TSTP Solution File: SEU294+3 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU294+3 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n014.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 08:48:34 EDT 2022
% Result : Theorem 19.11s 5.18s
% Output : Proof 22.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09 % Problem : SEU294+3 : TPTP v8.1.0. Released v3.2.0.
% 0.05/0.09 % Command : ePrincess-casc -timeout=%d %s
% 0.09/0.28 % Computer : n014.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8042.1875MB
% 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28 % CPULimit : 300
% 0.09/0.28 % WCLimit : 600
% 0.09/0.28 % DateTime : Mon Jun 20 09:23:47 EDT 2022
% 0.09/0.28 % CPUTime :
% 0.13/0.52 ____ _
% 0.13/0.52 ___ / __ \_____(_)___ ________ __________
% 0.13/0.52 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.13/0.52 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.13/0.52 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.13/0.52
% 0.13/0.52 A Theorem Prover for First-Order Logic
% 0.13/0.52 (ePrincess v.1.0)
% 0.13/0.52
% 0.13/0.52 (c) Philipp Rümmer, 2009-2015
% 0.13/0.52 (c) Peter Backeman, 2014-2015
% 0.13/0.52 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.13/0.52 Free software under GNU Lesser General Public License (LGPL).
% 0.13/0.52 Bug reports to peter@backeman.se
% 0.13/0.52
% 0.13/0.52 For more information, visit http://user.uu.se/~petba168/breu/
% 0.13/0.52
% 0.13/0.52 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.58/0.59 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.72/0.94 Prover 0: Preprocessing ...
% 2.13/1.14 Prover 0: Warning: ignoring some quantifiers
% 2.33/1.17 Prover 0: Constructing countermodel ...
% 3.52/1.45 Prover 0: gave up
% 3.52/1.45 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 3.65/1.50 Prover 1: Preprocessing ...
% 4.43/1.64 Prover 1: Warning: ignoring some quantifiers
% 4.43/1.65 Prover 1: Constructing countermodel ...
% 17.40/4.79 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 17.69/4.84 Prover 2: Preprocessing ...
% 18.20/4.99 Prover 2: Warning: ignoring some quantifiers
% 18.20/5.00 Prover 2: Constructing countermodel ...
% 19.11/5.18 Prover 2: proved (392ms)
% 19.11/5.18 Prover 1: stopped
% 19.11/5.18
% 19.11/5.18 No countermodel exists, formula is valid
% 19.11/5.18 % SZS status Theorem for theBenchmark
% 19.11/5.18
% 19.11/5.18 Generating proof ... Warning: ignoring some quantifiers
% 22.10/5.87 found it (size 30)
% 22.10/5.87
% 22.10/5.87 % SZS output start Proof for theBenchmark
% 22.10/5.87 Assumed formulas after preprocessing and simplification:
% 22.10/5.87 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : ? [v27] : ? [v28] : ? [v29] : ? [v30] : ( ~ (v30 = 0) & ~ (v28 = 0) & ~ (v20 = 0) & ~ (v15 = 0) & ~ (v13 = 0) & ~ (v9 = 0) & ~ (v3 = 0) & ~ (v0 = 0) & subset(v1, v2) = 0 & relation_non_empty(v4) = 0 & relation_empty_yielding(v7) = 0 & relation_empty_yielding(v6) = 0 & relation_empty_yielding(empty_set) = 0 & transfinite_sequence(v16) = 0 & transfinite_sequence(v5) = 0 & ordinal_yielding(v16) = 0 & being_limit_ordinal(v23) = 0 & function_yielding(v26) = 0 & one_to_one(v17) = 0 & one_to_one(v10) = 0 & one_to_one(empty_set) = 0 & natural(v29) = 0 & natural(v11) = 0 & relation(v26) = 0 & relation(v25) = 0 & relation(v22) = 0 & relation(v18) = 0 & relation(v17) = 0 & relation(v16) = 0 & relation(v14) = 0 & relation(v10) = 0 & relation(v7) = 0 & relation(v6) = 0 & relation(v5) = 0 & relation(v4) = 0 & relation(empty_set) = 0 & function(v26) = 0 & function(v25) = 0 & function(v18) = 0 & function(v17) = 0 & function(v16) = 0 & function(v10) = 0 & function(v6) = 0 & function(v5) = 0 & function(v4) = 0 & function(empty_set) = 0 & finite(v27) = 0 & finite(v2) = 0 & finite(v1) = v3 & empty(v29) = v30 & empty(v27) = v28 & empty(v22) = 0 & empty(v21) = 0 & empty(v19) = v20 & empty(v18) = 0 & empty(v17) = 0 & empty(v14) = v15 & empty(v12) = v13 & empty(v11) = 0 & empty(v8) = v9 & empty(empty_set) = 0 & empty(positive_rationals) = v0 & epsilon_connected(v29) = 0 & epsilon_connected(v24) = 0 & epsilon_connected(v23) = 0 & epsilon_connected(v19) = 0 & epsilon_connected(v17) = 0 & epsilon_connected(v11) = 0 & epsilon_connected(v8) = 0 & epsilon_connected(empty_set) = 0 & element(v19, positive_rationals) = 0 & element(v11, positive_rationals) = 0 & epsilon_transitive(v29) = 0 & epsilon_transitive(v24) = 0 & epsilon_transitive(v23) = 0 & epsilon_transitive(v19) = 0 & epsilon_transitive(v17) = 0 & epsilon_transitive(v11) = 0 & epsilon_transitive(v8) = 0 & epsilon_transitive(empty_set) = 0 & ordinal(v29) = 0 & ordinal(v24) = 0 & ordinal(v23) = 0 & ordinal(v19) = 0 & ordinal(v17) = 0 & ordinal(v11) = 0 & ordinal(v8) = 0 & ordinal(empty_set) = 0 & ! [v31] : ! [v32] : ! [v33] : ! [v34] : ! [v35] : (v35 = 0 | ~ (powerset(v33) = v34) | ~ (element(v32, v34) = 0) | ~ (element(v31, v33) = v35) | ? [v36] : ( ~ (v36 = 0) & in(v31, v32) = v36)) & ! [v31] : ! [v32] : ! [v33] : ! [v34] : (v34 = 0 | ~ (powerset(v32) = v33) | ~ (element(v31, v33) = v34) | ? [v35] : ( ~ (v35 = 0) & subset(v31, v32) = v35)) & ! [v31] : ! [v32] : ! [v33] : ! [v34] : (v34 = 0 | ~ (powerset(v31) = v32) | ~ (finite(v33) = v34) | ? [v35] : (( ~ (v35 = 0) & finite(v31) = v35) | ( ~ (v35 = 0) & element(v33, v32) = v35))) & ! [v31] : ! [v32] : ! [v33] : ! [v34] : (v34 = 0 | ~ (element(v31, v33) = v34) | ~ (in(v31, v32) = 0) | ? [v35] : ? [v36] : ( ~ (v36 = 0) & powerset(v33) = v35 & element(v32, v35) = v36)) & ! [v31] : ! [v32] : ! [v33] : ! [v34] : (v32 = v31 | ~ (subset(v34, v33) = v32) | ~ (subset(v34, v33) = v31)) & ! [v31] : ! [v32] : ! [v33] : ! [v34] : (v32 = v31 | ~ (element(v34, v33) = v32) | ~ (element(v34, v33) = v31)) & ! [v31] : ! [v32] : ! [v33] : ! [v34] : (v32 = v31 | ~ (in(v34, v33) = v32) | ~ (in(v34, v33) = v31)) & ! [v31] : ! [v32] : ! [v33] : ! [v34] : ( ~ (powerset(v33) = v34) | ~ (element(v32, v34) = 0) | ~ (in(v31, v32) = 0) | element(v31, v33) = 0) & ! [v31] : ! [v32] : ! [v33] : ! [v34] : ( ~ (powerset(v33) = v34) | ~ (element(v32, v34) = 0) | ~ (in(v31, v32) = 0) | ? [v35] : ( ~ (v35 = 0) & empty(v33) = v35)) & ! [v31] : ! [v32] : ! [v33] : (v33 = 0 | ~ (subset(v31, v32) = v33) | ? [v34] : ? [v35] : ( ~ (v35 = 0) & powerset(v32) = v34 & element(v31, v34) = v35)) & ! [v31] : ! [v32] : ! [v33] : (v33 = 0 | ~ (element(v31, v32) = v33) | ? [v34] : ( ~ (v34 = 0) & in(v31, v32) = v34)) & ! [v31] : ! [v32] : ! [v33] : (v33 = 0 | ~ (in(v31, v32) = v33) | ? [v34] : ((v34 = 0 & empty(v32) = 0) | ( ~ (v34 = 0) & element(v31, v32) = v34))) & ! [v31] : ! [v32] : ! [v33] : (v32 = v31 | ~ (relation_non_empty(v33) = v32) | ~ (relation_non_empty(v33) = v31)) & ! [v31] : ! [v32] : ! [v33] : (v32 = v31 | ~ (relation_empty_yielding(v33) = v32) | ~ (relation_empty_yielding(v33) = v31)) & ! [v31] : ! [v32] : ! [v33] : (v32 = v31 | ~ (transfinite_sequence(v33) = v32) | ~ (transfinite_sequence(v33) = v31)) & ! [v31] : ! [v32] : ! [v33] : (v32 = v31 | ~ (ordinal_yielding(v33) = v32) | ~ (ordinal_yielding(v33) = v31)) & ! [v31] : ! [v32] : ! [v33] : (v32 = v31 | ~ (being_limit_ordinal(v33) = v32) | ~ (being_limit_ordinal(v33) = v31)) & ! [v31] : ! [v32] : ! [v33] : (v32 = v31 | ~ (function_yielding(v33) = v32) | ~ (function_yielding(v33) = v31)) & ! [v31] : ! [v32] : ! [v33] : (v32 = v31 | ~ (one_to_one(v33) = v32) | ~ (one_to_one(v33) = v31)) & ! [v31] : ! [v32] : ! [v33] : (v32 = v31 | ~ (powerset(v33) = v32) | ~ (powerset(v33) = v31)) & ! [v31] : ! [v32] : ! [v33] : (v32 = v31 | ~ (natural(v33) = v32) | ~ (natural(v33) = v31)) & ! [v31] : ! [v32] : ! [v33] : (v32 = v31 | ~ (relation(v33) = v32) | ~ (relation(v33) = v31)) & ! [v31] : ! [v32] : ! [v33] : (v32 = v31 | ~ (function(v33) = v32) | ~ (function(v33) = v31)) & ! [v31] : ! [v32] : ! [v33] : (v32 = v31 | ~ (finite(v33) = v32) | ~ (finite(v33) = v31)) & ! [v31] : ! [v32] : ! [v33] : (v32 = v31 | ~ (empty(v33) = v32) | ~ (empty(v33) = v31)) & ! [v31] : ! [v32] : ! [v33] : (v32 = v31 | ~ (epsilon_connected(v33) = v32) | ~ (epsilon_connected(v33) = v31)) & ! [v31] : ! [v32] : ! [v33] : (v32 = v31 | ~ (epsilon_transitive(v33) = v32) | ~ (epsilon_transitive(v33) = v31)) & ! [v31] : ! [v32] : ! [v33] : (v32 = v31 | ~ (ordinal(v33) = v32) | ~ (ordinal(v33) = v31)) & ! [v31] : ! [v32] : ! [v33] : ( ~ (powerset(v32) = v33) | ~ (element(v31, v33) = 0) | subset(v31, v32) = 0) & ! [v31] : ! [v32] : ! [v33] : ( ~ (powerset(v31) = v32) | ~ (element(v33, v32) = 0) | ? [v34] : ((v34 = 0 & finite(v33) = 0) | ( ~ (v34 = 0) & finite(v31) = v34))) & ! [v31] : ! [v32] : ! [v33] : ( ~ (empty(v33) = 0) | ~ (in(v31, v32) = 0) | ? [v34] : ? [v35] : ( ~ (v35 = 0) & powerset(v33) = v34 & element(v32, v34) = v35)) & ! [v31] : ! [v32] : ! [v33] : ( ~ (epsilon_connected(v32) = v33) | ~ (ordinal(v31) = 0) | ? [v34] : ? [v35] : ((v35 = 0 & v34 = 0 & v33 = 0 & epsilon_transitive(v32) = 0 & ordinal(v32) = 0) | ( ~ (v34 = 0) & element(v32, v31) = v34))) & ! [v31] : ! [v32] : ! [v33] : ( ~ (epsilon_transitive(v32) = v33) | ~ (ordinal(v31) = 0) | ? [v34] : ? [v35] : ((v35 = 0 & v34 = 0 & v33 = 0 & epsilon_connected(v32) = 0 & ordinal(v32) = 0) | ( ~ (v34 = 0) & element(v32, v31) = v34))) & ! [v31] : ! [v32] : ! [v33] : ( ~ (ordinal(v32) = v33) | ~ (ordinal(v31) = 0) | ? [v34] : ? [v35] : ((v35 = 0 & v34 = 0 & v33 = 0 & epsilon_connected(v32) = 0 & epsilon_transitive(v32) = 0) | ( ~ (v34 = 0) & element(v32, v31) = v34))) & ! [v31] : ! [v32] : (v32 = v31 | ~ (empty(v32) = 0) | ~ (empty(v31) = 0)) & ! [v31] : ! [v32] : (v32 = 0 | ~ (subset(v31, v31) = v32)) & ! [v31] : ! [v32] : (v32 = 0 | ~ (relation(v31) = v32) | ? [v33] : ( ~ (v33 = 0) & empty(v31) = v33)) & ! [v31] : ! [v32] : (v32 = 0 | ~ (function(v31) = v32) | ? [v33] : ( ~ (v33 = 0) & empty(v31) = v33)) & ! [v31] : ! [v32] : (v32 = 0 | ~ (finite(v31) = v32) | ? [v33] : ( ~ (v33 = 0) & empty(v31) = v33)) & ! [v31] : ! [v32] : (v32 = 0 | ~ (empty(v31) = v32) | ? [v33] : ? [v34] : ? [v35] : ( ~ (v35 = 0) & powerset(v31) = v33 & finite(v34) = 0 & empty(v34) = v35 & element(v34, v33) = 0)) & ! [v31] : ! [v32] : (v32 = 0 | ~ (empty(v31) = v32) | ? [v33] : ? [v34] : ? [v35] : ( ~ (v35 = 0) & powerset(v31) = v33 & empty(v34) = v35 & element(v34, v33) = 0)) & ! [v31] : ! [v32] : (v32 = 0 | ~ (ordinal(v31) = v32) | ? [v33] : (( ~ (v33 = 0) & epsilon_connected(v31) = v33) | ( ~ (v33 = 0) & epsilon_transitive(v31) = v33))) & ! [v31] : ! [v32] : ( ~ (subset(v31, v32) = 0) | ? [v33] : (powerset(v32) = v33 & element(v31, v33) = 0)) & ! [v31] : ! [v32] : ( ~ (one_to_one(v31) = v32) | ? [v33] : ? [v34] : ((v34 = 0 & v33 = 0 & v32 = 0 & relation(v31) = 0 & function(v31) = 0) | ( ~ (v33 = 0) & relation(v31) = v33) | ( ~ (v33 = 0) & function(v31) = v33) | ( ~ (v33 = 0) & empty(v31) = v33))) & ! [v31] : ! [v32] : ( ~ (powerset(v31) = v32) | ? [v33] : ? [v34] : ? [v35] : ? [v36] : ((v36 = 0 & v34 = 0 & ~ (v35 = 0) & finite(v33) = 0 & empty(v33) = v35 & element(v33, v32) = 0) | (v33 = 0 & empty(v31) = 0))) & ! [v31] : ! [v32] : ( ~ (powerset(v31) = v32) | ? [v33] : ? [v34] : ? [v35] : ((v34 = 0 & ~ (v35 = 0) & empty(v33) = v35 & element(v33, v32) = 0) | (v33 = 0 & empty(v31) = 0))) & ! [v31] : ! [v32] : ( ~ (powerset(v31) = v32) | ? [v33] : ( ~ (v33 = 0) & empty(v32) = v33)) & ! [v31] : ! [v32] : ( ~ (powerset(v31) = v32) | ? [v33] : (one_to_one(v33) = 0 & natural(v33) = 0 & relation(v33) = 0 & function(v33) = 0 & finite(v33) = 0 & empty(v33) = 0 & epsilon_connected(v33) = 0 & element(v33, v32) = 0 & epsilon_transitive(v33) = 0 & ordinal(v33) = 0)) & ! [v31] : ! [v32] : ( ~ (powerset(v31) = v32) | ? [v33] : (empty(v33) = 0 & element(v33, v32) = 0)) & ! [v31] : ! [v32] : ( ~ (natural(v31) = v32) | ? [v33] : ? [v34] : ? [v35] : ((v35 = 0 & v34 = 0 & v33 = 0 & v32 = 0 & epsilon_connected(v31) = 0 & epsilon_transitive(v31) = 0 & ordinal(v31) = 0) | ( ~ (v33 = 0) & empty(v31) = v33) | ( ~ (v33 = 0) & ordinal(v31) = v33))) & ! [v31] : ! [v32] : ( ~ (natural(v31) = v32) | ? [v33] : ? [v34] : ? [v35] : ((v35 = 0 & v34 = 0 & v33 = 0 & v32 = 0 & epsilon_connected(v31) = 0 & epsilon_transitive(v31) = 0 & ordinal(v31) = 0) | ( ~ (v33 = 0) & element(v31, positive_rationals) = v33) | ( ~ (v33 = 0) & ordinal(v31) = v33))) & ! [v31] : ! [v32] : ( ~ (epsilon_connected(v31) = v32) | ? [v33] : ? [v34] : ? [v35] : ((v35 = 0 & v34 = 0 & v33 = 0 & v32 = 0 & natural(v31) = 0 & epsilon_transitive(v31) = 0 & ordinal(v31) = 0) | ( ~ (v33 = 0) & empty(v31) = v33) | ( ~ (v33 = 0) & ordinal(v31) = v33))) & ! [v31] : ! [v32] : ( ~ (epsilon_connected(v31) = v32) | ? [v33] : ? [v34] : ? [v35] : ((v35 = 0 & v34 = 0 & v33 = 0 & v32 = 0 & natural(v31) = 0 & epsilon_transitive(v31) = 0 & ordinal(v31) = 0) | ( ~ (v33 = 0) & element(v31, positive_rationals) = v33) | ( ~ (v33 = 0) & ordinal(v31) = v33))) & ! [v31] : ! [v32] : ( ~ (epsilon_connected(v31) = v32) | ? [v33] : ? [v34] : ((v34 = 0 & v33 = 0 & v32 = 0 & epsilon_transitive(v31) = 0 & ordinal(v31) = 0) | ( ~ (v33 = 0) & empty(v31) = v33))) & ! [v31] : ! [v32] : ( ~ (epsilon_connected(v31) = v32) | ? [v33] : ((v33 = 0 & v32 = 0 & epsilon_transitive(v31) = 0) | ( ~ (v33 = 0) & ordinal(v31) = v33))) & ! [v31] : ! [v32] : ( ~ (element(v32, v31) = 0) | ~ (ordinal(v31) = 0) | (epsilon_connected(v32) = 0 & epsilon_transitive(v32) = 0 & ordinal(v32) = 0)) & ! [v31] : ! [v32] : ( ~ (element(v31, v32) = 0) | ? [v33] : ((v33 = 0 & empty(v32) = 0) | (v33 = 0 & in(v31, v32) = 0))) & ! [v31] : ! [v32] : ( ~ (epsilon_transitive(v31) = v32) | ? [v33] : ? [v34] : ? [v35] : ((v35 = 0 & v34 = 0 & v33 = 0 & v32 = 0 & natural(v31) = 0 & epsilon_connected(v31) = 0 & ordinal(v31) = 0) | ( ~ (v33 = 0) & empty(v31) = v33) | ( ~ (v33 = 0) & ordinal(v31) = v33))) & ! [v31] : ! [v32] : ( ~ (epsilon_transitive(v31) = v32) | ? [v33] : ? [v34] : ? [v35] : ((v35 = 0 & v34 = 0 & v33 = 0 & v32 = 0 & natural(v31) = 0 & epsilon_connected(v31) = 0 & ordinal(v31) = 0) | ( ~ (v33 = 0) & element(v31, positive_rationals) = v33) | ( ~ (v33 = 0) & ordinal(v31) = v33))) & ! [v31] : ! [v32] : ( ~ (epsilon_transitive(v31) = v32) | ? [v33] : ? [v34] : ((v34 = 0 & v33 = 0 & v32 = 0 & epsilon_connected(v31) = 0 & ordinal(v31) = 0) | ( ~ (v33 = 0) & empty(v31) = v33))) & ! [v31] : ! [v32] : ( ~ (epsilon_transitive(v31) = v32) | ? [v33] : ((v33 = 0 & v32 = 0 & epsilon_connected(v31) = 0) | ( ~ (v33 = 0) & ordinal(v31) = v33))) & ! [v31] : ! [v32] : ( ~ (ordinal(v31) = v32) | ? [v33] : ? [v34] : ((v34 = 0 & v33 = 0 & v32 = 0 & epsilon_connected(v31) = 0 & epsilon_transitive(v31) = 0) | ( ~ (v33 = 0) & empty(v31) = v33))) & ! [v31] : ! [v32] : ( ~ (in(v32, v31) = 0) | ? [v33] : ( ~ (v33 = 0) & in(v31, v32) = v33)) & ! [v31] : ! [v32] : ( ~ (in(v31, v32) = 0) | element(v31, v32) = 0) & ! [v31] : ! [v32] : ( ~ (in(v31, v32) = 0) | ? [v33] : ( ~ (v33 = 0) & empty(v32) = v33)) & ! [v31] : ! [v32] : ( ~ (in(v31, v32) = 0) | ? [v33] : ( ~ (v33 = 0) & in(v32, v31) = v33)) & ! [v31] : (v31 = empty_set | ~ (empty(v31) = 0)) & ! [v31] : ( ~ (relation(v31) = 0) | ? [v32] : ? [v33] : ((v33 = 0 & v32 = 0 & one_to_one(v31) = 0 & function(v31) = 0) | ( ~ (v32 = 0) & function(v31) = v32) | ( ~ (v32 = 0) & empty(v31) = v32))) & ! [v31] : ( ~ (function(v31) = 0) | ? [v32] : ? [v33] : ((v33 = 0 & v32 = 0 & one_to_one(v31) = 0 & relation(v31) = 0) | ( ~ (v32 = 0) & relation(v31) = v32) | ( ~ (v32 = 0) & empty(v31) = v32))) & ! [v31] : ( ~ (finite(v31) = 0) | ? [v32] : (powerset(v31) = v32 & ! [v33] : ! [v34] : (v34 = 0 | ~ (finite(v33) = v34) | ? [v35] : ( ~ (v35 = 0) & element(v33, v32) = v35)) & ! [v33] : ( ~ (element(v33, v32) = 0) | finite(v33) = 0))) & ! [v31] : ( ~ (empty(v31) = 0) | relation(v31) = 0) & ! [v31] : ( ~ (empty(v31) = 0) | function(v31) = 0) & ! [v31] : ( ~ (empty(v31) = 0) | finite(v31) = 0) & ! [v31] : ( ~ (empty(v31) = 0) | ? [v32] : ? [v33] : ? [v34] : ? [v35] : (ordinal(v31) = v32 & ( ~ (v32 = 0) | (v35 = 0 & v34 = 0 & v33 = 0 & natural(v31) = 0 & epsilon_connected(v31) = 0 & epsilon_transitive(v31) = 0)))) & ! [v31] : ( ~ (empty(v31) = 0) | ? [v32] : ? [v33] : ? [v34] : ((v34 = 0 & v33 = 0 & v32 = 0 & one_to_one(v31) = 0 & relation(v31) = 0 & function(v31) = 0) | ( ~ (v32 = 0) & relation(v31) = v32) | ( ~ (v32 = 0) & function(v31) = v32))) & ! [v31] : ( ~ (empty(v31) = 0) | (epsilon_connected(v31) = 0 & epsilon_transitive(v31) = 0 & ordinal(v31) = 0)) & ! [v31] : ( ~ (epsilon_connected(v31) = 0) | ? [v32] : ((v32 = 0 & ordinal(v31) = 0) | ( ~ (v32 = 0) & epsilon_transitive(v31) = v32))) & ! [v31] : ( ~ (element(v31, positive_rationals) = 0) | ? [v32] : ? [v33] : ? [v34] : ? [v35] : (ordinal(v31) = v32 & ( ~ (v32 = 0) | (v35 = 0 & v34 = 0 & v33 = 0 & natural(v31) = 0 & epsilon_connected(v31) = 0 & epsilon_transitive(v31) = 0)))) & ! [v31] : ( ~ (epsilon_transitive(v31) = 0) | ? [v32] : ((v32 = 0 & ordinal(v31) = 0) | ( ~ (v32 = 0) & epsilon_connected(v31) = v32))) & ! [v31] : ( ~ (ordinal(v31) = 0) | ? [v32] : ? [v33] : ? [v34] : ((v34 = 0 & v33 = 0 & v32 = 0 & natural(v31) = 0 & epsilon_connected(v31) = 0 & epsilon_transitive(v31) = 0) | ( ~ (v32 = 0) & empty(v31) = v32))) & ! [v31] : ( ~ (ordinal(v31) = 0) | ? [v32] : ? [v33] : ? [v34] : ((v34 = 0 & v33 = 0 & v32 = 0 & natural(v31) = 0 & epsilon_connected(v31) = 0 & epsilon_transitive(v31) = 0) | ( ~ (v32 = 0) & element(v31, positive_rationals) = v32))) & ! [v31] : ( ~ (ordinal(v31) = 0) | (epsilon_connected(v31) = 0 & epsilon_transitive(v31) = 0)) & ? [v31] : ? [v32] : ? [v33] : subset(v32, v31) = v33 & ? [v31] : ? [v32] : ? [v33] : element(v32, v31) = v33 & ? [v31] : ? [v32] : ? [v33] : in(v32, v31) = v33 & ? [v31] : ? [v32] : relation_non_empty(v31) = v32 & ? [v31] : ? [v32] : relation_empty_yielding(v31) = v32 & ? [v31] : ? [v32] : transfinite_sequence(v31) = v32 & ? [v31] : ? [v32] : ordinal_yielding(v31) = v32 & ? [v31] : ? [v32] : being_limit_ordinal(v31) = v32 & ? [v31] : ? [v32] : function_yielding(v31) = v32 & ? [v31] : ? [v32] : one_to_one(v31) = v32 & ? [v31] : ? [v32] : powerset(v31) = v32 & ? [v31] : ? [v32] : natural(v31) = v32 & ? [v31] : ? [v32] : relation(v31) = v32 & ? [v31] : ? [v32] : function(v31) = v32 & ? [v31] : ? [v32] : finite(v31) = v32 & ? [v31] : ? [v32] : empty(v31) = v32 & ? [v31] : ? [v32] : epsilon_connected(v31) = v32 & ? [v31] : ? [v32] : element(v32, v31) = 0 & ? [v31] : ? [v32] : epsilon_transitive(v31) = v32 & ? [v31] : ? [v32] : ordinal(v31) = v32)
% 22.54/5.95 | 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, all_0_22_22, all_0_23_23, all_0_24_24, all_0_25_25, all_0_26_26, all_0_27_27, all_0_28_28, all_0_29_29, all_0_30_30 yields:
% 22.54/5.95 | (1) ~ (all_0_0_0 = 0) & ~ (all_0_2_2 = 0) & ~ (all_0_10_10 = 0) & ~ (all_0_15_15 = 0) & ~ (all_0_17_17 = 0) & ~ (all_0_21_21 = 0) & ~ (all_0_27_27 = 0) & ~ (all_0_30_30 = 0) & subset(all_0_29_29, all_0_28_28) = 0 & relation_non_empty(all_0_26_26) = 0 & relation_empty_yielding(all_0_23_23) = 0 & relation_empty_yielding(all_0_24_24) = 0 & relation_empty_yielding(empty_set) = 0 & transfinite_sequence(all_0_14_14) = 0 & transfinite_sequence(all_0_25_25) = 0 & ordinal_yielding(all_0_14_14) = 0 & being_limit_ordinal(all_0_7_7) = 0 & function_yielding(all_0_4_4) = 0 & one_to_one(all_0_13_13) = 0 & one_to_one(all_0_20_20) = 0 & one_to_one(empty_set) = 0 & natural(all_0_1_1) = 0 & natural(all_0_19_19) = 0 & relation(all_0_4_4) = 0 & relation(all_0_5_5) = 0 & relation(all_0_8_8) = 0 & relation(all_0_12_12) = 0 & relation(all_0_13_13) = 0 & relation(all_0_14_14) = 0 & relation(all_0_16_16) = 0 & relation(all_0_20_20) = 0 & relation(all_0_23_23) = 0 & relation(all_0_24_24) = 0 & relation(all_0_25_25) = 0 & relation(all_0_26_26) = 0 & relation(empty_set) = 0 & function(all_0_4_4) = 0 & function(all_0_5_5) = 0 & function(all_0_12_12) = 0 & function(all_0_13_13) = 0 & function(all_0_14_14) = 0 & function(all_0_20_20) = 0 & function(all_0_24_24) = 0 & function(all_0_25_25) = 0 & function(all_0_26_26) = 0 & function(empty_set) = 0 & finite(all_0_3_3) = 0 & finite(all_0_28_28) = 0 & finite(all_0_29_29) = all_0_27_27 & empty(all_0_1_1) = all_0_0_0 & empty(all_0_3_3) = all_0_2_2 & empty(all_0_8_8) = 0 & empty(all_0_9_9) = 0 & empty(all_0_11_11) = all_0_10_10 & empty(all_0_12_12) = 0 & empty(all_0_13_13) = 0 & empty(all_0_16_16) = all_0_15_15 & empty(all_0_18_18) = all_0_17_17 & empty(all_0_19_19) = 0 & empty(all_0_22_22) = all_0_21_21 & empty(empty_set) = 0 & empty(positive_rationals) = all_0_30_30 & epsilon_connected(all_0_1_1) = 0 & epsilon_connected(all_0_6_6) = 0 & epsilon_connected(all_0_7_7) = 0 & epsilon_connected(all_0_11_11) = 0 & epsilon_connected(all_0_13_13) = 0 & epsilon_connected(all_0_19_19) = 0 & epsilon_connected(all_0_22_22) = 0 & epsilon_connected(empty_set) = 0 & element(all_0_11_11, positive_rationals) = 0 & element(all_0_19_19, positive_rationals) = 0 & epsilon_transitive(all_0_1_1) = 0 & epsilon_transitive(all_0_6_6) = 0 & epsilon_transitive(all_0_7_7) = 0 & epsilon_transitive(all_0_11_11) = 0 & epsilon_transitive(all_0_13_13) = 0 & epsilon_transitive(all_0_19_19) = 0 & epsilon_transitive(all_0_22_22) = 0 & epsilon_transitive(empty_set) = 0 & ordinal(all_0_1_1) = 0 & ordinal(all_0_6_6) = 0 & ordinal(all_0_7_7) = 0 & ordinal(all_0_11_11) = 0 & ordinal(all_0_13_13) = 0 & ordinal(all_0_19_19) = 0 & ordinal(all_0_22_22) = 0 & ordinal(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 | ~ (powerset(v0) = v1) | ~ (finite(v2) = v3) | ? [v4] : (( ~ (v4 = 0) & finite(v0) = v4) | ( ~ (v4 = 0) & element(v2, 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 | ~ (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] : ( ~ (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_non_empty(v2) = v1) | ~ (relation_non_empty(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_empty_yielding(v2) = v1) | ~ (relation_empty_yielding(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (transfinite_sequence(v2) = v1) | ~ (transfinite_sequence(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ordinal_yielding(v2) = v1) | ~ (ordinal_yielding(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (being_limit_ordinal(v2) = v1) | ~ (being_limit_ordinal(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function_yielding(v2) = v1) | ~ (function_yielding(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 | ~ (natural(v2) = v1) | ~ (natural(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 | ~ (finite(v2) = v1) | ~ (finite(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (epsilon_connected(v2) = v1) | ~ (epsilon_connected(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] : ( ~ (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | subset(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ (element(v2, v1) = 0) | ? [v3] : ((v3 = 0 & finite(v2) = 0) | ( ~ (v3 = 0) & finite(v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (empty(v2) = 0) | ~ (in(v0, v1) = 0) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v2) = v3 & element(v1, v3) = v4)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (epsilon_connected(v1) = v2) | ~ (ordinal(v0) = 0) | ? [v3] : ? [v4] : ((v4 = 0 & v3 = 0 & v2 = 0 & epsilon_transitive(v1) = 0 & ordinal(v1) = 0) | ( ~ (v3 = 0) & element(v1, v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (epsilon_transitive(v1) = v2) | ~ (ordinal(v0) = 0) | ? [v3] : ? [v4] : ((v4 = 0 & v3 = 0 & v2 = 0 & epsilon_connected(v1) = 0 & ordinal(v1) = 0) | ( ~ (v3 = 0) & element(v1, v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordinal(v1) = v2) | ~ (ordinal(v0) = 0) | ? [v3] : ? [v4] : ((v4 = 0 & v3 = 0 & v2 = 0 & epsilon_connected(v1) = 0 & epsilon_transitive(v1) = 0) | ( ~ (v3 = 0) & element(v1, v0) = v3))) & ! [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 | ~ (function(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (finite(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (empty(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v0) = v2 & finite(v3) = 0 & empty(v3) = v4 & element(v3, v2) = 0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (empty(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v0) = v2 & empty(v3) = v4 & element(v3, v2) = 0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (ordinal(v0) = v1) | ? [v2] : (( ~ (v2 = 0) & epsilon_connected(v0) = v2) | ( ~ (v2 = 0) & epsilon_transitive(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (powerset(v1) = v2 & element(v0, v2) = 0)) & ! [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] : ? [v5] : ((v5 = 0 & v3 = 0 & ~ (v4 = 0) & finite(v2) = 0 & empty(v2) = v4 & element(v2, v1) = 0) | (v2 = 0 & empty(v0) = 0))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v3 = 0 & ~ (v4 = 0) & empty(v2) = v4 & element(v2, v1) = 0) | (v2 = 0 & empty(v0) = 0))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (one_to_one(v2) = 0 & natural(v2) = 0 & relation(v2) = 0 & function(v2) = 0 & finite(v2) = 0 & empty(v2) = 0 & epsilon_connected(v2) = 0 & element(v2, v1) = 0 & epsilon_transitive(v2) = 0 & ordinal(v2) = 0)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (empty(v2) = 0 & element(v2, v1) = 0)) & ! [v0] : ! [v1] : ( ~ (natural(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = 0 & v3 = 0 & v2 = 0 & v1 = 0 & epsilon_connected(v0) = 0 & epsilon_transitive(v0) = 0 & ordinal(v0) = 0) | ( ~ (v2 = 0) & empty(v0) = v2) | ( ~ (v2 = 0) & ordinal(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (natural(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = 0 & v3 = 0 & v2 = 0 & v1 = 0 & epsilon_connected(v0) = 0 & epsilon_transitive(v0) = 0 & ordinal(v0) = 0) | ( ~ (v2 = 0) & element(v0, positive_rationals) = v2) | ( ~ (v2 = 0) & ordinal(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (epsilon_connected(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = 0 & v3 = 0 & v2 = 0 & v1 = 0 & natural(v0) = 0 & epsilon_transitive(v0) = 0 & ordinal(v0) = 0) | ( ~ (v2 = 0) & empty(v0) = v2) | ( ~ (v2 = 0) & ordinal(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (epsilon_connected(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = 0 & v3 = 0 & v2 = 0 & v1 = 0 & natural(v0) = 0 & epsilon_transitive(v0) = 0 & ordinal(v0) = 0) | ( ~ (v2 = 0) & element(v0, positive_rationals) = v2) | ( ~ (v2 = 0) & ordinal(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] : ( ~ (element(v1, v0) = 0) | ~ (ordinal(v0) = 0) | (epsilon_connected(v1) = 0 & epsilon_transitive(v1) = 0 & ordinal(v1) = 0)) & ! [v0] : ! [v1] : ( ~ (element(v0, v1) = 0) | ? [v2] : ((v2 = 0 & empty(v1) = 0) | (v2 = 0 & in(v0, v1) = 0))) & ! [v0] : ! [v1] : ( ~ (epsilon_transitive(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = 0 & v3 = 0 & v2 = 0 & v1 = 0 & natural(v0) = 0 & epsilon_connected(v0) = 0 & ordinal(v0) = 0) | ( ~ (v2 = 0) & empty(v0) = v2) | ( ~ (v2 = 0) & ordinal(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (epsilon_transitive(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = 0 & v3 = 0 & v2 = 0 & v1 = 0 & natural(v0) = 0 & epsilon_connected(v0) = 0 & ordinal(v0) = 0) | ( ~ (v2 = 0) & element(v0, positive_rationals) = v2) | ( ~ (v2 = 0) & ordinal(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (epsilon_transitive(v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & epsilon_connected(v0) = 0 & ordinal(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_connected(v0) = 0 & epsilon_transitive(v0) = 0) | ( ~ (v2 = 0) & empty(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(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] : ( ~ (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] : ( ~ (finite(v0) = 0) | ? [v1] : (powerset(v0) = v1 & ! [v2] : ! [v3] : (v3 = 0 | ~ (finite(v2) = v3) | ? [v4] : ( ~ (v4 = 0) & element(v2, v1) = v4)) & ! [v2] : ( ~ (element(v2, v1) = 0) | finite(v2) = 0))) & ! [v0] : ( ~ (empty(v0) = 0) | relation(v0) = 0) & ! [v0] : ( ~ (empty(v0) = 0) | function(v0) = 0) & ! [v0] : ( ~ (empty(v0) = 0) | finite(v0) = 0) & ! [v0] : ( ~ (empty(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : (ordinal(v0) = v1 & ( ~ (v1 = 0) | (v4 = 0 & v3 = 0 & v2 = 0 & natural(v0) = 0 & epsilon_connected(v0) = 0 & epsilon_transitive(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) | (epsilon_connected(v0) = 0 & epsilon_transitive(v0) = 0 & ordinal(v0) = 0)) & ! [v0] : ( ~ (epsilon_connected(v0) = 0) | ? [v1] : ((v1 = 0 & ordinal(v0) = 0) | ( ~ (v1 = 0) & epsilon_transitive(v0) = v1))) & ! [v0] : ( ~ (element(v0, positive_rationals) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : (ordinal(v0) = v1 & ( ~ (v1 = 0) | (v4 = 0 & v3 = 0 & v2 = 0 & natural(v0) = 0 & epsilon_connected(v0) = 0 & epsilon_transitive(v0) = 0)))) & ! [v0] : ( ~ (epsilon_transitive(v0) = 0) | ? [v1] : ((v1 = 0 & ordinal(v0) = 0) | ( ~ (v1 = 0) & epsilon_connected(v0) = v1))) & ! [v0] : ( ~ (ordinal(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & natural(v0) = 0 & epsilon_connected(v0) = 0 & epsilon_transitive(v0) = 0) | ( ~ (v1 = 0) & empty(v0) = v1))) & ! [v0] : ( ~ (ordinal(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & natural(v0) = 0 & epsilon_connected(v0) = 0 & epsilon_transitive(v0) = 0) | ( ~ (v1 = 0) & element(v0, positive_rationals) = v1))) & ! [v0] : ( ~ (ordinal(v0) = 0) | (epsilon_connected(v0) = 0 & epsilon_transitive(v0) = 0)) & ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : element(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2 & ? [v0] : ? [v1] : relation_non_empty(v0) = v1 & ? [v0] : ? [v1] : relation_empty_yielding(v0) = v1 & ? [v0] : ? [v1] : transfinite_sequence(v0) = v1 & ? [v0] : ? [v1] : ordinal_yielding(v0) = v1 & ? [v0] : ? [v1] : being_limit_ordinal(v0) = v1 & ? [v0] : ? [v1] : function_yielding(v0) = v1 & ? [v0] : ? [v1] : one_to_one(v0) = v1 & ? [v0] : ? [v1] : powerset(v0) = v1 & ? [v0] : ? [v1] : natural(v0) = v1 & ? [v0] : ? [v1] : relation(v0) = v1 & ? [v0] : ? [v1] : function(v0) = v1 & ? [v0] : ? [v1] : finite(v0) = v1 & ? [v0] : ? [v1] : empty(v0) = v1 & ? [v0] : ? [v1] : epsilon_connected(v0) = v1 & ? [v0] : ? [v1] : element(v1, v0) = 0 & ? [v0] : ? [v1] : epsilon_transitive(v0) = v1 & ? [v0] : ? [v1] : ordinal(v0) = v1
% 22.54/5.98 |
% 22.54/5.98 | Applying alpha-rule on (1) yields:
% 22.54/5.98 | (2) ! [v0] : ! [v1] : ( ~ (epsilon_transitive(v0) = v1) | ? [v2] : ((v2 = 0 & v1 = 0 & epsilon_connected(v0) = 0) | ( ~ (v2 = 0) & ordinal(v0) = v2)))
% 22.54/5.98 | (3) subset(all_0_29_29, all_0_28_28) = 0
% 22.54/5.98 | (4) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0))
% 22.54/5.98 | (5) ! [v0] : ! [v1] : ( ~ (epsilon_transitive(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = 0 & v3 = 0 & v2 = 0 & v1 = 0 & natural(v0) = 0 & epsilon_connected(v0) = 0 & ordinal(v0) = 0) | ( ~ (v2 = 0) & empty(v0) = v2) | ( ~ (v2 = 0) & ordinal(v0) = v2)))
% 22.54/5.98 | (6) ? [v0] : ? [v1] : powerset(v0) = v1
% 22.54/5.98 | (7) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | element(v0, v1) = 0)
% 22.54/5.98 | (8) ! [v0] : ! [v1] : ( ~ (epsilon_connected(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = 0 & v3 = 0 & v2 = 0 & v1 = 0 & natural(v0) = 0 & epsilon_transitive(v0) = 0 & ordinal(v0) = 0) | ( ~ (v2 = 0) & element(v0, positive_rationals) = v2) | ( ~ (v2 = 0) & ordinal(v0) = v2)))
% 22.54/5.98 | (9) relation(all_0_26_26) = 0
% 22.54/5.98 | (10) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0))
% 22.54/5.98 | (11) epsilon_connected(all_0_6_6) = 0
% 22.54/5.98 | (12) epsilon_transitive(all_0_22_22) = 0
% 22.54/5.98 | (13) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0))
% 22.54/5.98 | (14) ! [v0] : ( ~ (ordinal(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & natural(v0) = 0 & epsilon_connected(v0) = 0 & epsilon_transitive(v0) = 0) | ( ~ (v1 = 0) & empty(v0) = v1)))
% 22.54/5.98 | (15) relation_empty_yielding(empty_set) = 0
% 22.54/5.98 | (16) epsilon_transitive(empty_set) = 0
% 22.54/5.98 | (17) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v1) = v3 & element(v0, v3) = v4))
% 22.54/5.98 | (18) empty(positive_rationals) = all_0_30_30
% 22.54/5.98 | (19) ~ (all_0_10_10 = 0)
% 22.54/5.98 | (20) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3))
% 22.54/5.98 | (21) relation(all_0_13_13) = 0
% 22.54/5.98 | (22) ordinal(all_0_13_13) = 0
% 22.54/5.98 | (23) ~ (all_0_30_30 = 0)
% 22.54/5.98 | (24) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | subset(v0, v1) = 0)
% 22.54/5.98 | (25) ordinal(empty_set) = 0
% 22.54/5.98 | (26) ordinal_yielding(all_0_14_14) = 0
% 22.54/5.98 | (27) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (epsilon_connected(v2) = v1) | ~ (epsilon_connected(v2) = v0))
% 22.54/5.98 | (28) function(all_0_4_4) = 0
% 22.54/5.98 | (29) ! [v0] : ( ~ (ordinal(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & natural(v0) = 0 & epsilon_connected(v0) = 0 & epsilon_transitive(v0) = 0) | ( ~ (v1 = 0) & element(v0, positive_rationals) = v1)))
% 22.54/5.98 | (30) ! [v0] : ! [v1] : ! [v2] : ( ~ (empty(v2) = 0) | ~ (in(v0, v1) = 0) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v2) = v3 & element(v1, v3) = v4))
% 22.54/5.98 | (31) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0))
% 22.54/5.98 | (32) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordinal(v1) = v2) | ~ (ordinal(v0) = 0) | ? [v3] : ? [v4] : ((v4 = 0 & v3 = 0 & v2 = 0 & epsilon_connected(v1) = 0 & epsilon_transitive(v1) = 0) | ( ~ (v3 = 0) & element(v1, v0) = v3)))
% 22.54/5.98 | (33) ? [v0] : ? [v1] : transfinite_sequence(v0) = v1
% 22.54/5.98 | (34) epsilon_transitive(all_0_13_13) = 0
% 22.54/5.98 | (35) ! [v0] : ! [v1] : (v1 = 0 | ~ (finite(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2))
% 22.54/5.98 | (36) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (epsilon_transitive(v2) = v1) | ~ (epsilon_transitive(v2) = v0))
% 22.54/5.98 | (37) ! [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))
% 22.54/5.98 | (38) ! [v0] : ( ~ (empty(v0) = 0) | relation(v0) = 0)
% 22.54/5.98 | (39) ! [v0] : ! [v1] : (v1 = 0 | ~ (empty(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v0) = v2 & empty(v3) = v4 & element(v3, v2) = 0))
% 22.54/5.98 | (40) relation(all_0_25_25) = 0
% 22.54/5.98 | (41) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ (element(v2, v1) = 0) | ? [v3] : ((v3 = 0 & finite(v2) = 0) | ( ~ (v3 = 0) & finite(v0) = v3)))
% 22.54/5.99 | (42) function(all_0_26_26) = 0
% 22.54/5.99 | (43) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 22.54/5.99 | (44) empty(all_0_1_1) = all_0_0_0
% 22.54/5.99 | (45) empty(all_0_13_13) = 0
% 22.54/5.99 | (46) ! [v0] : ( ~ (ordinal(v0) = 0) | (epsilon_connected(v0) = 0 & epsilon_transitive(v0) = 0))
% 22.54/5.99 | (47) function(all_0_25_25) = 0
% 22.54/5.99 | (48) element(all_0_11_11, positive_rationals) = 0
% 22.54/5.99 | (49) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 22.54/5.99 | (50) ? [v0] : ? [v1] : ? [v2] : element(v1, v0) = v2
% 22.54/5.99 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 22.54/5.99 | (52) ? [v0] : ? [v1] : function_yielding(v0) = v1
% 22.54/5.99 | (53) natural(all_0_19_19) = 0
% 22.54/5.99 | (54) ? [v0] : ? [v1] : relation_empty_yielding(v0) = v1
% 22.54/5.99 | (55) ! [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)))
% 22.54/5.99 | (56) empty(all_0_8_8) = 0
% 22.54/5.99 | (57) one_to_one(empty_set) = 0
% 22.54/5.99 | (58) ! [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)))
% 22.54/5.99 | (59) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v0, v1) = v2) | ? [v3] : ((v3 = 0 & empty(v1) = 0) | ( ~ (v3 = 0) & element(v0, v1) = v3)))
% 22.54/5.99 | (60) empty(all_0_19_19) = 0
% 22.54/5.99 | (61) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (transfinite_sequence(v2) = v1) | ~ (transfinite_sequence(v2) = v0))
% 22.54/5.99 | (62) ? [v0] : ? [v1] : natural(v0) = v1
% 22.54/5.99 | (63) ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2
% 22.54/5.99 | (64) relation(all_0_16_16) = 0
% 22.54/5.99 | (65) ! [v0] : ! [v1] : ( ~ (natural(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = 0 & v3 = 0 & v2 = 0 & v1 = 0 & epsilon_connected(v0) = 0 & epsilon_transitive(v0) = 0 & ordinal(v0) = 0) | ( ~ (v2 = 0) & element(v0, positive_rationals) = v2) | ( ~ (v2 = 0) & ordinal(v0) = v2)))
% 22.54/5.99 | (66) ~ (all_0_0_0 = 0)
% 22.54/5.99 | (67) empty(all_0_3_3) = all_0_2_2
% 22.54/5.99 | (68) empty(empty_set) = 0
% 22.54/5.99 | (69) ! [v0] : ( ~ (epsilon_transitive(v0) = 0) | ? [v1] : ((v1 = 0 & ordinal(v0) = 0) | ( ~ (v1 = 0) & epsilon_connected(v0) = v1)))
% 22.54/5.99 | (70) ! [v0] : ( ~ (epsilon_connected(v0) = 0) | ? [v1] : ((v1 = 0 & ordinal(v0) = 0) | ( ~ (v1 = 0) & epsilon_transitive(v0) = v1)))
% 22.54/5.99 | (71) relation_empty_yielding(all_0_23_23) = 0
% 22.54/5.99 | (72) ? [v0] : ? [v1] : empty(v0) = v1
% 22.54/5.99 | (73) ! [v0] : ( ~ (empty(v0) = 0) | (epsilon_connected(v0) = 0 & epsilon_transitive(v0) = 0 & ordinal(v0) = 0))
% 22.54/5.99 | (74) ! [v0] : ! [v1] : (v1 = 0 | ~ (relation(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2))
% 22.54/5.99 | (75) function(empty_set) = 0
% 22.54/5.99 | (76) function(all_0_12_12) = 0
% 22.54/5.99 | (77) ! [v0] : ! [v1] : ( ~ (epsilon_transitive(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = 0 & v3 = 0 & v2 = 0 & v1 = 0 & natural(v0) = 0 & epsilon_connected(v0) = 0 & ordinal(v0) = 0) | ( ~ (v2 = 0) & element(v0, positive_rationals) = v2) | ( ~ (v2 = 0) & ordinal(v0) = v2)))
% 22.54/5.99 | (78) finite(all_0_29_29) = all_0_27_27
% 22.54/5.99 | (79) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | element(v0, v2) = 0)
% 22.54/5.99 | (80) empty(all_0_18_18) = all_0_17_17
% 22.54/5.99 | (81) element(all_0_19_19, positive_rationals) = 0
% 22.54/5.99 | (82) ordinal(all_0_1_1) = 0
% 22.54/5.99 | (83) relation(empty_set) = 0
% 22.54/5.99 | (84) function(all_0_24_24) = 0
% 22.54/5.99 | (85) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ordinal_yielding(v2) = v1) | ~ (ordinal_yielding(v2) = v0))
% 22.54/5.99 | (86) ? [v0] : ? [v1] : being_limit_ordinal(v0) = v1
% 22.54/5.99 | (87) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 22.54/5.99 | (88) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v3 = 0 & ~ (v4 = 0) & empty(v2) = v4 & element(v2, v1) = 0) | (v2 = 0 & empty(v0) = 0)))
% 22.54/5.99 | (89) ! [v0] : ! [v1] : ! [v2] : ( ~ (epsilon_transitive(v1) = v2) | ~ (ordinal(v0) = 0) | ? [v3] : ? [v4] : ((v4 = 0 & v3 = 0 & v2 = 0 & epsilon_connected(v1) = 0 & ordinal(v1) = 0) | ( ~ (v3 = 0) & element(v1, v0) = v3)))
% 22.54/6.00 | (90) epsilon_connected(all_0_19_19) = 0
% 22.54/6.00 | (91) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0))
% 22.54/6.00 | (92) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_empty_yielding(v2) = v1) | ~ (relation_empty_yielding(v2) = v0))
% 22.54/6.00 | (93) ! [v0] : ! [v1] : ( ~ (element(v0, v1) = 0) | ? [v2] : ((v2 = 0 & empty(v1) = 0) | (v2 = 0 & in(v0, v1) = 0)))
% 22.54/6.00 | (94) ! [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)))
% 22.54/6.00 | (95) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4))
% 22.54/6.00 | (96) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_non_empty(v2) = v1) | ~ (relation_non_empty(v2) = v0))
% 22.54/6.00 | (97) epsilon_transitive(all_0_19_19) = 0
% 22.54/6.00 | (98) function_yielding(all_0_4_4) = 0
% 22.54/6.00 | (99) ? [v0] : ? [v1] : relation(v0) = v1
% 22.54/6.00 | (100) epsilon_transitive(all_0_11_11) = 0
% 22.54/6.00 | (101) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 22.54/6.00 | (102) ! [v0] : ! [v1] : (v1 = 0 | ~ (ordinal(v0) = v1) | ? [v2] : (( ~ (v2 = 0) & epsilon_connected(v0) = v2) | ( ~ (v2 = 0) & epsilon_transitive(v0) = v2)))
% 22.54/6.00 | (103) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 22.54/6.00 | (104) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0))
% 22.54/6.00 | (105) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & v3 = 0 & ~ (v4 = 0) & finite(v2) = 0 & empty(v2) = v4 & element(v2, v1) = 0) | (v2 = 0 & empty(v0) = 0)))
% 22.54/6.00 | (106) ! [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)))
% 22.54/6.00 | (107) transfinite_sequence(all_0_25_25) = 0
% 22.54/6.00 | (108) one_to_one(all_0_13_13) = 0
% 22.54/6.00 | (109) ! [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))
% 22.54/6.00 | (110) epsilon_connected(all_0_22_22) = 0
% 22.54/6.00 | (111) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (one_to_one(v2) = 0 & natural(v2) = 0 & relation(v2) = 0 & function(v2) = 0 & finite(v2) = 0 & empty(v2) = 0 & epsilon_connected(v2) = 0 & element(v2, v1) = 0 & epsilon_transitive(v2) = 0 & ordinal(v2) = 0))
% 22.54/6.00 | (112) ! [v0] : ! [v1] : (v1 = 0 | ~ (function(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2))
% 22.54/6.00 | (113) ~ (all_0_17_17 = 0)
% 22.54/6.00 | (114) function(all_0_13_13) = 0
% 22.54/6.00 | (115) ? [v0] : ? [v1] : epsilon_transitive(v0) = v1
% 22.54/6.00 | (116) relation(all_0_23_23) = 0
% 22.54/6.00 | (117) relation(all_0_5_5) = 0
% 22.54/6.00 | (118) finite(all_0_3_3) = 0
% 22.54/6.00 | (119) transfinite_sequence(all_0_14_14) = 0
% 22.54/6.00 | (120) empty(all_0_9_9) = 0
% 22.54/6.00 | (121) empty(all_0_16_16) = all_0_15_15
% 22.54/6.00 | (122) ! [v0] : ( ~ (element(v0, positive_rationals) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : (ordinal(v0) = v1 & ( ~ (v1 = 0) | (v4 = 0 & v3 = 0 & v2 = 0 & natural(v0) = 0 & epsilon_connected(v0) = 0 & epsilon_transitive(v0) = 0))))
% 22.54/6.00 | (123) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0))
% 22.54/6.00 | (124) natural(all_0_1_1) = 0
% 22.54/6.00 | (125) ? [v0] : ? [v1] : element(v1, v0) = 0
% 22.54/6.00 | (126) ~ (all_0_2_2 = 0)
% 22.84/6.00 | (127) ? [v0] : ? [v1] : relation_non_empty(v0) = v1
% 22.84/6.00 | (128) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function_yielding(v2) = v1) | ~ (function_yielding(v2) = v0))
% 22.84/6.00 | (129) ordinal(all_0_7_7) = 0
% 22.84/6.00 | (130) function(all_0_14_14) = 0
% 22.84/6.00 | (131) relation_non_empty(all_0_26_26) = 0
% 22.84/6.00 | (132) relation_empty_yielding(all_0_24_24) = 0
% 22.84/6.00 | (133) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (being_limit_ordinal(v2) = v1) | ~ (being_limit_ordinal(v2) = v0))
% 22.84/6.00 | (134) epsilon_connected(all_0_1_1) = 0
% 22.84/6.00 | (135) ordinal(all_0_6_6) = 0
% 22.84/6.00 | (136) ? [v0] : ? [v1] : ordinal_yielding(v0) = v1
% 22.84/6.00 | (137) ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2))
% 22.84/6.00 | (138) ! [v0] : ! [v1] : ( ~ (epsilon_connected(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = 0 & v3 = 0 & v2 = 0 & v1 = 0 & natural(v0) = 0 & epsilon_transitive(v0) = 0 & ordinal(v0) = 0) | ( ~ (v2 = 0) & empty(v0) = v2) | ( ~ (v2 = 0) & ordinal(v0) = v2)))
% 22.84/6.00 | (139) epsilon_transitive(all_0_1_1) = 0
% 22.84/6.00 | (140) epsilon_connected(all_0_11_11) = 0
% 22.84/6.00 | (141) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1))
% 22.84/6.00 | (142) one_to_one(all_0_20_20) = 0
% 22.84/6.00 | (143) ! [v0] : ! [v1] : ! [v2] : ( ~ (epsilon_connected(v1) = v2) | ~ (ordinal(v0) = 0) | ? [v3] : ? [v4] : ((v4 = 0 & v3 = 0 & v2 = 0 & epsilon_transitive(v1) = 0 & ordinal(v1) = 0) | ( ~ (v3 = 0) & element(v1, v0) = v3)))
% 22.84/6.00 | (144) ! [v0] : ! [v1] : ( ~ (epsilon_connected(v0) = v1) | ? [v2] : ((v2 = 0 & v1 = 0 & epsilon_transitive(v0) = 0) | ( ~ (v2 = 0) & ordinal(v0) = v2)))
% 22.84/6.01 | (145) epsilon_connected(all_0_13_13) = 0
% 22.84/6.01 | (146) relation(all_0_8_8) = 0
% 22.84/6.01 | (147) ! [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)))
% 22.84/6.01 | (148) function(all_0_5_5) = 0
% 22.84/6.01 | (149) ! [v0] : ! [v1] : ( ~ (ordinal(v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & epsilon_connected(v0) = 0 & epsilon_transitive(v0) = 0) | ( ~ (v2 = 0) & empty(v0) = v2)))
% 22.84/6.01 | (150) ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2
% 22.84/6.01 | (151) function(all_0_20_20) = 0
% 22.84/6.01 | (152) ordinal(all_0_19_19) = 0
% 22.84/6.01 | (153) ! [v0] : ( ~ (finite(v0) = 0) | ? [v1] : (powerset(v0) = v1 & ! [v2] : ! [v3] : (v3 = 0 | ~ (finite(v2) = v3) | ? [v4] : ( ~ (v4 = 0) & element(v2, v1) = v4)) & ! [v2] : ( ~ (element(v2, v1) = 0) | finite(v2) = 0)))
% 22.84/6.01 | (154) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (empty(v2) = 0 & element(v2, v1) = 0))
% 22.84/6.01 | (155) ! [v0] : ( ~ (empty(v0) = 0) | function(v0) = 0)
% 22.84/6.01 | (156) ordinal(all_0_22_22) = 0
% 22.84/6.01 | (157) epsilon_transitive(all_0_7_7) = 0
% 22.84/6.01 | (158) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v0) = v1) | ~ (finite(v2) = v3) | ? [v4] : (( ~ (v4 = 0) & finite(v0) = v4) | ( ~ (v4 = 0) & element(v2, v1) = v4)))
% 22.84/6.01 | (159) ! [v0] : ( ~ (empty(v0) = 0) | finite(v0) = 0)
% 22.84/6.01 | (160) empty(all_0_11_11) = all_0_10_10
% 22.84/6.01 | (161) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 22.84/6.01 | (162) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (finite(v2) = v1) | ~ (finite(v2) = v0))
% 22.84/6.01 | (163) relation(all_0_20_20) = 0
% 22.84/6.01 | (164) relation(all_0_14_14) = 0
% 22.84/6.01 | (165) ? [v0] : ? [v1] : finite(v0) = v1
% 22.84/6.01 | (166) epsilon_transitive(all_0_6_6) = 0
% 22.84/6.01 | (167) ! [v0] : ! [v1] : ( ~ (natural(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = 0 & v3 = 0 & v2 = 0 & v1 = 0 & epsilon_connected(v0) = 0 & epsilon_transitive(v0) = 0 & ordinal(v0) = 0) | ( ~ (v2 = 0) & empty(v0) = v2) | ( ~ (v2 = 0) & ordinal(v0) = v2)))
% 22.84/6.01 | (168) ? [v0] : ? [v1] : epsilon_connected(v0) = v1
% 22.84/6.01 | (169) epsilon_connected(all_0_7_7) = 0
% 22.84/6.01 | (170) being_limit_ordinal(all_0_7_7) = 0
% 22.84/6.01 | (171) ? [v0] : ? [v1] : function(v0) = v1
% 22.84/6.01 | (172) ! [v0] : ! [v1] : (v1 = 0 | ~ (empty(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v0) = v2 & finite(v3) = 0 & empty(v3) = v4 & element(v3, v2) = 0))
% 22.84/6.01 | (173) relation(all_0_4_4) = 0
% 22.84/6.01 | (174) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (natural(v2) = v1) | ~ (natural(v2) = v0))
% 22.84/6.01 | (175) ? [v0] : ? [v1] : ordinal(v0) = v1
% 22.84/6.01 | (176) finite(all_0_28_28) = 0
% 22.84/6.01 | (177) ~ (all_0_15_15 = 0)
% 22.84/6.01 | (178) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ordinal(v2) = v1) | ~ (ordinal(v2) = v0))
% 22.84/6.01 | (179) ~ (all_0_27_27 = 0)
% 22.84/6.01 | (180) ordinal(all_0_11_11) = 0
% 22.84/6.01 | (181) epsilon_connected(empty_set) = 0
% 22.84/6.01 | (182) empty(all_0_22_22) = all_0_21_21
% 22.84/6.01 | (183) ~ (all_0_21_21 = 0)
% 22.84/6.01 | (184) ! [v0] : ! [v1] : ( ~ (epsilon_transitive(v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & epsilon_connected(v0) = 0 & ordinal(v0) = 0) | ( ~ (v2 = 0) & empty(v0) = v2)))
% 22.84/6.01 | (185) relation(all_0_24_24) = 0
% 22.84/6.01 | (186) empty(all_0_12_12) = 0
% 22.84/6.01 | (187) ? [v0] : ? [v1] : one_to_one(v0) = v1
% 22.84/6.01 | (188) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (powerset(v1) = v2 & element(v0, v2) = 0))
% 22.84/6.01 | (189) ! [v0] : ( ~ (empty(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : (ordinal(v0) = v1 & ( ~ (v1 = 0) | (v4 = 0 & v3 = 0 & v2 = 0 & natural(v0) = 0 & epsilon_connected(v0) = 0 & epsilon_transitive(v0) = 0))))
% 22.84/6.01 | (190) relation(all_0_12_12) = 0
% 22.84/6.01 | (191) ! [v0] : ! [v1] : ( ~ (element(v1, v0) = 0) | ~ (ordinal(v0) = 0) | (epsilon_connected(v1) = 0 & epsilon_transitive(v1) = 0 & ordinal(v1) = 0))
% 22.84/6.01 |
% 22.84/6.01 | Instantiating formula (188) with all_0_28_28, all_0_29_29 and discharging atoms subset(all_0_29_29, all_0_28_28) = 0, yields:
% 22.84/6.01 | (192) ? [v0] : (powerset(all_0_28_28) = v0 & element(all_0_29_29, v0) = 0)
% 22.84/6.01 |
% 22.84/6.01 | Instantiating formula (153) with all_0_3_3 and discharging atoms finite(all_0_3_3) = 0, yields:
% 22.84/6.01 | (193) ? [v0] : (powerset(all_0_3_3) = v0 & ! [v1] : ! [v2] : (v2 = 0 | ~ (finite(v1) = v2) | ? [v3] : ( ~ (v3 = 0) & element(v1, v0) = v3)) & ! [v1] : ( ~ (element(v1, v0) = 0) | finite(v1) = 0))
% 22.84/6.01 |
% 22.84/6.01 | Instantiating formula (153) with all_0_28_28 and discharging atoms finite(all_0_28_28) = 0, yields:
% 22.84/6.01 | (194) ? [v0] : (powerset(all_0_28_28) = v0 & ! [v1] : ! [v2] : (v2 = 0 | ~ (finite(v1) = v2) | ? [v3] : ( ~ (v3 = 0) & element(v1, v0) = v3)) & ! [v1] : ( ~ (element(v1, v0) = 0) | finite(v1) = 0))
% 22.84/6.01 |
% 22.84/6.01 | Instantiating formula (35) with all_0_27_27, all_0_29_29 and discharging atoms finite(all_0_29_29) = all_0_27_27, yields:
% 22.84/6.01 | (195) all_0_27_27 = 0 | ? [v0] : ( ~ (v0 = 0) & empty(all_0_29_29) = v0)
% 22.84/6.01 |
% 22.84/6.01 | Instantiating (194) with all_163_0_311 yields:
% 22.84/6.01 | (196) powerset(all_0_28_28) = all_163_0_311 & ! [v0] : ! [v1] : (v1 = 0 | ~ (finite(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & element(v0, all_163_0_311) = v2)) & ! [v0] : ( ~ (element(v0, all_163_0_311) = 0) | finite(v0) = 0)
% 22.84/6.01 |
% 22.84/6.01 | Applying alpha-rule on (196) yields:
% 22.84/6.01 | (197) powerset(all_0_28_28) = all_163_0_311
% 22.84/6.01 | (198) ! [v0] : ! [v1] : (v1 = 0 | ~ (finite(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & element(v0, all_163_0_311) = v2))
% 22.84/6.01 | (199) ! [v0] : ( ~ (element(v0, all_163_0_311) = 0) | finite(v0) = 0)
% 22.84/6.01 |
% 22.84/6.01 | Instantiating formula (198) with all_0_27_27, all_0_29_29 and discharging atoms finite(all_0_29_29) = all_0_27_27, yields:
% 22.84/6.01 | (200) all_0_27_27 = 0 | ? [v0] : ( ~ (v0 = 0) & element(all_0_29_29, all_163_0_311) = v0)
% 22.84/6.01 |
% 22.84/6.01 | Instantiating (193) with all_186_0_357 yields:
% 22.84/6.01 | (201) powerset(all_0_3_3) = all_186_0_357 & ! [v0] : ! [v1] : (v1 = 0 | ~ (finite(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & element(v0, all_186_0_357) = v2)) & ! [v0] : ( ~ (element(v0, all_186_0_357) = 0) | finite(v0) = 0)
% 22.84/6.01 |
% 22.84/6.02 | Applying alpha-rule on (201) yields:
% 22.84/6.02 | (202) powerset(all_0_3_3) = all_186_0_357
% 22.84/6.02 | (203) ! [v0] : ! [v1] : (v1 = 0 | ~ (finite(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & element(v0, all_186_0_357) = v2))
% 22.84/6.02 | (204) ! [v0] : ( ~ (element(v0, all_186_0_357) = 0) | finite(v0) = 0)
% 22.84/6.02 |
% 22.84/6.02 | Instantiating formula (203) with all_0_27_27, all_0_29_29 and discharging atoms finite(all_0_29_29) = all_0_27_27, yields:
% 22.84/6.02 | (205) all_0_27_27 = 0 | ? [v0] : ( ~ (v0 = 0) & element(all_0_29_29, all_186_0_357) = v0)
% 22.84/6.02 |
% 22.84/6.02 | Instantiating (192) with all_231_0_449 yields:
% 22.84/6.02 | (206) powerset(all_0_28_28) = all_231_0_449 & element(all_0_29_29, all_231_0_449) = 0
% 22.84/6.02 |
% 22.84/6.02 | Applying alpha-rule on (206) yields:
% 22.84/6.02 | (207) powerset(all_0_28_28) = all_231_0_449
% 22.84/6.02 | (208) element(all_0_29_29, all_231_0_449) = 0
% 22.84/6.02 |
% 22.84/6.02 +-Applying beta-rule and splitting (195), into two cases.
% 22.84/6.02 |-Branch one:
% 22.84/6.02 | (209) all_0_27_27 = 0
% 22.84/6.02 |
% 22.84/6.02 | Equations (209) can reduce 179 to:
% 22.84/6.02 | (210) $false
% 22.84/6.02 |
% 22.84/6.02 |-The branch is then unsatisfiable
% 22.84/6.02 |-Branch two:
% 22.84/6.02 | (179) ~ (all_0_27_27 = 0)
% 22.84/6.02 | (212) ? [v0] : ( ~ (v0 = 0) & empty(all_0_29_29) = v0)
% 22.84/6.02 |
% 22.84/6.02 +-Applying beta-rule and splitting (205), into two cases.
% 22.84/6.02 |-Branch one:
% 22.84/6.02 | (209) all_0_27_27 = 0
% 22.84/6.02 |
% 22.84/6.02 | Equations (209) can reduce 179 to:
% 22.84/6.02 | (210) $false
% 22.84/6.02 |
% 22.84/6.02 |-The branch is then unsatisfiable
% 22.84/6.02 |-Branch two:
% 22.84/6.02 | (179) ~ (all_0_27_27 = 0)
% 22.84/6.02 | (216) ? [v0] : ( ~ (v0 = 0) & element(all_0_29_29, all_186_0_357) = v0)
% 22.84/6.02 |
% 22.84/6.02 +-Applying beta-rule and splitting (200), into two cases.
% 22.84/6.02 |-Branch one:
% 22.84/6.02 | (209) all_0_27_27 = 0
% 22.84/6.02 |
% 22.84/6.02 | Equations (209) can reduce 179 to:
% 22.84/6.02 | (210) $false
% 22.84/6.02 |
% 22.84/6.02 |-The branch is then unsatisfiable
% 22.84/6.02 |-Branch two:
% 22.84/6.02 | (179) ~ (all_0_27_27 = 0)
% 22.84/6.02 | (220) ? [v0] : ( ~ (v0 = 0) & element(all_0_29_29, all_163_0_311) = v0)
% 22.84/6.02 |
% 22.84/6.02 | Instantiating (220) with all_334_0_533 yields:
% 22.84/6.02 | (221) ~ (all_334_0_533 = 0) & element(all_0_29_29, all_163_0_311) = all_334_0_533
% 22.84/6.02 |
% 22.84/6.02 | Applying alpha-rule on (221) yields:
% 22.84/6.02 | (222) ~ (all_334_0_533 = 0)
% 22.84/6.02 | (223) element(all_0_29_29, all_163_0_311) = all_334_0_533
% 22.84/6.02 |
% 22.84/6.02 | Instantiating formula (31) with all_0_28_28, all_163_0_311, all_231_0_449 and discharging atoms powerset(all_0_28_28) = all_231_0_449, powerset(all_0_28_28) = all_163_0_311, yields:
% 22.84/6.02 | (224) all_231_0_449 = all_163_0_311
% 22.84/6.02 |
% 22.84/6.02 | From (224) and (208) follows:
% 22.84/6.02 | (225) element(all_0_29_29, all_163_0_311) = 0
% 22.84/6.02 |
% 22.84/6.02 | Instantiating formula (104) with all_0_29_29, all_163_0_311, 0, all_334_0_533 and discharging atoms element(all_0_29_29, all_163_0_311) = all_334_0_533, element(all_0_29_29, all_163_0_311) = 0, yields:
% 22.84/6.02 | (226) all_334_0_533 = 0
% 22.84/6.02 |
% 22.84/6.02 | Equations (226) can reduce 222 to:
% 22.84/6.02 | (210) $false
% 22.84/6.02 |
% 22.84/6.02 |-The branch is then unsatisfiable
% 22.84/6.02 % SZS output end Proof for theBenchmark
% 22.84/6.02
% 22.84/6.02 5475ms
%------------------------------------------------------------------------------