TSTP Solution File: SEU252+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU252+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n021.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 08:48:10 EDT 2022
% Result : Theorem 23.73s 6.51s
% Output : Proof 27.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU252+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n021.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sat Jun 18 22:07:32 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/sandbox2/benchmark/theBenchmark.p ...
% 0.64/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.47/0.93 Prover 0: Preprocessing ...
% 2.16/1.18 Prover 0: Warning: ignoring some quantifiers
% 2.33/1.21 Prover 0: Constructing countermodel ...
% 21.10/5.92 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 21.12/5.95 Prover 1: Preprocessing ...
% 21.53/6.03 Prover 1: Warning: ignoring some quantifiers
% 21.53/6.04 Prover 1: Constructing countermodel ...
% 22.46/6.22 Prover 1: gave up
% 22.46/6.22 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 22.46/6.24 Prover 2: Preprocessing ...
% 22.90/6.34 Prover 2: Warning: ignoring some quantifiers
% 22.90/6.35 Prover 2: Constructing countermodel ...
% 23.73/6.50 Prover 2: proved (282ms)
% 23.73/6.51 Prover 0: stopped
% 23.73/6.51
% 23.73/6.51 No countermodel exists, formula is valid
% 23.73/6.51 % SZS status Theorem for theBenchmark
% 23.73/6.51
% 23.73/6.51 Generating proof ... Warning: ignoring some quantifiers
% 26.77/7.28 found it (size 106)
% 26.77/7.28
% 26.77/7.28 % SZS output start Proof for theBenchmark
% 26.77/7.28 Assumed formulas after preprocessing and simplification:
% 26.77/7.28 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ( ~ (v6 = 0) & ~ (v3 = 0) & reflexive(v2) = v3 & reflexive(v1) = 0 & relation_restriction(v1, v0) = v2 & one_to_one(v4) = 0 & relation(v9) = 0 & relation(v7) = 0 & relation(v4) = 0 & relation(v1) = 0 & function(v9) = 0 & function(v7) = 0 & function(v4) = 0 & empty(v8) = 0 & empty(v7) = 0 & empty(v5) = v6 & empty(empty_set) = 0 & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (cartesian_product2(v12, v13) = v15) | ~ (ordered_pair(v10, v11) = v14) | ~ (in(v14, v15) = v16) | ? [v17] : (( ~ (v17 = 0) & in(v11, v13) = v17) | ( ~ (v17 = 0) & in(v10, v12) = v17))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (cartesian_product2(v12, v13) = v15) | ~ (ordered_pair(v10, v11) = v14) | ~ (in(v14, v15) = 0) | (in(v11, v13) = 0 & in(v10, v12) = 0)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (relation_restriction(v12, v11) = v13) | ~ (relation_field(v13) = v14) | ~ (in(v10, v14) = 0) | ? [v15] : ? [v16] : ? [v17] : ((v17 = 0 & v16 = 0 & relation_field(v12) = v15 & in(v10, v15) = 0 & in(v10, v11) = 0) | ( ~ (v15 = 0) & relation(v12) = v15))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (relation_restriction(v12, v11) = v13) | ~ (in(v10, v13) = v14) | ? [v15] : ? [v16] : ? [v17] : (( ~ (v15 = 0) & relation(v12) = v15) | (( ~ (v14 = 0) | (v17 = 0 & v15 = 0 & cartesian_product2(v11, v11) = v16 & in(v10, v16) = 0 & in(v10, v12) = 0)) & (v14 = 0 | ( ~ (v17 = 0) & cartesian_product2(v11, v11) = v16 & in(v10, v16) = v17) | ( ~ (v15 = 0) & in(v10, v12) = v15))))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (element(v13, v12) = v11) | ~ (element(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (cartesian_product2(v13, v12) = v11) | ~ (cartesian_product2(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (relation_restriction(v13, v12) = v11) | ~ (relation_restriction(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (ordered_pair(v13, v12) = v11) | ~ (ordered_pair(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (set_intersection2(v13, v12) = v11) | ~ (set_intersection2(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (set_union2(v13, v12) = v11) | ~ (set_union2(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (unordered_pair(v13, v12) = v11) | ~ (unordered_pair(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (in(v13, v12) = v11) | ~ (in(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (element(v10, v11) = v12) | ? [v13] : ( ~ (v13 = 0) & in(v10, v11) = v13)) & ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (in(v10, v11) = v12) | ? [v13] : ((v13 = 0 & empty(v11) = 0) | ( ~ (v13 = 0) & element(v10, v11) = v13))) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (reflexive(v12) = v11) | ~ (reflexive(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (relation_field(v12) = v11) | ~ (relation_field(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (relation_dom(v12) = v11) | ~ (relation_dom(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (relation_rng(v12) = v11) | ~ (relation_rng(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (singleton(v12) = v11) | ~ (singleton(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (one_to_one(v12) = v11) | ~ (one_to_one(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (relation(v12) = v11) | ~ (relation(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (function(v12) = v11) | ~ (function(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (empty(v12) = v11) | ~ (empty(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (cartesian_product2(v11, v11) = v12) | ~ (relation(v10) = 0) | ? [v13] : (relation_restriction(v10, v11) = v13 & set_intersection2(v10, v12) = v13)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (relation_restriction(v10, v11) = v12) | ~ (relation(v10) = 0) | ? [v13] : (cartesian_product2(v11, v11) = v13 & set_intersection2(v10, v13) = v12)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (relation_restriction(v10, v11) = v12) | ? [v13] : ((v13 = 0 & relation(v12) = 0) | ( ~ (v13 = 0) & relation(v10) = v13))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (ordered_pair(v10, v11) = v12) | ? [v13] : ? [v14] : (singleton(v10) = v14 & unordered_pair(v13, v14) = v12 & unordered_pair(v10, v11) = v13)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (ordered_pair(v10, v11) = v12) | ? [v13] : ( ~ (v13 = 0) & empty(v12) = v13)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (set_intersection2(v11, v10) = v12) | set_intersection2(v10, v11) = v12) & ! [v10] : ! [v11] : ! [v12] : ( ~ (set_intersection2(v10, v11) = v12) | set_intersection2(v11, v10) = v12) & ! [v10] : ! [v11] : ! [v12] : ( ~ (set_union2(v11, v10) = v12) | set_union2(v10, v11) = v12) & ! [v10] : ! [v11] : ! [v12] : ( ~ (set_union2(v11, v10) = v12) | ? [v13] : ((v13 = 0 & empty(v10) = 0) | ( ~ (v13 = 0) & empty(v12) = v13))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (set_union2(v10, v11) = v12) | set_union2(v11, v10) = v12) & ! [v10] : ! [v11] : ! [v12] : ( ~ (set_union2(v10, v11) = v12) | ? [v13] : ((v13 = 0 & empty(v10) = 0) | ( ~ (v13 = 0) & empty(v12) = v13))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (unordered_pair(v11, v10) = v12) | unordered_pair(v10, v11) = v12) & ! [v10] : ! [v11] : ! [v12] : ( ~ (unordered_pair(v10, v11) = v12) | unordered_pair(v11, v10) = v12) & ! [v10] : ! [v11] : ! [v12] : ( ~ (unordered_pair(v10, v11) = v12) | ? [v13] : ? [v14] : (ordered_pair(v10, v11) = v13 & singleton(v10) = v14 & unordered_pair(v12, v14) = v13)) & ! [v10] : ! [v11] : (v11 = v10 | ~ (set_intersection2(v10, v10) = v11)) & ! [v10] : ! [v11] : (v11 = v10 | ~ (set_union2(v10, v10) = v11)) & ! [v10] : ! [v11] : (v11 = v10 | ~ (set_union2(v10, empty_set) = v11)) & ! [v10] : ! [v11] : (v11 = v10 | ~ (empty(v11) = 0) | ~ (empty(v10) = 0)) & ! [v10] : ! [v11] : (v11 = empty_set | ~ (set_intersection2(v10, empty_set) = v11)) & ! [v10] : ! [v11] : (v11 = 0 | ~ (function(v10) = v11) | ? [v12] : ( ~ (v12 = 0) & empty(v10) = v12)) & ! [v10] : ! [v11] : ( ~ (reflexive(v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : (( ~ (v12 = 0) & relation(v10) = v12) | (( ~ (v11 = 0) | (relation_field(v10) = v12 & ! [v17] : ! [v18] : ( ~ (ordered_pair(v17, v17) = v18) | ? [v19] : ((v19 = 0 & in(v18, v10) = 0) | ( ~ (v19 = 0) & in(v17, v12) = v19))) & ! [v17] : ( ~ (in(v17, v12) = 0) | ? [v18] : (ordered_pair(v17, v17) = v18 & in(v18, v10) = 0)))) & (v11 = 0 | (v14 = 0 & ~ (v16 = 0) & relation_field(v10) = v12 & ordered_pair(v13, v13) = v15 & in(v15, v10) = v16 & in(v13, v12) = 0))))) & ! [v10] : ! [v11] : ( ~ (element(v10, v11) = 0) | ? [v12] : ((v12 = 0 & empty(v11) = 0) | (v12 = 0 & in(v10, v11) = 0))) & ! [v10] : ! [v11] : ( ~ (relation_field(v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : (( ~ (v12 = 0) & relation(v10) = v12) | (((v14 = 0 & ~ (v16 = 0) & ordered_pair(v13, v13) = v15 & in(v15, v10) = v16 & in(v13, v11) = 0) | (v12 = 0 & reflexive(v10) = 0)) & (( ~ (v12 = 0) & reflexive(v10) = v12) | ( ! [v17] : ! [v18] : ( ~ (ordered_pair(v17, v17) = v18) | ? [v19] : ((v19 = 0 & in(v18, v10) = 0) | ( ~ (v19 = 0) & in(v17, v11) = v19))) & ! [v17] : ( ~ (in(v17, v11) = 0) | ? [v18] : (ordered_pair(v17, v17) = v18 & in(v18, v10) = 0))))))) & ! [v10] : ! [v11] : ( ~ (relation_field(v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ((v14 = v11 & relation_dom(v10) = v12 & relation_rng(v10) = v13 & set_union2(v12, v13) = v11) | ( ~ (v12 = 0) & relation(v10) = v12))) & ! [v10] : ! [v11] : ( ~ (relation_dom(v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ((v14 = v12 & relation_field(v10) = v12 & relation_rng(v10) = v13 & set_union2(v11, v13) = v12) | ( ~ (v12 = 0) & relation(v10) = v12))) & ! [v10] : ! [v11] : ( ~ (relation_rng(v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ((v14 = v12 & relation_field(v10) = v12 & relation_dom(v10) = v13 & set_union2(v13, v11) = v12) | ( ~ (v12 = 0) & relation(v10) = v12))) & ! [v10] : ! [v11] : ( ~ (one_to_one(v10) = v11) | ? [v12] : ? [v13] : ((v13 = 0 & v12 = 0 & v11 = 0 & relation(v10) = 0 & function(v10) = 0) | ( ~ (v12 = 0) & relation(v10) = v12) | ( ~ (v12 = 0) & function(v10) = v12) | ( ~ (v12 = 0) & empty(v10) = v12))) & ! [v10] : ! [v11] : ( ~ (in(v11, v10) = 0) | ? [v12] : ( ~ (v12 = 0) & in(v10, v11) = v12)) & ! [v10] : ! [v11] : ( ~ (in(v10, v11) = 0) | element(v10, v11) = 0) & ! [v10] : ! [v11] : ( ~ (in(v10, v11) = 0) | ? [v12] : ( ~ (v12 = 0) & empty(v11) = v12)) & ! [v10] : ! [v11] : ( ~ (in(v10, v11) = 0) | ? [v12] : ( ~ (v12 = 0) & in(v11, v10) = v12)) & ! [v10] : (v10 = empty_set | ~ (empty(v10) = 0)) & ! [v10] : ( ~ (relation(v10) = 0) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : (((v14 = 0 & ~ (v16 = 0) & relation_field(v10) = v12 & ordered_pair(v13, v13) = v15 & in(v15, v10) = v16 & in(v13, v12) = 0) | (v11 = 0 & reflexive(v10) = 0)) & (( ~ (v11 = 0) & reflexive(v10) = v11) | (relation_field(v10) = v12 & ! [v17] : ! [v18] : ( ~ (ordered_pair(v17, v17) = v18) | ? [v19] : ((v19 = 0 & in(v18, v10) = 0) | ( ~ (v19 = 0) & in(v17, v12) = v19))) & ! [v17] : ( ~ (in(v17, v12) = 0) | ? [v18] : (ordered_pair(v17, v17) = v18 & in(v18, v10) = 0)))))) & ! [v10] : ( ~ (relation(v10) = 0) | ? [v11] : ? [v12] : ? [v13] : (relation_field(v10) = v11 & relation_dom(v10) = v12 & relation_rng(v10) = v13 & set_union2(v12, v13) = v11)) & ! [v10] : ( ~ (relation(v10) = 0) | ? [v11] : ? [v12] : ((v12 = 0 & v11 = 0 & one_to_one(v10) = 0 & function(v10) = 0) | ( ~ (v11 = 0) & function(v10) = v11) | ( ~ (v11 = 0) & empty(v10) = v11))) & ! [v10] : ( ~ (function(v10) = 0) | ? [v11] : ? [v12] : ((v12 = 0 & v11 = 0 & one_to_one(v10) = 0 & relation(v10) = 0) | ( ~ (v11 = 0) & relation(v10) = v11) | ( ~ (v11 = 0) & empty(v10) = v11))) & ! [v10] : ( ~ (empty(v10) = 0) | function(v10) = 0) & ! [v10] : ( ~ (empty(v10) = 0) | ? [v11] : ? [v12] : ? [v13] : ((v13 = 0 & v12 = 0 & v11 = 0 & one_to_one(v10) = 0 & relation(v10) = 0 & function(v10) = 0) | ( ~ (v11 = 0) & relation(v10) = v11) | ( ~ (v11 = 0) & function(v10) = v11))) & ? [v10] : ? [v11] : ? [v12] : element(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : cartesian_product2(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : relation_restriction(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : ordered_pair(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : set_intersection2(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : set_union2(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : unordered_pair(v11, v10) = v12 & ? [v10] : ? [v11] : ? [v12] : in(v11, v10) = v12 & ? [v10] : ? [v11] : reflexive(v10) = v11 & ? [v10] : ? [v11] : element(v11, v10) = 0 & ? [v10] : ? [v11] : relation_field(v10) = v11 & ? [v10] : ? [v11] : relation_dom(v10) = v11 & ? [v10] : ? [v11] : relation_rng(v10) = v11 & ? [v10] : ? [v11] : singleton(v10) = v11 & ? [v10] : ? [v11] : one_to_one(v10) = v11 & ? [v10] : ? [v11] : relation(v10) = v11 & ? [v10] : ? [v11] : function(v10) = v11 & ? [v10] : ? [v11] : empty(v10) = v11)
% 27.18/7.32 | 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 yields:
% 27.18/7.32 | (1) ~ (all_0_3_3 = 0) & ~ (all_0_6_6 = 0) & reflexive(all_0_7_7) = all_0_6_6 & reflexive(all_0_8_8) = 0 & relation_restriction(all_0_8_8, all_0_9_9) = all_0_7_7 & 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_8_8) = 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] : ! [v6] : (v6 = 0 | ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ (in(v4, v5) = v6) | ? [v7] : (( ~ (v7 = 0) & in(v1, v3) = v7) | ( ~ (v7 = 0) & in(v0, v2) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ (in(v4, v5) = 0) | (in(v1, v3) = 0 & in(v0, v2) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_restriction(v2, v1) = v3) | ~ (relation_field(v3) = v4) | ~ (in(v0, v4) = 0) | ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & relation_field(v2) = v5 & in(v0, v5) = 0 & in(v0, v1) = 0) | ( ~ (v5 = 0) & relation(v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_restriction(v2, v1) = v3) | ~ (in(v0, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : (( ~ (v5 = 0) & relation(v2) = v5) | (( ~ (v4 = 0) | (v7 = 0 & v5 = 0 & cartesian_product2(v1, v1) = v6 & in(v0, v6) = 0 & in(v0, v2) = 0)) & (v4 = 0 | ( ~ (v7 = 0) & cartesian_product2(v1, v1) = v6 & in(v0, v6) = v7) | ( ~ (v5 = 0) & in(v0, v2) = v5))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_restriction(v3, v2) = v1) | ~ (relation_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 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(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] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v0, v1) = v2) | ? [v3] : ((v3 = 0 & empty(v1) = 0) | ( ~ (v3 = 0) & element(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (reflexive(v2) = v1) | ~ (reflexive(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_field(v2) = v1) | ~ (relation_field(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(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] : ( ~ (cartesian_product2(v1, v1) = v2) | ~ (relation(v0) = 0) | ? [v3] : (relation_restriction(v0, v1) = v3 & set_intersection2(v0, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_restriction(v0, v1) = v2) | ~ (relation(v0) = 0) | ? [v3] : (cartesian_product2(v1, v1) = v3 & set_intersection2(v0, v3) = v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_restriction(v0, v1) = v2) | ? [v3] : ((v3 = 0 & relation(v2) = 0) | ( ~ (v3 = 0) & relation(v0) = 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] : ( ~ (set_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ? [v3] : ((v3 = 0 & empty(v0) = 0) | ( ~ (v3 = 0) & empty(v2) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : ((v3 = 0 & empty(v0) = 0) | ( ~ (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] : (ordered_pair(v0, v1) = v3 & singleton(v0) = v4 & unordered_pair(v2, v4) = v3)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)) & ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (function(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2)) & ! [v0] : ! [v1] : ( ~ (reflexive(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (( ~ (v2 = 0) & relation(v0) = v2) | (( ~ (v1 = 0) | (relation_field(v0) = v2 & ! [v7] : ! [v8] : ( ~ (ordered_pair(v7, v7) = v8) | ? [v9] : ((v9 = 0 & in(v8, v0) = 0) | ( ~ (v9 = 0) & in(v7, v2) = v9))) & ! [v7] : ( ~ (in(v7, v2) = 0) | ? [v8] : (ordered_pair(v7, v7) = v8 & in(v8, v0) = 0)))) & (v1 = 0 | (v4 = 0 & ~ (v6 = 0) & relation_field(v0) = v2 & ordered_pair(v3, v3) = v5 & in(v5, v0) = v6 & in(v3, v2) = 0))))) & ! [v0] : ! [v1] : ( ~ (element(v0, v1) = 0) | ? [v2] : ((v2 = 0 & empty(v1) = 0) | (v2 = 0 & in(v0, v1) = 0))) & ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (( ~ (v2 = 0) & relation(v0) = v2) | (((v4 = 0 & ~ (v6 = 0) & ordered_pair(v3, v3) = v5 & in(v5, v0) = v6 & in(v3, v1) = 0) | (v2 = 0 & reflexive(v0) = 0)) & (( ~ (v2 = 0) & reflexive(v0) = v2) | ( ! [v7] : ! [v8] : ( ~ (ordered_pair(v7, v7) = v8) | ? [v9] : ((v9 = 0 & in(v8, v0) = 0) | ( ~ (v9 = 0) & in(v7, v1) = v9))) & ! [v7] : ( ~ (in(v7, v1) = 0) | ? [v8] : (ordered_pair(v7, v7) = v8 & in(v8, v0) = 0))))))) & ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v1 & relation_dom(v0) = v2 & relation_rng(v0) = v3 & set_union2(v2, v3) = v1) | ( ~ (v2 = 0) & relation(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v2 & relation_field(v0) = v2 & relation_rng(v0) = v3 & set_union2(v1, v3) = v2) | ( ~ (v2 = 0) & relation(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v2 & relation_field(v0) = v2 & relation_dom(v0) = v3 & set_union2(v3, v1) = v2) | ( ~ (v2 = 0) & relation(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] : ( ~ (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] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (((v4 = 0 & ~ (v6 = 0) & relation_field(v0) = v2 & ordered_pair(v3, v3) = v5 & in(v5, v0) = v6 & in(v3, v2) = 0) | (v1 = 0 & reflexive(v0) = 0)) & (( ~ (v1 = 0) & reflexive(v0) = v1) | (relation_field(v0) = v2 & ! [v7] : ! [v8] : ( ~ (ordered_pair(v7, v7) = v8) | ? [v9] : ((v9 = 0 & in(v8, v0) = 0) | ( ~ (v9 = 0) & in(v7, v2) = v9))) & ! [v7] : ( ~ (in(v7, v2) = 0) | ? [v8] : (ordered_pair(v7, v7) = v8 & in(v8, v0) = 0)))))) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (relation_field(v0) = v1 & relation_dom(v0) = v2 & relation_rng(v0) = v3 & set_union2(v2, v3) = v1)) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ((v2 = 0 & v1 = 0 & one_to_one(v0) = 0 & function(v0) = 0) | ( ~ (v1 = 0) & function(v0) = v1) | ( ~ (v1 = 0) & empty(v0) = v1))) & ! [v0] : ( ~ (function(v0) = 0) | ? [v1] : ? [v2] : ((v2 = 0 & v1 = 0 & one_to_one(v0) = 0 & relation(v0) = 0) | ( ~ (v1 = 0) & relation(v0) = v1) | ( ~ (v1 = 0) & empty(v0) = v1))) & ! [v0] : ( ~ (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] : cartesian_product2(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : relation_restriction(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : ordered_pair(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : set_intersection2(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : set_union2(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : unordered_pair(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2 & ? [v0] : ? [v1] : reflexive(v0) = v1 & ? [v0] : ? [v1] : element(v1, v0) = 0 & ? [v0] : ? [v1] : relation_field(v0) = v1 & ? [v0] : ? [v1] : relation_dom(v0) = v1 & ? [v0] : ? [v1] : relation_rng(v0) = v1 & ? [v0] : ? [v1] : singleton(v0) = v1 & ? [v0] : ? [v1] : one_to_one(v0) = v1 & ? [v0] : ? [v1] : relation(v0) = v1 & ? [v0] : ? [v1] : function(v0) = v1 & ? [v0] : ? [v1] : empty(v0) = v1
% 27.18/7.33 |
% 27.18/7.33 | Applying alpha-rule on (1) yields:
% 27.18/7.33 | (2) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 27.18/7.33 | (3) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (reflexive(v2) = v1) | ~ (reflexive(v2) = v0))
% 27.18/7.33 | (4) ? [v0] : ? [v1] : function(v0) = v1
% 27.18/7.33 | (5) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2)
% 27.18/7.34 | (6) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2)
% 27.18/7.34 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ (in(v4, v5) = v6) | ? [v7] : (( ~ (v7 = 0) & in(v1, v3) = v7) | ( ~ (v7 = 0) & in(v0, v2) = v7)))
% 27.18/7.34 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : ((v3 = 0 & empty(v0) = 0) | ( ~ (v3 = 0) & empty(v2) = v3)))
% 27.18/7.34 | (9) ~ (all_0_3_3 = 0)
% 27.18/7.34 | (10) empty(all_0_2_2) = 0
% 27.18/7.34 | (11) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 27.18/7.34 | (12) relation(all_0_2_2) = 0
% 27.18/7.34 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_restriction(v2, v1) = v3) | ~ (relation_field(v3) = v4) | ~ (in(v0, v4) = 0) | ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & relation_field(v2) = v5 & in(v0, v5) = 0 & in(v0, v1) = 0) | ( ~ (v5 = 0) & relation(v2) = v5)))
% 27.18/7.34 | (14) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_field(v2) = v1) | ~ (relation_field(v2) = v0))
% 27.18/7.34 | (15) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v0, v1) = v2) | ? [v3] : ((v3 = 0 & empty(v1) = 0) | ( ~ (v3 = 0) & element(v0, v1) = v3)))
% 27.18/7.34 | (16) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2)
% 27.18/7.34 | (17) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2)
% 27.18/7.34 | (18) ? [v0] : ? [v1] : element(v1, v0) = 0
% 27.18/7.34 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0))
% 27.18/7.34 | (20) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1))
% 27.18/7.34 | (21) ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v1 & relation_dom(v0) = v2 & relation_rng(v0) = v3 & set_union2(v2, v3) = v1) | ( ~ (v2 = 0) & relation(v0) = v2)))
% 27.18/7.34 | (22) ! [v0] : ( ~ (empty(v0) = 0) | function(v0) = 0)
% 27.18/7.34 | (23) ! [v0] : ! [v1] : ( ~ (element(v0, v1) = 0) | ? [v2] : ((v2 = 0 & empty(v1) = 0) | (v2 = 0 & in(v0, v1) = 0)))
% 27.18/7.34 | (24) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0))
% 27.18/7.34 | (25) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (ordered_pair(v0, v1) = v3 & singleton(v0) = v4 & unordered_pair(v2, v4) = v3))
% 27.18/7.34 | (26) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0))
% 27.18/7.34 | (27) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ? [v3] : ((v3 = 0 & empty(v0) = 0) | ( ~ (v3 = 0) & empty(v2) = v3)))
% 27.18/7.34 | (28) ? [v0] : ? [v1] : empty(v0) = v1
% 27.18/7.34 | (29) relation_restriction(all_0_8_8, all_0_9_9) = all_0_7_7
% 27.18/7.34 | (30) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0))
% 27.18/7.34 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_restriction(v2, v1) = v3) | ~ (in(v0, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : (( ~ (v5 = 0) & relation(v2) = v5) | (( ~ (v4 = 0) | (v7 = 0 & v5 = 0 & cartesian_product2(v1, v1) = v6 & in(v0, v6) = 0 & in(v0, v2) = 0)) & (v4 = 0 | ( ~ (v7 = 0) & cartesian_product2(v1, v1) = v6 & in(v0, v6) = v7) | ( ~ (v5 = 0) & in(v0, v2) = v5)))))
% 27.18/7.34 | (32) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1))
% 27.18/7.34 | (33) one_to_one(all_0_5_5) = 0
% 27.18/7.34 | (34) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 27.18/7.34 | (35) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 27.18/7.34 | (36) ? [v0] : ? [v1] : reflexive(v0) = v1
% 27.18/7.34 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0))
% 27.18/7.34 | (38) ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2))
% 27.18/7.34 | (39) ? [v0] : ? [v1] : ? [v2] : unordered_pair(v1, v0) = v2
% 27.18/7.34 | (40) ? [v0] : ? [v1] : relation_rng(v0) = v1
% 27.18/7.34 | (41) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0))
% 27.18/7.34 | (42) reflexive(all_0_7_7) = all_0_6_6
% 27.18/7.34 | (43) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0))
% 27.18/7.34 | (44) ? [v0] : ? [v1] : ? [v2] : set_union2(v1, v0) = v2
% 27.18/7.34 | (45) ? [v0] : ? [v1] : relation(v0) = v1
% 27.18/7.34 | (46) ! [v0] : ! [v1] : ( ~ (reflexive(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (( ~ (v2 = 0) & relation(v0) = v2) | (( ~ (v1 = 0) | (relation_field(v0) = v2 & ! [v7] : ! [v8] : ( ~ (ordered_pair(v7, v7) = v8) | ? [v9] : ((v9 = 0 & in(v8, v0) = 0) | ( ~ (v9 = 0) & in(v7, v2) = v9))) & ! [v7] : ( ~ (in(v7, v2) = 0) | ? [v8] : (ordered_pair(v7, v7) = v8 & in(v8, v0) = 0)))) & (v1 = 0 | (v4 = 0 & ~ (v6 = 0) & relation_field(v0) = v2 & ordered_pair(v3, v3) = v5 & in(v5, v0) = v6 & in(v3, v2) = 0)))))
% 27.18/7.34 | (47) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (relation_field(v0) = v1 & relation_dom(v0) = v2 & relation_rng(v0) = v3 & set_union2(v2, v3) = v1))
% 27.18/7.34 | (48) ! [v0] : ! [v1] : ! [v2] : ( ~ (cartesian_product2(v1, v1) = v2) | ~ (relation(v0) = 0) | ? [v3] : (relation_restriction(v0, v1) = v3 & set_intersection2(v0, v2) = v3))
% 27.18/7.34 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0))
% 27.18/7.34 | (50) ~ (all_0_6_6 = 0)
% 27.18/7.34 | (51) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3))
% 27.18/7.34 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0))
% 27.18/7.34 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_restriction(v3, v2) = v1) | ~ (relation_restriction(v3, v2) = v0))
% 27.18/7.34 | (54) ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2
% 27.18/7.34 | (55) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v2 & relation_field(v0) = v2 & relation_dom(v0) = v3 & set_union2(v3, v1) = v2) | ( ~ (v2 = 0) & relation(v0) = v2)))
% 27.18/7.34 | (56) ? [v0] : ? [v1] : relation_field(v0) = v1
% 27.18/7.34 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 27.18/7.34 | (58) ! [v0] : ( ~ (function(v0) = 0) | ? [v1] : ? [v2] : ((v2 = 0 & v1 = 0 & one_to_one(v0) = 0 & relation(v0) = 0) | ( ~ (v1 = 0) & relation(v0) = v1) | ( ~ (v1 = 0) & empty(v0) = v1)))
% 27.18/7.35 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 27.18/7.35 | (60) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v2 & relation_field(v0) = v2 & relation_rng(v0) = v3 & set_union2(v1, v3) = v2) | ( ~ (v2 = 0) & relation(v0) = v2)))
% 27.18/7.35 | (61) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0))
% 27.18/7.35 | (62) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2)
% 27.18/7.35 | (63) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2)
% 27.18/7.35 | (64) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1))
% 27.18/7.35 | (65) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3))
% 27.18/7.35 | (66) empty(all_0_1_1) = 0
% 27.18/7.35 | (67) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ (in(v4, v5) = 0) | (in(v1, v3) = 0 & in(v0, v2) = 0))
% 27.18/7.35 | (68) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_restriction(v0, v1) = v2) | ? [v3] : ((v3 = 0 & relation(v2) = 0) | ( ~ (v3 = 0) & relation(v0) = v3)))
% 27.18/7.35 | (69) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (((v4 = 0 & ~ (v6 = 0) & relation_field(v0) = v2 & ordered_pair(v3, v3) = v5 & in(v5, v0) = v6 & in(v3, v2) = 0) | (v1 = 0 & reflexive(v0) = 0)) & (( ~ (v1 = 0) & reflexive(v0) = v1) | (relation_field(v0) = v2 & ! [v7] : ! [v8] : ( ~ (ordered_pair(v7, v7) = v8) | ? [v9] : ((v9 = 0 & in(v8, v0) = 0) | ( ~ (v9 = 0) & in(v7, v2) = v9))) & ! [v7] : ( ~ (in(v7, v2) = 0) | ? [v8] : (ordered_pair(v7, v7) = v8 & in(v8, v0) = 0))))))
% 27.18/7.35 | (70) ? [v0] : ? [v1] : relation_dom(v0) = v1
% 27.18/7.35 | (71) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3))
% 27.18/7.35 | (72) function(all_0_2_2) = 0
% 27.18/7.35 | (73) relation(all_0_8_8) = 0
% 27.18/7.35 | (74) function(all_0_5_5) = 0
% 27.18/7.35 | (75) relation(all_0_0_0) = 0
% 27.18/7.35 | (76) ! [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)))
% 27.18/7.35 | (77) ? [v0] : ? [v1] : ? [v2] : ordered_pair(v1, v0) = v2
% 27.18/7.35 | (78) empty(all_0_4_4) = all_0_3_3
% 27.18/7.35 | (79) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | element(v0, v1) = 0)
% 27.18/7.35 | (80) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0))
% 27.18/7.35 | (81) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0))
% 27.18/7.35 | (82) reflexive(all_0_8_8) = 0
% 27.18/7.35 | (83) ! [v0] : ! [v1] : (v1 = 0 | ~ (function(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2))
% 27.18/7.35 | (84) empty(empty_set) = 0
% 27.18/7.35 | (85) ? [v0] : ? [v1] : ? [v2] : set_intersection2(v1, v0) = v2
% 27.18/7.35 | (86) ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (( ~ (v2 = 0) & relation(v0) = v2) | (((v4 = 0 & ~ (v6 = 0) & ordered_pair(v3, v3) = v5 & in(v5, v0) = v6 & in(v3, v1) = 0) | (v2 = 0 & reflexive(v0) = 0)) & (( ~ (v2 = 0) & reflexive(v0) = v2) | ( ! [v7] : ! [v8] : ( ~ (ordered_pair(v7, v7) = v8) | ? [v9] : ((v9 = 0 & in(v8, v0) = 0) | ( ~ (v9 = 0) & in(v7, v1) = v9))) & ! [v7] : ( ~ (in(v7, v1) = 0) | ? [v8] : (ordered_pair(v7, v7) = v8 & in(v8, v0) = 0)))))))
% 27.18/7.35 | (87) ! [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)))
% 27.18/7.35 | (88) ? [v0] : ? [v1] : ? [v2] : element(v1, v0) = v2
% 27.18/7.35 | (89) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_restriction(v0, v1) = v2) | ~ (relation(v0) = 0) | ? [v3] : (cartesian_product2(v1, v1) = v3 & set_intersection2(v0, v3) = v2))
% 27.18/7.35 | (90) ? [v0] : ? [v1] : one_to_one(v0) = v1
% 27.18/7.35 | (91) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1))
% 27.18/7.35 | (92) ? [v0] : ? [v1] : ? [v2] : cartesian_product2(v1, v0) = v2
% 27.18/7.35 | (93) function(all_0_0_0) = 0
% 27.18/7.35 | (94) ? [v0] : ? [v1] : ? [v2] : relation_restriction(v1, v0) = v2
% 27.18/7.35 | (95) relation(all_0_5_5) = 0
% 27.18/7.35 | (96) ? [v0] : ? [v1] : singleton(v0) = v1
% 27.18/7.35 | (97) ! [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)))
% 27.18/7.35 |
% 27.18/7.35 | Instantiating formula (46) with all_0_6_6, all_0_7_7 and discharging atoms reflexive(all_0_7_7) = all_0_6_6, yields:
% 27.18/7.35 | (98) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (( ~ (v0 = 0) & relation(all_0_7_7) = v0) | (( ~ (all_0_6_6 = 0) | (relation_field(all_0_7_7) = v0 & ! [v5] : ! [v6] : ( ~ (ordered_pair(v5, v5) = v6) | ? [v7] : ((v7 = 0 & in(v6, all_0_7_7) = 0) | ( ~ (v7 = 0) & in(v5, v0) = v7))) & ! [v5] : ( ~ (in(v5, v0) = 0) | ? [v6] : (ordered_pair(v5, v5) = v6 & in(v6, all_0_7_7) = 0)))) & (all_0_6_6 = 0 | (v2 = 0 & ~ (v4 = 0) & relation_field(all_0_7_7) = v0 & ordered_pair(v1, v1) = v3 & in(v3, all_0_7_7) = v4 & in(v1, v0) = 0))))
% 27.18/7.35 |
% 27.18/7.35 | Instantiating formula (46) with 0, all_0_8_8 and discharging atoms reflexive(all_0_8_8) = 0, yields:
% 27.18/7.35 | (99) ? [v0] : (( ~ (v0 = 0) & relation(all_0_8_8) = v0) | (relation_field(all_0_8_8) = v0 & ! [v1] : ! [v2] : ( ~ (ordered_pair(v1, v1) = v2) | ? [v3] : ((v3 = 0 & in(v2, all_0_8_8) = 0) | ( ~ (v3 = 0) & in(v1, v0) = v3))) & ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : (ordered_pair(v1, v1) = v2 & in(v2, all_0_8_8) = 0))))
% 27.18/7.36 |
% 27.18/7.36 | Instantiating formula (68) with all_0_7_7, all_0_9_9, all_0_8_8 and discharging atoms relation_restriction(all_0_8_8, all_0_9_9) = all_0_7_7, yields:
% 27.18/7.36 | (100) ? [v0] : ((v0 = 0 & relation(all_0_7_7) = 0) | ( ~ (v0 = 0) & relation(all_0_8_8) = v0))
% 27.18/7.36 |
% 27.18/7.36 | Instantiating formula (89) with all_0_7_7, all_0_9_9, all_0_8_8 and discharging atoms relation_restriction(all_0_8_8, all_0_9_9) = all_0_7_7, relation(all_0_8_8) = 0, yields:
% 27.18/7.36 | (101) ? [v0] : (cartesian_product2(all_0_9_9, all_0_9_9) = v0 & set_intersection2(all_0_8_8, v0) = all_0_7_7)
% 27.18/7.36 |
% 27.18/7.36 | Instantiating formula (69) with all_0_8_8 and discharging atoms relation(all_0_8_8) = 0, yields:
% 27.18/7.36 | (102) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (((v3 = 0 & ~ (v5 = 0) & relation_field(all_0_8_8) = v1 & ordered_pair(v2, v2) = v4 & in(v4, all_0_8_8) = v5 & in(v2, v1) = 0) | (v0 = 0 & reflexive(all_0_8_8) = 0)) & (( ~ (v0 = 0) & reflexive(all_0_8_8) = v0) | (relation_field(all_0_8_8) = v1 & ! [v6] : ! [v7] : ( ~ (ordered_pair(v6, v6) = v7) | ? [v8] : ((v8 = 0 & in(v7, all_0_8_8) = 0) | ( ~ (v8 = 0) & in(v6, v1) = v8))) & ! [v6] : ( ~ (in(v6, v1) = 0) | ? [v7] : (ordered_pair(v6, v6) = v7 & in(v7, all_0_8_8) = 0)))))
% 27.18/7.36 |
% 27.18/7.36 | Instantiating formula (47) with all_0_8_8 and discharging atoms relation(all_0_8_8) = 0, yields:
% 27.18/7.36 | (103) ? [v0] : ? [v1] : ? [v2] : (relation_field(all_0_8_8) = v0 & relation_dom(all_0_8_8) = v1 & relation_rng(all_0_8_8) = v2 & set_union2(v1, v2) = v0)
% 27.18/7.36 |
% 27.18/7.36 | Instantiating (103) with all_57_0_76, all_57_1_77, all_57_2_78 yields:
% 27.18/7.36 | (104) relation_field(all_0_8_8) = all_57_2_78 & relation_dom(all_0_8_8) = all_57_1_77 & relation_rng(all_0_8_8) = all_57_0_76 & set_union2(all_57_1_77, all_57_0_76) = all_57_2_78
% 27.18/7.36 |
% 27.18/7.36 | Applying alpha-rule on (104) yields:
% 27.18/7.36 | (105) relation_field(all_0_8_8) = all_57_2_78
% 27.18/7.36 | (106) relation_dom(all_0_8_8) = all_57_1_77
% 27.18/7.36 | (107) relation_rng(all_0_8_8) = all_57_0_76
% 27.18/7.36 | (108) set_union2(all_57_1_77, all_57_0_76) = all_57_2_78
% 27.18/7.36 |
% 27.18/7.36 | Instantiating (102) with all_59_0_79, all_59_1_80, all_59_2_81, all_59_3_82, all_59_4_83, all_59_5_84 yields:
% 27.18/7.36 | (109) ((all_59_2_81 = 0 & ~ (all_59_0_79 = 0) & relation_field(all_0_8_8) = all_59_4_83 & ordered_pair(all_59_3_82, all_59_3_82) = all_59_1_80 & in(all_59_1_80, all_0_8_8) = all_59_0_79 & in(all_59_3_82, all_59_4_83) = 0) | (all_59_5_84 = 0 & reflexive(all_0_8_8) = 0)) & (( ~ (all_59_5_84 = 0) & reflexive(all_0_8_8) = all_59_5_84) | (relation_field(all_0_8_8) = all_59_4_83 & ! [v0] : ! [v1] : ( ~ (ordered_pair(v0, v0) = v1) | ? [v2] : ((v2 = 0 & in(v1, all_0_8_8) = 0) | ( ~ (v2 = 0) & in(v0, all_59_4_83) = v2))) & ! [v0] : ( ~ (in(v0, all_59_4_83) = 0) | ? [v1] : (ordered_pair(v0, v0) = v1 & in(v1, all_0_8_8) = 0))))
% 27.18/7.36 |
% 27.18/7.36 | Applying alpha-rule on (109) yields:
% 27.18/7.36 | (110) (all_59_2_81 = 0 & ~ (all_59_0_79 = 0) & relation_field(all_0_8_8) = all_59_4_83 & ordered_pair(all_59_3_82, all_59_3_82) = all_59_1_80 & in(all_59_1_80, all_0_8_8) = all_59_0_79 & in(all_59_3_82, all_59_4_83) = 0) | (all_59_5_84 = 0 & reflexive(all_0_8_8) = 0)
% 27.18/7.36 | (111) ( ~ (all_59_5_84 = 0) & reflexive(all_0_8_8) = all_59_5_84) | (relation_field(all_0_8_8) = all_59_4_83 & ! [v0] : ! [v1] : ( ~ (ordered_pair(v0, v0) = v1) | ? [v2] : ((v2 = 0 & in(v1, all_0_8_8) = 0) | ( ~ (v2 = 0) & in(v0, all_59_4_83) = v2))) & ! [v0] : ( ~ (in(v0, all_59_4_83) = 0) | ? [v1] : (ordered_pair(v0, v0) = v1 & in(v1, all_0_8_8) = 0)))
% 27.18/7.36 |
% 27.18/7.36 | Instantiating (101) with all_63_0_95 yields:
% 27.18/7.36 | (112) cartesian_product2(all_0_9_9, all_0_9_9) = all_63_0_95 & set_intersection2(all_0_8_8, all_63_0_95) = all_0_7_7
% 27.18/7.36 |
% 27.18/7.36 | Applying alpha-rule on (112) yields:
% 27.18/7.36 | (113) cartesian_product2(all_0_9_9, all_0_9_9) = all_63_0_95
% 27.18/7.36 | (114) set_intersection2(all_0_8_8, all_63_0_95) = all_0_7_7
% 27.18/7.36 |
% 27.18/7.36 | Instantiating (100) with all_71_0_110 yields:
% 27.18/7.36 | (115) (all_71_0_110 = 0 & relation(all_0_7_7) = 0) | ( ~ (all_71_0_110 = 0) & relation(all_0_8_8) = all_71_0_110)
% 27.18/7.36 |
% 27.18/7.36 | Instantiating (99) with all_73_0_112 yields:
% 27.18/7.36 | (116) ( ~ (all_73_0_112 = 0) & relation(all_0_8_8) = all_73_0_112) | (relation_field(all_0_8_8) = all_73_0_112 & ! [v0] : ! [v1] : ( ~ (ordered_pair(v0, v0) = v1) | ? [v2] : ((v2 = 0 & in(v1, all_0_8_8) = 0) | ( ~ (v2 = 0) & in(v0, all_73_0_112) = v2))) & ! [v0] : ( ~ (in(v0, all_73_0_112) = 0) | ? [v1] : (ordered_pair(v0, v0) = v1 & in(v1, all_0_8_8) = 0)))
% 27.18/7.36 |
% 27.18/7.36 | Instantiating (98) with all_74_0_113, all_74_1_114, all_74_2_115, all_74_3_116, all_74_4_117 yields:
% 27.18/7.36 | (117) ( ~ (all_74_4_117 = 0) & relation(all_0_7_7) = all_74_4_117) | (( ~ (all_0_6_6 = 0) | (relation_field(all_0_7_7) = all_74_4_117 & ! [v0] : ! [v1] : ( ~ (ordered_pair(v0, v0) = v1) | ? [v2] : ((v2 = 0 & in(v1, all_0_7_7) = 0) | ( ~ (v2 = 0) & in(v0, all_74_4_117) = v2))) & ! [v0] : ( ~ (in(v0, all_74_4_117) = 0) | ? [v1] : (ordered_pair(v0, v0) = v1 & in(v1, all_0_7_7) = 0)))) & (all_0_6_6 = 0 | (all_74_2_115 = 0 & ~ (all_74_0_113 = 0) & relation_field(all_0_7_7) = all_74_4_117 & ordered_pair(all_74_3_116, all_74_3_116) = all_74_1_114 & in(all_74_1_114, all_0_7_7) = all_74_0_113 & in(all_74_3_116, all_74_4_117) = 0)))
% 27.18/7.36 |
% 27.18/7.36 +-Applying beta-rule and splitting (116), into two cases.
% 27.18/7.36 |-Branch one:
% 27.18/7.36 | (118) ~ (all_73_0_112 = 0) & relation(all_0_8_8) = all_73_0_112
% 27.18/7.36 |
% 27.18/7.36 | Applying alpha-rule on (118) yields:
% 27.18/7.36 | (119) ~ (all_73_0_112 = 0)
% 27.18/7.36 | (120) relation(all_0_8_8) = all_73_0_112
% 27.18/7.36 |
% 27.18/7.36 | Instantiating formula (41) with all_0_8_8, all_73_0_112, 0 and discharging atoms relation(all_0_8_8) = all_73_0_112, relation(all_0_8_8) = 0, yields:
% 27.18/7.36 | (121) all_73_0_112 = 0
% 27.18/7.36 |
% 27.18/7.36 | Equations (121) can reduce 119 to:
% 27.18/7.36 | (122) $false
% 27.18/7.36 |
% 27.18/7.36 |-The branch is then unsatisfiable
% 27.18/7.36 |-Branch two:
% 27.18/7.36 | (123) relation_field(all_0_8_8) = all_73_0_112 & ! [v0] : ! [v1] : ( ~ (ordered_pair(v0, v0) = v1) | ? [v2] : ((v2 = 0 & in(v1, all_0_8_8) = 0) | ( ~ (v2 = 0) & in(v0, all_73_0_112) = v2))) & ! [v0] : ( ~ (in(v0, all_73_0_112) = 0) | ? [v1] : (ordered_pair(v0, v0) = v1 & in(v1, all_0_8_8) = 0))
% 27.18/7.36 |
% 27.18/7.36 | Applying alpha-rule on (123) yields:
% 27.18/7.36 | (124) relation_field(all_0_8_8) = all_73_0_112
% 27.18/7.36 | (125) ! [v0] : ! [v1] : ( ~ (ordered_pair(v0, v0) = v1) | ? [v2] : ((v2 = 0 & in(v1, all_0_8_8) = 0) | ( ~ (v2 = 0) & in(v0, all_73_0_112) = v2)))
% 27.18/7.36 | (126) ! [v0] : ( ~ (in(v0, all_73_0_112) = 0) | ? [v1] : (ordered_pair(v0, v0) = v1 & in(v1, all_0_8_8) = 0))
% 27.18/7.36 |
% 27.18/7.36 +-Applying beta-rule and splitting (111), into two cases.
% 27.18/7.36 |-Branch one:
% 27.18/7.36 | (127) ~ (all_59_5_84 = 0) & reflexive(all_0_8_8) = all_59_5_84
% 27.18/7.36 |
% 27.18/7.36 | Applying alpha-rule on (127) yields:
% 27.18/7.36 | (128) ~ (all_59_5_84 = 0)
% 27.18/7.36 | (129) reflexive(all_0_8_8) = all_59_5_84
% 27.18/7.36 |
% 27.18/7.36 | Instantiating formula (3) with all_0_8_8, all_59_5_84, 0 and discharging atoms reflexive(all_0_8_8) = all_59_5_84, reflexive(all_0_8_8) = 0, yields:
% 27.18/7.36 | (130) all_59_5_84 = 0
% 27.18/7.36 |
% 27.18/7.36 | Equations (130) can reduce 128 to:
% 27.18/7.36 | (122) $false
% 27.18/7.36 |
% 27.18/7.36 |-The branch is then unsatisfiable
% 27.18/7.36 |-Branch two:
% 27.18/7.37 | (132) relation_field(all_0_8_8) = all_59_4_83 & ! [v0] : ! [v1] : ( ~ (ordered_pair(v0, v0) = v1) | ? [v2] : ((v2 = 0 & in(v1, all_0_8_8) = 0) | ( ~ (v2 = 0) & in(v0, all_59_4_83) = v2))) & ! [v0] : ( ~ (in(v0, all_59_4_83) = 0) | ? [v1] : (ordered_pair(v0, v0) = v1 & in(v1, all_0_8_8) = 0))
% 27.18/7.37 |
% 27.18/7.37 | Applying alpha-rule on (132) yields:
% 27.18/7.37 | (133) relation_field(all_0_8_8) = all_59_4_83
% 27.18/7.37 | (134) ! [v0] : ! [v1] : ( ~ (ordered_pair(v0, v0) = v1) | ? [v2] : ((v2 = 0 & in(v1, all_0_8_8) = 0) | ( ~ (v2 = 0) & in(v0, all_59_4_83) = v2)))
% 27.18/7.37 | (135) ! [v0] : ( ~ (in(v0, all_59_4_83) = 0) | ? [v1] : (ordered_pair(v0, v0) = v1 & in(v1, all_0_8_8) = 0))
% 27.18/7.37 |
% 27.18/7.37 +-Applying beta-rule and splitting (115), into two cases.
% 27.18/7.37 |-Branch one:
% 27.18/7.37 | (136) all_71_0_110 = 0 & relation(all_0_7_7) = 0
% 27.18/7.37 |
% 27.18/7.37 | Applying alpha-rule on (136) yields:
% 27.18/7.37 | (137) all_71_0_110 = 0
% 27.18/7.37 | (138) relation(all_0_7_7) = 0
% 27.18/7.37 |
% 27.18/7.37 +-Applying beta-rule and splitting (117), into two cases.
% 27.18/7.37 |-Branch one:
% 27.18/7.37 | (139) ~ (all_74_4_117 = 0) & relation(all_0_7_7) = all_74_4_117
% 27.18/7.37 |
% 27.18/7.37 | Applying alpha-rule on (139) yields:
% 27.18/7.37 | (140) ~ (all_74_4_117 = 0)
% 27.18/7.37 | (141) relation(all_0_7_7) = all_74_4_117
% 27.18/7.37 |
% 27.18/7.37 | Instantiating formula (41) with all_0_7_7, 0, all_74_4_117 and discharging atoms relation(all_0_7_7) = all_74_4_117, relation(all_0_7_7) = 0, yields:
% 27.18/7.37 | (142) all_74_4_117 = 0
% 27.18/7.37 |
% 27.18/7.37 | Equations (142) can reduce 140 to:
% 27.18/7.37 | (122) $false
% 27.18/7.37 |
% 27.18/7.37 |-The branch is then unsatisfiable
% 27.18/7.37 |-Branch two:
% 27.18/7.37 | (144) ( ~ (all_0_6_6 = 0) | (relation_field(all_0_7_7) = all_74_4_117 & ! [v0] : ! [v1] : ( ~ (ordered_pair(v0, v0) = v1) | ? [v2] : ((v2 = 0 & in(v1, all_0_7_7) = 0) | ( ~ (v2 = 0) & in(v0, all_74_4_117) = v2))) & ! [v0] : ( ~ (in(v0, all_74_4_117) = 0) | ? [v1] : (ordered_pair(v0, v0) = v1 & in(v1, all_0_7_7) = 0)))) & (all_0_6_6 = 0 | (all_74_2_115 = 0 & ~ (all_74_0_113 = 0) & relation_field(all_0_7_7) = all_74_4_117 & ordered_pair(all_74_3_116, all_74_3_116) = all_74_1_114 & in(all_74_1_114, all_0_7_7) = all_74_0_113 & in(all_74_3_116, all_74_4_117) = 0))
% 27.18/7.37 |
% 27.18/7.37 | Applying alpha-rule on (144) yields:
% 27.18/7.37 | (145) ~ (all_0_6_6 = 0) | (relation_field(all_0_7_7) = all_74_4_117 & ! [v0] : ! [v1] : ( ~ (ordered_pair(v0, v0) = v1) | ? [v2] : ((v2 = 0 & in(v1, all_0_7_7) = 0) | ( ~ (v2 = 0) & in(v0, all_74_4_117) = v2))) & ! [v0] : ( ~ (in(v0, all_74_4_117) = 0) | ? [v1] : (ordered_pair(v0, v0) = v1 & in(v1, all_0_7_7) = 0)))
% 27.18/7.37 | (146) all_0_6_6 = 0 | (all_74_2_115 = 0 & ~ (all_74_0_113 = 0) & relation_field(all_0_7_7) = all_74_4_117 & ordered_pair(all_74_3_116, all_74_3_116) = all_74_1_114 & in(all_74_1_114, all_0_7_7) = all_74_0_113 & in(all_74_3_116, all_74_4_117) = 0)
% 27.18/7.37 |
% 27.18/7.37 +-Applying beta-rule and splitting (146), into two cases.
% 27.18/7.37 |-Branch one:
% 27.18/7.37 | (147) all_0_6_6 = 0
% 27.18/7.37 |
% 27.18/7.37 | Equations (147) can reduce 50 to:
% 27.18/7.37 | (122) $false
% 27.18/7.37 |
% 27.18/7.37 |-The branch is then unsatisfiable
% 27.18/7.37 |-Branch two:
% 27.18/7.37 | (50) ~ (all_0_6_6 = 0)
% 27.18/7.37 | (150) all_74_2_115 = 0 & ~ (all_74_0_113 = 0) & relation_field(all_0_7_7) = all_74_4_117 & ordered_pair(all_74_3_116, all_74_3_116) = all_74_1_114 & in(all_74_1_114, all_0_7_7) = all_74_0_113 & in(all_74_3_116, all_74_4_117) = 0
% 27.18/7.37 |
% 27.18/7.37 | Applying alpha-rule on (150) yields:
% 27.18/7.37 | (151) in(all_74_1_114, all_0_7_7) = all_74_0_113
% 27.18/7.37 | (152) all_74_2_115 = 0
% 27.18/7.37 | (153) in(all_74_3_116, all_74_4_117) = 0
% 27.18/7.37 | (154) relation_field(all_0_7_7) = all_74_4_117
% 27.18/7.37 | (155) ~ (all_74_0_113 = 0)
% 27.18/7.37 | (156) ordered_pair(all_74_3_116, all_74_3_116) = all_74_1_114
% 27.18/7.37 |
% 27.18/7.37 | Instantiating formula (14) with all_0_8_8, all_59_4_83, all_73_0_112 and discharging atoms relation_field(all_0_8_8) = all_73_0_112, relation_field(all_0_8_8) = all_59_4_83, yields:
% 27.18/7.37 | (157) all_73_0_112 = all_59_4_83
% 27.18/7.37 |
% 27.18/7.37 | Instantiating formula (14) with all_0_8_8, all_57_2_78, all_73_0_112 and discharging atoms relation_field(all_0_8_8) = all_73_0_112, relation_field(all_0_8_8) = all_57_2_78, yields:
% 27.18/7.37 | (158) all_73_0_112 = all_57_2_78
% 27.18/7.37 |
% 27.18/7.37 | Combining equations (157,158) yields a new equation:
% 27.18/7.37 | (159) all_59_4_83 = all_57_2_78
% 27.18/7.37 |
% 27.18/7.37 | Simplifying 159 yields:
% 27.18/7.37 | (160) all_59_4_83 = all_57_2_78
% 27.18/7.37 |
% 27.18/7.37 | From (160) and (133) follows:
% 27.18/7.37 | (105) relation_field(all_0_8_8) = all_57_2_78
% 27.18/7.37 |
% 27.18/7.37 | Instantiating formula (134) with all_74_1_114, all_74_3_116 and discharging atoms ordered_pair(all_74_3_116, all_74_3_116) = all_74_1_114, yields:
% 27.18/7.37 | (162) ? [v0] : ((v0 = 0 & in(all_74_1_114, all_0_8_8) = 0) | ( ~ (v0 = 0) & in(all_74_3_116, all_59_4_83) = v0))
% 27.18/7.37 |
% 27.18/7.37 | Instantiating formula (31) with all_74_0_113, all_0_7_7, all_0_8_8, all_0_9_9, all_74_1_114 and discharging atoms relation_restriction(all_0_8_8, all_0_9_9) = all_0_7_7, in(all_74_1_114, all_0_7_7) = all_74_0_113, yields:
% 27.18/7.37 | (163) ? [v0] : ? [v1] : ? [v2] : (( ~ (v0 = 0) & relation(all_0_8_8) = v0) | (( ~ (all_74_0_113 = 0) | (v2 = 0 & v0 = 0 & cartesian_product2(all_0_9_9, all_0_9_9) = v1 & in(all_74_1_114, v1) = 0 & in(all_74_1_114, all_0_8_8) = 0)) & (all_74_0_113 = 0 | ( ~ (v2 = 0) & cartesian_product2(all_0_9_9, all_0_9_9) = v1 & in(all_74_1_114, v1) = v2) | ( ~ (v0 = 0) & in(all_74_1_114, all_0_8_8) = v0))))
% 27.18/7.37 |
% 27.18/7.37 | Instantiating formula (15) with all_74_0_113, all_0_7_7, all_74_1_114 and discharging atoms in(all_74_1_114, all_0_7_7) = all_74_0_113, yields:
% 27.18/7.37 | (164) all_74_0_113 = 0 | ? [v0] : ((v0 = 0 & empty(all_0_7_7) = 0) | ( ~ (v0 = 0) & element(all_74_1_114, all_0_7_7) = v0))
% 27.18/7.37 |
% 27.18/7.37 | Instantiating formula (13) with all_74_4_117, all_0_7_7, all_0_8_8, all_0_9_9, all_74_3_116 and discharging atoms relation_restriction(all_0_8_8, all_0_9_9) = all_0_7_7, relation_field(all_0_7_7) = all_74_4_117, in(all_74_3_116, all_74_4_117) = 0, yields:
% 27.18/7.37 | (165) ? [v0] : ? [v1] : ? [v2] : ((v2 = 0 & v1 = 0 & relation_field(all_0_8_8) = v0 & in(all_74_3_116, v0) = 0 & in(all_74_3_116, all_0_9_9) = 0) | ( ~ (v0 = 0) & relation(all_0_8_8) = v0))
% 27.18/7.37 |
% 27.18/7.37 | Instantiating (163) with all_119_0_120, all_119_1_121, all_119_2_122 yields:
% 27.18/7.37 | (166) ( ~ (all_119_2_122 = 0) & relation(all_0_8_8) = all_119_2_122) | (( ~ (all_74_0_113 = 0) | (all_119_0_120 = 0 & all_119_2_122 = 0 & cartesian_product2(all_0_9_9, all_0_9_9) = all_119_1_121 & in(all_74_1_114, all_119_1_121) = 0 & in(all_74_1_114, all_0_8_8) = 0)) & (all_74_0_113 = 0 | ( ~ (all_119_0_120 = 0) & cartesian_product2(all_0_9_9, all_0_9_9) = all_119_1_121 & in(all_74_1_114, all_119_1_121) = all_119_0_120) | ( ~ (all_119_2_122 = 0) & in(all_74_1_114, all_0_8_8) = all_119_2_122)))
% 27.18/7.37 |
% 27.18/7.37 | Instantiating (165) with all_129_0_137, all_129_1_138, all_129_2_139 yields:
% 27.18/7.37 | (167) (all_129_0_137 = 0 & all_129_1_138 = 0 & relation_field(all_0_8_8) = all_129_2_139 & in(all_74_3_116, all_129_2_139) = 0 & in(all_74_3_116, all_0_9_9) = 0) | ( ~ (all_129_2_139 = 0) & relation(all_0_8_8) = all_129_2_139)
% 27.18/7.37 |
% 27.18/7.37 | Instantiating (162) with all_133_0_143 yields:
% 27.18/7.37 | (168) (all_133_0_143 = 0 & in(all_74_1_114, all_0_8_8) = 0) | ( ~ (all_133_0_143 = 0) & in(all_74_3_116, all_59_4_83) = all_133_0_143)
% 27.18/7.37 |
% 27.18/7.37 +-Applying beta-rule and splitting (167), into two cases.
% 27.18/7.37 |-Branch one:
% 27.18/7.37 | (169) all_129_0_137 = 0 & all_129_1_138 = 0 & relation_field(all_0_8_8) = all_129_2_139 & in(all_74_3_116, all_129_2_139) = 0 & in(all_74_3_116, all_0_9_9) = 0
% 27.18/7.37 |
% 27.18/7.37 | Applying alpha-rule on (169) yields:
% 27.18/7.37 | (170) in(all_74_3_116, all_0_9_9) = 0
% 27.18/7.37 | (171) all_129_0_137 = 0
% 27.18/7.37 | (172) relation_field(all_0_8_8) = all_129_2_139
% 27.18/7.38 | (173) all_129_1_138 = 0
% 27.18/7.38 | (174) in(all_74_3_116, all_129_2_139) = 0
% 27.18/7.38 |
% 27.18/7.38 +-Applying beta-rule and splitting (164), into two cases.
% 27.18/7.38 |-Branch one:
% 27.18/7.38 | (175) all_74_0_113 = 0
% 27.18/7.38 |
% 27.18/7.38 | Equations (175) can reduce 155 to:
% 27.18/7.38 | (122) $false
% 27.18/7.38 |
% 27.18/7.38 |-The branch is then unsatisfiable
% 27.18/7.38 |-Branch two:
% 27.18/7.38 | (155) ~ (all_74_0_113 = 0)
% 27.18/7.38 | (178) ? [v0] : ((v0 = 0 & empty(all_0_7_7) = 0) | ( ~ (v0 = 0) & element(all_74_1_114, all_0_7_7) = v0))
% 27.18/7.38 |
% 27.18/7.38 | Instantiating formula (14) with all_0_8_8, all_129_2_139, all_57_2_78 and discharging atoms relation_field(all_0_8_8) = all_129_2_139, relation_field(all_0_8_8) = all_57_2_78, yields:
% 27.18/7.38 | (179) all_129_2_139 = all_57_2_78
% 27.18/7.38 |
% 27.18/7.38 | From (179) and (174) follows:
% 27.18/7.38 | (180) in(all_74_3_116, all_57_2_78) = 0
% 27.18/7.38 |
% 27.18/7.38 +-Applying beta-rule and splitting (166), into two cases.
% 27.18/7.38 |-Branch one:
% 27.18/7.38 | (181) ~ (all_119_2_122 = 0) & relation(all_0_8_8) = all_119_2_122
% 27.18/7.38 |
% 27.18/7.38 | Applying alpha-rule on (181) yields:
% 27.18/7.38 | (182) ~ (all_119_2_122 = 0)
% 27.18/7.38 | (183) relation(all_0_8_8) = all_119_2_122
% 27.18/7.38 |
% 27.18/7.38 | Instantiating formula (41) with all_0_8_8, all_119_2_122, 0 and discharging atoms relation(all_0_8_8) = all_119_2_122, relation(all_0_8_8) = 0, yields:
% 27.18/7.38 | (184) all_119_2_122 = 0
% 27.18/7.38 |
% 27.18/7.38 | Equations (184) can reduce 182 to:
% 27.18/7.38 | (122) $false
% 27.18/7.38 |
% 27.18/7.38 |-The branch is then unsatisfiable
% 27.18/7.38 |-Branch two:
% 27.18/7.38 | (186) ( ~ (all_74_0_113 = 0) | (all_119_0_120 = 0 & all_119_2_122 = 0 & cartesian_product2(all_0_9_9, all_0_9_9) = all_119_1_121 & in(all_74_1_114, all_119_1_121) = 0 & in(all_74_1_114, all_0_8_8) = 0)) & (all_74_0_113 = 0 | ( ~ (all_119_0_120 = 0) & cartesian_product2(all_0_9_9, all_0_9_9) = all_119_1_121 & in(all_74_1_114, all_119_1_121) = all_119_0_120) | ( ~ (all_119_2_122 = 0) & in(all_74_1_114, all_0_8_8) = all_119_2_122))
% 27.18/7.38 |
% 27.18/7.38 | Applying alpha-rule on (186) yields:
% 27.18/7.38 | (187) ~ (all_74_0_113 = 0) | (all_119_0_120 = 0 & all_119_2_122 = 0 & cartesian_product2(all_0_9_9, all_0_9_9) = all_119_1_121 & in(all_74_1_114, all_119_1_121) = 0 & in(all_74_1_114, all_0_8_8) = 0)
% 27.18/7.38 | (188) all_74_0_113 = 0 | ( ~ (all_119_0_120 = 0) & cartesian_product2(all_0_9_9, all_0_9_9) = all_119_1_121 & in(all_74_1_114, all_119_1_121) = all_119_0_120) | ( ~ (all_119_2_122 = 0) & in(all_74_1_114, all_0_8_8) = all_119_2_122)
% 27.18/7.38 |
% 27.18/7.38 +-Applying beta-rule and splitting (168), into two cases.
% 27.18/7.38 |-Branch one:
% 27.18/7.38 | (189) all_133_0_143 = 0 & in(all_74_1_114, all_0_8_8) = 0
% 27.18/7.38 |
% 27.18/7.38 | Applying alpha-rule on (189) yields:
% 27.18/7.38 | (190) all_133_0_143 = 0
% 27.18/7.38 | (191) in(all_74_1_114, all_0_8_8) = 0
% 27.18/7.38 |
% 27.18/7.38 +-Applying beta-rule and splitting (188), into two cases.
% 27.18/7.38 |-Branch one:
% 27.18/7.38 | (175) all_74_0_113 = 0
% 27.18/7.38 |
% 27.18/7.38 | Equations (175) can reduce 155 to:
% 27.18/7.38 | (122) $false
% 27.18/7.38 |
% 27.18/7.38 |-The branch is then unsatisfiable
% 27.18/7.38 |-Branch two:
% 27.18/7.38 | (155) ~ (all_74_0_113 = 0)
% 27.18/7.38 | (195) ( ~ (all_119_0_120 = 0) & cartesian_product2(all_0_9_9, all_0_9_9) = all_119_1_121 & in(all_74_1_114, all_119_1_121) = all_119_0_120) | ( ~ (all_119_2_122 = 0) & in(all_74_1_114, all_0_8_8) = all_119_2_122)
% 27.18/7.38 |
% 27.18/7.38 +-Applying beta-rule and splitting (195), into two cases.
% 27.18/7.38 |-Branch one:
% 27.18/7.38 | (196) ~ (all_119_0_120 = 0) & cartesian_product2(all_0_9_9, all_0_9_9) = all_119_1_121 & in(all_74_1_114, all_119_1_121) = all_119_0_120
% 27.18/7.38 |
% 27.18/7.38 | Applying alpha-rule on (196) yields:
% 27.18/7.38 | (197) ~ (all_119_0_120 = 0)
% 27.18/7.38 | (198) cartesian_product2(all_0_9_9, all_0_9_9) = all_119_1_121
% 27.18/7.38 | (199) in(all_74_1_114, all_119_1_121) = all_119_0_120
% 27.18/7.38 |
% 27.18/7.38 | Instantiating formula (49) with all_0_9_9, all_0_9_9, all_119_1_121, all_63_0_95 and discharging atoms cartesian_product2(all_0_9_9, all_0_9_9) = all_119_1_121, cartesian_product2(all_0_9_9, all_0_9_9) = all_63_0_95, yields:
% 27.18/7.38 | (200) all_119_1_121 = all_63_0_95
% 27.18/7.38 |
% 27.18/7.38 | From (200) and (198) follows:
% 27.18/7.38 | (113) cartesian_product2(all_0_9_9, all_0_9_9) = all_63_0_95
% 27.18/7.38 |
% 27.18/7.38 | From (200) and (199) follows:
% 27.18/7.38 | (202) in(all_74_1_114, all_63_0_95) = all_119_0_120
% 27.18/7.38 |
% 27.18/7.38 | Instantiating formula (7) with all_119_0_120, all_63_0_95, all_74_1_114, all_0_9_9, all_0_9_9, all_74_3_116, all_74_3_116 and discharging atoms cartesian_product2(all_0_9_9, all_0_9_9) = all_63_0_95, ordered_pair(all_74_3_116, all_74_3_116) = all_74_1_114, in(all_74_1_114, all_63_0_95) = all_119_0_120, yields:
% 27.18/7.38 | (203) all_119_0_120 = 0 | ? [v0] : ( ~ (v0 = 0) & in(all_74_3_116, all_0_9_9) = v0)
% 27.18/7.38 |
% 27.18/7.38 | Instantiating formula (15) with all_119_0_120, all_63_0_95, all_74_1_114 and discharging atoms in(all_74_1_114, all_63_0_95) = all_119_0_120, yields:
% 27.18/7.38 | (204) all_119_0_120 = 0 | ? [v0] : ((v0 = 0 & empty(all_63_0_95) = 0) | ( ~ (v0 = 0) & element(all_74_1_114, all_63_0_95) = v0))
% 27.18/7.38 |
% 27.18/7.38 +-Applying beta-rule and splitting (204), into two cases.
% 27.18/7.38 |-Branch one:
% 27.18/7.38 | (205) all_119_0_120 = 0
% 27.18/7.38 |
% 27.18/7.38 | Equations (205) can reduce 197 to:
% 27.18/7.38 | (122) $false
% 27.18/7.38 |
% 27.18/7.38 |-The branch is then unsatisfiable
% 27.18/7.38 |-Branch two:
% 27.18/7.38 | (197) ~ (all_119_0_120 = 0)
% 27.18/7.38 | (208) ? [v0] : ((v0 = 0 & empty(all_63_0_95) = 0) | ( ~ (v0 = 0) & element(all_74_1_114, all_63_0_95) = v0))
% 27.18/7.38 |
% 27.18/7.38 +-Applying beta-rule and splitting (203), into two cases.
% 27.18/7.38 |-Branch one:
% 27.18/7.38 | (205) all_119_0_120 = 0
% 27.18/7.38 |
% 27.18/7.38 | Equations (205) can reduce 197 to:
% 27.18/7.38 | (122) $false
% 27.18/7.38 |
% 27.18/7.38 |-The branch is then unsatisfiable
% 27.18/7.38 |-Branch two:
% 27.18/7.38 | (197) ~ (all_119_0_120 = 0)
% 27.18/7.38 | (212) ? [v0] : ( ~ (v0 = 0) & in(all_74_3_116, all_0_9_9) = v0)
% 27.18/7.38 |
% 27.18/7.38 | Instantiating (212) with all_288_0_237 yields:
% 27.18/7.38 | (213) ~ (all_288_0_237 = 0) & in(all_74_3_116, all_0_9_9) = all_288_0_237
% 27.18/7.38 |
% 27.18/7.38 | Applying alpha-rule on (213) yields:
% 27.18/7.38 | (214) ~ (all_288_0_237 = 0)
% 27.18/7.38 | (215) in(all_74_3_116, all_0_9_9) = all_288_0_237
% 27.18/7.38 |
% 27.18/7.38 | Instantiating formula (57) with all_74_3_116, all_0_9_9, all_288_0_237, 0 and discharging atoms in(all_74_3_116, all_0_9_9) = all_288_0_237, in(all_74_3_116, all_0_9_9) = 0, yields:
% 27.18/7.38 | (216) all_288_0_237 = 0
% 27.18/7.38 |
% 27.18/7.38 | Equations (216) can reduce 214 to:
% 27.18/7.38 | (122) $false
% 27.18/7.38 |
% 27.18/7.38 |-The branch is then unsatisfiable
% 27.18/7.38 |-Branch two:
% 27.18/7.38 | (218) ~ (all_119_2_122 = 0) & in(all_74_1_114, all_0_8_8) = all_119_2_122
% 27.18/7.38 |
% 27.18/7.38 | Applying alpha-rule on (218) yields:
% 27.18/7.38 | (182) ~ (all_119_2_122 = 0)
% 27.18/7.38 | (220) in(all_74_1_114, all_0_8_8) = all_119_2_122
% 27.18/7.38 |
% 27.18/7.38 | Instantiating formula (57) with all_74_1_114, all_0_8_8, 0, all_119_2_122 and discharging atoms in(all_74_1_114, all_0_8_8) = all_119_2_122, in(all_74_1_114, all_0_8_8) = 0, yields:
% 27.18/7.38 | (184) all_119_2_122 = 0
% 27.18/7.38 |
% 27.18/7.38 | Equations (184) can reduce 182 to:
% 27.18/7.38 | (122) $false
% 27.18/7.38 |
% 27.18/7.38 |-The branch is then unsatisfiable
% 27.18/7.38 |-Branch two:
% 27.18/7.38 | (223) ~ (all_133_0_143 = 0) & in(all_74_3_116, all_59_4_83) = all_133_0_143
% 27.18/7.38 |
% 27.18/7.38 | Applying alpha-rule on (223) yields:
% 27.18/7.38 | (224) ~ (all_133_0_143 = 0)
% 27.18/7.38 | (225) in(all_74_3_116, all_59_4_83) = all_133_0_143
% 27.18/7.38 |
% 27.18/7.38 | From (160) and (225) follows:
% 27.18/7.38 | (226) in(all_74_3_116, all_57_2_78) = all_133_0_143
% 27.18/7.38 |
% 27.18/7.38 | Instantiating formula (57) with all_74_3_116, all_57_2_78, 0, all_133_0_143 and discharging atoms in(all_74_3_116, all_57_2_78) = all_133_0_143, in(all_74_3_116, all_57_2_78) = 0, yields:
% 27.18/7.38 | (190) all_133_0_143 = 0
% 27.18/7.38 |
% 27.18/7.38 | Equations (190) can reduce 224 to:
% 27.18/7.38 | (122) $false
% 27.18/7.38 |
% 27.18/7.38 |-The branch is then unsatisfiable
% 27.18/7.38 |-Branch two:
% 27.18/7.38 | (229) ~ (all_129_2_139 = 0) & relation(all_0_8_8) = all_129_2_139
% 27.18/7.38 |
% 27.18/7.38 | Applying alpha-rule on (229) yields:
% 27.18/7.38 | (230) ~ (all_129_2_139 = 0)
% 27.18/7.38 | (231) relation(all_0_8_8) = all_129_2_139
% 27.18/7.38 |
% 27.18/7.38 | Instantiating formula (41) with all_0_8_8, all_129_2_139, 0 and discharging atoms relation(all_0_8_8) = all_129_2_139, relation(all_0_8_8) = 0, yields:
% 27.18/7.38 | (232) all_129_2_139 = 0
% 27.18/7.38 |
% 27.18/7.38 | Equations (232) can reduce 230 to:
% 27.18/7.38 | (122) $false
% 27.18/7.38 |
% 27.18/7.38 |-The branch is then unsatisfiable
% 27.18/7.38 |-Branch two:
% 27.18/7.38 | (234) ~ (all_71_0_110 = 0) & relation(all_0_8_8) = all_71_0_110
% 27.18/7.38 |
% 27.18/7.38 | Applying alpha-rule on (234) yields:
% 27.18/7.38 | (235) ~ (all_71_0_110 = 0)
% 27.18/7.38 | (236) relation(all_0_8_8) = all_71_0_110
% 27.18/7.38 |
% 27.18/7.38 | Instantiating formula (41) with all_0_8_8, all_71_0_110, 0 and discharging atoms relation(all_0_8_8) = all_71_0_110, relation(all_0_8_8) = 0, yields:
% 27.18/7.38 | (137) all_71_0_110 = 0
% 27.18/7.38 |
% 27.18/7.38 | Equations (137) can reduce 235 to:
% 27.18/7.38 | (122) $false
% 27.18/7.38 |
% 27.18/7.38 |-The branch is then unsatisfiable
% 27.18/7.38 % SZS output end Proof for theBenchmark
% 27.18/7.38
% 27.18/7.38 6794ms
%------------------------------------------------------------------------------