TSTP Solution File: SEU343+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU343+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n007.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 7.10s 2.24s
% Output : Proof 13.25s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU343+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.14/0.35 % Computer : n007.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Mon Jun 20 04:29:59 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.60/0.60 ____ _
% 0.60/0.60 ___ / __ \_____(_)___ ________ __________
% 0.60/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.60/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.60/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.60/0.60
% 0.60/0.60 A Theorem Prover for First-Order Logic
% 0.60/0.60 (ePrincess v.1.0)
% 0.60/0.60
% 0.60/0.60 (c) Philipp Rümmer, 2009-2015
% 0.60/0.60 (c) Peter Backeman, 2014-2015
% 0.60/0.60 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.60/0.60 Free software under GNU Lesser General Public License (LGPL).
% 0.60/0.60 Bug reports to peter@backeman.se
% 0.60/0.60
% 0.60/0.60 For more information, visit http://user.uu.se/~petba168/breu/
% 0.60/0.60
% 0.60/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.73/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.71/1.02 Prover 0: Preprocessing ...
% 3.89/1.51 Prover 0: Warning: ignoring some quantifiers
% 4.11/1.55 Prover 0: Constructing countermodel ...
% 7.10/2.24 Prover 0: proved (1595ms)
% 7.10/2.24
% 7.10/2.24 No countermodel exists, formula is valid
% 7.10/2.24 % SZS status Theorem for theBenchmark
% 7.10/2.24
% 7.10/2.24 Generating proof ... Warning: ignoring some quantifiers
% 11.89/3.38 found it (size 383)
% 11.89/3.38
% 11.89/3.38 % SZS output start Proof for theBenchmark
% 11.89/3.38 Assumed formulas after preprocessing and simplification:
% 11.89/3.38 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : (meet(v2, v1, v4) = v7 & join(v2, v1, v4) = v5 & boole_lattice(v0) = v2 & set_intersection2(v1, v4) = v8 & set_union2(v1, v4) = v6 & the_carrier(v2) = v3 & one_sorted_str(v16) & one_sorted_str(v10) & empty(v13) & empty(empty_set) & meet_semilatt_str(v17) & join_semilatt_str(v15) & element(v4, v3) & element(v1, v3) & strict_latt_str(v11) & strict_latt_str(v9) & latt_str(v14) & latt_str(v11) & latt_str(v9) & ~ empty(v12) & ~ empty_carrier(v10) & ~ empty_carrier(v9) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : (v19 = v18 | ~ (apply_binary_as_element(v25, v24, v23, v22, v21, v20) = v19) | ~ (apply_binary_as_element(v25, v24, v23, v22, v21, v20) = v18)) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : (v24 = v20 | ~ (latt_str_of(v22, v23, v24) = v21) | ~ (latt_str_of(v18, v19, v20) = v21) | ~ function(v20) | ~ function(v19) | ? [v25] : (cartesian_product2(v18, v18) = v25 & ( ~ relation_of2(v20, v25, v18) | ~ relation_of2(v19, v25, v18) | ~ quasi_total(v20, v25, v18) | ~ quasi_total(v19, v25, v18)))) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : (v23 = v19 | ~ (latt_str_of(v22, v23, v24) = v21) | ~ (latt_str_of(v18, v19, v20) = v21) | ~ function(v20) | ~ function(v19) | ? [v25] : (cartesian_product2(v18, v18) = v25 & ( ~ relation_of2(v20, v25, v18) | ~ relation_of2(v19, v25, v18) | ~ quasi_total(v20, v25, v18) | ~ quasi_total(v19, v25, v18)))) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : (v22 = v18 | ~ (latt_str_of(v22, v23, v24) = v21) | ~ (latt_str_of(v18, v19, v20) = v21) | ~ function(v20) | ~ function(v19) | ? [v25] : (cartesian_product2(v18, v18) = v25 & ( ~ relation_of2(v20, v25, v18) | ~ relation_of2(v19, v25, v18) | ~ quasi_total(v20, v25, v18) | ~ quasi_total(v19, v25, v18)))) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ( ~ (apply_binary_as_element(v18, v19, v20, v21, v22, v23) = v24) | ~ function(v21) | ~ element(v23, v19) | ~ element(v22, v18) | empty(v19) | empty(v18) | element(v24, v20) | ? [v25] : (cartesian_product2(v18, v19) = v25 & ( ~ relation_of2(v21, v25, v20) | ~ quasi_total(v21, v25, v20)))) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ( ~ (apply_binary_as_element(v18, v19, v20, v21, v22, v23) = v24) | ~ function(v21) | ~ element(v23, v19) | ~ element(v22, v18) | empty(v19) | empty(v18) | ? [v25] : ? [v26] : (apply_binary(v21, v22, v23) = v26 & cartesian_product2(v18, v19) = v25 & (v26 = v24 | ~ relation_of2(v21, v25, v20) | ~ quasi_total(v21, v25, v20)))) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v22 = v18 | ~ (the_carrier(v18) = v19) | ~ (the_L_join(v18) = v20) | ~ (the_L_meet(v18) = v21) | ~ (latt_str_of(v19, v20, v21) = v22) | ~ strict_latt_str(v18) | ~ latt_str(v18)) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v19 = v18 | ~ (meet(v22, v21, v20) = v19) | ~ (meet(v22, v21, v20) = v18)) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v19 = v18 | ~ (join(v22, v21, v20) = v19) | ~ (join(v22, v21, v20) = v18)) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v19 = v18 | ~ (apply_binary(v22, v21, v20) = v19) | ~ (apply_binary(v22, v21, v20) = v18)) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v19 = v18 | ~ (subset_intersection2(v22, v21, v20) = v19) | ~ (subset_intersection2(v22, v21, v20) = v18)) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v19 = v18 | ~ (subset_union2(v22, v21, v20) = v19) | ~ (subset_union2(v22, v21, v20) = v18)) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v19 = v18 | ~ (latt_str_of(v22, v21, v20) = v19) | ~ (latt_str_of(v22, v21, v20) = v18)) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (singleton(v18) = v21) | ~ (unordered_pair(v20, v21) = v22) | ~ (unordered_pair(v18, v19) = v20) | ordered_pair(v18, v19) = v22) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (ordered_pair(v19, v20) = v21) | ~ (apply(v18, v21) = v22) | ~ function(v18) | ~ relation(v18) | apply_binary(v18, v19, v20) = v22) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (set_intersection2(v19, v20) = v22) | ~ (powerset(v18) = v21) | ~ element(v20, v21) | ~ element(v19, v21) | subset_intersection2(v18, v19, v20) = v22) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (set_union2(v19, v20) = v22) | ~ (powerset(v18) = v21) | ~ element(v20, v21) | ~ element(v19, v21) | subset_union2(v18, v19, v20) = v22) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v19 = v18 | ~ (ordered_pair(v21, v20) = v19) | ~ (ordered_pair(v21, v20) = v18)) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v19 = v18 | ~ (apply(v21, v20) = v19) | ~ (apply(v21, v20) = v18)) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v19 = v18 | ~ (set_intersection2(v21, v20) = v19) | ~ (set_intersection2(v21, v20) = v18)) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v19 = v18 | ~ (set_union2(v21, v20) = v19) | ~ (set_union2(v21, v20) = v18)) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v19 = v18 | ~ (unordered_pair(v21, v20) = v19) | ~ (unordered_pair(v21, v20) = v18)) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v19 = v18 | ~ (cartesian_product2(v21, v20) = v19) | ~ (cartesian_product2(v21, v20) = v18)) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (meet(v18, v19, v20) = v21) | ~ meet_semilatt_str(v18) | empty_carrier(v18) | ? [v22] : (the_carrier(v18) = v22 & ( ~ element(v20, v22) | ~ element(v19, v22) | element(v21, v22)))) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (join(v18, v19, v20) = v21) | ~ join_semilatt_str(v18) | empty_carrier(v18) | ? [v22] : (the_carrier(v18) = v22 & ( ~ element(v20, v22) | ~ element(v19, v22) | element(v21, v22)))) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (boole_lattice(v18) = v20) | ~ (the_carrier(v19) = v21) | ~ strict_latt_str(v19) | ~ latt_str(v19) | ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : ? [v27] : ? [v28] : ? [v29] : ? [v30] : (powerset(v18) = v22 & the_L_join(v19) = v23 & the_L_meet(v19) = v24 & ( ~ (v22 = v21) | v20 = v19 | (apply_binary(v24, v25, v26) = v29 & apply_binary(v23, v25, v26) = v27 & subset_intersection2(v18, v25, v26) = v30 & subset_union2(v18, v25, v26) = v28 & element(v26, v21) & element(v25, v21) & ( ~ (v30 = v29) | ~ (v28 = v27)))) & ( ~ (v20 = v19) | (v22 = v21 & ! [v31] : ! [v32] : ! [v33] : ( ~ (apply_binary(v24, v31, v32) = v33) | ~ element(v32, v21) | ~ element(v31, v21) | ? [v34] : (apply_binary(v23, v31, v32) = v34 & subset_intersection2(v18, v31, v32) = v33 & subset_union2(v18, v31, v32) = v34)) & ! [v31] : ! [v32] : ! [v33] : ( ~ (apply_binary(v23, v31, v32) = v33) | ~ element(v32, v21) | ~ element(v31, v21) | ? [v34] : (apply_binary(v24, v31, v32) = v34 & subset_intersection2(v18, v31, v32) = v34 & subset_union2(v18, v31, v32) = v33)) & ! [v31] : ! [v32] : ! [v33] : ( ~ (subset_intersection2(v18, v31, v32) = v33) | ~ element(v32, v21) | ~ element(v31, v21) | ? [v34] : (apply_binary(v24, v31, v32) = v33 & apply_binary(v23, v31, v32) = v34 & subset_union2(v18, v31, v32) = v34)) & ! [v31] : ! [v32] : ! [v33] : ( ~ (subset_union2(v18, v31, v32) = v33) | ~ element(v32, v21) | ~ element(v31, v21) | ? [v34] : (apply_binary(v24, v31, v32) = v34 & apply_binary(v23, v31, v32) = v33 & subset_intersection2(v18, v31, v32) = v34)))))) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (boole_lattice(v18) = v20) | ~ (the_L_join(v19) = v21) | ~ strict_latt_str(v19) | ~ latt_str(v19) | ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : ? [v27] : ? [v28] : ? [v29] : ? [v30] : (powerset(v18) = v23 & the_carrier(v19) = v22 & the_L_meet(v19) = v24 & ( ~ (v23 = v22) | v20 = v19 | (apply_binary(v24, v25, v26) = v29 & apply_binary(v21, v25, v26) = v27 & subset_intersection2(v18, v25, v26) = v30 & subset_union2(v18, v25, v26) = v28 & element(v26, v22) & element(v25, v22) & ( ~ (v30 = v29) | ~ (v28 = v27)))) & ( ~ (v20 = v19) | (v23 = v22 & ! [v31] : ! [v32] : ! [v33] : ( ~ (apply_binary(v24, v31, v32) = v33) | ~ element(v32, v22) | ~ element(v31, v22) | ? [v34] : (apply_binary(v21, v31, v32) = v34 & subset_intersection2(v18, v31, v32) = v33 & subset_union2(v18, v31, v32) = v34)) & ! [v31] : ! [v32] : ! [v33] : ( ~ (apply_binary(v21, v31, v32) = v33) | ~ element(v32, v22) | ~ element(v31, v22) | ? [v34] : (apply_binary(v24, v31, v32) = v34 & subset_intersection2(v18, v31, v32) = v34 & subset_union2(v18, v31, v32) = v33)) & ! [v31] : ! [v32] : ! [v33] : ( ~ (subset_intersection2(v18, v31, v32) = v33) | ~ element(v32, v22) | ~ element(v31, v22) | ? [v34] : (apply_binary(v24, v31, v32) = v33 & apply_binary(v21, v31, v32) = v34 & subset_union2(v18, v31, v32) = v34)) & ! [v31] : ! [v32] : ! [v33] : ( ~ (subset_union2(v18, v31, v32) = v33) | ~ element(v32, v22) | ~ element(v31, v22) | ? [v34] : (apply_binary(v24, v31, v32) = v34 & apply_binary(v21, v31, v32) = v33 & subset_intersection2(v18, v31, v32) = v34)))))) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (boole_lattice(v18) = v20) | ~ (the_L_meet(v19) = v21) | ~ strict_latt_str(v19) | ~ latt_str(v19) | ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : ? [v27] : ? [v28] : ? [v29] : ? [v30] : (powerset(v18) = v23 & the_carrier(v19) = v22 & the_L_join(v19) = v24 & ( ~ (v23 = v22) | v20 = v19 | (apply_binary(v24, v25, v26) = v27 & apply_binary(v21, v25, v26) = v29 & subset_intersection2(v18, v25, v26) = v30 & subset_union2(v18, v25, v26) = v28 & element(v26, v22) & element(v25, v22) & ( ~ (v30 = v29) | ~ (v28 = v27)))) & ( ~ (v20 = v19) | (v23 = v22 & ! [v31] : ! [v32] : ! [v33] : ( ~ (apply_binary(v24, v31, v32) = v33) | ~ element(v32, v22) | ~ element(v31, v22) | ? [v34] : (apply_binary(v21, v31, v32) = v34 & subset_intersection2(v18, v31, v32) = v34 & subset_union2(v18, v31, v32) = v33)) & ! [v31] : ! [v32] : ! [v33] : ( ~ (apply_binary(v21, v31, v32) = v33) | ~ element(v32, v22) | ~ element(v31, v22) | ? [v34] : (apply_binary(v24, v31, v32) = v34 & subset_intersection2(v18, v31, v32) = v33 & subset_union2(v18, v31, v32) = v34)) & ! [v31] : ! [v32] : ! [v33] : ( ~ (subset_intersection2(v18, v31, v32) = v33) | ~ element(v32, v22) | ~ element(v31, v22) | ? [v34] : (apply_binary(v24, v31, v32) = v34 & apply_binary(v21, v31, v32) = v33 & subset_union2(v18, v31, v32) = v34)) & ! [v31] : ! [v32] : ! [v33] : ( ~ (subset_union2(v18, v31, v32) = v33) | ~ element(v32, v22) | ~ element(v31, v22) | ? [v34] : (apply_binary(v24, v31, v32) = v33 & apply_binary(v21, v31, v32) = v34 & subset_intersection2(v18, v31, v32) = v34)))))) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (apply_binary(v18, v19, v20) = v21) | ~ function(v18) | ~ relation(v18) | ? [v22] : (ordered_pair(v19, v20) = v22 & apply(v18, v22) = v21)) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (subset_intersection2(v18, v20, v19) = v21) | ? [v22] : ? [v23] : (subset_intersection2(v18, v19, v20) = v23 & powerset(v18) = v22 & (v23 = v21 | ~ element(v20, v22) | ~ element(v19, v22)))) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (subset_intersection2(v18, v19, v20) = v21) | ? [v22] : ? [v23] : (subset_intersection2(v18, v20, v19) = v23 & powerset(v18) = v22 & (v23 = v21 | ~ element(v20, v22) | ~ element(v19, v22)))) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (subset_intersection2(v18, v19, v20) = v21) | ? [v22] : ? [v23] : (set_intersection2(v19, v20) = v23 & powerset(v18) = v22 & (v23 = v21 | ~ element(v20, v22) | ~ element(v19, v22)))) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (subset_intersection2(v18, v19, v20) = v21) | ? [v22] : (powerset(v18) = v22 & ( ~ element(v20, v22) | ~ element(v19, v22) | element(v21, v22)))) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (subset_union2(v18, v20, v19) = v21) | ? [v22] : ? [v23] : (subset_union2(v18, v19, v20) = v23 & powerset(v18) = v22 & (v23 = v21 | ~ element(v20, v22) | ~ element(v19, v22)))) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (subset_union2(v18, v19, v20) = v21) | ? [v22] : ? [v23] : (subset_union2(v18, v20, v19) = v23 & powerset(v18) = v22 & (v23 = v21 | ~ element(v20, v22) | ~ element(v19, v22)))) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (subset_union2(v18, v19, v20) = v21) | ? [v22] : ? [v23] : (set_union2(v19, v20) = v23 & powerset(v18) = v22 & (v23 = v21 | ~ element(v20, v22) | ~ element(v19, v22)))) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (subset_union2(v18, v19, v20) = v21) | ? [v22] : (powerset(v18) = v22 & ( ~ element(v20, v22) | ~ element(v19, v22) | element(v21, v22)))) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (cartesian_product2(v18, v19) = v21) | ~ relation_of2_as_subset(v20, v18, v19) | ? [v22] : (powerset(v21) = v22 & element(v20, v22))) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (powerset(v20) = v21) | ~ empty(v20) | ~ element(v19, v21) | ~ in(v18, v19)) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (powerset(v20) = v21) | ~ element(v19, v21) | ~ in(v18, v19) | element(v18, v20)) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (powerset(v18) = v21) | ~ (the_carrier(v19) = v20) | ~ strict_latt_str(v19) | ~ latt_str(v19) | ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : ? [v27] : ? [v28] : ? [v29] : ? [v30] : (boole_lattice(v18) = v22 & the_L_join(v19) = v23 & the_L_meet(v19) = v24 & ( ~ (v22 = v19) | (v21 = v20 & ! [v31] : ! [v32] : ! [v33] : ( ~ (apply_binary(v24, v31, v32) = v33) | ~ element(v32, v20) | ~ element(v31, v20) | ? [v34] : (apply_binary(v23, v31, v32) = v34 & subset_intersection2(v18, v31, v32) = v33 & subset_union2(v18, v31, v32) = v34)) & ! [v31] : ! [v32] : ! [v33] : ( ~ (apply_binary(v23, v31, v32) = v33) | ~ element(v32, v20) | ~ element(v31, v20) | ? [v34] : (apply_binary(v24, v31, v32) = v34 & subset_intersection2(v18, v31, v32) = v34 & subset_union2(v18, v31, v32) = v33)) & ! [v31] : ! [v32] : ! [v33] : ( ~ (subset_intersection2(v18, v31, v32) = v33) | ~ element(v32, v20) | ~ element(v31, v20) | ? [v34] : (apply_binary(v24, v31, v32) = v33 & apply_binary(v23, v31, v32) = v34 & subset_union2(v18, v31, v32) = v34)) & ! [v31] : ! [v32] : ! [v33] : ( ~ (subset_union2(v18, v31, v32) = v33) | ~ element(v32, v20) | ~ element(v31, v20) | ? [v34] : (apply_binary(v24, v31, v32) = v34 & apply_binary(v23, v31, v32) = v33 & subset_intersection2(v18, v31, v32) = v34)))) & ( ~ (v21 = v20) | v22 = v19 | (apply_binary(v24, v25, v26) = v29 & apply_binary(v23, v25, v26) = v27 & subset_intersection2(v18, v25, v26) = v30 & subset_union2(v18, v25, v26) = v28 & element(v26, v20) & element(v25, v20) & ( ~ (v30 = v29) | ~ (v28 = v27)))))) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (powerset(v18) = v20) | ~ (the_L_join(v19) = v21) | ~ strict_latt_str(v19) | ~ latt_str(v19) | ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : ? [v27] : ? [v28] : ? [v29] : ? [v30] : (boole_lattice(v18) = v22 & the_carrier(v19) = v23 & the_L_meet(v19) = v24 & ( ~ (v23 = v20) | v22 = v19 | (apply_binary(v24, v25, v26) = v29 & apply_binary(v21, v25, v26) = v27 & subset_intersection2(v18, v25, v26) = v30 & subset_union2(v18, v25, v26) = v28 & element(v26, v20) & element(v25, v20) & ( ~ (v30 = v29) | ~ (v28 = v27)))) & ( ~ (v22 = v19) | (v23 = v20 & ! [v31] : ! [v32] : ! [v33] : ( ~ (apply_binary(v24, v31, v32) = v33) | ~ element(v32, v20) | ~ element(v31, v20) | ? [v34] : (apply_binary(v21, v31, v32) = v34 & subset_intersection2(v18, v31, v32) = v33 & subset_union2(v18, v31, v32) = v34)) & ! [v31] : ! [v32] : ! [v33] : ( ~ (apply_binary(v21, v31, v32) = v33) | ~ element(v32, v20) | ~ element(v31, v20) | ? [v34] : (apply_binary(v24, v31, v32) = v34 & subset_intersection2(v18, v31, v32) = v34 & subset_union2(v18, v31, v32) = v33)) & ! [v31] : ! [v32] : ! [v33] : ( ~ (subset_intersection2(v18, v31, v32) = v33) | ~ element(v32, v20) | ~ element(v31, v20) | ? [v34] : (apply_binary(v24, v31, v32) = v33 & apply_binary(v21, v31, v32) = v34 & subset_union2(v18, v31, v32) = v34)) & ! [v31] : ! [v32] : ! [v33] : ( ~ (subset_union2(v18, v31, v32) = v33) | ~ element(v32, v20) | ~ element(v31, v20) | ? [v34] : (apply_binary(v24, v31, v32) = v34 & apply_binary(v21, v31, v32) = v33 & subset_intersection2(v18, v31, v32) = v34)))))) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (powerset(v18) = v20) | ~ (the_L_meet(v19) = v21) | ~ strict_latt_str(v19) | ~ latt_str(v19) | ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : ? [v27] : ? [v28] : ? [v29] : ? [v30] : (boole_lattice(v18) = v22 & the_carrier(v19) = v23 & the_L_join(v19) = v24 & ( ~ (v23 = v20) | v22 = v19 | (apply_binary(v24, v25, v26) = v27 & apply_binary(v21, v25, v26) = v29 & subset_intersection2(v18, v25, v26) = v30 & subset_union2(v18, v25, v26) = v28 & element(v26, v20) & element(v25, v20) & ( ~ (v30 = v29) | ~ (v28 = v27)))) & ( ~ (v22 = v19) | (v23 = v20 & ! [v31] : ! [v32] : ! [v33] : ( ~ (apply_binary(v24, v31, v32) = v33) | ~ element(v32, v20) | ~ element(v31, v20) | ? [v34] : (apply_binary(v21, v31, v32) = v34 & subset_intersection2(v18, v31, v32) = v34 & subset_union2(v18, v31, v32) = v33)) & ! [v31] : ! [v32] : ! [v33] : ( ~ (apply_binary(v21, v31, v32) = v33) | ~ element(v32, v20) | ~ element(v31, v20) | ? [v34] : (apply_binary(v24, v31, v32) = v34 & subset_intersection2(v18, v31, v32) = v33 & subset_union2(v18, v31, v32) = v34)) & ! [v31] : ! [v32] : ! [v33] : ( ~ (subset_intersection2(v18, v31, v32) = v33) | ~ element(v32, v20) | ~ element(v31, v20) | ? [v34] : (apply_binary(v24, v31, v32) = v34 & apply_binary(v21, v31, v32) = v33 & subset_union2(v18, v31, v32) = v34)) & ! [v31] : ! [v32] : ! [v33] : ( ~ (subset_union2(v18, v31, v32) = v33) | ~ element(v32, v20) | ~ element(v31, v20) | ? [v34] : (apply_binary(v24, v31, v32) = v33 & apply_binary(v21, v31, v32) = v34 & subset_intersection2(v18, v31, v32) = v34)))))) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (latt_str_of(v18, v19, v20) = v21) | ~ empty_carrier(v21) | ~ function(v20) | ~ function(v19) | empty(v18) | ? [v22] : (cartesian_product2(v18, v18) = v22 & ( ~ relation_of2(v20, v22, v18) | ~ relation_of2(v19, v22, v18) | ~ quasi_total(v20, v22, v18) | ~ quasi_total(v19, v22, v18)))) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (latt_str_of(v18, v19, v20) = v21) | ~ function(v20) | ~ function(v19) | empty(v18) | strict_latt_str(v21) | ? [v22] : (cartesian_product2(v18, v18) = v22 & ( ~ relation_of2(v20, v22, v18) | ~ relation_of2(v19, v22, v18) | ~ quasi_total(v20, v22, v18) | ~ quasi_total(v19, v22, v18)))) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (latt_str_of(v18, v19, v20) = v21) | ~ function(v20) | ~ function(v19) | strict_latt_str(v21) | ? [v22] : (cartesian_product2(v18, v18) = v22 & ( ~ relation_of2(v20, v22, v18) | ~ relation_of2(v19, v22, v18) | ~ quasi_total(v20, v22, v18) | ~ quasi_total(v19, v22, v18)))) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (latt_str_of(v18, v19, v20) = v21) | ~ function(v20) | ~ function(v19) | latt_str(v21) | ? [v22] : (cartesian_product2(v18, v18) = v22 & ( ~ relation_of2(v20, v22, v18) | ~ relation_of2(v19, v22, v18) | ~ quasi_total(v20, v22, v18) | ~ quasi_total(v19, v22, v18)))) & ? [v18] : ! [v19] : ! [v20] : ! [v21] : (v21 = v20 | ~ (subset_intersection2(v19, v20, v20) = v21) | ? [v22] : (powerset(v19) = v22 & ( ~ element(v20, v22) | ~ element(v18, v22)))) & ? [v18] : ! [v19] : ! [v20] : ! [v21] : (v21 = v20 | ~ (subset_union2(v19, v20, v20) = v21) | ? [v22] : (powerset(v19) = v22 & ( ~ element(v20, v22) | ~ element(v18, v22)))) & ? [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (cartesian_product2(v19, v20) = v21) | relation(v18) | ? [v22] : (powerset(v21) = v22 & ~ element(v18, v22))) & ! [v18] : ! [v19] : ! [v20] : (v19 = v18 | ~ (singleton(v20) = v19) | ~ (singleton(v20) = v18)) & ! [v18] : ! [v19] : ! [v20] : (v19 = v18 | ~ (boole_lattice(v20) = v19) | ~ (boole_lattice(v20) = v18)) & ! [v18] : ! [v19] : ! [v20] : (v19 = v18 | ~ (powerset(v20) = v19) | ~ (powerset(v20) = v18)) & ! [v18] : ! [v19] : ! [v20] : (v19 = v18 | ~ (the_carrier(v20) = v19) | ~ (the_carrier(v20) = v18)) & ! [v18] : ! [v19] : ! [v20] : (v19 = v18 | ~ (the_L_join(v20) = v19) | ~ (the_L_join(v20) = v18)) & ! [v18] : ! [v19] : ! [v20] : (v19 = v18 | ~ (the_L_meet(v20) = v19) | ~ (the_L_meet(v20) = v18)) & ! [v18] : ! [v19] : ! [v20] : ( ~ (ordered_pair(v18, v19) = v20) | ? [v21] : ? [v22] : (singleton(v18) = v22 & unordered_pair(v21, v22) = v20 & unordered_pair(v18, v19) = v21)) & ! [v18] : ! [v19] : ! [v20] : ( ~ (set_intersection2(v19, v18) = v20) | set_intersection2(v18, v19) = v20) & ! [v18] : ! [v19] : ! [v20] : ( ~ (set_intersection2(v18, v19) = v20) | set_intersection2(v19, v18) = v20) & ! [v18] : ! [v19] : ! [v20] : ( ~ (set_union2(v19, v18) = v20) | ~ empty(v20) | empty(v18)) & ! [v18] : ! [v19] : ! [v20] : ( ~ (set_union2(v19, v18) = v20) | set_union2(v18, v19) = v20) & ! [v18] : ! [v19] : ! [v20] : ( ~ (set_union2(v18, v19) = v20) | ~ empty(v20) | empty(v18)) & ! [v18] : ! [v19] : ! [v20] : ( ~ (set_union2(v18, v19) = v20) | set_union2(v19, v18) = v20) & ! [v18] : ! [v19] : ! [v20] : ( ~ (unordered_pair(v19, v18) = v20) | unordered_pair(v18, v19) = v20) & ! [v18] : ! [v19] : ! [v20] : ( ~ (unordered_pair(v18, v19) = v20) | ~ empty(v20)) & ! [v18] : ! [v19] : ! [v20] : ( ~ (unordered_pair(v18, v19) = v20) | unordered_pair(v19, v18) = v20) & ! [v18] : ! [v19] : ! [v20] : ( ~ (cartesian_product2(v19, v19) = v20) | ~ (the_carrier(v18) = v19) | ~ meet_semilatt_str(v18) | ? [v21] : (the_L_meet(v18) = v21 & relation_of2_as_subset(v21, v20, v19) & quasi_total(v21, v20, v19) & function(v21))) & ! [v18] : ! [v19] : ! [v20] : ( ~ (cartesian_product2(v19, v19) = v20) | ~ (the_carrier(v18) = v19) | ~ join_semilatt_str(v18) | ? [v21] : (the_L_join(v18) = v21 & relation_of2_as_subset(v21, v20, v19) & quasi_total(v21, v20, v19) & function(v21))) & ! [v18] : ! [v19] : ! [v20] : ( ~ (cartesian_product2(v18, v19) = v20) | ~ empty(v20) | empty(v19) | empty(v18)) & ! [v18] : ! [v19] : ! [v20] : ( ~ (powerset(v19) = v20) | ~ subset(v18, v19) | element(v18, v20)) & ! [v18] : ! [v19] : ! [v20] : ( ~ (powerset(v19) = v20) | ~ element(v18, v20) | subset(v18, v19)) & ! [v18] : ! [v19] : ! [v20] : ( ~ relation_of2_as_subset(v20, v18, v19) | relation_of2(v20, v18, v19)) & ! [v18] : ! [v19] : ! [v20] : ( ~ relation_of2(v20, v18, v19) | relation_of2_as_subset(v20, v18, v19)) & ! [v18] : ! [v19] : (v19 = v18 | ~ (set_intersection2(v18, v18) = v19)) & ! [v18] : ! [v19] : (v19 = v18 | ~ (set_union2(v18, v18) = v19)) & ! [v18] : ! [v19] : (v19 = v18 | ~ (set_union2(v18, empty_set) = v19)) & ! [v18] : ! [v19] : (v19 = v18 | ~ empty(v19) | ~ empty(v18)) & ! [v18] : ! [v19] : (v19 = empty_set | ~ (set_intersection2(v18, empty_set) = v19)) & ! [v18] : ! [v19] : ( ~ (singleton(v18) = v19) | ~ empty(v19)) & ! [v18] : ! [v19] : ( ~ (boole_lattice(v18) = v19) | ~ empty_carrier(v19)) & ! [v18] : ! [v19] : ( ~ (boole_lattice(v18) = v19) | strict_latt_str(v19)) & ! [v18] : ! [v19] : ( ~ (boole_lattice(v18) = v19) | latt_str(v19)) & ! [v18] : ! [v19] : ( ~ (powerset(v18) = v19) | ~ empty(v19)) & ! [v18] : ! [v19] : ( ~ (powerset(v18) = v19) | empty(v18) | ? [v20] : (element(v20, v19) & ~ empty(v20))) & ! [v18] : ! [v19] : ( ~ (powerset(v18) = v19) | ? [v20] : (empty(v20) & element(v20, v19))) & ! [v18] : ! [v19] : ( ~ (the_carrier(v18) = v19) | ~ one_sorted_str(v18) | ~ empty(v19) | empty_carrier(v18)) & ! [v18] : ! [v19] : ( ~ (the_carrier(v18) = v19) | ~ one_sorted_str(v18) | empty_carrier(v18) | ? [v20] : ? [v21] : (powerset(v19) = v20 & element(v21, v20) & ~ empty(v21))) & ! [v18] : ! [v19] : ( ~ (the_carrier(v18) = v19) | ~ meet_semilatt_str(v18) | empty_carrier(v18) | ? [v20] : (the_L_meet(v18) = v20 & ! [v21] : ! [v22] : ! [v23] : ( ~ (meet(v18, v21, v22) = v23) | ~ element(v22, v19) | ~ element(v21, v19) | apply_binary_as_element(v19, v19, v19, v20, v21, v22) = v23) & ! [v21] : ! [v22] : ! [v23] : ( ~ (apply_binary_as_element(v19, v19, v19, v20, v21, v22) = v23) | ~ element(v22, v19) | ~ element(v21, v19) | meet(v18, v21, v22) = v23))) & ! [v18] : ! [v19] : ( ~ (the_carrier(v18) = v19) | ~ meet_semilatt_str(v18) | ? [v20] : ? [v21] : (cartesian_product2(v19, v19) = v21 & the_L_meet(v18) = v20 & relation_of2_as_subset(v20, v21, v19) & quasi_total(v20, v21, v19) & function(v20))) & ! [v18] : ! [v19] : ( ~ (the_carrier(v18) = v19) | ~ join_semilatt_str(v18) | empty_carrier(v18) | ? [v20] : (the_L_join(v18) = v20 & ! [v21] : ! [v22] : ! [v23] : ( ~ (join(v18, v21, v22) = v23) | ~ element(v22, v19) | ~ element(v21, v19) | apply_binary_as_element(v19, v19, v19, v20, v21, v22) = v23) & ! [v21] : ! [v22] : ! [v23] : ( ~ (apply_binary_as_element(v19, v19, v19, v20, v21, v22) = v23) | ~ element(v22, v19) | ~ element(v21, v19) | join(v18, v21, v22) = v23))) & ! [v18] : ! [v19] : ( ~ (the_carrier(v18) = v19) | ~ join_semilatt_str(v18) | ? [v20] : ? [v21] : (cartesian_product2(v19, v19) = v21 & the_L_join(v18) = v20 & relation_of2_as_subset(v20, v21, v19) & quasi_total(v20, v21, v19) & function(v20))) & ! [v18] : ! [v19] : ( ~ (the_L_join(v18) = v19) | ~ join_semilatt_str(v18) | empty_carrier(v18) | ? [v20] : (the_carrier(v18) = v20 & ! [v21] : ! [v22] : ! [v23] : ( ~ (join(v18, v21, v22) = v23) | ~ element(v22, v20) | ~ element(v21, v20) | apply_binary_as_element(v20, v20, v20, v19, v21, v22) = v23) & ! [v21] : ! [v22] : ! [v23] : ( ~ (apply_binary_as_element(v20, v20, v20, v19, v21, v22) = v23) | ~ element(v22, v20) | ~ element(v21, v20) | join(v18, v21, v22) = v23))) & ! [v18] : ! [v19] : ( ~ (the_L_join(v18) = v19) | ~ join_semilatt_str(v18) | function(v19)) & ! [v18] : ! [v19] : ( ~ (the_L_join(v18) = v19) | ~ join_semilatt_str(v18) | ? [v20] : ? [v21] : (cartesian_product2(v20, v20) = v21 & the_carrier(v18) = v20 & relation_of2_as_subset(v19, v21, v20) & quasi_total(v19, v21, v20))) & ! [v18] : ! [v19] : ( ~ (the_L_meet(v18) = v19) | ~ meet_semilatt_str(v18) | empty_carrier(v18) | ? [v20] : (the_carrier(v18) = v20 & ! [v21] : ! [v22] : ! [v23] : ( ~ (meet(v18, v21, v22) = v23) | ~ element(v22, v20) | ~ element(v21, v20) | apply_binary_as_element(v20, v20, v20, v19, v21, v22) = v23) & ! [v21] : ! [v22] : ! [v23] : ( ~ (apply_binary_as_element(v20, v20, v20, v19, v21, v22) = v23) | ~ element(v22, v20) | ~ element(v21, v20) | meet(v18, v21, v22) = v23))) & ! [v18] : ! [v19] : ( ~ (the_L_meet(v18) = v19) | ~ meet_semilatt_str(v18) | function(v19)) & ! [v18] : ! [v19] : ( ~ (the_L_meet(v18) = v19) | ~ meet_semilatt_str(v18) | ? [v20] : ? [v21] : (cartesian_product2(v20, v20) = v21 & the_carrier(v18) = v20 & relation_of2_as_subset(v19, v21, v20) & quasi_total(v19, v21, v20))) & ! [v18] : ! [v19] : ( ~ empty(v19) | ~ in(v18, v19)) & ! [v18] : ! [v19] : ( ~ element(v18, v19) | empty(v19) | in(v18, v19)) & ! [v18] : ! [v19] : ( ~ in(v19, v18) | ~ in(v18, v19)) & ! [v18] : ! [v19] : ( ~ in(v18, v19) | element(v18, v19)) & ! [v18] : (v18 = empty_set | ~ empty(v18)) & ! [v18] : ( ~ meet_semilatt_str(v18) | one_sorted_str(v18)) & ! [v18] : ( ~ join_semilatt_str(v18) | one_sorted_str(v18)) & ! [v18] : ( ~ latt_str(v18) | meet_semilatt_str(v18)) & ! [v18] : ( ~ latt_str(v18) | join_semilatt_str(v18)) & ? [v18] : ? [v19] : ? [v20] : relation_of2_as_subset(v20, v18, v19) & ? [v18] : ? [v19] : ? [v20] : relation_of2(v20, v18, v19) & ? [v18] : ? [v19] : element(v19, v18) & ? [v18] : subset(v18, v18) & ( ~ (v8 = v7) | ~ (v6 = v5)))
% 12.27/3.46 | 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 yields:
% 12.27/3.46 | (1) meet(all_0_15_15, all_0_16_16, all_0_13_13) = all_0_10_10 & join(all_0_15_15, all_0_16_16, all_0_13_13) = all_0_12_12 & boole_lattice(all_0_17_17) = all_0_15_15 & set_intersection2(all_0_16_16, all_0_13_13) = all_0_9_9 & set_union2(all_0_16_16, all_0_13_13) = all_0_11_11 & the_carrier(all_0_15_15) = all_0_14_14 & one_sorted_str(all_0_1_1) & one_sorted_str(all_0_7_7) & empty(all_0_4_4) & empty(empty_set) & meet_semilatt_str(all_0_0_0) & join_semilatt_str(all_0_2_2) & element(all_0_13_13, all_0_14_14) & element(all_0_16_16, all_0_14_14) & strict_latt_str(all_0_6_6) & strict_latt_str(all_0_8_8) & latt_str(all_0_3_3) & latt_str(all_0_6_6) & latt_str(all_0_8_8) & ~ empty(all_0_5_5) & ~ empty_carrier(all_0_7_7) & ~ empty_carrier(all_0_8_8) & ! [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) | ~ function(v2) | ~ function(v1) | ? [v7] : (cartesian_product2(v0, v0) = v7 & ( ~ relation_of2(v2, v7, v0) | ~ relation_of2(v1, v7, v0) | ~ quasi_total(v2, v7, v0) | ~ quasi_total(v1, v7, v0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v5 = v1 | ~ (latt_str_of(v4, v5, v6) = v3) | ~ (latt_str_of(v0, v1, v2) = v3) | ~ function(v2) | ~ function(v1) | ? [v7] : (cartesian_product2(v0, v0) = v7 & ( ~ relation_of2(v2, v7, v0) | ~ relation_of2(v1, v7, v0) | ~ quasi_total(v2, v7, v0) | ~ quasi_total(v1, v7, v0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v0 | ~ (latt_str_of(v4, v5, v6) = v3) | ~ (latt_str_of(v0, v1, v2) = v3) | ~ function(v2) | ~ function(v1) | ? [v7] : (cartesian_product2(v0, v0) = v7 & ( ~ relation_of2(v2, v7, v0) | ~ relation_of2(v1, v7, v0) | ~ quasi_total(v2, v7, v0) | ~ quasi_total(v1, v7, v0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (apply_binary_as_element(v0, v1, v2, v3, v4, v5) = v6) | ~ function(v3) | ~ element(v5, v1) | ~ element(v4, v0) | empty(v1) | empty(v0) | element(v6, v2) | ? [v7] : (cartesian_product2(v0, v1) = v7 & ( ~ relation_of2(v3, v7, v2) | ~ quasi_total(v3, v7, v2)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (apply_binary_as_element(v0, v1, v2, v3, v4, v5) = v6) | ~ function(v3) | ~ element(v5, v1) | ~ element(v4, v0) | empty(v1) | empty(v0) | ? [v7] : ? [v8] : (apply_binary(v3, v4, v5) = v8 & cartesian_product2(v0, v1) = v7 & (v8 = v6 | ~ relation_of2(v3, v7, v2) | ~ quasi_total(v3, v7, v2)))) & ! [v0] : ! [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) = v4) | ~ strict_latt_str(v0) | ~ latt_str(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 | ~ (subset_intersection2(v4, v3, v2) = v1) | ~ (subset_intersection2(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (subset_union2(v4, v3, v2) = v1) | ~ (subset_union2(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] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (ordered_pair(v1, v2) = v3) | ~ (apply(v0, v3) = v4) | ~ function(v0) | ~ relation(v0) | apply_binary(v0, v1, v2) = v4) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_intersection2(v1, v2) = v4) | ~ (powerset(v0) = v3) | ~ element(v2, v3) | ~ element(v1, v3) | subset_intersection2(v0, v1, v2) = v4) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_union2(v1, v2) = v4) | ~ (powerset(v0) = v3) | ~ element(v2, v3) | ~ element(v1, v3) | subset_union2(v0, v1, v2) = v4) & ! [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] : ( ~ (meet(v0, v1, v2) = v3) | ~ meet_semilatt_str(v0) | empty_carrier(v0) | ? [v4] : (the_carrier(v0) = v4 & ( ~ element(v2, v4) | ~ element(v1, v4) | element(v3, v4)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (join(v0, v1, v2) = v3) | ~ join_semilatt_str(v0) | empty_carrier(v0) | ? [v4] : (the_carrier(v0) = v4 & ( ~ element(v2, v4) | ~ element(v1, v4) | element(v3, v4)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (boole_lattice(v0) = v2) | ~ (the_carrier(v1) = v3) | ~ strict_latt_str(v1) | ~ latt_str(v1) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : (powerset(v0) = v4 & the_L_join(v1) = v5 & the_L_meet(v1) = v6 & ( ~ (v4 = v3) | v2 = v1 | (apply_binary(v6, v7, v8) = v11 & apply_binary(v5, v7, v8) = v9 & subset_intersection2(v0, v7, v8) = v12 & subset_union2(v0, v7, v8) = v10 & element(v8, v3) & element(v7, v3) & ( ~ (v12 = v11) | ~ (v10 = v9)))) & ( ~ (v2 = v1) | (v4 = v3 & ! [v13] : ! [v14] : ! [v15] : ( ~ (apply_binary(v6, v13, v14) = v15) | ~ element(v14, v3) | ~ element(v13, v3) | ? [v16] : (apply_binary(v5, v13, v14) = v16 & subset_intersection2(v0, v13, v14) = v15 & subset_union2(v0, v13, v14) = v16)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (apply_binary(v5, v13, v14) = v15) | ~ element(v14, v3) | ~ element(v13, v3) | ? [v16] : (apply_binary(v6, v13, v14) = v16 & subset_intersection2(v0, v13, v14) = v16 & subset_union2(v0, v13, v14) = v15)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (subset_intersection2(v0, v13, v14) = v15) | ~ element(v14, v3) | ~ element(v13, v3) | ? [v16] : (apply_binary(v6, v13, v14) = v15 & apply_binary(v5, v13, v14) = v16 & subset_union2(v0, v13, v14) = v16)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (subset_union2(v0, v13, v14) = v15) | ~ element(v14, v3) | ~ element(v13, v3) | ? [v16] : (apply_binary(v6, v13, v14) = v16 & apply_binary(v5, v13, v14) = v15 & subset_intersection2(v0, v13, v14) = v16)))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (boole_lattice(v0) = v2) | ~ (the_L_join(v1) = v3) | ~ strict_latt_str(v1) | ~ latt_str(v1) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : (powerset(v0) = v5 & the_carrier(v1) = v4 & the_L_meet(v1) = v6 & ( ~ (v5 = v4) | v2 = v1 | (apply_binary(v6, v7, v8) = v11 & apply_binary(v3, v7, v8) = v9 & subset_intersection2(v0, v7, v8) = v12 & subset_union2(v0, v7, v8) = v10 & element(v8, v4) & element(v7, v4) & ( ~ (v12 = v11) | ~ (v10 = v9)))) & ( ~ (v2 = v1) | (v5 = v4 & ! [v13] : ! [v14] : ! [v15] : ( ~ (apply_binary(v6, v13, v14) = v15) | ~ element(v14, v4) | ~ element(v13, v4) | ? [v16] : (apply_binary(v3, v13, v14) = v16 & subset_intersection2(v0, v13, v14) = v15 & subset_union2(v0, v13, v14) = v16)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (apply_binary(v3, v13, v14) = v15) | ~ element(v14, v4) | ~ element(v13, v4) | ? [v16] : (apply_binary(v6, v13, v14) = v16 & subset_intersection2(v0, v13, v14) = v16 & subset_union2(v0, v13, v14) = v15)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (subset_intersection2(v0, v13, v14) = v15) | ~ element(v14, v4) | ~ element(v13, v4) | ? [v16] : (apply_binary(v6, v13, v14) = v15 & apply_binary(v3, v13, v14) = v16 & subset_union2(v0, v13, v14) = v16)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (subset_union2(v0, v13, v14) = v15) | ~ element(v14, v4) | ~ element(v13, v4) | ? [v16] : (apply_binary(v6, v13, v14) = v16 & apply_binary(v3, v13, v14) = v15 & subset_intersection2(v0, v13, v14) = v16)))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (boole_lattice(v0) = v2) | ~ (the_L_meet(v1) = v3) | ~ strict_latt_str(v1) | ~ latt_str(v1) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : (powerset(v0) = v5 & the_carrier(v1) = v4 & the_L_join(v1) = v6 & ( ~ (v5 = v4) | v2 = v1 | (apply_binary(v6, v7, v8) = v9 & apply_binary(v3, v7, v8) = v11 & subset_intersection2(v0, v7, v8) = v12 & subset_union2(v0, v7, v8) = v10 & element(v8, v4) & element(v7, v4) & ( ~ (v12 = v11) | ~ (v10 = v9)))) & ( ~ (v2 = v1) | (v5 = v4 & ! [v13] : ! [v14] : ! [v15] : ( ~ (apply_binary(v6, v13, v14) = v15) | ~ element(v14, v4) | ~ element(v13, v4) | ? [v16] : (apply_binary(v3, v13, v14) = v16 & subset_intersection2(v0, v13, v14) = v16 & subset_union2(v0, v13, v14) = v15)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (apply_binary(v3, v13, v14) = v15) | ~ element(v14, v4) | ~ element(v13, v4) | ? [v16] : (apply_binary(v6, v13, v14) = v16 & subset_intersection2(v0, v13, v14) = v15 & subset_union2(v0, v13, v14) = v16)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (subset_intersection2(v0, v13, v14) = v15) | ~ element(v14, v4) | ~ element(v13, v4) | ? [v16] : (apply_binary(v6, v13, v14) = v16 & apply_binary(v3, v13, v14) = v15 & subset_union2(v0, v13, v14) = v16)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (subset_union2(v0, v13, v14) = v15) | ~ element(v14, v4) | ~ element(v13, v4) | ? [v16] : (apply_binary(v6, v13, v14) = v15 & apply_binary(v3, v13, v14) = v16 & subset_intersection2(v0, v13, v14) = v16)))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (apply_binary(v0, v1, v2) = v3) | ~ function(v0) | ~ relation(v0) | ? [v4] : (ordered_pair(v1, v2) = v4 & apply(v0, v4) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_intersection2(v0, v2, v1) = v3) | ? [v4] : ? [v5] : (subset_intersection2(v0, v1, v2) = v5 & powerset(v0) = v4 & (v5 = v3 | ~ element(v2, v4) | ~ element(v1, v4)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_intersection2(v0, v1, v2) = v3) | ? [v4] : ? [v5] : (subset_intersection2(v0, v2, v1) = v5 & powerset(v0) = v4 & (v5 = v3 | ~ element(v2, v4) | ~ element(v1, v4)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_intersection2(v0, v1, v2) = v3) | ? [v4] : ? [v5] : (set_intersection2(v1, v2) = v5 & powerset(v0) = v4 & (v5 = v3 | ~ element(v2, v4) | ~ element(v1, v4)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_intersection2(v0, v1, v2) = v3) | ? [v4] : (powerset(v0) = v4 & ( ~ element(v2, v4) | ~ element(v1, v4) | element(v3, v4)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_union2(v0, v2, v1) = v3) | ? [v4] : ? [v5] : (subset_union2(v0, v1, v2) = v5 & powerset(v0) = v4 & (v5 = v3 | ~ element(v2, v4) | ~ element(v1, v4)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_union2(v0, v1, v2) = v3) | ? [v4] : ? [v5] : (subset_union2(v0, v2, v1) = v5 & powerset(v0) = v4 & (v5 = v3 | ~ element(v2, v4) | ~ element(v1, v4)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_union2(v0, v1, v2) = v3) | ? [v4] : ? [v5] : (set_union2(v1, v2) = v5 & powerset(v0) = v4 & (v5 = v3 | ~ element(v2, v4) | ~ element(v1, v4)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_union2(v0, v1, v2) = v3) | ? [v4] : (powerset(v0) = v4 & ( ~ element(v2, v4) | ~ element(v1, v4) | element(v3, v4)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cartesian_product2(v0, v1) = v3) | ~ relation_of2_as_subset(v2, v0, v1) | ? [v4] : (powerset(v3) = v4 & element(v2, v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ empty(v2) | ~ element(v1, v3) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ in(v0, v1) | element(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v0) = v3) | ~ (the_carrier(v1) = v2) | ~ strict_latt_str(v1) | ~ latt_str(v1) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : (boole_lattice(v0) = v4 & the_L_join(v1) = v5 & the_L_meet(v1) = v6 & ( ~ (v4 = v1) | (v3 = v2 & ! [v13] : ! [v14] : ! [v15] : ( ~ (apply_binary(v6, v13, v14) = v15) | ~ element(v14, v2) | ~ element(v13, v2) | ? [v16] : (apply_binary(v5, v13, v14) = v16 & subset_intersection2(v0, v13, v14) = v15 & subset_union2(v0, v13, v14) = v16)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (apply_binary(v5, v13, v14) = v15) | ~ element(v14, v2) | ~ element(v13, v2) | ? [v16] : (apply_binary(v6, v13, v14) = v16 & subset_intersection2(v0, v13, v14) = v16 & subset_union2(v0, v13, v14) = v15)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (subset_intersection2(v0, v13, v14) = v15) | ~ element(v14, v2) | ~ element(v13, v2) | ? [v16] : (apply_binary(v6, v13, v14) = v15 & apply_binary(v5, v13, v14) = v16 & subset_union2(v0, v13, v14) = v16)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (subset_union2(v0, v13, v14) = v15) | ~ element(v14, v2) | ~ element(v13, v2) | ? [v16] : (apply_binary(v6, v13, v14) = v16 & apply_binary(v5, v13, v14) = v15 & subset_intersection2(v0, v13, v14) = v16)))) & ( ~ (v3 = v2) | v4 = v1 | (apply_binary(v6, v7, v8) = v11 & apply_binary(v5, v7, v8) = v9 & subset_intersection2(v0, v7, v8) = v12 & subset_union2(v0, v7, v8) = v10 & element(v8, v2) & element(v7, v2) & ( ~ (v12 = v11) | ~ (v10 = v9)))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v0) = v2) | ~ (the_L_join(v1) = v3) | ~ strict_latt_str(v1) | ~ latt_str(v1) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : (boole_lattice(v0) = v4 & the_carrier(v1) = v5 & the_L_meet(v1) = v6 & ( ~ (v5 = v2) | v4 = v1 | (apply_binary(v6, v7, v8) = v11 & apply_binary(v3, v7, v8) = v9 & subset_intersection2(v0, v7, v8) = v12 & subset_union2(v0, v7, v8) = v10 & element(v8, v2) & element(v7, v2) & ( ~ (v12 = v11) | ~ (v10 = v9)))) & ( ~ (v4 = v1) | (v5 = v2 & ! [v13] : ! [v14] : ! [v15] : ( ~ (apply_binary(v6, v13, v14) = v15) | ~ element(v14, v2) | ~ element(v13, v2) | ? [v16] : (apply_binary(v3, v13, v14) = v16 & subset_intersection2(v0, v13, v14) = v15 & subset_union2(v0, v13, v14) = v16)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (apply_binary(v3, v13, v14) = v15) | ~ element(v14, v2) | ~ element(v13, v2) | ? [v16] : (apply_binary(v6, v13, v14) = v16 & subset_intersection2(v0, v13, v14) = v16 & subset_union2(v0, v13, v14) = v15)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (subset_intersection2(v0, v13, v14) = v15) | ~ element(v14, v2) | ~ element(v13, v2) | ? [v16] : (apply_binary(v6, v13, v14) = v15 & apply_binary(v3, v13, v14) = v16 & subset_union2(v0, v13, v14) = v16)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (subset_union2(v0, v13, v14) = v15) | ~ element(v14, v2) | ~ element(v13, v2) | ? [v16] : (apply_binary(v6, v13, v14) = v16 & apply_binary(v3, v13, v14) = v15 & subset_intersection2(v0, v13, v14) = v16)))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v0) = v2) | ~ (the_L_meet(v1) = v3) | ~ strict_latt_str(v1) | ~ latt_str(v1) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : (boole_lattice(v0) = v4 & the_carrier(v1) = v5 & the_L_join(v1) = v6 & ( ~ (v5 = v2) | v4 = v1 | (apply_binary(v6, v7, v8) = v9 & apply_binary(v3, v7, v8) = v11 & subset_intersection2(v0, v7, v8) = v12 & subset_union2(v0, v7, v8) = v10 & element(v8, v2) & element(v7, v2) & ( ~ (v12 = v11) | ~ (v10 = v9)))) & ( ~ (v4 = v1) | (v5 = v2 & ! [v13] : ! [v14] : ! [v15] : ( ~ (apply_binary(v6, v13, v14) = v15) | ~ element(v14, v2) | ~ element(v13, v2) | ? [v16] : (apply_binary(v3, v13, v14) = v16 & subset_intersection2(v0, v13, v14) = v16 & subset_union2(v0, v13, v14) = v15)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (apply_binary(v3, v13, v14) = v15) | ~ element(v14, v2) | ~ element(v13, v2) | ? [v16] : (apply_binary(v6, v13, v14) = v16 & subset_intersection2(v0, v13, v14) = v15 & subset_union2(v0, v13, v14) = v16)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (subset_intersection2(v0, v13, v14) = v15) | ~ element(v14, v2) | ~ element(v13, v2) | ? [v16] : (apply_binary(v6, v13, v14) = v16 & apply_binary(v3, v13, v14) = v15 & subset_union2(v0, v13, v14) = v16)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (subset_union2(v0, v13, v14) = v15) | ~ element(v14, v2) | ~ element(v13, v2) | ? [v16] : (apply_binary(v6, v13, v14) = v15 & apply_binary(v3, v13, v14) = v16 & subset_intersection2(v0, v13, v14) = v16)))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (latt_str_of(v0, v1, v2) = v3) | ~ empty_carrier(v3) | ~ function(v2) | ~ function(v1) | empty(v0) | ? [v4] : (cartesian_product2(v0, v0) = v4 & ( ~ relation_of2(v2, v4, v0) | ~ relation_of2(v1, v4, v0) | ~ quasi_total(v2, v4, v0) | ~ quasi_total(v1, v4, v0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (latt_str_of(v0, v1, v2) = v3) | ~ function(v2) | ~ function(v1) | empty(v0) | strict_latt_str(v3) | ? [v4] : (cartesian_product2(v0, v0) = v4 & ( ~ relation_of2(v2, v4, v0) | ~ relation_of2(v1, v4, v0) | ~ quasi_total(v2, v4, v0) | ~ quasi_total(v1, v4, v0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (latt_str_of(v0, v1, v2) = v3) | ~ function(v2) | ~ function(v1) | strict_latt_str(v3) | ? [v4] : (cartesian_product2(v0, v0) = v4 & ( ~ relation_of2(v2, v4, v0) | ~ relation_of2(v1, v4, v0) | ~ quasi_total(v2, v4, v0) | ~ quasi_total(v1, v4, v0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (latt_str_of(v0, v1, v2) = v3) | ~ function(v2) | ~ function(v1) | latt_str(v3) | ? [v4] : (cartesian_product2(v0, v0) = v4 & ( ~ relation_of2(v2, v4, v0) | ~ relation_of2(v1, v4, v0) | ~ quasi_total(v2, v4, v0) | ~ quasi_total(v1, v4, v0)))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (subset_intersection2(v1, v2, v2) = v3) | ? [v4] : (powerset(v1) = v4 & ( ~ element(v2, v4) | ~ element(v0, v4)))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (subset_union2(v1, v2, v2) = v3) | ? [v4] : (powerset(v1) = v4 & ( ~ element(v2, v4) | ~ element(v0, v4)))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cartesian_product2(v1, v2) = v3) | relation(v0) | ? [v4] : (powerset(v3) = v4 & ~ element(v0, v4))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (boole_lattice(v2) = v1) | ~ (boole_lattice(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(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] : ( ~ (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) | ~ empty(v2) | empty(v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ empty(v2) | empty(v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ~ empty(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (cartesian_product2(v1, v1) = v2) | ~ (the_carrier(v0) = v1) | ~ meet_semilatt_str(v0) | ? [v3] : (the_L_meet(v0) = v3 & relation_of2_as_subset(v3, v2, v1) & quasi_total(v3, v2, v1) & function(v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (cartesian_product2(v1, v1) = v2) | ~ (the_carrier(v0) = v1) | ~ join_semilatt_str(v0) | ? [v3] : (the_L_join(v0) = v3 & relation_of2_as_subset(v3, v2, v1) & quasi_total(v3, v2, v1) & function(v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (cartesian_product2(v0, v1) = v2) | ~ empty(v2) | empty(v1) | empty(v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ element(v0, v2) | subset(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ relation_of2_as_subset(v2, v0, v1) | relation_of2(v2, v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ relation_of2(v2, v0, v1) | relation_of2_as_subset(v2, v0, v1)) & ! [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 = v0 | ~ empty(v1) | ~ empty(v0)) & ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1)) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ~ empty(v1)) & ! [v0] : ! [v1] : ( ~ (boole_lattice(v0) = v1) | ~ empty_carrier(v1)) & ! [v0] : ! [v1] : ( ~ (boole_lattice(v0) = v1) | strict_latt_str(v1)) & ! [v0] : ! [v1] : ( ~ (boole_lattice(v0) = v1) | latt_str(v1)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ empty(v1)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (element(v2, v1) & ~ empty(v2))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (empty(v2) & element(v2, v1))) & ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ one_sorted_str(v0) | ~ empty(v1) | empty_carrier(v0)) & ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ one_sorted_str(v0) | empty_carrier(v0) | ? [v2] : ? [v3] : (powerset(v1) = v2 & element(v3, v2) & ~ empty(v3))) & ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ meet_semilatt_str(v0) | empty_carrier(v0) | ? [v2] : (the_L_meet(v0) = v2 & ! [v3] : ! [v4] : ! [v5] : ( ~ (meet(v0, v3, v4) = v5) | ~ element(v4, v1) | ~ element(v3, v1) | apply_binary_as_element(v1, v1, v1, v2, v3, v4) = v5) & ! [v3] : ! [v4] : ! [v5] : ( ~ (apply_binary_as_element(v1, v1, v1, v2, v3, v4) = v5) | ~ element(v4, v1) | ~ element(v3, v1) | meet(v0, v3, v4) = v5))) & ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ meet_semilatt_str(v0) | ? [v2] : ? [v3] : (cartesian_product2(v1, v1) = v3 & the_L_meet(v0) = v2 & relation_of2_as_subset(v2, v3, v1) & quasi_total(v2, v3, v1) & function(v2))) & ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ join_semilatt_str(v0) | empty_carrier(v0) | ? [v2] : (the_L_join(v0) = v2 & ! [v3] : ! [v4] : ! [v5] : ( ~ (join(v0, v3, v4) = v5) | ~ element(v4, v1) | ~ element(v3, v1) | apply_binary_as_element(v1, v1, v1, v2, v3, v4) = v5) & ! [v3] : ! [v4] : ! [v5] : ( ~ (apply_binary_as_element(v1, v1, v1, v2, v3, v4) = v5) | ~ element(v4, v1) | ~ element(v3, v1) | join(v0, v3, v4) = v5))) & ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ join_semilatt_str(v0) | ? [v2] : ? [v3] : (cartesian_product2(v1, v1) = v3 & the_L_join(v0) = v2 & relation_of2_as_subset(v2, v3, v1) & quasi_total(v2, v3, v1) & function(v2))) & ! [v0] : ! [v1] : ( ~ (the_L_join(v0) = v1) | ~ join_semilatt_str(v0) | empty_carrier(v0) | ? [v2] : (the_carrier(v0) = v2 & ! [v3] : ! [v4] : ! [v5] : ( ~ (join(v0, v3, v4) = v5) | ~ element(v4, v2) | ~ element(v3, v2) | apply_binary_as_element(v2, v2, v2, v1, v3, v4) = v5) & ! [v3] : ! [v4] : ! [v5] : ( ~ (apply_binary_as_element(v2, v2, v2, v1, v3, v4) = v5) | ~ element(v4, v2) | ~ element(v3, v2) | join(v0, v3, v4) = v5))) & ! [v0] : ! [v1] : ( ~ (the_L_join(v0) = v1) | ~ join_semilatt_str(v0) | function(v1)) & ! [v0] : ! [v1] : ( ~ (the_L_join(v0) = v1) | ~ join_semilatt_str(v0) | ? [v2] : ? [v3] : (cartesian_product2(v2, v2) = v3 & the_carrier(v0) = v2 & relation_of2_as_subset(v1, v3, v2) & quasi_total(v1, v3, v2))) & ! [v0] : ! [v1] : ( ~ (the_L_meet(v0) = v1) | ~ meet_semilatt_str(v0) | empty_carrier(v0) | ? [v2] : (the_carrier(v0) = v2 & ! [v3] : ! [v4] : ! [v5] : ( ~ (meet(v0, v3, v4) = v5) | ~ element(v4, v2) | ~ element(v3, v2) | apply_binary_as_element(v2, v2, v2, v1, v3, v4) = v5) & ! [v3] : ! [v4] : ! [v5] : ( ~ (apply_binary_as_element(v2, v2, v2, v1, v3, v4) = v5) | ~ element(v4, v2) | ~ element(v3, v2) | meet(v0, v3, v4) = v5))) & ! [v0] : ! [v1] : ( ~ (the_L_meet(v0) = v1) | ~ meet_semilatt_str(v0) | function(v1)) & ! [v0] : ! [v1] : ( ~ (the_L_meet(v0) = v1) | ~ meet_semilatt_str(v0) | ? [v2] : ? [v3] : (cartesian_product2(v2, v2) = v3 & the_carrier(v0) = v2 & relation_of2_as_subset(v1, v3, v2) & quasi_total(v1, v3, v2))) & ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1)) & ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1)) & ! [v0] : (v0 = empty_set | ~ empty(v0)) & ! [v0] : ( ~ meet_semilatt_str(v0) | one_sorted_str(v0)) & ! [v0] : ( ~ join_semilatt_str(v0) | one_sorted_str(v0)) & ! [v0] : ( ~ latt_str(v0) | meet_semilatt_str(v0)) & ! [v0] : ( ~ latt_str(v0) | join_semilatt_str(v0)) & ? [v0] : ? [v1] : ? [v2] : relation_of2_as_subset(v2, v0, v1) & ? [v0] : ? [v1] : ? [v2] : relation_of2(v2, v0, v1) & ? [v0] : ? [v1] : element(v1, v0) & ? [v0] : subset(v0, v0) & ( ~ (all_0_9_9 = all_0_10_10) | ~ (all_0_11_11 = all_0_12_12))
% 12.73/3.50 |
% 12.73/3.50 | Applying alpha-rule on (1) yields:
% 12.73/3.50 | (2) element(all_0_16_16, all_0_14_14)
% 12.73/3.50 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (join(v4, v3, v2) = v1) | ~ (join(v4, v3, v2) = v0))
% 12.73/3.50 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ empty(v2) | ~ element(v1, v3) | ~ in(v0, v1))
% 12.73/3.50 | (5) the_carrier(all_0_15_15) = all_0_14_14
% 12.73/3.50 | (6) ! [v0] : ( ~ join_semilatt_str(v0) | one_sorted_str(v0))
% 12.73/3.50 | (7) ! [v0] : ( ~ latt_str(v0) | meet_semilatt_str(v0))
% 12.73/3.50 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2)
% 12.73/3.50 | (9) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2)
% 12.73/3.50 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4)
% 12.73/3.50 | (11) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (element(v2, v1) & ~ empty(v2)))
% 12.73/3.50 | (12) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1))
% 12.73/3.50 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cartesian_product2(v0, v1) = v3) | ~ relation_of2_as_subset(v2, v0, v1) | ? [v4] : (powerset(v3) = v4 & element(v2, v4)))
% 12.73/3.50 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_intersection2(v0, v1, v2) = v3) | ? [v4] : ? [v5] : (set_intersection2(v1, v2) = v5 & powerset(v0) = v4 & (v5 = v3 | ~ element(v2, v4) | ~ element(v1, v4))))
% 12.73/3.50 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0))
% 12.73/3.50 | (16) ~ empty_carrier(all_0_8_8)
% 12.73/3.50 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (boole_lattice(v0) = v2) | ~ (the_L_join(v1) = v3) | ~ strict_latt_str(v1) | ~ latt_str(v1) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : (powerset(v0) = v5 & the_carrier(v1) = v4 & the_L_meet(v1) = v6 & ( ~ (v5 = v4) | v2 = v1 | (apply_binary(v6, v7, v8) = v11 & apply_binary(v3, v7, v8) = v9 & subset_intersection2(v0, v7, v8) = v12 & subset_union2(v0, v7, v8) = v10 & element(v8, v4) & element(v7, v4) & ( ~ (v12 = v11) | ~ (v10 = v9)))) & ( ~ (v2 = v1) | (v5 = v4 & ! [v13] : ! [v14] : ! [v15] : ( ~ (apply_binary(v6, v13, v14) = v15) | ~ element(v14, v4) | ~ element(v13, v4) | ? [v16] : (apply_binary(v3, v13, v14) = v16 & subset_intersection2(v0, v13, v14) = v15 & subset_union2(v0, v13, v14) = v16)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (apply_binary(v3, v13, v14) = v15) | ~ element(v14, v4) | ~ element(v13, v4) | ? [v16] : (apply_binary(v6, v13, v14) = v16 & subset_intersection2(v0, v13, v14) = v16 & subset_union2(v0, v13, v14) = v15)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (subset_intersection2(v0, v13, v14) = v15) | ~ element(v14, v4) | ~ element(v13, v4) | ? [v16] : (apply_binary(v6, v13, v14) = v15 & apply_binary(v3, v13, v14) = v16 & subset_union2(v0, v13, v14) = v16)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (subset_union2(v0, v13, v14) = v15) | ~ element(v14, v4) | ~ element(v13, v4) | ? [v16] : (apply_binary(v6, v13, v14) = v16 & apply_binary(v3, v13, v14) = v15 & subset_intersection2(v0, v13, v14) = v16))))))
% 12.73/3.50 | (18) latt_str(all_0_6_6)
% 12.73/3.50 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_union2(v0, v1, v2) = v3) | ? [v4] : ? [v5] : (subset_union2(v0, v2, v1) = v5 & powerset(v0) = v4 & (v5 = v3 | ~ element(v2, v4) | ~ element(v1, v4))))
% 12.73/3.50 | (20) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 12.73/3.50 | (21) ! [v0] : ! [v1] : ! [v2] : ( ~ relation_of2(v2, v0, v1) | relation_of2_as_subset(v2, v0, v1))
% 12.73/3.50 | (22) ! [v0] : ! [v1] : ! [v2] : ( ~ relation_of2_as_subset(v2, v0, v1) | relation_of2(v2, v0, v1))
% 12.73/3.50 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (apply_binary_as_element(v0, v1, v2, v3, v4, v5) = v6) | ~ function(v3) | ~ element(v5, v1) | ~ element(v4, v0) | empty(v1) | empty(v0) | element(v6, v2) | ? [v7] : (cartesian_product2(v0, v1) = v7 & ( ~ relation_of2(v3, v7, v2) | ~ quasi_total(v3, v7, v2))))
% 12.73/3.50 | (24) join_semilatt_str(all_0_2_2)
% 12.73/3.50 | (25) latt_str(all_0_8_8)
% 12.73/3.50 | (26) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (subset_intersection2(v1, v2, v2) = v3) | ? [v4] : (powerset(v1) = v4 & ( ~ element(v2, v4) | ~ element(v0, v4))))
% 12.73/3.50 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_union2(v0, v2, v1) = v3) | ? [v4] : ? [v5] : (subset_union2(v0, v1, v2) = v5 & powerset(v0) = v4 & (v5 = v3 | ~ element(v2, v4) | ~ element(v1, v4))))
% 12.73/3.50 | (28) ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ join_semilatt_str(v0) | ? [v2] : ? [v3] : (cartesian_product2(v1, v1) = v3 & the_L_join(v0) = v2 & relation_of2_as_subset(v2, v3, v1) & quasi_total(v2, v3, v1) & function(v2)))
% 12.73/3.50 | (29) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2)
% 12.73/3.50 | (30) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2)
% 12.73/3.50 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_union2(v0, v1, v2) = v3) | ? [v4] : (powerset(v0) = v4 & ( ~ element(v2, v4) | ~ element(v1, v4) | element(v3, v4))))
% 12.73/3.50 | (32) one_sorted_str(all_0_7_7)
% 12.73/3.50 | (33) ~ empty(all_0_5_5)
% 12.73/3.50 | (34) ! [v0] : ! [v1] : ( ~ (the_L_meet(v0) = v1) | ~ meet_semilatt_str(v0) | empty_carrier(v0) | ? [v2] : (the_carrier(v0) = v2 & ! [v3] : ! [v4] : ! [v5] : ( ~ (meet(v0, v3, v4) = v5) | ~ element(v4, v2) | ~ element(v3, v2) | apply_binary_as_element(v2, v2, v2, v1, v3, v4) = v5) & ! [v3] : ! [v4] : ! [v5] : ( ~ (apply_binary_as_element(v2, v2, v2, v1, v3, v4) = v5) | ~ element(v4, v2) | ~ element(v3, v2) | meet(v0, v3, v4) = v5)))
% 12.73/3.50 | (35) ! [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))
% 12.73/3.50 | (36) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (the_L_join(v2) = v1) | ~ (the_L_join(v2) = v0))
% 12.73/3.50 | (37) ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ one_sorted_str(v0) | empty_carrier(v0) | ? [v2] : ? [v3] : (powerset(v1) = v2 & element(v3, v2) & ~ empty(v3)))
% 12.73/3.50 | (38) ! [v0] : ( ~ latt_str(v0) | join_semilatt_str(v0))
% 12.73/3.50 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_intersection2(v0, v1, v2) = v3) | ? [v4] : ? [v5] : (subset_intersection2(v0, v2, v1) = v5 & powerset(v0) = v4 & (v5 = v3 | ~ element(v2, v4) | ~ element(v1, v4))))
% 12.73/3.50 | (40) strict_latt_str(all_0_8_8)
% 12.73/3.50 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (boole_lattice(v0) = v2) | ~ (the_carrier(v1) = v3) | ~ strict_latt_str(v1) | ~ latt_str(v1) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : (powerset(v0) = v4 & the_L_join(v1) = v5 & the_L_meet(v1) = v6 & ( ~ (v4 = v3) | v2 = v1 | (apply_binary(v6, v7, v8) = v11 & apply_binary(v5, v7, v8) = v9 & subset_intersection2(v0, v7, v8) = v12 & subset_union2(v0, v7, v8) = v10 & element(v8, v3) & element(v7, v3) & ( ~ (v12 = v11) | ~ (v10 = v9)))) & ( ~ (v2 = v1) | (v4 = v3 & ! [v13] : ! [v14] : ! [v15] : ( ~ (apply_binary(v6, v13, v14) = v15) | ~ element(v14, v3) | ~ element(v13, v3) | ? [v16] : (apply_binary(v5, v13, v14) = v16 & subset_intersection2(v0, v13, v14) = v15 & subset_union2(v0, v13, v14) = v16)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (apply_binary(v5, v13, v14) = v15) | ~ element(v14, v3) | ~ element(v13, v3) | ? [v16] : (apply_binary(v6, v13, v14) = v16 & subset_intersection2(v0, v13, v14) = v16 & subset_union2(v0, v13, v14) = v15)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (subset_intersection2(v0, v13, v14) = v15) | ~ element(v14, v3) | ~ element(v13, v3) | ? [v16] : (apply_binary(v6, v13, v14) = v15 & apply_binary(v5, v13, v14) = v16 & subset_union2(v0, v13, v14) = v16)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (subset_union2(v0, v13, v14) = v15) | ~ element(v14, v3) | ~ element(v13, v3) | ? [v16] : (apply_binary(v6, v13, v14) = v16 & apply_binary(v5, v13, v14) = v15 & subset_intersection2(v0, v13, v14) = v16))))))
% 12.73/3.51 | (42) ! [v0] : ! [v1] : ( ~ (the_L_meet(v0) = v1) | ~ meet_semilatt_str(v0) | function(v1))
% 12.73/3.51 | (43) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ empty(v1))
% 12.73/3.51 | (44) join(all_0_15_15, all_0_16_16, all_0_13_13) = all_0_12_12
% 12.73/3.51 | (45) ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ meet_semilatt_str(v0) | ? [v2] : ? [v3] : (cartesian_product2(v1, v1) = v3 & the_L_meet(v0) = v2 & relation_of2_as_subset(v2, v3, v1) & quasi_total(v2, v3, v1) & function(v2)))
% 12.73/3.51 | (46) empty(all_0_4_4)
% 12.73/3.51 | (47) ! [v0] : ! [v1] : ( ~ (the_L_meet(v0) = v1) | ~ meet_semilatt_str(v0) | ? [v2] : ? [v3] : (cartesian_product2(v2, v2) = v3 & the_carrier(v0) = v2 & relation_of2_as_subset(v1, v3, v2) & quasi_total(v1, v3, v2)))
% 12.73/3.51 | (48) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2)
% 12.73/3.51 | (49) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2)
% 12.73/3.51 | (50) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1))
% 12.73/3.51 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (apply_binary_as_element(v0, v1, v2, v3, v4, v5) = v6) | ~ function(v3) | ~ element(v5, v1) | ~ element(v4, v0) | empty(v1) | empty(v0) | ? [v7] : ? [v8] : (apply_binary(v3, v4, v5) = v8 & cartesian_product2(v0, v1) = v7 & (v8 = v6 | ~ relation_of2(v3, v7, v2) | ~ quasi_total(v3, v7, v2))))
% 12.83/3.51 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0))
% 12.83/3.51 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0))
% 12.83/3.51 | (54) ! [v0] : ! [v1] : ( ~ (the_L_join(v0) = v1) | ~ join_semilatt_str(v0) | empty_carrier(v0) | ? [v2] : (the_carrier(v0) = v2 & ! [v3] : ! [v4] : ! [v5] : ( ~ (join(v0, v3, v4) = v5) | ~ element(v4, v2) | ~ element(v3, v2) | apply_binary_as_element(v2, v2, v2, v1, v3, v4) = v5) & ! [v3] : ! [v4] : ! [v5] : ( ~ (apply_binary_as_element(v2, v2, v2, v1, v3, v4) = v5) | ~ element(v4, v2) | ~ element(v3, v2) | join(v0, v3, v4) = v5)))
% 12.83/3.51 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v5 = v1 | ~ (latt_str_of(v4, v5, v6) = v3) | ~ (latt_str_of(v0, v1, v2) = v3) | ~ function(v2) | ~ function(v1) | ? [v7] : (cartesian_product2(v0, v0) = v7 & ( ~ relation_of2(v2, v7, v0) | ~ relation_of2(v1, v7, v0) | ~ quasi_total(v2, v7, v0) | ~ quasi_total(v1, v7, v0))))
% 12.83/3.51 | (56) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ~ empty(v2) | empty(v0))
% 12.83/3.51 | (57) ! [v0] : ! [v1] : ! [v2] : ( ~ (cartesian_product2(v1, v1) = v2) | ~ (the_carrier(v0) = v1) | ~ meet_semilatt_str(v0) | ? [v3] : (the_L_meet(v0) = v3 & relation_of2_as_subset(v3, v2, v1) & quasi_total(v3, v2, v1) & function(v3)))
% 12.83/3.51 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 12.83/3.51 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_intersection2(v1, v2) = v4) | ~ (powerset(v0) = v3) | ~ element(v2, v3) | ~ element(v1, v3) | subset_intersection2(v0, v1, v2) = v4)
% 12.83/3.51 | (60) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1))
% 12.83/3.51 | (61) empty(empty_set)
% 12.83/3.51 | (62) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (the_carrier(v2) = v1) | ~ (the_carrier(v2) = v0))
% 12.83/3.51 | (63) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (ordered_pair(v1, v2) = v3) | ~ (apply(v0, v3) = v4) | ~ function(v0) | ~ relation(v0) | apply_binary(v0, v1, v2) = v4)
% 12.83/3.51 | (64) ! [v0] : ! [v1] : ( ~ (the_L_join(v0) = v1) | ~ join_semilatt_str(v0) | function(v1))
% 12.83/3.51 | (65) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v0 | ~ (latt_str_of(v4, v5, v6) = v3) | ~ (latt_str_of(v0, v1, v2) = v3) | ~ function(v2) | ~ function(v1) | ? [v7] : (cartesian_product2(v0, v0) = v7 & ( ~ relation_of2(v2, v7, v0) | ~ relation_of2(v1, v7, v0) | ~ quasi_total(v2, v7, v0) | ~ quasi_total(v1, v7, v0))))
% 12.83/3.51 | (66) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0))
% 12.83/3.51 | (67) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (empty(v2) & element(v2, v1)))
% 12.83/3.51 | (68) ! [v0] : ! [v1] : ( ~ (boole_lattice(v0) = v1) | latt_str(v1))
% 12.83/3.51 | (69) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (subset_union2(v4, v3, v2) = v1) | ~ (subset_union2(v4, v3, v2) = v0))
% 12.83/3.51 | (70) ~ empty_carrier(all_0_7_7)
% 12.83/3.51 | (71) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_intersection2(v0, v2, v1) = v3) | ? [v4] : ? [v5] : (subset_intersection2(v0, v1, v2) = v5 & powerset(v0) = v4 & (v5 = v3 | ~ element(v2, v4) | ~ element(v1, v4))))
% 12.83/3.51 | (72) ! [v0] : ! [v1] : ! [v2] : ( ~ (cartesian_product2(v1, v1) = v2) | ~ (the_carrier(v0) = v1) | ~ join_semilatt_str(v0) | ? [v3] : (the_L_join(v0) = v3 & relation_of2_as_subset(v3, v2, v1) & quasi_total(v3, v2, v1) & function(v3)))
% 12.83/3.51 | (73) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (the_L_meet(v2) = v1) | ~ (the_L_meet(v2) = v0))
% 12.83/3.51 | (74) ~ (all_0_9_9 = all_0_10_10) | ~ (all_0_11_11 = all_0_12_12)
% 12.83/3.51 | (75) boole_lattice(all_0_17_17) = all_0_15_15
% 12.83/3.51 | (76) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0))
% 12.83/3.51 | (77) ! [v0] : ! [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) = v4) | ~ strict_latt_str(v0) | ~ latt_str(v0))
% 12.83/3.51 | (78) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (latt_str_of(v0, v1, v2) = v3) | ~ function(v2) | ~ function(v1) | latt_str(v3) | ? [v4] : (cartesian_product2(v0, v0) = v4 & ( ~ relation_of2(v2, v4, v0) | ~ relation_of2(v1, v4, v0) | ~ quasi_total(v2, v4, v0) | ~ quasi_total(v1, v4, v0))))
% 12.83/3.51 | (79) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (latt_str_of(v4, v3, v2) = v1) | ~ (latt_str_of(v4, v3, v2) = v0))
% 12.83/3.51 | (80) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v0) = v2) | ~ (the_L_join(v1) = v3) | ~ strict_latt_str(v1) | ~ latt_str(v1) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : (boole_lattice(v0) = v4 & the_carrier(v1) = v5 & the_L_meet(v1) = v6 & ( ~ (v5 = v2) | v4 = v1 | (apply_binary(v6, v7, v8) = v11 & apply_binary(v3, v7, v8) = v9 & subset_intersection2(v0, v7, v8) = v12 & subset_union2(v0, v7, v8) = v10 & element(v8, v2) & element(v7, v2) & ( ~ (v12 = v11) | ~ (v10 = v9)))) & ( ~ (v4 = v1) | (v5 = v2 & ! [v13] : ! [v14] : ! [v15] : ( ~ (apply_binary(v6, v13, v14) = v15) | ~ element(v14, v2) | ~ element(v13, v2) | ? [v16] : (apply_binary(v3, v13, v14) = v16 & subset_intersection2(v0, v13, v14) = v15 & subset_union2(v0, v13, v14) = v16)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (apply_binary(v3, v13, v14) = v15) | ~ element(v14, v2) | ~ element(v13, v2) | ? [v16] : (apply_binary(v6, v13, v14) = v16 & subset_intersection2(v0, v13, v14) = v16 & subset_union2(v0, v13, v14) = v15)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (subset_intersection2(v0, v13, v14) = v15) | ~ element(v14, v2) | ~ element(v13, v2) | ? [v16] : (apply_binary(v6, v13, v14) = v15 & apply_binary(v3, v13, v14) = v16 & subset_union2(v0, v13, v14) = v16)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (subset_union2(v0, v13, v14) = v15) | ~ element(v14, v2) | ~ element(v13, v2) | ? [v16] : (apply_binary(v6, v13, v14) = v16 & apply_binary(v3, v13, v14) = v15 & subset_intersection2(v0, v13, v14) = v16))))))
% 12.83/3.51 | (81) ! [v0] : ! [v1] : ( ~ (boole_lattice(v0) = v1) | ~ empty_carrier(v1))
% 12.83/3.51 | (82) meet(all_0_15_15, all_0_16_16, all_0_13_13) = all_0_10_10
% 12.83/3.52 | (83) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = v2 | ~ (latt_str_of(v4, v5, v6) = v3) | ~ (latt_str_of(v0, v1, v2) = v3) | ~ function(v2) | ~ function(v1) | ? [v7] : (cartesian_product2(v0, v0) = v7 & ( ~ relation_of2(v2, v7, v0) | ~ relation_of2(v1, v7, v0) | ~ quasi_total(v2, v7, v0) | ~ quasi_total(v1, v7, v0))))
% 12.83/3.52 | (84) ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ join_semilatt_str(v0) | empty_carrier(v0) | ? [v2] : (the_L_join(v0) = v2 & ! [v3] : ! [v4] : ! [v5] : ( ~ (join(v0, v3, v4) = v5) | ~ element(v4, v1) | ~ element(v3, v1) | apply_binary_as_element(v1, v1, v1, v2, v3, v4) = v5) & ! [v3] : ! [v4] : ! [v5] : ( ~ (apply_binary_as_element(v1, v1, v1, v2, v3, v4) = v5) | ~ element(v4, v1) | ~ element(v3, v1) | join(v0, v3, v4) = v5)))
% 12.83/3.52 | (85) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (boole_lattice(v0) = v2) | ~ (the_L_meet(v1) = v3) | ~ strict_latt_str(v1) | ~ latt_str(v1) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : (powerset(v0) = v5 & the_carrier(v1) = v4 & the_L_join(v1) = v6 & ( ~ (v5 = v4) | v2 = v1 | (apply_binary(v6, v7, v8) = v9 & apply_binary(v3, v7, v8) = v11 & subset_intersection2(v0, v7, v8) = v12 & subset_union2(v0, v7, v8) = v10 & element(v8, v4) & element(v7, v4) & ( ~ (v12 = v11) | ~ (v10 = v9)))) & ( ~ (v2 = v1) | (v5 = v4 & ! [v13] : ! [v14] : ! [v15] : ( ~ (apply_binary(v6, v13, v14) = v15) | ~ element(v14, v4) | ~ element(v13, v4) | ? [v16] : (apply_binary(v3, v13, v14) = v16 & subset_intersection2(v0, v13, v14) = v16 & subset_union2(v0, v13, v14) = v15)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (apply_binary(v3, v13, v14) = v15) | ~ element(v14, v4) | ~ element(v13, v4) | ? [v16] : (apply_binary(v6, v13, v14) = v16 & subset_intersection2(v0, v13, v14) = v15 & subset_union2(v0, v13, v14) = v16)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (subset_intersection2(v0, v13, v14) = v15) | ~ element(v14, v4) | ~ element(v13, v4) | ? [v16] : (apply_binary(v6, v13, v14) = v16 & apply_binary(v3, v13, v14) = v15 & subset_union2(v0, v13, v14) = v16)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (subset_union2(v0, v13, v14) = v15) | ~ element(v14, v4) | ~ element(v13, v4) | ? [v16] : (apply_binary(v6, v13, v14) = v15 & apply_binary(v3, v13, v14) = v16 & subset_intersection2(v0, v13, v14) = v16))))))
% 12.83/3.52 | (86) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (latt_str_of(v0, v1, v2) = v3) | ~ function(v2) | ~ function(v1) | empty(v0) | strict_latt_str(v3) | ? [v4] : (cartesian_product2(v0, v0) = v4 & ( ~ relation_of2(v2, v4, v0) | ~ relation_of2(v1, v4, v0) | ~ quasi_total(v2, v4, v0) | ~ quasi_total(v1, v4, v0))))
% 12.88/3.52 | (87) ? [v0] : ? [v1] : element(v1, v0)
% 12.88/3.52 | (88) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (join(v0, v1, v2) = v3) | ~ join_semilatt_str(v0) | empty_carrier(v0) | ? [v4] : (the_carrier(v0) = v4 & ( ~ element(v2, v4) | ~ element(v1, v4) | element(v3, v4))))
% 12.88/3.52 | (89) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ~ empty(v1))
% 12.88/3.52 | (90) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3))
% 12.88/3.52 | (91) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (subset_union2(v1, v2, v2) = v3) | ? [v4] : (powerset(v1) = v4 & ( ~ element(v2, v4) | ~ element(v0, v4))))
% 12.88/3.52 | (92) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0))
% 12.88/3.52 | (93) strict_latt_str(all_0_6_6)
% 12.88/3.52 | (94) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (subset_intersection2(v4, v3, v2) = v1) | ~ (subset_intersection2(v4, v3, v2) = v0))
% 12.88/3.52 | (95) meet_semilatt_str(all_0_0_0)
% 12.88/3.52 | (96) ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ one_sorted_str(v0) | ~ empty(v1) | empty_carrier(v0))
% 12.88/3.52 | (97) ! [v0] : ! [v1] : ! [v2] : ( ~ (cartesian_product2(v0, v1) = v2) | ~ empty(v2) | empty(v1) | empty(v0))
% 12.88/3.52 | (98) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v0) = v2) | ~ (the_L_meet(v1) = v3) | ~ strict_latt_str(v1) | ~ latt_str(v1) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : (boole_lattice(v0) = v4 & the_carrier(v1) = v5 & the_L_join(v1) = v6 & ( ~ (v5 = v2) | v4 = v1 | (apply_binary(v6, v7, v8) = v9 & apply_binary(v3, v7, v8) = v11 & subset_intersection2(v0, v7, v8) = v12 & subset_union2(v0, v7, v8) = v10 & element(v8, v2) & element(v7, v2) & ( ~ (v12 = v11) | ~ (v10 = v9)))) & ( ~ (v4 = v1) | (v5 = v2 & ! [v13] : ! [v14] : ! [v15] : ( ~ (apply_binary(v6, v13, v14) = v15) | ~ element(v14, v2) | ~ element(v13, v2) | ? [v16] : (apply_binary(v3, v13, v14) = v16 & subset_intersection2(v0, v13, v14) = v16 & subset_union2(v0, v13, v14) = v15)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (apply_binary(v3, v13, v14) = v15) | ~ element(v14, v2) | ~ element(v13, v2) | ? [v16] : (apply_binary(v6, v13, v14) = v16 & subset_intersection2(v0, v13, v14) = v15 & subset_union2(v0, v13, v14) = v16)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (subset_intersection2(v0, v13, v14) = v15) | ~ element(v14, v2) | ~ element(v13, v2) | ? [v16] : (apply_binary(v6, v13, v14) = v16 & apply_binary(v3, v13, v14) = v15 & subset_union2(v0, v13, v14) = v16)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (subset_union2(v0, v13, v14) = v15) | ~ element(v14, v2) | ~ element(v13, v2) | ? [v16] : (apply_binary(v6, v13, v14) = v15 & apply_binary(v3, v13, v14) = v16 & subset_intersection2(v0, v13, v14) = v16))))))
% 12.88/3.52 | (99) set_union2(all_0_16_16, all_0_13_13) = all_0_11_11
% 12.88/3.52 | (100) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (boole_lattice(v2) = v1) | ~ (boole_lattice(v2) = v0))
% 12.88/3.52 | (101) element(all_0_13_13, all_0_14_14)
% 12.88/3.52 | (102) one_sorted_str(all_0_1_1)
% 12.88/3.52 | (103) ? [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cartesian_product2(v1, v2) = v3) | relation(v0) | ? [v4] : (powerset(v3) = v4 & ~ element(v0, v4)))
% 12.88/3.52 | (104) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ empty(v2) | empty(v0))
% 12.88/3.52 | (105) ? [v0] : subset(v0, v0)
% 12.88/3.52 | (106) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_union2(v1, v2) = v4) | ~ (powerset(v0) = v3) | ~ element(v2, v3) | ~ element(v1, v3) | subset_union2(v0, v1, v2) = v4)
% 12.88/3.52 | (107) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1))
% 12.88/3.52 | (108) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (latt_str_of(v0, v1, v2) = v3) | ~ empty_carrier(v3) | ~ function(v2) | ~ function(v1) | empty(v0) | ? [v4] : (cartesian_product2(v0, v0) = v4 & ( ~ relation_of2(v2, v4, v0) | ~ relation_of2(v1, v4, v0) | ~ quasi_total(v2, v4, v0) | ~ quasi_total(v1, v4, v0))))
% 12.88/3.52 | (109) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ element(v0, v2) | subset(v0, v1))
% 12.88/3.52 | (110) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2))
% 12.88/3.52 | (111) ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1))
% 12.88/3.52 | (112) ! [v0] : ! [v1] : ( ~ (the_L_join(v0) = v1) | ~ join_semilatt_str(v0) | ? [v2] : ? [v3] : (cartesian_product2(v2, v2) = v3 & the_carrier(v0) = v2 & relation_of2_as_subset(v1, v3, v2) & quasi_total(v1, v3, v2)))
% 12.88/3.52 | (113) set_intersection2(all_0_16_16, all_0_13_13) = all_0_9_9
% 12.88/3.52 | (114) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1))
% 12.88/3.52 | (115) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0))
% 12.88/3.52 | (116) ! [v0] : ( ~ meet_semilatt_str(v0) | one_sorted_str(v0))
% 12.88/3.52 | (117) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ in(v0, v1) | element(v0, v2))
% 12.88/3.52 | (118) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_intersection2(v0, v1, v2) = v3) | ? [v4] : (powerset(v0) = v4 & ( ~ element(v2, v4) | ~ element(v1, v4) | element(v3, v4))))
% 12.88/3.52 | (119) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (meet(v0, v1, v2) = v3) | ~ meet_semilatt_str(v0) | empty_carrier(v0) | ? [v4] : (the_carrier(v0) = v4 & ( ~ element(v2, v4) | ~ element(v1, v4) | element(v3, v4))))
% 12.88/3.52 | (120) ? [v0] : ? [v1] : ? [v2] : relation_of2_as_subset(v2, v0, v1)
% 12.88/3.52 | (121) ? [v0] : ? [v1] : ? [v2] : relation_of2(v2, v0, v1)
% 12.88/3.52 | (122) latt_str(all_0_3_3)
% 12.88/3.52 | (123) ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ meet_semilatt_str(v0) | empty_carrier(v0) | ? [v2] : (the_L_meet(v0) = v2 & ! [v3] : ! [v4] : ! [v5] : ( ~ (meet(v0, v3, v4) = v5) | ~ element(v4, v1) | ~ element(v3, v1) | apply_binary_as_element(v1, v1, v1, v2, v3, v4) = v5) & ! [v3] : ! [v4] : ! [v5] : ( ~ (apply_binary_as_element(v1, v1, v1, v2, v3, v4) = v5) | ~ element(v4, v1) | ~ element(v3, v1) | meet(v0, v3, v4) = v5)))
% 12.88/3.52 | (124) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1))
% 12.91/3.52 | (125) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (apply_binary(v0, v1, v2) = v3) | ~ function(v0) | ~ relation(v0) | ? [v4] : (ordered_pair(v1, v2) = v4 & apply(v0, v4) = v3))
% 12.91/3.52 | (126) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (apply_binary(v4, v3, v2) = v1) | ~ (apply_binary(v4, v3, v2) = v0))
% 12.91/3.52 | (127) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (latt_str_of(v0, v1, v2) = v3) | ~ function(v2) | ~ function(v1) | strict_latt_str(v3) | ? [v4] : (cartesian_product2(v0, v0) = v4 & ( ~ relation_of2(v2, v4, v0) | ~ relation_of2(v1, v4, v0) | ~ quasi_total(v2, v4, v0) | ~ quasi_total(v1, v4, v0))))
% 12.91/3.53 | (128) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (meet(v4, v3, v2) = v1) | ~ (meet(v4, v3, v2) = v0))
% 12.91/3.53 | (129) ! [v0] : (v0 = empty_set | ~ empty(v0))
% 12.91/3.53 | (130) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_union2(v0, v1, v2) = v3) | ? [v4] : ? [v5] : (set_union2(v1, v2) = v5 & powerset(v0) = v4 & (v5 = v3 | ~ element(v2, v4) | ~ element(v1, v4))))
% 12.91/3.53 | (131) ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1))
% 12.91/3.53 | (132) ! [v0] : ! [v1] : ( ~ (boole_lattice(v0) = v1) | strict_latt_str(v1))
% 12.91/3.53 | (133) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v0) = v3) | ~ (the_carrier(v1) = v2) | ~ strict_latt_str(v1) | ~ latt_str(v1) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : (boole_lattice(v0) = v4 & the_L_join(v1) = v5 & the_L_meet(v1) = v6 & ( ~ (v4 = v1) | (v3 = v2 & ! [v13] : ! [v14] : ! [v15] : ( ~ (apply_binary(v6, v13, v14) = v15) | ~ element(v14, v2) | ~ element(v13, v2) | ? [v16] : (apply_binary(v5, v13, v14) = v16 & subset_intersection2(v0, v13, v14) = v15 & subset_union2(v0, v13, v14) = v16)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (apply_binary(v5, v13, v14) = v15) | ~ element(v14, v2) | ~ element(v13, v2) | ? [v16] : (apply_binary(v6, v13, v14) = v16 & subset_intersection2(v0, v13, v14) = v16 & subset_union2(v0, v13, v14) = v15)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (subset_intersection2(v0, v13, v14) = v15) | ~ element(v14, v2) | ~ element(v13, v2) | ? [v16] : (apply_binary(v6, v13, v14) = v15 & apply_binary(v5, v13, v14) = v16 & subset_union2(v0, v13, v14) = v16)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (subset_union2(v0, v13, v14) = v15) | ~ element(v14, v2) | ~ element(v13, v2) | ? [v16] : (apply_binary(v6, v13, v14) = v16 & apply_binary(v5, v13, v14) = v15 & subset_intersection2(v0, v13, v14) = v16)))) & ( ~ (v3 = v2) | v4 = v1 | (apply_binary(v6, v7, v8) = v11 & apply_binary(v5, v7, v8) = v9 & subset_intersection2(v0, v7, v8) = v12 & subset_union2(v0, v7, v8) = v10 & element(v8, v2) & element(v7, v2) & ( ~ (v12 = v11) | ~ (v10 = v9))))))
% 12.91/3.53 | (134) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ~ empty(v2))
% 12.91/3.53 |
% 12.91/3.53 | Instantiating formula (132) with all_0_15_15, all_0_17_17 and discharging atoms boole_lattice(all_0_17_17) = all_0_15_15, yields:
% 12.91/3.53 | (135) strict_latt_str(all_0_15_15)
% 12.91/3.53 |
% 12.91/3.53 | Instantiating formula (68) with all_0_15_15, all_0_17_17 and discharging atoms boole_lattice(all_0_17_17) = all_0_15_15, yields:
% 12.91/3.53 | (136) latt_str(all_0_15_15)
% 12.91/3.53 |
% 12.91/3.53 | Instantiating formula (131) with all_0_14_14, all_0_13_13 and discharging atoms element(all_0_13_13, all_0_14_14), yields:
% 12.91/3.53 | (137) empty(all_0_14_14) | in(all_0_13_13, all_0_14_14)
% 12.91/3.53 |
% 12.91/3.53 | Instantiating formula (131) with all_0_14_14, all_0_16_16 and discharging atoms element(all_0_16_16, all_0_14_14), yields:
% 12.91/3.53 | (138) empty(all_0_14_14) | in(all_0_16_16, all_0_14_14)
% 12.91/3.53 |
% 12.91/3.53 | Instantiating formula (41) with all_0_14_14, all_0_15_15, all_0_15_15, all_0_17_17 and discharging atoms boole_lattice(all_0_17_17) = all_0_15_15, the_carrier(all_0_15_15) = all_0_14_14, strict_latt_str(all_0_15_15), latt_str(all_0_15_15), yields:
% 12.91/3.53 | (139) ? [v0] : ? [v1] : (powerset(all_0_17_17) = all_0_14_14 & the_L_join(all_0_15_15) = v0 & the_L_meet(all_0_15_15) = v1 & ! [v2] : ! [v3] : ! [v4] : ( ~ (apply_binary(v1, v2, v3) = v4) | ~ element(v3, all_0_14_14) | ~ element(v2, all_0_14_14) | ? [v5] : (apply_binary(v0, v2, v3) = v5 & subset_intersection2(all_0_17_17, v2, v3) = v4 & subset_union2(all_0_17_17, v2, v3) = v5)) & ! [v2] : ! [v3] : ! [v4] : ( ~ (apply_binary(v0, v2, v3) = v4) | ~ element(v3, all_0_14_14) | ~ element(v2, all_0_14_14) | ? [v5] : (apply_binary(v1, v2, v3) = v5 & subset_intersection2(all_0_17_17, v2, v3) = v5 & subset_union2(all_0_17_17, v2, v3) = v4)) & ! [v2] : ! [v3] : ! [v4] : ( ~ (subset_intersection2(all_0_17_17, v2, v3) = v4) | ~ element(v3, all_0_14_14) | ~ element(v2, all_0_14_14) | ? [v5] : (apply_binary(v1, v2, v3) = v4 & apply_binary(v0, v2, v3) = v5 & subset_union2(all_0_17_17, v2, v3) = v5)) & ! [v2] : ! [v3] : ! [v4] : ( ~ (subset_union2(all_0_17_17, v2, v3) = v4) | ~ element(v3, all_0_14_14) | ~ element(v2, all_0_14_14) | ? [v5] : (apply_binary(v1, v2, v3) = v5 & apply_binary(v0, v2, v3) = v4 & subset_intersection2(all_0_17_17, v2, v3) = v5)))
% 12.91/3.53 |
% 12.91/3.53 | Instantiating formula (7) with all_0_15_15 and discharging atoms latt_str(all_0_15_15), yields:
% 12.91/3.53 | (140) meet_semilatt_str(all_0_15_15)
% 12.91/3.53 |
% 12.91/3.53 | Instantiating formula (38) with all_0_15_15 and discharging atoms latt_str(all_0_15_15), yields:
% 12.91/3.53 | (141) join_semilatt_str(all_0_15_15)
% 12.91/3.53 |
% 12.91/3.53 | Instantiating (139) with all_33_0_30, all_33_1_31 yields:
% 12.91/3.53 | (142) powerset(all_0_17_17) = all_0_14_14 & the_L_join(all_0_15_15) = all_33_1_31 & the_L_meet(all_0_15_15) = all_33_0_30 & ! [v0] : ! [v1] : ! [v2] : ( ~ (apply_binary(all_33_0_30, v0, v1) = v2) | ~ element(v1, all_0_14_14) | ~ element(v0, all_0_14_14) | ? [v3] : (apply_binary(all_33_1_31, v0, v1) = v3 & subset_intersection2(all_0_17_17, v0, v1) = v2 & subset_union2(all_0_17_17, v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (apply_binary(all_33_1_31, v0, v1) = v2) | ~ element(v1, all_0_14_14) | ~ element(v0, all_0_14_14) | ? [v3] : (apply_binary(all_33_0_30, v0, v1) = v3 & subset_intersection2(all_0_17_17, v0, v1) = v3 & subset_union2(all_0_17_17, v0, v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_intersection2(all_0_17_17, v0, v1) = v2) | ~ element(v1, all_0_14_14) | ~ element(v0, all_0_14_14) | ? [v3] : (apply_binary(all_33_0_30, v0, v1) = v2 & apply_binary(all_33_1_31, v0, v1) = v3 & subset_union2(all_0_17_17, v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_union2(all_0_17_17, v0, v1) = v2) | ~ element(v1, all_0_14_14) | ~ element(v0, all_0_14_14) | ? [v3] : (apply_binary(all_33_0_30, v0, v1) = v3 & apply_binary(all_33_1_31, v0, v1) = v2 & subset_intersection2(all_0_17_17, v0, v1) = v3))
% 12.91/3.53 |
% 12.91/3.53 | Applying alpha-rule on (142) yields:
% 12.91/3.53 | (143) powerset(all_0_17_17) = all_0_14_14
% 12.91/3.53 | (144) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_union2(all_0_17_17, v0, v1) = v2) | ~ element(v1, all_0_14_14) | ~ element(v0, all_0_14_14) | ? [v3] : (apply_binary(all_33_0_30, v0, v1) = v3 & apply_binary(all_33_1_31, v0, v1) = v2 & subset_intersection2(all_0_17_17, v0, v1) = v3))
% 12.91/3.53 | (145) ! [v0] : ! [v1] : ! [v2] : ( ~ (apply_binary(all_33_0_30, v0, v1) = v2) | ~ element(v1, all_0_14_14) | ~ element(v0, all_0_14_14) | ? [v3] : (apply_binary(all_33_1_31, v0, v1) = v3 & subset_intersection2(all_0_17_17, v0, v1) = v2 & subset_union2(all_0_17_17, v0, v1) = v3))
% 12.91/3.53 | (146) ! [v0] : ! [v1] : ! [v2] : ( ~ (apply_binary(all_33_1_31, v0, v1) = v2) | ~ element(v1, all_0_14_14) | ~ element(v0, all_0_14_14) | ? [v3] : (apply_binary(all_33_0_30, v0, v1) = v3 & subset_intersection2(all_0_17_17, v0, v1) = v3 & subset_union2(all_0_17_17, v0, v1) = v2))
% 12.91/3.53 | (147) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_intersection2(all_0_17_17, v0, v1) = v2) | ~ element(v1, all_0_14_14) | ~ element(v0, all_0_14_14) | ? [v3] : (apply_binary(all_33_0_30, v0, v1) = v2 & apply_binary(all_33_1_31, v0, v1) = v3 & subset_union2(all_0_17_17, v0, v1) = v3))
% 12.91/3.53 | (148) the_L_join(all_0_15_15) = all_33_1_31
% 12.91/3.53 | (149) the_L_meet(all_0_15_15) = all_33_0_30
% 12.91/3.53 |
% 12.91/3.53 | Instantiating formula (59) with all_0_9_9, all_0_14_14, all_0_13_13, all_0_16_16, all_0_17_17 and discharging atoms set_intersection2(all_0_16_16, all_0_13_13) = all_0_9_9, powerset(all_0_17_17) = all_0_14_14, element(all_0_13_13, all_0_14_14), element(all_0_16_16, all_0_14_14), yields:
% 12.91/3.53 | (150) subset_intersection2(all_0_17_17, all_0_16_16, all_0_13_13) = all_0_9_9
% 12.91/3.53 |
% 12.91/3.53 | Instantiating formula (106) with all_0_11_11, all_0_14_14, all_0_13_13, all_0_16_16, all_0_17_17 and discharging atoms set_union2(all_0_16_16, all_0_13_13) = all_0_11_11, powerset(all_0_17_17) = all_0_14_14, element(all_0_13_13, all_0_14_14), element(all_0_16_16, all_0_14_14), yields:
% 12.91/3.53 | (151) subset_union2(all_0_17_17, all_0_16_16, all_0_13_13) = all_0_11_11
% 12.91/3.53 |
% 12.91/3.53 | Instantiating formula (133) with all_0_14_14, all_0_14_14, all_0_15_15, all_0_17_17 and discharging atoms powerset(all_0_17_17) = all_0_14_14, the_carrier(all_0_15_15) = all_0_14_14, strict_latt_str(all_0_15_15), latt_str(all_0_15_15), yields:
% 12.91/3.53 | (152) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (boole_lattice(all_0_17_17) = v0 & the_L_join(all_0_15_15) = v1 & the_L_meet(all_0_15_15) = v2 & ( ~ (v0 = all_0_15_15) | ( ! [v9] : ! [v10] : ! [v11] : ( ~ (apply_binary(v2, v9, v10) = v11) | ~ element(v10, all_0_14_14) | ~ element(v9, all_0_14_14) | ? [v12] : (apply_binary(v1, v9, v10) = v12 & subset_intersection2(all_0_17_17, v9, v10) = v11 & subset_union2(all_0_17_17, v9, v10) = v12)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (apply_binary(v1, v9, v10) = v11) | ~ element(v10, all_0_14_14) | ~ element(v9, all_0_14_14) | ? [v12] : (apply_binary(v2, v9, v10) = v12 & subset_intersection2(all_0_17_17, v9, v10) = v12 & subset_union2(all_0_17_17, v9, v10) = v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (subset_intersection2(all_0_17_17, v9, v10) = v11) | ~ element(v10, all_0_14_14) | ~ element(v9, all_0_14_14) | ? [v12] : (apply_binary(v2, v9, v10) = v11 & apply_binary(v1, v9, v10) = v12 & subset_union2(all_0_17_17, v9, v10) = v12)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (subset_union2(all_0_17_17, v9, v10) = v11) | ~ element(v10, all_0_14_14) | ~ element(v9, all_0_14_14) | ? [v12] : (apply_binary(v2, v9, v10) = v12 & apply_binary(v1, v9, v10) = v11 & subset_intersection2(all_0_17_17, v9, v10) = v12)))) & (v0 = all_0_15_15 | (apply_binary(v2, v3, v4) = v7 & apply_binary(v1, v3, v4) = v5 & subset_intersection2(all_0_17_17, v3, v4) = v8 & subset_union2(all_0_17_17, v3, v4) = v6 & element(v4, all_0_14_14) & element(v3, all_0_14_14) & ( ~ (v8 = v7) | ~ (v6 = v5)))))
% 12.91/3.53 |
% 12.91/3.53 | Instantiating formula (17) with all_33_1_31, all_0_15_15, all_0_15_15, all_0_17_17 and discharging atoms boole_lattice(all_0_17_17) = all_0_15_15, the_L_join(all_0_15_15) = all_33_1_31, strict_latt_str(all_0_15_15), latt_str(all_0_15_15), yields:
% 12.91/3.53 | (153) ? [v0] : ? [v1] : (powerset(all_0_17_17) = v0 & the_carrier(all_0_15_15) = v0 & the_L_meet(all_0_15_15) = v1 & ! [v2] : ! [v3] : ! [v4] : ( ~ (apply_binary(v1, v2, v3) = v4) | ~ element(v3, v0) | ~ element(v2, v0) | ? [v5] : (apply_binary(all_33_1_31, v2, v3) = v5 & subset_intersection2(all_0_17_17, v2, v3) = v4 & subset_union2(all_0_17_17, v2, v3) = v5)) & ! [v2] : ! [v3] : ! [v4] : ( ~ (apply_binary(all_33_1_31, v2, v3) = v4) | ~ element(v3, v0) | ~ element(v2, v0) | ? [v5] : (apply_binary(v1, v2, v3) = v5 & subset_intersection2(all_0_17_17, v2, v3) = v5 & subset_union2(all_0_17_17, v2, v3) = v4)) & ! [v2] : ! [v3] : ! [v4] : ( ~ (subset_intersection2(all_0_17_17, v2, v3) = v4) | ~ element(v3, v0) | ~ element(v2, v0) | ? [v5] : (apply_binary(v1, v2, v3) = v4 & apply_binary(all_33_1_31, v2, v3) = v5 & subset_union2(all_0_17_17, v2, v3) = v5)) & ! [v2] : ! [v3] : ! [v4] : ( ~ (subset_union2(all_0_17_17, v2, v3) = v4) | ~ element(v3, v0) | ~ element(v2, v0) | ? [v5] : (apply_binary(v1, v2, v3) = v5 & apply_binary(all_33_1_31, v2, v3) = v4 & subset_intersection2(all_0_17_17, v2, v3) = v5)))
% 12.91/3.53 |
% 12.91/3.53 | Instantiating formula (80) with all_33_1_31, all_0_14_14, all_0_15_15, all_0_17_17 and discharging atoms powerset(all_0_17_17) = all_0_14_14, the_L_join(all_0_15_15) = all_33_1_31, strict_latt_str(all_0_15_15), latt_str(all_0_15_15), yields:
% 12.91/3.53 | (154) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (boole_lattice(all_0_17_17) = v0 & the_carrier(all_0_15_15) = v1 & the_L_meet(all_0_15_15) = v2 & ( ~ (v1 = all_0_14_14) | v0 = all_0_15_15 | (apply_binary(v2, v3, v4) = v7 & apply_binary(all_33_1_31, v3, v4) = v5 & subset_intersection2(all_0_17_17, v3, v4) = v8 & subset_union2(all_0_17_17, v3, v4) = v6 & element(v4, all_0_14_14) & element(v3, all_0_14_14) & ( ~ (v8 = v7) | ~ (v6 = v5)))) & ( ~ (v0 = all_0_15_15) | (v1 = all_0_14_14 & ! [v9] : ! [v10] : ! [v11] : ( ~ (apply_binary(v2, v9, v10) = v11) | ~ element(v10, all_0_14_14) | ~ element(v9, all_0_14_14) | ? [v12] : (apply_binary(all_33_1_31, v9, v10) = v12 & subset_intersection2(all_0_17_17, v9, v10) = v11 & subset_union2(all_0_17_17, v9, v10) = v12)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (apply_binary(all_33_1_31, v9, v10) = v11) | ~ element(v10, all_0_14_14) | ~ element(v9, all_0_14_14) | ? [v12] : (apply_binary(v2, v9, v10) = v12 & subset_intersection2(all_0_17_17, v9, v10) = v12 & subset_union2(all_0_17_17, v9, v10) = v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (subset_intersection2(all_0_17_17, v9, v10) = v11) | ~ element(v10, all_0_14_14) | ~ element(v9, all_0_14_14) | ? [v12] : (apply_binary(v2, v9, v10) = v11 & apply_binary(all_33_1_31, v9, v10) = v12 & subset_union2(all_0_17_17, v9, v10) = v12)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (subset_union2(all_0_17_17, v9, v10) = v11) | ~ element(v10, all_0_14_14) | ~ element(v9, all_0_14_14) | ? [v12] : (apply_binary(v2, v9, v10) = v12 & apply_binary(all_33_1_31, v9, v10) = v11 & subset_intersection2(all_0_17_17, v9, v10) = v12)))))
% 12.91/3.54 |
% 12.91/3.54 | Instantiating formula (85) with all_33_0_30, all_0_15_15, all_0_15_15, all_0_17_17 and discharging atoms boole_lattice(all_0_17_17) = all_0_15_15, the_L_meet(all_0_15_15) = all_33_0_30, strict_latt_str(all_0_15_15), latt_str(all_0_15_15), yields:
% 12.91/3.54 | (155) ? [v0] : ? [v1] : (powerset(all_0_17_17) = v0 & the_carrier(all_0_15_15) = v0 & the_L_join(all_0_15_15) = v1 & ! [v2] : ! [v3] : ! [v4] : ( ~ (apply_binary(v1, v2, v3) = v4) | ~ element(v3, v0) | ~ element(v2, v0) | ? [v5] : (apply_binary(all_33_0_30, v2, v3) = v5 & subset_intersection2(all_0_17_17, v2, v3) = v5 & subset_union2(all_0_17_17, v2, v3) = v4)) & ! [v2] : ! [v3] : ! [v4] : ( ~ (apply_binary(all_33_0_30, v2, v3) = v4) | ~ element(v3, v0) | ~ element(v2, v0) | ? [v5] : (apply_binary(v1, v2, v3) = v5 & subset_intersection2(all_0_17_17, v2, v3) = v4 & subset_union2(all_0_17_17, v2, v3) = v5)) & ! [v2] : ! [v3] : ! [v4] : ( ~ (subset_intersection2(all_0_17_17, v2, v3) = v4) | ~ element(v3, v0) | ~ element(v2, v0) | ? [v5] : (apply_binary(v1, v2, v3) = v5 & apply_binary(all_33_0_30, v2, v3) = v4 & subset_union2(all_0_17_17, v2, v3) = v5)) & ! [v2] : ! [v3] : ! [v4] : ( ~ (subset_union2(all_0_17_17, v2, v3) = v4) | ~ element(v3, v0) | ~ element(v2, v0) | ? [v5] : (apply_binary(v1, v2, v3) = v4 & apply_binary(all_33_0_30, v2, v3) = v5 & subset_intersection2(all_0_17_17, v2, v3) = v5)))
% 12.91/3.54 |
% 12.91/3.54 | Instantiating formula (98) with all_33_0_30, all_0_14_14, all_0_15_15, all_0_17_17 and discharging atoms powerset(all_0_17_17) = all_0_14_14, the_L_meet(all_0_15_15) = all_33_0_30, strict_latt_str(all_0_15_15), latt_str(all_0_15_15), yields:
% 12.91/3.54 | (156) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (boole_lattice(all_0_17_17) = v0 & the_carrier(all_0_15_15) = v1 & the_L_join(all_0_15_15) = v2 & ( ~ (v1 = all_0_14_14) | v0 = all_0_15_15 | (apply_binary(v2, v3, v4) = v5 & apply_binary(all_33_0_30, v3, v4) = v7 & subset_intersection2(all_0_17_17, v3, v4) = v8 & subset_union2(all_0_17_17, v3, v4) = v6 & element(v4, all_0_14_14) & element(v3, all_0_14_14) & ( ~ (v8 = v7) | ~ (v6 = v5)))) & ( ~ (v0 = all_0_15_15) | (v1 = all_0_14_14 & ! [v9] : ! [v10] : ! [v11] : ( ~ (apply_binary(v2, v9, v10) = v11) | ~ element(v10, all_0_14_14) | ~ element(v9, all_0_14_14) | ? [v12] : (apply_binary(all_33_0_30, v9, v10) = v12 & subset_intersection2(all_0_17_17, v9, v10) = v12 & subset_union2(all_0_17_17, v9, v10) = v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (apply_binary(all_33_0_30, v9, v10) = v11) | ~ element(v10, all_0_14_14) | ~ element(v9, all_0_14_14) | ? [v12] : (apply_binary(v2, v9, v10) = v12 & subset_intersection2(all_0_17_17, v9, v10) = v11 & subset_union2(all_0_17_17, v9, v10) = v12)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (subset_intersection2(all_0_17_17, v9, v10) = v11) | ~ element(v10, all_0_14_14) | ~ element(v9, all_0_14_14) | ? [v12] : (apply_binary(v2, v9, v10) = v12 & apply_binary(all_33_0_30, v9, v10) = v11 & subset_union2(all_0_17_17, v9, v10) = v12)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (subset_union2(all_0_17_17, v9, v10) = v11) | ~ element(v10, all_0_14_14) | ~ element(v9, all_0_14_14) | ? [v12] : (apply_binary(v2, v9, v10) = v11 & apply_binary(all_33_0_30, v9, v10) = v12 & subset_intersection2(all_0_17_17, v9, v10) = v12)))))
% 12.91/3.54 |
% 12.91/3.54 | Instantiating formula (119) with all_0_10_10, all_0_13_13, all_0_16_16, all_0_15_15 and discharging atoms meet(all_0_15_15, all_0_16_16, all_0_13_13) = all_0_10_10, meet_semilatt_str(all_0_15_15), yields:
% 12.91/3.54 | (157) empty_carrier(all_0_15_15) | ? [v0] : (the_carrier(all_0_15_15) = v0 & ( ~ element(all_0_13_13, v0) | ~ element(all_0_16_16, v0) | element(all_0_10_10, v0)))
% 12.91/3.54 |
% 12.91/3.54 | Instantiating formula (123) with all_0_14_14, all_0_15_15 and discharging atoms the_carrier(all_0_15_15) = all_0_14_14, meet_semilatt_str(all_0_15_15), yields:
% 12.91/3.54 | (158) empty_carrier(all_0_15_15) | ? [v0] : (the_L_meet(all_0_15_15) = v0 & ! [v1] : ! [v2] : ! [v3] : ( ~ (meet(all_0_15_15, v1, v2) = v3) | ~ element(v2, all_0_14_14) | ~ element(v1, all_0_14_14) | apply_binary_as_element(all_0_14_14, all_0_14_14, all_0_14_14, v0, v1, v2) = v3) & ! [v1] : ! [v2] : ! [v3] : ( ~ (apply_binary_as_element(all_0_14_14, all_0_14_14, all_0_14_14, v0, v1, v2) = v3) | ~ element(v2, all_0_14_14) | ~ element(v1, all_0_14_14) | meet(all_0_15_15, v1, v2) = v3))
% 12.91/3.54 |
% 12.91/3.54 | Instantiating formula (45) with all_0_14_14, all_0_15_15 and discharging atoms the_carrier(all_0_15_15) = all_0_14_14, meet_semilatt_str(all_0_15_15), yields:
% 12.91/3.54 | (159) ? [v0] : ? [v1] : (cartesian_product2(all_0_14_14, all_0_14_14) = v1 & the_L_meet(all_0_15_15) = v0 & relation_of2_as_subset(v0, v1, all_0_14_14) & quasi_total(v0, v1, all_0_14_14) & function(v0))
% 12.91/3.54 |
% 12.91/3.54 | Instantiating formula (34) with all_33_0_30, all_0_15_15 and discharging atoms the_L_meet(all_0_15_15) = all_33_0_30, meet_semilatt_str(all_0_15_15), yields:
% 12.91/3.54 | (160) empty_carrier(all_0_15_15) | ? [v0] : (the_carrier(all_0_15_15) = v0 & ! [v1] : ! [v2] : ! [v3] : ( ~ (meet(all_0_15_15, v1, v2) = v3) | ~ element(v2, v0) | ~ element(v1, v0) | apply_binary_as_element(v0, v0, v0, all_33_0_30, v1, v2) = v3) & ! [v1] : ! [v2] : ! [v3] : ( ~ (apply_binary_as_element(v0, v0, v0, all_33_0_30, v1, v2) = v3) | ~ element(v2, v0) | ~ element(v1, v0) | meet(all_0_15_15, v1, v2) = v3))
% 12.91/3.54 |
% 12.91/3.54 | Instantiating formula (47) with all_33_0_30, all_0_15_15 and discharging atoms the_L_meet(all_0_15_15) = all_33_0_30, meet_semilatt_str(all_0_15_15), yields:
% 12.91/3.54 | (161) ? [v0] : ? [v1] : (cartesian_product2(v0, v0) = v1 & the_carrier(all_0_15_15) = v0 & relation_of2_as_subset(all_33_0_30, v1, v0) & quasi_total(all_33_0_30, v1, v0))
% 12.91/3.54 |
% 12.91/3.54 | Instantiating formula (88) with all_0_12_12, all_0_13_13, all_0_16_16, all_0_15_15 and discharging atoms join(all_0_15_15, all_0_16_16, all_0_13_13) = all_0_12_12, join_semilatt_str(all_0_15_15), yields:
% 12.91/3.54 | (162) empty_carrier(all_0_15_15) | ? [v0] : (the_carrier(all_0_15_15) = v0 & ( ~ element(all_0_13_13, v0) | ~ element(all_0_16_16, v0) | element(all_0_12_12, v0)))
% 12.91/3.54 |
% 12.91/3.54 | Instantiating formula (84) with all_0_14_14, all_0_15_15 and discharging atoms the_carrier(all_0_15_15) = all_0_14_14, join_semilatt_str(all_0_15_15), yields:
% 12.91/3.54 | (163) empty_carrier(all_0_15_15) | ? [v0] : (the_L_join(all_0_15_15) = v0 & ! [v1] : ! [v2] : ! [v3] : ( ~ (join(all_0_15_15, v1, v2) = v3) | ~ element(v2, all_0_14_14) | ~ element(v1, all_0_14_14) | apply_binary_as_element(all_0_14_14, all_0_14_14, all_0_14_14, v0, v1, v2) = v3) & ! [v1] : ! [v2] : ! [v3] : ( ~ (apply_binary_as_element(all_0_14_14, all_0_14_14, all_0_14_14, v0, v1, v2) = v3) | ~ element(v2, all_0_14_14) | ~ element(v1, all_0_14_14) | join(all_0_15_15, v1, v2) = v3))
% 12.91/3.54 |
% 12.91/3.54 | Instantiating formula (28) with all_0_14_14, all_0_15_15 and discharging atoms the_carrier(all_0_15_15) = all_0_14_14, join_semilatt_str(all_0_15_15), yields:
% 12.91/3.54 | (164) ? [v0] : ? [v1] : (cartesian_product2(all_0_14_14, all_0_14_14) = v1 & the_L_join(all_0_15_15) = v0 & relation_of2_as_subset(v0, v1, all_0_14_14) & quasi_total(v0, v1, all_0_14_14) & function(v0))
% 12.91/3.54 |
% 12.91/3.54 | Instantiating formula (54) with all_33_1_31, all_0_15_15 and discharging atoms the_L_join(all_0_15_15) = all_33_1_31, join_semilatt_str(all_0_15_15), yields:
% 12.91/3.54 | (165) empty_carrier(all_0_15_15) | ? [v0] : (the_carrier(all_0_15_15) = v0 & ! [v1] : ! [v2] : ! [v3] : ( ~ (join(all_0_15_15, v1, v2) = v3) | ~ element(v2, v0) | ~ element(v1, v0) | apply_binary_as_element(v0, v0, v0, all_33_1_31, v1, v2) = v3) & ! [v1] : ! [v2] : ! [v3] : ( ~ (apply_binary_as_element(v0, v0, v0, all_33_1_31, v1, v2) = v3) | ~ element(v2, v0) | ~ element(v1, v0) | join(all_0_15_15, v1, v2) = v3))
% 12.91/3.54 |
% 12.91/3.54 | Instantiating formula (112) with all_33_1_31, all_0_15_15 and discharging atoms the_L_join(all_0_15_15) = all_33_1_31, join_semilatt_str(all_0_15_15), yields:
% 12.91/3.54 | (166) ? [v0] : ? [v1] : (cartesian_product2(v0, v0) = v1 & the_carrier(all_0_15_15) = v0 & relation_of2_as_subset(all_33_1_31, v1, v0) & quasi_total(all_33_1_31, v1, v0))
% 12.91/3.54 |
% 12.91/3.54 | Instantiating formula (6) with all_0_15_15 and discharging atoms join_semilatt_str(all_0_15_15), yields:
% 12.91/3.54 | (167) one_sorted_str(all_0_15_15)
% 12.91/3.54 |
% 12.91/3.54 | Instantiating (161) with all_42_0_32, all_42_1_33 yields:
% 12.91/3.54 | (168) cartesian_product2(all_42_1_33, all_42_1_33) = all_42_0_32 & the_carrier(all_0_15_15) = all_42_1_33 & relation_of2_as_subset(all_33_0_30, all_42_0_32, all_42_1_33) & quasi_total(all_33_0_30, all_42_0_32, all_42_1_33)
% 12.91/3.54 |
% 12.91/3.54 | Applying alpha-rule on (168) yields:
% 12.91/3.54 | (169) cartesian_product2(all_42_1_33, all_42_1_33) = all_42_0_32
% 12.91/3.54 | (170) the_carrier(all_0_15_15) = all_42_1_33
% 12.91/3.54 | (171) relation_of2_as_subset(all_33_0_30, all_42_0_32, all_42_1_33)
% 12.91/3.54 | (172) quasi_total(all_33_0_30, all_42_0_32, all_42_1_33)
% 12.91/3.54 |
% 12.91/3.54 | Instantiating (159) with all_44_0_34, all_44_1_35 yields:
% 12.91/3.54 | (173) cartesian_product2(all_0_14_14, all_0_14_14) = all_44_0_34 & the_L_meet(all_0_15_15) = all_44_1_35 & relation_of2_as_subset(all_44_1_35, all_44_0_34, all_0_14_14) & quasi_total(all_44_1_35, all_44_0_34, all_0_14_14) & function(all_44_1_35)
% 12.91/3.54 |
% 12.91/3.54 | Applying alpha-rule on (173) yields:
% 12.91/3.54 | (174) the_L_meet(all_0_15_15) = all_44_1_35
% 12.91/3.54 | (175) relation_of2_as_subset(all_44_1_35, all_44_0_34, all_0_14_14)
% 12.91/3.54 | (176) quasi_total(all_44_1_35, all_44_0_34, all_0_14_14)
% 12.91/3.54 | (177) function(all_44_1_35)
% 12.91/3.54 | (178) cartesian_product2(all_0_14_14, all_0_14_14) = all_44_0_34
% 12.91/3.54 |
% 12.91/3.54 | Instantiating (156) with all_46_0_36, all_46_1_37, all_46_2_38, all_46_3_39, all_46_4_40, all_46_5_41, all_46_6_42, all_46_7_43, all_46_8_44 yields:
% 12.91/3.54 | (179) boole_lattice(all_0_17_17) = all_46_8_44 & the_carrier(all_0_15_15) = all_46_7_43 & the_L_join(all_0_15_15) = all_46_6_42 & ( ~ (all_46_7_43 = all_0_14_14) | all_46_8_44 = all_0_15_15 | (apply_binary(all_46_6_42, all_46_5_41, all_46_4_40) = all_46_3_39 & apply_binary(all_33_0_30, all_46_5_41, all_46_4_40) = all_46_1_37 & subset_intersection2(all_0_17_17, all_46_5_41, all_46_4_40) = all_46_0_36 & subset_union2(all_0_17_17, all_46_5_41, all_46_4_40) = all_46_2_38 & element(all_46_4_40, all_0_14_14) & element(all_46_5_41, all_0_14_14) & ( ~ (all_46_0_36 = all_46_1_37) | ~ (all_46_2_38 = all_46_3_39)))) & ( ~ (all_46_8_44 = all_0_15_15) | (all_46_7_43 = all_0_14_14 & ! [v0] : ! [v1] : ! [v2] : ( ~ (apply_binary(all_46_6_42, v0, v1) = v2) | ~ element(v1, all_0_14_14) | ~ element(v0, all_0_14_14) | ? [v3] : (apply_binary(all_33_0_30, v0, v1) = v3 & subset_intersection2(all_0_17_17, v0, v1) = v3 & subset_union2(all_0_17_17, v0, v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (apply_binary(all_33_0_30, v0, v1) = v2) | ~ element(v1, all_0_14_14) | ~ element(v0, all_0_14_14) | ? [v3] : (apply_binary(all_46_6_42, v0, v1) = v3 & subset_intersection2(all_0_17_17, v0, v1) = v2 & subset_union2(all_0_17_17, v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_intersection2(all_0_17_17, v0, v1) = v2) | ~ element(v1, all_0_14_14) | ~ element(v0, all_0_14_14) | ? [v3] : (apply_binary(all_46_6_42, v0, v1) = v3 & apply_binary(all_33_0_30, v0, v1) = v2 & subset_union2(all_0_17_17, v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_union2(all_0_17_17, v0, v1) = v2) | ~ element(v1, all_0_14_14) | ~ element(v0, all_0_14_14) | ? [v3] : (apply_binary(all_46_6_42, v0, v1) = v2 & apply_binary(all_33_0_30, v0, v1) = v3 & subset_intersection2(all_0_17_17, v0, v1) = v3))))
% 12.91/3.54 |
% 12.91/3.54 | Applying alpha-rule on (179) yields:
% 12.91/3.54 | (180) ~ (all_46_8_44 = all_0_15_15) | (all_46_7_43 = all_0_14_14 & ! [v0] : ! [v1] : ! [v2] : ( ~ (apply_binary(all_46_6_42, v0, v1) = v2) | ~ element(v1, all_0_14_14) | ~ element(v0, all_0_14_14) | ? [v3] : (apply_binary(all_33_0_30, v0, v1) = v3 & subset_intersection2(all_0_17_17, v0, v1) = v3 & subset_union2(all_0_17_17, v0, v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (apply_binary(all_33_0_30, v0, v1) = v2) | ~ element(v1, all_0_14_14) | ~ element(v0, all_0_14_14) | ? [v3] : (apply_binary(all_46_6_42, v0, v1) = v3 & subset_intersection2(all_0_17_17, v0, v1) = v2 & subset_union2(all_0_17_17, v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_intersection2(all_0_17_17, v0, v1) = v2) | ~ element(v1, all_0_14_14) | ~ element(v0, all_0_14_14) | ? [v3] : (apply_binary(all_46_6_42, v0, v1) = v3 & apply_binary(all_33_0_30, v0, v1) = v2 & subset_union2(all_0_17_17, v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_union2(all_0_17_17, v0, v1) = v2) | ~ element(v1, all_0_14_14) | ~ element(v0, all_0_14_14) | ? [v3] : (apply_binary(all_46_6_42, v0, v1) = v2 & apply_binary(all_33_0_30, v0, v1) = v3 & subset_intersection2(all_0_17_17, v0, v1) = v3)))
% 12.91/3.54 | (181) boole_lattice(all_0_17_17) = all_46_8_44
% 12.91/3.54 | (182) the_L_join(all_0_15_15) = all_46_6_42
% 12.91/3.54 | (183) the_carrier(all_0_15_15) = all_46_7_43
% 12.91/3.55 | (184) ~ (all_46_7_43 = all_0_14_14) | all_46_8_44 = all_0_15_15 | (apply_binary(all_46_6_42, all_46_5_41, all_46_4_40) = all_46_3_39 & apply_binary(all_33_0_30, all_46_5_41, all_46_4_40) = all_46_1_37 & subset_intersection2(all_0_17_17, all_46_5_41, all_46_4_40) = all_46_0_36 & subset_union2(all_0_17_17, all_46_5_41, all_46_4_40) = all_46_2_38 & element(all_46_4_40, all_0_14_14) & element(all_46_5_41, all_0_14_14) & ( ~ (all_46_0_36 = all_46_1_37) | ~ (all_46_2_38 = all_46_3_39)))
% 12.91/3.55 |
% 12.91/3.55 | Instantiating (152) with all_48_0_45, all_48_1_46, all_48_2_47, all_48_3_48, all_48_4_49, all_48_5_50, all_48_6_51, all_48_7_52, all_48_8_53 yields:
% 12.91/3.55 | (185) boole_lattice(all_0_17_17) = all_48_8_53 & the_L_join(all_0_15_15) = all_48_7_52 & the_L_meet(all_0_15_15) = all_48_6_51 & ( ~ (all_48_8_53 = all_0_15_15) | ( ! [v0] : ! [v1] : ! [v2] : ( ~ (apply_binary(all_48_6_51, v0, v1) = v2) | ~ element(v1, all_0_14_14) | ~ element(v0, all_0_14_14) | ? [v3] : (apply_binary(all_48_7_52, v0, v1) = v3 & subset_intersection2(all_0_17_17, v0, v1) = v2 & subset_union2(all_0_17_17, v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (apply_binary(all_48_7_52, v0, v1) = v2) | ~ element(v1, all_0_14_14) | ~ element(v0, all_0_14_14) | ? [v3] : (apply_binary(all_48_6_51, v0, v1) = v3 & subset_intersection2(all_0_17_17, v0, v1) = v3 & subset_union2(all_0_17_17, v0, v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_intersection2(all_0_17_17, v0, v1) = v2) | ~ element(v1, all_0_14_14) | ~ element(v0, all_0_14_14) | ? [v3] : (apply_binary(all_48_6_51, v0, v1) = v2 & apply_binary(all_48_7_52, v0, v1) = v3 & subset_union2(all_0_17_17, v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_union2(all_0_17_17, v0, v1) = v2) | ~ element(v1, all_0_14_14) | ~ element(v0, all_0_14_14) | ? [v3] : (apply_binary(all_48_6_51, v0, v1) = v3 & apply_binary(all_48_7_52, v0, v1) = v2 & subset_intersection2(all_0_17_17, v0, v1) = v3)))) & (all_48_8_53 = all_0_15_15 | (apply_binary(all_48_6_51, all_48_5_50, all_48_4_49) = all_48_1_46 & apply_binary(all_48_7_52, all_48_5_50, all_48_4_49) = all_48_3_48 & subset_intersection2(all_0_17_17, all_48_5_50, all_48_4_49) = all_48_0_45 & subset_union2(all_0_17_17, all_48_5_50, all_48_4_49) = all_48_2_47 & element(all_48_4_49, all_0_14_14) & element(all_48_5_50, all_0_14_14) & ( ~ (all_48_0_45 = all_48_1_46) | ~ (all_48_2_47 = all_48_3_48))))
% 12.91/3.55 |
% 12.91/3.55 | Applying alpha-rule on (185) yields:
% 12.91/3.55 | (186) the_L_join(all_0_15_15) = all_48_7_52
% 12.91/3.55 | (187) the_L_meet(all_0_15_15) = all_48_6_51
% 12.91/3.55 | (188) ~ (all_48_8_53 = all_0_15_15) | ( ! [v0] : ! [v1] : ! [v2] : ( ~ (apply_binary(all_48_6_51, v0, v1) = v2) | ~ element(v1, all_0_14_14) | ~ element(v0, all_0_14_14) | ? [v3] : (apply_binary(all_48_7_52, v0, v1) = v3 & subset_intersection2(all_0_17_17, v0, v1) = v2 & subset_union2(all_0_17_17, v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (apply_binary(all_48_7_52, v0, v1) = v2) | ~ element(v1, all_0_14_14) | ~ element(v0, all_0_14_14) | ? [v3] : (apply_binary(all_48_6_51, v0, v1) = v3 & subset_intersection2(all_0_17_17, v0, v1) = v3 & subset_union2(all_0_17_17, v0, v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_intersection2(all_0_17_17, v0, v1) = v2) | ~ element(v1, all_0_14_14) | ~ element(v0, all_0_14_14) | ? [v3] : (apply_binary(all_48_6_51, v0, v1) = v2 & apply_binary(all_48_7_52, v0, v1) = v3 & subset_union2(all_0_17_17, v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_union2(all_0_17_17, v0, v1) = v2) | ~ element(v1, all_0_14_14) | ~ element(v0, all_0_14_14) | ? [v3] : (apply_binary(all_48_6_51, v0, v1) = v3 & apply_binary(all_48_7_52, v0, v1) = v2 & subset_intersection2(all_0_17_17, v0, v1) = v3)))
% 12.91/3.55 | (189) boole_lattice(all_0_17_17) = all_48_8_53
% 12.91/3.55 | (190) all_48_8_53 = all_0_15_15 | (apply_binary(all_48_6_51, all_48_5_50, all_48_4_49) = all_48_1_46 & apply_binary(all_48_7_52, all_48_5_50, all_48_4_49) = all_48_3_48 & subset_intersection2(all_0_17_17, all_48_5_50, all_48_4_49) = all_48_0_45 & subset_union2(all_0_17_17, all_48_5_50, all_48_4_49) = all_48_2_47 & element(all_48_4_49, all_0_14_14) & element(all_48_5_50, all_0_14_14) & ( ~ (all_48_0_45 = all_48_1_46) | ~ (all_48_2_47 = all_48_3_48)))
% 12.91/3.55 |
% 12.91/3.55 | Instantiating (164) with all_50_0_54, all_50_1_55 yields:
% 12.91/3.55 | (191) cartesian_product2(all_0_14_14, all_0_14_14) = all_50_0_54 & the_L_join(all_0_15_15) = all_50_1_55 & relation_of2_as_subset(all_50_1_55, all_50_0_54, all_0_14_14) & quasi_total(all_50_1_55, all_50_0_54, all_0_14_14) & function(all_50_1_55)
% 12.91/3.55 |
% 12.91/3.55 | Applying alpha-rule on (191) yields:
% 12.91/3.55 | (192) function(all_50_1_55)
% 12.91/3.55 | (193) cartesian_product2(all_0_14_14, all_0_14_14) = all_50_0_54
% 12.91/3.55 | (194) the_L_join(all_0_15_15) = all_50_1_55
% 12.91/3.55 | (195) relation_of2_as_subset(all_50_1_55, all_50_0_54, all_0_14_14)
% 12.91/3.55 | (196) quasi_total(all_50_1_55, all_50_0_54, all_0_14_14)
% 12.91/3.55 |
% 12.91/3.55 | Instantiating (155) with all_52_0_56, all_52_1_57 yields:
% 12.91/3.55 | (197) powerset(all_0_17_17) = all_52_1_57 & the_carrier(all_0_15_15) = all_52_1_57 & the_L_join(all_0_15_15) = all_52_0_56 & ! [v0] : ! [v1] : ! [v2] : ( ~ (apply_binary(all_52_0_56, v0, v1) = v2) | ~ element(v1, all_52_1_57) | ~ element(v0, all_52_1_57) | ? [v3] : (apply_binary(all_33_0_30, v0, v1) = v3 & subset_intersection2(all_0_17_17, v0, v1) = v3 & subset_union2(all_0_17_17, v0, v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (apply_binary(all_33_0_30, v0, v1) = v2) | ~ element(v1, all_52_1_57) | ~ element(v0, all_52_1_57) | ? [v3] : (apply_binary(all_52_0_56, v0, v1) = v3 & subset_intersection2(all_0_17_17, v0, v1) = v2 & subset_union2(all_0_17_17, v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_intersection2(all_0_17_17, v0, v1) = v2) | ~ element(v1, all_52_1_57) | ~ element(v0, all_52_1_57) | ? [v3] : (apply_binary(all_52_0_56, v0, v1) = v3 & apply_binary(all_33_0_30, v0, v1) = v2 & subset_union2(all_0_17_17, v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_union2(all_0_17_17, v0, v1) = v2) | ~ element(v1, all_52_1_57) | ~ element(v0, all_52_1_57) | ? [v3] : (apply_binary(all_52_0_56, v0, v1) = v2 & apply_binary(all_33_0_30, v0, v1) = v3 & subset_intersection2(all_0_17_17, v0, v1) = v3))
% 12.91/3.55 |
% 12.91/3.55 | Applying alpha-rule on (197) yields:
% 12.91/3.55 | (198) ! [v0] : ! [v1] : ! [v2] : ( ~ (apply_binary(all_52_0_56, v0, v1) = v2) | ~ element(v1, all_52_1_57) | ~ element(v0, all_52_1_57) | ? [v3] : (apply_binary(all_33_0_30, v0, v1) = v3 & subset_intersection2(all_0_17_17, v0, v1) = v3 & subset_union2(all_0_17_17, v0, v1) = v2))
% 12.91/3.55 | (199) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_intersection2(all_0_17_17, v0, v1) = v2) | ~ element(v1, all_52_1_57) | ~ element(v0, all_52_1_57) | ? [v3] : (apply_binary(all_52_0_56, v0, v1) = v3 & apply_binary(all_33_0_30, v0, v1) = v2 & subset_union2(all_0_17_17, v0, v1) = v3))
% 12.91/3.55 | (200) ! [v0] : ! [v1] : ! [v2] : ( ~ (apply_binary(all_33_0_30, v0, v1) = v2) | ~ element(v1, all_52_1_57) | ~ element(v0, all_52_1_57) | ? [v3] : (apply_binary(all_52_0_56, v0, v1) = v3 & subset_intersection2(all_0_17_17, v0, v1) = v2 & subset_union2(all_0_17_17, v0, v1) = v3))
% 12.91/3.55 | (201) the_carrier(all_0_15_15) = all_52_1_57
% 12.91/3.55 | (202) the_L_join(all_0_15_15) = all_52_0_56
% 12.91/3.55 | (203) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_union2(all_0_17_17, v0, v1) = v2) | ~ element(v1, all_52_1_57) | ~ element(v0, all_52_1_57) | ? [v3] : (apply_binary(all_52_0_56, v0, v1) = v2 & apply_binary(all_33_0_30, v0, v1) = v3 & subset_intersection2(all_0_17_17, v0, v1) = v3))
% 12.91/3.55 | (204) powerset(all_0_17_17) = all_52_1_57
% 12.91/3.55 |
% 12.91/3.55 | Instantiating (154) with all_55_0_58, all_55_1_59, all_55_2_60, all_55_3_61, all_55_4_62, all_55_5_63, all_55_6_64, all_55_7_65, all_55_8_66 yields:
% 12.91/3.55 | (205) boole_lattice(all_0_17_17) = all_55_8_66 & the_carrier(all_0_15_15) = all_55_7_65 & the_L_meet(all_0_15_15) = all_55_6_64 & ( ~ (all_55_7_65 = all_0_14_14) | all_55_8_66 = all_0_15_15 | (apply_binary(all_55_6_64, all_55_5_63, all_55_4_62) = all_55_1_59 & apply_binary(all_33_1_31, all_55_5_63, all_55_4_62) = all_55_3_61 & subset_intersection2(all_0_17_17, all_55_5_63, all_55_4_62) = all_55_0_58 & subset_union2(all_0_17_17, all_55_5_63, all_55_4_62) = all_55_2_60 & element(all_55_4_62, all_0_14_14) & element(all_55_5_63, all_0_14_14) & ( ~ (all_55_0_58 = all_55_1_59) | ~ (all_55_2_60 = all_55_3_61)))) & ( ~ (all_55_8_66 = all_0_15_15) | (all_55_7_65 = all_0_14_14 & ! [v0] : ! [v1] : ! [v2] : ( ~ (apply_binary(all_55_6_64, v0, v1) = v2) | ~ element(v1, all_0_14_14) | ~ element(v0, all_0_14_14) | ? [v3] : (apply_binary(all_33_1_31, v0, v1) = v3 & subset_intersection2(all_0_17_17, v0, v1) = v2 & subset_union2(all_0_17_17, v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (apply_binary(all_33_1_31, v0, v1) = v2) | ~ element(v1, all_0_14_14) | ~ element(v0, all_0_14_14) | ? [v3] : (apply_binary(all_55_6_64, v0, v1) = v3 & subset_intersection2(all_0_17_17, v0, v1) = v3 & subset_union2(all_0_17_17, v0, v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_intersection2(all_0_17_17, v0, v1) = v2) | ~ element(v1, all_0_14_14) | ~ element(v0, all_0_14_14) | ? [v3] : (apply_binary(all_55_6_64, v0, v1) = v2 & apply_binary(all_33_1_31, v0, v1) = v3 & subset_union2(all_0_17_17, v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_union2(all_0_17_17, v0, v1) = v2) | ~ element(v1, all_0_14_14) | ~ element(v0, all_0_14_14) | ? [v3] : (apply_binary(all_55_6_64, v0, v1) = v3 & apply_binary(all_33_1_31, v0, v1) = v2 & subset_intersection2(all_0_17_17, v0, v1) = v3))))
% 12.91/3.55 |
% 12.91/3.55 | Applying alpha-rule on (205) yields:
% 12.91/3.55 | (206) the_carrier(all_0_15_15) = all_55_7_65
% 12.91/3.55 | (207) ~ (all_55_8_66 = all_0_15_15) | (all_55_7_65 = all_0_14_14 & ! [v0] : ! [v1] : ! [v2] : ( ~ (apply_binary(all_55_6_64, v0, v1) = v2) | ~ element(v1, all_0_14_14) | ~ element(v0, all_0_14_14) | ? [v3] : (apply_binary(all_33_1_31, v0, v1) = v3 & subset_intersection2(all_0_17_17, v0, v1) = v2 & subset_union2(all_0_17_17, v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (apply_binary(all_33_1_31, v0, v1) = v2) | ~ element(v1, all_0_14_14) | ~ element(v0, all_0_14_14) | ? [v3] : (apply_binary(all_55_6_64, v0, v1) = v3 & subset_intersection2(all_0_17_17, v0, v1) = v3 & subset_union2(all_0_17_17, v0, v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_intersection2(all_0_17_17, v0, v1) = v2) | ~ element(v1, all_0_14_14) | ~ element(v0, all_0_14_14) | ? [v3] : (apply_binary(all_55_6_64, v0, v1) = v2 & apply_binary(all_33_1_31, v0, v1) = v3 & subset_union2(all_0_17_17, v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_union2(all_0_17_17, v0, v1) = v2) | ~ element(v1, all_0_14_14) | ~ element(v0, all_0_14_14) | ? [v3] : (apply_binary(all_55_6_64, v0, v1) = v3 & apply_binary(all_33_1_31, v0, v1) = v2 & subset_intersection2(all_0_17_17, v0, v1) = v3)))
% 12.91/3.55 | (208) ~ (all_55_7_65 = all_0_14_14) | all_55_8_66 = all_0_15_15 | (apply_binary(all_55_6_64, all_55_5_63, all_55_4_62) = all_55_1_59 & apply_binary(all_33_1_31, all_55_5_63, all_55_4_62) = all_55_3_61 & subset_intersection2(all_0_17_17, all_55_5_63, all_55_4_62) = all_55_0_58 & subset_union2(all_0_17_17, all_55_5_63, all_55_4_62) = all_55_2_60 & element(all_55_4_62, all_0_14_14) & element(all_55_5_63, all_0_14_14) & ( ~ (all_55_0_58 = all_55_1_59) | ~ (all_55_2_60 = all_55_3_61)))
% 12.91/3.55 | (209) the_L_meet(all_0_15_15) = all_55_6_64
% 12.91/3.55 | (210) boole_lattice(all_0_17_17) = all_55_8_66
% 12.91/3.55 |
% 12.91/3.55 | Instantiating (153) with all_57_0_67, all_57_1_68 yields:
% 12.91/3.55 | (211) powerset(all_0_17_17) = all_57_1_68 & the_carrier(all_0_15_15) = all_57_1_68 & the_L_meet(all_0_15_15) = all_57_0_67 & ! [v0] : ! [v1] : ! [v2] : ( ~ (apply_binary(all_57_0_67, v0, v1) = v2) | ~ element(v1, all_57_1_68) | ~ element(v0, all_57_1_68) | ? [v3] : (apply_binary(all_33_1_31, v0, v1) = v3 & subset_intersection2(all_0_17_17, v0, v1) = v2 & subset_union2(all_0_17_17, v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (apply_binary(all_33_1_31, v0, v1) = v2) | ~ element(v1, all_57_1_68) | ~ element(v0, all_57_1_68) | ? [v3] : (apply_binary(all_57_0_67, v0, v1) = v3 & subset_intersection2(all_0_17_17, v0, v1) = v3 & subset_union2(all_0_17_17, v0, v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_intersection2(all_0_17_17, v0, v1) = v2) | ~ element(v1, all_57_1_68) | ~ element(v0, all_57_1_68) | ? [v3] : (apply_binary(all_57_0_67, v0, v1) = v2 & apply_binary(all_33_1_31, v0, v1) = v3 & subset_union2(all_0_17_17, v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_union2(all_0_17_17, v0, v1) = v2) | ~ element(v1, all_57_1_68) | ~ element(v0, all_57_1_68) | ? [v3] : (apply_binary(all_57_0_67, v0, v1) = v3 & apply_binary(all_33_1_31, v0, v1) = v2 & subset_intersection2(all_0_17_17, v0, v1) = v3))
% 12.91/3.55 |
% 12.91/3.55 | Applying alpha-rule on (211) yields:
% 12.91/3.55 | (212) the_carrier(all_0_15_15) = all_57_1_68
% 12.91/3.55 | (213) the_L_meet(all_0_15_15) = all_57_0_67
% 12.91/3.55 | (214) powerset(all_0_17_17) = all_57_1_68
% 12.91/3.55 | (215) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_intersection2(all_0_17_17, v0, v1) = v2) | ~ element(v1, all_57_1_68) | ~ element(v0, all_57_1_68) | ? [v3] : (apply_binary(all_57_0_67, v0, v1) = v2 & apply_binary(all_33_1_31, v0, v1) = v3 & subset_union2(all_0_17_17, v0, v1) = v3))
% 12.91/3.55 | (216) ! [v0] : ! [v1] : ! [v2] : ( ~ (apply_binary(all_57_0_67, v0, v1) = v2) | ~ element(v1, all_57_1_68) | ~ element(v0, all_57_1_68) | ? [v3] : (apply_binary(all_33_1_31, v0, v1) = v3 & subset_intersection2(all_0_17_17, v0, v1) = v2 & subset_union2(all_0_17_17, v0, v1) = v3))
% 12.91/3.55 | (217) ! [v0] : ! [v1] : ! [v2] : ( ~ (apply_binary(all_33_1_31, v0, v1) = v2) | ~ element(v1, all_57_1_68) | ~ element(v0, all_57_1_68) | ? [v3] : (apply_binary(all_57_0_67, v0, v1) = v3 & subset_intersection2(all_0_17_17, v0, v1) = v3 & subset_union2(all_0_17_17, v0, v1) = v2))
% 12.91/3.55 | (218) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_union2(all_0_17_17, v0, v1) = v2) | ~ element(v1, all_57_1_68) | ~ element(v0, all_57_1_68) | ? [v3] : (apply_binary(all_57_0_67, v0, v1) = v3 & apply_binary(all_33_1_31, v0, v1) = v2 & subset_intersection2(all_0_17_17, v0, v1) = v3))
% 12.91/3.55 |
% 12.91/3.55 | Instantiating (166) with all_62_0_70, all_62_1_71 yields:
% 12.91/3.55 | (219) cartesian_product2(all_62_1_71, all_62_1_71) = all_62_0_70 & the_carrier(all_0_15_15) = all_62_1_71 & relation_of2_as_subset(all_33_1_31, all_62_0_70, all_62_1_71) & quasi_total(all_33_1_31, all_62_0_70, all_62_1_71)
% 12.91/3.55 |
% 12.91/3.55 | Applying alpha-rule on (219) yields:
% 12.91/3.55 | (220) cartesian_product2(all_62_1_71, all_62_1_71) = all_62_0_70
% 12.91/3.55 | (221) the_carrier(all_0_15_15) = all_62_1_71
% 12.91/3.55 | (222) relation_of2_as_subset(all_33_1_31, all_62_0_70, all_62_1_71)
% 12.91/3.55 | (223) quasi_total(all_33_1_31, all_62_0_70, all_62_1_71)
% 12.91/3.55 |
% 12.91/3.56 | Instantiating formula (100) with all_0_17_17, all_48_8_53, all_0_15_15 and discharging atoms boole_lattice(all_0_17_17) = all_48_8_53, boole_lattice(all_0_17_17) = all_0_15_15, yields:
% 12.91/3.56 | (224) all_48_8_53 = all_0_15_15
% 12.91/3.56 |
% 12.91/3.56 | Instantiating formula (100) with all_0_17_17, all_48_8_53, all_55_8_66 and discharging atoms boole_lattice(all_0_17_17) = all_55_8_66, boole_lattice(all_0_17_17) = all_48_8_53, yields:
% 12.91/3.56 | (225) all_55_8_66 = all_48_8_53
% 12.91/3.56 |
% 12.91/3.56 | Instantiating formula (100) with all_0_17_17, all_46_8_44, all_55_8_66 and discharging atoms boole_lattice(all_0_17_17) = all_55_8_66, boole_lattice(all_0_17_17) = all_46_8_44, yields:
% 12.91/3.56 | (226) all_55_8_66 = all_46_8_44
% 12.91/3.56 |
% 12.91/3.56 | Instantiating formula (53) with all_0_14_14, all_0_14_14, all_44_0_34, all_50_0_54 and discharging atoms cartesian_product2(all_0_14_14, all_0_14_14) = all_50_0_54, cartesian_product2(all_0_14_14, all_0_14_14) = all_44_0_34, yields:
% 12.91/3.56 | (227) all_50_0_54 = all_44_0_34
% 12.91/3.56 |
% 12.91/3.56 | Instantiating formula (62) with all_0_15_15, all_55_7_65, all_62_1_71 and discharging atoms the_carrier(all_0_15_15) = all_62_1_71, the_carrier(all_0_15_15) = all_55_7_65, yields:
% 12.91/3.56 | (228) all_62_1_71 = all_55_7_65
% 12.91/3.56 |
% 12.91/3.56 | Instantiating formula (62) with all_0_15_15, all_55_7_65, all_57_1_68 and discharging atoms the_carrier(all_0_15_15) = all_57_1_68, the_carrier(all_0_15_15) = all_55_7_65, yields:
% 12.91/3.56 | (229) all_57_1_68 = all_55_7_65
% 12.91/3.56 |
% 12.91/3.56 | Instantiating formula (62) with all_0_15_15, all_52_1_57, all_0_14_14 and discharging atoms the_carrier(all_0_15_15) = all_52_1_57, the_carrier(all_0_15_15) = all_0_14_14, yields:
% 12.91/3.56 | (230) all_52_1_57 = all_0_14_14
% 12.91/3.56 |
% 12.91/3.56 | Instantiating formula (62) with all_0_15_15, all_52_1_57, all_55_7_65 and discharging atoms the_carrier(all_0_15_15) = all_55_7_65, the_carrier(all_0_15_15) = all_52_1_57, yields:
% 12.91/3.56 | (231) all_55_7_65 = all_52_1_57
% 12.91/3.56 |
% 12.91/3.56 | Instantiating formula (62) with all_0_15_15, all_46_7_43, all_57_1_68 and discharging atoms the_carrier(all_0_15_15) = all_57_1_68, the_carrier(all_0_15_15) = all_46_7_43, yields:
% 12.91/3.56 | (232) all_57_1_68 = all_46_7_43
% 12.91/3.56 |
% 12.91/3.56 | Instantiating formula (62) with all_0_15_15, all_42_1_33, all_62_1_71 and discharging atoms the_carrier(all_0_15_15) = all_62_1_71, the_carrier(all_0_15_15) = all_42_1_33, yields:
% 12.91/3.56 | (233) all_62_1_71 = all_42_1_33
% 12.91/3.56 |
% 12.91/3.56 | Instantiating formula (36) with all_0_15_15, all_52_0_56, all_33_1_31 and discharging atoms the_L_join(all_0_15_15) = all_52_0_56, the_L_join(all_0_15_15) = all_33_1_31, yields:
% 12.91/3.56 | (234) all_52_0_56 = all_33_1_31
% 12.91/3.56 |
% 12.91/3.56 | Instantiating formula (36) with all_0_15_15, all_50_1_55, all_52_0_56 and discharging atoms the_L_join(all_0_15_15) = all_52_0_56, the_L_join(all_0_15_15) = all_50_1_55, yields:
% 12.91/3.56 | (235) all_52_0_56 = all_50_1_55
% 12.91/3.56 |
% 12.91/3.56 | Instantiating formula (36) with all_0_15_15, all_48_7_52, all_50_1_55 and discharging atoms the_L_join(all_0_15_15) = all_50_1_55, the_L_join(all_0_15_15) = all_48_7_52, yields:
% 12.91/3.56 | (236) all_50_1_55 = all_48_7_52
% 12.91/3.56 |
% 12.91/3.56 | Instantiating formula (36) with all_0_15_15, all_46_6_42, all_48_7_52 and discharging atoms the_L_join(all_0_15_15) = all_48_7_52, the_L_join(all_0_15_15) = all_46_6_42, yields:
% 12.91/3.56 | (237) all_48_7_52 = all_46_6_42
% 12.91/3.56 |
% 12.91/3.56 | Instantiating formula (73) with all_0_15_15, all_57_0_67, all_33_0_30 and discharging atoms the_L_meet(all_0_15_15) = all_57_0_67, the_L_meet(all_0_15_15) = all_33_0_30, yields:
% 12.91/3.56 | (238) all_57_0_67 = all_33_0_30
% 12.91/3.56 |
% 12.91/3.56 | Instantiating formula (73) with all_0_15_15, all_55_6_64, all_57_0_67 and discharging atoms the_L_meet(all_0_15_15) = all_57_0_67, the_L_meet(all_0_15_15) = all_55_6_64, yields:
% 12.91/3.56 | (239) all_57_0_67 = all_55_6_64
% 12.91/3.56 |
% 12.91/3.56 | Instantiating formula (73) with all_0_15_15, all_48_6_51, all_55_6_64 and discharging atoms the_L_meet(all_0_15_15) = all_55_6_64, the_L_meet(all_0_15_15) = all_48_6_51, yields:
% 12.91/3.56 | (240) all_55_6_64 = all_48_6_51
% 12.91/3.56 |
% 12.91/3.56 | Instantiating formula (73) with all_0_15_15, all_44_1_35, all_48_6_51 and discharging atoms the_L_meet(all_0_15_15) = all_48_6_51, the_L_meet(all_0_15_15) = all_44_1_35, yields:
% 12.91/3.56 | (241) all_48_6_51 = all_44_1_35
% 12.91/3.56 |
% 12.91/3.56 | Combining equations (228,233) yields a new equation:
% 12.91/3.56 | (242) all_55_7_65 = all_42_1_33
% 12.91/3.56 |
% 12.91/3.56 | Simplifying 242 yields:
% 12.91/3.56 | (243) all_55_7_65 = all_42_1_33
% 12.91/3.56 |
% 12.91/3.56 | Combining equations (239,238) yields a new equation:
% 12.91/3.56 | (244) all_55_6_64 = all_33_0_30
% 12.91/3.56 |
% 12.91/3.56 | Simplifying 244 yields:
% 12.91/3.56 | (245) all_55_6_64 = all_33_0_30
% 12.91/3.56 |
% 12.91/3.56 | Combining equations (229,232) yields a new equation:
% 12.91/3.56 | (246) all_55_7_65 = all_46_7_43
% 12.91/3.56 |
% 12.91/3.56 | Simplifying 246 yields:
% 12.91/3.56 | (247) all_55_7_65 = all_46_7_43
% 12.91/3.56 |
% 12.91/3.56 | Combining equations (240,245) yields a new equation:
% 12.91/3.56 | (248) all_48_6_51 = all_33_0_30
% 12.91/3.56 |
% 12.91/3.56 | Simplifying 248 yields:
% 12.91/3.56 | (249) all_48_6_51 = all_33_0_30
% 12.91/3.56 |
% 12.91/3.56 | Combining equations (243,247) yields a new equation:
% 12.91/3.56 | (250) all_46_7_43 = all_42_1_33
% 12.91/3.56 |
% 12.91/3.56 | Combining equations (231,247) yields a new equation:
% 12.91/3.56 | (251) all_52_1_57 = all_46_7_43
% 12.91/3.56 |
% 12.91/3.56 | Simplifying 251 yields:
% 12.91/3.56 | (252) all_52_1_57 = all_46_7_43
% 12.91/3.56 |
% 12.91/3.56 | Combining equations (225,226) yields a new equation:
% 12.91/3.56 | (253) all_48_8_53 = all_46_8_44
% 12.91/3.56 |
% 12.91/3.56 | Simplifying 253 yields:
% 12.91/3.56 | (254) all_48_8_53 = all_46_8_44
% 12.91/3.56 |
% 12.91/3.56 | Combining equations (235,234) yields a new equation:
% 12.91/3.56 | (255) all_50_1_55 = all_33_1_31
% 12.91/3.56 |
% 12.91/3.56 | Simplifying 255 yields:
% 12.91/3.56 | (256) all_50_1_55 = all_33_1_31
% 12.91/3.56 |
% 12.91/3.56 | Combining equations (252,230) yields a new equation:
% 12.91/3.56 | (257) all_46_7_43 = all_0_14_14
% 12.91/3.56 |
% 12.91/3.56 | Simplifying 257 yields:
% 12.91/3.56 | (258) all_46_7_43 = all_0_14_14
% 12.91/3.56 |
% 12.91/3.56 | Combining equations (236,256) yields a new equation:
% 12.91/3.56 | (259) all_48_7_52 = all_33_1_31
% 12.91/3.56 |
% 12.91/3.56 | Simplifying 259 yields:
% 12.91/3.56 | (260) all_48_7_52 = all_33_1_31
% 12.91/3.56 |
% 12.91/3.56 | Combining equations (249,241) yields a new equation:
% 12.91/3.56 | (261) all_44_1_35 = all_33_0_30
% 12.91/3.56 |
% 12.91/3.56 | Combining equations (237,260) yields a new equation:
% 12.91/3.56 | (262) all_46_6_42 = all_33_1_31
% 12.91/3.56 |
% 12.91/3.56 | Simplifying 262 yields:
% 12.91/3.56 | (263) all_46_6_42 = all_33_1_31
% 12.91/3.56 |
% 12.91/3.56 | Combining equations (224,254) yields a new equation:
% 12.91/3.56 | (264) all_46_8_44 = all_0_15_15
% 12.91/3.56 |
% 12.91/3.56 | Combining equations (258,250) yields a new equation:
% 12.91/3.56 | (265) all_42_1_33 = all_0_14_14
% 12.91/3.56 |
% 12.91/3.56 | Combining equations (264,254) yields a new equation:
% 12.91/3.56 | (224) all_48_8_53 = all_0_15_15
% 12.91/3.56 |
% 12.91/3.56 | Combining equations (264,226) yields a new equation:
% 12.91/3.56 | (267) all_55_8_66 = all_0_15_15
% 12.91/3.56 |
% 12.91/3.56 | Combining equations (265,233) yields a new equation:
% 12.91/3.56 | (268) all_62_1_71 = all_0_14_14
% 12.91/3.56 |
% 12.91/3.56 | From (264) and (181) follows:
% 12.91/3.56 | (75) boole_lattice(all_0_17_17) = all_0_15_15
% 12.91/3.56 |
% 12.91/3.56 | From (268)(268) and (220) follows:
% 12.91/3.56 | (270) cartesian_product2(all_0_14_14, all_0_14_14) = all_62_0_70
% 12.91/3.56 |
% 12.91/3.56 | From (265)(265) and (169) follows:
% 12.91/3.56 | (271) cartesian_product2(all_0_14_14, all_0_14_14) = all_42_0_32
% 12.91/3.56 |
% 12.91/3.56 | From (227) and (193) follows:
% 12.91/3.56 | (178) cartesian_product2(all_0_14_14, all_0_14_14) = all_44_0_34
% 12.91/3.56 |
% 12.91/3.56 | From (230) and (204) follows:
% 12.91/3.56 | (143) powerset(all_0_17_17) = all_0_14_14
% 12.91/3.56 |
% 12.91/3.56 | From (265) and (170) follows:
% 12.91/3.56 | (5) the_carrier(all_0_15_15) = all_0_14_14
% 12.91/3.56 |
% 12.91/3.56 | From (263) and (182) follows:
% 12.91/3.56 | (148) the_L_join(all_0_15_15) = all_33_1_31
% 12.91/3.56 |
% 12.91/3.56 | From (261) and (174) follows:
% 12.91/3.56 | (149) the_L_meet(all_0_15_15) = all_33_0_30
% 12.91/3.56 |
% 12.91/3.56 | From (256)(227) and (195) follows:
% 12.91/3.56 | (277) relation_of2_as_subset(all_33_1_31, all_44_0_34, all_0_14_14)
% 12.91/3.56 |
% 12.91/3.56 | From (261) and (175) follows:
% 12.91/3.56 | (278) relation_of2_as_subset(all_33_0_30, all_44_0_34, all_0_14_14)
% 12.91/3.56 |
% 12.91/3.56 | From (256)(227) and (196) follows:
% 12.91/3.56 | (279) quasi_total(all_33_1_31, all_44_0_34, all_0_14_14)
% 12.91/3.56 |
% 12.91/3.56 | From (261) and (176) follows:
% 12.91/3.56 | (280) quasi_total(all_33_0_30, all_44_0_34, all_0_14_14)
% 12.91/3.56 |
% 12.91/3.56 | From (256) and (192) follows:
% 12.91/3.56 | (281) function(all_33_1_31)
% 12.91/3.56 |
% 12.91/3.56 | From (261) and (177) follows:
% 12.91/3.56 | (282) function(all_33_0_30)
% 12.91/3.56 |
% 12.91/3.56 +-Applying beta-rule and splitting (180), into two cases.
% 12.91/3.56 |-Branch one:
% 12.91/3.56 | (283) ~ (all_46_8_44 = all_0_15_15)
% 12.91/3.56 |
% 12.91/3.56 | Equations (264) can reduce 283 to:
% 12.91/3.56 | (284) $false
% 12.91/3.56 |
% 12.91/3.56 |-The branch is then unsatisfiable
% 12.91/3.56 |-Branch two:
% 12.91/3.56 | (264) all_46_8_44 = all_0_15_15
% 12.91/3.56 | (286) all_46_7_43 = all_0_14_14 & ! [v0] : ! [v1] : ! [v2] : ( ~ (apply_binary(all_46_6_42, v0, v1) = v2) | ~ element(v1, all_0_14_14) | ~ element(v0, all_0_14_14) | ? [v3] : (apply_binary(all_33_0_30, v0, v1) = v3 & subset_intersection2(all_0_17_17, v0, v1) = v3 & subset_union2(all_0_17_17, v0, v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (apply_binary(all_33_0_30, v0, v1) = v2) | ~ element(v1, all_0_14_14) | ~ element(v0, all_0_14_14) | ? [v3] : (apply_binary(all_46_6_42, v0, v1) = v3 & subset_intersection2(all_0_17_17, v0, v1) = v2 & subset_union2(all_0_17_17, v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_intersection2(all_0_17_17, v0, v1) = v2) | ~ element(v1, all_0_14_14) | ~ element(v0, all_0_14_14) | ? [v3] : (apply_binary(all_46_6_42, v0, v1) = v3 & apply_binary(all_33_0_30, v0, v1) = v2 & subset_union2(all_0_17_17, v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_union2(all_0_17_17, v0, v1) = v2) | ~ element(v1, all_0_14_14) | ~ element(v0, all_0_14_14) | ? [v3] : (apply_binary(all_46_6_42, v0, v1) = v2 & apply_binary(all_33_0_30, v0, v1) = v3 & subset_intersection2(all_0_17_17, v0, v1) = v3))
% 12.91/3.56 |
% 12.91/3.56 | Applying alpha-rule on (286) yields:
% 12.91/3.56 | (287) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_union2(all_0_17_17, v0, v1) = v2) | ~ element(v1, all_0_14_14) | ~ element(v0, all_0_14_14) | ? [v3] : (apply_binary(all_46_6_42, v0, v1) = v2 & apply_binary(all_33_0_30, v0, v1) = v3 & subset_intersection2(all_0_17_17, v0, v1) = v3))
% 12.91/3.57 | (288) ! [v0] : ! [v1] : ! [v2] : ( ~ (apply_binary(all_33_0_30, v0, v1) = v2) | ~ element(v1, all_0_14_14) | ~ element(v0, all_0_14_14) | ? [v3] : (apply_binary(all_46_6_42, v0, v1) = v3 & subset_intersection2(all_0_17_17, v0, v1) = v2 & subset_union2(all_0_17_17, v0, v1) = v3))
% 12.91/3.57 | (289) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_intersection2(all_0_17_17, v0, v1) = v2) | ~ element(v1, all_0_14_14) | ~ element(v0, all_0_14_14) | ? [v3] : (apply_binary(all_46_6_42, v0, v1) = v3 & apply_binary(all_33_0_30, v0, v1) = v2 & subset_union2(all_0_17_17, v0, v1) = v3))
% 12.91/3.57 | (258) all_46_7_43 = all_0_14_14
% 12.91/3.57 | (291) ! [v0] : ! [v1] : ! [v2] : ( ~ (apply_binary(all_46_6_42, v0, v1) = v2) | ~ element(v1, all_0_14_14) | ~ element(v0, all_0_14_14) | ? [v3] : (apply_binary(all_33_0_30, v0, v1) = v3 & subset_intersection2(all_0_17_17, v0, v1) = v3 & subset_union2(all_0_17_17, v0, v1) = v2))
% 12.91/3.57 |
% 12.91/3.57 +-Applying beta-rule and splitting (188), into two cases.
% 12.91/3.57 |-Branch one:
% 12.91/3.57 | (292) ~ (all_48_8_53 = all_0_15_15)
% 12.91/3.57 |
% 12.91/3.57 | Equations (224) can reduce 292 to:
% 12.91/3.57 | (284) $false
% 12.91/3.57 |
% 12.91/3.57 |-The branch is then unsatisfiable
% 12.91/3.57 |-Branch two:
% 12.91/3.57 | (224) all_48_8_53 = all_0_15_15
% 12.91/3.57 | (295) ! [v0] : ! [v1] : ! [v2] : ( ~ (apply_binary(all_48_6_51, v0, v1) = v2) | ~ element(v1, all_0_14_14) | ~ element(v0, all_0_14_14) | ? [v3] : (apply_binary(all_48_7_52, v0, v1) = v3 & subset_intersection2(all_0_17_17, v0, v1) = v2 & subset_union2(all_0_17_17, v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (apply_binary(all_48_7_52, v0, v1) = v2) | ~ element(v1, all_0_14_14) | ~ element(v0, all_0_14_14) | ? [v3] : (apply_binary(all_48_6_51, v0, v1) = v3 & subset_intersection2(all_0_17_17, v0, v1) = v3 & subset_union2(all_0_17_17, v0, v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_intersection2(all_0_17_17, v0, v1) = v2) | ~ element(v1, all_0_14_14) | ~ element(v0, all_0_14_14) | ? [v3] : (apply_binary(all_48_6_51, v0, v1) = v2 & apply_binary(all_48_7_52, v0, v1) = v3 & subset_union2(all_0_17_17, v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_union2(all_0_17_17, v0, v1) = v2) | ~ element(v1, all_0_14_14) | ~ element(v0, all_0_14_14) | ? [v3] : (apply_binary(all_48_6_51, v0, v1) = v3 & apply_binary(all_48_7_52, v0, v1) = v2 & subset_intersection2(all_0_17_17, v0, v1) = v3))
% 12.91/3.57 |
% 12.91/3.57 | Applying alpha-rule on (295) yields:
% 12.91/3.57 | (296) ! [v0] : ! [v1] : ! [v2] : ( ~ (apply_binary(all_48_6_51, v0, v1) = v2) | ~ element(v1, all_0_14_14) | ~ element(v0, all_0_14_14) | ? [v3] : (apply_binary(all_48_7_52, v0, v1) = v3 & subset_intersection2(all_0_17_17, v0, v1) = v2 & subset_union2(all_0_17_17, v0, v1) = v3))
% 12.91/3.57 | (297) ! [v0] : ! [v1] : ! [v2] : ( ~ (apply_binary(all_48_7_52, v0, v1) = v2) | ~ element(v1, all_0_14_14) | ~ element(v0, all_0_14_14) | ? [v3] : (apply_binary(all_48_6_51, v0, v1) = v3 & subset_intersection2(all_0_17_17, v0, v1) = v3 & subset_union2(all_0_17_17, v0, v1) = v2))
% 12.91/3.57 | (298) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_intersection2(all_0_17_17, v0, v1) = v2) | ~ element(v1, all_0_14_14) | ~ element(v0, all_0_14_14) | ? [v3] : (apply_binary(all_48_6_51, v0, v1) = v2 & apply_binary(all_48_7_52, v0, v1) = v3 & subset_union2(all_0_17_17, v0, v1) = v3))
% 12.91/3.57 | (299) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_union2(all_0_17_17, v0, v1) = v2) | ~ element(v1, all_0_14_14) | ~ element(v0, all_0_14_14) | ? [v3] : (apply_binary(all_48_6_51, v0, v1) = v3 & apply_binary(all_48_7_52, v0, v1) = v2 & subset_intersection2(all_0_17_17, v0, v1) = v3))
% 12.91/3.57 |
% 12.91/3.57 +-Applying beta-rule and splitting (207), into two cases.
% 12.91/3.57 |-Branch one:
% 12.91/3.57 | (300) ~ (all_55_8_66 = all_0_15_15)
% 12.91/3.57 |
% 12.91/3.57 | Equations (267) can reduce 300 to:
% 12.91/3.57 | (284) $false
% 12.91/3.57 |
% 12.91/3.57 |-The branch is then unsatisfiable
% 12.91/3.57 |-Branch two:
% 12.91/3.57 | (267) all_55_8_66 = all_0_15_15
% 12.91/3.57 | (303) all_55_7_65 = all_0_14_14 & ! [v0] : ! [v1] : ! [v2] : ( ~ (apply_binary(all_55_6_64, v0, v1) = v2) | ~ element(v1, all_0_14_14) | ~ element(v0, all_0_14_14) | ? [v3] : (apply_binary(all_33_1_31, v0, v1) = v3 & subset_intersection2(all_0_17_17, v0, v1) = v2 & subset_union2(all_0_17_17, v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (apply_binary(all_33_1_31, v0, v1) = v2) | ~ element(v1, all_0_14_14) | ~ element(v0, all_0_14_14) | ? [v3] : (apply_binary(all_55_6_64, v0, v1) = v3 & subset_intersection2(all_0_17_17, v0, v1) = v3 & subset_union2(all_0_17_17, v0, v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_intersection2(all_0_17_17, v0, v1) = v2) | ~ element(v1, all_0_14_14) | ~ element(v0, all_0_14_14) | ? [v3] : (apply_binary(all_55_6_64, v0, v1) = v2 & apply_binary(all_33_1_31, v0, v1) = v3 & subset_union2(all_0_17_17, v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_union2(all_0_17_17, v0, v1) = v2) | ~ element(v1, all_0_14_14) | ~ element(v0, all_0_14_14) | ? [v3] : (apply_binary(all_55_6_64, v0, v1) = v3 & apply_binary(all_33_1_31, v0, v1) = v2 & subset_intersection2(all_0_17_17, v0, v1) = v3))
% 12.91/3.57 |
% 12.91/3.57 | Applying alpha-rule on (303) yields:
% 12.91/3.57 | (304) ! [v0] : ! [v1] : ! [v2] : ( ~ (apply_binary(all_33_1_31, v0, v1) = v2) | ~ element(v1, all_0_14_14) | ~ element(v0, all_0_14_14) | ? [v3] : (apply_binary(all_55_6_64, v0, v1) = v3 & subset_intersection2(all_0_17_17, v0, v1) = v3 & subset_union2(all_0_17_17, v0, v1) = v2))
% 12.91/3.57 | (305) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_intersection2(all_0_17_17, v0, v1) = v2) | ~ element(v1, all_0_14_14) | ~ element(v0, all_0_14_14) | ? [v3] : (apply_binary(all_55_6_64, v0, v1) = v2 & apply_binary(all_33_1_31, v0, v1) = v3 & subset_union2(all_0_17_17, v0, v1) = v3))
% 12.91/3.57 | (306) ! [v0] : ! [v1] : ! [v2] : ( ~ (apply_binary(all_55_6_64, v0, v1) = v2) | ~ element(v1, all_0_14_14) | ~ element(v0, all_0_14_14) | ? [v3] : (apply_binary(all_33_1_31, v0, v1) = v3 & subset_intersection2(all_0_17_17, v0, v1) = v2 & subset_union2(all_0_17_17, v0, v1) = v3))
% 12.91/3.57 | (307) all_55_7_65 = all_0_14_14
% 12.91/3.57 | (308) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_union2(all_0_17_17, v0, v1) = v2) | ~ element(v1, all_0_14_14) | ~ element(v0, all_0_14_14) | ? [v3] : (apply_binary(all_55_6_64, v0, v1) = v3 & apply_binary(all_33_1_31, v0, v1) = v2 & subset_intersection2(all_0_17_17, v0, v1) = v3))
% 12.91/3.57 |
% 12.91/3.57 | Instantiating formula (53) with all_0_14_14, all_0_14_14, all_62_0_70, all_44_0_34 and discharging atoms cartesian_product2(all_0_14_14, all_0_14_14) = all_62_0_70, cartesian_product2(all_0_14_14, all_0_14_14) = all_44_0_34, yields:
% 12.91/3.57 | (309) all_62_0_70 = all_44_0_34
% 12.91/3.57 |
% 12.91/3.57 | Instantiating formula (53) with all_0_14_14, all_0_14_14, all_42_0_32, all_62_0_70 and discharging atoms cartesian_product2(all_0_14_14, all_0_14_14) = all_62_0_70, cartesian_product2(all_0_14_14, all_0_14_14) = all_42_0_32, yields:
% 12.91/3.57 | (310) all_62_0_70 = all_42_0_32
% 12.91/3.57 |
% 12.91/3.57 | Combining equations (309,310) yields a new equation:
% 12.91/3.57 | (311) all_44_0_34 = all_42_0_32
% 12.91/3.57 |
% 12.91/3.57 | Simplifying 311 yields:
% 12.91/3.57 | (312) all_44_0_34 = all_42_0_32
% 12.91/3.57 |
% 12.91/3.57 | From (312) and (178) follows:
% 12.91/3.57 | (271) cartesian_product2(all_0_14_14, all_0_14_14) = all_42_0_32
% 12.91/3.57 |
% 12.91/3.57 | From (312) and (278) follows:
% 12.91/3.57 | (314) relation_of2_as_subset(all_33_0_30, all_42_0_32, all_0_14_14)
% 12.91/3.57 |
% 12.91/3.57 | From (312) and (277) follows:
% 12.91/3.57 | (315) relation_of2_as_subset(all_33_1_31, all_42_0_32, all_0_14_14)
% 12.91/3.57 |
% 12.91/3.57 | From (312) and (280) follows:
% 12.91/3.57 | (316) quasi_total(all_33_0_30, all_42_0_32, all_0_14_14)
% 12.91/3.57 |
% 12.91/3.57 | From (312) and (279) follows:
% 12.91/3.57 | (317) quasi_total(all_33_1_31, all_42_0_32, all_0_14_14)
% 12.91/3.57 |
% 12.91/3.57 | Instantiating formula (305) with all_0_9_9, all_0_13_13, all_0_16_16 and discharging atoms subset_intersection2(all_0_17_17, all_0_16_16, all_0_13_13) = all_0_9_9, element(all_0_13_13, all_0_14_14), element(all_0_16_16, all_0_14_14), yields:
% 12.91/3.57 | (318) ? [v0] : (apply_binary(all_55_6_64, all_0_16_16, all_0_13_13) = all_0_9_9 & apply_binary(all_33_1_31, all_0_16_16, all_0_13_13) = v0 & subset_union2(all_0_17_17, all_0_16_16, all_0_13_13) = v0)
% 12.91/3.57 |
% 12.91/3.57 | Instantiating formula (298) with all_0_9_9, all_0_13_13, all_0_16_16 and discharging atoms subset_intersection2(all_0_17_17, all_0_16_16, all_0_13_13) = all_0_9_9, element(all_0_13_13, all_0_14_14), element(all_0_16_16, all_0_14_14), yields:
% 12.91/3.57 | (319) ? [v0] : (apply_binary(all_48_6_51, all_0_16_16, all_0_13_13) = all_0_9_9 & apply_binary(all_48_7_52, all_0_16_16, all_0_13_13) = v0 & subset_union2(all_0_17_17, all_0_16_16, all_0_13_13) = v0)
% 12.91/3.57 |
% 12.91/3.57 | Instantiating formula (289) with all_0_9_9, all_0_13_13, all_0_16_16 and discharging atoms subset_intersection2(all_0_17_17, all_0_16_16, all_0_13_13) = all_0_9_9, element(all_0_13_13, all_0_14_14), element(all_0_16_16, all_0_14_14), yields:
% 12.91/3.57 | (320) ? [v0] : (apply_binary(all_46_6_42, all_0_16_16, all_0_13_13) = v0 & apply_binary(all_33_0_30, all_0_16_16, all_0_13_13) = all_0_9_9 & subset_union2(all_0_17_17, all_0_16_16, all_0_13_13) = v0)
% 12.91/3.57 |
% 12.91/3.57 | Instantiating formula (147) with all_0_9_9, all_0_13_13, all_0_16_16 and discharging atoms subset_intersection2(all_0_17_17, all_0_16_16, all_0_13_13) = all_0_9_9, element(all_0_13_13, all_0_14_14), element(all_0_16_16, all_0_14_14), yields:
% 12.91/3.57 | (321) ? [v0] : (apply_binary(all_33_0_30, all_0_16_16, all_0_13_13) = all_0_9_9 & apply_binary(all_33_1_31, all_0_16_16, all_0_13_13) = v0 & subset_union2(all_0_17_17, all_0_16_16, all_0_13_13) = v0)
% 12.91/3.57 |
% 12.91/3.57 | Instantiating formula (118) with all_0_9_9, all_0_13_13, all_0_16_16, all_0_17_17 and discharging atoms subset_intersection2(all_0_17_17, all_0_16_16, all_0_13_13) = all_0_9_9, yields:
% 12.91/3.57 | (322) ? [v0] : (powerset(all_0_17_17) = v0 & ( ~ element(all_0_13_13, v0) | ~ element(all_0_16_16, v0) | element(all_0_9_9, v0)))
% 12.91/3.57 |
% 12.91/3.57 | Instantiating formula (308) with all_0_11_11, all_0_13_13, all_0_16_16 and discharging atoms subset_union2(all_0_17_17, all_0_16_16, all_0_13_13) = all_0_11_11, element(all_0_13_13, all_0_14_14), element(all_0_16_16, all_0_14_14), yields:
% 12.91/3.57 | (323) ? [v0] : (apply_binary(all_55_6_64, all_0_16_16, all_0_13_13) = v0 & apply_binary(all_33_1_31, all_0_16_16, all_0_13_13) = all_0_11_11 & subset_intersection2(all_0_17_17, all_0_16_16, all_0_13_13) = v0)
% 12.91/3.57 |
% 12.91/3.57 | Instantiating formula (299) with all_0_11_11, all_0_13_13, all_0_16_16 and discharging atoms subset_union2(all_0_17_17, all_0_16_16, all_0_13_13) = all_0_11_11, element(all_0_13_13, all_0_14_14), element(all_0_16_16, all_0_14_14), yields:
% 12.91/3.57 | (324) ? [v0] : (apply_binary(all_48_6_51, all_0_16_16, all_0_13_13) = v0 & apply_binary(all_48_7_52, all_0_16_16, all_0_13_13) = all_0_11_11 & subset_intersection2(all_0_17_17, all_0_16_16, all_0_13_13) = v0)
% 12.91/3.57 |
% 12.91/3.57 | Instantiating formula (287) with all_0_11_11, all_0_13_13, all_0_16_16 and discharging atoms subset_union2(all_0_17_17, all_0_16_16, all_0_13_13) = all_0_11_11, element(all_0_13_13, all_0_14_14), element(all_0_16_16, all_0_14_14), yields:
% 12.91/3.57 | (325) ? [v0] : (apply_binary(all_46_6_42, all_0_16_16, all_0_13_13) = all_0_11_11 & apply_binary(all_33_0_30, all_0_16_16, all_0_13_13) = v0 & subset_intersection2(all_0_17_17, all_0_16_16, all_0_13_13) = v0)
% 12.91/3.57 |
% 12.91/3.57 | Instantiating formula (144) with all_0_11_11, all_0_13_13, all_0_16_16 and discharging atoms subset_union2(all_0_17_17, all_0_16_16, all_0_13_13) = all_0_11_11, element(all_0_13_13, all_0_14_14), element(all_0_16_16, all_0_14_14), yields:
% 12.91/3.57 | (326) ? [v0] : (apply_binary(all_33_0_30, all_0_16_16, all_0_13_13) = v0 & apply_binary(all_33_1_31, all_0_16_16, all_0_13_13) = all_0_11_11 & subset_intersection2(all_0_17_17, all_0_16_16, all_0_13_13) = v0)
% 12.91/3.57 |
% 12.91/3.57 | Instantiating formula (31) with all_0_11_11, all_0_13_13, all_0_16_16, all_0_17_17 and discharging atoms subset_union2(all_0_17_17, all_0_16_16, all_0_13_13) = all_0_11_11, yields:
% 12.91/3.57 | (327) ? [v0] : (powerset(all_0_17_17) = v0 & ( ~ element(all_0_13_13, v0) | ~ element(all_0_16_16, v0) | element(all_0_11_11, v0)))
% 12.91/3.57 |
% 12.91/3.57 | Instantiating formula (22) with all_33_0_30, all_0_14_14, all_42_0_32 and discharging atoms relation_of2_as_subset(all_33_0_30, all_42_0_32, all_0_14_14), yields:
% 12.91/3.57 | (328) relation_of2(all_33_0_30, all_42_0_32, all_0_14_14)
% 12.91/3.57 |
% 12.91/3.57 | Instantiating formula (22) with all_33_1_31, all_0_14_14, all_42_0_32 and discharging atoms relation_of2_as_subset(all_33_1_31, all_42_0_32, all_0_14_14), yields:
% 12.91/3.57 | (329) relation_of2(all_33_1_31, all_42_0_32, all_0_14_14)
% 12.91/3.57 |
% 12.91/3.57 | Instantiating formula (37) with all_0_14_14, all_0_15_15 and discharging atoms the_carrier(all_0_15_15) = all_0_14_14, one_sorted_str(all_0_15_15), yields:
% 12.91/3.57 | (330) empty_carrier(all_0_15_15) | ? [v0] : ? [v1] : (powerset(all_0_14_14) = v0 & element(v1, v0) & ~ empty(v1))
% 12.91/3.57 |
% 12.91/3.57 | Instantiating (318) with all_97_0_75 yields:
% 12.91/3.57 | (331) apply_binary(all_55_6_64, all_0_16_16, all_0_13_13) = all_0_9_9 & apply_binary(all_33_1_31, all_0_16_16, all_0_13_13) = all_97_0_75 & subset_union2(all_0_17_17, all_0_16_16, all_0_13_13) = all_97_0_75
% 12.91/3.57 |
% 12.91/3.57 | Applying alpha-rule on (331) yields:
% 12.91/3.57 | (332) apply_binary(all_55_6_64, all_0_16_16, all_0_13_13) = all_0_9_9
% 12.91/3.57 | (333) apply_binary(all_33_1_31, all_0_16_16, all_0_13_13) = all_97_0_75
% 12.91/3.57 | (334) subset_union2(all_0_17_17, all_0_16_16, all_0_13_13) = all_97_0_75
% 12.91/3.57 |
% 12.91/3.57 | Instantiating (322) with all_99_0_76 yields:
% 12.91/3.57 | (335) powerset(all_0_17_17) = all_99_0_76 & ( ~ element(all_0_13_13, all_99_0_76) | ~ element(all_0_16_16, all_99_0_76) | element(all_0_9_9, all_99_0_76))
% 12.91/3.58 |
% 12.91/3.58 | Applying alpha-rule on (335) yields:
% 12.91/3.58 | (336) powerset(all_0_17_17) = all_99_0_76
% 12.91/3.58 | (337) ~ element(all_0_13_13, all_99_0_76) | ~ element(all_0_16_16, all_99_0_76) | element(all_0_9_9, all_99_0_76)
% 12.91/3.58 |
% 12.91/3.58 | Instantiating (321) with all_101_0_77 yields:
% 12.91/3.58 | (338) apply_binary(all_33_0_30, all_0_16_16, all_0_13_13) = all_0_9_9 & apply_binary(all_33_1_31, all_0_16_16, all_0_13_13) = all_101_0_77 & subset_union2(all_0_17_17, all_0_16_16, all_0_13_13) = all_101_0_77
% 12.91/3.58 |
% 12.91/3.58 | Applying alpha-rule on (338) yields:
% 12.91/3.58 | (339) apply_binary(all_33_0_30, all_0_16_16, all_0_13_13) = all_0_9_9
% 12.91/3.58 | (340) apply_binary(all_33_1_31, all_0_16_16, all_0_13_13) = all_101_0_77
% 12.91/3.58 | (341) subset_union2(all_0_17_17, all_0_16_16, all_0_13_13) = all_101_0_77
% 12.91/3.58 |
% 12.91/3.58 | Instantiating (326) with all_103_0_78 yields:
% 12.91/3.58 | (342) apply_binary(all_33_0_30, all_0_16_16, all_0_13_13) = all_103_0_78 & apply_binary(all_33_1_31, all_0_16_16, all_0_13_13) = all_0_11_11 & subset_intersection2(all_0_17_17, all_0_16_16, all_0_13_13) = all_103_0_78
% 12.91/3.58 |
% 12.91/3.58 | Applying alpha-rule on (342) yields:
% 12.91/3.58 | (343) apply_binary(all_33_0_30, all_0_16_16, all_0_13_13) = all_103_0_78
% 12.91/3.58 | (344) apply_binary(all_33_1_31, all_0_16_16, all_0_13_13) = all_0_11_11
% 12.91/3.58 | (345) subset_intersection2(all_0_17_17, all_0_16_16, all_0_13_13) = all_103_0_78
% 12.91/3.58 |
% 12.91/3.58 | Instantiating (325) with all_105_0_79 yields:
% 12.91/3.58 | (346) apply_binary(all_46_6_42, all_0_16_16, all_0_13_13) = all_0_11_11 & apply_binary(all_33_0_30, all_0_16_16, all_0_13_13) = all_105_0_79 & subset_intersection2(all_0_17_17, all_0_16_16, all_0_13_13) = all_105_0_79
% 12.91/3.58 |
% 12.91/3.58 | Applying alpha-rule on (346) yields:
% 12.91/3.58 | (347) apply_binary(all_46_6_42, all_0_16_16, all_0_13_13) = all_0_11_11
% 12.91/3.58 | (348) apply_binary(all_33_0_30, all_0_16_16, all_0_13_13) = all_105_0_79
% 12.91/3.58 | (349) subset_intersection2(all_0_17_17, all_0_16_16, all_0_13_13) = all_105_0_79
% 12.91/3.58 |
% 12.91/3.58 | Instantiating (327) with all_107_0_80 yields:
% 12.91/3.58 | (350) powerset(all_0_17_17) = all_107_0_80 & ( ~ element(all_0_13_13, all_107_0_80) | ~ element(all_0_16_16, all_107_0_80) | element(all_0_11_11, all_107_0_80))
% 12.91/3.58 |
% 12.91/3.58 | Applying alpha-rule on (350) yields:
% 12.91/3.58 | (351) powerset(all_0_17_17) = all_107_0_80
% 12.91/3.58 | (352) ~ element(all_0_13_13, all_107_0_80) | ~ element(all_0_16_16, all_107_0_80) | element(all_0_11_11, all_107_0_80)
% 12.91/3.58 |
% 12.91/3.58 | Instantiating (324) with all_115_0_84 yields:
% 12.91/3.58 | (353) apply_binary(all_48_6_51, all_0_16_16, all_0_13_13) = all_115_0_84 & apply_binary(all_48_7_52, all_0_16_16, all_0_13_13) = all_0_11_11 & subset_intersection2(all_0_17_17, all_0_16_16, all_0_13_13) = all_115_0_84
% 12.91/3.58 |
% 12.91/3.58 | Applying alpha-rule on (353) yields:
% 12.91/3.58 | (354) apply_binary(all_48_6_51, all_0_16_16, all_0_13_13) = all_115_0_84
% 12.91/3.58 | (355) apply_binary(all_48_7_52, all_0_16_16, all_0_13_13) = all_0_11_11
% 12.91/3.58 | (356) subset_intersection2(all_0_17_17, all_0_16_16, all_0_13_13) = all_115_0_84
% 12.91/3.58 |
% 12.91/3.58 | Instantiating (323) with all_117_0_85 yields:
% 12.91/3.58 | (357) apply_binary(all_55_6_64, all_0_16_16, all_0_13_13) = all_117_0_85 & apply_binary(all_33_1_31, all_0_16_16, all_0_13_13) = all_0_11_11 & subset_intersection2(all_0_17_17, all_0_16_16, all_0_13_13) = all_117_0_85
% 12.91/3.58 |
% 12.91/3.58 | Applying alpha-rule on (357) yields:
% 12.91/3.58 | (358) apply_binary(all_55_6_64, all_0_16_16, all_0_13_13) = all_117_0_85
% 12.91/3.58 | (344) apply_binary(all_33_1_31, all_0_16_16, all_0_13_13) = all_0_11_11
% 12.91/3.58 | (360) subset_intersection2(all_0_17_17, all_0_16_16, all_0_13_13) = all_117_0_85
% 12.91/3.58 |
% 12.91/3.58 | Instantiating (320) with all_119_0_86 yields:
% 12.91/3.58 | (361) apply_binary(all_46_6_42, all_0_16_16, all_0_13_13) = all_119_0_86 & apply_binary(all_33_0_30, all_0_16_16, all_0_13_13) = all_0_9_9 & subset_union2(all_0_17_17, all_0_16_16, all_0_13_13) = all_119_0_86
% 12.91/3.58 |
% 12.91/3.58 | Applying alpha-rule on (361) yields:
% 12.91/3.58 | (362) apply_binary(all_46_6_42, all_0_16_16, all_0_13_13) = all_119_0_86
% 12.91/3.58 | (339) apply_binary(all_33_0_30, all_0_16_16, all_0_13_13) = all_0_9_9
% 12.91/3.58 | (364) subset_union2(all_0_17_17, all_0_16_16, all_0_13_13) = all_119_0_86
% 12.91/3.58 |
% 12.91/3.58 | Instantiating (319) with all_121_0_87 yields:
% 12.91/3.58 | (365) apply_binary(all_48_6_51, all_0_16_16, all_0_13_13) = all_0_9_9 & apply_binary(all_48_7_52, all_0_16_16, all_0_13_13) = all_121_0_87 & subset_union2(all_0_17_17, all_0_16_16, all_0_13_13) = all_121_0_87
% 12.91/3.58 |
% 12.91/3.58 | Applying alpha-rule on (365) yields:
% 12.91/3.58 | (366) apply_binary(all_48_6_51, all_0_16_16, all_0_13_13) = all_0_9_9
% 12.91/3.58 | (367) apply_binary(all_48_7_52, all_0_16_16, all_0_13_13) = all_121_0_87
% 12.91/3.58 | (368) subset_union2(all_0_17_17, all_0_16_16, all_0_13_13) = all_121_0_87
% 12.91/3.58 |
% 12.91/3.58 | Instantiating formula (94) with all_0_17_17, all_0_16_16, all_0_13_13, all_115_0_84, all_0_9_9 and discharging atoms subset_intersection2(all_0_17_17, all_0_16_16, all_0_13_13) = all_115_0_84, subset_intersection2(all_0_17_17, all_0_16_16, all_0_13_13) = all_0_9_9, yields:
% 12.91/3.58 | (369) all_115_0_84 = all_0_9_9
% 12.91/3.58 |
% 12.91/3.58 | Instantiating formula (94) with all_0_17_17, all_0_16_16, all_0_13_13, all_105_0_79, all_117_0_85 and discharging atoms subset_intersection2(all_0_17_17, all_0_16_16, all_0_13_13) = all_117_0_85, subset_intersection2(all_0_17_17, all_0_16_16, all_0_13_13) = all_105_0_79, yields:
% 12.91/3.58 | (370) all_117_0_85 = all_105_0_79
% 12.91/3.58 |
% 12.91/3.58 | Instantiating formula (94) with all_0_17_17, all_0_16_16, all_0_13_13, all_105_0_79, all_115_0_84 and discharging atoms subset_intersection2(all_0_17_17, all_0_16_16, all_0_13_13) = all_115_0_84, subset_intersection2(all_0_17_17, all_0_16_16, all_0_13_13) = all_105_0_79, yields:
% 12.91/3.58 | (371) all_115_0_84 = all_105_0_79
% 12.91/3.58 |
% 12.91/3.58 | Instantiating formula (94) with all_0_17_17, all_0_16_16, all_0_13_13, all_103_0_78, all_117_0_85 and discharging atoms subset_intersection2(all_0_17_17, all_0_16_16, all_0_13_13) = all_117_0_85, subset_intersection2(all_0_17_17, all_0_16_16, all_0_13_13) = all_103_0_78, yields:
% 12.91/3.58 | (372) all_117_0_85 = all_103_0_78
% 12.91/3.58 |
% 12.91/3.58 | Instantiating formula (69) with all_0_17_17, all_0_16_16, all_0_13_13, all_121_0_87, all_0_11_11 and discharging atoms subset_union2(all_0_17_17, all_0_16_16, all_0_13_13) = all_121_0_87, subset_union2(all_0_17_17, all_0_16_16, all_0_13_13) = all_0_11_11, yields:
% 12.91/3.58 | (373) all_121_0_87 = all_0_11_11
% 12.91/3.58 |
% 12.91/3.58 | Instantiating formula (69) with all_0_17_17, all_0_16_16, all_0_13_13, all_119_0_86, all_121_0_87 and discharging atoms subset_union2(all_0_17_17, all_0_16_16, all_0_13_13) = all_121_0_87, subset_union2(all_0_17_17, all_0_16_16, all_0_13_13) = all_119_0_86, yields:
% 12.91/3.58 | (374) all_121_0_87 = all_119_0_86
% 12.91/3.58 |
% 12.91/3.58 | Instantiating formula (69) with all_0_17_17, all_0_16_16, all_0_13_13, all_101_0_77, all_119_0_86 and discharging atoms subset_union2(all_0_17_17, all_0_16_16, all_0_13_13) = all_119_0_86, subset_union2(all_0_17_17, all_0_16_16, all_0_13_13) = all_101_0_77, yields:
% 12.91/3.58 | (375) all_119_0_86 = all_101_0_77
% 12.91/3.58 |
% 12.91/3.58 | Instantiating formula (69) with all_0_17_17, all_0_16_16, all_0_13_13, all_97_0_75, all_119_0_86 and discharging atoms subset_union2(all_0_17_17, all_0_16_16, all_0_13_13) = all_119_0_86, subset_union2(all_0_17_17, all_0_16_16, all_0_13_13) = all_97_0_75, yields:
% 12.91/3.58 | (376) all_119_0_86 = all_97_0_75
% 12.91/3.58 |
% 12.91/3.58 | Instantiating formula (92) with all_0_17_17, all_107_0_80, all_0_14_14 and discharging atoms powerset(all_0_17_17) = all_107_0_80, powerset(all_0_17_17) = all_0_14_14, yields:
% 12.91/3.58 | (377) all_107_0_80 = all_0_14_14
% 12.91/3.58 |
% 12.91/3.58 | Instantiating formula (92) with all_0_17_17, all_99_0_76, all_107_0_80 and discharging atoms powerset(all_0_17_17) = all_107_0_80, powerset(all_0_17_17) = all_99_0_76, yields:
% 12.91/3.58 | (378) all_107_0_80 = all_99_0_76
% 12.91/3.58 |
% 12.91/3.58 | Combining equations (374,373) yields a new equation:
% 12.91/3.58 | (379) all_119_0_86 = all_0_11_11
% 12.91/3.58 |
% 12.91/3.58 | Simplifying 379 yields:
% 12.91/3.58 | (380) all_119_0_86 = all_0_11_11
% 12.91/3.58 |
% 12.91/3.58 | Combining equations (376,375) yields a new equation:
% 12.91/3.58 | (381) all_101_0_77 = all_97_0_75
% 12.91/3.58 |
% 12.91/3.58 | Combining equations (380,375) yields a new equation:
% 12.91/3.58 | (382) all_101_0_77 = all_0_11_11
% 12.91/3.58 |
% 12.91/3.58 | Combining equations (370,372) yields a new equation:
% 12.91/3.58 | (383) all_105_0_79 = all_103_0_78
% 12.91/3.58 |
% 12.91/3.58 | Simplifying 383 yields:
% 12.91/3.58 | (384) all_105_0_79 = all_103_0_78
% 12.91/3.58 |
% 12.91/3.58 | Combining equations (371,369) yields a new equation:
% 12.91/3.58 | (385) all_105_0_79 = all_0_9_9
% 12.91/3.58 |
% 12.91/3.58 | Simplifying 385 yields:
% 12.91/3.58 | (386) all_105_0_79 = all_0_9_9
% 12.91/3.58 |
% 12.91/3.58 | Combining equations (377,378) yields a new equation:
% 12.91/3.58 | (387) all_99_0_76 = all_0_14_14
% 12.91/3.58 |
% 12.91/3.58 | Combining equations (386,384) yields a new equation:
% 12.91/3.58 | (388) all_103_0_78 = all_0_9_9
% 12.91/3.58 |
% 12.91/3.58 | Combining equations (381,382) yields a new equation:
% 12.91/3.58 | (389) all_97_0_75 = all_0_11_11
% 12.91/3.58 |
% 12.91/3.58 | Simplifying 389 yields:
% 12.91/3.58 | (390) all_97_0_75 = all_0_11_11
% 12.91/3.58 |
% 12.91/3.58 | Combining equations (387,378) yields a new equation:
% 12.91/3.58 | (377) all_107_0_80 = all_0_14_14
% 12.91/3.58 |
% 12.91/3.58 | From (388) and (343) follows:
% 12.91/3.58 | (339) apply_binary(all_33_0_30, all_0_16_16, all_0_13_13) = all_0_9_9
% 12.91/3.58 |
% 12.91/3.58 | From (390) and (333) follows:
% 12.91/3.58 | (344) apply_binary(all_33_1_31, all_0_16_16, all_0_13_13) = all_0_11_11
% 12.91/3.58 |
% 12.91/3.58 | From (387) and (336) follows:
% 12.91/3.58 | (143) powerset(all_0_17_17) = all_0_14_14
% 12.91/3.58 |
% 12.91/3.58 +-Applying beta-rule and splitting (337), into two cases.
% 12.91/3.58 |-Branch one:
% 12.91/3.58 | (395) ~ element(all_0_13_13, all_99_0_76)
% 12.91/3.58 |
% 12.91/3.58 | From (387) and (395) follows:
% 12.91/3.58 | (396) ~ element(all_0_13_13, all_0_14_14)
% 12.91/3.58 |
% 12.91/3.58 | Using (101) and (396) yields:
% 12.91/3.58 | (397) $false
% 12.91/3.58 |
% 12.91/3.58 |-The branch is then unsatisfiable
% 12.91/3.58 |-Branch two:
% 12.91/3.58 | (398) element(all_0_13_13, all_99_0_76)
% 12.91/3.58 | (399) ~ element(all_0_16_16, all_99_0_76) | element(all_0_9_9, all_99_0_76)
% 12.91/3.58 |
% 12.91/3.58 | From (387) and (398) follows:
% 12.91/3.58 | (101) element(all_0_13_13, all_0_14_14)
% 12.91/3.58 |
% 12.91/3.58 +-Applying beta-rule and splitting (399), into two cases.
% 12.91/3.58 |-Branch one:
% 12.91/3.58 | (401) ~ element(all_0_16_16, all_99_0_76)
% 12.91/3.58 |
% 12.91/3.58 | From (387) and (401) follows:
% 12.91/3.58 | (402) ~ element(all_0_16_16, all_0_14_14)
% 12.91/3.58 |
% 12.91/3.58 | Using (2) and (402) yields:
% 12.91/3.58 | (397) $false
% 12.91/3.58 |
% 12.91/3.58 |-The branch is then unsatisfiable
% 12.91/3.58 |-Branch two:
% 12.91/3.58 | (404) element(all_0_16_16, all_99_0_76)
% 12.91/3.58 | (405) element(all_0_9_9, all_99_0_76)
% 12.91/3.58 |
% 12.91/3.58 | From (387) and (405) follows:
% 12.91/3.58 | (406) element(all_0_9_9, all_0_14_14)
% 12.91/3.58 |
% 12.91/3.58 | From (387) and (404) follows:
% 12.91/3.58 | (2) element(all_0_16_16, all_0_14_14)
% 12.91/3.58 |
% 12.91/3.58 +-Applying beta-rule and splitting (352), into two cases.
% 12.91/3.58 |-Branch one:
% 12.91/3.58 | (408) ~ element(all_0_13_13, all_107_0_80)
% 12.91/3.58 |
% 12.91/3.58 | From (377) and (408) follows:
% 12.91/3.58 | (396) ~ element(all_0_13_13, all_0_14_14)
% 12.91/3.58 |
% 12.91/3.58 | Using (101) and (396) yields:
% 12.91/3.58 | (397) $false
% 12.91/3.58 |
% 12.91/3.58 |-The branch is then unsatisfiable
% 12.91/3.58 |-Branch two:
% 12.91/3.58 | (411) element(all_0_13_13, all_107_0_80)
% 12.91/3.58 | (412) ~ element(all_0_16_16, all_107_0_80) | element(all_0_11_11, all_107_0_80)
% 12.91/3.58 |
% 12.91/3.58 | From (377) and (411) follows:
% 12.91/3.58 | (101) element(all_0_13_13, all_0_14_14)
% 12.91/3.58 |
% 12.91/3.58 +-Applying beta-rule and splitting (412), into two cases.
% 12.91/3.58 |-Branch one:
% 12.91/3.58 | (414) ~ element(all_0_16_16, all_107_0_80)
% 12.91/3.58 |
% 12.91/3.58 | From (377) and (414) follows:
% 12.91/3.58 | (402) ~ element(all_0_16_16, all_0_14_14)
% 12.91/3.58 |
% 12.91/3.59 | Using (2) and (402) yields:
% 12.91/3.59 | (397) $false
% 12.91/3.59 |
% 12.91/3.59 |-The branch is then unsatisfiable
% 12.91/3.59 |-Branch two:
% 12.91/3.59 | (417) element(all_0_16_16, all_107_0_80)
% 12.91/3.59 | (418) element(all_0_11_11, all_107_0_80)
% 12.91/3.59 |
% 12.91/3.59 | From (377) and (418) follows:
% 12.91/3.59 | (419) element(all_0_11_11, all_0_14_14)
% 12.91/3.59 |
% 12.91/3.59 | From (377) and (417) follows:
% 12.91/3.59 | (2) element(all_0_16_16, all_0_14_14)
% 12.91/3.59 |
% 12.91/3.59 | Instantiating formula (131) with all_0_14_14, all_0_9_9 and discharging atoms element(all_0_9_9, all_0_14_14), yields:
% 12.91/3.59 | (421) empty(all_0_14_14) | in(all_0_9_9, all_0_14_14)
% 12.91/3.59 |
% 12.91/3.59 | Instantiating formula (131) with all_0_14_14, all_0_11_11 and discharging atoms element(all_0_11_11, all_0_14_14), yields:
% 12.91/3.59 | (422) empty(all_0_14_14) | in(all_0_11_11, all_0_14_14)
% 12.91/3.59 |
% 12.91/3.59 +-Applying beta-rule and splitting (74), into two cases.
% 12.91/3.59 |-Branch one:
% 12.91/3.59 | (423) ~ (all_0_9_9 = all_0_10_10)
% 12.91/3.59 |
% 12.91/3.59 +-Applying beta-rule and splitting (138), into two cases.
% 12.91/3.59 |-Branch one:
% 12.91/3.59 | (424) empty(all_0_14_14)
% 12.91/3.59 |
% 12.91/3.59 | Instantiating formula (43) with all_0_14_14, all_0_17_17 and discharging atoms powerset(all_0_17_17) = all_0_14_14, empty(all_0_14_14), yields:
% 12.91/3.59 | (397) $false
% 12.91/3.59 |
% 12.91/3.59 |-The branch is then unsatisfiable
% 12.91/3.59 |-Branch two:
% 12.91/3.59 | (426) ~ empty(all_0_14_14)
% 12.91/3.59 | (427) in(all_0_16_16, all_0_14_14)
% 12.91/3.59 |
% 12.91/3.59 +-Applying beta-rule and splitting (137), into two cases.
% 12.91/3.59 |-Branch one:
% 12.91/3.59 | (424) empty(all_0_14_14)
% 12.91/3.59 |
% 12.91/3.59 | Using (424) and (426) yields:
% 12.91/3.59 | (397) $false
% 12.91/3.59 |
% 12.91/3.59 |-The branch is then unsatisfiable
% 12.91/3.59 |-Branch two:
% 12.91/3.59 | (426) ~ empty(all_0_14_14)
% 12.91/3.59 | (431) in(all_0_13_13, all_0_14_14)
% 12.91/3.59 |
% 12.91/3.59 +-Applying beta-rule and splitting (422), into two cases.
% 12.91/3.59 |-Branch one:
% 12.91/3.59 | (424) empty(all_0_14_14)
% 12.91/3.59 |
% 12.91/3.59 | Using (424) and (426) yields:
% 12.91/3.59 | (397) $false
% 12.91/3.59 |
% 12.91/3.59 |-The branch is then unsatisfiable
% 12.91/3.59 |-Branch two:
% 12.91/3.59 | (426) ~ empty(all_0_14_14)
% 12.91/3.59 | (435) in(all_0_11_11, all_0_14_14)
% 12.91/3.59 |
% 12.91/3.59 +-Applying beta-rule and splitting (421), into two cases.
% 12.91/3.59 |-Branch one:
% 12.91/3.59 | (424) empty(all_0_14_14)
% 12.91/3.59 |
% 12.91/3.59 | Using (424) and (426) yields:
% 12.91/3.59 | (397) $false
% 12.91/3.59 |
% 12.91/3.59 |-The branch is then unsatisfiable
% 12.91/3.59 |-Branch two:
% 12.91/3.59 | (426) ~ empty(all_0_14_14)
% 12.91/3.59 | (439) in(all_0_9_9, all_0_14_14)
% 12.91/3.59 |
% 12.91/3.59 +-Applying beta-rule and splitting (157), into two cases.
% 12.91/3.59 |-Branch one:
% 12.91/3.59 | (440) empty_carrier(all_0_15_15)
% 12.91/3.59 |
% 12.91/3.59 | Instantiating formula (81) with all_0_15_15, all_0_17_17 and discharging atoms boole_lattice(all_0_17_17) = all_0_15_15, empty_carrier(all_0_15_15), yields:
% 12.91/3.59 | (397) $false
% 12.91/3.59 |
% 12.91/3.59 |-The branch is then unsatisfiable
% 12.91/3.59 |-Branch two:
% 12.91/3.59 | (442) ~ empty_carrier(all_0_15_15)
% 12.91/3.59 | (443) ? [v0] : (the_carrier(all_0_15_15) = v0 & ( ~ element(all_0_13_13, v0) | ~ element(all_0_16_16, v0) | element(all_0_10_10, v0)))
% 12.91/3.59 |
% 12.91/3.59 | Instantiating (443) with all_197_0_90 yields:
% 12.91/3.59 | (444) the_carrier(all_0_15_15) = all_197_0_90 & ( ~ element(all_0_13_13, all_197_0_90) | ~ element(all_0_16_16, all_197_0_90) | element(all_0_10_10, all_197_0_90))
% 12.91/3.59 |
% 12.91/3.59 | Applying alpha-rule on (444) yields:
% 12.91/3.59 | (445) the_carrier(all_0_15_15) = all_197_0_90
% 12.91/3.59 | (446) ~ element(all_0_13_13, all_197_0_90) | ~ element(all_0_16_16, all_197_0_90) | element(all_0_10_10, all_197_0_90)
% 12.91/3.59 |
% 12.91/3.59 +-Applying beta-rule and splitting (160), into two cases.
% 12.91/3.59 |-Branch one:
% 12.91/3.59 | (440) empty_carrier(all_0_15_15)
% 12.91/3.59 |
% 12.91/3.59 | Using (440) and (442) yields:
% 12.91/3.59 | (397) $false
% 12.91/3.59 |
% 12.91/3.59 |-The branch is then unsatisfiable
% 12.91/3.59 |-Branch two:
% 12.91/3.59 | (442) ~ empty_carrier(all_0_15_15)
% 12.91/3.59 | (450) ? [v0] : (the_carrier(all_0_15_15) = v0 & ! [v1] : ! [v2] : ! [v3] : ( ~ (meet(all_0_15_15, v1, v2) = v3) | ~ element(v2, v0) | ~ element(v1, v0) | apply_binary_as_element(v0, v0, v0, all_33_0_30, v1, v2) = v3) & ! [v1] : ! [v2] : ! [v3] : ( ~ (apply_binary_as_element(v0, v0, v0, all_33_0_30, v1, v2) = v3) | ~ element(v2, v0) | ~ element(v1, v0) | meet(all_0_15_15, v1, v2) = v3))
% 12.91/3.59 |
% 12.91/3.59 +-Applying beta-rule and splitting (158), into two cases.
% 12.91/3.59 |-Branch one:
% 12.91/3.59 | (440) empty_carrier(all_0_15_15)
% 12.91/3.59 |
% 12.91/3.59 | Using (440) and (442) yields:
% 12.91/3.59 | (397) $false
% 12.91/3.59 |
% 12.91/3.59 |-The branch is then unsatisfiable
% 12.91/3.59 |-Branch two:
% 12.91/3.59 | (442) ~ empty_carrier(all_0_15_15)
% 12.91/3.59 | (454) ? [v0] : (the_L_meet(all_0_15_15) = v0 & ! [v1] : ! [v2] : ! [v3] : ( ~ (meet(all_0_15_15, v1, v2) = v3) | ~ element(v2, all_0_14_14) | ~ element(v1, all_0_14_14) | apply_binary_as_element(all_0_14_14, all_0_14_14, all_0_14_14, v0, v1, v2) = v3) & ! [v1] : ! [v2] : ! [v3] : ( ~ (apply_binary_as_element(all_0_14_14, all_0_14_14, all_0_14_14, v0, v1, v2) = v3) | ~ element(v2, all_0_14_14) | ~ element(v1, all_0_14_14) | meet(all_0_15_15, v1, v2) = v3))
% 12.91/3.59 |
% 12.91/3.59 +-Applying beta-rule and splitting (165), into two cases.
% 12.91/3.59 |-Branch one:
% 12.91/3.59 | (440) empty_carrier(all_0_15_15)
% 12.91/3.59 |
% 12.91/3.59 | Using (440) and (442) yields:
% 12.91/3.59 | (397) $false
% 12.91/3.59 |
% 12.91/3.59 |-The branch is then unsatisfiable
% 12.91/3.59 |-Branch two:
% 12.91/3.59 | (442) ~ empty_carrier(all_0_15_15)
% 12.91/3.59 | (458) ? [v0] : (the_carrier(all_0_15_15) = v0 & ! [v1] : ! [v2] : ! [v3] : ( ~ (join(all_0_15_15, v1, v2) = v3) | ~ element(v2, v0) | ~ element(v1, v0) | apply_binary_as_element(v0, v0, v0, all_33_1_31, v1, v2) = v3) & ! [v1] : ! [v2] : ! [v3] : ( ~ (apply_binary_as_element(v0, v0, v0, all_33_1_31, v1, v2) = v3) | ~ element(v2, v0) | ~ element(v1, v0) | join(all_0_15_15, v1, v2) = v3))
% 12.91/3.59 |
% 12.91/3.59 +-Applying beta-rule and splitting (163), into two cases.
% 12.91/3.59 |-Branch one:
% 12.91/3.59 | (440) empty_carrier(all_0_15_15)
% 12.91/3.59 |
% 12.91/3.59 | Using (440) and (442) yields:
% 12.91/3.59 | (397) $false
% 12.91/3.59 |
% 12.91/3.59 |-The branch is then unsatisfiable
% 12.91/3.59 |-Branch two:
% 12.91/3.59 | (442) ~ empty_carrier(all_0_15_15)
% 12.91/3.59 | (462) ? [v0] : (the_L_join(all_0_15_15) = v0 & ! [v1] : ! [v2] : ! [v3] : ( ~ (join(all_0_15_15, v1, v2) = v3) | ~ element(v2, all_0_14_14) | ~ element(v1, all_0_14_14) | apply_binary_as_element(all_0_14_14, all_0_14_14, all_0_14_14, v0, v1, v2) = v3) & ! [v1] : ! [v2] : ! [v3] : ( ~ (apply_binary_as_element(all_0_14_14, all_0_14_14, all_0_14_14, v0, v1, v2) = v3) | ~ element(v2, all_0_14_14) | ~ element(v1, all_0_14_14) | join(all_0_15_15, v1, v2) = v3))
% 12.91/3.59 |
% 12.91/3.59 | Instantiating (450) with all_212_0_91 yields:
% 12.91/3.59 | (463) the_carrier(all_0_15_15) = all_212_0_91 & ! [v0] : ! [v1] : ! [v2] : ( ~ (meet(all_0_15_15, v0, v1) = v2) | ~ element(v1, all_212_0_91) | ~ element(v0, all_212_0_91) | apply_binary_as_element(all_212_0_91, all_212_0_91, all_212_0_91, all_33_0_30, v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (apply_binary_as_element(all_212_0_91, all_212_0_91, all_212_0_91, all_33_0_30, v0, v1) = v2) | ~ element(v1, all_212_0_91) | ~ element(v0, all_212_0_91) | meet(all_0_15_15, v0, v1) = v2)
% 12.91/3.59 |
% 12.91/3.59 | Applying alpha-rule on (463) yields:
% 12.91/3.59 | (464) the_carrier(all_0_15_15) = all_212_0_91
% 12.91/3.59 | (465) ! [v0] : ! [v1] : ! [v2] : ( ~ (meet(all_0_15_15, v0, v1) = v2) | ~ element(v1, all_212_0_91) | ~ element(v0, all_212_0_91) | apply_binary_as_element(all_212_0_91, all_212_0_91, all_212_0_91, all_33_0_30, v0, v1) = v2)
% 12.91/3.59 | (466) ! [v0] : ! [v1] : ! [v2] : ( ~ (apply_binary_as_element(all_212_0_91, all_212_0_91, all_212_0_91, all_33_0_30, v0, v1) = v2) | ~ element(v1, all_212_0_91) | ~ element(v0, all_212_0_91) | meet(all_0_15_15, v0, v1) = v2)
% 12.91/3.59 |
% 12.91/3.59 | Instantiating (454) with all_215_0_92 yields:
% 12.91/3.59 | (467) the_L_meet(all_0_15_15) = all_215_0_92 & ! [v0] : ! [v1] : ! [v2] : ( ~ (meet(all_0_15_15, v0, v1) = v2) | ~ element(v1, all_0_14_14) | ~ element(v0, all_0_14_14) | apply_binary_as_element(all_0_14_14, all_0_14_14, all_0_14_14, all_215_0_92, v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (apply_binary_as_element(all_0_14_14, all_0_14_14, all_0_14_14, all_215_0_92, v0, v1) = v2) | ~ element(v1, all_0_14_14) | ~ element(v0, all_0_14_14) | meet(all_0_15_15, v0, v1) = v2)
% 12.91/3.59 |
% 12.91/3.59 | Applying alpha-rule on (467) yields:
% 12.91/3.59 | (468) the_L_meet(all_0_15_15) = all_215_0_92
% 12.91/3.59 | (469) ! [v0] : ! [v1] : ! [v2] : ( ~ (meet(all_0_15_15, v0, v1) = v2) | ~ element(v1, all_0_14_14) | ~ element(v0, all_0_14_14) | apply_binary_as_element(all_0_14_14, all_0_14_14, all_0_14_14, all_215_0_92, v0, v1) = v2)
% 12.91/3.59 | (470) ! [v0] : ! [v1] : ! [v2] : ( ~ (apply_binary_as_element(all_0_14_14, all_0_14_14, all_0_14_14, all_215_0_92, v0, v1) = v2) | ~ element(v1, all_0_14_14) | ~ element(v0, all_0_14_14) | meet(all_0_15_15, v0, v1) = v2)
% 12.91/3.59 |
% 12.91/3.59 | Instantiating formula (469) with all_0_10_10, all_0_13_13, all_0_16_16 and discharging atoms meet(all_0_15_15, all_0_16_16, all_0_13_13) = all_0_10_10, element(all_0_13_13, all_0_14_14), element(all_0_16_16, all_0_14_14), yields:
% 12.91/3.59 | (471) apply_binary_as_element(all_0_14_14, all_0_14_14, all_0_14_14, all_215_0_92, all_0_16_16, all_0_13_13) = all_0_10_10
% 12.91/3.59 |
% 12.91/3.59 | Instantiating (458) with all_219_0_93 yields:
% 12.91/3.59 | (472) the_carrier(all_0_15_15) = all_219_0_93 & ! [v0] : ! [v1] : ! [v2] : ( ~ (join(all_0_15_15, v0, v1) = v2) | ~ element(v1, all_219_0_93) | ~ element(v0, all_219_0_93) | apply_binary_as_element(all_219_0_93, all_219_0_93, all_219_0_93, all_33_1_31, v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (apply_binary_as_element(all_219_0_93, all_219_0_93, all_219_0_93, all_33_1_31, v0, v1) = v2) | ~ element(v1, all_219_0_93) | ~ element(v0, all_219_0_93) | join(all_0_15_15, v0, v1) = v2)
% 12.91/3.59 |
% 12.91/3.59 | Applying alpha-rule on (472) yields:
% 12.91/3.59 | (473) the_carrier(all_0_15_15) = all_219_0_93
% 12.91/3.59 | (474) ! [v0] : ! [v1] : ! [v2] : ( ~ (join(all_0_15_15, v0, v1) = v2) | ~ element(v1, all_219_0_93) | ~ element(v0, all_219_0_93) | apply_binary_as_element(all_219_0_93, all_219_0_93, all_219_0_93, all_33_1_31, v0, v1) = v2)
% 12.91/3.59 | (475) ! [v0] : ! [v1] : ! [v2] : ( ~ (apply_binary_as_element(all_219_0_93, all_219_0_93, all_219_0_93, all_33_1_31, v0, v1) = v2) | ~ element(v1, all_219_0_93) | ~ element(v0, all_219_0_93) | join(all_0_15_15, v0, v1) = v2)
% 12.91/3.59 |
% 12.91/3.59 | Instantiating (462) with all_222_0_94 yields:
% 12.91/3.59 | (476) the_L_join(all_0_15_15) = all_222_0_94 & ! [v0] : ! [v1] : ! [v2] : ( ~ (join(all_0_15_15, v0, v1) = v2) | ~ element(v1, all_0_14_14) | ~ element(v0, all_0_14_14) | apply_binary_as_element(all_0_14_14, all_0_14_14, all_0_14_14, all_222_0_94, v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (apply_binary_as_element(all_0_14_14, all_0_14_14, all_0_14_14, all_222_0_94, v0, v1) = v2) | ~ element(v1, all_0_14_14) | ~ element(v0, all_0_14_14) | join(all_0_15_15, v0, v1) = v2)
% 12.91/3.59 |
% 12.91/3.59 | Applying alpha-rule on (476) yields:
% 12.91/3.59 | (477) the_L_join(all_0_15_15) = all_222_0_94
% 12.91/3.59 | (478) ! [v0] : ! [v1] : ! [v2] : ( ~ (join(all_0_15_15, v0, v1) = v2) | ~ element(v1, all_0_14_14) | ~ element(v0, all_0_14_14) | apply_binary_as_element(all_0_14_14, all_0_14_14, all_0_14_14, all_222_0_94, v0, v1) = v2)
% 12.91/3.59 | (479) ! [v0] : ! [v1] : ! [v2] : ( ~ (apply_binary_as_element(all_0_14_14, all_0_14_14, all_0_14_14, all_222_0_94, v0, v1) = v2) | ~ element(v1, all_0_14_14) | ~ element(v0, all_0_14_14) | join(all_0_15_15, v0, v1) = v2)
% 12.91/3.59 |
% 12.91/3.59 | Instantiating formula (478) with all_0_12_12, all_0_13_13, all_0_16_16 and discharging atoms join(all_0_15_15, all_0_16_16, all_0_13_13) = all_0_12_12, element(all_0_13_13, all_0_14_14), element(all_0_16_16, all_0_14_14), yields:
% 12.91/3.59 | (480) apply_binary_as_element(all_0_14_14, all_0_14_14, all_0_14_14, all_222_0_94, all_0_16_16, all_0_13_13) = all_0_12_12
% 12.91/3.59 |
% 12.91/3.59 +-Applying beta-rule and splitting (330), into two cases.
% 12.91/3.59 |-Branch one:
% 12.91/3.60 | (440) empty_carrier(all_0_15_15)
% 12.91/3.60 |
% 12.91/3.60 | Using (440) and (442) yields:
% 12.91/3.60 | (397) $false
% 12.91/3.60 |
% 12.91/3.60 |-The branch is then unsatisfiable
% 12.91/3.60 |-Branch two:
% 12.91/3.60 | (442) ~ empty_carrier(all_0_15_15)
% 12.91/3.60 | (484) ? [v0] : ? [v1] : (powerset(all_0_14_14) = v0 & element(v1, v0) & ~ empty(v1))
% 12.91/3.60 |
% 12.91/3.60 | Instantiating formula (62) with all_0_15_15, all_219_0_93, all_0_14_14 and discharging atoms the_carrier(all_0_15_15) = all_219_0_93, the_carrier(all_0_15_15) = all_0_14_14, yields:
% 12.91/3.60 | (485) all_219_0_93 = all_0_14_14
% 12.91/3.60 |
% 12.91/3.60 | Instantiating formula (62) with all_0_15_15, all_212_0_91, all_219_0_93 and discharging atoms the_carrier(all_0_15_15) = all_219_0_93, the_carrier(all_0_15_15) = all_212_0_91, yields:
% 12.91/3.60 | (486) all_219_0_93 = all_212_0_91
% 12.91/3.60 |
% 12.91/3.60 | Instantiating formula (62) with all_0_15_15, all_197_0_90, all_212_0_91 and discharging atoms the_carrier(all_0_15_15) = all_212_0_91, the_carrier(all_0_15_15) = all_197_0_90, yields:
% 12.91/3.60 | (487) all_212_0_91 = all_197_0_90
% 12.91/3.60 |
% 12.91/3.60 | Instantiating formula (36) with all_0_15_15, all_222_0_94, all_33_1_31 and discharging atoms the_L_join(all_0_15_15) = all_222_0_94, the_L_join(all_0_15_15) = all_33_1_31, yields:
% 12.91/3.60 | (488) all_222_0_94 = all_33_1_31
% 12.91/3.60 |
% 12.91/3.60 | Instantiating formula (73) with all_0_15_15, all_215_0_92, all_33_0_30 and discharging atoms the_L_meet(all_0_15_15) = all_215_0_92, the_L_meet(all_0_15_15) = all_33_0_30, yields:
% 12.91/3.60 | (489) all_215_0_92 = all_33_0_30
% 12.91/3.60 |
% 12.91/3.60 | Combining equations (486,485) yields a new equation:
% 12.91/3.60 | (490) all_212_0_91 = all_0_14_14
% 12.91/3.60 |
% 12.91/3.60 | Simplifying 490 yields:
% 12.91/3.60 | (491) all_212_0_91 = all_0_14_14
% 12.91/3.60 |
% 12.91/3.60 | Combining equations (491,487) yields a new equation:
% 12.91/3.60 | (492) all_197_0_90 = all_0_14_14
% 12.91/3.60 |
% 12.91/3.60 | From (488) and (480) follows:
% 12.91/3.60 | (493) apply_binary_as_element(all_0_14_14, all_0_14_14, all_0_14_14, all_33_1_31, all_0_16_16, all_0_13_13) = all_0_12_12
% 12.91/3.60 |
% 12.91/3.60 | From (489) and (471) follows:
% 12.91/3.60 | (494) apply_binary_as_element(all_0_14_14, all_0_14_14, all_0_14_14, all_33_0_30, all_0_16_16, all_0_13_13) = all_0_10_10
% 12.91/3.60 |
% 12.91/3.60 | From (492) and (445) follows:
% 12.91/3.60 | (5) the_carrier(all_0_15_15) = all_0_14_14
% 12.91/3.60 |
% 12.91/3.60 +-Applying beta-rule and splitting (162), into two cases.
% 12.91/3.60 |-Branch one:
% 12.91/3.60 | (440) empty_carrier(all_0_15_15)
% 12.91/3.60 |
% 12.91/3.60 | Using (440) and (442) yields:
% 12.91/3.60 | (397) $false
% 12.91/3.60 |
% 12.91/3.60 |-The branch is then unsatisfiable
% 12.91/3.60 |-Branch two:
% 12.91/3.60 | (442) ~ empty_carrier(all_0_15_15)
% 12.91/3.60 | (499) ? [v0] : (the_carrier(all_0_15_15) = v0 & ( ~ element(all_0_13_13, v0) | ~ element(all_0_16_16, v0) | element(all_0_12_12, v0)))
% 12.91/3.60 |
% 12.91/3.60 | Instantiating (499) with all_239_0_97 yields:
% 12.91/3.60 | (500) the_carrier(all_0_15_15) = all_239_0_97 & ( ~ element(all_0_13_13, all_239_0_97) | ~ element(all_0_16_16, all_239_0_97) | element(all_0_12_12, all_239_0_97))
% 12.91/3.60 |
% 12.91/3.60 | Applying alpha-rule on (500) yields:
% 12.91/3.60 | (501) the_carrier(all_0_15_15) = all_239_0_97
% 12.91/3.60 | (502) ~ element(all_0_13_13, all_239_0_97) | ~ element(all_0_16_16, all_239_0_97) | element(all_0_12_12, all_239_0_97)
% 12.91/3.60 |
% 12.91/3.60 +-Applying beta-rule and splitting (446), into two cases.
% 12.91/3.60 |-Branch one:
% 12.91/3.60 | (503) ~ element(all_0_13_13, all_197_0_90)
% 12.91/3.60 |
% 12.91/3.60 | From (492) and (503) follows:
% 12.91/3.60 | (396) ~ element(all_0_13_13, all_0_14_14)
% 12.91/3.60 |
% 12.91/3.60 | Using (101) and (396) yields:
% 12.91/3.60 | (397) $false
% 12.91/3.60 |
% 12.91/3.60 |-The branch is then unsatisfiable
% 12.91/3.60 |-Branch two:
% 12.91/3.60 | (506) element(all_0_13_13, all_197_0_90)
% 12.91/3.60 | (507) ~ element(all_0_16_16, all_197_0_90) | element(all_0_10_10, all_197_0_90)
% 12.91/3.60 |
% 12.91/3.60 | From (492) and (506) follows:
% 12.91/3.60 | (101) element(all_0_13_13, all_0_14_14)
% 12.91/3.60 |
% 12.91/3.60 +-Applying beta-rule and splitting (507), into two cases.
% 12.91/3.60 |-Branch one:
% 12.91/3.60 | (509) ~ element(all_0_16_16, all_197_0_90)
% 12.91/3.60 |
% 12.91/3.60 | From (492) and (509) follows:
% 12.91/3.60 | (402) ~ element(all_0_16_16, all_0_14_14)
% 12.91/3.60 |
% 12.91/3.60 | Using (2) and (402) yields:
% 12.91/3.60 | (397) $false
% 12.91/3.60 |
% 12.91/3.60 |-The branch is then unsatisfiable
% 12.91/3.60 |-Branch two:
% 12.91/3.60 | (512) element(all_0_16_16, all_197_0_90)
% 12.91/3.60 | (513) element(all_0_10_10, all_197_0_90)
% 12.91/3.60 |
% 12.91/3.60 | From (492) and (512) follows:
% 12.91/3.60 | (2) element(all_0_16_16, all_0_14_14)
% 12.91/3.60 |
% 12.91/3.60 | Instantiating formula (62) with all_0_15_15, all_239_0_97, all_0_14_14 and discharging atoms the_carrier(all_0_15_15) = all_239_0_97, the_carrier(all_0_15_15) = all_0_14_14, yields:
% 12.91/3.60 | (515) all_239_0_97 = all_0_14_14
% 12.91/3.60 |
% 12.91/3.60 +-Applying beta-rule and splitting (502), into two cases.
% 12.91/3.60 |-Branch one:
% 12.91/3.60 | (516) ~ element(all_0_13_13, all_239_0_97)
% 12.91/3.60 |
% 12.91/3.60 | From (515) and (516) follows:
% 12.91/3.60 | (396) ~ element(all_0_13_13, all_0_14_14)
% 12.91/3.60 |
% 12.91/3.60 | Using (101) and (396) yields:
% 12.91/3.60 | (397) $false
% 12.91/3.60 |
% 12.91/3.60 |-The branch is then unsatisfiable
% 12.91/3.60 |-Branch two:
% 12.91/3.60 | (519) element(all_0_13_13, all_239_0_97)
% 12.91/3.60 | (520) ~ element(all_0_16_16, all_239_0_97) | element(all_0_12_12, all_239_0_97)
% 12.91/3.60 |
% 12.91/3.60 | From (515) and (519) follows:
% 12.91/3.60 | (101) element(all_0_13_13, all_0_14_14)
% 12.91/3.60 |
% 12.91/3.60 +-Applying beta-rule and splitting (520), into two cases.
% 12.91/3.60 |-Branch one:
% 12.91/3.60 | (522) ~ element(all_0_16_16, all_239_0_97)
% 12.91/3.60 |
% 12.91/3.60 | From (515) and (522) follows:
% 12.91/3.60 | (402) ~ element(all_0_16_16, all_0_14_14)
% 12.91/3.60 |
% 12.91/3.60 | Using (2) and (402) yields:
% 12.91/3.60 | (397) $false
% 12.91/3.60 |
% 12.91/3.60 |-The branch is then unsatisfiable
% 12.91/3.60 |-Branch two:
% 12.91/3.60 | (525) element(all_0_16_16, all_239_0_97)
% 12.91/3.60 | (526) element(all_0_12_12, all_239_0_97)
% 12.91/3.60 |
% 12.91/3.60 | From (515) and (525) follows:
% 12.91/3.60 | (2) element(all_0_16_16, all_0_14_14)
% 12.91/3.60 |
% 12.91/3.60 | Instantiating formula (51) with all_0_10_10, all_0_13_13, all_0_16_16, all_33_0_30, all_0_14_14, all_0_14_14, all_0_14_14 and discharging atoms apply_binary_as_element(all_0_14_14, all_0_14_14, all_0_14_14, all_33_0_30, all_0_16_16, all_0_13_13) = all_0_10_10, function(all_33_0_30), element(all_0_13_13, all_0_14_14), element(all_0_16_16, all_0_14_14), ~ empty(all_0_14_14), yields:
% 12.91/3.60 | (528) ? [v0] : ? [v1] : (apply_binary(all_33_0_30, all_0_16_16, all_0_13_13) = v1 & cartesian_product2(all_0_14_14, all_0_14_14) = v0 & (v1 = all_0_10_10 | ~ relation_of2(all_33_0_30, v0, all_0_14_14) | ~ quasi_total(all_33_0_30, v0, all_0_14_14)))
% 12.91/3.60 |
% 12.91/3.60 | Instantiating formula (51) with all_0_12_12, all_0_13_13, all_0_16_16, all_33_1_31, all_0_14_14, all_0_14_14, all_0_14_14 and discharging atoms apply_binary_as_element(all_0_14_14, all_0_14_14, all_0_14_14, all_33_1_31, all_0_16_16, all_0_13_13) = all_0_12_12, function(all_33_1_31), element(all_0_13_13, all_0_14_14), element(all_0_16_16, all_0_14_14), ~ empty(all_0_14_14), yields:
% 12.91/3.60 | (529) ? [v0] : ? [v1] : (apply_binary(all_33_1_31, all_0_16_16, all_0_13_13) = v1 & cartesian_product2(all_0_14_14, all_0_14_14) = v0 & (v1 = all_0_12_12 | ~ relation_of2(all_33_1_31, v0, all_0_14_14) | ~ quasi_total(all_33_1_31, v0, all_0_14_14)))
% 12.91/3.60 |
% 12.91/3.60 | Instantiating (529) with all_285_0_118, all_285_1_119 yields:
% 12.91/3.60 | (530) apply_binary(all_33_1_31, all_0_16_16, all_0_13_13) = all_285_0_118 & cartesian_product2(all_0_14_14, all_0_14_14) = all_285_1_119 & (all_285_0_118 = all_0_12_12 | ~ relation_of2(all_33_1_31, all_285_1_119, all_0_14_14) | ~ quasi_total(all_33_1_31, all_285_1_119, all_0_14_14))
% 12.91/3.60 |
% 12.91/3.60 | Applying alpha-rule on (530) yields:
% 12.91/3.60 | (531) apply_binary(all_33_1_31, all_0_16_16, all_0_13_13) = all_285_0_118
% 12.91/3.60 | (532) cartesian_product2(all_0_14_14, all_0_14_14) = all_285_1_119
% 12.91/3.60 | (533) all_285_0_118 = all_0_12_12 | ~ relation_of2(all_33_1_31, all_285_1_119, all_0_14_14) | ~ quasi_total(all_33_1_31, all_285_1_119, all_0_14_14)
% 12.91/3.60 |
% 12.91/3.60 | Instantiating (528) with all_287_0_120, all_287_1_121 yields:
% 12.91/3.60 | (534) apply_binary(all_33_0_30, all_0_16_16, all_0_13_13) = all_287_0_120 & cartesian_product2(all_0_14_14, all_0_14_14) = all_287_1_121 & (all_287_0_120 = all_0_10_10 | ~ relation_of2(all_33_0_30, all_287_1_121, all_0_14_14) | ~ quasi_total(all_33_0_30, all_287_1_121, all_0_14_14))
% 12.91/3.60 |
% 12.91/3.60 | Applying alpha-rule on (534) yields:
% 12.91/3.60 | (535) apply_binary(all_33_0_30, all_0_16_16, all_0_13_13) = all_287_0_120
% 12.91/3.60 | (536) cartesian_product2(all_0_14_14, all_0_14_14) = all_287_1_121
% 12.91/3.60 | (537) all_287_0_120 = all_0_10_10 | ~ relation_of2(all_33_0_30, all_287_1_121, all_0_14_14) | ~ quasi_total(all_33_0_30, all_287_1_121, all_0_14_14)
% 12.91/3.60 |
% 12.91/3.60 | Instantiating formula (126) with all_33_0_30, all_0_16_16, all_0_13_13, all_287_0_120, all_0_9_9 and discharging atoms apply_binary(all_33_0_30, all_0_16_16, all_0_13_13) = all_287_0_120, apply_binary(all_33_0_30, all_0_16_16, all_0_13_13) = all_0_9_9, yields:
% 12.91/3.60 | (538) all_287_0_120 = all_0_9_9
% 12.91/3.60 |
% 12.91/3.60 | Instantiating formula (53) with all_0_14_14, all_0_14_14, all_287_1_121, all_42_0_32 and discharging atoms cartesian_product2(all_0_14_14, all_0_14_14) = all_287_1_121, cartesian_product2(all_0_14_14, all_0_14_14) = all_42_0_32, yields:
% 12.91/3.60 | (539) all_287_1_121 = all_42_0_32
% 12.91/3.60 |
% 12.91/3.60 | Instantiating formula (53) with all_0_14_14, all_0_14_14, all_285_1_119, all_287_1_121 and discharging atoms cartesian_product2(all_0_14_14, all_0_14_14) = all_287_1_121, cartesian_product2(all_0_14_14, all_0_14_14) = all_285_1_119, yields:
% 13.25/3.60 | (540) all_287_1_121 = all_285_1_119
% 13.25/3.60 |
% 13.25/3.60 | Combining equations (539,540) yields a new equation:
% 13.25/3.60 | (541) all_285_1_119 = all_42_0_32
% 13.25/3.60 |
% 13.25/3.60 | Combining equations (541,540) yields a new equation:
% 13.25/3.60 | (539) all_287_1_121 = all_42_0_32
% 13.25/3.60 |
% 13.25/3.60 +-Applying beta-rule and splitting (537), into two cases.
% 13.25/3.60 |-Branch one:
% 13.25/3.60 | (543) ~ relation_of2(all_33_0_30, all_287_1_121, all_0_14_14)
% 13.25/3.60 |
% 13.25/3.60 | From (539) and (543) follows:
% 13.25/3.60 | (544) ~ relation_of2(all_33_0_30, all_42_0_32, all_0_14_14)
% 13.25/3.60 |
% 13.25/3.60 | Using (328) and (544) yields:
% 13.25/3.60 | (397) $false
% 13.25/3.60 |
% 13.25/3.60 |-The branch is then unsatisfiable
% 13.25/3.60 |-Branch two:
% 13.25/3.60 | (546) relation_of2(all_33_0_30, all_287_1_121, all_0_14_14)
% 13.25/3.60 | (547) all_287_0_120 = all_0_10_10 | ~ quasi_total(all_33_0_30, all_287_1_121, all_0_14_14)
% 13.25/3.60 |
% 13.25/3.60 +-Applying beta-rule and splitting (547), into two cases.
% 13.25/3.60 |-Branch one:
% 13.25/3.60 | (548) ~ quasi_total(all_33_0_30, all_287_1_121, all_0_14_14)
% 13.25/3.60 |
% 13.25/3.60 | From (539) and (548) follows:
% 13.25/3.61 | (549) ~ quasi_total(all_33_0_30, all_42_0_32, all_0_14_14)
% 13.25/3.61 |
% 13.25/3.61 | Using (316) and (549) yields:
% 13.25/3.61 | (397) $false
% 13.25/3.61 |
% 13.25/3.61 |-The branch is then unsatisfiable
% 13.25/3.61 |-Branch two:
% 13.25/3.61 | (551) quasi_total(all_33_0_30, all_287_1_121, all_0_14_14)
% 13.25/3.61 | (552) all_287_0_120 = all_0_10_10
% 13.25/3.61 |
% 13.25/3.61 | Combining equations (552,538) yields a new equation:
% 13.25/3.61 | (553) all_0_9_9 = all_0_10_10
% 13.25/3.61 |
% 13.25/3.61 | Equations (553) can reduce 423 to:
% 13.25/3.61 | (284) $false
% 13.25/3.61 |
% 13.25/3.61 |-The branch is then unsatisfiable
% 13.25/3.61 |-Branch two:
% 13.25/3.61 | (553) all_0_9_9 = all_0_10_10
% 13.25/3.61 | (556) ~ (all_0_11_11 = all_0_12_12)
% 13.25/3.61 |
% 13.25/3.61 +-Applying beta-rule and splitting (138), into two cases.
% 13.25/3.61 |-Branch one:
% 13.25/3.61 | (424) empty(all_0_14_14)
% 13.25/3.61 |
% 13.25/3.61 | Instantiating formula (43) with all_0_14_14, all_0_17_17 and discharging atoms powerset(all_0_17_17) = all_0_14_14, empty(all_0_14_14), yields:
% 13.25/3.61 | (397) $false
% 13.25/3.61 |
% 13.25/3.61 |-The branch is then unsatisfiable
% 13.25/3.61 |-Branch two:
% 13.25/3.61 | (426) ~ empty(all_0_14_14)
% 13.25/3.61 | (427) in(all_0_16_16, all_0_14_14)
% 13.25/3.61 |
% 13.25/3.61 +-Applying beta-rule and splitting (137), into two cases.
% 13.25/3.61 |-Branch one:
% 13.25/3.61 | (424) empty(all_0_14_14)
% 13.25/3.61 |
% 13.25/3.61 | Using (424) and (426) yields:
% 13.25/3.61 | (397) $false
% 13.25/3.61 |
% 13.25/3.61 |-The branch is then unsatisfiable
% 13.25/3.61 |-Branch two:
% 13.25/3.61 | (426) ~ empty(all_0_14_14)
% 13.25/3.61 | (431) in(all_0_13_13, all_0_14_14)
% 13.25/3.61 |
% 13.25/3.61 +-Applying beta-rule and splitting (422), into two cases.
% 13.25/3.61 |-Branch one:
% 13.25/3.61 | (424) empty(all_0_14_14)
% 13.25/3.61 |
% 13.25/3.61 | Using (424) and (426) yields:
% 13.25/3.61 | (397) $false
% 13.25/3.61 |
% 13.25/3.61 |-The branch is then unsatisfiable
% 13.25/3.61 |-Branch two:
% 13.25/3.61 | (426) ~ empty(all_0_14_14)
% 13.25/3.61 | (435) in(all_0_11_11, all_0_14_14)
% 13.25/3.61 |
% 13.25/3.61 +-Applying beta-rule and splitting (421), into two cases.
% 13.25/3.61 |-Branch one:
% 13.25/3.61 | (424) empty(all_0_14_14)
% 13.25/3.61 |
% 13.25/3.61 | Using (424) and (426) yields:
% 13.25/3.61 | (397) $false
% 13.25/3.61 |
% 13.25/3.61 |-The branch is then unsatisfiable
% 13.25/3.61 |-Branch two:
% 13.25/3.61 | (426) ~ empty(all_0_14_14)
% 13.25/3.61 | (439) in(all_0_9_9, all_0_14_14)
% 13.25/3.61 |
% 13.25/3.61 +-Applying beta-rule and splitting (162), into two cases.
% 13.25/3.61 |-Branch one:
% 13.25/3.61 | (440) empty_carrier(all_0_15_15)
% 13.25/3.61 |
% 13.25/3.61 | Instantiating formula (81) with all_0_15_15, all_0_17_17 and discharging atoms boole_lattice(all_0_17_17) = all_0_15_15, empty_carrier(all_0_15_15), yields:
% 13.25/3.61 | (397) $false
% 13.25/3.61 |
% 13.25/3.61 |-The branch is then unsatisfiable
% 13.25/3.61 |-Branch two:
% 13.25/3.61 | (442) ~ empty_carrier(all_0_15_15)
% 13.25/3.61 | (499) ? [v0] : (the_carrier(all_0_15_15) = v0 & ( ~ element(all_0_13_13, v0) | ~ element(all_0_16_16, v0) | element(all_0_12_12, v0)))
% 13.25/3.61 |
% 13.25/3.61 | Instantiating (499) with all_197_0_131 yields:
% 13.25/3.61 | (577) the_carrier(all_0_15_15) = all_197_0_131 & ( ~ element(all_0_13_13, all_197_0_131) | ~ element(all_0_16_16, all_197_0_131) | element(all_0_12_12, all_197_0_131))
% 13.25/3.61 |
% 13.25/3.61 | Applying alpha-rule on (577) yields:
% 13.25/3.61 | (578) the_carrier(all_0_15_15) = all_197_0_131
% 13.25/3.61 | (579) ~ element(all_0_13_13, all_197_0_131) | ~ element(all_0_16_16, all_197_0_131) | element(all_0_12_12, all_197_0_131)
% 13.25/3.61 |
% 13.25/3.61 +-Applying beta-rule and splitting (163), into two cases.
% 13.25/3.61 |-Branch one:
% 13.25/3.61 | (440) empty_carrier(all_0_15_15)
% 13.25/3.61 |
% 13.25/3.61 | Using (440) and (442) yields:
% 13.25/3.61 | (397) $false
% 13.25/3.61 |
% 13.25/3.61 |-The branch is then unsatisfiable
% 13.25/3.61 |-Branch two:
% 13.25/3.61 | (442) ~ empty_carrier(all_0_15_15)
% 13.25/3.61 | (462) ? [v0] : (the_L_join(all_0_15_15) = v0 & ! [v1] : ! [v2] : ! [v3] : ( ~ (join(all_0_15_15, v1, v2) = v3) | ~ element(v2, all_0_14_14) | ~ element(v1, all_0_14_14) | apply_binary_as_element(all_0_14_14, all_0_14_14, all_0_14_14, v0, v1, v2) = v3) & ! [v1] : ! [v2] : ! [v3] : ( ~ (apply_binary_as_element(all_0_14_14, all_0_14_14, all_0_14_14, v0, v1, v2) = v3) | ~ element(v2, all_0_14_14) | ~ element(v1, all_0_14_14) | join(all_0_15_15, v1, v2) = v3))
% 13.25/3.61 |
% 13.25/3.61 +-Applying beta-rule and splitting (158), into two cases.
% 13.25/3.61 |-Branch one:
% 13.25/3.61 | (440) empty_carrier(all_0_15_15)
% 13.25/3.61 |
% 13.25/3.61 | Using (440) and (442) yields:
% 13.25/3.61 | (397) $false
% 13.25/3.61 |
% 13.25/3.61 |-The branch is then unsatisfiable
% 13.25/3.61 |-Branch two:
% 13.25/3.61 | (442) ~ empty_carrier(all_0_15_15)
% 13.25/3.61 | (454) ? [v0] : (the_L_meet(all_0_15_15) = v0 & ! [v1] : ! [v2] : ! [v3] : ( ~ (meet(all_0_15_15, v1, v2) = v3) | ~ element(v2, all_0_14_14) | ~ element(v1, all_0_14_14) | apply_binary_as_element(all_0_14_14, all_0_14_14, all_0_14_14, v0, v1, v2) = v3) & ! [v1] : ! [v2] : ! [v3] : ( ~ (apply_binary_as_element(all_0_14_14, all_0_14_14, all_0_14_14, v0, v1, v2) = v3) | ~ element(v2, all_0_14_14) | ~ element(v1, all_0_14_14) | meet(all_0_15_15, v1, v2) = v3))
% 13.25/3.61 |
% 13.25/3.61 +-Applying beta-rule and splitting (165), into two cases.
% 13.25/3.61 |-Branch one:
% 13.25/3.61 | (440) empty_carrier(all_0_15_15)
% 13.25/3.61 |
% 13.25/3.61 | Using (440) and (442) yields:
% 13.25/3.61 | (397) $false
% 13.25/3.61 |
% 13.25/3.61 |-The branch is then unsatisfiable
% 13.25/3.61 |-Branch two:
% 13.25/3.61 | (442) ~ empty_carrier(all_0_15_15)
% 13.25/3.61 | (458) ? [v0] : (the_carrier(all_0_15_15) = v0 & ! [v1] : ! [v2] : ! [v3] : ( ~ (join(all_0_15_15, v1, v2) = v3) | ~ element(v2, v0) | ~ element(v1, v0) | apply_binary_as_element(v0, v0, v0, all_33_1_31, v1, v2) = v3) & ! [v1] : ! [v2] : ! [v3] : ( ~ (apply_binary_as_element(v0, v0, v0, all_33_1_31, v1, v2) = v3) | ~ element(v2, v0) | ~ element(v1, v0) | join(all_0_15_15, v1, v2) = v3))
% 13.25/3.61 |
% 13.25/3.61 +-Applying beta-rule and splitting (160), into two cases.
% 13.25/3.61 |-Branch one:
% 13.25/3.61 | (440) empty_carrier(all_0_15_15)
% 13.25/3.61 |
% 13.25/3.61 | Using (440) and (442) yields:
% 13.25/3.61 | (397) $false
% 13.25/3.61 |
% 13.25/3.61 |-The branch is then unsatisfiable
% 13.25/3.61 |-Branch two:
% 13.25/3.61 | (442) ~ empty_carrier(all_0_15_15)
% 13.25/3.61 | (450) ? [v0] : (the_carrier(all_0_15_15) = v0 & ! [v1] : ! [v2] : ! [v3] : ( ~ (meet(all_0_15_15, v1, v2) = v3) | ~ element(v2, v0) | ~ element(v1, v0) | apply_binary_as_element(v0, v0, v0, all_33_0_30, v1, v2) = v3) & ! [v1] : ! [v2] : ! [v3] : ( ~ (apply_binary_as_element(v0, v0, v0, all_33_0_30, v1, v2) = v3) | ~ element(v2, v0) | ~ element(v1, v0) | meet(all_0_15_15, v1, v2) = v3))
% 13.25/3.61 |
% 13.25/3.61 | Instantiating (462) with all_212_0_132 yields:
% 13.25/3.61 | (596) the_L_join(all_0_15_15) = all_212_0_132 & ! [v0] : ! [v1] : ! [v2] : ( ~ (join(all_0_15_15, v0, v1) = v2) | ~ element(v1, all_0_14_14) | ~ element(v0, all_0_14_14) | apply_binary_as_element(all_0_14_14, all_0_14_14, all_0_14_14, all_212_0_132, v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (apply_binary_as_element(all_0_14_14, all_0_14_14, all_0_14_14, all_212_0_132, v0, v1) = v2) | ~ element(v1, all_0_14_14) | ~ element(v0, all_0_14_14) | join(all_0_15_15, v0, v1) = v2)
% 13.25/3.61 |
% 13.25/3.61 | Applying alpha-rule on (596) yields:
% 13.25/3.61 | (597) the_L_join(all_0_15_15) = all_212_0_132
% 13.25/3.61 | (598) ! [v0] : ! [v1] : ! [v2] : ( ~ (join(all_0_15_15, v0, v1) = v2) | ~ element(v1, all_0_14_14) | ~ element(v0, all_0_14_14) | apply_binary_as_element(all_0_14_14, all_0_14_14, all_0_14_14, all_212_0_132, v0, v1) = v2)
% 13.25/3.61 | (599) ! [v0] : ! [v1] : ! [v2] : ( ~ (apply_binary_as_element(all_0_14_14, all_0_14_14, all_0_14_14, all_212_0_132, v0, v1) = v2) | ~ element(v1, all_0_14_14) | ~ element(v0, all_0_14_14) | join(all_0_15_15, v0, v1) = v2)
% 13.25/3.61 |
% 13.25/3.61 | Instantiating formula (598) with all_0_12_12, all_0_13_13, all_0_16_16 and discharging atoms join(all_0_15_15, all_0_16_16, all_0_13_13) = all_0_12_12, element(all_0_13_13, all_0_14_14), element(all_0_16_16, all_0_14_14), yields:
% 13.25/3.61 | (600) apply_binary_as_element(all_0_14_14, all_0_14_14, all_0_14_14, all_212_0_132, all_0_16_16, all_0_13_13) = all_0_12_12
% 13.25/3.61 |
% 13.25/3.61 | Instantiating (458) with all_220_0_134 yields:
% 13.25/3.61 | (601) the_carrier(all_0_15_15) = all_220_0_134 & ! [v0] : ! [v1] : ! [v2] : ( ~ (join(all_0_15_15, v0, v1) = v2) | ~ element(v1, all_220_0_134) | ~ element(v0, all_220_0_134) | apply_binary_as_element(all_220_0_134, all_220_0_134, all_220_0_134, all_33_1_31, v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (apply_binary_as_element(all_220_0_134, all_220_0_134, all_220_0_134, all_33_1_31, v0, v1) = v2) | ~ element(v1, all_220_0_134) | ~ element(v0, all_220_0_134) | join(all_0_15_15, v0, v1) = v2)
% 13.25/3.61 |
% 13.25/3.61 | Applying alpha-rule on (601) yields:
% 13.25/3.61 | (602) the_carrier(all_0_15_15) = all_220_0_134
% 13.25/3.61 | (603) ! [v0] : ! [v1] : ! [v2] : ( ~ (join(all_0_15_15, v0, v1) = v2) | ~ element(v1, all_220_0_134) | ~ element(v0, all_220_0_134) | apply_binary_as_element(all_220_0_134, all_220_0_134, all_220_0_134, all_33_1_31, v0, v1) = v2)
% 13.25/3.61 | (604) ! [v0] : ! [v1] : ! [v2] : ( ~ (apply_binary_as_element(all_220_0_134, all_220_0_134, all_220_0_134, all_33_1_31, v0, v1) = v2) | ~ element(v1, all_220_0_134) | ~ element(v0, all_220_0_134) | join(all_0_15_15, v0, v1) = v2)
% 13.25/3.61 |
% 13.25/3.61 | Instantiating (450) with all_223_0_135 yields:
% 13.25/3.61 | (605) the_carrier(all_0_15_15) = all_223_0_135 & ! [v0] : ! [v1] : ! [v2] : ( ~ (meet(all_0_15_15, v0, v1) = v2) | ~ element(v1, all_223_0_135) | ~ element(v0, all_223_0_135) | apply_binary_as_element(all_223_0_135, all_223_0_135, all_223_0_135, all_33_0_30, v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (apply_binary_as_element(all_223_0_135, all_223_0_135, all_223_0_135, all_33_0_30, v0, v1) = v2) | ~ element(v1, all_223_0_135) | ~ element(v0, all_223_0_135) | meet(all_0_15_15, v0, v1) = v2)
% 13.25/3.61 |
% 13.25/3.61 | Applying alpha-rule on (605) yields:
% 13.25/3.61 | (606) the_carrier(all_0_15_15) = all_223_0_135
% 13.25/3.61 | (607) ! [v0] : ! [v1] : ! [v2] : ( ~ (meet(all_0_15_15, v0, v1) = v2) | ~ element(v1, all_223_0_135) | ~ element(v0, all_223_0_135) | apply_binary_as_element(all_223_0_135, all_223_0_135, all_223_0_135, all_33_0_30, v0, v1) = v2)
% 13.25/3.61 | (608) ! [v0] : ! [v1] : ! [v2] : ( ~ (apply_binary_as_element(all_223_0_135, all_223_0_135, all_223_0_135, all_33_0_30, v0, v1) = v2) | ~ element(v1, all_223_0_135) | ~ element(v0, all_223_0_135) | meet(all_0_15_15, v0, v1) = v2)
% 13.25/3.62 |
% 13.25/3.62 | Instantiating formula (62) with all_0_15_15, all_223_0_135, all_0_14_14 and discharging atoms the_carrier(all_0_15_15) = all_223_0_135, the_carrier(all_0_15_15) = all_0_14_14, yields:
% 13.25/3.62 | (609) all_223_0_135 = all_0_14_14
% 13.25/3.62 |
% 13.25/3.62 | Instantiating formula (62) with all_0_15_15, all_220_0_134, all_223_0_135 and discharging atoms the_carrier(all_0_15_15) = all_223_0_135, the_carrier(all_0_15_15) = all_220_0_134, yields:
% 13.25/3.62 | (610) all_223_0_135 = all_220_0_134
% 13.25/3.62 |
% 13.25/3.62 | Instantiating formula (62) with all_0_15_15, all_197_0_131, all_220_0_134 and discharging atoms the_carrier(all_0_15_15) = all_220_0_134, the_carrier(all_0_15_15) = all_197_0_131, yields:
% 13.25/3.62 | (611) all_220_0_134 = all_197_0_131
% 13.25/3.62 |
% 13.25/3.62 | Instantiating formula (36) with all_0_15_15, all_212_0_132, all_33_1_31 and discharging atoms the_L_join(all_0_15_15) = all_212_0_132, the_L_join(all_0_15_15) = all_33_1_31, yields:
% 13.25/3.62 | (612) all_212_0_132 = all_33_1_31
% 13.25/3.62 |
% 13.25/3.62 | Combining equations (610,609) yields a new equation:
% 13.25/3.62 | (613) all_220_0_134 = all_0_14_14
% 13.25/3.62 |
% 13.25/3.62 | Simplifying 613 yields:
% 13.25/3.62 | (614) all_220_0_134 = all_0_14_14
% 13.25/3.62 |
% 13.25/3.62 | Combining equations (614,611) yields a new equation:
% 13.25/3.62 | (615) all_197_0_131 = all_0_14_14
% 13.25/3.62 |
% 13.25/3.62 | From (612) and (600) follows:
% 13.25/3.62 | (493) apply_binary_as_element(all_0_14_14, all_0_14_14, all_0_14_14, all_33_1_31, all_0_16_16, all_0_13_13) = all_0_12_12
% 13.25/3.62 |
% 13.25/3.62 +-Applying beta-rule and splitting (579), into two cases.
% 13.25/3.62 |-Branch one:
% 13.25/3.62 | (617) ~ element(all_0_13_13, all_197_0_131)
% 13.25/3.62 |
% 13.25/3.62 | From (615) and (617) follows:
% 13.25/3.62 | (396) ~ element(all_0_13_13, all_0_14_14)
% 13.25/3.62 |
% 13.25/3.62 | Using (101) and (396) yields:
% 13.25/3.62 | (397) $false
% 13.25/3.62 |
% 13.25/3.62 |-The branch is then unsatisfiable
% 13.25/3.62 |-Branch two:
% 13.25/3.62 | (620) element(all_0_13_13, all_197_0_131)
% 13.25/3.62 | (621) ~ element(all_0_16_16, all_197_0_131) | element(all_0_12_12, all_197_0_131)
% 13.25/3.62 |
% 13.25/3.62 | From (615) and (620) follows:
% 13.25/3.62 | (101) element(all_0_13_13, all_0_14_14)
% 13.25/3.62 |
% 13.25/3.62 +-Applying beta-rule and splitting (621), into two cases.
% 13.25/3.62 |-Branch one:
% 13.25/3.62 | (623) ~ element(all_0_16_16, all_197_0_131)
% 13.25/3.62 |
% 13.25/3.62 | From (615) and (623) follows:
% 13.25/3.62 | (402) ~ element(all_0_16_16, all_0_14_14)
% 13.25/3.62 |
% 13.25/3.62 | Using (2) and (402) yields:
% 13.25/3.62 | (397) $false
% 13.25/3.62 |
% 13.25/3.62 |-The branch is then unsatisfiable
% 13.25/3.62 |-Branch two:
% 13.25/3.62 | (626) element(all_0_16_16, all_197_0_131)
% 13.25/3.62 | (627) element(all_0_12_12, all_197_0_131)
% 13.25/3.62 |
% 13.25/3.62 | From (615) and (626) follows:
% 13.25/3.62 | (2) element(all_0_16_16, all_0_14_14)
% 13.25/3.62 |
% 13.25/3.62 | Instantiating formula (51) with all_0_12_12, all_0_13_13, all_0_16_16, all_33_1_31, all_0_14_14, all_0_14_14, all_0_14_14 and discharging atoms apply_binary_as_element(all_0_14_14, all_0_14_14, all_0_14_14, all_33_1_31, all_0_16_16, all_0_13_13) = all_0_12_12, function(all_33_1_31), element(all_0_13_13, all_0_14_14), element(all_0_16_16, all_0_14_14), ~ empty(all_0_14_14), yields:
% 13.25/3.62 | (529) ? [v0] : ? [v1] : (apply_binary(all_33_1_31, all_0_16_16, all_0_13_13) = v1 & cartesian_product2(all_0_14_14, all_0_14_14) = v0 & (v1 = all_0_12_12 | ~ relation_of2(all_33_1_31, v0, all_0_14_14) | ~ quasi_total(all_33_1_31, v0, all_0_14_14)))
% 13.25/3.62 |
% 13.25/3.62 | Instantiating (529) with all_263_0_148, all_263_1_149 yields:
% 13.25/3.62 | (630) apply_binary(all_33_1_31, all_0_16_16, all_0_13_13) = all_263_0_148 & cartesian_product2(all_0_14_14, all_0_14_14) = all_263_1_149 & (all_263_0_148 = all_0_12_12 | ~ relation_of2(all_33_1_31, all_263_1_149, all_0_14_14) | ~ quasi_total(all_33_1_31, all_263_1_149, all_0_14_14))
% 13.25/3.62 |
% 13.25/3.62 | Applying alpha-rule on (630) yields:
% 13.25/3.62 | (631) apply_binary(all_33_1_31, all_0_16_16, all_0_13_13) = all_263_0_148
% 13.25/3.62 | (632) cartesian_product2(all_0_14_14, all_0_14_14) = all_263_1_149
% 13.25/3.62 | (633) all_263_0_148 = all_0_12_12 | ~ relation_of2(all_33_1_31, all_263_1_149, all_0_14_14) | ~ quasi_total(all_33_1_31, all_263_1_149, all_0_14_14)
% 13.25/3.62 |
% 13.25/3.62 | Instantiating formula (126) with all_33_1_31, all_0_16_16, all_0_13_13, all_263_0_148, all_0_11_11 and discharging atoms apply_binary(all_33_1_31, all_0_16_16, all_0_13_13) = all_263_0_148, apply_binary(all_33_1_31, all_0_16_16, all_0_13_13) = all_0_11_11, yields:
% 13.25/3.62 | (634) all_263_0_148 = all_0_11_11
% 13.25/3.62 |
% 13.25/3.62 | Instantiating formula (53) with all_0_14_14, all_0_14_14, all_263_1_149, all_42_0_32 and discharging atoms cartesian_product2(all_0_14_14, all_0_14_14) = all_263_1_149, cartesian_product2(all_0_14_14, all_0_14_14) = all_42_0_32, yields:
% 13.25/3.62 | (635) all_263_1_149 = all_42_0_32
% 13.25/3.62 |
% 13.25/3.62 +-Applying beta-rule and splitting (633), into two cases.
% 13.25/3.62 |-Branch one:
% 13.25/3.62 | (636) ~ relation_of2(all_33_1_31, all_263_1_149, all_0_14_14)
% 13.25/3.62 |
% 13.25/3.62 | From (635) and (636) follows:
% 13.25/3.62 | (637) ~ relation_of2(all_33_1_31, all_42_0_32, all_0_14_14)
% 13.25/3.62 |
% 13.25/3.62 | Using (329) and (637) yields:
% 13.25/3.62 | (397) $false
% 13.25/3.62 |
% 13.25/3.62 |-The branch is then unsatisfiable
% 13.25/3.62 |-Branch two:
% 13.25/3.62 | (639) relation_of2(all_33_1_31, all_263_1_149, all_0_14_14)
% 13.25/3.62 | (640) all_263_0_148 = all_0_12_12 | ~ quasi_total(all_33_1_31, all_263_1_149, all_0_14_14)
% 13.25/3.62 |
% 13.25/3.62 +-Applying beta-rule and splitting (640), into two cases.
% 13.25/3.62 |-Branch one:
% 13.25/3.62 | (641) ~ quasi_total(all_33_1_31, all_263_1_149, all_0_14_14)
% 13.25/3.62 |
% 13.25/3.62 | From (635) and (641) follows:
% 13.25/3.62 | (642) ~ quasi_total(all_33_1_31, all_42_0_32, all_0_14_14)
% 13.25/3.62 |
% 13.25/3.62 | Using (317) and (642) yields:
% 13.25/3.62 | (397) $false
% 13.25/3.62 |
% 13.25/3.62 |-The branch is then unsatisfiable
% 13.25/3.62 |-Branch two:
% 13.25/3.62 | (644) quasi_total(all_33_1_31, all_263_1_149, all_0_14_14)
% 13.25/3.62 | (645) all_263_0_148 = all_0_12_12
% 13.25/3.62 |
% 13.25/3.62 | Combining equations (634,645) yields a new equation:
% 13.25/3.62 | (646) all_0_11_11 = all_0_12_12
% 13.25/3.62 |
% 13.25/3.62 | Simplifying 646 yields:
% 13.25/3.62 | (647) all_0_11_11 = all_0_12_12
% 13.25/3.62 |
% 13.25/3.62 | Equations (647) can reduce 556 to:
% 13.25/3.62 | (284) $false
% 13.25/3.62 |
% 13.25/3.62 |-The branch is then unsatisfiable
% 13.25/3.62 % SZS output end Proof for theBenchmark
% 13.25/3.62
% 13.25/3.62 3015ms
%------------------------------------------------------------------------------