TSTP Solution File: NUM388+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : NUM388+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n025.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 08:44:06 EDT 2022
% Result : Theorem 5.20s 1.89s
% Output : Proof 7.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : NUM388+1 : TPTP v8.1.0. Released v3.2.0.
% 0.10/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.32 % Computer : n025.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 600
% 0.12/0.32 % DateTime : Thu Jul 7 10:39:14 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.58 ____ _
% 0.18/0.58 ___ / __ \_____(_)___ ________ __________
% 0.18/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.18/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.18/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.18/0.58
% 0.18/0.58 A Theorem Prover for First-Order Logic
% 0.18/0.58 (ePrincess v.1.0)
% 0.18/0.58
% 0.18/0.58 (c) Philipp Rümmer, 2009-2015
% 0.18/0.58 (c) Peter Backeman, 2014-2015
% 0.18/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.18/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.18/0.58 Bug reports to peter@backeman.se
% 0.18/0.58
% 0.18/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.18/0.58
% 0.18/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.68/0.66 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.61/0.94 Prover 0: Preprocessing ...
% 2.02/1.08 Prover 0: Warning: ignoring some quantifiers
% 2.02/1.10 Prover 0: Constructing countermodel ...
% 2.57/1.31 Prover 0: gave up
% 2.57/1.31 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.89/1.34 Prover 1: Preprocessing ...
% 3.16/1.44 Prover 1: Warning: ignoring some quantifiers
% 3.16/1.45 Prover 1: Constructing countermodel ...
% 4.22/1.67 Prover 1: gave up
% 4.22/1.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 4.22/1.69 Prover 2: Preprocessing ...
% 4.54/1.78 Prover 2: Warning: ignoring some quantifiers
% 4.96/1.78 Prover 2: Constructing countermodel ...
% 5.20/1.89 Prover 2: proved (225ms)
% 5.20/1.89
% 5.20/1.89 No countermodel exists, formula is valid
% 5.20/1.89 % SZS status Theorem for theBenchmark
% 5.20/1.89
% 5.20/1.89 Generating proof ... Warning: ignoring some quantifiers
% 7.22/2.29 found it (size 34)
% 7.22/2.29
% 7.22/2.29 % SZS output start Proof for theBenchmark
% 7.22/2.30 Assumed formulas after preprocessing and simplification:
% 7.22/2.30 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ( ~ (v11 = 0) & ~ (v9 = 0) & ~ (v3 = 0) & relation_non_empty(v4) = 0 & relation_empty_yielding(v6) = 0 & relation_empty_yielding(v5) = 0 & relation_empty_yielding(empty_set) = 0 & one_to_one(v7) = 0 & relation(v16) = 0 & relation(v14) = 0 & relation(v12) = 0 & relation(v10) = 0 & relation(v7) = 0 & relation(v6) = 0 & relation(v5) = 0 & relation(v4) = 0 & relation(empty_set) = 0 & epsilon_transitive(v15) = 0 & epsilon_transitive(v2) = 0 & ordinal(v15) = 0 & ordinal(v1) = 0 & ordinal(v0) = 0 & epsilon_connected(v15) = 0 & function(v16) = 0 & function(v12) = 0 & function(v7) = 0 & function(v5) = 0 & function(v4) = 0 & empty(v14) = 0 & empty(v13) = 0 & empty(v12) = 0 & empty(v10) = v11 & empty(v8) = v9 & empty(empty_set) = 0 & in(v2, v1) = v3 & in(v2, v0) = 0 & in(v0, v1) = 0 & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v21 = 0 | ~ (powerset(v19) = v20) | ~ (element(v18, v20) = 0) | ~ (element(v17, v19) = v21) | ? [v22] : ( ~ (v22 = 0) & in(v17, v18) = v22)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v20 = 0 | ~ (powerset(v18) = v19) | ~ (element(v17, v19) = v20) | ? [v21] : ( ~ (v21 = 0) & subset(v17, v18) = v21)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v20 = 0 | ~ (element(v17, v19) = v20) | ~ (in(v17, v18) = 0) | ? [v21] : ? [v22] : ( ~ (v22 = 0) & powerset(v19) = v21 & element(v18, v21) = v22)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (element(v20, v19) = v18) | ~ (element(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (subset(v20, v19) = v18) | ~ (subset(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (in(v20, v19) = v18) | ~ (in(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (powerset(v19) = v20) | ~ (element(v18, v20) = 0) | ~ (in(v17, v18) = 0) | element(v17, v19) = 0) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (powerset(v19) = v20) | ~ (element(v18, v20) = 0) | ~ (in(v17, v18) = 0) | ? [v21] : ( ~ (v21 = 0) & empty(v19) = v21)) & ! [v17] : ! [v18] : ! [v19] : (v19 = 0 | ~ (element(v17, v18) = v19) | ? [v20] : ( ~ (v20 = 0) & in(v17, v18) = v20)) & ! [v17] : ! [v18] : ! [v19] : (v19 = 0 | ~ (subset(v18, v17) = v19) | ~ (epsilon_transitive(v17) = 0) | ? [v20] : ( ~ (v20 = 0) & in(v18, v17) = v20)) & ! [v17] : ! [v18] : ! [v19] : (v19 = 0 | ~ (subset(v17, v18) = v19) | ? [v20] : ? [v21] : ( ~ (v21 = 0) & powerset(v18) = v20 & element(v17, v20) = v21)) & ! [v17] : ! [v18] : ! [v19] : (v19 = 0 | ~ (in(v17, v18) = v19) | ? [v20] : ((v20 = 0 & empty(v18) = 0) | ( ~ (v20 = 0) & element(v17, v18) = v20))) & ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (powerset(v19) = v18) | ~ (powerset(v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (relation_non_empty(v19) = v18) | ~ (relation_non_empty(v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (relation_empty_yielding(v19) = v18) | ~ (relation_empty_yielding(v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (one_to_one(v19) = v18) | ~ (one_to_one(v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (relation(v19) = v18) | ~ (relation(v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (epsilon_transitive(v19) = v18) | ~ (epsilon_transitive(v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (ordinal(v19) = v18) | ~ (ordinal(v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (epsilon_connected(v19) = v18) | ~ (epsilon_connected(v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (function(v19) = v18) | ~ (function(v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (empty(v19) = v18) | ~ (empty(v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (powerset(v18) = v19) | ~ (element(v17, v19) = 0) | subset(v17, v18) = 0) & ! [v17] : ! [v18] : ! [v19] : ( ~ (empty(v19) = 0) | ~ (in(v17, v18) = 0) | ? [v20] : ? [v21] : ( ~ (v21 = 0) & powerset(v19) = v20 & element(v18, v20) = v21)) & ! [v17] : ! [v18] : (v18 = v17 | ~ (empty(v18) = 0) | ~ (empty(v17) = 0)) & ! [v17] : ! [v18] : (v18 = 0 | ~ (subset(v17, v17) = v18)) & ! [v17] : ! [v18] : (v18 = 0 | ~ (relation(v17) = v18) | ? [v19] : ( ~ (v19 = 0) & empty(v17) = v19)) & ! [v17] : ! [v18] : (v18 = 0 | ~ (epsilon_transitive(v17) = v18) | ? [v19] : ? [v20] : ( ~ (v20 = 0) & subset(v19, v17) = v20 & in(v19, v17) = 0)) & ! [v17] : ! [v18] : (v18 = 0 | ~ (ordinal(v17) = v18) | ? [v19] : (( ~ (v19 = 0) & epsilon_transitive(v17) = v19) | ( ~ (v19 = 0) & epsilon_connected(v17) = v19))) & ! [v17] : ! [v18] : (v18 = 0 | ~ (function(v17) = v18) | ? [v19] : ( ~ (v19 = 0) & empty(v17) = v19)) & ! [v17] : ! [v18] : ( ~ (element(v17, v18) = 0) | ? [v19] : ((v19 = 0 & empty(v18) = 0) | (v19 = 0 & in(v17, v18) = 0))) & ! [v17] : ! [v18] : ( ~ (subset(v17, v18) = 0) | ? [v19] : (powerset(v18) = v19 & element(v17, v19) = 0)) & ! [v17] : ! [v18] : ( ~ (one_to_one(v17) = v18) | ? [v19] : ? [v20] : ((v20 = 0 & v19 = 0 & v18 = 0 & relation(v17) = 0 & function(v17) = 0) | ( ~ (v19 = 0) & relation(v17) = v19) | ( ~ (v19 = 0) & function(v17) = v19) | ( ~ (v19 = 0) & empty(v17) = v19))) & ! [v17] : ! [v18] : ( ~ (epsilon_transitive(v17) = v18) | ? [v19] : ((v19 = 0 & v18 = 0 & epsilon_connected(v17) = 0) | ( ~ (v19 = 0) & ordinal(v17) = v19))) & ! [v17] : ! [v18] : ( ~ (epsilon_transitive(v17) = 0) | ~ (in(v18, v17) = 0) | subset(v18, v17) = 0) & ! [v17] : ! [v18] : ( ~ (epsilon_connected(v17) = v18) | ? [v19] : ((v19 = 0 & v18 = 0 & epsilon_transitive(v17) = 0) | ( ~ (v19 = 0) & ordinal(v17) = v19))) & ! [v17] : ! [v18] : ( ~ (in(v18, v17) = 0) | ? [v19] : ( ~ (v19 = 0) & in(v17, v18) = v19)) & ! [v17] : ! [v18] : ( ~ (in(v17, v18) = 0) | element(v17, v18) = 0) & ! [v17] : ! [v18] : ( ~ (in(v17, v18) = 0) | ? [v19] : ( ~ (v19 = 0) & empty(v18) = v19)) & ! [v17] : ! [v18] : ( ~ (in(v17, v18) = 0) | ? [v19] : ( ~ (v19 = 0) & in(v18, v17) = v19)) & ! [v17] : (v17 = empty_set | ~ (empty(v17) = 0)) & ! [v17] : ( ~ (relation(v17) = 0) | ? [v18] : ? [v19] : ((v19 = 0 & v18 = 0 & one_to_one(v17) = 0 & function(v17) = 0) | ( ~ (v18 = 0) & function(v17) = v18) | ( ~ (v18 = 0) & empty(v17) = v18))) & ! [v17] : ( ~ (epsilon_transitive(v17) = 0) | ? [v18] : ((v18 = 0 & ordinal(v17) = 0) | ( ~ (v18 = 0) & epsilon_connected(v17) = v18))) & ! [v17] : ( ~ (ordinal(v17) = 0) | (epsilon_transitive(v17) = 0 & epsilon_connected(v17) = 0)) & ! [v17] : ( ~ (epsilon_connected(v17) = 0) | ? [v18] : ((v18 = 0 & ordinal(v17) = 0) | ( ~ (v18 = 0) & epsilon_transitive(v17) = v18))) & ! [v17] : ( ~ (function(v17) = 0) | ? [v18] : ? [v19] : ((v19 = 0 & v18 = 0 & one_to_one(v17) = 0 & relation(v17) = 0) | ( ~ (v18 = 0) & relation(v17) = v18) | ( ~ (v18 = 0) & empty(v17) = v18))) & ! [v17] : ( ~ (empty(v17) = 0) | relation(v17) = 0) & ! [v17] : ( ~ (empty(v17) = 0) | function(v17) = 0) & ! [v17] : ( ~ (empty(v17) = 0) | ? [v18] : ? [v19] : ? [v20] : ((v20 = 0 & v19 = 0 & v18 = 0 & one_to_one(v17) = 0 & relation(v17) = 0 & function(v17) = 0) | ( ~ (v18 = 0) & relation(v17) = v18) | ( ~ (v18 = 0) & function(v17) = v18))) & ? [v17] : ? [v18] : ? [v19] : element(v18, v17) = v19 & ? [v17] : ? [v18] : ? [v19] : subset(v18, v17) = v19 & ? [v17] : ? [v18] : ? [v19] : in(v18, v17) = v19 & ? [v17] : ? [v18] : powerset(v17) = v18 & ? [v17] : ? [v18] : relation_non_empty(v17) = v18 & ? [v17] : ? [v18] : relation_empty_yielding(v17) = v18 & ? [v17] : ? [v18] : element(v18, v17) = 0 & ? [v17] : ? [v18] : one_to_one(v17) = v18 & ? [v17] : ? [v18] : relation(v17) = v18 & ? [v17] : ? [v18] : epsilon_transitive(v17) = v18 & ? [v17] : ? [v18] : ordinal(v17) = v18 & ? [v17] : ? [v18] : epsilon_connected(v17) = v18 & ? [v17] : ? [v18] : function(v17) = v18 & ? [v17] : ? [v18] : empty(v17) = v18)
% 7.22/2.34 | 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 yields:
% 7.22/2.34 | (1) ~ (all_0_5_5 = 0) & ~ (all_0_7_7 = 0) & ~ (all_0_13_13 = 0) & relation_non_empty(all_0_12_12) = 0 & relation_empty_yielding(all_0_10_10) = 0 & relation_empty_yielding(all_0_11_11) = 0 & relation_empty_yielding(empty_set) = 0 & one_to_one(all_0_9_9) = 0 & relation(all_0_0_0) = 0 & relation(all_0_2_2) = 0 & relation(all_0_4_4) = 0 & relation(all_0_6_6) = 0 & relation(all_0_9_9) = 0 & relation(all_0_10_10) = 0 & relation(all_0_11_11) = 0 & relation(all_0_12_12) = 0 & relation(empty_set) = 0 & epsilon_transitive(all_0_1_1) = 0 & epsilon_transitive(all_0_14_14) = 0 & ordinal(all_0_1_1) = 0 & ordinal(all_0_15_15) = 0 & ordinal(all_0_16_16) = 0 & epsilon_connected(all_0_1_1) = 0 & function(all_0_0_0) = 0 & function(all_0_4_4) = 0 & function(all_0_9_9) = 0 & function(all_0_11_11) = 0 & function(all_0_12_12) = 0 & empty(all_0_2_2) = 0 & empty(all_0_3_3) = 0 & empty(all_0_4_4) = 0 & empty(all_0_6_6) = all_0_5_5 & empty(all_0_8_8) = all_0_7_7 & empty(empty_set) = 0 & in(all_0_14_14, all_0_15_15) = all_0_13_13 & in(all_0_14_14, all_0_16_16) = 0 & in(all_0_16_16, all_0_15_15) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (element(v0, v2) = v4) | ? [v5] : ( ~ (v5 = 0) & in(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (element(v0, v2) = v3) | ~ (in(v0, v1) = 0) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & powerset(v2) = v4 & element(v1, v4) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (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 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v1, v0) = v2) | ~ (epsilon_transitive(v0) = 0) | ? [v3] : ( ~ (v3 = 0) & in(v1, v0) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v1) = v3 & element(v0, v3) = v4)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v0, v1) = v2) | ? [v3] : ((v3 = 0 & empty(v1) = 0) | ( ~ (v3 = 0) & element(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_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 | ~ (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] : ( ~ (empty(v2) = 0) | ~ (in(v0, v1) = 0) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v2) = v3 & element(v1, v3) = v4)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (relation(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (epsilon_transitive(v0) = v1) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & subset(v2, v0) = v3 & in(v2, v0) = 0)) & ! [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] : ( ~ (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] : ((v2 = 0 & v1 = 0 & epsilon_connected(v0) = 0) | ( ~ (v2 = 0) & ordinal(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (epsilon_transitive(v0) = 0) | ~ (in(v1, v0) = 0) | subset(v1, v0) = 0) & ! [v0] : ! [v1] : ( ~ (epsilon_connected(v0) = v1) | ? [v2] : ((v2 = 0 & v1 = 0 & epsilon_transitive(v0) = 0) | ( ~ (v2 = 0) & ordinal(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | element(v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) & ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0)) & ! [v0] : ( ~ (relation(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] : ? [v1] : ? [v2] : element(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : 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] : 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
% 7.22/2.35 |
% 7.22/2.35 | Applying alpha-rule on (1) yields:
% 7.22/2.35 | (2) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0))
% 7.22/2.35 | (3) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | subset(v0, v1) = 0)
% 7.22/2.35 | (4) in(all_0_14_14, all_0_16_16) = 0
% 7.22/2.35 | (5) ? [v0] : ? [v1] : epsilon_connected(v0) = v1
% 7.22/2.35 | (6) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (epsilon_transitive(v2) = v1) | ~ (epsilon_transitive(v2) = v0))
% 7.22/2.35 | (7) empty(all_0_2_2) = 0
% 7.22/2.35 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | element(v0, v2) = 0)
% 7.22/2.35 | (9) ordinal(all_0_16_16) = 0
% 7.22/2.35 | (10) ? [v0] : ? [v1] : relation(v0) = v1
% 7.22/2.35 | (11) ! [v0] : ! [v1] : ( ~ (epsilon_transitive(v0) = 0) | ~ (in(v1, v0) = 0) | subset(v1, v0) = 0)
% 7.22/2.35 | (12) relation_empty_yielding(all_0_10_10) = 0
% 7.22/2.36 | (13) ~ (all_0_13_13 = 0)
% 7.22/2.36 | (14) epsilon_transitive(all_0_14_14) = 0
% 7.22/2.36 | (15) relation(all_0_0_0) = 0
% 7.22/2.36 | (16) ! [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)))
% 7.22/2.36 | (17) ! [v0] : ! [v1] : ( ~ (element(v0, v1) = 0) | ? [v2] : ((v2 = 0 & empty(v1) = 0) | (v2 = 0 & in(v0, v1) = 0)))
% 7.22/2.36 | (18) empty(empty_set) = 0
% 7.22/2.36 | (19) empty(all_0_8_8) = all_0_7_7
% 7.22/2.36 | (20) function(all_0_9_9) = 0
% 7.22/2.36 | (21) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0))
% 7.22/2.36 | (22) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v1, v0) = v2) | ~ (epsilon_transitive(v0) = 0) | ? [v3] : ( ~ (v3 = 0) & in(v1, v0) = v3))
% 7.22/2.36 | (23) ! [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)))
% 7.22/2.36 | (24) ! [v0] : ! [v1] : ( ~ (epsilon_transitive(v0) = v1) | ? [v2] : ((v2 = 0 & v1 = 0 & epsilon_connected(v0) = 0) | ( ~ (v2 = 0) & ordinal(v0) = v2)))
% 7.22/2.36 | (25) relation(all_0_10_10) = 0
% 7.22/2.36 | (26) relation_empty_yielding(all_0_11_11) = 0
% 7.22/2.36 | (27) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 7.22/2.36 | (28) ? [v0] : ? [v1] : ? [v2] : element(v1, v0) = v2
% 7.22/2.36 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0))
% 7.22/2.36 | (30) ? [v0] : ? [v1] : one_to_one(v0) = v1
% 7.22/2.36 | (31) relation_non_empty(all_0_12_12) = 0
% 7.22/2.36 | (32) ? [v0] : ? [v1] : relation_non_empty(v0) = v1
% 7.22/2.36 | (33) empty(all_0_4_4) = 0
% 7.22/2.36 | (34) relation(all_0_6_6) = 0
% 7.22/2.36 | (35) ? [v0] : ? [v1] : ordinal(v0) = v1
% 7.22/2.36 | (36) ! [v0] : ( ~ (epsilon_connected(v0) = 0) | ? [v1] : ((v1 = 0 & ordinal(v0) = 0) | ( ~ (v1 = 0) & epsilon_transitive(v0) = v1)))
% 7.22/2.36 | (37) ! [v0] : ( ~ (epsilon_transitive(v0) = 0) | ? [v1] : ((v1 = 0 & ordinal(v0) = 0) | ( ~ (v1 = 0) & epsilon_connected(v0) = v1)))
% 7.22/2.36 | (38) in(all_0_16_16, all_0_15_15) = 0
% 7.22/2.36 | (39) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_empty_yielding(v2) = v1) | ~ (relation_empty_yielding(v2) = v0))
% 7.22/2.36 | (40) empty(all_0_3_3) = 0
% 7.22/2.36 | (41) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0))
% 7.22/2.36 | (42) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0))
% 7.22/2.36 | (43) relation(all_0_12_12) = 0
% 7.22/2.36 | (44) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (epsilon_connected(v2) = v1) | ~ (epsilon_connected(v2) = v0))
% 7.22/2.36 | (45) ! [v0] : ( ~ (ordinal(v0) = 0) | (epsilon_transitive(v0) = 0 & epsilon_connected(v0) = 0))
% 7.22/2.36 | (46) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 7.22/2.36 | (47) function(all_0_11_11) = 0
% 7.22/2.36 | (48) epsilon_transitive(all_0_1_1) = 0
% 7.22/2.36 | (49) relation(all_0_11_11) = 0
% 7.22/2.36 | (50) ordinal(all_0_1_1) = 0
% 7.22/2.36 | (51) ? [v0] : ? [v1] : powerset(v0) = v1
% 7.22/2.36 | (52) one_to_one(all_0_9_9) = 0
% 7.22/2.36 | (53) function(all_0_12_12) = 0
% 7.22/2.37 | (54) ? [v0] : ? [v1] : function(v0) = v1
% 7.22/2.37 | (55) ! [v0] : ! [v1] : (v1 = 0 | ~ (relation(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2))
% 7.22/2.37 | (56) ! [v0] : ! [v1] : ! [v2] : ( ~ (empty(v2) = 0) | ~ (in(v0, v1) = 0) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v2) = v3 & element(v1, v3) = v4))
% 7.22/2.37 | (57) in(all_0_14_14, all_0_15_15) = all_0_13_13
% 7.22/2.37 | (58) ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2
% 7.22/2.37 | (59) ~ (all_0_5_5 = 0)
% 7.22/2.37 | (60) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 7.22/2.37 | (61) ! [v0] : ! [v1] : ( ~ (epsilon_connected(v0) = v1) | ? [v2] : ((v2 = 0 & v1 = 0 & epsilon_transitive(v0) = 0) | ( ~ (v2 = 0) & ordinal(v0) = v2)))
% 7.22/2.37 | (62) function(all_0_0_0) = 0
% 7.22/2.37 | (63) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3))
% 7.22/2.37 | (64) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1))
% 7.22/2.37 | (65) ? [v0] : ? [v1] : epsilon_transitive(v0) = v1
% 7.22/2.37 | (66) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 7.22/2.37 | (67) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_non_empty(v2) = v1) | ~ (relation_non_empty(v2) = v0))
% 7.22/2.37 | (68) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v0, v1) = v2) | ? [v3] : ((v3 = 0 & empty(v1) = 0) | ( ~ (v3 = 0) & element(v0, v1) = v3)))
% 7.22/2.37 | (69) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 7.22/2.37 | (70) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ordinal(v2) = v1) | ~ (ordinal(v2) = v0))
% 7.22/2.37 | (71) ! [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))
% 7.22/2.37 | (72) ! [v0] : ! [v1] : (v1 = 0 | ~ (ordinal(v0) = v1) | ? [v2] : (( ~ (v2 = 0) & epsilon_transitive(v0) = v2) | ( ~ (v2 = 0) & epsilon_connected(v0) = v2)))
% 7.22/2.37 | (73) relation(all_0_2_2) = 0
% 7.22/2.37 | (74) function(all_0_4_4) = 0
% 7.22/2.37 | (75) relation(empty_set) = 0
% 7.22/2.37 | (76) relation(all_0_4_4) = 0
% 7.22/2.37 | (77) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v1) = v3 & element(v0, v3) = v4))
% 7.22/2.37 | (78) ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2
% 7.22/2.37 | (79) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0))
% 7.22/2.37 | (80) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | element(v0, v1) = 0)
% 7.22/2.37 | (81) ? [v0] : ? [v1] : relation_empty_yielding(v0) = v1
% 7.22/2.37 | (82) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0))
% 7.22/2.37 | (83) ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2))
% 7.22/2.37 | (84) epsilon_connected(all_0_1_1) = 0
% 7.22/2.37 | (85) ! [v0] : ! [v1] : (v1 = 0 | ~ (function(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2))
% 7.22/2.37 | (86) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 7.22/2.37 | (87) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (powerset(v1) = v2 & element(v0, v2) = 0))
% 7.22/2.37 | (88) ! [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)))
% 7.22/2.37 | (89) ! [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)))
% 7.22/2.37 | (90) ~ (all_0_7_7 = 0)
% 7.22/2.37 | (91) empty(all_0_6_6) = all_0_5_5
% 7.22/2.37 | (92) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4))
% 7.22/2.37 | (93) ? [v0] : ? [v1] : empty(v0) = v1
% 7.22/2.37 | (94) relation_empty_yielding(empty_set) = 0
% 7.22/2.37 | (95) relation(all_0_9_9) = 0
% 7.22/2.37 | (96) ! [v0] : ( ~ (empty(v0) = 0) | function(v0) = 0)
% 7.22/2.37 | (97) ! [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))
% 7.22/2.37 | (98) ! [v0] : ( ~ (empty(v0) = 0) | relation(v0) = 0)
% 7.22/2.37 | (99) ! [v0] : ! [v1] : (v1 = 0 | ~ (epsilon_transitive(v0) = v1) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & subset(v2, v0) = v3 & in(v2, v0) = 0))
% 7.22/2.37 | (100) ordinal(all_0_15_15) = 0
% 7.22/2.38 | (101) ? [v0] : ? [v1] : element(v1, v0) = 0
% 7.22/2.38 |
% 7.22/2.38 | Instantiating formula (45) with all_0_15_15 and discharging atoms ordinal(all_0_15_15) = 0, yields:
% 7.22/2.38 | (102) epsilon_transitive(all_0_15_15) = 0 & epsilon_connected(all_0_15_15) = 0
% 7.22/2.38 |
% 7.22/2.38 | Applying alpha-rule on (102) yields:
% 7.22/2.38 | (103) epsilon_transitive(all_0_15_15) = 0
% 7.22/2.38 | (104) epsilon_connected(all_0_15_15) = 0
% 7.22/2.38 |
% 7.22/2.38 | Instantiating formula (68) with all_0_13_13, all_0_15_15, all_0_14_14 and discharging atoms in(all_0_14_14, all_0_15_15) = all_0_13_13, yields:
% 7.22/2.38 | (105) all_0_13_13 = 0 | ? [v0] : ((v0 = 0 & empty(all_0_15_15) = 0) | ( ~ (v0 = 0) & element(all_0_14_14, all_0_15_15) = v0))
% 7.22/2.38 |
% 7.22/2.38 | Instantiating formula (46) with all_0_15_15, all_0_16_16 and discharging atoms in(all_0_16_16, all_0_15_15) = 0, yields:
% 7.22/2.38 | (106) ? [v0] : ( ~ (v0 = 0) & empty(all_0_15_15) = v0)
% 7.22/2.38 |
% 7.22/2.38 | Instantiating (106) with all_55_0_67 yields:
% 7.22/2.38 | (107) ~ (all_55_0_67 = 0) & empty(all_0_15_15) = all_55_0_67
% 7.22/2.38 |
% 7.22/2.38 | Applying alpha-rule on (107) yields:
% 7.22/2.38 | (108) ~ (all_55_0_67 = 0)
% 7.22/2.38 | (109) empty(all_0_15_15) = all_55_0_67
% 7.22/2.38 |
% 7.22/2.38 +-Applying beta-rule and splitting (105), into two cases.
% 7.22/2.38 |-Branch one:
% 7.22/2.38 | (110) all_0_13_13 = 0
% 7.22/2.38 |
% 7.22/2.38 | Equations (110) can reduce 13 to:
% 7.22/2.38 | (111) $false
% 7.22/2.38 |
% 7.22/2.38 |-The branch is then unsatisfiable
% 7.22/2.38 |-Branch two:
% 7.22/2.38 | (13) ~ (all_0_13_13 = 0)
% 7.22/2.38 | (113) ? [v0] : ((v0 = 0 & empty(all_0_15_15) = 0) | ( ~ (v0 = 0) & element(all_0_14_14, all_0_15_15) = v0))
% 7.66/2.38 |
% 7.66/2.38 | Instantiating (113) with all_81_0_88 yields:
% 7.66/2.38 | (114) (all_81_0_88 = 0 & empty(all_0_15_15) = 0) | ( ~ (all_81_0_88 = 0) & element(all_0_14_14, all_0_15_15) = all_81_0_88)
% 7.66/2.38 |
% 7.66/2.38 +-Applying beta-rule and splitting (114), into two cases.
% 7.66/2.38 |-Branch one:
% 7.66/2.38 | (115) all_81_0_88 = 0 & empty(all_0_15_15) = 0
% 7.66/2.38 |
% 7.66/2.38 | Applying alpha-rule on (115) yields:
% 7.66/2.38 | (116) all_81_0_88 = 0
% 7.66/2.38 | (117) empty(all_0_15_15) = 0
% 7.66/2.38 |
% 7.66/2.38 | Instantiating formula (60) with all_0_15_15, 0, all_55_0_67 and discharging atoms empty(all_0_15_15) = all_55_0_67, empty(all_0_15_15) = 0, yields:
% 7.66/2.38 | (118) all_55_0_67 = 0
% 7.66/2.38 |
% 7.66/2.38 | Equations (118) can reduce 108 to:
% 7.66/2.38 | (111) $false
% 7.66/2.38 |
% 7.66/2.38 |-The branch is then unsatisfiable
% 7.66/2.38 |-Branch two:
% 7.66/2.38 | (120) ~ (all_81_0_88 = 0) & element(all_0_14_14, all_0_15_15) = all_81_0_88
% 7.66/2.38 |
% 7.66/2.38 | Applying alpha-rule on (120) yields:
% 7.66/2.38 | (121) ~ (all_81_0_88 = 0)
% 7.66/2.38 | (122) element(all_0_14_14, all_0_15_15) = all_81_0_88
% 7.66/2.38 |
% 7.66/2.38 | Instantiating formula (71) with all_81_0_88, all_0_15_15, all_0_16_16, all_0_14_14 and discharging atoms element(all_0_14_14, all_0_15_15) = all_81_0_88, in(all_0_14_14, all_0_16_16) = 0, yields:
% 7.66/2.38 | (123) all_81_0_88 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & powerset(all_0_15_15) = v0 & element(all_0_16_16, v0) = v1)
% 7.66/2.38 |
% 7.66/2.38 | Instantiating formula (11) with all_0_16_16, all_0_15_15 and discharging atoms epsilon_transitive(all_0_15_15) = 0, in(all_0_16_16, all_0_15_15) = 0, yields:
% 7.66/2.38 | (124) subset(all_0_16_16, all_0_15_15) = 0
% 7.66/2.38 |
% 7.66/2.38 +-Applying beta-rule and splitting (123), into two cases.
% 7.66/2.38 |-Branch one:
% 7.66/2.38 | (116) all_81_0_88 = 0
% 7.66/2.38 |
% 7.66/2.38 | Equations (116) can reduce 121 to:
% 7.66/2.38 | (111) $false
% 7.66/2.38 |
% 7.66/2.38 |-The branch is then unsatisfiable
% 7.66/2.38 |-Branch two:
% 7.66/2.38 | (121) ~ (all_81_0_88 = 0)
% 7.66/2.38 | (128) ? [v0] : ? [v1] : ( ~ (v1 = 0) & powerset(all_0_15_15) = v0 & element(all_0_16_16, v0) = v1)
% 7.66/2.38 |
% 7.66/2.38 | Instantiating (128) with all_132_0_95, all_132_1_96 yields:
% 7.66/2.38 | (129) ~ (all_132_0_95 = 0) & powerset(all_0_15_15) = all_132_1_96 & element(all_0_16_16, all_132_1_96) = all_132_0_95
% 7.66/2.38 |
% 7.66/2.38 | Applying alpha-rule on (129) yields:
% 7.66/2.38 | (130) ~ (all_132_0_95 = 0)
% 7.66/2.38 | (131) powerset(all_0_15_15) = all_132_1_96
% 7.66/2.38 | (132) element(all_0_16_16, all_132_1_96) = all_132_0_95
% 7.66/2.38 |
% 7.66/2.38 | Instantiating formula (86) with all_132_0_95, all_132_1_96, all_0_15_15, all_0_16_16 and discharging atoms powerset(all_0_15_15) = all_132_1_96, element(all_0_16_16, all_132_1_96) = all_132_0_95, yields:
% 7.66/2.38 | (133) all_132_0_95 = 0 | ? [v0] : ( ~ (v0 = 0) & subset(all_0_16_16, all_0_15_15) = v0)
% 7.66/2.38 |
% 7.66/2.38 +-Applying beta-rule and splitting (133), into two cases.
% 7.66/2.38 |-Branch one:
% 7.66/2.38 | (134) all_132_0_95 = 0
% 7.66/2.38 |
% 7.66/2.38 | Equations (134) can reduce 130 to:
% 7.66/2.38 | (111) $false
% 7.66/2.38 |
% 7.66/2.38 |-The branch is then unsatisfiable
% 7.66/2.38 |-Branch two:
% 7.66/2.38 | (130) ~ (all_132_0_95 = 0)
% 7.66/2.38 | (137) ? [v0] : ( ~ (v0 = 0) & subset(all_0_16_16, all_0_15_15) = v0)
% 7.66/2.38 |
% 7.66/2.38 | Instantiating (137) with all_156_0_101 yields:
% 7.66/2.38 | (138) ~ (all_156_0_101 = 0) & subset(all_0_16_16, all_0_15_15) = all_156_0_101
% 7.66/2.38 |
% 7.66/2.38 | Applying alpha-rule on (138) yields:
% 7.66/2.38 | (139) ~ (all_156_0_101 = 0)
% 7.66/2.38 | (140) subset(all_0_16_16, all_0_15_15) = all_156_0_101
% 7.66/2.38 |
% 7.66/2.39 | Instantiating formula (66) with all_0_16_16, all_0_15_15, all_156_0_101, 0 and discharging atoms subset(all_0_16_16, all_0_15_15) = all_156_0_101, subset(all_0_16_16, all_0_15_15) = 0, yields:
% 7.66/2.39 | (141) all_156_0_101 = 0
% 7.66/2.39 |
% 7.66/2.39 | Equations (141) can reduce 139 to:
% 7.66/2.39 | (111) $false
% 7.66/2.39 |
% 7.66/2.39 |-The branch is then unsatisfiable
% 7.66/2.39 % SZS output end Proof for theBenchmark
% 7.66/2.39
% 7.66/2.39 1781ms
%------------------------------------------------------------------------------