TSTP Solution File: SEU242+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU242+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n017.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 08:48:04 EDT 2022
% Result : Theorem 6.30s 2.16s
% Output : Proof 10.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU242+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.33 % Computer : n017.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jun 19 21:08:58 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.59/0.59 ____ _
% 0.59/0.59 ___ / __ \_____(_)___ ________ __________
% 0.59/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.59/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.59/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.59/0.59
% 0.59/0.59 A Theorem Prover for First-Order Logic
% 0.59/0.59 (ePrincess v.1.0)
% 0.59/0.59
% 0.59/0.59 (c) Philipp Rümmer, 2009-2015
% 0.59/0.59 (c) Peter Backeman, 2014-2015
% 0.59/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.59/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.59/0.59 Bug reports to peter@backeman.se
% 0.59/0.59
% 0.59/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.59/0.59
% 0.59/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.75/0.66 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.55/0.97 Prover 0: Preprocessing ...
% 2.14/1.19 Prover 0: Warning: ignoring some quantifiers
% 2.21/1.21 Prover 0: Constructing countermodel ...
% 3.50/1.57 Prover 0: gave up
% 3.50/1.57 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 3.50/1.60 Prover 1: Preprocessing ...
% 4.23/1.69 Prover 1: Warning: ignoring some quantifiers
% 4.23/1.70 Prover 1: Constructing countermodel ...
% 4.84/1.88 Prover 1: gave up
% 4.84/1.88 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 4.84/1.90 Prover 2: Preprocessing ...
% 5.66/2.00 Prover 2: Warning: ignoring some quantifiers
% 5.66/2.01 Prover 2: Constructing countermodel ...
% 6.30/2.16 Prover 2: proved (283ms)
% 6.30/2.16
% 6.30/2.16 No countermodel exists, formula is valid
% 6.30/2.16 % SZS status Theorem for theBenchmark
% 6.30/2.16
% 6.30/2.16 Generating proof ... Warning: ignoring some quantifiers
% 9.67/2.91 found it (size 173)
% 9.67/2.91
% 9.67/2.91 % SZS output start Proof for theBenchmark
% 9.67/2.91 Assumed formulas after preprocessing and simplification:
% 9.67/2.91 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ( ~ (v13 = 0) & relation_field(v0) = v2 & connected(v0) = v1 & one_to_one(v11) = 0 & relation(v16) = 0 & relation(v14) = 0 & relation(v11) = 0 & relation(v0) = 0 & function(v16) = 0 & function(v14) = 0 & function(v11) = 0 & empty(v15) = 0 & empty(v14) = 0 & empty(v12) = v13 & empty(empty_set) = 0 & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v20 = v19 | ~ (ordered_pair(v20, v19) = v21) | ~ (is_connected_in(v17, v18) = 0) | ~ (relation(v17) = 0) | ? [v22] : ? [v23] : ((v23 = 0 & ordered_pair(v19, v20) = v22 & in(v22, v17) = 0) | (v22 = 0 & in(v21, v17) = 0) | ( ~ (v22 = 0) & in(v20, v18) = v22) | ( ~ (v22 = 0) & in(v19, v18) = v22))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v20 = v19 | ~ (ordered_pair(v19, v20) = v21) | ~ (is_connected_in(v17, v18) = 0) | ~ (relation(v17) = 0) | ? [v22] : ? [v23] : ((v23 = 0 & ordered_pair(v20, v19) = v22 & in(v22, v17) = 0) | (v22 = 0 & in(v21, v17) = 0) | ( ~ (v22 = 0) & in(v20, v18) = v22) | ( ~ (v22 = 0) & in(v19, v18) = v22))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (element(v20, v19) = v18) | ~ (element(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (ordered_pair(v20, v19) = v18) | ~ (ordered_pair(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (is_connected_in(v20, v19) = v18) | ~ (is_connected_in(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (set_union2(v20, v19) = v18) | ~ (set_union2(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (unordered_pair(v20, v19) = v18) | ~ (unordered_pair(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (in(v20, v19) = v18) | ~ (in(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : (v19 = 0 | ~ (element(v17, v18) = v19) | ? [v20] : ( ~ (v20 = 0) & in(v17, v18) = v20)) & ! [v17] : ! [v18] : ! [v19] : (v19 = 0 | ~ (is_connected_in(v17, v18) = v19) | ~ (relation(v17) = 0) | ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ( ~ (v25 = 0) & ~ (v23 = 0) & ~ (v21 = v20) & ordered_pair(v21, v20) = v24 & ordered_pair(v20, v21) = v22 & in(v24, v17) = v25 & in(v22, v17) = v23 & in(v21, v18) = 0 & in(v20, v18) = 0)) & ! [v17] : ! [v18] : ! [v19] : (v19 = 0 | ~ (in(v17, v18) = v19) | ? [v20] : ((v20 = 0 & empty(v18) = 0) | ( ~ (v20 = 0) & element(v17, v18) = v20))) & ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (relation_dom(v19) = v18) | ~ (relation_dom(v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (relation_rng(v19) = v18) | ~ (relation_rng(v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (singleton(v19) = v18) | ~ (singleton(v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (relation_field(v19) = v18) | ~ (relation_field(v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (connected(v19) = v18) | ~ (connected(v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (one_to_one(v19) = v18) | ~ (one_to_one(v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (relation(v19) = v18) | ~ (relation(v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (function(v19) = v18) | ~ (function(v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (empty(v19) = v18) | ~ (empty(v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (ordered_pair(v17, v18) = v19) | ? [v20] : ? [v21] : (singleton(v17) = v21 & unordered_pair(v20, v21) = v19 & unordered_pair(v17, v18) = v20)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (ordered_pair(v17, v18) = v19) | ? [v20] : ( ~ (v20 = 0) & empty(v19) = v20)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (set_union2(v18, v17) = v19) | set_union2(v17, v18) = v19) & ! [v17] : ! [v18] : ! [v19] : ( ~ (set_union2(v18, v17) = v19) | ? [v20] : ((v20 = 0 & empty(v17) = 0) | ( ~ (v20 = 0) & empty(v19) = v20))) & ! [v17] : ! [v18] : ! [v19] : ( ~ (set_union2(v17, v18) = v19) | set_union2(v18, v17) = v19) & ! [v17] : ! [v18] : ! [v19] : ( ~ (set_union2(v17, v18) = v19) | ? [v20] : ((v20 = 0 & empty(v17) = 0) | ( ~ (v20 = 0) & empty(v19) = v20))) & ! [v17] : ! [v18] : ! [v19] : ( ~ (unordered_pair(v18, v17) = v19) | unordered_pair(v17, v18) = v19) & ! [v17] : ! [v18] : ! [v19] : ( ~ (unordered_pair(v17, v18) = v19) | unordered_pair(v18, v17) = v19) & ! [v17] : ! [v18] : ! [v19] : ( ~ (unordered_pair(v17, v18) = v19) | ? [v20] : ? [v21] : (ordered_pair(v17, v18) = v20 & singleton(v17) = v21 & unordered_pair(v19, v21) = v20)) & ! [v17] : ! [v18] : (v18 = v17 | ~ (set_union2(v17, v17) = v18)) & ! [v17] : ! [v18] : (v18 = v17 | ~ (set_union2(v17, empty_set) = v18)) & ! [v17] : ! [v18] : (v18 = v17 | ~ (empty(v18) = 0) | ~ (empty(v17) = 0)) & ! [v17] : ! [v18] : (v18 = 0 | ~ (function(v17) = v18) | ? [v19] : ( ~ (v19 = 0) & empty(v17) = v19)) & ! [v17] : ! [v18] : ( ~ (element(v17, v18) = 0) | ? [v19] : ((v19 = 0 & empty(v18) = 0) | (v19 = 0 & in(v17, v18) = 0))) & ! [v17] : ! [v18] : ( ~ (relation_dom(v17) = v18) | ? [v19] : ? [v20] : ? [v21] : ((v21 = v19 & relation_rng(v17) = v20 & relation_field(v17) = v19 & set_union2(v18, v20) = v19) | ( ~ (v19 = 0) & relation(v17) = v19))) & ! [v17] : ! [v18] : ( ~ (relation_rng(v17) = v18) | ? [v19] : ? [v20] : ? [v21] : ((v21 = v19 & relation_dom(v17) = v20 & relation_field(v17) = v19 & set_union2(v20, v18) = v19) | ( ~ (v19 = 0) & relation(v17) = v19))) & ! [v17] : ! [v18] : ( ~ (relation_field(v17) = v18) | ? [v19] : ? [v20] : ? [v21] : ((v21 = v18 & relation_dom(v17) = v19 & relation_rng(v17) = v20 & set_union2(v19, v20) = v18) | ( ~ (v19 = 0) & relation(v17) = v19))) & ! [v17] : ! [v18] : ( ~ (relation_field(v17) = v18) | ? [v19] : ? [v20] : (( ~ (v19 = 0) & relation(v17) = v19) | (((v20 = 0 & is_connected_in(v17, v18) = 0) | ( ~ (v19 = 0) & connected(v17) = v19)) & ((v19 = 0 & connected(v17) = 0) | ( ~ (v20 = 0) & is_connected_in(v17, v18) = v20))))) & ! [v17] : ! [v18] : ( ~ (connected(v17) = v18) | ? [v19] : ? [v20] : (( ~ (v19 = 0) & relation(v17) = v19) | (( ~ (v18 = 0) | (v20 = 0 & relation_field(v17) = v19 & is_connected_in(v17, v19) = 0)) & (v18 = 0 | ( ~ (v20 = 0) & relation_field(v17) = v19 & is_connected_in(v17, v19) = v20))))) & ! [v17] : ! [v18] : ( ~ (one_to_one(v17) = v18) | ? [v19] : ? [v20] : ((v20 = 0 & v19 = 0 & v18 = 0 & relation(v17) = 0 & function(v17) = 0) | ( ~ (v19 = 0) & relation(v17) = v19) | ( ~ (v19 = 0) & function(v17) = v19) | ( ~ (v19 = 0) & empty(v17) = v19))) & ! [v17] : ! [v18] : ( ~ (in(v18, v17) = 0) | ? [v19] : ( ~ (v19 = 0) & in(v17, v18) = v19)) & ! [v17] : ! [v18] : ( ~ (in(v17, v18) = 0) | element(v17, v18) = 0) & ! [v17] : ! [v18] : ( ~ (in(v17, v18) = 0) | ? [v19] : ( ~ (v19 = 0) & empty(v18) = v19)) & ! [v17] : ! [v18] : ( ~ (in(v17, v18) = 0) | ? [v19] : ( ~ (v19 = 0) & in(v18, v17) = v19)) & ! [v17] : (v17 = empty_set | ~ (empty(v17) = 0)) & ! [v17] : ( ~ (relation(v17) = 0) | ? [v18] : ? [v19] : ? [v20] : (relation_dom(v17) = v19 & relation_rng(v17) = v20 & relation_field(v17) = v18 & set_union2(v19, v20) = v18)) & ! [v17] : ( ~ (relation(v17) = 0) | ? [v18] : ? [v19] : ? [v20] : (((v20 = 0 & relation_field(v17) = v19 & is_connected_in(v17, v19) = 0) | ( ~ (v18 = 0) & connected(v17) = v18)) & ((v18 = 0 & connected(v17) = 0) | ( ~ (v20 = 0) & relation_field(v17) = v19 & is_connected_in(v17, v19) = v20)))) & ! [v17] : ( ~ (relation(v17) = 0) | ? [v18] : ? [v19] : ((v19 = 0 & v18 = 0 & one_to_one(v17) = 0 & function(v17) = 0) | ( ~ (v18 = 0) & function(v17) = v18) | ( ~ (v18 = 0) & empty(v17) = v18))) & ! [v17] : ( ~ (function(v17) = 0) | ? [v18] : ? [v19] : ((v19 = 0 & v18 = 0 & one_to_one(v17) = 0 & relation(v17) = 0) | ( ~ (v18 = 0) & relation(v17) = v18) | ( ~ (v18 = 0) & empty(v17) = v18))) & ! [v17] : ( ~ (empty(v17) = 0) | function(v17) = 0) & ! [v17] : ( ~ (empty(v17) = 0) | ? [v18] : ? [v19] : ? [v20] : ((v20 = 0 & v19 = 0 & v18 = 0 & one_to_one(v17) = 0 & relation(v17) = 0 & function(v17) = 0) | ( ~ (v18 = 0) & relation(v17) = v18) | ( ~ (v18 = 0) & function(v17) = v18))) & ? [v17] : ? [v18] : ? [v19] : element(v18, v17) = v19 & ? [v17] : ? [v18] : ? [v19] : ordered_pair(v18, v17) = v19 & ? [v17] : ? [v18] : ? [v19] : is_connected_in(v18, v17) = v19 & ? [v17] : ? [v18] : ? [v19] : set_union2(v18, v17) = v19 & ? [v17] : ? [v18] : ? [v19] : unordered_pair(v18, v17) = v19 & ? [v17] : ? [v18] : ? [v19] : in(v18, v17) = v19 & ? [v17] : ? [v18] : element(v18, v17) = 0 & ? [v17] : ? [v18] : relation_dom(v17) = v18 & ? [v17] : ? [v18] : relation_rng(v17) = v18 & ? [v17] : ? [v18] : singleton(v17) = v18 & ? [v17] : ? [v18] : relation_field(v17) = v18 & ? [v17] : ? [v18] : connected(v17) = v18 & ? [v17] : ? [v18] : one_to_one(v17) = v18 & ? [v17] : ? [v18] : relation(v17) = v18 & ? [v17] : ? [v18] : function(v17) = v18 & ? [v17] : ? [v18] : empty(v17) = v18 & ((v6 = 0 & v5 = 0 & v1 = 0 & ~ (v10 = 0) & ~ (v8 = 0) & ~ (v4 = v3) & ordered_pair(v4, v3) = v9 & ordered_pair(v3, v4) = v7 & in(v9, v0) = v10 & in(v7, v0) = v8 & in(v4, v2) = 0 & in(v3, v2) = 0) | ( ~ (v1 = 0) & ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (ordered_pair(v18, v17) = v19) | ? [v20] : ? [v21] : ((v21 = 0 & ordered_pair(v17, v18) = v20 & in(v20, v0) = 0) | (v20 = 0 & in(v19, v0) = 0) | ( ~ (v20 = 0) & in(v18, v2) = v20) | ( ~ (v20 = 0) & in(v17, v2) = v20))) & ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (ordered_pair(v17, v18) = v19) | ? [v20] : ? [v21] : ((v21 = 0 & ordered_pair(v18, v17) = v20 & in(v20, v0) = 0) | (v20 = 0 & in(v19, v0) = 0) | ( ~ (v20 = 0) & in(v18, v2) = v20) | ( ~ (v20 = 0) & in(v17, v2) = v20))))))
% 9.67/2.96 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9, all_0_10_10, all_0_11_11, all_0_12_12, all_0_13_13, all_0_14_14, all_0_15_15, all_0_16_16 yields:
% 9.67/2.96 | (1) ~ (all_0_3_3 = 0) & relation_field(all_0_16_16) = all_0_14_14 & connected(all_0_16_16) = all_0_15_15 & 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_16_16) = 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] : (v3 = v2 | ~ (ordered_pair(v3, v2) = v4) | ~ (is_connected_in(v0, v1) = 0) | ~ (relation(v0) = 0) | ? [v5] : ? [v6] : ((v6 = 0 & ordered_pair(v2, v3) = v5 & in(v5, v0) = 0) | (v5 = 0 & in(v4, v0) = 0) | ( ~ (v5 = 0) & in(v3, v1) = v5) | ( ~ (v5 = 0) & in(v2, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (ordered_pair(v2, v3) = v4) | ~ (is_connected_in(v0, v1) = 0) | ~ (relation(v0) = 0) | ? [v5] : ? [v6] : ((v6 = 0 & ordered_pair(v3, v2) = v5 & in(v5, v0) = 0) | (v5 = 0 & in(v4, v0) = 0) | ( ~ (v5 = 0) & in(v3, v1) = v5) | ( ~ (v5 = 0) & in(v2, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(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 | ~ (is_connected_in(v3, v2) = v1) | ~ (is_connected_in(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 | ~ (is_connected_in(v0, v1) = v2) | ~ (relation(v0) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ( ~ (v8 = 0) & ~ (v6 = 0) & ~ (v4 = v3) & ordered_pair(v4, v3) = v7 & ordered_pair(v3, v4) = v5 & in(v7, v0) = v8 & in(v5, v0) = v6 & in(v4, v1) = 0 & 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 | ~ (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 | ~ (relation_field(v2) = v1) | ~ (relation_field(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (connected(v2) = v1) | ~ (connected(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] : ( ~ (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] : (ordered_pair(v0, v1) = v3 & singleton(v0) = v4 & 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] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v2 & relation_rng(v0) = v3 & relation_field(v0) = v2 & set_union2(v1, v3) = v2) | ( ~ (v2 = 0) & relation(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v2 & relation_dom(v0) = v3 & relation_field(v0) = v2 & set_union2(v3, v1) = v2) | ( ~ (v2 = 0) & relation(v0) = v2))) & ! [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_connected_in(v0, v1) = 0) | ( ~ (v2 = 0) & connected(v0) = v2)) & ((v2 = 0 & connected(v0) = 0) | ( ~ (v3 = 0) & is_connected_in(v0, v1) = v3))))) & ! [v0] : ! [v1] : ( ~ (connected(v0) = v1) | ? [v2] : ? [v3] : (( ~ (v2 = 0) & relation(v0) = v2) | (( ~ (v1 = 0) | (v3 = 0 & relation_field(v0) = v2 & is_connected_in(v0, v2) = 0)) & (v1 = 0 | ( ~ (v3 = 0) & relation_field(v0) = v2 & is_connected_in(v0, v2) = v3))))) & ! [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_dom(v0) = v2 & relation_rng(v0) = v3 & relation_field(v0) = v1 & set_union2(v2, v3) = v1)) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (((v3 = 0 & relation_field(v0) = v2 & is_connected_in(v0, v2) = 0) | ( ~ (v1 = 0) & connected(v0) = v1)) & ((v1 = 0 & connected(v0) = 0) | ( ~ (v3 = 0) & relation_field(v0) = v2 & is_connected_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] : ordered_pair(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : is_connected_in(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] : relation_dom(v0) = v1 & ? [v0] : ? [v1] : relation_rng(v0) = v1 & ? [v0] : ? [v1] : singleton(v0) = v1 & ? [v0] : ? [v1] : relation_field(v0) = v1 & ? [v0] : ? [v1] : connected(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_10_10 = 0 & all_0_11_11 = 0 & all_0_15_15 = 0 & ~ (all_0_6_6 = 0) & ~ (all_0_8_8 = 0) & ~ (all_0_12_12 = all_0_13_13) & ordered_pair(all_0_12_12, all_0_13_13) = all_0_7_7 & ordered_pair(all_0_13_13, all_0_12_12) = all_0_9_9 & in(all_0_7_7, all_0_16_16) = all_0_6_6 & in(all_0_9_9, all_0_16_16) = all_0_8_8 & in(all_0_12_12, all_0_14_14) = 0 & in(all_0_13_13, all_0_14_14) = 0) | ( ~ (all_0_15_15 = 0) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ordered_pair(v1, v0) = v2) | ? [v3] : ? [v4] : ((v4 = 0 & ordered_pair(v0, v1) = v3 & in(v3, all_0_16_16) = 0) | (v3 = 0 & in(v2, all_0_16_16) = 0) | ( ~ (v3 = 0) & in(v1, all_0_14_14) = v3) | ( ~ (v3 = 0) & in(v0, all_0_14_14) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : ((v4 = 0 & ordered_pair(v1, v0) = v3 & in(v3, all_0_16_16) = 0) | (v3 = 0 & in(v2, all_0_16_16) = 0) | ( ~ (v3 = 0) & in(v1, all_0_14_14) = v3) | ( ~ (v3 = 0) & in(v0, all_0_14_14) = v3)))))
% 9.98/2.98 |
% 9.98/2.98 | Applying alpha-rule on (1) yields:
% 9.98/2.98 | (2) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2)
% 9.98/2.98 | (3) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2)
% 9.98/2.98 | (4) relation(all_0_5_5) = 0
% 9.98/2.98 | (5) ! [v0] : ! [v1] : ( ~ (element(v0, v1) = 0) | ? [v2] : ((v2 = 0 & empty(v1) = 0) | (v2 = 0 & in(v0, v1) = 0)))
% 9.98/2.98 | (6) ? [v0] : ? [v1] : one_to_one(v0) = v1
% 9.98/2.98 | (7) connected(all_0_16_16) = all_0_15_15
% 9.98/2.98 | (8) ? [v0] : ? [v1] : relation_dom(v0) = v1
% 9.98/2.98 | (9) ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2
% 9.98/2.98 | (10) function(all_0_0_0) = 0
% 9.98/2.98 | (11) relation_field(all_0_16_16) = all_0_14_14
% 9.98/2.98 | (12) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 9.98/2.98 | (13) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0))
% 9.98/2.98 | (14) ? [v0] : ? [v1] : relation(v0) = v1
% 9.98/2.98 | (15) ! [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)))
% 9.98/2.98 | (16) empty(all_0_2_2) = 0
% 9.98/2.98 | (17) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (relation_dom(v0) = v2 & relation_rng(v0) = v3 & relation_field(v0) = v1 & set_union2(v2, v3) = v1))
% 9.98/2.99 | (18) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0))
% 9.98/2.99 | (19) ! [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)))
% 9.98/2.99 | (20) ! [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)))
% 9.98/2.99 | (21) ! [v0] : ( ~ (empty(v0) = 0) | function(v0) = 0)
% 9.98/2.99 | (22) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (((v3 = 0 & relation_field(v0) = v2 & is_connected_in(v0, v2) = 0) | ( ~ (v1 = 0) & connected(v0) = v1)) & ((v1 = 0 & connected(v0) = 0) | ( ~ (v3 = 0) & relation_field(v0) = v2 & is_connected_in(v0, v2) = v3))))
% 9.98/2.99 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (ordered_pair(v3, v2) = v4) | ~ (is_connected_in(v0, v1) = 0) | ~ (relation(v0) = 0) | ? [v5] : ? [v6] : ((v6 = 0 & ordered_pair(v2, v3) = v5 & in(v5, v0) = 0) | (v5 = 0 & in(v4, v0) = 0) | ( ~ (v5 = 0) & in(v3, v1) = v5) | ( ~ (v5 = 0) & in(v2, v1) = v5)))
% 9.98/2.99 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (ordered_pair(v2, v3) = v4) | ~ (is_connected_in(v0, v1) = 0) | ~ (relation(v0) = 0) | ? [v5] : ? [v6] : ((v6 = 0 & ordered_pair(v3, v2) = v5 & in(v5, v0) = 0) | (v5 = 0 & in(v4, v0) = 0) | ( ~ (v5 = 0) & in(v3, v1) = v5) | ( ~ (v5 = 0) & in(v2, v1) = v5)))
% 9.98/2.99 | (25) ! [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)))
% 9.98/2.99 | (26) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2)
% 9.98/2.99 | (27) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2)
% 9.98/2.99 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 9.98/2.99 | (29) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 9.98/2.99 | (30) ! [v0] : ! [v1] : (v1 = 0 | ~ (function(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2))
% 9.98/2.99 | (31) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (ordered_pair(v0, v1) = v3 & singleton(v0) = v4 & unordered_pair(v2, v4) = v3))
% 9.98/2.99 | (32) ? [v0] : ? [v1] : ? [v2] : element(v1, v0) = v2
% 9.98/2.99 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0))
% 9.98/2.99 | (34) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1))
% 9.98/2.99 | (35) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1))
% 9.98/2.99 | (36) ! [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)))
% 9.98/2.99 | (37) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (connected(v2) = v1) | ~ (connected(v2) = v0))
% 9.98/2.99 | (38) one_to_one(all_0_5_5) = 0
% 9.98/2.99 | (39) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0))
% 9.98/2.99 | (40) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3))
% 9.98/2.99 | (41) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0))
% 9.98/2.99 | (42) ~ (all_0_3_3 = 0)
% 9.98/2.99 | (43) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_field(v2) = v1) | ~ (relation_field(v2) = v0))
% 9.98/3.00 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0))
% 9.98/3.00 | (45) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v2 & relation_rng(v0) = v3 & relation_field(v0) = v2 & set_union2(v1, v3) = v2) | ( ~ (v2 = 0) & relation(v0) = v2)))
% 9.98/3.00 | (46) ? [v0] : ? [v1] : connected(v0) = v1
% 9.98/3.00 | (47) empty(all_0_4_4) = all_0_3_3
% 9.98/3.00 | (48) ? [v0] : ? [v1] : empty(v0) = v1
% 9.98/3.00 | (49) function(all_0_2_2) = 0
% 9.98/3.00 | (50) (all_0_10_10 = 0 & all_0_11_11 = 0 & all_0_15_15 = 0 & ~ (all_0_6_6 = 0) & ~ (all_0_8_8 = 0) & ~ (all_0_12_12 = all_0_13_13) & ordered_pair(all_0_12_12, all_0_13_13) = all_0_7_7 & ordered_pair(all_0_13_13, all_0_12_12) = all_0_9_9 & in(all_0_7_7, all_0_16_16) = all_0_6_6 & in(all_0_9_9, all_0_16_16) = all_0_8_8 & in(all_0_12_12, all_0_14_14) = 0 & in(all_0_13_13, all_0_14_14) = 0) | ( ~ (all_0_15_15 = 0) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ordered_pair(v1, v0) = v2) | ? [v3] : ? [v4] : ((v4 = 0 & ordered_pair(v0, v1) = v3 & in(v3, all_0_16_16) = 0) | (v3 = 0 & in(v2, all_0_16_16) = 0) | ( ~ (v3 = 0) & in(v1, all_0_14_14) = v3) | ( ~ (v3 = 0) & in(v0, all_0_14_14) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : ((v4 = 0 & ordered_pair(v1, v0) = v3 & in(v3, all_0_16_16) = 0) | (v3 = 0 & in(v2, all_0_16_16) = 0) | ( ~ (v3 = 0) & in(v1, all_0_14_14) = v3) | ( ~ (v3 = 0) & in(v0, all_0_14_14) = v3))))
% 9.98/3.00 | (51) ? [v0] : ? [v1] : relation_rng(v0) = v1
% 9.98/3.00 | (52) ? [v0] : ? [v1] : ? [v2] : is_connected_in(v1, v0) = v2
% 9.98/3.00 | (53) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0))
% 9.98/3.00 | (54) ? [v0] : ? [v1] : function(v0) = v1
% 9.98/3.00 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0))
% 9.98/3.00 | (56) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v2 & relation_dom(v0) = v3 & relation_field(v0) = v2 & set_union2(v3, v1) = v2) | ( ~ (v2 = 0) & relation(v0) = v2)))
% 9.98/3.00 | (57) ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ? [v2] : ? [v3] : (( ~ (v2 = 0) & relation(v0) = v2) | (((v3 = 0 & is_connected_in(v0, v1) = 0) | ( ~ (v2 = 0) & connected(v0) = v2)) & ((v2 = 0 & connected(v0) = 0) | ( ~ (v3 = 0) & is_connected_in(v0, v1) = v3)))))
% 9.98/3.00 | (58) ? [v0] : ? [v1] : singleton(v0) = v1
% 9.98/3.00 | (59) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v0, v1) = v2) | ? [v3] : ((v3 = 0 & empty(v1) = 0) | ( ~ (v3 = 0) & element(v0, v1) = v3)))
% 9.98/3.00 | (60) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ? [v3] : ((v3 = 0 & empty(v0) = 0) | ( ~ (v3 = 0) & empty(v2) = v3)))
% 9.98/3.00 | (61) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 9.98/3.00 | (62) empty(empty_set) = 0
% 9.98/3.00 | (63) function(all_0_5_5) = 0
% 9.98/3.00 | (64) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3))
% 9.98/3.00 | (65) relation(all_0_16_16) = 0
% 9.98/3.00 | (66) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 9.98/3.00 | (67) ? [v0] : ? [v1] : relation_field(v0) = v1
% 9.98/3.00 | (68) relation(all_0_0_0) = 0
% 9.98/3.00 | (69) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0))
% 9.98/3.00 | (70) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | element(v0, v1) = 0)
% 9.98/3.00 | (71) ? [v0] : ? [v1] : element(v1, v0) = 0
% 9.98/3.00 | (72) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : ((v3 = 0 & empty(v0) = 0) | ( ~ (v3 = 0) & empty(v2) = v3)))
% 9.98/3.00 | (73) ! [v0] : ! [v1] : ( ~ (connected(v0) = v1) | ? [v2] : ? [v3] : (( ~ (v2 = 0) & relation(v0) = v2) | (( ~ (v1 = 0) | (v3 = 0 & relation_field(v0) = v2 & is_connected_in(v0, v2) = 0)) & (v1 = 0 | ( ~ (v3 = 0) & relation_field(v0) = v2 & is_connected_in(v0, v2) = v3)))))
% 9.98/3.00 | (74) empty(all_0_1_1) = 0
% 9.98/3.00 | (75) relation(all_0_2_2) = 0
% 9.98/3.00 | (76) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0))
% 9.98/3.01 | (77) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3))
% 9.98/3.01 | (78) ? [v0] : ? [v1] : ? [v2] : unordered_pair(v1, v0) = v2
% 9.98/3.01 | (79) ? [v0] : ? [v1] : ? [v2] : set_union2(v1, v0) = v2
% 9.98/3.01 | (80) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (is_connected_in(v0, v1) = v2) | ~ (relation(v0) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ( ~ (v8 = 0) & ~ (v6 = 0) & ~ (v4 = v3) & ordered_pair(v4, v3) = v7 & ordered_pair(v3, v4) = v5 & in(v7, v0) = v8 & in(v5, v0) = v6 & in(v4, v1) = 0 & in(v3, v1) = 0))
% 9.98/3.01 | (81) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (is_connected_in(v3, v2) = v1) | ~ (is_connected_in(v3, v2) = v0))
% 9.98/3.01 | (82) ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2))
% 9.98/3.01 | (83) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 9.98/3.01 | (84) ? [v0] : ? [v1] : ? [v2] : ordered_pair(v1, v0) = v2
% 9.98/3.01 |
% 9.98/3.01 | Instantiating formula (57) with all_0_14_14, all_0_16_16 and discharging atoms relation_field(all_0_16_16) = all_0_14_14, yields:
% 9.98/3.01 | (85) ? [v0] : ? [v1] : (( ~ (v0 = 0) & relation(all_0_16_16) = v0) | (((v1 = 0 & is_connected_in(all_0_16_16, all_0_14_14) = 0) | ( ~ (v0 = 0) & connected(all_0_16_16) = v0)) & ((v0 = 0 & connected(all_0_16_16) = 0) | ( ~ (v1 = 0) & is_connected_in(all_0_16_16, all_0_14_14) = v1))))
% 9.98/3.01 |
% 9.98/3.01 | Instantiating formula (73) with all_0_15_15, all_0_16_16 and discharging atoms connected(all_0_16_16) = all_0_15_15, yields:
% 9.98/3.01 | (86) ? [v0] : ? [v1] : (( ~ (v0 = 0) & relation(all_0_16_16) = v0) | (( ~ (all_0_15_15 = 0) | (v1 = 0 & relation_field(all_0_16_16) = v0 & is_connected_in(all_0_16_16, v0) = 0)) & (all_0_15_15 = 0 | ( ~ (v1 = 0) & relation_field(all_0_16_16) = v0 & is_connected_in(all_0_16_16, v0) = v1))))
% 9.98/3.01 |
% 9.98/3.01 | Instantiating formula (17) with all_0_16_16 and discharging atoms relation(all_0_16_16) = 0, yields:
% 9.98/3.01 | (87) ? [v0] : ? [v1] : ? [v2] : (relation_dom(all_0_16_16) = v1 & relation_rng(all_0_16_16) = v2 & relation_field(all_0_16_16) = v0 & set_union2(v1, v2) = v0)
% 9.98/3.01 |
% 9.98/3.01 | Instantiating formula (22) with all_0_16_16 and discharging atoms relation(all_0_16_16) = 0, yields:
% 9.98/3.01 | (88) ? [v0] : ? [v1] : ? [v2] : (((v2 = 0 & relation_field(all_0_16_16) = v1 & is_connected_in(all_0_16_16, v1) = 0) | ( ~ (v0 = 0) & connected(all_0_16_16) = v0)) & ((v0 = 0 & connected(all_0_16_16) = 0) | ( ~ (v2 = 0) & relation_field(all_0_16_16) = v1 & is_connected_in(all_0_16_16, v1) = v2)))
% 9.98/3.01 |
% 9.98/3.01 | Instantiating (88) with all_53_0_74, all_53_1_75, all_53_2_76 yields:
% 9.98/3.01 | (89) ((all_53_0_74 = 0 & relation_field(all_0_16_16) = all_53_1_75 & is_connected_in(all_0_16_16, all_53_1_75) = 0) | ( ~ (all_53_2_76 = 0) & connected(all_0_16_16) = all_53_2_76)) & ((all_53_2_76 = 0 & connected(all_0_16_16) = 0) | ( ~ (all_53_0_74 = 0) & relation_field(all_0_16_16) = all_53_1_75 & is_connected_in(all_0_16_16, all_53_1_75) = all_53_0_74))
% 9.98/3.01 |
% 9.98/3.01 | Applying alpha-rule on (89) yields:
% 9.98/3.01 | (90) (all_53_0_74 = 0 & relation_field(all_0_16_16) = all_53_1_75 & is_connected_in(all_0_16_16, all_53_1_75) = 0) | ( ~ (all_53_2_76 = 0) & connected(all_0_16_16) = all_53_2_76)
% 9.98/3.01 | (91) (all_53_2_76 = 0 & connected(all_0_16_16) = 0) | ( ~ (all_53_0_74 = 0) & relation_field(all_0_16_16) = all_53_1_75 & is_connected_in(all_0_16_16, all_53_1_75) = all_53_0_74)
% 9.98/3.01 |
% 9.98/3.01 | Instantiating (87) with all_54_0_77, all_54_1_78, all_54_2_79 yields:
% 9.98/3.01 | (92) relation_dom(all_0_16_16) = all_54_1_78 & relation_rng(all_0_16_16) = all_54_0_77 & relation_field(all_0_16_16) = all_54_2_79 & set_union2(all_54_1_78, all_54_0_77) = all_54_2_79
% 9.98/3.01 |
% 9.98/3.01 | Applying alpha-rule on (92) yields:
% 9.98/3.01 | (93) relation_dom(all_0_16_16) = all_54_1_78
% 9.98/3.01 | (94) relation_rng(all_0_16_16) = all_54_0_77
% 9.98/3.01 | (95) relation_field(all_0_16_16) = all_54_2_79
% 9.98/3.01 | (96) set_union2(all_54_1_78, all_54_0_77) = all_54_2_79
% 9.98/3.01 |
% 9.98/3.01 | Instantiating (85) with all_59_0_86, all_59_1_87 yields:
% 9.98/3.01 | (97) ( ~ (all_59_1_87 = 0) & relation(all_0_16_16) = all_59_1_87) | (((all_59_0_86 = 0 & is_connected_in(all_0_16_16, all_0_14_14) = 0) | ( ~ (all_59_1_87 = 0) & connected(all_0_16_16) = all_59_1_87)) & ((all_59_1_87 = 0 & connected(all_0_16_16) = 0) | ( ~ (all_59_0_86 = 0) & is_connected_in(all_0_16_16, all_0_14_14) = all_59_0_86)))
% 9.98/3.01 |
% 9.98/3.01 | Instantiating (86) with all_63_0_94, all_63_1_95 yields:
% 9.98/3.01 | (98) ( ~ (all_63_1_95 = 0) & relation(all_0_16_16) = all_63_1_95) | (( ~ (all_0_15_15 = 0) | (all_63_0_94 = 0 & relation_field(all_0_16_16) = all_63_1_95 & is_connected_in(all_0_16_16, all_63_1_95) = 0)) & (all_0_15_15 = 0 | ( ~ (all_63_0_94 = 0) & relation_field(all_0_16_16) = all_63_1_95 & is_connected_in(all_0_16_16, all_63_1_95) = all_63_0_94)))
% 9.98/3.01 |
% 9.98/3.01 | Instantiating formula (43) with all_0_16_16, all_54_2_79, all_0_14_14 and discharging atoms relation_field(all_0_16_16) = all_54_2_79, relation_field(all_0_16_16) = all_0_14_14, yields:
% 9.98/3.01 | (99) all_54_2_79 = all_0_14_14
% 9.98/3.01 |
% 9.98/3.02 | From (99) and (95) follows:
% 9.98/3.02 | (11) relation_field(all_0_16_16) = all_0_14_14
% 9.98/3.02 |
% 9.98/3.02 +-Applying beta-rule and splitting (50), into two cases.
% 9.98/3.02 |-Branch one:
% 9.98/3.02 | (101) all_0_10_10 = 0 & all_0_11_11 = 0 & all_0_15_15 = 0 & ~ (all_0_6_6 = 0) & ~ (all_0_8_8 = 0) & ~ (all_0_12_12 = all_0_13_13) & ordered_pair(all_0_12_12, all_0_13_13) = all_0_7_7 & ordered_pair(all_0_13_13, all_0_12_12) = all_0_9_9 & in(all_0_7_7, all_0_16_16) = all_0_6_6 & in(all_0_9_9, all_0_16_16) = all_0_8_8 & in(all_0_12_12, all_0_14_14) = 0 & in(all_0_13_13, all_0_14_14) = 0
% 9.98/3.02 |
% 9.98/3.02 | Applying alpha-rule on (101) yields:
% 9.98/3.02 | (102) all_0_11_11 = 0
% 9.98/3.02 | (103) ~ (all_0_6_6 = 0)
% 9.98/3.02 | (104) ~ (all_0_12_12 = all_0_13_13)
% 9.98/3.02 | (105) in(all_0_7_7, all_0_16_16) = all_0_6_6
% 9.98/3.02 | (106) in(all_0_9_9, all_0_16_16) = all_0_8_8
% 9.98/3.02 | (107) all_0_10_10 = 0
% 9.98/3.02 | (108) in(all_0_13_13, all_0_14_14) = 0
% 9.98/3.02 | (109) all_0_15_15 = 0
% 9.98/3.02 | (110) in(all_0_12_12, all_0_14_14) = 0
% 9.98/3.02 | (111) ~ (all_0_8_8 = 0)
% 9.98/3.02 | (112) ordered_pair(all_0_13_13, all_0_12_12) = all_0_9_9
% 9.98/3.02 | (113) ordered_pair(all_0_12_12, all_0_13_13) = all_0_7_7
% 9.98/3.02 |
% 9.98/3.02 | From (109) and (7) follows:
% 9.98/3.02 | (114) connected(all_0_16_16) = 0
% 9.98/3.02 |
% 9.98/3.02 +-Applying beta-rule and splitting (90), into two cases.
% 9.98/3.02 |-Branch one:
% 9.98/3.02 | (115) all_53_0_74 = 0 & relation_field(all_0_16_16) = all_53_1_75 & is_connected_in(all_0_16_16, all_53_1_75) = 0
% 9.98/3.02 |
% 9.98/3.02 | Applying alpha-rule on (115) yields:
% 9.98/3.02 | (116) all_53_0_74 = 0
% 9.98/3.02 | (117) relation_field(all_0_16_16) = all_53_1_75
% 9.98/3.02 | (118) is_connected_in(all_0_16_16, all_53_1_75) = 0
% 9.98/3.02 |
% 9.98/3.02 +-Applying beta-rule and splitting (98), into two cases.
% 9.98/3.02 |-Branch one:
% 9.98/3.02 | (119) ~ (all_63_1_95 = 0) & relation(all_0_16_16) = all_63_1_95
% 9.98/3.02 |
% 9.98/3.02 | Applying alpha-rule on (119) yields:
% 9.98/3.02 | (120) ~ (all_63_1_95 = 0)
% 9.98/3.02 | (121) relation(all_0_16_16) = all_63_1_95
% 9.98/3.02 |
% 9.98/3.02 | Instantiating formula (13) with all_0_16_16, all_63_1_95, 0 and discharging atoms relation(all_0_16_16) = all_63_1_95, relation(all_0_16_16) = 0, yields:
% 9.98/3.02 | (122) all_63_1_95 = 0
% 9.98/3.02 |
% 9.98/3.02 | Equations (122) can reduce 120 to:
% 9.98/3.02 | (123) $false
% 9.98/3.02 |
% 9.98/3.02 |-The branch is then unsatisfiable
% 9.98/3.02 |-Branch two:
% 9.98/3.02 | (124) ( ~ (all_0_15_15 = 0) | (all_63_0_94 = 0 & relation_field(all_0_16_16) = all_63_1_95 & is_connected_in(all_0_16_16, all_63_1_95) = 0)) & (all_0_15_15 = 0 | ( ~ (all_63_0_94 = 0) & relation_field(all_0_16_16) = all_63_1_95 & is_connected_in(all_0_16_16, all_63_1_95) = all_63_0_94))
% 9.98/3.02 |
% 9.98/3.02 | Applying alpha-rule on (124) yields:
% 9.98/3.02 | (125) ~ (all_0_15_15 = 0) | (all_63_0_94 = 0 & relation_field(all_0_16_16) = all_63_1_95 & is_connected_in(all_0_16_16, all_63_1_95) = 0)
% 9.98/3.02 | (126) all_0_15_15 = 0 | ( ~ (all_63_0_94 = 0) & relation_field(all_0_16_16) = all_63_1_95 & is_connected_in(all_0_16_16, all_63_1_95) = all_63_0_94)
% 9.98/3.02 |
% 9.98/3.02 +-Applying beta-rule and splitting (125), into two cases.
% 9.98/3.02 |-Branch one:
% 9.98/3.02 | (127) ~ (all_0_15_15 = 0)
% 9.98/3.02 |
% 9.98/3.02 | Equations (109) can reduce 127 to:
% 9.98/3.02 | (123) $false
% 9.98/3.02 |
% 9.98/3.02 |-The branch is then unsatisfiable
% 9.98/3.02 |-Branch two:
% 9.98/3.02 | (109) all_0_15_15 = 0
% 9.98/3.02 | (130) all_63_0_94 = 0 & relation_field(all_0_16_16) = all_63_1_95 & is_connected_in(all_0_16_16, all_63_1_95) = 0
% 9.98/3.02 |
% 9.98/3.02 | Applying alpha-rule on (130) yields:
% 9.98/3.02 | (131) all_63_0_94 = 0
% 9.98/3.02 | (132) relation_field(all_0_16_16) = all_63_1_95
% 9.98/3.02 | (133) is_connected_in(all_0_16_16, all_63_1_95) = 0
% 9.98/3.02 |
% 9.98/3.02 | Instantiating formula (43) with all_0_16_16, all_63_1_95, all_0_14_14 and discharging atoms relation_field(all_0_16_16) = all_63_1_95, relation_field(all_0_16_16) = all_0_14_14, yields:
% 9.98/3.02 | (134) all_63_1_95 = all_0_14_14
% 9.98/3.02 |
% 9.98/3.02 | Instantiating formula (43) with all_0_16_16, all_53_1_75, all_63_1_95 and discharging atoms relation_field(all_0_16_16) = all_63_1_95, relation_field(all_0_16_16) = all_53_1_75, yields:
% 9.98/3.02 | (135) all_63_1_95 = all_53_1_75
% 9.98/3.02 |
% 9.98/3.02 | Combining equations (134,135) yields a new equation:
% 9.98/3.02 | (136) all_53_1_75 = all_0_14_14
% 9.98/3.02 |
% 9.98/3.02 | From (136) and (118) follows:
% 9.98/3.02 | (137) is_connected_in(all_0_16_16, all_0_14_14) = 0
% 9.98/3.02 |
% 9.98/3.02 | Instantiating formula (23) with all_0_7_7, all_0_12_12, all_0_13_13, all_0_14_14, all_0_16_16 and discharging atoms ordered_pair(all_0_12_12, all_0_13_13) = all_0_7_7, is_connected_in(all_0_16_16, all_0_14_14) = 0, relation(all_0_16_16) = 0, yields:
% 9.98/3.02 | (138) all_0_12_12 = all_0_13_13 | ? [v0] : ? [v1] : ((v1 = 0 & ordered_pair(all_0_13_13, all_0_12_12) = v0 & in(v0, all_0_16_16) = 0) | (v0 = 0 & in(all_0_7_7, all_0_16_16) = 0) | ( ~ (v0 = 0) & in(all_0_12_12, all_0_14_14) = v0) | ( ~ (v0 = 0) & in(all_0_13_13, all_0_14_14) = v0))
% 9.98/3.03 |
% 9.98/3.03 | Instantiating formula (23) with all_0_9_9, all_0_13_13, all_0_12_12, all_0_14_14, all_0_16_16 and discharging atoms ordered_pair(all_0_13_13, all_0_12_12) = all_0_9_9, is_connected_in(all_0_16_16, all_0_14_14) = 0, relation(all_0_16_16) = 0, yields:
% 9.98/3.03 | (139) all_0_12_12 = all_0_13_13 | ? [v0] : ? [v1] : ((v1 = 0 & ordered_pair(all_0_12_12, all_0_13_13) = v0 & in(v0, all_0_16_16) = 0) | (v0 = 0 & in(all_0_9_9, all_0_16_16) = 0) | ( ~ (v0 = 0) & in(all_0_12_12, all_0_14_14) = v0) | ( ~ (v0 = 0) & in(all_0_13_13, all_0_14_14) = v0))
% 9.98/3.03 |
% 9.98/3.03 | Instantiating formula (59) with all_0_6_6, all_0_16_16, all_0_7_7 and discharging atoms in(all_0_7_7, all_0_16_16) = all_0_6_6, yields:
% 9.98/3.03 | (140) all_0_6_6 = 0 | ? [v0] : ((v0 = 0 & empty(all_0_16_16) = 0) | ( ~ (v0 = 0) & element(all_0_7_7, all_0_16_16) = v0))
% 9.98/3.03 |
% 9.98/3.03 | Instantiating formula (59) with all_0_8_8, all_0_16_16, all_0_9_9 and discharging atoms in(all_0_9_9, all_0_16_16) = all_0_8_8, yields:
% 9.98/3.03 | (141) all_0_8_8 = 0 | ? [v0] : ((v0 = 0 & empty(all_0_16_16) = 0) | ( ~ (v0 = 0) & element(all_0_9_9, all_0_16_16) = v0))
% 9.98/3.03 |
% 9.98/3.03 +-Applying beta-rule and splitting (139), into two cases.
% 9.98/3.03 |-Branch one:
% 9.98/3.03 | (142) all_0_12_12 = all_0_13_13
% 9.98/3.03 |
% 9.98/3.03 | Equations (142) can reduce 104 to:
% 9.98/3.03 | (123) $false
% 9.98/3.03 |
% 9.98/3.03 |-The branch is then unsatisfiable
% 9.98/3.03 |-Branch two:
% 9.98/3.03 | (104) ~ (all_0_12_12 = all_0_13_13)
% 9.98/3.03 | (145) ? [v0] : ? [v1] : ((v1 = 0 & ordered_pair(all_0_12_12, all_0_13_13) = v0 & in(v0, all_0_16_16) = 0) | (v0 = 0 & in(all_0_9_9, all_0_16_16) = 0) | ( ~ (v0 = 0) & in(all_0_12_12, all_0_14_14) = v0) | ( ~ (v0 = 0) & in(all_0_13_13, all_0_14_14) = v0))
% 9.98/3.03 |
% 9.98/3.03 +-Applying beta-rule and splitting (138), into two cases.
% 9.98/3.03 |-Branch one:
% 9.98/3.03 | (142) all_0_12_12 = all_0_13_13
% 9.98/3.03 |
% 9.98/3.03 | Equations (142) can reduce 104 to:
% 9.98/3.03 | (123) $false
% 9.98/3.03 |
% 9.98/3.03 |-The branch is then unsatisfiable
% 9.98/3.03 |-Branch two:
% 9.98/3.03 | (104) ~ (all_0_12_12 = all_0_13_13)
% 9.98/3.03 | (149) ? [v0] : ? [v1] : ((v1 = 0 & ordered_pair(all_0_13_13, all_0_12_12) = v0 & in(v0, all_0_16_16) = 0) | (v0 = 0 & in(all_0_7_7, all_0_16_16) = 0) | ( ~ (v0 = 0) & in(all_0_12_12, all_0_14_14) = v0) | ( ~ (v0 = 0) & in(all_0_13_13, all_0_14_14) = v0))
% 9.98/3.03 |
% 9.98/3.03 | Instantiating (149) with all_178_0_139, all_178_1_140 yields:
% 9.98/3.03 | (150) (all_178_0_139 = 0 & ordered_pair(all_0_13_13, all_0_12_12) = all_178_1_140 & in(all_178_1_140, all_0_16_16) = 0) | (all_178_1_140 = 0 & in(all_0_7_7, all_0_16_16) = 0) | ( ~ (all_178_1_140 = 0) & in(all_0_12_12, all_0_14_14) = all_178_1_140) | ( ~ (all_178_1_140 = 0) & in(all_0_13_13, all_0_14_14) = all_178_1_140)
% 9.98/3.03 |
% 9.98/3.03 +-Applying beta-rule and splitting (140), into two cases.
% 9.98/3.03 |-Branch one:
% 9.98/3.03 | (151) all_0_6_6 = 0
% 9.98/3.03 |
% 9.98/3.03 | Equations (151) can reduce 103 to:
% 9.98/3.03 | (123) $false
% 9.98/3.03 |
% 9.98/3.03 |-The branch is then unsatisfiable
% 9.98/3.03 |-Branch two:
% 9.98/3.03 | (103) ~ (all_0_6_6 = 0)
% 9.98/3.03 | (154) ? [v0] : ((v0 = 0 & empty(all_0_16_16) = 0) | ( ~ (v0 = 0) & element(all_0_7_7, all_0_16_16) = v0))
% 9.98/3.03 |
% 9.98/3.03 +-Applying beta-rule and splitting (141), into two cases.
% 9.98/3.03 |-Branch one:
% 9.98/3.03 | (155) all_0_8_8 = 0
% 9.98/3.03 |
% 9.98/3.03 | Equations (155) can reduce 111 to:
% 9.98/3.03 | (123) $false
% 9.98/3.03 |
% 9.98/3.03 |-The branch is then unsatisfiable
% 9.98/3.03 |-Branch two:
% 9.98/3.03 | (111) ~ (all_0_8_8 = 0)
% 9.98/3.03 | (158) ? [v0] : ((v0 = 0 & empty(all_0_16_16) = 0) | ( ~ (v0 = 0) & element(all_0_9_9, all_0_16_16) = v0))
% 9.98/3.03 |
% 9.98/3.03 +-Applying beta-rule and splitting (150), into two cases.
% 9.98/3.03 |-Branch one:
% 9.98/3.03 | (159) (all_178_0_139 = 0 & ordered_pair(all_0_13_13, all_0_12_12) = all_178_1_140 & in(all_178_1_140, all_0_16_16) = 0) | (all_178_1_140 = 0 & in(all_0_7_7, all_0_16_16) = 0) | ( ~ (all_178_1_140 = 0) & in(all_0_12_12, all_0_14_14) = all_178_1_140)
% 9.98/3.03 |
% 9.98/3.03 +-Applying beta-rule and splitting (159), into two cases.
% 9.98/3.03 |-Branch one:
% 9.98/3.03 | (160) (all_178_0_139 = 0 & ordered_pair(all_0_13_13, all_0_12_12) = all_178_1_140 & in(all_178_1_140, all_0_16_16) = 0) | (all_178_1_140 = 0 & in(all_0_7_7, all_0_16_16) = 0)
% 9.98/3.03 |
% 9.98/3.03 +-Applying beta-rule and splitting (160), into two cases.
% 9.98/3.03 |-Branch one:
% 9.98/3.03 | (161) all_178_0_139 = 0 & ordered_pair(all_0_13_13, all_0_12_12) = all_178_1_140 & in(all_178_1_140, all_0_16_16) = 0
% 9.98/3.03 |
% 9.98/3.03 | Applying alpha-rule on (161) yields:
% 9.98/3.03 | (162) all_178_0_139 = 0
% 9.98/3.03 | (163) ordered_pair(all_0_13_13, all_0_12_12) = all_178_1_140
% 9.98/3.03 | (164) in(all_178_1_140, all_0_16_16) = 0
% 9.98/3.03 |
% 9.98/3.03 | Instantiating formula (44) with all_0_13_13, all_0_12_12, all_178_1_140, all_0_9_9 and discharging atoms ordered_pair(all_0_13_13, all_0_12_12) = all_178_1_140, ordered_pair(all_0_13_13, all_0_12_12) = all_0_9_9, yields:
% 9.98/3.03 | (165) all_178_1_140 = all_0_9_9
% 9.98/3.03 |
% 9.98/3.03 | From (165) and (164) follows:
% 9.98/3.03 | (166) in(all_0_9_9, all_0_16_16) = 0
% 9.98/3.03 |
% 9.98/3.03 | Instantiating formula (61) with all_0_9_9, all_0_16_16, 0, all_0_8_8 and discharging atoms in(all_0_9_9, all_0_16_16) = all_0_8_8, in(all_0_9_9, all_0_16_16) = 0, yields:
% 9.98/3.03 | (155) all_0_8_8 = 0
% 9.98/3.03 |
% 9.98/3.03 | Equations (155) can reduce 111 to:
% 9.98/3.03 | (123) $false
% 9.98/3.03 |
% 9.98/3.03 |-The branch is then unsatisfiable
% 9.98/3.03 |-Branch two:
% 9.98/3.03 | (169) all_178_1_140 = 0 & in(all_0_7_7, all_0_16_16) = 0
% 9.98/3.03 |
% 9.98/3.03 | Applying alpha-rule on (169) yields:
% 9.98/3.03 | (170) all_178_1_140 = 0
% 9.98/3.03 | (171) in(all_0_7_7, all_0_16_16) = 0
% 9.98/3.04 |
% 9.98/3.04 | Instantiating formula (61) with all_0_7_7, all_0_16_16, 0, all_0_6_6 and discharging atoms in(all_0_7_7, all_0_16_16) = all_0_6_6, in(all_0_7_7, all_0_16_16) = 0, yields:
% 9.98/3.04 | (151) all_0_6_6 = 0
% 9.98/3.04 |
% 9.98/3.04 | Equations (151) can reduce 103 to:
% 9.98/3.04 | (123) $false
% 9.98/3.04 |
% 9.98/3.04 |-The branch is then unsatisfiable
% 9.98/3.04 |-Branch two:
% 9.98/3.04 | (174) ~ (all_178_1_140 = 0) & in(all_0_12_12, all_0_14_14) = all_178_1_140
% 9.98/3.04 |
% 9.98/3.04 | Applying alpha-rule on (174) yields:
% 9.98/3.04 | (175) ~ (all_178_1_140 = 0)
% 9.98/3.04 | (176) in(all_0_12_12, all_0_14_14) = all_178_1_140
% 9.98/3.04 |
% 9.98/3.04 | Instantiating formula (61) with all_0_12_12, all_0_14_14, all_178_1_140, 0 and discharging atoms in(all_0_12_12, all_0_14_14) = all_178_1_140, in(all_0_12_12, all_0_14_14) = 0, yields:
% 9.98/3.04 | (170) all_178_1_140 = 0
% 9.98/3.04 |
% 9.98/3.04 | Equations (170) can reduce 175 to:
% 9.98/3.04 | (123) $false
% 9.98/3.04 |
% 9.98/3.04 |-The branch is then unsatisfiable
% 9.98/3.04 |-Branch two:
% 9.98/3.04 | (179) ~ (all_178_1_140 = 0) & in(all_0_13_13, all_0_14_14) = all_178_1_140
% 9.98/3.04 |
% 9.98/3.04 | Applying alpha-rule on (179) yields:
% 9.98/3.04 | (175) ~ (all_178_1_140 = 0)
% 9.98/3.04 | (181) in(all_0_13_13, all_0_14_14) = all_178_1_140
% 9.98/3.04 |
% 9.98/3.04 | Instantiating formula (61) with all_0_13_13, all_0_14_14, all_178_1_140, 0 and discharging atoms in(all_0_13_13, all_0_14_14) = all_178_1_140, in(all_0_13_13, all_0_14_14) = 0, yields:
% 9.98/3.04 | (170) all_178_1_140 = 0
% 9.98/3.04 |
% 9.98/3.04 | Equations (170) can reduce 175 to:
% 9.98/3.04 | (123) $false
% 9.98/3.04 |
% 9.98/3.04 |-The branch is then unsatisfiable
% 9.98/3.04 |-Branch two:
% 9.98/3.04 | (184) ~ (all_53_2_76 = 0) & connected(all_0_16_16) = all_53_2_76
% 9.98/3.04 |
% 9.98/3.04 | Applying alpha-rule on (184) yields:
% 9.98/3.04 | (185) ~ (all_53_2_76 = 0)
% 9.98/3.04 | (186) connected(all_0_16_16) = all_53_2_76
% 9.98/3.04 |
% 9.98/3.04 | Instantiating formula (37) with all_0_16_16, 0, all_53_2_76 and discharging atoms connected(all_0_16_16) = all_53_2_76, connected(all_0_16_16) = 0, yields:
% 9.98/3.04 | (187) all_53_2_76 = 0
% 9.98/3.04 |
% 9.98/3.04 | Equations (187) can reduce 185 to:
% 9.98/3.04 | (123) $false
% 9.98/3.04 |
% 9.98/3.04 |-The branch is then unsatisfiable
% 9.98/3.04 |-Branch two:
% 9.98/3.04 | (189) ~ (all_0_15_15 = 0) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ordered_pair(v1, v0) = v2) | ? [v3] : ? [v4] : ((v4 = 0 & ordered_pair(v0, v1) = v3 & in(v3, all_0_16_16) = 0) | (v3 = 0 & in(v2, all_0_16_16) = 0) | ( ~ (v3 = 0) & in(v1, all_0_14_14) = v3) | ( ~ (v3 = 0) & in(v0, all_0_14_14) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : ((v4 = 0 & ordered_pair(v1, v0) = v3 & in(v3, all_0_16_16) = 0) | (v3 = 0 & in(v2, all_0_16_16) = 0) | ( ~ (v3 = 0) & in(v1, all_0_14_14) = v3) | ( ~ (v3 = 0) & in(v0, all_0_14_14) = v3)))
% 9.98/3.04 |
% 9.98/3.04 | Applying alpha-rule on (189) yields:
% 9.98/3.04 | (127) ~ (all_0_15_15 = 0)
% 9.98/3.04 | (191) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ordered_pair(v1, v0) = v2) | ? [v3] : ? [v4] : ((v4 = 0 & ordered_pair(v0, v1) = v3 & in(v3, all_0_16_16) = 0) | (v3 = 0 & in(v2, all_0_16_16) = 0) | ( ~ (v3 = 0) & in(v1, all_0_14_14) = v3) | ( ~ (v3 = 0) & in(v0, all_0_14_14) = v3)))
% 9.98/3.04 | (192) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : ((v4 = 0 & ordered_pair(v1, v0) = v3 & in(v3, all_0_16_16) = 0) | (v3 = 0 & in(v2, all_0_16_16) = 0) | ( ~ (v3 = 0) & in(v1, all_0_14_14) = v3) | ( ~ (v3 = 0) & in(v0, all_0_14_14) = v3)))
% 9.98/3.04 |
% 9.98/3.04 +-Applying beta-rule and splitting (98), into two cases.
% 9.98/3.04 |-Branch one:
% 9.98/3.04 | (119) ~ (all_63_1_95 = 0) & relation(all_0_16_16) = all_63_1_95
% 9.98/3.04 |
% 9.98/3.04 | Applying alpha-rule on (119) yields:
% 9.98/3.04 | (120) ~ (all_63_1_95 = 0)
% 9.98/3.04 | (121) relation(all_0_16_16) = all_63_1_95
% 9.98/3.04 |
% 9.98/3.04 | Instantiating formula (13) with all_0_16_16, all_63_1_95, 0 and discharging atoms relation(all_0_16_16) = all_63_1_95, relation(all_0_16_16) = 0, yields:
% 9.98/3.04 | (122) all_63_1_95 = 0
% 9.98/3.04 |
% 9.98/3.04 | Equations (122) can reduce 120 to:
% 9.98/3.04 | (123) $false
% 9.98/3.04 |
% 9.98/3.04 |-The branch is then unsatisfiable
% 9.98/3.04 |-Branch two:
% 9.98/3.04 | (124) ( ~ (all_0_15_15 = 0) | (all_63_0_94 = 0 & relation_field(all_0_16_16) = all_63_1_95 & is_connected_in(all_0_16_16, all_63_1_95) = 0)) & (all_0_15_15 = 0 | ( ~ (all_63_0_94 = 0) & relation_field(all_0_16_16) = all_63_1_95 & is_connected_in(all_0_16_16, all_63_1_95) = all_63_0_94))
% 9.98/3.04 |
% 9.98/3.04 | Applying alpha-rule on (124) yields:
% 9.98/3.04 | (125) ~ (all_0_15_15 = 0) | (all_63_0_94 = 0 & relation_field(all_0_16_16) = all_63_1_95 & is_connected_in(all_0_16_16, all_63_1_95) = 0)
% 9.98/3.04 | (126) all_0_15_15 = 0 | ( ~ (all_63_0_94 = 0) & relation_field(all_0_16_16) = all_63_1_95 & is_connected_in(all_0_16_16, all_63_1_95) = all_63_0_94)
% 9.98/3.05 |
% 9.98/3.05 +-Applying beta-rule and splitting (97), into two cases.
% 9.98/3.05 |-Branch one:
% 9.98/3.05 | (201) ~ (all_59_1_87 = 0) & relation(all_0_16_16) = all_59_1_87
% 9.98/3.05 |
% 9.98/3.05 | Applying alpha-rule on (201) yields:
% 9.98/3.05 | (202) ~ (all_59_1_87 = 0)
% 9.98/3.05 | (203) relation(all_0_16_16) = all_59_1_87
% 9.98/3.05 |
% 9.98/3.05 | Instantiating formula (13) with all_0_16_16, all_59_1_87, 0 and discharging atoms relation(all_0_16_16) = all_59_1_87, relation(all_0_16_16) = 0, yields:
% 9.98/3.05 | (204) all_59_1_87 = 0
% 9.98/3.05 |
% 9.98/3.05 | Equations (204) can reduce 202 to:
% 9.98/3.05 | (123) $false
% 9.98/3.05 |
% 9.98/3.05 |-The branch is then unsatisfiable
% 9.98/3.05 |-Branch two:
% 9.98/3.05 | (206) ((all_59_0_86 = 0 & is_connected_in(all_0_16_16, all_0_14_14) = 0) | ( ~ (all_59_1_87 = 0) & connected(all_0_16_16) = all_59_1_87)) & ((all_59_1_87 = 0 & connected(all_0_16_16) = 0) | ( ~ (all_59_0_86 = 0) & is_connected_in(all_0_16_16, all_0_14_14) = all_59_0_86))
% 9.98/3.05 |
% 9.98/3.05 | Applying alpha-rule on (206) yields:
% 9.98/3.05 | (207) (all_59_0_86 = 0 & is_connected_in(all_0_16_16, all_0_14_14) = 0) | ( ~ (all_59_1_87 = 0) & connected(all_0_16_16) = all_59_1_87)
% 9.98/3.05 | (208) (all_59_1_87 = 0 & connected(all_0_16_16) = 0) | ( ~ (all_59_0_86 = 0) & is_connected_in(all_0_16_16, all_0_14_14) = all_59_0_86)
% 9.98/3.05 |
% 9.98/3.05 +-Applying beta-rule and splitting (91), into two cases.
% 9.98/3.05 |-Branch one:
% 9.98/3.05 | (209) all_53_2_76 = 0 & connected(all_0_16_16) = 0
% 9.98/3.05 |
% 9.98/3.05 | Applying alpha-rule on (209) yields:
% 9.98/3.05 | (187) all_53_2_76 = 0
% 9.98/3.05 | (114) connected(all_0_16_16) = 0
% 9.98/3.05 |
% 9.98/3.05 +-Applying beta-rule and splitting (126), into two cases.
% 9.98/3.05 |-Branch one:
% 9.98/3.05 | (109) all_0_15_15 = 0
% 9.98/3.05 |
% 9.98/3.05 | Equations (109) can reduce 127 to:
% 9.98/3.05 | (123) $false
% 9.98/3.05 |
% 9.98/3.05 |-The branch is then unsatisfiable
% 9.98/3.05 |-Branch two:
% 9.98/3.05 | (127) ~ (all_0_15_15 = 0)
% 9.98/3.05 | (215) ~ (all_63_0_94 = 0) & relation_field(all_0_16_16) = all_63_1_95 & is_connected_in(all_0_16_16, all_63_1_95) = all_63_0_94
% 9.98/3.05 |
% 9.98/3.05 | Instantiating formula (37) with all_0_16_16, 0, all_0_15_15 and discharging atoms connected(all_0_16_16) = all_0_15_15, connected(all_0_16_16) = 0, yields:
% 9.98/3.05 | (109) all_0_15_15 = 0
% 9.98/3.05 |
% 9.98/3.05 | Equations (109) can reduce 127 to:
% 9.98/3.05 | (123) $false
% 9.98/3.05 |
% 9.98/3.05 |-The branch is then unsatisfiable
% 9.98/3.05 |-Branch two:
% 9.98/3.05 | (218) ~ (all_53_0_74 = 0) & relation_field(all_0_16_16) = all_53_1_75 & is_connected_in(all_0_16_16, all_53_1_75) = all_53_0_74
% 9.98/3.05 |
% 9.98/3.05 | Applying alpha-rule on (218) yields:
% 9.98/3.05 | (219) ~ (all_53_0_74 = 0)
% 9.98/3.05 | (117) relation_field(all_0_16_16) = all_53_1_75
% 9.98/3.05 | (221) is_connected_in(all_0_16_16, all_53_1_75) = all_53_0_74
% 9.98/3.05 |
% 9.98/3.05 +-Applying beta-rule and splitting (208), into two cases.
% 9.98/3.05 |-Branch one:
% 9.98/3.05 | (222) all_59_1_87 = 0 & connected(all_0_16_16) = 0
% 9.98/3.05 |
% 9.98/3.05 | Applying alpha-rule on (222) yields:
% 9.98/3.05 | (204) all_59_1_87 = 0
% 9.98/3.05 | (114) connected(all_0_16_16) = 0
% 9.98/3.05 |
% 9.98/3.05 +-Applying beta-rule and splitting (90), into two cases.
% 9.98/3.05 |-Branch one:
% 9.98/3.05 | (115) all_53_0_74 = 0 & relation_field(all_0_16_16) = all_53_1_75 & is_connected_in(all_0_16_16, all_53_1_75) = 0
% 9.98/3.05 |
% 9.98/3.05 | Applying alpha-rule on (115) yields:
% 9.98/3.05 | (116) all_53_0_74 = 0
% 9.98/3.05 | (117) relation_field(all_0_16_16) = all_53_1_75
% 9.98/3.05 | (118) is_connected_in(all_0_16_16, all_53_1_75) = 0
% 9.98/3.05 |
% 9.98/3.05 | Equations (116) can reduce 219 to:
% 9.98/3.05 | (123) $false
% 9.98/3.05 |
% 9.98/3.05 |-The branch is then unsatisfiable
% 9.98/3.05 |-Branch two:
% 9.98/3.05 | (184) ~ (all_53_2_76 = 0) & connected(all_0_16_16) = all_53_2_76
% 9.98/3.05 |
% 9.98/3.05 | Applying alpha-rule on (184) yields:
% 9.98/3.05 | (185) ~ (all_53_2_76 = 0)
% 9.98/3.05 | (186) connected(all_0_16_16) = all_53_2_76
% 9.98/3.05 |
% 9.98/3.05 +-Applying beta-rule and splitting (126), into two cases.
% 9.98/3.05 |-Branch one:
% 9.98/3.05 | (109) all_0_15_15 = 0
% 9.98/3.05 |
% 9.98/3.05 | Equations (109) can reduce 127 to:
% 9.98/3.05 | (123) $false
% 9.98/3.05 |
% 9.98/3.05 |-The branch is then unsatisfiable
% 9.98/3.05 |-Branch two:
% 9.98/3.05 | (127) ~ (all_0_15_15 = 0)
% 9.98/3.05 | (215) ~ (all_63_0_94 = 0) & relation_field(all_0_16_16) = all_63_1_95 & is_connected_in(all_0_16_16, all_63_1_95) = all_63_0_94
% 9.98/3.05 |
% 9.98/3.05 | Instantiating formula (37) with all_0_16_16, all_53_2_76, all_0_15_15 and discharging atoms connected(all_0_16_16) = all_53_2_76, connected(all_0_16_16) = all_0_15_15, yields:
% 9.98/3.05 | (237) all_53_2_76 = all_0_15_15
% 9.98/3.05 |
% 9.98/3.05 | Instantiating formula (37) with all_0_16_16, 0, all_53_2_76 and discharging atoms connected(all_0_16_16) = all_53_2_76, connected(all_0_16_16) = 0, yields:
% 9.98/3.05 | (187) all_53_2_76 = 0
% 9.98/3.05 |
% 9.98/3.05 | Combining equations (187,237) yields a new equation:
% 9.98/3.05 | (109) all_0_15_15 = 0
% 9.98/3.05 |
% 9.98/3.05 | Equations (109) can reduce 127 to:
% 9.98/3.05 | (123) $false
% 9.98/3.05 |
% 9.98/3.05 |-The branch is then unsatisfiable
% 9.98/3.05 |-Branch two:
% 9.98/3.05 | (241) ~ (all_59_0_86 = 0) & is_connected_in(all_0_16_16, all_0_14_14) = all_59_0_86
% 9.98/3.05 |
% 9.98/3.05 | Applying alpha-rule on (241) yields:
% 9.98/3.05 | (242) ~ (all_59_0_86 = 0)
% 9.98/3.05 | (243) is_connected_in(all_0_16_16, all_0_14_14) = all_59_0_86
% 9.98/3.05 |
% 9.98/3.05 +-Applying beta-rule and splitting (126), into two cases.
% 9.98/3.05 |-Branch one:
% 9.98/3.05 | (109) all_0_15_15 = 0
% 9.98/3.05 |
% 9.98/3.05 | Equations (109) can reduce 127 to:
% 9.98/3.05 | (123) $false
% 9.98/3.05 |
% 9.98/3.05 |-The branch is then unsatisfiable
% 9.98/3.05 |-Branch two:
% 9.98/3.05 | (127) ~ (all_0_15_15 = 0)
% 9.98/3.05 | (215) ~ (all_63_0_94 = 0) & relation_field(all_0_16_16) = all_63_1_95 & is_connected_in(all_0_16_16, all_63_1_95) = all_63_0_94
% 9.98/3.05 |
% 9.98/3.05 | Applying alpha-rule on (215) yields:
% 9.98/3.05 | (248) ~ (all_63_0_94 = 0)
% 9.98/3.05 | (132) relation_field(all_0_16_16) = all_63_1_95
% 9.98/3.05 | (250) is_connected_in(all_0_16_16, all_63_1_95) = all_63_0_94
% 9.98/3.05 |
% 9.98/3.05 | Instantiating formula (43) with all_0_16_16, all_63_1_95, all_0_14_14 and discharging atoms relation_field(all_0_16_16) = all_63_1_95, relation_field(all_0_16_16) = all_0_14_14, yields:
% 9.98/3.05 | (134) all_63_1_95 = all_0_14_14
% 9.98/3.05 |
% 9.98/3.05 | Instantiating formula (43) with all_0_16_16, all_53_1_75, all_63_1_95 and discharging atoms relation_field(all_0_16_16) = all_63_1_95, relation_field(all_0_16_16) = all_53_1_75, yields:
% 9.98/3.05 | (135) all_63_1_95 = all_53_1_75
% 9.98/3.05 |
% 9.98/3.05 | Combining equations (134,135) yields a new equation:
% 9.98/3.05 | (136) all_53_1_75 = all_0_14_14
% 9.98/3.05 |
% 9.98/3.05 | Combining equations (136,135) yields a new equation:
% 9.98/3.05 | (134) all_63_1_95 = all_0_14_14
% 9.98/3.05 |
% 9.98/3.05 | From (134) and (250) follows:
% 9.98/3.05 | (255) is_connected_in(all_0_16_16, all_0_14_14) = all_63_0_94
% 9.98/3.05 |
% 9.98/3.05 | From (136) and (221) follows:
% 9.98/3.05 | (256) is_connected_in(all_0_16_16, all_0_14_14) = all_53_0_74
% 9.98/3.05 |
% 9.98/3.05 | Instantiating formula (81) with all_0_16_16, all_0_14_14, all_63_0_94, all_59_0_86 and discharging atoms is_connected_in(all_0_16_16, all_0_14_14) = all_63_0_94, is_connected_in(all_0_16_16, all_0_14_14) = all_59_0_86, yields:
% 9.98/3.05 | (257) all_63_0_94 = all_59_0_86
% 9.98/3.05 |
% 9.98/3.05 | Instantiating formula (81) with all_0_16_16, all_0_14_14, all_53_0_74, all_63_0_94 and discharging atoms is_connected_in(all_0_16_16, all_0_14_14) = all_63_0_94, is_connected_in(all_0_16_16, all_0_14_14) = all_53_0_74, yields:
% 9.98/3.05 | (258) all_63_0_94 = all_53_0_74
% 9.98/3.05 |
% 9.98/3.05 | Combining equations (257,258) yields a new equation:
% 9.98/3.05 | (259) all_59_0_86 = all_53_0_74
% 9.98/3.05 |
% 9.98/3.05 | Simplifying 259 yields:
% 9.98/3.05 | (260) all_59_0_86 = all_53_0_74
% 9.98/3.05 |
% 9.98/3.06 | Equations (260) can reduce 242 to:
% 9.98/3.06 | (219) ~ (all_53_0_74 = 0)
% 9.98/3.06 |
% 9.98/3.06 | From (260) and (243) follows:
% 9.98/3.06 | (256) is_connected_in(all_0_16_16, all_0_14_14) = all_53_0_74
% 9.98/3.06 |
% 9.98/3.06 | Instantiating formula (80) with all_53_0_74, all_0_14_14, all_0_16_16 and discharging atoms is_connected_in(all_0_16_16, all_0_14_14) = all_53_0_74, relation(all_0_16_16) = 0, yields:
% 9.98/3.06 | (263) all_53_0_74 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = 0) & ~ (v3 = 0) & ~ (v1 = v0) & ordered_pair(v1, v0) = v4 & ordered_pair(v0, v1) = v2 & in(v4, all_0_16_16) = v5 & in(v2, all_0_16_16) = v3 & in(v1, all_0_14_14) = 0 & in(v0, all_0_14_14) = 0)
% 9.98/3.06 |
% 9.98/3.06 +-Applying beta-rule and splitting (263), into two cases.
% 9.98/3.06 |-Branch one:
% 9.98/3.06 | (116) all_53_0_74 = 0
% 9.98/3.06 |
% 9.98/3.06 | Equations (116) can reduce 219 to:
% 9.98/3.06 | (123) $false
% 9.98/3.06 |
% 9.98/3.06 |-The branch is then unsatisfiable
% 9.98/3.06 |-Branch two:
% 9.98/3.06 | (219) ~ (all_53_0_74 = 0)
% 9.98/3.06 | (267) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = 0) & ~ (v3 = 0) & ~ (v1 = v0) & ordered_pair(v1, v0) = v4 & ordered_pair(v0, v1) = v2 & in(v4, all_0_16_16) = v5 & in(v2, all_0_16_16) = v3 & in(v1, all_0_14_14) = 0 & in(v0, all_0_14_14) = 0)
% 9.98/3.06 |
% 9.98/3.06 | Instantiating (267) with all_170_0_149, all_170_1_150, all_170_2_151, all_170_3_152, all_170_4_153, all_170_5_154 yields:
% 9.98/3.06 | (268) ~ (all_170_0_149 = 0) & ~ (all_170_2_151 = 0) & ~ (all_170_4_153 = all_170_5_154) & ordered_pair(all_170_4_153, all_170_5_154) = all_170_1_150 & ordered_pair(all_170_5_154, all_170_4_153) = all_170_3_152 & in(all_170_1_150, all_0_16_16) = all_170_0_149 & in(all_170_3_152, all_0_16_16) = all_170_2_151 & in(all_170_4_153, all_0_14_14) = 0 & in(all_170_5_154, all_0_14_14) = 0
% 9.98/3.06 |
% 9.98/3.06 | Applying alpha-rule on (268) yields:
% 9.98/3.06 | (269) in(all_170_4_153, all_0_14_14) = 0
% 9.98/3.06 | (270) in(all_170_5_154, all_0_14_14) = 0
% 9.98/3.06 | (271) ordered_pair(all_170_4_153, all_170_5_154) = all_170_1_150
% 9.98/3.06 | (272) in(all_170_3_152, all_0_16_16) = all_170_2_151
% 9.98/3.06 | (273) ordered_pair(all_170_5_154, all_170_4_153) = all_170_3_152
% 9.98/3.06 | (274) in(all_170_1_150, all_0_16_16) = all_170_0_149
% 9.98/3.06 | (275) ~ (all_170_0_149 = 0)
% 9.98/3.06 | (276) ~ (all_170_4_153 = all_170_5_154)
% 9.98/3.06 | (277) ~ (all_170_2_151 = 0)
% 9.98/3.06 |
% 10.45/3.06 | Instantiating formula (191) with all_170_1_150, all_170_4_153, all_170_5_154 and discharging atoms ordered_pair(all_170_4_153, all_170_5_154) = all_170_1_150, yields:
% 10.45/3.06 | (278) all_170_4_153 = all_170_5_154 | ? [v0] : ? [v1] : ((v1 = 0 & ordered_pair(all_170_5_154, all_170_4_153) = v0 & in(v0, all_0_16_16) = 0) | (v0 = 0 & in(all_170_1_150, all_0_16_16) = 0) | ( ~ (v0 = 0) & in(all_170_4_153, all_0_14_14) = v0) | ( ~ (v0 = 0) & in(all_170_5_154, all_0_14_14) = v0))
% 10.45/3.06 |
% 10.45/3.06 | Instantiating formula (191) with all_170_3_152, all_170_5_154, all_170_4_153 and discharging atoms ordered_pair(all_170_5_154, all_170_4_153) = all_170_3_152, yields:
% 10.45/3.06 | (279) all_170_4_153 = all_170_5_154 | ? [v0] : ? [v1] : ((v1 = 0 & ordered_pair(all_170_4_153, all_170_5_154) = v0 & in(v0, all_0_16_16) = 0) | (v0 = 0 & in(all_170_3_152, all_0_16_16) = 0) | ( ~ (v0 = 0) & in(all_170_4_153, all_0_14_14) = v0) | ( ~ (v0 = 0) & in(all_170_5_154, all_0_14_14) = v0))
% 10.45/3.06 |
% 10.45/3.06 | Instantiating formula (59) with all_170_0_149, all_0_16_16, all_170_1_150 and discharging atoms in(all_170_1_150, all_0_16_16) = all_170_0_149, yields:
% 10.45/3.06 | (280) all_170_0_149 = 0 | ? [v0] : ((v0 = 0 & empty(all_0_16_16) = 0) | ( ~ (v0 = 0) & element(all_170_1_150, all_0_16_16) = v0))
% 10.45/3.06 |
% 10.45/3.06 | Instantiating formula (59) with all_170_2_151, all_0_16_16, all_170_3_152 and discharging atoms in(all_170_3_152, all_0_16_16) = all_170_2_151, yields:
% 10.45/3.06 | (281) all_170_2_151 = 0 | ? [v0] : ((v0 = 0 & empty(all_0_16_16) = 0) | ( ~ (v0 = 0) & element(all_170_3_152, all_0_16_16) = v0))
% 10.45/3.06 |
% 10.45/3.06 +-Applying beta-rule and splitting (279), into two cases.
% 10.45/3.06 |-Branch one:
% 10.45/3.06 | (282) all_170_4_153 = all_170_5_154
% 10.45/3.06 |
% 10.45/3.06 | Equations (282) can reduce 276 to:
% 10.45/3.06 | (123) $false
% 10.45/3.06 |
% 10.45/3.06 |-The branch is then unsatisfiable
% 10.45/3.06 |-Branch two:
% 10.45/3.06 | (276) ~ (all_170_4_153 = all_170_5_154)
% 10.45/3.06 | (285) ? [v0] : ? [v1] : ((v1 = 0 & ordered_pair(all_170_4_153, all_170_5_154) = v0 & in(v0, all_0_16_16) = 0) | (v0 = 0 & in(all_170_3_152, all_0_16_16) = 0) | ( ~ (v0 = 0) & in(all_170_4_153, all_0_14_14) = v0) | ( ~ (v0 = 0) & in(all_170_5_154, all_0_14_14) = v0))
% 10.45/3.06 |
% 10.45/3.06 +-Applying beta-rule and splitting (280), into two cases.
% 10.45/3.06 |-Branch one:
% 10.45/3.06 | (286) all_170_0_149 = 0
% 10.45/3.06 |
% 10.45/3.06 | Equations (286) can reduce 275 to:
% 10.45/3.06 | (123) $false
% 10.45/3.06 |
% 10.45/3.06 |-The branch is then unsatisfiable
% 10.45/3.06 |-Branch two:
% 10.45/3.06 | (275) ~ (all_170_0_149 = 0)
% 10.45/3.06 | (289) ? [v0] : ((v0 = 0 & empty(all_0_16_16) = 0) | ( ~ (v0 = 0) & element(all_170_1_150, all_0_16_16) = v0))
% 10.45/3.06 |
% 10.45/3.06 +-Applying beta-rule and splitting (278), into two cases.
% 10.45/3.06 |-Branch one:
% 10.45/3.06 | (282) all_170_4_153 = all_170_5_154
% 10.45/3.06 |
% 10.45/3.06 | Equations (282) can reduce 276 to:
% 10.45/3.06 | (123) $false
% 10.45/3.06 |
% 10.45/3.06 |-The branch is then unsatisfiable
% 10.45/3.06 |-Branch two:
% 10.45/3.06 | (276) ~ (all_170_4_153 = all_170_5_154)
% 10.45/3.06 | (293) ? [v0] : ? [v1] : ((v1 = 0 & ordered_pair(all_170_5_154, all_170_4_153) = v0 & in(v0, all_0_16_16) = 0) | (v0 = 0 & in(all_170_1_150, all_0_16_16) = 0) | ( ~ (v0 = 0) & in(all_170_4_153, all_0_14_14) = v0) | ( ~ (v0 = 0) & in(all_170_5_154, all_0_14_14) = v0))
% 10.45/3.06 |
% 10.45/3.06 | Instantiating (293) with all_234_0_169, all_234_1_170 yields:
% 10.45/3.06 | (294) (all_234_0_169 = 0 & ordered_pair(all_170_5_154, all_170_4_153) = all_234_1_170 & in(all_234_1_170, all_0_16_16) = 0) | (all_234_1_170 = 0 & in(all_170_1_150, all_0_16_16) = 0) | ( ~ (all_234_1_170 = 0) & in(all_170_4_153, all_0_14_14) = all_234_1_170) | ( ~ (all_234_1_170 = 0) & in(all_170_5_154, all_0_14_14) = all_234_1_170)
% 10.45/3.06 |
% 10.45/3.06 +-Applying beta-rule and splitting (294), into two cases.
% 10.45/3.06 |-Branch one:
% 10.45/3.06 | (295) (all_234_0_169 = 0 & ordered_pair(all_170_5_154, all_170_4_153) = all_234_1_170 & in(all_234_1_170, all_0_16_16) = 0) | (all_234_1_170 = 0 & in(all_170_1_150, all_0_16_16) = 0) | ( ~ (all_234_1_170 = 0) & in(all_170_4_153, all_0_14_14) = all_234_1_170)
% 10.45/3.06 |
% 10.45/3.06 +-Applying beta-rule and splitting (295), into two cases.
% 10.45/3.06 |-Branch one:
% 10.45/3.06 | (296) (all_234_0_169 = 0 & ordered_pair(all_170_5_154, all_170_4_153) = all_234_1_170 & in(all_234_1_170, all_0_16_16) = 0) | (all_234_1_170 = 0 & in(all_170_1_150, all_0_16_16) = 0)
% 10.45/3.06 |
% 10.45/3.06 +-Applying beta-rule and splitting (296), into two cases.
% 10.45/3.06 |-Branch one:
% 10.45/3.06 | (297) all_234_0_169 = 0 & ordered_pair(all_170_5_154, all_170_4_153) = all_234_1_170 & in(all_234_1_170, all_0_16_16) = 0
% 10.45/3.06 |
% 10.45/3.06 | Applying alpha-rule on (297) yields:
% 10.45/3.06 | (298) all_234_0_169 = 0
% 10.45/3.06 | (299) ordered_pair(all_170_5_154, all_170_4_153) = all_234_1_170
% 10.45/3.06 | (300) in(all_234_1_170, all_0_16_16) = 0
% 10.45/3.06 |
% 10.45/3.06 +-Applying beta-rule and splitting (281), into two cases.
% 10.45/3.06 |-Branch one:
% 10.45/3.06 | (301) all_170_2_151 = 0
% 10.45/3.06 |
% 10.45/3.06 | Equations (301) can reduce 277 to:
% 10.45/3.06 | (123) $false
% 10.45/3.06 |
% 10.45/3.06 |-The branch is then unsatisfiable
% 10.45/3.06 |-Branch two:
% 10.45/3.06 | (277) ~ (all_170_2_151 = 0)
% 10.45/3.06 | (304) ? [v0] : ((v0 = 0 & empty(all_0_16_16) = 0) | ( ~ (v0 = 0) & element(all_170_3_152, all_0_16_16) = v0))
% 10.45/3.07 |
% 10.45/3.07 | Instantiating formula (44) with all_170_5_154, all_170_4_153, all_234_1_170, all_170_3_152 and discharging atoms ordered_pair(all_170_5_154, all_170_4_153) = all_234_1_170, ordered_pair(all_170_5_154, all_170_4_153) = all_170_3_152, yields:
% 10.45/3.07 | (305) all_234_1_170 = all_170_3_152
% 10.45/3.07 |
% 10.45/3.07 | From (305) and (300) follows:
% 10.45/3.07 | (306) in(all_170_3_152, all_0_16_16) = 0
% 10.45/3.07 |
% 10.45/3.07 | Instantiating formula (61) with all_170_3_152, all_0_16_16, 0, all_170_2_151 and discharging atoms in(all_170_3_152, all_0_16_16) = all_170_2_151, in(all_170_3_152, all_0_16_16) = 0, yields:
% 10.45/3.07 | (301) all_170_2_151 = 0
% 10.45/3.07 |
% 10.45/3.07 | Equations (301) can reduce 277 to:
% 10.45/3.07 | (123) $false
% 10.45/3.07 |
% 10.45/3.07 |-The branch is then unsatisfiable
% 10.45/3.07 |-Branch two:
% 10.45/3.07 | (309) all_234_1_170 = 0 & in(all_170_1_150, all_0_16_16) = 0
% 10.45/3.07 |
% 10.45/3.07 | Applying alpha-rule on (309) yields:
% 10.45/3.07 | (310) all_234_1_170 = 0
% 10.45/3.07 | (311) in(all_170_1_150, all_0_16_16) = 0
% 10.45/3.07 |
% 10.45/3.07 | Instantiating formula (61) with all_170_1_150, all_0_16_16, 0, all_170_0_149 and discharging atoms in(all_170_1_150, all_0_16_16) = all_170_0_149, in(all_170_1_150, all_0_16_16) = 0, yields:
% 10.45/3.07 | (286) all_170_0_149 = 0
% 10.45/3.07 |
% 10.45/3.07 | Equations (286) can reduce 275 to:
% 10.45/3.07 | (123) $false
% 10.45/3.07 |
% 10.45/3.07 |-The branch is then unsatisfiable
% 10.45/3.07 |-Branch two:
% 10.45/3.07 | (314) ~ (all_234_1_170 = 0) & in(all_170_4_153, all_0_14_14) = all_234_1_170
% 10.45/3.07 |
% 10.45/3.07 | Applying alpha-rule on (314) yields:
% 10.45/3.07 | (315) ~ (all_234_1_170 = 0)
% 10.45/3.07 | (316) in(all_170_4_153, all_0_14_14) = all_234_1_170
% 10.45/3.07 |
% 10.45/3.07 | Instantiating formula (61) with all_170_4_153, all_0_14_14, all_234_1_170, 0 and discharging atoms in(all_170_4_153, all_0_14_14) = all_234_1_170, in(all_170_4_153, all_0_14_14) = 0, yields:
% 10.45/3.07 | (310) all_234_1_170 = 0
% 10.45/3.07 |
% 10.45/3.07 | Equations (310) can reduce 315 to:
% 10.45/3.07 | (123) $false
% 10.45/3.07 |
% 10.45/3.07 |-The branch is then unsatisfiable
% 10.45/3.07 |-Branch two:
% 10.45/3.07 | (319) ~ (all_234_1_170 = 0) & in(all_170_5_154, all_0_14_14) = all_234_1_170
% 10.45/3.07 |
% 10.45/3.07 | Applying alpha-rule on (319) yields:
% 10.45/3.07 | (315) ~ (all_234_1_170 = 0)
% 10.45/3.07 | (321) in(all_170_5_154, all_0_14_14) = all_234_1_170
% 10.45/3.07 |
% 10.45/3.07 | Instantiating formula (61) with all_170_5_154, all_0_14_14, all_234_1_170, 0 and discharging atoms in(all_170_5_154, all_0_14_14) = all_234_1_170, in(all_170_5_154, all_0_14_14) = 0, yields:
% 10.45/3.07 | (310) all_234_1_170 = 0
% 10.45/3.07 |
% 10.45/3.07 | Equations (310) can reduce 315 to:
% 10.45/3.07 | (123) $false
% 10.45/3.07 |
% 10.45/3.07 |-The branch is then unsatisfiable
% 10.45/3.07 % SZS output end Proof for theBenchmark
% 10.45/3.07
% 10.45/3.07 2465ms
%------------------------------------------------------------------------------