Solution File: NUM410+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : NUM410+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n020.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 : Mon Jul 18 08:44:13 EDT 2022
% Result : Theorem 9.35s 2.85s
% Output : Proof 20.98s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : NUM410+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.14/0.35 % Computer : n020.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Tue Jul 5 15:09:59 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.21/0.60 ____ _
% 0.21/0.60 ___ / __ \_____(_)___ ________ __________
% 0.21/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.21/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.21/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.21/0.60
% 0.21/0.60 A Theorem Prover for First-Order Logic
% 0.21/0.60 (ePrincess v.1.0)
% 0.21/0.60
% 0.21/0.60 (c) Philipp Rümmer, 2009-2015
% 0.21/0.60 (c) Peter Backeman, 2014-2015
% 0.21/0.60 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.21/0.60 Free software under GNU Lesser General Public License (LGPL).
% 0.21/0.60 Bug reports to peter@backeman.se
% 0.21/0.60
% 0.21/0.60 For more information, visit http://user.uu.se/~petba168/breu/
% 0.21/0.60
% 0.21/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.70/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.67/0.99 Prover 0: Preprocessing ...
% 2.32/1.19 Prover 0: Warning: ignoring some quantifiers
% 2.40/1.22 Prover 0: Constructing countermodel ...
% 4.81/1.86 Prover 0: gave up
% 4.81/1.86 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 5.17/1.90 Prover 1: Preprocessing ...
% 5.45/2.01 Prover 1: Warning: ignoring some quantifiers
% 5.84/2.02 Prover 1: Constructing countermodel ...
% 8.00/2.53 Prover 1: gave up
% 8.00/2.53 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 8.00/2.57 Prover 2: Preprocessing ...
% 8.74/2.70 Prover 2: Warning: ignoring some quantifiers
% 8.74/2.70 Prover 2: Constructing countermodel ...
% 9.35/2.85 Prover 2: proved (320ms)
% 9.35/2.85
% 9.35/2.85 No countermodel exists, formula is valid
% 9.35/2.85 % SZS status Theorem for theBenchmark
% 9.35/2.85
% 9.35/2.85 Generating proof ... Warning: ignoring some quantifiers
% 20.31/5.48 found it (size 112)
% 20.31/5.48
% 20.31/5.48 % SZS output start Proof for theBenchmark
% 20.31/5.48 Assumed formulas after preprocessing and simplification:
% 20.31/5.48 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ( ~ (v14 = 0) & ~ (v12 = 0) & ~ (v9 = 0) & ~ (v3 = 0) & relation_empty_yielding(v7) = 0 & relation_empty_yielding(v6) = 0 & relation_empty_yielding(empty_set) = 0 & relation_non_empty(v4) = 0 & relation_rng(v0) = v2 & transfinite_sequence_of(v0, v2) = v3 & relation_dom(v0) = v1 & transfinite_sequence(v5) = 0 & one_to_one(v15) = 0 & one_to_one(v10) = 0 & one_to_one(empty_set) = 0 & relation(v20) = 0 & relation(v18) = 0 & relation(v16) = 0 & relation(v15) = 0 & relation(v13) = 0 & relation(v10) = 0 & relation(v7) = 0 & relation(v6) = 0 & relation(v5) = 0 & relation(v4) = 0 & relation(v0) = 0 & relation(empty_set) = 0 & epsilon_transitive(v19) = 0 & epsilon_transitive(v15) = 0 & epsilon_transitive(v8) = 0 & epsilon_transitive(empty_set) = 0 & ordinal(v19) = 0 & ordinal(v15) = 0 & ordinal(v8) = 0 & ordinal(v1) = 0 & ordinal(empty_set) = 0 & epsilon_connected(v19) = 0 & epsilon_connected(v15) = 0 & epsilon_connected(v8) = 0 & epsilon_connected(empty_set) = 0 & function(v20) = 0 & function(v16) = 0 & function(v15) = 0 & function(v10) = 0 & function(v6) = 0 & function(v5) = 0 & function(v4) = 0 & function(v0) = 0 & function(empty_set) = 0 & empty(v18) = 0 & empty(v17) = 0 & empty(v16) = 0 & empty(v15) = 0 & empty(v13) = v14 & empty(v11) = v12 & empty(v8) = v9 & empty(empty_set) = 0 & ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : (v25 = 0 | ~ (powerset(v23) = v24) | ~ (element(v22, v24) = 0) | ~ (element(v21, v23) = v25) | ? [v26] : ( ~ (v26 = 0) & in(v21, v22) = v26)) & ! [v21] : ! [v22] : ! [v23] : ! [v24] : (v24 = 0 | ~ (powerset(v22) = v23) | ~ (element(v21, v23) = v24) | ? [v25] : ( ~ (v25 = 0) & subset(v21, v22) = v25)) & ! [v21] : ! [v22] : ! [v23] : ! [v24] : (v24 = 0 | ~ (element(v21, v23) = v24) | ~ (in(v21, v22) = 0) | ? [v25] : ? [v26] : ( ~ (v26 = 0) & powerset(v23) = v25 & element(v22, v25) = v26)) & ! [v21] : ! [v22] : ! [v23] : ! [v24] : (v22 = v21 | ~ (element(v24, v23) = v22) | ~ (element(v24, v23) = v21)) & ! [v21] : ! [v22] : ! [v23] : ! [v24] : (v22 = v21 | ~ (subset(v24, v23) = v22) | ~ (subset(v24, v23) = v21)) & ! [v21] : ! [v22] : ! [v23] : ! [v24] : (v22 = v21 | ~ (transfinite_sequence_of(v24, v23) = v22) | ~ (transfinite_sequence_of(v24, v23) = v21)) & ! [v21] : ! [v22] : ! [v23] : ! [v24] : (v22 = v21 | ~ (in(v24, v23) = v22) | ~ (in(v24, v23) = v21)) & ! [v21] : ! [v22] : ! [v23] : ! [v24] : ( ~ (powerset(v23) = v24) | ~ (element(v22, v24) = 0) | ~ (in(v21, v22) = 0) | element(v21, v23) = 0) & ! [v21] : ! [v22] : ! [v23] : ! [v24] : ( ~ (powerset(v23) = v24) | ~ (element(v22, v24) = 0) | ~ (in(v21, v22) = 0) | ? [v25] : ( ~ (v25 = 0) & empty(v23) = v25)) & ! [v21] : ! [v22] : ! [v23] : ! [v24] : ( ~ (relation_rng(v22) = v23) | ~ (subset(v23, v21) = v24) | ? [v25] : (( ~ (v25 = 0) & transfinite_sequence(v22) = v25) | ( ~ (v25 = 0) & relation(v22) = v25) | ( ~ (v25 = 0) & function(v22) = v25) | (( ~ (v24 = 0) | (v25 = 0 & transfinite_sequence_of(v22, v21) = 0)) & (v24 = 0 | ( ~ (v25 = 0) & transfinite_sequence_of(v22, v21) = v25))))) & ! [v21] : ! [v22] : ! [v23] : (v23 = 0 | ~ (element(v21, v22) = v23) | ? [v24] : ( ~ (v24 = 0) & in(v21, v22) = v24)) & ! [v21] : ! [v22] : ! [v23] : (v23 = 0 | ~ (subset(v21, v22) = v23) | ? [v24] : ? [v25] : ( ~ (v25 = 0) & powerset(v22) = v24 & element(v21, v24) = v25)) & ! [v21] : ! [v22] : ! [v23] : (v23 = 0 | ~ (in(v21, v22) = v23) | ? [v24] : ((v24 = 0 & empty(v22) = 0) | ( ~ (v24 = 0) & element(v21, v22) = v24))) & ! [v21] : ! [v22] : ! [v23] : (v22 = v21 | ~ (powerset(v23) = v22) | ~ (powerset(v23) = v21)) & ! [v21] : ! [v22] : ! [v23] : (v22 = v21 | ~ (relation_empty_yielding(v23) = v22) | ~ (relation_empty_yielding(v23) = v21)) & ! [v21] : ! [v22] : ! [v23] : (v22 = v21 | ~ (relation_non_empty(v23) = v22) | ~ (relation_non_empty(v23) = v21)) & ! [v21] : ! [v22] : ! [v23] : (v22 = v21 | ~ (with_non_empty_elements(v23) = v22) | ~ (with_non_empty_elements(v23) = v21)) & ! [v21] : ! [v22] : ! [v23] : (v22 = v21 | ~ (relation_rng(v23) = v22) | ~ (relation_rng(v23) = v21)) & ! [v21] : ! [v22] : ! [v23] : (v22 = v21 | ~ (relation_dom(v23) = v22) | ~ (relation_dom(v23) = v21)) & ! [v21] : ! [v22] : ! [v23] : (v22 = v21 | ~ (transfinite_sequence(v23) = v22) | ~ (transfinite_sequence(v23) = v21)) & ! [v21] : ! [v22] : ! [v23] : (v22 = v21 | ~ (one_to_one(v23) = v22) | ~ (one_to_one(v23) = v21)) & ! [v21] : ! [v22] : ! [v23] : (v22 = v21 | ~ (relation(v23) = v22) | ~ (relation(v23) = v21)) & ! [v21] : ! [v22] : ! [v23] : (v22 = v21 | ~ (epsilon_transitive(v23) = v22) | ~ (epsilon_transitive(v23) = v21)) & ! [v21] : ! [v22] : ! [v23] : (v22 = v21 | ~ (ordinal(v23) = v22) | ~ (ordinal(v23) = v21)) & ! [v21] : ! [v22] : ! [v23] : (v22 = v21 | ~ (epsilon_connected(v23) = v22) | ~ (epsilon_connected(v23) = v21)) & ! [v21] : ! [v22] : ! [v23] : (v22 = v21 | ~ (function(v23) = v22) | ~ (function(v23) = v21)) & ! [v21] : ! [v22] : ! [v23] : (v22 = v21 | ~ (empty(v23) = v22) | ~ (empty(v23) = v21)) & ! [v21] : ! [v22] : ! [v23] : ( ~ (powerset(v22) = v23) | ~ (element(v21, v23) = 0) | subset(v21, v22) = 0) & ! [v21] : ! [v22] : ! [v23] : ( ~ (transfinite_sequence_of(v22, v21) = v23) | ? [v24] : ? [v25] : (( ~ (v24 = 0) & transfinite_sequence(v22) = v24) | ( ~ (v24 = 0) & relation(v22) = v24) | ( ~ (v24 = 0) & function(v22) = v24) | (( ~ (v23 = 0) | (v25 = 0 & relation_rng(v22) = v24 & subset(v24, v21) = 0)) & (v23 = 0 | ( ~ (v25 = 0) & relation_rng(v22) = v24 & subset(v24, v21) = v25))))) & ! [v21] : ! [v22] : ! [v23] : ( ~ (empty(v23) = 0) | ~ (in(v21, v22) = 0) | ? [v24] : ? [v25] : ( ~ (v25 = 0) & powerset(v23) = v24 & element(v22, v24) = v25)) & ! [v21] : ! [v22] : (v22 = v21 | ~ (empty(v22) = 0) | ~ (empty(v21) = 0)) & ! [v21] : ! [v22] : (v22 = 0 | ~ (subset(v21, v21) = v22)) & ! [v21] : ! [v22] : (v22 = 0 | ~ (relation(v21) = v22) | ? [v23] : ( ~ (v23 = 0) & empty(v21) = v23)) & ! [v21] : ! [v22] : (v22 = 0 | ~ (ordinal(v21) = v22) | ? [v23] : (( ~ (v23 = 0) & epsilon_transitive(v21) = v23) | ( ~ (v23 = 0) & epsilon_connected(v21) = v23))) & ! [v21] : ! [v22] : (v22 = 0 | ~ (function(v21) = v22) | ? [v23] : ( ~ (v23 = 0) & empty(v21) = v23)) & ! [v21] : ! [v22] : (v22 = 0 | ~ (empty(v21) = v22) | ? [v23] : ? [v24] : (( ~ (v24 = 0) & relation_rng(v21) = v23 & empty(v23) = v24) | ( ~ (v23 = 0) & relation(v21) = v23))) & ! [v21] : ! [v22] : (v22 = 0 | ~ (empty(v21) = v22) | ? [v23] : ? [v24] : (( ~ (v24 = 0) & relation_dom(v21) = v23 & empty(v23) = v24) | ( ~ (v23 = 0) & relation(v21) = v23))) & ! [v21] : ! [v22] : ( ~ (element(v21, v22) = 0) | ? [v23] : ((v23 = 0 & empty(v22) = 0) | (v23 = 0 & in(v21, v22) = 0))) & ! [v21] : ! [v22] : ( ~ (relation_rng(v21) = v22) | ? [v23] : ? [v24] : ((v24 = 0 & v23 = 0 & relation(v22) = 0 & empty(v22) = 0) | ( ~ (v23 = 0) & empty(v21) = v23))) & ! [v21] : ! [v22] : ( ~ (relation_rng(v21) = v22) | ? [v23] : ((v23 = 0 & with_non_empty_elements(v22) = 0) | ( ~ (v23 = 0) & relation_non_empty(v21) = v23) | ( ~ (v23 = 0) & relation(v21) = v23) | ( ~ (v23 = 0) & function(v21) = v23))) & ! [v21] : ! [v22] : ( ~ (relation_rng(v21) = v22) | ? [v23] : ((v23 = 0 & empty(v21) = 0) | ( ~ (v23 = 0) & relation(v21) = v23) | ( ~ (v23 = 0) & empty(v22) = v23))) & ! [v21] : ! [v22] : ( ~ (subset(v21, v22) = 0) | ? [v23] : (powerset(v22) = v23 & element(v21, v23) = 0)) & ! [v21] : ! [v22] : ( ~ (transfinite_sequence_of(v22, v21) = 0) | (transfinite_sequence(v22) = 0 & relation(v22) = 0 & function(v22) = 0)) & ! [v21] : ! [v22] : ( ~ (relation_dom(v21) = v22) | ? [v23] : ? [v24] : ((v24 = 0 & v23 = 0 & relation(v22) = 0 & empty(v22) = 0) | ( ~ (v23 = 0) & empty(v21) = v23))) & ! [v21] : ! [v22] : ( ~ (relation_dom(v21) = v22) | ? [v23] : ? [v24] : (( ~ (v23 = 0) & relation(v21) = v23) | ( ~ (v23 = 0) & function(v21) = v23) | (((v24 = 0 & ordinal(v22) = 0) | ( ~ (v23 = 0) & transfinite_sequence(v21) = v23)) & ((v23 = 0 & transfinite_sequence(v21) = 0) | ( ~ (v24 = 0) & ordinal(v22) = v24))))) & ! [v21] : ! [v22] : ( ~ (relation_dom(v21) = v22) | ? [v23] : ((v23 = 0 & empty(v21) = 0) | ( ~ (v23 = 0) & relation(v21) = v23) | ( ~ (v23 = 0) & empty(v22) = v23))) & ! [v21] : ! [v22] : ( ~ (transfinite_sequence(v21) = v22) | ? [v23] : ? [v24] : (( ~ (v23 = 0) & relation(v21) = v23) | ( ~ (v23 = 0) & function(v21) = v23) | (( ~ (v22 = 0) | (v24 = 0 & relation_dom(v21) = v23 & ordinal(v23) = 0)) & (v22 = 0 | ( ~ (v24 = 0) & relation_dom(v21) = v23 & ordinal(v23) = v24))))) & ! [v21] : ! [v22] : ( ~ (one_to_one(v21) = v22) | ? [v23] : ? [v24] : ((v24 = 0 & v23 = 0 & v22 = 0 & relation(v21) = 0 & function(v21) = 0) | ( ~ (v23 = 0) & relation(v21) = v23) | ( ~ (v23 = 0) & function(v21) = v23) | ( ~ (v23 = 0) & empty(v21) = v23))) & ! [v21] : ! [v22] : ( ~ (epsilon_transitive(v21) = v22) | ? [v23] : ? [v24] : ((v24 = 0 & v23 = 0 & v22 = 0 & ordinal(v21) = 0 & epsilon_connected(v21) = 0) | ( ~ (v23 = 0) & empty(v21) = v23))) & ! [v21] : ! [v22] : ( ~ (epsilon_transitive(v21) = v22) | ? [v23] : ((v23 = 0 & v22 = 0 & epsilon_connected(v21) = 0) | ( ~ (v23 = 0) & ordinal(v21) = v23))) & ! [v21] : ! [v22] : ( ~ (ordinal(v21) = v22) | ? [v23] : ? [v24] : ((v24 = 0 & v23 = 0 & v22 = 0 & epsilon_transitive(v21) = 0 & epsilon_connected(v21) = 0) | ( ~ (v23 = 0) & empty(v21) = v23))) & ! [v21] : ! [v22] : ( ~ (epsilon_connected(v21) = v22) | ? [v23] : ? [v24] : ((v24 = 0 & v23 = 0 & v22 = 0 & epsilon_transitive(v21) = 0 & ordinal(v21) = 0) | ( ~ (v23 = 0) & empty(v21) = v23))) & ! [v21] : ! [v22] : ( ~ (epsilon_connected(v21) = v22) | ? [v23] : ((v23 = 0 & v22 = 0 & epsilon_transitive(v21) = 0) | ( ~ (v23 = 0) & ordinal(v21) = v23))) & ! [v21] : ! [v22] : ( ~ (in(v22, v21) = 0) | ? [v23] : ( ~ (v23 = 0) & in(v21, v22) = v23)) & ! [v21] : ! [v22] : ( ~ (in(v21, v22) = 0) | element(v21, v22) = 0) & ! [v21] : ! [v22] : ( ~ (in(v21, v22) = 0) | ? [v23] : ( ~ (v23 = 0) & empty(v22) = v23)) & ! [v21] : ! [v22] : ( ~ (in(v21, v22) = 0) | ? [v23] : ( ~ (v23 = 0) & in(v22, v21) = v23)) & ! [v21] : (v21 = empty_set | ~ (empty(v21) = 0)) & ! [v21] : ( ~ (relation_non_empty(v21) = 0) | ? [v22] : ? [v23] : ((v23 = 0 & with_non_empty_elements(v22) = 0 & relation_rng(v21) = v22) | ( ~ (v22 = 0) & relation(v21) = v22) | ( ~ (v22 = 0) & function(v21) = v22))) & ! [v21] : ( ~ (relation(v21) = 0) | ? [v22] : ? [v23] : ? [v24] : (( ~ (v22 = 0) & function(v21) = v22) | (((v24 = 0 & relation_dom(v21) = v23 & ordinal(v23) = 0) | ( ~ (v22 = 0) & transfinite_sequence(v21) = v22)) & ((v22 = 0 & transfinite_sequence(v21) = 0) | ( ~ (v24 = 0) & relation_dom(v21) = v23 & ordinal(v23) = v24))))) & ! [v21] : ( ~ (relation(v21) = 0) | ? [v22] : ? [v23] : ((v23 = 0 & v22 = 0 & one_to_one(v21) = 0 & function(v21) = 0) | ( ~ (v22 = 0) & function(v21) = v22) | ( ~ (v22 = 0) & empty(v21) = v22))) & ! [v21] : ( ~ (relation(v21) = 0) | ? [v22] : ? [v23] : ((v23 = 0 & with_non_empty_elements(v22) = 0 & relation_rng(v21) = v22) | ( ~ (v22 = 0) & relation_non_empty(v21) = v22) | ( ~ (v22 = 0) & function(v21) = v22))) & ! [v21] : ( ~ (relation(v21) = 0) | ? [v22] : ? [v23] : ((v22 = 0 & empty(v21) = 0) | ( ~ (v23 = 0) & relation_rng(v21) = v22 & empty(v22) = v23))) & ! [v21] : ( ~ (relation(v21) = 0) | ? [v22] : ? [v23] : ((v22 = 0 & empty(v21) = 0) | ( ~ (v23 = 0) & relation_dom(v21) = v22 & empty(v22) = v23))) & ! [v21] : ( ~ (epsilon_transitive(v21) = 0) | ? [v22] : ((v22 = 0 & ordinal(v21) = 0) | ( ~ (v22 = 0) & epsilon_connected(v21) = v22))) & ! [v21] : ( ~ (ordinal(v21) = 0) | (epsilon_transitive(v21) = 0 & epsilon_connected(v21) = 0)) & ! [v21] : ( ~ (epsilon_connected(v21) = 0) | ? [v22] : ((v22 = 0 & ordinal(v21) = 0) | ( ~ (v22 = 0) & epsilon_transitive(v21) = v22))) & ! [v21] : ( ~ (function(v21) = 0) | ? [v22] : ? [v23] : ? [v24] : (( ~ (v22 = 0) & relation(v21) = v22) | (((v24 = 0 & relation_dom(v21) = v23 & ordinal(v23) = 0) | ( ~ (v22 = 0) & transfinite_sequence(v21) = v22)) & ((v22 = 0 & transfinite_sequence(v21) = 0) | ( ~ (v24 = 0) & relation_dom(v21) = v23 & ordinal(v23) = v24))))) & ! [v21] : ( ~ (function(v21) = 0) | ? [v22] : ? [v23] : ((v23 = 0 & v22 = 0 & one_to_one(v21) = 0 & relation(v21) = 0) | ( ~ (v22 = 0) & relation(v21) = v22) | ( ~ (v22 = 0) & empty(v21) = v22))) & ! [v21] : ( ~ (function(v21) = 0) | ? [v22] : ? [v23] : ((v23 = 0 & with_non_empty_elements(v22) = 0 & relation_rng(v21) = v22) | ( ~ (v22 = 0) & relation_non_empty(v21) = v22) | ( ~ (v22 = 0) & relation(v21) = v22))) & ! [v21] : ( ~ (empty(v21) = 0) | relation(v21) = 0) & ! [v21] : ( ~ (empty(v21) = 0) | function(v21) = 0) & ! [v21] : ( ~ (empty(v21) = 0) | ? [v22] : ? [v23] : ? [v24] : ((v24 = 0 & v23 = 0 & v22 = 0 & one_to_one(v21) = 0 & relation(v21) = 0 & function(v21) = 0) | ( ~ (v22 = 0) & relation(v21) = v22) | ( ~ (v22 = 0) & function(v21) = v22))) & ! [v21] : ( ~ (empty(v21) = 0) | ? [v22] : (relation_rng(v21) = v22 & relation(v22) = 0 & empty(v22) = 0)) & ! [v21] : ( ~ (empty(v21) = 0) | ? [v22] : (relation_dom(v21) = v22 & relation(v22) = 0 & empty(v22) = 0)) & ! [v21] : ( ~ (empty(v21) = 0) | (epsilon_transitive(v21) = 0 & ordinal(v21) = 0 & epsilon_connected(v21) = 0)) & ? [v21] : ? [v22] : ? [v23] : element(v22, v21) = v23 & ? [v21] : ? [v22] : ? [v23] : subset(v22, v21) = v23 & ? [v21] : ? [v22] : ? [v23] : transfinite_sequence_of(v22, v21) = v23 & ? [v21] : ? [v22] : ? [v23] : in(v22, v21) = v23 & ? [v21] : ? [v22] : powerset(v21) = v22 & ? [v21] : ? [v22] : relation_empty_yielding(v21) = v22 & ? [v21] : ? [v22] : relation_non_empty(v21) = v22 & ? [v21] : ? [v22] : with_non_empty_elements(v21) = v22 & ? [v21] : ? [v22] : element(v22, v21) = 0 & ? [v21] : ? [v22] : relation_rng(v21) = v22 & ? [v21] : ? [v22] : transfinite_sequence_of(v22, v21) = 0 & ? [v21] : ? [v22] : relation_dom(v21) = v22 & ? [v21] : ? [v22] : transfinite_sequence(v21) = v22 & ? [v21] : ? [v22] : one_to_one(v21) = v22 & ? [v21] : ? [v22] : relation(v21) = v22 & ? [v21] : ? [v22] : epsilon_transitive(v21) = v22 & ? [v21] : ? [v22] : ordinal(v21) = v22 & ? [v21] : ? [v22] : epsilon_connected(v21) = v22 & ? [v21] : ? [v22] : function(v21) = v22 & ? [v21] : ? [v22] : empty(v21) = v22)
% 20.67/5.56 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9, all_0_10_10, all_0_11_11, all_0_12_12, all_0_13_13, all_0_14_14, all_0_15_15, all_0_16_16, all_0_17_17, all_0_18_18, all_0_19_19, all_0_20_20 yields:
% 20.67/5.56 | (1) ~ (all_0_6_6 = 0) & ~ (all_0_8_8 = 0) & ~ (all_0_11_11 = 0) & ~ (all_0_17_17 = 0) & relation_empty_yielding(all_0_13_13) = 0 & relation_empty_yielding(all_0_14_14) = 0 & relation_empty_yielding(empty_set) = 0 & relation_non_empty(all_0_16_16) = 0 & relation_rng(all_0_20_20) = all_0_18_18 & transfinite_sequence_of(all_0_20_20, all_0_18_18) = all_0_17_17 & relation_dom(all_0_20_20) = all_0_19_19 & transfinite_sequence(all_0_15_15) = 0 & one_to_one(all_0_5_5) = 0 & one_to_one(all_0_10_10) = 0 & one_to_one(empty_set) = 0 & relation(all_0_0_0) = 0 & relation(all_0_2_2) = 0 & relation(all_0_4_4) = 0 & relation(all_0_5_5) = 0 & relation(all_0_7_7) = 0 & relation(all_0_10_10) = 0 & relation(all_0_13_13) = 0 & relation(all_0_14_14) = 0 & relation(all_0_15_15) = 0 & relation(all_0_16_16) = 0 & relation(all_0_20_20) = 0 & relation(empty_set) = 0 & epsilon_transitive(all_0_1_1) = 0 & epsilon_transitive(all_0_5_5) = 0 & epsilon_transitive(all_0_12_12) = 0 & epsilon_transitive(empty_set) = 0 & ordinal(all_0_1_1) = 0 & ordinal(all_0_5_5) = 0 & ordinal(all_0_12_12) = 0 & ordinal(all_0_19_19) = 0 & ordinal(empty_set) = 0 & epsilon_connected(all_0_1_1) = 0 & epsilon_connected(all_0_5_5) = 0 & epsilon_connected(all_0_12_12) = 0 & epsilon_connected(empty_set) = 0 & function(all_0_0_0) = 0 & function(all_0_4_4) = 0 & function(all_0_5_5) = 0 & function(all_0_10_10) = 0 & function(all_0_14_14) = 0 & function(all_0_15_15) = 0 & function(all_0_16_16) = 0 & function(all_0_20_20) = 0 & function(empty_set) = 0 & empty(all_0_2_2) = 0 & empty(all_0_3_3) = 0 & empty(all_0_4_4) = 0 & empty(all_0_5_5) = 0 & empty(all_0_7_7) = all_0_6_6 & empty(all_0_9_9) = all_0_8_8 & empty(all_0_12_12) = all_0_11_11 & empty(empty_set) = 0 & ! [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] : (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 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (transfinite_sequence_of(v3, v2) = v1) | ~ (transfinite_sequence_of(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [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] : ! [v3] : ( ~ (relation_rng(v1) = v2) | ~ (subset(v2, v0) = v3) | ? [v4] : (( ~ (v4 = 0) & transfinite_sequence(v1) = v4) | ( ~ (v4 = 0) & relation(v1) = v4) | ( ~ (v4 = 0) & function(v1) = v4) | (( ~ (v3 = 0) | (v4 = 0 & transfinite_sequence_of(v1, v0) = 0)) & (v3 = 0 | ( ~ (v4 = 0) & transfinite_sequence_of(v1, v0) = v4))))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3)) & ! [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 | ~ (in(v0, v1) = v2) | ? [v3] : ((v3 = 0 & empty(v1) = 0) | ( ~ (v3 = 0) & element(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_empty_yielding(v2) = v1) | ~ (relation_empty_yielding(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_non_empty(v2) = v1) | ~ (relation_non_empty(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (with_non_empty_elements(v2) = v1) | ~ (with_non_empty_elements(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (transfinite_sequence(v2) = v1) | ~ (transfinite_sequence(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (epsilon_transitive(v2) = v1) | ~ (epsilon_transitive(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ordinal(v2) = v1) | ~ (ordinal(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (epsilon_connected(v2) = v1) | ~ (epsilon_connected(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] : ( ~ (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | subset(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (transfinite_sequence_of(v1, v0) = v2) | ? [v3] : ? [v4] : (( ~ (v3 = 0) & transfinite_sequence(v1) = v3) | ( ~ (v3 = 0) & relation(v1) = v3) | ( ~ (v3 = 0) & function(v1) = v3) | (( ~ (v2 = 0) | (v4 = 0 & relation_rng(v1) = v3 & subset(v3, v0) = 0)) & (v2 = 0 | ( ~ (v4 = 0) & relation_rng(v1) = v3 & subset(v3, v0) = v4))))) & ! [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 = 0 | ~ (subset(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (relation(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (ordinal(v0) = v1) | ? [v2] : (( ~ (v2 = 0) & epsilon_transitive(v0) = v2) | ( ~ (v2 = 0) & epsilon_connected(v0) = v2))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (function(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (empty(v0) = v1) | ? [v2] : ? [v3] : (( ~ (v3 = 0) & relation_rng(v0) = v2 & empty(v2) = v3) | ( ~ (v2 = 0) & relation(v0) = v2))) & ! [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] : ( ~ (element(v0, v1) = 0) | ? [v2] : ((v2 = 0 & empty(v1) = 0) | (v2 = 0 & in(v0, v1) = 0))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & relation(v1) = 0 & empty(v1) = 0) | ( ~ (v2 = 0) & empty(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ((v2 = 0 & with_non_empty_elements(v1) = 0) | ( ~ (v2 = 0) & relation_non_empty(v0) = v2) | ( ~ (v2 = 0) & relation(v0) = v2) | ( ~ (v2 = 0) & function(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ((v2 = 0 & empty(v0) = 0) | ( ~ (v2 = 0) & relation(v0) = v2) | ( ~ (v2 = 0) & empty(v1) = v2))) & ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (powerset(v1) = v2 & element(v0, v2) = 0)) & ! [v0] : ! [v1] : ( ~ (transfinite_sequence_of(v1, v0) = 0) | (transfinite_sequence(v1) = 0 & relation(v1) = 0 & function(v1) = 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] : ? [v3] : (( ~ (v2 = 0) & relation(v0) = v2) | ( ~ (v2 = 0) & function(v0) = v2) | (((v3 = 0 & ordinal(v1) = 0) | ( ~ (v2 = 0) & transfinite_sequence(v0) = v2)) & ((v2 = 0 & transfinite_sequence(v0) = 0) | ( ~ (v3 = 0) & ordinal(v1) = v3))))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ((v2 = 0 & empty(v0) = 0) | ( ~ (v2 = 0) & relation(v0) = v2) | ( ~ (v2 = 0) & empty(v1) = v2))) & ! [v0] : ! [v1] : ( ~ (transfinite_sequence(v0) = v1) | ? [v2] : ? [v3] : (( ~ (v2 = 0) & relation(v0) = v2) | ( ~ (v2 = 0) & function(v0) = v2) | (( ~ (v1 = 0) | (v3 = 0 & relation_dom(v0) = v2 & ordinal(v2) = 0)) & (v1 = 0 | ( ~ (v3 = 0) & relation_dom(v0) = v2 & ordinal(v2) = v3))))) & ! [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] : ( ~ (epsilon_transitive(v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & ordinal(v0) = 0 & epsilon_connected(v0) = 0) | ( ~ (v2 = 0) & empty(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (epsilon_transitive(v0) = v1) | ? [v2] : ((v2 = 0 & v1 = 0 & epsilon_connected(v0) = 0) | ( ~ (v2 = 0) & ordinal(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (ordinal(v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & epsilon_transitive(v0) = 0 & epsilon_connected(v0) = 0) | ( ~ (v2 = 0) & empty(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (epsilon_connected(v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & epsilon_transitive(v0) = 0 & ordinal(v0) = 0) | ( ~ (v2 = 0) & empty(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (epsilon_connected(v0) = v1) | ? [v2] : ((v2 = 0 & v1 = 0 & epsilon_transitive(v0) = 0) | ( ~ (v2 = 0) & ordinal(v0) = v2))) & ! [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_non_empty(v0) = 0) | ? [v1] : ? [v2] : ((v2 = 0 & with_non_empty_elements(v1) = 0 & relation_rng(v0) = v1) | ( ~ (v1 = 0) & relation(v0) = v1) | ( ~ (v1 = 0) & function(v0) = v1))) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (( ~ (v1 = 0) & function(v0) = v1) | (((v3 = 0 & relation_dom(v0) = v2 & ordinal(v2) = 0) | ( ~ (v1 = 0) & transfinite_sequence(v0) = v1)) & ((v1 = 0 & transfinite_sequence(v0) = 0) | ( ~ (v3 = 0) & relation_dom(v0) = v2 & ordinal(v2) = v3))))) & ! [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] : ((v2 = 0 & with_non_empty_elements(v1) = 0 & relation_rng(v0) = v1) | ( ~ (v1 = 0) & relation_non_empty(v0) = v1) | ( ~ (v1 = 0) & function(v0) = v1))) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ((v1 = 0 & empty(v0) = 0) | ( ~ (v2 = 0) & relation_rng(v0) = v1 & empty(v1) = v2))) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ((v1 = 0 & empty(v0) = 0) | ( ~ (v2 = 0) & relation_dom(v0) = v1 & empty(v1) = v2))) & ! [v0] : ( ~ (epsilon_transitive(v0) = 0) | ? [v1] : ((v1 = 0 & ordinal(v0) = 0) | ( ~ (v1 = 0) & epsilon_connected(v0) = v1))) & ! [v0] : ( ~ (ordinal(v0) = 0) | (epsilon_transitive(v0) = 0 & epsilon_connected(v0) = 0)) & ! [v0] : ( ~ (epsilon_connected(v0) = 0) | ? [v1] : ((v1 = 0 & ordinal(v0) = 0) | ( ~ (v1 = 0) & epsilon_transitive(v0) = v1))) & ! [v0] : ( ~ (function(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (( ~ (v1 = 0) & relation(v0) = v1) | (((v3 = 0 & relation_dom(v0) = v2 & ordinal(v2) = 0) | ( ~ (v1 = 0) & transfinite_sequence(v0) = v1)) & ((v1 = 0 & transfinite_sequence(v0) = 0) | ( ~ (v3 = 0) & relation_dom(v0) = v2 & ordinal(v2) = v3))))) & ! [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] : ? [v2] : ((v2 = 0 & with_non_empty_elements(v1) = 0 & relation_rng(v0) = v1) | ( ~ (v1 = 0) & relation_non_empty(v0) = v1) | ( ~ (v1 = 0) & relation(v0) = v1))) & ! [v0] : ( ~ (empty(v0) = 0) | relation(v0) = 0) & ! [v0] : ( ~ (empty(v0) = 0) | function(v0) = 0) & ! [v0] : ( ~ (empty(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & one_to_one(v0) = 0 & relation(v0) = 0 & function(v0) = 0) | ( ~ (v1 = 0) & relation(v0) = v1) | ( ~ (v1 = 0) & function(v0) = v1))) & ! [v0] : ( ~ (empty(v0) = 0) | ? [v1] : (relation_rng(v0) = v1 & relation(v1) = 0 & empty(v1) = 0)) & ! [v0] : ( ~ (empty(v0) = 0) | ? [v1] : (relation_dom(v0) = v1 & relation(v1) = 0 & empty(v1) = 0)) & ! [v0] : ( ~ (empty(v0) = 0) | (epsilon_transitive(v0) = 0 & ordinal(v0) = 0 & epsilon_connected(v0) = 0)) & ? [v0] : ? [v1] : ? [v2] : element(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : transfinite_sequence_of(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2 & ? [v0] : ? [v1] : powerset(v0) = v1 & ? [v0] : ? [v1] : relation_empty_yielding(v0) = v1 & ? [v0] : ? [v1] : relation_non_empty(v0) = v1 & ? [v0] : ? [v1] : with_non_empty_elements(v0) = v1 & ? [v0] : ? [v1] : element(v1, v0) = 0 & ? [v0] : ? [v1] : relation_rng(v0) = v1 & ? [v0] : ? [v1] : transfinite_sequence_of(v1, v0) = 0 & ? [v0] : ? [v1] : relation_dom(v0) = v1 & ? [v0] : ? [v1] : transfinite_sequence(v0) = v1 & ? [v0] : ? [v1] : one_to_one(v0) = v1 & ? [v0] : ? [v1] : relation(v0) = v1 & ? [v0] : ? [v1] : epsilon_transitive(v0) = v1 & ? [v0] : ? [v1] : ordinal(v0) = v1 & ? [v0] : ? [v1] : epsilon_connected(v0) = v1 & ? [v0] : ? [v1] : function(v0) = v1 & ? [v0] : ? [v1] : empty(v0) = v1
% 20.98/5.58 |
% 20.98/5.58 | Applying alpha-rule on (1) yields:
% 20.98/5.58 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4))
% 20.98/5.59 | (3) function(all_0_16_16) = 0
% 20.98/5.59 | (4) ? [v0] : ? [v1] : with_non_empty_elements(v0) = v1
% 20.98/5.59 | (5) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0))
% 20.98/5.59 | (6) ordinal(empty_set) = 0
% 20.98/5.59 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng(v1) = v2) | ~ (subset(v2, v0) = v3) | ? [v4] : (( ~ (v4 = 0) & transfinite_sequence(v1) = v4) | ( ~ (v4 = 0) & relation(v1) = v4) | ( ~ (v4 = 0) & function(v1) = v4) | (( ~ (v3 = 0) | (v4 = 0 & transfinite_sequence_of(v1, v0) = 0)) & (v3 = 0 | ( ~ (v4 = 0) & transfinite_sequence_of(v1, v0) = v4)))))
% 20.98/5.59 | (8) ! [v0] : ( ~ (function(v0) = 0) | ? [v1] : ? [v2] : ((v2 = 0 & with_non_empty_elements(v1) = 0 & relation_rng(v0) = v1) | ( ~ (v1 = 0) & relation_non_empty(v0) = v1) | ( ~ (v1 = 0) & relation(v0) = v1)))
% 20.98/5.59 | (9) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ((v2 = 0 & with_non_empty_elements(v1) = 0 & relation_rng(v0) = v1) | ( ~ (v1 = 0) & relation_non_empty(v0) = v1) | ( ~ (v1 = 0) & function(v0) = v1)))
% 20.98/5.59 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | element(v0, v2) = 0)
% 20.98/5.59 | (11) ~ (all_0_17_17 = 0)
% 20.98/5.59 | (12) ! [v0] : ( ~ (empty(v0) = 0) | (epsilon_transitive(v0) = 0 & ordinal(v0) = 0 & epsilon_connected(v0) = 0))
% 20.98/5.59 | (13) ! [v0] : ! [v1] : ( ~ (epsilon_transitive(v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & ordinal(v0) = 0 & epsilon_connected(v0) = 0) | ( ~ (v2 = 0) & empty(v0) = v2)))
% 20.98/5.59 | (14) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 20.98/5.59 | (15) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0))
% 20.98/5.59 | (16) ? [v0] : ? [v1] : relation_rng(v0) = v1
% 20.98/5.59 | (17) empty(empty_set) = 0
% 20.98/5.59 | (18) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 20.98/5.59 | (19) ! [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))
% 20.98/5.59 | (20) ! [v0] : ( ~ (epsilon_connected(v0) = 0) | ? [v1] : ((v1 = 0 & ordinal(v0) = 0) | ( ~ (v1 = 0) & epsilon_transitive(v0) = v1)))
% 20.98/5.59 | (21) ! [v0] : ( ~ (epsilon_transitive(v0) = 0) | ? [v1] : ((v1 = 0 & ordinal(v0) = 0) | ( ~ (v1 = 0) & epsilon_connected(v0) = v1)))
% 20.98/5.59 | (22) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0))
% 20.98/5.59 | (23) relation(all_0_20_20) = 0
% 20.98/5.59 | (24) function(all_0_10_10) = 0
% 20.98/5.59 | (25) ? [v0] : ? [v1] : empty(v0) = v1
% 20.98/5.59 | (26) relation_empty_yielding(all_0_13_13) = 0
% 20.98/5.59 | (27) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ordinal(v2) = v1) | ~ (ordinal(v2) = v0))
% 20.98/5.59 | (28) ? [v0] : ? [v1] : relation_dom(v0) = v1
% 20.98/5.59 | (29) relation_empty_yielding(all_0_14_14) = 0
% 20.98/5.59 | (30) ! [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)))
% 20.98/5.59 | (31) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3))
% 20.98/5.59 | (32) ! [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)))
% 20.98/5.59 | (33) ! [v0] : ( ~ (empty(v0) = 0) | ? [v1] : (relation_dom(v0) = v1 & relation(v1) = 0 & empty(v1) = 0))
% 20.98/5.59 | (34) ? [v0] : ? [v1] : relation_non_empty(v0) = v1
% 20.98/5.59 | (35) ? [v0] : ? [v1] : relation(v0) = v1
% 20.98/5.59 | (36) ! [v0] : ! [v1] : ( ~ (epsilon_connected(v0) = v1) | ? [v2] : ((v2 = 0 & v1 = 0 & epsilon_transitive(v0) = 0) | ( ~ (v2 = 0) & ordinal(v0) = v2)))
% 20.98/5.59 | (37) empty(all_0_2_2) = 0
% 20.98/5.59 | (38) relation(all_0_5_5) = 0
% 20.98/5.59 | (39) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (transfinite_sequence(v2) = v1) | ~ (transfinite_sequence(v2) = v0))
% 20.98/5.59 | (40) function(all_0_0_0) = 0
% 20.98/5.59 | (41) relation(all_0_2_2) = 0
% 20.98/5.59 | (42) ! [v0] : ( ~ (empty(v0) = 0) | function(v0) = 0)
% 20.98/5.59 | (43) relation(all_0_15_15) = 0
% 20.98/5.59 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 20.98/5.59 | (45) ! [v0] : ! [v1] : ! [v2] : ( ~ (transfinite_sequence_of(v1, v0) = v2) | ? [v3] : ? [v4] : (( ~ (v3 = 0) & transfinite_sequence(v1) = v3) | ( ~ (v3 = 0) & relation(v1) = v3) | ( ~ (v3 = 0) & function(v1) = v3) | (( ~ (v2 = 0) | (v4 = 0 & relation_rng(v1) = v3 & subset(v3, v0) = 0)) & (v2 = 0 | ( ~ (v4 = 0) & relation_rng(v1) = v3 & subset(v3, v0) = v4)))))
% 20.98/5.59 | (46) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1))
% 20.98/5.60 | (47) empty(all_0_7_7) = all_0_6_6
% 20.98/5.60 | (48) function(all_0_4_4) = 0
% 20.98/5.60 | (49) ordinal(all_0_5_5) = 0
% 20.98/5.60 | (50) function(all_0_20_20) = 0
% 20.98/5.60 | (51) relation(all_0_4_4) = 0
% 20.98/5.60 | (52) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0))
% 20.98/5.60 | (53) one_to_one(all_0_10_10) = 0
% 20.98/5.60 | (54) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_non_empty(v2) = v1) | ~ (relation_non_empty(v2) = v0))
% 20.98/5.60 | (55) ! [v0] : ! [v1] : (v1 = 0 | ~ (empty(v0) = v1) | ? [v2] : ? [v3] : (( ~ (v3 = 0) & relation_rng(v0) = v2 & empty(v2) = v3) | ( ~ (v2 = 0) & relation(v0) = v2)))
% 20.98/5.60 | (56) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (epsilon_connected(v2) = v1) | ~ (epsilon_connected(v2) = v0))
% 20.98/5.60 | (57) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ((v2 = 0 & with_non_empty_elements(v1) = 0) | ( ~ (v2 = 0) & relation_non_empty(v0) = v2) | ( ~ (v2 = 0) & relation(v0) = v2) | ( ~ (v2 = 0) & function(v0) = v2)))
% 20.98/5.60 | (58) ! [v0] : ! [v1] : ( ~ (transfinite_sequence_of(v1, v0) = 0) | (transfinite_sequence(v1) = 0 & relation(v1) = 0 & function(v1) = 0))
% 20.98/5.60 | (59) ! [v0] : ( ~ (empty(v0) = 0) | ? [v1] : (relation_rng(v0) = v1 & relation(v1) = 0 & empty(v1) = 0))
% 20.98/5.60 | (60) function(all_0_5_5) = 0
% 20.98/5.60 | (61) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & relation(v1) = 0 & empty(v1) = 0) | ( ~ (v2 = 0) & empty(v0) = v2)))
% 20.98/5.60 | (62) ? [v0] : ? [v1] : epsilon_transitive(v0) = v1
% 20.98/5.60 | (63) ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2
% 20.98/5.60 | (64) relation_rng(all_0_20_20) = all_0_18_18
% 20.98/5.60 | (65) empty(all_0_4_4) = 0
% 20.98/5.60 | (66) ordinal(all_0_19_19) = 0
% 20.98/5.60 | (67) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0))
% 20.98/5.60 | (68) relation_non_empty(all_0_16_16) = 0
% 20.98/5.60 | (69) epsilon_connected(empty_set) = 0
% 20.98/5.60 | (70) relation(empty_set) = 0
% 20.98/5.60 | (71) relation(all_0_16_16) = 0
% 20.98/5.60 | (72) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (epsilon_transitive(v2) = v1) | ~ (epsilon_transitive(v2) = v0))
% 20.98/5.60 | (73) ! [v0] : ! [v1] : ( ~ (epsilon_connected(v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & epsilon_transitive(v0) = 0 & ordinal(v0) = 0) | ( ~ (v2 = 0) & empty(v0) = v2)))
% 20.98/5.60 | (74) ! [v0] : ! [v1] : ! [v2] : ( ~ (empty(v2) = 0) | ~ (in(v0, v1) = 0) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v2) = v3 & element(v1, v3) = v4))
% 20.98/5.60 | (75) ? [v0] : ? [v1] : function(v0) = v1
% 20.98/5.60 | (76) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ((v2 = 0 & empty(v0) = 0) | ( ~ (v2 = 0) & relation(v0) = v2) | ( ~ (v2 = 0) & empty(v1) = v2)))
% 20.98/5.60 | (77) ? [v0] : ? [v1] : one_to_one(v0) = v1
% 20.98/5.60 | (78) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (transfinite_sequence_of(v3, v2) = v1) | ~ (transfinite_sequence_of(v3, v2) = v0))
% 20.98/5.60 | (79) ? [v0] : ? [v1] : epsilon_connected(v0) = v1
% 20.98/5.60 | (80) ! [v0] : ( ~ (empty(v0) = 0) | relation(v0) = 0)
% 20.98/5.60 | (81) epsilon_transitive(all_0_1_1) = 0
% 20.98/5.60 | (82) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v0, v1) = v2) | ? [v3] : ((v3 = 0 & empty(v1) = 0) | ( ~ (v3 = 0) & element(v0, v1) = v3)))
% 20.98/5.60 | (83) ! [v0] : ! [v1] : ( ~ (element(v0, v1) = 0) | ? [v2] : ((v2 = 0 & empty(v1) = 0) | (v2 = 0 & in(v0, v1) = 0)))
% 20.98/5.60 | (84) ! [v0] : ( ~ (function(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (( ~ (v1 = 0) & relation(v0) = v1) | (((v3 = 0 & relation_dom(v0) = v2 & ordinal(v2) = 0) | ( ~ (v1 = 0) & transfinite_sequence(v0) = v1)) & ((v1 = 0 & transfinite_sequence(v0) = 0) | ( ~ (v3 = 0) & relation_dom(v0) = v2 & ordinal(v2) = v3)))))
% 20.98/5.60 | (85) function(all_0_15_15) = 0
% 20.98/5.60 | (86) ! [v0] : ! [v1] : ( ~ (epsilon_transitive(v0) = v1) | ? [v2] : ((v2 = 0 & v1 = 0 & epsilon_connected(v0) = 0) | ( ~ (v2 = 0) & ordinal(v0) = v2)))
% 20.98/5.60 | (87) ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2))
% 20.98/5.60 | (88) ordinal(all_0_1_1) = 0
% 20.98/5.60 | (89) ! [v0] : ! [v1] : ( ~ (transfinite_sequence(v0) = v1) | ? [v2] : ? [v3] : (( ~ (v2 = 0) & relation(v0) = v2) | ( ~ (v2 = 0) & function(v0) = v2) | (( ~ (v1 = 0) | (v3 = 0 & relation_dom(v0) = v2 & ordinal(v2) = 0)) & (v1 = 0 | ( ~ (v3 = 0) & relation_dom(v0) = v2 & ordinal(v2) = v3)))))
% 20.98/5.60 | (90) epsilon_transitive(empty_set) = 0
% 20.98/5.60 | (91) ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2
% 20.98/5.60 | (92) ~ (all_0_6_6 = 0)
% 20.98/5.60 | (93) ordinal(all_0_12_12) = 0
% 20.98/5.60 | (94) epsilon_connected(all_0_5_5) = 0
% 20.98/5.60 | (95) ! [v0] : ( ~ (ordinal(v0) = 0) | (epsilon_transitive(v0) = 0 & epsilon_connected(v0) = 0))
% 20.98/5.60 | (96) transfinite_sequence(all_0_15_15) = 0
% 20.98/5.60 | (97) ? [v0] : ? [v1] : ? [v2] : element(v1, v0) = v2
% 20.98/5.60 | (98) ? [v0] : ? [v1] : ? [v2] : transfinite_sequence_of(v1, v0) = v2
% 20.98/5.60 | (99) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (with_non_empty_elements(v2) = v1) | ~ (with_non_empty_elements(v2) = v0))
% 20.98/5.61 | (100) epsilon_connected(all_0_1_1) = 0
% 20.98/5.61 | (101) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ((v1 = 0 & empty(v0) = 0) | ( ~ (v2 = 0) & relation_dom(v0) = v1 & empty(v1) = v2)))
% 20.98/5.61 | (102) ? [v0] : ? [v1] : transfinite_sequence_of(v1, v0) = 0
% 20.98/5.61 | (103) ! [v0] : ( ~ (relation_non_empty(v0) = 0) | ? [v1] : ? [v2] : ((v2 = 0 & with_non_empty_elements(v1) = 0 & relation_rng(v0) = v1) | ( ~ (v1 = 0) & relation(v0) = v1) | ( ~ (v1 = 0) & function(v0) = v1)))
% 20.98/5.61 | (104) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 20.98/5.61 | (105) ~ (all_0_11_11 = 0)
% 20.98/5.61 | (106) relation(all_0_0_0) = 0
% 20.98/5.61 | (107) empty(all_0_12_12) = all_0_11_11
% 20.98/5.61 | (108) transfinite_sequence_of(all_0_20_20, all_0_18_18) = all_0_17_17
% 20.98/5.61 | (109) function(all_0_14_14) = 0
% 20.98/5.61 | (110) ? [v0] : ? [v1] : powerset(v0) = v1
% 20.98/5.61 | (111) ! [v0] : ! [v1] : (v1 = 0 | ~ (ordinal(v0) = v1) | ? [v2] : (( ~ (v2 = 0) & epsilon_transitive(v0) = v2) | ( ~ (v2 = 0) & epsilon_connected(v0) = v2)))
% 20.98/5.61 | (112) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (powerset(v1) = v2 & element(v0, v2) = 0))
% 20.98/5.61 | (113) ? [v0] : ? [v1] : transfinite_sequence(v0) = v1
% 20.98/5.61 | (114) relation(all_0_10_10) = 0
% 20.98/5.61 | (115) ! [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))
% 20.98/5.61 | (116) relation(all_0_14_14) = 0
% 20.98/5.61 | (117) function(empty_set) = 0
% 20.98/5.61 | (118) empty(all_0_9_9) = all_0_8_8
% 20.98/5.61 | (119) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (( ~ (v1 = 0) & function(v0) = v1) | (((v3 = 0 & relation_dom(v0) = v2 & ordinal(v2) = 0) | ( ~ (v1 = 0) & transfinite_sequence(v0) = v1)) & ((v1 = 0 & transfinite_sequence(v0) = 0) | ( ~ (v3 = 0) & relation_dom(v0) = v2 & ordinal(v2) = v3)))))
% 20.98/5.61 | (120) ? [v0] : ? [v1] : ordinal(v0) = v1
% 20.98/5.61 | (121) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & relation(v1) = 0 & empty(v1) = 0) | ( ~ (v2 = 0) & empty(v0) = v2)))
% 20.98/5.61 | (122) relation(all_0_13_13) = 0
% 20.98/5.61 | (123) relation_empty_yielding(empty_set) = 0
% 20.98/5.61 | (124) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | element(v0, v1) = 0)
% 20.98/5.61 | (125) epsilon_transitive(all_0_12_12) = 0
% 20.98/5.61 | (126) ~ (all_0_8_8 = 0)
% 20.98/5.61 | (127) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0))
% 20.98/5.61 | (128) ? [v0] : ? [v1] : element(v1, v0) = 0
% 20.98/5.61 | (129) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ((v1 = 0 & empty(v0) = 0) | ( ~ (v2 = 0) & relation_rng(v0) = v1 & empty(v1) = v2)))
% 20.98/5.61 | (130) one_to_one(empty_set) = 0
% 20.98/5.61 | (131) epsilon_connected(all_0_12_12) = 0
% 20.98/5.61 | (132) empty(all_0_5_5) = 0
% 20.98/5.61 | (133) ! [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)))
% 20.98/5.61 | (134) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0))
% 20.98/5.61 | (135) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : (( ~ (v2 = 0) & relation(v0) = v2) | ( ~ (v2 = 0) & function(v0) = v2) | (((v3 = 0 & ordinal(v1) = 0) | ( ~ (v2 = 0) & transfinite_sequence(v0) = v2)) & ((v2 = 0 & transfinite_sequence(v0) = 0) | ( ~ (v3 = 0) & ordinal(v1) = v3)))))
% 20.98/5.61 | (136) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0))
% 20.98/5.61 | (137) one_to_one(all_0_5_5) = 0
% 20.98/5.61 | (138) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0))
% 20.98/5.61 | (139) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ((v2 = 0 & empty(v0) = 0) | ( ~ (v2 = 0) & relation(v0) = v2) | ( ~ (v2 = 0) & empty(v1) = v2)))
% 20.98/5.61 | (140) ! [v0] : ! [v1] : (v1 = 0 | ~ (empty(v0) = v1) | ? [v2] : ? [v3] : (( ~ (v3 = 0) & relation_dom(v0) = v2 & empty(v2) = v3) | ( ~ (v2 = 0) & relation(v0) = v2)))
% 20.98/5.61 | (141) ! [v0] : ! [v1] : (v1 = 0 | ~ (function(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2))
% 20.98/5.61 | (142) epsilon_transitive(all_0_5_5) = 0
% 20.98/5.61 | (143) relation_dom(all_0_20_20) = all_0_19_19
% 20.98/5.61 | (144) ? [v0] : ? [v1] : relation_empty_yielding(v0) = v1
% 20.98/5.61 | (145) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 20.98/5.61 | (146) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v1) = v3 & element(v0, v3) = v4))
% 20.98/5.62 | (147) ! [v0] : ! [v1] : (v1 = 0 | ~ (relation(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2))
% 20.98/5.62 | (148) ! [v0] : ! [v1] : ( ~ (ordinal(v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & epsilon_transitive(v0) = 0 & epsilon_connected(v0) = 0) | ( ~ (v2 = 0) & empty(v0) = v2)))
% 20.98/5.62 | (149) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | subset(v0, v1) = 0)
% 20.98/5.62 | (150) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 20.98/5.62 | (151) empty(all_0_3_3) = 0
% 20.98/5.62 | (152) relation(all_0_7_7) = 0
% 20.98/5.62 | (153) ! [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)))
% 20.98/5.62 | (154) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_empty_yielding(v2) = v1) | ~ (relation_empty_yielding(v2) = v0))
% 20.98/5.62 |
% 20.98/5.62 | Instantiating formula (45) with all_0_17_17, all_0_20_20, all_0_18_18 and discharging atoms transfinite_sequence_of(all_0_20_20, all_0_18_18) = all_0_17_17, yields:
% 20.98/5.62 | (155) ? [v0] : ? [v1] : (( ~ (v0 = 0) & transfinite_sequence(all_0_20_20) = v0) | ( ~ (v0 = 0) & relation(all_0_20_20) = v0) | ( ~ (v0 = 0) & function(all_0_20_20) = v0) | (( ~ (all_0_17_17 = 0) | (v1 = 0 & relation_rng(all_0_20_20) = v0 & subset(v0, all_0_18_18) = 0)) & (all_0_17_17 = 0 | ( ~ (v1 = 0) & relation_rng(all_0_20_20) = v0 & subset(v0, all_0_18_18) = v1))))
% 20.98/5.62 |
% 20.98/5.62 | Instantiating formula (135) with all_0_19_19, all_0_20_20 and discharging atoms relation_dom(all_0_20_20) = all_0_19_19, yields:
% 20.98/5.62 | (156) ? [v0] : ? [v1] : (( ~ (v0 = 0) & relation(all_0_20_20) = v0) | ( ~ (v0 = 0) & function(all_0_20_20) = v0) | (((v1 = 0 & ordinal(all_0_19_19) = 0) | ( ~ (v0 = 0) & transfinite_sequence(all_0_20_20) = v0)) & ((v0 = 0 & transfinite_sequence(all_0_20_20) = 0) | ( ~ (v1 = 0) & ordinal(all_0_19_19) = v1))))
% 20.98/5.62 |
% 20.98/5.62 | Instantiating formula (119) with all_0_20_20 and discharging atoms relation(all_0_20_20) = 0, yields:
% 20.98/5.62 | (157) ? [v0] : ? [v1] : ? [v2] : (( ~ (v0 = 0) & function(all_0_20_20) = v0) | (((v2 = 0 & relation_dom(all_0_20_20) = v1 & ordinal(v1) = 0) | ( ~ (v0 = 0) & transfinite_sequence(all_0_20_20) = v0)) & ((v0 = 0 & transfinite_sequence(all_0_20_20) = 0) | ( ~ (v2 = 0) & relation_dom(all_0_20_20) = v1 & ordinal(v1) = v2))))
% 20.98/5.62 |
% 20.98/5.62 | Instantiating formula (84) with all_0_20_20 and discharging atoms function(all_0_20_20) = 0, yields:
% 20.98/5.62 | (158) ? [v0] : ? [v1] : ? [v2] : (( ~ (v0 = 0) & relation(all_0_20_20) = v0) | (((v2 = 0 & relation_dom(all_0_20_20) = v1 & ordinal(v1) = 0) | ( ~ (v0 = 0) & transfinite_sequence(all_0_20_20) = v0)) & ((v0 = 0 & transfinite_sequence(all_0_20_20) = 0) | ( ~ (v2 = 0) & relation_dom(all_0_20_20) = v1 & ordinal(v1) = v2))))
% 20.98/5.62 |
% 20.98/5.62 | Instantiating (158) with all_72_0_99, all_72_1_100, all_72_2_101 yields:
% 20.98/5.62 | (159) ( ~ (all_72_2_101 = 0) & relation(all_0_20_20) = all_72_2_101) | (((all_72_0_99 = 0 & relation_dom(all_0_20_20) = all_72_1_100 & ordinal(all_72_1_100) = 0) | ( ~ (all_72_2_101 = 0) & transfinite_sequence(all_0_20_20) = all_72_2_101)) & ((all_72_2_101 = 0 & transfinite_sequence(all_0_20_20) = 0) | ( ~ (all_72_0_99 = 0) & relation_dom(all_0_20_20) = all_72_1_100 & ordinal(all_72_1_100) = all_72_0_99)))
% 20.98/5.62 |
% 20.98/5.62 | Instantiating (157) with all_96_0_148, all_96_1_149, all_96_2_150 yields:
% 20.98/5.62 | (160) ( ~ (all_96_2_150 = 0) & function(all_0_20_20) = all_96_2_150) | (((all_96_0_148 = 0 & relation_dom(all_0_20_20) = all_96_1_149 & ordinal(all_96_1_149) = 0) | ( ~ (all_96_2_150 = 0) & transfinite_sequence(all_0_20_20) = all_96_2_150)) & ((all_96_2_150 = 0 & transfinite_sequence(all_0_20_20) = 0) | ( ~ (all_96_0_148 = 0) & relation_dom(all_0_20_20) = all_96_1_149 & ordinal(all_96_1_149) = all_96_0_148)))
% 20.98/5.62 |
% 20.98/5.62 | Instantiating (155) with all_102_0_161, all_102_1_162 yields:
% 20.98/5.62 | (161) ( ~ (all_102_1_162 = 0) & transfinite_sequence(all_0_20_20) = all_102_1_162) | ( ~ (all_102_1_162 = 0) & relation(all_0_20_20) = all_102_1_162) | ( ~ (all_102_1_162 = 0) & function(all_0_20_20) = all_102_1_162) | (( ~ (all_0_17_17 = 0) | (all_102_0_161 = 0 & relation_rng(all_0_20_20) = all_102_1_162 & subset(all_102_1_162, all_0_18_18) = 0)) & (all_0_17_17 = 0 | ( ~ (all_102_0_161 = 0) & relation_rng(all_0_20_20) = all_102_1_162 & subset(all_102_1_162, all_0_18_18) = all_102_0_161)))
% 20.98/5.62 |
% 20.98/5.62 | Instantiating (156) with all_105_0_167, all_105_1_168 yields:
% 20.98/5.62 | (162) ( ~ (all_105_1_168 = 0) & relation(all_0_20_20) = all_105_1_168) | ( ~ (all_105_1_168 = 0) & function(all_0_20_20) = all_105_1_168) | (((all_105_0_167 = 0 & ordinal(all_0_19_19) = 0) | ( ~ (all_105_1_168 = 0) & transfinite_sequence(all_0_20_20) = all_105_1_168)) & ((all_105_1_168 = 0 & transfinite_sequence(all_0_20_20) = 0) | ( ~ (all_105_0_167 = 0) & ordinal(all_0_19_19) = all_105_0_167)))
% 20.98/5.62 |
% 20.98/5.62 +-Applying beta-rule and splitting (159), into two cases.
% 20.98/5.62 |-Branch one:
% 20.98/5.62 | (163) ~ (all_72_2_101 = 0) & relation(all_0_20_20) = all_72_2_101
% 20.98/5.62 |
% 20.98/5.62 | Applying alpha-rule on (163) yields:
% 20.98/5.62 | (164) ~ (all_72_2_101 = 0)
% 20.98/5.62 | (165) relation(all_0_20_20) = all_72_2_101
% 20.98/5.62 |
% 20.98/5.62 | Instantiating formula (22) with all_0_20_20, all_72_2_101, 0 and discharging atoms relation(all_0_20_20) = all_72_2_101, relation(all_0_20_20) = 0, yields:
% 20.98/5.62 | (166) all_72_2_101 = 0
% 20.98/5.62 |
% 20.98/5.62 | Equations (166) can reduce 164 to:
% 20.98/5.62 | (167) $false
% 20.98/5.62 |
% 20.98/5.63 |-The branch is then unsatisfiable
% 20.98/5.63 |-Branch two:
% 20.98/5.63 | (168) ((all_72_0_99 = 0 & relation_dom(all_0_20_20) = all_72_1_100 & ordinal(all_72_1_100) = 0) | ( ~ (all_72_2_101 = 0) & transfinite_sequence(all_0_20_20) = all_72_2_101)) & ((all_72_2_101 = 0 & transfinite_sequence(all_0_20_20) = 0) | ( ~ (all_72_0_99 = 0) & relation_dom(all_0_20_20) = all_72_1_100 & ordinal(all_72_1_100) = all_72_0_99))
% 20.98/5.63 |
% 20.98/5.63 | Applying alpha-rule on (168) yields:
% 20.98/5.63 | (169) (all_72_0_99 = 0 & relation_dom(all_0_20_20) = all_72_1_100 & ordinal(all_72_1_100) = 0) | ( ~ (all_72_2_101 = 0) & transfinite_sequence(all_0_20_20) = all_72_2_101)
% 20.98/5.63 | (170) (all_72_2_101 = 0 & transfinite_sequence(all_0_20_20) = 0) | ( ~ (all_72_0_99 = 0) & relation_dom(all_0_20_20) = all_72_1_100 & ordinal(all_72_1_100) = all_72_0_99)
% 20.98/5.63 |
% 20.98/5.63 +-Applying beta-rule and splitting (170), into two cases.
% 20.98/5.63 |-Branch one:
% 20.98/5.63 | (171) all_72_2_101 = 0 & transfinite_sequence(all_0_20_20) = 0
% 20.98/5.63 |
% 20.98/5.63 | Applying alpha-rule on (171) yields:
% 20.98/5.63 | (166) all_72_2_101 = 0
% 20.98/5.63 | (173) transfinite_sequence(all_0_20_20) = 0
% 20.98/5.63 |
% 20.98/5.63 +-Applying beta-rule and splitting (161), into two cases.
% 20.98/5.63 |-Branch one:
% 20.98/5.63 | (174) ( ~ (all_102_1_162 = 0) & transfinite_sequence(all_0_20_20) = all_102_1_162) | ( ~ (all_102_1_162 = 0) & relation(all_0_20_20) = all_102_1_162) | ( ~ (all_102_1_162 = 0) & function(all_0_20_20) = all_102_1_162)
% 20.98/5.63 |
% 20.98/5.63 +-Applying beta-rule and splitting (174), into two cases.
% 20.98/5.63 |-Branch one:
% 20.98/5.63 | (175) ( ~ (all_102_1_162 = 0) & transfinite_sequence(all_0_20_20) = all_102_1_162) | ( ~ (all_102_1_162 = 0) & relation(all_0_20_20) = all_102_1_162)
% 20.98/5.63 |
% 20.98/5.63 +-Applying beta-rule and splitting (175), into two cases.
% 20.98/5.63 |-Branch one:
% 20.98/5.63 | (176) ~ (all_102_1_162 = 0) & transfinite_sequence(all_0_20_20) = all_102_1_162
% 20.98/5.63 |
% 20.98/5.63 | Applying alpha-rule on (176) yields:
% 20.98/5.63 | (177) ~ (all_102_1_162 = 0)
% 20.98/5.63 | (178) transfinite_sequence(all_0_20_20) = all_102_1_162
% 20.98/5.63 |
% 20.98/5.63 +-Applying beta-rule and splitting (160), into two cases.
% 20.98/5.63 |-Branch one:
% 20.98/5.63 | (179) ~ (all_96_2_150 = 0) & function(all_0_20_20) = all_96_2_150
% 20.98/5.63 |
% 20.98/5.63 | Applying alpha-rule on (179) yields:
% 20.98/5.63 | (180) ~ (all_96_2_150 = 0)
% 20.98/5.63 | (181) function(all_0_20_20) = all_96_2_150
% 20.98/5.63 |
% 20.98/5.63 | Instantiating formula (134) with all_0_20_20, all_96_2_150, 0 and discharging atoms function(all_0_20_20) = all_96_2_150, function(all_0_20_20) = 0, yields:
% 20.98/5.63 | (182) all_96_2_150 = 0
% 20.98/5.63 |
% 20.98/5.63 | Equations (182) can reduce 180 to:
% 20.98/5.63 | (167) $false
% 20.98/5.63 |
% 20.98/5.63 |-The branch is then unsatisfiable
% 20.98/5.63 |-Branch two:
% 20.98/5.63 | (184) ((all_96_0_148 = 0 & relation_dom(all_0_20_20) = all_96_1_149 & ordinal(all_96_1_149) = 0) | ( ~ (all_96_2_150 = 0) & transfinite_sequence(all_0_20_20) = all_96_2_150)) & ((all_96_2_150 = 0 & transfinite_sequence(all_0_20_20) = 0) | ( ~ (all_96_0_148 = 0) & relation_dom(all_0_20_20) = all_96_1_149 & ordinal(all_96_1_149) = all_96_0_148))
% 20.98/5.63 |
% 20.98/5.63 | Applying alpha-rule on (184) yields:
% 20.98/5.63 | (185) (all_96_0_148 = 0 & relation_dom(all_0_20_20) = all_96_1_149 & ordinal(all_96_1_149) = 0) | ( ~ (all_96_2_150 = 0) & transfinite_sequence(all_0_20_20) = all_96_2_150)
% 20.98/5.63 | (186) (all_96_2_150 = 0 & transfinite_sequence(all_0_20_20) = 0) | ( ~ (all_96_0_148 = 0) & relation_dom(all_0_20_20) = all_96_1_149 & ordinal(all_96_1_149) = all_96_0_148)
% 20.98/5.63 |
% 20.98/5.63 +-Applying beta-rule and splitting (186), into two cases.
% 20.98/5.63 |-Branch one:
% 20.98/5.63 | (187) all_96_2_150 = 0 & transfinite_sequence(all_0_20_20) = 0
% 20.98/5.63 |
% 20.98/5.63 | Applying alpha-rule on (187) yields:
% 20.98/5.63 | (182) all_96_2_150 = 0
% 20.98/5.63 | (173) transfinite_sequence(all_0_20_20) = 0
% 20.98/5.63 |
% 20.98/5.63 | Instantiating formula (39) with all_0_20_20, 0, all_102_1_162 and discharging atoms transfinite_sequence(all_0_20_20) = all_102_1_162, transfinite_sequence(all_0_20_20) = 0, yields:
% 20.98/5.63 | (190) all_102_1_162 = 0
% 20.98/5.63 |
% 20.98/5.63 | Equations (190) can reduce 177 to:
% 20.98/5.63 | (167) $false
% 20.98/5.63 |
% 20.98/5.63 |-The branch is then unsatisfiable
% 20.98/5.63 |-Branch two:
% 20.98/5.63 | (192) ~ (all_96_0_148 = 0) & relation_dom(all_0_20_20) = all_96_1_149 & ordinal(all_96_1_149) = all_96_0_148
% 20.98/5.63 |
% 20.98/5.63 | Applying alpha-rule on (192) yields:
% 20.98/5.63 | (193) ~ (all_96_0_148 = 0)
% 20.98/5.63 | (194) relation_dom(all_0_20_20) = all_96_1_149
% 20.98/5.63 | (195) ordinal(all_96_1_149) = all_96_0_148
% 20.98/5.63 |
% 20.98/5.63 +-Applying beta-rule and splitting (185), into two cases.
% 20.98/5.63 |-Branch one:
% 20.98/5.63 | (196) all_96_0_148 = 0 & relation_dom(all_0_20_20) = all_96_1_149 & ordinal(all_96_1_149) = 0
% 20.98/5.63 |
% 20.98/5.63 | Applying alpha-rule on (196) yields:
% 20.98/5.63 | (197) all_96_0_148 = 0
% 20.98/5.63 | (194) relation_dom(all_0_20_20) = all_96_1_149
% 20.98/5.63 | (199) ordinal(all_96_1_149) = 0
% 20.98/5.63 |
% 20.98/5.63 | Equations (197) can reduce 193 to:
% 20.98/5.63 | (167) $false
% 20.98/5.63 |
% 20.98/5.63 |-The branch is then unsatisfiable
% 20.98/5.63 |-Branch two:
% 20.98/5.63 | (201) ~ (all_96_2_150 = 0) & transfinite_sequence(all_0_20_20) = all_96_2_150
% 20.98/5.63 |
% 20.98/5.63 | Applying alpha-rule on (201) yields:
% 20.98/5.63 | (180) ~ (all_96_2_150 = 0)
% 20.98/5.63 | (203) transfinite_sequence(all_0_20_20) = all_96_2_150
% 20.98/5.63 |
% 20.98/5.63 | Instantiating formula (39) with all_0_20_20, all_96_2_150, all_102_1_162 and discharging atoms transfinite_sequence(all_0_20_20) = all_102_1_162, transfinite_sequence(all_0_20_20) = all_96_2_150, yields:
% 20.98/5.63 | (204) all_102_1_162 = all_96_2_150
% 20.98/5.63 |
% 20.98/5.63 | Instantiating formula (39) with all_0_20_20, 0, all_102_1_162 and discharging atoms transfinite_sequence(all_0_20_20) = all_102_1_162, transfinite_sequence(all_0_20_20) = 0, yields:
% 20.98/5.63 | (190) all_102_1_162 = 0
% 20.98/5.63 |
% 20.98/5.63 | Combining equations (190,204) yields a new equation:
% 20.98/5.63 | (182) all_96_2_150 = 0
% 20.98/5.63 |
% 20.98/5.63 | Equations (182) can reduce 180 to:
% 20.98/5.63 | (167) $false
% 20.98/5.63 |
% 20.98/5.63 |-The branch is then unsatisfiable
% 20.98/5.63 |-Branch two:
% 20.98/5.63 | (208) ~ (all_102_1_162 = 0) & relation(all_0_20_20) = all_102_1_162
% 20.98/5.63 |
% 20.98/5.63 | Applying alpha-rule on (208) yields:
% 20.98/5.63 | (177) ~ (all_102_1_162 = 0)
% 20.98/5.63 | (210) relation(all_0_20_20) = all_102_1_162
% 20.98/5.63 |
% 20.98/5.63 | Instantiating formula (22) with all_0_20_20, all_102_1_162, 0 and discharging atoms relation(all_0_20_20) = all_102_1_162, relation(all_0_20_20) = 0, yields:
% 20.98/5.63 | (190) all_102_1_162 = 0
% 20.98/5.63 |
% 20.98/5.63 | Equations (190) can reduce 177 to:
% 20.98/5.63 | (167) $false
% 20.98/5.63 |
% 20.98/5.63 |-The branch is then unsatisfiable
% 20.98/5.64 |-Branch two:
% 20.98/5.64 | (213) ~ (all_102_1_162 = 0) & function(all_0_20_20) = all_102_1_162
% 20.98/5.64 |
% 20.98/5.64 | Applying alpha-rule on (213) yields:
% 20.98/5.64 | (177) ~ (all_102_1_162 = 0)
% 20.98/5.64 | (215) function(all_0_20_20) = all_102_1_162
% 20.98/5.64 |
% 20.98/5.64 | Instantiating formula (134) with all_0_20_20, all_102_1_162, 0 and discharging atoms function(all_0_20_20) = all_102_1_162, function(all_0_20_20) = 0, yields:
% 20.98/5.64 | (190) all_102_1_162 = 0
% 20.98/5.64 |
% 20.98/5.64 | Equations (190) can reduce 177 to:
% 20.98/5.64 | (167) $false
% 20.98/5.64 |
% 20.98/5.64 |-The branch is then unsatisfiable
% 20.98/5.64 |-Branch two:
% 20.98/5.64 | (218) ( ~ (all_0_17_17 = 0) | (all_102_0_161 = 0 & relation_rng(all_0_20_20) = all_102_1_162 & subset(all_102_1_162, all_0_18_18) = 0)) & (all_0_17_17 = 0 | ( ~ (all_102_0_161 = 0) & relation_rng(all_0_20_20) = all_102_1_162 & subset(all_102_1_162, all_0_18_18) = all_102_0_161))
% 20.98/5.64 |
% 20.98/5.64 | Applying alpha-rule on (218) yields:
% 20.98/5.64 | (219) ~ (all_0_17_17 = 0) | (all_102_0_161 = 0 & relation_rng(all_0_20_20) = all_102_1_162 & subset(all_102_1_162, all_0_18_18) = 0)
% 20.98/5.64 | (220) all_0_17_17 = 0 | ( ~ (all_102_0_161 = 0) & relation_rng(all_0_20_20) = all_102_1_162 & subset(all_102_1_162, all_0_18_18) = all_102_0_161)
% 20.98/5.64 |
% 20.98/5.64 +-Applying beta-rule and splitting (220), into two cases.
% 20.98/5.64 |-Branch one:
% 20.98/5.64 | (221) all_0_17_17 = 0
% 20.98/5.64 |
% 20.98/5.64 | Equations (221) can reduce 11 to:
% 20.98/5.64 | (167) $false
% 20.98/5.64 |
% 20.98/5.64 |-The branch is then unsatisfiable
% 20.98/5.64 |-Branch two:
% 20.98/5.64 | (11) ~ (all_0_17_17 = 0)
% 20.98/5.64 | (224) ~ (all_102_0_161 = 0) & relation_rng(all_0_20_20) = all_102_1_162 & subset(all_102_1_162, all_0_18_18) = all_102_0_161
% 20.98/5.64 |
% 20.98/5.64 | Applying alpha-rule on (224) yields:
% 20.98/5.64 | (225) ~ (all_102_0_161 = 0)
% 20.98/5.64 | (226) relation_rng(all_0_20_20) = all_102_1_162
% 20.98/5.64 | (227) subset(all_102_1_162, all_0_18_18) = all_102_0_161
% 20.98/5.64 |
% 20.98/5.64 | Instantiating formula (67) with all_0_20_20, all_102_1_162, all_0_18_18 and discharging atoms relation_rng(all_0_20_20) = all_102_1_162, relation_rng(all_0_20_20) = all_0_18_18, yields:
% 20.98/5.64 | (228) all_102_1_162 = all_0_18_18
% 20.98/5.64 |
% 20.98/5.64 | From (228) and (227) follows:
% 20.98/5.64 | (229) subset(all_0_18_18, all_0_18_18) = all_102_0_161
% 20.98/5.64 |
% 20.98/5.64 | Instantiating formula (46) with all_102_0_161, all_0_18_18 and discharging atoms subset(all_0_18_18, all_0_18_18) = all_102_0_161, yields:
% 20.98/5.64 | (230) all_102_0_161 = 0
% 20.98/5.64 |
% 20.98/5.64 | Equations (230) can reduce 225 to:
% 20.98/5.64 | (167) $false
% 20.98/5.64 |
% 20.98/5.64 |-The branch is then unsatisfiable
% 20.98/5.64 |-Branch two:
% 20.98/5.64 | (232) ~ (all_72_0_99 = 0) & relation_dom(all_0_20_20) = all_72_1_100 & ordinal(all_72_1_100) = all_72_0_99
% 20.98/5.64 |
% 20.98/5.64 | Applying alpha-rule on (232) yields:
% 20.98/5.64 | (233) ~ (all_72_0_99 = 0)
% 20.98/5.64 | (234) relation_dom(all_0_20_20) = all_72_1_100
% 20.98/5.64 | (235) ordinal(all_72_1_100) = all_72_0_99
% 20.98/5.64 |
% 20.98/5.64 +-Applying beta-rule and splitting (160), into two cases.
% 20.98/5.64 |-Branch one:
% 20.98/5.64 | (179) ~ (all_96_2_150 = 0) & function(all_0_20_20) = all_96_2_150
% 20.98/5.64 |
% 20.98/5.64 | Applying alpha-rule on (179) yields:
% 20.98/5.64 | (180) ~ (all_96_2_150 = 0)
% 20.98/5.64 | (181) function(all_0_20_20) = all_96_2_150
% 20.98/5.64 |
% 20.98/5.64 | Instantiating formula (134) with all_0_20_20, all_96_2_150, 0 and discharging atoms function(all_0_20_20) = all_96_2_150, function(all_0_20_20) = 0, yields:
% 20.98/5.64 | (182) all_96_2_150 = 0
% 20.98/5.64 |
% 20.98/5.64 | Equations (182) can reduce 180 to:
% 20.98/5.64 | (167) $false
% 20.98/5.64 |
% 20.98/5.64 |-The branch is then unsatisfiable
% 20.98/5.64 |-Branch two:
% 20.98/5.64 | (184) ((all_96_0_148 = 0 & relation_dom(all_0_20_20) = all_96_1_149 & ordinal(all_96_1_149) = 0) | ( ~ (all_96_2_150 = 0) & transfinite_sequence(all_0_20_20) = all_96_2_150)) & ((all_96_2_150 = 0 & transfinite_sequence(all_0_20_20) = 0) | ( ~ (all_96_0_148 = 0) & relation_dom(all_0_20_20) = all_96_1_149 & ordinal(all_96_1_149) = all_96_0_148))
% 20.98/5.64 |
% 20.98/5.64 | Applying alpha-rule on (184) yields:
% 20.98/5.64 | (185) (all_96_0_148 = 0 & relation_dom(all_0_20_20) = all_96_1_149 & ordinal(all_96_1_149) = 0) | ( ~ (all_96_2_150 = 0) & transfinite_sequence(all_0_20_20) = all_96_2_150)
% 20.98/5.64 | (186) (all_96_2_150 = 0 & transfinite_sequence(all_0_20_20) = 0) | ( ~ (all_96_0_148 = 0) & relation_dom(all_0_20_20) = all_96_1_149 & ordinal(all_96_1_149) = all_96_0_148)
% 20.98/5.64 |
% 20.98/5.64 +-Applying beta-rule and splitting (185), into two cases.
% 20.98/5.64 |-Branch one:
% 20.98/5.64 | (196) all_96_0_148 = 0 & relation_dom(all_0_20_20) = all_96_1_149 & ordinal(all_96_1_149) = 0
% 20.98/5.64 |
% 20.98/5.64 | Applying alpha-rule on (196) yields:
% 20.98/5.64 | (197) all_96_0_148 = 0
% 20.98/5.64 | (194) relation_dom(all_0_20_20) = all_96_1_149
% 20.98/5.64 | (199) ordinal(all_96_1_149) = 0
% 20.98/5.64 |
% 20.98/5.64 +-Applying beta-rule and splitting (186), into two cases.
% 20.98/5.64 |-Branch one:
% 20.98/5.64 | (187) all_96_2_150 = 0 & transfinite_sequence(all_0_20_20) = 0
% 20.98/5.64 |
% 20.98/5.64 | Applying alpha-rule on (187) yields:
% 20.98/5.64 | (182) all_96_2_150 = 0
% 20.98/5.64 | (173) transfinite_sequence(all_0_20_20) = 0
% 20.98/5.64 |
% 20.98/5.64 +-Applying beta-rule and splitting (169), into two cases.
% 20.98/5.64 |-Branch one:
% 20.98/5.64 | (251) all_72_0_99 = 0 & relation_dom(all_0_20_20) = all_72_1_100 & ordinal(all_72_1_100) = 0
% 20.98/5.64 |
% 20.98/5.64 | Applying alpha-rule on (251) yields:
% 20.98/5.64 | (252) all_72_0_99 = 0
% 20.98/5.64 | (234) relation_dom(all_0_20_20) = all_72_1_100
% 20.98/5.64 | (254) ordinal(all_72_1_100) = 0
% 20.98/5.64 |
% 20.98/5.64 | Equations (252) can reduce 233 to:
% 20.98/5.64 | (167) $false
% 20.98/5.64 |
% 20.98/5.64 |-The branch is then unsatisfiable
% 20.98/5.64 |-Branch two:
% 20.98/5.64 | (256) ~ (all_72_2_101 = 0) & transfinite_sequence(all_0_20_20) = all_72_2_101
% 20.98/5.64 |
% 20.98/5.64 | Applying alpha-rule on (256) yields:
% 20.98/5.64 | (164) ~ (all_72_2_101 = 0)
% 20.98/5.64 | (258) transfinite_sequence(all_0_20_20) = all_72_2_101
% 20.98/5.64 |
% 20.98/5.64 | Instantiating formula (39) with all_0_20_20, 0, all_72_2_101 and discharging atoms transfinite_sequence(all_0_20_20) = all_72_2_101, transfinite_sequence(all_0_20_20) = 0, yields:
% 20.98/5.64 | (166) all_72_2_101 = 0
% 20.98/5.64 |
% 20.98/5.64 | Equations (166) can reduce 164 to:
% 20.98/5.64 | (167) $false
% 20.98/5.64 |
% 20.98/5.64 |-The branch is then unsatisfiable
% 20.98/5.64 |-Branch two:
% 20.98/5.64 | (192) ~ (all_96_0_148 = 0) & relation_dom(all_0_20_20) = all_96_1_149 & ordinal(all_96_1_149) = all_96_0_148
% 20.98/5.64 |
% 20.98/5.64 | Applying alpha-rule on (192) yields:
% 20.98/5.64 | (193) ~ (all_96_0_148 = 0)
% 20.98/5.64 | (194) relation_dom(all_0_20_20) = all_96_1_149
% 20.98/5.64 | (195) ordinal(all_96_1_149) = all_96_0_148
% 20.98/5.64 |
% 20.98/5.64 | Equations (197) can reduce 193 to:
% 20.98/5.64 | (167) $false
% 20.98/5.64 |
% 20.98/5.64 |-The branch is then unsatisfiable
% 20.98/5.64 |-Branch two:
% 20.98/5.64 | (201) ~ (all_96_2_150 = 0) & transfinite_sequence(all_0_20_20) = all_96_2_150
% 20.98/5.64 |
% 20.98/5.64 | Applying alpha-rule on (201) yields:
% 20.98/5.64 | (180) ~ (all_96_2_150 = 0)
% 20.98/5.64 | (203) transfinite_sequence(all_0_20_20) = all_96_2_150
% 20.98/5.64 |
% 20.98/5.64 +-Applying beta-rule and splitting (162), into two cases.
% 20.98/5.64 |-Branch one:
% 20.98/5.64 | (269) ( ~ (all_105_1_168 = 0) & relation(all_0_20_20) = all_105_1_168) | ( ~ (all_105_1_168 = 0) & function(all_0_20_20) = all_105_1_168)
% 20.98/5.64 |
% 20.98/5.64 +-Applying beta-rule and splitting (269), into two cases.
% 20.98/5.64 |-Branch one:
% 20.98/5.64 | (270) ~ (all_105_1_168 = 0) & relation(all_0_20_20) = all_105_1_168
% 20.98/5.64 |
% 20.98/5.64 | Applying alpha-rule on (270) yields:
% 20.98/5.64 | (271) ~ (all_105_1_168 = 0)
% 20.98/5.64 | (272) relation(all_0_20_20) = all_105_1_168
% 20.98/5.64 |
% 20.98/5.64 | Instantiating formula (22) with all_0_20_20, all_105_1_168, 0 and discharging atoms relation(all_0_20_20) = all_105_1_168, relation(all_0_20_20) = 0, yields:
% 20.98/5.64 | (273) all_105_1_168 = 0
% 20.98/5.64 |
% 20.98/5.64 | Equations (273) can reduce 271 to:
% 20.98/5.64 | (167) $false
% 20.98/5.64 |
% 20.98/5.64 |-The branch is then unsatisfiable
% 20.98/5.64 |-Branch two:
% 20.98/5.64 | (275) ~ (all_105_1_168 = 0) & function(all_0_20_20) = all_105_1_168
% 20.98/5.64 |
% 20.98/5.64 | Applying alpha-rule on (275) yields:
% 20.98/5.64 | (271) ~ (all_105_1_168 = 0)
% 20.98/5.64 | (277) function(all_0_20_20) = all_105_1_168
% 20.98/5.64 |
% 20.98/5.64 | Instantiating formula (134) with all_0_20_20, all_105_1_168, 0 and discharging atoms function(all_0_20_20) = all_105_1_168, function(all_0_20_20) = 0, yields:
% 20.98/5.64 | (273) all_105_1_168 = 0
% 20.98/5.64 |
% 20.98/5.64 | Equations (273) can reduce 271 to:
% 20.98/5.64 | (167) $false
% 20.98/5.64 |
% 20.98/5.64 |-The branch is then unsatisfiable
% 20.98/5.64 |-Branch two:
% 20.98/5.64 | (280) ((all_105_0_167 = 0 & ordinal(all_0_19_19) = 0) | ( ~ (all_105_1_168 = 0) & transfinite_sequence(all_0_20_20) = all_105_1_168)) & ((all_105_1_168 = 0 & transfinite_sequence(all_0_20_20) = 0) | ( ~ (all_105_0_167 = 0) & ordinal(all_0_19_19) = all_105_0_167))
% 20.98/5.64 |
% 20.98/5.64 | Applying alpha-rule on (280) yields:
% 20.98/5.64 | (281) (all_105_0_167 = 0 & ordinal(all_0_19_19) = 0) | ( ~ (all_105_1_168 = 0) & transfinite_sequence(all_0_20_20) = all_105_1_168)
% 20.98/5.64 | (282) (all_105_1_168 = 0 & transfinite_sequence(all_0_20_20) = 0) | ( ~ (all_105_0_167 = 0) & ordinal(all_0_19_19) = all_105_0_167)
% 20.98/5.64 |
% 20.98/5.64 +-Applying beta-rule and splitting (169), into two cases.
% 20.98/5.64 |-Branch one:
% 20.98/5.64 | (251) all_72_0_99 = 0 & relation_dom(all_0_20_20) = all_72_1_100 & ordinal(all_72_1_100) = 0
% 20.98/5.64 |
% 20.98/5.64 | Applying alpha-rule on (251) yields:
% 20.98/5.64 | (252) all_72_0_99 = 0
% 20.98/5.64 | (234) relation_dom(all_0_20_20) = all_72_1_100
% 20.98/5.64 | (254) ordinal(all_72_1_100) = 0
% 20.98/5.64 |
% 20.98/5.64 | Equations (252) can reduce 233 to:
% 20.98/5.64 | (167) $false
% 20.98/5.64 |
% 20.98/5.64 |-The branch is then unsatisfiable
% 20.98/5.64 |-Branch two:
% 20.98/5.64 | (256) ~ (all_72_2_101 = 0) & transfinite_sequence(all_0_20_20) = all_72_2_101
% 20.98/5.64 |
% 20.98/5.64 | Applying alpha-rule on (256) yields:
% 20.98/5.64 | (164) ~ (all_72_2_101 = 0)
% 20.98/5.64 | (258) transfinite_sequence(all_0_20_20) = all_72_2_101
% 20.98/5.64 |
% 20.98/5.64 +-Applying beta-rule and splitting (282), into two cases.
% 20.98/5.64 |-Branch one:
% 20.98/5.64 | (291) all_105_1_168 = 0 & transfinite_sequence(all_0_20_20) = 0
% 20.98/5.64 |
% 20.98/5.64 | Applying alpha-rule on (291) yields:
% 20.98/5.64 | (273) all_105_1_168 = 0
% 20.98/5.64 | (173) transfinite_sequence(all_0_20_20) = 0
% 20.98/5.64 |
% 20.98/5.64 | Instantiating formula (39) with all_0_20_20, all_72_2_101, all_96_2_150 and discharging atoms transfinite_sequence(all_0_20_20) = all_96_2_150, transfinite_sequence(all_0_20_20) = all_72_2_101, yields:
% 20.98/5.64 | (294) all_96_2_150 = all_72_2_101
% 20.98/5.64 |
% 20.98/5.64 | Instantiating formula (39) with all_0_20_20, 0, all_96_2_150 and discharging atoms transfinite_sequence(all_0_20_20) = all_96_2_150, transfinite_sequence(all_0_20_20) = 0, yields:
% 20.98/5.65 | (182) all_96_2_150 = 0
% 20.98/5.65 |
% 20.98/5.65 | Combining equations (182,294) yields a new equation:
% 20.98/5.65 | (166) all_72_2_101 = 0
% 20.98/5.65 |
% 20.98/5.65 | Equations (166) can reduce 164 to:
% 20.98/5.65 | (167) $false
% 20.98/5.65 |
% 20.98/5.65 |-The branch is then unsatisfiable
% 20.98/5.65 |-Branch two:
% 20.98/5.65 | (298) ~ (all_105_0_167 = 0) & ordinal(all_0_19_19) = all_105_0_167
% 20.98/5.65 |
% 20.98/5.65 | Applying alpha-rule on (298) yields:
% 20.98/5.65 | (299) ~ (all_105_0_167 = 0)
% 20.98/5.65 | (300) ordinal(all_0_19_19) = all_105_0_167
% 20.98/5.65 |
% 20.98/5.65 | Instantiating formula (27) with all_0_19_19, all_105_0_167, 0 and discharging atoms ordinal(all_0_19_19) = all_105_0_167, ordinal(all_0_19_19) = 0, yields:
% 20.98/5.65 | (301) all_105_0_167 = 0
% 20.98/5.65 |
% 20.98/5.65 | Equations (301) can reduce 299 to:
% 20.98/5.65 | (167) $false
% 20.98/5.65 |
% 20.98/5.65 |-The branch is then unsatisfiable
% 20.98/5.65 % SZS output end Proof for theBenchmark
% 20.98/5.65
% 20.98/5.65 5033ms
%------------------------------------------------------------------------------