TSTP Solution File: SEU239+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU239+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n008.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 08:48:02 EDT 2022
% Result : Theorem 5.79s 1.99s
% Output : Proof 8.91s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SEU239+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.11/0.32 % Computer : n008.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 600
% 0.11/0.32 % DateTime : Sun Jun 19 23:52:52 EDT 2022
% 0.11/0.32 % CPUTime :
% 0.17/0.57 ____ _
% 0.17/0.57 ___ / __ \_____(_)___ ________ __________
% 0.17/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.17/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.17/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.17/0.57
% 0.17/0.57 A Theorem Prover for First-Order Logic
% 0.17/0.57 (ePrincess v.1.0)
% 0.17/0.57
% 0.17/0.57 (c) Philipp Rümmer, 2009-2015
% 0.17/0.57 (c) Peter Backeman, 2014-2015
% 0.17/0.57 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.17/0.57 Free software under GNU Lesser General Public License (LGPL).
% 0.17/0.57 Bug reports to peter@backeman.se
% 0.17/0.57
% 0.17/0.57 For more information, visit http://user.uu.se/~petba168/breu/
% 0.17/0.57
% 0.17/0.57 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.65/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.51/0.93 Prover 0: Preprocessing ...
% 1.99/1.13 Prover 0: Warning: ignoring some quantifiers
% 1.99/1.15 Prover 0: Constructing countermodel ...
% 3.37/1.48 Prover 0: gave up
% 3.37/1.48 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 3.46/1.51 Prover 1: Preprocessing ...
% 3.66/1.59 Prover 1: Warning: ignoring some quantifiers
% 3.66/1.60 Prover 1: Constructing countermodel ...
% 4.40/1.73 Prover 1: gave up
% 4.40/1.73 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 4.40/1.75 Prover 2: Preprocessing ...
% 5.01/1.84 Prover 2: Warning: ignoring some quantifiers
% 5.01/1.85 Prover 2: Constructing countermodel ...
% 5.79/1.99 Prover 2: proved (259ms)
% 5.79/1.99
% 5.79/1.99 No countermodel exists, formula is valid
% 5.79/1.99 % SZS status Theorem for theBenchmark
% 5.79/1.99
% 5.79/1.99 Generating proof ... Warning: ignoring some quantifiers
% 8.44/2.60 found it (size 121)
% 8.44/2.60
% 8.44/2.60 % SZS output start Proof for theBenchmark
% 8.44/2.60 Assumed formulas after preprocessing and simplification:
% 8.44/2.60 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ( ~ (v9 = 0) & reflexive(v0) = v1 & relation_field(v0) = v2 & one_to_one(v7) = 0 & relation(v12) = 0 & relation(v10) = 0 & relation(v7) = 0 & relation(v0) = 0 & function(v12) = 0 & function(v10) = 0 & function(v7) = 0 & empty(v11) = 0 & empty(v10) = 0 & empty(v8) = v9 & empty(empty_set) = 0 & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v14 = v13 | ~ (element(v16, v15) = v14) | ~ (element(v16, v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v14 = v13 | ~ (is_reflexive_in(v16, v15) = v14) | ~ (is_reflexive_in(v16, v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v14 = v13 | ~ (ordered_pair(v16, v15) = v14) | ~ (ordered_pair(v16, v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v14 = v13 | ~ (set_union2(v16, v15) = v14) | ~ (set_union2(v16, v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v14 = v13 | ~ (unordered_pair(v16, v15) = v14) | ~ (unordered_pair(v16, v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v14 = v13 | ~ (in(v16, v15) = v14) | ~ (in(v16, v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (is_reflexive_in(v13, v14) = 0) | ~ (ordered_pair(v15, v15) = v16) | ~ (relation(v13) = 0) | ? [v17] : ((v17 = 0 & in(v16, v13) = 0) | ( ~ (v17 = 0) & in(v15, v14) = v17))) & ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (element(v13, v14) = v15) | ? [v16] : ( ~ (v16 = 0) & in(v13, v14) = v16)) & ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (is_reflexive_in(v13, v14) = v15) | ~ (relation(v13) = 0) | ? [v16] : ? [v17] : ? [v18] : ( ~ (v18 = 0) & ordered_pair(v16, v16) = v17 & in(v17, v13) = v18 & in(v16, v14) = 0)) & ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (in(v13, v14) = v15) | ? [v16] : ((v16 = 0 & empty(v14) = 0) | ( ~ (v16 = 0) & element(v13, v14) = v16))) & ! [v13] : ! [v14] : ! [v15] : (v14 = v13 | ~ (reflexive(v15) = v14) | ~ (reflexive(v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : (v14 = v13 | ~ (relation_field(v15) = v14) | ~ (relation_field(v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : (v14 = v13 | ~ (relation_dom(v15) = v14) | ~ (relation_dom(v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : (v14 = v13 | ~ (relation_rng(v15) = v14) | ~ (relation_rng(v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : (v14 = v13 | ~ (singleton(v15) = v14) | ~ (singleton(v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : (v14 = v13 | ~ (one_to_one(v15) = v14) | ~ (one_to_one(v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : (v14 = v13 | ~ (relation(v15) = v14) | ~ (relation(v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : (v14 = v13 | ~ (function(v15) = v14) | ~ (function(v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : (v14 = v13 | ~ (empty(v15) = v14) | ~ (empty(v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (is_reflexive_in(v13, v14) = 0) | ~ (relation(v13) = 0) | ~ (in(v15, v14) = 0) | ? [v16] : (ordered_pair(v15, v15) = v16 & in(v16, v13) = 0)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (ordered_pair(v13, v14) = v15) | ? [v16] : ? [v17] : (singleton(v13) = v17 & unordered_pair(v16, v17) = v15 & unordered_pair(v13, v14) = v16)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (ordered_pair(v13, v14) = v15) | ? [v16] : ( ~ (v16 = 0) & empty(v15) = v16)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (set_union2(v14, v13) = v15) | set_union2(v13, v14) = v15) & ! [v13] : ! [v14] : ! [v15] : ( ~ (set_union2(v14, v13) = v15) | ? [v16] : ((v16 = 0 & empty(v13) = 0) | ( ~ (v16 = 0) & empty(v15) = v16))) & ! [v13] : ! [v14] : ! [v15] : ( ~ (set_union2(v13, v14) = v15) | set_union2(v14, v13) = v15) & ! [v13] : ! [v14] : ! [v15] : ( ~ (set_union2(v13, v14) = v15) | ? [v16] : ((v16 = 0 & empty(v13) = 0) | ( ~ (v16 = 0) & empty(v15) = v16))) & ! [v13] : ! [v14] : ! [v15] : ( ~ (unordered_pair(v14, v13) = v15) | unordered_pair(v13, v14) = v15) & ! [v13] : ! [v14] : ! [v15] : ( ~ (unordered_pair(v13, v14) = v15) | unordered_pair(v14, v13) = v15) & ! [v13] : ! [v14] : ! [v15] : ( ~ (unordered_pair(v13, v14) = v15) | ? [v16] : ? [v17] : (singleton(v13) = v17 & ordered_pair(v13, v14) = v16 & unordered_pair(v15, v17) = v16)) & ! [v13] : ! [v14] : (v14 = v13 | ~ (set_union2(v13, v13) = v14)) & ! [v13] : ! [v14] : (v14 = v13 | ~ (set_union2(v13, empty_set) = v14)) & ! [v13] : ! [v14] : (v14 = v13 | ~ (empty(v14) = 0) | ~ (empty(v13) = 0)) & ! [v13] : ! [v14] : (v14 = 0 | ~ (function(v13) = v14) | ? [v15] : ( ~ (v15 = 0) & empty(v13) = v15)) & ! [v13] : ! [v14] : ( ~ (element(v13, v14) = 0) | ? [v15] : ((v15 = 0 & empty(v14) = 0) | (v15 = 0 & in(v13, v14) = 0))) & ! [v13] : ! [v14] : ( ~ (reflexive(v13) = v14) | ? [v15] : ? [v16] : (( ~ (v15 = 0) & relation(v13) = v15) | (( ~ (v14 = 0) | (v16 = 0 & relation_field(v13) = v15 & is_reflexive_in(v13, v15) = 0)) & (v14 = 0 | ( ~ (v16 = 0) & relation_field(v13) = v15 & is_reflexive_in(v13, v15) = v16))))) & ! [v13] : ! [v14] : ( ~ (relation_field(v13) = v14) | ? [v15] : ? [v16] : ? [v17] : ((v17 = v14 & relation_dom(v13) = v15 & relation_rng(v13) = v16 & set_union2(v15, v16) = v14) | ( ~ (v15 = 0) & relation(v13) = v15))) & ! [v13] : ! [v14] : ( ~ (relation_field(v13) = v14) | ? [v15] : ? [v16] : (( ~ (v15 = 0) & relation(v13) = v15) | (((v16 = 0 & is_reflexive_in(v13, v14) = 0) | ( ~ (v15 = 0) & reflexive(v13) = v15)) & ((v15 = 0 & reflexive(v13) = 0) | ( ~ (v16 = 0) & is_reflexive_in(v13, v14) = v16))))) & ! [v13] : ! [v14] : ( ~ (relation_dom(v13) = v14) | ? [v15] : ? [v16] : ? [v17] : ((v17 = v15 & relation_field(v13) = v15 & relation_rng(v13) = v16 & set_union2(v14, v16) = v15) | ( ~ (v15 = 0) & relation(v13) = v15))) & ! [v13] : ! [v14] : ( ~ (relation_rng(v13) = v14) | ? [v15] : ? [v16] : ? [v17] : ((v17 = v15 & relation_field(v13) = v15 & relation_dom(v13) = v16 & set_union2(v16, v14) = v15) | ( ~ (v15 = 0) & relation(v13) = v15))) & ! [v13] : ! [v14] : ( ~ (one_to_one(v13) = v14) | ? [v15] : ? [v16] : ((v16 = 0 & v15 = 0 & v14 = 0 & relation(v13) = 0 & function(v13) = 0) | ( ~ (v15 = 0) & relation(v13) = v15) | ( ~ (v15 = 0) & function(v13) = v15) | ( ~ (v15 = 0) & empty(v13) = v15))) & ! [v13] : ! [v14] : ( ~ (in(v14, v13) = 0) | ? [v15] : ( ~ (v15 = 0) & in(v13, v14) = v15)) & ! [v13] : ! [v14] : ( ~ (in(v13, v14) = 0) | element(v13, v14) = 0) & ! [v13] : ! [v14] : ( ~ (in(v13, v14) = 0) | ? [v15] : ( ~ (v15 = 0) & empty(v14) = v15)) & ! [v13] : ! [v14] : ( ~ (in(v13, v14) = 0) | ? [v15] : ( ~ (v15 = 0) & in(v14, v13) = v15)) & ! [v13] : (v13 = empty_set | ~ (empty(v13) = 0)) & ! [v13] : ( ~ (relation(v13) = 0) | ? [v14] : ? [v15] : ? [v16] : (relation_field(v13) = v14 & relation_dom(v13) = v15 & relation_rng(v13) = v16 & set_union2(v15, v16) = v14)) & ! [v13] : ( ~ (relation(v13) = 0) | ? [v14] : ? [v15] : ? [v16] : (((v16 = 0 & relation_field(v13) = v15 & is_reflexive_in(v13, v15) = 0) | ( ~ (v14 = 0) & reflexive(v13) = v14)) & ((v14 = 0 & reflexive(v13) = 0) | ( ~ (v16 = 0) & relation_field(v13) = v15 & is_reflexive_in(v13, v15) = v16)))) & ! [v13] : ( ~ (relation(v13) = 0) | ? [v14] : ? [v15] : ((v15 = 0 & v14 = 0 & one_to_one(v13) = 0 & function(v13) = 0) | ( ~ (v14 = 0) & function(v13) = v14) | ( ~ (v14 = 0) & empty(v13) = v14))) & ! [v13] : ( ~ (function(v13) = 0) | ? [v14] : ? [v15] : ((v15 = 0 & v14 = 0 & one_to_one(v13) = 0 & relation(v13) = 0) | ( ~ (v14 = 0) & relation(v13) = v14) | ( ~ (v14 = 0) & empty(v13) = v14))) & ! [v13] : ( ~ (empty(v13) = 0) | function(v13) = 0) & ! [v13] : ( ~ (empty(v13) = 0) | ? [v14] : ? [v15] : ? [v16] : ((v16 = 0 & v15 = 0 & v14 = 0 & one_to_one(v13) = 0 & relation(v13) = 0 & function(v13) = 0) | ( ~ (v14 = 0) & relation(v13) = v14) | ( ~ (v14 = 0) & function(v13) = v14))) & ? [v13] : ? [v14] : ? [v15] : element(v14, v13) = v15 & ? [v13] : ? [v14] : ? [v15] : is_reflexive_in(v14, v13) = v15 & ? [v13] : ? [v14] : ? [v15] : ordered_pair(v14, v13) = v15 & ? [v13] : ? [v14] : ? [v15] : set_union2(v14, v13) = v15 & ? [v13] : ? [v14] : ? [v15] : unordered_pair(v14, v13) = v15 & ? [v13] : ? [v14] : ? [v15] : in(v14, v13) = v15 & ? [v13] : ? [v14] : element(v14, v13) = 0 & ? [v13] : ? [v14] : reflexive(v13) = v14 & ? [v13] : ? [v14] : relation_field(v13) = v14 & ? [v13] : ? [v14] : relation_dom(v13) = v14 & ? [v13] : ? [v14] : relation_rng(v13) = v14 & ? [v13] : ? [v14] : singleton(v13) = v14 & ? [v13] : ? [v14] : one_to_one(v13) = v14 & ? [v13] : ? [v14] : relation(v13) = v14 & ? [v13] : ? [v14] : function(v13) = v14 & ? [v13] : ? [v14] : empty(v13) = v14 & ((v4 = 0 & v1 = 0 & ~ (v6 = 0) & ordered_pair(v3, v3) = v5 & in(v5, v0) = v6 & in(v3, v2) = 0) | ( ~ (v1 = 0) & ! [v13] : ! [v14] : ( ~ (ordered_pair(v13, v13) = v14) | ? [v15] : ((v15 = 0 & in(v14, v0) = 0) | ( ~ (v15 = 0) & in(v13, v2) = v15))) & ! [v13] : ( ~ (in(v13, v2) = 0) | ? [v14] : (ordered_pair(v13, v13) = v14 & in(v14, v0) = 0)))))
% 8.44/2.65 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9, all_0_10_10, all_0_11_11, all_0_12_12 yields:
% 8.44/2.65 | (1) ~ (all_0_3_3 = 0) & reflexive(all_0_12_12) = all_0_11_11 & relation_field(all_0_12_12) = all_0_10_10 & 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_12_12) = 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] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (is_reflexive_in(v3, v2) = v1) | ~ (is_reflexive_in(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_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] : ! [v3] : ( ~ (is_reflexive_in(v0, v1) = 0) | ~ (ordered_pair(v2, v2) = v3) | ~ (relation(v0) = 0) | ? [v4] : ((v4 = 0 & in(v3, v0) = 0) | ( ~ (v4 = 0) & in(v2, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (is_reflexive_in(v0, v1) = v2) | ~ (relation(v0) = 0) | ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = 0) & ordered_pair(v3, v3) = v4 & in(v4, v0) = v5 & in(v3, v1) = 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 | ~ (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] : ( ~ (is_reflexive_in(v0, v1) = 0) | ~ (relation(v0) = 0) | ~ (in(v2, v1) = 0) | ? [v3] : (ordered_pair(v2, v2) = v3 & in(v3, v0) = 0)) & ! [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_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] : (singleton(v0) = v4 & ordered_pair(v0, v1) = v3 & unordered_pair(v2, v4) = v3)) & ! [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 = 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] : ( ~ (reflexive(v0) = v1) | ? [v2] : ? [v3] : (( ~ (v2 = 0) & relation(v0) = v2) | (( ~ (v1 = 0) | (v3 = 0 & relation_field(v0) = v2 & is_reflexive_in(v0, v2) = 0)) & (v1 = 0 | ( ~ (v3 = 0) & relation_field(v0) = v2 & is_reflexive_in(v0, v2) = v3))))) & ! [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_field(v0) = v1) | ? [v2] : ? [v3] : (( ~ (v2 = 0) & relation(v0) = v2) | (((v3 = 0 & is_reflexive_in(v0, v1) = 0) | ( ~ (v2 = 0) & reflexive(v0) = v2)) & ((v2 = 0 & reflexive(v0) = 0) | ( ~ (v3 = 0) & is_reflexive_in(v0, v1) = v3))))) & ! [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] : (relation_field(v0) = v1 & relation_dom(v0) = v2 & relation_rng(v0) = v3 & set_union2(v2, v3) = v1)) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (((v3 = 0 & relation_field(v0) = v2 & is_reflexive_in(v0, v2) = 0) | ( ~ (v1 = 0) & reflexive(v0) = v1)) & ((v1 = 0 & reflexive(v0) = 0) | ( ~ (v3 = 0) & relation_field(v0) = v2 & is_reflexive_in(v0, v2) = v3)))) & ! [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] : is_reflexive_in(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : ordered_pair(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] : element(v1, v0) = 0 & ? [v0] : ? [v1] : reflexive(v0) = v1 & ? [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 & ((all_0_8_8 = 0 & all_0_11_11 = 0 & ~ (all_0_6_6 = 0) & ordered_pair(all_0_9_9, all_0_9_9) = all_0_7_7 & in(all_0_7_7, all_0_12_12) = all_0_6_6 & in(all_0_9_9, all_0_10_10) = 0) | ( ~ (all_0_11_11 = 0) & ! [v0] : ! [v1] : ( ~ (ordered_pair(v0, v0) = v1) | ? [v2] : ((v2 = 0 & in(v1, all_0_12_12) = 0) | ( ~ (v2 = 0) & in(v0, all_0_10_10) = v2))) & ! [v0] : ( ~ (in(v0, all_0_10_10) = 0) | ? [v1] : (ordered_pair(v0, v0) = v1 & in(v1, all_0_12_12) = 0))))
% 8.44/2.67 |
% 8.44/2.67 | Applying alpha-rule on (1) yields:
% 8.44/2.67 | (2) ? [v0] : ? [v1] : ? [v2] : ordered_pair(v1, v0) = v2
% 8.44/2.67 | (3) empty(all_0_4_4) = all_0_3_3
% 8.44/2.67 | (4) ! [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)))
% 8.44/2.67 | (5) ? [v0] : ? [v1] : relation(v0) = v1
% 8.44/2.67 | (6) ? [v0] : ? [v1] : ? [v2] : is_reflexive_in(v1, v0) = v2
% 8.44/2.67 | (7) ! [v0] : ! [v1] : ! [v2] : ( ~ (is_reflexive_in(v0, v1) = 0) | ~ (relation(v0) = 0) | ~ (in(v2, v1) = 0) | ? [v3] : (ordered_pair(v2, v2) = v3 & in(v3, v0) = 0))
% 8.44/2.67 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2)
% 8.44/2.67 | (9) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2)
% 8.44/2.67 | (10) ? [v0] : ? [v1] : singleton(v0) = v1
% 8.44/2.67 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0))
% 8.44/2.67 | (12) relation(all_0_12_12) = 0
% 8.44/2.67 | (13) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0))
% 8.44/2.67 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 8.44/2.67 | (15) ! [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)))
% 8.44/2.67 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0))
% 8.44/2.67 | (17) ? [v0] : ? [v1] : element(v1, v0) = 0
% 8.44/2.67 | (18) ? [v0] : ? [v1] : function(v0) = v1
% 8.44/2.67 | (19) empty(all_0_1_1) = 0
% 8.44/2.67 | (20) empty(all_0_2_2) = 0
% 8.44/2.67 | (21) reflexive(all_0_12_12) = all_0_11_11
% 8.44/2.67 | (22) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (is_reflexive_in(v0, v1) = v2) | ~ (relation(v0) = 0) | ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = 0) & ordered_pair(v3, v3) = v4 & in(v4, v0) = v5 & in(v3, v1) = 0))
% 8.44/2.67 | (23) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3))
% 8.44/2.67 | (24) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_field(v2) = v1) | ~ (relation_field(v2) = v0))
% 8.44/2.67 | (25) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (((v3 = 0 & relation_field(v0) = v2 & is_reflexive_in(v0, v2) = 0) | ( ~ (v1 = 0) & reflexive(v0) = v1)) & ((v1 = 0 & reflexive(v0) = 0) | ( ~ (v3 = 0) & relation_field(v0) = v2 & is_reflexive_in(v0, v2) = v3))))
% 8.44/2.67 | (26) ? [v0] : ? [v1] : relation_field(v0) = v1
% 8.44/2.67 | (27) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0))
% 8.44/2.67 | (28) ? [v0] : ? [v1] : ? [v2] : set_union2(v1, v0) = v2
% 8.44/2.67 | (29) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 8.44/2.67 | (30) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : ((v3 = 0 & empty(v0) = 0) | ( ~ (v3 = 0) & empty(v2) = v3)))
% 8.44/2.68 | (31) ! [v0] : ( ~ (empty(v0) = 0) | function(v0) = 0)
% 8.44/2.68 | (32) ! [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)))
% 8.44/2.68 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 8.44/2.68 | (34) ? [v0] : ? [v1] : reflexive(v0) = v1
% 8.44/2.68 | (35) ~ (all_0_3_3 = 0)
% 8.44/2.68 | (36) ? [v0] : ? [v1] : one_to_one(v0) = v1
% 8.44/2.68 | (37) ! [v0] : ! [v1] : ( ~ (element(v0, v1) = 0) | ? [v2] : ((v2 = 0 & empty(v1) = 0) | (v2 = 0 & in(v0, v1) = 0)))
% 8.44/2.68 | (38) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (relation_field(v0) = v1 & relation_dom(v0) = v2 & relation_rng(v0) = v3 & set_union2(v2, v3) = v1))
% 8.44/2.68 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (is_reflexive_in(v3, v2) = v1) | ~ (is_reflexive_in(v3, v2) = v0))
% 8.44/2.68 | (40) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0))
% 8.44/2.68 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0))
% 8.44/2.68 | (42) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ? [v3] : ((v3 = 0 & empty(v0) = 0) | ( ~ (v3 = 0) & empty(v2) = v3)))
% 8.44/2.68 | (43) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0))
% 8.44/2.68 | (44) relation_field(all_0_12_12) = all_0_10_10
% 8.44/2.68 | (45) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1))
% 8.44/2.68 | (46) one_to_one(all_0_5_5) = 0
% 8.44/2.68 | (47) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 8.44/2.68 | (48) ! [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)))
% 8.44/2.68 | (49) ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ? [v2] : ? [v3] : (( ~ (v2 = 0) & relation(v0) = v2) | (((v3 = 0 & is_reflexive_in(v0, v1) = 0) | ( ~ (v2 = 0) & reflexive(v0) = v2)) & ((v2 = 0 & reflexive(v0) = 0) | ( ~ (v3 = 0) & is_reflexive_in(v0, v1) = v3)))))
% 8.44/2.68 | (50) empty(empty_set) = 0
% 8.44/2.68 | (51) relation(all_0_2_2) = 0
% 8.44/2.68 | (52) ! [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)))
% 8.44/2.68 | (53) relation(all_0_5_5) = 0
% 8.44/2.68 | (54) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1))
% 8.44/2.68 | (55) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2)
% 8.44/2.68 | (56) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2)
% 8.44/2.68 | (57) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | element(v0, v1) = 0)
% 8.44/2.68 | (58) relation(all_0_0_0) = 0
% 8.44/2.68 | (59) ? [v0] : ? [v1] : ? [v2] : element(v1, v0) = v2
% 8.44/2.68 | (60) ? [v0] : ? [v1] : empty(v0) = v1
% 8.44/2.68 | (61) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0))
% 8.44/2.68 | (62) ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2
% 8.44/2.68 | (63) function(all_0_0_0) = 0
% 8.44/2.68 | (64) ? [v0] : ? [v1] : relation_rng(v0) = v1
% 8.44/2.68 | (65) ? [v0] : ? [v1] : relation_dom(v0) = v1
% 8.44/2.68 | (66) ! [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)))
% 8.44/2.68 | (67) function(all_0_2_2) = 0
% 8.44/2.68 | (68) ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2))
% 8.44/2.69 | (69) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0))
% 8.44/2.69 | (70) (all_0_8_8 = 0 & all_0_11_11 = 0 & ~ (all_0_6_6 = 0) & ordered_pair(all_0_9_9, all_0_9_9) = all_0_7_7 & in(all_0_7_7, all_0_12_12) = all_0_6_6 & in(all_0_9_9, all_0_10_10) = 0) | ( ~ (all_0_11_11 = 0) & ! [v0] : ! [v1] : ( ~ (ordered_pair(v0, v0) = v1) | ? [v2] : ((v2 = 0 & in(v1, all_0_12_12) = 0) | ( ~ (v2 = 0) & in(v0, all_0_10_10) = v2))) & ! [v0] : ( ~ (in(v0, all_0_10_10) = 0) | ? [v1] : (ordered_pair(v0, v0) = v1 & in(v1, all_0_12_12) = 0)))
% 8.44/2.69 | (71) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v0, v1) = v2) | ? [v3] : ((v3 = 0 & empty(v1) = 0) | ( ~ (v3 = 0) & element(v0, v1) = v3)))
% 8.44/2.69 | (72) ! [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)))
% 8.44/2.69 | (73) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 8.44/2.69 | (74) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3))
% 8.44/2.69 | (75) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (is_reflexive_in(v0, v1) = 0) | ~ (ordered_pair(v2, v2) = v3) | ~ (relation(v0) = 0) | ? [v4] : ((v4 = 0 & in(v3, v0) = 0) | ( ~ (v4 = 0) & in(v2, v1) = v4)))
% 8.44/2.69 | (76) ! [v0] : ! [v1] : (v1 = 0 | ~ (function(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2))
% 8.44/2.69 | (77) ! [v0] : ! [v1] : ( ~ (reflexive(v0) = v1) | ? [v2] : ? [v3] : (( ~ (v2 = 0) & relation(v0) = v2) | (( ~ (v1 = 0) | (v3 = 0 & relation_field(v0) = v2 & is_reflexive_in(v0, v2) = 0)) & (v1 = 0 | ( ~ (v3 = 0) & relation_field(v0) = v2 & is_reflexive_in(v0, v2) = v3)))))
% 8.44/2.69 | (78) function(all_0_5_5) = 0
% 8.44/2.69 | (79) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & ordered_pair(v0, v1) = v3 & unordered_pair(v2, v4) = v3))
% 8.44/2.69 | (80) ? [v0] : ? [v1] : ? [v2] : unordered_pair(v1, v0) = v2
% 8.44/2.69 | (81) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0))
% 8.44/2.69 | (82) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (reflexive(v2) = v1) | ~ (reflexive(v2) = v0))
% 8.44/2.69 | (83) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 8.44/2.69 | (84) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3))
% 8.44/2.69 |
% 8.91/2.69 | Instantiating formula (77) with all_0_11_11, all_0_12_12 and discharging atoms reflexive(all_0_12_12) = all_0_11_11, yields:
% 8.91/2.69 | (85) ? [v0] : ? [v1] : (( ~ (v0 = 0) & relation(all_0_12_12) = v0) | (( ~ (all_0_11_11 = 0) | (v1 = 0 & relation_field(all_0_12_12) = v0 & is_reflexive_in(all_0_12_12, v0) = 0)) & (all_0_11_11 = 0 | ( ~ (v1 = 0) & relation_field(all_0_12_12) = v0 & is_reflexive_in(all_0_12_12, v0) = v1))))
% 8.91/2.69 |
% 8.91/2.69 | Instantiating formula (49) with all_0_10_10, all_0_12_12 and discharging atoms relation_field(all_0_12_12) = all_0_10_10, yields:
% 8.91/2.69 | (86) ? [v0] : ? [v1] : (( ~ (v0 = 0) & relation(all_0_12_12) = v0) | (((v1 = 0 & is_reflexive_in(all_0_12_12, all_0_10_10) = 0) | ( ~ (v0 = 0) & reflexive(all_0_12_12) = v0)) & ((v0 = 0 & reflexive(all_0_12_12) = 0) | ( ~ (v1 = 0) & is_reflexive_in(all_0_12_12, all_0_10_10) = v1))))
% 8.91/2.69 |
% 8.91/2.69 | Instantiating formula (38) with all_0_12_12 and discharging atoms relation(all_0_12_12) = 0, yields:
% 8.91/2.69 | (87) ? [v0] : ? [v1] : ? [v2] : (relation_field(all_0_12_12) = v0 & relation_dom(all_0_12_12) = v1 & relation_rng(all_0_12_12) = v2 & set_union2(v1, v2) = v0)
% 8.91/2.69 |
% 8.91/2.69 | Instantiating formula (25) with all_0_12_12 and discharging atoms relation(all_0_12_12) = 0, yields:
% 8.91/2.69 | (88) ? [v0] : ? [v1] : ? [v2] : (((v2 = 0 & relation_field(all_0_12_12) = v1 & is_reflexive_in(all_0_12_12, v1) = 0) | ( ~ (v0 = 0) & reflexive(all_0_12_12) = v0)) & ((v0 = 0 & reflexive(all_0_12_12) = 0) | ( ~ (v2 = 0) & relation_field(all_0_12_12) = v1 & is_reflexive_in(all_0_12_12, v1) = v2)))
% 8.91/2.70 |
% 8.91/2.70 | Instantiating (88) with all_53_0_70, all_53_1_71, all_53_2_72 yields:
% 8.91/2.70 | (89) ((all_53_0_70 = 0 & relation_field(all_0_12_12) = all_53_1_71 & is_reflexive_in(all_0_12_12, all_53_1_71) = 0) | ( ~ (all_53_2_72 = 0) & reflexive(all_0_12_12) = all_53_2_72)) & ((all_53_2_72 = 0 & reflexive(all_0_12_12) = 0) | ( ~ (all_53_0_70 = 0) & relation_field(all_0_12_12) = all_53_1_71 & is_reflexive_in(all_0_12_12, all_53_1_71) = all_53_0_70))
% 8.91/2.70 |
% 8.91/2.70 | Applying alpha-rule on (89) yields:
% 8.91/2.70 | (90) (all_53_0_70 = 0 & relation_field(all_0_12_12) = all_53_1_71 & is_reflexive_in(all_0_12_12, all_53_1_71) = 0) | ( ~ (all_53_2_72 = 0) & reflexive(all_0_12_12) = all_53_2_72)
% 8.91/2.70 | (91) (all_53_2_72 = 0 & reflexive(all_0_12_12) = 0) | ( ~ (all_53_0_70 = 0) & relation_field(all_0_12_12) = all_53_1_71 & is_reflexive_in(all_0_12_12, all_53_1_71) = all_53_0_70)
% 8.91/2.70 |
% 8.91/2.70 | Instantiating (87) with all_54_0_73, all_54_1_74, all_54_2_75 yields:
% 8.91/2.70 | (92) relation_field(all_0_12_12) = all_54_2_75 & relation_dom(all_0_12_12) = all_54_1_74 & relation_rng(all_0_12_12) = all_54_0_73 & set_union2(all_54_1_74, all_54_0_73) = all_54_2_75
% 8.91/2.70 |
% 8.91/2.70 | Applying alpha-rule on (92) yields:
% 8.91/2.70 | (93) relation_field(all_0_12_12) = all_54_2_75
% 8.91/2.70 | (94) relation_dom(all_0_12_12) = all_54_1_74
% 8.91/2.70 | (95) relation_rng(all_0_12_12) = all_54_0_73
% 8.91/2.70 | (96) set_union2(all_54_1_74, all_54_0_73) = all_54_2_75
% 8.91/2.70 |
% 8.91/2.70 | Instantiating (85) with all_61_0_86, all_61_1_87 yields:
% 8.91/2.70 | (97) ( ~ (all_61_1_87 = 0) & relation(all_0_12_12) = all_61_1_87) | (( ~ (all_0_11_11 = 0) | (all_61_0_86 = 0 & relation_field(all_0_12_12) = all_61_1_87 & is_reflexive_in(all_0_12_12, all_61_1_87) = 0)) & (all_0_11_11 = 0 | ( ~ (all_61_0_86 = 0) & relation_field(all_0_12_12) = all_61_1_87 & is_reflexive_in(all_0_12_12, all_61_1_87) = all_61_0_86)))
% 8.91/2.70 |
% 8.91/2.70 | Instantiating (86) with all_63_0_90, all_63_1_91 yields:
% 8.91/2.70 | (98) ( ~ (all_63_1_91 = 0) & relation(all_0_12_12) = all_63_1_91) | (((all_63_0_90 = 0 & is_reflexive_in(all_0_12_12, all_0_10_10) = 0) | ( ~ (all_63_1_91 = 0) & reflexive(all_0_12_12) = all_63_1_91)) & ((all_63_1_91 = 0 & reflexive(all_0_12_12) = 0) | ( ~ (all_63_0_90 = 0) & is_reflexive_in(all_0_12_12, all_0_10_10) = all_63_0_90)))
% 8.91/2.70 |
% 8.91/2.70 | Instantiating formula (24) with all_0_12_12, all_54_2_75, all_0_10_10 and discharging atoms relation_field(all_0_12_12) = all_54_2_75, relation_field(all_0_12_12) = all_0_10_10, yields:
% 8.91/2.70 | (99) all_54_2_75 = all_0_10_10
% 8.91/2.70 |
% 8.91/2.70 | From (99) and (93) follows:
% 8.91/2.70 | (44) relation_field(all_0_12_12) = all_0_10_10
% 8.91/2.70 |
% 8.91/2.70 +-Applying beta-rule and splitting (70), into two cases.
% 8.91/2.70 |-Branch one:
% 8.91/2.70 | (101) all_0_8_8 = 0 & all_0_11_11 = 0 & ~ (all_0_6_6 = 0) & ordered_pair(all_0_9_9, all_0_9_9) = all_0_7_7 & in(all_0_7_7, all_0_12_12) = all_0_6_6 & in(all_0_9_9, all_0_10_10) = 0
% 8.91/2.70 |
% 8.91/2.70 | Applying alpha-rule on (101) yields:
% 8.91/2.70 | (102) all_0_11_11 = 0
% 8.91/2.70 | (103) ~ (all_0_6_6 = 0)
% 8.91/2.70 | (104) in(all_0_9_9, all_0_10_10) = 0
% 8.91/2.70 | (105) all_0_8_8 = 0
% 8.91/2.70 | (106) in(all_0_7_7, all_0_12_12) = all_0_6_6
% 8.91/2.70 | (107) ordered_pair(all_0_9_9, all_0_9_9) = all_0_7_7
% 8.91/2.70 |
% 8.91/2.70 | From (102) and (21) follows:
% 8.91/2.70 | (108) reflexive(all_0_12_12) = 0
% 8.91/2.70 |
% 8.91/2.70 +-Applying beta-rule and splitting (90), into two cases.
% 8.91/2.70 |-Branch one:
% 8.91/2.70 | (109) all_53_0_70 = 0 & relation_field(all_0_12_12) = all_53_1_71 & is_reflexive_in(all_0_12_12, all_53_1_71) = 0
% 8.91/2.70 |
% 8.91/2.70 | Applying alpha-rule on (109) yields:
% 8.91/2.70 | (110) all_53_0_70 = 0
% 8.91/2.70 | (111) relation_field(all_0_12_12) = all_53_1_71
% 8.91/2.70 | (112) is_reflexive_in(all_0_12_12, all_53_1_71) = 0
% 8.91/2.70 |
% 8.91/2.70 +-Applying beta-rule and splitting (97), into two cases.
% 8.91/2.70 |-Branch one:
% 8.91/2.70 | (113) ~ (all_61_1_87 = 0) & relation(all_0_12_12) = all_61_1_87
% 8.91/2.70 |
% 8.91/2.70 | Applying alpha-rule on (113) yields:
% 8.91/2.70 | (114) ~ (all_61_1_87 = 0)
% 8.91/2.71 | (115) relation(all_0_12_12) = all_61_1_87
% 8.91/2.71 |
% 8.91/2.71 | Instantiating formula (43) with all_0_12_12, all_61_1_87, 0 and discharging atoms relation(all_0_12_12) = all_61_1_87, relation(all_0_12_12) = 0, yields:
% 8.91/2.71 | (116) all_61_1_87 = 0
% 8.91/2.71 |
% 8.91/2.71 | Equations (116) can reduce 114 to:
% 8.91/2.71 | (117) $false
% 8.91/2.71 |
% 8.91/2.71 |-The branch is then unsatisfiable
% 8.91/2.71 |-Branch two:
% 8.91/2.71 | (118) ( ~ (all_0_11_11 = 0) | (all_61_0_86 = 0 & relation_field(all_0_12_12) = all_61_1_87 & is_reflexive_in(all_0_12_12, all_61_1_87) = 0)) & (all_0_11_11 = 0 | ( ~ (all_61_0_86 = 0) & relation_field(all_0_12_12) = all_61_1_87 & is_reflexive_in(all_0_12_12, all_61_1_87) = all_61_0_86))
% 8.91/2.71 |
% 8.91/2.71 | Applying alpha-rule on (118) yields:
% 8.91/2.71 | (119) ~ (all_0_11_11 = 0) | (all_61_0_86 = 0 & relation_field(all_0_12_12) = all_61_1_87 & is_reflexive_in(all_0_12_12, all_61_1_87) = 0)
% 8.91/2.71 | (120) all_0_11_11 = 0 | ( ~ (all_61_0_86 = 0) & relation_field(all_0_12_12) = all_61_1_87 & is_reflexive_in(all_0_12_12, all_61_1_87) = all_61_0_86)
% 8.91/2.71 |
% 8.91/2.71 +-Applying beta-rule and splitting (119), into two cases.
% 8.91/2.71 |-Branch one:
% 8.91/2.71 | (121) ~ (all_0_11_11 = 0)
% 8.91/2.71 |
% 8.91/2.71 | Equations (102) can reduce 121 to:
% 8.91/2.71 | (117) $false
% 8.91/2.71 |
% 8.91/2.71 |-The branch is then unsatisfiable
% 8.91/2.71 |-Branch two:
% 8.91/2.71 | (102) all_0_11_11 = 0
% 8.91/2.71 | (124) all_61_0_86 = 0 & relation_field(all_0_12_12) = all_61_1_87 & is_reflexive_in(all_0_12_12, all_61_1_87) = 0
% 8.91/2.71 |
% 8.91/2.71 | Applying alpha-rule on (124) yields:
% 8.91/2.71 | (125) all_61_0_86 = 0
% 8.91/2.71 | (126) relation_field(all_0_12_12) = all_61_1_87
% 8.91/2.71 | (127) is_reflexive_in(all_0_12_12, all_61_1_87) = 0
% 8.91/2.71 |
% 8.91/2.71 | Instantiating formula (24) with all_0_12_12, all_61_1_87, all_0_10_10 and discharging atoms relation_field(all_0_12_12) = all_61_1_87, relation_field(all_0_12_12) = all_0_10_10, yields:
% 8.91/2.71 | (128) all_61_1_87 = all_0_10_10
% 8.91/2.71 |
% 8.91/2.71 | Instantiating formula (24) with all_0_12_12, all_53_1_71, all_61_1_87 and discharging atoms relation_field(all_0_12_12) = all_61_1_87, relation_field(all_0_12_12) = all_53_1_71, yields:
% 8.91/2.71 | (129) all_61_1_87 = all_53_1_71
% 8.91/2.71 |
% 8.91/2.71 | Combining equations (128,129) yields a new equation:
% 8.91/2.71 | (130) all_53_1_71 = all_0_10_10
% 8.91/2.71 |
% 8.91/2.71 | From (130) and (112) follows:
% 8.91/2.71 | (131) is_reflexive_in(all_0_12_12, all_0_10_10) = 0
% 8.91/2.71 |
% 8.91/2.71 | Instantiating formula (75) with all_0_7_7, all_0_9_9, all_0_10_10, all_0_12_12 and discharging atoms is_reflexive_in(all_0_12_12, all_0_10_10) = 0, ordered_pair(all_0_9_9, all_0_9_9) = all_0_7_7, relation(all_0_12_12) = 0, yields:
% 8.91/2.71 | (132) ? [v0] : ((v0 = 0 & in(all_0_7_7, all_0_12_12) = 0) | ( ~ (v0 = 0) & in(all_0_9_9, all_0_10_10) = v0))
% 8.91/2.71 |
% 8.91/2.71 | Instantiating formula (71) with all_0_6_6, all_0_12_12, all_0_7_7 and discharging atoms in(all_0_7_7, all_0_12_12) = all_0_6_6, yields:
% 8.91/2.71 | (133) all_0_6_6 = 0 | ? [v0] : ((v0 = 0 & empty(all_0_12_12) = 0) | ( ~ (v0 = 0) & element(all_0_7_7, all_0_12_12) = v0))
% 8.91/2.71 |
% 8.91/2.71 | Instantiating (132) with all_165_0_130 yields:
% 8.91/2.71 | (134) (all_165_0_130 = 0 & in(all_0_7_7, all_0_12_12) = 0) | ( ~ (all_165_0_130 = 0) & in(all_0_9_9, all_0_10_10) = all_165_0_130)
% 8.91/2.71 |
% 8.91/2.71 +-Applying beta-rule and splitting (134), into two cases.
% 8.91/2.71 |-Branch one:
% 8.91/2.71 | (135) all_165_0_130 = 0 & in(all_0_7_7, all_0_12_12) = 0
% 8.91/2.71 |
% 8.91/2.71 | Applying alpha-rule on (135) yields:
% 8.91/2.71 | (136) all_165_0_130 = 0
% 8.91/2.71 | (137) in(all_0_7_7, all_0_12_12) = 0
% 8.91/2.71 |
% 8.91/2.71 +-Applying beta-rule and splitting (133), into two cases.
% 8.91/2.71 |-Branch one:
% 8.91/2.71 | (138) all_0_6_6 = 0
% 8.91/2.71 |
% 8.91/2.71 | Equations (138) can reduce 103 to:
% 8.91/2.71 | (117) $false
% 8.91/2.71 |
% 8.91/2.71 |-The branch is then unsatisfiable
% 8.91/2.71 |-Branch two:
% 8.91/2.71 | (103) ~ (all_0_6_6 = 0)
% 8.91/2.71 | (141) ? [v0] : ((v0 = 0 & empty(all_0_12_12) = 0) | ( ~ (v0 = 0) & element(all_0_7_7, all_0_12_12) = v0))
% 8.91/2.71 |
% 8.91/2.71 | Instantiating formula (33) with all_0_7_7, all_0_12_12, 0, all_0_6_6 and discharging atoms in(all_0_7_7, all_0_12_12) = all_0_6_6, in(all_0_7_7, all_0_12_12) = 0, yields:
% 8.91/2.71 | (138) all_0_6_6 = 0
% 8.91/2.71 |
% 8.91/2.71 | Equations (138) can reduce 103 to:
% 8.91/2.71 | (117) $false
% 8.91/2.71 |
% 8.91/2.71 |-The branch is then unsatisfiable
% 8.91/2.71 |-Branch two:
% 8.91/2.71 | (144) ~ (all_165_0_130 = 0) & in(all_0_9_9, all_0_10_10) = all_165_0_130
% 8.91/2.71 |
% 8.91/2.71 | Applying alpha-rule on (144) yields:
% 8.91/2.71 | (145) ~ (all_165_0_130 = 0)
% 8.91/2.71 | (146) in(all_0_9_9, all_0_10_10) = all_165_0_130
% 8.91/2.71 |
% 8.91/2.71 | Instantiating formula (33) with all_0_9_9, all_0_10_10, all_165_0_130, 0 and discharging atoms in(all_0_9_9, all_0_10_10) = all_165_0_130, in(all_0_9_9, all_0_10_10) = 0, yields:
% 8.91/2.71 | (136) all_165_0_130 = 0
% 8.91/2.71 |
% 8.91/2.71 | Equations (136) can reduce 145 to:
% 8.91/2.71 | (117) $false
% 8.91/2.71 |
% 8.91/2.71 |-The branch is then unsatisfiable
% 8.91/2.71 |-Branch two:
% 8.91/2.71 | (149) ~ (all_53_2_72 = 0) & reflexive(all_0_12_12) = all_53_2_72
% 8.91/2.71 |
% 8.91/2.71 | Applying alpha-rule on (149) yields:
% 8.91/2.71 | (150) ~ (all_53_2_72 = 0)
% 8.91/2.71 | (151) reflexive(all_0_12_12) = all_53_2_72
% 8.91/2.71 |
% 8.91/2.71 | Instantiating formula (82) with all_0_12_12, 0, all_53_2_72 and discharging atoms reflexive(all_0_12_12) = all_53_2_72, reflexive(all_0_12_12) = 0, yields:
% 8.91/2.72 | (152) all_53_2_72 = 0
% 8.91/2.72 |
% 8.91/2.72 | Equations (152) can reduce 150 to:
% 8.91/2.72 | (117) $false
% 8.91/2.72 |
% 8.91/2.72 |-The branch is then unsatisfiable
% 8.91/2.72 |-Branch two:
% 8.91/2.72 | (154) ~ (all_0_11_11 = 0) & ! [v0] : ! [v1] : ( ~ (ordered_pair(v0, v0) = v1) | ? [v2] : ((v2 = 0 & in(v1, all_0_12_12) = 0) | ( ~ (v2 = 0) & in(v0, all_0_10_10) = v2))) & ! [v0] : ( ~ (in(v0, all_0_10_10) = 0) | ? [v1] : (ordered_pair(v0, v0) = v1 & in(v1, all_0_12_12) = 0))
% 8.91/2.72 |
% 8.91/2.72 | Applying alpha-rule on (154) yields:
% 8.91/2.72 | (121) ~ (all_0_11_11 = 0)
% 8.91/2.72 | (156) ! [v0] : ! [v1] : ( ~ (ordered_pair(v0, v0) = v1) | ? [v2] : ((v2 = 0 & in(v1, all_0_12_12) = 0) | ( ~ (v2 = 0) & in(v0, all_0_10_10) = v2)))
% 8.91/2.72 | (157) ! [v0] : ( ~ (in(v0, all_0_10_10) = 0) | ? [v1] : (ordered_pair(v0, v0) = v1 & in(v1, all_0_12_12) = 0))
% 8.91/2.72 |
% 8.91/2.72 +-Applying beta-rule and splitting (91), into two cases.
% 8.91/2.72 |-Branch one:
% 8.91/2.72 | (158) all_53_2_72 = 0 & reflexive(all_0_12_12) = 0
% 8.91/2.72 |
% 8.91/2.72 | Applying alpha-rule on (158) yields:
% 8.91/2.72 | (152) all_53_2_72 = 0
% 8.91/2.72 | (108) reflexive(all_0_12_12) = 0
% 8.91/2.72 |
% 8.91/2.72 | Instantiating formula (82) with all_0_12_12, 0, all_0_11_11 and discharging atoms reflexive(all_0_12_12) = all_0_11_11, reflexive(all_0_12_12) = 0, yields:
% 8.91/2.72 | (102) all_0_11_11 = 0
% 8.91/2.72 |
% 8.91/2.72 | Equations (102) can reduce 121 to:
% 8.91/2.72 | (117) $false
% 8.91/2.72 |
% 8.91/2.72 |-The branch is then unsatisfiable
% 8.91/2.72 |-Branch two:
% 8.91/2.72 | (163) ~ (all_53_0_70 = 0) & relation_field(all_0_12_12) = all_53_1_71 & is_reflexive_in(all_0_12_12, all_53_1_71) = all_53_0_70
% 8.91/2.72 |
% 8.91/2.72 | Applying alpha-rule on (163) yields:
% 8.91/2.72 | (164) ~ (all_53_0_70 = 0)
% 8.91/2.72 | (111) relation_field(all_0_12_12) = all_53_1_71
% 8.91/2.72 | (166) is_reflexive_in(all_0_12_12, all_53_1_71) = all_53_0_70
% 8.91/2.72 |
% 8.91/2.72 +-Applying beta-rule and splitting (97), into two cases.
% 8.91/2.72 |-Branch one:
% 8.91/2.72 | (113) ~ (all_61_1_87 = 0) & relation(all_0_12_12) = all_61_1_87
% 8.91/2.72 |
% 8.91/2.72 | Applying alpha-rule on (113) yields:
% 8.91/2.72 | (114) ~ (all_61_1_87 = 0)
% 8.91/2.72 | (115) relation(all_0_12_12) = all_61_1_87
% 8.91/2.72 |
% 8.91/2.72 | Instantiating formula (43) with all_0_12_12, all_61_1_87, 0 and discharging atoms relation(all_0_12_12) = all_61_1_87, relation(all_0_12_12) = 0, yields:
% 8.91/2.72 | (116) all_61_1_87 = 0
% 8.91/2.72 |
% 8.91/2.72 | Equations (116) can reduce 114 to:
% 8.91/2.72 | (117) $false
% 8.91/2.72 |
% 8.91/2.72 |-The branch is then unsatisfiable
% 8.91/2.72 |-Branch two:
% 8.91/2.72 | (118) ( ~ (all_0_11_11 = 0) | (all_61_0_86 = 0 & relation_field(all_0_12_12) = all_61_1_87 & is_reflexive_in(all_0_12_12, all_61_1_87) = 0)) & (all_0_11_11 = 0 | ( ~ (all_61_0_86 = 0) & relation_field(all_0_12_12) = all_61_1_87 & is_reflexive_in(all_0_12_12, all_61_1_87) = all_61_0_86))
% 8.91/2.72 |
% 8.91/2.72 | Applying alpha-rule on (118) yields:
% 8.91/2.72 | (119) ~ (all_0_11_11 = 0) | (all_61_0_86 = 0 & relation_field(all_0_12_12) = all_61_1_87 & is_reflexive_in(all_0_12_12, all_61_1_87) = 0)
% 8.91/2.72 | (120) all_0_11_11 = 0 | ( ~ (all_61_0_86 = 0) & relation_field(all_0_12_12) = all_61_1_87 & is_reflexive_in(all_0_12_12, all_61_1_87) = all_61_0_86)
% 8.91/2.72 |
% 8.91/2.72 +-Applying beta-rule and splitting (90), into two cases.
% 8.91/2.72 |-Branch one:
% 8.91/2.72 | (109) all_53_0_70 = 0 & relation_field(all_0_12_12) = all_53_1_71 & is_reflexive_in(all_0_12_12, all_53_1_71) = 0
% 8.91/2.72 |
% 8.91/2.72 | Applying alpha-rule on (109) yields:
% 8.91/2.72 | (110) all_53_0_70 = 0
% 8.91/2.72 | (111) relation_field(all_0_12_12) = all_53_1_71
% 8.91/2.72 | (112) is_reflexive_in(all_0_12_12, all_53_1_71) = 0
% 8.91/2.72 |
% 8.91/2.72 | Equations (110) can reduce 164 to:
% 8.91/2.72 | (117) $false
% 8.91/2.72 |
% 8.91/2.72 |-The branch is then unsatisfiable
% 8.91/2.72 |-Branch two:
% 8.91/2.72 | (149) ~ (all_53_2_72 = 0) & reflexive(all_0_12_12) = all_53_2_72
% 8.91/2.72 |
% 8.91/2.72 | Applying alpha-rule on (149) yields:
% 8.91/2.72 | (150) ~ (all_53_2_72 = 0)
% 8.91/2.72 | (151) reflexive(all_0_12_12) = all_53_2_72
% 8.91/2.72 |
% 8.91/2.72 +-Applying beta-rule and splitting (120), into two cases.
% 8.91/2.72 |-Branch one:
% 8.91/2.72 | (102) all_0_11_11 = 0
% 8.91/2.72 |
% 8.91/2.72 | Equations (102) can reduce 121 to:
% 8.91/2.72 | (117) $false
% 8.91/2.72 |
% 8.91/2.72 |-The branch is then unsatisfiable
% 8.91/2.72 |-Branch two:
% 8.91/2.72 | (121) ~ (all_0_11_11 = 0)
% 8.91/2.72 | (186) ~ (all_61_0_86 = 0) & relation_field(all_0_12_12) = all_61_1_87 & is_reflexive_in(all_0_12_12, all_61_1_87) = all_61_0_86
% 8.91/2.72 |
% 8.91/2.72 | Applying alpha-rule on (186) yields:
% 8.91/2.72 | (187) ~ (all_61_0_86 = 0)
% 8.91/2.72 | (126) relation_field(all_0_12_12) = all_61_1_87
% 8.91/2.72 | (189) is_reflexive_in(all_0_12_12, all_61_1_87) = all_61_0_86
% 8.91/2.72 |
% 8.91/2.72 +-Applying beta-rule and splitting (98), into two cases.
% 8.91/2.72 |-Branch one:
% 8.91/2.72 | (190) ~ (all_63_1_91 = 0) & relation(all_0_12_12) = all_63_1_91
% 8.91/2.72 |
% 8.91/2.72 | Applying alpha-rule on (190) yields:
% 8.91/2.72 | (191) ~ (all_63_1_91 = 0)
% 8.91/2.72 | (192) relation(all_0_12_12) = all_63_1_91
% 8.91/2.72 |
% 8.91/2.72 | Instantiating formula (43) with all_0_12_12, all_63_1_91, 0 and discharging atoms relation(all_0_12_12) = all_63_1_91, relation(all_0_12_12) = 0, yields:
% 8.91/2.72 | (193) all_63_1_91 = 0
% 8.91/2.72 |
% 8.91/2.72 | Equations (193) can reduce 191 to:
% 8.91/2.72 | (117) $false
% 8.91/2.72 |
% 8.91/2.72 |-The branch is then unsatisfiable
% 8.91/2.72 |-Branch two:
% 8.91/2.72 | (195) ((all_63_0_90 = 0 & is_reflexive_in(all_0_12_12, all_0_10_10) = 0) | ( ~ (all_63_1_91 = 0) & reflexive(all_0_12_12) = all_63_1_91)) & ((all_63_1_91 = 0 & reflexive(all_0_12_12) = 0) | ( ~ (all_63_0_90 = 0) & is_reflexive_in(all_0_12_12, all_0_10_10) = all_63_0_90))
% 8.91/2.72 |
% 8.91/2.72 | Applying alpha-rule on (195) yields:
% 8.91/2.72 | (196) (all_63_0_90 = 0 & is_reflexive_in(all_0_12_12, all_0_10_10) = 0) | ( ~ (all_63_1_91 = 0) & reflexive(all_0_12_12) = all_63_1_91)
% 8.91/2.72 | (197) (all_63_1_91 = 0 & reflexive(all_0_12_12) = 0) | ( ~ (all_63_0_90 = 0) & is_reflexive_in(all_0_12_12, all_0_10_10) = all_63_0_90)
% 8.91/2.72 |
% 8.91/2.72 +-Applying beta-rule and splitting (197), into two cases.
% 8.91/2.72 |-Branch one:
% 8.91/2.72 | (198) all_63_1_91 = 0 & reflexive(all_0_12_12) = 0
% 8.91/2.72 |
% 8.91/2.72 | Applying alpha-rule on (198) yields:
% 8.91/2.72 | (193) all_63_1_91 = 0
% 8.91/2.72 | (108) reflexive(all_0_12_12) = 0
% 8.91/2.72 |
% 8.91/2.72 | Instantiating formula (82) with all_0_12_12, all_53_2_72, all_0_11_11 and discharging atoms reflexive(all_0_12_12) = all_53_2_72, reflexive(all_0_12_12) = all_0_11_11, yields:
% 8.91/2.72 | (201) all_53_2_72 = all_0_11_11
% 8.91/2.72 |
% 8.91/2.72 | Instantiating formula (82) with all_0_12_12, 0, all_53_2_72 and discharging atoms reflexive(all_0_12_12) = all_53_2_72, reflexive(all_0_12_12) = 0, yields:
% 8.91/2.72 | (152) all_53_2_72 = 0
% 8.91/2.72 |
% 8.91/2.72 | Combining equations (152,201) yields a new equation:
% 8.91/2.72 | (102) all_0_11_11 = 0
% 8.91/2.72 |
% 8.91/2.72 | Equations (102) can reduce 121 to:
% 8.91/2.72 | (117) $false
% 8.91/2.72 |
% 8.91/2.72 |-The branch is then unsatisfiable
% 8.91/2.72 |-Branch two:
% 8.91/2.72 | (205) ~ (all_63_0_90 = 0) & is_reflexive_in(all_0_12_12, all_0_10_10) = all_63_0_90
% 8.91/2.72 |
% 8.91/2.72 | Applying alpha-rule on (205) yields:
% 8.91/2.72 | (206) ~ (all_63_0_90 = 0)
% 8.91/2.72 | (207) is_reflexive_in(all_0_12_12, all_0_10_10) = all_63_0_90
% 8.91/2.72 |
% 8.91/2.72 | Instantiating formula (24) with all_0_12_12, all_61_1_87, all_0_10_10 and discharging atoms relation_field(all_0_12_12) = all_61_1_87, relation_field(all_0_12_12) = all_0_10_10, yields:
% 8.91/2.72 | (128) all_61_1_87 = all_0_10_10
% 8.91/2.72 |
% 8.91/2.72 | Instantiating formula (24) with all_0_12_12, all_53_1_71, all_61_1_87 and discharging atoms relation_field(all_0_12_12) = all_61_1_87, relation_field(all_0_12_12) = all_53_1_71, yields:
% 8.91/2.72 | (129) all_61_1_87 = all_53_1_71
% 8.91/2.72 |
% 8.91/2.72 | Combining equations (129,128) yields a new equation:
% 8.91/2.72 | (210) all_53_1_71 = all_0_10_10
% 8.91/2.72 |
% 8.91/2.72 | Simplifying 210 yields:
% 8.91/2.72 | (130) all_53_1_71 = all_0_10_10
% 8.91/2.72 |
% 8.91/2.72 | From (128) and (189) follows:
% 8.91/2.72 | (212) is_reflexive_in(all_0_12_12, all_0_10_10) = all_61_0_86
% 8.91/2.72 |
% 8.91/2.72 | From (130) and (166) follows:
% 8.91/2.72 | (213) is_reflexive_in(all_0_12_12, all_0_10_10) = all_53_0_70
% 8.91/2.72 |
% 8.91/2.72 | Instantiating formula (39) with all_0_12_12, all_0_10_10, all_61_0_86, all_63_0_90 and discharging atoms is_reflexive_in(all_0_12_12, all_0_10_10) = all_63_0_90, is_reflexive_in(all_0_12_12, all_0_10_10) = all_61_0_86, yields:
% 8.91/2.72 | (214) all_63_0_90 = all_61_0_86
% 8.91/2.72 |
% 8.91/2.72 | Instantiating formula (39) with all_0_12_12, all_0_10_10, all_53_0_70, all_63_0_90 and discharging atoms is_reflexive_in(all_0_12_12, all_0_10_10) = all_63_0_90, is_reflexive_in(all_0_12_12, all_0_10_10) = all_53_0_70, yields:
% 8.91/2.72 | (215) all_63_0_90 = all_53_0_70
% 8.91/2.72 |
% 8.91/2.72 | Combining equations (214,215) yields a new equation:
% 8.91/2.72 | (216) all_61_0_86 = all_53_0_70
% 8.91/2.73 |
% 8.91/2.73 | Simplifying 216 yields:
% 8.91/2.73 | (217) all_61_0_86 = all_53_0_70
% 8.91/2.73 |
% 8.91/2.73 | Equations (217) can reduce 187 to:
% 8.91/2.73 | (164) ~ (all_53_0_70 = 0)
% 8.91/2.73 |
% 8.91/2.73 | From (217) and (212) follows:
% 8.91/2.73 | (213) is_reflexive_in(all_0_12_12, all_0_10_10) = all_53_0_70
% 8.91/2.73 |
% 8.91/2.73 | Instantiating formula (22) with all_53_0_70, all_0_10_10, all_0_12_12 and discharging atoms is_reflexive_in(all_0_12_12, all_0_10_10) = all_53_0_70, relation(all_0_12_12) = 0, yields:
% 8.91/2.73 | (220) all_53_0_70 = 0 | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = 0) & ordered_pair(v0, v0) = v1 & in(v1, all_0_12_12) = v2 & in(v0, all_0_10_10) = 0)
% 8.91/2.73 |
% 8.91/2.73 +-Applying beta-rule and splitting (220), into two cases.
% 8.91/2.73 |-Branch one:
% 8.91/2.73 | (110) all_53_0_70 = 0
% 8.91/2.73 |
% 8.91/2.73 | Equations (110) can reduce 164 to:
% 8.91/2.73 | (117) $false
% 8.91/2.73 |
% 8.91/2.73 |-The branch is then unsatisfiable
% 8.91/2.73 |-Branch two:
% 8.91/2.73 | (164) ~ (all_53_0_70 = 0)
% 8.91/2.73 | (224) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = 0) & ordered_pair(v0, v0) = v1 & in(v1, all_0_12_12) = v2 & in(v0, all_0_10_10) = 0)
% 8.91/2.73 |
% 8.91/2.73 | Instantiating (224) with all_170_0_136, all_170_1_137, all_170_2_138 yields:
% 8.91/2.73 | (225) ~ (all_170_0_136 = 0) & ordered_pair(all_170_2_138, all_170_2_138) = all_170_1_137 & in(all_170_1_137, all_0_12_12) = all_170_0_136 & in(all_170_2_138, all_0_10_10) = 0
% 8.91/2.73 |
% 8.91/2.73 | Applying alpha-rule on (225) yields:
% 8.91/2.73 | (226) ~ (all_170_0_136 = 0)
% 8.91/2.73 | (227) ordered_pair(all_170_2_138, all_170_2_138) = all_170_1_137
% 8.91/2.73 | (228) in(all_170_1_137, all_0_12_12) = all_170_0_136
% 8.91/2.73 | (229) in(all_170_2_138, all_0_10_10) = 0
% 8.91/2.73 |
% 8.91/2.73 | Instantiating formula (156) with all_170_1_137, all_170_2_138 and discharging atoms ordered_pair(all_170_2_138, all_170_2_138) = all_170_1_137, yields:
% 8.91/2.73 | (230) ? [v0] : ((v0 = 0 & in(all_170_1_137, all_0_12_12) = 0) | ( ~ (v0 = 0) & in(all_170_2_138, all_0_10_10) = v0))
% 8.91/2.73 |
% 8.91/2.73 | Instantiating formula (71) with all_170_0_136, all_0_12_12, all_170_1_137 and discharging atoms in(all_170_1_137, all_0_12_12) = all_170_0_136, yields:
% 8.91/2.73 | (231) all_170_0_136 = 0 | ? [v0] : ((v0 = 0 & empty(all_0_12_12) = 0) | ( ~ (v0 = 0) & element(all_170_1_137, all_0_12_12) = v0))
% 8.91/2.73 |
% 8.91/2.73 | Instantiating (230) with all_217_0_145 yields:
% 8.91/2.73 | (232) (all_217_0_145 = 0 & in(all_170_1_137, all_0_12_12) = 0) | ( ~ (all_217_0_145 = 0) & in(all_170_2_138, all_0_10_10) = all_217_0_145)
% 8.91/2.73 |
% 8.91/2.73 +-Applying beta-rule and splitting (232), into two cases.
% 8.91/2.73 |-Branch one:
% 8.91/2.73 | (233) all_217_0_145 = 0 & in(all_170_1_137, all_0_12_12) = 0
% 8.91/2.73 |
% 8.91/2.73 | Applying alpha-rule on (233) yields:
% 8.91/2.73 | (234) all_217_0_145 = 0
% 8.91/2.73 | (235) in(all_170_1_137, all_0_12_12) = 0
% 8.91/2.73 |
% 8.91/2.73 +-Applying beta-rule and splitting (231), into two cases.
% 8.91/2.73 |-Branch one:
% 8.91/2.73 | (236) all_170_0_136 = 0
% 8.91/2.73 |
% 8.91/2.73 | Equations (236) can reduce 226 to:
% 8.91/2.73 | (117) $false
% 8.91/2.73 |
% 8.91/2.73 |-The branch is then unsatisfiable
% 8.91/2.73 |-Branch two:
% 8.91/2.73 | (226) ~ (all_170_0_136 = 0)
% 8.91/2.73 | (239) ? [v0] : ((v0 = 0 & empty(all_0_12_12) = 0) | ( ~ (v0 = 0) & element(all_170_1_137, all_0_12_12) = v0))
% 8.91/2.73 |
% 8.91/2.73 | Instantiating formula (33) with all_170_1_137, all_0_12_12, 0, all_170_0_136 and discharging atoms in(all_170_1_137, all_0_12_12) = all_170_0_136, in(all_170_1_137, all_0_12_12) = 0, yields:
% 8.91/2.73 | (236) all_170_0_136 = 0
% 8.91/2.73 |
% 8.91/2.73 | Equations (236) can reduce 226 to:
% 8.91/2.73 | (117) $false
% 8.91/2.73 |
% 8.91/2.73 |-The branch is then unsatisfiable
% 8.91/2.73 |-Branch two:
% 8.91/2.73 | (242) ~ (all_217_0_145 = 0) & in(all_170_2_138, all_0_10_10) = all_217_0_145
% 8.91/2.73 |
% 8.91/2.73 | Applying alpha-rule on (242) yields:
% 8.91/2.73 | (243) ~ (all_217_0_145 = 0)
% 8.91/2.73 | (244) in(all_170_2_138, all_0_10_10) = all_217_0_145
% 8.91/2.73 |
% 8.91/2.73 | Instantiating formula (33) with all_170_2_138, all_0_10_10, all_217_0_145, 0 and discharging atoms in(all_170_2_138, all_0_10_10) = all_217_0_145, in(all_170_2_138, all_0_10_10) = 0, yields:
% 8.91/2.73 | (234) all_217_0_145 = 0
% 8.91/2.73 |
% 8.91/2.73 | Equations (234) can reduce 243 to:
% 8.91/2.73 | (117) $false
% 8.91/2.73 |
% 8.91/2.73 |-The branch is then unsatisfiable
% 8.91/2.73 % SZS output end Proof for theBenchmark
% 8.91/2.73
% 8.91/2.73 2149ms
%------------------------------------------------------------------------------