TSTP Solution File: SEU240+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU240+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n010.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 08:48:03 EDT 2022
% Result : Theorem 23.20s 6.53s
% Output : Proof 26.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU240+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.34 % Computer : n010.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 20 01:08:22 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.56/0.59 ____ _
% 0.56/0.59 ___ / __ \_____(_)___ ________ __________
% 0.56/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.56/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.56/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.56/0.59
% 0.56/0.59 A Theorem Prover for First-Order Logic
% 0.56/0.60 (ePrincess v.1.0)
% 0.56/0.60
% 0.56/0.60 (c) Philipp Rümmer, 2009-2015
% 0.56/0.60 (c) Peter Backeman, 2014-2015
% 0.56/0.60 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.56/0.60 Free software under GNU Lesser General Public License (LGPL).
% 0.56/0.60 Bug reports to peter@backeman.se
% 0.56/0.60
% 0.56/0.60 For more information, visit http://user.uu.se/~petba168/breu/
% 0.56/0.60
% 0.56/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.73/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.55/0.93 Prover 0: Preprocessing ...
% 2.28/1.17 Prover 0: Warning: ignoring some quantifiers
% 2.28/1.19 Prover 0: Constructing countermodel ...
% 20.52/5.94 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 20.52/5.99 Prover 1: Preprocessing ...
% 21.28/6.11 Prover 1: Warning: ignoring some quantifiers
% 21.28/6.11 Prover 1: Constructing countermodel ...
% 22.03/6.25 Prover 1: gave up
% 22.03/6.25 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 22.03/6.28 Prover 2: Preprocessing ...
% 22.45/6.38 Prover 2: Warning: ignoring some quantifiers
% 22.68/6.39 Prover 2: Constructing countermodel ...
% 23.20/6.53 Prover 2: proved (275ms)
% 23.20/6.53 Prover 0: stopped
% 23.20/6.53
% 23.20/6.53 No countermodel exists, formula is valid
% 23.20/6.53 % SZS status Theorem for theBenchmark
% 23.20/6.53
% 23.20/6.53 Generating proof ... Warning: ignoring some quantifiers
% 26.07/7.19 found it (size 188)
% 26.07/7.19
% 26.07/7.19 % SZS output start Proof for theBenchmark
% 26.07/7.19 Assumed formulas after preprocessing and simplification:
% 26.07/7.19 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ( ~ (v13 = 0) & transitive(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] : ! [v22] : ! [v23] : ! [v24] : (v24 = 0 | ~ (ordered_pair(v20, v21) = v22) | ~ (ordered_pair(v19, v21) = v23) | ~ (is_transitive_in(v17, v18) = 0) | ~ (relation(v17) = 0) | ~ (in(v23, v17) = v24) | ~ (in(v22, v17) = 0) | ? [v25] : ? [v26] : (( ~ (v26 = 0) & ordered_pair(v19, v20) = v25 & in(v25, v17) = v26) | ( ~ (v25 = 0) & in(v21, v18) = v25) | ( ~ (v25 = 0) & in(v20, v18) = v25) | ( ~ (v25 = 0) & in(v19, v18) = v25))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : (v24 = 0 | ~ (ordered_pair(v19, v21) = v23) | ~ (ordered_pair(v19, v20) = v22) | ~ (is_transitive_in(v17, v18) = 0) | ~ (relation(v17) = 0) | ~ (in(v23, v17) = v24) | ~ (in(v22, v17) = 0) | ? [v25] : ? [v26] : (( ~ (v26 = 0) & ordered_pair(v20, v21) = v25 & in(v25, v17) = v26) | ( ~ (v25 = 0) & in(v21, v18) = v25) | ( ~ (v25 = 0) & in(v20, v18) = v25) | ( ~ (v25 = 0) & in(v19, v18) = v25))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v23 = 0 | ~ (ordered_pair(v19, v21) = v22) | ~ (is_transitive_in(v17, v18) = 0) | ~ (relation(v17) = 0) | ~ (in(v22, v17) = v23) | ~ (in(v20, v18) = 0) | ? [v24] : ? [v25] : (( ~ (v25 = 0) & ordered_pair(v20, v21) = v24 & in(v24, v17) = v25) | ( ~ (v25 = 0) & ordered_pair(v19, v20) = v24 & in(v24, v17) = v25) | ( ~ (v24 = 0) & in(v21, v18) = v24) | ( ~ (v24 = 0) & in(v19, v18) = v24))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ( ~ (ordered_pair(v20, v21) = v23) | ~ (ordered_pair(v19, v20) = v22) | ~ (is_transitive_in(v17, v18) = 0) | ~ (relation(v17) = 0) | ~ (in(v23, v17) = 0) | ~ (in(v22, v17) = 0) | ? [v24] : ? [v25] : ((v25 = 0 & ordered_pair(v19, v21) = v24 & in(v24, v17) = 0) | ( ~ (v24 = 0) & in(v21, v18) = v24) | ( ~ (v24 = 0) & in(v20, v18) = v24) | ( ~ (v24 = 0) & in(v19, v18) = v24))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (ordered_pair(v20, v21) = v22) | ~ (is_transitive_in(v17, v18) = 0) | ~ (relation(v17) = 0) | ~ (in(v22, v17) = 0) | ~ (in(v19, v18) = 0) | ? [v23] : ? [v24] : ((v24 = 0 & ordered_pair(v19, v21) = v23 & in(v23, v17) = 0) | ( ~ (v24 = 0) & ordered_pair(v19, v20) = v23 & in(v23, v17) = v24) | ( ~ (v23 = 0) & in(v21, v18) = v23) | ( ~ (v23 = 0) & in(v20, v18) = v23))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (ordered_pair(v19, v20) = v22) | ~ (is_transitive_in(v17, v18) = 0) | ~ (relation(v17) = 0) | ~ (in(v22, v17) = 0) | ~ (in(v21, v18) = 0) | ? [v23] : ? [v24] : ((v24 = 0 & ordered_pair(v19, v21) = v23 & in(v23, v17) = 0) | ( ~ (v24 = 0) & ordered_pair(v20, v21) = v23 & in(v23, v17) = v24) | ( ~ (v23 = 0) & in(v20, v18) = v23) | ( ~ (v23 = 0) & in(v19, v18) = v23))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (is_transitive_in(v17, v18) = 0) | ~ (relation(v17) = 0) | ~ (in(v21, v18) = 0) | ~ (in(v20, v18) = 0) | ~ (in(v19, v18) = 0) | ? [v22] : ? [v23] : ((v23 = 0 & ordered_pair(v19, v21) = v22 & in(v22, v17) = 0) | ( ~ (v23 = 0) & ordered_pair(v20, v21) = v22 & in(v22, v17) = v23) | ( ~ (v23 = 0) & ordered_pair(v19, v20) = v22 & in(v22, v17) = v23))) & ! [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_transitive_in(v20, v19) = v18) | ~ (is_transitive_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] : ! [v20] : ( ~ (ordered_pair(v17, v18) = v20) | ~ (in(v20, v19) = 0) | ? [v21] : ? [v22] : ? [v23] : ((v23 = 0 & v22 = 0 & relation_field(v19) = v21 & in(v18, v21) = 0 & in(v17, v21) = 0) | ( ~ (v21 = 0) & relation(v19) = v21))) & ! [v17] : ! [v18] : ! [v19] : (v19 = 0 | ~ (element(v17, v18) = v19) | ? [v20] : ( ~ (v20 = 0) & in(v17, v18) = v20)) & ! [v17] : ! [v18] : ! [v19] : (v19 = 0 | ~ (is_transitive_in(v17, v18) = v19) | ~ (relation(v17) = 0) | ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : ( ~ (v26 = 0) & ordered_pair(v21, v22) = v24 & ordered_pair(v20, v22) = v25 & ordered_pair(v20, v21) = v23 & in(v25, v17) = v26 & in(v24, v17) = 0 & in(v23, v17) = 0 & in(v22, v18) = 0 & 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 | ~ (transitive(v19) = v18) | ~ (transitive(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_transitive_in(v17, v18) = 0) | ( ~ (v19 = 0) & transitive(v17) = v19)) & ((v19 = 0 & transitive(v17) = 0) | ( ~ (v20 = 0) & is_transitive_in(v17, v18) = v20))))) & ! [v17] : ! [v18] : ( ~ (transitive(v17) = v18) | ? [v19] : ? [v20] : (( ~ (v19 = 0) & relation(v17) = v19) | (( ~ (v18 = 0) | (v20 = 0 & relation_field(v17) = v19 & is_transitive_in(v17, v19) = 0)) & (v18 = 0 | ( ~ (v20 = 0) & relation_field(v17) = v19 & is_transitive_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_transitive_in(v17, v19) = 0) | ( ~ (v18 = 0) & transitive(v17) = v18)) & ((v18 = 0 & transitive(v17) = 0) | ( ~ (v20 = 0) & relation_field(v17) = v19 & is_transitive_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_transitive_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] : transitive(v17) = v18 & ? [v17] : ? [v18] : one_to_one(v17) = v18 & ? [v17] : ? [v18] : relation(v17) = v18 & ? [v17] : ? [v18] : function(v17) = v18 & ? [v17] : ? [v18] : empty(v17) = v18 & ((v8 = 0 & v6 = 0 & v1 = 0 & ~ (v10 = 0) & ordered_pair(v3, v4) = v7 & ordered_pair(v2, v4) = v9 & ordered_pair(v2, v3) = v5 & in(v9, v0) = v10 & in(v7, v0) = 0 & in(v5, v0) = 0) | ( ~ (v1 = 0) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v22 = 0 | ~ (ordered_pair(v18, v19) = v20) | ~ (ordered_pair(v17, v19) = v21) | ~ (in(v21, v0) = v22) | ~ (in(v20, v0) = 0) | ? [v23] : ? [v24] : ( ~ (v24 = 0) & ordered_pair(v17, v18) = v23 & in(v23, v0) = v24)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v22 = 0 | ~ (ordered_pair(v17, v19) = v21) | ~ (ordered_pair(v17, v18) = v20) | ~ (in(v21, v0) = v22) | ~ (in(v20, v0) = 0) | ? [v23] : ? [v24] : ( ~ (v24 = 0) & ordered_pair(v18, v19) = v23 & in(v23, v0) = v24)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (ordered_pair(v18, v19) = v21) | ~ (ordered_pair(v17, v18) = v20) | ~ (in(v21, v0) = 0) | ~ (in(v20, v0) = 0) | ? [v22] : (ordered_pair(v17, v19) = v22 & in(v22, v0) = 0)))))
% 26.40/7.25 | 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:
% 26.40/7.25 | (1) ~ (all_0_3_3 = 0) & transitive(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] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (ordered_pair(v3, v4) = v5) | ~ (ordered_pair(v2, v4) = v6) | ~ (is_transitive_in(v0, v1) = 0) | ~ (relation(v0) = 0) | ~ (in(v6, v0) = v7) | ~ (in(v5, v0) = 0) | ? [v8] : ? [v9] : (( ~ (v9 = 0) & ordered_pair(v2, v3) = v8 & in(v8, v0) = v9) | ( ~ (v8 = 0) & in(v4, v1) = v8) | ( ~ (v8 = 0) & in(v3, v1) = v8) | ( ~ (v8 = 0) & in(v2, v1) = v8))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (ordered_pair(v2, v4) = v6) | ~ (ordered_pair(v2, v3) = v5) | ~ (is_transitive_in(v0, v1) = 0) | ~ (relation(v0) = 0) | ~ (in(v6, v0) = v7) | ~ (in(v5, v0) = 0) | ? [v8] : ? [v9] : (( ~ (v9 = 0) & ordered_pair(v3, v4) = v8 & in(v8, v0) = v9) | ( ~ (v8 = 0) & in(v4, v1) = v8) | ( ~ (v8 = 0) & in(v3, v1) = v8) | ( ~ (v8 = 0) & in(v2, v1) = v8))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (ordered_pair(v2, v4) = v5) | ~ (is_transitive_in(v0, v1) = 0) | ~ (relation(v0) = 0) | ~ (in(v5, v0) = v6) | ~ (in(v3, v1) = 0) | ? [v7] : ? [v8] : (( ~ (v8 = 0) & ordered_pair(v3, v4) = v7 & in(v7, v0) = v8) | ( ~ (v8 = 0) & ordered_pair(v2, v3) = v7 & in(v7, v0) = v8) | ( ~ (v7 = 0) & in(v4, v1) = v7) | ( ~ (v7 = 0) & in(v2, v1) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (ordered_pair(v3, v4) = v6) | ~ (ordered_pair(v2, v3) = v5) | ~ (is_transitive_in(v0, v1) = 0) | ~ (relation(v0) = 0) | ~ (in(v6, v0) = 0) | ~ (in(v5, v0) = 0) | ? [v7] : ? [v8] : ((v8 = 0 & ordered_pair(v2, v4) = v7 & in(v7, v0) = 0) | ( ~ (v7 = 0) & in(v4, v1) = v7) | ( ~ (v7 = 0) & in(v3, v1) = v7) | ( ~ (v7 = 0) & in(v2, v1) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (ordered_pair(v3, v4) = v5) | ~ (is_transitive_in(v0, v1) = 0) | ~ (relation(v0) = 0) | ~ (in(v5, v0) = 0) | ~ (in(v2, v1) = 0) | ? [v6] : ? [v7] : ((v7 = 0 & ordered_pair(v2, v4) = v6 & in(v6, v0) = 0) | ( ~ (v7 = 0) & ordered_pair(v2, v3) = v6 & in(v6, v0) = v7) | ( ~ (v6 = 0) & in(v4, v1) = v6) | ( ~ (v6 = 0) & in(v3, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (ordered_pair(v2, v3) = v5) | ~ (is_transitive_in(v0, v1) = 0) | ~ (relation(v0) = 0) | ~ (in(v5, v0) = 0) | ~ (in(v4, v1) = 0) | ? [v6] : ? [v7] : ((v7 = 0 & ordered_pair(v2, v4) = v6 & in(v6, v0) = 0) | ( ~ (v7 = 0) & ordered_pair(v3, v4) = v6 & in(v6, v0) = v7) | ( ~ (v6 = 0) & in(v3, v1) = v6) | ( ~ (v6 = 0) & in(v2, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (is_transitive_in(v0, v1) = 0) | ~ (relation(v0) = 0) | ~ (in(v4, v1) = 0) | ~ (in(v3, v1) = 0) | ~ (in(v2, v1) = 0) | ? [v5] : ? [v6] : ((v6 = 0 & ordered_pair(v2, v4) = v5 & in(v5, v0) = 0) | ( ~ (v6 = 0) & ordered_pair(v3, v4) = v5 & in(v5, v0) = v6) | ( ~ (v6 = 0) & ordered_pair(v2, v3) = v5 & in(v5, v0) = v6))) & ! [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_transitive_in(v3, v2) = v1) | ~ (is_transitive_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] : ! [v3] : ( ~ (ordered_pair(v0, v1) = v3) | ~ (in(v3, v2) = 0) | ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & relation_field(v2) = v4 & in(v1, v4) = 0 & in(v0, v4) = 0) | ( ~ (v4 = 0) & relation(v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (is_transitive_in(v0, v1) = v2) | ~ (relation(v0) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ( ~ (v9 = 0) & ordered_pair(v4, v5) = v7 & ordered_pair(v3, v5) = v8 & ordered_pair(v3, v4) = v6 & in(v8, v0) = v9 & in(v7, v0) = 0 & in(v6, v0) = 0 & in(v5, v1) = 0 & 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 | ~ (transitive(v2) = v1) | ~ (transitive(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_transitive_in(v0, v1) = 0) | ( ~ (v2 = 0) & transitive(v0) = v2)) & ((v2 = 0 & transitive(v0) = 0) | ( ~ (v3 = 0) & is_transitive_in(v0, v1) = v3))))) & ! [v0] : ! [v1] : ( ~ (transitive(v0) = v1) | ? [v2] : ? [v3] : (( ~ (v2 = 0) & relation(v0) = v2) | (( ~ (v1 = 0) | (v3 = 0 & relation_field(v0) = v2 & is_transitive_in(v0, v2) = 0)) & (v1 = 0 | ( ~ (v3 = 0) & relation_field(v0) = v2 & is_transitive_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_transitive_in(v0, v2) = 0) | ( ~ (v1 = 0) & transitive(v0) = v1)) & ((v1 = 0 & transitive(v0) = 0) | ( ~ (v3 = 0) & relation_field(v0) = v2 & is_transitive_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_transitive_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] : transitive(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_10_10 = 0 & all_0_15_15 = 0 & ~ (all_0_6_6 = 0) & ordered_pair(all_0_13_13, all_0_12_12) = all_0_9_9 & ordered_pair(all_0_14_14, all_0_12_12) = all_0_7_7 & ordered_pair(all_0_14_14, all_0_13_13) = all_0_11_11 & in(all_0_7_7, all_0_16_16) = all_0_6_6 & in(all_0_9_9, all_0_16_16) = 0 & in(all_0_11_11, all_0_16_16) = 0) | ( ~ (all_0_15_15 = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (ordered_pair(v1, v2) = v3) | ~ (ordered_pair(v0, v2) = v4) | ~ (in(v4, all_0_16_16) = v5) | ~ (in(v3, all_0_16_16) = 0) | ? [v6] : ? [v7] : ( ~ (v7 = 0) & ordered_pair(v0, v1) = v6 & in(v6, all_0_16_16) = v7)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (ordered_pair(v0, v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ (in(v4, all_0_16_16) = v5) | ~ (in(v3, all_0_16_16) = 0) | ? [v6] : ? [v7] : ( ~ (v7 = 0) & ordered_pair(v1, v2) = v6 & in(v6, all_0_16_16) = v7)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (ordered_pair(v1, v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ (in(v4, all_0_16_16) = 0) | ~ (in(v3, all_0_16_16) = 0) | ? [v5] : (ordered_pair(v0, v2) = v5 & in(v5, all_0_16_16) = 0))))
% 26.40/7.27 |
% 26.40/7.27 | Applying alpha-rule on (1) yields:
% 26.57/7.27 | (2) empty(all_0_1_1) = 0
% 26.57/7.27 | (3) ? [v0] : ? [v1] : transitive(v0) = v1
% 26.57/7.27 | (4) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (((v3 = 0 & relation_field(v0) = v2 & is_transitive_in(v0, v2) = 0) | ( ~ (v1 = 0) & transitive(v0) = v1)) & ((v1 = 0 & transitive(v0) = 0) | ( ~ (v3 = 0) & relation_field(v0) = v2 & is_transitive_in(v0, v2) = v3))))
% 26.57/7.27 | (5) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0))
% 26.57/7.27 | (6) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0))
% 26.57/7.27 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (ordered_pair(v2, v4) = v5) | ~ (is_transitive_in(v0, v1) = 0) | ~ (relation(v0) = 0) | ~ (in(v5, v0) = v6) | ~ (in(v3, v1) = 0) | ? [v7] : ? [v8] : (( ~ (v8 = 0) & ordered_pair(v3, v4) = v7 & in(v7, v0) = v8) | ( ~ (v8 = 0) & ordered_pair(v2, v3) = v7 & in(v7, v0) = v8) | ( ~ (v7 = 0) & in(v4, v1) = v7) | ( ~ (v7 = 0) & in(v2, v1) = v7)))
% 26.57/7.27 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (ordered_pair(v2, v3) = v5) | ~ (is_transitive_in(v0, v1) = 0) | ~ (relation(v0) = 0) | ~ (in(v5, v0) = 0) | ~ (in(v4, v1) = 0) | ? [v6] : ? [v7] : ((v7 = 0 & ordered_pair(v2, v4) = v6 & in(v6, v0) = 0) | ( ~ (v7 = 0) & ordered_pair(v3, v4) = v6 & in(v6, v0) = v7) | ( ~ (v6 = 0) & in(v3, v1) = v6) | ( ~ (v6 = 0) & in(v2, v1) = v6)))
% 26.57/7.27 | (9) empty(all_0_4_4) = all_0_3_3
% 26.57/7.27 | (10) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0))
% 26.57/7.27 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (ordered_pair(v3, v4) = v5) | ~ (is_transitive_in(v0, v1) = 0) | ~ (relation(v0) = 0) | ~ (in(v5, v0) = 0) | ~ (in(v2, v1) = 0) | ? [v6] : ? [v7] : ((v7 = 0 & ordered_pair(v2, v4) = v6 & in(v6, v0) = 0) | ( ~ (v7 = 0) & ordered_pair(v2, v3) = v6 & in(v6, v0) = v7) | ( ~ (v6 = 0) & in(v4, v1) = v6) | ( ~ (v6 = 0) & in(v3, v1) = v6)))
% 26.57/7.28 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ? [v3] : ((v3 = 0 & empty(v0) = 0) | ( ~ (v3 = 0) & empty(v2) = v3)))
% 26.57/7.28 | (13) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 26.57/7.28 | (14) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (ordered_pair(v0, v1) = v3 & singleton(v0) = v4 & unordered_pair(v2, v4) = v3))
% 26.57/7.28 | (15) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_field(v2) = v1) | ~ (relation_field(v2) = v0))
% 26.57/7.28 | (16) ? [v0] : ? [v1] : relation_dom(v0) = v1
% 26.57/7.28 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (ordered_pair(v3, v4) = v6) | ~ (ordered_pair(v2, v3) = v5) | ~ (is_transitive_in(v0, v1) = 0) | ~ (relation(v0) = 0) | ~ (in(v6, v0) = 0) | ~ (in(v5, v0) = 0) | ? [v7] : ? [v8] : ((v8 = 0 & ordered_pair(v2, v4) = v7 & in(v7, v0) = 0) | ( ~ (v7 = 0) & in(v4, v1) = v7) | ( ~ (v7 = 0) & in(v3, v1) = v7) | ( ~ (v7 = 0) & in(v2, v1) = v7)))
% 26.57/7.28 | (18) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2)
% 26.57/7.28 | (19) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2)
% 26.57/7.28 | (20) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0))
% 26.57/7.28 | (21) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (transitive(v2) = v1) | ~ (transitive(v2) = v0))
% 26.57/7.28 | (22) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (relation_dom(v0) = v2 & relation_rng(v0) = v3 & relation_field(v0) = v1 & set_union2(v2, v3) = v1))
% 26.57/7.28 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0))
% 26.57/7.28 | (24) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3))
% 26.57/7.28 | (25) ? [v0] : ? [v1] : singleton(v0) = v1
% 26.57/7.28 | (26) relation(all_0_0_0) = 0
% 26.57/7.28 | (27) ? [v0] : ? [v1] : empty(v0) = v1
% 26.57/7.28 | (28) ? [v0] : ? [v1] : relation_field(v0) = v1
% 26.57/7.28 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (is_transitive_in(v0, v1) = 0) | ~ (relation(v0) = 0) | ~ (in(v4, v1) = 0) | ~ (in(v3, v1) = 0) | ~ (in(v2, v1) = 0) | ? [v5] : ? [v6] : ((v6 = 0 & ordered_pair(v2, v4) = v5 & in(v5, v0) = 0) | ( ~ (v6 = 0) & ordered_pair(v3, v4) = v5 & in(v5, v0) = v6) | ( ~ (v6 = 0) & ordered_pair(v2, v3) = v5 & in(v5, v0) = v6)))
% 26.57/7.28 | (30) ? [v0] : ? [v1] : one_to_one(v0) = v1
% 26.57/7.28 | (31) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0))
% 26.57/7.28 | (32) ! [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)))
% 26.57/7.28 | (33) ? [v0] : ? [v1] : relation_rng(v0) = v1
% 26.57/7.28 | (34) empty(all_0_2_2) = 0
% 26.57/7.28 | (35) relation(all_0_5_5) = 0
% 26.57/7.28 | (36) ! [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)))
% 26.57/7.28 | (37) ! [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)))
% 26.57/7.28 | (38) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0))
% 26.57/7.28 | (39) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0))
% 26.57/7.28 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (ordered_pair(v0, v1) = v3) | ~ (in(v3, v2) = 0) | ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & relation_field(v2) = v4 & in(v1, v4) = 0 & in(v0, v4) = 0) | ( ~ (v4 = 0) & relation(v2) = v4)))
% 26.57/7.28 | (41) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v0, v1) = v2) | ? [v3] : ((v3 = 0 & empty(v1) = 0) | ( ~ (v3 = 0) & element(v0, v1) = v3)))
% 26.57/7.28 | (42) ! [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)))
% 26.57/7.28 | (43) ? [v0] : ? [v1] : function(v0) = v1
% 26.57/7.28 | (44) ? [v0] : ? [v1] : ? [v2] : set_union2(v1, v0) = v2
% 26.57/7.29 | (45) ! [v0] : ! [v1] : (v1 = 0 | ~ (function(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2))
% 26.57/7.29 | (46) ? [v0] : ? [v1] : ? [v2] : ordered_pair(v1, v0) = v2
% 26.57/7.29 | (47) one_to_one(all_0_5_5) = 0
% 26.57/7.29 | (48) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1))
% 26.57/7.29 | (49) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 26.57/7.29 | (50) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (ordered_pair(v2, v4) = v6) | ~ (ordered_pair(v2, v3) = v5) | ~ (is_transitive_in(v0, v1) = 0) | ~ (relation(v0) = 0) | ~ (in(v6, v0) = v7) | ~ (in(v5, v0) = 0) | ? [v8] : ? [v9] : (( ~ (v9 = 0) & ordered_pair(v3, v4) = v8 & in(v8, v0) = v9) | ( ~ (v8 = 0) & in(v4, v1) = v8) | ( ~ (v8 = 0) & in(v3, v1) = v8) | ( ~ (v8 = 0) & in(v2, v1) = v8)))
% 26.57/7.29 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0))
% 26.57/7.29 | (52) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1))
% 26.57/7.29 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (is_transitive_in(v3, v2) = v1) | ~ (is_transitive_in(v3, v2) = v0))
% 26.57/7.29 | (54) ? [v0] : ? [v1] : relation(v0) = v1
% 26.57/7.29 | (55) ! [v0] : ( ~ (empty(v0) = 0) | function(v0) = 0)
% 26.57/7.29 | (56) ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2
% 26.57/7.29 | (57) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | element(v0, v1) = 0)
% 26.57/7.29 | (58) ! [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)))
% 26.57/7.29 | (59) ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2))
% 26.57/7.29 | (60) ! [v0] : ! [v1] : ( ~ (element(v0, v1) = 0) | ? [v2] : ((v2 = 0 & empty(v1) = 0) | (v2 = 0 & in(v0, v1) = 0)))
% 26.57/7.29 | (61) ? [v0] : ? [v1] : ? [v2] : is_transitive_in(v1, v0) = v2
% 26.57/7.29 | (62) function(all_0_0_0) = 0
% 26.57/7.29 | (63) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 26.57/7.29 | (64) relation(all_0_2_2) = 0
% 26.57/7.29 | (65) relation(all_0_16_16) = 0
% 26.57/7.29 | (66) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0))
% 26.57/7.29 | (67) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (is_transitive_in(v0, v1) = v2) | ~ (relation(v0) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ( ~ (v9 = 0) & ordered_pair(v4, v5) = v7 & ordered_pair(v3, v5) = v8 & ordered_pair(v3, v4) = v6 & in(v8, v0) = v9 & in(v7, v0) = 0 & in(v6, v0) = 0 & in(v5, v1) = 0 & in(v4, v1) = 0 & in(v3, v1) = 0))
% 26.57/7.29 | (68) empty(empty_set) = 0
% 26.57/7.29 | (69) function(all_0_5_5) = 0
% 26.57/7.29 | (70) ! [v0] : ! [v1] : ( ~ (transitive(v0) = v1) | ? [v2] : ? [v3] : (( ~ (v2 = 0) & relation(v0) = v2) | (( ~ (v1 = 0) | (v3 = 0 & relation_field(v0) = v2 & is_transitive_in(v0, v2) = 0)) & (v1 = 0 | ( ~ (v3 = 0) & relation_field(v0) = v2 & is_transitive_in(v0, v2) = v3)))))
% 26.57/7.29 | (71) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2)
% 26.57/7.29 | (72) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2)
% 26.57/7.29 | (73) ~ (all_0_3_3 = 0)
% 26.57/7.29 | (74) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 26.57/7.29 | (75) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3))
% 26.57/7.29 | (76) ? [v0] : ? [v1] : ? [v2] : unordered_pair(v1, v0) = v2
% 26.57/7.29 | (77) ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ? [v2] : ? [v3] : (( ~ (v2 = 0) & relation(v0) = v2) | (((v3 = 0 & is_transitive_in(v0, v1) = 0) | ( ~ (v2 = 0) & transitive(v0) = v2)) & ((v2 = 0 & transitive(v0) = 0) | ( ~ (v3 = 0) & is_transitive_in(v0, v1) = v3)))))
% 26.57/7.29 | (78) (all_0_8_8 = 0 & all_0_10_10 = 0 & all_0_15_15 = 0 & ~ (all_0_6_6 = 0) & ordered_pair(all_0_13_13, all_0_12_12) = all_0_9_9 & ordered_pair(all_0_14_14, all_0_12_12) = all_0_7_7 & ordered_pair(all_0_14_14, all_0_13_13) = all_0_11_11 & in(all_0_7_7, all_0_16_16) = all_0_6_6 & in(all_0_9_9, all_0_16_16) = 0 & in(all_0_11_11, all_0_16_16) = 0) | ( ~ (all_0_15_15 = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (ordered_pair(v1, v2) = v3) | ~ (ordered_pair(v0, v2) = v4) | ~ (in(v4, all_0_16_16) = v5) | ~ (in(v3, all_0_16_16) = 0) | ? [v6] : ? [v7] : ( ~ (v7 = 0) & ordered_pair(v0, v1) = v6 & in(v6, all_0_16_16) = v7)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (ordered_pair(v0, v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ (in(v4, all_0_16_16) = v5) | ~ (in(v3, all_0_16_16) = 0) | ? [v6] : ? [v7] : ( ~ (v7 = 0) & ordered_pair(v1, v2) = v6 & in(v6, all_0_16_16) = v7)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (ordered_pair(v1, v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ (in(v4, all_0_16_16) = 0) | ~ (in(v3, all_0_16_16) = 0) | ? [v5] : (ordered_pair(v0, v2) = v5 & in(v5, all_0_16_16) = 0)))
% 26.57/7.30 | (79) ! [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)))
% 26.57/7.30 | (80) function(all_0_2_2) = 0
% 26.57/7.30 | (81) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3))
% 26.57/7.30 | (82) ? [v0] : ? [v1] : element(v1, v0) = 0
% 26.57/7.30 | (83) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : ((v3 = 0 & empty(v0) = 0) | ( ~ (v3 = 0) & empty(v2) = v3)))
% 26.57/7.30 | (84) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 26.57/7.30 | (85) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 26.57/7.30 | (86) transitive(all_0_16_16) = all_0_15_15
% 26.57/7.30 | (87) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (ordered_pair(v3, v4) = v5) | ~ (ordered_pair(v2, v4) = v6) | ~ (is_transitive_in(v0, v1) = 0) | ~ (relation(v0) = 0) | ~ (in(v6, v0) = v7) | ~ (in(v5, v0) = 0) | ? [v8] : ? [v9] : (( ~ (v9 = 0) & ordered_pair(v2, v3) = v8 & in(v8, v0) = v9) | ( ~ (v8 = 0) & in(v4, v1) = v8) | ( ~ (v8 = 0) & in(v3, v1) = v8) | ( ~ (v8 = 0) & in(v2, v1) = v8)))
% 26.57/7.30 | (88) ! [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)))
% 26.57/7.30 | (89) ? [v0] : ? [v1] : ? [v2] : element(v1, v0) = v2
% 26.57/7.30 |
% 26.57/7.30 | Instantiating formula (70) with all_0_15_15, all_0_16_16 and discharging atoms transitive(all_0_16_16) = all_0_15_15, yields:
% 26.57/7.30 | (90) ? [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_transitive_in(all_0_16_16, v0) = 0)) & (all_0_15_15 = 0 | ( ~ (v1 = 0) & relation_field(all_0_16_16) = v0 & is_transitive_in(all_0_16_16, v0) = v1))))
% 26.57/7.30 |
% 26.57/7.30 | Instantiating formula (22) with all_0_16_16 and discharging atoms relation(all_0_16_16) = 0, yields:
% 26.57/7.30 | (91) ? [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)
% 26.57/7.30 |
% 26.57/7.30 | Instantiating formula (4) with all_0_16_16 and discharging atoms relation(all_0_16_16) = 0, yields:
% 26.57/7.30 | (92) ? [v0] : ? [v1] : ? [v2] : (((v2 = 0 & relation_field(all_0_16_16) = v1 & is_transitive_in(all_0_16_16, v1) = 0) | ( ~ (v0 = 0) & transitive(all_0_16_16) = v0)) & ((v0 = 0 & transitive(all_0_16_16) = 0) | ( ~ (v2 = 0) & relation_field(all_0_16_16) = v1 & is_transitive_in(all_0_16_16, v1) = v2)))
% 26.57/7.30 |
% 26.57/7.30 | Instantiating (92) with all_50_0_69, all_50_1_70, all_50_2_71 yields:
% 26.57/7.30 | (93) ((all_50_0_69 = 0 & relation_field(all_0_16_16) = all_50_1_70 & is_transitive_in(all_0_16_16, all_50_1_70) = 0) | ( ~ (all_50_2_71 = 0) & transitive(all_0_16_16) = all_50_2_71)) & ((all_50_2_71 = 0 & transitive(all_0_16_16) = 0) | ( ~ (all_50_0_69 = 0) & relation_field(all_0_16_16) = all_50_1_70 & is_transitive_in(all_0_16_16, all_50_1_70) = all_50_0_69))
% 26.57/7.30 |
% 26.57/7.30 | Applying alpha-rule on (93) yields:
% 26.57/7.30 | (94) (all_50_0_69 = 0 & relation_field(all_0_16_16) = all_50_1_70 & is_transitive_in(all_0_16_16, all_50_1_70) = 0) | ( ~ (all_50_2_71 = 0) & transitive(all_0_16_16) = all_50_2_71)
% 26.57/7.30 | (95) (all_50_2_71 = 0 & transitive(all_0_16_16) = 0) | ( ~ (all_50_0_69 = 0) & relation_field(all_0_16_16) = all_50_1_70 & is_transitive_in(all_0_16_16, all_50_1_70) = all_50_0_69)
% 26.57/7.30 |
% 26.57/7.30 | Instantiating (91) with all_51_0_72, all_51_1_73, all_51_2_74 yields:
% 26.57/7.30 | (96) relation_dom(all_0_16_16) = all_51_1_73 & relation_rng(all_0_16_16) = all_51_0_72 & relation_field(all_0_16_16) = all_51_2_74 & set_union2(all_51_1_73, all_51_0_72) = all_51_2_74
% 26.57/7.30 |
% 26.57/7.30 | Applying alpha-rule on (96) yields:
% 26.57/7.30 | (97) relation_dom(all_0_16_16) = all_51_1_73
% 26.57/7.30 | (98) relation_rng(all_0_16_16) = all_51_0_72
% 26.57/7.30 | (99) relation_field(all_0_16_16) = all_51_2_74
% 26.57/7.30 | (100) set_union2(all_51_1_73, all_51_0_72) = all_51_2_74
% 26.57/7.30 |
% 26.57/7.30 | Instantiating (90) with all_60_0_87, all_60_1_88 yields:
% 26.57/7.30 | (101) ( ~ (all_60_1_88 = 0) & relation(all_0_16_16) = all_60_1_88) | (( ~ (all_0_15_15 = 0) | (all_60_0_87 = 0 & relation_field(all_0_16_16) = all_60_1_88 & is_transitive_in(all_0_16_16, all_60_1_88) = 0)) & (all_0_15_15 = 0 | ( ~ (all_60_0_87 = 0) & relation_field(all_0_16_16) = all_60_1_88 & is_transitive_in(all_0_16_16, all_60_1_88) = all_60_0_87)))
% 26.57/7.30 |
% 26.57/7.30 | Instantiating formula (77) with all_51_2_74, all_0_16_16 and discharging atoms relation_field(all_0_16_16) = all_51_2_74, yields:
% 26.57/7.30 | (102) ? [v0] : ? [v1] : (( ~ (v0 = 0) & relation(all_0_16_16) = v0) | (((v1 = 0 & is_transitive_in(all_0_16_16, all_51_2_74) = 0) | ( ~ (v0 = 0) & transitive(all_0_16_16) = v0)) & ((v0 = 0 & transitive(all_0_16_16) = 0) | ( ~ (v1 = 0) & is_transitive_in(all_0_16_16, all_51_2_74) = v1))))
% 26.57/7.30 |
% 26.57/7.30 | Instantiating (102) with all_93_0_110, all_93_1_111 yields:
% 26.57/7.30 | (103) ( ~ (all_93_1_111 = 0) & relation(all_0_16_16) = all_93_1_111) | (((all_93_0_110 = 0 & is_transitive_in(all_0_16_16, all_51_2_74) = 0) | ( ~ (all_93_1_111 = 0) & transitive(all_0_16_16) = all_93_1_111)) & ((all_93_1_111 = 0 & transitive(all_0_16_16) = 0) | ( ~ (all_93_0_110 = 0) & is_transitive_in(all_0_16_16, all_51_2_74) = all_93_0_110)))
% 26.57/7.30 |
% 26.57/7.30 +-Applying beta-rule and splitting (78), into two cases.
% 26.57/7.30 |-Branch one:
% 26.57/7.30 | (104) all_0_8_8 = 0 & all_0_10_10 = 0 & all_0_15_15 = 0 & ~ (all_0_6_6 = 0) & ordered_pair(all_0_13_13, all_0_12_12) = all_0_9_9 & ordered_pair(all_0_14_14, all_0_12_12) = all_0_7_7 & ordered_pair(all_0_14_14, all_0_13_13) = all_0_11_11 & in(all_0_7_7, all_0_16_16) = all_0_6_6 & in(all_0_9_9, all_0_16_16) = 0 & in(all_0_11_11, all_0_16_16) = 0
% 26.57/7.31 |
% 26.57/7.31 | Applying alpha-rule on (104) yields:
% 26.57/7.31 | (105) in(all_0_9_9, all_0_16_16) = 0
% 26.57/7.31 | (106) ordered_pair(all_0_14_14, all_0_13_13) = all_0_11_11
% 26.57/7.31 | (107) ordered_pair(all_0_13_13, all_0_12_12) = all_0_9_9
% 26.57/7.31 | (108) all_0_8_8 = 0
% 26.57/7.31 | (109) in(all_0_11_11, all_0_16_16) = 0
% 26.57/7.31 | (110) all_0_15_15 = 0
% 26.57/7.31 | (111) ordered_pair(all_0_14_14, all_0_12_12) = all_0_7_7
% 26.57/7.31 | (112) all_0_10_10 = 0
% 26.57/7.31 | (113) in(all_0_7_7, all_0_16_16) = all_0_6_6
% 26.57/7.31 | (114) ~ (all_0_6_6 = 0)
% 26.57/7.31 |
% 26.57/7.31 | From (110) and (86) follows:
% 26.57/7.31 | (115) transitive(all_0_16_16) = 0
% 26.57/7.31 |
% 26.57/7.31 +-Applying beta-rule and splitting (101), into two cases.
% 26.57/7.31 |-Branch one:
% 26.57/7.31 | (116) ~ (all_60_1_88 = 0) & relation(all_0_16_16) = all_60_1_88
% 26.57/7.31 |
% 26.57/7.31 | Applying alpha-rule on (116) yields:
% 26.57/7.31 | (117) ~ (all_60_1_88 = 0)
% 26.57/7.31 | (118) relation(all_0_16_16) = all_60_1_88
% 26.57/7.31 |
% 26.57/7.31 | Instantiating formula (6) with all_0_16_16, all_60_1_88, 0 and discharging atoms relation(all_0_16_16) = all_60_1_88, relation(all_0_16_16) = 0, yields:
% 26.57/7.31 | (119) all_60_1_88 = 0
% 26.57/7.31 |
% 26.57/7.31 | Equations (119) can reduce 117 to:
% 26.57/7.31 | (120) $false
% 26.57/7.31 |
% 26.57/7.31 |-The branch is then unsatisfiable
% 26.57/7.31 |-Branch two:
% 26.57/7.31 | (121) ( ~ (all_0_15_15 = 0) | (all_60_0_87 = 0 & relation_field(all_0_16_16) = all_60_1_88 & is_transitive_in(all_0_16_16, all_60_1_88) = 0)) & (all_0_15_15 = 0 | ( ~ (all_60_0_87 = 0) & relation_field(all_0_16_16) = all_60_1_88 & is_transitive_in(all_0_16_16, all_60_1_88) = all_60_0_87))
% 26.57/7.31 |
% 26.57/7.31 | Applying alpha-rule on (121) yields:
% 26.57/7.31 | (122) ~ (all_0_15_15 = 0) | (all_60_0_87 = 0 & relation_field(all_0_16_16) = all_60_1_88 & is_transitive_in(all_0_16_16, all_60_1_88) = 0)
% 26.57/7.31 | (123) all_0_15_15 = 0 | ( ~ (all_60_0_87 = 0) & relation_field(all_0_16_16) = all_60_1_88 & is_transitive_in(all_0_16_16, all_60_1_88) = all_60_0_87)
% 26.57/7.31 |
% 26.57/7.31 +-Applying beta-rule and splitting (94), into two cases.
% 26.57/7.31 |-Branch one:
% 26.57/7.31 | (124) all_50_0_69 = 0 & relation_field(all_0_16_16) = all_50_1_70 & is_transitive_in(all_0_16_16, all_50_1_70) = 0
% 26.57/7.31 |
% 26.57/7.31 | Applying alpha-rule on (124) yields:
% 26.57/7.31 | (125) all_50_0_69 = 0
% 26.57/7.31 | (126) relation_field(all_0_16_16) = all_50_1_70
% 26.57/7.31 | (127) is_transitive_in(all_0_16_16, all_50_1_70) = 0
% 26.57/7.31 |
% 26.57/7.31 +-Applying beta-rule and splitting (95), into two cases.
% 26.57/7.31 |-Branch one:
% 26.57/7.31 | (128) all_50_2_71 = 0 & transitive(all_0_16_16) = 0
% 26.57/7.31 |
% 26.57/7.31 | Applying alpha-rule on (128) yields:
% 26.57/7.31 | (129) all_50_2_71 = 0
% 26.57/7.31 | (115) transitive(all_0_16_16) = 0
% 26.57/7.31 |
% 26.57/7.31 +-Applying beta-rule and splitting (103), into two cases.
% 26.57/7.31 |-Branch one:
% 26.57/7.31 | (131) ~ (all_93_1_111 = 0) & relation(all_0_16_16) = all_93_1_111
% 26.57/7.31 |
% 26.57/7.31 | Applying alpha-rule on (131) yields:
% 26.57/7.31 | (132) ~ (all_93_1_111 = 0)
% 26.57/7.31 | (133) relation(all_0_16_16) = all_93_1_111
% 26.57/7.31 |
% 26.57/7.31 | Instantiating formula (6) with all_0_16_16, all_93_1_111, 0 and discharging atoms relation(all_0_16_16) = all_93_1_111, relation(all_0_16_16) = 0, yields:
% 26.57/7.31 | (134) all_93_1_111 = 0
% 26.57/7.31 |
% 26.57/7.31 | Equations (134) can reduce 132 to:
% 26.57/7.31 | (120) $false
% 26.57/7.31 |
% 26.57/7.31 |-The branch is then unsatisfiable
% 26.57/7.31 |-Branch two:
% 26.57/7.31 | (136) ((all_93_0_110 = 0 & is_transitive_in(all_0_16_16, all_51_2_74) = 0) | ( ~ (all_93_1_111 = 0) & transitive(all_0_16_16) = all_93_1_111)) & ((all_93_1_111 = 0 & transitive(all_0_16_16) = 0) | ( ~ (all_93_0_110 = 0) & is_transitive_in(all_0_16_16, all_51_2_74) = all_93_0_110))
% 26.57/7.31 |
% 26.57/7.31 | Applying alpha-rule on (136) yields:
% 26.57/7.31 | (137) (all_93_0_110 = 0 & is_transitive_in(all_0_16_16, all_51_2_74) = 0) | ( ~ (all_93_1_111 = 0) & transitive(all_0_16_16) = all_93_1_111)
% 26.57/7.31 | (138) (all_93_1_111 = 0 & transitive(all_0_16_16) = 0) | ( ~ (all_93_0_110 = 0) & is_transitive_in(all_0_16_16, all_51_2_74) = all_93_0_110)
% 26.57/7.31 |
% 26.57/7.31 +-Applying beta-rule and splitting (122), into two cases.
% 26.57/7.31 |-Branch one:
% 26.57/7.31 | (139) ~ (all_0_15_15 = 0)
% 26.57/7.31 |
% 26.57/7.31 | Equations (110) can reduce 139 to:
% 26.57/7.31 | (120) $false
% 26.57/7.31 |
% 26.57/7.31 |-The branch is then unsatisfiable
% 26.57/7.31 |-Branch two:
% 26.57/7.31 | (110) all_0_15_15 = 0
% 26.57/7.31 | (142) all_60_0_87 = 0 & relation_field(all_0_16_16) = all_60_1_88 & is_transitive_in(all_0_16_16, all_60_1_88) = 0
% 26.57/7.31 |
% 26.57/7.31 | Applying alpha-rule on (142) yields:
% 26.57/7.31 | (143) all_60_0_87 = 0
% 26.57/7.31 | (144) relation_field(all_0_16_16) = all_60_1_88
% 26.57/7.31 | (145) is_transitive_in(all_0_16_16, all_60_1_88) = 0
% 26.57/7.31 |
% 26.57/7.31 +-Applying beta-rule and splitting (137), into two cases.
% 26.57/7.31 |-Branch one:
% 26.57/7.31 | (146) all_93_0_110 = 0 & is_transitive_in(all_0_16_16, all_51_2_74) = 0
% 26.57/7.31 |
% 26.57/7.31 | Applying alpha-rule on (146) yields:
% 26.57/7.31 | (147) all_93_0_110 = 0
% 26.57/7.31 | (148) is_transitive_in(all_0_16_16, all_51_2_74) = 0
% 26.57/7.31 |
% 26.57/7.31 | Instantiating formula (15) with all_0_16_16, all_60_1_88, all_51_2_74 and discharging atoms relation_field(all_0_16_16) = all_60_1_88, relation_field(all_0_16_16) = all_51_2_74, yields:
% 26.57/7.31 | (149) all_60_1_88 = all_51_2_74
% 26.57/7.31 |
% 26.57/7.31 | Instantiating formula (15) with all_0_16_16, all_50_1_70, all_60_1_88 and discharging atoms relation_field(all_0_16_16) = all_60_1_88, relation_field(all_0_16_16) = all_50_1_70, yields:
% 26.57/7.31 | (150) all_60_1_88 = all_50_1_70
% 26.57/7.31 |
% 26.57/7.31 | Combining equations (149,150) yields a new equation:
% 26.57/7.31 | (151) all_51_2_74 = all_50_1_70
% 26.57/7.31 |
% 26.57/7.31 | Simplifying 151 yields:
% 26.57/7.31 | (152) all_51_2_74 = all_50_1_70
% 26.57/7.31 |
% 26.57/7.31 | From (152) and (99) follows:
% 26.57/7.31 | (126) relation_field(all_0_16_16) = all_50_1_70
% 26.57/7.31 |
% 26.57/7.31 | From (152) and (148) follows:
% 26.57/7.31 | (127) is_transitive_in(all_0_16_16, all_50_1_70) = 0
% 26.57/7.31 |
% 26.57/7.31 | Instantiating formula (41) 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:
% 26.57/7.31 | (155) 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))
% 26.57/7.31 |
% 26.57/7.31 | Instantiating formula (87) with all_0_6_6, all_0_7_7, all_0_9_9, all_0_12_12, all_0_13_13, all_0_14_14, all_50_1_70, all_0_16_16 and discharging atoms ordered_pair(all_0_13_13, all_0_12_12) = all_0_9_9, ordered_pair(all_0_14_14, all_0_12_12) = all_0_7_7, is_transitive_in(all_0_16_16, all_50_1_70) = 0, relation(all_0_16_16) = 0, in(all_0_7_7, all_0_16_16) = all_0_6_6, in(all_0_9_9, all_0_16_16) = 0, yields:
% 26.57/7.31 | (156) all_0_6_6 = 0 | ? [v0] : ? [v1] : (( ~ (v1 = 0) & ordered_pair(all_0_14_14, all_0_13_13) = v0 & in(v0, all_0_16_16) = v1) | ( ~ (v0 = 0) & in(all_0_12_12, all_50_1_70) = v0) | ( ~ (v0 = 0) & in(all_0_13_13, all_50_1_70) = v0) | ( ~ (v0 = 0) & in(all_0_14_14, all_50_1_70) = v0))
% 26.57/7.31 |
% 26.57/7.31 | Instantiating formula (40) with all_0_9_9, all_0_16_16, all_0_12_12, all_0_13_13 and discharging atoms ordered_pair(all_0_13_13, all_0_12_12) = all_0_9_9, in(all_0_9_9, all_0_16_16) = 0, yields:
% 26.57/7.31 | (157) ? [v0] : ? [v1] : ? [v2] : ((v2 = 0 & v1 = 0 & relation_field(all_0_16_16) = v0 & in(all_0_12_12, v0) = 0 & in(all_0_13_13, v0) = 0) | ( ~ (v0 = 0) & relation(all_0_16_16) = v0))
% 26.57/7.31 |
% 26.57/7.31 | Instantiating formula (17) with all_0_9_9, all_0_11_11, all_0_12_12, all_0_13_13, all_0_14_14, all_50_1_70, all_0_16_16 and discharging atoms ordered_pair(all_0_13_13, all_0_12_12) = all_0_9_9, ordered_pair(all_0_14_14, all_0_13_13) = all_0_11_11, is_transitive_in(all_0_16_16, all_50_1_70) = 0, relation(all_0_16_16) = 0, in(all_0_9_9, all_0_16_16) = 0, in(all_0_11_11, all_0_16_16) = 0, yields:
% 26.57/7.32 | (158) ? [v0] : ? [v1] : ((v1 = 0 & ordered_pair(all_0_14_14, all_0_12_12) = v0 & in(v0, all_0_16_16) = 0) | ( ~ (v0 = 0) & in(all_0_12_12, all_50_1_70) = v0) | ( ~ (v0 = 0) & in(all_0_13_13, all_50_1_70) = v0) | ( ~ (v0 = 0) & in(all_0_14_14, all_50_1_70) = v0))
% 26.57/7.32 |
% 26.57/7.32 | Instantiating formula (50) with all_0_6_6, all_0_7_7, all_0_11_11, all_0_12_12, all_0_13_13, all_0_14_14, all_50_1_70, all_0_16_16 and discharging atoms ordered_pair(all_0_14_14, all_0_12_12) = all_0_7_7, ordered_pair(all_0_14_14, all_0_13_13) = all_0_11_11, is_transitive_in(all_0_16_16, all_50_1_70) = 0, relation(all_0_16_16) = 0, in(all_0_7_7, all_0_16_16) = all_0_6_6, in(all_0_11_11, all_0_16_16) = 0, yields:
% 26.57/7.32 | (159) all_0_6_6 = 0 | ? [v0] : ? [v1] : (( ~ (v1 = 0) & ordered_pair(all_0_13_13, all_0_12_12) = v0 & in(v0, all_0_16_16) = v1) | ( ~ (v0 = 0) & in(all_0_12_12, all_50_1_70) = v0) | ( ~ (v0 = 0) & in(all_0_13_13, all_50_1_70) = v0) | ( ~ (v0 = 0) & in(all_0_14_14, all_50_1_70) = v0))
% 26.57/7.32 |
% 26.57/7.32 | Instantiating formula (40) with all_0_11_11, all_0_16_16, all_0_13_13, all_0_14_14 and discharging atoms ordered_pair(all_0_14_14, all_0_13_13) = all_0_11_11, in(all_0_11_11, all_0_16_16) = 0, yields:
% 26.57/7.32 | (160) ? [v0] : ? [v1] : ? [v2] : ((v2 = 0 & v1 = 0 & relation_field(all_0_16_16) = v0 & in(all_0_13_13, v0) = 0 & in(all_0_14_14, v0) = 0) | ( ~ (v0 = 0) & relation(all_0_16_16) = v0))
% 26.57/7.32 |
% 26.57/7.32 | Instantiating (158) with all_148_0_126, all_148_1_127 yields:
% 26.57/7.32 | (161) (all_148_0_126 = 0 & ordered_pair(all_0_14_14, all_0_12_12) = all_148_1_127 & in(all_148_1_127, all_0_16_16) = 0) | ( ~ (all_148_1_127 = 0) & in(all_0_12_12, all_50_1_70) = all_148_1_127) | ( ~ (all_148_1_127 = 0) & in(all_0_13_13, all_50_1_70) = all_148_1_127) | ( ~ (all_148_1_127 = 0) & in(all_0_14_14, all_50_1_70) = all_148_1_127)
% 26.57/7.32 |
% 26.57/7.32 | Instantiating (160) with all_149_0_128, all_149_1_129, all_149_2_130 yields:
% 26.57/7.32 | (162) (all_149_0_128 = 0 & all_149_1_129 = 0 & relation_field(all_0_16_16) = all_149_2_130 & in(all_0_13_13, all_149_2_130) = 0 & in(all_0_14_14, all_149_2_130) = 0) | ( ~ (all_149_2_130 = 0) & relation(all_0_16_16) = all_149_2_130)
% 26.57/7.32 |
% 26.57/7.32 | Instantiating (157) with all_160_0_137, all_160_1_138, all_160_2_139 yields:
% 26.57/7.32 | (163) (all_160_0_137 = 0 & all_160_1_138 = 0 & relation_field(all_0_16_16) = all_160_2_139 & in(all_0_12_12, all_160_2_139) = 0 & in(all_0_13_13, all_160_2_139) = 0) | ( ~ (all_160_2_139 = 0) & relation(all_0_16_16) = all_160_2_139)
% 26.57/7.32 |
% 26.57/7.32 +-Applying beta-rule and splitting (162), into two cases.
% 26.57/7.32 |-Branch one:
% 26.57/7.32 | (164) all_149_0_128 = 0 & all_149_1_129 = 0 & relation_field(all_0_16_16) = all_149_2_130 & in(all_0_13_13, all_149_2_130) = 0 & in(all_0_14_14, all_149_2_130) = 0
% 26.57/7.32 |
% 26.57/7.32 | Applying alpha-rule on (164) yields:
% 26.57/7.32 | (165) in(all_0_13_13, all_149_2_130) = 0
% 26.57/7.32 | (166) in(all_0_14_14, all_149_2_130) = 0
% 26.57/7.32 | (167) relation_field(all_0_16_16) = all_149_2_130
% 26.57/7.32 | (168) all_149_1_129 = 0
% 26.57/7.32 | (169) all_149_0_128 = 0
% 26.57/7.32 |
% 26.57/7.32 +-Applying beta-rule and splitting (156), into two cases.
% 26.57/7.32 |-Branch one:
% 26.57/7.32 | (170) all_0_6_6 = 0
% 26.57/7.32 |
% 26.57/7.32 | Equations (170) can reduce 114 to:
% 26.57/7.32 | (120) $false
% 26.57/7.32 |
% 26.57/7.32 |-The branch is then unsatisfiable
% 26.57/7.32 |-Branch two:
% 26.57/7.32 | (114) ~ (all_0_6_6 = 0)
% 26.57/7.32 | (173) ? [v0] : ? [v1] : (( ~ (v1 = 0) & ordered_pair(all_0_14_14, all_0_13_13) = v0 & in(v0, all_0_16_16) = v1) | ( ~ (v0 = 0) & in(all_0_12_12, all_50_1_70) = v0) | ( ~ (v0 = 0) & in(all_0_13_13, all_50_1_70) = v0) | ( ~ (v0 = 0) & in(all_0_14_14, all_50_1_70) = v0))
% 26.57/7.32 |
% 26.57/7.32 +-Applying beta-rule and splitting (163), into two cases.
% 26.57/7.32 |-Branch one:
% 26.57/7.32 | (174) all_160_0_137 = 0 & all_160_1_138 = 0 & relation_field(all_0_16_16) = all_160_2_139 & in(all_0_12_12, all_160_2_139) = 0 & in(all_0_13_13, all_160_2_139) = 0
% 26.57/7.32 |
% 26.57/7.32 | Applying alpha-rule on (174) yields:
% 26.57/7.32 | (175) in(all_0_12_12, all_160_2_139) = 0
% 26.57/7.32 | (176) in(all_0_13_13, all_160_2_139) = 0
% 26.57/7.32 | (177) relation_field(all_0_16_16) = all_160_2_139
% 26.57/7.32 | (178) all_160_0_137 = 0
% 26.57/7.32 | (179) all_160_1_138 = 0
% 26.57/7.32 |
% 26.57/7.32 +-Applying beta-rule and splitting (155), into two cases.
% 26.57/7.32 |-Branch one:
% 26.57/7.32 | (170) all_0_6_6 = 0
% 26.57/7.32 |
% 26.57/7.32 | Equations (170) can reduce 114 to:
% 26.57/7.32 | (120) $false
% 26.57/7.32 |
% 26.57/7.32 |-The branch is then unsatisfiable
% 26.57/7.32 |-Branch two:
% 26.57/7.32 | (114) ~ (all_0_6_6 = 0)
% 26.57/7.32 | (183) ? [v0] : ((v0 = 0 & empty(all_0_16_16) = 0) | ( ~ (v0 = 0) & element(all_0_7_7, all_0_16_16) = v0))
% 26.57/7.32 |
% 26.57/7.32 +-Applying beta-rule and splitting (159), into two cases.
% 26.57/7.32 |-Branch one:
% 26.57/7.32 | (170) all_0_6_6 = 0
% 26.57/7.32 |
% 26.57/7.32 | Equations (170) can reduce 114 to:
% 26.57/7.32 | (120) $false
% 26.57/7.32 |
% 26.57/7.32 |-The branch is then unsatisfiable
% 26.57/7.32 |-Branch two:
% 26.57/7.32 | (114) ~ (all_0_6_6 = 0)
% 26.57/7.32 | (187) ? [v0] : ? [v1] : (( ~ (v1 = 0) & ordered_pair(all_0_13_13, all_0_12_12) = v0 & in(v0, all_0_16_16) = v1) | ( ~ (v0 = 0) & in(all_0_12_12, all_50_1_70) = v0) | ( ~ (v0 = 0) & in(all_0_13_13, all_50_1_70) = v0) | ( ~ (v0 = 0) & in(all_0_14_14, all_50_1_70) = v0))
% 26.57/7.32 |
% 26.57/7.32 | Instantiating formula (15) with all_0_16_16, all_160_2_139, all_50_1_70 and discharging atoms relation_field(all_0_16_16) = all_160_2_139, relation_field(all_0_16_16) = all_50_1_70, yields:
% 26.57/7.32 | (188) all_160_2_139 = all_50_1_70
% 26.57/7.32 |
% 26.57/7.32 | Instantiating formula (15) with all_0_16_16, all_149_2_130, all_160_2_139 and discharging atoms relation_field(all_0_16_16) = all_160_2_139, relation_field(all_0_16_16) = all_149_2_130, yields:
% 26.57/7.32 | (189) all_160_2_139 = all_149_2_130
% 26.57/7.32 |
% 26.57/7.32 | Combining equations (189,188) yields a new equation:
% 26.57/7.32 | (190) all_149_2_130 = all_50_1_70
% 26.57/7.32 |
% 26.57/7.32 | Simplifying 190 yields:
% 26.57/7.32 | (191) all_149_2_130 = all_50_1_70
% 26.57/7.32 |
% 26.57/7.32 | From (188) and (175) follows:
% 26.57/7.32 | (192) in(all_0_12_12, all_50_1_70) = 0
% 26.57/7.32 |
% 26.57/7.32 | From (191) and (165) follows:
% 26.57/7.32 | (193) in(all_0_13_13, all_50_1_70) = 0
% 26.57/7.32 |
% 26.57/7.32 | From (191) and (166) follows:
% 26.57/7.32 | (194) in(all_0_14_14, all_50_1_70) = 0
% 26.57/7.32 |
% 26.57/7.32 +-Applying beta-rule and splitting (161), into two cases.
% 26.57/7.32 |-Branch one:
% 26.57/7.32 | (195) (all_148_0_126 = 0 & ordered_pair(all_0_14_14, all_0_12_12) = all_148_1_127 & in(all_148_1_127, all_0_16_16) = 0) | ( ~ (all_148_1_127 = 0) & in(all_0_12_12, all_50_1_70) = all_148_1_127) | ( ~ (all_148_1_127 = 0) & in(all_0_13_13, all_50_1_70) = all_148_1_127)
% 26.57/7.32 |
% 26.57/7.32 +-Applying beta-rule and splitting (195), into two cases.
% 26.57/7.32 |-Branch one:
% 26.57/7.32 | (196) (all_148_0_126 = 0 & ordered_pair(all_0_14_14, all_0_12_12) = all_148_1_127 & in(all_148_1_127, all_0_16_16) = 0) | ( ~ (all_148_1_127 = 0) & in(all_0_12_12, all_50_1_70) = all_148_1_127)
% 26.57/7.32 |
% 26.57/7.32 +-Applying beta-rule and splitting (196), into two cases.
% 26.57/7.32 |-Branch one:
% 26.57/7.32 | (197) all_148_0_126 = 0 & ordered_pair(all_0_14_14, all_0_12_12) = all_148_1_127 & in(all_148_1_127, all_0_16_16) = 0
% 26.57/7.32 |
% 26.57/7.32 | Applying alpha-rule on (197) yields:
% 26.57/7.32 | (198) all_148_0_126 = 0
% 26.57/7.32 | (199) ordered_pair(all_0_14_14, all_0_12_12) = all_148_1_127
% 26.57/7.32 | (200) in(all_148_1_127, all_0_16_16) = 0
% 26.57/7.32 |
% 26.57/7.32 | Instantiating formula (23) with all_0_14_14, all_0_12_12, all_148_1_127, all_0_7_7 and discharging atoms ordered_pair(all_0_14_14, all_0_12_12) = all_148_1_127, ordered_pair(all_0_14_14, all_0_12_12) = all_0_7_7, yields:
% 26.57/7.32 | (201) all_148_1_127 = all_0_7_7
% 26.57/7.32 |
% 26.57/7.32 | From (201) and (200) follows:
% 26.57/7.32 | (202) in(all_0_7_7, all_0_16_16) = 0
% 26.57/7.32 |
% 26.57/7.32 | Instantiating formula (85) 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:
% 26.57/7.32 | (170) all_0_6_6 = 0
% 26.57/7.32 |
% 26.57/7.32 | Equations (170) can reduce 114 to:
% 26.57/7.32 | (120) $false
% 26.57/7.32 |
% 26.57/7.32 |-The branch is then unsatisfiable
% 26.57/7.32 |-Branch two:
% 26.57/7.32 | (205) ~ (all_148_1_127 = 0) & in(all_0_12_12, all_50_1_70) = all_148_1_127
% 26.57/7.32 |
% 26.57/7.32 | Applying alpha-rule on (205) yields:
% 26.57/7.32 | (206) ~ (all_148_1_127 = 0)
% 26.57/7.32 | (207) in(all_0_12_12, all_50_1_70) = all_148_1_127
% 26.57/7.32 |
% 26.57/7.32 | Instantiating formula (85) with all_0_12_12, all_50_1_70, 0, all_148_1_127 and discharging atoms in(all_0_12_12, all_50_1_70) = all_148_1_127, in(all_0_12_12, all_50_1_70) = 0, yields:
% 26.57/7.32 | (208) all_148_1_127 = 0
% 26.57/7.32 |
% 26.57/7.32 | Equations (208) can reduce 206 to:
% 26.57/7.32 | (120) $false
% 26.57/7.32 |
% 26.57/7.32 |-The branch is then unsatisfiable
% 26.57/7.32 |-Branch two:
% 26.57/7.32 | (210) ~ (all_148_1_127 = 0) & in(all_0_13_13, all_50_1_70) = all_148_1_127
% 26.57/7.32 |
% 26.57/7.32 | Applying alpha-rule on (210) yields:
% 26.57/7.32 | (206) ~ (all_148_1_127 = 0)
% 26.57/7.32 | (212) in(all_0_13_13, all_50_1_70) = all_148_1_127
% 26.57/7.32 |
% 26.57/7.32 | Instantiating formula (85) with all_0_13_13, all_50_1_70, 0, all_148_1_127 and discharging atoms in(all_0_13_13, all_50_1_70) = all_148_1_127, in(all_0_13_13, all_50_1_70) = 0, yields:
% 26.57/7.32 | (208) all_148_1_127 = 0
% 26.57/7.32 |
% 26.57/7.32 | Equations (208) can reduce 206 to:
% 26.57/7.32 | (120) $false
% 26.57/7.32 |
% 26.57/7.32 |-The branch is then unsatisfiable
% 26.57/7.32 |-Branch two:
% 26.57/7.32 | (215) ~ (all_148_1_127 = 0) & in(all_0_14_14, all_50_1_70) = all_148_1_127
% 26.57/7.32 |
% 26.57/7.32 | Applying alpha-rule on (215) yields:
% 26.57/7.32 | (206) ~ (all_148_1_127 = 0)
% 26.57/7.32 | (217) in(all_0_14_14, all_50_1_70) = all_148_1_127
% 26.57/7.32 |
% 26.57/7.32 | Instantiating formula (85) with all_0_14_14, all_50_1_70, 0, all_148_1_127 and discharging atoms in(all_0_14_14, all_50_1_70) = all_148_1_127, in(all_0_14_14, all_50_1_70) = 0, yields:
% 26.57/7.32 | (208) all_148_1_127 = 0
% 26.57/7.32 |
% 26.57/7.32 | Equations (208) can reduce 206 to:
% 26.57/7.32 | (120) $false
% 26.57/7.32 |
% 26.57/7.32 |-The branch is then unsatisfiable
% 26.57/7.32 |-Branch two:
% 26.57/7.32 | (220) ~ (all_160_2_139 = 0) & relation(all_0_16_16) = all_160_2_139
% 26.57/7.32 |
% 26.57/7.32 | Applying alpha-rule on (220) yields:
% 26.57/7.32 | (221) ~ (all_160_2_139 = 0)
% 26.57/7.32 | (222) relation(all_0_16_16) = all_160_2_139
% 26.57/7.32 |
% 26.57/7.32 | Instantiating formula (6) with all_0_16_16, all_160_2_139, 0 and discharging atoms relation(all_0_16_16) = all_160_2_139, relation(all_0_16_16) = 0, yields:
% 26.57/7.32 | (223) all_160_2_139 = 0
% 26.57/7.32 |
% 26.57/7.32 | Equations (223) can reduce 221 to:
% 26.57/7.32 | (120) $false
% 26.57/7.32 |
% 26.57/7.32 |-The branch is then unsatisfiable
% 26.57/7.32 |-Branch two:
% 26.57/7.32 | (225) ~ (all_149_2_130 = 0) & relation(all_0_16_16) = all_149_2_130
% 26.57/7.33 |
% 26.57/7.33 | Applying alpha-rule on (225) yields:
% 26.57/7.33 | (226) ~ (all_149_2_130 = 0)
% 26.57/7.33 | (227) relation(all_0_16_16) = all_149_2_130
% 26.57/7.33 |
% 26.57/7.33 | Instantiating formula (6) with all_0_16_16, all_149_2_130, 0 and discharging atoms relation(all_0_16_16) = all_149_2_130, relation(all_0_16_16) = 0, yields:
% 26.57/7.33 | (228) all_149_2_130 = 0
% 26.57/7.33 |
% 26.57/7.33 | Equations (228) can reduce 226 to:
% 26.57/7.33 | (120) $false
% 26.57/7.33 |
% 26.57/7.33 |-The branch is then unsatisfiable
% 26.57/7.33 |-Branch two:
% 26.57/7.33 | (230) ~ (all_93_1_111 = 0) & transitive(all_0_16_16) = all_93_1_111
% 26.57/7.33 |
% 26.57/7.33 | Applying alpha-rule on (230) yields:
% 26.57/7.33 | (132) ~ (all_93_1_111 = 0)
% 26.57/7.33 | (232) transitive(all_0_16_16) = all_93_1_111
% 26.57/7.33 |
% 26.57/7.33 | Instantiating formula (21) with all_0_16_16, 0, all_93_1_111 and discharging atoms transitive(all_0_16_16) = all_93_1_111, transitive(all_0_16_16) = 0, yields:
% 26.57/7.33 | (134) all_93_1_111 = 0
% 26.57/7.33 |
% 26.57/7.33 | Equations (134) can reduce 132 to:
% 26.57/7.33 | (120) $false
% 26.57/7.33 |
% 26.57/7.33 |-The branch is then unsatisfiable
% 26.57/7.33 |-Branch two:
% 26.57/7.33 | (235) ~ (all_50_0_69 = 0) & relation_field(all_0_16_16) = all_50_1_70 & is_transitive_in(all_0_16_16, all_50_1_70) = all_50_0_69
% 26.57/7.33 |
% 26.57/7.33 | Applying alpha-rule on (235) yields:
% 26.57/7.33 | (236) ~ (all_50_0_69 = 0)
% 26.57/7.33 | (126) relation_field(all_0_16_16) = all_50_1_70
% 26.57/7.33 | (238) is_transitive_in(all_0_16_16, all_50_1_70) = all_50_0_69
% 26.57/7.33 |
% 26.57/7.33 | Equations (125) can reduce 236 to:
% 26.57/7.33 | (120) $false
% 26.57/7.33 |
% 26.57/7.33 |-The branch is then unsatisfiable
% 26.57/7.33 |-Branch two:
% 26.57/7.33 | (240) ~ (all_50_2_71 = 0) & transitive(all_0_16_16) = all_50_2_71
% 26.57/7.33 |
% 26.57/7.33 | Applying alpha-rule on (240) yields:
% 26.57/7.33 | (241) ~ (all_50_2_71 = 0)
% 26.57/7.33 | (242) transitive(all_0_16_16) = all_50_2_71
% 26.57/7.33 |
% 26.57/7.33 | Instantiating formula (21) with all_0_16_16, 0, all_50_2_71 and discharging atoms transitive(all_0_16_16) = all_50_2_71, transitive(all_0_16_16) = 0, yields:
% 26.57/7.33 | (129) all_50_2_71 = 0
% 26.57/7.33 |
% 26.57/7.33 | Equations (129) can reduce 241 to:
% 26.57/7.33 | (120) $false
% 26.57/7.33 |
% 26.57/7.33 |-The branch is then unsatisfiable
% 26.57/7.33 |-Branch two:
% 26.57/7.33 | (245) ~ (all_0_15_15 = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (ordered_pair(v1, v2) = v3) | ~ (ordered_pair(v0, v2) = v4) | ~ (in(v4, all_0_16_16) = v5) | ~ (in(v3, all_0_16_16) = 0) | ? [v6] : ? [v7] : ( ~ (v7 = 0) & ordered_pair(v0, v1) = v6 & in(v6, all_0_16_16) = v7)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (ordered_pair(v0, v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ (in(v4, all_0_16_16) = v5) | ~ (in(v3, all_0_16_16) = 0) | ? [v6] : ? [v7] : ( ~ (v7 = 0) & ordered_pair(v1, v2) = v6 & in(v6, all_0_16_16) = v7)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (ordered_pair(v1, v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ (in(v4, all_0_16_16) = 0) | ~ (in(v3, all_0_16_16) = 0) | ? [v5] : (ordered_pair(v0, v2) = v5 & in(v5, all_0_16_16) = 0))
% 26.57/7.33 |
% 26.57/7.33 | Applying alpha-rule on (245) yields:
% 26.57/7.33 | (139) ~ (all_0_15_15 = 0)
% 26.57/7.33 | (247) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (ordered_pair(v1, v2) = v3) | ~ (ordered_pair(v0, v2) = v4) | ~ (in(v4, all_0_16_16) = v5) | ~ (in(v3, all_0_16_16) = 0) | ? [v6] : ? [v7] : ( ~ (v7 = 0) & ordered_pair(v0, v1) = v6 & in(v6, all_0_16_16) = v7))
% 26.57/7.33 | (248) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (ordered_pair(v0, v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ (in(v4, all_0_16_16) = v5) | ~ (in(v3, all_0_16_16) = 0) | ? [v6] : ? [v7] : ( ~ (v7 = 0) & ordered_pair(v1, v2) = v6 & in(v6, all_0_16_16) = v7))
% 26.57/7.33 | (249) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (ordered_pair(v1, v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ (in(v4, all_0_16_16) = 0) | ~ (in(v3, all_0_16_16) = 0) | ? [v5] : (ordered_pair(v0, v2) = v5 & in(v5, all_0_16_16) = 0))
% 26.57/7.33 |
% 26.57/7.33 +-Applying beta-rule and splitting (101), into two cases.
% 26.57/7.33 |-Branch one:
% 26.57/7.33 | (116) ~ (all_60_1_88 = 0) & relation(all_0_16_16) = all_60_1_88
% 26.57/7.33 |
% 26.57/7.33 | Applying alpha-rule on (116) yields:
% 26.57/7.33 | (117) ~ (all_60_1_88 = 0)
% 26.57/7.33 | (118) relation(all_0_16_16) = all_60_1_88
% 26.57/7.33 |
% 26.57/7.33 | Instantiating formula (6) with all_0_16_16, all_60_1_88, 0 and discharging atoms relation(all_0_16_16) = all_60_1_88, relation(all_0_16_16) = 0, yields:
% 26.57/7.33 | (119) all_60_1_88 = 0
% 26.57/7.33 |
% 26.57/7.33 | Equations (119) can reduce 117 to:
% 26.57/7.33 | (120) $false
% 26.57/7.33 |
% 26.57/7.33 |-The branch is then unsatisfiable
% 26.57/7.33 |-Branch two:
% 26.57/7.33 | (121) ( ~ (all_0_15_15 = 0) | (all_60_0_87 = 0 & relation_field(all_0_16_16) = all_60_1_88 & is_transitive_in(all_0_16_16, all_60_1_88) = 0)) & (all_0_15_15 = 0 | ( ~ (all_60_0_87 = 0) & relation_field(all_0_16_16) = all_60_1_88 & is_transitive_in(all_0_16_16, all_60_1_88) = all_60_0_87))
% 26.57/7.33 |
% 26.57/7.33 | Applying alpha-rule on (121) yields:
% 26.57/7.33 | (122) ~ (all_0_15_15 = 0) | (all_60_0_87 = 0 & relation_field(all_0_16_16) = all_60_1_88 & is_transitive_in(all_0_16_16, all_60_1_88) = 0)
% 26.57/7.33 | (123) all_0_15_15 = 0 | ( ~ (all_60_0_87 = 0) & relation_field(all_0_16_16) = all_60_1_88 & is_transitive_in(all_0_16_16, all_60_1_88) = all_60_0_87)
% 26.57/7.33 |
% 26.57/7.33 +-Applying beta-rule and splitting (95), into two cases.
% 26.57/7.33 |-Branch one:
% 26.57/7.33 | (128) all_50_2_71 = 0 & transitive(all_0_16_16) = 0
% 26.57/7.33 |
% 26.57/7.33 | Applying alpha-rule on (128) yields:
% 26.57/7.33 | (129) all_50_2_71 = 0
% 26.57/7.33 | (115) transitive(all_0_16_16) = 0
% 26.57/7.33 |
% 26.57/7.33 +-Applying beta-rule and splitting (123), into two cases.
% 26.57/7.33 |-Branch one:
% 26.57/7.33 | (110) all_0_15_15 = 0
% 26.57/7.33 |
% 26.57/7.33 | Equations (110) can reduce 139 to:
% 26.57/7.33 | (120) $false
% 26.57/7.33 |
% 26.57/7.33 |-The branch is then unsatisfiable
% 26.57/7.33 |-Branch two:
% 26.57/7.33 | (139) ~ (all_0_15_15 = 0)
% 26.57/7.33 | (264) ~ (all_60_0_87 = 0) & relation_field(all_0_16_16) = all_60_1_88 & is_transitive_in(all_0_16_16, all_60_1_88) = all_60_0_87
% 26.57/7.33 |
% 26.57/7.33 | Instantiating formula (21) with all_0_16_16, 0, all_0_15_15 and discharging atoms transitive(all_0_16_16) = all_0_15_15, transitive(all_0_16_16) = 0, yields:
% 26.57/7.33 | (110) all_0_15_15 = 0
% 26.57/7.33 |
% 26.57/7.33 | Equations (110) can reduce 139 to:
% 26.57/7.33 | (120) $false
% 26.57/7.33 |
% 26.57/7.33 |-The branch is then unsatisfiable
% 26.57/7.33 |-Branch two:
% 26.57/7.33 | (235) ~ (all_50_0_69 = 0) & relation_field(all_0_16_16) = all_50_1_70 & is_transitive_in(all_0_16_16, all_50_1_70) = all_50_0_69
% 26.57/7.33 |
% 26.57/7.33 | Applying alpha-rule on (235) yields:
% 26.57/7.33 | (236) ~ (all_50_0_69 = 0)
% 26.57/7.33 | (126) relation_field(all_0_16_16) = all_50_1_70
% 26.57/7.33 | (238) is_transitive_in(all_0_16_16, all_50_1_70) = all_50_0_69
% 26.57/7.33 |
% 26.57/7.33 +-Applying beta-rule and splitting (123), into two cases.
% 26.57/7.33 |-Branch one:
% 26.57/7.33 | (110) all_0_15_15 = 0
% 26.57/7.33 |
% 26.57/7.33 | Equations (110) can reduce 139 to:
% 26.57/7.33 | (120) $false
% 26.57/7.33 |
% 26.57/7.33 |-The branch is then unsatisfiable
% 26.57/7.33 |-Branch two:
% 26.57/7.33 | (139) ~ (all_0_15_15 = 0)
% 26.57/7.33 | (264) ~ (all_60_0_87 = 0) & relation_field(all_0_16_16) = all_60_1_88 & is_transitive_in(all_0_16_16, all_60_1_88) = all_60_0_87
% 26.57/7.33 |
% 26.57/7.33 | Applying alpha-rule on (264) yields:
% 26.57/7.33 | (275) ~ (all_60_0_87 = 0)
% 26.57/7.33 | (144) relation_field(all_0_16_16) = all_60_1_88
% 26.57/7.33 | (277) is_transitive_in(all_0_16_16, all_60_1_88) = all_60_0_87
% 26.57/7.33 |
% 26.57/7.33 +-Applying beta-rule and splitting (94), into two cases.
% 26.57/7.33 |-Branch one:
% 26.57/7.33 | (124) all_50_0_69 = 0 & relation_field(all_0_16_16) = all_50_1_70 & is_transitive_in(all_0_16_16, all_50_1_70) = 0
% 26.57/7.33 |
% 26.57/7.33 | Applying alpha-rule on (124) yields:
% 26.57/7.33 | (125) all_50_0_69 = 0
% 26.57/7.33 | (126) relation_field(all_0_16_16) = all_50_1_70
% 26.57/7.33 | (127) is_transitive_in(all_0_16_16, all_50_1_70) = 0
% 26.57/7.33 |
% 26.57/7.33 | Equations (125) can reduce 236 to:
% 26.57/7.33 | (120) $false
% 26.57/7.33 |
% 26.57/7.33 |-The branch is then unsatisfiable
% 26.57/7.33 |-Branch two:
% 26.57/7.33 | (240) ~ (all_50_2_71 = 0) & transitive(all_0_16_16) = all_50_2_71
% 26.57/7.33 |
% 26.57/7.33 | Applying alpha-rule on (240) yields:
% 26.57/7.33 | (241) ~ (all_50_2_71 = 0)
% 26.57/7.33 | (242) transitive(all_0_16_16) = all_50_2_71
% 26.57/7.33 |
% 26.57/7.33 +-Applying beta-rule and splitting (103), into two cases.
% 26.57/7.33 |-Branch one:
% 26.57/7.33 | (131) ~ (all_93_1_111 = 0) & relation(all_0_16_16) = all_93_1_111
% 26.57/7.33 |
% 26.57/7.33 | Applying alpha-rule on (131) yields:
% 26.57/7.33 | (132) ~ (all_93_1_111 = 0)
% 26.57/7.33 | (133) relation(all_0_16_16) = all_93_1_111
% 26.57/7.33 |
% 26.57/7.33 | Instantiating formula (6) with all_0_16_16, all_93_1_111, 0 and discharging atoms relation(all_0_16_16) = all_93_1_111, relation(all_0_16_16) = 0, yields:
% 26.57/7.33 | (134) all_93_1_111 = 0
% 26.57/7.33 |
% 26.57/7.33 | Equations (134) can reduce 132 to:
% 26.57/7.33 | (120) $false
% 26.57/7.33 |
% 26.57/7.33 |-The branch is then unsatisfiable
% 26.57/7.33 |-Branch two:
% 26.57/7.33 | (136) ((all_93_0_110 = 0 & is_transitive_in(all_0_16_16, all_51_2_74) = 0) | ( ~ (all_93_1_111 = 0) & transitive(all_0_16_16) = all_93_1_111)) & ((all_93_1_111 = 0 & transitive(all_0_16_16) = 0) | ( ~ (all_93_0_110 = 0) & is_transitive_in(all_0_16_16, all_51_2_74) = all_93_0_110))
% 26.57/7.33 |
% 26.57/7.33 | Applying alpha-rule on (136) yields:
% 26.57/7.33 | (137) (all_93_0_110 = 0 & is_transitive_in(all_0_16_16, all_51_2_74) = 0) | ( ~ (all_93_1_111 = 0) & transitive(all_0_16_16) = all_93_1_111)
% 26.57/7.33 | (138) (all_93_1_111 = 0 & transitive(all_0_16_16) = 0) | ( ~ (all_93_0_110 = 0) & is_transitive_in(all_0_16_16, all_51_2_74) = all_93_0_110)
% 26.57/7.33 |
% 26.57/7.33 +-Applying beta-rule and splitting (138), into two cases.
% 26.57/7.33 |-Branch one:
% 26.57/7.33 | (294) all_93_1_111 = 0 & transitive(all_0_16_16) = 0
% 26.57/7.33 |
% 26.57/7.33 | Applying alpha-rule on (294) yields:
% 26.57/7.33 | (134) all_93_1_111 = 0
% 26.57/7.33 | (115) transitive(all_0_16_16) = 0
% 26.57/7.33 |
% 26.57/7.33 | Instantiating formula (21) with all_0_16_16, all_50_2_71, all_0_15_15 and discharging atoms transitive(all_0_16_16) = all_50_2_71, transitive(all_0_16_16) = all_0_15_15, yields:
% 26.57/7.33 | (297) all_50_2_71 = all_0_15_15
% 26.57/7.33 |
% 26.57/7.33 | Instantiating formula (21) with all_0_16_16, 0, all_50_2_71 and discharging atoms transitive(all_0_16_16) = all_50_2_71, transitive(all_0_16_16) = 0, yields:
% 26.57/7.33 | (129) all_50_2_71 = 0
% 26.57/7.33 |
% 26.57/7.33 | Combining equations (129,297) yields a new equation:
% 26.57/7.33 | (110) all_0_15_15 = 0
% 26.57/7.33 |
% 26.57/7.33 | Equations (110) can reduce 139 to:
% 26.57/7.33 | (120) $false
% 26.57/7.33 |
% 26.57/7.33 |-The branch is then unsatisfiable
% 26.57/7.33 |-Branch two:
% 26.57/7.34 | (301) ~ (all_93_0_110 = 0) & is_transitive_in(all_0_16_16, all_51_2_74) = all_93_0_110
% 26.57/7.34 |
% 26.57/7.34 | Applying alpha-rule on (301) yields:
% 26.57/7.34 | (302) ~ (all_93_0_110 = 0)
% 26.57/7.34 | (303) is_transitive_in(all_0_16_16, all_51_2_74) = all_93_0_110
% 26.57/7.34 |
% 26.57/7.34 | Instantiating formula (15) with all_0_16_16, all_60_1_88, all_51_2_74 and discharging atoms relation_field(all_0_16_16) = all_60_1_88, relation_field(all_0_16_16) = all_51_2_74, yields:
% 26.57/7.34 | (149) all_60_1_88 = all_51_2_74
% 26.57/7.34 |
% 26.57/7.34 | Instantiating formula (15) with all_0_16_16, all_50_1_70, all_60_1_88 and discharging atoms relation_field(all_0_16_16) = all_60_1_88, relation_field(all_0_16_16) = all_50_1_70, yields:
% 26.57/7.34 | (150) all_60_1_88 = all_50_1_70
% 26.57/7.34 |
% 26.57/7.34 | Combining equations (150,149) yields a new equation:
% 26.57/7.34 | (152) all_51_2_74 = all_50_1_70
% 26.57/7.34 |
% 26.57/7.34 | Combining equations (152,149) yields a new equation:
% 26.57/7.34 | (150) all_60_1_88 = all_50_1_70
% 26.57/7.34 |
% 26.57/7.34 | From (150) and (277) follows:
% 26.57/7.34 | (308) is_transitive_in(all_0_16_16, all_50_1_70) = all_60_0_87
% 26.57/7.34 |
% 26.57/7.34 | From (152) and (303) follows:
% 26.57/7.34 | (309) is_transitive_in(all_0_16_16, all_50_1_70) = all_93_0_110
% 26.57/7.34 |
% 26.57/7.34 | Instantiating formula (53) with all_0_16_16, all_50_1_70, all_93_0_110, all_50_0_69 and discharging atoms is_transitive_in(all_0_16_16, all_50_1_70) = all_93_0_110, is_transitive_in(all_0_16_16, all_50_1_70) = all_50_0_69, yields:
% 26.57/7.34 | (310) all_93_0_110 = all_50_0_69
% 26.57/7.34 |
% 26.57/7.34 | Instantiating formula (53) with all_0_16_16, all_50_1_70, all_60_0_87, all_93_0_110 and discharging atoms is_transitive_in(all_0_16_16, all_50_1_70) = all_93_0_110, is_transitive_in(all_0_16_16, all_50_1_70) = all_60_0_87, yields:
% 26.57/7.34 | (311) all_93_0_110 = all_60_0_87
% 26.57/7.34 |
% 26.57/7.34 | Combining equations (310,311) yields a new equation:
% 26.57/7.34 | (312) all_60_0_87 = all_50_0_69
% 26.57/7.34 |
% 26.57/7.34 | Equations (312) can reduce 275 to:
% 26.57/7.34 | (236) ~ (all_50_0_69 = 0)
% 26.57/7.34 |
% 26.57/7.34 | From (312) and (308) follows:
% 26.57/7.34 | (238) is_transitive_in(all_0_16_16, all_50_1_70) = all_50_0_69
% 26.57/7.34 |
% 26.57/7.34 | Instantiating formula (67) with all_50_0_69, all_50_1_70, all_0_16_16 and discharging atoms is_transitive_in(all_0_16_16, all_50_1_70) = all_50_0_69, relation(all_0_16_16) = 0, yields:
% 26.57/7.34 | (315) all_50_0_69 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = 0) & ordered_pair(v1, v2) = v4 & ordered_pair(v0, v2) = v5 & ordered_pair(v0, v1) = v3 & in(v5, all_0_16_16) = v6 & in(v4, all_0_16_16) = 0 & in(v3, all_0_16_16) = 0 & in(v2, all_50_1_70) = 0 & in(v1, all_50_1_70) = 0 & in(v0, all_50_1_70) = 0)
% 26.57/7.34 |
% 26.57/7.34 +-Applying beta-rule and splitting (315), into two cases.
% 26.57/7.34 |-Branch one:
% 26.57/7.34 | (125) all_50_0_69 = 0
% 26.57/7.34 |
% 26.57/7.34 | Equations (125) can reduce 236 to:
% 26.57/7.34 | (120) $false
% 26.57/7.34 |
% 26.57/7.34 |-The branch is then unsatisfiable
% 26.57/7.34 |-Branch two:
% 26.57/7.34 | (236) ~ (all_50_0_69 = 0)
% 26.57/7.34 | (319) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = 0) & ordered_pair(v1, v2) = v4 & ordered_pair(v0, v2) = v5 & ordered_pair(v0, v1) = v3 & in(v5, all_0_16_16) = v6 & in(v4, all_0_16_16) = 0 & in(v3, all_0_16_16) = 0 & in(v2, all_50_1_70) = 0 & in(v1, all_50_1_70) = 0 & in(v0, all_50_1_70) = 0)
% 26.57/7.34 |
% 26.57/7.34 | Instantiating (319) with all_161_0_167, all_161_1_168, all_161_2_169, all_161_3_170, all_161_4_171, all_161_5_172, all_161_6_173 yields:
% 26.57/7.34 | (320) ~ (all_161_0_167 = 0) & ordered_pair(all_161_5_172, all_161_4_171) = all_161_2_169 & ordered_pair(all_161_6_173, all_161_4_171) = all_161_1_168 & ordered_pair(all_161_6_173, all_161_5_172) = all_161_3_170 & in(all_161_1_168, all_0_16_16) = all_161_0_167 & in(all_161_2_169, all_0_16_16) = 0 & in(all_161_3_170, all_0_16_16) = 0 & in(all_161_4_171, all_50_1_70) = 0 & in(all_161_5_172, all_50_1_70) = 0 & in(all_161_6_173, all_50_1_70) = 0
% 26.57/7.34 |
% 26.57/7.34 | Applying alpha-rule on (320) yields:
% 26.57/7.34 | (321) in(all_161_1_168, all_0_16_16) = all_161_0_167
% 26.57/7.34 | (322) in(all_161_5_172, all_50_1_70) = 0
% 26.57/7.34 | (323) in(all_161_6_173, all_50_1_70) = 0
% 26.57/7.34 | (324) in(all_161_3_170, all_0_16_16) = 0
% 26.57/7.34 | (325) ordered_pair(all_161_6_173, all_161_4_171) = all_161_1_168
% 26.57/7.34 | (326) in(all_161_4_171, all_50_1_70) = 0
% 26.57/7.34 | (327) in(all_161_2_169, all_0_16_16) = 0
% 26.57/7.34 | (328) ordered_pair(all_161_5_172, all_161_4_171) = all_161_2_169
% 26.57/7.34 | (329) ordered_pair(all_161_6_173, all_161_5_172) = all_161_3_170
% 26.57/7.34 | (330) ~ (all_161_0_167 = 0)
% 26.57/7.34 |
% 26.57/7.34 | Instantiating formula (41) with all_161_0_167, all_0_16_16, all_161_1_168 and discharging atoms in(all_161_1_168, all_0_16_16) = all_161_0_167, yields:
% 26.57/7.34 | (331) all_161_0_167 = 0 | ? [v0] : ((v0 = 0 & empty(all_0_16_16) = 0) | ( ~ (v0 = 0) & element(all_161_1_168, all_0_16_16) = v0))
% 26.57/7.34 |
% 26.57/7.34 | Instantiating formula (247) with all_161_0_167, all_161_1_168, all_161_2_169, all_161_4_171, all_161_5_172, all_161_6_173 and discharging atoms ordered_pair(all_161_5_172, all_161_4_171) = all_161_2_169, ordered_pair(all_161_6_173, all_161_4_171) = all_161_1_168, in(all_161_1_168, all_0_16_16) = all_161_0_167, in(all_161_2_169, all_0_16_16) = 0, yields:
% 26.57/7.34 | (332) all_161_0_167 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & ordered_pair(all_161_6_173, all_161_5_172) = v0 & in(v0, all_0_16_16) = v1)
% 26.57/7.34 |
% 26.57/7.34 | Instantiating formula (249) with all_161_2_169, all_161_3_170, all_161_4_171, all_161_5_172, all_161_6_173 and discharging atoms ordered_pair(all_161_5_172, all_161_4_171) = all_161_2_169, ordered_pair(all_161_6_173, all_161_5_172) = all_161_3_170, in(all_161_2_169, all_0_16_16) = 0, in(all_161_3_170, all_0_16_16) = 0, yields:
% 26.57/7.34 | (333) ? [v0] : (ordered_pair(all_161_6_173, all_161_4_171) = v0 & in(v0, all_0_16_16) = 0)
% 26.57/7.34 |
% 26.57/7.34 | Instantiating formula (248) with all_161_0_167, all_161_1_168, all_161_3_170, all_161_4_171, all_161_5_172, all_161_6_173 and discharging atoms ordered_pair(all_161_6_173, all_161_4_171) = all_161_1_168, ordered_pair(all_161_6_173, all_161_5_172) = all_161_3_170, in(all_161_1_168, all_0_16_16) = all_161_0_167, in(all_161_3_170, all_0_16_16) = 0, yields:
% 26.57/7.34 | (334) all_161_0_167 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & ordered_pair(all_161_5_172, all_161_4_171) = v0 & in(v0, all_0_16_16) = v1)
% 26.57/7.34 |
% 26.57/7.34 | Instantiating (333) with all_195_0_182 yields:
% 26.57/7.34 | (335) ordered_pair(all_161_6_173, all_161_4_171) = all_195_0_182 & in(all_195_0_182, all_0_16_16) = 0
% 26.57/7.34 |
% 26.57/7.34 | Applying alpha-rule on (335) yields:
% 26.57/7.34 | (336) ordered_pair(all_161_6_173, all_161_4_171) = all_195_0_182
% 26.57/7.34 | (337) in(all_195_0_182, all_0_16_16) = 0
% 26.57/7.34 |
% 26.57/7.34 +-Applying beta-rule and splitting (334), into two cases.
% 26.57/7.34 |-Branch one:
% 26.57/7.34 | (338) all_161_0_167 = 0
% 26.57/7.34 |
% 26.57/7.34 | Equations (338) can reduce 330 to:
% 26.57/7.34 | (120) $false
% 26.57/7.34 |
% 26.57/7.34 |-The branch is then unsatisfiable
% 26.57/7.34 |-Branch two:
% 26.57/7.34 | (330) ~ (all_161_0_167 = 0)
% 26.57/7.34 | (341) ? [v0] : ? [v1] : ( ~ (v1 = 0) & ordered_pair(all_161_5_172, all_161_4_171) = v0 & in(v0, all_0_16_16) = v1)
% 26.57/7.34 |
% 26.57/7.34 +-Applying beta-rule and splitting (332), into two cases.
% 26.57/7.34 |-Branch one:
% 26.57/7.34 | (338) all_161_0_167 = 0
% 26.57/7.34 |
% 26.57/7.34 | Equations (338) can reduce 330 to:
% 26.57/7.34 | (120) $false
% 26.57/7.34 |
% 26.57/7.34 |-The branch is then unsatisfiable
% 26.57/7.34 |-Branch two:
% 26.57/7.34 | (330) ~ (all_161_0_167 = 0)
% 26.57/7.34 | (345) ? [v0] : ? [v1] : ( ~ (v1 = 0) & ordered_pair(all_161_6_173, all_161_5_172) = v0 & in(v0, all_0_16_16) = v1)
% 26.57/7.34 |
% 26.57/7.34 +-Applying beta-rule and splitting (331), into two cases.
% 26.57/7.34 |-Branch one:
% 26.57/7.34 | (338) all_161_0_167 = 0
% 26.57/7.34 |
% 26.57/7.34 | Equations (338) can reduce 330 to:
% 26.57/7.34 | (120) $false
% 26.57/7.34 |
% 26.57/7.34 |-The branch is then unsatisfiable
% 26.57/7.34 |-Branch two:
% 26.57/7.34 | (330) ~ (all_161_0_167 = 0)
% 26.57/7.34 | (349) ? [v0] : ((v0 = 0 & empty(all_0_16_16) = 0) | ( ~ (v0 = 0) & element(all_161_1_168, all_0_16_16) = v0))
% 26.57/7.34 |
% 26.57/7.34 | Instantiating formula (23) with all_161_6_173, all_161_4_171, all_195_0_182, all_161_1_168 and discharging atoms ordered_pair(all_161_6_173, all_161_4_171) = all_195_0_182, ordered_pair(all_161_6_173, all_161_4_171) = all_161_1_168, yields:
% 26.57/7.34 | (350) all_195_0_182 = all_161_1_168
% 26.57/7.34 |
% 26.57/7.34 | From (350) and (337) follows:
% 26.57/7.34 | (351) in(all_161_1_168, all_0_16_16) = 0
% 26.57/7.34 |
% 26.57/7.34 | Instantiating formula (85) with all_161_1_168, all_0_16_16, 0, all_161_0_167 and discharging atoms in(all_161_1_168, all_0_16_16) = all_161_0_167, in(all_161_1_168, all_0_16_16) = 0, yields:
% 26.57/7.34 | (338) all_161_0_167 = 0
% 26.57/7.34 |
% 26.57/7.34 | Equations (338) can reduce 330 to:
% 26.57/7.34 | (120) $false
% 26.57/7.34 |
% 26.57/7.34 |-The branch is then unsatisfiable
% 26.57/7.34 % SZS output end Proof for theBenchmark
% 26.57/7.34
% 26.57/7.34 6738ms
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