TSTP Solution File: SEU362+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU362+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n027.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 08:49:11 EDT 2022
% Result : Theorem 29.81s 9.23s
% Output : Proof 66.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU362+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n027.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jun 19 00:44:23 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.51/0.57 ____ _
% 0.51/0.57 ___ / __ \_____(_)___ ________ __________
% 0.51/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.51/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.51/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.51/0.57
% 0.51/0.57 A Theorem Prover for First-Order Logic
% 0.51/0.57 (ePrincess v.1.0)
% 0.51/0.57
% 0.51/0.57 (c) Philipp Rümmer, 2009-2015
% 0.51/0.57 (c) Peter Backeman, 2014-2015
% 0.51/0.57 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.51/0.57 Free software under GNU Lesser General Public License (LGPL).
% 0.51/0.57 Bug reports to peter@backeman.se
% 0.51/0.57
% 0.51/0.57 For more information, visit http://user.uu.se/~petba168/breu/
% 0.51/0.57
% 0.51/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.51/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.64/0.96 Prover 0: Preprocessing ...
% 2.43/1.23 Prover 0: Warning: ignoring some quantifiers
% 2.43/1.26 Prover 0: Constructing countermodel ...
% 17.23/5.92 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 17.40/5.97 Prover 1: Preprocessing ...
% 17.93/6.10 Prover 1: Warning: ignoring some quantifiers
% 17.93/6.11 Prover 1: Constructing countermodel ...
% 26.62/8.51 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 26.75/8.55 Prover 2: Preprocessing ...
% 27.46/8.74 Prover 2: Warning: ignoring some quantifiers
% 27.46/8.75 Prover 2: Constructing countermodel ...
% 29.65/9.23 Prover 2: proved (716ms)
% 29.81/9.23 Prover 0: stopped
% 29.81/9.23 Prover 1: stopped
% 29.81/9.23
% 29.81/9.23 No countermodel exists, formula is valid
% 29.81/9.23 % SZS status Theorem for theBenchmark
% 29.81/9.23
% 29.81/9.23 Generating proof ... Warning: ignoring some quantifiers
% 65.61/30.67 found it (size 208)
% 65.61/30.67
% 65.61/30.67 % SZS output start Proof for theBenchmark
% 65.61/30.67 Assumed formulas after preprocessing and simplification:
% 65.61/30.67 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ( ~ (v11 = 0) & ~ (v8 = 0) & ~ (v6 = 0) & one_sorted_str(v12) = 0 & related(v2, v4, v5) = 0 & related(v0, v4, v5) = v6 & the_carrier(v2) = v3 & the_carrier(v0) = v1 & rel_str(v13) = 0 & rel_str(v0) = 0 & subrelstr(v2, v0) = 0 & element(v5, v3) = 0 & element(v5, v1) = 0 & element(v4, v3) = 0 & element(v4, v1) = 0 & finite(v10) = 0 & empty(v10) = v11 & empty(v9) = 0 & empty(v7) = v8 & empty(empty_set) = 0 & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v19 = 0 | ~ (cartesian_product2(v14, v15) = v17) | ~ (powerset(v17) = v18) | ~ (element(v16, v18) = v19) | ? [v20] : ( ~ (v20 = 0) & relation_of2_as_subset(v16, v14, v15) = v20)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = 0 | ~ (powerset(v16) = v17) | ~ (element(v15, v17) = 0) | ~ (element(v14, v16) = v18) | ? [v19] : ( ~ (v19 = 0) & in(v14, v15) = v19)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v15 = v14 | ~ (relation_of2(v18, v17, v16) = v15) | ~ (relation_of2(v18, v17, v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v15 = v14 | ~ (relation_of2_as_subset(v18, v17, v16) = v15) | ~ (relation_of2_as_subset(v18, v17, v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v15 = v14 | ~ (related(v18, v17, v16) = v15) | ~ (related(v18, v17, v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (cartesian_product2(v14, v15) = v17) | ~ (powerset(v17) = v18) | ~ (element(v16, v18) = 0) | relation(v16) = 0) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v17 = 0 | ~ (relation_of2(v16, v14, v15) = v17) | ? [v18] : ( ~ (v18 = 0) & relation_of2_as_subset(v16, v14, v15) = v18)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v17 = 0 | ~ (relation_of2_as_subset(v16, v14, v15) = v17) | ? [v18] : ( ~ (v18 = 0) & relation_of2(v16, v14, v15) = v18)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v17 = 0 | ~ (powerset(v15) = v16) | ~ (element(v14, v16) = v17) | ? [v18] : ( ~ (v18 = 0) & subset(v14, v15) = v18)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v17 = 0 | ~ (powerset(v14) = v15) | ~ (finite(v16) = v17) | ? [v18] : (( ~ (v18 = 0) & element(v16, v15) = v18) | ( ~ (v18 = 0) & finite(v14) = v18))) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v17 = 0 | ~ (element(v14, v16) = v17) | ~ (in(v14, v15) = 0) | ? [v18] : ? [v19] : ( ~ (v19 = 0) & powerset(v16) = v18 & element(v15, v18) = v19)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v15 = v14 | ~ (ordered_pair(v17, v16) = v15) | ~ (ordered_pair(v17, v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v15 = v14 | ~ (subrelstr(v17, v16) = v15) | ~ (subrelstr(v17, v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v15 = v14 | ~ (subset(v17, v16) = v15) | ~ (subset(v17, v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v15 = v14 | ~ (cartesian_product2(v17, v16) = v15) | ~ (cartesian_product2(v17, v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v15 = v14 | ~ (element(v17, v16) = v15) | ~ (element(v17, v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v15 = v14 | ~ (in(v17, v16) = v15) | ~ (in(v17, v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (powerset(v16) = v17) | ~ (element(v15, v17) = 0) | ~ (in(v14, v15) = 0) | element(v14, v16) = 0) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (powerset(v16) = v17) | ~ (element(v15, v17) = 0) | ~ (in(v14, v15) = 0) | ? [v18] : ( ~ (v18 = 0) & empty(v16) = v18)) & ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (rel_str(v15) = v16) | ~ (rel_str(v14) = 0) | ? [v17] : ( ~ (v17 = 0) & subrelstr(v15, v14) = v17)) & ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (subset(v14, v15) = v16) | ? [v17] : ? [v18] : ( ~ (v18 = 0) & powerset(v15) = v17 & element(v14, v17) = v18)) & ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (element(v14, v15) = v16) | ? [v17] : ( ~ (v17 = 0) & in(v14, v15) = v17)) & ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (in(v14, v15) = v16) | ? [v17] : ((v17 = 0 & empty(v15) = 0) | ( ~ (v17 = 0) & element(v14, v15) = v17))) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (one_sorted_str(v16) = v15) | ~ (one_sorted_str(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (the_carrier(v16) = v15) | ~ (the_carrier(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (rel_str(v16) = v15) | ~ (rel_str(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (the_InternalRel(v16) = v15) | ~ (the_InternalRel(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (powerset(v16) = v15) | ~ (powerset(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (relation(v16) = v15) | ~ (relation(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (finite(v16) = v15) | ~ (finite(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (empty(v16) = v15) | ~ (empty(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : ( ~ (relation_of2(v16, v14, v15) = 0) | relation_of2_as_subset(v16, v14, v15) = 0) & ! [v14] : ! [v15] : ! [v16] : ( ~ (relation_of2_as_subset(v16, v14, v15) = 0) | relation_of2(v16, v14, v15) = 0) & ! [v14] : ! [v15] : ! [v16] : ( ~ (relation_of2_as_subset(v16, v14, v15) = 0) | ? [v17] : ? [v18] : (cartesian_product2(v14, v15) = v17 & powerset(v17) = v18 & element(v16, v18) = 0)) & ! [v14] : ! [v15] : ! [v16] : ( ~ (cartesian_product2(v14, v15) = v16) | ? [v17] : ((v17 = 0 & finite(v16) = 0) | ( ~ (v17 = 0) & finite(v15) = v17) | ( ~ (v17 = 0) & finite(v14) = v17))) & ! [v14] : ! [v15] : ! [v16] : ( ~ (powerset(v15) = v16) | ~ (element(v14, v16) = 0) | subset(v14, v15) = 0) & ! [v14] : ! [v15] : ! [v16] : ( ~ (powerset(v14) = v15) | ~ (element(v16, v15) = 0) | ? [v17] : ((v17 = 0 & finite(v16) = 0) | ( ~ (v17 = 0) & finite(v14) = v17))) & ! [v14] : ! [v15] : ! [v16] : ( ~ (empty(v16) = 0) | ~ (in(v14, v15) = 0) | ? [v17] : ? [v18] : ( ~ (v18 = 0) & powerset(v16) = v17 & element(v15, v17) = v18)) & ! [v14] : ! [v15] : (v15 = v14 | ~ (empty(v15) = 0) | ~ (empty(v14) = 0)) & ! [v14] : ! [v15] : (v15 = 0 | ~ (one_sorted_str(v14) = v15) | ? [v16] : ( ~ (v16 = 0) & rel_str(v14) = v16)) & ! [v14] : ! [v15] : (v15 = 0 | ~ (subset(v14, v14) = v15)) & ! [v14] : ! [v15] : (v15 = 0 | ~ (finite(v14) = v15) | ? [v16] : ( ~ (v16 = 0) & empty(v14) = v16)) & ! [v14] : ! [v15] : (v15 = 0 | ~ (empty(v14) = v15) | ? [v16] : ? [v17] : ? [v18] : ( ~ (v18 = 0) & powerset(v14) = v16 & element(v17, v16) = 0 & finite(v17) = 0 & empty(v17) = v18)) & ! [v14] : ! [v15] : ( ~ (the_carrier(v14) = v15) | ? [v16] : ? [v17] : ((v17 = 0 & relation_of2_as_subset(v16, v15, v15) = 0 & the_InternalRel(v14) = v16) | ( ~ (v16 = 0) & rel_str(v14) = v16))) & ! [v14] : ! [v15] : ( ~ (the_carrier(v14) = v15) | ? [v16] : (( ~ (v16 = 0) & rel_str(v14) = v16) | (the_InternalRel(v14) = v16 & ! [v17] : ! [v18] : ! [v19] : ( ~ (ordered_pair(v17, v18) = v19) | ~ (element(v17, v15) = 0) | ? [v20] : ? [v21] : (( ~ (v20 = 0) & element(v18, v15) = v20) | (((v21 = 0 & in(v19, v16) = 0) | ( ~ (v20 = 0) & related(v14, v17, v18) = v20)) & ((v20 = 0 & related(v14, v17, v18) = 0) | ( ~ (v21 = 0) & in(v19, v16) = v21))))) & ! [v17] : ! [v18] : ! [v19] : ( ~ (related(v14, v17, v18) = v19) | ~ (element(v17, v15) = 0) | ? [v20] : ? [v21] : (( ~ (v20 = 0) & element(v18, v15) = v20) | (( ~ (v19 = 0) | (v21 = 0 & ordered_pair(v17, v18) = v20 & in(v20, v16) = 0)) & (v19 = 0 | ( ~ (v21 = 0) & ordered_pair(v17, v18) = v20 & in(v20, v16) = v21))))) & ! [v17] : ! [v18] : ( ~ (element(v18, v15) = 0) | ~ (element(v17, v15) = 0) | ? [v19] : ? [v20] : ? [v21] : (((v21 = 0 & ordered_pair(v17, v18) = v20 & in(v20, v16) = 0) | ( ~ (v19 = 0) & related(v14, v17, v18) = v19)) & ((v19 = 0 & related(v14, v17, v18) = 0) | ( ~ (v21 = 0) & ordered_pair(v17, v18) = v20 & in(v20, v16) = v21))))))) & ! [v14] : ! [v15] : ( ~ (the_carrier(v14) = v15) | ? [v16] : (( ~ (v16 = 0) & rel_str(v14) = v16) | (the_InternalRel(v14) = v16 & ! [v17] : ! [v18] : ( ~ (the_carrier(v17) = v18) | ? [v19] : ? [v20] : ? [v21] : ? [v22] : (( ~ (v19 = 0) & rel_str(v17) = v19) | (((v22 = 0 & v20 = 0 & the_InternalRel(v17) = v21 & subset(v21, v16) = 0 & subset(v18, v15) = 0) | ( ~ (v19 = 0) & subrelstr(v17, v14) = v19)) & ((v19 = 0 & subrelstr(v17, v14) = 0) | ( ~ (v22 = 0) & the_InternalRel(v17) = v21 & subset(v21, v16) = v22) | ( ~ (v20 = 0) & subset(v18, v15) = v20))))) & ! [v17] : ! [v18] : ( ~ (subrelstr(v17, v14) = v18) | ? [v19] : ? [v20] : ? [v21] : ? [v22] : (( ~ (v19 = 0) & rel_str(v17) = v19) | (( ~ (v18 = 0) | (v22 = 0 & v20 = 0 & the_carrier(v17) = v19 & the_InternalRel(v17) = v21 & subset(v21, v16) = 0 & subset(v19, v15) = 0)) & (v18 = 0 | ( ~ (v22 = 0) & the_InternalRel(v17) = v21 & subset(v21, v16) = v22) | ( ~ (v20 = 0) & the_carrier(v17) = v19 & subset(v19, v15) = v20))))) & ! [v17] : ! [v18] : ( ~ (the_InternalRel(v17) = v18) | ? [v19] : ? [v20] : ? [v21] : ? [v22] : (( ~ (v19 = 0) & rel_str(v17) = v19) | (((v22 = 0 & v21 = 0 & the_carrier(v17) = v20 & subset(v20, v15) = 0 & subset(v18, v16) = 0) | ( ~ (v19 = 0) & subrelstr(v17, v14) = v19)) & ((v19 = 0 & subrelstr(v17, v14) = 0) | ( ~ (v22 = 0) & subset(v18, v16) = v22) | ( ~ (v21 = 0) & the_carrier(v17) = v20 & subset(v20, v15) = v21))))) & ! [v17] : ( ~ (rel_str(v17) = 0) | ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : (((v22 = 0 & v20 = 0 & the_carrier(v17) = v19 & the_InternalRel(v17) = v21 & subset(v21, v16) = 0 & subset(v19, v15) = 0) | ( ~ (v18 = 0) & subrelstr(v17, v14) = v18)) & ((v18 = 0 & subrelstr(v17, v14) = 0) | ( ~ (v22 = 0) & the_InternalRel(v17) = v21 & subset(v21, v16) = v22) | ( ~ (v20 = 0) & the_carrier(v17) = v19 & subset(v19, v15) = v20))))))) & ! [v14] : ! [v15] : ( ~ (rel_str(v14) = 0) | ~ (subrelstr(v15, v14) = 0) | rel_str(v15) = 0) & ! [v14] : ! [v15] : ( ~ (the_InternalRel(v14) = v15) | ? [v16] : ? [v17] : ((v17 = 0 & relation_of2_as_subset(v15, v16, v16) = 0 & the_carrier(v14) = v16) | ( ~ (v16 = 0) & rel_str(v14) = v16))) & ! [v14] : ! [v15] : ( ~ (the_InternalRel(v14) = v15) | ? [v16] : (( ~ (v16 = 0) & rel_str(v14) = v16) | (the_carrier(v14) = v16 & ! [v17] : ! [v18] : ! [v19] : ( ~ (ordered_pair(v17, v18) = v19) | ~ (element(v17, v16) = 0) | ? [v20] : ? [v21] : (( ~ (v20 = 0) & element(v18, v16) = v20) | (((v21 = 0 & in(v19, v15) = 0) | ( ~ (v20 = 0) & related(v14, v17, v18) = v20)) & ((v20 = 0 & related(v14, v17, v18) = 0) | ( ~ (v21 = 0) & in(v19, v15) = v21))))) & ! [v17] : ! [v18] : ! [v19] : ( ~ (related(v14, v17, v18) = v19) | ~ (element(v17, v16) = 0) | ? [v20] : ? [v21] : (( ~ (v20 = 0) & element(v18, v16) = v20) | (( ~ (v19 = 0) | (v21 = 0 & ordered_pair(v17, v18) = v20 & in(v20, v15) = 0)) & (v19 = 0 | ( ~ (v21 = 0) & ordered_pair(v17, v18) = v20 & in(v20, v15) = v21))))) & ! [v17] : ! [v18] : ( ~ (element(v18, v16) = 0) | ~ (element(v17, v16) = 0) | ? [v19] : ? [v20] : ? [v21] : (((v21 = 0 & ordered_pair(v17, v18) = v20 & in(v20, v15) = 0) | ( ~ (v19 = 0) & related(v14, v17, v18) = v19)) & ((v19 = 0 & related(v14, v17, v18) = 0) | ( ~ (v21 = 0) & ordered_pair(v17, v18) = v20 & in(v20, v15) = v21))))))) & ! [v14] : ! [v15] : ( ~ (the_InternalRel(v14) = v15) | ? [v16] : (( ~ (v16 = 0) & rel_str(v14) = v16) | (the_carrier(v14) = v16 & ! [v17] : ! [v18] : ( ~ (the_carrier(v17) = v18) | ? [v19] : ? [v20] : ? [v21] : ? [v22] : (( ~ (v19 = 0) & rel_str(v17) = v19) | (((v22 = 0 & v20 = 0 & the_InternalRel(v17) = v21 & subset(v21, v15) = 0 & subset(v18, v16) = 0) | ( ~ (v19 = 0) & subrelstr(v17, v14) = v19)) & ((v19 = 0 & subrelstr(v17, v14) = 0) | ( ~ (v22 = 0) & the_InternalRel(v17) = v21 & subset(v21, v15) = v22) | ( ~ (v20 = 0) & subset(v18, v16) = v20))))) & ! [v17] : ! [v18] : ( ~ (subrelstr(v17, v14) = v18) | ? [v19] : ? [v20] : ? [v21] : ? [v22] : (( ~ (v19 = 0) & rel_str(v17) = v19) | (( ~ (v18 = 0) | (v22 = 0 & v20 = 0 & the_carrier(v17) = v19 & the_InternalRel(v17) = v21 & subset(v21, v15) = 0 & subset(v19, v16) = 0)) & (v18 = 0 | ( ~ (v22 = 0) & the_InternalRel(v17) = v21 & subset(v21, v15) = v22) | ( ~ (v20 = 0) & the_carrier(v17) = v19 & subset(v19, v16) = v20))))) & ! [v17] : ! [v18] : ( ~ (the_InternalRel(v17) = v18) | ? [v19] : ? [v20] : ? [v21] : ? [v22] : (( ~ (v19 = 0) & rel_str(v17) = v19) | (((v22 = 0 & v21 = 0 & the_carrier(v17) = v20 & subset(v20, v16) = 0 & subset(v18, v15) = 0) | ( ~ (v19 = 0) & subrelstr(v17, v14) = v19)) & ((v19 = 0 & subrelstr(v17, v14) = 0) | ( ~ (v22 = 0) & subset(v18, v15) = v22) | ( ~ (v21 = 0) & the_carrier(v17) = v20 & subset(v20, v16) = v21))))) & ! [v17] : ( ~ (rel_str(v17) = 0) | ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : (((v22 = 0 & v20 = 0 & the_carrier(v17) = v19 & the_InternalRel(v17) = v21 & subset(v21, v15) = 0 & subset(v19, v16) = 0) | ( ~ (v18 = 0) & subrelstr(v17, v14) = v18)) & ((v18 = 0 & subrelstr(v17, v14) = 0) | ( ~ (v22 = 0) & the_InternalRel(v17) = v21 & subset(v21, v15) = v22) | ( ~ (v20 = 0) & the_carrier(v17) = v19 & subset(v19, v16) = v20))))))) & ! [v14] : ! [v15] : ( ~ (subset(v14, v15) = 0) | ? [v16] : (powerset(v15) = v16 & element(v14, v16) = 0)) & ! [v14] : ! [v15] : ( ~ (powerset(v14) = v15) | ? [v16] : ? [v17] : ? [v18] : ? [v19] : ((v19 = 0 & v17 = 0 & ~ (v18 = 0) & element(v16, v15) = 0 & finite(v16) = 0 & empty(v16) = v18) | (v16 = 0 & empty(v14) = 0))) & ! [v14] : ! [v15] : ( ~ (element(v14, v15) = 0) | ? [v16] : ((v16 = 0 & empty(v15) = 0) | (v16 = 0 & in(v14, v15) = 0))) & ! [v14] : ! [v15] : ( ~ (in(v15, v14) = 0) | ? [v16] : ( ~ (v16 = 0) & in(v14, v15) = v16)) & ! [v14] : ! [v15] : ( ~ (in(v14, v15) = 0) | element(v14, v15) = 0) & ! [v14] : ! [v15] : ( ~ (in(v14, v15) = 0) | ? [v16] : ( ~ (v16 = 0) & empty(v15) = v16)) & ! [v14] : ! [v15] : ( ~ (in(v14, v15) = 0) | ? [v16] : ( ~ (v16 = 0) & in(v15, v14) = v16)) & ! [v14] : (v14 = empty_set | ~ (empty(v14) = 0)) & ! [v14] : ( ~ (rel_str(v14) = 0) | one_sorted_str(v14) = 0) & ! [v14] : ( ~ (rel_str(v14) = 0) | ? [v15] : ? [v16] : (relation_of2_as_subset(v15, v16, v16) = 0 & the_carrier(v14) = v16 & the_InternalRel(v14) = v15)) & ! [v14] : ( ~ (rel_str(v14) = 0) | ? [v15] : ? [v16] : (the_carrier(v14) = v15 & the_InternalRel(v14) = v16 & ! [v17] : ! [v18] : ! [v19] : ( ~ (ordered_pair(v17, v18) = v19) | ~ (element(v17, v15) = 0) | ? [v20] : ? [v21] : (( ~ (v20 = 0) & element(v18, v15) = v20) | (((v21 = 0 & in(v19, v16) = 0) | ( ~ (v20 = 0) & related(v14, v17, v18) = v20)) & ((v20 = 0 & related(v14, v17, v18) = 0) | ( ~ (v21 = 0) & in(v19, v16) = v21))))) & ! [v17] : ! [v18] : ! [v19] : ( ~ (related(v14, v17, v18) = v19) | ~ (element(v17, v15) = 0) | ? [v20] : ? [v21] : (( ~ (v20 = 0) & element(v18, v15) = v20) | (( ~ (v19 = 0) | (v21 = 0 & ordered_pair(v17, v18) = v20 & in(v20, v16) = 0)) & (v19 = 0 | ( ~ (v21 = 0) & ordered_pair(v17, v18) = v20 & in(v20, v16) = v21))))) & ! [v17] : ! [v18] : ( ~ (element(v18, v15) = 0) | ~ (element(v17, v15) = 0) | ? [v19] : ? [v20] : ? [v21] : (((v21 = 0 & ordered_pair(v17, v18) = v20 & in(v20, v16) = 0) | ( ~ (v19 = 0) & related(v14, v17, v18) = v19)) & ((v19 = 0 & related(v14, v17, v18) = 0) | ( ~ (v21 = 0) & ordered_pair(v17, v18) = v20 & in(v20, v16) = v21)))))) & ! [v14] : ( ~ (rel_str(v14) = 0) | ? [v15] : ? [v16] : (the_carrier(v14) = v15 & the_InternalRel(v14) = v16 & ! [v17] : ! [v18] : ( ~ (the_carrier(v17) = v18) | ? [v19] : ? [v20] : ? [v21] : ? [v22] : (( ~ (v19 = 0) & rel_str(v17) = v19) | (((v22 = 0 & v20 = 0 & the_InternalRel(v17) = v21 & subset(v21, v16) = 0 & subset(v18, v15) = 0) | ( ~ (v19 = 0) & subrelstr(v17, v14) = v19)) & ((v19 = 0 & subrelstr(v17, v14) = 0) | ( ~ (v22 = 0) & the_InternalRel(v17) = v21 & subset(v21, v16) = v22) | ( ~ (v20 = 0) & subset(v18, v15) = v20))))) & ! [v17] : ! [v18] : ( ~ (subrelstr(v17, v14) = v18) | ? [v19] : ? [v20] : ? [v21] : ? [v22] : (( ~ (v19 = 0) & rel_str(v17) = v19) | (( ~ (v18 = 0) | (v22 = 0 & v20 = 0 & the_carrier(v17) = v19 & the_InternalRel(v17) = v21 & subset(v21, v16) = 0 & subset(v19, v15) = 0)) & (v18 = 0 | ( ~ (v22 = 0) & the_InternalRel(v17) = v21 & subset(v21, v16) = v22) | ( ~ (v20 = 0) & the_carrier(v17) = v19 & subset(v19, v15) = v20))))) & ! [v17] : ! [v18] : ( ~ (the_InternalRel(v17) = v18) | ? [v19] : ? [v20] : ? [v21] : ? [v22] : (( ~ (v19 = 0) & rel_str(v17) = v19) | (((v22 = 0 & v21 = 0 & the_carrier(v17) = v20 & subset(v20, v15) = 0 & subset(v18, v16) = 0) | ( ~ (v19 = 0) & subrelstr(v17, v14) = v19)) & ((v19 = 0 & subrelstr(v17, v14) = 0) | ( ~ (v22 = 0) & subset(v18, v16) = v22) | ( ~ (v21 = 0) & the_carrier(v17) = v20 & subset(v20, v15) = v21))))) & ! [v17] : ( ~ (rel_str(v17) = 0) | ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : (((v22 = 0 & v20 = 0 & the_carrier(v17) = v19 & the_InternalRel(v17) = v21 & subset(v21, v16) = 0 & subset(v19, v15) = 0) | ( ~ (v18 = 0) & subrelstr(v17, v14) = v18)) & ((v18 = 0 & subrelstr(v17, v14) = 0) | ( ~ (v22 = 0) & the_InternalRel(v17) = v21 & subset(v21, v16) = v22) | ( ~ (v20 = 0) & the_carrier(v17) = v19 & subset(v19, v15) = v20)))))) & ! [v14] : ( ~ (rel_str(v14) = 0) | ? [v15] : subrelstr(v15, v14) = 0) & ! [v14] : ( ~ (finite(v14) = 0) | ? [v15] : (powerset(v14) = v15 & ! [v16] : ! [v17] : (v17 = 0 | ~ (finite(v16) = v17) | ? [v18] : ( ~ (v18 = 0) & element(v16, v15) = v18)) & ! [v16] : ( ~ (element(v16, v15) = 0) | finite(v16) = 0))) & ! [v14] : ( ~ (empty(v14) = 0) | finite(v14) = 0) & ? [v14] : ? [v15] : ? [v16] : ? [v17] : relation_of2(v16, v15, v14) = v17 & ? [v14] : ? [v15] : ? [v16] : ? [v17] : relation_of2_as_subset(v16, v15, v14) = v17 & ? [v14] : ? [v15] : ? [v16] : ? [v17] : related(v16, v15, v14) = v17 & ? [v14] : ? [v15] : ? [v16] : relation_of2(v16, v14, v15) = 0 & ? [v14] : ? [v15] : ? [v16] : relation_of2_as_subset(v16, v14, v15) = 0 & ? [v14] : ? [v15] : ? [v16] : ordered_pair(v15, v14) = v16 & ? [v14] : ? [v15] : ? [v16] : subrelstr(v15, v14) = v16 & ? [v14] : ? [v15] : ? [v16] : subset(v15, v14) = v16 & ? [v14] : ? [v15] : ? [v16] : cartesian_product2(v15, v14) = v16 & ? [v14] : ? [v15] : ? [v16] : element(v15, v14) = v16 & ? [v14] : ? [v15] : ? [v16] : in(v15, v14) = v16 & ? [v14] : ? [v15] : one_sorted_str(v14) = v15 & ? [v14] : ? [v15] : the_carrier(v14) = v15 & ? [v14] : ? [v15] : rel_str(v14) = v15 & ? [v14] : ? [v15] : the_InternalRel(v14) = v15 & ? [v14] : ? [v15] : powerset(v14) = v15 & ? [v14] : ? [v15] : element(v15, v14) = 0 & ? [v14] : ? [v15] : relation(v14) = v15 & ? [v14] : ? [v15] : finite(v14) = v15 & ? [v14] : ? [v15] : empty(v14) = v15)
% 65.93/30.75 | 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 yields:
% 65.93/30.75 | (1) ~ (all_0_2_2 = 0) & ~ (all_0_5_5 = 0) & ~ (all_0_7_7 = 0) & one_sorted_str(all_0_1_1) = 0 & related(all_0_11_11, all_0_9_9, all_0_8_8) = 0 & related(all_0_13_13, all_0_9_9, all_0_8_8) = all_0_7_7 & the_carrier(all_0_11_11) = all_0_10_10 & the_carrier(all_0_13_13) = all_0_12_12 & rel_str(all_0_0_0) = 0 & rel_str(all_0_13_13) = 0 & subrelstr(all_0_11_11, all_0_13_13) = 0 & element(all_0_8_8, all_0_10_10) = 0 & element(all_0_8_8, all_0_12_12) = 0 & element(all_0_9_9, all_0_10_10) = 0 & element(all_0_9_9, all_0_12_12) = 0 & finite(all_0_3_3) = 0 & empty(all_0_3_3) = all_0_2_2 & empty(all_0_4_4) = 0 & empty(all_0_6_6) = all_0_5_5 & empty(empty_set) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (cartesian_product2(v0, v1) = v3) | ~ (powerset(v3) = v4) | ~ (element(v2, v4) = v5) | ? [v6] : ( ~ (v6 = 0) & relation_of2_as_subset(v2, v0, v1) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (element(v0, v2) = v4) | ? [v5] : ( ~ (v5 = 0) & in(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (relation_of2(v4, v3, v2) = v1) | ~ (relation_of2(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (relation_of2_as_subset(v4, v3, v2) = v1) | ~ (relation_of2_as_subset(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (related(v4, v3, v2) = v1) | ~ (related(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v0, v1) = v3) | ~ (powerset(v3) = v4) | ~ (element(v2, v4) = 0) | relation(v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (relation_of2(v2, v0, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & relation_of2_as_subset(v2, v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (relation_of2_as_subset(v2, v0, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & relation_of2(v2, v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v0) = v1) | ~ (finite(v2) = v3) | ? [v4] : (( ~ (v4 = 0) & element(v2, v1) = v4) | ( ~ (v4 = 0) & finite(v0) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (element(v0, v2) = v3) | ~ (in(v0, v1) = 0) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & powerset(v2) = v4 & element(v1, v4) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subrelstr(v3, v2) = v1) | ~ (subrelstr(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | element(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (rel_str(v1) = v2) | ~ (rel_str(v0) = 0) | ? [v3] : ( ~ (v3 = 0) & subrelstr(v1, v0) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v1) = v3 & element(v0, v3) = v4)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v0, v1) = v2) | ? [v3] : ((v3 = 0 & empty(v1) = 0) | ( ~ (v3 = 0) & element(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (one_sorted_str(v2) = v1) | ~ (one_sorted_str(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (the_carrier(v2) = v1) | ~ (the_carrier(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (rel_str(v2) = v1) | ~ (rel_str(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (the_InternalRel(v2) = v1) | ~ (the_InternalRel(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (finite(v2) = v1) | ~ (finite(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_of2(v2, v0, v1) = 0) | relation_of2_as_subset(v2, v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_of2_as_subset(v2, v0, v1) = 0) | relation_of2(v2, v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_of2_as_subset(v2, v0, v1) = 0) | ? [v3] : ? [v4] : (cartesian_product2(v0, v1) = v3 & powerset(v3) = v4 & element(v2, v4) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (cartesian_product2(v0, v1) = v2) | ? [v3] : ((v3 = 0 & finite(v2) = 0) | ( ~ (v3 = 0) & finite(v1) = v3) | ( ~ (v3 = 0) & finite(v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | subset(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ (element(v2, v1) = 0) | ? [v3] : ((v3 = 0 & finite(v2) = 0) | ( ~ (v3 = 0) & finite(v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (empty(v2) = 0) | ~ (in(v0, v1) = 0) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v2) = v3 & element(v1, v3) = v4)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (one_sorted_str(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & rel_str(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (finite(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (empty(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v0) = v2 & element(v3, v2) = 0 & finite(v3) = 0 & empty(v3) = v4)) & ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & relation_of2_as_subset(v2, v1, v1) = 0 & the_InternalRel(v0) = v2) | ( ~ (v2 = 0) & rel_str(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ? [v2] : (( ~ (v2 = 0) & rel_str(v0) = v2) | (the_InternalRel(v0) = v2 & ! [v3] : ! [v4] : ! [v5] : ( ~ (ordered_pair(v3, v4) = v5) | ~ (element(v3, v1) = 0) | ? [v6] : ? [v7] : (( ~ (v6 = 0) & element(v4, v1) = v6) | (((v7 = 0 & in(v5, v2) = 0) | ( ~ (v6 = 0) & related(v0, v3, v4) = v6)) & ((v6 = 0 & related(v0, v3, v4) = 0) | ( ~ (v7 = 0) & in(v5, v2) = v7))))) & ! [v3] : ! [v4] : ! [v5] : ( ~ (related(v0, v3, v4) = v5) | ~ (element(v3, v1) = 0) | ? [v6] : ? [v7] : (( ~ (v6 = 0) & element(v4, v1) = v6) | (( ~ (v5 = 0) | (v7 = 0 & ordered_pair(v3, v4) = v6 & in(v6, v2) = 0)) & (v5 = 0 | ( ~ (v7 = 0) & ordered_pair(v3, v4) = v6 & in(v6, v2) = v7))))) & ! [v3] : ! [v4] : ( ~ (element(v4, v1) = 0) | ~ (element(v3, v1) = 0) | ? [v5] : ? [v6] : ? [v7] : (((v7 = 0 & ordered_pair(v3, v4) = v6 & in(v6, v2) = 0) | ( ~ (v5 = 0) & related(v0, v3, v4) = v5)) & ((v5 = 0 & related(v0, v3, v4) = 0) | ( ~ (v7 = 0) & ordered_pair(v3, v4) = v6 & in(v6, v2) = v7))))))) & ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ? [v2] : (( ~ (v2 = 0) & rel_str(v0) = v2) | (the_InternalRel(v0) = v2 & ! [v3] : ! [v4] : ( ~ (the_carrier(v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (( ~ (v5 = 0) & rel_str(v3) = v5) | (((v8 = 0 & v6 = 0 & the_InternalRel(v3) = v7 & subset(v7, v2) = 0 & subset(v4, v1) = 0) | ( ~ (v5 = 0) & subrelstr(v3, v0) = v5)) & ((v5 = 0 & subrelstr(v3, v0) = 0) | ( ~ (v8 = 0) & the_InternalRel(v3) = v7 & subset(v7, v2) = v8) | ( ~ (v6 = 0) & subset(v4, v1) = v6))))) & ! [v3] : ! [v4] : ( ~ (subrelstr(v3, v0) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (( ~ (v5 = 0) & rel_str(v3) = v5) | (( ~ (v4 = 0) | (v8 = 0 & v6 = 0 & the_carrier(v3) = v5 & the_InternalRel(v3) = v7 & subset(v7, v2) = 0 & subset(v5, v1) = 0)) & (v4 = 0 | ( ~ (v8 = 0) & the_InternalRel(v3) = v7 & subset(v7, v2) = v8) | ( ~ (v6 = 0) & the_carrier(v3) = v5 & subset(v5, v1) = v6))))) & ! [v3] : ! [v4] : ( ~ (the_InternalRel(v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (( ~ (v5 = 0) & rel_str(v3) = v5) | (((v8 = 0 & v7 = 0 & the_carrier(v3) = v6 & subset(v6, v1) = 0 & subset(v4, v2) = 0) | ( ~ (v5 = 0) & subrelstr(v3, v0) = v5)) & ((v5 = 0 & subrelstr(v3, v0) = 0) | ( ~ (v8 = 0) & subset(v4, v2) = v8) | ( ~ (v7 = 0) & the_carrier(v3) = v6 & subset(v6, v1) = v7))))) & ! [v3] : ( ~ (rel_str(v3) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (((v8 = 0 & v6 = 0 & the_carrier(v3) = v5 & the_InternalRel(v3) = v7 & subset(v7, v2) = 0 & subset(v5, v1) = 0) | ( ~ (v4 = 0) & subrelstr(v3, v0) = v4)) & ((v4 = 0 & subrelstr(v3, v0) = 0) | ( ~ (v8 = 0) & the_InternalRel(v3) = v7 & subset(v7, v2) = v8) | ( ~ (v6 = 0) & the_carrier(v3) = v5 & subset(v5, v1) = v6))))))) & ! [v0] : ! [v1] : ( ~ (rel_str(v0) = 0) | ~ (subrelstr(v1, v0) = 0) | rel_str(v1) = 0) & ! [v0] : ! [v1] : ( ~ (the_InternalRel(v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & relation_of2_as_subset(v1, v2, v2) = 0 & the_carrier(v0) = v2) | ( ~ (v2 = 0) & rel_str(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (the_InternalRel(v0) = v1) | ? [v2] : (( ~ (v2 = 0) & rel_str(v0) = v2) | (the_carrier(v0) = v2 & ! [v3] : ! [v4] : ! [v5] : ( ~ (ordered_pair(v3, v4) = v5) | ~ (element(v3, v2) = 0) | ? [v6] : ? [v7] : (( ~ (v6 = 0) & element(v4, v2) = v6) | (((v7 = 0 & in(v5, v1) = 0) | ( ~ (v6 = 0) & related(v0, v3, v4) = v6)) & ((v6 = 0 & related(v0, v3, v4) = 0) | ( ~ (v7 = 0) & in(v5, v1) = v7))))) & ! [v3] : ! [v4] : ! [v5] : ( ~ (related(v0, v3, v4) = v5) | ~ (element(v3, v2) = 0) | ? [v6] : ? [v7] : (( ~ (v6 = 0) & element(v4, v2) = v6) | (( ~ (v5 = 0) | (v7 = 0 & ordered_pair(v3, v4) = v6 & in(v6, v1) = 0)) & (v5 = 0 | ( ~ (v7 = 0) & ordered_pair(v3, v4) = v6 & in(v6, v1) = v7))))) & ! [v3] : ! [v4] : ( ~ (element(v4, v2) = 0) | ~ (element(v3, v2) = 0) | ? [v5] : ? [v6] : ? [v7] : (((v7 = 0 & ordered_pair(v3, v4) = v6 & in(v6, v1) = 0) | ( ~ (v5 = 0) & related(v0, v3, v4) = v5)) & ((v5 = 0 & related(v0, v3, v4) = 0) | ( ~ (v7 = 0) & ordered_pair(v3, v4) = v6 & in(v6, v1) = v7))))))) & ! [v0] : ! [v1] : ( ~ (the_InternalRel(v0) = v1) | ? [v2] : (( ~ (v2 = 0) & rel_str(v0) = v2) | (the_carrier(v0) = v2 & ! [v3] : ! [v4] : ( ~ (the_carrier(v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (( ~ (v5 = 0) & rel_str(v3) = v5) | (((v8 = 0 & v6 = 0 & the_InternalRel(v3) = v7 & subset(v7, v1) = 0 & subset(v4, v2) = 0) | ( ~ (v5 = 0) & subrelstr(v3, v0) = v5)) & ((v5 = 0 & subrelstr(v3, v0) = 0) | ( ~ (v8 = 0) & the_InternalRel(v3) = v7 & subset(v7, v1) = v8) | ( ~ (v6 = 0) & subset(v4, v2) = v6))))) & ! [v3] : ! [v4] : ( ~ (subrelstr(v3, v0) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (( ~ (v5 = 0) & rel_str(v3) = v5) | (( ~ (v4 = 0) | (v8 = 0 & v6 = 0 & the_carrier(v3) = v5 & the_InternalRel(v3) = v7 & subset(v7, v1) = 0 & subset(v5, v2) = 0)) & (v4 = 0 | ( ~ (v8 = 0) & the_InternalRel(v3) = v7 & subset(v7, v1) = v8) | ( ~ (v6 = 0) & the_carrier(v3) = v5 & subset(v5, v2) = v6))))) & ! [v3] : ! [v4] : ( ~ (the_InternalRel(v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (( ~ (v5 = 0) & rel_str(v3) = v5) | (((v8 = 0 & v7 = 0 & the_carrier(v3) = v6 & subset(v6, v2) = 0 & subset(v4, v1) = 0) | ( ~ (v5 = 0) & subrelstr(v3, v0) = v5)) & ((v5 = 0 & subrelstr(v3, v0) = 0) | ( ~ (v8 = 0) & subset(v4, v1) = v8) | ( ~ (v7 = 0) & the_carrier(v3) = v6 & subset(v6, v2) = v7))))) & ! [v3] : ( ~ (rel_str(v3) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (((v8 = 0 & v6 = 0 & the_carrier(v3) = v5 & the_InternalRel(v3) = v7 & subset(v7, v1) = 0 & subset(v5, v2) = 0) | ( ~ (v4 = 0) & subrelstr(v3, v0) = v4)) & ((v4 = 0 & subrelstr(v3, v0) = 0) | ( ~ (v8 = 0) & the_InternalRel(v3) = v7 & subset(v7, v1) = v8) | ( ~ (v6 = 0) & the_carrier(v3) = v5 & subset(v5, v2) = v6))))))) & ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (powerset(v1) = v2 & element(v0, v2) = 0)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & v3 = 0 & ~ (v4 = 0) & element(v2, v1) = 0 & finite(v2) = 0 & empty(v2) = v4) | (v2 = 0 & empty(v0) = 0))) & ! [v0] : ! [v1] : ( ~ (element(v0, v1) = 0) | ? [v2] : ((v2 = 0 & empty(v1) = 0) | (v2 = 0 & in(v0, v1) = 0))) & ! [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] : ( ~ (rel_str(v0) = 0) | one_sorted_str(v0) = 0) & ! [v0] : ( ~ (rel_str(v0) = 0) | ? [v1] : ? [v2] : (relation_of2_as_subset(v1, v2, v2) = 0 & the_carrier(v0) = v2 & the_InternalRel(v0) = v1)) & ! [v0] : ( ~ (rel_str(v0) = 0) | ? [v1] : ? [v2] : (the_carrier(v0) = v1 & the_InternalRel(v0) = v2 & ! [v3] : ! [v4] : ! [v5] : ( ~ (ordered_pair(v3, v4) = v5) | ~ (element(v3, v1) = 0) | ? [v6] : ? [v7] : (( ~ (v6 = 0) & element(v4, v1) = v6) | (((v7 = 0 & in(v5, v2) = 0) | ( ~ (v6 = 0) & related(v0, v3, v4) = v6)) & ((v6 = 0 & related(v0, v3, v4) = 0) | ( ~ (v7 = 0) & in(v5, v2) = v7))))) & ! [v3] : ! [v4] : ! [v5] : ( ~ (related(v0, v3, v4) = v5) | ~ (element(v3, v1) = 0) | ? [v6] : ? [v7] : (( ~ (v6 = 0) & element(v4, v1) = v6) | (( ~ (v5 = 0) | (v7 = 0 & ordered_pair(v3, v4) = v6 & in(v6, v2) = 0)) & (v5 = 0 | ( ~ (v7 = 0) & ordered_pair(v3, v4) = v6 & in(v6, v2) = v7))))) & ! [v3] : ! [v4] : ( ~ (element(v4, v1) = 0) | ~ (element(v3, v1) = 0) | ? [v5] : ? [v6] : ? [v7] : (((v7 = 0 & ordered_pair(v3, v4) = v6 & in(v6, v2) = 0) | ( ~ (v5 = 0) & related(v0, v3, v4) = v5)) & ((v5 = 0 & related(v0, v3, v4) = 0) | ( ~ (v7 = 0) & ordered_pair(v3, v4) = v6 & in(v6, v2) = v7)))))) & ! [v0] : ( ~ (rel_str(v0) = 0) | ? [v1] : ? [v2] : (the_carrier(v0) = v1 & the_InternalRel(v0) = v2 & ! [v3] : ! [v4] : ( ~ (the_carrier(v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (( ~ (v5 = 0) & rel_str(v3) = v5) | (((v8 = 0 & v6 = 0 & the_InternalRel(v3) = v7 & subset(v7, v2) = 0 & subset(v4, v1) = 0) | ( ~ (v5 = 0) & subrelstr(v3, v0) = v5)) & ((v5 = 0 & subrelstr(v3, v0) = 0) | ( ~ (v8 = 0) & the_InternalRel(v3) = v7 & subset(v7, v2) = v8) | ( ~ (v6 = 0) & subset(v4, v1) = v6))))) & ! [v3] : ! [v4] : ( ~ (subrelstr(v3, v0) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (( ~ (v5 = 0) & rel_str(v3) = v5) | (( ~ (v4 = 0) | (v8 = 0 & v6 = 0 & the_carrier(v3) = v5 & the_InternalRel(v3) = v7 & subset(v7, v2) = 0 & subset(v5, v1) = 0)) & (v4 = 0 | ( ~ (v8 = 0) & the_InternalRel(v3) = v7 & subset(v7, v2) = v8) | ( ~ (v6 = 0) & the_carrier(v3) = v5 & subset(v5, v1) = v6))))) & ! [v3] : ! [v4] : ( ~ (the_InternalRel(v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (( ~ (v5 = 0) & rel_str(v3) = v5) | (((v8 = 0 & v7 = 0 & the_carrier(v3) = v6 & subset(v6, v1) = 0 & subset(v4, v2) = 0) | ( ~ (v5 = 0) & subrelstr(v3, v0) = v5)) & ((v5 = 0 & subrelstr(v3, v0) = 0) | ( ~ (v8 = 0) & subset(v4, v2) = v8) | ( ~ (v7 = 0) & the_carrier(v3) = v6 & subset(v6, v1) = v7))))) & ! [v3] : ( ~ (rel_str(v3) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (((v8 = 0 & v6 = 0 & the_carrier(v3) = v5 & the_InternalRel(v3) = v7 & subset(v7, v2) = 0 & subset(v5, v1) = 0) | ( ~ (v4 = 0) & subrelstr(v3, v0) = v4)) & ((v4 = 0 & subrelstr(v3, v0) = 0) | ( ~ (v8 = 0) & the_InternalRel(v3) = v7 & subset(v7, v2) = v8) | ( ~ (v6 = 0) & the_carrier(v3) = v5 & subset(v5, v1) = v6)))))) & ! [v0] : ( ~ (rel_str(v0) = 0) | ? [v1] : subrelstr(v1, v0) = 0) & ! [v0] : ( ~ (finite(v0) = 0) | ? [v1] : (powerset(v0) = v1 & ! [v2] : ! [v3] : (v3 = 0 | ~ (finite(v2) = v3) | ? [v4] : ( ~ (v4 = 0) & element(v2, v1) = v4)) & ! [v2] : ( ~ (element(v2, v1) = 0) | finite(v2) = 0))) & ! [v0] : ( ~ (empty(v0) = 0) | finite(v0) = 0) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : relation_of2(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : relation_of2_as_subset(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : related(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : relation_of2(v2, v0, v1) = 0 & ? [v0] : ? [v1] : ? [v2] : relation_of2_as_subset(v2, v0, v1) = 0 & ? [v0] : ? [v1] : ? [v2] : ordered_pair(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : subrelstr(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : cartesian_product2(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : element(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2 & ? [v0] : ? [v1] : one_sorted_str(v0) = v1 & ? [v0] : ? [v1] : the_carrier(v0) = v1 & ? [v0] : ? [v1] : rel_str(v0) = v1 & ? [v0] : ? [v1] : the_InternalRel(v0) = v1 & ? [v0] : ? [v1] : powerset(v0) = v1 & ? [v0] : ? [v1] : element(v1, v0) = 0 & ? [v0] : ? [v1] : relation(v0) = v1 & ? [v0] : ? [v1] : finite(v0) = v1 & ? [v0] : ? [v1] : empty(v0) = v1
% 66.14/30.79 |
% 66.14/30.79 | Applying alpha-rule on (1) yields:
% 66.14/30.79 | (2) finite(all_0_3_3) = 0
% 66.14/30.79 | (3) ? [v0] : ? [v1] : ? [v2] : cartesian_product2(v1, v0) = v2
% 66.14/30.79 | (4) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | element(v0, v1) = 0)
% 66.14/30.79 | (5) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & v3 = 0 & ~ (v4 = 0) & element(v2, v1) = 0 & finite(v2) = 0 & empty(v2) = v4) | (v2 = 0 & empty(v0) = 0)))
% 66.14/30.79 | (6) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v1) = v3 & element(v0, v3) = v4))
% 66.14/30.79 | (7) ! [v0] : ( ~ (finite(v0) = 0) | ? [v1] : (powerset(v0) = v1 & ! [v2] : ! [v3] : (v3 = 0 | ~ (finite(v2) = v3) | ? [v4] : ( ~ (v4 = 0) & element(v2, v1) = v4)) & ! [v2] : ( ~ (element(v2, v1) = 0) | finite(v2) = 0)))
% 66.14/30.79 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 66.14/30.79 | (9) ! [v0] : ! [v1] : ( ~ (the_InternalRel(v0) = v1) | ? [v2] : (( ~ (v2 = 0) & rel_str(v0) = v2) | (the_carrier(v0) = v2 & ! [v3] : ! [v4] : ( ~ (the_carrier(v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (( ~ (v5 = 0) & rel_str(v3) = v5) | (((v8 = 0 & v6 = 0 & the_InternalRel(v3) = v7 & subset(v7, v1) = 0 & subset(v4, v2) = 0) | ( ~ (v5 = 0) & subrelstr(v3, v0) = v5)) & ((v5 = 0 & subrelstr(v3, v0) = 0) | ( ~ (v8 = 0) & the_InternalRel(v3) = v7 & subset(v7, v1) = v8) | ( ~ (v6 = 0) & subset(v4, v2) = v6))))) & ! [v3] : ! [v4] : ( ~ (subrelstr(v3, v0) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (( ~ (v5 = 0) & rel_str(v3) = v5) | (( ~ (v4 = 0) | (v8 = 0 & v6 = 0 & the_carrier(v3) = v5 & the_InternalRel(v3) = v7 & subset(v7, v1) = 0 & subset(v5, v2) = 0)) & (v4 = 0 | ( ~ (v8 = 0) & the_InternalRel(v3) = v7 & subset(v7, v1) = v8) | ( ~ (v6 = 0) & the_carrier(v3) = v5 & subset(v5, v2) = v6))))) & ! [v3] : ! [v4] : ( ~ (the_InternalRel(v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (( ~ (v5 = 0) & rel_str(v3) = v5) | (((v8 = 0 & v7 = 0 & the_carrier(v3) = v6 & subset(v6, v2) = 0 & subset(v4, v1) = 0) | ( ~ (v5 = 0) & subrelstr(v3, v0) = v5)) & ((v5 = 0 & subrelstr(v3, v0) = 0) | ( ~ (v8 = 0) & subset(v4, v1) = v8) | ( ~ (v7 = 0) & the_carrier(v3) = v6 & subset(v6, v2) = v7))))) & ! [v3] : ( ~ (rel_str(v3) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (((v8 = 0 & v6 = 0 & the_carrier(v3) = v5 & the_InternalRel(v3) = v7 & subset(v7, v1) = 0 & subset(v5, v2) = 0) | ( ~ (v4 = 0) & subrelstr(v3, v0) = v4)) & ((v4 = 0 & subrelstr(v3, v0) = 0) | ( ~ (v8 = 0) & the_InternalRel(v3) = v7 & subset(v7, v1) = v8) | ( ~ (v6 = 0) & the_carrier(v3) = v5 & subset(v5, v2) = v6)))))))
% 66.14/30.80 | (10) one_sorted_str(all_0_1_1) = 0
% 66.14/30.80 | (11) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 66.14/30.80 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4))
% 66.14/30.80 | (13) ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2
% 66.14/30.80 | (14) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | subset(v0, v1) = 0)
% 66.14/30.80 | (15) ? [v0] : ? [v1] : ? [v2] : ? [v3] : related(v2, v1, v0) = v3
% 66.14/30.80 | (16) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v0, v1) = v2) | ? [v3] : ((v3 = 0 & empty(v1) = 0) | ( ~ (v3 = 0) & element(v0, v1) = v3)))
% 66.14/30.80 | (17) related(all_0_13_13, all_0_9_9, all_0_8_8) = all_0_7_7
% 66.14/30.80 | (18) empty(all_0_3_3) = all_0_2_2
% 66.14/30.80 | (19) ! [v0] : ( ~ (rel_str(v0) = 0) | ? [v1] : ? [v2] : (the_carrier(v0) = v1 & the_InternalRel(v0) = v2 & ! [v3] : ! [v4] : ! [v5] : ( ~ (ordered_pair(v3, v4) = v5) | ~ (element(v3, v1) = 0) | ? [v6] : ? [v7] : (( ~ (v6 = 0) & element(v4, v1) = v6) | (((v7 = 0 & in(v5, v2) = 0) | ( ~ (v6 = 0) & related(v0, v3, v4) = v6)) & ((v6 = 0 & related(v0, v3, v4) = 0) | ( ~ (v7 = 0) & in(v5, v2) = v7))))) & ! [v3] : ! [v4] : ! [v5] : ( ~ (related(v0, v3, v4) = v5) | ~ (element(v3, v1) = 0) | ? [v6] : ? [v7] : (( ~ (v6 = 0) & element(v4, v1) = v6) | (( ~ (v5 = 0) | (v7 = 0 & ordered_pair(v3, v4) = v6 & in(v6, v2) = 0)) & (v5 = 0 | ( ~ (v7 = 0) & ordered_pair(v3, v4) = v6 & in(v6, v2) = v7))))) & ! [v3] : ! [v4] : ( ~ (element(v4, v1) = 0) | ~ (element(v3, v1) = 0) | ? [v5] : ? [v6] : ? [v7] : (((v7 = 0 & ordered_pair(v3, v4) = v6 & in(v6, v2) = 0) | ( ~ (v5 = 0) & related(v0, v3, v4) = v5)) & ((v5 = 0 & related(v0, v3, v4) = 0) | ( ~ (v7 = 0) & ordered_pair(v3, v4) = v6 & in(v6, v2) = v7))))))
% 66.14/30.80 | (20) ! [v0] : ( ~ (rel_str(v0) = 0) | ? [v1] : subrelstr(v1, v0) = 0)
% 66.14/30.80 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0))
% 66.14/30.80 | (22) ? [v0] : ? [v1] : relation(v0) = v1
% 66.14/30.80 | (23) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 66.14/30.80 | (24) ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & relation_of2_as_subset(v2, v1, v1) = 0 & the_InternalRel(v0) = v2) | ( ~ (v2 = 0) & rel_str(v0) = v2)))
% 66.14/30.80 | (25) ! [v0] : ! [v1] : ( ~ (element(v0, v1) = 0) | ? [v2] : ((v2 = 0 & empty(v1) = 0) | (v2 = 0 & in(v0, v1) = 0)))
% 66.14/30.80 | (26) ? [v0] : ? [v1] : ? [v2] : ordered_pair(v1, v0) = v2
% 66.14/30.80 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0))
% 66.14/30.80 | (28) the_carrier(all_0_13_13) = all_0_12_12
% 66.14/30.80 | (29) ? [v0] : ? [v1] : the_InternalRel(v0) = v1
% 66.14/30.80 | (30) ! [v0] : ! [v1] : (v1 = 0 | ~ (finite(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2))
% 66.14/30.80 | (31) ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ? [v2] : (( ~ (v2 = 0) & rel_str(v0) = v2) | (the_InternalRel(v0) = v2 & ! [v3] : ! [v4] : ( ~ (the_carrier(v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (( ~ (v5 = 0) & rel_str(v3) = v5) | (((v8 = 0 & v6 = 0 & the_InternalRel(v3) = v7 & subset(v7, v2) = 0 & subset(v4, v1) = 0) | ( ~ (v5 = 0) & subrelstr(v3, v0) = v5)) & ((v5 = 0 & subrelstr(v3, v0) = 0) | ( ~ (v8 = 0) & the_InternalRel(v3) = v7 & subset(v7, v2) = v8) | ( ~ (v6 = 0) & subset(v4, v1) = v6))))) & ! [v3] : ! [v4] : ( ~ (subrelstr(v3, v0) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (( ~ (v5 = 0) & rel_str(v3) = v5) | (( ~ (v4 = 0) | (v8 = 0 & v6 = 0 & the_carrier(v3) = v5 & the_InternalRel(v3) = v7 & subset(v7, v2) = 0 & subset(v5, v1) = 0)) & (v4 = 0 | ( ~ (v8 = 0) & the_InternalRel(v3) = v7 & subset(v7, v2) = v8) | ( ~ (v6 = 0) & the_carrier(v3) = v5 & subset(v5, v1) = v6))))) & ! [v3] : ! [v4] : ( ~ (the_InternalRel(v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (( ~ (v5 = 0) & rel_str(v3) = v5) | (((v8 = 0 & v7 = 0 & the_carrier(v3) = v6 & subset(v6, v1) = 0 & subset(v4, v2) = 0) | ( ~ (v5 = 0) & subrelstr(v3, v0) = v5)) & ((v5 = 0 & subrelstr(v3, v0) = 0) | ( ~ (v8 = 0) & subset(v4, v2) = v8) | ( ~ (v7 = 0) & the_carrier(v3) = v6 & subset(v6, v1) = v7))))) & ! [v3] : ( ~ (rel_str(v3) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (((v8 = 0 & v6 = 0 & the_carrier(v3) = v5 & the_InternalRel(v3) = v7 & subset(v7, v2) = 0 & subset(v5, v1) = 0) | ( ~ (v4 = 0) & subrelstr(v3, v0) = v4)) & ((v4 = 0 & subrelstr(v3, v0) = 0) | ( ~ (v8 = 0) & the_InternalRel(v3) = v7 & subset(v7, v2) = v8) | ( ~ (v6 = 0) & the_carrier(v3) = v5 & subset(v5, v1) = v6)))))))
% 66.14/30.81 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (related(v4, v3, v2) = v1) | ~ (related(v4, v3, v2) = v0))
% 66.14/30.81 | (33) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (rel_str(v1) = v2) | ~ (rel_str(v0) = 0) | ? [v3] : ( ~ (v3 = 0) & subrelstr(v1, v0) = v3))
% 66.14/30.81 | (34) element(all_0_8_8, all_0_10_10) = 0
% 66.14/30.81 | (35) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (rel_str(v2) = v1) | ~ (rel_str(v2) = v0))
% 66.14/30.81 | (36) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1))
% 66.14/30.81 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (relation_of2_as_subset(v2, v0, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & relation_of2(v2, v0, v1) = v4))
% 66.14/30.81 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (relation_of2(v2, v0, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & relation_of2_as_subset(v2, v0, v1) = v4))
% 66.14/30.81 | (39) ! [v0] : ! [v1] : ! [v2] : ( ~ (empty(v2) = 0) | ~ (in(v0, v1) = 0) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v2) = v3 & element(v1, v3) = v4))
% 66.14/30.81 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v0) = v1) | ~ (finite(v2) = v3) | ? [v4] : (( ~ (v4 = 0) & element(v2, v1) = v4) | ( ~ (v4 = 0) & finite(v0) = v4)))
% 66.14/30.81 | (41) ! [v0] : ! [v1] : ! [v2] : ( ~ (cartesian_product2(v0, v1) = v2) | ? [v3] : ((v3 = 0 & finite(v2) = 0) | ( ~ (v3 = 0) & finite(v1) = v3) | ( ~ (v3 = 0) & finite(v0) = v3)))
% 66.14/30.81 | (42) ! [v0] : ! [v1] : (v1 = 0 | ~ (one_sorted_str(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & rel_str(v0) = v2))
% 66.14/30.81 | (43) empty(empty_set) = 0
% 66.14/30.81 | (44) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (finite(v2) = v1) | ~ (finite(v2) = v0))
% 66.14/30.81 | (45) ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ? [v2] : (( ~ (v2 = 0) & rel_str(v0) = v2) | (the_InternalRel(v0) = v2 & ! [v3] : ! [v4] : ! [v5] : ( ~ (ordered_pair(v3, v4) = v5) | ~ (element(v3, v1) = 0) | ? [v6] : ? [v7] : (( ~ (v6 = 0) & element(v4, v1) = v6) | (((v7 = 0 & in(v5, v2) = 0) | ( ~ (v6 = 0) & related(v0, v3, v4) = v6)) & ((v6 = 0 & related(v0, v3, v4) = 0) | ( ~ (v7 = 0) & in(v5, v2) = v7))))) & ! [v3] : ! [v4] : ! [v5] : ( ~ (related(v0, v3, v4) = v5) | ~ (element(v3, v1) = 0) | ? [v6] : ? [v7] : (( ~ (v6 = 0) & element(v4, v1) = v6) | (( ~ (v5 = 0) | (v7 = 0 & ordered_pair(v3, v4) = v6 & in(v6, v2) = 0)) & (v5 = 0 | ( ~ (v7 = 0) & ordered_pair(v3, v4) = v6 & in(v6, v2) = v7))))) & ! [v3] : ! [v4] : ( ~ (element(v4, v1) = 0) | ~ (element(v3, v1) = 0) | ? [v5] : ? [v6] : ? [v7] : (((v7 = 0 & ordered_pair(v3, v4) = v6 & in(v6, v2) = 0) | ( ~ (v5 = 0) & related(v0, v3, v4) = v5)) & ((v5 = 0 & related(v0, v3, v4) = 0) | ( ~ (v7 = 0) & ordered_pair(v3, v4) = v6 & in(v6, v2) = v7)))))))
% 66.14/30.81 | (46) subrelstr(all_0_11_11, all_0_13_13) = 0
% 66.14/30.81 | (47) ! [v0] : ! [v1] : ( ~ (the_InternalRel(v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & relation_of2_as_subset(v1, v2, v2) = 0 & the_carrier(v0) = v2) | ( ~ (v2 = 0) & rel_str(v0) = v2)))
% 66.14/30.81 | (48) empty(all_0_6_6) = all_0_5_5
% 66.14/30.81 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 66.14/30.81 | (50) ? [v0] : ? [v1] : one_sorted_str(v0) = v1
% 66.14/30.81 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v0, v1) = v3) | ~ (powerset(v3) = v4) | ~ (element(v2, v4) = 0) | relation(v2) = 0)
% 66.14/30.81 | (52) empty(all_0_4_4) = 0
% 66.14/30.81 | (53) ? [v0] : ? [v1] : ? [v2] : ? [v3] : relation_of2_as_subset(v2, v1, v0) = v3
% 66.14/30.81 | (54) ~ (all_0_5_5 = 0)
% 66.14/30.81 | (55) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3))
% 66.14/30.81 | (56) ? [v0] : ? [v1] : ? [v2] : relation_of2(v2, v0, v1) = 0
% 66.14/30.81 | (57) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 66.14/30.81 | (58) ~ (all_0_2_2 = 0)
% 66.14/30.81 | (59) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0))
% 66.14/30.82 | (60) related(all_0_11_11, all_0_9_9, all_0_8_8) = 0
% 66.14/30.82 | (61) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0))
% 66.14/30.82 | (62) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0))
% 66.14/30.82 | (63) ? [v0] : ? [v1] : ? [v2] : subrelstr(v1, v0) = v2
% 66.14/30.82 | (64) rel_str(all_0_13_13) = 0
% 66.14/30.82 | (65) ! [v0] : ( ~ (empty(v0) = 0) | finite(v0) = 0)
% 66.14/30.82 | (66) ? [v0] : ? [v1] : ? [v2] : relation_of2_as_subset(v2, v0, v1) = 0
% 66.14/30.82 | (67) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (relation_of2_as_subset(v4, v3, v2) = v1) | ~ (relation_of2_as_subset(v4, v3, v2) = v0))
% 66.14/30.82 | (68) ? [v0] : ? [v1] : the_carrier(v0) = v1
% 66.14/30.82 | (69) element(all_0_9_9, all_0_12_12) = 0
% 66.14/30.82 | (70) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (the_carrier(v2) = v1) | ~ (the_carrier(v2) = v0))
% 66.14/30.82 | (71) ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2
% 66.14/30.82 | (72) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0))
% 66.14/30.82 | (73) ! [v0] : ( ~ (rel_str(v0) = 0) | one_sorted_str(v0) = 0)
% 66.14/30.82 | (74) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ (element(v2, v1) = 0) | ? [v3] : ((v3 = 0 & finite(v2) = 0) | ( ~ (v3 = 0) & finite(v0) = v3)))
% 66.14/30.82 | (75) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 66.14/30.82 | (76) ? [v0] : ? [v1] : ? [v2] : ? [v3] : relation_of2(v2, v1, v0) = v3
% 66.14/30.82 | (77) ! [v0] : ( ~ (rel_str(v0) = 0) | ? [v1] : ? [v2] : (relation_of2_as_subset(v1, v2, v2) = 0 & the_carrier(v0) = v2 & the_InternalRel(v0) = v1))
% 66.14/30.82 | (78) rel_str(all_0_0_0) = 0
% 66.14/30.82 | (79) element(all_0_8_8, all_0_12_12) = 0
% 66.14/30.82 | (80) ~ (all_0_7_7 = 0)
% 66.14/30.82 | (81) ! [v0] : ! [v1] : ( ~ (rel_str(v0) = 0) | ~ (subrelstr(v1, v0) = 0) | rel_str(v1) = 0)
% 66.14/30.82 | (82) ? [v0] : ? [v1] : finite(v0) = v1
% 66.14/30.82 | (83) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (cartesian_product2(v0, v1) = v3) | ~ (powerset(v3) = v4) | ~ (element(v2, v4) = v5) | ? [v6] : ( ~ (v6 = 0) & relation_of2_as_subset(v2, v0, v1) = v6))
% 66.14/30.82 | (84) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (element(v0, v2) = v4) | ? [v5] : ( ~ (v5 = 0) & in(v0, v1) = v5))
% 66.14/30.82 | (85) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (relation_of2(v4, v3, v2) = v1) | ~ (relation_of2(v4, v3, v2) = v0))
% 66.14/30.82 | (86) ? [v0] : ? [v1] : ? [v2] : element(v1, v0) = v2
% 66.14/30.82 | (87) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (the_InternalRel(v2) = v1) | ~ (the_InternalRel(v2) = v0))
% 66.14/30.82 | (88) ! [v0] : ! [v1] : (v1 = 0 | ~ (empty(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v0) = v2 & element(v3, v2) = 0 & finite(v3) = 0 & empty(v3) = v4))
% 66.14/30.82 | (89) ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2))
% 66.14/30.82 | (90) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (one_sorted_str(v2) = v1) | ~ (one_sorted_str(v2) = v0))
% 66.14/30.82 | (91) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (element(v0, v2) = v3) | ~ (in(v0, v1) = 0) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & powerset(v2) = v4 & element(v1, v4) = v5))
% 66.14/30.82 | (92) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subrelstr(v3, v2) = v1) | ~ (subrelstr(v3, v2) = v0))
% 66.14/30.82 | (93) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | element(v0, v2) = 0)
% 66.14/30.82 | (94) ! [v0] : ( ~ (rel_str(v0) = 0) | ? [v1] : ? [v2] : (the_carrier(v0) = v1 & the_InternalRel(v0) = v2 & ! [v3] : ! [v4] : ( ~ (the_carrier(v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (( ~ (v5 = 0) & rel_str(v3) = v5) | (((v8 = 0 & v6 = 0 & the_InternalRel(v3) = v7 & subset(v7, v2) = 0 & subset(v4, v1) = 0) | ( ~ (v5 = 0) & subrelstr(v3, v0) = v5)) & ((v5 = 0 & subrelstr(v3, v0) = 0) | ( ~ (v8 = 0) & the_InternalRel(v3) = v7 & subset(v7, v2) = v8) | ( ~ (v6 = 0) & subset(v4, v1) = v6))))) & ! [v3] : ! [v4] : ( ~ (subrelstr(v3, v0) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (( ~ (v5 = 0) & rel_str(v3) = v5) | (( ~ (v4 = 0) | (v8 = 0 & v6 = 0 & the_carrier(v3) = v5 & the_InternalRel(v3) = v7 & subset(v7, v2) = 0 & subset(v5, v1) = 0)) & (v4 = 0 | ( ~ (v8 = 0) & the_InternalRel(v3) = v7 & subset(v7, v2) = v8) | ( ~ (v6 = 0) & the_carrier(v3) = v5 & subset(v5, v1) = v6))))) & ! [v3] : ! [v4] : ( ~ (the_InternalRel(v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (( ~ (v5 = 0) & rel_str(v3) = v5) | (((v8 = 0 & v7 = 0 & the_carrier(v3) = v6 & subset(v6, v1) = 0 & subset(v4, v2) = 0) | ( ~ (v5 = 0) & subrelstr(v3, v0) = v5)) & ((v5 = 0 & subrelstr(v3, v0) = 0) | ( ~ (v8 = 0) & subset(v4, v2) = v8) | ( ~ (v7 = 0) & the_carrier(v3) = v6 & subset(v6, v1) = v7))))) & ! [v3] : ( ~ (rel_str(v3) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (((v8 = 0 & v6 = 0 & the_carrier(v3) = v5 & the_InternalRel(v3) = v7 & subset(v7, v2) = 0 & subset(v5, v1) = 0) | ( ~ (v4 = 0) & subrelstr(v3, v0) = v4)) & ((v4 = 0 & subrelstr(v3, v0) = 0) | ( ~ (v8 = 0) & the_InternalRel(v3) = v7 & subset(v7, v2) = v8) | ( ~ (v6 = 0) & the_carrier(v3) = v5 & subset(v5, v1) = v6))))))
% 66.14/30.83 | (95) the_carrier(all_0_11_11) = all_0_10_10
% 66.14/30.83 | (96) ? [v0] : ? [v1] : powerset(v0) = v1
% 66.14/30.83 | (97) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_of2_as_subset(v2, v0, v1) = 0) | relation_of2(v2, v0, v1) = 0)
% 66.14/30.83 | (98) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_of2(v2, v0, v1) = 0) | relation_of2_as_subset(v2, v0, v1) = 0)
% 66.14/30.83 | (99) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0))
% 66.14/30.83 | (100) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (powerset(v1) = v2 & element(v0, v2) = 0))
% 66.14/30.83 | (101) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_of2_as_subset(v2, v0, v1) = 0) | ? [v3] : ? [v4] : (cartesian_product2(v0, v1) = v3 & powerset(v3) = v4 & element(v2, v4) = 0))
% 66.14/30.83 | (102) ? [v0] : ? [v1] : empty(v0) = v1
% 66.14/30.83 | (103) ! [v0] : ! [v1] : ( ~ (the_InternalRel(v0) = v1) | ? [v2] : (( ~ (v2 = 0) & rel_str(v0) = v2) | (the_carrier(v0) = v2 & ! [v3] : ! [v4] : ! [v5] : ( ~ (ordered_pair(v3, v4) = v5) | ~ (element(v3, v2) = 0) | ? [v6] : ? [v7] : (( ~ (v6 = 0) & element(v4, v2) = v6) | (((v7 = 0 & in(v5, v1) = 0) | ( ~ (v6 = 0) & related(v0, v3, v4) = v6)) & ((v6 = 0 & related(v0, v3, v4) = 0) | ( ~ (v7 = 0) & in(v5, v1) = v7))))) & ! [v3] : ! [v4] : ! [v5] : ( ~ (related(v0, v3, v4) = v5) | ~ (element(v3, v2) = 0) | ? [v6] : ? [v7] : (( ~ (v6 = 0) & element(v4, v2) = v6) | (( ~ (v5 = 0) | (v7 = 0 & ordered_pair(v3, v4) = v6 & in(v6, v1) = 0)) & (v5 = 0 | ( ~ (v7 = 0) & ordered_pair(v3, v4) = v6 & in(v6, v1) = v7))))) & ! [v3] : ! [v4] : ( ~ (element(v4, v2) = 0) | ~ (element(v3, v2) = 0) | ? [v5] : ? [v6] : ? [v7] : (((v7 = 0 & ordered_pair(v3, v4) = v6 & in(v6, v1) = 0) | ( ~ (v5 = 0) & related(v0, v3, v4) = v5)) & ((v5 = 0 & related(v0, v3, v4) = 0) | ( ~ (v7 = 0) & ordered_pair(v3, v4) = v6 & in(v6, v1) = v7)))))))
% 66.14/30.83 | (104) ? [v0] : ? [v1] : element(v1, v0) = 0
% 66.14/30.83 | (105) element(all_0_9_9, all_0_10_10) = 0
% 66.14/30.83 | (106) ? [v0] : ? [v1] : rel_str(v0) = v1
% 66.14/30.83 |
% 66.14/30.83 | Instantiating formula (24) with all_0_10_10, all_0_11_11 and discharging atoms the_carrier(all_0_11_11) = all_0_10_10, yields:
% 66.14/30.83 | (107) ? [v0] : ? [v1] : ((v1 = 0 & relation_of2_as_subset(v0, all_0_10_10, all_0_10_10) = 0 & the_InternalRel(all_0_11_11) = v0) | ( ~ (v0 = 0) & rel_str(all_0_11_11) = v0))
% 66.14/30.83 |
% 66.14/30.83 | Instantiating formula (45) with all_0_10_10, all_0_11_11 and discharging atoms the_carrier(all_0_11_11) = all_0_10_10, yields:
% 66.14/30.83 | (108) ? [v0] : (( ~ (v0 = 0) & rel_str(all_0_11_11) = v0) | (the_InternalRel(all_0_11_11) = v0 & ! [v1] : ! [v2] : ! [v3] : ( ~ (ordered_pair(v1, v2) = v3) | ~ (element(v1, all_0_10_10) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & element(v2, all_0_10_10) = v4) | (((v5 = 0 & in(v3, v0) = 0) | ( ~ (v4 = 0) & related(all_0_11_11, v1, v2) = v4)) & ((v4 = 0 & related(all_0_11_11, v1, v2) = 0) | ( ~ (v5 = 0) & in(v3, v0) = v5))))) & ! [v1] : ! [v2] : ! [v3] : ( ~ (related(all_0_11_11, v1, v2) = v3) | ~ (element(v1, all_0_10_10) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & element(v2, all_0_10_10) = v4) | (( ~ (v3 = 0) | (v5 = 0 & ordered_pair(v1, v2) = v4 & in(v4, v0) = 0)) & (v3 = 0 | ( ~ (v5 = 0) & ordered_pair(v1, v2) = v4 & in(v4, v0) = v5))))) & ! [v1] : ! [v2] : ( ~ (element(v2, all_0_10_10) = 0) | ~ (element(v1, all_0_10_10) = 0) | ? [v3] : ? [v4] : ? [v5] : (((v5 = 0 & ordered_pair(v1, v2) = v4 & in(v4, v0) = 0) | ( ~ (v3 = 0) & related(all_0_11_11, v1, v2) = v3)) & ((v3 = 0 & related(all_0_11_11, v1, v2) = 0) | ( ~ (v5 = 0) & ordered_pair(v1, v2) = v4 & in(v4, v0) = v5))))))
% 66.14/30.83 |
% 66.14/30.83 | Instantiating formula (31) with all_0_10_10, all_0_11_11 and discharging atoms the_carrier(all_0_11_11) = all_0_10_10, yields:
% 66.14/30.83 | (109) ? [v0] : (( ~ (v0 = 0) & rel_str(all_0_11_11) = v0) | (the_InternalRel(all_0_11_11) = v0 & ! [v1] : ! [v2] : ( ~ (the_carrier(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (( ~ (v3 = 0) & rel_str(v1) = v3) | (((v6 = 0 & v4 = 0 & the_InternalRel(v1) = v5 & subset(v5, v0) = 0 & subset(v2, all_0_10_10) = 0) | ( ~ (v3 = 0) & subrelstr(v1, all_0_11_11) = v3)) & ((v3 = 0 & subrelstr(v1, all_0_11_11) = 0) | ( ~ (v6 = 0) & the_InternalRel(v1) = v5 & subset(v5, v0) = v6) | ( ~ (v4 = 0) & subset(v2, all_0_10_10) = v4))))) & ! [v1] : ! [v2] : ( ~ (subrelstr(v1, all_0_11_11) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (( ~ (v3 = 0) & rel_str(v1) = v3) | (( ~ (v2 = 0) | (v6 = 0 & v4 = 0 & the_carrier(v1) = v3 & the_InternalRel(v1) = v5 & subset(v5, v0) = 0 & subset(v3, all_0_10_10) = 0)) & (v2 = 0 | ( ~ (v6 = 0) & the_InternalRel(v1) = v5 & subset(v5, v0) = v6) | ( ~ (v4 = 0) & the_carrier(v1) = v3 & subset(v3, all_0_10_10) = v4))))) & ! [v1] : ! [v2] : ( ~ (the_InternalRel(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (( ~ (v3 = 0) & rel_str(v1) = v3) | (((v6 = 0 & v5 = 0 & the_carrier(v1) = v4 & subset(v4, all_0_10_10) = 0 & subset(v2, v0) = 0) | ( ~ (v3 = 0) & subrelstr(v1, all_0_11_11) = v3)) & ((v3 = 0 & subrelstr(v1, all_0_11_11) = 0) | ( ~ (v6 = 0) & subset(v2, v0) = v6) | ( ~ (v5 = 0) & the_carrier(v1) = v4 & subset(v4, all_0_10_10) = v5))))) & ! [v1] : ( ~ (rel_str(v1) = 0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (((v6 = 0 & v4 = 0 & the_carrier(v1) = v3 & the_InternalRel(v1) = v5 & subset(v5, v0) = 0 & subset(v3, all_0_10_10) = 0) | ( ~ (v2 = 0) & subrelstr(v1, all_0_11_11) = v2)) & ((v2 = 0 & subrelstr(v1, all_0_11_11) = 0) | ( ~ (v6 = 0) & the_InternalRel(v1) = v5 & subset(v5, v0) = v6) | ( ~ (v4 = 0) & the_carrier(v1) = v3 & subset(v3, all_0_10_10) = v4))))))
% 66.14/30.84 |
% 66.14/30.84 | Instantiating formula (24) with all_0_12_12, all_0_13_13 and discharging atoms the_carrier(all_0_13_13) = all_0_12_12, yields:
% 66.14/30.84 | (110) ? [v0] : ? [v1] : ((v1 = 0 & relation_of2_as_subset(v0, all_0_12_12, all_0_12_12) = 0 & the_InternalRel(all_0_13_13) = v0) | ( ~ (v0 = 0) & rel_str(all_0_13_13) = v0))
% 66.14/30.84 |
% 66.14/30.84 | Instantiating formula (45) with all_0_12_12, all_0_13_13 and discharging atoms the_carrier(all_0_13_13) = all_0_12_12, yields:
% 66.14/30.84 | (111) ? [v0] : (( ~ (v0 = 0) & rel_str(all_0_13_13) = v0) | (the_InternalRel(all_0_13_13) = v0 & ! [v1] : ! [v2] : ! [v3] : ( ~ (ordered_pair(v1, v2) = v3) | ~ (element(v1, all_0_12_12) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & element(v2, all_0_12_12) = v4) | (((v5 = 0 & in(v3, v0) = 0) | ( ~ (v4 = 0) & related(all_0_13_13, v1, v2) = v4)) & ((v4 = 0 & related(all_0_13_13, v1, v2) = 0) | ( ~ (v5 = 0) & in(v3, v0) = v5))))) & ! [v1] : ! [v2] : ! [v3] : ( ~ (related(all_0_13_13, v1, v2) = v3) | ~ (element(v1, all_0_12_12) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & element(v2, all_0_12_12) = v4) | (( ~ (v3 = 0) | (v5 = 0 & ordered_pair(v1, v2) = v4 & in(v4, v0) = 0)) & (v3 = 0 | ( ~ (v5 = 0) & ordered_pair(v1, v2) = v4 & in(v4, v0) = v5))))) & ! [v1] : ! [v2] : ( ~ (element(v2, all_0_12_12) = 0) | ~ (element(v1, all_0_12_12) = 0) | ? [v3] : ? [v4] : ? [v5] : (((v5 = 0 & ordered_pair(v1, v2) = v4 & in(v4, v0) = 0) | ( ~ (v3 = 0) & related(all_0_13_13, v1, v2) = v3)) & ((v3 = 0 & related(all_0_13_13, v1, v2) = 0) | ( ~ (v5 = 0) & ordered_pair(v1, v2) = v4 & in(v4, v0) = v5))))))
% 66.14/30.84 |
% 66.14/30.84 | Instantiating formula (31) with all_0_12_12, all_0_13_13 and discharging atoms the_carrier(all_0_13_13) = all_0_12_12, yields:
% 66.14/30.84 | (112) ? [v0] : (( ~ (v0 = 0) & rel_str(all_0_13_13) = v0) | (the_InternalRel(all_0_13_13) = v0 & ! [v1] : ! [v2] : ( ~ (the_carrier(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (( ~ (v3 = 0) & rel_str(v1) = v3) | (((v6 = 0 & v4 = 0 & the_InternalRel(v1) = v5 & subset(v5, v0) = 0 & subset(v2, all_0_12_12) = 0) | ( ~ (v3 = 0) & subrelstr(v1, all_0_13_13) = v3)) & ((v3 = 0 & subrelstr(v1, all_0_13_13) = 0) | ( ~ (v6 = 0) & the_InternalRel(v1) = v5 & subset(v5, v0) = v6) | ( ~ (v4 = 0) & subset(v2, all_0_12_12) = v4))))) & ! [v1] : ! [v2] : ( ~ (subrelstr(v1, all_0_13_13) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (( ~ (v3 = 0) & rel_str(v1) = v3) | (( ~ (v2 = 0) | (v6 = 0 & v4 = 0 & the_carrier(v1) = v3 & the_InternalRel(v1) = v5 & subset(v5, v0) = 0 & subset(v3, all_0_12_12) = 0)) & (v2 = 0 | ( ~ (v6 = 0) & the_InternalRel(v1) = v5 & subset(v5, v0) = v6) | ( ~ (v4 = 0) & the_carrier(v1) = v3 & subset(v3, all_0_12_12) = v4))))) & ! [v1] : ! [v2] : ( ~ (the_InternalRel(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (( ~ (v3 = 0) & rel_str(v1) = v3) | (((v6 = 0 & v5 = 0 & the_carrier(v1) = v4 & subset(v4, all_0_12_12) = 0 & subset(v2, v0) = 0) | ( ~ (v3 = 0) & subrelstr(v1, all_0_13_13) = v3)) & ((v3 = 0 & subrelstr(v1, all_0_13_13) = 0) | ( ~ (v6 = 0) & subset(v2, v0) = v6) | ( ~ (v5 = 0) & the_carrier(v1) = v4 & subset(v4, all_0_12_12) = v5))))) & ! [v1] : ( ~ (rel_str(v1) = 0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (((v6 = 0 & v4 = 0 & the_carrier(v1) = v3 & the_InternalRel(v1) = v5 & subset(v5, v0) = 0 & subset(v3, all_0_12_12) = 0) | ( ~ (v2 = 0) & subrelstr(v1, all_0_13_13) = v2)) & ((v2 = 0 & subrelstr(v1, all_0_13_13) = 0) | ( ~ (v6 = 0) & the_InternalRel(v1) = v5 & subset(v5, v0) = v6) | ( ~ (v4 = 0) & the_carrier(v1) = v3 & subset(v3, all_0_12_12) = v4))))))
% 66.14/30.85 |
% 66.14/30.85 | Instantiating formula (77) with all_0_13_13 and discharging atoms rel_str(all_0_13_13) = 0, yields:
% 66.14/30.85 | (113) ? [v0] : ? [v1] : (relation_of2_as_subset(v0, v1, v1) = 0 & the_carrier(all_0_13_13) = v1 & the_InternalRel(all_0_13_13) = v0)
% 66.14/30.85 |
% 66.14/30.85 | Instantiating formula (19) with all_0_13_13 and discharging atoms rel_str(all_0_13_13) = 0, yields:
% 66.14/30.85 | (114) ? [v0] : ? [v1] : (the_carrier(all_0_13_13) = v0 & the_InternalRel(all_0_13_13) = v1 & ! [v2] : ! [v3] : ! [v4] : ( ~ (ordered_pair(v2, v3) = v4) | ~ (element(v2, v0) = 0) | ? [v5] : ? [v6] : (( ~ (v5 = 0) & element(v3, v0) = v5) | (((v6 = 0 & in(v4, v1) = 0) | ( ~ (v5 = 0) & related(all_0_13_13, v2, v3) = v5)) & ((v5 = 0 & related(all_0_13_13, v2, v3) = 0) | ( ~ (v6 = 0) & in(v4, v1) = v6))))) & ! [v2] : ! [v3] : ! [v4] : ( ~ (related(all_0_13_13, v2, v3) = v4) | ~ (element(v2, v0) = 0) | ? [v5] : ? [v6] : (( ~ (v5 = 0) & element(v3, v0) = v5) | (( ~ (v4 = 0) | (v6 = 0 & ordered_pair(v2, v3) = v5 & in(v5, v1) = 0)) & (v4 = 0 | ( ~ (v6 = 0) & ordered_pair(v2, v3) = v5 & in(v5, v1) = v6))))) & ! [v2] : ! [v3] : ( ~ (element(v3, v0) = 0) | ~ (element(v2, v0) = 0) | ? [v4] : ? [v5] : ? [v6] : (((v6 = 0 & ordered_pair(v2, v3) = v5 & in(v5, v1) = 0) | ( ~ (v4 = 0) & related(all_0_13_13, v2, v3) = v4)) & ((v4 = 0 & related(all_0_13_13, v2, v3) = 0) | ( ~ (v6 = 0) & ordered_pair(v2, v3) = v5 & in(v5, v1) = v6)))))
% 66.14/30.85 |
% 66.14/30.85 | Instantiating formula (94) with all_0_13_13 and discharging atoms rel_str(all_0_13_13) = 0, yields:
% 66.14/30.85 | (115) ? [v0] : ? [v1] : (the_carrier(all_0_13_13) = v0 & the_InternalRel(all_0_13_13) = v1 & ! [v2] : ! [v3] : ( ~ (the_carrier(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (( ~ (v4 = 0) & rel_str(v2) = v4) | (((v7 = 0 & v5 = 0 & the_InternalRel(v2) = v6 & subset(v6, v1) = 0 & subset(v3, v0) = 0) | ( ~ (v4 = 0) & subrelstr(v2, all_0_13_13) = v4)) & ((v4 = 0 & subrelstr(v2, all_0_13_13) = 0) | ( ~ (v7 = 0) & the_InternalRel(v2) = v6 & subset(v6, v1) = v7) | ( ~ (v5 = 0) & subset(v3, v0) = v5))))) & ! [v2] : ! [v3] : ( ~ (subrelstr(v2, all_0_13_13) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (( ~ (v4 = 0) & rel_str(v2) = v4) | (( ~ (v3 = 0) | (v7 = 0 & v5 = 0 & the_carrier(v2) = v4 & the_InternalRel(v2) = v6 & subset(v6, v1) = 0 & subset(v4, v0) = 0)) & (v3 = 0 | ( ~ (v7 = 0) & the_InternalRel(v2) = v6 & subset(v6, v1) = v7) | ( ~ (v5 = 0) & the_carrier(v2) = v4 & subset(v4, v0) = v5))))) & ! [v2] : ! [v3] : ( ~ (the_InternalRel(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (( ~ (v4 = 0) & rel_str(v2) = v4) | (((v7 = 0 & v6 = 0 & the_carrier(v2) = v5 & subset(v5, v0) = 0 & subset(v3, v1) = 0) | ( ~ (v4 = 0) & subrelstr(v2, all_0_13_13) = v4)) & ((v4 = 0 & subrelstr(v2, all_0_13_13) = 0) | ( ~ (v7 = 0) & subset(v3, v1) = v7) | ( ~ (v6 = 0) & the_carrier(v2) = v5 & subset(v5, v0) = v6))))) & ! [v2] : ( ~ (rel_str(v2) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (((v7 = 0 & v5 = 0 & the_carrier(v2) = v4 & the_InternalRel(v2) = v6 & subset(v6, v1) = 0 & subset(v4, v0) = 0) | ( ~ (v3 = 0) & subrelstr(v2, all_0_13_13) = v3)) & ((v3 = 0 & subrelstr(v2, all_0_13_13) = 0) | ( ~ (v7 = 0) & the_InternalRel(v2) = v6 & subset(v6, v1) = v7) | ( ~ (v5 = 0) & the_carrier(v2) = v4 & subset(v4, v0) = v5)))))
% 66.14/30.85 |
% 66.14/30.85 | Instantiating formula (81) with all_0_11_11, all_0_13_13 and discharging atoms rel_str(all_0_13_13) = 0, subrelstr(all_0_11_11, all_0_13_13) = 0, yields:
% 66.14/30.85 | (116) rel_str(all_0_11_11) = 0
% 66.14/30.85 |
% 66.14/30.85 | Instantiating (111) with all_59_0_72 yields:
% 66.14/30.85 | (117) ( ~ (all_59_0_72 = 0) & rel_str(all_0_13_13) = all_59_0_72) | (the_InternalRel(all_0_13_13) = all_59_0_72 & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ (element(v0, all_0_12_12) = 0) | ? [v3] : ? [v4] : (( ~ (v3 = 0) & element(v1, all_0_12_12) = v3) | (((v4 = 0 & in(v2, all_59_0_72) = 0) | ( ~ (v3 = 0) & related(all_0_13_13, v0, v1) = v3)) & ((v3 = 0 & related(all_0_13_13, v0, v1) = 0) | ( ~ (v4 = 0) & in(v2, all_59_0_72) = v4))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (related(all_0_13_13, v0, v1) = v2) | ~ (element(v0, all_0_12_12) = 0) | ? [v3] : ? [v4] : (( ~ (v3 = 0) & element(v1, all_0_12_12) = v3) | (( ~ (v2 = 0) | (v4 = 0 & ordered_pair(v0, v1) = v3 & in(v3, all_59_0_72) = 0)) & (v2 = 0 | ( ~ (v4 = 0) & ordered_pair(v0, v1) = v3 & in(v3, all_59_0_72) = v4))))) & ! [v0] : ! [v1] : ( ~ (element(v1, all_0_12_12) = 0) | ~ (element(v0, all_0_12_12) = 0) | ? [v2] : ? [v3] : ? [v4] : (((v4 = 0 & ordered_pair(v0, v1) = v3 & in(v3, all_59_0_72) = 0) | ( ~ (v2 = 0) & related(all_0_13_13, v0, v1) = v2)) & ((v2 = 0 & related(all_0_13_13, v0, v1) = 0) | ( ~ (v4 = 0) & ordered_pair(v0, v1) = v3 & in(v3, all_59_0_72) = v4)))))
% 66.14/30.85 |
% 66.14/30.85 | Instantiating (110) with all_60_0_73, all_60_1_74 yields:
% 66.14/30.85 | (118) (all_60_0_73 = 0 & relation_of2_as_subset(all_60_1_74, all_0_12_12, all_0_12_12) = 0 & the_InternalRel(all_0_13_13) = all_60_1_74) | ( ~ (all_60_1_74 = 0) & rel_str(all_0_13_13) = all_60_1_74)
% 66.14/30.85 |
% 66.14/30.85 | Instantiating (109) with all_61_0_75 yields:
% 66.14/30.85 | (119) ( ~ (all_61_0_75 = 0) & rel_str(all_0_11_11) = all_61_0_75) | (the_InternalRel(all_0_11_11) = all_61_0_75 & ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (( ~ (v2 = 0) & rel_str(v0) = v2) | (((v5 = 0 & v3 = 0 & the_InternalRel(v0) = v4 & subset(v4, all_61_0_75) = 0 & subset(v1, all_0_10_10) = 0) | ( ~ (v2 = 0) & subrelstr(v0, all_0_11_11) = v2)) & ((v2 = 0 & subrelstr(v0, all_0_11_11) = 0) | ( ~ (v5 = 0) & the_InternalRel(v0) = v4 & subset(v4, all_61_0_75) = v5) | ( ~ (v3 = 0) & subset(v1, all_0_10_10) = v3))))) & ! [v0] : ! [v1] : ( ~ (subrelstr(v0, all_0_11_11) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (( ~ (v2 = 0) & rel_str(v0) = v2) | (( ~ (v1 = 0) | (v5 = 0 & v3 = 0 & the_carrier(v0) = v2 & the_InternalRel(v0) = v4 & subset(v4, all_61_0_75) = 0 & subset(v2, all_0_10_10) = 0)) & (v1 = 0 | ( ~ (v5 = 0) & the_InternalRel(v0) = v4 & subset(v4, all_61_0_75) = v5) | ( ~ (v3 = 0) & the_carrier(v0) = v2 & subset(v2, all_0_10_10) = v3))))) & ! [v0] : ! [v1] : ( ~ (the_InternalRel(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (( ~ (v2 = 0) & rel_str(v0) = v2) | (((v5 = 0 & v4 = 0 & the_carrier(v0) = v3 & subset(v3, all_0_10_10) = 0 & subset(v1, all_61_0_75) = 0) | ( ~ (v2 = 0) & subrelstr(v0, all_0_11_11) = v2)) & ((v2 = 0 & subrelstr(v0, all_0_11_11) = 0) | ( ~ (v5 = 0) & subset(v1, all_61_0_75) = v5) | ( ~ (v4 = 0) & the_carrier(v0) = v3 & subset(v3, all_0_10_10) = v4))))) & ! [v0] : ( ~ (rel_str(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (((v5 = 0 & v3 = 0 & the_carrier(v0) = v2 & the_InternalRel(v0) = v4 & subset(v4, all_61_0_75) = 0 & subset(v2, all_0_10_10) = 0) | ( ~ (v1 = 0) & subrelstr(v0, all_0_11_11) = v1)) & ((v1 = 0 & subrelstr(v0, all_0_11_11) = 0) | ( ~ (v5 = 0) & the_InternalRel(v0) = v4 & subset(v4, all_61_0_75) = v5) | ( ~ (v3 = 0) & the_carrier(v0) = v2 & subset(v2, all_0_10_10) = v3)))))
% 66.14/30.85 |
% 66.14/30.85 | Instantiating (108) with all_62_0_76 yields:
% 66.14/30.85 | (120) ( ~ (all_62_0_76 = 0) & rel_str(all_0_11_11) = all_62_0_76) | (the_InternalRel(all_0_11_11) = all_62_0_76 & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ (element(v0, all_0_10_10) = 0) | ? [v3] : ? [v4] : (( ~ (v3 = 0) & element(v1, all_0_10_10) = v3) | (((v4 = 0 & in(v2, all_62_0_76) = 0) | ( ~ (v3 = 0) & related(all_0_11_11, v0, v1) = v3)) & ((v3 = 0 & related(all_0_11_11, v0, v1) = 0) | ( ~ (v4 = 0) & in(v2, all_62_0_76) = v4))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (related(all_0_11_11, v0, v1) = v2) | ~ (element(v0, all_0_10_10) = 0) | ? [v3] : ? [v4] : (( ~ (v3 = 0) & element(v1, all_0_10_10) = v3) | (( ~ (v2 = 0) | (v4 = 0 & ordered_pair(v0, v1) = v3 & in(v3, all_62_0_76) = 0)) & (v2 = 0 | ( ~ (v4 = 0) & ordered_pair(v0, v1) = v3 & in(v3, all_62_0_76) = v4))))) & ! [v0] : ! [v1] : ( ~ (element(v1, all_0_10_10) = 0) | ~ (element(v0, all_0_10_10) = 0) | ? [v2] : ? [v3] : ? [v4] : (((v4 = 0 & ordered_pair(v0, v1) = v3 & in(v3, all_62_0_76) = 0) | ( ~ (v2 = 0) & related(all_0_11_11, v0, v1) = v2)) & ((v2 = 0 & related(all_0_11_11, v0, v1) = 0) | ( ~ (v4 = 0) & ordered_pair(v0, v1) = v3 & in(v3, all_62_0_76) = v4)))))
% 66.14/30.85 |
% 66.14/30.85 | Instantiating (115) with all_70_0_82, all_70_1_83 yields:
% 66.14/30.85 | (121) the_carrier(all_0_13_13) = all_70_1_83 & the_InternalRel(all_0_13_13) = all_70_0_82 & ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (( ~ (v2 = 0) & rel_str(v0) = v2) | (((v5 = 0 & v3 = 0 & the_InternalRel(v0) = v4 & subset(v4, all_70_0_82) = 0 & subset(v1, all_70_1_83) = 0) | ( ~ (v2 = 0) & subrelstr(v0, all_0_13_13) = v2)) & ((v2 = 0 & subrelstr(v0, all_0_13_13) = 0) | ( ~ (v5 = 0) & the_InternalRel(v0) = v4 & subset(v4, all_70_0_82) = v5) | ( ~ (v3 = 0) & subset(v1, all_70_1_83) = v3))))) & ! [v0] : ! [v1] : ( ~ (subrelstr(v0, all_0_13_13) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (( ~ (v2 = 0) & rel_str(v0) = v2) | (( ~ (v1 = 0) | (v5 = 0 & v3 = 0 & the_carrier(v0) = v2 & the_InternalRel(v0) = v4 & subset(v4, all_70_0_82) = 0 & subset(v2, all_70_1_83) = 0)) & (v1 = 0 | ( ~ (v5 = 0) & the_InternalRel(v0) = v4 & subset(v4, all_70_0_82) = v5) | ( ~ (v3 = 0) & the_carrier(v0) = v2 & subset(v2, all_70_1_83) = v3))))) & ! [v0] : ! [v1] : ( ~ (the_InternalRel(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (( ~ (v2 = 0) & rel_str(v0) = v2) | (((v5 = 0 & v4 = 0 & the_carrier(v0) = v3 & subset(v3, all_70_1_83) = 0 & subset(v1, all_70_0_82) = 0) | ( ~ (v2 = 0) & subrelstr(v0, all_0_13_13) = v2)) & ((v2 = 0 & subrelstr(v0, all_0_13_13) = 0) | ( ~ (v5 = 0) & subset(v1, all_70_0_82) = v5) | ( ~ (v4 = 0) & the_carrier(v0) = v3 & subset(v3, all_70_1_83) = v4))))) & ! [v0] : ( ~ (rel_str(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (((v5 = 0 & v3 = 0 & the_carrier(v0) = v2 & the_InternalRel(v0) = v4 & subset(v4, all_70_0_82) = 0 & subset(v2, all_70_1_83) = 0) | ( ~ (v1 = 0) & subrelstr(v0, all_0_13_13) = v1)) & ((v1 = 0 & subrelstr(v0, all_0_13_13) = 0) | ( ~ (v5 = 0) & the_InternalRel(v0) = v4 & subset(v4, all_70_0_82) = v5) | ( ~ (v3 = 0) & the_carrier(v0) = v2 & subset(v2, all_70_1_83) = v3))))
% 66.14/30.85 |
% 66.14/30.85 | Applying alpha-rule on (121) yields:
% 66.14/30.85 | (122) the_carrier(all_0_13_13) = all_70_1_83
% 66.14/30.85 | (123) ! [v0] : ( ~ (rel_str(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (((v5 = 0 & v3 = 0 & the_carrier(v0) = v2 & the_InternalRel(v0) = v4 & subset(v4, all_70_0_82) = 0 & subset(v2, all_70_1_83) = 0) | ( ~ (v1 = 0) & subrelstr(v0, all_0_13_13) = v1)) & ((v1 = 0 & subrelstr(v0, all_0_13_13) = 0) | ( ~ (v5 = 0) & the_InternalRel(v0) = v4 & subset(v4, all_70_0_82) = v5) | ( ~ (v3 = 0) & the_carrier(v0) = v2 & subset(v2, all_70_1_83) = v3))))
% 66.14/30.85 | (124) the_InternalRel(all_0_13_13) = all_70_0_82
% 66.14/30.85 | (125) ! [v0] : ! [v1] : ( ~ (the_InternalRel(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (( ~ (v2 = 0) & rel_str(v0) = v2) | (((v5 = 0 & v4 = 0 & the_carrier(v0) = v3 & subset(v3, all_70_1_83) = 0 & subset(v1, all_70_0_82) = 0) | ( ~ (v2 = 0) & subrelstr(v0, all_0_13_13) = v2)) & ((v2 = 0 & subrelstr(v0, all_0_13_13) = 0) | ( ~ (v5 = 0) & subset(v1, all_70_0_82) = v5) | ( ~ (v4 = 0) & the_carrier(v0) = v3 & subset(v3, all_70_1_83) = v4)))))
% 66.14/30.85 | (126) ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (( ~ (v2 = 0) & rel_str(v0) = v2) | (((v5 = 0 & v3 = 0 & the_InternalRel(v0) = v4 & subset(v4, all_70_0_82) = 0 & subset(v1, all_70_1_83) = 0) | ( ~ (v2 = 0) & subrelstr(v0, all_0_13_13) = v2)) & ((v2 = 0 & subrelstr(v0, all_0_13_13) = 0) | ( ~ (v5 = 0) & the_InternalRel(v0) = v4 & subset(v4, all_70_0_82) = v5) | ( ~ (v3 = 0) & subset(v1, all_70_1_83) = v3)))))
% 66.14/30.85 | (127) ! [v0] : ! [v1] : ( ~ (subrelstr(v0, all_0_13_13) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (( ~ (v2 = 0) & rel_str(v0) = v2) | (( ~ (v1 = 0) | (v5 = 0 & v3 = 0 & the_carrier(v0) = v2 & the_InternalRel(v0) = v4 & subset(v4, all_70_0_82) = 0 & subset(v2, all_70_1_83) = 0)) & (v1 = 0 | ( ~ (v5 = 0) & the_InternalRel(v0) = v4 & subset(v4, all_70_0_82) = v5) | ( ~ (v3 = 0) & the_carrier(v0) = v2 & subset(v2, all_70_1_83) = v3)))))
% 66.14/30.85 |
% 66.14/30.85 | Instantiating formula (126) with all_0_10_10, all_0_11_11 and discharging atoms the_carrier(all_0_11_11) = all_0_10_10, yields:
% 66.14/30.85 | (128) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (( ~ (v0 = 0) & rel_str(all_0_11_11) = v0) | (((v3 = 0 & v1 = 0 & the_InternalRel(all_0_11_11) = v2 & subset(v2, all_70_0_82) = 0 & subset(all_0_10_10, all_70_1_83) = 0) | ( ~ (v0 = 0) & subrelstr(all_0_11_11, all_0_13_13) = v0)) & ((v0 = 0 & subrelstr(all_0_11_11, all_0_13_13) = 0) | ( ~ (v3 = 0) & the_InternalRel(all_0_11_11) = v2 & subset(v2, all_70_0_82) = v3) | ( ~ (v1 = 0) & subset(all_0_10_10, all_70_1_83) = v1))))
% 66.14/30.85 |
% 66.14/30.85 | Instantiating formula (127) with 0, all_0_11_11 and discharging atoms subrelstr(all_0_11_11, all_0_13_13) = 0, yields:
% 66.14/30.86 | (129) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ((v3 = 0 & v1 = 0 & the_carrier(all_0_11_11) = v0 & the_InternalRel(all_0_11_11) = v2 & subset(v2, all_70_0_82) = 0 & subset(v0, all_70_1_83) = 0) | ( ~ (v0 = 0) & rel_str(all_0_11_11) = v0))
% 66.14/30.86 |
% 66.14/30.86 | Instantiating (107) with all_75_0_85, all_75_1_86 yields:
% 66.14/30.86 | (130) (all_75_0_85 = 0 & relation_of2_as_subset(all_75_1_86, all_0_10_10, all_0_10_10) = 0 & the_InternalRel(all_0_11_11) = all_75_1_86) | ( ~ (all_75_1_86 = 0) & rel_str(all_0_11_11) = all_75_1_86)
% 66.14/30.86 |
% 66.14/30.86 | Instantiating (114) with all_81_0_91, all_81_1_92 yields:
% 66.14/30.86 | (131) the_carrier(all_0_13_13) = all_81_1_92 & the_InternalRel(all_0_13_13) = all_81_0_91 & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ (element(v0, all_81_1_92) = 0) | ? [v3] : ? [v4] : (( ~ (v3 = 0) & element(v1, all_81_1_92) = v3) | (((v4 = 0 & in(v2, all_81_0_91) = 0) | ( ~ (v3 = 0) & related(all_0_13_13, v0, v1) = v3)) & ((v3 = 0 & related(all_0_13_13, v0, v1) = 0) | ( ~ (v4 = 0) & in(v2, all_81_0_91) = v4))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (related(all_0_13_13, v0, v1) = v2) | ~ (element(v0, all_81_1_92) = 0) | ? [v3] : ? [v4] : (( ~ (v3 = 0) & element(v1, all_81_1_92) = v3) | (( ~ (v2 = 0) | (v4 = 0 & ordered_pair(v0, v1) = v3 & in(v3, all_81_0_91) = 0)) & (v2 = 0 | ( ~ (v4 = 0) & ordered_pair(v0, v1) = v3 & in(v3, all_81_0_91) = v4))))) & ! [v0] : ! [v1] : ( ~ (element(v1, all_81_1_92) = 0) | ~ (element(v0, all_81_1_92) = 0) | ? [v2] : ? [v3] : ? [v4] : (((v4 = 0 & ordered_pair(v0, v1) = v3 & in(v3, all_81_0_91) = 0) | ( ~ (v2 = 0) & related(all_0_13_13, v0, v1) = v2)) & ((v2 = 0 & related(all_0_13_13, v0, v1) = 0) | ( ~ (v4 = 0) & ordered_pair(v0, v1) = v3 & in(v3, all_81_0_91) = v4))))
% 66.49/30.86 |
% 66.49/30.86 | Applying alpha-rule on (131) yields:
% 66.49/30.86 | (132) ! [v0] : ! [v1] : ( ~ (element(v1, all_81_1_92) = 0) | ~ (element(v0, all_81_1_92) = 0) | ? [v2] : ? [v3] : ? [v4] : (((v4 = 0 & ordered_pair(v0, v1) = v3 & in(v3, all_81_0_91) = 0) | ( ~ (v2 = 0) & related(all_0_13_13, v0, v1) = v2)) & ((v2 = 0 & related(all_0_13_13, v0, v1) = 0) | ( ~ (v4 = 0) & ordered_pair(v0, v1) = v3 & in(v3, all_81_0_91) = v4))))
% 66.49/30.86 | (133) the_InternalRel(all_0_13_13) = all_81_0_91
% 66.49/30.86 | (134) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ (element(v0, all_81_1_92) = 0) | ? [v3] : ? [v4] : (( ~ (v3 = 0) & element(v1, all_81_1_92) = v3) | (((v4 = 0 & in(v2, all_81_0_91) = 0) | ( ~ (v3 = 0) & related(all_0_13_13, v0, v1) = v3)) & ((v3 = 0 & related(all_0_13_13, v0, v1) = 0) | ( ~ (v4 = 0) & in(v2, all_81_0_91) = v4)))))
% 66.49/30.86 | (135) the_carrier(all_0_13_13) = all_81_1_92
% 66.49/30.86 | (136) ! [v0] : ! [v1] : ! [v2] : ( ~ (related(all_0_13_13, v0, v1) = v2) | ~ (element(v0, all_81_1_92) = 0) | ? [v3] : ? [v4] : (( ~ (v3 = 0) & element(v1, all_81_1_92) = v3) | (( ~ (v2 = 0) | (v4 = 0 & ordered_pair(v0, v1) = v3 & in(v3, all_81_0_91) = 0)) & (v2 = 0 | ( ~ (v4 = 0) & ordered_pair(v0, v1) = v3 & in(v3, all_81_0_91) = v4)))))
% 66.49/30.86 |
% 66.49/30.86 | Instantiating (113) with all_86_0_95, all_86_1_96 yields:
% 66.49/30.86 | (137) relation_of2_as_subset(all_86_1_96, all_86_0_95, all_86_0_95) = 0 & the_carrier(all_0_13_13) = all_86_0_95 & the_InternalRel(all_0_13_13) = all_86_1_96
% 66.49/30.86 |
% 66.49/30.86 | Applying alpha-rule on (137) yields:
% 66.49/30.86 | (138) relation_of2_as_subset(all_86_1_96, all_86_0_95, all_86_0_95) = 0
% 66.49/30.86 | (139) the_carrier(all_0_13_13) = all_86_0_95
% 66.49/30.86 | (140) the_InternalRel(all_0_13_13) = all_86_1_96
% 66.49/30.86 |
% 66.49/30.86 | Instantiating (112) with all_88_0_97 yields:
% 66.49/30.86 | (141) ( ~ (all_88_0_97 = 0) & rel_str(all_0_13_13) = all_88_0_97) | (the_InternalRel(all_0_13_13) = all_88_0_97 & ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (( ~ (v2 = 0) & rel_str(v0) = v2) | (((v5 = 0 & v3 = 0 & the_InternalRel(v0) = v4 & subset(v4, all_88_0_97) = 0 & subset(v1, all_0_12_12) = 0) | ( ~ (v2 = 0) & subrelstr(v0, all_0_13_13) = v2)) & ((v2 = 0 & subrelstr(v0, all_0_13_13) = 0) | ( ~ (v5 = 0) & the_InternalRel(v0) = v4 & subset(v4, all_88_0_97) = v5) | ( ~ (v3 = 0) & subset(v1, all_0_12_12) = v3))))) & ! [v0] : ! [v1] : ( ~ (subrelstr(v0, all_0_13_13) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (( ~ (v2 = 0) & rel_str(v0) = v2) | (( ~ (v1 = 0) | (v5 = 0 & v3 = 0 & the_carrier(v0) = v2 & the_InternalRel(v0) = v4 & subset(v4, all_88_0_97) = 0 & subset(v2, all_0_12_12) = 0)) & (v1 = 0 | ( ~ (v5 = 0) & the_InternalRel(v0) = v4 & subset(v4, all_88_0_97) = v5) | ( ~ (v3 = 0) & the_carrier(v0) = v2 & subset(v2, all_0_12_12) = v3))))) & ! [v0] : ! [v1] : ( ~ (the_InternalRel(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (( ~ (v2 = 0) & rel_str(v0) = v2) | (((v5 = 0 & v4 = 0 & the_carrier(v0) = v3 & subset(v3, all_0_12_12) = 0 & subset(v1, all_88_0_97) = 0) | ( ~ (v2 = 0) & subrelstr(v0, all_0_13_13) = v2)) & ((v2 = 0 & subrelstr(v0, all_0_13_13) = 0) | ( ~ (v5 = 0) & subset(v1, all_88_0_97) = v5) | ( ~ (v4 = 0) & the_carrier(v0) = v3 & subset(v3, all_0_12_12) = v4))))) & ! [v0] : ( ~ (rel_str(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (((v5 = 0 & v3 = 0 & the_carrier(v0) = v2 & the_InternalRel(v0) = v4 & subset(v4, all_88_0_97) = 0 & subset(v2, all_0_12_12) = 0) | ( ~ (v1 = 0) & subrelstr(v0, all_0_13_13) = v1)) & ((v1 = 0 & subrelstr(v0, all_0_13_13) = 0) | ( ~ (v5 = 0) & the_InternalRel(v0) = v4 & subset(v4, all_88_0_97) = v5) | ( ~ (v3 = 0) & the_carrier(v0) = v2 & subset(v2, all_0_12_12) = v3)))))
% 66.49/30.86 |
% 66.49/30.86 | Instantiating (129) with all_89_0_98, all_89_1_99, all_89_2_100, all_89_3_101 yields:
% 66.49/30.86 | (142) (all_89_0_98 = 0 & all_89_2_100 = 0 & the_carrier(all_0_11_11) = all_89_3_101 & the_InternalRel(all_0_11_11) = all_89_1_99 & subset(all_89_1_99, all_70_0_82) = 0 & subset(all_89_3_101, all_70_1_83) = 0) | ( ~ (all_89_3_101 = 0) & rel_str(all_0_11_11) = all_89_3_101)
% 66.49/30.86 |
% 66.49/30.86 | Instantiating (128) with all_93_0_116, all_93_1_117, all_93_2_118, all_93_3_119 yields:
% 66.49/30.86 | (143) ( ~ (all_93_3_119 = 0) & rel_str(all_0_11_11) = all_93_3_119) | (((all_93_0_116 = 0 & all_93_2_118 = 0 & the_InternalRel(all_0_11_11) = all_93_1_117 & subset(all_93_1_117, all_70_0_82) = 0 & subset(all_0_10_10, all_70_1_83) = 0) | ( ~ (all_93_3_119 = 0) & subrelstr(all_0_11_11, all_0_13_13) = all_93_3_119)) & ((all_93_3_119 = 0 & subrelstr(all_0_11_11, all_0_13_13) = 0) | ( ~ (all_93_0_116 = 0) & the_InternalRel(all_0_11_11) = all_93_1_117 & subset(all_93_1_117, all_70_0_82) = all_93_0_116) | ( ~ (all_93_2_118 = 0) & subset(all_0_10_10, all_70_1_83) = all_93_2_118)))
% 66.49/30.86 |
% 66.49/30.86 +-Applying beta-rule and splitting (120), into two cases.
% 66.49/30.86 |-Branch one:
% 66.49/30.86 | (144) ~ (all_62_0_76 = 0) & rel_str(all_0_11_11) = all_62_0_76
% 66.49/30.86 |
% 66.49/30.86 | Applying alpha-rule on (144) yields:
% 66.49/30.86 | (145) ~ (all_62_0_76 = 0)
% 66.49/30.86 | (146) rel_str(all_0_11_11) = all_62_0_76
% 66.49/30.86 |
% 66.49/30.86 | Instantiating formula (35) with all_0_11_11, 0, all_62_0_76 and discharging atoms rel_str(all_0_11_11) = all_62_0_76, rel_str(all_0_11_11) = 0, yields:
% 66.49/30.86 | (147) all_62_0_76 = 0
% 66.49/30.86 |
% 66.49/30.86 | Equations (147) can reduce 145 to:
% 66.49/30.86 | (148) $false
% 66.49/30.86 |
% 66.49/30.86 |-The branch is then unsatisfiable
% 66.49/30.86 |-Branch two:
% 66.49/30.86 | (149) the_InternalRel(all_0_11_11) = all_62_0_76 & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ (element(v0, all_0_10_10) = 0) | ? [v3] : ? [v4] : (( ~ (v3 = 0) & element(v1, all_0_10_10) = v3) | (((v4 = 0 & in(v2, all_62_0_76) = 0) | ( ~ (v3 = 0) & related(all_0_11_11, v0, v1) = v3)) & ((v3 = 0 & related(all_0_11_11, v0, v1) = 0) | ( ~ (v4 = 0) & in(v2, all_62_0_76) = v4))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (related(all_0_11_11, v0, v1) = v2) | ~ (element(v0, all_0_10_10) = 0) | ? [v3] : ? [v4] : (( ~ (v3 = 0) & element(v1, all_0_10_10) = v3) | (( ~ (v2 = 0) | (v4 = 0 & ordered_pair(v0, v1) = v3 & in(v3, all_62_0_76) = 0)) & (v2 = 0 | ( ~ (v4 = 0) & ordered_pair(v0, v1) = v3 & in(v3, all_62_0_76) = v4))))) & ! [v0] : ! [v1] : ( ~ (element(v1, all_0_10_10) = 0) | ~ (element(v0, all_0_10_10) = 0) | ? [v2] : ? [v3] : ? [v4] : (((v4 = 0 & ordered_pair(v0, v1) = v3 & in(v3, all_62_0_76) = 0) | ( ~ (v2 = 0) & related(all_0_11_11, v0, v1) = v2)) & ((v2 = 0 & related(all_0_11_11, v0, v1) = 0) | ( ~ (v4 = 0) & ordered_pair(v0, v1) = v3 & in(v3, all_62_0_76) = v4))))
% 66.49/30.86 |
% 66.49/30.86 | Applying alpha-rule on (149) yields:
% 66.49/30.86 | (150) the_InternalRel(all_0_11_11) = all_62_0_76
% 66.49/30.86 | (151) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ (element(v0, all_0_10_10) = 0) | ? [v3] : ? [v4] : (( ~ (v3 = 0) & element(v1, all_0_10_10) = v3) | (((v4 = 0 & in(v2, all_62_0_76) = 0) | ( ~ (v3 = 0) & related(all_0_11_11, v0, v1) = v3)) & ((v3 = 0 & related(all_0_11_11, v0, v1) = 0) | ( ~ (v4 = 0) & in(v2, all_62_0_76) = v4)))))
% 66.49/30.86 | (152) ! [v0] : ! [v1] : ! [v2] : ( ~ (related(all_0_11_11, v0, v1) = v2) | ~ (element(v0, all_0_10_10) = 0) | ? [v3] : ? [v4] : (( ~ (v3 = 0) & element(v1, all_0_10_10) = v3) | (( ~ (v2 = 0) | (v4 = 0 & ordered_pair(v0, v1) = v3 & in(v3, all_62_0_76) = 0)) & (v2 = 0 | ( ~ (v4 = 0) & ordered_pair(v0, v1) = v3 & in(v3, all_62_0_76) = v4)))))
% 66.49/30.87 | (153) ! [v0] : ! [v1] : ( ~ (element(v1, all_0_10_10) = 0) | ~ (element(v0, all_0_10_10) = 0) | ? [v2] : ? [v3] : ? [v4] : (((v4 = 0 & ordered_pair(v0, v1) = v3 & in(v3, all_62_0_76) = 0) | ( ~ (v2 = 0) & related(all_0_11_11, v0, v1) = v2)) & ((v2 = 0 & related(all_0_11_11, v0, v1) = 0) | ( ~ (v4 = 0) & ordered_pair(v0, v1) = v3 & in(v3, all_62_0_76) = v4))))
% 66.49/30.87 |
% 66.49/30.87 | Instantiating formula (153) with all_0_8_8, all_0_9_9 and discharging atoms element(all_0_8_8, all_0_10_10) = 0, element(all_0_9_9, all_0_10_10) = 0, yields:
% 66.49/30.87 | (154) ? [v0] : ? [v1] : ? [v2] : (((v2 = 0 & ordered_pair(all_0_9_9, all_0_8_8) = v1 & in(v1, all_62_0_76) = 0) | ( ~ (v0 = 0) & related(all_0_11_11, all_0_9_9, all_0_8_8) = v0)) & ((v0 = 0 & related(all_0_11_11, all_0_9_9, all_0_8_8) = 0) | ( ~ (v2 = 0) & ordered_pair(all_0_9_9, all_0_8_8) = v1 & in(v1, all_62_0_76) = v2)))
% 66.49/30.87 |
% 66.49/30.87 | Instantiating (154) with all_104_0_167, all_104_1_168, all_104_2_169 yields:
% 66.49/30.87 | (155) ((all_104_0_167 = 0 & ordered_pair(all_0_9_9, all_0_8_8) = all_104_1_168 & in(all_104_1_168, all_62_0_76) = 0) | ( ~ (all_104_2_169 = 0) & related(all_0_11_11, all_0_9_9, all_0_8_8) = all_104_2_169)) & ((all_104_2_169 = 0 & related(all_0_11_11, all_0_9_9, all_0_8_8) = 0) | ( ~ (all_104_0_167 = 0) & ordered_pair(all_0_9_9, all_0_8_8) = all_104_1_168 & in(all_104_1_168, all_62_0_76) = all_104_0_167))
% 66.49/30.87 |
% 66.49/30.87 | Applying alpha-rule on (155) yields:
% 66.49/30.87 | (156) (all_104_0_167 = 0 & ordered_pair(all_0_9_9, all_0_8_8) = all_104_1_168 & in(all_104_1_168, all_62_0_76) = 0) | ( ~ (all_104_2_169 = 0) & related(all_0_11_11, all_0_9_9, all_0_8_8) = all_104_2_169)
% 66.49/30.87 | (157) (all_104_2_169 = 0 & related(all_0_11_11, all_0_9_9, all_0_8_8) = 0) | ( ~ (all_104_0_167 = 0) & ordered_pair(all_0_9_9, all_0_8_8) = all_104_1_168 & in(all_104_1_168, all_62_0_76) = all_104_0_167)
% 66.49/30.87 |
% 66.49/30.87 +-Applying beta-rule and splitting (118), into two cases.
% 66.49/30.87 |-Branch one:
% 66.49/30.87 | (158) all_60_0_73 = 0 & relation_of2_as_subset(all_60_1_74, all_0_12_12, all_0_12_12) = 0 & the_InternalRel(all_0_13_13) = all_60_1_74
% 66.49/30.87 |
% 66.49/30.87 | Applying alpha-rule on (158) yields:
% 66.49/30.87 | (159) all_60_0_73 = 0
% 66.49/30.87 | (160) relation_of2_as_subset(all_60_1_74, all_0_12_12, all_0_12_12) = 0
% 66.49/30.87 | (161) the_InternalRel(all_0_13_13) = all_60_1_74
% 66.49/30.87 |
% 66.49/30.87 +-Applying beta-rule and splitting (156), into two cases.
% 66.49/30.87 |-Branch one:
% 66.49/30.87 | (162) all_104_0_167 = 0 & ordered_pair(all_0_9_9, all_0_8_8) = all_104_1_168 & in(all_104_1_168, all_62_0_76) = 0
% 66.49/30.87 |
% 66.49/30.87 | Applying alpha-rule on (162) yields:
% 66.49/30.87 | (163) all_104_0_167 = 0
% 66.49/30.87 | (164) ordered_pair(all_0_9_9, all_0_8_8) = all_104_1_168
% 66.49/30.87 | (165) in(all_104_1_168, all_62_0_76) = 0
% 66.49/30.87 |
% 66.49/30.87 +-Applying beta-rule and splitting (143), into two cases.
% 66.49/30.87 |-Branch one:
% 66.49/30.87 | (166) ~ (all_93_3_119 = 0) & rel_str(all_0_11_11) = all_93_3_119
% 66.49/30.87 |
% 66.49/30.87 | Applying alpha-rule on (166) yields:
% 66.49/30.87 | (167) ~ (all_93_3_119 = 0)
% 66.49/30.87 | (168) rel_str(all_0_11_11) = all_93_3_119
% 66.49/30.87 |
% 66.49/30.87 | Instantiating formula (35) with all_0_11_11, 0, all_93_3_119 and discharging atoms rel_str(all_0_11_11) = all_93_3_119, rel_str(all_0_11_11) = 0, yields:
% 66.49/30.87 | (169) all_93_3_119 = 0
% 66.49/30.87 |
% 66.49/30.87 | Equations (169) can reduce 167 to:
% 66.49/30.87 | (148) $false
% 66.49/30.87 |
% 66.49/30.87 |-The branch is then unsatisfiable
% 66.49/30.87 |-Branch two:
% 66.49/30.87 | (171) ((all_93_0_116 = 0 & all_93_2_118 = 0 & the_InternalRel(all_0_11_11) = all_93_1_117 & subset(all_93_1_117, all_70_0_82) = 0 & subset(all_0_10_10, all_70_1_83) = 0) | ( ~ (all_93_3_119 = 0) & subrelstr(all_0_11_11, all_0_13_13) = all_93_3_119)) & ((all_93_3_119 = 0 & subrelstr(all_0_11_11, all_0_13_13) = 0) | ( ~ (all_93_0_116 = 0) & the_InternalRel(all_0_11_11) = all_93_1_117 & subset(all_93_1_117, all_70_0_82) = all_93_0_116) | ( ~ (all_93_2_118 = 0) & subset(all_0_10_10, all_70_1_83) = all_93_2_118))
% 66.49/30.87 |
% 66.49/30.87 | Applying alpha-rule on (171) yields:
% 66.49/30.87 | (172) (all_93_0_116 = 0 & all_93_2_118 = 0 & the_InternalRel(all_0_11_11) = all_93_1_117 & subset(all_93_1_117, all_70_0_82) = 0 & subset(all_0_10_10, all_70_1_83) = 0) | ( ~ (all_93_3_119 = 0) & subrelstr(all_0_11_11, all_0_13_13) = all_93_3_119)
% 66.49/30.87 | (173) (all_93_3_119 = 0 & subrelstr(all_0_11_11, all_0_13_13) = 0) | ( ~ (all_93_0_116 = 0) & the_InternalRel(all_0_11_11) = all_93_1_117 & subset(all_93_1_117, all_70_0_82) = all_93_0_116) | ( ~ (all_93_2_118 = 0) & subset(all_0_10_10, all_70_1_83) = all_93_2_118)
% 66.49/30.87 |
% 66.49/30.87 +-Applying beta-rule and splitting (172), into two cases.
% 66.49/30.87 |-Branch one:
% 66.49/30.87 | (174) all_93_0_116 = 0 & all_93_2_118 = 0 & the_InternalRel(all_0_11_11) = all_93_1_117 & subset(all_93_1_117, all_70_0_82) = 0 & subset(all_0_10_10, all_70_1_83) = 0
% 66.49/30.87 |
% 66.49/30.87 | Applying alpha-rule on (174) yields:
% 66.49/30.87 | (175) subset(all_0_10_10, all_70_1_83) = 0
% 66.49/30.87 | (176) subset(all_93_1_117, all_70_0_82) = 0
% 66.49/30.87 | (177) the_InternalRel(all_0_11_11) = all_93_1_117
% 66.55/30.87 | (178) all_93_2_118 = 0
% 66.55/30.87 | (179) all_93_0_116 = 0
% 66.55/30.87 |
% 66.55/30.87 +-Applying beta-rule and splitting (173), into two cases.
% 66.55/30.87 |-Branch one:
% 66.55/30.87 | (180) (all_93_3_119 = 0 & subrelstr(all_0_11_11, all_0_13_13) = 0) | ( ~ (all_93_0_116 = 0) & the_InternalRel(all_0_11_11) = all_93_1_117 & subset(all_93_1_117, all_70_0_82) = all_93_0_116)
% 66.55/30.87 |
% 66.55/30.87 +-Applying beta-rule and splitting (180), into two cases.
% 66.55/30.87 |-Branch one:
% 66.55/30.87 | (181) all_93_3_119 = 0 & subrelstr(all_0_11_11, all_0_13_13) = 0
% 66.55/30.87 |
% 66.55/30.87 | Applying alpha-rule on (181) yields:
% 66.55/30.87 | (169) all_93_3_119 = 0
% 66.55/30.87 | (46) subrelstr(all_0_11_11, all_0_13_13) = 0
% 66.55/30.87 |
% 66.55/30.87 +-Applying beta-rule and splitting (117), into two cases.
% 66.55/30.87 |-Branch one:
% 66.55/30.87 | (184) ~ (all_59_0_72 = 0) & rel_str(all_0_13_13) = all_59_0_72
% 66.55/30.87 |
% 66.55/30.87 | Applying alpha-rule on (184) yields:
% 66.55/30.87 | (185) ~ (all_59_0_72 = 0)
% 66.55/30.87 | (186) rel_str(all_0_13_13) = all_59_0_72
% 66.55/30.87 |
% 66.55/30.87 | Instantiating formula (35) with all_0_13_13, all_59_0_72, 0 and discharging atoms rel_str(all_0_13_13) = all_59_0_72, rel_str(all_0_13_13) = 0, yields:
% 66.55/30.87 | (187) all_59_0_72 = 0
% 66.55/30.87 |
% 66.55/30.87 | Equations (187) can reduce 185 to:
% 66.55/30.87 | (148) $false
% 66.55/30.87 |
% 66.55/30.87 |-The branch is then unsatisfiable
% 66.55/30.87 |-Branch two:
% 66.55/30.87 | (189) the_InternalRel(all_0_13_13) = all_59_0_72 & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ (element(v0, all_0_12_12) = 0) | ? [v3] : ? [v4] : (( ~ (v3 = 0) & element(v1, all_0_12_12) = v3) | (((v4 = 0 & in(v2, all_59_0_72) = 0) | ( ~ (v3 = 0) & related(all_0_13_13, v0, v1) = v3)) & ((v3 = 0 & related(all_0_13_13, v0, v1) = 0) | ( ~ (v4 = 0) & in(v2, all_59_0_72) = v4))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (related(all_0_13_13, v0, v1) = v2) | ~ (element(v0, all_0_12_12) = 0) | ? [v3] : ? [v4] : (( ~ (v3 = 0) & element(v1, all_0_12_12) = v3) | (( ~ (v2 = 0) | (v4 = 0 & ordered_pair(v0, v1) = v3 & in(v3, all_59_0_72) = 0)) & (v2 = 0 | ( ~ (v4 = 0) & ordered_pair(v0, v1) = v3 & in(v3, all_59_0_72) = v4))))) & ! [v0] : ! [v1] : ( ~ (element(v1, all_0_12_12) = 0) | ~ (element(v0, all_0_12_12) = 0) | ? [v2] : ? [v3] : ? [v4] : (((v4 = 0 & ordered_pair(v0, v1) = v3 & in(v3, all_59_0_72) = 0) | ( ~ (v2 = 0) & related(all_0_13_13, v0, v1) = v2)) & ((v2 = 0 & related(all_0_13_13, v0, v1) = 0) | ( ~ (v4 = 0) & ordered_pair(v0, v1) = v3 & in(v3, all_59_0_72) = v4))))
% 66.55/30.87 |
% 66.55/30.87 | Applying alpha-rule on (189) yields:
% 66.55/30.87 | (190) the_InternalRel(all_0_13_13) = all_59_0_72
% 66.55/30.87 | (191) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ (element(v0, all_0_12_12) = 0) | ? [v3] : ? [v4] : (( ~ (v3 = 0) & element(v1, all_0_12_12) = v3) | (((v4 = 0 & in(v2, all_59_0_72) = 0) | ( ~ (v3 = 0) & related(all_0_13_13, v0, v1) = v3)) & ((v3 = 0 & related(all_0_13_13, v0, v1) = 0) | ( ~ (v4 = 0) & in(v2, all_59_0_72) = v4)))))
% 66.55/30.87 | (192) ! [v0] : ! [v1] : ! [v2] : ( ~ (related(all_0_13_13, v0, v1) = v2) | ~ (element(v0, all_0_12_12) = 0) | ? [v3] : ? [v4] : (( ~ (v3 = 0) & element(v1, all_0_12_12) = v3) | (( ~ (v2 = 0) | (v4 = 0 & ordered_pair(v0, v1) = v3 & in(v3, all_59_0_72) = 0)) & (v2 = 0 | ( ~ (v4 = 0) & ordered_pair(v0, v1) = v3 & in(v3, all_59_0_72) = v4)))))
% 66.55/30.87 | (193) ! [v0] : ! [v1] : ( ~ (element(v1, all_0_12_12) = 0) | ~ (element(v0, all_0_12_12) = 0) | ? [v2] : ? [v3] : ? [v4] : (((v4 = 0 & ordered_pair(v0, v1) = v3 & in(v3, all_59_0_72) = 0) | ( ~ (v2 = 0) & related(all_0_13_13, v0, v1) = v2)) & ((v2 = 0 & related(all_0_13_13, v0, v1) = 0) | ( ~ (v4 = 0) & ordered_pair(v0, v1) = v3 & in(v3, all_59_0_72) = v4))))
% 66.55/30.87 |
% 66.55/30.87 | Instantiating formula (192) with all_0_7_7, all_0_8_8, all_0_9_9 and discharging atoms related(all_0_13_13, all_0_9_9, all_0_8_8) = all_0_7_7, element(all_0_9_9, all_0_12_12) = 0, yields:
% 66.55/30.87 | (194) ? [v0] : ? [v1] : (( ~ (v0 = 0) & element(all_0_8_8, all_0_12_12) = v0) | (( ~ (all_0_7_7 = 0) | (v1 = 0 & ordered_pair(all_0_9_9, all_0_8_8) = v0 & in(v0, all_59_0_72) = 0)) & (all_0_7_7 = 0 | ( ~ (v1 = 0) & ordered_pair(all_0_9_9, all_0_8_8) = v0 & in(v0, all_59_0_72) = v1))))
% 66.55/30.87 |
% 66.55/30.87 | Instantiating formula (193) with all_0_8_8, all_0_9_9 and discharging atoms element(all_0_8_8, all_0_12_12) = 0, element(all_0_9_9, all_0_12_12) = 0, yields:
% 66.55/30.87 | (195) ? [v0] : ? [v1] : ? [v2] : (((v2 = 0 & ordered_pair(all_0_9_9, all_0_8_8) = v1 & in(v1, all_59_0_72) = 0) | ( ~ (v0 = 0) & related(all_0_13_13, all_0_9_9, all_0_8_8) = v0)) & ((v0 = 0 & related(all_0_13_13, all_0_9_9, all_0_8_8) = 0) | ( ~ (v2 = 0) & ordered_pair(all_0_9_9, all_0_8_8) = v1 & in(v1, all_59_0_72) = v2)))
% 66.55/30.87 |
% 66.55/30.87 | Instantiating (195) with all_145_0_232, all_145_1_233, all_145_2_234 yields:
% 66.55/30.87 | (196) ((all_145_0_232 = 0 & ordered_pair(all_0_9_9, all_0_8_8) = all_145_1_233 & in(all_145_1_233, all_59_0_72) = 0) | ( ~ (all_145_2_234 = 0) & related(all_0_13_13, all_0_9_9, all_0_8_8) = all_145_2_234)) & ((all_145_2_234 = 0 & related(all_0_13_13, all_0_9_9, all_0_8_8) = 0) | ( ~ (all_145_0_232 = 0) & ordered_pair(all_0_9_9, all_0_8_8) = all_145_1_233 & in(all_145_1_233, all_59_0_72) = all_145_0_232))
% 66.55/30.87 |
% 66.55/30.87 | Applying alpha-rule on (196) yields:
% 66.55/30.87 | (197) (all_145_0_232 = 0 & ordered_pair(all_0_9_9, all_0_8_8) = all_145_1_233 & in(all_145_1_233, all_59_0_72) = 0) | ( ~ (all_145_2_234 = 0) & related(all_0_13_13, all_0_9_9, all_0_8_8) = all_145_2_234)
% 66.55/30.87 | (198) (all_145_2_234 = 0 & related(all_0_13_13, all_0_9_9, all_0_8_8) = 0) | ( ~ (all_145_0_232 = 0) & ordered_pair(all_0_9_9, all_0_8_8) = all_145_1_233 & in(all_145_1_233, all_59_0_72) = all_145_0_232)
% 66.55/30.88 |
% 66.55/30.88 | Instantiating (194) with all_146_0_235, all_146_1_236 yields:
% 66.55/30.88 | (199) ( ~ (all_146_1_236 = 0) & element(all_0_8_8, all_0_12_12) = all_146_1_236) | (( ~ (all_0_7_7 = 0) | (all_146_0_235 = 0 & ordered_pair(all_0_9_9, all_0_8_8) = all_146_1_236 & in(all_146_1_236, all_59_0_72) = 0)) & (all_0_7_7 = 0 | ( ~ (all_146_0_235 = 0) & ordered_pair(all_0_9_9, all_0_8_8) = all_146_1_236 & in(all_146_1_236, all_59_0_72) = all_146_0_235)))
% 66.55/30.88 |
% 66.55/30.88 +-Applying beta-rule and splitting (119), into two cases.
% 66.55/30.88 |-Branch one:
% 66.55/30.88 | (200) ~ (all_61_0_75 = 0) & rel_str(all_0_11_11) = all_61_0_75
% 66.55/30.88 |
% 66.55/30.88 | Applying alpha-rule on (200) yields:
% 66.55/30.88 | (201) ~ (all_61_0_75 = 0)
% 66.55/30.88 | (202) rel_str(all_0_11_11) = all_61_0_75
% 66.55/30.88 |
% 66.55/30.88 | Instantiating formula (35) with all_0_11_11, 0, all_61_0_75 and discharging atoms rel_str(all_0_11_11) = all_61_0_75, rel_str(all_0_11_11) = 0, yields:
% 66.55/30.88 | (203) all_61_0_75 = 0
% 66.55/30.88 |
% 66.55/30.88 | Equations (203) can reduce 201 to:
% 66.55/30.88 | (148) $false
% 66.55/30.88 |
% 66.55/30.88 |-The branch is then unsatisfiable
% 66.55/30.88 |-Branch two:
% 66.55/30.88 | (205) the_InternalRel(all_0_11_11) = all_61_0_75 & ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (( ~ (v2 = 0) & rel_str(v0) = v2) | (((v5 = 0 & v3 = 0 & the_InternalRel(v0) = v4 & subset(v4, all_61_0_75) = 0 & subset(v1, all_0_10_10) = 0) | ( ~ (v2 = 0) & subrelstr(v0, all_0_11_11) = v2)) & ((v2 = 0 & subrelstr(v0, all_0_11_11) = 0) | ( ~ (v5 = 0) & the_InternalRel(v0) = v4 & subset(v4, all_61_0_75) = v5) | ( ~ (v3 = 0) & subset(v1, all_0_10_10) = v3))))) & ! [v0] : ! [v1] : ( ~ (subrelstr(v0, all_0_11_11) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (( ~ (v2 = 0) & rel_str(v0) = v2) | (( ~ (v1 = 0) | (v5 = 0 & v3 = 0 & the_carrier(v0) = v2 & the_InternalRel(v0) = v4 & subset(v4, all_61_0_75) = 0 & subset(v2, all_0_10_10) = 0)) & (v1 = 0 | ( ~ (v5 = 0) & the_InternalRel(v0) = v4 & subset(v4, all_61_0_75) = v5) | ( ~ (v3 = 0) & the_carrier(v0) = v2 & subset(v2, all_0_10_10) = v3))))) & ! [v0] : ! [v1] : ( ~ (the_InternalRel(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (( ~ (v2 = 0) & rel_str(v0) = v2) | (((v5 = 0 & v4 = 0 & the_carrier(v0) = v3 & subset(v3, all_0_10_10) = 0 & subset(v1, all_61_0_75) = 0) | ( ~ (v2 = 0) & subrelstr(v0, all_0_11_11) = v2)) & ((v2 = 0 & subrelstr(v0, all_0_11_11) = 0) | ( ~ (v5 = 0) & subset(v1, all_61_0_75) = v5) | ( ~ (v4 = 0) & the_carrier(v0) = v3 & subset(v3, all_0_10_10) = v4))))) & ! [v0] : ( ~ (rel_str(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (((v5 = 0 & v3 = 0 & the_carrier(v0) = v2 & the_InternalRel(v0) = v4 & subset(v4, all_61_0_75) = 0 & subset(v2, all_0_10_10) = 0) | ( ~ (v1 = 0) & subrelstr(v0, all_0_11_11) = v1)) & ((v1 = 0 & subrelstr(v0, all_0_11_11) = 0) | ( ~ (v5 = 0) & the_InternalRel(v0) = v4 & subset(v4, all_61_0_75) = v5) | ( ~ (v3 = 0) & the_carrier(v0) = v2 & subset(v2, all_0_10_10) = v3))))
% 66.55/30.88 |
% 66.55/30.88 | Applying alpha-rule on (205) yields:
% 66.55/30.88 | (206) ! [v0] : ! [v1] : ( ~ (subrelstr(v0, all_0_11_11) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (( ~ (v2 = 0) & rel_str(v0) = v2) | (( ~ (v1 = 0) | (v5 = 0 & v3 = 0 & the_carrier(v0) = v2 & the_InternalRel(v0) = v4 & subset(v4, all_61_0_75) = 0 & subset(v2, all_0_10_10) = 0)) & (v1 = 0 | ( ~ (v5 = 0) & the_InternalRel(v0) = v4 & subset(v4, all_61_0_75) = v5) | ( ~ (v3 = 0) & the_carrier(v0) = v2 & subset(v2, all_0_10_10) = v3)))))
% 66.55/30.88 | (207) ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (( ~ (v2 = 0) & rel_str(v0) = v2) | (((v5 = 0 & v3 = 0 & the_InternalRel(v0) = v4 & subset(v4, all_61_0_75) = 0 & subset(v1, all_0_10_10) = 0) | ( ~ (v2 = 0) & subrelstr(v0, all_0_11_11) = v2)) & ((v2 = 0 & subrelstr(v0, all_0_11_11) = 0) | ( ~ (v5 = 0) & the_InternalRel(v0) = v4 & subset(v4, all_61_0_75) = v5) | ( ~ (v3 = 0) & subset(v1, all_0_10_10) = v3)))))
% 66.55/30.88 | (208) ! [v0] : ! [v1] : ( ~ (the_InternalRel(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (( ~ (v2 = 0) & rel_str(v0) = v2) | (((v5 = 0 & v4 = 0 & the_carrier(v0) = v3 & subset(v3, all_0_10_10) = 0 & subset(v1, all_61_0_75) = 0) | ( ~ (v2 = 0) & subrelstr(v0, all_0_11_11) = v2)) & ((v2 = 0 & subrelstr(v0, all_0_11_11) = 0) | ( ~ (v5 = 0) & subset(v1, all_61_0_75) = v5) | ( ~ (v4 = 0) & the_carrier(v0) = v3 & subset(v3, all_0_10_10) = v4)))))
% 66.55/30.88 | (209) the_InternalRel(all_0_11_11) = all_61_0_75
% 66.55/30.88 | (210) ! [v0] : ( ~ (rel_str(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (((v5 = 0 & v3 = 0 & the_carrier(v0) = v2 & the_InternalRel(v0) = v4 & subset(v4, all_61_0_75) = 0 & subset(v2, all_0_10_10) = 0) | ( ~ (v1 = 0) & subrelstr(v0, all_0_11_11) = v1)) & ((v1 = 0 & subrelstr(v0, all_0_11_11) = 0) | ( ~ (v5 = 0) & the_InternalRel(v0) = v4 & subset(v4, all_61_0_75) = v5) | ( ~ (v3 = 0) & the_carrier(v0) = v2 & subset(v2, all_0_10_10) = v3))))
% 66.55/30.88 |
% 66.55/30.88 +-Applying beta-rule and splitting (130), into two cases.
% 66.55/30.88 |-Branch one:
% 66.55/30.88 | (211) all_75_0_85 = 0 & relation_of2_as_subset(all_75_1_86, all_0_10_10, all_0_10_10) = 0 & the_InternalRel(all_0_11_11) = all_75_1_86
% 66.55/30.88 |
% 66.55/30.88 | Applying alpha-rule on (211) yields:
% 66.55/30.88 | (212) all_75_0_85 = 0
% 66.55/30.88 | (213) relation_of2_as_subset(all_75_1_86, all_0_10_10, all_0_10_10) = 0
% 66.55/30.88 | (214) the_InternalRel(all_0_11_11) = all_75_1_86
% 66.55/30.88 |
% 66.55/30.88 +-Applying beta-rule and splitting (141), into two cases.
% 66.55/30.88 |-Branch one:
% 66.55/30.88 | (215) ~ (all_88_0_97 = 0) & rel_str(all_0_13_13) = all_88_0_97
% 66.55/30.88 |
% 66.55/30.88 | Applying alpha-rule on (215) yields:
% 66.55/30.88 | (216) ~ (all_88_0_97 = 0)
% 66.55/30.88 | (217) rel_str(all_0_13_13) = all_88_0_97
% 66.55/30.88 |
% 66.55/30.88 | Instantiating formula (35) with all_0_13_13, all_88_0_97, 0 and discharging atoms rel_str(all_0_13_13) = all_88_0_97, rel_str(all_0_13_13) = 0, yields:
% 66.55/30.88 | (218) all_88_0_97 = 0
% 66.55/30.88 |
% 66.55/30.88 | Equations (218) can reduce 216 to:
% 66.55/30.88 | (148) $false
% 66.55/30.88 |
% 66.55/30.88 |-The branch is then unsatisfiable
% 66.55/30.88 |-Branch two:
% 66.55/30.88 | (220) the_InternalRel(all_0_13_13) = all_88_0_97 & ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (( ~ (v2 = 0) & rel_str(v0) = v2) | (((v5 = 0 & v3 = 0 & the_InternalRel(v0) = v4 & subset(v4, all_88_0_97) = 0 & subset(v1, all_0_12_12) = 0) | ( ~ (v2 = 0) & subrelstr(v0, all_0_13_13) = v2)) & ((v2 = 0 & subrelstr(v0, all_0_13_13) = 0) | ( ~ (v5 = 0) & the_InternalRel(v0) = v4 & subset(v4, all_88_0_97) = v5) | ( ~ (v3 = 0) & subset(v1, all_0_12_12) = v3))))) & ! [v0] : ! [v1] : ( ~ (subrelstr(v0, all_0_13_13) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (( ~ (v2 = 0) & rel_str(v0) = v2) | (( ~ (v1 = 0) | (v5 = 0 & v3 = 0 & the_carrier(v0) = v2 & the_InternalRel(v0) = v4 & subset(v4, all_88_0_97) = 0 & subset(v2, all_0_12_12) = 0)) & (v1 = 0 | ( ~ (v5 = 0) & the_InternalRel(v0) = v4 & subset(v4, all_88_0_97) = v5) | ( ~ (v3 = 0) & the_carrier(v0) = v2 & subset(v2, all_0_12_12) = v3))))) & ! [v0] : ! [v1] : ( ~ (the_InternalRel(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (( ~ (v2 = 0) & rel_str(v0) = v2) | (((v5 = 0 & v4 = 0 & the_carrier(v0) = v3 & subset(v3, all_0_12_12) = 0 & subset(v1, all_88_0_97) = 0) | ( ~ (v2 = 0) & subrelstr(v0, all_0_13_13) = v2)) & ((v2 = 0 & subrelstr(v0, all_0_13_13) = 0) | ( ~ (v5 = 0) & subset(v1, all_88_0_97) = v5) | ( ~ (v4 = 0) & the_carrier(v0) = v3 & subset(v3, all_0_12_12) = v4))))) & ! [v0] : ( ~ (rel_str(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (((v5 = 0 & v3 = 0 & the_carrier(v0) = v2 & the_InternalRel(v0) = v4 & subset(v4, all_88_0_97) = 0 & subset(v2, all_0_12_12) = 0) | ( ~ (v1 = 0) & subrelstr(v0, all_0_13_13) = v1)) & ((v1 = 0 & subrelstr(v0, all_0_13_13) = 0) | ( ~ (v5 = 0) & the_InternalRel(v0) = v4 & subset(v4, all_88_0_97) = v5) | ( ~ (v3 = 0) & the_carrier(v0) = v2 & subset(v2, all_0_12_12) = v3))))
% 66.55/30.88 |
% 66.55/30.88 | Applying alpha-rule on (220) yields:
% 66.55/30.88 | (221) the_InternalRel(all_0_13_13) = all_88_0_97
% 66.55/30.88 | (222) ! [v0] : ! [v1] : ( ~ (subrelstr(v0, all_0_13_13) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (( ~ (v2 = 0) & rel_str(v0) = v2) | (( ~ (v1 = 0) | (v5 = 0 & v3 = 0 & the_carrier(v0) = v2 & the_InternalRel(v0) = v4 & subset(v4, all_88_0_97) = 0 & subset(v2, all_0_12_12) = 0)) & (v1 = 0 | ( ~ (v5 = 0) & the_InternalRel(v0) = v4 & subset(v4, all_88_0_97) = v5) | ( ~ (v3 = 0) & the_carrier(v0) = v2 & subset(v2, all_0_12_12) = v3)))))
% 66.55/30.88 | (223) ! [v0] : ! [v1] : ( ~ (the_InternalRel(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (( ~ (v2 = 0) & rel_str(v0) = v2) | (((v5 = 0 & v4 = 0 & the_carrier(v0) = v3 & subset(v3, all_0_12_12) = 0 & subset(v1, all_88_0_97) = 0) | ( ~ (v2 = 0) & subrelstr(v0, all_0_13_13) = v2)) & ((v2 = 0 & subrelstr(v0, all_0_13_13) = 0) | ( ~ (v5 = 0) & subset(v1, all_88_0_97) = v5) | ( ~ (v4 = 0) & the_carrier(v0) = v3 & subset(v3, all_0_12_12) = v4)))))
% 66.55/30.88 | (224) ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (( ~ (v2 = 0) & rel_str(v0) = v2) | (((v5 = 0 & v3 = 0 & the_InternalRel(v0) = v4 & subset(v4, all_88_0_97) = 0 & subset(v1, all_0_12_12) = 0) | ( ~ (v2 = 0) & subrelstr(v0, all_0_13_13) = v2)) & ((v2 = 0 & subrelstr(v0, all_0_13_13) = 0) | ( ~ (v5 = 0) & the_InternalRel(v0) = v4 & subset(v4, all_88_0_97) = v5) | ( ~ (v3 = 0) & subset(v1, all_0_12_12) = v3)))))
% 66.55/30.88 | (225) ! [v0] : ( ~ (rel_str(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (((v5 = 0 & v3 = 0 & the_carrier(v0) = v2 & the_InternalRel(v0) = v4 & subset(v4, all_88_0_97) = 0 & subset(v2, all_0_12_12) = 0) | ( ~ (v1 = 0) & subrelstr(v0, all_0_13_13) = v1)) & ((v1 = 0 & subrelstr(v0, all_0_13_13) = 0) | ( ~ (v5 = 0) & the_InternalRel(v0) = v4 & subset(v4, all_88_0_97) = v5) | ( ~ (v3 = 0) & the_carrier(v0) = v2 & subset(v2, all_0_12_12) = v3))))
% 66.55/30.88 |
% 66.55/30.88 | Instantiating formula (224) with all_0_10_10, all_0_11_11 and discharging atoms the_carrier(all_0_11_11) = all_0_10_10, yields:
% 66.55/30.88 | (226) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (( ~ (v0 = 0) & rel_str(all_0_11_11) = v0) | (((v3 = 0 & v1 = 0 & the_InternalRel(all_0_11_11) = v2 & subset(v2, all_88_0_97) = 0 & subset(all_0_10_10, all_0_12_12) = 0) | ( ~ (v0 = 0) & subrelstr(all_0_11_11, all_0_13_13) = v0)) & ((v0 = 0 & subrelstr(all_0_11_11, all_0_13_13) = 0) | ( ~ (v3 = 0) & the_InternalRel(all_0_11_11) = v2 & subset(v2, all_88_0_97) = v3) | ( ~ (v1 = 0) & subset(all_0_10_10, all_0_12_12) = v1))))
% 66.55/30.89 |
% 66.55/30.89 | Instantiating formula (222) with 0, all_0_11_11 and discharging atoms subrelstr(all_0_11_11, all_0_13_13) = 0, yields:
% 66.55/30.89 | (227) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ((v3 = 0 & v1 = 0 & the_carrier(all_0_11_11) = v0 & the_InternalRel(all_0_11_11) = v2 & subset(v2, all_88_0_97) = 0 & subset(v0, all_0_12_12) = 0) | ( ~ (v0 = 0) & rel_str(all_0_11_11) = v0))
% 66.55/30.89 |
% 66.55/30.89 | Instantiating (227) with all_172_0_264, all_172_1_265, all_172_2_266, all_172_3_267 yields:
% 66.55/30.89 | (228) (all_172_0_264 = 0 & all_172_2_266 = 0 & the_carrier(all_0_11_11) = all_172_3_267 & the_InternalRel(all_0_11_11) = all_172_1_265 & subset(all_172_1_265, all_88_0_97) = 0 & subset(all_172_3_267, all_0_12_12) = 0) | ( ~ (all_172_3_267 = 0) & rel_str(all_0_11_11) = all_172_3_267)
% 66.55/30.89 |
% 66.55/30.89 | Instantiating (226) with all_175_0_277, all_175_1_278, all_175_2_279, all_175_3_280 yields:
% 66.55/30.89 | (229) ( ~ (all_175_3_280 = 0) & rel_str(all_0_11_11) = all_175_3_280) | (((all_175_0_277 = 0 & all_175_2_279 = 0 & the_InternalRel(all_0_11_11) = all_175_1_278 & subset(all_175_1_278, all_88_0_97) = 0 & subset(all_0_10_10, all_0_12_12) = 0) | ( ~ (all_175_3_280 = 0) & subrelstr(all_0_11_11, all_0_13_13) = all_175_3_280)) & ((all_175_3_280 = 0 & subrelstr(all_0_11_11, all_0_13_13) = 0) | ( ~ (all_175_0_277 = 0) & the_InternalRel(all_0_11_11) = all_175_1_278 & subset(all_175_1_278, all_88_0_97) = all_175_0_277) | ( ~ (all_175_2_279 = 0) & subset(all_0_10_10, all_0_12_12) = all_175_2_279)))
% 66.55/30.89 |
% 66.55/30.89 +-Applying beta-rule and splitting (228), into two cases.
% 66.55/30.89 |-Branch one:
% 66.55/30.89 | (230) all_172_0_264 = 0 & all_172_2_266 = 0 & the_carrier(all_0_11_11) = all_172_3_267 & the_InternalRel(all_0_11_11) = all_172_1_265 & subset(all_172_1_265, all_88_0_97) = 0 & subset(all_172_3_267, all_0_12_12) = 0
% 66.55/30.89 |
% 66.55/30.89 | Applying alpha-rule on (230) yields:
% 66.55/30.89 | (231) all_172_2_266 = 0
% 66.55/30.89 | (232) the_carrier(all_0_11_11) = all_172_3_267
% 66.55/30.89 | (233) subset(all_172_1_265, all_88_0_97) = 0
% 66.55/30.89 | (234) subset(all_172_3_267, all_0_12_12) = 0
% 66.55/30.89 | (235) the_InternalRel(all_0_11_11) = all_172_1_265
% 66.55/30.89 | (236) all_172_0_264 = 0
% 66.55/30.89 |
% 66.55/30.89 +-Applying beta-rule and splitting (142), into two cases.
% 66.55/30.89 |-Branch one:
% 66.55/30.89 | (237) all_89_0_98 = 0 & all_89_2_100 = 0 & the_carrier(all_0_11_11) = all_89_3_101 & the_InternalRel(all_0_11_11) = all_89_1_99 & subset(all_89_1_99, all_70_0_82) = 0 & subset(all_89_3_101, all_70_1_83) = 0
% 66.55/30.89 |
% 66.55/30.89 | Applying alpha-rule on (237) yields:
% 66.55/30.89 | (238) subset(all_89_1_99, all_70_0_82) = 0
% 66.55/30.89 | (239) all_89_2_100 = 0
% 66.55/30.89 | (240) the_carrier(all_0_11_11) = all_89_3_101
% 66.55/30.89 | (241) subset(all_89_3_101, all_70_1_83) = 0
% 66.55/30.89 | (242) the_InternalRel(all_0_11_11) = all_89_1_99
% 66.55/30.89 | (243) all_89_0_98 = 0
% 66.55/30.89 |
% 66.55/30.89 +-Applying beta-rule and splitting (229), into two cases.
% 66.55/30.89 |-Branch one:
% 66.55/30.89 | (244) ~ (all_175_3_280 = 0) & rel_str(all_0_11_11) = all_175_3_280
% 66.55/30.89 |
% 66.55/30.89 | Applying alpha-rule on (244) yields:
% 66.55/30.89 | (245) ~ (all_175_3_280 = 0)
% 66.55/30.89 | (246) rel_str(all_0_11_11) = all_175_3_280
% 66.55/30.89 |
% 66.55/30.89 | Instantiating formula (35) with all_0_11_11, 0, all_175_3_280 and discharging atoms rel_str(all_0_11_11) = all_175_3_280, rel_str(all_0_11_11) = 0, yields:
% 66.55/30.89 | (247) all_175_3_280 = 0
% 66.55/30.89 |
% 66.55/30.89 | Equations (247) can reduce 245 to:
% 66.55/30.89 | (148) $false
% 66.55/30.89 |
% 66.55/30.89 |-The branch is then unsatisfiable
% 66.55/30.89 |-Branch two:
% 66.55/30.89 | (249) ((all_175_0_277 = 0 & all_175_2_279 = 0 & the_InternalRel(all_0_11_11) = all_175_1_278 & subset(all_175_1_278, all_88_0_97) = 0 & subset(all_0_10_10, all_0_12_12) = 0) | ( ~ (all_175_3_280 = 0) & subrelstr(all_0_11_11, all_0_13_13) = all_175_3_280)) & ((all_175_3_280 = 0 & subrelstr(all_0_11_11, all_0_13_13) = 0) | ( ~ (all_175_0_277 = 0) & the_InternalRel(all_0_11_11) = all_175_1_278 & subset(all_175_1_278, all_88_0_97) = all_175_0_277) | ( ~ (all_175_2_279 = 0) & subset(all_0_10_10, all_0_12_12) = all_175_2_279))
% 66.55/30.89 |
% 66.55/30.89 | Applying alpha-rule on (249) yields:
% 66.55/30.89 | (250) (all_175_0_277 = 0 & all_175_2_279 = 0 & the_InternalRel(all_0_11_11) = all_175_1_278 & subset(all_175_1_278, all_88_0_97) = 0 & subset(all_0_10_10, all_0_12_12) = 0) | ( ~ (all_175_3_280 = 0) & subrelstr(all_0_11_11, all_0_13_13) = all_175_3_280)
% 66.55/30.89 | (251) (all_175_3_280 = 0 & subrelstr(all_0_11_11, all_0_13_13) = 0) | ( ~ (all_175_0_277 = 0) & the_InternalRel(all_0_11_11) = all_175_1_278 & subset(all_175_1_278, all_88_0_97) = all_175_0_277) | ( ~ (all_175_2_279 = 0) & subset(all_0_10_10, all_0_12_12) = all_175_2_279)
% 66.55/30.89 |
% 66.55/30.89 +-Applying beta-rule and splitting (199), into two cases.
% 66.55/30.89 |-Branch one:
% 66.55/30.89 | (252) ~ (all_146_1_236 = 0) & element(all_0_8_8, all_0_12_12) = all_146_1_236
% 66.55/30.89 |
% 66.55/30.89 | Applying alpha-rule on (252) yields:
% 66.55/30.89 | (253) ~ (all_146_1_236 = 0)
% 66.55/30.89 | (254) element(all_0_8_8, all_0_12_12) = all_146_1_236
% 66.55/30.89 |
% 66.55/30.89 | Instantiating formula (27) with all_0_8_8, all_0_12_12, all_146_1_236, 0 and discharging atoms element(all_0_8_8, all_0_12_12) = all_146_1_236, element(all_0_8_8, all_0_12_12) = 0, yields:
% 66.55/30.89 | (255) all_146_1_236 = 0
% 66.55/30.89 |
% 66.55/30.89 | Equations (255) can reduce 253 to:
% 66.55/30.89 | (148) $false
% 66.55/30.89 |
% 66.55/30.89 |-The branch is then unsatisfiable
% 66.55/30.89 |-Branch two:
% 66.55/30.89 | (257) ( ~ (all_0_7_7 = 0) | (all_146_0_235 = 0 & ordered_pair(all_0_9_9, all_0_8_8) = all_146_1_236 & in(all_146_1_236, all_59_0_72) = 0)) & (all_0_7_7 = 0 | ( ~ (all_146_0_235 = 0) & ordered_pair(all_0_9_9, all_0_8_8) = all_146_1_236 & in(all_146_1_236, all_59_0_72) = all_146_0_235))
% 66.55/30.89 |
% 66.55/30.89 | Applying alpha-rule on (257) yields:
% 66.55/30.89 | (258) ~ (all_0_7_7 = 0) | (all_146_0_235 = 0 & ordered_pair(all_0_9_9, all_0_8_8) = all_146_1_236 & in(all_146_1_236, all_59_0_72) = 0)
% 66.55/30.89 | (259) all_0_7_7 = 0 | ( ~ (all_146_0_235 = 0) & ordered_pair(all_0_9_9, all_0_8_8) = all_146_1_236 & in(all_146_1_236, all_59_0_72) = all_146_0_235)
% 66.55/30.89 |
% 66.55/30.89 +-Applying beta-rule and splitting (198), into two cases.
% 66.55/30.89 |-Branch one:
% 66.55/30.89 | (260) all_145_2_234 = 0 & related(all_0_13_13, all_0_9_9, all_0_8_8) = 0
% 66.55/30.89 |
% 66.55/30.89 | Applying alpha-rule on (260) yields:
% 66.55/30.89 | (261) all_145_2_234 = 0
% 66.55/30.89 | (262) related(all_0_13_13, all_0_9_9, all_0_8_8) = 0
% 66.55/30.89 |
% 66.55/30.89 +-Applying beta-rule and splitting (259), into two cases.
% 66.55/30.89 |-Branch one:
% 66.55/30.89 | (263) all_0_7_7 = 0
% 66.55/30.89 |
% 66.55/30.89 | Equations (263) can reduce 80 to:
% 66.55/30.89 | (148) $false
% 66.55/30.89 |
% 66.55/30.89 |-The branch is then unsatisfiable
% 66.55/30.89 |-Branch two:
% 66.55/30.89 | (80) ~ (all_0_7_7 = 0)
% 66.55/30.89 | (266) ~ (all_146_0_235 = 0) & ordered_pair(all_0_9_9, all_0_8_8) = all_146_1_236 & in(all_146_1_236, all_59_0_72) = all_146_0_235
% 66.55/30.89 |
% 66.55/30.89 | Instantiating formula (32) with all_0_13_13, all_0_9_9, all_0_8_8, 0, all_0_7_7 and discharging atoms related(all_0_13_13, all_0_9_9, all_0_8_8) = all_0_7_7, related(all_0_13_13, all_0_9_9, all_0_8_8) = 0, yields:
% 66.55/30.89 | (263) all_0_7_7 = 0
% 66.55/30.89 |
% 66.55/30.89 | Equations (263) can reduce 80 to:
% 66.55/30.89 | (148) $false
% 66.55/30.89 |
% 66.55/30.89 |-The branch is then unsatisfiable
% 66.55/30.89 |-Branch two:
% 66.55/30.89 | (269) ~ (all_145_0_232 = 0) & ordered_pair(all_0_9_9, all_0_8_8) = all_145_1_233 & in(all_145_1_233, all_59_0_72) = all_145_0_232
% 66.55/30.89 |
% 66.55/30.89 | Applying alpha-rule on (269) yields:
% 66.55/30.89 | (270) ~ (all_145_0_232 = 0)
% 66.55/30.89 | (271) ordered_pair(all_0_9_9, all_0_8_8) = all_145_1_233
% 66.55/30.89 | (272) in(all_145_1_233, all_59_0_72) = all_145_0_232
% 66.55/30.89 |
% 66.55/30.89 +-Applying beta-rule and splitting (250), into two cases.
% 66.55/30.89 |-Branch one:
% 66.55/30.89 | (273) all_175_0_277 = 0 & all_175_2_279 = 0 & the_InternalRel(all_0_11_11) = all_175_1_278 & subset(all_175_1_278, all_88_0_97) = 0 & subset(all_0_10_10, all_0_12_12) = 0
% 66.55/30.89 |
% 66.55/30.89 | Applying alpha-rule on (273) yields:
% 66.55/30.89 | (274) subset(all_175_1_278, all_88_0_97) = 0
% 66.55/30.89 | (275) the_InternalRel(all_0_11_11) = all_175_1_278
% 66.55/30.89 | (276) all_175_0_277 = 0
% 66.55/30.89 | (277) all_175_2_279 = 0
% 66.55/30.89 | (278) subset(all_0_10_10, all_0_12_12) = 0
% 66.55/30.89 |
% 66.55/30.89 +-Applying beta-rule and splitting (259), into two cases.
% 66.55/30.89 |-Branch one:
% 66.55/30.89 | (263) all_0_7_7 = 0
% 66.55/30.89 |
% 66.55/30.89 | Equations (263) can reduce 80 to:
% 66.55/30.89 | (148) $false
% 66.55/30.89 |
% 66.55/30.89 |-The branch is then unsatisfiable
% 66.55/30.89 |-Branch two:
% 66.55/30.89 | (80) ~ (all_0_7_7 = 0)
% 66.55/30.89 | (266) ~ (all_146_0_235 = 0) & ordered_pair(all_0_9_9, all_0_8_8) = all_146_1_236 & in(all_146_1_236, all_59_0_72) = all_146_0_235
% 66.55/30.89 |
% 66.55/30.89 | Applying alpha-rule on (266) yields:
% 66.55/30.89 | (283) ~ (all_146_0_235 = 0)
% 66.55/30.89 | (284) ordered_pair(all_0_9_9, all_0_8_8) = all_146_1_236
% 66.55/30.89 | (285) in(all_146_1_236, all_59_0_72) = all_146_0_235
% 66.55/30.89 |
% 66.55/30.89 | Instantiating formula (72) with all_0_9_9, all_0_8_8, all_145_1_233, all_146_1_236 and discharging atoms ordered_pair(all_0_9_9, all_0_8_8) = all_146_1_236, ordered_pair(all_0_9_9, all_0_8_8) = all_145_1_233, yields:
% 66.55/30.89 | (286) all_146_1_236 = all_145_1_233
% 66.55/30.89 |
% 66.55/30.89 | Instantiating formula (72) with all_0_9_9, all_0_8_8, all_104_1_168, all_146_1_236 and discharging atoms ordered_pair(all_0_9_9, all_0_8_8) = all_146_1_236, ordered_pair(all_0_9_9, all_0_8_8) = all_104_1_168, yields:
% 66.55/30.89 | (287) all_146_1_236 = all_104_1_168
% 66.55/30.89 |
% 66.55/30.89 | Instantiating formula (87) with all_0_11_11, all_172_1_265, all_175_1_278 and discharging atoms the_InternalRel(all_0_11_11) = all_175_1_278, the_InternalRel(all_0_11_11) = all_172_1_265, yields:
% 66.55/30.89 | (288) all_175_1_278 = all_172_1_265
% 66.55/30.89 |
% 66.55/30.89 | Instantiating formula (87) with all_0_11_11, all_93_1_117, all_175_1_278 and discharging atoms the_InternalRel(all_0_11_11) = all_175_1_278, the_InternalRel(all_0_11_11) = all_93_1_117, yields:
% 66.55/30.89 | (289) all_175_1_278 = all_93_1_117
% 66.55/30.89 |
% 66.55/30.89 | Instantiating formula (87) with all_0_11_11, all_89_1_99, all_172_1_265 and discharging atoms the_InternalRel(all_0_11_11) = all_172_1_265, the_InternalRel(all_0_11_11) = all_89_1_99, yields:
% 66.55/30.89 | (290) all_172_1_265 = all_89_1_99
% 66.55/30.89 |
% 66.55/30.89 | Instantiating formula (87) with all_0_11_11, all_75_1_86, all_89_1_99 and discharging atoms the_InternalRel(all_0_11_11) = all_89_1_99, the_InternalRel(all_0_11_11) = all_75_1_86, yields:
% 66.55/30.89 | (291) all_89_1_99 = all_75_1_86
% 66.55/30.89 |
% 66.55/30.89 | Instantiating formula (87) with all_0_11_11, all_62_0_76, all_75_1_86 and discharging atoms the_InternalRel(all_0_11_11) = all_75_1_86, the_InternalRel(all_0_11_11) = all_62_0_76, yields:
% 66.55/30.89 | (292) all_75_1_86 = all_62_0_76
% 66.55/30.89 |
% 66.55/30.89 | Instantiating formula (87) with all_0_11_11, all_61_0_75, all_172_1_265 and discharging atoms the_InternalRel(all_0_11_11) = all_172_1_265, the_InternalRel(all_0_11_11) = all_61_0_75, yields:
% 66.55/30.89 | (293) all_172_1_265 = all_61_0_75
% 66.55/30.89 |
% 66.55/30.89 | Instantiating formula (87) with all_0_13_13, all_86_1_96, all_88_0_97 and discharging atoms the_InternalRel(all_0_13_13) = all_88_0_97, the_InternalRel(all_0_13_13) = all_86_1_96, yields:
% 66.55/30.89 | (294) all_88_0_97 = all_86_1_96
% 66.55/30.89 |
% 66.55/30.89 | Instantiating formula (87) with all_0_13_13, all_81_0_91, all_86_1_96 and discharging atoms the_InternalRel(all_0_13_13) = all_86_1_96, the_InternalRel(all_0_13_13) = all_81_0_91, yields:
% 66.55/30.89 | (295) all_86_1_96 = all_81_0_91
% 66.55/30.89 |
% 66.55/30.89 | Instantiating formula (87) with all_0_13_13, all_70_0_82, all_88_0_97 and discharging atoms the_InternalRel(all_0_13_13) = all_88_0_97, the_InternalRel(all_0_13_13) = all_70_0_82, yields:
% 66.55/30.89 | (296) all_88_0_97 = all_70_0_82
% 66.55/30.89 |
% 66.55/30.89 | Instantiating formula (87) with all_0_13_13, all_60_1_74, all_86_1_96 and discharging atoms the_InternalRel(all_0_13_13) = all_86_1_96, the_InternalRel(all_0_13_13) = all_60_1_74, yields:
% 66.55/30.90 | (297) all_86_1_96 = all_60_1_74
% 66.55/30.90 |
% 66.55/30.90 | Instantiating formula (87) with all_0_13_13, all_59_0_72, all_88_0_97 and discharging atoms the_InternalRel(all_0_13_13) = all_88_0_97, the_InternalRel(all_0_13_13) = all_59_0_72, yields:
% 66.55/30.90 | (298) all_88_0_97 = all_59_0_72
% 66.55/30.90 |
% 66.55/30.90 | Combining equations (288,289) yields a new equation:
% 66.55/30.90 | (299) all_172_1_265 = all_93_1_117
% 66.55/30.90 |
% 66.55/30.90 | Simplifying 299 yields:
% 66.55/30.90 | (300) all_172_1_265 = all_93_1_117
% 66.55/30.90 |
% 66.55/30.90 | Combining equations (293,300) yields a new equation:
% 66.55/30.90 | (301) all_93_1_117 = all_61_0_75
% 66.55/30.90 |
% 66.55/30.90 | Combining equations (290,300) yields a new equation:
% 66.55/30.90 | (302) all_93_1_117 = all_89_1_99
% 66.55/30.90 |
% 66.55/30.90 | Combining equations (286,287) yields a new equation:
% 66.55/30.90 | (303) all_145_1_233 = all_104_1_168
% 66.55/30.90 |
% 66.55/30.90 | Simplifying 303 yields:
% 66.55/30.90 | (304) all_145_1_233 = all_104_1_168
% 66.55/30.90 |
% 66.55/30.90 | Combining equations (302,301) yields a new equation:
% 66.55/30.90 | (305) all_89_1_99 = all_61_0_75
% 66.55/30.90 |
% 66.55/30.90 | Simplifying 305 yields:
% 66.55/30.90 | (306) all_89_1_99 = all_61_0_75
% 66.55/30.90 |
% 66.55/30.90 | Combining equations (291,306) yields a new equation:
% 66.55/30.90 | (307) all_75_1_86 = all_61_0_75
% 66.55/30.90 |
% 66.55/30.90 | Simplifying 307 yields:
% 66.55/30.90 | (308) all_75_1_86 = all_61_0_75
% 66.55/30.90 |
% 66.55/30.90 | Combining equations (298,296) yields a new equation:
% 66.55/30.90 | (309) all_70_0_82 = all_59_0_72
% 66.55/30.90 |
% 66.55/30.90 | Combining equations (294,296) yields a new equation:
% 66.55/30.90 | (310) all_86_1_96 = all_70_0_82
% 66.55/30.90 |
% 66.55/30.90 | Simplifying 310 yields:
% 66.55/30.90 | (311) all_86_1_96 = all_70_0_82
% 66.55/30.90 |
% 66.55/30.90 | Combining equations (297,295) yields a new equation:
% 66.55/30.90 | (312) all_81_0_91 = all_60_1_74
% 66.55/30.90 |
% 66.55/30.90 | Combining equations (311,295) yields a new equation:
% 66.55/30.90 | (313) all_81_0_91 = all_70_0_82
% 66.55/30.90 |
% 66.55/30.90 | Combining equations (313,312) yields a new equation:
% 66.55/30.90 | (314) all_70_0_82 = all_60_1_74
% 66.55/30.90 |
% 66.55/30.90 | Simplifying 314 yields:
% 66.55/30.90 | (315) all_70_0_82 = all_60_1_74
% 66.55/30.90 |
% 66.55/30.90 | Combining equations (292,308) yields a new equation:
% 66.55/30.90 | (316) all_62_0_76 = all_61_0_75
% 66.55/30.90 |
% 66.55/30.90 | Simplifying 316 yields:
% 66.55/30.90 | (317) all_62_0_76 = all_61_0_75
% 66.55/30.90 |
% 66.55/30.90 | Combining equations (309,315) yields a new equation:
% 66.55/30.90 | (318) all_60_1_74 = all_59_0_72
% 66.55/30.90 |
% 66.55/30.90 | Combining equations (318,315) yields a new equation:
% 66.55/30.90 | (309) all_70_0_82 = all_59_0_72
% 66.55/30.90 |
% 66.55/30.90 | From (306)(309) and (238) follows:
% 66.55/30.90 | (320) subset(all_61_0_75, all_59_0_72) = 0
% 66.55/30.90 |
% 66.55/30.90 | From (287) and (285) follows:
% 66.55/30.90 | (321) in(all_104_1_168, all_59_0_72) = all_146_0_235
% 66.55/30.90 |
% 66.55/30.90 | From (304) and (272) follows:
% 66.55/30.90 | (322) in(all_104_1_168, all_59_0_72) = all_145_0_232
% 66.55/30.90 |
% 66.55/30.90 | From (317) and (165) follows:
% 66.55/30.90 | (323) in(all_104_1_168, all_61_0_75) = 0
% 66.55/30.90 |
% 66.55/30.90 | Instantiating formula (8) with all_104_1_168, all_59_0_72, all_145_0_232, all_146_0_235 and discharging atoms in(all_104_1_168, all_59_0_72) = all_146_0_235, in(all_104_1_168, all_59_0_72) = all_145_0_232, yields:
% 66.55/30.90 | (324) all_146_0_235 = all_145_0_232
% 66.55/30.90 |
% 66.55/30.90 | Equations (324) can reduce 283 to:
% 66.55/30.90 | (270) ~ (all_145_0_232 = 0)
% 66.55/30.90 |
% 66.55/30.90 | From (324) and (321) follows:
% 66.55/30.90 | (322) in(all_104_1_168, all_59_0_72) = all_145_0_232
% 66.55/30.90 |
% 66.55/30.90 | Instantiating formula (100) with all_59_0_72, all_61_0_75 and discharging atoms subset(all_61_0_75, all_59_0_72) = 0, yields:
% 66.55/30.90 | (327) ? [v0] : (powerset(all_59_0_72) = v0 & element(all_61_0_75, v0) = 0)
% 66.55/30.90 |
% 66.55/30.90 | Instantiating formula (16) with all_145_0_232, all_59_0_72, all_104_1_168 and discharging atoms in(all_104_1_168, all_59_0_72) = all_145_0_232, yields:
% 66.55/30.90 | (328) all_145_0_232 = 0 | ? [v0] : ((v0 = 0 & empty(all_59_0_72) = 0) | ( ~ (v0 = 0) & element(all_104_1_168, all_59_0_72) = v0))
% 66.55/30.90 |
% 66.55/30.90 | Instantiating (327) with all_292_0_411 yields:
% 66.55/30.90 | (329) powerset(all_59_0_72) = all_292_0_411 & element(all_61_0_75, all_292_0_411) = 0
% 66.55/30.90 |
% 66.55/30.90 | Applying alpha-rule on (329) yields:
% 66.55/30.90 | (330) powerset(all_59_0_72) = all_292_0_411
% 66.55/30.90 | (331) element(all_61_0_75, all_292_0_411) = 0
% 66.55/30.90 |
% 66.55/30.90 +-Applying beta-rule and splitting (328), into two cases.
% 66.55/30.90 |-Branch one:
% 66.55/30.90 | (332) all_145_0_232 = 0
% 66.55/30.90 |
% 66.55/30.90 | Equations (332) can reduce 270 to:
% 66.55/30.90 | (148) $false
% 66.55/30.90 |
% 66.55/30.90 |-The branch is then unsatisfiable
% 66.55/30.90 |-Branch two:
% 66.55/30.90 | (270) ~ (all_145_0_232 = 0)
% 66.55/30.90 | (335) ? [v0] : ((v0 = 0 & empty(all_59_0_72) = 0) | ( ~ (v0 = 0) & element(all_104_1_168, all_59_0_72) = v0))
% 66.55/30.90 |
% 66.55/30.90 | Instantiating (335) with all_402_0_820 yields:
% 66.55/30.90 | (336) (all_402_0_820 = 0 & empty(all_59_0_72) = 0) | ( ~ (all_402_0_820 = 0) & element(all_104_1_168, all_59_0_72) = all_402_0_820)
% 66.55/30.90 |
% 66.55/30.90 | Instantiating formula (93) with all_292_0_411, all_59_0_72, all_61_0_75, all_104_1_168 and discharging atoms powerset(all_59_0_72) = all_292_0_411, element(all_61_0_75, all_292_0_411) = 0, in(all_104_1_168, all_61_0_75) = 0, yields:
% 66.55/30.90 | (337) element(all_104_1_168, all_59_0_72) = 0
% 66.55/30.90 |
% 66.55/30.90 | Instantiating formula (12) with all_292_0_411, all_59_0_72, all_61_0_75, all_104_1_168 and discharging atoms powerset(all_59_0_72) = all_292_0_411, element(all_61_0_75, all_292_0_411) = 0, in(all_104_1_168, all_61_0_75) = 0, yields:
% 66.55/30.90 | (338) ? [v0] : ( ~ (v0 = 0) & empty(all_59_0_72) = v0)
% 66.55/30.90 |
% 66.55/30.90 | Instantiating (338) with all_996_0_5420 yields:
% 66.55/30.90 | (339) ~ (all_996_0_5420 = 0) & empty(all_59_0_72) = all_996_0_5420
% 66.55/30.90 |
% 66.55/30.90 | Applying alpha-rule on (339) yields:
% 66.55/30.90 | (340) ~ (all_996_0_5420 = 0)
% 66.55/30.90 | (341) empty(all_59_0_72) = all_996_0_5420
% 66.55/30.90 |
% 66.55/30.90 +-Applying beta-rule and splitting (336), into two cases.
% 66.55/30.90 |-Branch one:
% 66.55/30.90 | (342) all_402_0_820 = 0 & empty(all_59_0_72) = 0
% 66.55/30.90 |
% 66.55/30.90 | Applying alpha-rule on (342) yields:
% 66.55/30.90 | (343) all_402_0_820 = 0
% 66.55/30.90 | (344) empty(all_59_0_72) = 0
% 66.55/30.90 |
% 66.55/30.90 | Instantiating formula (23) with all_59_0_72, 0, all_996_0_5420 and discharging atoms empty(all_59_0_72) = all_996_0_5420, empty(all_59_0_72) = 0, yields:
% 66.55/30.90 | (345) all_996_0_5420 = 0
% 66.55/30.90 |
% 66.55/30.90 | Equations (345) can reduce 340 to:
% 66.55/30.90 | (148) $false
% 66.55/30.90 |
% 66.55/30.90 |-The branch is then unsatisfiable
% 66.55/30.90 |-Branch two:
% 66.55/30.90 | (347) ~ (all_402_0_820 = 0) & element(all_104_1_168, all_59_0_72) = all_402_0_820
% 66.55/30.90 |
% 66.55/30.90 | Applying alpha-rule on (347) yields:
% 66.55/30.90 | (348) ~ (all_402_0_820 = 0)
% 66.55/30.90 | (349) element(all_104_1_168, all_59_0_72) = all_402_0_820
% 66.55/30.90 |
% 66.55/30.90 | Instantiating formula (27) with all_104_1_168, all_59_0_72, 0, all_402_0_820 and discharging atoms element(all_104_1_168, all_59_0_72) = all_402_0_820, element(all_104_1_168, all_59_0_72) = 0, yields:
% 66.55/30.90 | (343) all_402_0_820 = 0
% 66.55/30.90 |
% 66.55/30.90 | Equations (343) can reduce 348 to:
% 66.55/30.90 | (148) $false
% 66.55/30.90 |
% 66.55/30.90 |-The branch is then unsatisfiable
% 66.55/30.90 |-Branch two:
% 66.55/30.90 | (352) ~ (all_175_3_280 = 0) & subrelstr(all_0_11_11, all_0_13_13) = all_175_3_280
% 66.55/30.90 |
% 66.55/30.90 | Applying alpha-rule on (352) yields:
% 66.55/30.90 | (245) ~ (all_175_3_280 = 0)
% 66.55/30.90 | (354) subrelstr(all_0_11_11, all_0_13_13) = all_175_3_280
% 66.55/30.90 |
% 66.55/30.90 | Instantiating formula (92) with all_0_11_11, all_0_13_13, all_175_3_280, 0 and discharging atoms subrelstr(all_0_11_11, all_0_13_13) = all_175_3_280, subrelstr(all_0_11_11, all_0_13_13) = 0, yields:
% 66.55/30.90 | (247) all_175_3_280 = 0
% 66.55/30.90 |
% 66.55/30.90 | Equations (247) can reduce 245 to:
% 66.55/30.90 | (148) $false
% 66.55/30.90 |
% 66.55/30.90 |-The branch is then unsatisfiable
% 66.55/30.90 |-Branch two:
% 66.55/30.90 | (357) ~ (all_89_3_101 = 0) & rel_str(all_0_11_11) = all_89_3_101
% 66.55/30.90 |
% 66.55/30.90 | Applying alpha-rule on (357) yields:
% 66.55/30.90 | (358) ~ (all_89_3_101 = 0)
% 66.55/30.90 | (359) rel_str(all_0_11_11) = all_89_3_101
% 66.55/30.90 |
% 66.55/30.90 | Instantiating formula (35) with all_0_11_11, 0, all_89_3_101 and discharging atoms rel_str(all_0_11_11) = all_89_3_101, rel_str(all_0_11_11) = 0, yields:
% 66.55/30.90 | (360) all_89_3_101 = 0
% 66.55/30.90 |
% 66.55/30.90 | Equations (360) can reduce 358 to:
% 66.55/30.90 | (148) $false
% 66.55/30.90 |
% 66.55/30.90 |-The branch is then unsatisfiable
% 66.55/30.90 |-Branch two:
% 66.55/30.90 | (362) ~ (all_172_3_267 = 0) & rel_str(all_0_11_11) = all_172_3_267
% 66.55/30.90 |
% 66.55/30.90 | Applying alpha-rule on (362) yields:
% 66.55/30.90 | (363) ~ (all_172_3_267 = 0)
% 66.55/30.90 | (364) rel_str(all_0_11_11) = all_172_3_267
% 66.55/30.90 |
% 66.55/30.90 | Instantiating formula (35) with all_0_11_11, 0, all_172_3_267 and discharging atoms rel_str(all_0_11_11) = all_172_3_267, rel_str(all_0_11_11) = 0, yields:
% 66.55/30.90 | (365) all_172_3_267 = 0
% 66.55/30.90 |
% 66.55/30.90 | Equations (365) can reduce 363 to:
% 66.55/30.90 | (148) $false
% 66.55/30.90 |
% 66.55/30.90 |-The branch is then unsatisfiable
% 66.55/30.90 |-Branch two:
% 66.55/30.90 | (367) ~ (all_75_1_86 = 0) & rel_str(all_0_11_11) = all_75_1_86
% 66.55/30.90 |
% 66.55/30.90 | Applying alpha-rule on (367) yields:
% 66.55/30.90 | (368) ~ (all_75_1_86 = 0)
% 66.55/30.90 | (369) rel_str(all_0_11_11) = all_75_1_86
% 66.55/30.90 |
% 66.55/30.90 | Instantiating formula (35) with all_0_11_11, 0, all_75_1_86 and discharging atoms rel_str(all_0_11_11) = all_75_1_86, rel_str(all_0_11_11) = 0, yields:
% 66.55/30.91 | (370) all_75_1_86 = 0
% 66.55/30.91 |
% 66.55/30.91 | Equations (370) can reduce 368 to:
% 66.55/30.91 | (148) $false
% 66.55/30.91 |
% 66.55/30.91 |-The branch is then unsatisfiable
% 66.55/30.91 |-Branch two:
% 66.55/30.91 | (372) ~ (all_93_0_116 = 0) & the_InternalRel(all_0_11_11) = all_93_1_117 & subset(all_93_1_117, all_70_0_82) = all_93_0_116
% 66.55/30.91 |
% 66.55/30.91 | Applying alpha-rule on (372) yields:
% 66.55/30.91 | (373) ~ (all_93_0_116 = 0)
% 66.55/30.91 | (177) the_InternalRel(all_0_11_11) = all_93_1_117
% 66.55/30.91 | (375) subset(all_93_1_117, all_70_0_82) = all_93_0_116
% 66.55/30.91 |
% 66.55/30.91 | Equations (179) can reduce 373 to:
% 66.55/30.91 | (148) $false
% 66.55/30.91 |
% 66.55/30.91 |-The branch is then unsatisfiable
% 66.55/30.91 |-Branch two:
% 66.55/30.91 | (377) ~ (all_93_2_118 = 0) & subset(all_0_10_10, all_70_1_83) = all_93_2_118
% 66.55/30.91 |
% 66.55/30.91 | Applying alpha-rule on (377) yields:
% 66.55/30.91 | (378) ~ (all_93_2_118 = 0)
% 66.55/30.91 | (379) subset(all_0_10_10, all_70_1_83) = all_93_2_118
% 66.55/30.91 |
% 66.55/30.91 | Equations (178) can reduce 378 to:
% 66.55/30.91 | (148) $false
% 66.55/30.91 |
% 66.55/30.91 |-The branch is then unsatisfiable
% 66.55/30.91 |-Branch two:
% 66.55/30.91 | (381) ~ (all_93_3_119 = 0) & subrelstr(all_0_11_11, all_0_13_13) = all_93_3_119
% 66.55/30.91 |
% 66.55/30.91 | Applying alpha-rule on (381) yields:
% 66.55/30.91 | (167) ~ (all_93_3_119 = 0)
% 66.55/30.91 | (383) subrelstr(all_0_11_11, all_0_13_13) = all_93_3_119
% 66.55/30.91 |
% 66.55/30.91 | Instantiating formula (92) with all_0_11_11, all_0_13_13, all_93_3_119, 0 and discharging atoms subrelstr(all_0_11_11, all_0_13_13) = all_93_3_119, subrelstr(all_0_11_11, all_0_13_13) = 0, yields:
% 66.55/30.91 | (169) all_93_3_119 = 0
% 66.55/30.91 |
% 66.55/30.91 | Equations (169) can reduce 167 to:
% 66.55/30.91 | (148) $false
% 66.55/30.91 |
% 66.55/30.91 |-The branch is then unsatisfiable
% 66.55/30.91 |-Branch two:
% 66.55/30.91 | (386) ~ (all_104_2_169 = 0) & related(all_0_11_11, all_0_9_9, all_0_8_8) = all_104_2_169
% 66.55/30.91 |
% 66.55/30.91 | Applying alpha-rule on (386) yields:
% 66.55/30.91 | (387) ~ (all_104_2_169 = 0)
% 66.55/30.91 | (388) related(all_0_11_11, all_0_9_9, all_0_8_8) = all_104_2_169
% 66.55/30.91 |
% 66.55/30.91 | Instantiating formula (32) with all_0_11_11, all_0_9_9, all_0_8_8, all_104_2_169, 0 and discharging atoms related(all_0_11_11, all_0_9_9, all_0_8_8) = all_104_2_169, related(all_0_11_11, all_0_9_9, all_0_8_8) = 0, yields:
% 66.55/30.91 | (389) all_104_2_169 = 0
% 66.55/30.91 |
% 66.55/30.91 | Equations (389) can reduce 387 to:
% 66.55/30.91 | (148) $false
% 66.55/30.91 |
% 66.55/30.91 |-The branch is then unsatisfiable
% 66.55/30.91 |-Branch two:
% 66.55/30.91 | (391) ~ (all_60_1_74 = 0) & rel_str(all_0_13_13) = all_60_1_74
% 66.55/30.91 |
% 66.55/30.91 | Applying alpha-rule on (391) yields:
% 66.55/30.91 | (392) ~ (all_60_1_74 = 0)
% 66.55/30.91 | (393) rel_str(all_0_13_13) = all_60_1_74
% 66.55/30.91 |
% 66.55/30.91 | Instantiating formula (35) with all_0_13_13, all_60_1_74, 0 and discharging atoms rel_str(all_0_13_13) = all_60_1_74, rel_str(all_0_13_13) = 0, yields:
% 66.55/30.91 | (394) all_60_1_74 = 0
% 66.55/30.91 |
% 66.55/30.91 | Equations (394) can reduce 392 to:
% 66.55/30.91 | (148) $false
% 66.55/30.91 |
% 66.55/30.91 |-The branch is then unsatisfiable
% 66.55/30.91 % SZS output end Proof for theBenchmark
% 66.55/30.91
% 66.55/30.91 30327ms
%------------------------------------------------------------------------------