TSTP Solution File: NUM414+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : NUM414+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n005.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 08:44:14 EDT 2022
% Result : Theorem 20.41s 6.55s
% Output : Proof 23.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM414+1 : TPTP v8.1.0. Released v3.2.0.
% 0.13/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.34 % Computer : n005.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue Jul 5 18:41:52 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.54/0.62 ____ _
% 0.54/0.62 ___ / __ \_____(_)___ ________ __________
% 0.54/0.62 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.54/0.62 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.54/0.62 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.54/0.62
% 0.54/0.62 A Theorem Prover for First-Order Logic
% 0.54/0.63 (ePrincess v.1.0)
% 0.54/0.63
% 0.54/0.63 (c) Philipp Rümmer, 2009-2015
% 0.54/0.63 (c) Peter Backeman, 2014-2015
% 0.54/0.63 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.54/0.63 Free software under GNU Lesser General Public License (LGPL).
% 0.54/0.63 Bug reports to peter@backeman.se
% 0.65/0.63
% 0.65/0.63 For more information, visit http://user.uu.se/~petba168/breu/
% 0.65/0.63
% 0.65/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.69/0.68 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.70/0.98 Prover 0: Preprocessing ...
% 2.06/1.15 Prover 0: Warning: ignoring some quantifiers
% 2.28/1.17 Prover 0: Constructing countermodel ...
% 17.66/5.97 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 18.05/6.03 Prover 1: Preprocessing ...
% 18.59/6.17 Prover 1: Warning: ignoring some quantifiers
% 18.59/6.17 Prover 1: Constructing countermodel ...
% 19.43/6.32 Prover 1: gave up
% 19.43/6.32 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 19.43/6.35 Prover 2: Preprocessing ...
% 19.97/6.45 Prover 2: Warning: ignoring some quantifiers
% 19.97/6.45 Prover 2: Constructing countermodel ...
% 20.41/6.54 Prover 2: proved (223ms)
% 20.41/6.55 Prover 0: stopped
% 20.41/6.55
% 20.41/6.55 No countermodel exists, formula is valid
% 20.41/6.55 % SZS status Theorem for theBenchmark
% 20.41/6.55
% 20.41/6.55 Generating proof ... Warning: ignoring some quantifiers
% 22.69/7.03 found it (size 85)
% 22.69/7.03
% 22.69/7.03 % SZS output start Proof for theBenchmark
% 22.69/7.03 Assumed formulas after preprocessing and simplification:
% 22.69/7.03 | (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) & ~ (v2 = 0) & ~ (v1 = v0) & relation_non_empty(v4) = 0 & transfinite_sequence(v5) = 0 & relation_empty_yielding(v7) = 0 & relation_empty_yielding(v6) = 0 & relation_empty_yielding(empty_set) = 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(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(v0) = 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(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 & proper_subset(v1, v0) = v3 & proper_subset(v0, v1) = v2 & ! [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 | ~ (ordinal_subset(v24, v23) = v22) | ~ (ordinal_subset(v24, v23) = v21)) & ! [v21] : ! [v22] : ! [v23] : ! [v24] : (v22 = v21 | ~ (proper_subset(v24, v23) = v22) | ~ (proper_subset(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] : (v23 = 0 | v22 = v21 | ~ (proper_subset(v21, v22) = v23) | ? [v24] : ( ~ (v24 = 0) & subset(v21, v22) = v24)) & ! [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 | ~ (subset(v21, v22) = v23) | ? [v24] : ( ~ (v24 = 0) & proper_subset(v21, v22) = v24)) & ! [v21] : ! [v22] : ! [v23] : (v23 = 0 | ~ (ordinal_subset(v22, v21) = v23) | ? [v24] : ((v24 = 0 & ordinal_subset(v21, v22) = 0) | ( ~ (v24 = 0) & ordinal(v22) = v24) | ( ~ (v24 = 0) & ordinal(v21) = v24))) & ! [v21] : ! [v22] : ! [v23] : (v23 = 0 | ~ (ordinal_subset(v21, v22) = v23) | ? [v24] : ((v24 = 0 & ordinal_subset(v22, v21) = 0) | ( ~ (v24 = 0) & ordinal(v22) = v24) | ( ~ (v24 = 0) & ordinal(v21) = v24))) & ! [v21] : ! [v22] : ! [v23] : (v23 = 0 | ~ (ordinal_subset(v21, v21) = v23) | ~ (ordinal(v22) = 0) | ? [v24] : ( ~ (v24 = 0) & ordinal(v21) = v24)) & ! [v21] : ! [v22] : ! [v23] : (v23 = 0 | ~ (in(v21, v22) = v23) | ? [v24] : ((v24 = 0 & empty(v22) = 0) | ( ~ (v24 = 0) & element(v21, v22) = v24))) & ! [v21] : ! [v22] : ! [v23] : (v22 = v21 | ~ (powerset(v23) = v22) | ~ (powerset(v23) = v21)) & ! [v21] : ! [v22] : ! [v23] : (v22 = v21 | ~ (relation_non_empty(v23) = v22) | ~ (relation_non_empty(v23) = v21)) & ! [v21] : ! [v22] : ! [v23] : (v22 = v21 | ~ (transfinite_sequence(v23) = v22) | ~ (transfinite_sequence(v23) = v21)) & ! [v21] : ! [v22] : ! [v23] : (v22 = v21 | ~ (relation_empty_yielding(v23) = v22) | ~ (relation_empty_yielding(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] : ( ~ (subset(v21, v22) = v23) | ? [v24] : (( ~ (v24 = 0) & ordinal(v22) = v24) | ( ~ (v24 = 0) & ordinal(v21) = v24) | (( ~ (v23 = 0) | (v24 = 0 & ordinal_subset(v21, v22) = 0)) & (v23 = 0 | ( ~ (v24 = 0) & ordinal_subset(v21, v22) = v24))))) & ! [v21] : ! [v22] : ! [v23] : ( ~ (ordinal_subset(v21, v22) = v23) | ? [v24] : (( ~ (v24 = 0) & ordinal(v22) = v24) | ( ~ (v24 = 0) & ordinal(v21) = v24) | (( ~ (v23 = 0) | (v24 = 0 & subset(v21, v22) = 0)) & (v23 = 0 | ( ~ (v24 = 0) & subset(v21, v22) = v24))))) & ! [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 | ~ (subset(v21, v22) = 0) | proper_subset(v21, v22) = 0) & ! [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] : ( ~ (element(v21, v22) = 0) | ? [v23] : ((v23 = 0 & empty(v22) = 0) | (v23 = 0 & in(v21, v22) = 0))) & ! [v21] : ! [v22] : ( ~ (subset(v21, v22) = 0) | ? [v23] : (powerset(v22) = v23 & element(v21, v23) = 0)) & ! [v21] : ! [v22] : ( ~ (subset(v21, v21) = v22) | ? [v23] : ( ~ (v23 = 0) & proper_subset(v21, v21) = v23)) & ! [v21] : ! [v22] : ( ~ (one_to_one(v21) = v22) | ? [v23] : ? [v24] : ((v24 = 0 & v23 = 0 & v22 = 0 & relation(v21) = 0 & function(v21) = 0) | ( ~ (v23 = 0) & relation(v21) = v23) | ( ~ (v23 = 0) & function(v21) = v23) | ( ~ (v23 = 0) & empty(v21) = v23))) & ! [v21] : ! [v22] : ( ~ (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(v22) = 0) | ~ (ordinal(v21) = 0) | ordinal_subset(v21, v21) = 0) & ! [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] : ( ~ (proper_subset(v22, v21) = 0) | ? [v23] : ( ~ (v23 = 0) & proper_subset(v21, v22) = v23)) & ! [v21] : ! [v22] : ( ~ (proper_subset(v21, v22) = 0) | subset(v21, v22) = 0) & ! [v21] : ! [v22] : ( ~ (proper_subset(v21, v22) = 0) | ? [v23] : ( ~ (v23 = 0) & proper_subset(v22, 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(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] : ( ~ (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] : ((v23 = 0 & v22 = 0 & one_to_one(v21) = 0 & relation(v21) = 0) | ( ~ (v22 = 0) & relation(v21) = v22) | ( ~ (v22 = 0) & empty(v21) = v22))) & ! [v21] : ( ~ (empty(v21) = 0) | relation(v21) = 0) & ! [v21] : ( ~ (empty(v21) = 0) | function(v21) = 0) & ! [v21] : ( ~ (empty(v21) = 0) | ? [v22] : ? [v23] : ? [v24] : ((v24 = 0 & v23 = 0 & v22 = 0 & one_to_one(v21) = 0 & relation(v21) = 0 & function(v21) = 0) | ( ~ (v22 = 0) & relation(v21) = v22) | ( ~ (v22 = 0) & function(v21) = v22))) & ! [v21] : ( ~ (empty(v21) = 0) | (epsilon_transitive(v21) = 0 & ordinal(v21) = 0 & epsilon_connected(v21) = 0)) & ! [v21] : ~ (proper_subset(v21, v21) = 0) & ? [v21] : ? [v22] : ? [v23] : element(v22, v21) = v23 & ? [v21] : ? [v22] : ? [v23] : subset(v22, v21) = v23 & ? [v21] : ? [v22] : ? [v23] : ordinal_subset(v22, v21) = v23 & ? [v21] : ? [v22] : ? [v23] : proper_subset(v22, v21) = v23 & ? [v21] : ? [v22] : ? [v23] : in(v22, v21) = v23 & ? [v21] : ? [v22] : powerset(v21) = v22 & ? [v21] : ? [v22] : relation_non_empty(v21) = v22 & ? [v21] : ? [v22] : transfinite_sequence(v21) = v22 & ? [v21] : ? [v22] : relation_empty_yielding(v21) = v22 & ? [v21] : ? [v22] : element(v22, v21) = 0 & ? [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)
% 22.69/7.08 | 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:
% 22.69/7.08 | (1) ~ (all_0_6_6 = 0) & ~ (all_0_8_8 = 0) & ~ (all_0_11_11 = 0) & ~ (all_0_17_17 = 0) & ~ (all_0_18_18 = 0) & ~ (all_0_19_19 = all_0_20_20) & relation_non_empty(all_0_16_16) = 0 & transfinite_sequence(all_0_15_15) = 0 & relation_empty_yielding(all_0_13_13) = 0 & relation_empty_yielding(all_0_14_14) = 0 & relation_empty_yielding(empty_set) = 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(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(all_0_20_20) = 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(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 & proper_subset(all_0_19_19, all_0_20_20) = all_0_17_17 & proper_subset(all_0_20_20, all_0_19_19) = all_0_18_18 & ! [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 | ~ (ordinal_subset(v3, v2) = v1) | ~ (ordinal_subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (proper_subset(v3, v2) = v1) | ~ (proper_subset(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 | v1 = v0 | ~ (proper_subset(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3)) & ! [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 | ~ (subset(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & proper_subset(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (ordinal_subset(v1, v0) = v2) | ? [v3] : ((v3 = 0 & ordinal_subset(v0, v1) = 0) | ( ~ (v3 = 0) & ordinal(v1) = v3) | ( ~ (v3 = 0) & ordinal(v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (ordinal_subset(v0, v1) = v2) | ? [v3] : ((v3 = 0 & ordinal_subset(v1, v0) = 0) | ( ~ (v3 = 0) & ordinal(v1) = v3) | ( ~ (v3 = 0) & ordinal(v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (ordinal_subset(v0, v0) = v2) | ~ (ordinal(v1) = 0) | ? [v3] : ( ~ (v3 = 0) & ordinal(v0) = 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 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_non_empty(v2) = v1) | ~ (relation_non_empty(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (transfinite_sequence(v2) = v1) | ~ (transfinite_sequence(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_empty_yielding(v2) = v1) | ~ (relation_empty_yielding(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] : ( ~ (subset(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & ordinal(v1) = v3) | ( ~ (v3 = 0) & ordinal(v0) = v3) | (( ~ (v2 = 0) | (v3 = 0 & ordinal_subset(v0, v1) = 0)) & (v2 = 0 | ( ~ (v3 = 0) & ordinal_subset(v0, v1) = v3))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordinal_subset(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & ordinal(v1) = v3) | ( ~ (v3 = 0) & ordinal(v0) = v3) | (( ~ (v2 = 0) | (v3 = 0 & subset(v0, v1) = 0)) & (v2 = 0 | ( ~ (v3 = 0) & subset(v0, v1) = v3))))) & ! [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 | ~ (subset(v0, v1) = 0) | proper_subset(v0, v1) = 0) & ! [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] : ( ~ (element(v0, v1) = 0) | ? [v2] : ((v2 = 0 & empty(v1) = 0) | (v2 = 0 & in(v0, v1) = 0))) & ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (powerset(v1) = v2 & element(v0, v2) = 0)) & ! [v0] : ! [v1] : ( ~ (subset(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & proper_subset(v0, v0) = v2)) & ! [v0] : ! [v1] : ( ~ (one_to_one(v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & relation(v0) = 0 & function(v0) = 0) | ( ~ (v2 = 0) & relation(v0) = v2) | ( ~ (v2 = 0) & function(v0) = v2) | ( ~ (v2 = 0) & empty(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (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(v1) = 0) | ~ (ordinal(v0) = 0) | ordinal_subset(v0, v0) = 0) & ! [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] : ( ~ (proper_subset(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & proper_subset(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (proper_subset(v0, v1) = 0) | subset(v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (proper_subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & proper_subset(v1, 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] : ( ~ (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] : ((v2 = 0 & v1 = 0 & one_to_one(v0) = 0 & relation(v0) = 0) | ( ~ (v1 = 0) & relation(v0) = v1) | ( ~ (v1 = 0) & empty(v0) = v1))) & ! [v0] : ( ~ (empty(v0) = 0) | relation(v0) = 0) & ! [v0] : ( ~ (empty(v0) = 0) | function(v0) = 0) & ! [v0] : ( ~ (empty(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & one_to_one(v0) = 0 & relation(v0) = 0 & function(v0) = 0) | ( ~ (v1 = 0) & relation(v0) = v1) | ( ~ (v1 = 0) & function(v0) = v1))) & ! [v0] : ( ~ (empty(v0) = 0) | (epsilon_transitive(v0) = 0 & ordinal(v0) = 0 & epsilon_connected(v0) = 0)) & ! [v0] : ~ (proper_subset(v0, v0) = 0) & ? [v0] : ? [v1] : ? [v2] : element(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : ordinal_subset(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : proper_subset(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2 & ? [v0] : ? [v1] : powerset(v0) = v1 & ? [v0] : ? [v1] : relation_non_empty(v0) = v1 & ? [v0] : ? [v1] : transfinite_sequence(v0) = v1 & ? [v0] : ? [v1] : relation_empty_yielding(v0) = v1 & ? [v0] : ? [v1] : element(v1, v0) = 0 & ? [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
% 22.69/7.10 |
% 22.69/7.10 | Applying alpha-rule on (1) yields:
% 22.69/7.10 | (2) ? [v0] : ? [v1] : ? [v2] : ordinal_subset(v1, v0) = v2
% 22.69/7.10 | (3) ! [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))
% 22.69/7.10 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | subset(v0, v1) = 0)
% 22.69/7.10 | (5) ! [v0] : ! [v1] : (v1 = v0 | ~ (subset(v0, v1) = 0) | proper_subset(v0, v1) = 0)
% 22.69/7.10 | (6) relation_empty_yielding(empty_set) = 0
% 22.69/7.10 | (7) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordinal_subset(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & ordinal(v1) = v3) | ( ~ (v3 = 0) & ordinal(v0) = v3) | (( ~ (v2 = 0) | (v3 = 0 & subset(v0, v1) = 0)) & (v2 = 0 | ( ~ (v3 = 0) & subset(v0, v1) = v3)))))
% 22.69/7.10 | (8) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (proper_subset(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3))
% 22.69/7.10 | (9) ! [v0] : ! [v1] : ( ~ (epsilon_transitive(v0) = v1) | ? [v2] : ((v2 = 0 & v1 = 0 & epsilon_connected(v0) = 0) | ( ~ (v2 = 0) & ordinal(v0) = v2)))
% 22.69/7.10 | (10) ! [v0] : ~ (proper_subset(v0, v0) = 0)
% 22.69/7.10 | (11) ! [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))
% 22.69/7.10 | (12) function(all_0_0_0) = 0
% 22.69/7.10 | (13) ordinal(empty_set) = 0
% 22.69/7.10 | (14) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & proper_subset(v0, v1) = v3))
% 22.69/7.10 | (15) ~ (all_0_6_6 = 0)
% 22.69/7.10 | (16) ~ (all_0_18_18 = 0)
% 22.69/7.10 | (17) epsilon_transitive(all_0_1_1) = 0
% 22.69/7.10 | (18) ! [v0] : ( ~ (empty(v0) = 0) | (epsilon_transitive(v0) = 0 & ordinal(v0) = 0 & epsilon_connected(v0) = 0))
% 22.69/7.10 | (19) function(all_0_15_15) = 0
% 22.69/7.10 | (20) epsilon_connected(empty_set) = 0
% 22.69/7.10 | (21) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v1) = v3 & element(v0, v3) = v4))
% 22.69/7.10 | (22) ! [v0] : ! [v1] : (v1 = 0 | ~ (relation(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2))
% 22.69/7.10 | (23) ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2
% 22.69/7.10 | (24) transfinite_sequence(all_0_15_15) = 0
% 22.69/7.10 | (25) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (powerset(v1) = v2 & element(v0, v2) = 0))
% 22.69/7.10 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 22.69/7.10 | (27) ? [v0] : ? [v1] : ? [v2] : proper_subset(v1, v0) = v2
% 22.69/7.10 | (28) ? [v0] : ? [v1] : ordinal(v0) = v1
% 22.69/7.10 | (29) empty(all_0_5_5) = 0
% 22.69/7.10 | (30) relation_empty_yielding(all_0_14_14) = 0
% 22.69/7.11 | (31) relation(all_0_4_4) = 0
% 22.69/7.11 | (32) ! [v0] : ( ~ (epsilon_connected(v0) = 0) | ? [v1] : ((v1 = 0 & ordinal(v0) = 0) | ( ~ (v1 = 0) & epsilon_transitive(v0) = v1)))
% 22.69/7.11 | (33) ! [v0] : ( ~ (epsilon_transitive(v0) = 0) | ? [v1] : ((v1 = 0 & ordinal(v0) = 0) | ( ~ (v1 = 0) & epsilon_connected(v0) = v1)))
% 22.69/7.11 | (34) empty(all_0_2_2) = 0
% 22.69/7.11 | (35) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | element(v0, v1) = 0)
% 22.69/7.11 | (36) ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2))
% 22.69/7.11 | (37) one_to_one(empty_set) = 0
% 22.69/7.11 | (38) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0))
% 22.69/7.11 | (39) ? [v0] : ? [v1] : function(v0) = v1
% 22.69/7.11 | (40) ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2
% 22.69/7.11 | (41) ~ (all_0_19_19 = all_0_20_20)
% 22.69/7.11 | (42) proper_subset(all_0_19_19, all_0_20_20) = all_0_17_17
% 22.69/7.11 | (43) empty(all_0_4_4) = 0
% 22.69/7.11 | (44) ! [v0] : ( ~ (empty(v0) = 0) | function(v0) = 0)
% 22.69/7.11 | (45) relation(empty_set) = 0
% 22.69/7.11 | (46) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (ordinal_subset(v0, v1) = v2) | ? [v3] : ((v3 = 0 & ordinal_subset(v1, v0) = 0) | ( ~ (v3 = 0) & ordinal(v1) = v3) | ( ~ (v3 = 0) & ordinal(v0) = v3)))
% 22.69/7.11 | (47) ? [v0] : ? [v1] : powerset(v0) = v1
% 22.69/7.11 | (48) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0))
% 22.69/7.11 | (49) ! [v0] : ! [v1] : ( ~ (proper_subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & proper_subset(v1, v0) = v2))
% 22.69/7.11 | (50) function(all_0_5_5) = 0
% 22.69/7.11 | (51) ordinal(all_0_20_20) = 0
% 22.69/7.11 | (52) ! [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)))
% 22.69/7.11 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 22.69/7.11 | (54) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 22.69/7.11 | (55) ! [v0] : ! [v1] : ( ~ (epsilon_connected(v0) = v1) | ? [v2] : ((v2 = 0 & v1 = 0 & epsilon_transitive(v0) = 0) | ( ~ (v2 = 0) & ordinal(v0) = v2)))
% 22.69/7.11 | (56) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (ordinal_subset(v1, v0) = v2) | ? [v3] : ((v3 = 0 & ordinal_subset(v0, v1) = 0) | ( ~ (v3 = 0) & ordinal(v1) = v3) | ( ~ (v3 = 0) & ordinal(v0) = v3)))
% 22.69/7.11 | (57) ? [v0] : ? [v1] : element(v1, v0) = 0
% 22.69/7.11 | (58) epsilon_connected(all_0_12_12) = 0
% 22.69/7.11 | (59) ! [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)))
% 22.69/7.11 | (60) ! [v0] : ( ~ (ordinal(v0) = 0) | (epsilon_transitive(v0) = 0 & epsilon_connected(v0) = 0))
% 22.69/7.11 | (61) ordinal(all_0_1_1) = 0
% 22.69/7.11 | (62) ! [v0] : ! [v1] : ! [v2] : ( ~ (empty(v2) = 0) | ~ (in(v0, v1) = 0) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v2) = v3 & element(v1, v3) = v4))
% 22.69/7.11 | (63) ! [v0] : ! [v1] : (v1 = 0 | ~ (ordinal(v0) = v1) | ? [v2] : (( ~ (v2 = 0) & epsilon_transitive(v0) = v2) | ( ~ (v2 = 0) & epsilon_connected(v0) = v2)))
% 22.69/7.11 | (64) function(all_0_14_14) = 0
% 22.69/7.11 | (65) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 22.69/7.11 | (66) function(all_0_4_4) = 0
% 22.69/7.11 | (67) ~ (all_0_11_11 = 0)
% 22.69/7.11 | (68) proper_subset(all_0_20_20, all_0_19_19) = all_0_18_18
% 22.69/7.11 | (69) ! [v0] : ! [v1] : ( ~ (element(v0, v1) = 0) | ? [v2] : ((v2 = 0 & empty(v1) = 0) | (v2 = 0 & in(v0, v1) = 0)))
% 22.69/7.11 | (70) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (ordinal_subset(v0, v0) = v2) | ~ (ordinal(v1) = 0) | ? [v3] : ( ~ (v3 = 0) & ordinal(v0) = v3))
% 22.69/7.11 | (71) ? [v0] : ? [v1] : empty(v0) = v1
% 22.69/7.11 | (72) relation(all_0_15_15) = 0
% 22.69/7.11 | (73) epsilon_transitive(empty_set) = 0
% 22.69/7.11 | (74) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 22.69/7.11 | (75) empty(all_0_3_3) = 0
% 22.69/7.11 | (76) ordinal(all_0_12_12) = 0
% 22.69/7.11 | (77) one_to_one(all_0_10_10) = 0
% 22.69/7.11 | (78) relation(all_0_7_7) = 0
% 22.69/7.11 | (79) relation(all_0_10_10) = 0
% 22.69/7.12 | (80) function(all_0_10_10) = 0
% 22.69/7.12 | (81) ! [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)))
% 22.69/7.12 | (82) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0))
% 22.69/7.12 | (83) epsilon_transitive(all_0_5_5) = 0
% 22.69/7.12 | (84) relation_empty_yielding(all_0_13_13) = 0
% 22.69/7.12 | (85) relation(all_0_2_2) = 0
% 22.69/7.12 | (86) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (proper_subset(v3, v2) = v1) | ~ (proper_subset(v3, v2) = v0))
% 22.69/7.12 | (87) ? [v0] : ? [v1] : ? [v2] : element(v1, v0) = v2
% 22.69/7.12 | (88) relation(all_0_0_0) = 0
% 22.69/7.12 | (89) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ordinal(v2) = v1) | ~ (ordinal(v2) = v0))
% 22.69/7.12 | (90) ! [v0] : ! [v1] : ( ~ (proper_subset(v0, v1) = 0) | subset(v0, v1) = 0)
% 22.69/7.12 | (91) ! [v0] : ! [v1] : (v1 = 0 | ~ (function(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2))
% 22.69/7.12 | (92) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordinal_subset(v3, v2) = v1) | ~ (ordinal_subset(v3, v2) = v0))
% 22.69/7.12 | (93) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v0, v1) = v2) | ? [v3] : ((v3 = 0 & empty(v1) = 0) | ( ~ (v3 = 0) & element(v0, v1) = v3)))
% 22.69/7.12 | (94) relation(all_0_5_5) = 0
% 22.69/7.12 | (95) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3))
% 22.69/7.12 | (96) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_empty_yielding(v2) = v1) | ~ (relation_empty_yielding(v2) = v0))
% 22.69/7.12 | (97) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_non_empty(v2) = v1) | ~ (relation_non_empty(v2) = v0))
% 22.69/7.12 | (98) ! [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)))
% 22.69/7.12 | (99) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 22.69/7.12 | (100) ~ (all_0_8_8 = 0)
% 22.69/7.12 | (101) ! [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)))
% 22.69/7.12 | (102) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1))
% 22.69/7.12 | (103) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0))
% 22.69/7.12 | (104) relation(all_0_14_14) = 0
% 22.69/7.12 | (105) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4))
% 22.69/7.12 | (106) ! [v0] : ! [v1] : ( ~ (ordinal(v1) = 0) | ~ (ordinal(v0) = 0) | ordinal_subset(v0, v0) = 0)
% 22.69/7.12 | (107) ? [v0] : ? [v1] : relation_non_empty(v0) = v1
% 22.69/7.12 | (108) relation(all_0_16_16) = 0
% 22.69/7.12 | (109) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0))
% 22.69/7.12 | (110) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0))
% 22.69/7.12 | (111) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & ordinal(v1) = v3) | ( ~ (v3 = 0) & ordinal(v0) = v3) | (( ~ (v2 = 0) | (v3 = 0 & ordinal_subset(v0, v1) = 0)) & (v2 = 0 | ( ~ (v3 = 0) & ordinal_subset(v0, v1) = v3)))))
% 22.69/7.12 | (112) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (epsilon_transitive(v2) = v1) | ~ (epsilon_transitive(v2) = v0))
% 22.69/7.12 | (113) ! [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)))
% 22.69/7.12 | (114) function(empty_set) = 0
% 22.69/7.12 | (115) empty(all_0_12_12) = all_0_11_11
% 22.69/7.12 | (116) empty(all_0_7_7) = all_0_6_6
% 22.69/7.12 | (117) ~ (all_0_17_17 = 0)
% 22.69/7.12 | (118) ! [v0] : ( ~ (empty(v0) = 0) | relation(v0) = 0)
% 22.69/7.12 | (119) ? [v0] : ? [v1] : relation(v0) = v1
% 22.69/7.12 | (120) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0))
% 22.69/7.12 | (121) relation(all_0_13_13) = 0
% 22.69/7.12 | (122) epsilon_connected(all_0_5_5) = 0
% 22.69/7.12 | (123) empty(all_0_9_9) = all_0_8_8
% 22.69/7.12 | (124) function(all_0_16_16) = 0
% 22.69/7.12 | (125) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | element(v0, v2) = 0)
% 22.69/7.12 | (126) ? [v0] : ? [v1] : epsilon_transitive(v0) = v1
% 22.69/7.12 | (127) ? [v0] : ? [v1] : epsilon_connected(v0) = v1
% 22.69/7.12 | (128) ! [v0] : ! [v1] : ( ~ (proper_subset(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & proper_subset(v0, v1) = v2))
% 22.69/7.12 | (129) one_to_one(all_0_5_5) = 0
% 22.69/7.12 | (130) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (transfinite_sequence(v2) = v1) | ~ (transfinite_sequence(v2) = v0))
% 22.69/7.12 | (131) epsilon_transitive(all_0_12_12) = 0
% 22.69/7.12 | (132) ordinal(all_0_19_19) = 0
% 22.69/7.12 | (133) ! [v0] : ! [v1] : ( ~ (subset(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & proper_subset(v0, v0) = v2))
% 22.69/7.12 | (134) epsilon_connected(all_0_1_1) = 0
% 22.69/7.12 | (135) ! [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)))
% 22.69/7.12 | (136) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (epsilon_connected(v2) = v1) | ~ (epsilon_connected(v2) = v0))
% 22.69/7.12 | (137) ? [v0] : ? [v1] : transfinite_sequence(v0) = v1
% 22.69/7.12 | (138) empty(empty_set) = 0
% 22.69/7.12 | (139) ? [v0] : ? [v1] : relation_empty_yielding(v0) = v1
% 22.69/7.12 | (140) relation_non_empty(all_0_16_16) = 0
% 22.69/7.12 | (141) ordinal(all_0_5_5) = 0
% 22.69/7.12 | (142) ? [v0] : ? [v1] : one_to_one(v0) = v1
% 22.69/7.12 |
% 23.17/7.13 | Instantiating formula (8) with all_0_17_17, all_0_20_20, all_0_19_19 and discharging atoms proper_subset(all_0_19_19, all_0_20_20) = all_0_17_17, yields:
% 23.17/7.13 | (143) all_0_17_17 = 0 | all_0_19_19 = all_0_20_20 | ? [v0] : ( ~ (v0 = 0) & subset(all_0_19_19, all_0_20_20) = v0)
% 23.17/7.13 |
% 23.17/7.13 | Instantiating formula (8) with all_0_18_18, all_0_19_19, all_0_20_20 and discharging atoms proper_subset(all_0_20_20, all_0_19_19) = all_0_18_18, yields:
% 23.17/7.13 | (144) all_0_18_18 = 0 | all_0_19_19 = all_0_20_20 | ? [v0] : ( ~ (v0 = 0) & subset(all_0_20_20, all_0_19_19) = v0)
% 23.17/7.13 |
% 23.17/7.13 +-Applying beta-rule and splitting (144), into two cases.
% 23.17/7.13 |-Branch one:
% 23.17/7.13 | (145) all_0_18_18 = 0
% 23.17/7.13 |
% 23.17/7.13 | Equations (145) can reduce 16 to:
% 23.17/7.13 | (146) $false
% 23.17/7.13 |
% 23.17/7.13 |-The branch is then unsatisfiable
% 23.17/7.13 |-Branch two:
% 23.17/7.13 | (16) ~ (all_0_18_18 = 0)
% 23.17/7.13 | (148) all_0_19_19 = all_0_20_20 | ? [v0] : ( ~ (v0 = 0) & subset(all_0_20_20, all_0_19_19) = v0)
% 23.17/7.13 |
% 23.17/7.13 +-Applying beta-rule and splitting (143), into two cases.
% 23.17/7.13 |-Branch one:
% 23.17/7.13 | (149) all_0_17_17 = 0
% 23.17/7.13 |
% 23.17/7.13 | Equations (149) can reduce 117 to:
% 23.17/7.13 | (146) $false
% 23.17/7.13 |
% 23.17/7.13 |-The branch is then unsatisfiable
% 23.17/7.13 |-Branch two:
% 23.17/7.13 | (117) ~ (all_0_17_17 = 0)
% 23.17/7.13 | (152) all_0_19_19 = all_0_20_20 | ? [v0] : ( ~ (v0 = 0) & subset(all_0_19_19, all_0_20_20) = v0)
% 23.17/7.13 |
% 23.17/7.13 +-Applying beta-rule and splitting (148), into two cases.
% 23.17/7.13 |-Branch one:
% 23.17/7.13 | (153) all_0_19_19 = all_0_20_20
% 23.17/7.13 |
% 23.17/7.13 | Equations (153) can reduce 41 to:
% 23.17/7.13 | (146) $false
% 23.17/7.13 |
% 23.17/7.13 |-The branch is then unsatisfiable
% 23.17/7.13 |-Branch two:
% 23.17/7.13 | (41) ~ (all_0_19_19 = all_0_20_20)
% 23.17/7.13 | (156) ? [v0] : ( ~ (v0 = 0) & subset(all_0_20_20, all_0_19_19) = v0)
% 23.17/7.13 |
% 23.17/7.13 | Instantiating (156) with all_80_0_103 yields:
% 23.17/7.13 | (157) ~ (all_80_0_103 = 0) & subset(all_0_20_20, all_0_19_19) = all_80_0_103
% 23.17/7.13 |
% 23.17/7.13 | Applying alpha-rule on (157) yields:
% 23.17/7.13 | (158) ~ (all_80_0_103 = 0)
% 23.17/7.13 | (159) subset(all_0_20_20, all_0_19_19) = all_80_0_103
% 23.17/7.13 |
% 23.17/7.13 +-Applying beta-rule and splitting (152), into two cases.
% 23.17/7.13 |-Branch one:
% 23.17/7.13 | (153) all_0_19_19 = all_0_20_20
% 23.17/7.13 |
% 23.17/7.13 | Equations (153) can reduce 41 to:
% 23.17/7.13 | (146) $false
% 23.17/7.13 |
% 23.17/7.13 |-The branch is then unsatisfiable
% 23.17/7.13 |-Branch two:
% 23.17/7.13 | (41) ~ (all_0_19_19 = all_0_20_20)
% 23.17/7.13 | (163) ? [v0] : ( ~ (v0 = 0) & subset(all_0_19_19, all_0_20_20) = v0)
% 23.17/7.13 |
% 23.17/7.13 | Instantiating (163) with all_85_0_104 yields:
% 23.17/7.13 | (164) ~ (all_85_0_104 = 0) & subset(all_0_19_19, all_0_20_20) = all_85_0_104
% 23.17/7.13 |
% 23.17/7.13 | Applying alpha-rule on (164) yields:
% 23.17/7.13 | (165) ~ (all_85_0_104 = 0)
% 23.17/7.13 | (166) subset(all_0_19_19, all_0_20_20) = all_85_0_104
% 23.17/7.13 |
% 23.17/7.13 | Instantiating formula (21) with all_85_0_104, all_0_20_20, all_0_19_19 and discharging atoms subset(all_0_19_19, all_0_20_20) = all_85_0_104, yields:
% 23.17/7.13 | (167) all_85_0_104 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & powerset(all_0_20_20) = v0 & element(all_0_19_19, v0) = v1)
% 23.17/7.13 |
% 23.17/7.13 | Instantiating formula (111) with all_85_0_104, all_0_20_20, all_0_19_19 and discharging atoms subset(all_0_19_19, all_0_20_20) = all_85_0_104, yields:
% 23.17/7.13 | (168) ? [v0] : (( ~ (v0 = 0) & ordinal(all_0_19_19) = v0) | ( ~ (v0 = 0) & ordinal(all_0_20_20) = v0) | (( ~ (all_85_0_104 = 0) | (v0 = 0 & ordinal_subset(all_0_19_19, all_0_20_20) = 0)) & (all_85_0_104 = 0 | ( ~ (v0 = 0) & ordinal_subset(all_0_19_19, all_0_20_20) = v0))))
% 23.17/7.13 |
% 23.17/7.13 | Instantiating formula (21) with all_80_0_103, all_0_19_19, all_0_20_20 and discharging atoms subset(all_0_20_20, all_0_19_19) = all_80_0_103, yields:
% 23.17/7.13 | (169) all_80_0_103 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & powerset(all_0_19_19) = v0 & element(all_0_20_20, v0) = v1)
% 23.17/7.13 |
% 23.17/7.13 | Instantiating formula (111) with all_80_0_103, all_0_19_19, all_0_20_20 and discharging atoms subset(all_0_20_20, all_0_19_19) = all_80_0_103, yields:
% 23.17/7.13 | (170) ? [v0] : (( ~ (v0 = 0) & ordinal(all_0_19_19) = v0) | ( ~ (v0 = 0) & ordinal(all_0_20_20) = v0) | (( ~ (all_80_0_103 = 0) | (v0 = 0 & ordinal_subset(all_0_20_20, all_0_19_19) = 0)) & (all_80_0_103 = 0 | ( ~ (v0 = 0) & ordinal_subset(all_0_20_20, all_0_19_19) = v0))))
% 23.17/7.13 |
% 23.17/7.13 | Instantiating (170) with all_101_0_118 yields:
% 23.17/7.13 | (171) ( ~ (all_101_0_118 = 0) & ordinal(all_0_19_19) = all_101_0_118) | ( ~ (all_101_0_118 = 0) & ordinal(all_0_20_20) = all_101_0_118) | (( ~ (all_80_0_103 = 0) | (all_101_0_118 = 0 & ordinal_subset(all_0_20_20, all_0_19_19) = 0)) & (all_80_0_103 = 0 | ( ~ (all_101_0_118 = 0) & ordinal_subset(all_0_20_20, all_0_19_19) = all_101_0_118)))
% 23.17/7.13 |
% 23.17/7.13 | Instantiating (168) with all_102_0_119 yields:
% 23.17/7.13 | (172) ( ~ (all_102_0_119 = 0) & ordinal(all_0_19_19) = all_102_0_119) | ( ~ (all_102_0_119 = 0) & ordinal(all_0_20_20) = all_102_0_119) | (( ~ (all_85_0_104 = 0) | (all_102_0_119 = 0 & ordinal_subset(all_0_19_19, all_0_20_20) = 0)) & (all_85_0_104 = 0 | ( ~ (all_102_0_119 = 0) & ordinal_subset(all_0_19_19, all_0_20_20) = all_102_0_119)))
% 23.17/7.13 |
% 23.17/7.13 +-Applying beta-rule and splitting (172), into two cases.
% 23.17/7.13 |-Branch one:
% 23.17/7.13 | (173) ( ~ (all_102_0_119 = 0) & ordinal(all_0_19_19) = all_102_0_119) | ( ~ (all_102_0_119 = 0) & ordinal(all_0_20_20) = all_102_0_119)
% 23.17/7.13 |
% 23.17/7.13 +-Applying beta-rule and splitting (173), into two cases.
% 23.17/7.13 |-Branch one:
% 23.17/7.13 | (174) ~ (all_102_0_119 = 0) & ordinal(all_0_19_19) = all_102_0_119
% 23.17/7.13 |
% 23.17/7.13 | Applying alpha-rule on (174) yields:
% 23.17/7.13 | (175) ~ (all_102_0_119 = 0)
% 23.17/7.13 | (176) ordinal(all_0_19_19) = all_102_0_119
% 23.17/7.13 |
% 23.17/7.13 | Instantiating formula (89) with all_0_19_19, all_102_0_119, 0 and discharging atoms ordinal(all_0_19_19) = all_102_0_119, ordinal(all_0_19_19) = 0, yields:
% 23.17/7.13 | (177) all_102_0_119 = 0
% 23.17/7.13 |
% 23.17/7.13 | Equations (177) can reduce 175 to:
% 23.17/7.13 | (146) $false
% 23.17/7.13 |
% 23.17/7.13 |-The branch is then unsatisfiable
% 23.17/7.13 |-Branch two:
% 23.17/7.13 | (179) ~ (all_102_0_119 = 0) & ordinal(all_0_20_20) = all_102_0_119
% 23.17/7.13 |
% 23.17/7.13 | Applying alpha-rule on (179) yields:
% 23.17/7.13 | (175) ~ (all_102_0_119 = 0)
% 23.17/7.13 | (181) ordinal(all_0_20_20) = all_102_0_119
% 23.17/7.13 |
% 23.17/7.13 | Instantiating formula (89) with all_0_20_20, all_102_0_119, 0 and discharging atoms ordinal(all_0_20_20) = all_102_0_119, ordinal(all_0_20_20) = 0, yields:
% 23.17/7.13 | (177) all_102_0_119 = 0
% 23.17/7.13 |
% 23.17/7.13 | Equations (177) can reduce 175 to:
% 23.17/7.13 | (146) $false
% 23.17/7.13 |
% 23.17/7.13 |-The branch is then unsatisfiable
% 23.17/7.13 |-Branch two:
% 23.17/7.13 | (184) ( ~ (all_85_0_104 = 0) | (all_102_0_119 = 0 & ordinal_subset(all_0_19_19, all_0_20_20) = 0)) & (all_85_0_104 = 0 | ( ~ (all_102_0_119 = 0) & ordinal_subset(all_0_19_19, all_0_20_20) = all_102_0_119))
% 23.17/7.13 |
% 23.17/7.13 | Applying alpha-rule on (184) yields:
% 23.17/7.13 | (185) ~ (all_85_0_104 = 0) | (all_102_0_119 = 0 & ordinal_subset(all_0_19_19, all_0_20_20) = 0)
% 23.17/7.13 | (186) all_85_0_104 = 0 | ( ~ (all_102_0_119 = 0) & ordinal_subset(all_0_19_19, all_0_20_20) = all_102_0_119)
% 23.17/7.13 |
% 23.17/7.13 +-Applying beta-rule and splitting (169), into two cases.
% 23.17/7.13 |-Branch one:
% 23.17/7.13 | (187) all_80_0_103 = 0
% 23.17/7.13 |
% 23.17/7.13 | Equations (187) can reduce 158 to:
% 23.17/7.13 | (146) $false
% 23.17/7.13 |
% 23.17/7.13 |-The branch is then unsatisfiable
% 23.17/7.13 |-Branch two:
% 23.17/7.13 | (158) ~ (all_80_0_103 = 0)
% 23.17/7.13 | (190) ? [v0] : ? [v1] : ( ~ (v1 = 0) & powerset(all_0_19_19) = v0 & element(all_0_20_20, v0) = v1)
% 23.17/7.13 |
% 23.17/7.13 +-Applying beta-rule and splitting (167), into two cases.
% 23.17/7.13 |-Branch one:
% 23.17/7.13 | (191) all_85_0_104 = 0
% 23.17/7.13 |
% 23.17/7.13 | Equations (191) can reduce 165 to:
% 23.17/7.13 | (146) $false
% 23.17/7.13 |
% 23.17/7.13 |-The branch is then unsatisfiable
% 23.17/7.13 |-Branch two:
% 23.17/7.13 | (165) ~ (all_85_0_104 = 0)
% 23.17/7.13 | (194) ? [v0] : ? [v1] : ( ~ (v1 = 0) & powerset(all_0_20_20) = v0 & element(all_0_19_19, v0) = v1)
% 23.17/7.13 |
% 23.17/7.13 +-Applying beta-rule and splitting (186), into two cases.
% 23.17/7.13 |-Branch one:
% 23.17/7.13 | (191) all_85_0_104 = 0
% 23.17/7.13 |
% 23.17/7.13 | Equations (191) can reduce 165 to:
% 23.17/7.13 | (146) $false
% 23.17/7.13 |
% 23.17/7.13 |-The branch is then unsatisfiable
% 23.17/7.13 |-Branch two:
% 23.17/7.13 | (165) ~ (all_85_0_104 = 0)
% 23.17/7.13 | (198) ~ (all_102_0_119 = 0) & ordinal_subset(all_0_19_19, all_0_20_20) = all_102_0_119
% 23.17/7.13 |
% 23.17/7.13 | Applying alpha-rule on (198) yields:
% 23.17/7.13 | (175) ~ (all_102_0_119 = 0)
% 23.17/7.13 | (200) ordinal_subset(all_0_19_19, all_0_20_20) = all_102_0_119
% 23.17/7.13 |
% 23.17/7.13 +-Applying beta-rule and splitting (171), into two cases.
% 23.17/7.13 |-Branch one:
% 23.17/7.13 | (201) ( ~ (all_101_0_118 = 0) & ordinal(all_0_19_19) = all_101_0_118) | ( ~ (all_101_0_118 = 0) & ordinal(all_0_20_20) = all_101_0_118)
% 23.17/7.13 |
% 23.17/7.13 +-Applying beta-rule and splitting (201), into two cases.
% 23.17/7.13 |-Branch one:
% 23.17/7.13 | (202) ~ (all_101_0_118 = 0) & ordinal(all_0_19_19) = all_101_0_118
% 23.17/7.13 |
% 23.17/7.13 | Applying alpha-rule on (202) yields:
% 23.17/7.13 | (203) ~ (all_101_0_118 = 0)
% 23.17/7.13 | (204) ordinal(all_0_19_19) = all_101_0_118
% 23.17/7.13 |
% 23.17/7.13 | Instantiating formula (89) with all_0_19_19, all_101_0_118, 0 and discharging atoms ordinal(all_0_19_19) = all_101_0_118, ordinal(all_0_19_19) = 0, yields:
% 23.17/7.13 | (205) all_101_0_118 = 0
% 23.17/7.13 |
% 23.17/7.13 | Equations (205) can reduce 203 to:
% 23.17/7.13 | (146) $false
% 23.17/7.13 |
% 23.17/7.13 |-The branch is then unsatisfiable
% 23.17/7.13 |-Branch two:
% 23.17/7.13 | (207) ~ (all_101_0_118 = 0) & ordinal(all_0_20_20) = all_101_0_118
% 23.17/7.13 |
% 23.17/7.13 | Applying alpha-rule on (207) yields:
% 23.17/7.13 | (203) ~ (all_101_0_118 = 0)
% 23.17/7.13 | (209) ordinal(all_0_20_20) = all_101_0_118
% 23.17/7.13 |
% 23.17/7.13 | Instantiating formula (89) with all_0_20_20, all_101_0_118, 0 and discharging atoms ordinal(all_0_20_20) = all_101_0_118, ordinal(all_0_20_20) = 0, yields:
% 23.17/7.13 | (205) all_101_0_118 = 0
% 23.17/7.13 |
% 23.17/7.13 | Equations (205) can reduce 203 to:
% 23.17/7.13 | (146) $false
% 23.17/7.13 |
% 23.17/7.13 |-The branch is then unsatisfiable
% 23.17/7.13 |-Branch two:
% 23.17/7.13 | (212) ( ~ (all_80_0_103 = 0) | (all_101_0_118 = 0 & ordinal_subset(all_0_20_20, all_0_19_19) = 0)) & (all_80_0_103 = 0 | ( ~ (all_101_0_118 = 0) & ordinal_subset(all_0_20_20, all_0_19_19) = all_101_0_118))
% 23.17/7.13 |
% 23.17/7.13 | Applying alpha-rule on (212) yields:
% 23.17/7.13 | (213) ~ (all_80_0_103 = 0) | (all_101_0_118 = 0 & ordinal_subset(all_0_20_20, all_0_19_19) = 0)
% 23.17/7.13 | (214) all_80_0_103 = 0 | ( ~ (all_101_0_118 = 0) & ordinal_subset(all_0_20_20, all_0_19_19) = all_101_0_118)
% 23.17/7.13 |
% 23.17/7.13 +-Applying beta-rule and splitting (214), into two cases.
% 23.17/7.13 |-Branch one:
% 23.17/7.13 | (187) all_80_0_103 = 0
% 23.17/7.13 |
% 23.17/7.13 | Equations (187) can reduce 158 to:
% 23.17/7.13 | (146) $false
% 23.17/7.13 |
% 23.17/7.13 |-The branch is then unsatisfiable
% 23.17/7.13 |-Branch two:
% 23.17/7.13 | (158) ~ (all_80_0_103 = 0)
% 23.17/7.13 | (218) ~ (all_101_0_118 = 0) & ordinal_subset(all_0_20_20, all_0_19_19) = all_101_0_118
% 23.17/7.13 |
% 23.17/7.13 | Applying alpha-rule on (218) yields:
% 23.17/7.13 | (203) ~ (all_101_0_118 = 0)
% 23.17/7.14 | (220) ordinal_subset(all_0_20_20, all_0_19_19) = all_101_0_118
% 23.17/7.14 |
% 23.17/7.14 | Instantiating formula (56) with all_102_0_119, all_0_19_19, all_0_20_20 and discharging atoms ordinal_subset(all_0_19_19, all_0_20_20) = all_102_0_119, yields:
% 23.17/7.14 | (221) all_102_0_119 = 0 | ? [v0] : ((v0 = 0 & ordinal_subset(all_0_20_20, all_0_19_19) = 0) | ( ~ (v0 = 0) & ordinal(all_0_19_19) = v0) | ( ~ (v0 = 0) & ordinal(all_0_20_20) = v0))
% 23.17/7.14 |
% 23.17/7.14 | Instantiating formula (56) with all_101_0_118, all_0_20_20, all_0_19_19 and discharging atoms ordinal_subset(all_0_20_20, all_0_19_19) = all_101_0_118, yields:
% 23.17/7.14 | (222) all_101_0_118 = 0 | ? [v0] : ((v0 = 0 & ordinal_subset(all_0_19_19, all_0_20_20) = 0) | ( ~ (v0 = 0) & ordinal(all_0_19_19) = v0) | ( ~ (v0 = 0) & ordinal(all_0_20_20) = v0))
% 23.17/7.14 |
% 23.17/7.14 +-Applying beta-rule and splitting (222), into two cases.
% 23.17/7.14 |-Branch one:
% 23.17/7.14 | (205) all_101_0_118 = 0
% 23.17/7.14 |
% 23.17/7.14 | Equations (205) can reduce 203 to:
% 23.17/7.14 | (146) $false
% 23.17/7.14 |
% 23.17/7.14 |-The branch is then unsatisfiable
% 23.17/7.14 |-Branch two:
% 23.17/7.14 | (203) ~ (all_101_0_118 = 0)
% 23.17/7.14 | (226) ? [v0] : ((v0 = 0 & ordinal_subset(all_0_19_19, all_0_20_20) = 0) | ( ~ (v0 = 0) & ordinal(all_0_19_19) = v0) | ( ~ (v0 = 0) & ordinal(all_0_20_20) = v0))
% 23.17/7.14 |
% 23.17/7.14 | Instantiating (226) with all_177_0_144 yields:
% 23.17/7.14 | (227) (all_177_0_144 = 0 & ordinal_subset(all_0_19_19, all_0_20_20) = 0) | ( ~ (all_177_0_144 = 0) & ordinal(all_0_19_19) = all_177_0_144) | ( ~ (all_177_0_144 = 0) & ordinal(all_0_20_20) = all_177_0_144)
% 23.17/7.14 |
% 23.17/7.14 +-Applying beta-rule and splitting (227), into two cases.
% 23.17/7.14 |-Branch one:
% 23.17/7.14 | (228) (all_177_0_144 = 0 & ordinal_subset(all_0_19_19, all_0_20_20) = 0) | ( ~ (all_177_0_144 = 0) & ordinal(all_0_19_19) = all_177_0_144)
% 23.17/7.14 |
% 23.17/7.14 +-Applying beta-rule and splitting (228), into two cases.
% 23.17/7.14 |-Branch one:
% 23.17/7.14 | (229) all_177_0_144 = 0 & ordinal_subset(all_0_19_19, all_0_20_20) = 0
% 23.17/7.14 |
% 23.17/7.14 | Applying alpha-rule on (229) yields:
% 23.17/7.14 | (230) all_177_0_144 = 0
% 23.17/7.14 | (231) ordinal_subset(all_0_19_19, all_0_20_20) = 0
% 23.17/7.14 |
% 23.17/7.14 +-Applying beta-rule and splitting (221), into two cases.
% 23.17/7.14 |-Branch one:
% 23.17/7.14 | (177) all_102_0_119 = 0
% 23.17/7.14 |
% 23.17/7.14 | Equations (177) can reduce 175 to:
% 23.17/7.14 | (146) $false
% 23.17/7.14 |
% 23.17/7.14 |-The branch is then unsatisfiable
% 23.17/7.14 |-Branch two:
% 23.17/7.14 | (175) ~ (all_102_0_119 = 0)
% 23.17/7.14 | (235) ? [v0] : ((v0 = 0 & ordinal_subset(all_0_20_20, all_0_19_19) = 0) | ( ~ (v0 = 0) & ordinal(all_0_19_19) = v0) | ( ~ (v0 = 0) & ordinal(all_0_20_20) = v0))
% 23.17/7.14 |
% 23.17/7.14 | Instantiating formula (92) with all_0_19_19, all_0_20_20, 0, all_102_0_119 and discharging atoms ordinal_subset(all_0_19_19, all_0_20_20) = all_102_0_119, ordinal_subset(all_0_19_19, all_0_20_20) = 0, yields:
% 23.17/7.14 | (177) all_102_0_119 = 0
% 23.17/7.14 |
% 23.17/7.14 | Equations (177) can reduce 175 to:
% 23.17/7.14 | (146) $false
% 23.17/7.14 |
% 23.17/7.14 |-The branch is then unsatisfiable
% 23.17/7.14 |-Branch two:
% 23.17/7.14 | (238) ~ (all_177_0_144 = 0) & ordinal(all_0_19_19) = all_177_0_144
% 23.17/7.14 |
% 23.17/7.14 | Applying alpha-rule on (238) yields:
% 23.17/7.14 | (239) ~ (all_177_0_144 = 0)
% 23.17/7.14 | (240) ordinal(all_0_19_19) = all_177_0_144
% 23.17/7.14 |
% 23.17/7.14 | Instantiating formula (89) with all_0_19_19, all_177_0_144, 0 and discharging atoms ordinal(all_0_19_19) = all_177_0_144, ordinal(all_0_19_19) = 0, yields:
% 23.17/7.14 | (230) all_177_0_144 = 0
% 23.17/7.14 |
% 23.17/7.14 | Equations (230) can reduce 239 to:
% 23.17/7.14 | (146) $false
% 23.17/7.14 |
% 23.17/7.14 |-The branch is then unsatisfiable
% 23.17/7.14 |-Branch two:
% 23.17/7.14 | (243) ~ (all_177_0_144 = 0) & ordinal(all_0_20_20) = all_177_0_144
% 23.17/7.14 |
% 23.17/7.14 | Applying alpha-rule on (243) yields:
% 23.17/7.14 | (239) ~ (all_177_0_144 = 0)
% 23.17/7.14 | (245) ordinal(all_0_20_20) = all_177_0_144
% 23.17/7.14 |
% 23.17/7.14 | Instantiating formula (89) with all_0_20_20, all_177_0_144, 0 and discharging atoms ordinal(all_0_20_20) = all_177_0_144, ordinal(all_0_20_20) = 0, yields:
% 23.17/7.14 | (230) all_177_0_144 = 0
% 23.17/7.14 |
% 23.17/7.14 | Equations (230) can reduce 239 to:
% 23.17/7.14 | (146) $false
% 23.17/7.14 |
% 23.17/7.14 |-The branch is then unsatisfiable
% 23.17/7.14 % SZS output end Proof for theBenchmark
% 23.17/7.14
% 23.17/7.14 6503ms
%------------------------------------------------------------------------------