TSTP Solution File: SEU344+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU344+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n004.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 08:49:02 EDT 2022
% Result : Theorem 13.75s 3.83s
% Output : Proof 111.03s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU344+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.34 % Computer : n004.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 20 11:22:08 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.52/0.59 ____ _
% 0.52/0.59 ___ / __ \_____(_)___ ________ __________
% 0.52/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.52/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.52/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.52/0.59
% 0.52/0.59 A Theorem Prover for First-Order Logic
% 0.52/0.59 (ePrincess v.1.0)
% 0.52/0.59
% 0.52/0.59 (c) Philipp Rümmer, 2009-2015
% 0.52/0.59 (c) Peter Backeman, 2014-2015
% 0.52/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.52/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.52/0.59 Bug reports to peter@backeman.se
% 0.52/0.59
% 0.52/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.52/0.59
% 0.52/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.73/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.86/1.03 Prover 0: Preprocessing ...
% 3.60/1.45 Prover 0: Warning: ignoring some quantifiers
% 3.69/1.49 Prover 0: Constructing countermodel ...
% 5.96/2.03 Prover 0: gave up
% 5.96/2.03 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 6.38/2.09 Prover 1: Preprocessing ...
% 7.15/2.26 Prover 1: Warning: ignoring some quantifiers
% 7.15/2.27 Prover 1: Constructing countermodel ...
% 10.62/3.06 Prover 1: gave up
% 10.62/3.06 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 10.62/3.12 Prover 2: Preprocessing ...
% 11.84/3.32 Prover 2: Warning: ignoring some quantifiers
% 11.84/3.34 Prover 2: Constructing countermodel ...
% 13.75/3.83 Prover 2: proved (763ms)
% 13.75/3.83
% 13.75/3.83 No countermodel exists, formula is valid
% 13.75/3.83 % SZS status Theorem for theBenchmark
% 13.75/3.83
% 13.75/3.83 Generating proof ... Warning: ignoring some quantifiers
% 109.38/75.38 found it (size 400)
% 109.38/75.38
% 109.38/75.38 % SZS output start Proof for theBenchmark
% 109.38/75.38 Assumed formulas after preprocessing and simplification:
% 109.38/75.38 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ( ~ (v13 = 0) & ~ (v10 = 0) & ~ (v8 = 0) & subset(v1, v4) = v6 & one_sorted_str(v17) = 0 & one_sorted_str(v9) = 0 & empty(v14) = 0 & empty(v12) = v13 & empty(empty_set) = 0 & boole_lattice(v0) = v2 & below(v2, v1, v4) = v5 & meet_semilatt_str(v18) = 0 & empty_carrier(v9) = v10 & empty_carrier(v7) = v8 & join_semilatt_str(v16) = 0 & element(v4, v3) = 0 & element(v1, v3) = 0 & strict_latt_str(v11) = 0 & strict_latt_str(v7) = 0 & latt_str(v15) = 0 & latt_str(v11) = 0 & latt_str(v7) = 0 & the_carrier(v2) = v3 & ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : (v20 = v19 | ~ (apply_binary_as_element(v26, v25, v24, v23, v22, v21) = v20) | ~ (apply_binary_as_element(v26, v25, v24, v23, v22, v21) = v19)) & ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : (v25 = v21 | ~ (latt_str_of(v23, v24, v25) = v22) | ~ (latt_str_of(v19, v20, v21) = v22) | ? [v26] : ? [v27] : (( ~ (v27 = 0) & quasi_total(v21, v26, v19) = v27 & cartesian_product2(v19, v19) = v26) | ( ~ (v27 = 0) & quasi_total(v20, v26, v19) = v27 & cartesian_product2(v19, v19) = v26) | ( ~ (v27 = 0) & relation_of2(v21, v26, v19) = v27 & cartesian_product2(v19, v19) = v26) | ( ~ (v27 = 0) & relation_of2(v20, v26, v19) = v27 & cartesian_product2(v19, v19) = v26) | ( ~ (v26 = 0) & function(v21) = v26) | ( ~ (v26 = 0) & function(v20) = v26))) & ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : (v24 = v20 | ~ (latt_str_of(v23, v24, v25) = v22) | ~ (latt_str_of(v19, v20, v21) = v22) | ? [v26] : ? [v27] : (( ~ (v27 = 0) & quasi_total(v21, v26, v19) = v27 & cartesian_product2(v19, v19) = v26) | ( ~ (v27 = 0) & quasi_total(v20, v26, v19) = v27 & cartesian_product2(v19, v19) = v26) | ( ~ (v27 = 0) & relation_of2(v21, v26, v19) = v27 & cartesian_product2(v19, v19) = v26) | ( ~ (v27 = 0) & relation_of2(v20, v26, v19) = v27 & cartesian_product2(v19, v19) = v26) | ( ~ (v26 = 0) & function(v21) = v26) | ( ~ (v26 = 0) & function(v20) = v26))) & ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : (v23 = v19 | ~ (latt_str_of(v23, v24, v25) = v22) | ~ (latt_str_of(v19, v20, v21) = v22) | ? [v26] : ? [v27] : (( ~ (v27 = 0) & quasi_total(v21, v26, v19) = v27 & cartesian_product2(v19, v19) = v26) | ( ~ (v27 = 0) & quasi_total(v20, v26, v19) = v27 & cartesian_product2(v19, v19) = v26) | ( ~ (v27 = 0) & relation_of2(v21, v26, v19) = v27 & cartesian_product2(v19, v19) = v26) | ( ~ (v27 = 0) & relation_of2(v20, v26, v19) = v27 & cartesian_product2(v19, v19) = v26) | ( ~ (v26 = 0) & function(v21) = v26) | ( ~ (v26 = 0) & function(v20) = v26))) & ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : ( ~ (apply_binary_as_element(v19, v20, v21, v22, v23, v24) = v25) | ? [v26] : ? [v27] : ((v26 = v25 & apply_binary(v22, v23, v24) = v25) | (v26 = 0 & empty(v20) = 0) | (v26 = 0 & empty(v19) = 0) | ( ~ (v27 = 0) & quasi_total(v22, v26, v21) = v27 & cartesian_product2(v19, v20) = v26) | ( ~ (v27 = 0) & relation_of2(v22, v26, v21) = v27 & cartesian_product2(v19, v20) = v26) | ( ~ (v26 = 0) & function(v22) = v26) | ( ~ (v26 = 0) & element(v24, v20) = v26) | ( ~ (v26 = 0) & element(v23, v19) = v26))) & ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : ( ~ (apply_binary_as_element(v19, v20, v21, v22, v23, v24) = v25) | ? [v26] : ? [v27] : ((v26 = 0 & empty(v20) = 0) | (v26 = 0 & empty(v19) = 0) | (v26 = 0 & element(v25, v21) = 0) | ( ~ (v27 = 0) & quasi_total(v22, v26, v21) = v27 & cartesian_product2(v19, v20) = v26) | ( ~ (v27 = 0) & relation_of2(v22, v26, v21) = v27 & cartesian_product2(v19, v20) = v26) | ( ~ (v26 = 0) & function(v22) = v26) | ( ~ (v26 = 0) & element(v24, v20) = v26) | ( ~ (v26 = 0) & element(v23, v19) = v26))) & ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : (v24 = 0 | ~ (cartesian_product2(v19, v20) = v22) | ~ (powerset(v22) = v23) | ~ (element(v21, v23) = v24) | ? [v25] : ( ~ (v25 = 0) & relation_of2_as_subset(v21, v19, v20) = v25)) & ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ( ~ (boole_lattice(v19) = v21) | ~ (meet(v21, v20, v23) = v24) | ~ (element(v20, v22) = 0) | ~ (the_carrier(v21) = v22) | ? [v25] : ? [v26] : ? [v27] : ((v27 = v24 & v26 = v25 & join(v21, v20, v23) = v25 & set_intersection2(v20, v23) = v24 & set_union2(v20, v23) = v25) | ( ~ (v25 = 0) & element(v23, v22) = v25))) & ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ( ~ (boole_lattice(v19) = v21) | ~ (join(v21, v20, v23) = v24) | ~ (element(v20, v22) = 0) | ~ (the_carrier(v21) = v22) | ? [v25] : ? [v26] : ? [v27] : ((v27 = v26 & v25 = v24 & meet(v21, v20, v23) = v26 & set_intersection2(v20, v23) = v26 & set_union2(v20, v23) = v24) | ( ~ (v25 = 0) & element(v23, v22) = v25))) & ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ( ~ (boole_lattice(v19) = v21) | ~ (set_intersection2(v20, v23) = v24) | ~ (element(v20, v22) = 0) | ~ (the_carrier(v21) = v22) | ? [v25] : ? [v26] : ? [v27] : ((v27 = v24 & v26 = v25 & meet(v21, v20, v23) = v24 & join(v21, v20, v23) = v25 & set_union2(v20, v23) = v25) | ( ~ (v25 = 0) & element(v23, v22) = v25))) & ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ( ~ (boole_lattice(v19) = v21) | ~ (set_union2(v20, v23) = v24) | ~ (element(v20, v22) = 0) | ~ (the_carrier(v21) = v22) | ? [v25] : ? [v26] : ? [v27] : ((v27 = v26 & v25 = v24 & meet(v21, v20, v23) = v26 & join(v21, v20, v23) = v24 & set_intersection2(v20, v23) = v26) | ( ~ (v25 = 0) & element(v23, v22) = v25))) & ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v23 = 0 | ~ (powerset(v21) = v22) | ~ (element(v20, v22) = 0) | ~ (element(v19, v21) = v23) | ? [v24] : ( ~ (v24 = 0) & in(v19, v20) = v24)) & ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v20 = v19 | ~ (relation_of2_as_subset(v23, v22, v21) = v20) | ~ (relation_of2_as_subset(v23, v22, v21) = v19)) & ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v20 = v19 | ~ (quasi_total(v23, v22, v21) = v20) | ~ (quasi_total(v23, v22, v21) = v19)) & ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v20 = v19 | ~ (relation_of2(v23, v22, v21) = v20) | ~ (relation_of2(v23, v22, v21) = v19)) & ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v20 = v19 | ~ (below(v23, v22, v21) = v20) | ~ (below(v23, v22, v21) = v19)) & ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v20 = v19 | ~ (meet(v23, v22, v21) = v20) | ~ (meet(v23, v22, v21) = v19)) & ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v20 = v19 | ~ (join(v23, v22, v21) = v20) | ~ (join(v23, v22, v21) = v19)) & ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v20 = v19 | ~ (apply_binary(v23, v22, v21) = v20) | ~ (apply_binary(v23, v22, v21) = v19)) & ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v20 = v19 | ~ (latt_str_of(v23, v22, v21) = v20) | ~ (latt_str_of(v23, v22, v21) = v19)) & ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ( ~ (boole_lattice(v19) = v21) | ~ (element(v23, v22) = 0) | ~ (element(v20, v22) = 0) | ~ (the_carrier(v21) = v22) | ? [v24] : ? [v25] : (meet(v21, v20, v23) = v25 & join(v21, v20, v23) = v24 & set_intersection2(v20, v23) = v25 & set_union2(v20, v23) = v24)) & ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ( ~ (below(v19, v21, v22) = v23) | ~ (element(v21, v20) = 0) | ~ (the_carrier(v19) = v20) | ? [v24] : ((v24 = 0 & empty_carrier(v19) = 0) | ( ~ (v24 = 0) & join_semilatt_str(v19) = v24) | ( ~ (v24 = 0) & element(v22, v20) = v24) | (( ~ (v23 = 0) | (v24 = v22 & join(v19, v21, v22) = v22)) & (v23 = 0 | ( ~ (v24 = v22) & join(v19, v21, v22) = v24))))) & ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ( ~ (join(v19, v21, v22) = v23) | ~ (element(v21, v20) = 0) | ~ (the_carrier(v19) = v20) | ? [v24] : ((v24 = 0 & empty_carrier(v19) = 0) | ( ~ (v24 = 0) & join_semilatt_str(v19) = v24) | ( ~ (v24 = 0) & element(v22, v20) = v24) | (( ~ (v23 = v22) | (v24 = 0 & below(v19, v21, v22) = 0)) & (v23 = v22 | ( ~ (v24 = 0) & below(v19, v21, v22) = v24))))) & ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ( ~ (cartesian_product2(v19, v20) = v22) | ~ (powerset(v22) = v23) | ~ (element(v21, v23) = 0) | relation(v21) = 0) & ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v22 = 0 | ~ (relation_of2_as_subset(v21, v19, v20) = v22) | ? [v23] : ( ~ (v23 = 0) & relation_of2(v21, v19, v20) = v23)) & ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v22 = 0 | ~ (relation_of2(v21, v19, v20) = v22) | ? [v23] : ( ~ (v23 = 0) & relation_of2_as_subset(v21, v19, v20) = v23)) & ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v22 = 0 | ~ (powerset(v20) = v21) | ~ (element(v19, v21) = v22) | ? [v23] : ( ~ (v23 = 0) & subset(v19, v20) = v23)) & ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v22 = 0 | ~ (element(v19, v21) = v22) | ~ (in(v19, v20) = 0) | ? [v23] : ? [v24] : ( ~ (v24 = 0) & powerset(v21) = v23 & element(v20, v23) = v24)) & ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v20 = v19 | ~ (subset(v22, v21) = v20) | ~ (subset(v22, v21) = v19)) & ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v20 = v19 | ~ (ordered_pair(v22, v21) = v20) | ~ (ordered_pair(v22, v21) = v19)) & ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v20 = v19 | ~ (apply(v22, v21) = v20) | ~ (apply(v22, v21) = v19)) & ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v20 = v19 | ~ (set_intersection2(v22, v21) = v20) | ~ (set_intersection2(v22, v21) = v19)) & ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v20 = v19 | ~ (set_union2(v22, v21) = v20) | ~ (set_union2(v22, v21) = v19)) & ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v20 = v19 | ~ (unordered_pair(v22, v21) = v20) | ~ (unordered_pair(v22, v21) = v19)) & ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v20 = v19 | ~ (cartesian_product2(v22, v21) = v20) | ~ (cartesian_product2(v22, v21) = v19)) & ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v20 = v19 | ~ (element(v22, v21) = v20) | ~ (element(v22, v21) = v19)) & ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v20 = v19 | ~ (in(v22, v21) = v20) | ~ (in(v22, v21) = v19)) & ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (meet(v19, v20, v21) = v22) | ? [v23] : ? [v24] : ((v24 = 0 & element(v22, v23) = 0 & the_carrier(v19) = v23) | (v23 = 0 & empty_carrier(v19) = 0) | ( ~ (v24 = 0) & element(v21, v23) = v24 & the_carrier(v19) = v23) | ( ~ (v24 = 0) & element(v20, v23) = v24 & the_carrier(v19) = v23) | ( ~ (v23 = 0) & meet_semilatt_str(v19) = v23))) & ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (join(v19, v20, v21) = v22) | ? [v23] : ? [v24] : ((v24 = 0 & element(v22, v23) = 0 & the_carrier(v19) = v23) | (v23 = 0 & empty_carrier(v19) = 0) | ( ~ (v24 = 0) & element(v21, v23) = v24 & the_carrier(v19) = v23) | ( ~ (v24 = 0) & element(v20, v23) = v24 & the_carrier(v19) = v23) | ( ~ (v23 = 0) & join_semilatt_str(v19) = v23))) & ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (function(v19) = 0) | ~ (ordered_pair(v20, v21) = v22) | ? [v23] : ? [v24] : ((v24 = v23 & apply_binary(v19, v20, v21) = v23 & apply(v19, v22) = v23) | ( ~ (v23 = 0) & relation(v19) = v23))) & ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (function(v19) = 0) | ~ (apply_binary(v19, v20, v21) = v22) | ? [v23] : ? [v24] : ((v24 = v22 & ordered_pair(v20, v21) = v23 & apply(v19, v23) = v22) | ( ~ (v23 = 0) & relation(v19) = v23))) & ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (ordered_pair(v20, v21) = v22) | ~ (relation(v19) = 0) | ? [v23] : ? [v24] : ((v24 = v23 & apply_binary(v19, v20, v21) = v23 & apply(v19, v22) = v23) | ( ~ (v23 = 0) & function(v19) = v23))) & ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (apply_binary(v19, v20, v21) = v22) | ~ (relation(v19) = 0) | ? [v23] : ? [v24] : ((v24 = v22 & ordered_pair(v20, v21) = v23 & apply(v19, v23) = v22) | ( ~ (v23 = 0) & function(v19) = v23))) & ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (powerset(v21) = v22) | ~ (element(v20, v22) = 0) | ~ (in(v19, v20) = 0) | element(v19, v21) = 0) & ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (powerset(v21) = v22) | ~ (element(v20, v22) = 0) | ~ (in(v19, v20) = 0) | ? [v23] : ( ~ (v23 = 0) & empty(v21) = v23)) & ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (element(v22, v20) = 0) | ~ (element(v21, v20) = 0) | ~ (the_carrier(v19) = v20) | ? [v23] : ? [v24] : ((v23 = 0 & empty_carrier(v19) = 0) | ( ~ (v23 = 0) & join_semilatt_str(v19) = v23) | (((v24 = v22 & join(v19, v21, v22) = v22) | ( ~ (v23 = 0) & below(v19, v21, v22) = v23)) & ((v23 = 0 & below(v19, v21, v22) = 0) | ( ~ (v24 = v22) & join(v19, v21, v22) = v24))))) & ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (latt_str_of(v19, v20, v21) = v22) | ? [v23] : ? [v24] : ((v24 = 0 & v23 = 0 & strict_latt_str(v22) = 0 & latt_str(v22) = 0) | ( ~ (v24 = 0) & quasi_total(v21, v23, v19) = v24 & cartesian_product2(v19, v19) = v23) | ( ~ (v24 = 0) & quasi_total(v20, v23, v19) = v24 & cartesian_product2(v19, v19) = v23) | ( ~ (v24 = 0) & relation_of2(v21, v23, v19) = v24 & cartesian_product2(v19, v19) = v23) | ( ~ (v24 = 0) & relation_of2(v20, v23, v19) = v24 & cartesian_product2(v19, v19) = v23) | ( ~ (v23 = 0) & function(v21) = v23) | ( ~ (v23 = 0) & function(v20) = v23))) & ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (latt_str_of(v19, v20, v21) = v22) | ? [v23] : ? [v24] : ((v24 = 0 & ~ (v23 = 0) & empty_carrier(v22) = v23 & strict_latt_str(v22) = 0) | (v23 = 0 & empty(v19) = 0) | ( ~ (v24 = 0) & quasi_total(v21, v23, v19) = v24 & cartesian_product2(v19, v19) = v23) | ( ~ (v24 = 0) & quasi_total(v20, v23, v19) = v24 & cartesian_product2(v19, v19) = v23) | ( ~ (v24 = 0) & relation_of2(v21, v23, v19) = v24 & cartesian_product2(v19, v19) = v23) | ( ~ (v24 = 0) & relation_of2(v20, v23, v19) = v24 & cartesian_product2(v19, v19) = v23) | ( ~ (v23 = 0) & function(v21) = v23) | ( ~ (v23 = 0) & function(v20) = v23))) & ! [v19] : ! [v20] : ! [v21] : (v21 = v20 | ~ (set_union2(v19, v20) = v21) | ? [v22] : ( ~ (v22 = 0) & subset(v19, v20) = v22)) & ! [v19] : ! [v20] : ! [v21] : (v21 = 0 | ~ (subset(v19, v20) = v21) | ? [v22] : ? [v23] : ( ~ (v23 = 0) & powerset(v20) = v22 & element(v19, v22) = v23)) & ! [v19] : ! [v20] : ! [v21] : (v21 = 0 | ~ (element(v19, v20) = v21) | ? [v22] : ( ~ (v22 = 0) & in(v19, v20) = v22)) & ! [v19] : ! [v20] : ! [v21] : (v21 = 0 | ~ (in(v19, v20) = v21) | ? [v22] : ((v22 = 0 & empty(v20) = 0) | ( ~ (v22 = 0) & element(v19, v20) = v22))) & ! [v19] : ! [v20] : ! [v21] : (v20 = v19 | ~ (one_sorted_str(v21) = v20) | ~ (one_sorted_str(v21) = v19)) & ! [v19] : ! [v20] : ! [v21] : (v20 = v19 | ~ (empty(v21) = v20) | ~ (empty(v21) = v19)) & ! [v19] : ! [v20] : ! [v21] : (v20 = v19 | ~ (boole_lattice(v21) = v20) | ~ (boole_lattice(v21) = v19)) & ! [v19] : ! [v20] : ! [v21] : (v20 = v19 | ~ (singleton(v21) = v20) | ~ (singleton(v21) = v19)) & ! [v19] : ! [v20] : ! [v21] : (v20 = v19 | ~ (meet_semilatt_str(v21) = v20) | ~ (meet_semilatt_str(v21) = v19)) & ! [v19] : ! [v20] : ! [v21] : (v20 = v19 | ~ (empty_carrier(v21) = v20) | ~ (empty_carrier(v21) = v19)) & ! [v19] : ! [v20] : ! [v21] : (v20 = v19 | ~ (join_semilatt_str(v21) = v20) | ~ (join_semilatt_str(v21) = v19)) & ! [v19] : ! [v20] : ! [v21] : (v20 = v19 | ~ (function(v21) = v20) | ~ (function(v21) = v19)) & ! [v19] : ! [v20] : ! [v21] : (v20 = v19 | ~ (powerset(v21) = v20) | ~ (powerset(v21) = v19)) & ! [v19] : ! [v20] : ! [v21] : (v20 = v19 | ~ (relation(v21) = v20) | ~ (relation(v21) = v19)) & ! [v19] : ! [v20] : ! [v21] : (v20 = v19 | ~ (strict_latt_str(v21) = v20) | ~ (strict_latt_str(v21) = v19)) & ! [v19] : ! [v20] : ! [v21] : (v20 = v19 | ~ (latt_str(v21) = v20) | ~ (latt_str(v21) = v19)) & ! [v19] : ! [v20] : ! [v21] : (v20 = v19 | ~ (the_carrier(v21) = v20) | ~ (the_carrier(v21) = v19)) & ! [v19] : ! [v20] : ! [v21] : (v20 = v19 | ~ (the_L_join(v21) = v20) | ~ (the_L_join(v21) = v19)) & ! [v19] : ! [v20] : ! [v21] : (v20 = v19 | ~ (the_L_meet(v21) = v20) | ~ (the_L_meet(v21) = v19)) & ! [v19] : ! [v20] : ! [v21] : ( ~ (relation_of2_as_subset(v21, v19, v20) = 0) | relation_of2(v21, v19, v20) = 0) & ! [v19] : ! [v20] : ! [v21] : ( ~ (relation_of2_as_subset(v21, v19, v20) = 0) | ? [v22] : ? [v23] : (cartesian_product2(v19, v20) = v22 & powerset(v22) = v23 & element(v21, v23) = 0)) & ! [v19] : ! [v20] : ! [v21] : ( ~ (empty(v21) = 0) | ~ (in(v19, v20) = 0) | ? [v22] : ? [v23] : ( ~ (v23 = 0) & powerset(v21) = v22 & element(v20, v22) = v23)) & ! [v19] : ! [v20] : ! [v21] : ( ~ (relation_of2(v21, v19, v20) = 0) | relation_of2_as_subset(v21, v19, v20) = 0) & ! [v19] : ! [v20] : ! [v21] : ( ~ (ordered_pair(v19, v20) = v21) | ? [v22] : ? [v23] : (singleton(v19) = v23 & unordered_pair(v22, v23) = v21 & unordered_pair(v19, v20) = v22)) & ! [v19] : ! [v20] : ! [v21] : ( ~ (set_intersection2(v20, v19) = v21) | set_intersection2(v19, v20) = v21) & ! [v19] : ! [v20] : ! [v21] : ( ~ (set_intersection2(v19, v20) = v21) | set_intersection2(v20, v19) = v21) & ! [v19] : ! [v20] : ! [v21] : ( ~ (set_union2(v20, v19) = v21) | set_union2(v19, v20) = v21) & ! [v19] : ! [v20] : ! [v21] : ( ~ (set_union2(v20, v19) = v21) | ? [v22] : ((v22 = 0 & empty(v19) = 0) | ( ~ (v22 = 0) & empty(v21) = v22))) & ! [v19] : ! [v20] : ! [v21] : ( ~ (set_union2(v19, v20) = v21) | subset(v19, v21) = 0) & ! [v19] : ! [v20] : ! [v21] : ( ~ (set_union2(v19, v20) = v21) | set_union2(v20, v19) = v21) & ! [v19] : ! [v20] : ! [v21] : ( ~ (set_union2(v19, v20) = v21) | ? [v22] : ((v22 = 0 & empty(v19) = 0) | ( ~ (v22 = 0) & empty(v21) = v22))) & ! [v19] : ! [v20] : ! [v21] : ( ~ (unordered_pair(v20, v19) = v21) | unordered_pair(v19, v20) = v21) & ! [v19] : ! [v20] : ! [v21] : ( ~ (unordered_pair(v19, v20) = v21) | unordered_pair(v20, v19) = v21) & ! [v19] : ! [v20] : ! [v21] : ( ~ (unordered_pair(v19, v20) = v21) | ? [v22] : ? [v23] : (singleton(v19) = v23 & ordered_pair(v19, v20) = v22 & unordered_pair(v21, v23) = v22)) & ! [v19] : ! [v20] : ! [v21] : ( ~ (unordered_pair(v19, v20) = v21) | ? [v22] : ( ~ (v22 = 0) & empty(v21) = v22)) & ! [v19] : ! [v20] : ! [v21] : ( ~ (cartesian_product2(v19, v20) = v21) | ? [v22] : ((v22 = 0 & empty(v20) = 0) | (v22 = 0 & empty(v19) = 0) | ( ~ (v22 = 0) & empty(v21) = v22))) & ! [v19] : ! [v20] : ! [v21] : ( ~ (powerset(v20) = v21) | ~ (element(v19, v21) = 0) | subset(v19, v20) = 0) & ! [v19] : ! [v20] : (v20 = v19 | ~ (empty(v20) = 0) | ~ (empty(v19) = 0)) & ! [v19] : ! [v20] : (v20 = v19 | ~ (set_intersection2(v19, v19) = v20)) & ! [v19] : ! [v20] : (v20 = v19 | ~ (set_union2(v19, v19) = v20)) & ! [v19] : ! [v20] : (v20 = v19 | ~ (set_union2(v19, empty_set) = v20)) & ! [v19] : ! [v20] : (v20 = empty_set | ~ (set_intersection2(v19, empty_set) = v20)) & ! [v19] : ! [v20] : (v20 = 0 | ~ (subset(v19, v19) = v20)) & ! [v19] : ! [v20] : (v20 = 0 | ~ (one_sorted_str(v19) = v20) | ? [v21] : ( ~ (v21 = 0) & meet_semilatt_str(v19) = v21)) & ! [v19] : ! [v20] : (v20 = 0 | ~ (one_sorted_str(v19) = v20) | ? [v21] : ( ~ (v21 = 0) & join_semilatt_str(v19) = v21)) & ! [v19] : ! [v20] : (v20 = 0 | ~ (empty(v19) = v20) | ? [v21] : ? [v22] : ? [v23] : ( ~ (v23 = 0) & empty(v22) = v23 & powerset(v19) = v21 & element(v22, v21) = 0)) & ! [v19] : ! [v20] : (v20 = 0 | ~ (empty_carrier(v19) = v20) | ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ((v24 = 0 & ~ (v25 = 0) & empty(v23) = v25 & powerset(v21) = v22 & element(v23, v22) = 0 & the_carrier(v19) = v21) | ( ~ (v21 = 0) & one_sorted_str(v19) = v21))) & ! [v19] : ! [v20] : (v20 = 0 | ~ (empty_carrier(v19) = v20) | ? [v21] : ? [v22] : (( ~ (v22 = 0) & empty(v21) = v22 & the_carrier(v19) = v21) | ( ~ (v21 = 0) & one_sorted_str(v19) = v21))) & ! [v19] : ! [v20] : (v20 = 0 | ~ (empty_carrier(v19) = v20) | ? [v21] : ? [v22] : (( ~ (v21 = 0) & meet_semilatt_str(v19) = v21) | (the_carrier(v19) = v21 & the_L_meet(v19) = v22 & ! [v23] : ! [v24] : ! [v25] : ( ~ (meet(v19, v23, v24) = v25) | ~ (element(v23, v21) = 0) | ? [v26] : ((v26 = v25 & apply_binary_as_element(v21, v21, v21, v22, v23, v24) = v25) | ( ~ (v26 = 0) & element(v24, v21) = v26))) & ! [v23] : ! [v24] : ! [v25] : ( ~ (apply_binary_as_element(v21, v21, v21, v22, v23, v24) = v25) | ~ (element(v23, v21) = 0) | ? [v26] : ((v26 = v25 & meet(v19, v23, v24) = v25) | ( ~ (v26 = 0) & element(v24, v21) = v26))) & ! [v23] : ! [v24] : ( ~ (element(v24, v21) = 0) | ~ (element(v23, v21) = 0) | ? [v25] : (meet(v19, v23, v24) = v25 & apply_binary_as_element(v21, v21, v21, v22, v23, v24) = v25))))) & ! [v19] : ! [v20] : (v20 = 0 | ~ (empty_carrier(v19) = v20) | ? [v21] : ? [v22] : (( ~ (v21 = 0) & join_semilatt_str(v19) = v21) | (the_carrier(v19) = v21 & the_L_join(v19) = v22 & ! [v23] : ! [v24] : ! [v25] : ( ~ (join(v19, v23, v24) = v25) | ~ (element(v23, v21) = 0) | ? [v26] : ((v26 = v25 & apply_binary_as_element(v21, v21, v21, v22, v23, v24) = v25) | ( ~ (v26 = 0) & element(v24, v21) = v26))) & ! [v23] : ! [v24] : ! [v25] : ( ~ (apply_binary_as_element(v21, v21, v21, v22, v23, v24) = v25) | ~ (element(v23, v21) = 0) | ? [v26] : ((v26 = v25 & join(v19, v23, v24) = v25) | ( ~ (v26 = 0) & element(v24, v21) = v26))) & ! [v23] : ! [v24] : ( ~ (element(v24, v21) = 0) | ~ (element(v23, v21) = 0) | ? [v25] : (join(v19, v23, v24) = v25 & apply_binary_as_element(v21, v21, v21, v22, v23, v24) = v25))))) & ! [v19] : ! [v20] : (v20 = 0 | ~ (empty_carrier(v19) = v20) | ? [v21] : (( ~ (v21 = 0) & join_semilatt_str(v19) = v21) | (the_carrier(v19) = v21 & ! [v22] : ! [v23] : ! [v24] : ( ~ (below(v19, v22, v23) = v24) | ~ (element(v22, v21) = 0) | ? [v25] : (( ~ (v25 = 0) & element(v23, v21) = v25) | (( ~ (v24 = 0) | (v25 = v23 & join(v19, v22, v23) = v23)) & (v24 = 0 | ( ~ (v25 = v23) & join(v19, v22, v23) = v25))))) & ! [v22] : ! [v23] : ! [v24] : ( ~ (join(v19, v22, v23) = v24) | ~ (element(v22, v21) = 0) | ? [v25] : (( ~ (v25 = 0) & element(v23, v21) = v25) | (( ~ (v24 = v23) | (v25 = 0 & below(v19, v22, v23) = 0)) & (v24 = v23 | ( ~ (v25 = 0) & below(v19, v22, v23) = v25))))) & ! [v22] : ! [v23] : ( ~ (element(v23, v21) = 0) | ~ (element(v22, v21) = 0) | ? [v24] : ? [v25] : (((v25 = v23 & join(v19, v22, v23) = v23) | ( ~ (v24 = 0) & below(v19, v22, v23) = v24)) & ((v24 = 0 & below(v19, v22, v23) = 0) | ( ~ (v25 = v23) & join(v19, v22, v23) = v25))))))) & ! [v19] : ! [v20] : ( ~ (subset(v19, v20) = 0) | set_union2(v19, v20) = v20) & ! [v19] : ! [v20] : ( ~ (subset(v19, v20) = 0) | ? [v21] : (powerset(v20) = v21 & element(v19, v21) = 0)) & ! [v19] : ! [v20] : ( ~ (boole_lattice(v19) = v20) | strict_latt_str(v20) = 0) & ! [v19] : ! [v20] : ( ~ (boole_lattice(v19) = v20) | latt_str(v20) = 0) & ! [v19] : ! [v20] : ( ~ (boole_lattice(v19) = v20) | ? [v21] : ( ~ (v21 = 0) & empty_carrier(v20) = v21)) & ! [v19] : ! [v20] : ( ~ (singleton(v19) = v20) | ? [v21] : ( ~ (v21 = 0) & empty(v20) = v21)) & ! [v19] : ! [v20] : ( ~ (meet_semilatt_str(v19) = v20) | ? [v21] : ((v21 = 0 & v20 = 0 & join_semilatt_str(v19) = 0) | ( ~ (v21 = 0) & latt_str(v19) = v21))) & ! [v19] : ! [v20] : ( ~ (join_semilatt_str(v19) = v20) | ? [v21] : ((v21 = 0 & v20 = 0 & meet_semilatt_str(v19) = 0) | ( ~ (v21 = 0) & latt_str(v19) = v21))) & ! [v19] : ! [v20] : ( ~ (powerset(v19) = v20) | ? [v21] : ? [v22] : ? [v23] : ((v22 = 0 & ~ (v23 = 0) & empty(v21) = v23 & element(v21, v20) = 0) | (v21 = 0 & empty(v19) = 0))) & ! [v19] : ! [v20] : ( ~ (powerset(v19) = v20) | ? [v21] : ( ~ (v21 = 0) & empty(v20) = v21)) & ! [v19] : ! [v20] : ( ~ (powerset(v19) = v20) | ? [v21] : (empty(v21) = 0 & element(v21, v20) = 0)) & ! [v19] : ! [v20] : ( ~ (element(v19, v20) = 0) | ? [v21] : ((v21 = 0 & empty(v20) = 0) | (v21 = 0 & in(v19, v20) = 0))) & ! [v19] : ! [v20] : ( ~ (in(v20, v19) = 0) | ? [v21] : ( ~ (v21 = 0) & in(v19, v20) = v21)) & ! [v19] : ! [v20] : ( ~ (in(v19, v20) = 0) | element(v19, v20) = 0) & ! [v19] : ! [v20] : ( ~ (in(v19, v20) = 0) | ? [v21] : ( ~ (v21 = 0) & empty(v20) = v21)) & ! [v19] : ! [v20] : ( ~ (in(v19, v20) = 0) | ? [v21] : ( ~ (v21 = 0) & in(v20, v19) = v21)) & ! [v19] : ! [v20] : ( ~ (the_carrier(v19) = v20) | ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ((v25 = 0 & v24 = 0 & v22 = 0 & relation_of2_as_subset(v21, v23, v20) = 0 & quasi_total(v21, v23, v20) = 0 & function(v21) = 0 & cartesian_product2(v20, v20) = v23 & the_L_join(v19) = v21) | ( ~ (v21 = 0) & join_semilatt_str(v19) = v21))) & ! [v19] : ! [v20] : ( ~ (the_carrier(v19) = v20) | ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ((v25 = 0 & v24 = 0 & v22 = 0 & relation_of2_as_subset(v21, v23, v20) = 0 & quasi_total(v21, v23, v20) = 0 & function(v21) = 0 & cartesian_product2(v20, v20) = v23 & the_L_meet(v19) = v21) | ( ~ (v21 = 0) & meet_semilatt_str(v19) = v21))) & ! [v19] : ! [v20] : ( ~ (the_carrier(v19) = v20) | ? [v21] : ? [v22] : ? [v23] : ? [v24] : ((v23 = 0 & ~ (v24 = 0) & empty(v22) = v24 & powerset(v20) = v21 & element(v22, v21) = 0) | (v21 = 0 & empty_carrier(v19) = 0) | ( ~ (v21 = 0) & one_sorted_str(v19) = v21))) & ! [v19] : ! [v20] : ( ~ (the_carrier(v19) = v20) | ? [v21] : ? [v22] : ? [v23] : ((v23 = v19 & the_L_join(v19) = v21 & the_L_meet(v19) = v22 & latt_str_of(v20, v21, v22) = v19) | ( ~ (v21 = 0) & strict_latt_str(v19) = v21) | ( ~ (v21 = 0) & latt_str(v19) = v21))) & ! [v19] : ! [v20] : ( ~ (the_carrier(v19) = v20) | ? [v21] : ((v21 = 0 & empty_carrier(v19) = 0) | ( ~ (v21 = 0) & one_sorted_str(v19) = v21) | ( ~ (v21 = 0) & empty(v20) = v21))) & ! [v19] : ! [v20] : ( ~ (the_carrier(v19) = v20) | ? [v21] : ((v21 = 0 & empty_carrier(v19) = 0) | ( ~ (v21 = 0) & meet_semilatt_str(v19) = v21) | (the_L_meet(v19) = v21 & ! [v22] : ! [v23] : ! [v24] : ( ~ (meet(v19, v22, v23) = v24) | ~ (element(v22, v20) = 0) | ? [v25] : ((v25 = v24 & apply_binary_as_element(v20, v20, v20, v21, v22, v23) = v24) | ( ~ (v25 = 0) & element(v23, v20) = v25))) & ! [v22] : ! [v23] : ! [v24] : ( ~ (apply_binary_as_element(v20, v20, v20, v21, v22, v23) = v24) | ~ (element(v22, v20) = 0) | ? [v25] : ((v25 = v24 & meet(v19, v22, v23) = v24) | ( ~ (v25 = 0) & element(v23, v20) = v25))) & ! [v22] : ! [v23] : ( ~ (element(v23, v20) = 0) | ~ (element(v22, v20) = 0) | ? [v24] : (meet(v19, v22, v23) = v24 & apply_binary_as_element(v20, v20, v20, v21, v22, v23) = v24))))) & ! [v19] : ! [v20] : ( ~ (the_carrier(v19) = v20) | ? [v21] : ((v21 = 0 & empty_carrier(v19) = 0) | ( ~ (v21 = 0) & join_semilatt_str(v19) = v21) | (the_L_join(v19) = v21 & ! [v22] : ! [v23] : ! [v24] : ( ~ (join(v19, v22, v23) = v24) | ~ (element(v22, v20) = 0) | ? [v25] : ((v25 = v24 & apply_binary_as_element(v20, v20, v20, v21, v22, v23) = v24) | ( ~ (v25 = 0) & element(v23, v20) = v25))) & ! [v22] : ! [v23] : ! [v24] : ( ~ (apply_binary_as_element(v20, v20, v20, v21, v22, v23) = v24) | ~ (element(v22, v20) = 0) | ? [v25] : ((v25 = v24 & join(v19, v22, v23) = v24) | ( ~ (v25 = 0) & element(v23, v20) = v25))) & ! [v22] : ! [v23] : ( ~ (element(v23, v20) = 0) | ~ (element(v22, v20) = 0) | ? [v24] : (join(v19, v22, v23) = v24 & apply_binary_as_element(v20, v20, v20, v21, v22, v23) = v24))))) & ! [v19] : ! [v20] : ( ~ (the_L_join(v19) = v20) | ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ((v25 = 0 & v24 = 0 & v21 = 0 & relation_of2_as_subset(v20, v23, v22) = 0 & quasi_total(v20, v23, v22) = 0 & function(v20) = 0 & cartesian_product2(v22, v22) = v23 & the_carrier(v19) = v22) | ( ~ (v21 = 0) & join_semilatt_str(v19) = v21))) & ! [v19] : ! [v20] : ( ~ (the_L_join(v19) = v20) | ? [v21] : ? [v22] : ? [v23] : ((v23 = v19 & the_carrier(v19) = v21 & the_L_meet(v19) = v22 & latt_str_of(v21, v20, v22) = v19) | ( ~ (v21 = 0) & strict_latt_str(v19) = v21) | ( ~ (v21 = 0) & latt_str(v19) = v21))) & ! [v19] : ! [v20] : ( ~ (the_L_join(v19) = v20) | ? [v21] : ((v21 = 0 & empty_carrier(v19) = 0) | ( ~ (v21 = 0) & join_semilatt_str(v19) = v21) | (the_carrier(v19) = v21 & ! [v22] : ! [v23] : ! [v24] : ( ~ (join(v19, v22, v23) = v24) | ~ (element(v22, v21) = 0) | ? [v25] : ((v25 = v24 & apply_binary_as_element(v21, v21, v21, v20, v22, v23) = v24) | ( ~ (v25 = 0) & element(v23, v21) = v25))) & ! [v22] : ! [v23] : ! [v24] : ( ~ (apply_binary_as_element(v21, v21, v21, v20, v22, v23) = v24) | ~ (element(v22, v21) = 0) | ? [v25] : ((v25 = v24 & join(v19, v22, v23) = v24) | ( ~ (v25 = 0) & element(v23, v21) = v25))) & ! [v22] : ! [v23] : ( ~ (element(v23, v21) = 0) | ~ (element(v22, v21) = 0) | ? [v24] : (join(v19, v22, v23) = v24 & apply_binary_as_element(v21, v21, v21, v20, v22, v23) = v24))))) & ! [v19] : ! [v20] : ( ~ (the_L_meet(v19) = v20) | ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ((v25 = 0 & v24 = 0 & v21 = 0 & relation_of2_as_subset(v20, v23, v22) = 0 & quasi_total(v20, v23, v22) = 0 & function(v20) = 0 & cartesian_product2(v22, v22) = v23 & the_carrier(v19) = v22) | ( ~ (v21 = 0) & meet_semilatt_str(v19) = v21))) & ! [v19] : ! [v20] : ( ~ (the_L_meet(v19) = v20) | ? [v21] : ? [v22] : ? [v23] : ((v23 = v19 & the_carrier(v19) = v21 & the_L_join(v19) = v22 & latt_str_of(v21, v22, v20) = v19) | ( ~ (v21 = 0) & strict_latt_str(v19) = v21) | ( ~ (v21 = 0) & latt_str(v19) = v21))) & ! [v19] : ! [v20] : ( ~ (the_L_meet(v19) = v20) | ? [v21] : ((v21 = 0 & empty_carrier(v19) = 0) | ( ~ (v21 = 0) & meet_semilatt_str(v19) = v21) | (the_carrier(v19) = v21 & ! [v22] : ! [v23] : ! [v24] : ( ~ (meet(v19, v22, v23) = v24) | ~ (element(v22, v21) = 0) | ? [v25] : ((v25 = v24 & apply_binary_as_element(v21, v21, v21, v20, v22, v23) = v24) | ( ~ (v25 = 0) & element(v23, v21) = v25))) & ! [v22] : ! [v23] : ! [v24] : ( ~ (apply_binary_as_element(v21, v21, v21, v20, v22, v23) = v24) | ~ (element(v22, v21) = 0) | ? [v25] : ((v25 = v24 & meet(v19, v22, v23) = v24) | ( ~ (v25 = 0) & element(v23, v21) = v25))) & ! [v22] : ! [v23] : ( ~ (element(v23, v21) = 0) | ~ (element(v22, v21) = 0) | ? [v24] : (meet(v19, v22, v23) = v24 & apply_binary_as_element(v21, v21, v21, v20, v22, v23) = v24))))) & ! [v19] : (v19 = empty_set | ~ (empty(v19) = 0)) & ! [v19] : ( ~ (one_sorted_str(v19) = 0) | ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ((v23 = 0 & ~ (v24 = 0) & empty(v22) = v24 & powerset(v20) = v21 & element(v22, v21) = 0 & the_carrier(v19) = v20) | (v20 = 0 & empty_carrier(v19) = 0))) & ! [v19] : ( ~ (one_sorted_str(v19) = 0) | ? [v20] : ? [v21] : ((v20 = 0 & empty_carrier(v19) = 0) | ( ~ (v21 = 0) & empty(v20) = v21 & the_carrier(v19) = v20))) & ! [v19] : ( ~ (meet_semilatt_str(v19) = 0) | one_sorted_str(v19) = 0) & ! [v19] : ( ~ (meet_semilatt_str(v19) = 0) | ? [v20] : ? [v21] : ? [v22] : (relation_of2_as_subset(v20, v22, v21) = 0 & quasi_total(v20, v22, v21) = 0 & function(v20) = 0 & cartesian_product2(v21, v21) = v22 & the_carrier(v19) = v21 & the_L_meet(v19) = v20)) & ! [v19] : ( ~ (meet_semilatt_str(v19) = 0) | ? [v20] : ? [v21] : ((v20 = 0 & empty_carrier(v19) = 0) | (the_carrier(v19) = v20 & the_L_meet(v19) = v21 & ! [v22] : ! [v23] : ! [v24] : ( ~ (meet(v19, v22, v23) = v24) | ~ (element(v22, v20) = 0) | ? [v25] : ((v25 = v24 & apply_binary_as_element(v20, v20, v20, v21, v22, v23) = v24) | ( ~ (v25 = 0) & element(v23, v20) = v25))) & ! [v22] : ! [v23] : ! [v24] : ( ~ (apply_binary_as_element(v20, v20, v20, v21, v22, v23) = v24) | ~ (element(v22, v20) = 0) | ? [v25] : ((v25 = v24 & meet(v19, v22, v23) = v24) | ( ~ (v25 = 0) & element(v23, v20) = v25))) & ! [v22] : ! [v23] : ( ~ (element(v23, v20) = 0) | ~ (element(v22, v20) = 0) | ? [v24] : (meet(v19, v22, v23) = v24 & apply_binary_as_element(v20, v20, v20, v21, v22, v23) = v24))))) & ! [v19] : ( ~ (join_semilatt_str(v19) = 0) | one_sorted_str(v19) = 0) & ! [v19] : ( ~ (join_semilatt_str(v19) = 0) | ? [v20] : ? [v21] : ? [v22] : (relation_of2_as_subset(v20, v22, v21) = 0 & quasi_total(v20, v22, v21) = 0 & function(v20) = 0 & cartesian_product2(v21, v21) = v22 & the_carrier(v19) = v21 & the_L_join(v19) = v20)) & ! [v19] : ( ~ (join_semilatt_str(v19) = 0) | ? [v20] : ? [v21] : ((v20 = 0 & empty_carrier(v19) = 0) | (the_carrier(v19) = v20 & the_L_join(v19) = v21 & ! [v22] : ! [v23] : ! [v24] : ( ~ (join(v19, v22, v23) = v24) | ~ (element(v22, v20) = 0) | ? [v25] : ((v25 = v24 & apply_binary_as_element(v20, v20, v20, v21, v22, v23) = v24) | ( ~ (v25 = 0) & element(v23, v20) = v25))) & ! [v22] : ! [v23] : ! [v24] : ( ~ (apply_binary_as_element(v20, v20, v20, v21, v22, v23) = v24) | ~ (element(v22, v20) = 0) | ? [v25] : ((v25 = v24 & join(v19, v22, v23) = v24) | ( ~ (v25 = 0) & element(v23, v20) = v25))) & ! [v22] : ! [v23] : ( ~ (element(v23, v20) = 0) | ~ (element(v22, v20) = 0) | ? [v24] : (join(v19, v22, v23) = v24 & apply_binary_as_element(v20, v20, v20, v21, v22, v23) = v24))))) & ! [v19] : ( ~ (join_semilatt_str(v19) = 0) | ? [v20] : ((v20 = 0 & empty_carrier(v19) = 0) | (the_carrier(v19) = v20 & ! [v21] : ! [v22] : ! [v23] : ( ~ (below(v19, v21, v22) = v23) | ~ (element(v21, v20) = 0) | ? [v24] : (( ~ (v24 = 0) & element(v22, v20) = v24) | (( ~ (v23 = 0) | (v24 = v22 & join(v19, v21, v22) = v22)) & (v23 = 0 | ( ~ (v24 = v22) & join(v19, v21, v22) = v24))))) & ! [v21] : ! [v22] : ! [v23] : ( ~ (join(v19, v21, v22) = v23) | ~ (element(v21, v20) = 0) | ? [v24] : (( ~ (v24 = 0) & element(v22, v20) = v24) | (( ~ (v23 = v22) | (v24 = 0 & below(v19, v21, v22) = 0)) & (v23 = v22 | ( ~ (v24 = 0) & below(v19, v21, v22) = v24))))) & ! [v21] : ! [v22] : ( ~ (element(v22, v20) = 0) | ~ (element(v21, v20) = 0) | ? [v23] : ? [v24] : (((v24 = v22 & join(v19, v21, v22) = v22) | ( ~ (v23 = 0) & below(v19, v21, v22) = v23)) & ((v23 = 0 & below(v19, v21, v22) = 0) | ( ~ (v24 = v22) & join(v19, v21, v22) = v24))))))) & ! [v19] : ( ~ (strict_latt_str(v19) = 0) | ? [v20] : ? [v21] : ? [v22] : ? [v23] : ((v23 = v19 & the_carrier(v19) = v20 & the_L_join(v19) = v21 & the_L_meet(v19) = v22 & latt_str_of(v20, v21, v22) = v19) | ( ~ (v20 = 0) & latt_str(v19) = v20))) & ! [v19] : ( ~ (latt_str(v19) = 0) | ? [v20] : ? [v21] : ? [v22] : ? [v23] : ((v23 = v19 & the_carrier(v19) = v20 & the_L_join(v19) = v21 & the_L_meet(v19) = v22 & latt_str_of(v20, v21, v22) = v19) | ( ~ (v20 = 0) & strict_latt_str(v19) = v20))) & ! [v19] : ( ~ (latt_str(v19) = 0) | (meet_semilatt_str(v19) = 0 & join_semilatt_str(v19) = 0)) & ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : apply_binary_as_element(v24, v23, v22, v21, v20, v19) = v25 & ? [v19] : ? [v20] : ? [v21] : ? [v22] : relation_of2_as_subset(v21, v20, v19) = v22 & ? [v19] : ? [v20] : ? [v21] : ? [v22] : quasi_total(v21, v20, v19) = v22 & ? [v19] : ? [v20] : ? [v21] : ? [v22] : relation_of2(v21, v20, v19) = v22 & ? [v19] : ? [v20] : ? [v21] : ? [v22] : below(v21, v20, v19) = v22 & ? [v19] : ? [v20] : ? [v21] : ? [v22] : meet(v21, v20, v19) = v22 & ? [v19] : ? [v20] : ? [v21] : ? [v22] : join(v21, v20, v19) = v22 & ? [v19] : ? [v20] : ? [v21] : ? [v22] : apply_binary(v21, v20, v19) = v22 & ? [v19] : ? [v20] : ? [v21] : ? [v22] : latt_str_of(v21, v20, v19) = v22 & ? [v19] : ? [v20] : ? [v21] : subset(v20, v19) = v21 & ? [v19] : ? [v20] : ? [v21] : relation_of2_as_subset(v21, v19, v20) = 0 & ? [v19] : ? [v20] : ? [v21] : relation_of2(v21, v19, v20) = 0 & ? [v19] : ? [v20] : ? [v21] : ordered_pair(v20, v19) = v21 & ? [v19] : ? [v20] : ? [v21] : apply(v20, v19) = v21 & ? [v19] : ? [v20] : ? [v21] : set_intersection2(v20, v19) = v21 & ? [v19] : ? [v20] : ? [v21] : set_union2(v20, v19) = v21 & ? [v19] : ? [v20] : ? [v21] : unordered_pair(v20, v19) = v21 & ? [v19] : ? [v20] : ? [v21] : cartesian_product2(v20, v19) = v21 & ? [v19] : ? [v20] : ? [v21] : element(v20, v19) = v21 & ? [v19] : ? [v20] : ? [v21] : in(v20, v19) = v21 & ? [v19] : ? [v20] : one_sorted_str(v19) = v20 & ? [v19] : ? [v20] : empty(v19) = v20 & ? [v19] : ? [v20] : boole_lattice(v19) = v20 & ? [v19] : ? [v20] : singleton(v19) = v20 & ? [v19] : ? [v20] : meet_semilatt_str(v19) = v20 & ? [v19] : ? [v20] : empty_carrier(v19) = v20 & ? [v19] : ? [v20] : join_semilatt_str(v19) = v20 & ? [v19] : ? [v20] : function(v19) = v20 & ? [v19] : ? [v20] : powerset(v19) = v20 & ? [v19] : ? [v20] : element(v20, v19) = 0 & ? [v19] : ? [v20] : relation(v19) = v20 & ? [v19] : ? [v20] : strict_latt_str(v19) = v20 & ? [v19] : ? [v20] : latt_str(v19) = v20 & ? [v19] : ? [v20] : the_carrier(v19) = v20 & ? [v19] : ? [v20] : the_L_join(v19) = v20 & ? [v19] : ? [v20] : the_L_meet(v19) = v20 & ((v6 = 0 & ~ (v5 = 0)) | (v5 = 0 & ~ (v6 = 0))))
% 109.79/75.49 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9, all_0_10_10, all_0_11_11, all_0_12_12, all_0_13_13, all_0_14_14, all_0_15_15, all_0_16_16, all_0_17_17, all_0_18_18 yields:
% 109.79/75.49 | (1) ~ (all_0_5_5 = 0) & ~ (all_0_8_8 = 0) & ~ (all_0_10_10 = 0) & subset(all_0_17_17, all_0_14_14) = all_0_12_12 & one_sorted_str(all_0_1_1) = 0 & one_sorted_str(all_0_9_9) = 0 & empty(all_0_4_4) = 0 & empty(all_0_6_6) = all_0_5_5 & empty(empty_set) = 0 & boole_lattice(all_0_18_18) = all_0_16_16 & below(all_0_16_16, all_0_17_17, all_0_14_14) = all_0_13_13 & meet_semilatt_str(all_0_0_0) = 0 & empty_carrier(all_0_9_9) = all_0_8_8 & empty_carrier(all_0_11_11) = all_0_10_10 & join_semilatt_str(all_0_2_2) = 0 & element(all_0_14_14, all_0_15_15) = 0 & element(all_0_17_17, all_0_15_15) = 0 & strict_latt_str(all_0_7_7) = 0 & strict_latt_str(all_0_11_11) = 0 & latt_str(all_0_3_3) = 0 & latt_str(all_0_7_7) = 0 & latt_str(all_0_11_11) = 0 & the_carrier(all_0_16_16) = all_0_15_15 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v1 = v0 | ~ (apply_binary_as_element(v7, v6, v5, v4, v3, v2) = v1) | ~ (apply_binary_as_element(v7, v6, v5, v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = v2 | ~ (latt_str_of(v4, v5, v6) = v3) | ~ (latt_str_of(v0, v1, v2) = v3) | ? [v7] : ? [v8] : (( ~ (v8 = 0) & quasi_total(v2, v7, v0) = v8 & cartesian_product2(v0, v0) = v7) | ( ~ (v8 = 0) & quasi_total(v1, v7, v0) = v8 & cartesian_product2(v0, v0) = v7) | ( ~ (v8 = 0) & relation_of2(v2, v7, v0) = v8 & cartesian_product2(v0, v0) = v7) | ( ~ (v8 = 0) & relation_of2(v1, v7, v0) = v8 & cartesian_product2(v0, v0) = v7) | ( ~ (v7 = 0) & function(v2) = v7) | ( ~ (v7 = 0) & function(v1) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v5 = v1 | ~ (latt_str_of(v4, v5, v6) = v3) | ~ (latt_str_of(v0, v1, v2) = v3) | ? [v7] : ? [v8] : (( ~ (v8 = 0) & quasi_total(v2, v7, v0) = v8 & cartesian_product2(v0, v0) = v7) | ( ~ (v8 = 0) & quasi_total(v1, v7, v0) = v8 & cartesian_product2(v0, v0) = v7) | ( ~ (v8 = 0) & relation_of2(v2, v7, v0) = v8 & cartesian_product2(v0, v0) = v7) | ( ~ (v8 = 0) & relation_of2(v1, v7, v0) = v8 & cartesian_product2(v0, v0) = v7) | ( ~ (v7 = 0) & function(v2) = v7) | ( ~ (v7 = 0) & function(v1) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v0 | ~ (latt_str_of(v4, v5, v6) = v3) | ~ (latt_str_of(v0, v1, v2) = v3) | ? [v7] : ? [v8] : (( ~ (v8 = 0) & quasi_total(v2, v7, v0) = v8 & cartesian_product2(v0, v0) = v7) | ( ~ (v8 = 0) & quasi_total(v1, v7, v0) = v8 & cartesian_product2(v0, v0) = v7) | ( ~ (v8 = 0) & relation_of2(v2, v7, v0) = v8 & cartesian_product2(v0, v0) = v7) | ( ~ (v8 = 0) & relation_of2(v1, v7, v0) = v8 & cartesian_product2(v0, v0) = v7) | ( ~ (v7 = 0) & function(v2) = v7) | ( ~ (v7 = 0) & function(v1) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (apply_binary_as_element(v0, v1, v2, v3, v4, v5) = v6) | ? [v7] : ? [v8] : ((v7 = v6 & apply_binary(v3, v4, v5) = v6) | (v7 = 0 & empty(v1) = 0) | (v7 = 0 & empty(v0) = 0) | ( ~ (v8 = 0) & quasi_total(v3, v7, v2) = v8 & cartesian_product2(v0, v1) = v7) | ( ~ (v8 = 0) & relation_of2(v3, v7, v2) = v8 & cartesian_product2(v0, v1) = v7) | ( ~ (v7 = 0) & function(v3) = v7) | ( ~ (v7 = 0) & element(v5, v1) = v7) | ( ~ (v7 = 0) & element(v4, v0) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (apply_binary_as_element(v0, v1, v2, v3, v4, v5) = v6) | ? [v7] : ? [v8] : ((v7 = 0 & empty(v1) = 0) | (v7 = 0 & empty(v0) = 0) | (v7 = 0 & element(v6, v2) = 0) | ( ~ (v8 = 0) & quasi_total(v3, v7, v2) = v8 & cartesian_product2(v0, v1) = v7) | ( ~ (v8 = 0) & relation_of2(v3, v7, v2) = v8 & cartesian_product2(v0, v1) = v7) | ( ~ (v7 = 0) & function(v3) = v7) | ( ~ (v7 = 0) & element(v5, v1) = v7) | ( ~ (v7 = 0) & element(v4, v0) = v7))) & ! [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] : ! [v5] : ( ~ (boole_lattice(v0) = v2) | ~ (meet(v2, v1, v4) = v5) | ~ (element(v1, v3) = 0) | ~ (the_carrier(v2) = v3) | ? [v6] : ? [v7] : ? [v8] : ((v8 = v5 & v7 = v6 & join(v2, v1, v4) = v6 & set_intersection2(v1, v4) = v5 & set_union2(v1, v4) = v6) | ( ~ (v6 = 0) & element(v4, v3) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (boole_lattice(v0) = v2) | ~ (join(v2, v1, v4) = v5) | ~ (element(v1, v3) = 0) | ~ (the_carrier(v2) = v3) | ? [v6] : ? [v7] : ? [v8] : ((v8 = v7 & v6 = v5 & meet(v2, v1, v4) = v7 & set_intersection2(v1, v4) = v7 & set_union2(v1, v4) = v5) | ( ~ (v6 = 0) & element(v4, v3) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (boole_lattice(v0) = v2) | ~ (set_intersection2(v1, v4) = v5) | ~ (element(v1, v3) = 0) | ~ (the_carrier(v2) = v3) | ? [v6] : ? [v7] : ? [v8] : ((v8 = v5 & v7 = v6 & meet(v2, v1, v4) = v5 & join(v2, v1, v4) = v6 & set_union2(v1, v4) = v6) | ( ~ (v6 = 0) & element(v4, v3) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (boole_lattice(v0) = v2) | ~ (set_union2(v1, v4) = v5) | ~ (element(v1, v3) = 0) | ~ (the_carrier(v2) = v3) | ? [v6] : ? [v7] : ? [v8] : ((v8 = v7 & v6 = v5 & meet(v2, v1, v4) = v7 & join(v2, v1, v4) = v5 & set_intersection2(v1, v4) = v7) | ( ~ (v6 = 0) & element(v4, v3) = 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_as_subset(v4, v3, v2) = v1) | ~ (relation_of2_as_subset(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (quasi_total(v4, v3, v2) = v1) | ~ (quasi_total(v4, v3, v2) = v0)) & ! [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 | ~ (below(v4, v3, v2) = v1) | ~ (below(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (meet(v4, v3, v2) = v1) | ~ (meet(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (join(v4, v3, v2) = v1) | ~ (join(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (apply_binary(v4, v3, v2) = v1) | ~ (apply_binary(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (latt_str_of(v4, v3, v2) = v1) | ~ (latt_str_of(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (boole_lattice(v0) = v2) | ~ (element(v4, v3) = 0) | ~ (element(v1, v3) = 0) | ~ (the_carrier(v2) = v3) | ? [v5] : ? [v6] : (meet(v2, v1, v4) = v6 & join(v2, v1, v4) = v5 & set_intersection2(v1, v4) = v6 & set_union2(v1, v4) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (below(v0, v2, v3) = v4) | ~ (element(v2, v1) = 0) | ~ (the_carrier(v0) = v1) | ? [v5] : ((v5 = 0 & empty_carrier(v0) = 0) | ( ~ (v5 = 0) & join_semilatt_str(v0) = v5) | ( ~ (v5 = 0) & element(v3, v1) = v5) | (( ~ (v4 = 0) | (v5 = v3 & join(v0, v2, v3) = v3)) & (v4 = 0 | ( ~ (v5 = v3) & join(v0, v2, v3) = v5))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (join(v0, v2, v3) = v4) | ~ (element(v2, v1) = 0) | ~ (the_carrier(v0) = v1) | ? [v5] : ((v5 = 0 & empty_carrier(v0) = 0) | ( ~ (v5 = 0) & join_semilatt_str(v0) = v5) | ( ~ (v5 = 0) & element(v3, v1) = v5) | (( ~ (v4 = v3) | (v5 = 0 & below(v0, v2, v3) = 0)) & (v4 = v3 | ( ~ (v5 = 0) & below(v0, v2, v3) = v5))))) & ! [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_as_subset(v2, v0, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & relation_of2(v2, v0, v1) = v4)) & ! [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 | ~ (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = 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 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (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] : ( ~ (meet(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & element(v3, v4) = 0 & the_carrier(v0) = v4) | (v4 = 0 & empty_carrier(v0) = 0) | ( ~ (v5 = 0) & element(v2, v4) = v5 & the_carrier(v0) = v4) | ( ~ (v5 = 0) & element(v1, v4) = v5 & the_carrier(v0) = v4) | ( ~ (v4 = 0) & meet_semilatt_str(v0) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (join(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & element(v3, v4) = 0 & the_carrier(v0) = v4) | (v4 = 0 & empty_carrier(v0) = 0) | ( ~ (v5 = 0) & element(v2, v4) = v5 & the_carrier(v0) = v4) | ( ~ (v5 = 0) & element(v1, v4) = v5 & the_carrier(v0) = v4) | ( ~ (v4 = 0) & join_semilatt_str(v0) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (function(v0) = 0) | ~ (ordered_pair(v1, v2) = v3) | ? [v4] : ? [v5] : ((v5 = v4 & apply_binary(v0, v1, v2) = v4 & apply(v0, v3) = v4) | ( ~ (v4 = 0) & relation(v0) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (function(v0) = 0) | ~ (apply_binary(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ((v5 = v3 & ordered_pair(v1, v2) = v4 & apply(v0, v4) = v3) | ( ~ (v4 = 0) & relation(v0) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (ordered_pair(v1, v2) = v3) | ~ (relation(v0) = 0) | ? [v4] : ? [v5] : ((v5 = v4 & apply_binary(v0, v1, v2) = v4 & apply(v0, v3) = v4) | ( ~ (v4 = 0) & function(v0) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (apply_binary(v0, v1, v2) = v3) | ~ (relation(v0) = 0) | ? [v4] : ? [v5] : ((v5 = v3 & ordered_pair(v1, v2) = v4 & apply(v0, v4) = v3) | ( ~ (v4 = 0) & function(v0) = v4))) & ! [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] : ! [v3] : ( ~ (element(v3, v1) = 0) | ~ (element(v2, v1) = 0) | ~ (the_carrier(v0) = v1) | ? [v4] : ? [v5] : ((v4 = 0 & empty_carrier(v0) = 0) | ( ~ (v4 = 0) & join_semilatt_str(v0) = v4) | (((v5 = v3 & join(v0, v2, v3) = v3) | ( ~ (v4 = 0) & below(v0, v2, v3) = v4)) & ((v4 = 0 & below(v0, v2, v3) = 0) | ( ~ (v5 = v3) & join(v0, v2, v3) = v5))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (latt_str_of(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & strict_latt_str(v3) = 0 & latt_str(v3) = 0) | ( ~ (v5 = 0) & quasi_total(v2, v4, v0) = v5 & cartesian_product2(v0, v0) = v4) | ( ~ (v5 = 0) & quasi_total(v1, v4, v0) = v5 & cartesian_product2(v0, v0) = v4) | ( ~ (v5 = 0) & relation_of2(v2, v4, v0) = v5 & cartesian_product2(v0, v0) = v4) | ( ~ (v5 = 0) & relation_of2(v1, v4, v0) = v5 & cartesian_product2(v0, v0) = v4) | ( ~ (v4 = 0) & function(v2) = v4) | ( ~ (v4 = 0) & function(v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (latt_str_of(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & ~ (v4 = 0) & empty_carrier(v3) = v4 & strict_latt_str(v3) = 0) | (v4 = 0 & empty(v0) = 0) | ( ~ (v5 = 0) & quasi_total(v2, v4, v0) = v5 & cartesian_product2(v0, v0) = v4) | ( ~ (v5 = 0) & quasi_total(v1, v4, v0) = v5 & cartesian_product2(v0, v0) = v4) | ( ~ (v5 = 0) & relation_of2(v2, v4, v0) = v5 & cartesian_product2(v0, v0) = v4) | ( ~ (v5 = 0) & relation_of2(v1, v4, v0) = v5 & cartesian_product2(v0, v0) = v4) | ( ~ (v4 = 0) & function(v2) = v4) | ( ~ (v4 = 0) & function(v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (set_union2(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = 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 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (boole_lattice(v2) = v1) | ~ (boole_lattice(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (meet_semilatt_str(v2) = v1) | ~ (meet_semilatt_str(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty_carrier(v2) = v1) | ~ (empty_carrier(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (join_semilatt_str(v2) = v1) | ~ (join_semilatt_str(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(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 | ~ (strict_latt_str(v2) = v1) | ~ (strict_latt_str(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (latt_str(v2) = v1) | ~ (latt_str(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (the_carrier(v2) = v1) | ~ (the_carrier(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (the_L_join(v2) = v1) | ~ (the_L_join(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (the_L_meet(v2) = v1) | ~ (the_L_meet(v2) = v0)) & ! [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] : ( ~ (empty(v2) = 0) | ~ (in(v0, v1) = 0) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v2) = v3 & element(v1, v3) = v4)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_of2(v2, v0, v1) = 0) | relation_of2_as_subset(v2, v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ? [v3] : ((v3 = 0 & empty(v0) = 0) | ( ~ (v3 = 0) & empty(v2) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | subset(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : ((v3 = 0 & empty(v0) = 0) | ( ~ (v3 = 0) & empty(v2) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & ordered_pair(v0, v1) = v3 & unordered_pair(v2, v4) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (cartesian_product2(v0, v1) = v2) | ? [v3] : ((v3 = 0 & empty(v1) = 0) | (v3 = 0 & empty(v0) = 0) | ( ~ (v3 = 0) & empty(v2) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | subset(v0, v1) = 0) & ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1)) & ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (one_sorted_str(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & meet_semilatt_str(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (one_sorted_str(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & join_semilatt_str(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (empty(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & empty(v3) = v4 & powerset(v0) = v2 & element(v3, v2) = 0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (empty_carrier(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ((v5 = 0 & ~ (v6 = 0) & empty(v4) = v6 & powerset(v2) = v3 & element(v4, v3) = 0 & the_carrier(v0) = v2) | ( ~ (v2 = 0) & one_sorted_str(v0) = v2))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (empty_carrier(v0) = v1) | ? [v2] : ? [v3] : (( ~ (v3 = 0) & empty(v2) = v3 & the_carrier(v0) = v2) | ( ~ (v2 = 0) & one_sorted_str(v0) = v2))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (empty_carrier(v0) = v1) | ? [v2] : ? [v3] : (( ~ (v2 = 0) & meet_semilatt_str(v0) = v2) | (the_carrier(v0) = v2 & the_L_meet(v0) = v3 & ! [v4] : ! [v5] : ! [v6] : ( ~ (meet(v0, v4, v5) = v6) | ~ (element(v4, v2) = 0) | ? [v7] : ((v7 = v6 & apply_binary_as_element(v2, v2, v2, v3, v4, v5) = v6) | ( ~ (v7 = 0) & element(v5, v2) = v7))) & ! [v4] : ! [v5] : ! [v6] : ( ~ (apply_binary_as_element(v2, v2, v2, v3, v4, v5) = v6) | ~ (element(v4, v2) = 0) | ? [v7] : ((v7 = v6 & meet(v0, v4, v5) = v6) | ( ~ (v7 = 0) & element(v5, v2) = v7))) & ! [v4] : ! [v5] : ( ~ (element(v5, v2) = 0) | ~ (element(v4, v2) = 0) | ? [v6] : (meet(v0, v4, v5) = v6 & apply_binary_as_element(v2, v2, v2, v3, v4, v5) = v6))))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (empty_carrier(v0) = v1) | ? [v2] : ? [v3] : (( ~ (v2 = 0) & join_semilatt_str(v0) = v2) | (the_carrier(v0) = v2 & the_L_join(v0) = v3 & ! [v4] : ! [v5] : ! [v6] : ( ~ (join(v0, v4, v5) = v6) | ~ (element(v4, v2) = 0) | ? [v7] : ((v7 = v6 & apply_binary_as_element(v2, v2, v2, v3, v4, v5) = v6) | ( ~ (v7 = 0) & element(v5, v2) = v7))) & ! [v4] : ! [v5] : ! [v6] : ( ~ (apply_binary_as_element(v2, v2, v2, v3, v4, v5) = v6) | ~ (element(v4, v2) = 0) | ? [v7] : ((v7 = v6 & join(v0, v4, v5) = v6) | ( ~ (v7 = 0) & element(v5, v2) = v7))) & ! [v4] : ! [v5] : ( ~ (element(v5, v2) = 0) | ~ (element(v4, v2) = 0) | ? [v6] : (join(v0, v4, v5) = v6 & apply_binary_as_element(v2, v2, v2, v3, v4, v5) = v6))))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (empty_carrier(v0) = v1) | ? [v2] : (( ~ (v2 = 0) & join_semilatt_str(v0) = v2) | (the_carrier(v0) = v2 & ! [v3] : ! [v4] : ! [v5] : ( ~ (below(v0, v3, v4) = v5) | ~ (element(v3, v2) = 0) | ? [v6] : (( ~ (v6 = 0) & element(v4, v2) = v6) | (( ~ (v5 = 0) | (v6 = v4 & join(v0, v3, v4) = v4)) & (v5 = 0 | ( ~ (v6 = v4) & join(v0, v3, v4) = v6))))) & ! [v3] : ! [v4] : ! [v5] : ( ~ (join(v0, v3, v4) = v5) | ~ (element(v3, v2) = 0) | ? [v6] : (( ~ (v6 = 0) & element(v4, v2) = v6) | (( ~ (v5 = v4) | (v6 = 0 & below(v0, v3, v4) = 0)) & (v5 = v4 | ( ~ (v6 = 0) & below(v0, v3, v4) = v6))))) & ! [v3] : ! [v4] : ( ~ (element(v4, v2) = 0) | ~ (element(v3, v2) = 0) | ? [v5] : ? [v6] : (((v6 = v4 & join(v0, v3, v4) = v4) | ( ~ (v5 = 0) & below(v0, v3, v4) = v5)) & ((v5 = 0 & below(v0, v3, v4) = 0) | ( ~ (v6 = v4) & join(v0, v3, v4) = v6))))))) & ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | set_union2(v0, v1) = v1) & ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (powerset(v1) = v2 & element(v0, v2) = 0)) & ! [v0] : ! [v1] : ( ~ (boole_lattice(v0) = v1) | strict_latt_str(v1) = 0) & ! [v0] : ! [v1] : ( ~ (boole_lattice(v0) = v1) | latt_str(v1) = 0) & ! [v0] : ! [v1] : ( ~ (boole_lattice(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty_carrier(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (meet_semilatt_str(v0) = v1) | ? [v2] : ((v2 = 0 & v1 = 0 & join_semilatt_str(v0) = 0) | ( ~ (v2 = 0) & latt_str(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (join_semilatt_str(v0) = v1) | ? [v2] : ((v2 = 0 & v1 = 0 & meet_semilatt_str(v0) = 0) | ( ~ (v2 = 0) & latt_str(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v3 = 0 & ~ (v4 = 0) & empty(v2) = v4 & element(v2, v1) = 0) | (v2 = 0 & empty(v0) = 0))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (empty(v2) = 0 & element(v2, v1) = 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] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & v3 = 0 & relation_of2_as_subset(v2, v4, v1) = 0 & quasi_total(v2, v4, v1) = 0 & function(v2) = 0 & cartesian_product2(v1, v1) = v4 & the_L_join(v0) = v2) | ( ~ (v2 = 0) & join_semilatt_str(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & v3 = 0 & relation_of2_as_subset(v2, v4, v1) = 0 & quasi_total(v2, v4, v1) = 0 & function(v2) = 0 & cartesian_product2(v1, v1) = v4 & the_L_meet(v0) = v2) | ( ~ (v2 = 0) & meet_semilatt_str(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ((v4 = 0 & ~ (v5 = 0) & empty(v3) = v5 & powerset(v1) = v2 & element(v3, v2) = 0) | (v2 = 0 & empty_carrier(v0) = 0) | ( ~ (v2 = 0) & one_sorted_str(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v0 & the_L_join(v0) = v2 & the_L_meet(v0) = v3 & latt_str_of(v1, v2, v3) = v0) | ( ~ (v2 = 0) & strict_latt_str(v0) = v2) | ( ~ (v2 = 0) & latt_str(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ? [v2] : ((v2 = 0 & empty_carrier(v0) = 0) | ( ~ (v2 = 0) & one_sorted_str(v0) = v2) | ( ~ (v2 = 0) & empty(v1) = v2))) & ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ? [v2] : ((v2 = 0 & empty_carrier(v0) = 0) | ( ~ (v2 = 0) & meet_semilatt_str(v0) = v2) | (the_L_meet(v0) = v2 & ! [v3] : ! [v4] : ! [v5] : ( ~ (meet(v0, v3, v4) = v5) | ~ (element(v3, v1) = 0) | ? [v6] : ((v6 = v5 & apply_binary_as_element(v1, v1, v1, v2, v3, v4) = v5) | ( ~ (v6 = 0) & element(v4, v1) = v6))) & ! [v3] : ! [v4] : ! [v5] : ( ~ (apply_binary_as_element(v1, v1, v1, v2, v3, v4) = v5) | ~ (element(v3, v1) = 0) | ? [v6] : ((v6 = v5 & meet(v0, v3, v4) = v5) | ( ~ (v6 = 0) & element(v4, v1) = v6))) & ! [v3] : ! [v4] : ( ~ (element(v4, v1) = 0) | ~ (element(v3, v1) = 0) | ? [v5] : (meet(v0, v3, v4) = v5 & apply_binary_as_element(v1, v1, v1, v2, v3, v4) = v5))))) & ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ? [v2] : ((v2 = 0 & empty_carrier(v0) = 0) | ( ~ (v2 = 0) & join_semilatt_str(v0) = v2) | (the_L_join(v0) = v2 & ! [v3] : ! [v4] : ! [v5] : ( ~ (join(v0, v3, v4) = v5) | ~ (element(v3, v1) = 0) | ? [v6] : ((v6 = v5 & apply_binary_as_element(v1, v1, v1, v2, v3, v4) = v5) | ( ~ (v6 = 0) & element(v4, v1) = v6))) & ! [v3] : ! [v4] : ! [v5] : ( ~ (apply_binary_as_element(v1, v1, v1, v2, v3, v4) = v5) | ~ (element(v3, v1) = 0) | ? [v6] : ((v6 = v5 & join(v0, v3, v4) = v5) | ( ~ (v6 = 0) & element(v4, v1) = v6))) & ! [v3] : ! [v4] : ( ~ (element(v4, v1) = 0) | ~ (element(v3, v1) = 0) | ? [v5] : (join(v0, v3, v4) = v5 & apply_binary_as_element(v1, v1, v1, v2, v3, v4) = v5))))) & ! [v0] : ! [v1] : ( ~ (the_L_join(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & v2 = 0 & relation_of2_as_subset(v1, v4, v3) = 0 & quasi_total(v1, v4, v3) = 0 & function(v1) = 0 & cartesian_product2(v3, v3) = v4 & the_carrier(v0) = v3) | ( ~ (v2 = 0) & join_semilatt_str(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (the_L_join(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v0 & the_carrier(v0) = v2 & the_L_meet(v0) = v3 & latt_str_of(v2, v1, v3) = v0) | ( ~ (v2 = 0) & strict_latt_str(v0) = v2) | ( ~ (v2 = 0) & latt_str(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (the_L_join(v0) = v1) | ? [v2] : ((v2 = 0 & empty_carrier(v0) = 0) | ( ~ (v2 = 0) & join_semilatt_str(v0) = v2) | (the_carrier(v0) = v2 & ! [v3] : ! [v4] : ! [v5] : ( ~ (join(v0, v3, v4) = v5) | ~ (element(v3, v2) = 0) | ? [v6] : ((v6 = v5 & apply_binary_as_element(v2, v2, v2, v1, v3, v4) = v5) | ( ~ (v6 = 0) & element(v4, v2) = v6))) & ! [v3] : ! [v4] : ! [v5] : ( ~ (apply_binary_as_element(v2, v2, v2, v1, v3, v4) = v5) | ~ (element(v3, v2) = 0) | ? [v6] : ((v6 = v5 & join(v0, v3, v4) = v5) | ( ~ (v6 = 0) & element(v4, v2) = v6))) & ! [v3] : ! [v4] : ( ~ (element(v4, v2) = 0) | ~ (element(v3, v2) = 0) | ? [v5] : (join(v0, v3, v4) = v5 & apply_binary_as_element(v2, v2, v2, v1, v3, v4) = v5))))) & ! [v0] : ! [v1] : ( ~ (the_L_meet(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & v2 = 0 & relation_of2_as_subset(v1, v4, v3) = 0 & quasi_total(v1, v4, v3) = 0 & function(v1) = 0 & cartesian_product2(v3, v3) = v4 & the_carrier(v0) = v3) | ( ~ (v2 = 0) & meet_semilatt_str(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (the_L_meet(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v0 & the_carrier(v0) = v2 & the_L_join(v0) = v3 & latt_str_of(v2, v3, v1) = v0) | ( ~ (v2 = 0) & strict_latt_str(v0) = v2) | ( ~ (v2 = 0) & latt_str(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (the_L_meet(v0) = v1) | ? [v2] : ((v2 = 0 & empty_carrier(v0) = 0) | ( ~ (v2 = 0) & meet_semilatt_str(v0) = v2) | (the_carrier(v0) = v2 & ! [v3] : ! [v4] : ! [v5] : ( ~ (meet(v0, v3, v4) = v5) | ~ (element(v3, v2) = 0) | ? [v6] : ((v6 = v5 & apply_binary_as_element(v2, v2, v2, v1, v3, v4) = v5) | ( ~ (v6 = 0) & element(v4, v2) = v6))) & ! [v3] : ! [v4] : ! [v5] : ( ~ (apply_binary_as_element(v2, v2, v2, v1, v3, v4) = v5) | ~ (element(v3, v2) = 0) | ? [v6] : ((v6 = v5 & meet(v0, v3, v4) = v5) | ( ~ (v6 = 0) & element(v4, v2) = v6))) & ! [v3] : ! [v4] : ( ~ (element(v4, v2) = 0) | ~ (element(v3, v2) = 0) | ? [v5] : (meet(v0, v3, v4) = v5 & apply_binary_as_element(v2, v2, v2, v1, v3, v4) = v5))))) & ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0)) & ! [v0] : ( ~ (one_sorted_str(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ((v4 = 0 & ~ (v5 = 0) & empty(v3) = v5 & powerset(v1) = v2 & element(v3, v2) = 0 & the_carrier(v0) = v1) | (v1 = 0 & empty_carrier(v0) = 0))) & ! [v0] : ( ~ (one_sorted_str(v0) = 0) | ? [v1] : ? [v2] : ((v1 = 0 & empty_carrier(v0) = 0) | ( ~ (v2 = 0) & empty(v1) = v2 & the_carrier(v0) = v1))) & ! [v0] : ( ~ (meet_semilatt_str(v0) = 0) | one_sorted_str(v0) = 0) & ! [v0] : ( ~ (meet_semilatt_str(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (relation_of2_as_subset(v1, v3, v2) = 0 & quasi_total(v1, v3, v2) = 0 & function(v1) = 0 & cartesian_product2(v2, v2) = v3 & the_carrier(v0) = v2 & the_L_meet(v0) = v1)) & ! [v0] : ( ~ (meet_semilatt_str(v0) = 0) | ? [v1] : ? [v2] : ((v1 = 0 & empty_carrier(v0) = 0) | (the_carrier(v0) = v1 & the_L_meet(v0) = v2 & ! [v3] : ! [v4] : ! [v5] : ( ~ (meet(v0, v3, v4) = v5) | ~ (element(v3, v1) = 0) | ? [v6] : ((v6 = v5 & apply_binary_as_element(v1, v1, v1, v2, v3, v4) = v5) | ( ~ (v6 = 0) & element(v4, v1) = v6))) & ! [v3] : ! [v4] : ! [v5] : ( ~ (apply_binary_as_element(v1, v1, v1, v2, v3, v4) = v5) | ~ (element(v3, v1) = 0) | ? [v6] : ((v6 = v5 & meet(v0, v3, v4) = v5) | ( ~ (v6 = 0) & element(v4, v1) = v6))) & ! [v3] : ! [v4] : ( ~ (element(v4, v1) = 0) | ~ (element(v3, v1) = 0) | ? [v5] : (meet(v0, v3, v4) = v5 & apply_binary_as_element(v1, v1, v1, v2, v3, v4) = v5))))) & ! [v0] : ( ~ (join_semilatt_str(v0) = 0) | one_sorted_str(v0) = 0) & ! [v0] : ( ~ (join_semilatt_str(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (relation_of2_as_subset(v1, v3, v2) = 0 & quasi_total(v1, v3, v2) = 0 & function(v1) = 0 & cartesian_product2(v2, v2) = v3 & the_carrier(v0) = v2 & the_L_join(v0) = v1)) & ! [v0] : ( ~ (join_semilatt_str(v0) = 0) | ? [v1] : ? [v2] : ((v1 = 0 & empty_carrier(v0) = 0) | (the_carrier(v0) = v1 & the_L_join(v0) = v2 & ! [v3] : ! [v4] : ! [v5] : ( ~ (join(v0, v3, v4) = v5) | ~ (element(v3, v1) = 0) | ? [v6] : ((v6 = v5 & apply_binary_as_element(v1, v1, v1, v2, v3, v4) = v5) | ( ~ (v6 = 0) & element(v4, v1) = v6))) & ! [v3] : ! [v4] : ! [v5] : ( ~ (apply_binary_as_element(v1, v1, v1, v2, v3, v4) = v5) | ~ (element(v3, v1) = 0) | ? [v6] : ((v6 = v5 & join(v0, v3, v4) = v5) | ( ~ (v6 = 0) & element(v4, v1) = v6))) & ! [v3] : ! [v4] : ( ~ (element(v4, v1) = 0) | ~ (element(v3, v1) = 0) | ? [v5] : (join(v0, v3, v4) = v5 & apply_binary_as_element(v1, v1, v1, v2, v3, v4) = v5))))) & ! [v0] : ( ~ (join_semilatt_str(v0) = 0) | ? [v1] : ((v1 = 0 & empty_carrier(v0) = 0) | (the_carrier(v0) = v1 & ! [v2] : ! [v3] : ! [v4] : ( ~ (below(v0, v2, v3) = v4) | ~ (element(v2, v1) = 0) | ? [v5] : (( ~ (v5 = 0) & element(v3, v1) = v5) | (( ~ (v4 = 0) | (v5 = v3 & join(v0, v2, v3) = v3)) & (v4 = 0 | ( ~ (v5 = v3) & join(v0, v2, v3) = v5))))) & ! [v2] : ! [v3] : ! [v4] : ( ~ (join(v0, v2, v3) = v4) | ~ (element(v2, v1) = 0) | ? [v5] : (( ~ (v5 = 0) & element(v3, v1) = v5) | (( ~ (v4 = v3) | (v5 = 0 & below(v0, v2, v3) = 0)) & (v4 = v3 | ( ~ (v5 = 0) & below(v0, v2, v3) = v5))))) & ! [v2] : ! [v3] : ( ~ (element(v3, v1) = 0) | ~ (element(v2, v1) = 0) | ? [v4] : ? [v5] : (((v5 = v3 & join(v0, v2, v3) = v3) | ( ~ (v4 = 0) & below(v0, v2, v3) = v4)) & ((v4 = 0 & below(v0, v2, v3) = 0) | ( ~ (v5 = v3) & join(v0, v2, v3) = v5))))))) & ! [v0] : ( ~ (strict_latt_str(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ((v4 = v0 & the_carrier(v0) = v1 & the_L_join(v0) = v2 & the_L_meet(v0) = v3 & latt_str_of(v1, v2, v3) = v0) | ( ~ (v1 = 0) & latt_str(v0) = v1))) & ! [v0] : ( ~ (latt_str(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ((v4 = v0 & the_carrier(v0) = v1 & the_L_join(v0) = v2 & the_L_meet(v0) = v3 & latt_str_of(v1, v2, v3) = v0) | ( ~ (v1 = 0) & strict_latt_str(v0) = v1))) & ! [v0] : ( ~ (latt_str(v0) = 0) | (meet_semilatt_str(v0) = 0 & join_semilatt_str(v0) = 0)) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : apply_binary_as_element(v5, v4, v3, v2, v1, v0) = v6 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : relation_of2_as_subset(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : quasi_total(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : relation_of2(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : below(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : meet(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : join(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : apply_binary(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : latt_str_of(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : relation_of2_as_subset(v2, v0, v1) = 0 & ? [v0] : ? [v1] : ? [v2] : relation_of2(v2, v0, v1) = 0 & ? [v0] : ? [v1] : ? [v2] : ordered_pair(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : apply(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : set_intersection2(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : set_union2(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : unordered_pair(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : 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] : empty(v0) = v1 & ? [v0] : ? [v1] : boole_lattice(v0) = v1 & ? [v0] : ? [v1] : singleton(v0) = v1 & ? [v0] : ? [v1] : meet_semilatt_str(v0) = v1 & ? [v0] : ? [v1] : empty_carrier(v0) = v1 & ? [v0] : ? [v1] : join_semilatt_str(v0) = v1 & ? [v0] : ? [v1] : function(v0) = v1 & ? [v0] : ? [v1] : powerset(v0) = v1 & ? [v0] : ? [v1] : element(v1, v0) = 0 & ? [v0] : ? [v1] : relation(v0) = v1 & ? [v0] : ? [v1] : strict_latt_str(v0) = v1 & ? [v0] : ? [v1] : latt_str(v0) = v1 & ? [v0] : ? [v1] : the_carrier(v0) = v1 & ? [v0] : ? [v1] : the_L_join(v0) = v1 & ? [v0] : ? [v1] : the_L_meet(v0) = v1 & ((all_0_12_12 = 0 & ~ (all_0_13_13 = 0)) | (all_0_13_13 = 0 & ~ (all_0_12_12 = 0)))
% 110.18/75.55 |
% 110.18/75.55 | Applying alpha-rule on (1) yields:
% 110.18/75.55 | (2) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (the_carrier(v2) = v1) | ~ (the_carrier(v2) = v0))
% 110.18/75.55 | (3) the_carrier(all_0_16_16) = all_0_15_15
% 110.18/75.55 | (4) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1))
% 110.18/75.55 | (5) ! [v0] : ( ~ (join_semilatt_str(v0) = 0) | ? [v1] : ? [v2] : ((v1 = 0 & empty_carrier(v0) = 0) | (the_carrier(v0) = v1 & the_L_join(v0) = v2 & ! [v3] : ! [v4] : ! [v5] : ( ~ (join(v0, v3, v4) = v5) | ~ (element(v3, v1) = 0) | ? [v6] : ((v6 = v5 & apply_binary_as_element(v1, v1, v1, v2, v3, v4) = v5) | ( ~ (v6 = 0) & element(v4, v1) = v6))) & ! [v3] : ! [v4] : ! [v5] : ( ~ (apply_binary_as_element(v1, v1, v1, v2, v3, v4) = v5) | ~ (element(v3, v1) = 0) | ? [v6] : ((v6 = v5 & join(v0, v3, v4) = v5) | ( ~ (v6 = 0) & element(v4, v1) = v6))) & ! [v3] : ! [v4] : ( ~ (element(v4, v1) = 0) | ~ (element(v3, v1) = 0) | ? [v5] : (join(v0, v3, v4) = v5 & apply_binary_as_element(v1, v1, v1, v2, v3, v4) = v5)))))
% 110.18/75.55 | (6) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v1) = v3 & element(v0, v3) = v4))
% 110.18/75.55 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v0 | ~ (latt_str_of(v4, v5, v6) = v3) | ~ (latt_str_of(v0, v1, v2) = v3) | ? [v7] : ? [v8] : (( ~ (v8 = 0) & quasi_total(v2, v7, v0) = v8 & cartesian_product2(v0, v0) = v7) | ( ~ (v8 = 0) & quasi_total(v1, v7, v0) = v8 & cartesian_product2(v0, v0) = v7) | ( ~ (v8 = 0) & relation_of2(v2, v7, v0) = v8 & cartesian_product2(v0, v0) = v7) | ( ~ (v8 = 0) & relation_of2(v1, v7, v0) = v8 & cartesian_product2(v0, v0) = v7) | ( ~ (v7 = 0) & function(v2) = v7) | ( ~ (v7 = 0) & function(v1) = v7)))
% 110.18/75.56 | (8) ! [v0] : ! [v1] : ( ~ (the_L_join(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & v2 = 0 & relation_of2_as_subset(v1, v4, v3) = 0 & quasi_total(v1, v4, v3) = 0 & function(v1) = 0 & cartesian_product2(v3, v3) = v4 & the_carrier(v0) = v3) | ( ~ (v2 = 0) & join_semilatt_str(v0) = v2)))
% 110.18/75.56 | (9) subset(all_0_17_17, all_0_14_14) = all_0_12_12
% 110.18/75.56 | (10) ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & v3 = 0 & relation_of2_as_subset(v2, v4, v1) = 0 & quasi_total(v2, v4, v1) = 0 & function(v2) = 0 & cartesian_product2(v1, v1) = v4 & the_L_join(v0) = v2) | ( ~ (v2 = 0) & join_semilatt_str(v0) = v2)))
% 110.18/75.56 | (11) ? [v0] : ? [v1] : ? [v2] : cartesian_product2(v1, v0) = v2
% 110.18/75.56 | (12) strict_latt_str(all_0_7_7) = 0
% 110.18/75.56 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 110.18/75.56 | (14) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2)
% 110.18/75.56 | (15) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2)
% 110.18/75.56 | (16) join_semilatt_str(all_0_2_2) = 0
% 110.18/75.56 | (17) empty_carrier(all_0_11_11) = all_0_10_10
% 110.18/75.56 | (18) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1))
% 110.18/75.56 | (19) ~ (all_0_10_10 = 0)
% 110.18/75.56 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (boole_lattice(v0) = v2) | ~ (meet(v2, v1, v4) = v5) | ~ (element(v1, v3) = 0) | ~ (the_carrier(v2) = v3) | ? [v6] : ? [v7] : ? [v8] : ((v8 = v5 & v7 = v6 & join(v2, v1, v4) = v6 & set_intersection2(v1, v4) = v5 & set_union2(v1, v4) = v6) | ( ~ (v6 = 0) & element(v4, v3) = v6)))
% 110.18/75.56 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (element(v3, v1) = 0) | ~ (element(v2, v1) = 0) | ~ (the_carrier(v0) = v1) | ? [v4] : ? [v5] : ((v4 = 0 & empty_carrier(v0) = 0) | ( ~ (v4 = 0) & join_semilatt_str(v0) = v4) | (((v5 = v3 & join(v0, v2, v3) = v3) | ( ~ (v4 = 0) & below(v0, v2, v3) = v4)) & ((v4 = 0 & below(v0, v2, v3) = 0) | ( ~ (v5 = v3) & join(v0, v2, v3) = v5)))))
% 110.18/75.56 | (22) ? [v0] : ? [v1] : singleton(v0) = v1
% 110.18/75.56 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0))
% 110.18/75.56 | (24) ? [v0] : ? [v1] : strict_latt_str(v0) = v1
% 110.18/75.56 | (25) ! [v0] : ! [v1] : ( ~ (element(v0, v1) = 0) | ? [v2] : ((v2 = 0 & empty(v1) = 0) | (v2 = 0 & in(v0, v1) = 0)))
% 110.18/75.56 | (26) ? [v0] : ? [v1] : one_sorted_str(v0) = v1
% 110.18/75.56 | (27) ! [v0] : ! [v1] : ! [v2] : ( ~ (empty(v2) = 0) | ~ (in(v0, v1) = 0) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v2) = v3 & element(v1, v3) = v4))
% 110.18/75.56 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (latt_str_of(v4, v3, v2) = v1) | ~ (latt_str_of(v4, v3, v2) = v0))
% 110.18/75.56 | (29) ! [v0] : ( ~ (meet_semilatt_str(v0) = 0) | ? [v1] : ? [v2] : ((v1 = 0 & empty_carrier(v0) = 0) | (the_carrier(v0) = v1 & the_L_meet(v0) = v2 & ! [v3] : ! [v4] : ! [v5] : ( ~ (meet(v0, v3, v4) = v5) | ~ (element(v3, v1) = 0) | ? [v6] : ((v6 = v5 & apply_binary_as_element(v1, v1, v1, v2, v3, v4) = v5) | ( ~ (v6 = 0) & element(v4, v1) = v6))) & ! [v3] : ! [v4] : ! [v5] : ( ~ (apply_binary_as_element(v1, v1, v1, v2, v3, v4) = v5) | ~ (element(v3, v1) = 0) | ? [v6] : ((v6 = v5 & meet(v0, v3, v4) = v5) | ( ~ (v6 = 0) & element(v4, v1) = v6))) & ! [v3] : ! [v4] : ( ~ (element(v4, v1) = 0) | ~ (element(v3, v1) = 0) | ? [v5] : (meet(v0, v3, v4) = v5 & apply_binary_as_element(v1, v1, v1, v2, v3, v4) = v5)))))
% 110.18/75.56 | (30) ! [v0] : ( ~ (one_sorted_str(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ((v4 = 0 & ~ (v5 = 0) & empty(v3) = v5 & powerset(v1) = v2 & element(v3, v2) = 0 & the_carrier(v0) = v1) | (v1 = 0 & empty_carrier(v0) = 0)))
% 110.18/75.56 | (31) ? [v0] : ? [v1] : the_L_join(v0) = v1
% 110.18/75.56 | (32) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 110.18/75.56 | (33) ~ (all_0_5_5 = 0)
% 110.18/75.56 | (34) ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ? [v2] : ((v2 = 0 & empty_carrier(v0) = 0) | ( ~ (v2 = 0) & one_sorted_str(v0) = v2) | ( ~ (v2 = 0) & empty(v1) = v2)))
% 110.18/75.56 | (35) ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ? [v2] : ((v2 = 0 & empty_carrier(v0) = 0) | ( ~ (v2 = 0) & join_semilatt_str(v0) = v2) | (the_L_join(v0) = v2 & ! [v3] : ! [v4] : ! [v5] : ( ~ (join(v0, v3, v4) = v5) | ~ (element(v3, v1) = 0) | ? [v6] : ((v6 = v5 & apply_binary_as_element(v1, v1, v1, v2, v3, v4) = v5) | ( ~ (v6 = 0) & element(v4, v1) = v6))) & ! [v3] : ! [v4] : ! [v5] : ( ~ (apply_binary_as_element(v1, v1, v1, v2, v3, v4) = v5) | ~ (element(v3, v1) = 0) | ? [v6] : ((v6 = v5 & join(v0, v3, v4) = v5) | ( ~ (v6 = 0) & element(v4, v1) = v6))) & ! [v3] : ! [v4] : ( ~ (element(v4, v1) = 0) | ~ (element(v3, v1) = 0) | ? [v5] : (join(v0, v3, v4) = v5 & apply_binary_as_element(v1, v1, v1, v2, v3, v4) = v5)))))
% 110.18/75.57 | (36) ! [v0] : ! [v1] : ! [v2] : ( ~ (cartesian_product2(v0, v1) = v2) | ? [v3] : ((v3 = 0 & empty(v1) = 0) | (v3 = 0 & empty(v0) = 0) | ( ~ (v3 = 0) & empty(v2) = v3)))
% 110.18/75.57 | (37) ? [v0] : ? [v1] : latt_str(v0) = v1
% 110.18/75.57 | (38) ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ? [v2] : ((v2 = 0 & empty_carrier(v0) = 0) | ( ~ (v2 = 0) & meet_semilatt_str(v0) = v2) | (the_L_meet(v0) = v2 & ! [v3] : ! [v4] : ! [v5] : ( ~ (meet(v0, v3, v4) = v5) | ~ (element(v3, v1) = 0) | ? [v6] : ((v6 = v5 & apply_binary_as_element(v1, v1, v1, v2, v3, v4) = v5) | ( ~ (v6 = 0) & element(v4, v1) = v6))) & ! [v3] : ! [v4] : ! [v5] : ( ~ (apply_binary_as_element(v1, v1, v1, v2, v3, v4) = v5) | ~ (element(v3, v1) = 0) | ? [v6] : ((v6 = v5 & meet(v0, v3, v4) = v5) | ( ~ (v6 = 0) & element(v4, v1) = v6))) & ! [v3] : ! [v4] : ( ~ (element(v4, v1) = 0) | ~ (element(v3, v1) = 0) | ? [v5] : (meet(v0, v3, v4) = v5 & apply_binary_as_element(v1, v1, v1, v2, v3, v4) = v5)))))
% 110.18/75.57 | (39) ? [v0] : ? [v1] : element(v1, v0) = 0
% 110.18/75.57 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (apply_binary(v0, v1, v2) = v3) | ~ (relation(v0) = 0) | ? [v4] : ? [v5] : ((v5 = v3 & ordered_pair(v1, v2) = v4 & apply(v0, v4) = v3) | ( ~ (v4 = 0) & function(v0) = v4)))
% 110.18/75.57 | (41) empty(all_0_6_6) = all_0_5_5
% 110.18/75.57 | (42) (all_0_12_12 = 0 & ~ (all_0_13_13 = 0)) | (all_0_13_13 = 0 & ~ (all_0_12_12 = 0))
% 110.18/75.57 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (boole_lattice(v0) = v2) | ~ (set_intersection2(v1, v4) = v5) | ~ (element(v1, v3) = 0) | ~ (the_carrier(v2) = v3) | ? [v6] : ? [v7] : ? [v8] : ((v8 = v5 & v7 = v6 & meet(v2, v1, v4) = v5 & join(v2, v1, v4) = v6 & set_union2(v1, v4) = v6) | ( ~ (v6 = 0) & element(v4, v3) = v6)))
% 110.18/75.57 | (44) meet_semilatt_str(all_0_0_0) = 0
% 110.18/75.57 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (join(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & element(v3, v4) = 0 & the_carrier(v0) = v4) | (v4 = 0 & empty_carrier(v0) = 0) | ( ~ (v5 = 0) & element(v2, v4) = v5 & the_carrier(v0) = v4) | ( ~ (v5 = 0) & element(v1, v4) = v5 & the_carrier(v0) = v4) | ( ~ (v4 = 0) & join_semilatt_str(v0) = v4)))
% 110.18/75.57 | (46) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0))
% 110.18/75.57 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 110.18/75.57 | (48) ! [v0] : ! [v1] : ( ~ (the_L_meet(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v0 & the_carrier(v0) = v2 & the_L_join(v0) = v3 & latt_str_of(v2, v3, v1) = v0) | ( ~ (v2 = 0) & strict_latt_str(v0) = v2) | ( ~ (v2 = 0) & latt_str(v0) = v2)))
% 110.18/75.57 | (49) ! [v0] : ! [v1] : ( ~ (boole_lattice(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty_carrier(v1) = v2))
% 110.18/75.57 | (50) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 110.18/75.57 | (51) ! [v0] : ! [v1] : (v1 = 0 | ~ (one_sorted_str(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & join_semilatt_str(v0) = v2))
% 110.18/75.57 | (52) ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2
% 110.18/75.57 | (53) ! [v0] : ! [v1] : (v1 = 0 | ~ (empty_carrier(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ((v5 = 0 & ~ (v6 = 0) & empty(v4) = v6 & powerset(v2) = v3 & element(v4, v3) = 0 & the_carrier(v0) = v2) | ( ~ (v2 = 0) & one_sorted_str(v0) = v2)))
% 110.18/75.57 | (54) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : ((v3 = 0 & empty(v0) = 0) | ( ~ (v3 = 0) & empty(v2) = v3)))
% 110.18/75.57 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0))
% 110.18/75.57 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (apply_binary_as_element(v0, v1, v2, v3, v4, v5) = v6) | ? [v7] : ? [v8] : ((v7 = 0 & empty(v1) = 0) | (v7 = 0 & empty(v0) = 0) | (v7 = 0 & element(v6, v2) = 0) | ( ~ (v8 = 0) & quasi_total(v3, v7, v2) = v8 & cartesian_product2(v0, v1) = v7) | ( ~ (v8 = 0) & relation_of2(v3, v7, v2) = v8 & cartesian_product2(v0, v1) = v7) | ( ~ (v7 = 0) & function(v3) = v7) | ( ~ (v7 = 0) & element(v5, v1) = v7) | ( ~ (v7 = 0) & element(v4, v0) = v7)))
% 110.18/75.57 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0))
% 110.18/75.57 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | element(v0, v2) = 0)
% 110.18/75.57 | (59) ? [v0] : ? [v1] : function(v0) = v1
% 110.18/75.57 | (60) ! [v0] : ! [v1] : ( ~ (meet_semilatt_str(v0) = v1) | ? [v2] : ((v2 = 0 & v1 = 0 & join_semilatt_str(v0) = 0) | ( ~ (v2 = 0) & latt_str(v0) = v2)))
% 110.18/75.57 | (61) ! [v0] : ( ~ (latt_str(v0) = 0) | (meet_semilatt_str(v0) = 0 & join_semilatt_str(v0) = 0))
% 110.18/75.57 | (62) ? [v0] : ? [v1] : ? [v2] : ? [v3] : meet(v2, v1, v0) = v3
% 110.18/75.57 | (63) ! [v0] : ( ~ (meet_semilatt_str(v0) = 0) | one_sorted_str(v0) = 0)
% 110.18/75.57 | (64) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1))
% 110.18/75.57 | (65) ? [v0] : ? [v1] : ? [v2] : apply(v1, v0) = v2
% 110.18/75.57 | (66) ! [v0] : ! [v1] : (v1 = 0 | ~ (empty_carrier(v0) = v1) | ? [v2] : ? [v3] : (( ~ (v2 = 0) & meet_semilatt_str(v0) = v2) | (the_carrier(v0) = v2 & the_L_meet(v0) = v3 & ! [v4] : ! [v5] : ! [v6] : ( ~ (meet(v0, v4, v5) = v6) | ~ (element(v4, v2) = 0) | ? [v7] : ((v7 = v6 & apply_binary_as_element(v2, v2, v2, v3, v4, v5) = v6) | ( ~ (v7 = 0) & element(v5, v2) = v7))) & ! [v4] : ! [v5] : ! [v6] : ( ~ (apply_binary_as_element(v2, v2, v2, v3, v4, v5) = v6) | ~ (element(v4, v2) = 0) | ? [v7] : ((v7 = v6 & meet(v0, v4, v5) = v6) | ( ~ (v7 = 0) & element(v5, v2) = v7))) & ! [v4] : ! [v5] : ( ~ (element(v5, v2) = 0) | ~ (element(v4, v2) = 0) | ? [v6] : (meet(v0, v4, v5) = v6 & apply_binary_as_element(v2, v2, v2, v3, v4, v5) = v6)))))
% 110.18/75.58 | (67) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2)
% 110.18/75.58 | (68) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2)
% 110.18/75.58 | (69) ? [v0] : ? [v1] : ? [v2] : ? [v3] : relation_of2_as_subset(v2, v1, v0) = v3
% 110.18/75.58 | (70) ? [v0] : ? [v1] : ? [v2] : element(v1, v0) = v2
% 110.39/75.58 | (71) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (join(v4, v3, v2) = v1) | ~ (join(v4, v3, v2) = v0))
% 110.39/75.58 | (72) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (boole_lattice(v0) = v2) | ~ (join(v2, v1, v4) = v5) | ~ (element(v1, v3) = 0) | ~ (the_carrier(v2) = v3) | ? [v6] : ? [v7] : ? [v8] : ((v8 = v7 & v6 = v5 & meet(v2, v1, v4) = v7 & set_intersection2(v1, v4) = v7 & set_union2(v1, v4) = v5) | ( ~ (v6 = 0) & element(v4, v3) = v6)))
% 110.39/75.58 | (73) ? [v0] : ? [v1] : ? [v2] : ? [v3] : below(v2, v1, v0) = v3
% 110.39/75.58 | (74) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | set_union2(v0, v1) = v1)
% 110.39/75.58 | (75) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4))
% 110.39/75.58 | (76) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v5 = v1 | ~ (latt_str_of(v4, v5, v6) = v3) | ~ (latt_str_of(v0, v1, v2) = v3) | ? [v7] : ? [v8] : (( ~ (v8 = 0) & quasi_total(v2, v7, v0) = v8 & cartesian_product2(v0, v0) = v7) | ( ~ (v8 = 0) & quasi_total(v1, v7, v0) = v8 & cartesian_product2(v0, v0) = v7) | ( ~ (v8 = 0) & relation_of2(v2, v7, v0) = v8 & cartesian_product2(v0, v0) = v7) | ( ~ (v8 = 0) & relation_of2(v1, v7, v0) = v8 & cartesian_product2(v0, v0) = v7) | ( ~ (v7 = 0) & function(v2) = v7) | ( ~ (v7 = 0) & function(v1) = v7)))
% 110.39/75.58 | (77) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (meet(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & element(v3, v4) = 0 & the_carrier(v0) = v4) | (v4 = 0 & empty_carrier(v0) = 0) | ( ~ (v5 = 0) & element(v2, v4) = v5 & the_carrier(v0) = v4) | ( ~ (v5 = 0) & element(v1, v4) = v5 & the_carrier(v0) = v4) | ( ~ (v4 = 0) & meet_semilatt_str(v0) = v4)))
% 110.39/75.58 | (78) ! [v0] : ! [v1] : ( ~ (join_semilatt_str(v0) = v1) | ? [v2] : ((v2 = 0 & v1 = 0 & meet_semilatt_str(v0) = 0) | ( ~ (v2 = 0) & latt_str(v0) = v2)))
% 110.39/75.58 | (79) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (latt_str(v2) = v1) | ~ (latt_str(v2) = v0))
% 110.39/75.58 | (80) ? [v0] : ? [v1] : ? [v2] : relation_of2(v2, v0, v1) = 0
% 110.39/75.58 | (81) latt_str(all_0_3_3) = 0
% 110.39/75.58 | (82) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (join(v0, v2, v3) = v4) | ~ (element(v2, v1) = 0) | ~ (the_carrier(v0) = v1) | ? [v5] : ((v5 = 0 & empty_carrier(v0) = 0) | ( ~ (v5 = 0) & join_semilatt_str(v0) = v5) | ( ~ (v5 = 0) & element(v3, v1) = v5) | (( ~ (v4 = v3) | (v5 = 0 & below(v0, v2, v3) = 0)) & (v4 = v3 | ( ~ (v5 = 0) & below(v0, v2, v3) = v5)))))
% 110.39/75.58 | (83) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | subset(v0, v2) = 0)
% 110.39/75.58 | (84) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (empty(v2) = 0 & element(v2, v1) = 0))
% 110.39/75.58 | (85) ? [v0] : ? [v1] : ? [v2] : ? [v3] : quasi_total(v2, v1, v0) = v3
% 110.39/75.58 | (86) latt_str(all_0_7_7) = 0
% 110.39/75.58 | (87) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (boole_lattice(v0) = v2) | ~ (set_union2(v1, v4) = v5) | ~ (element(v1, v3) = 0) | ~ (the_carrier(v2) = v3) | ? [v6] : ? [v7] : ? [v8] : ((v8 = v7 & v6 = v5 & meet(v2, v1, v4) = v7 & join(v2, v1, v4) = v5 & set_intersection2(v1, v4) = v7) | ( ~ (v6 = 0) & element(v4, v3) = v6)))
% 110.39/75.58 | (88) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (relation_of2(v4, v3, v2) = v1) | ~ (relation_of2(v4, v3, v2) = v0))
% 110.39/75.58 | (89) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (ordered_pair(v1, v2) = v3) | ~ (relation(v0) = 0) | ? [v4] : ? [v5] : ((v5 = v4 & apply_binary(v0, v1, v2) = v4 & apply(v0, v3) = v4) | ( ~ (v4 = 0) & function(v0) = v4)))
% 110.39/75.58 | (90) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (below(v0, v2, v3) = v4) | ~ (element(v2, v1) = 0) | ~ (the_carrier(v0) = v1) | ? [v5] : ((v5 = 0 & empty_carrier(v0) = 0) | ( ~ (v5 = 0) & join_semilatt_str(v0) = v5) | ( ~ (v5 = 0) & element(v3, v1) = v5) | (( ~ (v4 = 0) | (v5 = v3 & join(v0, v2, v3) = v3)) & (v4 = 0 | ( ~ (v5 = v3) & join(v0, v2, v3) = v5)))))
% 110.39/75.58 | (91) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1))
% 110.39/75.58 | (92) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (function(v0) = 0) | ~ (apply_binary(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ((v5 = v3 & ordered_pair(v1, v2) = v4 & apply(v0, v4) = v3) | ( ~ (v4 = 0) & relation(v0) = v4)))
% 110.39/75.58 | (93) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty_carrier(v2) = v1) | ~ (empty_carrier(v2) = v0))
% 110.39/75.58 | (94) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3))
% 110.39/75.58 | (95) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 110.39/75.58 | (96) ! [v0] : ( ~ (join_semilatt_str(v0) = 0) | ? [v1] : ((v1 = 0 & empty_carrier(v0) = 0) | (the_carrier(v0) = v1 & ! [v2] : ! [v3] : ! [v4] : ( ~ (below(v0, v2, v3) = v4) | ~ (element(v2, v1) = 0) | ? [v5] : (( ~ (v5 = 0) & element(v3, v1) = v5) | (( ~ (v4 = 0) | (v5 = v3 & join(v0, v2, v3) = v3)) & (v4 = 0 | ( ~ (v5 = v3) & join(v0, v2, v3) = v5))))) & ! [v2] : ! [v3] : ! [v4] : ( ~ (join(v0, v2, v3) = v4) | ~ (element(v2, v1) = 0) | ? [v5] : (( ~ (v5 = 0) & element(v3, v1) = v5) | (( ~ (v4 = v3) | (v5 = 0 & below(v0, v2, v3) = 0)) & (v4 = v3 | ( ~ (v5 = 0) & below(v0, v2, v3) = v5))))) & ! [v2] : ! [v3] : ( ~ (element(v3, v1) = 0) | ~ (element(v2, v1) = 0) | ? [v4] : ? [v5] : (((v5 = v3 & join(v0, v2, v3) = v3) | ( ~ (v4 = 0) & below(v0, v2, v3) = v4)) & ((v4 = 0 & below(v0, v2, v3) = 0) | ( ~ (v5 = v3) & join(v0, v2, v3) = v5)))))))
% 110.39/75.58 | (97) ? [v0] : ? [v1] : ? [v2] : ? [v3] : apply_binary(v2, v1, v0) = v3
% 110.39/75.58 | (98) boole_lattice(all_0_18_18) = all_0_16_16
% 110.39/75.58 | (99) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & ordered_pair(v0, v1) = v3 & unordered_pair(v2, v4) = v3))
% 110.39/75.58 | (100) empty(empty_set) = 0
% 110.39/75.58 | (101) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3))
% 110.39/75.59 | (102) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 110.39/75.59 | (103) ? [v0] : ? [v1] : ? [v2] : ? [v3] : latt_str_of(v2, v1, v0) = v3
% 110.39/75.59 | (104) ! [v0] : ! [v1] : (v1 = 0 | ~ (empty(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & empty(v3) = v4 & powerset(v0) = v2 & element(v3, v2) = 0))
% 110.39/75.59 | (105) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0))
% 110.39/75.59 | (106) ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ((v4 = 0 & ~ (v5 = 0) & empty(v3) = v5 & powerset(v1) = v2 & element(v3, v2) = 0) | (v2 = 0 & empty_carrier(v0) = 0) | ( ~ (v2 = 0) & one_sorted_str(v0) = v2)))
% 110.39/75.59 | (107) one_sorted_str(all_0_1_1) = 0
% 110.39/75.59 | (108) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (apply_binary_as_element(v0, v1, v2, v3, v4, v5) = v6) | ? [v7] : ? [v8] : ((v7 = v6 & apply_binary(v3, v4, v5) = v6) | (v7 = 0 & empty(v1) = 0) | (v7 = 0 & empty(v0) = 0) | ( ~ (v8 = 0) & quasi_total(v3, v7, v2) = v8 & cartesian_product2(v0, v1) = v7) | ( ~ (v8 = 0) & relation_of2(v3, v7, v2) = v8 & cartesian_product2(v0, v1) = v7) | ( ~ (v7 = 0) & function(v3) = v7) | ( ~ (v7 = 0) & element(v5, v1) = v7) | ( ~ (v7 = 0) & element(v4, v0) = v7)))
% 110.39/75.59 | (109) ? [v0] : ? [v1] : ? [v2] : ? [v3] : join(v2, v1, v0) = v3
% 110.39/75.59 | (110) ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2))
% 110.39/75.59 | (111) ? [v0] : ? [v1] : boole_lattice(v0) = v1
% 110.39/75.59 | (112) ? [v0] : ? [v1] : empty_carrier(v0) = v1
% 110.39/75.59 | (113) ! [v0] : ! [v1] : ( ~ (boole_lattice(v0) = v1) | strict_latt_str(v1) = 0)
% 110.39/75.59 | (114) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0))
% 110.39/75.59 | (115) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 110.39/75.59 | (116) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (relation_of2(v2, v0, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & relation_of2_as_subset(v2, v0, v1) = v4))
% 110.39/75.59 | (117) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (relation_of2_as_subset(v2, v0, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & relation_of2(v2, v0, v1) = v4))
% 110.39/75.59 | (118) ~ (all_0_8_8 = 0)
% 110.39/75.59 | (119) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (the_L_join(v2) = v1) | ~ (the_L_join(v2) = v0))
% 110.39/75.59 | (120) ! [v0] : ! [v1] : ( ~ (boole_lattice(v0) = v1) | latt_str(v1) = 0)
% 110.39/75.59 | (121) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (boole_lattice(v2) = v1) | ~ (boole_lattice(v2) = v0))
% 110.39/75.59 | (122) ! [v0] : ( ~ (one_sorted_str(v0) = 0) | ? [v1] : ? [v2] : ((v1 = 0 & empty_carrier(v0) = 0) | ( ~ (v2 = 0) & empty(v1) = v2 & the_carrier(v0) = v1)))
% 110.39/75.59 | (123) ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v0 & the_L_join(v0) = v2 & the_L_meet(v0) = v3 & latt_str_of(v1, v2, v3) = v0) | ( ~ (v2 = 0) & strict_latt_str(v0) = v2) | ( ~ (v2 = 0) & latt_str(v0) = v2)))
% 110.39/75.59 | (124) ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2
% 110.39/75.59 | (125) ! [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))
% 110.39/75.59 | (126) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 110.39/75.59 | (127) empty(all_0_4_4) = 0
% 110.39/75.59 | (128) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (strict_latt_str(v2) = v1) | ~ (strict_latt_str(v2) = v0))
% 110.39/75.59 | (129) empty_carrier(all_0_9_9) = all_0_8_8
% 110.39/75.59 | (130) ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & v3 = 0 & relation_of2_as_subset(v2, v4, v1) = 0 & quasi_total(v2, v4, v1) = 0 & function(v2) = 0 & cartesian_product2(v1, v1) = v4 & the_L_meet(v0) = v2) | ( ~ (v2 = 0) & meet_semilatt_str(v0) = v2)))
% 110.39/75.59 | (131) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (relation_of2_as_subset(v4, v3, v2) = v1) | ~ (relation_of2_as_subset(v4, v3, v2) = v0))
% 110.39/75.59 | (132) ! [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))
% 110.39/75.59 | (133) one_sorted_str(all_0_9_9) = 0
% 110.39/75.59 | (134) ? [v0] : ? [v1] : relation(v0) = v1
% 110.39/75.59 | (135) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (join_semilatt_str(v2) = v1) | ~ (join_semilatt_str(v2) = v0))
% 110.39/75.59 | (136) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | element(v0, v1) = 0)
% 110.39/75.59 | (137) ! [v0] : ! [v1] : ( ~ (the_L_meet(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & v2 = 0 & relation_of2_as_subset(v1, v4, v3) = 0 & quasi_total(v1, v4, v3) = 0 & function(v1) = 0 & cartesian_product2(v3, v3) = v4 & the_carrier(v0) = v3) | ( ~ (v2 = 0) & meet_semilatt_str(v0) = v2)))
% 110.39/75.59 | (138) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (latt_str_of(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & ~ (v4 = 0) & empty_carrier(v3) = v4 & strict_latt_str(v3) = 0) | (v4 = 0 & empty(v0) = 0) | ( ~ (v5 = 0) & quasi_total(v2, v4, v0) = v5 & cartesian_product2(v0, v0) = v4) | ( ~ (v5 = 0) & quasi_total(v1, v4, v0) = v5 & cartesian_product2(v0, v0) = v4) | ( ~ (v5 = 0) & relation_of2(v2, v4, v0) = v5 & cartesian_product2(v0, v0) = v4) | ( ~ (v5 = 0) & relation_of2(v1, v4, v0) = v5 & cartesian_product2(v0, v0) = v4) | ( ~ (v4 = 0) & function(v2) = v4) | ( ~ (v4 = 0) & function(v1) = v4)))
% 110.39/75.59 | (139) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v0, v1) = v2) | ? [v3] : ((v3 = 0 & empty(v1) = 0) | ( ~ (v3 = 0) & element(v0, v1) = v3)))
% 110.39/75.59 | (140) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v3 = 0 & ~ (v4 = 0) & empty(v2) = v4 & element(v2, v1) = 0) | (v2 = 0 & empty(v0) = 0)))
% 110.39/75.59 | (141) strict_latt_str(all_0_11_11) = 0
% 110.39/75.59 | (142) ? [v0] : ? [v1] : ? [v2] : ? [v3] : relation_of2(v2, v1, v0) = v3
% 110.39/75.59 | (143) ! [v0] : ! [v1] : (v1 = 0 | ~ (empty_carrier(v0) = v1) | ? [v2] : ? [v3] : (( ~ (v2 = 0) & join_semilatt_str(v0) = v2) | (the_carrier(v0) = v2 & the_L_join(v0) = v3 & ! [v4] : ! [v5] : ! [v6] : ( ~ (join(v0, v4, v5) = v6) | ~ (element(v4, v2) = 0) | ? [v7] : ((v7 = v6 & apply_binary_as_element(v2, v2, v2, v3, v4, v5) = v6) | ( ~ (v7 = 0) & element(v5, v2) = v7))) & ! [v4] : ! [v5] : ! [v6] : ( ~ (apply_binary_as_element(v2, v2, v2, v3, v4, v5) = v6) | ~ (element(v4, v2) = 0) | ? [v7] : ((v7 = v6 & join(v0, v4, v5) = v6) | ( ~ (v7 = 0) & element(v5, v2) = v7))) & ! [v4] : ! [v5] : ( ~ (element(v5, v2) = 0) | ~ (element(v4, v2) = 0) | ? [v6] : (join(v0, v4, v5) = v6 & apply_binary_as_element(v2, v2, v2, v3, v4, v5) = v6)))))
% 110.39/75.59 | (144) element(all_0_17_17, all_0_15_15) = 0
% 110.39/75.59 | (145) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0))
% 110.39/75.59 | (146) ! [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))
% 110.39/75.60 | (147) ? [v0] : ? [v1] : ? [v2] : relation_of2_as_subset(v2, v0, v1) = 0
% 110.39/75.60 | (148) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (function(v0) = 0) | ~ (ordered_pair(v1, v2) = v3) | ? [v4] : ? [v5] : ((v5 = v4 & apply_binary(v0, v1, v2) = v4 & apply(v0, v3) = v4) | ( ~ (v4 = 0) & relation(v0) = v4)))
% 110.39/75.60 | (149) ? [v0] : ? [v1] : empty(v0) = v1
% 110.39/75.60 | (150) ! [v0] : ! [v1] : ( ~ (the_L_join(v0) = v1) | ? [v2] : ((v2 = 0 & empty_carrier(v0) = 0) | ( ~ (v2 = 0) & join_semilatt_str(v0) = v2) | (the_carrier(v0) = v2 & ! [v3] : ! [v4] : ! [v5] : ( ~ (join(v0, v3, v4) = v5) | ~ (element(v3, v2) = 0) | ? [v6] : ((v6 = v5 & apply_binary_as_element(v2, v2, v2, v1, v3, v4) = v5) | ( ~ (v6 = 0) & element(v4, v2) = v6))) & ! [v3] : ! [v4] : ! [v5] : ( ~ (apply_binary_as_element(v2, v2, v2, v1, v3, v4) = v5) | ~ (element(v3, v2) = 0) | ? [v6] : ((v6 = v5 & join(v0, v3, v4) = v5) | ( ~ (v6 = 0) & element(v4, v2) = v6))) & ! [v3] : ! [v4] : ( ~ (element(v4, v2) = 0) | ~ (element(v3, v2) = 0) | ? [v5] : (join(v0, v3, v4) = v5 & apply_binary_as_element(v2, v2, v2, v1, v3, v4) = v5)))))
% 110.39/75.60 | (151) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0))
% 110.39/75.60 | (152) ? [v0] : ? [v1] : the_carrier(v0) = v1
% 110.39/75.60 | (153) latt_str(all_0_11_11) = 0
% 110.39/75.60 | (154) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = v2 | ~ (latt_str_of(v4, v5, v6) = v3) | ~ (latt_str_of(v0, v1, v2) = v3) | ? [v7] : ? [v8] : (( ~ (v8 = 0) & quasi_total(v2, v7, v0) = v8 & cartesian_product2(v0, v0) = v7) | ( ~ (v8 = 0) & quasi_total(v1, v7, v0) = v8 & cartesian_product2(v0, v0) = v7) | ( ~ (v8 = 0) & relation_of2(v2, v7, v0) = v8 & cartesian_product2(v0, v0) = v7) | ( ~ (v8 = 0) & relation_of2(v1, v7, v0) = v8 & cartesian_product2(v0, v0) = v7) | ( ~ (v7 = 0) & function(v2) = v7) | ( ~ (v7 = 0) & function(v1) = v7)))
% 110.39/75.60 | (155) ! [v0] : ! [v1] : ( ~ (the_L_join(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v0 & the_carrier(v0) = v2 & the_L_meet(v0) = v3 & latt_str_of(v2, v1, v3) = v0) | ( ~ (v2 = 0) & strict_latt_str(v0) = v2) | ( ~ (v2 = 0) & latt_str(v0) = v2)))
% 110.39/75.60 | (156) ! [v0] : ! [v1] : (v1 = 0 | ~ (empty_carrier(v0) = v1) | ? [v2] : ? [v3] : (( ~ (v3 = 0) & empty(v2) = v3 & the_carrier(v0) = v2) | ( ~ (v2 = 0) & one_sorted_str(v0) = v2)))
% 110.39/75.60 | (157) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (latt_str_of(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & strict_latt_str(v3) = 0 & latt_str(v3) = 0) | ( ~ (v5 = 0) & quasi_total(v2, v4, v0) = v5 & cartesian_product2(v0, v0) = v4) | ( ~ (v5 = 0) & quasi_total(v1, v4, v0) = v5 & cartesian_product2(v0, v0) = v4) | ( ~ (v5 = 0) & relation_of2(v2, v4, v0) = v5 & cartesian_product2(v0, v0) = v4) | ( ~ (v5 = 0) & relation_of2(v1, v4, v0) = v5 & cartesian_product2(v0, v0) = v4) | ( ~ (v4 = 0) & function(v2) = v4) | ( ~ (v4 = 0) & function(v1) = v4)))
% 110.39/75.60 | (158) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 110.39/75.60 | (159) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ? [v3] : ((v3 = 0 & empty(v0) = 0) | ( ~ (v3 = 0) & empty(v2) = v3)))
% 110.39/75.60 | (160) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v1 = v0 | ~ (apply_binary_as_element(v7, v6, v5, v4, v3, v2) = v1) | ~ (apply_binary_as_element(v7, v6, v5, v4, v3, v2) = v0))
% 110.39/75.60 | (161) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (set_union2(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3))
% 110.39/75.60 | (162) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (powerset(v1) = v2 & element(v0, v2) = 0))
% 110.39/75.60 | (163) ? [v0] : ? [v1] : powerset(v0) = v1
% 110.39/75.60 | (164) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (boole_lattice(v0) = v2) | ~ (element(v4, v3) = 0) | ~ (element(v1, v3) = 0) | ~ (the_carrier(v2) = v3) | ? [v5] : ? [v6] : (meet(v2, v1, v4) = v6 & join(v2, v1, v4) = v5 & set_intersection2(v1, v4) = v6 & set_union2(v1, v4) = v5))
% 110.39/75.60 | (165) ? [v0] : ? [v1] : ? [v2] : set_intersection2(v1, v0) = v2
% 110.39/75.60 | (166) ? [v0] : ? [v1] : join_semilatt_str(v0) = v1
% 110.39/75.60 | (167) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (quasi_total(v4, v3, v2) = v1) | ~ (quasi_total(v4, v3, v2) = v0))
% 110.39/75.60 | (168) ? [v0] : ? [v1] : ? [v2] : unordered_pair(v1, v0) = v2
% 110.39/75.60 | (169) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (below(v4, v3, v2) = v1) | ~ (below(v4, v3, v2) = v0))
% 110.39/75.60 | (170) below(all_0_16_16, all_0_17_17, all_0_14_14) = all_0_13_13
% 110.39/75.60 | (171) ! [v0] : ! [v1] : ( ~ (the_L_meet(v0) = v1) | ? [v2] : ((v2 = 0 & empty_carrier(v0) = 0) | ( ~ (v2 = 0) & meet_semilatt_str(v0) = v2) | (the_carrier(v0) = v2 & ! [v3] : ! [v4] : ! [v5] : ( ~ (meet(v0, v3, v4) = v5) | ~ (element(v3, v2) = 0) | ? [v6] : ((v6 = v5 & apply_binary_as_element(v2, v2, v2, v1, v3, v4) = v5) | ( ~ (v6 = 0) & element(v4, v2) = v6))) & ! [v3] : ! [v4] : ! [v5] : ( ~ (apply_binary_as_element(v2, v2, v2, v1, v3, v4) = v5) | ~ (element(v3, v2) = 0) | ? [v6] : ((v6 = v5 & meet(v0, v3, v4) = v5) | ( ~ (v6 = 0) & element(v4, v2) = v6))) & ! [v3] : ! [v4] : ( ~ (element(v4, v2) = 0) | ~ (element(v3, v2) = 0) | ? [v5] : (meet(v0, v3, v4) = v5 & apply_binary_as_element(v2, v2, v2, v1, v3, v4) = v5)))))
% 110.39/75.60 | (172) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0))
% 110.39/75.60 | (173) element(all_0_14_14, all_0_15_15) = 0
% 110.39/75.60 | (174) ? [v0] : ? [v1] : ? [v2] : set_union2(v1, v0) = v2
% 110.39/75.60 | (175) ? [v0] : ? [v1] : ? [v2] : ordered_pair(v1, v0) = v2
% 110.39/75.60 | (176) ! [v0] : ! [v1] : (v1 = 0 | ~ (one_sorted_str(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & meet_semilatt_str(v0) = v2))
% 110.39/75.60 | (177) ? [v0] : ? [v1] : the_L_meet(v0) = v1
% 110.39/75.60 | (178) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (meet_semilatt_str(v2) = v1) | ~ (meet_semilatt_str(v2) = v0))
% 110.39/75.60 | (179) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 110.39/75.60 | (180) ! [v0] : ( ~ (join_semilatt_str(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (relation_of2_as_subset(v1, v3, v2) = 0 & quasi_total(v1, v3, v2) = 0 & function(v1) = 0 & cartesian_product2(v2, v2) = v3 & the_carrier(v0) = v2 & the_L_join(v0) = v1))
% 110.39/75.60 | (181) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2)
% 110.39/75.60 | (182) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2)
% 110.39/75.60 | (183) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0))
% 110.39/75.60 | (184) ! [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))
% 110.39/75.60 | (185) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (one_sorted_str(v2) = v1) | ~ (one_sorted_str(v2) = v0))
% 110.39/75.60 | (186) ! [v0] : ( ~ (latt_str(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ((v4 = v0 & the_carrier(v0) = v1 & the_L_join(v0) = v2 & the_L_meet(v0) = v3 & latt_str_of(v1, v2, v3) = v0) | ( ~ (v1 = 0) & strict_latt_str(v0) = v1)))
% 110.39/75.60 | (187) ! [v0] : ( ~ (strict_latt_str(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ((v4 = v0 & the_carrier(v0) = v1 & the_L_join(v0) = v2 & the_L_meet(v0) = v3 & latt_str_of(v1, v2, v3) = v0) | ( ~ (v1 = 0) & latt_str(v0) = v1)))
% 110.39/75.60 | (188) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_of2(v2, v0, v1) = 0) | relation_of2_as_subset(v2, v0, v1) = 0)
% 110.39/75.60 | (189) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_of2_as_subset(v2, v0, v1) = 0) | relation_of2(v2, v0, v1) = 0)
% 110.39/75.61 | (190) ! [v0] : ! [v1] : (v1 = 0 | ~ (empty_carrier(v0) = v1) | ? [v2] : (( ~ (v2 = 0) & join_semilatt_str(v0) = v2) | (the_carrier(v0) = v2 & ! [v3] : ! [v4] : ! [v5] : ( ~ (below(v0, v3, v4) = v5) | ~ (element(v3, v2) = 0) | ? [v6] : (( ~ (v6 = 0) & element(v4, v2) = v6) | (( ~ (v5 = 0) | (v6 = v4 & join(v0, v3, v4) = v4)) & (v5 = 0 | ( ~ (v6 = v4) & join(v0, v3, v4) = v6))))) & ! [v3] : ! [v4] : ! [v5] : ( ~ (join(v0, v3, v4) = v5) | ~ (element(v3, v2) = 0) | ? [v6] : (( ~ (v6 = 0) & element(v4, v2) = v6) | (( ~ (v5 = v4) | (v6 = 0 & below(v0, v3, v4) = 0)) & (v5 = v4 | ( ~ (v6 = 0) & below(v0, v3, v4) = v6))))) & ! [v3] : ! [v4] : ( ~ (element(v4, v2) = 0) | ~ (element(v3, v2) = 0) | ? [v5] : ? [v6] : (((v6 = v4 & join(v0, v3, v4) = v4) | ( ~ (v5 = 0) & below(v0, v3, v4) = v5)) & ((v5 = 0 & below(v0, v3, v4) = 0) | ( ~ (v6 = v4) & join(v0, v3, v4) = v6)))))))
% 110.39/75.61 | (191) ! [v0] : ( ~ (join_semilatt_str(v0) = 0) | one_sorted_str(v0) = 0)
% 110.39/75.61 | (192) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0))
% 110.39/75.61 | (193) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (meet(v4, v3, v2) = v1) | ~ (meet(v4, v3, v2) = v0))
% 110.39/75.61 | (194) ? [v0] : ? [v1] : meet_semilatt_str(v0) = v1
% 110.39/75.61 | (195) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (the_L_meet(v2) = v1) | ~ (the_L_meet(v2) = v0))
% 110.39/75.61 | (196) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3))
% 110.39/75.61 | (197) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (apply_binary(v4, v3, v2) = v1) | ~ (apply_binary(v4, v3, v2) = v0))
% 110.39/75.61 | (198) ! [v0] : ( ~ (meet_semilatt_str(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (relation_of2_as_subset(v1, v3, v2) = 0 & quasi_total(v1, v3, v2) = 0 & function(v1) = 0 & cartesian_product2(v2, v2) = v3 & the_carrier(v0) = v2 & the_L_meet(v0) = v1))
% 110.39/75.61 | (199) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : apply_binary_as_element(v5, v4, v3, v2, v1, v0) = v6
% 110.39/75.61 | (200) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v0, v1) = v3) | ~ (powerset(v3) = v4) | ~ (element(v2, v4) = 0) | relation(v2) = 0)
% 110.39/75.61 | (201) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1))
% 110.39/75.61 | (202) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | subset(v0, v1) = 0)
% 110.39/75.61 |
% 110.39/75.61 | Instantiating formula (6) with all_0_12_12, all_0_14_14, all_0_17_17 and discharging atoms subset(all_0_17_17, all_0_14_14) = all_0_12_12, yields:
% 110.39/75.61 | (203) all_0_12_12 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & powerset(all_0_14_14) = v0 & element(all_0_17_17, v0) = v1)
% 110.39/75.61 |
% 110.39/75.61 | Instantiating formula (113) with all_0_16_16, all_0_18_18 and discharging atoms boole_lattice(all_0_18_18) = all_0_16_16, yields:
% 110.39/75.61 | (204) strict_latt_str(all_0_16_16) = 0
% 110.39/75.61 |
% 110.39/75.61 | Instantiating formula (120) with all_0_16_16, all_0_18_18 and discharging atoms boole_lattice(all_0_18_18) = all_0_16_16, yields:
% 110.39/75.61 | (205) latt_str(all_0_16_16) = 0
% 110.39/75.61 |
% 110.39/75.61 | Instantiating formula (49) with all_0_16_16, all_0_18_18 and discharging atoms boole_lattice(all_0_18_18) = all_0_16_16, yields:
% 110.39/75.61 | (206) ? [v0] : ( ~ (v0 = 0) & empty_carrier(all_0_16_16) = v0)
% 110.39/75.61 |
% 110.39/75.61 | Instantiating formula (164) with all_0_14_14, all_0_15_15, all_0_16_16, all_0_14_14, all_0_18_18 and discharging atoms boole_lattice(all_0_18_18) = all_0_16_16, element(all_0_14_14, all_0_15_15) = 0, the_carrier(all_0_16_16) = all_0_15_15, yields:
% 110.39/75.61 | (207) ? [v0] : ? [v1] : (meet(all_0_16_16, all_0_14_14, all_0_14_14) = v1 & join(all_0_16_16, all_0_14_14, all_0_14_14) = v0 & set_intersection2(all_0_14_14, all_0_14_14) = v1 & set_union2(all_0_14_14, all_0_14_14) = v0)
% 110.39/75.61 |
% 110.39/75.61 | Instantiating formula (164) with all_0_14_14, all_0_15_15, all_0_16_16, all_0_17_17, all_0_18_18 and discharging atoms boole_lattice(all_0_18_18) = all_0_16_16, element(all_0_14_14, all_0_15_15) = 0, element(all_0_17_17, all_0_15_15) = 0, the_carrier(all_0_16_16) = all_0_15_15, yields:
% 110.39/75.61 | (208) ? [v0] : ? [v1] : (meet(all_0_16_16, all_0_17_17, all_0_14_14) = v1 & join(all_0_16_16, all_0_17_17, all_0_14_14) = v0 & set_intersection2(all_0_17_17, all_0_14_14) = v1 & set_union2(all_0_17_17, all_0_14_14) = v0)
% 110.39/75.61 |
% 110.39/75.61 | Instantiating formula (164) with all_0_17_17, all_0_15_15, all_0_16_16, all_0_14_14, all_0_18_18 and discharging atoms boole_lattice(all_0_18_18) = all_0_16_16, element(all_0_14_14, all_0_15_15) = 0, element(all_0_17_17, all_0_15_15) = 0, the_carrier(all_0_16_16) = all_0_15_15, yields:
% 110.39/75.61 | (209) ? [v0] : ? [v1] : (meet(all_0_16_16, all_0_14_14, all_0_17_17) = v1 & join(all_0_16_16, all_0_14_14, all_0_17_17) = v0 & set_intersection2(all_0_14_14, all_0_17_17) = v1 & set_union2(all_0_14_14, all_0_17_17) = v0)
% 110.39/75.61 |
% 110.39/75.61 | Instantiating formula (90) with all_0_13_13, all_0_14_14, all_0_17_17, all_0_15_15, all_0_16_16 and discharging atoms below(all_0_16_16, all_0_17_17, all_0_14_14) = all_0_13_13, element(all_0_17_17, all_0_15_15) = 0, the_carrier(all_0_16_16) = all_0_15_15, yields:
% 110.39/75.61 | (210) ? [v0] : ((v0 = 0 & empty_carrier(all_0_16_16) = 0) | ( ~ (v0 = 0) & join_semilatt_str(all_0_16_16) = v0) | ( ~ (v0 = 0) & element(all_0_14_14, all_0_15_15) = v0) | (( ~ (all_0_13_13 = 0) | (v0 = all_0_14_14 & join(all_0_16_16, all_0_17_17, all_0_14_14) = all_0_14_14)) & (all_0_13_13 = 0 | ( ~ (v0 = all_0_14_14) & join(all_0_16_16, all_0_17_17, all_0_14_14) = v0))))
% 110.39/75.61 |
% 110.39/75.61 | Instantiating formula (21) with all_0_14_14, all_0_17_17, all_0_15_15, all_0_16_16 and discharging atoms element(all_0_14_14, all_0_15_15) = 0, element(all_0_17_17, all_0_15_15) = 0, the_carrier(all_0_16_16) = all_0_15_15, yields:
% 110.39/75.61 | (211) ? [v0] : ? [v1] : ((v0 = 0 & empty_carrier(all_0_16_16) = 0) | ( ~ (v0 = 0) & join_semilatt_str(all_0_16_16) = v0) | (((v1 = all_0_14_14 & join(all_0_16_16, all_0_17_17, all_0_14_14) = all_0_14_14) | ( ~ (v0 = 0) & below(all_0_16_16, all_0_17_17, all_0_14_14) = v0)) & ((v0 = 0 & below(all_0_16_16, all_0_17_17, all_0_14_14) = 0) | ( ~ (v1 = all_0_14_14) & join(all_0_16_16, all_0_17_17, all_0_14_14) = v1))))
% 110.39/75.61 |
% 110.39/75.61 | Instantiating formula (123) with all_0_15_15, all_0_16_16 and discharging atoms the_carrier(all_0_16_16) = all_0_15_15, yields:
% 110.39/75.61 | (212) ? [v0] : ? [v1] : ? [v2] : ((v2 = all_0_16_16 & the_L_join(all_0_16_16) = v0 & the_L_meet(all_0_16_16) = v1 & latt_str_of(all_0_15_15, v0, v1) = all_0_16_16) | ( ~ (v0 = 0) & strict_latt_str(all_0_16_16) = v0) | ( ~ (v0 = 0) & latt_str(all_0_16_16) = v0))
% 110.39/75.61 |
% 110.39/75.61 | Instantiating (206) with all_88_0_128 yields:
% 110.39/75.61 | (213) ~ (all_88_0_128 = 0) & empty_carrier(all_0_16_16) = all_88_0_128
% 110.39/75.61 |
% 110.39/75.61 | Applying alpha-rule on (213) yields:
% 110.39/75.61 | (214) ~ (all_88_0_128 = 0)
% 110.39/75.61 | (215) empty_carrier(all_0_16_16) = all_88_0_128
% 110.39/75.61 |
% 110.39/75.61 | Instantiating (212) with all_111_0_177, all_111_1_178, all_111_2_179 yields:
% 110.39/75.61 | (216) (all_111_0_177 = all_0_16_16 & the_L_join(all_0_16_16) = all_111_2_179 & the_L_meet(all_0_16_16) = all_111_1_178 & latt_str_of(all_0_15_15, all_111_2_179, all_111_1_178) = all_0_16_16) | ( ~ (all_111_2_179 = 0) & strict_latt_str(all_0_16_16) = all_111_2_179) | ( ~ (all_111_2_179 = 0) & latt_str(all_0_16_16) = all_111_2_179)
% 110.39/75.61 |
% 110.39/75.61 | Instantiating (210) with all_115_0_187 yields:
% 110.39/75.61 | (217) (all_115_0_187 = 0 & empty_carrier(all_0_16_16) = 0) | ( ~ (all_115_0_187 = 0) & join_semilatt_str(all_0_16_16) = all_115_0_187) | ( ~ (all_115_0_187 = 0) & element(all_0_14_14, all_0_15_15) = all_115_0_187) | (( ~ (all_0_13_13 = 0) | (all_115_0_187 = all_0_14_14 & join(all_0_16_16, all_0_17_17, all_0_14_14) = all_0_14_14)) & (all_0_13_13 = 0 | ( ~ (all_115_0_187 = all_0_14_14) & join(all_0_16_16, all_0_17_17, all_0_14_14) = all_115_0_187)))
% 110.39/75.61 |
% 110.39/75.61 | Instantiating (209) with all_116_0_188, all_116_1_189 yields:
% 110.39/75.61 | (218) meet(all_0_16_16, all_0_14_14, all_0_17_17) = all_116_0_188 & join(all_0_16_16, all_0_14_14, all_0_17_17) = all_116_1_189 & set_intersection2(all_0_14_14, all_0_17_17) = all_116_0_188 & set_union2(all_0_14_14, all_0_17_17) = all_116_1_189
% 110.39/75.61 |
% 110.39/75.61 | Applying alpha-rule on (218) yields:
% 110.39/75.61 | (219) meet(all_0_16_16, all_0_14_14, all_0_17_17) = all_116_0_188
% 110.39/75.61 | (220) join(all_0_16_16, all_0_14_14, all_0_17_17) = all_116_1_189
% 110.39/75.61 | (221) set_intersection2(all_0_14_14, all_0_17_17) = all_116_0_188
% 110.39/75.61 | (222) set_union2(all_0_14_14, all_0_17_17) = all_116_1_189
% 110.39/75.61 |
% 110.39/75.61 | Instantiating (208) with all_118_0_190, all_118_1_191 yields:
% 110.39/75.62 | (223) meet(all_0_16_16, all_0_17_17, all_0_14_14) = all_118_0_190 & join(all_0_16_16, all_0_17_17, all_0_14_14) = all_118_1_191 & set_intersection2(all_0_17_17, all_0_14_14) = all_118_0_190 & set_union2(all_0_17_17, all_0_14_14) = all_118_1_191
% 110.39/75.62 |
% 110.39/75.62 | Applying alpha-rule on (223) yields:
% 110.39/75.62 | (224) meet(all_0_16_16, all_0_17_17, all_0_14_14) = all_118_0_190
% 110.39/75.62 | (225) join(all_0_16_16, all_0_17_17, all_0_14_14) = all_118_1_191
% 110.39/75.62 | (226) set_intersection2(all_0_17_17, all_0_14_14) = all_118_0_190
% 110.39/75.62 | (227) set_union2(all_0_17_17, all_0_14_14) = all_118_1_191
% 110.39/75.62 |
% 110.39/75.62 | Instantiating (207) with all_124_0_203, all_124_1_204 yields:
% 110.39/75.62 | (228) meet(all_0_16_16, all_0_14_14, all_0_14_14) = all_124_0_203 & join(all_0_16_16, all_0_14_14, all_0_14_14) = all_124_1_204 & set_intersection2(all_0_14_14, all_0_14_14) = all_124_0_203 & set_union2(all_0_14_14, all_0_14_14) = all_124_1_204
% 110.39/75.62 |
% 110.39/75.62 | Applying alpha-rule on (228) yields:
% 110.39/75.62 | (229) meet(all_0_16_16, all_0_14_14, all_0_14_14) = all_124_0_203
% 110.39/75.62 | (230) join(all_0_16_16, all_0_14_14, all_0_14_14) = all_124_1_204
% 110.39/75.62 | (231) set_intersection2(all_0_14_14, all_0_14_14) = all_124_0_203
% 110.39/75.62 | (232) set_union2(all_0_14_14, all_0_14_14) = all_124_1_204
% 110.39/75.62 |
% 110.39/75.62 | Instantiating (211) with all_128_0_209, all_128_1_210 yields:
% 110.39/75.62 | (233) (all_128_1_210 = 0 & empty_carrier(all_0_16_16) = 0) | ( ~ (all_128_1_210 = 0) & join_semilatt_str(all_0_16_16) = all_128_1_210) | (((all_128_0_209 = all_0_14_14 & join(all_0_16_16, all_0_17_17, all_0_14_14) = all_0_14_14) | ( ~ (all_128_1_210 = 0) & below(all_0_16_16, all_0_17_17, all_0_14_14) = all_128_1_210)) & ((all_128_1_210 = 0 & below(all_0_16_16, all_0_17_17, all_0_14_14) = 0) | ( ~ (all_128_0_209 = all_0_14_14) & join(all_0_16_16, all_0_17_17, all_0_14_14) = all_128_0_209)))
% 110.39/75.62 |
% 110.39/75.62 +-Applying beta-rule and splitting (216), into two cases.
% 110.39/75.62 |-Branch one:
% 110.39/75.62 | (234) (all_111_0_177 = all_0_16_16 & the_L_join(all_0_16_16) = all_111_2_179 & the_L_meet(all_0_16_16) = all_111_1_178 & latt_str_of(all_0_15_15, all_111_2_179, all_111_1_178) = all_0_16_16) | ( ~ (all_111_2_179 = 0) & strict_latt_str(all_0_16_16) = all_111_2_179)
% 110.39/75.62 |
% 110.39/75.62 +-Applying beta-rule and splitting (234), into two cases.
% 110.39/75.62 |-Branch one:
% 110.39/75.62 | (235) all_111_0_177 = all_0_16_16 & the_L_join(all_0_16_16) = all_111_2_179 & the_L_meet(all_0_16_16) = all_111_1_178 & latt_str_of(all_0_15_15, all_111_2_179, all_111_1_178) = all_0_16_16
% 110.39/75.62 |
% 110.39/75.62 | Applying alpha-rule on (235) yields:
% 110.39/75.62 | (236) all_111_0_177 = all_0_16_16
% 110.39/75.62 | (237) the_L_join(all_0_16_16) = all_111_2_179
% 110.39/75.62 | (238) the_L_meet(all_0_16_16) = all_111_1_178
% 110.39/75.62 | (239) latt_str_of(all_0_15_15, all_111_2_179, all_111_1_178) = all_0_16_16
% 110.39/75.62 |
% 110.39/75.62 | Instantiating formula (201) with all_124_0_203, all_0_14_14 and discharging atoms set_intersection2(all_0_14_14, all_0_14_14) = all_124_0_203, yields:
% 110.39/75.62 | (240) all_124_0_203 = all_0_14_14
% 110.39/75.62 |
% 110.39/75.62 | Instantiating formula (91) with all_124_1_204, all_0_14_14 and discharging atoms set_union2(all_0_14_14, all_0_14_14) = all_124_1_204, yields:
% 110.39/75.62 | (241) all_124_1_204 = all_0_14_14
% 110.39/75.62 |
% 110.39/75.62 | From (240) and (229) follows:
% 110.39/75.62 | (242) meet(all_0_16_16, all_0_14_14, all_0_14_14) = all_0_14_14
% 110.39/75.62 |
% 110.39/75.62 | From (241) and (230) follows:
% 110.39/75.62 | (243) join(all_0_16_16, all_0_14_14, all_0_14_14) = all_0_14_14
% 110.39/75.62 |
% 110.39/75.62 | Instantiating formula (77) with all_0_14_14, all_0_14_14, all_0_14_14, all_0_16_16 and discharging atoms meet(all_0_16_16, all_0_14_14, all_0_14_14) = all_0_14_14, yields:
% 110.39/75.62 | (244) ? [v0] : ? [v1] : ((v1 = 0 & element(all_0_14_14, v0) = 0 & the_carrier(all_0_16_16) = v0) | (v0 = 0 & empty_carrier(all_0_16_16) = 0) | ( ~ (v1 = 0) & element(all_0_14_14, v0) = v1 & the_carrier(all_0_16_16) = v0) | ( ~ (v0 = 0) & meet_semilatt_str(all_0_16_16) = v0))
% 110.39/75.62 |
% 110.39/75.62 | Instantiating formula (53) with all_88_0_128, all_0_16_16 and discharging atoms empty_carrier(all_0_16_16) = all_88_0_128, yields:
% 110.39/75.62 | (245) all_88_0_128 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ((v3 = 0 & ~ (v4 = 0) & empty(v2) = v4 & powerset(v0) = v1 & element(v2, v1) = 0 & the_carrier(all_0_16_16) = v0) | ( ~ (v0 = 0) & one_sorted_str(all_0_16_16) = v0))
% 110.39/75.62 |
% 110.39/75.62 | Instantiating formula (156) with all_88_0_128, all_0_16_16 and discharging atoms empty_carrier(all_0_16_16) = all_88_0_128, yields:
% 110.39/75.62 | (246) all_88_0_128 = 0 | ? [v0] : ? [v1] : (( ~ (v1 = 0) & empty(v0) = v1 & the_carrier(all_0_16_16) = v0) | ( ~ (v0 = 0) & one_sorted_str(all_0_16_16) = v0))
% 110.39/75.62 |
% 110.39/75.62 | Instantiating formula (66) with all_88_0_128, all_0_16_16 and discharging atoms empty_carrier(all_0_16_16) = all_88_0_128, yields:
% 110.39/75.62 | (247) all_88_0_128 = 0 | ? [v0] : ? [v1] : (( ~ (v0 = 0) & meet_semilatt_str(all_0_16_16) = v0) | (the_carrier(all_0_16_16) = v0 & the_L_meet(all_0_16_16) = v1 & ! [v2] : ! [v3] : ! [v4] : ( ~ (meet(all_0_16_16, v2, v3) = v4) | ~ (element(v2, v0) = 0) | ? [v5] : ((v5 = v4 & apply_binary_as_element(v0, v0, v0, v1, v2, v3) = v4) | ( ~ (v5 = 0) & element(v3, v0) = v5))) & ! [v2] : ! [v3] : ! [v4] : ( ~ (apply_binary_as_element(v0, v0, v0, v1, v2, v3) = v4) | ~ (element(v2, v0) = 0) | ? [v5] : ((v5 = v4 & meet(all_0_16_16, v2, v3) = v4) | ( ~ (v5 = 0) & element(v3, v0) = v5))) & ! [v2] : ! [v3] : ( ~ (element(v3, v0) = 0) | ~ (element(v2, v0) = 0) | ? [v4] : (meet(all_0_16_16, v2, v3) = v4 & apply_binary_as_element(v0, v0, v0, v1, v2, v3) = v4))))
% 110.39/75.62 |
% 110.39/75.62 | Instantiating formula (143) with all_88_0_128, all_0_16_16 and discharging atoms empty_carrier(all_0_16_16) = all_88_0_128, yields:
% 110.39/75.62 | (248) all_88_0_128 = 0 | ? [v0] : ? [v1] : (( ~ (v0 = 0) & join_semilatt_str(all_0_16_16) = v0) | (the_carrier(all_0_16_16) = v0 & the_L_join(all_0_16_16) = v1 & ! [v2] : ! [v3] : ! [v4] : ( ~ (join(all_0_16_16, v2, v3) = v4) | ~ (element(v2, v0) = 0) | ? [v5] : ((v5 = v4 & apply_binary_as_element(v0, v0, v0, v1, v2, v3) = v4) | ( ~ (v5 = 0) & element(v3, v0) = v5))) & ! [v2] : ! [v3] : ! [v4] : ( ~ (apply_binary_as_element(v0, v0, v0, v1, v2, v3) = v4) | ~ (element(v2, v0) = 0) | ? [v5] : ((v5 = v4 & join(all_0_16_16, v2, v3) = v4) | ( ~ (v5 = 0) & element(v3, v0) = v5))) & ! [v2] : ! [v3] : ( ~ (element(v3, v0) = 0) | ~ (element(v2, v0) = 0) | ? [v4] : (join(all_0_16_16, v2, v3) = v4 & apply_binary_as_element(v0, v0, v0, v1, v2, v3) = v4))))
% 110.39/75.62 |
% 110.39/75.62 | Instantiating formula (190) with all_88_0_128, all_0_16_16 and discharging atoms empty_carrier(all_0_16_16) = all_88_0_128, yields:
% 110.39/75.62 | (249) all_88_0_128 = 0 | ? [v0] : (( ~ (v0 = 0) & join_semilatt_str(all_0_16_16) = v0) | (the_carrier(all_0_16_16) = v0 & ! [v1] : ! [v2] : ! [v3] : ( ~ (below(all_0_16_16, v1, v2) = v3) | ~ (element(v1, v0) = 0) | ? [v4] : (( ~ (v4 = 0) & element(v2, v0) = v4) | (( ~ (v3 = 0) | (v4 = v2 & join(all_0_16_16, v1, v2) = v2)) & (v3 = 0 | ( ~ (v4 = v2) & join(all_0_16_16, v1, v2) = v4))))) & ! [v1] : ! [v2] : ! [v3] : ( ~ (join(all_0_16_16, v1, v2) = v3) | ~ (element(v1, v0) = 0) | ? [v4] : (( ~ (v4 = 0) & element(v2, v0) = v4) | (( ~ (v3 = v2) | (v4 = 0 & below(all_0_16_16, v1, v2) = 0)) & (v3 = v2 | ( ~ (v4 = 0) & below(all_0_16_16, v1, v2) = v4))))) & ! [v1] : ! [v2] : ( ~ (element(v2, v0) = 0) | ~ (element(v1, v0) = 0) | ? [v3] : ? [v4] : (((v4 = v2 & join(all_0_16_16, v1, v2) = v2) | ( ~ (v3 = 0) & below(all_0_16_16, v1, v2) = v3)) & ((v3 = 0 & below(all_0_16_16, v1, v2) = 0) | ( ~ (v4 = v2) & join(all_0_16_16, v1, v2) = v4))))))
% 110.39/75.62 |
% 110.39/75.62 | Instantiating formula (45) with all_0_14_14, all_0_14_14, all_0_14_14, all_0_16_16 and discharging atoms join(all_0_16_16, all_0_14_14, all_0_14_14) = all_0_14_14, yields:
% 110.39/75.62 | (250) ? [v0] : ? [v1] : ((v1 = 0 & element(all_0_14_14, v0) = 0 & the_carrier(all_0_16_16) = v0) | (v0 = 0 & empty_carrier(all_0_16_16) = 0) | ( ~ (v1 = 0) & element(all_0_14_14, v0) = v1 & the_carrier(all_0_16_16) = v0) | ( ~ (v0 = 0) & join_semilatt_str(all_0_16_16) = v0))
% 110.39/75.62 |
% 110.39/75.62 | Instantiating formula (82) with all_118_1_191, all_0_14_14, all_0_17_17, all_0_15_15, all_0_16_16 and discharging atoms join(all_0_16_16, all_0_17_17, all_0_14_14) = all_118_1_191, element(all_0_17_17, all_0_15_15) = 0, the_carrier(all_0_16_16) = all_0_15_15, yields:
% 110.39/75.62 | (251) ? [v0] : ((v0 = 0 & empty_carrier(all_0_16_16) = 0) | ( ~ (v0 = 0) & join_semilatt_str(all_0_16_16) = v0) | ( ~ (v0 = 0) & element(all_0_14_14, all_0_15_15) = v0) | (( ~ (all_118_1_191 = all_0_14_14) | (v0 = 0 & below(all_0_16_16, all_0_17_17, all_0_14_14) = 0)) & (all_118_1_191 = all_0_14_14 | ( ~ (v0 = 0) & below(all_0_16_16, all_0_17_17, all_0_14_14) = v0))))
% 110.39/75.62 |
% 110.39/75.62 | Instantiating formula (15) with all_116_1_189, all_0_14_14, all_0_17_17 and discharging atoms set_union2(all_0_14_14, all_0_17_17) = all_116_1_189, yields:
% 110.39/75.62 | (252) set_union2(all_0_17_17, all_0_14_14) = all_116_1_189
% 110.39/75.62 |
% 110.39/75.62 | Instantiating formula (161) with all_118_1_191, all_0_14_14, all_0_17_17 and discharging atoms set_union2(all_0_17_17, all_0_14_14) = all_118_1_191, yields:
% 110.39/75.62 | (253) all_118_1_191 = all_0_14_14 | ? [v0] : ( ~ (v0 = 0) & subset(all_0_17_17, all_0_14_14) = v0)
% 110.39/75.63 |
% 110.39/75.63 | Instantiating formula (83) with all_118_1_191, all_0_14_14, all_0_17_17 and discharging atoms set_union2(all_0_17_17, all_0_14_14) = all_118_1_191, yields:
% 110.39/75.63 | (254) subset(all_0_17_17, all_118_1_191) = 0
% 110.39/75.63 |
% 110.39/75.63 | Instantiating formula (61) with all_0_16_16 and discharging atoms latt_str(all_0_16_16) = 0, yields:
% 110.39/75.63 | (255) meet_semilatt_str(all_0_16_16) = 0 & join_semilatt_str(all_0_16_16) = 0
% 110.39/75.63 |
% 110.39/75.63 | Applying alpha-rule on (255) yields:
% 110.39/75.63 | (256) meet_semilatt_str(all_0_16_16) = 0
% 110.39/75.63 | (257) join_semilatt_str(all_0_16_16) = 0
% 110.39/75.63 |
% 110.39/75.63 | Instantiating formula (8) with all_111_2_179, all_0_16_16 and discharging atoms the_L_join(all_0_16_16) = all_111_2_179, yields:
% 110.39/75.63 | (258) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ((v4 = 0 & v3 = 0 & v0 = 0 & relation_of2_as_subset(all_111_2_179, v2, v1) = 0 & quasi_total(all_111_2_179, v2, v1) = 0 & function(all_111_2_179) = 0 & cartesian_product2(v1, v1) = v2 & the_carrier(all_0_16_16) = v1) | ( ~ (v0 = 0) & join_semilatt_str(all_0_16_16) = v0))
% 110.39/75.63 |
% 110.39/75.63 | Instantiating formula (150) with all_111_2_179, all_0_16_16 and discharging atoms the_L_join(all_0_16_16) = all_111_2_179, yields:
% 110.39/75.63 | (259) ? [v0] : ((v0 = 0 & empty_carrier(all_0_16_16) = 0) | ( ~ (v0 = 0) & join_semilatt_str(all_0_16_16) = v0) | (the_carrier(all_0_16_16) = v0 & ! [v1] : ! [v2] : ! [v3] : ( ~ (join(all_0_16_16, v1, v2) = v3) | ~ (element(v1, v0) = 0) | ? [v4] : ((v4 = v3 & apply_binary_as_element(v0, v0, v0, all_111_2_179, v1, v2) = v3) | ( ~ (v4 = 0) & element(v2, v0) = v4))) & ! [v1] : ! [v2] : ! [v3] : ( ~ (apply_binary_as_element(v0, v0, v0, all_111_2_179, v1, v2) = v3) | ~ (element(v1, v0) = 0) | ? [v4] : ((v4 = v3 & join(all_0_16_16, v1, v2) = v3) | ( ~ (v4 = 0) & element(v2, v0) = v4))) & ! [v1] : ! [v2] : ( ~ (element(v2, v0) = 0) | ~ (element(v1, v0) = 0) | ? [v3] : (join(all_0_16_16, v1, v2) = v3 & apply_binary_as_element(v0, v0, v0, all_111_2_179, v1, v2) = v3))))
% 110.39/75.63 |
% 110.39/75.63 | Instantiating formula (137) with all_111_1_178, all_0_16_16 and discharging atoms the_L_meet(all_0_16_16) = all_111_1_178, yields:
% 110.39/75.63 | (260) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ((v4 = 0 & v3 = 0 & v0 = 0 & relation_of2_as_subset(all_111_1_178, v2, v1) = 0 & quasi_total(all_111_1_178, v2, v1) = 0 & function(all_111_1_178) = 0 & cartesian_product2(v1, v1) = v2 & the_carrier(all_0_16_16) = v1) | ( ~ (v0 = 0) & meet_semilatt_str(all_0_16_16) = v0))
% 110.39/75.63 |
% 110.39/75.63 | Instantiating formula (171) with all_111_1_178, all_0_16_16 and discharging atoms the_L_meet(all_0_16_16) = all_111_1_178, yields:
% 110.39/75.63 | (261) ? [v0] : ((v0 = 0 & empty_carrier(all_0_16_16) = 0) | ( ~ (v0 = 0) & meet_semilatt_str(all_0_16_16) = v0) | (the_carrier(all_0_16_16) = v0 & ! [v1] : ! [v2] : ! [v3] : ( ~ (meet(all_0_16_16, v1, v2) = v3) | ~ (element(v1, v0) = 0) | ? [v4] : ((v4 = v3 & apply_binary_as_element(v0, v0, v0, all_111_1_178, v1, v2) = v3) | ( ~ (v4 = 0) & element(v2, v0) = v4))) & ! [v1] : ! [v2] : ! [v3] : ( ~ (apply_binary_as_element(v0, v0, v0, all_111_1_178, v1, v2) = v3) | ~ (element(v1, v0) = 0) | ? [v4] : ((v4 = v3 & meet(all_0_16_16, v1, v2) = v3) | ( ~ (v4 = 0) & element(v2, v0) = v4))) & ! [v1] : ! [v2] : ( ~ (element(v2, v0) = 0) | ~ (element(v1, v0) = 0) | ? [v3] : (meet(all_0_16_16, v1, v2) = v3 & apply_binary_as_element(v0, v0, v0, all_111_1_178, v1, v2) = v3))))
% 110.39/75.63 |
% 110.39/75.63 | Instantiating (261) with all_248_0_306 yields:
% 110.39/75.63 | (262) (all_248_0_306 = 0 & empty_carrier(all_0_16_16) = 0) | ( ~ (all_248_0_306 = 0) & meet_semilatt_str(all_0_16_16) = all_248_0_306) | (the_carrier(all_0_16_16) = all_248_0_306 & ! [v0] : ! [v1] : ! [v2] : ( ~ (meet(all_0_16_16, v0, v1) = v2) | ~ (element(v0, all_248_0_306) = 0) | ? [v3] : ((v3 = v2 & apply_binary_as_element(all_248_0_306, all_248_0_306, all_248_0_306, all_111_1_178, v0, v1) = v2) | ( ~ (v3 = 0) & element(v1, all_248_0_306) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (apply_binary_as_element(all_248_0_306, all_248_0_306, all_248_0_306, all_111_1_178, v0, v1) = v2) | ~ (element(v0, all_248_0_306) = 0) | ? [v3] : ((v3 = v2 & meet(all_0_16_16, v0, v1) = v2) | ( ~ (v3 = 0) & element(v1, all_248_0_306) = v3))) & ! [v0] : ! [v1] : ( ~ (element(v1, all_248_0_306) = 0) | ~ (element(v0, all_248_0_306) = 0) | ? [v2] : (meet(all_0_16_16, v0, v1) = v2 & apply_binary_as_element(all_248_0_306, all_248_0_306, all_248_0_306, all_111_1_178, v0, v1) = v2)))
% 110.39/75.63 |
% 110.39/75.63 | Instantiating (260) with all_249_0_307, all_249_1_308, all_249_2_309, all_249_3_310, all_249_4_311 yields:
% 110.39/75.63 | (263) (all_249_0_307 = 0 & all_249_1_308 = 0 & all_249_4_311 = 0 & relation_of2_as_subset(all_111_1_178, all_249_2_309, all_249_3_310) = 0 & quasi_total(all_111_1_178, all_249_2_309, all_249_3_310) = 0 & function(all_111_1_178) = 0 & cartesian_product2(all_249_3_310, all_249_3_310) = all_249_2_309 & the_carrier(all_0_16_16) = all_249_3_310) | ( ~ (all_249_4_311 = 0) & meet_semilatt_str(all_0_16_16) = all_249_4_311)
% 110.39/75.63 |
% 110.39/75.63 | Instantiating (244) with all_254_0_318, all_254_1_319 yields:
% 110.39/75.63 | (264) (all_254_0_318 = 0 & element(all_0_14_14, all_254_1_319) = 0 & the_carrier(all_0_16_16) = all_254_1_319) | (all_254_1_319 = 0 & empty_carrier(all_0_16_16) = 0) | ( ~ (all_254_0_318 = 0) & element(all_0_14_14, all_254_1_319) = all_254_0_318 & the_carrier(all_0_16_16) = all_254_1_319) | ( ~ (all_254_1_319 = 0) & meet_semilatt_str(all_0_16_16) = all_254_1_319)
% 110.39/75.63 |
% 110.39/75.63 | Instantiating (259) with all_285_0_364 yields:
% 110.39/75.63 | (265) (all_285_0_364 = 0 & empty_carrier(all_0_16_16) = 0) | ( ~ (all_285_0_364 = 0) & join_semilatt_str(all_0_16_16) = all_285_0_364) | (the_carrier(all_0_16_16) = all_285_0_364 & ! [v0] : ! [v1] : ! [v2] : ( ~ (join(all_0_16_16, v0, v1) = v2) | ~ (element(v0, all_285_0_364) = 0) | ? [v3] : ((v3 = v2 & apply_binary_as_element(all_285_0_364, all_285_0_364, all_285_0_364, all_111_2_179, v0, v1) = v2) | ( ~ (v3 = 0) & element(v1, all_285_0_364) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (apply_binary_as_element(all_285_0_364, all_285_0_364, all_285_0_364, all_111_2_179, v0, v1) = v2) | ~ (element(v0, all_285_0_364) = 0) | ? [v3] : ((v3 = v2 & join(all_0_16_16, v0, v1) = v2) | ( ~ (v3 = 0) & element(v1, all_285_0_364) = v3))) & ! [v0] : ! [v1] : ( ~ (element(v1, all_285_0_364) = 0) | ~ (element(v0, all_285_0_364) = 0) | ? [v2] : (join(all_0_16_16, v0, v1) = v2 & apply_binary_as_element(all_285_0_364, all_285_0_364, all_285_0_364, all_111_2_179, v0, v1) = v2)))
% 110.39/75.63 |
% 110.39/75.63 | Instantiating (258) with all_286_0_365, all_286_1_366, all_286_2_367, all_286_3_368, all_286_4_369 yields:
% 110.39/75.63 | (266) (all_286_0_365 = 0 & all_286_1_366 = 0 & all_286_4_369 = 0 & relation_of2_as_subset(all_111_2_179, all_286_2_367, all_286_3_368) = 0 & quasi_total(all_111_2_179, all_286_2_367, all_286_3_368) = 0 & function(all_111_2_179) = 0 & cartesian_product2(all_286_3_368, all_286_3_368) = all_286_2_367 & the_carrier(all_0_16_16) = all_286_3_368) | ( ~ (all_286_4_369 = 0) & join_semilatt_str(all_0_16_16) = all_286_4_369)
% 110.39/75.63 |
% 110.39/75.63 | Instantiating (251) with all_311_0_412 yields:
% 110.39/75.63 | (267) (all_311_0_412 = 0 & empty_carrier(all_0_16_16) = 0) | ( ~ (all_311_0_412 = 0) & join_semilatt_str(all_0_16_16) = all_311_0_412) | ( ~ (all_311_0_412 = 0) & element(all_0_14_14, all_0_15_15) = all_311_0_412) | (( ~ (all_118_1_191 = all_0_14_14) | (all_311_0_412 = 0 & below(all_0_16_16, all_0_17_17, all_0_14_14) = 0)) & (all_118_1_191 = all_0_14_14 | ( ~ (all_311_0_412 = 0) & below(all_0_16_16, all_0_17_17, all_0_14_14) = all_311_0_412)))
% 110.39/75.63 |
% 110.39/75.63 | Instantiating (250) with all_341_0_487, all_341_1_488 yields:
% 110.39/75.63 | (268) (all_341_0_487 = 0 & element(all_0_14_14, all_341_1_488) = 0 & the_carrier(all_0_16_16) = all_341_1_488) | (all_341_1_488 = 0 & empty_carrier(all_0_16_16) = 0) | ( ~ (all_341_0_487 = 0) & element(all_0_14_14, all_341_1_488) = all_341_0_487 & the_carrier(all_0_16_16) = all_341_1_488) | ( ~ (all_341_1_488 = 0) & join_semilatt_str(all_0_16_16) = all_341_1_488)
% 110.39/75.63 |
% 110.39/75.63 +-Applying beta-rule and splitting (262), into two cases.
% 110.39/75.63 |-Branch one:
% 110.39/75.63 | (269) (all_248_0_306 = 0 & empty_carrier(all_0_16_16) = 0) | ( ~ (all_248_0_306 = 0) & meet_semilatt_str(all_0_16_16) = all_248_0_306)
% 110.39/75.63 |
% 110.39/75.63 +-Applying beta-rule and splitting (269), into two cases.
% 110.39/75.63 |-Branch one:
% 110.39/75.63 | (270) all_248_0_306 = 0 & empty_carrier(all_0_16_16) = 0
% 110.39/75.63 |
% 110.39/75.63 | Applying alpha-rule on (270) yields:
% 110.39/75.63 | (271) all_248_0_306 = 0
% 110.39/75.63 | (272) empty_carrier(all_0_16_16) = 0
% 110.39/75.63 |
% 110.39/75.63 +-Applying beta-rule and splitting (249), into two cases.
% 110.39/75.63 |-Branch one:
% 110.39/75.63 | (273) all_88_0_128 = 0
% 110.39/75.63 |
% 110.39/75.63 | Equations (273) can reduce 214 to:
% 110.39/75.63 | (274) $false
% 110.39/75.63 |
% 110.39/75.63 |-The branch is then unsatisfiable
% 110.39/75.63 |-Branch two:
% 110.39/75.63 | (214) ~ (all_88_0_128 = 0)
% 110.39/75.63 | (276) ? [v0] : (( ~ (v0 = 0) & join_semilatt_str(all_0_16_16) = v0) | (the_carrier(all_0_16_16) = v0 & ! [v1] : ! [v2] : ! [v3] : ( ~ (below(all_0_16_16, v1, v2) = v3) | ~ (element(v1, v0) = 0) | ? [v4] : (( ~ (v4 = 0) & element(v2, v0) = v4) | (( ~ (v3 = 0) | (v4 = v2 & join(all_0_16_16, v1, v2) = v2)) & (v3 = 0 | ( ~ (v4 = v2) & join(all_0_16_16, v1, v2) = v4))))) & ! [v1] : ! [v2] : ! [v3] : ( ~ (join(all_0_16_16, v1, v2) = v3) | ~ (element(v1, v0) = 0) | ? [v4] : (( ~ (v4 = 0) & element(v2, v0) = v4) | (( ~ (v3 = v2) | (v4 = 0 & below(all_0_16_16, v1, v2) = 0)) & (v3 = v2 | ( ~ (v4 = 0) & below(all_0_16_16, v1, v2) = v4))))) & ! [v1] : ! [v2] : ( ~ (element(v2, v0) = 0) | ~ (element(v1, v0) = 0) | ? [v3] : ? [v4] : (((v4 = v2 & join(all_0_16_16, v1, v2) = v2) | ( ~ (v3 = 0) & below(all_0_16_16, v1, v2) = v3)) & ((v3 = 0 & below(all_0_16_16, v1, v2) = 0) | ( ~ (v4 = v2) & join(all_0_16_16, v1, v2) = v4))))))
% 110.39/75.64 |
% 110.39/75.64 +-Applying beta-rule and splitting (247), into two cases.
% 110.39/75.64 |-Branch one:
% 110.39/75.64 | (273) all_88_0_128 = 0
% 110.39/75.64 |
% 110.39/75.64 | Equations (273) can reduce 214 to:
% 110.39/75.64 | (274) $false
% 110.39/75.64 |
% 110.39/75.64 |-The branch is then unsatisfiable
% 110.39/75.64 |-Branch two:
% 110.39/75.64 | (214) ~ (all_88_0_128 = 0)
% 110.39/75.64 | (280) ? [v0] : ? [v1] : (( ~ (v0 = 0) & meet_semilatt_str(all_0_16_16) = v0) | (the_carrier(all_0_16_16) = v0 & the_L_meet(all_0_16_16) = v1 & ! [v2] : ! [v3] : ! [v4] : ( ~ (meet(all_0_16_16, v2, v3) = v4) | ~ (element(v2, v0) = 0) | ? [v5] : ((v5 = v4 & apply_binary_as_element(v0, v0, v0, v1, v2, v3) = v4) | ( ~ (v5 = 0) & element(v3, v0) = v5))) & ! [v2] : ! [v3] : ! [v4] : ( ~ (apply_binary_as_element(v0, v0, v0, v1, v2, v3) = v4) | ~ (element(v2, v0) = 0) | ? [v5] : ((v5 = v4 & meet(all_0_16_16, v2, v3) = v4) | ( ~ (v5 = 0) & element(v3, v0) = v5))) & ! [v2] : ! [v3] : ( ~ (element(v3, v0) = 0) | ~ (element(v2, v0) = 0) | ? [v4] : (meet(all_0_16_16, v2, v3) = v4 & apply_binary_as_element(v0, v0, v0, v1, v2, v3) = v4))))
% 110.39/75.64 |
% 110.39/75.64 +-Applying beta-rule and splitting (248), into two cases.
% 110.39/75.64 |-Branch one:
% 110.39/75.64 | (273) all_88_0_128 = 0
% 110.39/75.64 |
% 110.39/75.64 | Equations (273) can reduce 214 to:
% 110.39/75.64 | (274) $false
% 110.39/75.64 |
% 110.39/75.64 |-The branch is then unsatisfiable
% 110.39/75.64 |-Branch two:
% 110.39/75.64 | (214) ~ (all_88_0_128 = 0)
% 110.39/75.64 | (284) ? [v0] : ? [v1] : (( ~ (v0 = 0) & join_semilatt_str(all_0_16_16) = v0) | (the_carrier(all_0_16_16) = v0 & the_L_join(all_0_16_16) = v1 & ! [v2] : ! [v3] : ! [v4] : ( ~ (join(all_0_16_16, v2, v3) = v4) | ~ (element(v2, v0) = 0) | ? [v5] : ((v5 = v4 & apply_binary_as_element(v0, v0, v0, v1, v2, v3) = v4) | ( ~ (v5 = 0) & element(v3, v0) = v5))) & ! [v2] : ! [v3] : ! [v4] : ( ~ (apply_binary_as_element(v0, v0, v0, v1, v2, v3) = v4) | ~ (element(v2, v0) = 0) | ? [v5] : ((v5 = v4 & join(all_0_16_16, v2, v3) = v4) | ( ~ (v5 = 0) & element(v3, v0) = v5))) & ! [v2] : ! [v3] : ( ~ (element(v3, v0) = 0) | ~ (element(v2, v0) = 0) | ? [v4] : (join(all_0_16_16, v2, v3) = v4 & apply_binary_as_element(v0, v0, v0, v1, v2, v3) = v4))))
% 110.39/75.64 |
% 110.39/75.64 +-Applying beta-rule and splitting (245), into two cases.
% 110.39/75.64 |-Branch one:
% 110.39/75.64 | (273) all_88_0_128 = 0
% 110.39/75.64 |
% 110.39/75.64 | Equations (273) can reduce 214 to:
% 110.39/75.64 | (274) $false
% 110.39/75.64 |
% 110.39/75.64 |-The branch is then unsatisfiable
% 110.39/75.64 |-Branch two:
% 110.39/75.64 | (214) ~ (all_88_0_128 = 0)
% 110.39/75.64 | (288) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ((v3 = 0 & ~ (v4 = 0) & empty(v2) = v4 & powerset(v0) = v1 & element(v2, v1) = 0 & the_carrier(all_0_16_16) = v0) | ( ~ (v0 = 0) & one_sorted_str(all_0_16_16) = v0))
% 110.39/75.64 |
% 110.66/75.64 +-Applying beta-rule and splitting (246), into two cases.
% 110.66/75.64 |-Branch one:
% 110.66/75.64 | (273) all_88_0_128 = 0
% 110.66/75.64 |
% 110.66/75.64 | Equations (273) can reduce 214 to:
% 110.66/75.64 | (274) $false
% 110.66/75.64 |
% 110.66/75.64 |-The branch is then unsatisfiable
% 110.66/75.64 |-Branch two:
% 110.66/75.64 | (214) ~ (all_88_0_128 = 0)
% 110.66/75.64 | (292) ? [v0] : ? [v1] : (( ~ (v1 = 0) & empty(v0) = v1 & the_carrier(all_0_16_16) = v0) | ( ~ (v0 = 0) & one_sorted_str(all_0_16_16) = v0))
% 110.66/75.64 |
% 110.66/75.64 | Instantiating formula (93) with all_0_16_16, 0, all_88_0_128 and discharging atoms empty_carrier(all_0_16_16) = all_88_0_128, empty_carrier(all_0_16_16) = 0, yields:
% 110.66/75.64 | (273) all_88_0_128 = 0
% 110.66/75.64 |
% 110.66/75.64 | Equations (273) can reduce 214 to:
% 110.66/75.64 | (274) $false
% 110.66/75.64 |
% 110.66/75.64 |-The branch is then unsatisfiable
% 110.66/75.64 |-Branch two:
% 110.66/75.64 | (295) ~ (all_248_0_306 = 0) & meet_semilatt_str(all_0_16_16) = all_248_0_306
% 110.66/75.64 |
% 110.66/75.64 | Applying alpha-rule on (295) yields:
% 110.66/75.64 | (296) ~ (all_248_0_306 = 0)
% 110.66/75.64 | (297) meet_semilatt_str(all_0_16_16) = all_248_0_306
% 110.66/75.64 |
% 110.66/75.64 | Instantiating formula (178) with all_0_16_16, 0, all_248_0_306 and discharging atoms meet_semilatt_str(all_0_16_16) = all_248_0_306, meet_semilatt_str(all_0_16_16) = 0, yields:
% 110.66/75.64 | (271) all_248_0_306 = 0
% 110.66/75.64 |
% 110.66/75.64 | Equations (271) can reduce 296 to:
% 110.66/75.64 | (274) $false
% 110.66/75.64 |
% 110.66/75.64 |-The branch is then unsatisfiable
% 110.66/75.64 |-Branch two:
% 110.66/75.64 | (300) the_carrier(all_0_16_16) = all_248_0_306 & ! [v0] : ! [v1] : ! [v2] : ( ~ (meet(all_0_16_16, v0, v1) = v2) | ~ (element(v0, all_248_0_306) = 0) | ? [v3] : ((v3 = v2 & apply_binary_as_element(all_248_0_306, all_248_0_306, all_248_0_306, all_111_1_178, v0, v1) = v2) | ( ~ (v3 = 0) & element(v1, all_248_0_306) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (apply_binary_as_element(all_248_0_306, all_248_0_306, all_248_0_306, all_111_1_178, v0, v1) = v2) | ~ (element(v0, all_248_0_306) = 0) | ? [v3] : ((v3 = v2 & meet(all_0_16_16, v0, v1) = v2) | ( ~ (v3 = 0) & element(v1, all_248_0_306) = v3))) & ! [v0] : ! [v1] : ( ~ (element(v1, all_248_0_306) = 0) | ~ (element(v0, all_248_0_306) = 0) | ? [v2] : (meet(all_0_16_16, v0, v1) = v2 & apply_binary_as_element(all_248_0_306, all_248_0_306, all_248_0_306, all_111_1_178, v0, v1) = v2))
% 110.66/75.64 |
% 110.66/75.64 | Applying alpha-rule on (300) yields:
% 110.66/75.64 | (301) the_carrier(all_0_16_16) = all_248_0_306
% 110.66/75.64 | (302) ! [v0] : ! [v1] : ! [v2] : ( ~ (meet(all_0_16_16, v0, v1) = v2) | ~ (element(v0, all_248_0_306) = 0) | ? [v3] : ((v3 = v2 & apply_binary_as_element(all_248_0_306, all_248_0_306, all_248_0_306, all_111_1_178, v0, v1) = v2) | ( ~ (v3 = 0) & element(v1, all_248_0_306) = v3)))
% 110.66/75.64 | (303) ! [v0] : ! [v1] : ! [v2] : ( ~ (apply_binary_as_element(all_248_0_306, all_248_0_306, all_248_0_306, all_111_1_178, v0, v1) = v2) | ~ (element(v0, all_248_0_306) = 0) | ? [v3] : ((v3 = v2 & meet(all_0_16_16, v0, v1) = v2) | ( ~ (v3 = 0) & element(v1, all_248_0_306) = v3)))
% 110.66/75.64 | (304) ! [v0] : ! [v1] : ( ~ (element(v1, all_248_0_306) = 0) | ~ (element(v0, all_248_0_306) = 0) | ? [v2] : (meet(all_0_16_16, v0, v1) = v2 & apply_binary_as_element(all_248_0_306, all_248_0_306, all_248_0_306, all_111_1_178, v0, v1) = v2))
% 110.66/75.64 |
% 110.66/75.64 +-Applying beta-rule and splitting (249), into two cases.
% 110.66/75.64 |-Branch one:
% 110.66/75.64 | (273) all_88_0_128 = 0
% 110.66/75.64 |
% 110.66/75.64 | Equations (273) can reduce 214 to:
% 110.66/75.64 | (274) $false
% 110.66/75.64 |
% 110.66/75.64 |-The branch is then unsatisfiable
% 110.66/75.64 |-Branch two:
% 110.66/75.64 | (214) ~ (all_88_0_128 = 0)
% 110.66/75.64 | (276) ? [v0] : (( ~ (v0 = 0) & join_semilatt_str(all_0_16_16) = v0) | (the_carrier(all_0_16_16) = v0 & ! [v1] : ! [v2] : ! [v3] : ( ~ (below(all_0_16_16, v1, v2) = v3) | ~ (element(v1, v0) = 0) | ? [v4] : (( ~ (v4 = 0) & element(v2, v0) = v4) | (( ~ (v3 = 0) | (v4 = v2 & join(all_0_16_16, v1, v2) = v2)) & (v3 = 0 | ( ~ (v4 = v2) & join(all_0_16_16, v1, v2) = v4))))) & ! [v1] : ! [v2] : ! [v3] : ( ~ (join(all_0_16_16, v1, v2) = v3) | ~ (element(v1, v0) = 0) | ? [v4] : (( ~ (v4 = 0) & element(v2, v0) = v4) | (( ~ (v3 = v2) | (v4 = 0 & below(all_0_16_16, v1, v2) = 0)) & (v3 = v2 | ( ~ (v4 = 0) & below(all_0_16_16, v1, v2) = v4))))) & ! [v1] : ! [v2] : ( ~ (element(v2, v0) = 0) | ~ (element(v1, v0) = 0) | ? [v3] : ? [v4] : (((v4 = v2 & join(all_0_16_16, v1, v2) = v2) | ( ~ (v3 = 0) & below(all_0_16_16, v1, v2) = v3)) & ((v3 = 0 & below(all_0_16_16, v1, v2) = 0) | ( ~ (v4 = v2) & join(all_0_16_16, v1, v2) = v4))))))
% 110.66/75.64 |
% 110.66/75.64 | Instantiating (276) with all_447_0_1607 yields:
% 110.66/75.64 | (309) ( ~ (all_447_0_1607 = 0) & join_semilatt_str(all_0_16_16) = all_447_0_1607) | (the_carrier(all_0_16_16) = all_447_0_1607 & ! [v0] : ! [v1] : ! [v2] : ( ~ (below(all_0_16_16, v0, v1) = v2) | ~ (element(v0, all_447_0_1607) = 0) | ? [v3] : (( ~ (v3 = 0) & element(v1, all_447_0_1607) = v3) | (( ~ (v2 = 0) | (v3 = v1 & join(all_0_16_16, v0, v1) = v1)) & (v2 = 0 | ( ~ (v3 = v1) & join(all_0_16_16, v0, v1) = v3))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (join(all_0_16_16, v0, v1) = v2) | ~ (element(v0, all_447_0_1607) = 0) | ? [v3] : (( ~ (v3 = 0) & element(v1, all_447_0_1607) = v3) | (( ~ (v2 = v1) | (v3 = 0 & below(all_0_16_16, v0, v1) = 0)) & (v2 = v1 | ( ~ (v3 = 0) & below(all_0_16_16, v0, v1) = v3))))) & ! [v0] : ! [v1] : ( ~ (element(v1, all_447_0_1607) = 0) | ~ (element(v0, all_447_0_1607) = 0) | ? [v2] : ? [v3] : (((v3 = v1 & join(all_0_16_16, v0, v1) = v1) | ( ~ (v2 = 0) & below(all_0_16_16, v0, v1) = v2)) & ((v2 = 0 & below(all_0_16_16, v0, v1) = 0) | ( ~ (v3 = v1) & join(all_0_16_16, v0, v1) = v3)))))
% 110.66/75.65 |
% 110.66/75.65 +-Applying beta-rule and splitting (309), into two cases.
% 110.66/75.65 |-Branch one:
% 110.66/75.65 | (310) ~ (all_447_0_1607 = 0) & join_semilatt_str(all_0_16_16) = all_447_0_1607
% 110.66/75.65 |
% 110.66/75.65 | Applying alpha-rule on (310) yields:
% 110.66/75.65 | (311) ~ (all_447_0_1607 = 0)
% 110.66/75.65 | (312) join_semilatt_str(all_0_16_16) = all_447_0_1607
% 110.66/75.65 |
% 110.66/75.65 | Instantiating formula (135) with all_0_16_16, 0, all_447_0_1607 and discharging atoms join_semilatt_str(all_0_16_16) = all_447_0_1607, join_semilatt_str(all_0_16_16) = 0, yields:
% 110.66/75.65 | (313) all_447_0_1607 = 0
% 110.66/75.65 |
% 110.66/75.65 | Equations (313) can reduce 311 to:
% 110.66/75.65 | (274) $false
% 110.66/75.65 |
% 110.66/75.65 |-The branch is then unsatisfiable
% 110.66/75.65 |-Branch two:
% 110.66/75.65 | (315) the_carrier(all_0_16_16) = all_447_0_1607 & ! [v0] : ! [v1] : ! [v2] : ( ~ (below(all_0_16_16, v0, v1) = v2) | ~ (element(v0, all_447_0_1607) = 0) | ? [v3] : (( ~ (v3 = 0) & element(v1, all_447_0_1607) = v3) | (( ~ (v2 = 0) | (v3 = v1 & join(all_0_16_16, v0, v1) = v1)) & (v2 = 0 | ( ~ (v3 = v1) & join(all_0_16_16, v0, v1) = v3))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (join(all_0_16_16, v0, v1) = v2) | ~ (element(v0, all_447_0_1607) = 0) | ? [v3] : (( ~ (v3 = 0) & element(v1, all_447_0_1607) = v3) | (( ~ (v2 = v1) | (v3 = 0 & below(all_0_16_16, v0, v1) = 0)) & (v2 = v1 | ( ~ (v3 = 0) & below(all_0_16_16, v0, v1) = v3))))) & ! [v0] : ! [v1] : ( ~ (element(v1, all_447_0_1607) = 0) | ~ (element(v0, all_447_0_1607) = 0) | ? [v2] : ? [v3] : (((v3 = v1 & join(all_0_16_16, v0, v1) = v1) | ( ~ (v2 = 0) & below(all_0_16_16, v0, v1) = v2)) & ((v2 = 0 & below(all_0_16_16, v0, v1) = 0) | ( ~ (v3 = v1) & join(all_0_16_16, v0, v1) = v3))))
% 110.66/75.65 |
% 110.66/75.65 | Applying alpha-rule on (315) yields:
% 110.66/75.65 | (316) the_carrier(all_0_16_16) = all_447_0_1607
% 110.66/75.65 | (317) ! [v0] : ! [v1] : ! [v2] : ( ~ (below(all_0_16_16, v0, v1) = v2) | ~ (element(v0, all_447_0_1607) = 0) | ? [v3] : (( ~ (v3 = 0) & element(v1, all_447_0_1607) = v3) | (( ~ (v2 = 0) | (v3 = v1 & join(all_0_16_16, v0, v1) = v1)) & (v2 = 0 | ( ~ (v3 = v1) & join(all_0_16_16, v0, v1) = v3)))))
% 110.66/75.65 | (318) ! [v0] : ! [v1] : ! [v2] : ( ~ (join(all_0_16_16, v0, v1) = v2) | ~ (element(v0, all_447_0_1607) = 0) | ? [v3] : (( ~ (v3 = 0) & element(v1, all_447_0_1607) = v3) | (( ~ (v2 = v1) | (v3 = 0 & below(all_0_16_16, v0, v1) = 0)) & (v2 = v1 | ( ~ (v3 = 0) & below(all_0_16_16, v0, v1) = v3)))))
% 110.66/75.65 | (319) ! [v0] : ! [v1] : ( ~ (element(v1, all_447_0_1607) = 0) | ~ (element(v0, all_447_0_1607) = 0) | ? [v2] : ? [v3] : (((v3 = v1 & join(all_0_16_16, v0, v1) = v1) | ( ~ (v2 = 0) & below(all_0_16_16, v0, v1) = v2)) & ((v2 = 0 & below(all_0_16_16, v0, v1) = 0) | ( ~ (v3 = v1) & join(all_0_16_16, v0, v1) = v3))))
% 110.66/75.65 |
% 110.66/75.65 +-Applying beta-rule and splitting (266), into two cases.
% 110.66/75.65 |-Branch one:
% 110.66/75.65 | (320) all_286_0_365 = 0 & all_286_1_366 = 0 & all_286_4_369 = 0 & relation_of2_as_subset(all_111_2_179, all_286_2_367, all_286_3_368) = 0 & quasi_total(all_111_2_179, all_286_2_367, all_286_3_368) = 0 & function(all_111_2_179) = 0 & cartesian_product2(all_286_3_368, all_286_3_368) = all_286_2_367 & the_carrier(all_0_16_16) = all_286_3_368
% 110.66/75.65 |
% 110.66/75.65 | Applying alpha-rule on (320) yields:
% 110.66/75.65 | (321) all_286_4_369 = 0
% 110.66/75.65 | (322) relation_of2_as_subset(all_111_2_179, all_286_2_367, all_286_3_368) = 0
% 110.66/75.65 | (323) all_286_1_366 = 0
% 110.66/75.65 | (324) the_carrier(all_0_16_16) = all_286_3_368
% 110.66/75.65 | (325) cartesian_product2(all_286_3_368, all_286_3_368) = all_286_2_367
% 110.66/75.65 | (326) all_286_0_365 = 0
% 110.66/75.65 | (327) quasi_total(all_111_2_179, all_286_2_367, all_286_3_368) = 0
% 110.66/75.65 | (328) function(all_111_2_179) = 0
% 110.66/75.65 |
% 110.66/75.65 +-Applying beta-rule and splitting (245), into two cases.
% 110.66/75.65 |-Branch one:
% 110.66/75.65 | (273) all_88_0_128 = 0
% 110.66/75.65 |
% 110.66/75.65 | Equations (273) can reduce 214 to:
% 110.66/75.65 | (274) $false
% 110.66/75.65 |
% 110.66/75.65 |-The branch is then unsatisfiable
% 110.66/75.65 |-Branch two:
% 110.66/75.65 | (214) ~ (all_88_0_128 = 0)
% 110.66/75.65 | (288) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ((v3 = 0 & ~ (v4 = 0) & empty(v2) = v4 & powerset(v0) = v1 & element(v2, v1) = 0 & the_carrier(all_0_16_16) = v0) | ( ~ (v0 = 0) & one_sorted_str(all_0_16_16) = v0))
% 110.66/75.65 |
% 110.66/75.65 +-Applying beta-rule and splitting (246), into two cases.
% 110.66/75.65 |-Branch one:
% 110.66/75.65 | (273) all_88_0_128 = 0
% 110.66/75.65 |
% 110.66/75.65 | Equations (273) can reduce 214 to:
% 110.66/75.65 | (274) $false
% 110.66/75.65 |
% 110.66/75.65 |-The branch is then unsatisfiable
% 110.66/75.65 |-Branch two:
% 110.66/75.65 | (214) ~ (all_88_0_128 = 0)
% 110.66/75.65 | (292) ? [v0] : ? [v1] : (( ~ (v1 = 0) & empty(v0) = v1 & the_carrier(all_0_16_16) = v0) | ( ~ (v0 = 0) & one_sorted_str(all_0_16_16) = v0))
% 110.66/75.65 |
% 110.66/75.65 +-Applying beta-rule and splitting (263), into two cases.
% 110.66/75.65 |-Branch one:
% 110.66/75.65 | (337) all_249_0_307 = 0 & all_249_1_308 = 0 & all_249_4_311 = 0 & relation_of2_as_subset(all_111_1_178, all_249_2_309, all_249_3_310) = 0 & quasi_total(all_111_1_178, all_249_2_309, all_249_3_310) = 0 & function(all_111_1_178) = 0 & cartesian_product2(all_249_3_310, all_249_3_310) = all_249_2_309 & the_carrier(all_0_16_16) = all_249_3_310
% 110.66/75.65 |
% 110.66/75.65 | Applying alpha-rule on (337) yields:
% 110.66/75.65 | (338) the_carrier(all_0_16_16) = all_249_3_310
% 110.66/75.65 | (339) quasi_total(all_111_1_178, all_249_2_309, all_249_3_310) = 0
% 110.66/75.65 | (340) all_249_1_308 = 0
% 110.66/75.65 | (341) all_249_0_307 = 0
% 110.66/75.65 | (342) function(all_111_1_178) = 0
% 110.66/75.65 | (343) relation_of2_as_subset(all_111_1_178, all_249_2_309, all_249_3_310) = 0
% 110.66/75.65 | (344) all_249_4_311 = 0
% 110.66/75.65 | (345) cartesian_product2(all_249_3_310, all_249_3_310) = all_249_2_309
% 110.66/75.65 |
% 110.66/75.65 +-Applying beta-rule and splitting (247), into two cases.
% 110.66/75.65 |-Branch one:
% 110.66/75.65 | (273) all_88_0_128 = 0
% 110.66/75.65 |
% 110.66/75.65 | Equations (273) can reduce 214 to:
% 110.66/75.65 | (274) $false
% 110.66/75.65 |
% 110.66/75.65 |-The branch is then unsatisfiable
% 110.66/75.65 |-Branch two:
% 110.66/75.65 | (214) ~ (all_88_0_128 = 0)
% 110.66/75.65 | (280) ? [v0] : ? [v1] : (( ~ (v0 = 0) & meet_semilatt_str(all_0_16_16) = v0) | (the_carrier(all_0_16_16) = v0 & the_L_meet(all_0_16_16) = v1 & ! [v2] : ! [v3] : ! [v4] : ( ~ (meet(all_0_16_16, v2, v3) = v4) | ~ (element(v2, v0) = 0) | ? [v5] : ((v5 = v4 & apply_binary_as_element(v0, v0, v0, v1, v2, v3) = v4) | ( ~ (v5 = 0) & element(v3, v0) = v5))) & ! [v2] : ! [v3] : ! [v4] : ( ~ (apply_binary_as_element(v0, v0, v0, v1, v2, v3) = v4) | ~ (element(v2, v0) = 0) | ? [v5] : ((v5 = v4 & meet(all_0_16_16, v2, v3) = v4) | ( ~ (v5 = 0) & element(v3, v0) = v5))) & ! [v2] : ! [v3] : ( ~ (element(v3, v0) = 0) | ~ (element(v2, v0) = 0) | ? [v4] : (meet(all_0_16_16, v2, v3) = v4 & apply_binary_as_element(v0, v0, v0, v1, v2, v3) = v4))))
% 110.66/75.65 |
% 110.66/75.65 +-Applying beta-rule and splitting (248), into two cases.
% 110.66/75.65 |-Branch one:
% 110.66/75.65 | (273) all_88_0_128 = 0
% 110.66/75.65 |
% 110.66/75.65 | Equations (273) can reduce 214 to:
% 110.66/75.65 | (274) $false
% 110.66/75.65 |
% 110.66/75.65 |-The branch is then unsatisfiable
% 110.66/75.65 |-Branch two:
% 110.66/75.65 | (214) ~ (all_88_0_128 = 0)
% 110.66/75.65 | (284) ? [v0] : ? [v1] : (( ~ (v0 = 0) & join_semilatt_str(all_0_16_16) = v0) | (the_carrier(all_0_16_16) = v0 & the_L_join(all_0_16_16) = v1 & ! [v2] : ! [v3] : ! [v4] : ( ~ (join(all_0_16_16, v2, v3) = v4) | ~ (element(v2, v0) = 0) | ? [v5] : ((v5 = v4 & apply_binary_as_element(v0, v0, v0, v1, v2, v3) = v4) | ( ~ (v5 = 0) & element(v3, v0) = v5))) & ! [v2] : ! [v3] : ! [v4] : ( ~ (apply_binary_as_element(v0, v0, v0, v1, v2, v3) = v4) | ~ (element(v2, v0) = 0) | ? [v5] : ((v5 = v4 & join(all_0_16_16, v2, v3) = v4) | ( ~ (v5 = 0) & element(v3, v0) = v5))) & ! [v2] : ! [v3] : ( ~ (element(v3, v0) = 0) | ~ (element(v2, v0) = 0) | ? [v4] : (join(all_0_16_16, v2, v3) = v4 & apply_binary_as_element(v0, v0, v0, v1, v2, v3) = v4))))
% 110.66/75.65 |
% 110.66/75.65 | Instantiating (280) with all_559_0_2634, all_559_1_2635 yields:
% 110.66/75.65 | (354) ( ~ (all_559_1_2635 = 0) & meet_semilatt_str(all_0_16_16) = all_559_1_2635) | (the_carrier(all_0_16_16) = all_559_1_2635 & the_L_meet(all_0_16_16) = all_559_0_2634 & ! [v0] : ! [v1] : ! [v2] : ( ~ (meet(all_0_16_16, v0, v1) = v2) | ~ (element(v0, all_559_1_2635) = 0) | ? [v3] : ((v3 = v2 & apply_binary_as_element(all_559_1_2635, all_559_1_2635, all_559_1_2635, all_559_0_2634, v0, v1) = v2) | ( ~ (v3 = 0) & element(v1, all_559_1_2635) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (apply_binary_as_element(all_559_1_2635, all_559_1_2635, all_559_1_2635, all_559_0_2634, v0, v1) = v2) | ~ (element(v0, all_559_1_2635) = 0) | ? [v3] : ((v3 = v2 & meet(all_0_16_16, v0, v1) = v2) | ( ~ (v3 = 0) & element(v1, all_559_1_2635) = v3))) & ! [v0] : ! [v1] : ( ~ (element(v1, all_559_1_2635) = 0) | ~ (element(v0, all_559_1_2635) = 0) | ? [v2] : (meet(all_0_16_16, v0, v1) = v2 & apply_binary_as_element(all_559_1_2635, all_559_1_2635, all_559_1_2635, all_559_0_2634, v0, v1) = v2)))
% 110.66/75.65 |
% 110.66/75.65 | Instantiating (284) with all_560_0_2636, all_560_1_2637 yields:
% 110.66/75.65 | (355) ( ~ (all_560_1_2637 = 0) & join_semilatt_str(all_0_16_16) = all_560_1_2637) | (the_carrier(all_0_16_16) = all_560_1_2637 & the_L_join(all_0_16_16) = all_560_0_2636 & ! [v0] : ! [v1] : ! [v2] : ( ~ (join(all_0_16_16, v0, v1) = v2) | ~ (element(v0, all_560_1_2637) = 0) | ? [v3] : ((v3 = v2 & apply_binary_as_element(all_560_1_2637, all_560_1_2637, all_560_1_2637, all_560_0_2636, v0, v1) = v2) | ( ~ (v3 = 0) & element(v1, all_560_1_2637) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (apply_binary_as_element(all_560_1_2637, all_560_1_2637, all_560_1_2637, all_560_0_2636, v0, v1) = v2) | ~ (element(v0, all_560_1_2637) = 0) | ? [v3] : ((v3 = v2 & join(all_0_16_16, v0, v1) = v2) | ( ~ (v3 = 0) & element(v1, all_560_1_2637) = v3))) & ! [v0] : ! [v1] : ( ~ (element(v1, all_560_1_2637) = 0) | ~ (element(v0, all_560_1_2637) = 0) | ? [v2] : (join(all_0_16_16, v0, v1) = v2 & apply_binary_as_element(all_560_1_2637, all_560_1_2637, all_560_1_2637, all_560_0_2636, v0, v1) = v2)))
% 110.66/75.66 |
% 110.66/75.66 +-Applying beta-rule and splitting (354), into two cases.
% 110.66/75.66 |-Branch one:
% 110.66/75.66 | (356) ~ (all_559_1_2635 = 0) & meet_semilatt_str(all_0_16_16) = all_559_1_2635
% 110.66/75.66 |
% 110.66/75.66 | Applying alpha-rule on (356) yields:
% 110.66/75.66 | (357) ~ (all_559_1_2635 = 0)
% 110.66/75.66 | (358) meet_semilatt_str(all_0_16_16) = all_559_1_2635
% 110.66/75.66 |
% 110.66/75.66 | Instantiating formula (178) with all_0_16_16, 0, all_559_1_2635 and discharging atoms meet_semilatt_str(all_0_16_16) = all_559_1_2635, meet_semilatt_str(all_0_16_16) = 0, yields:
% 110.66/75.66 | (359) all_559_1_2635 = 0
% 110.66/75.66 |
% 110.66/75.66 | Equations (359) can reduce 357 to:
% 110.66/75.66 | (274) $false
% 110.66/75.66 |
% 110.66/75.66 |-The branch is then unsatisfiable
% 110.66/75.66 |-Branch two:
% 110.66/75.66 | (361) the_carrier(all_0_16_16) = all_559_1_2635 & the_L_meet(all_0_16_16) = all_559_0_2634 & ! [v0] : ! [v1] : ! [v2] : ( ~ (meet(all_0_16_16, v0, v1) = v2) | ~ (element(v0, all_559_1_2635) = 0) | ? [v3] : ((v3 = v2 & apply_binary_as_element(all_559_1_2635, all_559_1_2635, all_559_1_2635, all_559_0_2634, v0, v1) = v2) | ( ~ (v3 = 0) & element(v1, all_559_1_2635) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (apply_binary_as_element(all_559_1_2635, all_559_1_2635, all_559_1_2635, all_559_0_2634, v0, v1) = v2) | ~ (element(v0, all_559_1_2635) = 0) | ? [v3] : ((v3 = v2 & meet(all_0_16_16, v0, v1) = v2) | ( ~ (v3 = 0) & element(v1, all_559_1_2635) = v3))) & ! [v0] : ! [v1] : ( ~ (element(v1, all_559_1_2635) = 0) | ~ (element(v0, all_559_1_2635) = 0) | ? [v2] : (meet(all_0_16_16, v0, v1) = v2 & apply_binary_as_element(all_559_1_2635, all_559_1_2635, all_559_1_2635, all_559_0_2634, v0, v1) = v2))
% 110.66/75.66 |
% 110.66/75.66 | Applying alpha-rule on (361) yields:
% 110.66/75.66 | (362) ! [v0] : ! [v1] : ( ~ (element(v1, all_559_1_2635) = 0) | ~ (element(v0, all_559_1_2635) = 0) | ? [v2] : (meet(all_0_16_16, v0, v1) = v2 & apply_binary_as_element(all_559_1_2635, all_559_1_2635, all_559_1_2635, all_559_0_2634, v0, v1) = v2))
% 110.66/75.66 | (363) the_carrier(all_0_16_16) = all_559_1_2635
% 110.66/75.66 | (364) ! [v0] : ! [v1] : ! [v2] : ( ~ (apply_binary_as_element(all_559_1_2635, all_559_1_2635, all_559_1_2635, all_559_0_2634, v0, v1) = v2) | ~ (element(v0, all_559_1_2635) = 0) | ? [v3] : ((v3 = v2 & meet(all_0_16_16, v0, v1) = v2) | ( ~ (v3 = 0) & element(v1, all_559_1_2635) = v3)))
% 110.66/75.66 | (365) the_L_meet(all_0_16_16) = all_559_0_2634
% 110.66/75.66 | (366) ! [v0] : ! [v1] : ! [v2] : ( ~ (meet(all_0_16_16, v0, v1) = v2) | ~ (element(v0, all_559_1_2635) = 0) | ? [v3] : ((v3 = v2 & apply_binary_as_element(all_559_1_2635, all_559_1_2635, all_559_1_2635, all_559_0_2634, v0, v1) = v2) | ( ~ (v3 = 0) & element(v1, all_559_1_2635) = v3)))
% 110.66/75.66 |
% 110.66/75.66 +-Applying beta-rule and splitting (355), into two cases.
% 110.66/75.66 |-Branch one:
% 110.66/75.66 | (367) ~ (all_560_1_2637 = 0) & join_semilatt_str(all_0_16_16) = all_560_1_2637
% 110.66/75.66 |
% 110.66/75.66 | Applying alpha-rule on (367) yields:
% 110.66/75.66 | (368) ~ (all_560_1_2637 = 0)
% 110.66/75.66 | (369) join_semilatt_str(all_0_16_16) = all_560_1_2637
% 110.66/75.66 |
% 110.66/75.66 | Instantiating formula (135) with all_0_16_16, 0, all_560_1_2637 and discharging atoms join_semilatt_str(all_0_16_16) = all_560_1_2637, join_semilatt_str(all_0_16_16) = 0, yields:
% 110.66/75.66 | (370) all_560_1_2637 = 0
% 110.66/75.66 |
% 110.66/75.66 | Equations (370) can reduce 368 to:
% 110.66/75.66 | (274) $false
% 110.66/75.66 |
% 110.66/75.66 |-The branch is then unsatisfiable
% 110.66/75.66 |-Branch two:
% 110.66/75.66 | (372) the_carrier(all_0_16_16) = all_560_1_2637 & the_L_join(all_0_16_16) = all_560_0_2636 & ! [v0] : ! [v1] : ! [v2] : ( ~ (join(all_0_16_16, v0, v1) = v2) | ~ (element(v0, all_560_1_2637) = 0) | ? [v3] : ((v3 = v2 & apply_binary_as_element(all_560_1_2637, all_560_1_2637, all_560_1_2637, all_560_0_2636, v0, v1) = v2) | ( ~ (v3 = 0) & element(v1, all_560_1_2637) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (apply_binary_as_element(all_560_1_2637, all_560_1_2637, all_560_1_2637, all_560_0_2636, v0, v1) = v2) | ~ (element(v0, all_560_1_2637) = 0) | ? [v3] : ((v3 = v2 & join(all_0_16_16, v0, v1) = v2) | ( ~ (v3 = 0) & element(v1, all_560_1_2637) = v3))) & ! [v0] : ! [v1] : ( ~ (element(v1, all_560_1_2637) = 0) | ~ (element(v0, all_560_1_2637) = 0) | ? [v2] : (join(all_0_16_16, v0, v1) = v2 & apply_binary_as_element(all_560_1_2637, all_560_1_2637, all_560_1_2637, all_560_0_2636, v0, v1) = v2))
% 110.75/75.66 |
% 110.75/75.66 | Applying alpha-rule on (372) yields:
% 110.75/75.66 | (373) ! [v0] : ! [v1] : ( ~ (element(v1, all_560_1_2637) = 0) | ~ (element(v0, all_560_1_2637) = 0) | ? [v2] : (join(all_0_16_16, v0, v1) = v2 & apply_binary_as_element(all_560_1_2637, all_560_1_2637, all_560_1_2637, all_560_0_2636, v0, v1) = v2))
% 110.75/75.66 | (374) ! [v0] : ! [v1] : ! [v2] : ( ~ (join(all_0_16_16, v0, v1) = v2) | ~ (element(v0, all_560_1_2637) = 0) | ? [v3] : ((v3 = v2 & apply_binary_as_element(all_560_1_2637, all_560_1_2637, all_560_1_2637, all_560_0_2636, v0, v1) = v2) | ( ~ (v3 = 0) & element(v1, all_560_1_2637) = v3)))
% 110.75/75.66 | (375) the_L_join(all_0_16_16) = all_560_0_2636
% 110.75/75.66 | (376) ! [v0] : ! [v1] : ! [v2] : ( ~ (apply_binary_as_element(all_560_1_2637, all_560_1_2637, all_560_1_2637, all_560_0_2636, v0, v1) = v2) | ~ (element(v0, all_560_1_2637) = 0) | ? [v3] : ((v3 = v2 & join(all_0_16_16, v0, v1) = v2) | ( ~ (v3 = 0) & element(v1, all_560_1_2637) = v3)))
% 110.75/75.66 | (377) the_carrier(all_0_16_16) = all_560_1_2637
% 110.75/75.66 |
% 110.75/75.66 +-Applying beta-rule and splitting (265), into two cases.
% 110.75/75.66 |-Branch one:
% 110.75/75.66 | (378) (all_285_0_364 = 0 & empty_carrier(all_0_16_16) = 0) | ( ~ (all_285_0_364 = 0) & join_semilatt_str(all_0_16_16) = all_285_0_364)
% 110.75/75.66 |
% 110.75/75.66 +-Applying beta-rule and splitting (378), into two cases.
% 110.75/75.66 |-Branch one:
% 110.75/75.66 | (379) all_285_0_364 = 0 & empty_carrier(all_0_16_16) = 0
% 110.75/75.66 |
% 110.75/75.66 | Applying alpha-rule on (379) yields:
% 110.75/75.66 | (380) all_285_0_364 = 0
% 110.75/75.66 | (272) empty_carrier(all_0_16_16) = 0
% 110.75/75.66 |
% 110.75/75.66 | Instantiating formula (93) with all_0_16_16, 0, all_88_0_128 and discharging atoms empty_carrier(all_0_16_16) = all_88_0_128, empty_carrier(all_0_16_16) = 0, yields:
% 110.75/75.66 | (273) all_88_0_128 = 0
% 110.75/75.66 |
% 110.75/75.66 | Equations (273) can reduce 214 to:
% 110.75/75.66 | (274) $false
% 110.75/75.66 |
% 110.75/75.66 |-The branch is then unsatisfiable
% 110.75/75.66 |-Branch two:
% 110.75/75.66 | (384) ~ (all_285_0_364 = 0) & join_semilatt_str(all_0_16_16) = all_285_0_364
% 110.75/75.66 |
% 110.75/75.66 | Applying alpha-rule on (384) yields:
% 110.75/75.66 | (385) ~ (all_285_0_364 = 0)
% 110.75/75.66 | (386) join_semilatt_str(all_0_16_16) = all_285_0_364
% 110.75/75.66 |
% 110.75/75.66 | Instantiating formula (135) with all_0_16_16, 0, all_285_0_364 and discharging atoms join_semilatt_str(all_0_16_16) = all_285_0_364, join_semilatt_str(all_0_16_16) = 0, yields:
% 110.75/75.66 | (380) all_285_0_364 = 0
% 110.75/75.66 |
% 110.75/75.66 | Equations (380) can reduce 385 to:
% 110.75/75.66 | (274) $false
% 110.75/75.66 |
% 110.75/75.66 |-The branch is then unsatisfiable
% 110.75/75.66 |-Branch two:
% 110.75/75.66 | (389) the_carrier(all_0_16_16) = all_285_0_364 & ! [v0] : ! [v1] : ! [v2] : ( ~ (join(all_0_16_16, v0, v1) = v2) | ~ (element(v0, all_285_0_364) = 0) | ? [v3] : ((v3 = v2 & apply_binary_as_element(all_285_0_364, all_285_0_364, all_285_0_364, all_111_2_179, v0, v1) = v2) | ( ~ (v3 = 0) & element(v1, all_285_0_364) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (apply_binary_as_element(all_285_0_364, all_285_0_364, all_285_0_364, all_111_2_179, v0, v1) = v2) | ~ (element(v0, all_285_0_364) = 0) | ? [v3] : ((v3 = v2 & join(all_0_16_16, v0, v1) = v2) | ( ~ (v3 = 0) & element(v1, all_285_0_364) = v3))) & ! [v0] : ! [v1] : ( ~ (element(v1, all_285_0_364) = 0) | ~ (element(v0, all_285_0_364) = 0) | ? [v2] : (join(all_0_16_16, v0, v1) = v2 & apply_binary_as_element(all_285_0_364, all_285_0_364, all_285_0_364, all_111_2_179, v0, v1) = v2))
% 110.75/75.66 |
% 110.75/75.66 | Applying alpha-rule on (389) yields:
% 110.75/75.66 | (390) the_carrier(all_0_16_16) = all_285_0_364
% 110.75/75.66 | (391) ! [v0] : ! [v1] : ! [v2] : ( ~ (join(all_0_16_16, v0, v1) = v2) | ~ (element(v0, all_285_0_364) = 0) | ? [v3] : ((v3 = v2 & apply_binary_as_element(all_285_0_364, all_285_0_364, all_285_0_364, all_111_2_179, v0, v1) = v2) | ( ~ (v3 = 0) & element(v1, all_285_0_364) = v3)))
% 110.75/75.66 | (392) ! [v0] : ! [v1] : ! [v2] : ( ~ (apply_binary_as_element(all_285_0_364, all_285_0_364, all_285_0_364, all_111_2_179, v0, v1) = v2) | ~ (element(v0, all_285_0_364) = 0) | ? [v3] : ((v3 = v2 & join(all_0_16_16, v0, v1) = v2) | ( ~ (v3 = 0) & element(v1, all_285_0_364) = v3)))
% 110.75/75.66 | (393) ! [v0] : ! [v1] : ( ~ (element(v1, all_285_0_364) = 0) | ~ (element(v0, all_285_0_364) = 0) | ? [v2] : (join(all_0_16_16, v0, v1) = v2 & apply_binary_as_element(all_285_0_364, all_285_0_364, all_285_0_364, all_111_2_179, v0, v1) = v2))
% 110.75/75.66 |
% 110.75/75.66 | Instantiating formula (55) with all_0_17_17, all_0_14_14, all_116_1_189, all_118_1_191 and discharging atoms set_union2(all_0_17_17, all_0_14_14) = all_118_1_191, set_union2(all_0_17_17, all_0_14_14) = all_116_1_189, yields:
% 110.75/75.66 | (394) all_118_1_191 = all_116_1_189
% 110.75/75.66 |
% 110.75/75.66 | Instantiating formula (2) with all_0_16_16, all_560_1_2637, all_0_15_15 and discharging atoms the_carrier(all_0_16_16) = all_560_1_2637, the_carrier(all_0_16_16) = all_0_15_15, yields:
% 110.75/75.66 | (395) all_560_1_2637 = all_0_15_15
% 110.75/75.66 |
% 110.75/75.66 | Instantiating formula (2) with all_0_16_16, all_286_3_368, all_560_1_2637 and discharging atoms the_carrier(all_0_16_16) = all_560_1_2637, the_carrier(all_0_16_16) = all_286_3_368, yields:
% 110.75/75.67 | (396) all_560_1_2637 = all_286_3_368
% 110.75/75.67 |
% 110.75/75.67 | Instantiating formula (2) with all_0_16_16, all_286_3_368, all_559_1_2635 and discharging atoms the_carrier(all_0_16_16) = all_559_1_2635, the_carrier(all_0_16_16) = all_286_3_368, yields:
% 110.75/75.67 | (397) all_559_1_2635 = all_286_3_368
% 110.75/75.67 |
% 110.75/75.67 | Instantiating formula (2) with all_0_16_16, all_286_3_368, all_447_0_1607 and discharging atoms the_carrier(all_0_16_16) = all_447_0_1607, the_carrier(all_0_16_16) = all_286_3_368, yields:
% 110.75/75.67 | (398) all_447_0_1607 = all_286_3_368
% 110.75/75.67 |
% 110.75/75.67 | Instantiating formula (2) with all_0_16_16, all_285_0_364, all_559_1_2635 and discharging atoms the_carrier(all_0_16_16) = all_559_1_2635, the_carrier(all_0_16_16) = all_285_0_364, yields:
% 110.75/75.67 | (399) all_559_1_2635 = all_285_0_364
% 110.75/75.67 |
% 110.75/75.67 | Instantiating formula (2) with all_0_16_16, all_249_3_310, all_447_0_1607 and discharging atoms the_carrier(all_0_16_16) = all_447_0_1607, the_carrier(all_0_16_16) = all_249_3_310, yields:
% 110.75/75.67 | (400) all_447_0_1607 = all_249_3_310
% 110.75/75.67 |
% 110.75/75.67 | Instantiating formula (2) with all_0_16_16, all_248_0_306, all_286_3_368 and discharging atoms the_carrier(all_0_16_16) = all_286_3_368, the_carrier(all_0_16_16) = all_248_0_306, yields:
% 110.75/75.67 | (401) all_286_3_368 = all_248_0_306
% 110.75/75.67 |
% 110.75/75.67 | Combining equations (396,395) yields a new equation:
% 110.75/75.67 | (402) all_286_3_368 = all_0_15_15
% 110.75/75.67 |
% 110.75/75.67 | Simplifying 402 yields:
% 110.75/75.67 | (403) all_286_3_368 = all_0_15_15
% 110.75/75.67 |
% 110.75/75.67 | Combining equations (397,399) yields a new equation:
% 110.75/75.67 | (404) all_286_3_368 = all_285_0_364
% 110.75/75.67 |
% 110.75/75.67 | Simplifying 404 yields:
% 110.75/75.67 | (405) all_286_3_368 = all_285_0_364
% 110.75/75.67 |
% 110.75/75.67 | Combining equations (398,400) yields a new equation:
% 110.75/75.67 | (406) all_286_3_368 = all_249_3_310
% 110.75/75.67 |
% 110.75/75.67 | Simplifying 406 yields:
% 110.75/75.67 | (407) all_286_3_368 = all_249_3_310
% 110.75/75.67 |
% 110.75/75.67 | Combining equations (401,405) yields a new equation:
% 110.75/75.67 | (408) all_285_0_364 = all_248_0_306
% 110.75/75.67 |
% 110.75/75.67 | Combining equations (403,405) yields a new equation:
% 110.75/75.67 | (409) all_285_0_364 = all_0_15_15
% 110.75/75.67 |
% 110.75/75.67 | Combining equations (407,405) yields a new equation:
% 110.75/75.67 | (410) all_285_0_364 = all_249_3_310
% 110.75/75.67 |
% 110.75/75.67 | Combining equations (408,410) yields a new equation:
% 110.75/75.67 | (411) all_249_3_310 = all_248_0_306
% 110.75/75.67 |
% 110.75/75.67 | Combining equations (409,410) yields a new equation:
% 110.75/75.67 | (412) all_249_3_310 = all_0_15_15
% 110.75/75.67 |
% 110.75/75.67 | Combining equations (412,411) yields a new equation:
% 110.75/75.67 | (413) all_248_0_306 = all_0_15_15
% 110.75/75.67 |
% 110.75/75.67 | From (394) and (254) follows:
% 110.75/75.67 | (414) subset(all_0_17_17, all_116_1_189) = 0
% 110.75/75.67 |
% 110.75/75.67 | From (394) and (225) follows:
% 110.75/75.67 | (415) join(all_0_16_16, all_0_17_17, all_0_14_14) = all_116_1_189
% 110.75/75.67 |
% 110.75/75.67 | From (413) and (301) follows:
% 110.75/75.67 | (3) the_carrier(all_0_16_16) = all_0_15_15
% 110.75/75.67 |
% 110.75/75.67 +-Applying beta-rule and splitting (264), into two cases.
% 110.75/75.67 |-Branch one:
% 110.75/75.67 | (417) (all_254_0_318 = 0 & element(all_0_14_14, all_254_1_319) = 0 & the_carrier(all_0_16_16) = all_254_1_319) | (all_254_1_319 = 0 & empty_carrier(all_0_16_16) = 0) | ( ~ (all_254_0_318 = 0) & element(all_0_14_14, all_254_1_319) = all_254_0_318 & the_carrier(all_0_16_16) = all_254_1_319)
% 110.75/75.67 |
% 110.75/75.67 +-Applying beta-rule and splitting (417), into two cases.
% 110.75/75.67 |-Branch one:
% 110.75/75.67 | (418) (all_254_0_318 = 0 & element(all_0_14_14, all_254_1_319) = 0 & the_carrier(all_0_16_16) = all_254_1_319) | (all_254_1_319 = 0 & empty_carrier(all_0_16_16) = 0)
% 110.75/75.67 |
% 110.75/75.67 +-Applying beta-rule and splitting (418), into two cases.
% 110.75/75.67 |-Branch one:
% 110.75/75.67 | (419) all_254_0_318 = 0 & element(all_0_14_14, all_254_1_319) = 0 & the_carrier(all_0_16_16) = all_254_1_319
% 110.75/75.67 |
% 110.75/75.67 | Applying alpha-rule on (419) yields:
% 110.75/75.67 | (420) all_254_0_318 = 0
% 110.75/75.67 | (421) element(all_0_14_14, all_254_1_319) = 0
% 110.75/75.67 | (422) the_carrier(all_0_16_16) = all_254_1_319
% 110.75/75.67 |
% 110.75/75.67 +-Applying beta-rule and splitting (268), into two cases.
% 110.75/75.67 |-Branch one:
% 110.75/75.67 | (423) (all_341_0_487 = 0 & element(all_0_14_14, all_341_1_488) = 0 & the_carrier(all_0_16_16) = all_341_1_488) | (all_341_1_488 = 0 & empty_carrier(all_0_16_16) = 0) | ( ~ (all_341_0_487 = 0) & element(all_0_14_14, all_341_1_488) = all_341_0_487 & the_carrier(all_0_16_16) = all_341_1_488)
% 110.75/75.67 |
% 110.75/75.67 +-Applying beta-rule and splitting (423), into two cases.
% 110.75/75.67 |-Branch one:
% 110.75/75.67 | (424) (all_341_0_487 = 0 & element(all_0_14_14, all_341_1_488) = 0 & the_carrier(all_0_16_16) = all_341_1_488) | (all_341_1_488 = 0 & empty_carrier(all_0_16_16) = 0)
% 110.75/75.67 |
% 110.75/75.67 +-Applying beta-rule and splitting (424), into two cases.
% 110.75/75.67 |-Branch one:
% 110.75/75.67 | (425) all_341_0_487 = 0 & element(all_0_14_14, all_341_1_488) = 0 & the_carrier(all_0_16_16) = all_341_1_488
% 110.75/75.67 |
% 110.75/75.67 | Applying alpha-rule on (425) yields:
% 110.75/75.67 | (426) all_341_0_487 = 0
% 110.75/75.67 | (427) element(all_0_14_14, all_341_1_488) = 0
% 110.75/75.67 | (428) the_carrier(all_0_16_16) = all_341_1_488
% 110.75/75.67 |
% 110.75/75.67 | Instantiating formula (2) with all_0_16_16, all_341_1_488, all_0_15_15 and discharging atoms the_carrier(all_0_16_16) = all_341_1_488, the_carrier(all_0_16_16) = all_0_15_15, yields:
% 110.75/75.67 | (429) all_341_1_488 = all_0_15_15
% 110.75/75.67 |
% 110.75/75.67 | Instantiating formula (2) with all_0_16_16, all_254_1_319, all_341_1_488 and discharging atoms the_carrier(all_0_16_16) = all_341_1_488, the_carrier(all_0_16_16) = all_254_1_319, yields:
% 110.75/75.67 | (430) all_341_1_488 = all_254_1_319
% 110.75/75.67 |
% 110.75/75.67 | Combining equations (430,429) yields a new equation:
% 110.75/75.67 | (431) all_254_1_319 = all_0_15_15
% 110.75/75.67 |
% 110.75/75.67 | Simplifying 431 yields:
% 110.75/75.67 | (432) all_254_1_319 = all_0_15_15
% 110.75/75.67 |
% 110.75/75.67 | From (432) and (421) follows:
% 110.75/75.67 | (173) element(all_0_14_14, all_0_15_15) = 0
% 110.75/75.68 |
% 110.75/75.68 +-Applying beta-rule and splitting (42), into two cases.
% 110.75/75.68 |-Branch one:
% 110.75/75.68 | (434) all_0_12_12 = 0 & ~ (all_0_13_13 = 0)
% 110.75/75.68 |
% 110.75/75.68 | Applying alpha-rule on (434) yields:
% 110.75/75.68 | (435) all_0_12_12 = 0
% 110.75/75.68 | (436) ~ (all_0_13_13 = 0)
% 110.75/75.68 |
% 110.75/75.68 | From (435) and (9) follows:
% 110.75/75.68 | (437) subset(all_0_17_17, all_0_14_14) = 0
% 110.75/75.68 |
% 110.75/75.68 +-Applying beta-rule and splitting (217), into two cases.
% 110.75/75.68 |-Branch one:
% 110.75/75.68 | (438) (all_115_0_187 = 0 & empty_carrier(all_0_16_16) = 0) | ( ~ (all_115_0_187 = 0) & join_semilatt_str(all_0_16_16) = all_115_0_187) | ( ~ (all_115_0_187 = 0) & element(all_0_14_14, all_0_15_15) = all_115_0_187)
% 110.75/75.68 |
% 110.75/75.68 +-Applying beta-rule and splitting (438), into two cases.
% 110.75/75.68 |-Branch one:
% 110.75/75.68 | (439) (all_115_0_187 = 0 & empty_carrier(all_0_16_16) = 0) | ( ~ (all_115_0_187 = 0) & join_semilatt_str(all_0_16_16) = all_115_0_187)
% 110.75/75.68 |
% 110.75/75.68 +-Applying beta-rule and splitting (439), into two cases.
% 110.75/75.68 |-Branch one:
% 110.75/75.68 | (440) all_115_0_187 = 0 & empty_carrier(all_0_16_16) = 0
% 110.75/75.68 |
% 110.75/75.68 | Applying alpha-rule on (440) yields:
% 110.75/75.68 | (441) all_115_0_187 = 0
% 110.75/75.68 | (272) empty_carrier(all_0_16_16) = 0
% 110.75/75.68 |
% 110.75/75.68 | Instantiating formula (93) with all_0_16_16, 0, all_88_0_128 and discharging atoms empty_carrier(all_0_16_16) = all_88_0_128, empty_carrier(all_0_16_16) = 0, yields:
% 110.75/75.68 | (273) all_88_0_128 = 0
% 110.75/75.68 |
% 110.75/75.68 | Equations (273) can reduce 214 to:
% 110.75/75.68 | (274) $false
% 110.75/75.68 |
% 110.75/75.68 |-The branch is then unsatisfiable
% 110.75/75.68 |-Branch two:
% 110.75/75.68 | (445) ~ (all_115_0_187 = 0) & join_semilatt_str(all_0_16_16) = all_115_0_187
% 110.75/75.68 |
% 110.75/75.68 | Applying alpha-rule on (445) yields:
% 110.75/75.68 | (446) ~ (all_115_0_187 = 0)
% 110.75/75.68 | (447) join_semilatt_str(all_0_16_16) = all_115_0_187
% 110.75/75.68 |
% 110.75/75.68 | Instantiating formula (135) with all_0_16_16, all_115_0_187, 0 and discharging atoms join_semilatt_str(all_0_16_16) = all_115_0_187, join_semilatt_str(all_0_16_16) = 0, yields:
% 110.75/75.68 | (441) all_115_0_187 = 0
% 110.75/75.68 |
% 110.75/75.68 | Equations (441) can reduce 446 to:
% 110.75/75.68 | (274) $false
% 110.75/75.68 |
% 110.75/75.68 |-The branch is then unsatisfiable
% 110.75/75.68 |-Branch two:
% 110.75/75.68 | (450) ~ (all_115_0_187 = 0) & element(all_0_14_14, all_0_15_15) = all_115_0_187
% 110.75/75.68 |
% 110.75/75.68 | Applying alpha-rule on (450) yields:
% 110.75/75.68 | (446) ~ (all_115_0_187 = 0)
% 110.75/75.68 | (452) element(all_0_14_14, all_0_15_15) = all_115_0_187
% 110.75/75.68 |
% 110.75/75.68 | Instantiating formula (172) with all_0_14_14, all_0_15_15, all_115_0_187, 0 and discharging atoms element(all_0_14_14, all_0_15_15) = all_115_0_187, element(all_0_14_14, all_0_15_15) = 0, yields:
% 110.75/75.68 | (441) all_115_0_187 = 0
% 110.75/75.68 |
% 110.75/75.68 | Equations (441) can reduce 446 to:
% 110.75/75.68 | (274) $false
% 110.75/75.68 |
% 110.75/75.68 |-The branch is then unsatisfiable
% 110.75/75.68 |-Branch two:
% 110.75/75.68 | (455) ( ~ (all_0_13_13 = 0) | (all_115_0_187 = all_0_14_14 & join(all_0_16_16, all_0_17_17, all_0_14_14) = all_0_14_14)) & (all_0_13_13 = 0 | ( ~ (all_115_0_187 = all_0_14_14) & join(all_0_16_16, all_0_17_17, all_0_14_14) = all_115_0_187))
% 110.75/75.68 |
% 110.75/75.68 | Applying alpha-rule on (455) yields:
% 110.75/75.68 | (456) ~ (all_0_13_13 = 0) | (all_115_0_187 = all_0_14_14 & join(all_0_16_16, all_0_17_17, all_0_14_14) = all_0_14_14)
% 110.75/75.68 | (457) all_0_13_13 = 0 | ( ~ (all_115_0_187 = all_0_14_14) & join(all_0_16_16, all_0_17_17, all_0_14_14) = all_115_0_187)
% 110.75/75.68 |
% 110.75/75.68 +-Applying beta-rule and splitting (267), into two cases.
% 110.75/75.68 |-Branch one:
% 110.75/75.68 | (458) (all_311_0_412 = 0 & empty_carrier(all_0_16_16) = 0) | ( ~ (all_311_0_412 = 0) & join_semilatt_str(all_0_16_16) = all_311_0_412) | ( ~ (all_311_0_412 = 0) & element(all_0_14_14, all_0_15_15) = all_311_0_412)
% 110.75/75.68 |
% 110.75/75.68 +-Applying beta-rule and splitting (458), into two cases.
% 110.75/75.68 |-Branch one:
% 110.75/75.68 | (459) (all_311_0_412 = 0 & empty_carrier(all_0_16_16) = 0) | ( ~ (all_311_0_412 = 0) & join_semilatt_str(all_0_16_16) = all_311_0_412)
% 110.75/75.68 |
% 110.75/75.68 +-Applying beta-rule and splitting (459), into two cases.
% 110.75/75.68 |-Branch one:
% 110.75/75.68 | (460) all_311_0_412 = 0 & empty_carrier(all_0_16_16) = 0
% 110.75/75.68 |
% 110.75/75.68 | Applying alpha-rule on (460) yields:
% 110.75/75.68 | (461) all_311_0_412 = 0
% 110.75/75.68 | (272) empty_carrier(all_0_16_16) = 0
% 110.75/75.68 |
% 110.75/75.68 | Instantiating formula (93) with all_0_16_16, 0, all_88_0_128 and discharging atoms empty_carrier(all_0_16_16) = all_88_0_128, empty_carrier(all_0_16_16) = 0, yields:
% 110.75/75.68 | (273) all_88_0_128 = 0
% 110.75/75.68 |
% 110.75/75.68 | Equations (273) can reduce 214 to:
% 110.75/75.68 | (274) $false
% 110.75/75.68 |
% 110.75/75.68 |-The branch is then unsatisfiable
% 110.75/75.68 |-Branch two:
% 110.75/75.68 | (465) ~ (all_311_0_412 = 0) & join_semilatt_str(all_0_16_16) = all_311_0_412
% 110.75/75.68 |
% 110.75/75.68 | Applying alpha-rule on (465) yields:
% 110.75/75.68 | (466) ~ (all_311_0_412 = 0)
% 110.75/75.68 | (467) join_semilatt_str(all_0_16_16) = all_311_0_412
% 110.75/75.68 |
% 110.75/75.68 | Instantiating formula (135) with all_0_16_16, all_311_0_412, 0 and discharging atoms join_semilatt_str(all_0_16_16) = all_311_0_412, join_semilatt_str(all_0_16_16) = 0, yields:
% 110.75/75.68 | (461) all_311_0_412 = 0
% 110.75/75.68 |
% 110.75/75.68 | Equations (461) can reduce 466 to:
% 110.75/75.68 | (274) $false
% 110.75/75.68 |
% 110.75/75.68 |-The branch is then unsatisfiable
% 110.75/75.68 |-Branch two:
% 110.75/75.68 | (470) ~ (all_311_0_412 = 0) & element(all_0_14_14, all_0_15_15) = all_311_0_412
% 110.75/75.68 |
% 110.75/75.68 | Applying alpha-rule on (470) yields:
% 110.75/75.69 | (466) ~ (all_311_0_412 = 0)
% 110.75/75.69 | (472) element(all_0_14_14, all_0_15_15) = all_311_0_412
% 110.75/75.69 |
% 110.75/75.69 | Instantiating formula (172) with all_0_14_14, all_0_15_15, all_311_0_412, 0 and discharging atoms element(all_0_14_14, all_0_15_15) = all_311_0_412, element(all_0_14_14, all_0_15_15) = 0, yields:
% 110.75/75.69 | (461) all_311_0_412 = 0
% 110.75/75.69 |
% 110.75/75.69 | Equations (461) can reduce 466 to:
% 110.75/75.69 | (274) $false
% 110.75/75.69 |
% 110.75/75.69 |-The branch is then unsatisfiable
% 110.75/75.69 |-Branch two:
% 110.75/75.69 | (475) ( ~ (all_118_1_191 = all_0_14_14) | (all_311_0_412 = 0 & below(all_0_16_16, all_0_17_17, all_0_14_14) = 0)) & (all_118_1_191 = all_0_14_14 | ( ~ (all_311_0_412 = 0) & below(all_0_16_16, all_0_17_17, all_0_14_14) = all_311_0_412))
% 110.75/75.69 |
% 110.75/75.69 | Applying alpha-rule on (475) yields:
% 110.75/75.69 | (476) ~ (all_118_1_191 = all_0_14_14) | (all_311_0_412 = 0 & below(all_0_16_16, all_0_17_17, all_0_14_14) = 0)
% 110.75/75.69 | (477) all_118_1_191 = all_0_14_14 | ( ~ (all_311_0_412 = 0) & below(all_0_16_16, all_0_17_17, all_0_14_14) = all_311_0_412)
% 110.75/75.69 |
% 110.75/75.69 +-Applying beta-rule and splitting (233), into two cases.
% 110.75/75.69 |-Branch one:
% 110.75/75.69 | (478) (all_128_1_210 = 0 & empty_carrier(all_0_16_16) = 0) | ( ~ (all_128_1_210 = 0) & join_semilatt_str(all_0_16_16) = all_128_1_210)
% 110.75/75.69 |
% 110.75/75.69 +-Applying beta-rule and splitting (478), into two cases.
% 110.75/75.69 |-Branch one:
% 110.75/75.69 | (479) all_128_1_210 = 0 & empty_carrier(all_0_16_16) = 0
% 110.75/75.69 |
% 110.75/75.69 | Applying alpha-rule on (479) yields:
% 110.75/75.69 | (480) all_128_1_210 = 0
% 110.75/75.69 | (272) empty_carrier(all_0_16_16) = 0
% 110.75/75.69 |
% 110.75/75.69 | Instantiating formula (93) with all_0_16_16, 0, all_88_0_128 and discharging atoms empty_carrier(all_0_16_16) = all_88_0_128, empty_carrier(all_0_16_16) = 0, yields:
% 110.75/75.69 | (273) all_88_0_128 = 0
% 110.75/75.69 |
% 110.75/75.69 | Equations (273) can reduce 214 to:
% 110.75/75.69 | (274) $false
% 110.75/75.69 |
% 110.75/75.69 |-The branch is then unsatisfiable
% 110.75/75.69 |-Branch two:
% 110.75/75.69 | (484) ~ (all_128_1_210 = 0) & join_semilatt_str(all_0_16_16) = all_128_1_210
% 110.75/75.69 |
% 110.75/75.69 | Applying alpha-rule on (484) yields:
% 110.75/75.69 | (485) ~ (all_128_1_210 = 0)
% 110.75/75.69 | (486) join_semilatt_str(all_0_16_16) = all_128_1_210
% 110.75/75.69 |
% 110.75/75.69 | Instantiating formula (135) with all_0_16_16, all_128_1_210, 0 and discharging atoms join_semilatt_str(all_0_16_16) = all_128_1_210, join_semilatt_str(all_0_16_16) = 0, yields:
% 110.75/75.69 | (480) all_128_1_210 = 0
% 110.75/75.69 |
% 110.75/75.69 | Equations (480) can reduce 485 to:
% 110.75/75.69 | (274) $false
% 110.75/75.69 |
% 110.75/75.69 |-The branch is then unsatisfiable
% 110.75/75.69 |-Branch two:
% 110.75/75.69 | (489) ((all_128_0_209 = all_0_14_14 & join(all_0_16_16, all_0_17_17, all_0_14_14) = all_0_14_14) | ( ~ (all_128_1_210 = 0) & below(all_0_16_16, all_0_17_17, all_0_14_14) = all_128_1_210)) & ((all_128_1_210 = 0 & below(all_0_16_16, all_0_17_17, all_0_14_14) = 0) | ( ~ (all_128_0_209 = all_0_14_14) & join(all_0_16_16, all_0_17_17, all_0_14_14) = all_128_0_209))
% 110.75/75.69 |
% 110.75/75.69 | Applying alpha-rule on (489) yields:
% 110.75/75.69 | (490) (all_128_0_209 = all_0_14_14 & join(all_0_16_16, all_0_17_17, all_0_14_14) = all_0_14_14) | ( ~ (all_128_1_210 = 0) & below(all_0_16_16, all_0_17_17, all_0_14_14) = all_128_1_210)
% 110.75/75.69 | (491) (all_128_1_210 = 0 & below(all_0_16_16, all_0_17_17, all_0_14_14) = 0) | ( ~ (all_128_0_209 = all_0_14_14) & join(all_0_16_16, all_0_17_17, all_0_14_14) = all_128_0_209)
% 110.75/75.69 |
% 110.75/75.69 +-Applying beta-rule and splitting (491), into two cases.
% 110.75/75.69 |-Branch one:
% 110.75/75.69 | (492) all_128_1_210 = 0 & below(all_0_16_16, all_0_17_17, all_0_14_14) = 0
% 110.75/75.69 |
% 110.75/75.69 | Applying alpha-rule on (492) yields:
% 110.75/75.69 | (480) all_128_1_210 = 0
% 110.75/75.69 | (494) below(all_0_16_16, all_0_17_17, all_0_14_14) = 0
% 110.75/75.69 |
% 110.75/75.69 +-Applying beta-rule and splitting (457), into two cases.
% 110.75/75.69 |-Branch one:
% 110.75/75.69 | (495) all_0_13_13 = 0
% 110.75/75.69 |
% 110.75/75.69 | Equations (495) can reduce 436 to:
% 110.75/75.69 | (274) $false
% 110.75/75.69 |
% 110.75/75.69 |-The branch is then unsatisfiable
% 110.75/75.69 |-Branch two:
% 110.75/75.69 | (436) ~ (all_0_13_13 = 0)
% 110.75/75.69 | (498) ~ (all_115_0_187 = all_0_14_14) & join(all_0_16_16, all_0_17_17, all_0_14_14) = all_115_0_187
% 110.75/75.69 |
% 110.75/75.69 +-Applying beta-rule and splitting (253), into two cases.
% 110.75/75.69 |-Branch one:
% 110.75/75.69 | (499) all_118_1_191 = all_0_14_14
% 110.75/75.69 |
% 110.75/75.69 | Combining equations (499,394) yields a new equation:
% 110.75/75.69 | (500) all_116_1_189 = all_0_14_14
% 110.75/75.69 |
% 110.75/75.69 | Combining equations (500,394) yields a new equation:
% 110.75/75.69 | (499) all_118_1_191 = all_0_14_14
% 110.75/75.69 |
% 110.75/75.69 +-Applying beta-rule and splitting (476), into two cases.
% 110.75/75.69 |-Branch one:
% 110.75/75.69 | (502) ~ (all_118_1_191 = all_0_14_14)
% 110.75/75.69 |
% 110.75/75.69 | Equations (499) can reduce 502 to:
% 110.75/75.69 | (274) $false
% 110.75/75.69 |
% 110.75/75.69 |-The branch is then unsatisfiable
% 110.75/75.69 |-Branch two:
% 110.75/75.69 | (499) all_118_1_191 = all_0_14_14
% 110.75/75.69 | (505) all_311_0_412 = 0 & below(all_0_16_16, all_0_17_17, all_0_14_14) = 0
% 110.75/75.69 |
% 110.75/75.69 | Applying alpha-rule on (505) yields:
% 110.75/75.69 | (461) all_311_0_412 = 0
% 110.75/75.69 | (494) below(all_0_16_16, all_0_17_17, all_0_14_14) = 0
% 110.75/75.69 |
% 110.75/75.69 | Instantiating formula (169) with all_0_16_16, all_0_17_17, all_0_14_14, 0, all_0_13_13 and discharging atoms below(all_0_16_16, all_0_17_17, all_0_14_14) = all_0_13_13, below(all_0_16_16, all_0_17_17, all_0_14_14) = 0, yields:
% 110.75/75.69 | (495) all_0_13_13 = 0
% 110.75/75.69 |
% 110.75/75.70 | Equations (495) can reduce 436 to:
% 110.75/75.70 | (274) $false
% 110.75/75.70 |
% 110.75/75.70 |-The branch is then unsatisfiable
% 110.75/75.70 |-Branch two:
% 110.75/75.70 | (502) ~ (all_118_1_191 = all_0_14_14)
% 110.75/75.70 | (511) ? [v0] : ( ~ (v0 = 0) & subset(all_0_17_17, all_0_14_14) = v0)
% 110.75/75.70 |
% 110.75/75.70 | Equations (394) can reduce 502 to:
% 110.75/75.70 | (512) ~ (all_116_1_189 = all_0_14_14)
% 110.75/75.70 |
% 110.75/75.70 +-Applying beta-rule and splitting (477), into two cases.
% 110.75/75.70 |-Branch one:
% 110.75/75.70 | (499) all_118_1_191 = all_0_14_14
% 110.75/75.70 |
% 110.75/75.70 | Combining equations (499,394) yields a new equation:
% 110.75/75.70 | (500) all_116_1_189 = all_0_14_14
% 110.75/75.70 |
% 110.75/75.70 | Equations (500) can reduce 512 to:
% 110.75/75.70 | (274) $false
% 110.75/75.70 |
% 110.75/75.70 |-The branch is then unsatisfiable
% 110.75/75.70 |-Branch two:
% 110.75/75.70 | (502) ~ (all_118_1_191 = all_0_14_14)
% 110.75/75.70 | (517) ~ (all_311_0_412 = 0) & below(all_0_16_16, all_0_17_17, all_0_14_14) = all_311_0_412
% 110.75/75.70 |
% 110.75/75.70 | Applying alpha-rule on (517) yields:
% 110.75/75.70 | (466) ~ (all_311_0_412 = 0)
% 110.75/75.70 | (519) below(all_0_16_16, all_0_17_17, all_0_14_14) = all_311_0_412
% 110.75/75.70 |
% 110.75/75.70 | Instantiating formula (169) with all_0_16_16, all_0_17_17, all_0_14_14, all_311_0_412, all_0_13_13 and discharging atoms below(all_0_16_16, all_0_17_17, all_0_14_14) = all_311_0_412, below(all_0_16_16, all_0_17_17, all_0_14_14) = all_0_13_13, yields:
% 110.75/75.70 | (520) all_311_0_412 = all_0_13_13
% 110.75/75.70 |
% 110.75/75.70 | Instantiating formula (169) with all_0_16_16, all_0_17_17, all_0_14_14, 0, all_311_0_412 and discharging atoms below(all_0_16_16, all_0_17_17, all_0_14_14) = all_311_0_412, below(all_0_16_16, all_0_17_17, all_0_14_14) = 0, yields:
% 110.75/75.70 | (461) all_311_0_412 = 0
% 110.75/75.70 |
% 110.75/75.70 | Combining equations (461,520) yields a new equation:
% 110.75/75.70 | (495) all_0_13_13 = 0
% 110.75/75.70 |
% 110.75/75.70 | Equations (495) can reduce 436 to:
% 110.75/75.70 | (274) $false
% 110.75/75.70 |
% 110.75/75.70 |-The branch is then unsatisfiable
% 110.75/75.70 |-Branch two:
% 110.75/75.70 | (524) ~ (all_128_0_209 = all_0_14_14) & join(all_0_16_16, all_0_17_17, all_0_14_14) = all_128_0_209
% 110.75/75.70 |
% 110.75/75.70 | Applying alpha-rule on (524) yields:
% 110.75/75.70 | (525) ~ (all_128_0_209 = all_0_14_14)
% 110.75/75.70 | (526) join(all_0_16_16, all_0_17_17, all_0_14_14) = all_128_0_209
% 110.75/75.70 |
% 110.75/75.70 +-Applying beta-rule and splitting (476), into two cases.
% 110.75/75.70 |-Branch one:
% 110.75/75.70 | (502) ~ (all_118_1_191 = all_0_14_14)
% 110.75/75.70 |
% 110.75/75.70 | Equations (394) can reduce 502 to:
% 110.75/75.70 | (512) ~ (all_116_1_189 = all_0_14_14)
% 110.75/75.70 |
% 110.75/75.70 +-Applying beta-rule and splitting (477), into two cases.
% 110.75/75.70 |-Branch one:
% 110.75/75.70 | (499) all_118_1_191 = all_0_14_14
% 110.75/75.70 |
% 110.75/75.70 | Combining equations (394,499) yields a new equation:
% 110.75/75.70 | (530) all_116_1_189 = all_0_14_14
% 110.75/75.70 |
% 110.75/75.70 | Simplifying 530 yields:
% 110.75/75.70 | (500) all_116_1_189 = all_0_14_14
% 110.75/75.70 |
% 110.75/75.70 | Equations (500) can reduce 512 to:
% 110.75/75.70 | (274) $false
% 110.75/75.70 |
% 110.75/75.70 |-The branch is then unsatisfiable
% 110.75/75.70 |-Branch two:
% 110.75/75.70 | (502) ~ (all_118_1_191 = all_0_14_14)
% 110.75/75.70 | (517) ~ (all_311_0_412 = 0) & below(all_0_16_16, all_0_17_17, all_0_14_14) = all_311_0_412
% 110.75/75.70 |
% 110.75/75.70 | Equations (394) can reduce 502 to:
% 110.75/75.70 | (512) ~ (all_116_1_189 = all_0_14_14)
% 110.75/75.70 |
% 110.75/75.70 +-Applying beta-rule and splitting (253), into two cases.
% 110.75/75.70 |-Branch one:
% 110.75/75.70 | (499) all_118_1_191 = all_0_14_14
% 110.75/75.70 |
% 110.75/75.70 | Combining equations (394,499) yields a new equation:
% 110.75/75.70 | (530) all_116_1_189 = all_0_14_14
% 110.75/75.70 |
% 110.75/75.70 | Simplifying 530 yields:
% 110.75/75.70 | (500) all_116_1_189 = all_0_14_14
% 110.75/75.70 |
% 110.75/75.70 | Equations (500) can reduce 512 to:
% 110.75/75.70 | (274) $false
% 110.75/75.70 |
% 110.75/75.70 |-The branch is then unsatisfiable
% 110.75/75.70 |-Branch two:
% 110.75/75.70 | (502) ~ (all_118_1_191 = all_0_14_14)
% 110.75/75.70 | (511) ? [v0] : ( ~ (v0 = 0) & subset(all_0_17_17, all_0_14_14) = v0)
% 110.75/75.70 |
% 110.75/75.70 | Instantiating (511) with all_741_0_2657 yields:
% 110.75/75.70 | (542) ~ (all_741_0_2657 = 0) & subset(all_0_17_17, all_0_14_14) = all_741_0_2657
% 110.75/75.70 |
% 110.75/75.70 | Applying alpha-rule on (542) yields:
% 110.75/75.70 | (543) ~ (all_741_0_2657 = 0)
% 110.75/75.70 | (544) subset(all_0_17_17, all_0_14_14) = all_741_0_2657
% 110.75/75.70 |
% 110.75/75.70 | Instantiating formula (13) with all_0_17_17, all_0_14_14, 0, all_741_0_2657 and discharging atoms subset(all_0_17_17, all_0_14_14) = all_741_0_2657, subset(all_0_17_17, all_0_14_14) = 0, yields:
% 110.75/75.70 | (545) all_741_0_2657 = 0
% 110.75/75.70 |
% 110.75/75.70 | Equations (545) can reduce 543 to:
% 110.75/75.70 | (274) $false
% 110.75/75.70 |
% 110.75/75.70 |-The branch is then unsatisfiable
% 110.75/75.70 |-Branch two:
% 110.75/75.70 | (499) all_118_1_191 = all_0_14_14
% 110.75/75.71 | (505) all_311_0_412 = 0 & below(all_0_16_16, all_0_17_17, all_0_14_14) = 0
% 110.75/75.71 |
% 110.75/75.71 | Applying alpha-rule on (505) yields:
% 110.75/75.71 | (461) all_311_0_412 = 0
% 110.75/75.71 | (494) below(all_0_16_16, all_0_17_17, all_0_14_14) = 0
% 110.75/75.71 |
% 110.75/75.71 +-Applying beta-rule and splitting (490), into two cases.
% 110.75/75.71 |-Branch one:
% 110.75/75.71 | (551) all_128_0_209 = all_0_14_14 & join(all_0_16_16, all_0_17_17, all_0_14_14) = all_0_14_14
% 110.75/75.71 |
% 110.75/75.71 | Applying alpha-rule on (551) yields:
% 110.75/75.71 | (552) all_128_0_209 = all_0_14_14
% 110.75/75.71 | (553) join(all_0_16_16, all_0_17_17, all_0_14_14) = all_0_14_14
% 110.75/75.71 |
% 110.75/75.71 | Equations (552) can reduce 525 to:
% 110.75/75.71 | (274) $false
% 110.75/75.71 |
% 110.75/75.71 |-The branch is then unsatisfiable
% 110.75/75.71 |-Branch two:
% 110.75/75.71 | (555) ~ (all_128_1_210 = 0) & below(all_0_16_16, all_0_17_17, all_0_14_14) = all_128_1_210
% 110.75/75.71 |
% 110.75/75.71 | Applying alpha-rule on (555) yields:
% 110.75/75.71 | (485) ~ (all_128_1_210 = 0)
% 110.75/75.71 | (557) below(all_0_16_16, all_0_17_17, all_0_14_14) = all_128_1_210
% 110.75/75.71 |
% 110.75/75.71 +-Applying beta-rule and splitting (457), into two cases.
% 110.75/75.71 |-Branch one:
% 110.75/75.71 | (495) all_0_13_13 = 0
% 110.75/75.71 |
% 110.75/75.71 | Equations (495) can reduce 436 to:
% 110.75/75.71 | (274) $false
% 110.75/75.71 |
% 110.75/75.71 |-The branch is then unsatisfiable
% 110.75/75.71 |-Branch two:
% 110.75/75.71 | (436) ~ (all_0_13_13 = 0)
% 110.75/75.71 | (498) ~ (all_115_0_187 = all_0_14_14) & join(all_0_16_16, all_0_17_17, all_0_14_14) = all_115_0_187
% 110.75/75.71 |
% 110.75/75.71 | Instantiating formula (169) with all_0_16_16, all_0_17_17, all_0_14_14, all_128_1_210, all_0_13_13 and discharging atoms below(all_0_16_16, all_0_17_17, all_0_14_14) = all_128_1_210, below(all_0_16_16, all_0_17_17, all_0_14_14) = all_0_13_13, yields:
% 110.75/75.71 | (562) all_128_1_210 = all_0_13_13
% 110.75/75.71 |
% 110.75/75.71 | Instantiating formula (169) with all_0_16_16, all_0_17_17, all_0_14_14, 0, all_128_1_210 and discharging atoms below(all_0_16_16, all_0_17_17, all_0_14_14) = all_128_1_210, below(all_0_16_16, all_0_17_17, all_0_14_14) = 0, yields:
% 110.75/75.71 | (480) all_128_1_210 = 0
% 110.75/75.71 |
% 110.75/75.71 | Combining equations (562,480) yields a new equation:
% 110.75/75.71 | (564) all_0_13_13 = 0
% 110.75/75.71 |
% 110.75/75.71 | Simplifying 564 yields:
% 110.75/75.71 | (495) all_0_13_13 = 0
% 110.75/75.71 |
% 110.75/75.71 | Equations (495) can reduce 436 to:
% 110.75/75.71 | (274) $false
% 110.75/75.71 |
% 110.75/75.71 |-The branch is then unsatisfiable
% 110.75/75.71 |-Branch two:
% 110.75/75.71 | (567) all_0_13_13 = 0 & ~ (all_0_12_12 = 0)
% 110.75/75.71 |
% 110.75/75.71 | Applying alpha-rule on (567) yields:
% 110.75/75.71 | (495) all_0_13_13 = 0
% 110.75/75.71 | (569) ~ (all_0_12_12 = 0)
% 110.75/75.71 |
% 110.75/75.71 +-Applying beta-rule and splitting (217), into two cases.
% 110.75/75.71 |-Branch one:
% 110.75/75.71 | (438) (all_115_0_187 = 0 & empty_carrier(all_0_16_16) = 0) | ( ~ (all_115_0_187 = 0) & join_semilatt_str(all_0_16_16) = all_115_0_187) | ( ~ (all_115_0_187 = 0) & element(all_0_14_14, all_0_15_15) = all_115_0_187)
% 110.75/75.71 |
% 110.75/75.71 +-Applying beta-rule and splitting (438), into two cases.
% 110.75/75.71 |-Branch one:
% 110.75/75.71 | (439) (all_115_0_187 = 0 & empty_carrier(all_0_16_16) = 0) | ( ~ (all_115_0_187 = 0) & join_semilatt_str(all_0_16_16) = all_115_0_187)
% 110.75/75.71 |
% 110.75/75.71 +-Applying beta-rule and splitting (439), into two cases.
% 110.75/75.71 |-Branch one:
% 110.75/75.71 | (440) all_115_0_187 = 0 & empty_carrier(all_0_16_16) = 0
% 110.75/75.71 |
% 110.75/75.71 | Applying alpha-rule on (440) yields:
% 110.75/75.71 | (441) all_115_0_187 = 0
% 110.75/75.71 | (272) empty_carrier(all_0_16_16) = 0
% 110.75/75.71 |
% 110.75/75.71 | Instantiating formula (93) with all_0_16_16, 0, all_88_0_128 and discharging atoms empty_carrier(all_0_16_16) = all_88_0_128, empty_carrier(all_0_16_16) = 0, yields:
% 110.75/75.71 | (273) all_88_0_128 = 0
% 110.75/75.71 |
% 110.75/75.71 | Equations (273) can reduce 214 to:
% 110.75/75.71 | (274) $false
% 110.75/75.71 |
% 110.75/75.71 |-The branch is then unsatisfiable
% 110.75/75.71 |-Branch two:
% 110.75/75.71 | (445) ~ (all_115_0_187 = 0) & join_semilatt_str(all_0_16_16) = all_115_0_187
% 110.75/75.71 |
% 110.75/75.71 | Applying alpha-rule on (445) yields:
% 110.75/75.71 | (446) ~ (all_115_0_187 = 0)
% 110.75/75.71 | (447) join_semilatt_str(all_0_16_16) = all_115_0_187
% 110.75/75.71 |
% 110.75/75.71 | Instantiating formula (135) with all_0_16_16, all_115_0_187, 0 and discharging atoms join_semilatt_str(all_0_16_16) = all_115_0_187, join_semilatt_str(all_0_16_16) = 0, yields:
% 110.75/75.71 | (441) all_115_0_187 = 0
% 110.75/75.71 |
% 110.75/75.71 | Equations (441) can reduce 446 to:
% 110.75/75.71 | (274) $false
% 110.75/75.71 |
% 110.75/75.71 |-The branch is then unsatisfiable
% 110.75/75.71 |-Branch two:
% 110.75/75.71 | (450) ~ (all_115_0_187 = 0) & element(all_0_14_14, all_0_15_15) = all_115_0_187
% 110.75/75.71 |
% 110.75/75.71 | Applying alpha-rule on (450) yields:
% 110.75/75.71 | (446) ~ (all_115_0_187 = 0)
% 110.75/75.72 | (452) element(all_0_14_14, all_0_15_15) = all_115_0_187
% 110.75/75.72 |
% 110.75/75.72 | Instantiating formula (172) with all_0_14_14, all_0_15_15, all_115_0_187, 0 and discharging atoms element(all_0_14_14, all_0_15_15) = all_115_0_187, element(all_0_14_14, all_0_15_15) = 0, yields:
% 110.75/75.72 | (441) all_115_0_187 = 0
% 110.75/75.72 |
% 110.75/75.72 | Equations (441) can reduce 446 to:
% 110.75/75.72 | (274) $false
% 110.75/75.72 |
% 110.75/75.72 |-The branch is then unsatisfiable
% 110.75/75.72 |-Branch two:
% 110.75/75.72 | (455) ( ~ (all_0_13_13 = 0) | (all_115_0_187 = all_0_14_14 & join(all_0_16_16, all_0_17_17, all_0_14_14) = all_0_14_14)) & (all_0_13_13 = 0 | ( ~ (all_115_0_187 = all_0_14_14) & join(all_0_16_16, all_0_17_17, all_0_14_14) = all_115_0_187))
% 110.75/75.72 |
% 110.75/75.72 | Applying alpha-rule on (455) yields:
% 110.75/75.72 | (456) ~ (all_0_13_13 = 0) | (all_115_0_187 = all_0_14_14 & join(all_0_16_16, all_0_17_17, all_0_14_14) = all_0_14_14)
% 110.75/75.72 | (457) all_0_13_13 = 0 | ( ~ (all_115_0_187 = all_0_14_14) & join(all_0_16_16, all_0_17_17, all_0_14_14) = all_115_0_187)
% 110.75/75.72 |
% 110.75/75.72 +-Applying beta-rule and splitting (203), into two cases.
% 110.75/75.72 |-Branch one:
% 110.75/75.72 | (435) all_0_12_12 = 0
% 110.75/75.72 |
% 110.75/75.72 | Equations (435) can reduce 569 to:
% 110.75/75.72 | (274) $false
% 110.75/75.72 |
% 110.75/75.72 |-The branch is then unsatisfiable
% 110.75/75.72 |-Branch two:
% 110.75/75.72 | (569) ~ (all_0_12_12 = 0)
% 110.75/75.72 | (593) ? [v0] : ? [v1] : ( ~ (v1 = 0) & powerset(all_0_14_14) = v0 & element(all_0_17_17, v0) = v1)
% 110.75/75.72 |
% 110.75/75.72 +-Applying beta-rule and splitting (456), into two cases.
% 110.75/75.72 |-Branch one:
% 110.75/75.72 | (436) ~ (all_0_13_13 = 0)
% 110.75/75.72 |
% 110.75/75.72 | Equations (495) can reduce 436 to:
% 110.75/75.72 | (274) $false
% 110.75/75.72 |
% 110.75/75.72 |-The branch is then unsatisfiable
% 110.75/75.72 |-Branch two:
% 110.75/75.72 | (495) all_0_13_13 = 0
% 110.75/75.72 | (597) all_115_0_187 = all_0_14_14 & join(all_0_16_16, all_0_17_17, all_0_14_14) = all_0_14_14
% 110.75/75.72 |
% 110.75/75.72 | Applying alpha-rule on (597) yields:
% 110.75/75.72 | (598) all_115_0_187 = all_0_14_14
% 110.75/75.72 | (553) join(all_0_16_16, all_0_17_17, all_0_14_14) = all_0_14_14
% 110.75/75.72 |
% 110.75/75.72 +-Applying beta-rule and splitting (267), into two cases.
% 110.75/75.72 |-Branch one:
% 110.75/75.72 | (458) (all_311_0_412 = 0 & empty_carrier(all_0_16_16) = 0) | ( ~ (all_311_0_412 = 0) & join_semilatt_str(all_0_16_16) = all_311_0_412) | ( ~ (all_311_0_412 = 0) & element(all_0_14_14, all_0_15_15) = all_311_0_412)
% 110.75/75.72 |
% 110.75/75.72 +-Applying beta-rule and splitting (458), into two cases.
% 110.75/75.72 |-Branch one:
% 110.75/75.72 | (459) (all_311_0_412 = 0 & empty_carrier(all_0_16_16) = 0) | ( ~ (all_311_0_412 = 0) & join_semilatt_str(all_0_16_16) = all_311_0_412)
% 110.75/75.72 |
% 110.75/75.72 +-Applying beta-rule and splitting (459), into two cases.
% 110.75/75.72 |-Branch one:
% 110.75/75.72 | (460) all_311_0_412 = 0 & empty_carrier(all_0_16_16) = 0
% 110.75/75.72 |
% 110.75/75.72 | Applying alpha-rule on (460) yields:
% 110.75/75.72 | (461) all_311_0_412 = 0
% 110.75/75.72 | (272) empty_carrier(all_0_16_16) = 0
% 110.75/75.72 |
% 110.75/75.72 | Instantiating formula (93) with all_0_16_16, 0, all_88_0_128 and discharging atoms empty_carrier(all_0_16_16) = all_88_0_128, empty_carrier(all_0_16_16) = 0, yields:
% 110.75/75.72 | (273) all_88_0_128 = 0
% 110.75/75.72 |
% 110.75/75.72 | Equations (273) can reduce 214 to:
% 110.75/75.72 | (274) $false
% 110.75/75.72 |
% 110.75/75.72 |-The branch is then unsatisfiable
% 110.75/75.72 |-Branch two:
% 110.75/75.72 | (465) ~ (all_311_0_412 = 0) & join_semilatt_str(all_0_16_16) = all_311_0_412
% 110.75/75.72 |
% 110.75/75.72 | Applying alpha-rule on (465) yields:
% 110.75/75.72 | (466) ~ (all_311_0_412 = 0)
% 110.75/75.72 | (467) join_semilatt_str(all_0_16_16) = all_311_0_412
% 110.75/75.72 |
% 110.75/75.72 | Instantiating formula (135) with all_0_16_16, all_311_0_412, 0 and discharging atoms join_semilatt_str(all_0_16_16) = all_311_0_412, join_semilatt_str(all_0_16_16) = 0, yields:
% 110.75/75.72 | (461) all_311_0_412 = 0
% 110.75/75.72 |
% 110.75/75.72 | Equations (461) can reduce 466 to:
% 110.75/75.72 | (274) $false
% 110.75/75.72 |
% 110.75/75.72 |-The branch is then unsatisfiable
% 110.75/75.72 |-Branch two:
% 110.75/75.72 | (470) ~ (all_311_0_412 = 0) & element(all_0_14_14, all_0_15_15) = all_311_0_412
% 110.75/75.72 |
% 110.75/75.72 | Applying alpha-rule on (470) yields:
% 110.75/75.72 | (466) ~ (all_311_0_412 = 0)
% 110.75/75.72 | (472) element(all_0_14_14, all_0_15_15) = all_311_0_412
% 110.75/75.72 |
% 110.75/75.72 | Instantiating formula (172) with all_0_14_14, all_0_15_15, all_311_0_412, 0 and discharging atoms element(all_0_14_14, all_0_15_15) = all_311_0_412, element(all_0_14_14, all_0_15_15) = 0, yields:
% 110.75/75.72 | (461) all_311_0_412 = 0
% 110.75/75.72 |
% 110.75/75.72 | Equations (461) can reduce 466 to:
% 110.75/75.72 | (274) $false
% 110.75/75.72 |
% 110.75/75.72 |-The branch is then unsatisfiable
% 110.75/75.72 |-Branch two:
% 110.75/75.72 | (475) ( ~ (all_118_1_191 = all_0_14_14) | (all_311_0_412 = 0 & below(all_0_16_16, all_0_17_17, all_0_14_14) = 0)) & (all_118_1_191 = all_0_14_14 | ( ~ (all_311_0_412 = 0) & below(all_0_16_16, all_0_17_17, all_0_14_14) = all_311_0_412))
% 110.75/75.72 |
% 110.75/75.72 | Applying alpha-rule on (475) yields:
% 110.75/75.72 | (476) ~ (all_118_1_191 = all_0_14_14) | (all_311_0_412 = 0 & below(all_0_16_16, all_0_17_17, all_0_14_14) = 0)
% 110.75/75.72 | (477) all_118_1_191 = all_0_14_14 | ( ~ (all_311_0_412 = 0) & below(all_0_16_16, all_0_17_17, all_0_14_14) = all_311_0_412)
% 110.75/75.72 |
% 110.75/75.72 +-Applying beta-rule and splitting (477), into two cases.
% 110.75/75.72 |-Branch one:
% 110.75/75.72 | (499) all_118_1_191 = all_0_14_14
% 110.75/75.72 |
% 110.75/75.73 | Combining equations (394,499) yields a new equation:
% 110.75/75.73 | (530) all_116_1_189 = all_0_14_14
% 110.75/75.73 |
% 110.75/75.73 | Simplifying 530 yields:
% 110.75/75.73 | (500) all_116_1_189 = all_0_14_14
% 110.75/75.73 |
% 110.75/75.73 | From (500) and (414) follows:
% 110.75/75.73 | (437) subset(all_0_17_17, all_0_14_14) = 0
% 110.75/75.73 |
% 110.75/75.73 | Instantiating formula (13) with all_0_17_17, all_0_14_14, 0, all_0_12_12 and discharging atoms subset(all_0_17_17, all_0_14_14) = all_0_12_12, subset(all_0_17_17, all_0_14_14) = 0, yields:
% 110.75/75.73 | (435) all_0_12_12 = 0
% 110.75/75.73 |
% 110.75/75.73 | Equations (435) can reduce 569 to:
% 110.75/75.73 | (274) $false
% 110.75/75.73 |
% 110.75/75.73 |-The branch is then unsatisfiable
% 110.75/75.73 |-Branch two:
% 110.75/75.73 | (502) ~ (all_118_1_191 = all_0_14_14)
% 110.75/75.73 | (517) ~ (all_311_0_412 = 0) & below(all_0_16_16, all_0_17_17, all_0_14_14) = all_311_0_412
% 110.75/75.73 |
% 110.75/75.73 | Equations (394) can reduce 502 to:
% 110.75/75.73 | (512) ~ (all_116_1_189 = all_0_14_14)
% 110.75/75.73 |
% 110.75/75.73 | Instantiating formula (71) with all_0_16_16, all_0_17_17, all_0_14_14, all_0_14_14, all_116_1_189 and discharging atoms join(all_0_16_16, all_0_17_17, all_0_14_14) = all_116_1_189, join(all_0_16_16, all_0_17_17, all_0_14_14) = all_0_14_14, yields:
% 110.75/75.73 | (500) all_116_1_189 = all_0_14_14
% 110.75/75.73 |
% 110.75/75.73 | Equations (500) can reduce 512 to:
% 110.75/75.73 | (274) $false
% 110.75/75.73 |
% 110.75/75.73 |-The branch is then unsatisfiable
% 110.75/75.73 |-Branch two:
% 110.75/75.73 | (631) all_341_1_488 = 0 & empty_carrier(all_0_16_16) = 0
% 110.75/75.73 |
% 110.75/75.73 | Applying alpha-rule on (631) yields:
% 110.75/75.73 | (632) all_341_1_488 = 0
% 110.75/75.73 | (272) empty_carrier(all_0_16_16) = 0
% 110.75/75.73 |
% 110.75/75.73 | Instantiating formula (93) with all_0_16_16, 0, all_88_0_128 and discharging atoms empty_carrier(all_0_16_16) = all_88_0_128, empty_carrier(all_0_16_16) = 0, yields:
% 110.75/75.73 | (273) all_88_0_128 = 0
% 110.75/75.73 |
% 110.75/75.73 | Equations (273) can reduce 214 to:
% 110.75/75.73 | (274) $false
% 110.75/75.73 |
% 110.75/75.73 |-The branch is then unsatisfiable
% 110.75/75.73 |-Branch two:
% 110.75/75.73 | (636) ~ (all_341_0_487 = 0) & element(all_0_14_14, all_341_1_488) = all_341_0_487 & the_carrier(all_0_16_16) = all_341_1_488
% 110.75/75.73 |
% 110.75/75.73 | Applying alpha-rule on (636) yields:
% 110.75/75.73 | (637) ~ (all_341_0_487 = 0)
% 110.75/75.73 | (638) element(all_0_14_14, all_341_1_488) = all_341_0_487
% 110.75/75.73 | (428) the_carrier(all_0_16_16) = all_341_1_488
% 110.75/75.73 |
% 110.75/75.73 | Instantiating formula (2) with all_0_16_16, all_341_1_488, all_0_15_15 and discharging atoms the_carrier(all_0_16_16) = all_341_1_488, the_carrier(all_0_16_16) = all_0_15_15, yields:
% 110.75/75.73 | (429) all_341_1_488 = all_0_15_15
% 110.75/75.73 |
% 110.75/75.73 | Instantiating formula (2) with all_0_16_16, all_254_1_319, all_341_1_488 and discharging atoms the_carrier(all_0_16_16) = all_341_1_488, the_carrier(all_0_16_16) = all_254_1_319, yields:
% 110.75/75.73 | (430) all_341_1_488 = all_254_1_319
% 110.75/75.73 |
% 110.75/75.73 | Combining equations (430,429) yields a new equation:
% 110.75/75.73 | (431) all_254_1_319 = all_0_15_15
% 110.75/75.73 |
% 110.75/75.73 | Simplifying 431 yields:
% 110.75/75.73 | (432) all_254_1_319 = all_0_15_15
% 110.75/75.73 |
% 110.75/75.73 | From (429) and (638) follows:
% 110.75/75.73 | (644) element(all_0_14_14, all_0_15_15) = all_341_0_487
% 110.75/75.73 |
% 110.75/75.73 | From (432) and (421) follows:
% 110.75/75.73 | (173) element(all_0_14_14, all_0_15_15) = 0
% 110.75/75.73 |
% 110.75/75.73 | Instantiating formula (172) with all_0_14_14, all_0_15_15, all_341_0_487, 0 and discharging atoms element(all_0_14_14, all_0_15_15) = all_341_0_487, element(all_0_14_14, all_0_15_15) = 0, yields:
% 110.75/75.73 | (426) all_341_0_487 = 0
% 110.75/75.73 |
% 110.75/75.73 | Equations (426) can reduce 637 to:
% 110.75/75.73 | (274) $false
% 110.75/75.73 |
% 110.75/75.73 |-The branch is then unsatisfiable
% 110.75/75.73 |-Branch two:
% 110.75/75.73 | (648) ~ (all_341_1_488 = 0) & join_semilatt_str(all_0_16_16) = all_341_1_488
% 110.75/75.73 |
% 110.75/75.73 | Applying alpha-rule on (648) yields:
% 110.75/75.73 | (649) ~ (all_341_1_488 = 0)
% 110.75/75.73 | (650) join_semilatt_str(all_0_16_16) = all_341_1_488
% 110.75/75.73 |
% 110.75/75.73 | Instantiating formula (135) with all_0_16_16, all_341_1_488, 0 and discharging atoms join_semilatt_str(all_0_16_16) = all_341_1_488, join_semilatt_str(all_0_16_16) = 0, yields:
% 111.03/75.73 | (632) all_341_1_488 = 0
% 111.03/75.73 |
% 111.03/75.73 | Equations (632) can reduce 649 to:
% 111.03/75.73 | (274) $false
% 111.03/75.73 |
% 111.03/75.73 |-The branch is then unsatisfiable
% 111.03/75.73 |-Branch two:
% 111.03/75.73 | (653) all_254_1_319 = 0 & empty_carrier(all_0_16_16) = 0
% 111.03/75.73 |
% 111.03/75.73 | Applying alpha-rule on (653) yields:
% 111.03/75.73 | (654) all_254_1_319 = 0
% 111.03/75.73 | (272) empty_carrier(all_0_16_16) = 0
% 111.03/75.74 |
% 111.03/75.74 | Instantiating formula (93) with all_0_16_16, 0, all_88_0_128 and discharging atoms empty_carrier(all_0_16_16) = all_88_0_128, empty_carrier(all_0_16_16) = 0, yields:
% 111.03/75.74 | (273) all_88_0_128 = 0
% 111.03/75.74 |
% 111.03/75.74 | Equations (273) can reduce 214 to:
% 111.03/75.74 | (274) $false
% 111.03/75.74 |
% 111.03/75.74 |-The branch is then unsatisfiable
% 111.03/75.74 |-Branch two:
% 111.03/75.74 | (658) ~ (all_254_0_318 = 0) & element(all_0_14_14, all_254_1_319) = all_254_0_318 & the_carrier(all_0_16_16) = all_254_1_319
% 111.03/75.74 |
% 111.03/75.74 | Applying alpha-rule on (658) yields:
% 111.03/75.74 | (659) ~ (all_254_0_318 = 0)
% 111.03/75.74 | (660) element(all_0_14_14, all_254_1_319) = all_254_0_318
% 111.03/75.74 | (422) the_carrier(all_0_16_16) = all_254_1_319
% 111.03/75.74 |
% 111.03/75.74 +-Applying beta-rule and splitting (268), into two cases.
% 111.03/75.74 |-Branch one:
% 111.03/75.74 | (423) (all_341_0_487 = 0 & element(all_0_14_14, all_341_1_488) = 0 & the_carrier(all_0_16_16) = all_341_1_488) | (all_341_1_488 = 0 & empty_carrier(all_0_16_16) = 0) | ( ~ (all_341_0_487 = 0) & element(all_0_14_14, all_341_1_488) = all_341_0_487 & the_carrier(all_0_16_16) = all_341_1_488)
% 111.03/75.74 |
% 111.03/75.74 +-Applying beta-rule and splitting (423), into two cases.
% 111.03/75.74 |-Branch one:
% 111.03/75.74 | (424) (all_341_0_487 = 0 & element(all_0_14_14, all_341_1_488) = 0 & the_carrier(all_0_16_16) = all_341_1_488) | (all_341_1_488 = 0 & empty_carrier(all_0_16_16) = 0)
% 111.03/75.74 |
% 111.03/75.74 +-Applying beta-rule and splitting (424), into two cases.
% 111.03/75.74 |-Branch one:
% 111.03/75.74 | (425) all_341_0_487 = 0 & element(all_0_14_14, all_341_1_488) = 0 & the_carrier(all_0_16_16) = all_341_1_488
% 111.03/75.74 |
% 111.03/75.74 | Applying alpha-rule on (425) yields:
% 111.03/75.74 | (426) all_341_0_487 = 0
% 111.03/75.74 | (427) element(all_0_14_14, all_341_1_488) = 0
% 111.03/75.74 | (428) the_carrier(all_0_16_16) = all_341_1_488
% 111.03/75.74 |
% 111.03/75.74 | Instantiating formula (2) with all_0_16_16, all_341_1_488, all_0_15_15 and discharging atoms the_carrier(all_0_16_16) = all_341_1_488, the_carrier(all_0_16_16) = all_0_15_15, yields:
% 111.03/75.74 | (429) all_341_1_488 = all_0_15_15
% 111.03/75.74 |
% 111.03/75.74 | Instantiating formula (2) with all_0_16_16, all_254_1_319, all_341_1_488 and discharging atoms the_carrier(all_0_16_16) = all_341_1_488, the_carrier(all_0_16_16) = all_254_1_319, yields:
% 111.03/75.74 | (430) all_341_1_488 = all_254_1_319
% 111.03/75.74 |
% 111.03/75.74 | Combining equations (430,429) yields a new equation:
% 111.03/75.74 | (431) all_254_1_319 = all_0_15_15
% 111.03/75.74 |
% 111.03/75.74 | Simplifying 431 yields:
% 111.03/75.74 | (432) all_254_1_319 = all_0_15_15
% 111.03/75.74 |
% 111.03/75.74 | From (429) and (427) follows:
% 111.03/75.74 | (173) element(all_0_14_14, all_0_15_15) = 0
% 111.03/75.74 |
% 111.03/75.74 | From (432) and (660) follows:
% 111.03/75.74 | (673) element(all_0_14_14, all_0_15_15) = all_254_0_318
% 111.03/75.74 |
% 111.03/75.74 | Instantiating formula (172) with all_0_14_14, all_0_15_15, all_254_0_318, 0 and discharging atoms element(all_0_14_14, all_0_15_15) = all_254_0_318, element(all_0_14_14, all_0_15_15) = 0, yields:
% 111.03/75.74 | (420) all_254_0_318 = 0
% 111.03/75.74 |
% 111.03/75.74 | Equations (420) can reduce 659 to:
% 111.03/75.74 | (274) $false
% 111.03/75.74 |
% 111.03/75.74 |-The branch is then unsatisfiable
% 111.03/75.74 |-Branch two:
% 111.03/75.74 | (631) all_341_1_488 = 0 & empty_carrier(all_0_16_16) = 0
% 111.03/75.74 |
% 111.03/75.74 | Applying alpha-rule on (631) yields:
% 111.03/75.74 | (632) all_341_1_488 = 0
% 111.03/75.74 | (272) empty_carrier(all_0_16_16) = 0
% 111.03/75.74 |
% 111.03/75.74 | Instantiating formula (93) with all_0_16_16, 0, all_88_0_128 and discharging atoms empty_carrier(all_0_16_16) = all_88_0_128, empty_carrier(all_0_16_16) = 0, yields:
% 111.03/75.74 | (273) all_88_0_128 = 0
% 111.03/75.74 |
% 111.03/75.74 | Equations (273) can reduce 214 to:
% 111.03/75.74 | (274) $false
% 111.03/75.74 |
% 111.03/75.74 |-The branch is then unsatisfiable
% 111.03/75.74 |-Branch two:
% 111.03/75.74 | (636) ~ (all_341_0_487 = 0) & element(all_0_14_14, all_341_1_488) = all_341_0_487 & the_carrier(all_0_16_16) = all_341_1_488
% 111.03/75.74 |
% 111.03/75.74 | Applying alpha-rule on (636) yields:
% 111.03/75.74 | (637) ~ (all_341_0_487 = 0)
% 111.03/75.74 | (638) element(all_0_14_14, all_341_1_488) = all_341_0_487
% 111.03/75.74 | (428) the_carrier(all_0_16_16) = all_341_1_488
% 111.03/75.74 |
% 111.03/75.74 | Instantiating formula (2) with all_0_16_16, all_341_1_488, all_0_15_15 and discharging atoms the_carrier(all_0_16_16) = all_341_1_488, the_carrier(all_0_16_16) = all_0_15_15, yields:
% 111.03/75.74 | (429) all_341_1_488 = all_0_15_15
% 111.03/75.74 |
% 111.03/75.74 | Instantiating formula (2) with all_0_16_16, all_254_1_319, all_341_1_488 and discharging atoms the_carrier(all_0_16_16) = all_341_1_488, the_carrier(all_0_16_16) = all_254_1_319, yields:
% 111.03/75.74 | (430) all_341_1_488 = all_254_1_319
% 111.03/75.74 |
% 111.03/75.74 | Combining equations (430,429) yields a new equation:
% 111.03/75.74 | (431) all_254_1_319 = all_0_15_15
% 111.03/75.74 |
% 111.03/75.74 | Simplifying 431 yields:
% 111.03/75.74 | (432) all_254_1_319 = all_0_15_15
% 111.03/75.74 |
% 111.03/75.74 | From (429) and (638) follows:
% 111.03/75.74 | (644) element(all_0_14_14, all_0_15_15) = all_341_0_487
% 111.03/75.74 |
% 111.03/75.74 | From (432) and (660) follows:
% 111.03/75.74 | (673) element(all_0_14_14, all_0_15_15) = all_254_0_318
% 111.03/75.74 |
% 111.03/75.74 | Instantiating formula (172) with all_0_14_14, all_0_15_15, all_341_0_487, 0 and discharging atoms element(all_0_14_14, all_0_15_15) = all_341_0_487, element(all_0_14_14, all_0_15_15) = 0, yields:
% 111.03/75.74 | (426) all_341_0_487 = 0
% 111.03/75.75 |
% 111.03/75.75 | Instantiating formula (172) with all_0_14_14, all_0_15_15, all_254_0_318, all_341_0_487 and discharging atoms element(all_0_14_14, all_0_15_15) = all_341_0_487, element(all_0_14_14, all_0_15_15) = all_254_0_318, yields:
% 111.03/75.75 | (692) all_341_0_487 = all_254_0_318
% 111.03/75.75 |
% 111.03/75.75 | Combining equations (426,692) yields a new equation:
% 111.03/75.75 | (420) all_254_0_318 = 0
% 111.03/75.75 |
% 111.03/75.75 | Equations (420) can reduce 659 to:
% 111.03/75.75 | (274) $false
% 111.03/75.75 |
% 111.03/75.75 |-The branch is then unsatisfiable
% 111.03/75.75 |-Branch two:
% 111.03/75.75 | (648) ~ (all_341_1_488 = 0) & join_semilatt_str(all_0_16_16) = all_341_1_488
% 111.03/75.75 |
% 111.03/75.75 | Applying alpha-rule on (648) yields:
% 111.03/75.75 | (649) ~ (all_341_1_488 = 0)
% 111.03/75.75 | (650) join_semilatt_str(all_0_16_16) = all_341_1_488
% 111.03/75.75 |
% 111.03/75.75 | Instantiating formula (135) with all_0_16_16, all_341_1_488, 0 and discharging atoms join_semilatt_str(all_0_16_16) = all_341_1_488, join_semilatt_str(all_0_16_16) = 0, yields:
% 111.03/75.75 | (632) all_341_1_488 = 0
% 111.03/75.75 |
% 111.03/75.75 | Equations (632) can reduce 649 to:
% 111.03/75.75 | (274) $false
% 111.03/75.75 |
% 111.03/75.75 |-The branch is then unsatisfiable
% 111.03/75.75 |-Branch two:
% 111.03/75.75 | (700) ~ (all_254_1_319 = 0) & meet_semilatt_str(all_0_16_16) = all_254_1_319
% 111.03/75.75 |
% 111.03/75.75 | Applying alpha-rule on (700) yields:
% 111.03/75.75 | (701) ~ (all_254_1_319 = 0)
% 111.03/75.75 | (702) meet_semilatt_str(all_0_16_16) = all_254_1_319
% 111.03/75.75 |
% 111.03/75.75 | Instantiating formula (178) with all_0_16_16, all_254_1_319, 0 and discharging atoms meet_semilatt_str(all_0_16_16) = all_254_1_319, meet_semilatt_str(all_0_16_16) = 0, yields:
% 111.03/75.75 | (654) all_254_1_319 = 0
% 111.03/75.75 |
% 111.03/75.75 | Equations (654) can reduce 701 to:
% 111.03/75.75 | (274) $false
% 111.03/75.75 |
% 111.03/75.75 |-The branch is then unsatisfiable
% 111.03/75.75 |-Branch two:
% 111.03/75.75 | (705) ~ (all_249_4_311 = 0) & meet_semilatt_str(all_0_16_16) = all_249_4_311
% 111.03/75.75 |
% 111.03/75.75 | Applying alpha-rule on (705) yields:
% 111.03/75.75 | (706) ~ (all_249_4_311 = 0)
% 111.03/75.75 | (707) meet_semilatt_str(all_0_16_16) = all_249_4_311
% 111.03/75.75 |
% 111.03/75.75 | Instantiating formula (178) with all_0_16_16, 0, all_249_4_311 and discharging atoms meet_semilatt_str(all_0_16_16) = all_249_4_311, meet_semilatt_str(all_0_16_16) = 0, yields:
% 111.03/75.75 | (344) all_249_4_311 = 0
% 111.03/75.75 |
% 111.03/75.75 | Equations (344) can reduce 706 to:
% 111.03/75.75 | (274) $false
% 111.03/75.75 |
% 111.03/75.75 |-The branch is then unsatisfiable
% 111.03/75.75 |-Branch two:
% 111.03/75.75 | (710) ~ (all_286_4_369 = 0) & join_semilatt_str(all_0_16_16) = all_286_4_369
% 111.03/75.75 |
% 111.03/75.75 | Applying alpha-rule on (710) yields:
% 111.03/75.75 | (711) ~ (all_286_4_369 = 0)
% 111.03/75.75 | (712) join_semilatt_str(all_0_16_16) = all_286_4_369
% 111.03/75.75 |
% 111.03/75.75 | Instantiating formula (135) with all_0_16_16, 0, all_286_4_369 and discharging atoms join_semilatt_str(all_0_16_16) = all_286_4_369, join_semilatt_str(all_0_16_16) = 0, yields:
% 111.03/75.75 | (321) all_286_4_369 = 0
% 111.03/75.75 |
% 111.03/75.75 | Equations (321) can reduce 711 to:
% 111.03/75.75 | (274) $false
% 111.03/75.75 |
% 111.03/75.75 |-The branch is then unsatisfiable
% 111.03/75.75 |-Branch two:
% 111.03/75.75 | (715) ~ (all_111_2_179 = 0) & strict_latt_str(all_0_16_16) = all_111_2_179
% 111.03/75.75 |
% 111.03/75.75 | Applying alpha-rule on (715) yields:
% 111.03/75.75 | (716) ~ (all_111_2_179 = 0)
% 111.03/75.75 | (717) strict_latt_str(all_0_16_16) = all_111_2_179
% 111.03/75.75 |
% 111.03/75.75 | Instantiating formula (128) with all_0_16_16, 0, all_111_2_179 and discharging atoms strict_latt_str(all_0_16_16) = all_111_2_179, strict_latt_str(all_0_16_16) = 0, yields:
% 111.03/75.75 | (718) all_111_2_179 = 0
% 111.03/75.75 |
% 111.03/75.76 | Equations (718) can reduce 716 to:
% 111.03/75.76 | (274) $false
% 111.03/75.76 |
% 111.03/75.76 |-The branch is then unsatisfiable
% 111.03/75.76 |-Branch two:
% 111.03/75.76 | (720) ~ (all_111_2_179 = 0) & latt_str(all_0_16_16) = all_111_2_179
% 111.03/75.76 |
% 111.03/75.76 | Applying alpha-rule on (720) yields:
% 111.03/75.76 | (716) ~ (all_111_2_179 = 0)
% 111.03/75.76 | (722) latt_str(all_0_16_16) = all_111_2_179
% 111.03/75.76 |
% 111.03/75.76 | Instantiating formula (79) with all_0_16_16, 0, all_111_2_179 and discharging atoms latt_str(all_0_16_16) = all_111_2_179, latt_str(all_0_16_16) = 0, yields:
% 111.03/75.76 | (718) all_111_2_179 = 0
% 111.03/75.76 |
% 111.03/75.76 | Equations (718) can reduce 716 to:
% 111.03/75.76 | (274) $false
% 111.03/75.76 |
% 111.03/75.76 |-The branch is then unsatisfiable
% 111.03/75.76 % SZS output end Proof for theBenchmark
% 111.03/75.76
% 111.03/75.76 75153ms
%------------------------------------------------------------------------------