TSTP Solution File: SEU248+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU248+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n024.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 08:48:08 EDT 2022
% Result : Theorem 10.69s 3.17s
% Output : Proof 13.98s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU248+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.33 % Computer : n024.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jun 19 13:11:02 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.49/0.59 ____ _
% 0.49/0.59 ___ / __ \_____(_)___ ________ __________
% 0.49/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.49/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.49/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.49/0.59
% 0.49/0.59 A Theorem Prover for First-Order Logic
% 0.49/0.59 (ePrincess v.1.0)
% 0.49/0.59
% 0.49/0.59 (c) Philipp Rümmer, 2009-2015
% 0.49/0.59 (c) Peter Backeman, 2014-2015
% 0.49/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.49/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.49/0.59 Bug reports to peter@backeman.se
% 0.49/0.59
% 0.49/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.49/0.59
% 0.49/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.72/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.53/0.97 Prover 0: Preprocessing ...
% 2.17/1.20 Prover 0: Warning: ignoring some quantifiers
% 2.17/1.23 Prover 0: Constructing countermodel ...
% 3.54/1.55 Prover 0: gave up
% 3.54/1.55 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 3.71/1.58 Prover 1: Preprocessing ...
% 4.23/1.68 Prover 1: Warning: ignoring some quantifiers
% 4.23/1.69 Prover 1: Constructing countermodel ...
% 9.53/2.93 Prover 1: gave up
% 9.53/2.93 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 9.64/2.96 Prover 2: Preprocessing ...
% 10.05/3.04 Prover 2: Warning: ignoring some quantifiers
% 10.05/3.05 Prover 2: Constructing countermodel ...
% 10.69/3.17 Prover 2: proved (242ms)
% 10.69/3.17
% 10.69/3.17 No countermodel exists, formula is valid
% 10.69/3.17 % SZS status Theorem for theBenchmark
% 10.69/3.18
% 10.69/3.18 Generating proof ... Warning: ignoring some quantifiers
% 13.05/3.75 found it (size 73)
% 13.05/3.75
% 13.05/3.75 % SZS output start Proof for theBenchmark
% 13.05/3.75 Assumed formulas after preprocessing and simplification:
% 13.05/3.75 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ( ~ (v8 = 0) & ~ (v5 = 0) & relation_dom(v2) = v3 & relation_dom(v1) = v4 & subset(v3, v4) = v5 & relation_rng_restriction(v0, v1) = v2 & one_to_one(v6) = 0 & relation(v11) = 0 & relation(v9) = 0 & relation(v6) = 0 & relation(v1) = 0 & function(v11) = 0 & function(v9) = 0 & function(v6) = 0 & empty(v10) = 0 & empty(v9) = 0 & empty(v7) = v8 & empty(empty_set) = 0 & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v15 = 0 | ~ (relation_dom(v12) = v13) | ~ (ordered_pair(v14, v16) = v17) | ~ (in(v14, v13) = v15) | ? [v18] : (( ~ (v18 = 0) & relation(v12) = v18) | ( ~ (v18 = 0) & in(v17, v12) = v18))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_rng_restriction(v12, v13) = v14) | ~ (ordered_pair(v15, v16) = v17) | ~ (relation(v14) = 0) | ? [v18] : ? [v19] : ((v19 = 0 & v18 = 0 & in(v17, v13) = 0 & in(v16, v12) = 0) | ( ~ (v18 = 0) & relation(v13) = v18) | ( ~ (v18 = 0) & in(v17, v14) = v18))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_rng_restriction(v12, v13) = v14) | ~ (ordered_pair(v15, v16) = v17) | ~ (relation(v14) = 0) | ? [v18] : ((v18 = 0 & in(v17, v14) = 0) | ( ~ (v18 = 0) & relation(v13) = v18) | ( ~ (v18 = 0) & in(v17, v13) = v18) | ( ~ (v18 = 0) & in(v16, v12) = v18))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (powerset(v14) = v15) | ~ (element(v13, v15) = 0) | ~ (element(v12, v14) = v16) | ? [v17] : ( ~ (v17 = 0) & in(v12, v13) = v17)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = v14 | ~ (relation_rng_restriction(v12, v13) = v14) | ~ (relation(v15) = 0) | ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : (( ~ (v16 = 0) & relation(v13) = v16) | (ordered_pair(v16, v17) = v18 & ((v21 = 0 & v20 = 0 & in(v18, v13) = 0 & in(v17, v12) = 0) | (v19 = 0 & in(v18, v15) = 0)) & (( ~ (v21 = 0) & in(v18, v13) = v21) | ( ~ (v20 = 0) & in(v17, v12) = v20) | ( ~ (v19 = 0) & in(v18, v15) = v19))))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (powerset(v13) = v14) | ~ (element(v12, v14) = v15) | ? [v16] : ( ~ (v16 = 0) & subset(v12, v13) = v16)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (element(v12, v14) = v15) | ~ (in(v12, v13) = 0) | ? [v16] : ? [v17] : ( ~ (v17 = 0) & powerset(v14) = v16 & element(v13, v16) = v17)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (subset(v12, v13) = 0) | ~ (in(v14, v13) = v15) | ? [v16] : ( ~ (v16 = 0) & in(v14, v12) = v16)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (element(v15, v14) = v13) | ~ (element(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (subset(v15, v14) = v13) | ~ (subset(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (relation_rng_restriction(v15, v14) = v13) | ~ (relation_rng_restriction(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (ordered_pair(v15, v14) = v13) | ~ (ordered_pair(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (unordered_pair(v15, v14) = v13) | ~ (unordered_pair(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (in(v15, v14) = v13) | ~ (in(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (powerset(v14) = v15) | ~ (element(v13, v15) = 0) | ~ (in(v12, v13) = 0) | element(v12, v14) = 0) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (powerset(v14) = v15) | ~ (element(v13, v15) = 0) | ~ (in(v12, v13) = 0) | ? [v16] : ( ~ (v16 = 0) & empty(v14) = v16)) & ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (element(v12, v13) = v14) | ? [v15] : ( ~ (v15 = 0) & in(v12, v13) = v15)) & ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (subset(v12, v13) = v14) | ? [v15] : ? [v16] : ( ~ (v16 = 0) & powerset(v13) = v15 & element(v12, v15) = v16)) & ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (subset(v12, v13) = v14) | ? [v15] : ? [v16] : ( ~ (v16 = 0) & in(v15, v13) = v16 & in(v15, v12) = 0)) & ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (in(v12, v13) = v14) | ? [v15] : ((v15 = 0 & empty(v13) = 0) | ( ~ (v15 = 0) & element(v12, v13) = v15))) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (powerset(v14) = v13) | ~ (powerset(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (singleton(v14) = v13) | ~ (singleton(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (relation_dom(v14) = v13) | ~ (relation_dom(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (one_to_one(v14) = v13) | ~ (one_to_one(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (relation(v14) = v13) | ~ (relation(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (function(v14) = v13) | ~ (function(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (empty(v14) = v13) | ~ (empty(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (powerset(v13) = v14) | ~ (element(v12, v14) = 0) | subset(v12, v13) = 0) & ! [v12] : ! [v13] : ! [v14] : ( ~ (relation_dom(v12) = v13) | ~ (in(v14, v13) = 0) | ? [v15] : ? [v16] : ? [v17] : ((v17 = 0 & ordered_pair(v14, v15) = v16 & in(v16, v12) = 0) | ( ~ (v15 = 0) & relation(v12) = v15))) & ! [v12] : ! [v13] : ! [v14] : ( ~ (subset(v12, v13) = 0) | ~ (in(v14, v12) = 0) | in(v14, v13) = 0) & ! [v12] : ! [v13] : ! [v14] : ( ~ (relation_rng_restriction(v12, v13) = v14) | ? [v15] : ? [v16] : ((v16 = 0 & v15 = 0 & relation(v14) = 0 & function(v14) = 0) | ( ~ (v15 = 0) & relation(v13) = v15) | ( ~ (v15 = 0) & function(v13) = v15))) & ! [v12] : ! [v13] : ! [v14] : ( ~ (relation_rng_restriction(v12, v13) = v14) | ? [v15] : ((v15 = 0 & relation(v14) = 0) | ( ~ (v15 = 0) & relation(v13) = v15))) & ! [v12] : ! [v13] : ! [v14] : ( ~ (ordered_pair(v12, v13) = v14) | ? [v15] : ? [v16] : (singleton(v12) = v16 & unordered_pair(v15, v16) = v14 & unordered_pair(v12, v13) = v15)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (ordered_pair(v12, v13) = v14) | ? [v15] : ( ~ (v15 = 0) & empty(v14) = v15)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (unordered_pair(v13, v12) = v14) | unordered_pair(v12, v13) = v14) & ! [v12] : ! [v13] : ! [v14] : ( ~ (unordered_pair(v12, v13) = v14) | unordered_pair(v13, v12) = v14) & ! [v12] : ! [v13] : ! [v14] : ( ~ (unordered_pair(v12, v13) = v14) | ? [v15] : ? [v16] : (singleton(v12) = v16 & ordered_pair(v12, v13) = v15 & unordered_pair(v14, v16) = v15)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (empty(v14) = 0) | ~ (in(v12, v13) = 0) | ? [v15] : ? [v16] : ( ~ (v16 = 0) & powerset(v14) = v15 & element(v13, v15) = v16)) & ? [v12] : ! [v13] : ! [v14] : (v14 = v12 | ~ (relation_dom(v13) = v14) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : (( ~ (v15 = 0) & relation(v13) = v15) | (( ! [v20] : ! [v21] : ( ~ (ordered_pair(v15, v20) = v21) | ? [v22] : ( ~ (v22 = 0) & in(v21, v13) = v22)) | ( ~ (v16 = 0) & in(v15, v12) = v16)) & ((v19 = 0 & ordered_pair(v15, v17) = v18 & in(v18, v13) = 0) | (v16 = 0 & in(v15, v12) = 0))))) & ! [v12] : ! [v13] : (v13 = v12 | ~ (empty(v13) = 0) | ~ (empty(v12) = 0)) & ! [v12] : ! [v13] : (v13 = 0 | ~ (subset(v12, v12) = v13)) & ! [v12] : ! [v13] : (v13 = 0 | ~ (function(v12) = v13) | ? [v14] : ( ~ (v14 = 0) & empty(v12) = v14)) & ! [v12] : ! [v13] : ( ~ (element(v12, v13) = 0) | ? [v14] : ((v14 = 0 & empty(v13) = 0) | (v14 = 0 & in(v12, v13) = 0))) & ! [v12] : ! [v13] : ( ~ (subset(v12, v13) = 0) | ? [v14] : (powerset(v13) = v14 & element(v12, v14) = 0)) & ! [v12] : ! [v13] : ( ~ (one_to_one(v12) = v13) | ? [v14] : ? [v15] : ((v15 = 0 & v14 = 0 & v13 = 0 & relation(v12) = 0 & function(v12) = 0) | ( ~ (v14 = 0) & relation(v12) = v14) | ( ~ (v14 = 0) & function(v12) = v14) | ( ~ (v14 = 0) & empty(v12) = v14))) & ! [v12] : ! [v13] : ( ~ (in(v13, v12) = 0) | ? [v14] : ( ~ (v14 = 0) & in(v12, v13) = v14)) & ! [v12] : ! [v13] : ( ~ (in(v12, v13) = 0) | element(v12, v13) = 0) & ! [v12] : ! [v13] : ( ~ (in(v12, v13) = 0) | ? [v14] : ( ~ (v14 = 0) & empty(v13) = v14)) & ! [v12] : ! [v13] : ( ~ (in(v12, v13) = 0) | ? [v14] : ( ~ (v14 = 0) & in(v13, v12) = v14)) & ! [v12] : (v12 = empty_set | ~ (empty(v12) = 0)) & ! [v12] : ( ~ (relation(v12) = 0) | ? [v13] : ? [v14] : ((v14 = 0 & v13 = 0 & one_to_one(v12) = 0 & function(v12) = 0) | ( ~ (v13 = 0) & function(v12) = v13) | ( ~ (v13 = 0) & empty(v12) = v13))) & ! [v12] : ( ~ (relation(v12) = 0) | ? [v13] : (relation_dom(v12) = v13 & ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v15 = 0 | ~ (ordered_pair(v14, v16) = v17) | ~ (in(v14, v13) = v15) | ? [v18] : ( ~ (v18 = 0) & in(v17, v12) = v18)) & ! [v14] : ( ~ (in(v14, v13) = 0) | ? [v15] : ? [v16] : (ordered_pair(v14, v15) = v16 & in(v16, v12) = 0)) & ? [v14] : (v14 = v13 | ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : (( ! [v20] : ! [v21] : ( ~ (ordered_pair(v15, v20) = v21) | ? [v22] : ( ~ (v22 = 0) & in(v21, v12) = v22)) | ( ~ (v16 = 0) & in(v15, v14) = v16)) & ((v19 = 0 & ordered_pair(v15, v17) = v18 & in(v18, v12) = 0) | (v16 = 0 & in(v15, v14) = 0)))))) & ! [v12] : ( ~ (function(v12) = 0) | ? [v13] : ? [v14] : ((v14 = 0 & v13 = 0 & one_to_one(v12) = 0 & relation(v12) = 0) | ( ~ (v13 = 0) & relation(v12) = v13) | ( ~ (v13 = 0) & empty(v12) = v13))) & ! [v12] : ( ~ (empty(v12) = 0) | function(v12) = 0) & ! [v12] : ( ~ (empty(v12) = 0) | ? [v13] : ? [v14] : ? [v15] : ((v15 = 0 & v14 = 0 & v13 = 0 & one_to_one(v12) = 0 & relation(v12) = 0 & function(v12) = 0) | ( ~ (v13 = 0) & relation(v12) = v13) | ( ~ (v13 = 0) & function(v12) = v13))) & ? [v12] : ? [v13] : ? [v14] : element(v13, v12) = v14 & ? [v12] : ? [v13] : ? [v14] : subset(v13, v12) = v14 & ? [v12] : ? [v13] : ? [v14] : relation_rng_restriction(v13, v12) = v14 & ? [v12] : ? [v13] : ? [v14] : ordered_pair(v13, v12) = v14 & ? [v12] : ? [v13] : ? [v14] : unordered_pair(v13, v12) = v14 & ? [v12] : ? [v13] : ? [v14] : in(v13, v12) = v14 & ? [v12] : ? [v13] : powerset(v12) = v13 & ? [v12] : ? [v13] : element(v13, v12) = 0 & ? [v12] : ? [v13] : singleton(v12) = v13 & ? [v12] : ? [v13] : relation_dom(v12) = v13 & ? [v12] : ? [v13] : one_to_one(v12) = v13 & ? [v12] : ? [v13] : relation(v12) = v13 & ? [v12] : ? [v13] : function(v12) = v13 & ? [v12] : ? [v13] : empty(v12) = v13)
% 13.38/3.80 | 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 yields:
% 13.38/3.80 | (1) ~ (all_0_3_3 = 0) & ~ (all_0_6_6 = 0) & relation_dom(all_0_9_9) = all_0_8_8 & relation_dom(all_0_10_10) = all_0_7_7 & subset(all_0_8_8, all_0_7_7) = all_0_6_6 & relation_rng_restriction(all_0_11_11, all_0_10_10) = all_0_9_9 & one_to_one(all_0_5_5) = 0 & relation(all_0_0_0) = 0 & relation(all_0_2_2) = 0 & relation(all_0_5_5) = 0 & relation(all_0_10_10) = 0 & function(all_0_0_0) = 0 & function(all_0_2_2) = 0 & function(all_0_5_5) = 0 & empty(all_0_1_1) = 0 & empty(all_0_2_2) = 0 & empty(all_0_4_4) = all_0_3_3 & empty(empty_set) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = 0 | ~ (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v4) = v5) | ~ (in(v2, v1) = v3) | ? [v6] : (( ~ (v6 = 0) & relation(v0) = v6) | ( ~ (v6 = 0) & in(v5, v0) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ (relation(v2) = 0) | ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & in(v5, v1) = 0 & in(v4, v0) = 0) | ( ~ (v6 = 0) & relation(v1) = v6) | ( ~ (v6 = 0) & in(v5, v2) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ (relation(v2) = 0) | ? [v6] : ((v6 = 0 & in(v5, v2) = 0) | ( ~ (v6 = 0) & relation(v1) = v6) | ( ~ (v6 = 0) & in(v5, v1) = v6) | ( ~ (v6 = 0) & in(v4, v0) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (element(v0, v2) = v4) | ? [v5] : ( ~ (v5 = 0) & in(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (relation_rng_restriction(v0, v1) = v2) | ~ (relation(v3) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (( ~ (v4 = 0) & relation(v1) = v4) | (ordered_pair(v4, v5) = v6 & ((v9 = 0 & v8 = 0 & in(v6, v1) = 0 & in(v5, v0) = 0) | (v7 = 0 & in(v6, v3) = 0)) & (( ~ (v9 = 0) & in(v6, v1) = v9) | ( ~ (v8 = 0) & in(v5, v0) = v8) | ( ~ (v7 = 0) & in(v6, v3) = v7))))) & ! [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] : (v3 = 0 | ~ (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v2, v0) = v4)) & ! [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 | ~ (relation_rng_restriction(v3, v2) = v1) | ~ (relation_rng_restriction(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(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(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v1) = v3 & element(v0, v3) = v4)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0)) & ! [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 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | subset(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom(v0) = v1) | ~ (in(v2, v1) = 0) | ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & ordered_pair(v2, v3) = v4 & in(v4, v0) = 0) | ( ~ (v3 = 0) & relation(v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ? [v3] : ? [v4] : ((v4 = 0 & v3 = 0 & relation(v2) = 0 & function(v2) = 0) | ( ~ (v3 = 0) & relation(v1) = v3) | ( ~ (v3 = 0) & function(v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ? [v3] : ((v3 = 0 & relation(v2) = 0) | ( ~ (v3 = 0) & relation(v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & ordered_pair(v0, v1) = v3 & unordered_pair(v2, v4) = 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] : (v2 = v0 | ~ (relation_dom(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (( ~ (v3 = 0) & relation(v1) = v3) | (( ! [v8] : ! [v9] : ( ~ (ordered_pair(v3, v8) = v9) | ? [v10] : ( ~ (v10 = 0) & in(v9, v1) = v10)) | ( ~ (v4 = 0) & in(v3, v0) = v4)) & ((v7 = 0 & ordered_pair(v3, v5) = v6 & in(v6, v1) = 0) | (v4 = 0 & in(v3, v0) = 0))))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) & ! [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] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | element(v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) & ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0)) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ((v2 = 0 & v1 = 0 & one_to_one(v0) = 0 & function(v0) = 0) | ( ~ (v1 = 0) & function(v0) = v1) | ( ~ (v1 = 0) & empty(v0) = v1))) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : (relation_dom(v0) = v1 & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = 0 | ~ (ordered_pair(v2, v4) = v5) | ~ (in(v2, v1) = v3) | ? [v6] : ( ~ (v6 = 0) & in(v5, v0) = v6)) & ! [v2] : ( ~ (in(v2, v1) = 0) | ? [v3] : ? [v4] : (ordered_pair(v2, v3) = v4 & in(v4, v0) = 0)) & ? [v2] : (v2 = v1 | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (( ! [v8] : ! [v9] : ( ~ (ordered_pair(v3, v8) = v9) | ? [v10] : ( ~ (v10 = 0) & in(v9, v0) = v10)) | ( ~ (v4 = 0) & in(v3, v2) = v4)) & ((v7 = 0 & ordered_pair(v3, v5) = v6 & in(v6, v0) = 0) | (v4 = 0 & in(v3, v2) = 0)))))) & ! [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) | 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] : relation_rng_restriction(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : ordered_pair(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : unordered_pair(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2 & ? [v0] : ? [v1] : powerset(v0) = v1 & ? [v0] : ? [v1] : element(v1, v0) = 0 & ? [v0] : ? [v1] : singleton(v0) = v1 & ? [v0] : ? [v1] : relation_dom(v0) = v1 & ? [v0] : ? [v1] : one_to_one(v0) = v1 & ? [v0] : ? [v1] : relation(v0) = v1 & ? [v0] : ? [v1] : function(v0) = v1 & ? [v0] : ? [v1] : empty(v0) = v1
% 13.38/3.81 |
% 13.38/3.81 | Applying alpha-rule on (1) yields:
% 13.38/3.81 | (2) relation(all_0_10_10) = 0
% 13.38/3.81 | (3) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_dom(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (( ~ (v3 = 0) & relation(v1) = v3) | (( ! [v8] : ! [v9] : ( ~ (ordered_pair(v3, v8) = v9) | ? [v10] : ( ~ (v10 = 0) & in(v9, v1) = v10)) | ( ~ (v4 = 0) & in(v3, v0) = v4)) & ((v7 = 0 & ordered_pair(v3, v5) = v6 & in(v6, v1) = 0) | (v4 = 0 & in(v3, v0) = 0)))))
% 13.38/3.82 | (4) ? [v0] : ? [v1] : empty(v0) = v1
% 13.38/3.82 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ (relation(v2) = 0) | ? [v6] : ((v6 = 0 & in(v5, v2) = 0) | ( ~ (v6 = 0) & relation(v1) = v6) | ( ~ (v6 = 0) & in(v5, v1) = v6) | ( ~ (v6 = 0) & in(v4, v0) = v6)))
% 13.38/3.82 | (6) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | subset(v0, v1) = 0)
% 13.38/3.82 | (7) ? [v0] : ? [v1] : one_to_one(v0) = v1
% 13.38/3.82 | (8) ! [v0] : ! [v1] : (v1 = 0 | ~ (function(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2))
% 13.38/3.82 | (9) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (powerset(v1) = v2 & element(v0, v2) = 0))
% 13.38/3.82 | (10) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0))
% 13.38/3.82 | (11) ? [v0] : ? [v1] : function(v0) = v1
% 13.38/3.82 | (12) ? [v0] : ? [v1] : relation(v0) = v1
% 13.38/3.82 | (13) relation_rng_restriction(all_0_11_11, all_0_10_10) = all_0_9_9
% 13.38/3.82 | (14) ? [v0] : ? [v1] : singleton(v0) = v1
% 13.38/3.82 | (15) ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2
% 13.38/3.82 | (16) ! [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)))
% 13.38/3.82 | (17) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 13.38/3.82 | (18) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0))
% 13.38/3.82 | (19) ! [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)))
% 13.38/3.82 | (20) relation_dom(all_0_10_10) = all_0_7_7
% 13.38/3.82 | (21) ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2))
% 13.38/3.82 | (22) function(all_0_0_0) = 0
% 13.38/3.82 | (23) ! [v0] : ! [v1] : ! [v2] : ( ~ (empty(v2) = 0) | ~ (in(v0, v1) = 0) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v2) = v3 & element(v1, v3) = v4))
% 13.38/3.82 | (24) one_to_one(all_0_5_5) = 0
% 13.38/3.82 | (25) ! [v0] : ! [v1] : ( ~ (element(v0, v1) = 0) | ? [v2] : ((v2 = 0 & empty(v1) = 0) | (v2 = 0 & in(v0, v1) = 0)))
% 13.38/3.82 | (26) ? [v0] : ? [v1] : ? [v2] : ordered_pair(v1, v0) = v2
% 13.38/3.82 | (27) empty(empty_set) = 0
% 13.38/3.82 | (28) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0))
% 13.38/3.83 | (29) ? [v0] : ? [v1] : ? [v2] : element(v1, v0) = v2
% 13.38/3.83 | (30) function(all_0_5_5) = 0
% 13.38/3.83 | (31) relation(all_0_2_2) = 0
% 13.38/3.83 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 13.38/3.83 | (33) ~ (all_0_3_3 = 0)
% 13.38/3.83 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0))
% 13.38/3.83 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0))
% 13.38/3.83 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4))
% 13.38/3.83 | (37) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 13.38/3.83 | (38) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0))
% 13.38/3.83 | (39) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | element(v0, v1) = 0)
% 13.38/3.83 | (40) ~ (all_0_6_6 = 0)
% 13.38/3.83 | (41) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0)
% 13.38/3.83 | (42) relation(all_0_5_5) = 0
% 13.38/3.83 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_rng_restriction(v3, v2) = v1) | ~ (relation_rng_restriction(v3, v2) = v0))
% 13.38/3.83 | (44) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom(v0) = v1) | ~ (in(v2, v1) = 0) | ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & ordered_pair(v2, v3) = v4 & in(v4, v0) = 0) | ( ~ (v3 = 0) & relation(v0) = v3)))
% 13.38/3.83 | (45) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0))
% 13.38/3.83 | (46) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ? [v3] : ((v3 = 0 & relation(v2) = 0) | ( ~ (v3 = 0) & relation(v1) = v3)))
% 13.38/3.83 | (47) ! [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))
% 13.38/3.84 | (48) ! [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)))
% 13.38/3.84 | (49) relation(all_0_0_0) = 0
% 13.38/3.84 | (50) subset(all_0_8_8, all_0_7_7) = all_0_6_6
% 13.38/3.84 | (51) ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2
% 13.38/3.84 | (52) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ? [v3] : ? [v4] : ((v4 = 0 & v3 = 0 & relation(v2) = 0 & function(v2) = 0) | ( ~ (v3 = 0) & relation(v1) = v3) | ( ~ (v3 = 0) & function(v1) = v3)))
% 13.38/3.84 | (53) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 13.38/3.84 | (54) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0))
% 13.38/3.84 | (55) relation_dom(all_0_9_9) = all_0_8_8
% 13.38/3.84 | (56) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v1) = v3 & element(v0, v3) = v4))
% 13.38/3.84 | (57) ! [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))
% 13.38/3.84 | (58) ? [v0] : ? [v1] : ? [v2] : relation_rng_restriction(v1, v0) = v2
% 13.38/3.84 | (59) function(all_0_2_2) = 0
% 13.38/3.84 | (60) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0))
% 13.38/3.84 | (61) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2)
% 13.38/3.84 | (62) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2)
% 13.38/3.84 | (63) ! [v0] : ( ~ (empty(v0) = 0) | function(v0) = 0)
% 13.38/3.85 | (64) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 13.38/3.85 | (65) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3))
% 13.38/3.85 | (66) ? [v0] : ? [v1] : powerset(v0) = v1
% 13.38/3.85 | (67) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v2, v0) = v4))
% 13.38/3.85 | (68) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (relation_rng_restriction(v0, v1) = v2) | ~ (relation(v3) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (( ~ (v4 = 0) & relation(v1) = v4) | (ordered_pair(v4, v5) = v6 & ((v9 = 0 & v8 = 0 & in(v6, v1) = 0 & in(v5, v0) = 0) | (v7 = 0 & in(v6, v3) = 0)) & (( ~ (v9 = 0) & in(v6, v1) = v9) | ( ~ (v8 = 0) & in(v5, v0) = v8) | ( ~ (v7 = 0) & in(v6, v3) = v7)))))
% 13.38/3.85 | (69) ? [v0] : ? [v1] : element(v1, v0) = 0
% 13.38/3.85 | (70) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & ordered_pair(v0, v1) = v3 & unordered_pair(v2, v4) = v3))
% 13.38/3.85 | (71) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 13.38/3.85 | (72) ! [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)))
% 13.38/3.85 | (73) ? [v0] : ? [v1] : relation_dom(v0) = v1
% 13.38/3.85 | (74) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3))
% 13.38/3.86 | (75) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3))
% 13.38/3.86 | (76) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 13.38/3.86 | (77) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | element(v0, v2) = 0)
% 13.38/3.86 | (78) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ (relation(v2) = 0) | ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & in(v5, v1) = 0 & in(v4, v0) = 0) | ( ~ (v6 = 0) & relation(v1) = v6) | ( ~ (v6 = 0) & in(v5, v2) = v6)))
% 13.38/3.86 | (79) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : (relation_dom(v0) = v1 & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = 0 | ~ (ordered_pair(v2, v4) = v5) | ~ (in(v2, v1) = v3) | ? [v6] : ( ~ (v6 = 0) & in(v5, v0) = v6)) & ! [v2] : ( ~ (in(v2, v1) = 0) | ? [v3] : ? [v4] : (ordered_pair(v2, v3) = v4 & in(v4, v0) = 0)) & ? [v2] : (v2 = v1 | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (( ! [v8] : ! [v9] : ( ~ (ordered_pair(v3, v8) = v9) | ? [v10] : ( ~ (v10 = 0) & in(v9, v0) = v10)) | ( ~ (v4 = 0) & in(v3, v2) = v4)) & ((v7 = 0 & ordered_pair(v3, v5) = v6 & in(v6, v0) = 0) | (v4 = 0 & in(v3, v2) = 0))))))
% 13.38/3.86 | (80) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v0, v1) = v2) | ? [v3] : ((v3 = 0 & empty(v1) = 0) | ( ~ (v3 = 0) & element(v0, v1) = v3)))
% 13.38/3.86 | (81) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0))
% 13.38/3.86 | (82) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1))
% 13.38/3.86 | (83) empty(all_0_2_2) = 0
% 13.38/3.86 | (84) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = 0 | ~ (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v4) = v5) | ~ (in(v2, v1) = v3) | ? [v6] : (( ~ (v6 = 0) & relation(v0) = v6) | ( ~ (v6 = 0) & in(v5, v0) = v6)))
% 13.38/3.86 | (85) empty(all_0_4_4) = all_0_3_3
% 13.38/3.87 | (86) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 13.38/3.87 | (87) ? [v0] : ? [v1] : ? [v2] : unordered_pair(v1, v0) = v2
% 13.38/3.87 | (88) empty(all_0_1_1) = 0
% 13.38/3.87 |
% 13.38/3.87 | Instantiating formula (60) with all_0_6_6, all_0_7_7, all_0_8_8 and discharging atoms subset(all_0_8_8, all_0_7_7) = all_0_6_6, yields:
% 13.38/3.87 | (89) all_0_6_6 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_7_7) = v1 & in(v0, all_0_8_8) = 0)
% 13.38/3.87 |
% 13.38/3.87 | Instantiating formula (46) with all_0_9_9, all_0_10_10, all_0_11_11 and discharging atoms relation_rng_restriction(all_0_11_11, all_0_10_10) = all_0_9_9, yields:
% 13.38/3.87 | (90) ? [v0] : ((v0 = 0 & relation(all_0_9_9) = 0) | ( ~ (v0 = 0) & relation(all_0_10_10) = v0))
% 13.38/3.87 |
% 13.38/3.87 | Instantiating formula (79) with all_0_10_10 and discharging atoms relation(all_0_10_10) = 0, yields:
% 13.38/3.87 | (91) ? [v0] : (relation_dom(all_0_10_10) = v0 & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = 0 | ~ (ordered_pair(v1, v3) = v4) | ~ (in(v1, v0) = v2) | ? [v5] : ( ~ (v5 = 0) & in(v4, all_0_10_10) = v5)) & ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ? [v3] : (ordered_pair(v1, v2) = v3 & in(v3, all_0_10_10) = 0)) & ? [v1] : (v1 = v0 | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (( ! [v7] : ! [v8] : ( ~ (ordered_pair(v2, v7) = v8) | ? [v9] : ( ~ (v9 = 0) & in(v8, all_0_10_10) = v9)) | ( ~ (v3 = 0) & in(v2, v1) = v3)) & ((v6 = 0 & ordered_pair(v2, v4) = v5 & in(v5, all_0_10_10) = 0) | (v3 = 0 & in(v2, v1) = 0)))))
% 13.87/3.87 |
% 13.87/3.87 | Instantiating (90) with all_49_0_57 yields:
% 13.87/3.87 | (92) (all_49_0_57 = 0 & relation(all_0_9_9) = 0) | ( ~ (all_49_0_57 = 0) & relation(all_0_10_10) = all_49_0_57)
% 13.87/3.87 |
% 13.87/3.87 | Instantiating (91) with all_63_0_73 yields:
% 13.87/3.87 | (93) relation_dom(all_0_10_10) = all_63_0_73 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = 0 | ~ (ordered_pair(v0, v2) = v3) | ~ (in(v0, all_63_0_73) = v1) | ? [v4] : ( ~ (v4 = 0) & in(v3, all_0_10_10) = v4)) & ! [v0] : ( ~ (in(v0, all_63_0_73) = 0) | ? [v1] : ? [v2] : (ordered_pair(v0, v1) = v2 & in(v2, all_0_10_10) = 0)) & ? [v0] : (v0 = all_63_0_73 | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (( ! [v6] : ! [v7] : ( ~ (ordered_pair(v1, v6) = v7) | ? [v8] : ( ~ (v8 = 0) & in(v7, all_0_10_10) = v8)) | ( ~ (v2 = 0) & in(v1, v0) = v2)) & ((v5 = 0 & ordered_pair(v1, v3) = v4 & in(v4, all_0_10_10) = 0) | (v2 = 0 & in(v1, v0) = 0))))
% 13.87/3.88 |
% 13.87/3.88 | Applying alpha-rule on (93) yields:
% 13.87/3.88 | (94) relation_dom(all_0_10_10) = all_63_0_73
% 13.87/3.88 | (95) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = 0 | ~ (ordered_pair(v0, v2) = v3) | ~ (in(v0, all_63_0_73) = v1) | ? [v4] : ( ~ (v4 = 0) & in(v3, all_0_10_10) = v4))
% 13.87/3.88 | (96) ! [v0] : ( ~ (in(v0, all_63_0_73) = 0) | ? [v1] : ? [v2] : (ordered_pair(v0, v1) = v2 & in(v2, all_0_10_10) = 0))
% 13.87/3.88 | (97) ? [v0] : (v0 = all_63_0_73 | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (( ! [v6] : ! [v7] : ( ~ (ordered_pair(v1, v6) = v7) | ? [v8] : ( ~ (v8 = 0) & in(v7, all_0_10_10) = v8)) | ( ~ (v2 = 0) & in(v1, v0) = v2)) & ((v5 = 0 & ordered_pair(v1, v3) = v4 & in(v4, all_0_10_10) = 0) | (v2 = 0 & in(v1, v0) = 0))))
% 13.87/3.88 |
% 13.87/3.88 +-Applying beta-rule and splitting (89), into two cases.
% 13.87/3.88 |-Branch one:
% 13.87/3.88 | (98) all_0_6_6 = 0
% 13.87/3.88 |
% 13.87/3.88 | Equations (98) can reduce 40 to:
% 13.87/3.88 | (99) $false
% 13.87/3.88 |
% 13.87/3.88 |-The branch is then unsatisfiable
% 13.87/3.88 |-Branch two:
% 13.87/3.88 | (40) ~ (all_0_6_6 = 0)
% 13.87/3.88 | (101) ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_7_7) = v1 & in(v0, all_0_8_8) = 0)
% 13.87/3.88 |
% 13.87/3.88 | Instantiating (101) with all_85_0_78, all_85_1_79 yields:
% 13.87/3.88 | (102) ~ (all_85_0_78 = 0) & in(all_85_1_79, all_0_7_7) = all_85_0_78 & in(all_85_1_79, all_0_8_8) = 0
% 13.87/3.88 |
% 13.87/3.88 | Applying alpha-rule on (102) yields:
% 13.87/3.88 | (103) ~ (all_85_0_78 = 0)
% 13.87/3.88 | (104) in(all_85_1_79, all_0_7_7) = all_85_0_78
% 13.87/3.88 | (105) in(all_85_1_79, all_0_8_8) = 0
% 13.87/3.88 |
% 13.87/3.88 +-Applying beta-rule and splitting (92), into two cases.
% 13.87/3.88 |-Branch one:
% 13.87/3.88 | (106) all_49_0_57 = 0 & relation(all_0_9_9) = 0
% 13.87/3.88 |
% 13.87/3.88 | Applying alpha-rule on (106) yields:
% 13.87/3.88 | (107) all_49_0_57 = 0
% 13.87/3.88 | (108) relation(all_0_9_9) = 0
% 13.87/3.89 |
% 13.87/3.89 | Instantiating formula (38) with all_0_10_10, all_63_0_73, all_0_7_7 and discharging atoms relation_dom(all_0_10_10) = all_63_0_73, relation_dom(all_0_10_10) = all_0_7_7, yields:
% 13.87/3.89 | (109) all_63_0_73 = all_0_7_7
% 13.87/3.89 |
% 13.87/3.89 | From (109) and (94) follows:
% 13.87/3.89 | (20) relation_dom(all_0_10_10) = all_0_7_7
% 13.87/3.89 |
% 13.87/3.89 | Instantiating formula (80) with all_85_0_78, all_0_7_7, all_85_1_79 and discharging atoms in(all_85_1_79, all_0_7_7) = all_85_0_78, yields:
% 13.87/3.89 | (111) all_85_0_78 = 0 | ? [v0] : ((v0 = 0 & empty(all_0_7_7) = 0) | ( ~ (v0 = 0) & element(all_85_1_79, all_0_7_7) = v0))
% 13.87/3.89 |
% 13.87/3.89 | Instantiating formula (44) with all_85_1_79, all_0_8_8, all_0_9_9 and discharging atoms relation_dom(all_0_9_9) = all_0_8_8, in(all_85_1_79, all_0_8_8) = 0, yields:
% 13.87/3.89 | (112) ? [v0] : ? [v1] : ? [v2] : ((v2 = 0 & ordered_pair(all_85_1_79, v0) = v1 & in(v1, all_0_9_9) = 0) | ( ~ (v0 = 0) & relation(all_0_9_9) = v0))
% 13.87/3.89 |
% 13.87/3.89 | Instantiating (112) with all_112_0_86, all_112_1_87, all_112_2_88 yields:
% 13.87/3.89 | (113) (all_112_0_86 = 0 & ordered_pair(all_85_1_79, all_112_2_88) = all_112_1_87 & in(all_112_1_87, all_0_9_9) = 0) | ( ~ (all_112_2_88 = 0) & relation(all_0_9_9) = all_112_2_88)
% 13.87/3.89 |
% 13.87/3.89 +-Applying beta-rule and splitting (113), into two cases.
% 13.87/3.89 |-Branch one:
% 13.87/3.89 | (114) all_112_0_86 = 0 & ordered_pair(all_85_1_79, all_112_2_88) = all_112_1_87 & in(all_112_1_87, all_0_9_9) = 0
% 13.87/3.89 |
% 13.87/3.89 | Applying alpha-rule on (114) yields:
% 13.87/3.89 | (115) all_112_0_86 = 0
% 13.87/3.89 | (116) ordered_pair(all_85_1_79, all_112_2_88) = all_112_1_87
% 13.87/3.89 | (117) in(all_112_1_87, all_0_9_9) = 0
% 13.87/3.89 |
% 13.87/3.89 +-Applying beta-rule and splitting (111), into two cases.
% 13.87/3.89 |-Branch one:
% 13.87/3.89 | (118) all_85_0_78 = 0
% 13.87/3.89 |
% 13.87/3.89 | Equations (118) can reduce 103 to:
% 13.87/3.89 | (99) $false
% 13.87/3.89 |
% 13.87/3.89 |-The branch is then unsatisfiable
% 13.87/3.89 |-Branch two:
% 13.87/3.89 | (103) ~ (all_85_0_78 = 0)
% 13.87/3.89 | (121) ? [v0] : ((v0 = 0 & empty(all_0_7_7) = 0) | ( ~ (v0 = 0) & element(all_85_1_79, all_0_7_7) = v0))
% 13.87/3.89 |
% 13.87/3.89 | Instantiating formula (84) with all_112_1_87, all_112_2_88, all_85_0_78, all_85_1_79, all_0_7_7, all_0_10_10 and discharging atoms relation_dom(all_0_10_10) = all_0_7_7, ordered_pair(all_85_1_79, all_112_2_88) = all_112_1_87, in(all_85_1_79, all_0_7_7) = all_85_0_78, yields:
% 13.87/3.89 | (122) all_85_0_78 = 0 | ? [v0] : (( ~ (v0 = 0) & relation(all_0_10_10) = v0) | ( ~ (v0 = 0) & in(all_112_1_87, all_0_10_10) = v0))
% 13.87/3.89 |
% 13.87/3.89 | Instantiating formula (78) with all_112_1_87, all_112_2_88, all_85_1_79, all_0_9_9, all_0_10_10, all_0_11_11 and discharging atoms relation_rng_restriction(all_0_11_11, all_0_10_10) = all_0_9_9, ordered_pair(all_85_1_79, all_112_2_88) = all_112_1_87, relation(all_0_9_9) = 0, yields:
% 13.87/3.89 | (123) ? [v0] : ? [v1] : ((v1 = 0 & v0 = 0 & in(all_112_1_87, all_0_10_10) = 0 & in(all_112_2_88, all_0_11_11) = 0) | ( ~ (v0 = 0) & relation(all_0_10_10) = v0) | ( ~ (v0 = 0) & in(all_112_1_87, all_0_9_9) = v0))
% 13.87/3.89 |
% 13.87/3.89 | Instantiating formula (95) with all_112_1_87, all_112_2_88, all_85_0_78, all_85_1_79 and discharging atoms ordered_pair(all_85_1_79, all_112_2_88) = all_112_1_87, yields:
% 13.87/3.89 | (124) all_85_0_78 = 0 | ~ (in(all_85_1_79, all_63_0_73) = all_85_0_78) | ? [v0] : ( ~ (v0 = 0) & in(all_112_1_87, all_0_10_10) = v0)
% 13.87/3.89 |
% 13.87/3.89 | Instantiating (123) with all_150_0_100, all_150_1_101 yields:
% 13.98/3.89 | (125) (all_150_0_100 = 0 & all_150_1_101 = 0 & in(all_112_1_87, all_0_10_10) = 0 & in(all_112_2_88, all_0_11_11) = 0) | ( ~ (all_150_1_101 = 0) & relation(all_0_10_10) = all_150_1_101) | ( ~ (all_150_1_101 = 0) & in(all_112_1_87, all_0_9_9) = all_150_1_101)
% 13.98/3.90 |
% 13.98/3.90 +-Applying beta-rule and splitting (125), into two cases.
% 13.98/3.90 |-Branch one:
% 13.98/3.90 | (126) (all_150_0_100 = 0 & all_150_1_101 = 0 & in(all_112_1_87, all_0_10_10) = 0 & in(all_112_2_88, all_0_11_11) = 0) | ( ~ (all_150_1_101 = 0) & relation(all_0_10_10) = all_150_1_101)
% 13.98/3.90 |
% 13.98/3.90 +-Applying beta-rule and splitting (126), into two cases.
% 13.98/3.90 |-Branch one:
% 13.98/3.90 | (127) all_150_0_100 = 0 & all_150_1_101 = 0 & in(all_112_1_87, all_0_10_10) = 0 & in(all_112_2_88, all_0_11_11) = 0
% 13.98/3.90 |
% 13.98/3.90 | Applying alpha-rule on (127) yields:
% 13.98/3.90 | (128) all_150_0_100 = 0
% 13.98/3.90 | (129) all_150_1_101 = 0
% 13.98/3.90 | (130) in(all_112_1_87, all_0_10_10) = 0
% 13.98/3.90 | (131) in(all_112_2_88, all_0_11_11) = 0
% 13.98/3.90 |
% 13.98/3.90 +-Applying beta-rule and splitting (124), into two cases.
% 13.98/3.90 |-Branch one:
% 13.98/3.90 | (132) ~ (in(all_85_1_79, all_63_0_73) = all_85_0_78)
% 13.98/3.90 |
% 13.98/3.90 | From (109) and (132) follows:
% 13.98/3.90 | (133) ~ (in(all_85_1_79, all_0_7_7) = all_85_0_78)
% 13.98/3.90 |
% 13.98/3.90 | Using (104) and (133) yields:
% 13.98/3.90 | (134) $false
% 13.98/3.90 |
% 13.98/3.90 |-The branch is then unsatisfiable
% 13.98/3.90 |-Branch two:
% 13.98/3.90 | (135) in(all_85_1_79, all_63_0_73) = all_85_0_78
% 13.98/3.90 | (136) all_85_0_78 = 0 | ? [v0] : ( ~ (v0 = 0) & in(all_112_1_87, all_0_10_10) = v0)
% 13.98/3.90 |
% 13.98/3.90 +-Applying beta-rule and splitting (122), into two cases.
% 13.98/3.90 |-Branch one:
% 13.98/3.90 | (118) all_85_0_78 = 0
% 13.98/3.90 |
% 13.98/3.90 | Equations (118) can reduce 103 to:
% 13.98/3.90 | (99) $false
% 13.98/3.90 |
% 13.98/3.90 |-The branch is then unsatisfiable
% 13.98/3.90 |-Branch two:
% 13.98/3.90 | (103) ~ (all_85_0_78 = 0)
% 13.98/3.90 | (140) ? [v0] : (( ~ (v0 = 0) & relation(all_0_10_10) = v0) | ( ~ (v0 = 0) & in(all_112_1_87, all_0_10_10) = v0))
% 13.98/3.90 |
% 13.98/3.90 | Instantiating (140) with all_174_0_107 yields:
% 13.98/3.90 | (141) ( ~ (all_174_0_107 = 0) & relation(all_0_10_10) = all_174_0_107) | ( ~ (all_174_0_107 = 0) & in(all_112_1_87, all_0_10_10) = all_174_0_107)
% 13.98/3.90 |
% 13.98/3.90 +-Applying beta-rule and splitting (136), into two cases.
% 13.98/3.90 |-Branch one:
% 13.98/3.90 | (118) all_85_0_78 = 0
% 13.98/3.90 |
% 13.98/3.90 | Equations (118) can reduce 103 to:
% 13.98/3.90 | (99) $false
% 13.98/3.90 |
% 13.98/3.90 |-The branch is then unsatisfiable
% 13.98/3.90 |-Branch two:
% 13.98/3.90 | (103) ~ (all_85_0_78 = 0)
% 13.98/3.90 | (145) ? [v0] : ( ~ (v0 = 0) & in(all_112_1_87, all_0_10_10) = v0)
% 13.98/3.90 |
% 13.98/3.90 | Instantiating (145) with all_187_0_110 yields:
% 13.98/3.90 | (146) ~ (all_187_0_110 = 0) & in(all_112_1_87, all_0_10_10) = all_187_0_110
% 13.98/3.90 |
% 13.98/3.90 | Applying alpha-rule on (146) yields:
% 13.98/3.90 | (147) ~ (all_187_0_110 = 0)
% 13.98/3.90 | (148) in(all_112_1_87, all_0_10_10) = all_187_0_110
% 13.98/3.90 |
% 13.98/3.90 +-Applying beta-rule and splitting (141), into two cases.
% 13.98/3.90 |-Branch one:
% 13.98/3.90 | (149) ~ (all_174_0_107 = 0) & relation(all_0_10_10) = all_174_0_107
% 13.98/3.90 |
% 13.98/3.90 | Applying alpha-rule on (149) yields:
% 13.98/3.90 | (150) ~ (all_174_0_107 = 0)
% 13.98/3.90 | (151) relation(all_0_10_10) = all_174_0_107
% 13.98/3.90 |
% 13.98/3.90 | Instantiating formula (81) with all_0_10_10, all_174_0_107, 0 and discharging atoms relation(all_0_10_10) = all_174_0_107, relation(all_0_10_10) = 0, yields:
% 13.98/3.90 | (152) all_174_0_107 = 0
% 13.98/3.90 |
% 13.98/3.90 | Equations (152) can reduce 150 to:
% 13.98/3.90 | (99) $false
% 13.98/3.90 |
% 13.98/3.90 |-The branch is then unsatisfiable
% 13.98/3.90 |-Branch two:
% 13.98/3.90 | (154) ~ (all_174_0_107 = 0) & in(all_112_1_87, all_0_10_10) = all_174_0_107
% 13.98/3.90 |
% 13.98/3.90 | Applying alpha-rule on (154) yields:
% 13.98/3.90 | (150) ~ (all_174_0_107 = 0)
% 13.98/3.90 | (156) in(all_112_1_87, all_0_10_10) = all_174_0_107
% 13.98/3.90 |
% 13.98/3.90 | Instantiating formula (32) with all_112_1_87, all_0_10_10, all_174_0_107, all_187_0_110 and discharging atoms in(all_112_1_87, all_0_10_10) = all_187_0_110, in(all_112_1_87, all_0_10_10) = all_174_0_107, yields:
% 13.98/3.90 | (157) all_187_0_110 = all_174_0_107
% 13.98/3.90 |
% 13.98/3.90 | Instantiating formula (32) with all_112_1_87, all_0_10_10, 0, all_187_0_110 and discharging atoms in(all_112_1_87, all_0_10_10) = all_187_0_110, in(all_112_1_87, all_0_10_10) = 0, yields:
% 13.98/3.90 | (158) all_187_0_110 = 0
% 13.98/3.90 |
% 13.98/3.91 | Combining equations (157,158) yields a new equation:
% 13.98/3.91 | (159) all_174_0_107 = 0
% 13.98/3.91 |
% 13.98/3.91 | Simplifying 159 yields:
% 13.98/3.91 | (152) all_174_0_107 = 0
% 13.98/3.91 |
% 13.98/3.91 | Equations (152) can reduce 150 to:
% 13.98/3.91 | (99) $false
% 13.98/3.91 |
% 13.98/3.91 |-The branch is then unsatisfiable
% 13.98/3.91 |-Branch two:
% 13.98/3.91 | (162) ~ (all_150_1_101 = 0) & relation(all_0_10_10) = all_150_1_101
% 13.98/3.91 |
% 13.98/3.91 | Applying alpha-rule on (162) yields:
% 13.98/3.91 | (163) ~ (all_150_1_101 = 0)
% 13.98/3.91 | (164) relation(all_0_10_10) = all_150_1_101
% 13.98/3.91 |
% 13.98/3.91 | Instantiating formula (81) with all_0_10_10, all_150_1_101, 0 and discharging atoms relation(all_0_10_10) = all_150_1_101, relation(all_0_10_10) = 0, yields:
% 13.98/3.91 | (129) all_150_1_101 = 0
% 13.98/3.91 |
% 13.98/3.91 | Equations (129) can reduce 163 to:
% 13.98/3.91 | (99) $false
% 13.98/3.91 |
% 13.98/3.91 |-The branch is then unsatisfiable
% 13.98/3.91 |-Branch two:
% 13.98/3.91 | (167) ~ (all_150_1_101 = 0) & in(all_112_1_87, all_0_9_9) = all_150_1_101
% 13.98/3.91 |
% 13.98/3.91 | Applying alpha-rule on (167) yields:
% 13.98/3.91 | (163) ~ (all_150_1_101 = 0)
% 13.98/3.91 | (169) in(all_112_1_87, all_0_9_9) = all_150_1_101
% 13.98/3.91 |
% 13.98/3.91 | Instantiating formula (32) with all_112_1_87, all_0_9_9, all_150_1_101, 0 and discharging atoms in(all_112_1_87, all_0_9_9) = all_150_1_101, in(all_112_1_87, all_0_9_9) = 0, yields:
% 13.98/3.91 | (129) all_150_1_101 = 0
% 13.98/3.91 |
% 13.98/3.91 | Equations (129) can reduce 163 to:
% 13.98/3.91 | (99) $false
% 13.98/3.91 |
% 13.98/3.91 |-The branch is then unsatisfiable
% 13.98/3.91 |-Branch two:
% 13.98/3.91 | (172) ~ (all_112_2_88 = 0) & relation(all_0_9_9) = all_112_2_88
% 13.98/3.91 |
% 13.98/3.91 | Applying alpha-rule on (172) yields:
% 13.98/3.91 | (173) ~ (all_112_2_88 = 0)
% 13.98/3.91 | (174) relation(all_0_9_9) = all_112_2_88
% 13.98/3.91 |
% 13.98/3.91 | Instantiating formula (81) with all_0_9_9, all_112_2_88, 0 and discharging atoms relation(all_0_9_9) = all_112_2_88, relation(all_0_9_9) = 0, yields:
% 13.98/3.91 | (175) all_112_2_88 = 0
% 13.98/3.91 |
% 13.98/3.91 | Equations (175) can reduce 173 to:
% 13.98/3.91 | (99) $false
% 13.98/3.91 |
% 13.98/3.91 |-The branch is then unsatisfiable
% 13.98/3.91 |-Branch two:
% 13.98/3.91 | (177) ~ (all_49_0_57 = 0) & relation(all_0_10_10) = all_49_0_57
% 13.98/3.91 |
% 13.98/3.91 | Applying alpha-rule on (177) yields:
% 13.98/3.91 | (178) ~ (all_49_0_57 = 0)
% 13.98/3.91 | (179) relation(all_0_10_10) = all_49_0_57
% 13.98/3.91 |
% 13.98/3.91 | Instantiating formula (81) with all_0_10_10, all_49_0_57, 0 and discharging atoms relation(all_0_10_10) = all_49_0_57, relation(all_0_10_10) = 0, yields:
% 13.98/3.91 | (107) all_49_0_57 = 0
% 13.98/3.91 |
% 13.98/3.91 | Equations (107) can reduce 178 to:
% 13.98/3.91 | (99) $false
% 13.98/3.91 |
% 13.98/3.91 |-The branch is then unsatisfiable
% 13.98/3.91 % SZS output end Proof for theBenchmark
% 13.98/3.91
% 13.98/3.91 3313ms
%------------------------------------------------------------------------------