TSTP Solution File: SEU305+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU305+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 08:48:41 EDT 2022
% Result : Theorem 5.45s 1.98s
% Output : Proof 9.00s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.14 % Problem : SEU305+1 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.14 % Command : ePrincess-casc -timeout=%d %s
% 0.15/0.36 % Computer : n029.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Sat Jun 18 19:19:14 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.57/0.61 ____ _
% 0.57/0.61 ___ / __ \_____(_)___ ________ __________
% 0.57/0.61 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.57/0.61 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.57/0.61 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.57/0.61
% 0.57/0.61 A Theorem Prover for First-Order Logic
% 0.57/0.61 (ePrincess v.1.0)
% 0.57/0.61
% 0.57/0.61 (c) Philipp Rümmer, 2009-2015
% 0.57/0.61 (c) Peter Backeman, 2014-2015
% 0.57/0.61 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.57/0.61 Free software under GNU Lesser General Public License (LGPL).
% 0.57/0.61 Bug reports to peter@backeman.se
% 0.57/0.61
% 0.57/0.61 For more information, visit http://user.uu.se/~petba168/breu/
% 0.57/0.61
% 0.57/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.72/0.66 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.74/1.01 Prover 0: Preprocessing ...
% 2.57/1.31 Prover 0: Warning: ignoring some quantifiers
% 2.89/1.33 Prover 0: Constructing countermodel ...
% 4.51/1.74 Prover 0: gave up
% 4.51/1.74 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 4.83/1.78 Prover 1: Preprocessing ...
% 5.45/1.91 Prover 1: Warning: ignoring some quantifiers
% 5.45/1.92 Prover 1: Constructing countermodel ...
% 5.45/1.98 Prover 1: proved (242ms)
% 5.45/1.98
% 5.45/1.98 No countermodel exists, formula is valid
% 5.45/1.98 % SZS status Theorem for theBenchmark
% 5.45/1.98
% 5.45/1.98 Generating proof ... Warning: ignoring some quantifiers
% 8.13/2.60 found it (size 219)
% 8.13/2.60
% 8.13/2.60 % SZS output start Proof for theBenchmark
% 8.13/2.60 Assumed formulas after preprocessing and simplification:
% 8.13/2.60 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ( ~ (v6 = 0) & ~ (v4 = v3) & ~ (v1 = 0) & one_sorted_str(v8) = 0 & one_sorted_str(v5) = 0 & below(v0, v4, v3) = 0 & below(v0, v3, v4) = 0 & the_carrier(v0) = v2 & element(v4, v2) = 0 & element(v3, v2) = 0 & empty_carrier(v5) = v6 & empty_carrier(v0) = v1 & join_commutative(v0) = 0 & join_semilatt_str(v7) = 0 & join_semilatt_str(v0) = 0 & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v10 = v9 | ~ (apply_binary_as_element(v16, v15, v14, v13, v12, v11) = v10) | ~ (apply_binary_as_element(v16, v15, v14, v13, v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (apply_binary(v12, v13, v14) = v16) | ~ (cartesian_product2(v9, v10) = v15) | ~ (quasi_total(v12, v15, v11) = 0) | ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : (empty(v10) = v18 & empty(v9) = v17 & function(v12) = v19 & relation_of2(v12, v15, v11) = v20 & apply_binary_as_element(v9, v10, v11, v12, v13, v14) = v23 & element(v14, v10) = v22 & element(v13, v9) = v21 & ( ~ (v22 = 0) | ~ (v21 = 0) | ~ (v20 = 0) | ~ (v19 = 0) | v23 = v16 | v18 = 0 | v17 = 0))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (cartesian_product2(v9, v10) = v15) | ~ (quasi_total(v12, v15, v11) = 0) | ~ (element(v14, v10) = 0) | ~ (element(v13, v9) = 0) | ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : (empty(v10) = v17 & empty(v9) = v16 & function(v12) = v18 & relation_of2(v12, v15, v11) = v19 & apply_binary_as_element(v9, v10, v11, v12, v13, v14) = v20 & element(v20, v11) = v21 & ( ~ (v19 = 0) | ~ (v18 = 0) | v21 = 0 | v17 = 0 | v16 = 0))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (powerset(v12) = v13) | ~ (cartesian_product2(v9, v10) = v12) | ~ (element(v11, v13) = v14) | ? [v15] : ( ~ (v15 = 0) & relation_of2_as_subset(v11, v9, v10) = v15)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (join(v9, v10, v11) = v13) | ~ (the_carrier(v9) = v12) | ~ (element(v13, v12) = v14) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : (element(v11, v12) = v18 & element(v10, v12) = v17 & empty_carrier(v9) = v15 & join_semilatt_str(v9) = v16 & ( ~ (v18 = 0) | ~ (v17 = 0) | ~ (v16 = 0) | v15 = 0))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (the_carrier(v9) = v12) | ~ (element(v13, v12) = v14) | ~ (join_commut(v9, v10, v11) = v13) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : (element(v11, v12) = v19 & element(v10, v12) = v18 & empty_carrier(v9) = v15 & join_commutative(v9) = v16 & join_semilatt_str(v9) = v17 & ( ~ (v19 = 0) | ~ (v18 = 0) | ~ (v17 = 0) | ~ (v16 = 0) | v15 = 0))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v10 = v9 | ~ (apply_binary(v13, v12, v11) = v10) | ~ (apply_binary(v13, v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v10 = v9 | ~ (relation_of2_as_subset(v13, v12, v11) = v10) | ~ (relation_of2_as_subset(v13, v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v10 = v9 | ~ (quasi_total(v13, v12, v11) = v10) | ~ (quasi_total(v13, v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v10 = v9 | ~ (relation_of2(v13, v12, v11) = v10) | ~ (relation_of2(v13, v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v10 = v9 | ~ (below(v13, v12, v11) = v10) | ~ (below(v13, v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v10 = v9 | ~ (join(v13, v12, v11) = v10) | ~ (join(v13, v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v10 = v9 | ~ (join_commut(v13, v12, v11) = v10) | ~ (join_commut(v13, v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (cartesian_product2(v11, v11) = v12) | ~ (quasi_total(v10, v12, v11) = v13) | ~ (the_L_join(v9) = v10) | ~ (the_carrier(v9) = v11) | ? [v14] : ? [v15] : ? [v16] : (relation_of2_as_subset(v10, v12, v11) = v16 & function(v10) = v15 & join_semilatt_str(v9) = v14 & ( ~ (v14 = 0) | (v16 = 0 & v15 = 0 & v13 = 0)))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (powerset(v10) = v11) | ~ (element(v9, v11) = v12) | ? [v13] : ( ~ (v13 = 0) & subset(v9, v10) = v13)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (relation_of2_as_subset(v11, v9, v10) = v12) | ? [v13] : ( ~ (v13 = 0) & relation_of2(v11, v9, v10) = v13)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (subset(v12, v11) = v10) | ~ (subset(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (cartesian_product2(v12, v11) = v10) | ~ (cartesian_product2(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (element(v12, v11) = v10) | ~ (element(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (in(v12, v11) = v10) | ~ (in(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (powerset(v11) = v12) | ~ (element(v10, v12) = 0) | ~ (in(v9, v10) = 0) | element(v9, v11) = 0) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (powerset(v11) = v12) | ~ (element(v10, v12) = 0) | ~ (in(v9, v10) = 0) | ? [v13] : ( ~ (v13 = 0) & empty(v11) = v13)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (the_carrier(v9) = v12) | ~ (element(v11, v12) = 0) | ~ (element(v10, v12) = 0) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : (join(v9, v10, v11) = v17 & empty_carrier(v9) = v13 & join_commutative(v9) = v14 & join_semilatt_str(v9) = v15 & join_commut(v9, v10, v11) = v16 & ( ~ (v15 = 0) | ~ (v14 = 0) | v17 = v16 | v13 = 0))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (the_carrier(v9) = v12) | ~ (element(v11, v12) = 0) | ~ (element(v10, v12) = 0) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : (empty_carrier(v9) = v13 & join_commutative(v9) = v14 & join_semilatt_str(v9) = v15 & join_commut(v9, v11, v10) = v17 & join_commut(v9, v10, v11) = v16 & ( ~ (v15 = 0) | ~ (v14 = 0) | v17 = v16 | v13 = 0))) & ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (in(v9, v10) = v11) | ? [v12] : ? [v13] : (empty(v10) = v13 & element(v9, v10) = v12 & ( ~ (v12 = 0) | v13 = 0))) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (powerset(v11) = v10) | ~ (powerset(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (one_sorted_str(v11) = v10) | ~ (one_sorted_str(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (empty(v11) = v10) | ~ (empty(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (function(v11) = v10) | ~ (function(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (the_L_join(v11) = v10) | ~ (the_L_join(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (the_carrier(v11) = v10) | ~ (the_carrier(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (empty_carrier(v11) = v10) | ~ (empty_carrier(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (join_commutative(v11) = v10) | ~ (join_commutative(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (join_semilatt_str(v11) = v10) | ~ (join_semilatt_str(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (preboolean(v11) = v10) | ~ (preboolean(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (cup_closed(v11) = v10) | ~ (cup_closed(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (diff_closed(v11) = v10) | ~ (diff_closed(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (powerset(v10) = v11) | ~ (element(v9, v11) = 0) | subset(v9, v10) = 0) & ! [v9] : ! [v10] : ! [v11] : ( ~ (relation_of2_as_subset(v11, v9, v10) = 0) | relation_of2(v11, v9, v10) = 0) & ! [v9] : ! [v10] : (v10 = v9 | ~ (empty(v10) = 0) | ~ (empty(v9) = 0)) & ! [v9] : ! [v10] : (v10 = 0 | ~ (subset(v9, v9) = v10)) & ! [v9] : ! [v10] : (v10 = 0 | ~ (one_sorted_str(v9) = v10) | ? [v11] : ( ~ (v11 = 0) & join_semilatt_str(v9) = v11)) & ! [v9] : ! [v10] : (v10 = 0 | ~ (preboolean(v9) = v10) | ? [v11] : ? [v12] : (cup_closed(v9) = v11 & diff_closed(v9) = v12 & ( ~ (v12 = 0) | ~ (v11 = 0)))) & ! [v9] : ! [v10] : ( ~ (powerset(v9) = v10) | preboolean(v10) = 0) & ! [v9] : ! [v10] : ( ~ (powerset(v9) = v10) | cup_closed(v10) = 0) & ! [v9] : ! [v10] : ( ~ (powerset(v9) = v10) | diff_closed(v10) = 0) & ! [v9] : ! [v10] : ( ~ (powerset(v9) = v10) | ? [v11] : ( ~ (v11 = 0) & empty(v10) = v11)) & ! [v9] : ! [v10] : ( ~ (the_L_join(v9) = v10) | ? [v11] : ? [v12] : ? [v13] : (the_carrier(v9) = v13 & empty_carrier(v9) = v11 & join_semilatt_str(v9) = v12 & ( ~ (v12 = 0) | v11 = 0 | ! [v14] : ! [v15] : ! [v16] : ( ~ (apply_binary_as_element(v13, v13, v13, v10, v14, v15) = v16) | ~ (element(v14, v13) = 0) | ? [v17] : ? [v18] : (join(v9, v14, v15) = v18 & element(v15, v13) = v17 & ( ~ (v17 = 0) | v18 = v16)))))) & ! [v9] : ! [v10] : ( ~ (in(v9, v10) = 0) | element(v9, v10) = 0) & ! [v9] : ! [v10] : ( ~ (in(v9, v10) = 0) | ? [v11] : ( ~ (v11 = 0) & empty(v10) = v11)) & ! [v9] : ! [v10] : ( ~ (in(v9, v10) = 0) | ? [v11] : ( ~ (v11 = 0) & in(v10, v9) = v11)) & ! [v9] : (v9 = empty_set | ~ (empty(v9) = 0)) & ! [v9] : ( ~ (one_sorted_str(v9) = 0) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : (powerset(v11) = v12 & the_carrier(v9) = v11 & empty_carrier(v9) = v10 & (v10 = 0 | (v14 = 0 & ~ (v15 = 0) & empty(v13) = v15 & element(v13, v12) = 0)))) & ! [v9] : ( ~ (one_sorted_str(v9) = 0) | ? [v10] : ? [v11] : ? [v12] : (empty(v11) = v12 & the_carrier(v9) = v11 & empty_carrier(v9) = v10 & ( ~ (v12 = 0) | v10 = 0))) & ! [v9] : ( ~ (join_semilatt_str(v9) = 0) | ? [v10] : ? [v11] : (the_carrier(v9) = v11 & empty_carrier(v9) = v10 & (v10 = 0 | ! [v12] : ! [v13] : ( ~ (element(v13, v11) = 0) | ~ (element(v12, v11) = 0) | ? [v14] : ? [v15] : (below(v9, v12, v13) = v14 & join(v9, v12, v13) = v15 & ( ~ (v15 = v13) | v14 = 0) & ( ~ (v14 = 0) | v15 = v13)))))) & ! [v9] : ( ~ (preboolean(v9) = 0) | (cup_closed(v9) = 0 & diff_closed(v9) = 0)) & ? [v9] : ? [v10] : ? [v11] : relation_of2_as_subset(v11, v9, v10) = 0 & ? [v9] : ? [v10] : ? [v11] : relation_of2(v11, v9, v10) = 0 & ? [v9] : ? [v10] : element(v10, v9) = 0)
% 8.56/2.64 | 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 yields:
% 8.56/2.64 | (1) ~ (all_0_2_2 = 0) & ~ (all_0_4_4 = all_0_5_5) & ~ (all_0_7_7 = 0) & one_sorted_str(all_0_0_0) = 0 & one_sorted_str(all_0_3_3) = 0 & below(all_0_8_8, all_0_4_4, all_0_5_5) = 0 & below(all_0_8_8, all_0_5_5, all_0_4_4) = 0 & the_carrier(all_0_8_8) = all_0_6_6 & element(all_0_4_4, all_0_6_6) = 0 & element(all_0_5_5, all_0_6_6) = 0 & empty_carrier(all_0_3_3) = all_0_2_2 & empty_carrier(all_0_8_8) = all_0_7_7 & join_commutative(all_0_8_8) = 0 & join_semilatt_str(all_0_1_1) = 0 & join_semilatt_str(all_0_8_8) = 0 & ! [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] : ! [v7] : ( ~ (apply_binary(v3, v4, v5) = v7) | ~ (cartesian_product2(v0, v1) = v6) | ~ (quasi_total(v3, v6, v2) = 0) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (empty(v1) = v9 & empty(v0) = v8 & function(v3) = v10 & relation_of2(v3, v6, v2) = v11 & apply_binary_as_element(v0, v1, v2, v3, v4, v5) = v14 & element(v5, v1) = v13 & element(v4, v0) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0) | ~ (v10 = 0) | v14 = v7 | v9 = 0 | v8 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (cartesian_product2(v0, v1) = v6) | ~ (quasi_total(v3, v6, v2) = 0) | ~ (element(v5, v1) = 0) | ~ (element(v4, v0) = 0) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : (empty(v1) = v8 & empty(v0) = v7 & function(v3) = v9 & relation_of2(v3, v6, v2) = v10 & apply_binary_as_element(v0, v1, v2, v3, v4, v5) = v11 & element(v11, v2) = v12 & ( ~ (v10 = 0) | ~ (v9 = 0) | v12 = 0 | v8 = 0 | v7 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (powerset(v3) = v4) | ~ (cartesian_product2(v0, v1) = v3) | ~ (element(v2, v4) = v5) | ? [v6] : ( ~ (v6 = 0) & relation_of2_as_subset(v2, v0, v1) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (join(v0, v1, v2) = v4) | ~ (the_carrier(v0) = v3) | ~ (element(v4, v3) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (element(v2, v3) = v9 & element(v1, v3) = v8 & empty_carrier(v0) = v6 & join_semilatt_str(v0) = v7 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (the_carrier(v0) = v3) | ~ (element(v4, v3) = v5) | ~ (join_commut(v0, v1, v2) = v4) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (element(v2, v3) = v10 & element(v1, v3) = v9 & empty_carrier(v0) = v6 & join_commutative(v0) = v7 & join_semilatt_str(v0) = v8 & ( ~ (v10 = 0) | ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | v6 = 0))) & ! [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 | ~ (relation_of2_as_subset(v4, v3, v2) = v1) | ~ (relation_of2_as_subset(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (quasi_total(v4, v3, v2) = v1) | ~ (quasi_total(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (relation_of2(v4, v3, v2) = v1) | ~ (relation_of2(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (below(v4, v3, v2) = v1) | ~ (below(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (join(v4, v3, v2) = v1) | ~ (join(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (join_commut(v4, v3, v2) = v1) | ~ (join_commut(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v2, v2) = v3) | ~ (quasi_total(v1, v3, v2) = v4) | ~ (the_L_join(v0) = v1) | ~ (the_carrier(v0) = v2) | ? [v5] : ? [v6] : ? [v7] : (relation_of2_as_subset(v1, v3, v2) = v7 & function(v1) = v6 & join_semilatt_str(v0) = v5 & ( ~ (v5 = 0) | (v7 = 0 & v6 = 0 & v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (relation_of2_as_subset(v2, v0, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & relation_of2(v2, v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | element(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (the_carrier(v0) = v3) | ~ (element(v2, v3) = 0) | ~ (element(v1, v3) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (join(v0, v1, v2) = v8 & empty_carrier(v0) = v4 & join_commutative(v0) = v5 & join_semilatt_str(v0) = v6 & join_commut(v0, v1, v2) = v7 & ( ~ (v6 = 0) | ~ (v5 = 0) | v8 = v7 | v4 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (the_carrier(v0) = v3) | ~ (element(v2, v3) = 0) | ~ (element(v1, v3) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (empty_carrier(v0) = v4 & join_commutative(v0) = v5 & join_semilatt_str(v0) = v6 & join_commut(v0, v2, v1) = v8 & join_commut(v0, v1, v2) = v7 & ( ~ (v6 = 0) | ~ (v5 = 0) | v8 = v7 | v4 = 0))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v0, v1) = v2) | ? [v3] : ? [v4] : (empty(v1) = v4 & element(v0, v1) = v3 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (one_sorted_str(v2) = v1) | ~ (one_sorted_str(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (the_L_join(v2) = v1) | ~ (the_L_join(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (the_carrier(v2) = v1) | ~ (the_carrier(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty_carrier(v2) = v1) | ~ (empty_carrier(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (join_commutative(v2) = v1) | ~ (join_commutative(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (join_semilatt_str(v2) = v1) | ~ (join_semilatt_str(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (preboolean(v2) = v1) | ~ (preboolean(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cup_closed(v2) = v1) | ~ (cup_closed(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (diff_closed(v2) = v1) | ~ (diff_closed(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | subset(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_of2_as_subset(v2, v0, v1) = 0) | relation_of2(v2, v0, v1) = 0) & ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (one_sorted_str(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & join_semilatt_str(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (preboolean(v0) = v1) | ? [v2] : ? [v3] : (cup_closed(v0) = v2 & diff_closed(v0) = v3 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | preboolean(v1) = 0) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | cup_closed(v1) = 0) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | diff_closed(v1) = 0) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (the_L_join(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (the_carrier(v0) = v4 & empty_carrier(v0) = v2 & join_semilatt_str(v0) = v3 & ( ~ (v3 = 0) | v2 = 0 | ! [v5] : ! [v6] : ! [v7] : ( ~ (apply_binary_as_element(v4, v4, v4, v1, v5, v6) = v7) | ~ (element(v5, v4) = 0) | ? [v8] : ? [v9] : (join(v0, v5, v6) = v9 & element(v6, v4) = v8 & ( ~ (v8 = 0) | v9 = v7)))))) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | element(v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) & ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0)) & ! [v0] : ( ~ (one_sorted_str(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (powerset(v2) = v3 & the_carrier(v0) = v2 & empty_carrier(v0) = v1 & (v1 = 0 | (v5 = 0 & ~ (v6 = 0) & empty(v4) = v6 & element(v4, v3) = 0)))) & ! [v0] : ( ~ (one_sorted_str(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (empty(v2) = v3 & the_carrier(v0) = v2 & empty_carrier(v0) = v1 & ( ~ (v3 = 0) | v1 = 0))) & ! [v0] : ( ~ (join_semilatt_str(v0) = 0) | ? [v1] : ? [v2] : (the_carrier(v0) = v2 & empty_carrier(v0) = v1 & (v1 = 0 | ! [v3] : ! [v4] : ( ~ (element(v4, v2) = 0) | ~ (element(v3, v2) = 0) | ? [v5] : ? [v6] : (below(v0, v3, v4) = v5 & join(v0, v3, v4) = v6 & ( ~ (v6 = v4) | v5 = 0) & ( ~ (v5 = 0) | v6 = v4)))))) & ! [v0] : ( ~ (preboolean(v0) = 0) | (cup_closed(v0) = 0 & diff_closed(v0) = 0)) & ? [v0] : ? [v1] : ? [v2] : relation_of2_as_subset(v2, v0, v1) = 0 & ? [v0] : ? [v1] : ? [v2] : relation_of2(v2, v0, v1) = 0 & ? [v0] : ? [v1] : element(v1, v0) = 0
% 8.56/2.66 |
% 8.56/2.66 | Applying alpha-rule on (1) yields:
% 8.56/2.66 | (2) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cup_closed(v2) = v1) | ~ (cup_closed(v2) = v0))
% 8.56/2.66 | (3) one_sorted_str(all_0_3_3) = 0
% 8.56/2.66 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (powerset(v3) = v4) | ~ (cartesian_product2(v0, v1) = v3) | ~ (element(v2, v4) = v5) | ? [v6] : ( ~ (v6 = 0) & relation_of2_as_subset(v2, v0, v1) = v6))
% 8.56/2.66 | (5) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 8.56/2.66 | (6) ? [v0] : ? [v1] : ? [v2] : relation_of2_as_subset(v2, v0, v1) = 0
% 8.56/2.66 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (relation_of2_as_subset(v2, v0, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & relation_of2(v2, v0, v1) = v4))
% 8.56/2.66 | (8) ? [v0] : ? [v1] : ? [v2] : relation_of2(v2, v0, v1) = 0
% 8.56/2.66 | (9) empty_carrier(all_0_3_3) = all_0_2_2
% 8.56/2.66 | (10) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0))
% 8.56/2.66 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (join_commut(v4, v3, v2) = v1) | ~ (join_commut(v4, v3, v2) = v0))
% 8.56/2.66 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (the_carrier(v0) = v3) | ~ (element(v2, v3) = 0) | ~ (element(v1, v3) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (empty_carrier(v0) = v4 & join_commutative(v0) = v5 & join_semilatt_str(v0) = v6 & join_commut(v0, v2, v1) = v8 & join_commut(v0, v1, v2) = v7 & ( ~ (v6 = 0) | ~ (v5 = 0) | v8 = v7 | v4 = 0)))
% 8.56/2.66 | (13) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 8.56/2.66 | (14) ~ (all_0_7_7 = 0)
% 8.56/2.66 | (15) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_of2_as_subset(v2, v0, v1) = 0) | relation_of2(v2, v0, v1) = 0)
% 8.56/2.66 | (16) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 8.56/2.66 | (17) element(all_0_5_5, all_0_6_6) = 0
% 8.56/2.66 | (18) ? [v0] : ? [v1] : element(v1, v0) = 0
% 8.56/2.66 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (join(v0, v1, v2) = v4) | ~ (the_carrier(v0) = v3) | ~ (element(v4, v3) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (element(v2, v3) = v9 & element(v1, v3) = v8 & empty_carrier(v0) = v6 & join_semilatt_str(v0) = v7 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | v6 = 0)))
% 8.56/2.66 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0))
% 8.56/2.66 | (21) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v0, v1) = v2) | ? [v3] : ? [v4] : (empty(v1) = v4 & element(v0, v1) = v3 & ( ~ (v3 = 0) | v4 = 0)))
% 8.56/2.66 | (22) ! [v0] : ( ~ (one_sorted_str(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (empty(v2) = v3 & the_carrier(v0) = v2 & empty_carrier(v0) = v1 & ( ~ (v3 = 0) | v1 = 0)))
% 8.56/2.66 | (23) ~ (all_0_4_4 = all_0_5_5)
% 8.56/2.66 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (cartesian_product2(v0, v1) = v6) | ~ (quasi_total(v3, v6, v2) = 0) | ~ (element(v5, v1) = 0) | ~ (element(v4, v0) = 0) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : (empty(v1) = v8 & empty(v0) = v7 & function(v3) = v9 & relation_of2(v3, v6, v2) = v10 & apply_binary_as_element(v0, v1, v2, v3, v4, v5) = v11 & element(v11, v2) = v12 & ( ~ (v10 = 0) | ~ (v9 = 0) | v12 = 0 | v8 = 0 | v7 = 0)))
% 8.56/2.66 | (25) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | subset(v0, v1) = 0)
% 8.56/2.66 | (26) ! [v0] : ! [v1] : (v1 = 0 | ~ (preboolean(v0) = v1) | ? [v2] : ? [v3] : (cup_closed(v0) = v2 & diff_closed(v0) = v3 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 8.56/2.66 | (27) below(all_0_8_8, all_0_5_5, all_0_4_4) = 0
% 8.56/2.66 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4))
% 8.56/2.66 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 8.56/2.66 | (30) below(all_0_8_8, all_0_4_4, all_0_5_5) = 0
% 8.56/2.66 | (31) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (the_carrier(v2) = v1) | ~ (the_carrier(v2) = v0))
% 8.56/2.66 | (32) the_carrier(all_0_8_8) = all_0_6_6
% 8.56/2.66 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (the_carrier(v0) = v3) | ~ (element(v2, v3) = 0) | ~ (element(v1, v3) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (join(v0, v1, v2) = v8 & empty_carrier(v0) = v4 & join_commutative(v0) = v5 & join_semilatt_str(v0) = v6 & join_commut(v0, v1, v2) = v7 & ( ~ (v6 = 0) | ~ (v5 = 0) | v8 = v7 | v4 = 0)))
% 8.56/2.67 | (34) join_commutative(all_0_8_8) = 0
% 8.56/2.67 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (below(v4, v3, v2) = v1) | ~ (below(v4, v3, v2) = v0))
% 8.56/2.67 | (36) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0))
% 8.56/2.67 | (37) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (join_semilatt_str(v2) = v1) | ~ (join_semilatt_str(v2) = v0))
% 8.56/2.67 | (38) one_sorted_str(all_0_0_0) = 0
% 8.56/2.67 | (39) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0))
% 8.56/2.67 | (40) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (the_L_join(v2) = v1) | ~ (the_L_join(v2) = v0))
% 8.56/2.67 | (41) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | preboolean(v1) = 0)
% 8.56/2.67 | (42) join_semilatt_str(all_0_1_1) = 0
% 8.56/2.67 | (43) ! [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))
% 8.56/2.67 | (44) ! [v0] : ! [v1] : ( ~ (the_L_join(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (the_carrier(v0) = v4 & empty_carrier(v0) = v2 & join_semilatt_str(v0) = v3 & ( ~ (v3 = 0) | v2 = 0 | ! [v5] : ! [v6] : ! [v7] : ( ~ (apply_binary_as_element(v4, v4, v4, v1, v5, v6) = v7) | ~ (element(v5, v4) = 0) | ? [v8] : ? [v9] : (join(v0, v5, v6) = v9 & element(v6, v4) = v8 & ( ~ (v8 = 0) | v9 = v7))))))
% 8.56/2.67 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (relation_of2(v4, v3, v2) = v1) | ~ (relation_of2(v4, v3, v2) = v0))
% 8.56/2.67 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (apply_binary(v3, v4, v5) = v7) | ~ (cartesian_product2(v0, v1) = v6) | ~ (quasi_total(v3, v6, v2) = 0) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (empty(v1) = v9 & empty(v0) = v8 & function(v3) = v10 & relation_of2(v3, v6, v2) = v11 & apply_binary_as_element(v0, v1, v2, v3, v4, v5) = v14 & element(v5, v1) = v13 & element(v4, v0) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0) | ~ (v11 = 0) | ~ (v10 = 0) | v14 = v7 | v9 = 0 | v8 = 0)))
% 8.56/2.67 | (47) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 8.56/2.67 | (48) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | element(v0, v1) = 0)
% 8.56/2.67 | (49) empty_carrier(all_0_8_8) = all_0_7_7
% 8.56/2.67 | (50) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 8.56/2.67 | (51) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (diff_closed(v2) = v1) | ~ (diff_closed(v2) = v0))
% 8.56/2.67 | (52) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | cup_closed(v1) = 0)
% 8.56/2.67 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (the_carrier(v0) = v3) | ~ (element(v4, v3) = v5) | ~ (join_commut(v0, v1, v2) = v4) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (element(v2, v3) = v10 & element(v1, v3) = v9 & empty_carrier(v0) = v6 & join_commutative(v0) = v7 & join_semilatt_str(v0) = v8 & ( ~ (v10 = 0) | ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | v6 = 0)))
% 8.56/2.67 | (54) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty_carrier(v2) = v1) | ~ (empty_carrier(v2) = v0))
% 8.56/2.67 | (55) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | diff_closed(v1) = 0)
% 8.56/2.67 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (quasi_total(v4, v3, v2) = v1) | ~ (quasi_total(v4, v3, v2) = v0))
% 8.56/2.67 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | element(v0, v2) = 0)
% 8.56/2.67 | (58) ~ (all_0_2_2 = 0)
% 8.56/2.67 | (59) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (join_commutative(v2) = v1) | ~ (join_commutative(v2) = v0))
% 8.56/2.67 | (60) ! [v0] : ( ~ (join_semilatt_str(v0) = 0) | ? [v1] : ? [v2] : (the_carrier(v0) = v2 & empty_carrier(v0) = v1 & (v1 = 0 | ! [v3] : ! [v4] : ( ~ (element(v4, v2) = 0) | ~ (element(v3, v2) = 0) | ? [v5] : ? [v6] : (below(v0, v3, v4) = v5 & join(v0, v3, v4) = v6 & ( ~ (v6 = v4) | v5 = 0) & ( ~ (v5 = 0) | v6 = v4))))))
% 8.56/2.67 | (61) join_semilatt_str(all_0_8_8) = 0
% 8.56/2.67 | (62) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (join(v4, v3, v2) = v1) | ~ (join(v4, v3, v2) = v0))
% 8.56/2.67 | (63) ! [v0] : ( ~ (preboolean(v0) = 0) | (cup_closed(v0) = 0 & diff_closed(v0) = 0))
% 8.56/2.67 | (64) ! [v0] : ( ~ (one_sorted_str(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (powerset(v2) = v3 & the_carrier(v0) = v2 & empty_carrier(v0) = v1 & (v1 = 0 | (v5 = 0 & ~ (v6 = 0) & empty(v4) = v6 & element(v4, v3) = 0))))
% 8.56/2.67 | (65) element(all_0_4_4, all_0_6_6) = 0
% 8.56/2.67 | (66) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (relation_of2_as_subset(v4, v3, v2) = v1) | ~ (relation_of2_as_subset(v4, v3, v2) = v0))
% 8.56/2.67 | (67) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 8.56/2.67 | (68) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1))
% 8.56/2.67 | (69) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (preboolean(v2) = v1) | ~ (preboolean(v2) = v0))
% 8.56/2.67 | (70) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0))
% 8.56/2.67 | (71) ! [v0] : ! [v1] : (v1 = 0 | ~ (one_sorted_str(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & join_semilatt_str(v0) = v2))
% 8.56/2.67 | (72) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0))
% 8.56/2.67 | (73) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (one_sorted_str(v2) = v1) | ~ (one_sorted_str(v2) = v0))
% 8.56/2.68 | (74) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v2, v2) = v3) | ~ (quasi_total(v1, v3, v2) = v4) | ~ (the_L_join(v0) = v1) | ~ (the_carrier(v0) = v2) | ? [v5] : ? [v6] : ? [v7] : (relation_of2_as_subset(v1, v3, v2) = v7 & function(v1) = v6 & join_semilatt_str(v0) = v5 & ( ~ (v5 = 0) | (v7 = 0 & v6 = 0 & v4 = 0))))
% 8.56/2.68 | (75) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (apply_binary(v4, v3, v2) = v1) | ~ (apply_binary(v4, v3, v2) = v0))
% 8.56/2.68 |
% 8.56/2.68 | Instantiating formula (33) with all_0_6_6, all_0_4_4, all_0_4_4, all_0_8_8 and discharging atoms the_carrier(all_0_8_8) = all_0_6_6, element(all_0_4_4, all_0_6_6) = 0, yields:
% 8.56/2.68 | (76) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (join(all_0_8_8, all_0_4_4, all_0_4_4) = v4 & empty_carrier(all_0_8_8) = v0 & join_commutative(all_0_8_8) = v1 & join_semilatt_str(all_0_8_8) = v2 & join_commut(all_0_8_8, all_0_4_4, all_0_4_4) = v3 & ( ~ (v2 = 0) | ~ (v1 = 0) | v4 = v3 | v0 = 0))
% 8.56/2.68 |
% 8.56/2.68 | Instantiating formula (12) with all_0_6_6, all_0_4_4, all_0_4_4, all_0_8_8 and discharging atoms the_carrier(all_0_8_8) = all_0_6_6, element(all_0_4_4, all_0_6_6) = 0, yields:
% 8.56/2.68 | (77) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (empty_carrier(all_0_8_8) = v0 & join_commutative(all_0_8_8) = v1 & join_semilatt_str(all_0_8_8) = v2 & join_commut(all_0_8_8, all_0_4_4, all_0_4_4) = v4 & join_commut(all_0_8_8, all_0_4_4, all_0_4_4) = v3 & ( ~ (v2 = 0) | ~ (v1 = 0) | v4 = v3 | v0 = 0))
% 8.56/2.68 |
% 8.56/2.68 | Instantiating formula (33) with all_0_6_6, all_0_5_5, all_0_4_4, all_0_8_8 and discharging atoms the_carrier(all_0_8_8) = all_0_6_6, element(all_0_4_4, all_0_6_6) = 0, element(all_0_5_5, all_0_6_6) = 0, yields:
% 8.56/2.68 | (78) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (join(all_0_8_8, all_0_4_4, all_0_5_5) = v4 & empty_carrier(all_0_8_8) = v0 & join_commutative(all_0_8_8) = v1 & join_semilatt_str(all_0_8_8) = v2 & join_commut(all_0_8_8, all_0_4_4, all_0_5_5) = v3 & ( ~ (v2 = 0) | ~ (v1 = 0) | v4 = v3 | v0 = 0))
% 8.56/2.68 |
% 8.56/2.68 | Instantiating formula (33) with all_0_6_6, all_0_4_4, all_0_5_5, all_0_8_8 and discharging atoms the_carrier(all_0_8_8) = all_0_6_6, element(all_0_4_4, all_0_6_6) = 0, element(all_0_5_5, all_0_6_6) = 0, yields:
% 8.56/2.68 | (79) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (join(all_0_8_8, all_0_5_5, all_0_4_4) = v4 & empty_carrier(all_0_8_8) = v0 & join_commutative(all_0_8_8) = v1 & join_semilatt_str(all_0_8_8) = v2 & join_commut(all_0_8_8, all_0_5_5, all_0_4_4) = v3 & ( ~ (v2 = 0) | ~ (v1 = 0) | v4 = v3 | v0 = 0))
% 8.56/2.68 |
% 8.56/2.68 | Instantiating formula (12) with all_0_6_6, all_0_5_5, all_0_4_4, all_0_8_8 and discharging atoms the_carrier(all_0_8_8) = all_0_6_6, element(all_0_4_4, all_0_6_6) = 0, element(all_0_5_5, all_0_6_6) = 0, yields:
% 8.56/2.68 | (80) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (empty_carrier(all_0_8_8) = v0 & join_commutative(all_0_8_8) = v1 & join_semilatt_str(all_0_8_8) = v2 & join_commut(all_0_8_8, all_0_4_4, all_0_5_5) = v3 & join_commut(all_0_8_8, all_0_5_5, all_0_4_4) = v4 & ( ~ (v2 = 0) | ~ (v1 = 0) | v4 = v3 | v0 = 0))
% 8.56/2.68 |
% 8.56/2.68 | Instantiating formula (12) with all_0_6_6, all_0_4_4, all_0_5_5, all_0_8_8 and discharging atoms the_carrier(all_0_8_8) = all_0_6_6, element(all_0_4_4, all_0_6_6) = 0, element(all_0_5_5, all_0_6_6) = 0, yields:
% 8.56/2.68 | (81) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (empty_carrier(all_0_8_8) = v0 & join_commutative(all_0_8_8) = v1 & join_semilatt_str(all_0_8_8) = v2 & join_commut(all_0_8_8, all_0_4_4, all_0_5_5) = v4 & join_commut(all_0_8_8, all_0_5_5, all_0_4_4) = v3 & ( ~ (v2 = 0) | ~ (v1 = 0) | v4 = v3 | v0 = 0))
% 8.56/2.68 |
% 8.56/2.68 | Instantiating formula (33) with all_0_6_6, all_0_5_5, all_0_5_5, all_0_8_8 and discharging atoms the_carrier(all_0_8_8) = all_0_6_6, element(all_0_5_5, all_0_6_6) = 0, yields:
% 8.56/2.68 | (82) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (join(all_0_8_8, all_0_5_5, all_0_5_5) = v4 & empty_carrier(all_0_8_8) = v0 & join_commutative(all_0_8_8) = v1 & join_semilatt_str(all_0_8_8) = v2 & join_commut(all_0_8_8, all_0_5_5, all_0_5_5) = v3 & ( ~ (v2 = 0) | ~ (v1 = 0) | v4 = v3 | v0 = 0))
% 8.56/2.68 |
% 8.56/2.68 | Instantiating formula (12) with all_0_6_6, all_0_5_5, all_0_5_5, all_0_8_8 and discharging atoms the_carrier(all_0_8_8) = all_0_6_6, element(all_0_5_5, all_0_6_6) = 0, yields:
% 8.56/2.68 | (83) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (empty_carrier(all_0_8_8) = v0 & join_commutative(all_0_8_8) = v1 & join_semilatt_str(all_0_8_8) = v2 & join_commut(all_0_8_8, all_0_5_5, all_0_5_5) = v4 & join_commut(all_0_8_8, all_0_5_5, all_0_5_5) = v3 & ( ~ (v2 = 0) | ~ (v1 = 0) | v4 = v3 | v0 = 0))
% 8.56/2.68 |
% 8.56/2.68 | Instantiating formula (60) with all_0_8_8 and discharging atoms join_semilatt_str(all_0_8_8) = 0, yields:
% 8.56/2.68 | (84) ? [v0] : ? [v1] : (the_carrier(all_0_8_8) = v1 & empty_carrier(all_0_8_8) = v0 & (v0 = 0 | ! [v2] : ! [v3] : ( ~ (element(v3, v1) = 0) | ~ (element(v2, v1) = 0) | ? [v4] : ? [v5] : (below(all_0_8_8, v2, v3) = v4 & join(all_0_8_8, v2, v3) = v5 & ( ~ (v5 = v3) | v4 = 0) & ( ~ (v4 = 0) | v5 = v3)))))
% 8.56/2.68 |
% 8.56/2.68 | Instantiating (84) with all_15_0_17, all_15_1_18 yields:
% 8.56/2.68 | (85) the_carrier(all_0_8_8) = all_15_0_17 & empty_carrier(all_0_8_8) = all_15_1_18 & (all_15_1_18 = 0 | ! [v0] : ! [v1] : ( ~ (element(v1, all_15_0_17) = 0) | ~ (element(v0, all_15_0_17) = 0) | ? [v2] : ? [v3] : (below(all_0_8_8, v0, v1) = v2 & join(all_0_8_8, v0, v1) = v3 & ( ~ (v3 = v1) | v2 = 0) & ( ~ (v2 = 0) | v3 = v1))))
% 8.56/2.68 |
% 8.56/2.68 | Applying alpha-rule on (85) yields:
% 8.56/2.68 | (86) the_carrier(all_0_8_8) = all_15_0_17
% 8.56/2.68 | (87) empty_carrier(all_0_8_8) = all_15_1_18
% 8.56/2.68 | (88) all_15_1_18 = 0 | ! [v0] : ! [v1] : ( ~ (element(v1, all_15_0_17) = 0) | ~ (element(v0, all_15_0_17) = 0) | ? [v2] : ? [v3] : (below(all_0_8_8, v0, v1) = v2 & join(all_0_8_8, v0, v1) = v3 & ( ~ (v3 = v1) | v2 = 0) & ( ~ (v2 = 0) | v3 = v1)))
% 8.56/2.68 |
% 8.56/2.68 | Instantiating (77) with all_19_0_21, all_19_1_22, all_19_2_23, all_19_3_24, all_19_4_25 yields:
% 8.56/2.68 | (89) empty_carrier(all_0_8_8) = all_19_4_25 & join_commutative(all_0_8_8) = all_19_3_24 & join_semilatt_str(all_0_8_8) = all_19_2_23 & join_commut(all_0_8_8, all_0_4_4, all_0_4_4) = all_19_0_21 & join_commut(all_0_8_8, all_0_4_4, all_0_4_4) = all_19_1_22 & ( ~ (all_19_2_23 = 0) | ~ (all_19_3_24 = 0) | all_19_0_21 = all_19_1_22 | all_19_4_25 = 0)
% 8.56/2.68 |
% 8.56/2.68 | Applying alpha-rule on (89) yields:
% 8.56/2.68 | (90) join_commut(all_0_8_8, all_0_4_4, all_0_4_4) = all_19_0_21
% 8.56/2.68 | (91) join_commutative(all_0_8_8) = all_19_3_24
% 8.56/2.68 | (92) join_semilatt_str(all_0_8_8) = all_19_2_23
% 8.56/2.68 | (93) empty_carrier(all_0_8_8) = all_19_4_25
% 8.56/2.68 | (94) join_commut(all_0_8_8, all_0_4_4, all_0_4_4) = all_19_1_22
% 8.56/2.68 | (95) ~ (all_19_2_23 = 0) | ~ (all_19_3_24 = 0) | all_19_0_21 = all_19_1_22 | all_19_4_25 = 0
% 8.56/2.68 |
% 8.56/2.68 | Instantiating (76) with all_25_0_35, all_25_1_36, all_25_2_37, all_25_3_38, all_25_4_39 yields:
% 8.56/2.68 | (96) join(all_0_8_8, all_0_4_4, all_0_4_4) = all_25_0_35 & empty_carrier(all_0_8_8) = all_25_4_39 & join_commutative(all_0_8_8) = all_25_3_38 & join_semilatt_str(all_0_8_8) = all_25_2_37 & join_commut(all_0_8_8, all_0_4_4, all_0_4_4) = all_25_1_36 & ( ~ (all_25_2_37 = 0) | ~ (all_25_3_38 = 0) | all_25_0_35 = all_25_1_36 | all_25_4_39 = 0)
% 8.56/2.69 |
% 8.56/2.69 | Applying alpha-rule on (96) yields:
% 8.56/2.69 | (97) empty_carrier(all_0_8_8) = all_25_4_39
% 8.56/2.69 | (98) ~ (all_25_2_37 = 0) | ~ (all_25_3_38 = 0) | all_25_0_35 = all_25_1_36 | all_25_4_39 = 0
% 8.56/2.69 | (99) join(all_0_8_8, all_0_4_4, all_0_4_4) = all_25_0_35
% 8.56/2.69 | (100) join_semilatt_str(all_0_8_8) = all_25_2_37
% 8.56/2.69 | (101) join_commutative(all_0_8_8) = all_25_3_38
% 8.56/2.69 | (102) join_commut(all_0_8_8, all_0_4_4, all_0_4_4) = all_25_1_36
% 8.56/2.69 |
% 8.56/2.69 | Instantiating (81) with all_27_0_40, all_27_1_41, all_27_2_42, all_27_3_43, all_27_4_44 yields:
% 8.56/2.69 | (103) empty_carrier(all_0_8_8) = all_27_4_44 & join_commutative(all_0_8_8) = all_27_3_43 & join_semilatt_str(all_0_8_8) = all_27_2_42 & join_commut(all_0_8_8, all_0_4_4, all_0_5_5) = all_27_0_40 & join_commut(all_0_8_8, all_0_5_5, all_0_4_4) = all_27_1_41 & ( ~ (all_27_2_42 = 0) | ~ (all_27_3_43 = 0) | all_27_0_40 = all_27_1_41 | all_27_4_44 = 0)
% 8.56/2.69 |
% 8.56/2.69 | Applying alpha-rule on (103) yields:
% 8.56/2.69 | (104) ~ (all_27_2_42 = 0) | ~ (all_27_3_43 = 0) | all_27_0_40 = all_27_1_41 | all_27_4_44 = 0
% 8.56/2.69 | (105) empty_carrier(all_0_8_8) = all_27_4_44
% 8.56/2.69 | (106) join_commut(all_0_8_8, all_0_4_4, all_0_5_5) = all_27_0_40
% 8.56/2.69 | (107) join_commutative(all_0_8_8) = all_27_3_43
% 8.56/2.69 | (108) join_commut(all_0_8_8, all_0_5_5, all_0_4_4) = all_27_1_41
% 8.56/2.69 | (109) join_semilatt_str(all_0_8_8) = all_27_2_42
% 8.56/2.69 |
% 8.56/2.69 | Instantiating (80) with all_29_0_45, all_29_1_46, all_29_2_47, all_29_3_48, all_29_4_49 yields:
% 8.56/2.69 | (110) empty_carrier(all_0_8_8) = all_29_4_49 & join_commutative(all_0_8_8) = all_29_3_48 & join_semilatt_str(all_0_8_8) = all_29_2_47 & join_commut(all_0_8_8, all_0_4_4, all_0_5_5) = all_29_1_46 & join_commut(all_0_8_8, all_0_5_5, all_0_4_4) = all_29_0_45 & ( ~ (all_29_2_47 = 0) | ~ (all_29_3_48 = 0) | all_29_0_45 = all_29_1_46 | all_29_4_49 = 0)
% 8.56/2.69 |
% 8.56/2.69 | Applying alpha-rule on (110) yields:
% 8.56/2.69 | (111) join_commutative(all_0_8_8) = all_29_3_48
% 8.56/2.69 | (112) join_commut(all_0_8_8, all_0_4_4, all_0_5_5) = all_29_1_46
% 8.56/2.69 | (113) ~ (all_29_2_47 = 0) | ~ (all_29_3_48 = 0) | all_29_0_45 = all_29_1_46 | all_29_4_49 = 0
% 8.56/2.69 | (114) empty_carrier(all_0_8_8) = all_29_4_49
% 8.56/2.69 | (115) join_commut(all_0_8_8, all_0_5_5, all_0_4_4) = all_29_0_45
% 8.56/2.69 | (116) join_semilatt_str(all_0_8_8) = all_29_2_47
% 8.56/2.69 |
% 8.56/2.69 | Instantiating (83) with all_31_0_50, all_31_1_51, all_31_2_52, all_31_3_53, all_31_4_54 yields:
% 8.56/2.69 | (117) empty_carrier(all_0_8_8) = all_31_4_54 & join_commutative(all_0_8_8) = all_31_3_53 & join_semilatt_str(all_0_8_8) = all_31_2_52 & join_commut(all_0_8_8, all_0_5_5, all_0_5_5) = all_31_0_50 & join_commut(all_0_8_8, all_0_5_5, all_0_5_5) = all_31_1_51 & ( ~ (all_31_2_52 = 0) | ~ (all_31_3_53 = 0) | all_31_0_50 = all_31_1_51 | all_31_4_54 = 0)
% 8.56/2.69 |
% 8.56/2.69 | Applying alpha-rule on (117) yields:
% 8.56/2.69 | (118) ~ (all_31_2_52 = 0) | ~ (all_31_3_53 = 0) | all_31_0_50 = all_31_1_51 | all_31_4_54 = 0
% 8.56/2.69 | (119) join_commutative(all_0_8_8) = all_31_3_53
% 8.56/2.69 | (120) join_commut(all_0_8_8, all_0_5_5, all_0_5_5) = all_31_1_51
% 8.56/2.69 | (121) join_semilatt_str(all_0_8_8) = all_31_2_52
% 8.56/2.69 | (122) join_commut(all_0_8_8, all_0_5_5, all_0_5_5) = all_31_0_50
% 8.56/2.69 | (123) empty_carrier(all_0_8_8) = all_31_4_54
% 8.56/2.69 |
% 8.56/2.69 | Instantiating (79) with all_35_0_58, all_35_1_59, all_35_2_60, all_35_3_61, all_35_4_62 yields:
% 8.56/2.69 | (124) join(all_0_8_8, all_0_5_5, all_0_4_4) = all_35_0_58 & empty_carrier(all_0_8_8) = all_35_4_62 & join_commutative(all_0_8_8) = all_35_3_61 & join_semilatt_str(all_0_8_8) = all_35_2_60 & join_commut(all_0_8_8, all_0_5_5, all_0_4_4) = all_35_1_59 & ( ~ (all_35_2_60 = 0) | ~ (all_35_3_61 = 0) | all_35_0_58 = all_35_1_59 | all_35_4_62 = 0)
% 8.56/2.69 |
% 8.56/2.69 | Applying alpha-rule on (124) yields:
% 8.56/2.69 | (125) join_commutative(all_0_8_8) = all_35_3_61
% 8.56/2.69 | (126) join_semilatt_str(all_0_8_8) = all_35_2_60
% 8.56/2.69 | (127) join(all_0_8_8, all_0_5_5, all_0_4_4) = all_35_0_58
% 8.56/2.69 | (128) empty_carrier(all_0_8_8) = all_35_4_62
% 8.56/2.69 | (129) join_commut(all_0_8_8, all_0_5_5, all_0_4_4) = all_35_1_59
% 8.56/2.69 | (130) ~ (all_35_2_60 = 0) | ~ (all_35_3_61 = 0) | all_35_0_58 = all_35_1_59 | all_35_4_62 = 0
% 8.56/2.69 |
% 8.56/2.69 | Instantiating (78) with all_37_0_63, all_37_1_64, all_37_2_65, all_37_3_66, all_37_4_67 yields:
% 8.56/2.69 | (131) join(all_0_8_8, all_0_4_4, all_0_5_5) = all_37_0_63 & empty_carrier(all_0_8_8) = all_37_4_67 & join_commutative(all_0_8_8) = all_37_3_66 & join_semilatt_str(all_0_8_8) = all_37_2_65 & join_commut(all_0_8_8, all_0_4_4, all_0_5_5) = all_37_1_64 & ( ~ (all_37_2_65 = 0) | ~ (all_37_3_66 = 0) | all_37_0_63 = all_37_1_64 | all_37_4_67 = 0)
% 8.56/2.69 |
% 8.56/2.69 | Applying alpha-rule on (131) yields:
% 8.56/2.69 | (132) join_semilatt_str(all_0_8_8) = all_37_2_65
% 8.56/2.69 | (133) empty_carrier(all_0_8_8) = all_37_4_67
% 8.56/2.69 | (134) join_commut(all_0_8_8, all_0_4_4, all_0_5_5) = all_37_1_64
% 8.56/2.69 | (135) join_commutative(all_0_8_8) = all_37_3_66
% 8.56/2.69 | (136) join(all_0_8_8, all_0_4_4, all_0_5_5) = all_37_0_63
% 8.56/2.69 | (137) ~ (all_37_2_65 = 0) | ~ (all_37_3_66 = 0) | all_37_0_63 = all_37_1_64 | all_37_4_67 = 0
% 8.56/2.69 |
% 8.56/2.69 | Instantiating (82) with all_41_0_74, all_41_1_75, all_41_2_76, all_41_3_77, all_41_4_78 yields:
% 8.56/2.69 | (138) join(all_0_8_8, all_0_5_5, all_0_5_5) = all_41_0_74 & empty_carrier(all_0_8_8) = all_41_4_78 & join_commutative(all_0_8_8) = all_41_3_77 & join_semilatt_str(all_0_8_8) = all_41_2_76 & join_commut(all_0_8_8, all_0_5_5, all_0_5_5) = all_41_1_75 & ( ~ (all_41_2_76 = 0) | ~ (all_41_3_77 = 0) | all_41_0_74 = all_41_1_75 | all_41_4_78 = 0)
% 8.56/2.69 |
% 8.56/2.69 | Applying alpha-rule on (138) yields:
% 8.56/2.69 | (139) join(all_0_8_8, all_0_5_5, all_0_5_5) = all_41_0_74
% 8.56/2.69 | (140) join_commut(all_0_8_8, all_0_5_5, all_0_5_5) = all_41_1_75
% 8.56/2.69 | (141) join_semilatt_str(all_0_8_8) = all_41_2_76
% 8.56/2.69 | (142) ~ (all_41_2_76 = 0) | ~ (all_41_3_77 = 0) | all_41_0_74 = all_41_1_75 | all_41_4_78 = 0
% 8.56/2.69 | (143) empty_carrier(all_0_8_8) = all_41_4_78
% 8.56/2.69 | (144) join_commutative(all_0_8_8) = all_41_3_77
% 8.56/2.69 |
% 8.56/2.69 | Instantiating formula (31) with all_0_8_8, all_15_0_17, all_0_6_6 and discharging atoms the_carrier(all_0_8_8) = all_15_0_17, the_carrier(all_0_8_8) = all_0_6_6, yields:
% 8.56/2.69 | (145) all_15_0_17 = all_0_6_6
% 8.56/2.69 |
% 8.56/2.69 | Instantiating formula (54) with all_0_8_8, all_37_4_67, all_41_4_78 and discharging atoms empty_carrier(all_0_8_8) = all_41_4_78, empty_carrier(all_0_8_8) = all_37_4_67, yields:
% 8.56/2.69 | (146) all_41_4_78 = all_37_4_67
% 8.56/2.69 |
% 8.56/2.69 | Instantiating formula (54) with all_0_8_8, all_35_4_62, all_41_4_78 and discharging atoms empty_carrier(all_0_8_8) = all_41_4_78, empty_carrier(all_0_8_8) = all_35_4_62, yields:
% 8.56/2.69 | (147) all_41_4_78 = all_35_4_62
% 8.56/2.69 |
% 8.56/2.69 | Instantiating formula (54) with all_0_8_8, all_31_4_54, all_37_4_67 and discharging atoms empty_carrier(all_0_8_8) = all_37_4_67, empty_carrier(all_0_8_8) = all_31_4_54, yields:
% 8.56/2.69 | (148) all_37_4_67 = all_31_4_54
% 8.56/2.69 |
% 8.56/2.69 | Instantiating formula (54) with all_0_8_8, all_29_4_49, all_37_4_67 and discharging atoms empty_carrier(all_0_8_8) = all_37_4_67, empty_carrier(all_0_8_8) = all_29_4_49, yields:
% 8.56/2.69 | (149) all_37_4_67 = all_29_4_49
% 8.56/2.69 |
% 8.56/2.69 | Instantiating formula (54) with all_0_8_8, all_27_4_44, all_37_4_67 and discharging atoms empty_carrier(all_0_8_8) = all_37_4_67, empty_carrier(all_0_8_8) = all_27_4_44, yields:
% 8.56/2.69 | (150) all_37_4_67 = all_27_4_44
% 8.56/2.69 |
% 8.56/2.69 | Instantiating formula (54) with all_0_8_8, all_25_4_39, all_37_4_67 and discharging atoms empty_carrier(all_0_8_8) = all_37_4_67, empty_carrier(all_0_8_8) = all_25_4_39, yields:
% 8.56/2.69 | (151) all_37_4_67 = all_25_4_39
% 8.56/2.69 |
% 8.56/2.69 | Instantiating formula (54) with all_0_8_8, all_19_4_25, all_0_7_7 and discharging atoms empty_carrier(all_0_8_8) = all_19_4_25, empty_carrier(all_0_8_8) = all_0_7_7, yields:
% 8.56/2.69 | (152) all_19_4_25 = all_0_7_7
% 8.56/2.69 |
% 8.56/2.69 | Instantiating formula (54) with all_0_8_8, all_19_4_25, all_25_4_39 and discharging atoms empty_carrier(all_0_8_8) = all_25_4_39, empty_carrier(all_0_8_8) = all_19_4_25, yields:
% 8.56/2.69 | (153) all_25_4_39 = all_19_4_25
% 8.56/2.69 |
% 8.56/2.69 | Instantiating formula (54) with all_0_8_8, all_15_1_18, all_31_4_54 and discharging atoms empty_carrier(all_0_8_8) = all_31_4_54, empty_carrier(all_0_8_8) = all_15_1_18, yields:
% 8.56/2.69 | (154) all_31_4_54 = all_15_1_18
% 8.56/2.69 |
% 8.56/2.69 | Instantiating formula (59) with all_0_8_8, all_35_3_61, all_37_3_66 and discharging atoms join_commutative(all_0_8_8) = all_37_3_66, join_commutative(all_0_8_8) = all_35_3_61, yields:
% 8.56/2.69 | (155) all_37_3_66 = all_35_3_61
% 8.56/2.69 |
% 8.56/2.69 | Instantiating formula (59) with all_0_8_8, all_31_3_53, all_41_3_77 and discharging atoms join_commutative(all_0_8_8) = all_41_3_77, join_commutative(all_0_8_8) = all_31_3_53, yields:
% 8.56/2.69 | (156) all_41_3_77 = all_31_3_53
% 8.56/2.69 |
% 8.56/2.69 | Instantiating formula (59) with all_0_8_8, all_29_3_48, all_35_3_61 and discharging atoms join_commutative(all_0_8_8) = all_35_3_61, join_commutative(all_0_8_8) = all_29_3_48, yields:
% 8.56/2.69 | (157) all_35_3_61 = all_29_3_48
% 8.56/2.69 |
% 8.56/2.69 | Instantiating formula (59) with all_0_8_8, all_29_3_48, all_31_3_53 and discharging atoms join_commutative(all_0_8_8) = all_31_3_53, join_commutative(all_0_8_8) = all_29_3_48, yields:
% 8.56/2.69 | (158) all_31_3_53 = all_29_3_48
% 8.56/2.69 |
% 8.56/2.69 | Instantiating formula (59) with all_0_8_8, all_27_3_43, all_41_3_77 and discharging atoms join_commutative(all_0_8_8) = all_41_3_77, join_commutative(all_0_8_8) = all_27_3_43, yields:
% 8.56/2.69 | (159) all_41_3_77 = all_27_3_43
% 8.56/2.69 |
% 8.56/2.69 | Instantiating formula (59) with all_0_8_8, all_25_3_38, 0 and discharging atoms join_commutative(all_0_8_8) = all_25_3_38, join_commutative(all_0_8_8) = 0, yields:
% 8.56/2.69 | (160) all_25_3_38 = 0
% 8.56/2.69 |
% 8.56/2.69 | Instantiating formula (59) with all_0_8_8, all_25_3_38, all_29_3_48 and discharging atoms join_commutative(all_0_8_8) = all_29_3_48, join_commutative(all_0_8_8) = all_25_3_38, yields:
% 8.56/2.69 | (161) all_29_3_48 = all_25_3_38
% 8.56/2.69 |
% 8.56/2.69 | Instantiating formula (59) with all_0_8_8, all_19_3_24, all_37_3_66 and discharging atoms join_commutative(all_0_8_8) = all_37_3_66, join_commutative(all_0_8_8) = all_19_3_24, yields:
% 8.56/2.69 | (162) all_37_3_66 = all_19_3_24
% 8.56/2.69 |
% 8.56/2.69 | Instantiating formula (37) with all_0_8_8, all_37_2_65, all_41_2_76 and discharging atoms join_semilatt_str(all_0_8_8) = all_41_2_76, join_semilatt_str(all_0_8_8) = all_37_2_65, yields:
% 8.56/2.69 | (163) all_41_2_76 = all_37_2_65
% 8.56/2.69 |
% 8.56/2.69 | Instantiating formula (37) with all_0_8_8, all_31_2_52, all_35_2_60 and discharging atoms join_semilatt_str(all_0_8_8) = all_35_2_60, join_semilatt_str(all_0_8_8) = all_31_2_52, yields:
% 9.00/2.69 | (164) all_35_2_60 = all_31_2_52
% 9.00/2.69 |
% 9.00/2.70 | Instantiating formula (37) with all_0_8_8, all_29_2_47, 0 and discharging atoms join_semilatt_str(all_0_8_8) = all_29_2_47, join_semilatt_str(all_0_8_8) = 0, yields:
% 9.00/2.70 | (165) all_29_2_47 = 0
% 9.00/2.70 |
% 9.00/2.70 | Instantiating formula (37) with all_0_8_8, all_29_2_47, all_31_2_52 and discharging atoms join_semilatt_str(all_0_8_8) = all_31_2_52, join_semilatt_str(all_0_8_8) = all_29_2_47, yields:
% 9.00/2.70 | (166) all_31_2_52 = all_29_2_47
% 9.00/2.70 |
% 9.00/2.70 | Instantiating formula (37) with all_0_8_8, all_27_2_42, all_37_2_65 and discharging atoms join_semilatt_str(all_0_8_8) = all_37_2_65, join_semilatt_str(all_0_8_8) = all_27_2_42, yields:
% 9.00/2.70 | (167) all_37_2_65 = all_27_2_42
% 9.00/2.70 |
% 9.00/2.70 | Instantiating formula (37) with all_0_8_8, all_27_2_42, all_29_2_47 and discharging atoms join_semilatt_str(all_0_8_8) = all_29_2_47, join_semilatt_str(all_0_8_8) = all_27_2_42, yields:
% 9.00/2.70 | (168) all_29_2_47 = all_27_2_42
% 9.00/2.70 |
% 9.00/2.70 | Instantiating formula (37) with all_0_8_8, all_25_2_37, all_35_2_60 and discharging atoms join_semilatt_str(all_0_8_8) = all_35_2_60, join_semilatt_str(all_0_8_8) = all_25_2_37, yields:
% 9.00/2.70 | (169) all_35_2_60 = all_25_2_37
% 9.00/2.70 |
% 9.00/2.70 | Instantiating formula (37) with all_0_8_8, all_19_2_23, all_41_2_76 and discharging atoms join_semilatt_str(all_0_8_8) = all_41_2_76, join_semilatt_str(all_0_8_8) = all_19_2_23, yields:
% 9.00/2.70 | (170) all_41_2_76 = all_19_2_23
% 9.00/2.70 |
% 9.00/2.70 | Instantiating formula (11) with all_0_8_8, all_0_4_4, all_0_5_5, all_29_1_46, all_37_1_64 and discharging atoms join_commut(all_0_8_8, all_0_4_4, all_0_5_5) = all_37_1_64, join_commut(all_0_8_8, all_0_4_4, all_0_5_5) = all_29_1_46, yields:
% 9.00/2.70 | (171) all_37_1_64 = all_29_1_46
% 9.00/2.70 |
% 9.00/2.70 | Instantiating formula (11) with all_0_8_8, all_0_4_4, all_0_5_5, all_27_0_40, all_37_1_64 and discharging atoms join_commut(all_0_8_8, all_0_4_4, all_0_5_5) = all_37_1_64, join_commut(all_0_8_8, all_0_4_4, all_0_5_5) = all_27_0_40, yields:
% 9.00/2.70 | (172) all_37_1_64 = all_27_0_40
% 9.00/2.70 |
% 9.00/2.70 | Instantiating formula (11) with all_0_8_8, all_0_5_5, all_0_4_4, all_29_0_45, all_35_1_59 and discharging atoms join_commut(all_0_8_8, all_0_5_5, all_0_4_4) = all_35_1_59, join_commut(all_0_8_8, all_0_5_5, all_0_4_4) = all_29_0_45, yields:
% 9.00/2.70 | (173) all_35_1_59 = all_29_0_45
% 9.00/2.70 |
% 9.00/2.70 | Instantiating formula (11) with all_0_8_8, all_0_5_5, all_0_4_4, all_27_1_41, all_35_1_59 and discharging atoms join_commut(all_0_8_8, all_0_5_5, all_0_4_4) = all_35_1_59, join_commut(all_0_8_8, all_0_5_5, all_0_4_4) = all_27_1_41, yields:
% 9.00/2.70 | (174) all_35_1_59 = all_27_1_41
% 9.00/2.70 |
% 9.00/2.70 | Combining equations (163,170) yields a new equation:
% 9.00/2.70 | (175) all_37_2_65 = all_19_2_23
% 9.00/2.70 |
% 9.00/2.70 | Simplifying 175 yields:
% 9.00/2.70 | (176) all_37_2_65 = all_19_2_23
% 9.00/2.70 |
% 9.00/2.70 | Combining equations (156,159) yields a new equation:
% 9.00/2.70 | (177) all_31_3_53 = all_27_3_43
% 9.00/2.70 |
% 9.00/2.70 | Simplifying 177 yields:
% 9.00/2.70 | (178) all_31_3_53 = all_27_3_43
% 9.00/2.70 |
% 9.00/2.70 | Combining equations (146,147) yields a new equation:
% 9.00/2.70 | (179) all_37_4_67 = all_35_4_62
% 9.00/2.70 |
% 9.00/2.70 | Simplifying 179 yields:
% 9.00/2.70 | (180) all_37_4_67 = all_35_4_62
% 9.00/2.70 |
% 9.00/2.70 | Combining equations (171,172) yields a new equation:
% 9.00/2.70 | (181) all_29_1_46 = all_27_0_40
% 9.00/2.70 |
% 9.00/2.70 | Simplifying 181 yields:
% 9.00/2.70 | (182) all_29_1_46 = all_27_0_40
% 9.00/2.70 |
% 9.00/2.70 | Combining equations (167,176) yields a new equation:
% 9.00/2.70 | (183) all_27_2_42 = all_19_2_23
% 9.00/2.70 |
% 9.00/2.70 | Simplifying 183 yields:
% 9.00/2.70 | (184) all_27_2_42 = all_19_2_23
% 9.00/2.70 |
% 9.00/2.70 | Combining equations (155,162) yields a new equation:
% 9.00/2.70 | (185) all_35_3_61 = all_19_3_24
% 9.00/2.70 |
% 9.00/2.70 | Simplifying 185 yields:
% 9.00/2.70 | (186) all_35_3_61 = all_19_3_24
% 9.00/2.70 |
% 9.00/2.70 | Combining equations (149,180) yields a new equation:
% 9.00/2.70 | (187) all_35_4_62 = all_29_4_49
% 9.00/2.70 |
% 9.00/2.70 | Combining equations (150,180) yields a new equation:
% 9.00/2.70 | (188) all_35_4_62 = all_27_4_44
% 9.00/2.70 |
% 9.00/2.70 | Combining equations (148,180) yields a new equation:
% 9.00/2.70 | (189) all_35_4_62 = all_31_4_54
% 9.00/2.70 |
% 9.00/2.70 | Combining equations (151,180) yields a new equation:
% 9.00/2.70 | (190) all_35_4_62 = all_25_4_39
% 9.00/2.70 |
% 9.00/2.70 | Combining equations (174,173) yields a new equation:
% 9.00/2.70 | (191) all_29_0_45 = all_27_1_41
% 9.00/2.70 |
% 9.00/2.70 | Combining equations (164,169) yields a new equation:
% 9.00/2.70 | (192) all_31_2_52 = all_25_2_37
% 9.00/2.70 |
% 9.00/2.70 | Simplifying 192 yields:
% 9.00/2.70 | (193) all_31_2_52 = all_25_2_37
% 9.00/2.70 |
% 9.00/2.70 | Combining equations (157,186) yields a new equation:
% 9.00/2.70 | (194) all_29_3_48 = all_19_3_24
% 9.00/2.70 |
% 9.00/2.70 | Simplifying 194 yields:
% 9.00/2.70 | (195) all_29_3_48 = all_19_3_24
% 9.00/2.70 |
% 9.00/2.70 | Combining equations (189,187) yields a new equation:
% 9.00/2.70 | (196) all_31_4_54 = all_29_4_49
% 9.00/2.70 |
% 9.00/2.70 | Simplifying 196 yields:
% 9.00/2.70 | (197) all_31_4_54 = all_29_4_49
% 9.00/2.70 |
% 9.00/2.70 | Combining equations (188,187) yields a new equation:
% 9.00/2.70 | (198) all_29_4_49 = all_27_4_44
% 9.00/2.70 |
% 9.00/2.70 | Combining equations (190,187) yields a new equation:
% 9.00/2.70 | (199) all_29_4_49 = all_25_4_39
% 9.00/2.70 |
% 9.00/2.70 | Combining equations (166,193) yields a new equation:
% 9.00/2.70 | (200) all_29_2_47 = all_25_2_37
% 9.00/2.70 |
% 9.00/2.70 | Simplifying 200 yields:
% 9.00/2.70 | (201) all_29_2_47 = all_25_2_37
% 9.00/2.70 |
% 9.00/2.70 | Combining equations (158,178) yields a new equation:
% 9.00/2.70 | (202) all_29_3_48 = all_27_3_43
% 9.00/2.70 |
% 9.00/2.70 | Simplifying 202 yields:
% 9.00/2.70 | (203) all_29_3_48 = all_27_3_43
% 9.00/2.70 |
% 9.00/2.70 | Combining equations (197,154) yields a new equation:
% 9.00/2.70 | (204) all_29_4_49 = all_15_1_18
% 9.00/2.70 |
% 9.00/2.70 | Simplifying 204 yields:
% 9.00/2.70 | (205) all_29_4_49 = all_15_1_18
% 9.00/2.70 |
% 9.00/2.70 | Combining equations (165,201) yields a new equation:
% 9.00/2.70 | (206) all_25_2_37 = 0
% 9.00/2.70 |
% 9.00/2.70 | Combining equations (168,201) yields a new equation:
% 9.00/2.70 | (207) all_27_2_42 = all_25_2_37
% 9.00/2.70 |
% 9.00/2.70 | Simplifying 207 yields:
% 9.00/2.70 | (208) all_27_2_42 = all_25_2_37
% 9.00/2.70 |
% 9.00/2.70 | Combining equations (195,203) yields a new equation:
% 9.00/2.70 | (209) all_27_3_43 = all_19_3_24
% 9.00/2.70 |
% 9.00/2.70 | Combining equations (161,203) yields a new equation:
% 9.00/2.70 | (210) all_27_3_43 = all_25_3_38
% 9.00/2.70 |
% 9.00/2.70 | Combining equations (205,198) yields a new equation:
% 9.00/2.70 | (211) all_27_4_44 = all_15_1_18
% 9.00/2.70 |
% 9.00/2.70 | Combining equations (199,198) yields a new equation:
% 9.00/2.70 | (212) all_27_4_44 = all_25_4_39
% 9.00/2.70 |
% 9.00/2.70 | Combining equations (208,184) yields a new equation:
% 9.00/2.70 | (213) all_25_2_37 = all_19_2_23
% 9.00/2.70 |
% 9.00/2.70 | Simplifying 213 yields:
% 9.00/2.70 | (214) all_25_2_37 = all_19_2_23
% 9.00/2.70 |
% 9.00/2.70 | Combining equations (210,209) yields a new equation:
% 9.00/2.70 | (215) all_25_3_38 = all_19_3_24
% 9.00/2.70 |
% 9.00/2.70 | Simplifying 215 yields:
% 9.00/2.70 | (216) all_25_3_38 = all_19_3_24
% 9.00/2.70 |
% 9.00/2.70 | Combining equations (212,211) yields a new equation:
% 9.00/2.70 | (217) all_25_4_39 = all_15_1_18
% 9.00/2.70 |
% 9.00/2.70 | Simplifying 217 yields:
% 9.00/2.70 | (218) all_25_4_39 = all_15_1_18
% 9.00/2.70 |
% 9.00/2.70 | Combining equations (206,214) yields a new equation:
% 9.00/2.70 | (219) all_19_2_23 = 0
% 9.00/2.70 |
% 9.00/2.70 | Combining equations (160,216) yields a new equation:
% 9.00/2.70 | (220) all_19_3_24 = 0
% 9.00/2.70 |
% 9.00/2.70 | Combining equations (153,218) yields a new equation:
% 9.00/2.70 | (221) all_19_4_25 = all_15_1_18
% 9.00/2.70 |
% 9.00/2.70 | Simplifying 221 yields:
% 9.00/2.70 | (222) all_19_4_25 = all_15_1_18
% 9.00/2.70 |
% 9.00/2.70 | Combining equations (152,222) yields a new equation:
% 9.00/2.70 | (223) all_15_1_18 = all_0_7_7
% 9.00/2.70 |
% 9.00/2.70 | Combining equations (219,214) yields a new equation:
% 9.00/2.70 | (206) all_25_2_37 = 0
% 9.00/2.70 |
% 9.00/2.70 | Combining equations (223,211) yields a new equation:
% 9.00/2.70 | (225) all_27_4_44 = all_0_7_7
% 9.00/2.70 |
% 9.00/2.70 | Combining equations (220,209) yields a new equation:
% 9.00/2.70 | (226) all_27_3_43 = 0
% 9.00/2.70 |
% 9.00/2.70 | Combining equations (225,198) yields a new equation:
% 9.00/2.70 | (227) all_29_4_49 = all_0_7_7
% 9.00/2.70 |
% 9.00/2.70 | Combining equations (226,203) yields a new equation:
% 9.00/2.70 | (228) all_29_3_48 = 0
% 9.00/2.70 |
% 9.00/2.70 | Combining equations (206,201) yields a new equation:
% 9.00/2.70 | (165) all_29_2_47 = 0
% 9.00/2.70 |
% 9.00/2.70 | Combining equations (227,187) yields a new equation:
% 9.00/2.70 | (230) all_35_4_62 = all_0_7_7
% 9.00/2.70 |
% 9.00/2.70 | Combining equations (220,186) yields a new equation:
% 9.00/2.70 | (231) all_35_3_61 = 0
% 9.00/2.70 |
% 9.00/2.70 | Combining equations (206,169) yields a new equation:
% 9.00/2.70 | (232) all_35_2_60 = 0
% 9.00/2.70 |
% 9.00/2.70 | Combining equations (191,173) yields a new equation:
% 9.00/2.70 | (174) all_35_1_59 = all_27_1_41
% 9.00/2.70 |
% 9.00/2.70 | Combining equations (230,180) yields a new equation:
% 9.00/2.70 | (234) all_37_4_67 = all_0_7_7
% 9.00/2.70 |
% 9.00/2.70 | Combining equations (220,162) yields a new equation:
% 9.00/2.70 | (235) all_37_3_66 = 0
% 9.00/2.70 |
% 9.00/2.70 | Combining equations (219,176) yields a new equation:
% 9.00/2.70 | (236) all_37_2_65 = 0
% 9.00/2.70 |
% 9.00/2.70 +-Applying beta-rule and splitting (88), into two cases.
% 9.00/2.70 |-Branch one:
% 9.00/2.70 | (237) all_15_1_18 = 0
% 9.00/2.70 |
% 9.00/2.70 | Combining equations (237,223) yields a new equation:
% 9.00/2.70 | (238) all_0_7_7 = 0
% 9.00/2.70 |
% 9.00/2.70 | Equations (238) can reduce 14 to:
% 9.00/2.70 | (239) $false
% 9.00/2.70 |
% 9.00/2.71 |-The branch is then unsatisfiable
% 9.00/2.71 |-Branch two:
% 9.00/2.71 | (240) ~ (all_15_1_18 = 0)
% 9.00/2.71 | (241) ! [v0] : ! [v1] : ( ~ (element(v1, all_15_0_17) = 0) | ~ (element(v0, all_15_0_17) = 0) | ? [v2] : ? [v3] : (below(all_0_8_8, v0, v1) = v2 & join(all_0_8_8, v0, v1) = v3 & ( ~ (v3 = v1) | v2 = 0) & ( ~ (v2 = 0) | v3 = v1)))
% 9.00/2.71 |
% 9.00/2.71 | Instantiating formula (241) with all_0_4_4, all_0_4_4 yields:
% 9.00/2.71 | (242) ~ (element(all_0_4_4, all_15_0_17) = 0) | ? [v0] : ? [v1] : (below(all_0_8_8, all_0_4_4, all_0_4_4) = v0 & join(all_0_8_8, all_0_4_4, all_0_4_4) = v1 & ( ~ (v1 = all_0_4_4) | v0 = 0) & ( ~ (v0 = 0) | v1 = all_0_4_4))
% 9.00/2.71 |
% 9.00/2.71 | Instantiating formula (241) with all_0_5_5, all_0_4_4 yields:
% 9.00/2.71 | (243) ~ (element(all_0_4_4, all_15_0_17) = 0) | ~ (element(all_0_5_5, all_15_0_17) = 0) | ? [v0] : ? [v1] : (below(all_0_8_8, all_0_4_4, all_0_5_5) = v0 & join(all_0_8_8, all_0_4_4, all_0_5_5) = v1 & ( ~ (v1 = all_0_5_5) | v0 = 0) & ( ~ (v0 = 0) | v1 = all_0_5_5))
% 9.00/2.71 |
% 9.00/2.71 | Instantiating formula (241) with all_0_4_4, all_0_5_5 yields:
% 9.00/2.71 | (244) ~ (element(all_0_4_4, all_15_0_17) = 0) | ~ (element(all_0_5_5, all_15_0_17) = 0) | ? [v0] : ? [v1] : (below(all_0_8_8, all_0_5_5, all_0_4_4) = v0 & join(all_0_8_8, all_0_5_5, all_0_4_4) = v1 & ( ~ (v1 = all_0_4_4) | v0 = 0) & ( ~ (v0 = 0) | v1 = all_0_4_4))
% 9.00/2.71 |
% 9.00/2.71 | Instantiating formula (241) with all_0_5_5, all_0_5_5 yields:
% 9.00/2.71 | (245) ~ (element(all_0_5_5, all_15_0_17) = 0) | ? [v0] : ? [v1] : (below(all_0_8_8, all_0_5_5, all_0_5_5) = v0 & join(all_0_8_8, all_0_5_5, all_0_5_5) = v1 & ( ~ (v1 = all_0_5_5) | v0 = 0) & ( ~ (v0 = 0) | v1 = all_0_5_5))
% 9.00/2.71 |
% 9.00/2.71 | Equations (223) can reduce 240 to:
% 9.00/2.71 | (14) ~ (all_0_7_7 = 0)
% 9.00/2.71 |
% 9.00/2.71 +-Applying beta-rule and splitting (137), into two cases.
% 9.00/2.71 |-Branch one:
% 9.00/2.71 | (247) ~ (all_37_2_65 = 0)
% 9.00/2.71 |
% 9.00/2.71 | Equations (236) can reduce 247 to:
% 9.00/2.71 | (239) $false
% 9.00/2.71 |
% 9.00/2.71 |-The branch is then unsatisfiable
% 9.00/2.71 |-Branch two:
% 9.00/2.71 | (236) all_37_2_65 = 0
% 9.00/2.71 | (250) ~ (all_37_3_66 = 0) | all_37_0_63 = all_37_1_64 | all_37_4_67 = 0
% 9.00/2.71 |
% 9.00/2.71 +-Applying beta-rule and splitting (250), into two cases.
% 9.00/2.71 |-Branch one:
% 9.00/2.71 | (251) ~ (all_37_3_66 = 0)
% 9.00/2.71 |
% 9.00/2.71 | Equations (235) can reduce 251 to:
% 9.00/2.71 | (239) $false
% 9.00/2.71 |
% 9.00/2.71 |-The branch is then unsatisfiable
% 9.00/2.71 |-Branch two:
% 9.00/2.71 | (235) all_37_3_66 = 0
% 9.00/2.71 | (254) all_37_0_63 = all_37_1_64 | all_37_4_67 = 0
% 9.00/2.71 |
% 9.00/2.71 +-Applying beta-rule and splitting (254), into two cases.
% 9.00/2.71 |-Branch one:
% 9.00/2.71 | (255) all_37_4_67 = 0
% 9.00/2.71 |
% 9.00/2.71 | Combining equations (255,234) yields a new equation:
% 9.00/2.71 | (238) all_0_7_7 = 0
% 9.00/2.71 |
% 9.00/2.71 | Equations (238) can reduce 14 to:
% 9.00/2.71 | (239) $false
% 9.00/2.71 |
% 9.00/2.71 |-The branch is then unsatisfiable
% 9.00/2.71 |-Branch two:
% 9.00/2.71 | (258) ~ (all_37_4_67 = 0)
% 9.00/2.71 | (259) all_37_0_63 = all_37_1_64
% 9.00/2.71 |
% 9.00/2.71 | Combining equations (172,259) yields a new equation:
% 9.00/2.71 | (260) all_37_0_63 = all_27_0_40
% 9.00/2.71 |
% 9.00/2.71 | Equations (234) can reduce 258 to:
% 9.00/2.71 | (14) ~ (all_0_7_7 = 0)
% 9.00/2.71 |
% 9.00/2.71 | From (260) and (136) follows:
% 9.00/2.71 | (262) join(all_0_8_8, all_0_4_4, all_0_5_5) = all_27_0_40
% 9.00/2.71 |
% 9.00/2.71 +-Applying beta-rule and splitting (113), into two cases.
% 9.00/2.71 |-Branch one:
% 9.00/2.71 | (263) ~ (all_29_2_47 = 0)
% 9.00/2.71 |
% 9.00/2.71 | Equations (165) can reduce 263 to:
% 9.00/2.71 | (239) $false
% 9.00/2.71 |
% 9.00/2.71 |-The branch is then unsatisfiable
% 9.00/2.71 |-Branch two:
% 9.00/2.71 | (165) all_29_2_47 = 0
% 9.00/2.71 | (266) ~ (all_29_3_48 = 0) | all_29_0_45 = all_29_1_46 | all_29_4_49 = 0
% 9.00/2.71 |
% 9.00/2.71 +-Applying beta-rule and splitting (266), into two cases.
% 9.00/2.71 |-Branch one:
% 9.00/2.71 | (267) ~ (all_29_3_48 = 0)
% 9.00/2.71 |
% 9.00/2.71 | Equations (228) can reduce 267 to:
% 9.00/2.71 | (239) $false
% 9.00/2.71 |
% 9.00/2.71 |-The branch is then unsatisfiable
% 9.00/2.71 |-Branch two:
% 9.00/2.71 | (228) all_29_3_48 = 0
% 9.00/2.71 | (270) all_29_0_45 = all_29_1_46 | all_29_4_49 = 0
% 9.00/2.71 |
% 9.00/2.71 +-Applying beta-rule and splitting (270), into two cases.
% 9.00/2.71 |-Branch one:
% 9.00/2.71 | (271) all_29_4_49 = 0
% 9.00/2.71 |
% 9.00/2.71 | Combining equations (227,271) yields a new equation:
% 9.00/2.71 | (272) all_0_7_7 = 0
% 9.00/2.71 |
% 9.00/2.71 | Simplifying 272 yields:
% 9.00/2.71 | (238) all_0_7_7 = 0
% 9.00/2.71 |
% 9.00/2.71 | Equations (238) can reduce 14 to:
% 9.00/2.71 | (239) $false
% 9.00/2.71 |
% 9.00/2.71 |-The branch is then unsatisfiable
% 9.00/2.71 |-Branch two:
% 9.00/2.71 | (275) ~ (all_29_4_49 = 0)
% 9.00/2.71 | (276) all_29_0_45 = all_29_1_46
% 9.00/2.71 |
% 9.00/2.71 | Combining equations (276,191) yields a new equation:
% 9.00/2.71 | (277) all_29_1_46 = all_27_1_41
% 9.00/2.71 |
% 9.00/2.71 | Simplifying 277 yields:
% 9.00/2.71 | (278) all_29_1_46 = all_27_1_41
% 9.00/2.71 |
% 9.00/2.71 | Combining equations (278,182) yields a new equation:
% 9.00/2.71 | (279) all_27_0_40 = all_27_1_41
% 9.00/2.71 |
% 9.00/2.71 | Equations (227) can reduce 275 to:
% 9.00/2.71 | (14) ~ (all_0_7_7 = 0)
% 9.00/2.71 |
% 9.00/2.71 | From (279) and (262) follows:
% 9.00/2.71 | (281) join(all_0_8_8, all_0_4_4, all_0_5_5) = all_27_1_41
% 9.00/2.71 |
% 9.00/2.71 +-Applying beta-rule and splitting (130), into two cases.
% 9.00/2.71 |-Branch one:
% 9.00/2.71 | (282) ~ (all_35_2_60 = 0)
% 9.00/2.71 |
% 9.00/2.71 | Equations (232) can reduce 282 to:
% 9.00/2.71 | (239) $false
% 9.00/2.71 |
% 9.00/2.71 |-The branch is then unsatisfiable
% 9.00/2.71 |-Branch two:
% 9.00/2.71 | (232) all_35_2_60 = 0
% 9.00/2.71 | (285) ~ (all_35_3_61 = 0) | all_35_0_58 = all_35_1_59 | all_35_4_62 = 0
% 9.00/2.71 |
% 9.00/2.71 +-Applying beta-rule and splitting (243), into two cases.
% 9.00/2.71 |-Branch one:
% 9.00/2.71 | (286) ~ (element(all_0_4_4, all_15_0_17) = 0)
% 9.00/2.71 |
% 9.00/2.71 | From (145) and (286) follows:
% 9.00/2.71 | (287) ~ (element(all_0_4_4, all_0_6_6) = 0)
% 9.00/2.71 |
% 9.00/2.71 | Using (65) and (287) yields:
% 9.00/2.71 | (288) $false
% 9.00/2.71 |
% 9.00/2.71 |-The branch is then unsatisfiable
% 9.00/2.71 |-Branch two:
% 9.00/2.71 | (289) element(all_0_4_4, all_15_0_17) = 0
% 9.00/2.71 | (290) ~ (element(all_0_5_5, all_15_0_17) = 0) | ? [v0] : ? [v1] : (below(all_0_8_8, all_0_4_4, all_0_5_5) = v0 & join(all_0_8_8, all_0_4_4, all_0_5_5) = v1 & ( ~ (v1 = all_0_5_5) | v0 = 0) & ( ~ (v0 = 0) | v1 = all_0_5_5))
% 9.00/2.71 |
% 9.00/2.71 | From (145) and (289) follows:
% 9.00/2.71 | (65) element(all_0_4_4, all_0_6_6) = 0
% 9.00/2.71 |
% 9.00/2.71 +-Applying beta-rule and splitting (242), into two cases.
% 9.00/2.71 |-Branch one:
% 9.00/2.71 | (286) ~ (element(all_0_4_4, all_15_0_17) = 0)
% 9.00/2.71 |
% 9.00/2.71 | From (145) and (286) follows:
% 9.00/2.71 | (287) ~ (element(all_0_4_4, all_0_6_6) = 0)
% 9.00/2.71 |
% 9.00/2.71 | Using (65) and (287) yields:
% 9.00/2.71 | (288) $false
% 9.00/2.71 |
% 9.00/2.71 |-The branch is then unsatisfiable
% 9.00/2.71 |-Branch two:
% 9.00/2.71 | (289) element(all_0_4_4, all_15_0_17) = 0
% 9.00/2.71 | (296) ? [v0] : ? [v1] : (below(all_0_8_8, all_0_4_4, all_0_4_4) = v0 & join(all_0_8_8, all_0_4_4, all_0_4_4) = v1 & ( ~ (v1 = all_0_4_4) | v0 = 0) & ( ~ (v0 = 0) | v1 = all_0_4_4))
% 9.00/2.71 |
% 9.00/2.71 | From (145) and (289) follows:
% 9.00/2.71 | (65) element(all_0_4_4, all_0_6_6) = 0
% 9.00/2.71 |
% 9.00/2.71 +-Applying beta-rule and splitting (245), into two cases.
% 9.00/2.71 |-Branch one:
% 9.00/2.71 | (298) ~ (element(all_0_5_5, all_15_0_17) = 0)
% 9.00/2.71 |
% 9.00/2.71 | From (145) and (298) follows:
% 9.00/2.71 | (299) ~ (element(all_0_5_5, all_0_6_6) = 0)
% 9.00/2.71 |
% 9.00/2.71 | Using (17) and (299) yields:
% 9.00/2.71 | (288) $false
% 9.00/2.71 |
% 9.00/2.71 |-The branch is then unsatisfiable
% 9.00/2.71 |-Branch two:
% 9.00/2.71 | (301) element(all_0_5_5, all_15_0_17) = 0
% 9.00/2.71 | (302) ? [v0] : ? [v1] : (below(all_0_8_8, all_0_5_5, all_0_5_5) = v0 & join(all_0_8_8, all_0_5_5, all_0_5_5) = v1 & ( ~ (v1 = all_0_5_5) | v0 = 0) & ( ~ (v0 = 0) | v1 = all_0_5_5))
% 9.00/2.71 |
% 9.00/2.71 | From (145) and (301) follows:
% 9.00/2.71 | (17) element(all_0_5_5, all_0_6_6) = 0
% 9.00/2.71 |
% 9.00/2.71 +-Applying beta-rule and splitting (285), into two cases.
% 9.00/2.71 |-Branch one:
% 9.00/2.71 | (304) ~ (all_35_3_61 = 0)
% 9.00/2.71 |
% 9.00/2.71 | Equations (231) can reduce 304 to:
% 9.00/2.71 | (239) $false
% 9.00/2.71 |
% 9.00/2.71 |-The branch is then unsatisfiable
% 9.00/2.71 |-Branch two:
% 9.00/2.71 | (231) all_35_3_61 = 0
% 9.00/2.71 | (307) all_35_0_58 = all_35_1_59 | all_35_4_62 = 0
% 9.00/2.71 |
% 9.00/2.71 +-Applying beta-rule and splitting (244), into two cases.
% 9.00/2.71 |-Branch one:
% 9.00/2.71 | (286) ~ (element(all_0_4_4, all_15_0_17) = 0)
% 9.00/2.71 |
% 9.00/2.71 | From (145) and (286) follows:
% 9.00/2.71 | (287) ~ (element(all_0_4_4, all_0_6_6) = 0)
% 9.00/2.71 |
% 9.00/2.71 | Using (65) and (287) yields:
% 9.00/2.71 | (288) $false
% 9.00/2.71 |
% 9.00/2.71 |-The branch is then unsatisfiable
% 9.00/2.71 |-Branch two:
% 9.00/2.71 | (289) element(all_0_4_4, all_15_0_17) = 0
% 9.00/2.71 | (312) ~ (element(all_0_5_5, all_15_0_17) = 0) | ? [v0] : ? [v1] : (below(all_0_8_8, all_0_5_5, all_0_4_4) = v0 & join(all_0_8_8, all_0_5_5, all_0_4_4) = v1 & ( ~ (v1 = all_0_4_4) | v0 = 0) & ( ~ (v0 = 0) | v1 = all_0_4_4))
% 9.00/2.72 |
% 9.00/2.72 +-Applying beta-rule and splitting (307), into two cases.
% 9.00/2.72 |-Branch one:
% 9.00/2.72 | (313) all_35_4_62 = 0
% 9.00/2.72 |
% 9.00/2.72 | Combining equations (230,313) yields a new equation:
% 9.00/2.72 | (272) all_0_7_7 = 0
% 9.00/2.72 |
% 9.00/2.72 | Simplifying 272 yields:
% 9.00/2.72 | (238) all_0_7_7 = 0
% 9.00/2.72 |
% 9.00/2.72 | Equations (238) can reduce 14 to:
% 9.00/2.72 | (239) $false
% 9.00/2.72 |
% 9.00/2.72 |-The branch is then unsatisfiable
% 9.00/2.72 |-Branch two:
% 9.00/2.72 | (317) ~ (all_35_4_62 = 0)
% 9.00/2.72 | (318) all_35_0_58 = all_35_1_59
% 9.00/2.72 |
% 9.00/2.72 | Combining equations (174,318) yields a new equation:
% 9.00/2.72 | (319) all_35_0_58 = all_27_1_41
% 9.00/2.72 |
% 9.00/2.72 | From (319) and (127) follows:
% 9.00/2.72 | (320) join(all_0_8_8, all_0_5_5, all_0_4_4) = all_27_1_41
% 9.00/2.72 |
% 9.00/2.72 +-Applying beta-rule and splitting (290), into two cases.
% 9.00/2.72 |-Branch one:
% 9.00/2.72 | (298) ~ (element(all_0_5_5, all_15_0_17) = 0)
% 9.00/2.72 |
% 9.00/2.72 | From (145) and (298) follows:
% 9.00/2.72 | (299) ~ (element(all_0_5_5, all_0_6_6) = 0)
% 9.00/2.72 |
% 9.00/2.72 | Using (17) and (299) yields:
% 9.00/2.72 | (288) $false
% 9.00/2.72 |
% 9.00/2.72 |-The branch is then unsatisfiable
% 9.00/2.72 |-Branch two:
% 9.00/2.72 | (301) element(all_0_5_5, all_15_0_17) = 0
% 9.00/2.72 | (325) ? [v0] : ? [v1] : (below(all_0_8_8, all_0_4_4, all_0_5_5) = v0 & join(all_0_8_8, all_0_4_4, all_0_5_5) = v1 & ( ~ (v1 = all_0_5_5) | v0 = 0) & ( ~ (v0 = 0) | v1 = all_0_5_5))
% 9.00/2.72 |
% 9.00/2.72 | Instantiating (325) with all_129_0_83, all_129_1_84 yields:
% 9.00/2.72 | (326) below(all_0_8_8, all_0_4_4, all_0_5_5) = all_129_1_84 & join(all_0_8_8, all_0_4_4, all_0_5_5) = all_129_0_83 & ( ~ (all_129_0_83 = all_0_5_5) | all_129_1_84 = 0) & ( ~ (all_129_1_84 = 0) | all_129_0_83 = all_0_5_5)
% 9.00/2.72 |
% 9.00/2.72 | Applying alpha-rule on (326) yields:
% 9.00/2.72 | (327) below(all_0_8_8, all_0_4_4, all_0_5_5) = all_129_1_84
% 9.00/2.72 | (328) join(all_0_8_8, all_0_4_4, all_0_5_5) = all_129_0_83
% 9.00/2.72 | (329) ~ (all_129_0_83 = all_0_5_5) | all_129_1_84 = 0
% 9.00/2.72 | (330) ~ (all_129_1_84 = 0) | all_129_0_83 = all_0_5_5
% 9.00/2.72 |
% 9.00/2.72 | From (145) and (301) follows:
% 9.00/2.72 | (17) element(all_0_5_5, all_0_6_6) = 0
% 9.00/2.72 |
% 9.00/2.72 +-Applying beta-rule and splitting (312), into two cases.
% 9.00/2.72 |-Branch one:
% 9.00/2.72 | (298) ~ (element(all_0_5_5, all_15_0_17) = 0)
% 9.00/2.72 |
% 9.00/2.72 | From (145) and (298) follows:
% 9.00/2.72 | (299) ~ (element(all_0_5_5, all_0_6_6) = 0)
% 9.00/2.72 |
% 9.00/2.72 | Using (17) and (299) yields:
% 9.00/2.72 | (288) $false
% 9.00/2.72 |
% 9.00/2.72 |-The branch is then unsatisfiable
% 9.00/2.72 |-Branch two:
% 9.00/2.72 | (301) element(all_0_5_5, all_15_0_17) = 0
% 9.00/2.72 | (336) ? [v0] : ? [v1] : (below(all_0_8_8, all_0_5_5, all_0_4_4) = v0 & join(all_0_8_8, all_0_5_5, all_0_4_4) = v1 & ( ~ (v1 = all_0_4_4) | v0 = 0) & ( ~ (v0 = 0) | v1 = all_0_4_4))
% 9.00/2.72 |
% 9.00/2.72 | Instantiating (336) with all_147_0_85, all_147_1_86 yields:
% 9.00/2.72 | (337) below(all_0_8_8, all_0_5_5, all_0_4_4) = all_147_1_86 & join(all_0_8_8, all_0_5_5, all_0_4_4) = all_147_0_85 & ( ~ (all_147_0_85 = all_0_4_4) | all_147_1_86 = 0) & ( ~ (all_147_1_86 = 0) | all_147_0_85 = all_0_4_4)
% 9.00/2.72 |
% 9.00/2.72 | Applying alpha-rule on (337) yields:
% 9.00/2.72 | (338) below(all_0_8_8, all_0_5_5, all_0_4_4) = all_147_1_86
% 9.00/2.72 | (339) join(all_0_8_8, all_0_5_5, all_0_4_4) = all_147_0_85
% 9.00/2.72 | (340) ~ (all_147_0_85 = all_0_4_4) | all_147_1_86 = 0
% 9.00/2.72 | (341) ~ (all_147_1_86 = 0) | all_147_0_85 = all_0_4_4
% 9.00/2.72 |
% 9.00/2.72 | Instantiating formula (35) with all_0_8_8, all_0_4_4, all_0_5_5, all_129_1_84, 0 and discharging atoms below(all_0_8_8, all_0_4_4, all_0_5_5) = all_129_1_84, below(all_0_8_8, all_0_4_4, all_0_5_5) = 0, yields:
% 9.00/2.72 | (342) all_129_1_84 = 0
% 9.00/2.72 |
% 9.00/2.72 | Instantiating formula (35) with all_0_8_8, all_0_5_5, all_0_4_4, all_147_1_86, 0 and discharging atoms below(all_0_8_8, all_0_5_5, all_0_4_4) = all_147_1_86, below(all_0_8_8, all_0_5_5, all_0_4_4) = 0, yields:
% 9.00/2.72 | (343) all_147_1_86 = 0
% 9.00/2.72 |
% 9.00/2.72 | Instantiating formula (62) with all_0_8_8, all_0_4_4, all_0_5_5, all_27_1_41, all_129_0_83 and discharging atoms join(all_0_8_8, all_0_4_4, all_0_5_5) = all_129_0_83, join(all_0_8_8, all_0_4_4, all_0_5_5) = all_27_1_41, yields:
% 9.00/2.72 | (344) all_129_0_83 = all_27_1_41
% 9.00/2.72 |
% 9.00/2.72 | Instantiating formula (62) with all_0_8_8, all_0_5_5, all_0_4_4, all_27_1_41, all_147_0_85 and discharging atoms join(all_0_8_8, all_0_5_5, all_0_4_4) = all_147_0_85, join(all_0_8_8, all_0_5_5, all_0_4_4) = all_27_1_41, yields:
% 9.00/2.72 | (345) all_147_0_85 = all_27_1_41
% 9.00/2.72 |
% 9.00/2.72 +-Applying beta-rule and splitting (341), into two cases.
% 9.00/2.72 |-Branch one:
% 9.00/2.72 | (346) ~ (all_147_1_86 = 0)
% 9.00/2.72 |
% 9.00/2.72 | Equations (343) can reduce 346 to:
% 9.00/2.72 | (239) $false
% 9.00/2.72 |
% 9.00/2.72 |-The branch is then unsatisfiable
% 9.00/2.72 |-Branch two:
% 9.00/2.72 | (343) all_147_1_86 = 0
% 9.00/2.72 | (349) all_147_0_85 = all_0_4_4
% 9.00/2.72 |
% 9.00/2.72 | Combining equations (349,345) yields a new equation:
% 9.00/2.72 | (350) all_27_1_41 = all_0_4_4
% 9.00/2.72 |
% 9.00/2.72 | Combining equations (350,344) yields a new equation:
% 9.00/2.72 | (351) all_129_0_83 = all_0_4_4
% 9.00/2.72 |
% 9.00/2.72 +-Applying beta-rule and splitting (330), into two cases.
% 9.00/2.72 |-Branch one:
% 9.00/2.72 | (352) ~ (all_129_1_84 = 0)
% 9.00/2.72 |
% 9.00/2.72 | Equations (342) can reduce 352 to:
% 9.00/2.72 | (239) $false
% 9.00/2.72 |
% 9.00/2.72 |-The branch is then unsatisfiable
% 9.00/2.72 |-Branch two:
% 9.00/2.72 | (342) all_129_1_84 = 0
% 9.00/2.72 | (355) all_129_0_83 = all_0_5_5
% 9.00/2.72 |
% 9.00/2.72 | Combining equations (355,351) yields a new equation:
% 9.00/2.72 | (356) all_0_4_4 = all_0_5_5
% 9.00/2.72 |
% 9.00/2.72 | Equations (356) can reduce 23 to:
% 9.00/2.72 | (239) $false
% 9.00/2.72 |
% 9.00/2.72 |-The branch is then unsatisfiable
% 9.00/2.72 % SZS output end Proof for theBenchmark
% 9.00/2.72
% 9.00/2.72 2101ms
%------------------------------------------------------------------------------