%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU342+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n003.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 08:49:01 EDT 2022 % Result : Theorem 10.03s 2.95s % Output : Proof 22.23s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SEU342+1 : TPTP v8.1.0. Released v3.3.0. % 0.06/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n003.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Mon Jun 20 04:15:59 EDT 2022 % 0.12/0.33 % CPUTime : % 0.18/0.58 ____ _ % 0.18/0.58 ___ / __ \_____(_)___ ________ __________ % 0.18/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.18/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.18/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.18/0.58 % 0.18/0.58 A Theorem Prover for First-Order Logic % 0.18/0.58 (ePrincess v.1.0) % 0.18/0.58 % 0.18/0.58 (c) Philipp Rümmer, 2009-2015 % 0.18/0.58 (c) Peter Backeman, 2014-2015 % 0.18/0.58 (contributions by Angelo Brillout, Peter Baumgartner) % 0.18/0.58 Free software under GNU Lesser General Public License (LGPL). % 0.18/0.58 Bug reports to peter@backeman.se % 0.18/0.58 % 0.18/0.58 For more information, visit http://user.uu.se/~petba168/breu/ % 0.18/0.58 % 0.18/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.74/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.62/0.96 Prover 0: Preprocessing ... % 2.49/1.23 Prover 0: Warning: ignoring some quantifiers % 2.61/1.26 Prover 0: Constructing countermodel ... % 4.98/1.77 Prover 0: gave up % 4.98/1.77 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 5.05/1.81 Prover 1: Preprocessing ... % 5.67/1.93 Prover 1: Warning: ignoring some quantifiers % 5.67/1.93 Prover 1: Constructing countermodel ... % 7.86/2.52 Prover 1: gave up % 7.86/2.52 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 8.29/2.55 Prover 2: Preprocessing ... % 8.92/2.69 Prover 2: Warning: ignoring some quantifiers % 8.92/2.70 Prover 2: Constructing countermodel ... % 10.03/2.94 Prover 2: proved (423ms) % 10.03/2.95 % 10.03/2.95 No countermodel exists, formula is valid % 10.03/2.95 % SZS status Theorem for theBenchmark % 10.03/2.95 % 10.03/2.95 Generating proof ... Warning: ignoring some quantifiers % 21.09/5.60 found it (size 440) % 21.09/5.60 % 21.09/5.60 % SZS output start Proof for theBenchmark % 21.09/5.60 Assumed formulas after preprocessing and simplification: % 21.09/5.60 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ( ~ (v12 = 0) & ~ (v10 = 0) & ~ (v1 = 0) & below_refl(v0, v4, v5) = v8 & the_carrier(v0) = v2 & join_semilatt_str(v15) = 0 & one_sorted_str(v16) = 0 & one_sorted_str(v9) = 0 & meet_semilatt_str(v17) = 0 & ordered_pair_as_product_element(v2, v2, v4, v5) = v6 & empty(v13) = 0 & empty(v11) = v12 & empty(empty_set) = 0 & element(v5, v2) = 0 & element(v4, v2) = 0 & relation_of_lattice(v0) = v3 & lattice(v0) = 0 & latt_str(v14) = 0 & latt_str(v0) = 0 & empty_carrier(v9) = v10 & empty_carrier(v0) = v1 & in(v6, v3) = v7 & ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v19 = v18 | ~ (ordered_pair_as_product_element(v23, v22, v21, v20) = v19) | ~ (ordered_pair_as_product_element(v23, v22, v21, v20) = v18)) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v22 = 0 | ~ (below_refl(v18, v19, v19) = v22) | ~ (the_carrier(v18) = v21) | ~ (element(v20, v21) = 0) | ? [v23] : ((v23 = 0 & empty_carrier(v18) = 0) | ( ~ (v23 = 0) & element(v19, v21) = v23) | ( ~ (v23 = 0) & latt_str(v18) = v23) | ( ~ (v23 = 0) & meet_commutative(v18) = v23) | ( ~ (v23 = 0) & meet_absorbing(v18) = v23) | ( ~ (v23 = 0) & join_absorbing(v18) = v23))) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v21 = v19 | ~ (ordered_pair(v20, v21) = v22) | ~ (ordered_pair(v18, v19) = v22)) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v20 = v18 | ~ (ordered_pair(v20, v21) = v22) | ~ (ordered_pair(v18, v19) = v22)) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v19 = v18 | ~ (below(v22, v21, v20) = v19) | ~ (below(v22, v21, v20) = v18)) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v19 = v18 | ~ (below_refl(v22, v21, v20) = v19) | ~ (below_refl(v22, v21, v20) = v18)) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (ordered_pair_as_product_element(v18, v19, v20, v21) = v22) | ? [v23] : ? [v24] : ((v24 = 0 & cartesian_product2(v18, v19) = v23 & element(v22, v23) = 0) | (v23 = 0 & empty(v19) = 0) | (v23 = 0 & empty(v18) = 0) | ( ~ (v23 = 0) & element(v21, v19) = v23) | ( ~ (v23 = 0) & element(v20, v18) = v23))) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (ordered_pair_as_product_element(v18, v19, v20, v21) = v22) | ? [v23] : ((v23 = v22 & ordered_pair(v20, v21) = v22) | (v23 = 0 & empty(v19) = 0) | (v23 = 0 & empty(v18) = 0) | ( ~ (v23 = 0) & element(v21, v19) = v23) | ( ~ (v23 = 0) & element(v20, v18) = v23))) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v19 = v18 | ~ (cartesian_product2(v21, v20) = v19) | ~ (cartesian_product2(v21, v20) = v18)) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v19 = v18 | ~ (element(v21, v20) = v19) | ~ (element(v21, v20) = v18)) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v19 = v18 | ~ (ordered_pair(v21, v20) = v19) | ~ (ordered_pair(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 | ~ (in(v21, v20) = v19) | ~ (in(v21, v20) = v18)) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (below(v18, v19, v20) = v21) | ? [v22] : ? [v23] : ((v22 = 0 & empty_carrier(v18) = 0) | ( ~ (v23 = 0) & the_carrier(v18) = v22 & element(v20, v22) = v23) | ( ~ (v23 = 0) & the_carrier(v18) = v22 & element(v19, v22) = v23) | ( ~ (v22 = 0) & latt_str(v18) = v22) | ( ~ (v22 = 0) & meet_commutative(v18) = v22) | ( ~ (v22 = 0) & meet_absorbing(v18) = v22) | ( ~ (v22 = 0) & join_absorbing(v18) = v22) | (( ~ (v21 = 0) | (v22 = 0 & below_refl(v18, v19, v20) = 0)) & (v21 = 0 | ( ~ (v22 = 0) & below_refl(v18, v19, v20) = v22))))) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (below_refl(v18, v19, v20) = v21) | ? [v22] : ? [v23] : ((v22 = 0 & empty_carrier(v18) = 0) | ( ~ (v23 = 0) & the_carrier(v18) = v22 & element(v20, v22) = v23) | ( ~ (v23 = 0) & the_carrier(v18) = v22 & element(v19, v22) = v23) | ( ~ (v22 = 0) & latt_str(v18) = v22) | ( ~ (v22 = 0) & meet_commutative(v18) = v22) | ( ~ (v22 = 0) & meet_absorbing(v18) = v22) | ( ~ (v22 = 0) & join_absorbing(v18) = v22) | (( ~ (v21 = 0) | (v22 = 0 & below(v18, v19, v20) = 0)) & (v21 = 0 | ( ~ (v22 = 0) & below(v18, v19, v20) = v22))))) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (the_carrier(v18) = v21) | ~ (element(v20, v21) = 0) | ~ (element(v19, v21) = 0) | ? [v22] : ((v22 = 0 & below_refl(v18, v19, v19) = 0) | (v22 = 0 & empty_carrier(v18) = 0) | ( ~ (v22 = 0) & latt_str(v18) = v22) | ( ~ (v22 = 0) & meet_commutative(v18) = v22) | ( ~ (v22 = 0) & meet_absorbing(v18) = v22) | ( ~ (v22 = 0) & join_absorbing(v18) = v22))) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (a_1_0_filter_1(v19) = v20) | ~ (in(v18, v20) = v21) | ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : ? [v27] : ? [v28] : ((v22 = 0 & empty_carrier(v19) = 0) | ( ~ (v22 = 0) & lattice(v19) = v22) | ( ~ (v22 = 0) & latt_str(v19) = v22) | (( ~ (v21 = 0) | (v28 = 0 & v27 = v18 & v26 = 0 & v25 = 0 & below_refl(v19, v23, v24) = 0 & the_carrier(v19) = v22 & ordered_pair_as_product_element(v22, v22, v23, v24) = v18 & element(v24, v22) = 0 & element(v23, v22) = 0)) & (v21 = 0 | (the_carrier(v19) = v22 & ! [v29] : ! [v30] : ( ~ (below_refl(v19, v29, v30) = 0) | ? [v31] : (( ~ (v31 = v18) & ordered_pair_as_product_element(v22, v22, v29, v30) = v31) | ( ~ (v31 = 0) & element(v30, v22) = v31) | ( ~ (v31 = 0) & element(v29, v22) = v31))) & ! [v29] : ! [v30] : ( ~ (ordered_pair_as_product_element(v22, v22, v29, v30) = v18) | ? [v31] : (( ~ (v31 = 0) & below_refl(v19, v29, v30) = v31) | ( ~ (v31 = 0) & element(v30, v22) = v31) | ( ~ (v31 = 0) & element(v29, v22) = v31)))))))) & ! [v18] : ! [v19] : ! [v20] : (v20 = 0 | ~ (element(v18, v19) = v20) | ? [v21] : ( ~ (v21 = 0) & in(v18, v19) = v21)) & ! [v18] : ! [v19] : ! [v20] : (v20 = 0 | ~ (in(v18, v19) = v20) | ? [v21] : ((v21 = 0 & empty(v19) = 0) | ( ~ (v21 = 0) & element(v18, v19) = v21))) & ! [v18] : ! [v19] : ! [v20] : (v19 = v18 | ~ (the_carrier(v20) = v19) | ~ (the_carrier(v20) = v18)) & ! [v18] : ! [v19] : ! [v20] : (v19 = v18 | ~ (join_semilatt_str(v20) = v19) | ~ (join_semilatt_str(v20) = v18)) & ! [v18] : ! [v19] : ! [v20] : (v19 = v18 | ~ (one_sorted_str(v20) = v19) | ~ (one_sorted_str(v20) = v18)) & ! [v18] : ! [v19] : ! [v20] : (v19 = v18 | ~ (meet_semilatt_str(v20) = v19) | ~ (meet_semilatt_str(v20) = v18)) & ! [v18] : ! [v19] : ! [v20] : (v19 = v18 | ~ (relation(v20) = v19) | ~ (relation(v20) = v18)) & ! [v18] : ! [v19] : ! [v20] : (v19 = v18 | ~ (empty(v20) = v19) | ~ (empty(v20) = v18)) & ! [v18] : ! [v19] : ! [v20] : (v19 = v18 | ~ (relation_of_lattice(v20) = v19) | ~ (relation_of_lattice(v20) = v18)) & ! [v18] : ! [v19] : ! [v20] : (v19 = v18 | ~ (a_1_0_filter_1(v20) = v19) | ~ (a_1_0_filter_1(v20) = v18)) & ! [v18] : ! [v19] : ! [v20] : (v19 = v18 | ~ (singleton(v20) = v19) | ~ (singleton(v20) = v18)) & ! [v18] : ! [v19] : ! [v20] : (v19 = v18 | ~ (lattice(v20) = v19) | ~ (lattice(v20) = v18)) & ! [v18] : ! [v19] : ! [v20] : (v19 = v18 | ~ (latt_str(v20) = v19) | ~ (latt_str(v20) = v18)) & ! [v18] : ! [v19] : ! [v20] : (v19 = v18 | ~ (empty_carrier(v20) = v19) | ~ (empty_carrier(v20) = v18)) & ! [v18] : ! [v19] : ! [v20] : (v19 = v18 | ~ (join_commutative(v20) = v19) | ~ (join_commutative(v20) = v18)) & ! [v18] : ! [v19] : ! [v20] : (v19 = v18 | ~ (join_associative(v20) = v19) | ~ (join_associative(v20) = v18)) & ! [v18] : ! [v19] : ! [v20] : (v19 = v18 | ~ (meet_commutative(v20) = v19) | ~ (meet_commutative(v20) = v18)) & ! [v18] : ! [v19] : ! [v20] : (v19 = v18 | ~ (meet_associative(v20) = v19) | ~ (meet_associative(v20) = v18)) & ! [v18] : ! [v19] : ! [v20] : (v19 = v18 | ~ (meet_absorbing(v20) = v19) | ~ (meet_absorbing(v20) = v18)) & ! [v18] : ! [v19] : ! [v20] : (v19 = v18 | ~ (join_absorbing(v20) = v19) | ~ (join_absorbing(v20) = v18)) & ! [v18] : ! [v19] : ! [v20] : ( ~ (cartesian_product2(v18, v19) = v20) | ? [v21] : ((v21 = 0 & empty(v19) = 0) | (v21 = 0 & empty(v18) = 0) | ( ~ (v21 = 0) & empty(v20) = v21))) & ! [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] : ( ~ (unordered_pair(v19, v18) = v20) | unordered_pair(v18, v19) = v20) & ! [v18] : ! [v19] : ! [v20] : ( ~ (unordered_pair(v18, v19) = v20) | unordered_pair(v19, v18) = v20) & ! [v18] : ! [v19] : ! [v20] : ( ~ (unordered_pair(v18, v19) = v20) | ? [v21] : ? [v22] : (ordered_pair(v18, v19) = v21 & singleton(v18) = v22 & unordered_pair(v20, v22) = v21)) & ! [v18] : ! [v19] : ! [v20] : ( ~ (unordered_pair(v18, v19) = v20) | ? [v21] : ( ~ (v21 = 0) & empty(v20) = v21)) & ! [v18] : ! [v19] : (v19 = v18 | ~ (empty(v19) = 0) | ~ (empty(v18) = 0)) & ! [v18] : ! [v19] : (v19 = 0 | ~ (one_sorted_str(v18) = v19) | ? [v20] : ( ~ (v20 = 0) & join_semilatt_str(v18) = v20)) & ! [v18] : ! [v19] : (v19 = 0 | ~ (one_sorted_str(v18) = v19) | ? [v20] : ( ~ (v20 = 0) & meet_semilatt_str(v18) = v20)) & ! [v18] : ! [v19] : (v19 = 0 | ~ (empty_carrier(v18) = v19) | ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ((v25 = 0 & v24 = 0 & v23 = 0 & v22 = 0 & v21 = 0 & v20 = 0 & join_commutative(v18) = 0 & join_associative(v18) = 0 & meet_commutative(v18) = 0 & meet_associative(v18) = 0 & meet_absorbing(v18) = 0 & join_absorbing(v18) = 0) | ( ~ (v20 = 0) & lattice(v18) = v20) | ( ~ (v20 = 0) & latt_str(v18) = v20))) & ! [v18] : ! [v19] : (v19 = 0 | ~ (empty_carrier(v18) = v19) | ? [v20] : ? [v21] : ((v21 = v20 & relation_of_lattice(v18) = v20 & a_1_0_filter_1(v18) = v20) | ( ~ (v20 = 0) & lattice(v18) = v20) | ( ~ (v20 = 0) & latt_str(v18) = v20))) & ! [v18] : ! [v19] : (v19 = 0 | ~ (empty_carrier(v18) = v19) | ? [v20] : ? [v21] : ((v21 = 0 & relation(v20) = 0 & relation_of_lattice(v18) = v20) | ( ~ (v20 = 0) & lattice(v18) = v20) | ( ~ (v20 = 0) & latt_str(v18) = v20))) & ! [v18] : ! [v19] : (v19 = 0 | ~ (empty_carrier(v18) = v19) | ? [v20] : ? [v21] : (( ~ (v21 = 0) & the_carrier(v18) = v20 & empty(v20) = v21) | ( ~ (v20 = 0) & one_sorted_str(v18) = v20))) & ! [v18] : ! [v19] : (v19 = 0 | ~ (empty_carrier(v18) = v19) | ? [v20] : ((v20 = 0 & lattice(v18) = 0) | ( ~ (v20 = 0) & latt_str(v18) = v20) | ( ~ (v20 = 0) & join_commutative(v18) = v20) | ( ~ (v20 = 0) & join_associative(v18) = v20) | ( ~ (v20 = 0) & meet_commutative(v18) = v20) | ( ~ (v20 = 0) & meet_associative(v18) = v20) | ( ~ (v20 = 0) & meet_absorbing(v18) = v20) | ( ~ (v20 = 0) & join_absorbing(v18) = v20))) & ! [v18] : ! [v19] : ( ~ (the_carrier(v18) = v19) | ? [v20] : ((v20 = 0 & empty_carrier(v18) = 0) | ( ~ (v20 = 0) & one_sorted_str(v18) = v20) | ( ~ (v20 = 0) & empty(v19) = v20))) & ! [v18] : ! [v19] : ( ~ (join_semilatt_str(v18) = v19) | ? [v20] : ((v20 = 0 & v19 = 0 & meet_semilatt_str(v18) = 0) | ( ~ (v20 = 0) & latt_str(v18) = v20))) & ! [v18] : ! [v19] : ( ~ (meet_semilatt_str(v18) = v19) | ? [v20] : ((v20 = 0 & v19 = 0 & join_semilatt_str(v18) = 0) | ( ~ (v20 = 0) & latt_str(v18) = v20))) & ! [v18] : ! [v19] : ( ~ (element(v18, v19) = 0) | ? [v20] : ((v20 = 0 & empty(v19) = 0) | (v20 = 0 & in(v18, v19) = 0))) & ! [v18] : ! [v19] : ( ~ (relation_of_lattice(v18) = v19) | ? [v20] : ((v20 = v19 & a_1_0_filter_1(v18) = v19) | (v20 = 0 & empty_carrier(v18) = 0) | ( ~ (v20 = 0) & lattice(v18) = v20) | ( ~ (v20 = 0) & latt_str(v18) = v20))) & ! [v18] : ! [v19] : ( ~ (relation_of_lattice(v18) = v19) | ? [v20] : ((v20 = 0 & relation(v19) = 0) | (v20 = 0 & empty_carrier(v18) = 0) | ( ~ (v20 = 0) & lattice(v18) = v20) | ( ~ (v20 = 0) & latt_str(v18) = v20))) & ! [v18] : ! [v19] : ( ~ (a_1_0_filter_1(v18) = v19) | ? [v20] : ((v20 = v19 & relation_of_lattice(v18) = v19) | (v20 = 0 & empty_carrier(v18) = 0) | ( ~ (v20 = 0) & lattice(v18) = v20) | ( ~ (v20 = 0) & latt_str(v18) = v20))) & ! [v18] : ! [v19] : ( ~ (singleton(v18) = v19) | ? [v20] : ( ~ (v20 = 0) & empty(v19) = v20)) & ! [v18] : ! [v19] : ( ~ (lattice(v18) = v19) | ? [v20] : ((v20 = 0 & empty_carrier(v18) = 0) | (v19 = 0 & ~ (v20 = 0) & empty_carrier(v18) = v20) | ( ~ (v20 = 0) & latt_str(v18) = v20) | ( ~ (v20 = 0) & join_commutative(v18) = v20) | ( ~ (v20 = 0) & join_associative(v18) = v20) | ( ~ (v20 = 0) & meet_commutative(v18) = v20) | ( ~ (v20 = 0) & meet_associative(v18) = v20) | ( ~ (v20 = 0) & meet_absorbing(v18) = v20) | ( ~ (v20 = 0) & join_absorbing(v18) = v20))) & ! [v18] : ! [v19] : ( ~ (join_commutative(v18) = v19) | ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ((v25 = 0 & v24 = 0 & v23 = 0 & v22 = 0 & v21 = 0 & v19 = 0 & ~ (v20 = 0) & empty_carrier(v18) = v20 & join_associative(v18) = 0 & meet_commutative(v18) = 0 & meet_associative(v18) = 0 & meet_absorbing(v18) = 0 & join_absorbing(v18) = 0) | (v20 = 0 & empty_carrier(v18) = 0) | ( ~ (v20 = 0) & lattice(v18) = v20) | ( ~ (v20 = 0) & latt_str(v18) = v20))) & ! [v18] : ! [v19] : ( ~ (join_associative(v18) = v19) | ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ((v25 = 0 & v24 = 0 & v23 = 0 & v22 = 0 & v21 = 0 & v19 = 0 & ~ (v20 = 0) & empty_carrier(v18) = v20 & join_commutative(v18) = 0 & meet_commutative(v18) = 0 & meet_associative(v18) = 0 & meet_absorbing(v18) = 0 & join_absorbing(v18) = 0) | (v20 = 0 & empty_carrier(v18) = 0) | ( ~ (v20 = 0) & lattice(v18) = v20) | ( ~ (v20 = 0) & latt_str(v18) = v20))) & ! [v18] : ! [v19] : ( ~ (meet_commutative(v18) = v19) | ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ((v25 = 0 & v24 = 0 & v23 = 0 & v22 = 0 & v21 = 0 & v19 = 0 & ~ (v20 = 0) & empty_carrier(v18) = v20 & join_commutative(v18) = 0 & join_associative(v18) = 0 & meet_associative(v18) = 0 & meet_absorbing(v18) = 0 & join_absorbing(v18) = 0) | (v20 = 0 & empty_carrier(v18) = 0) | ( ~ (v20 = 0) & lattice(v18) = v20) | ( ~ (v20 = 0) & latt_str(v18) = v20))) & ! [v18] : ! [v19] : ( ~ (meet_associative(v18) = v19) | ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ((v25 = 0 & v24 = 0 & v23 = 0 & v22 = 0 & v21 = 0 & v19 = 0 & ~ (v20 = 0) & empty_carrier(v18) = v20 & join_commutative(v18) = 0 & join_associative(v18) = 0 & meet_commutative(v18) = 0 & meet_absorbing(v18) = 0 & join_absorbing(v18) = 0) | (v20 = 0 & empty_carrier(v18) = 0) | ( ~ (v20 = 0) & lattice(v18) = v20) | ( ~ (v20 = 0) & latt_str(v18) = v20))) & ! [v18] : ! [v19] : ( ~ (meet_absorbing(v18) = v19) | ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ((v25 = 0 & v24 = 0 & v23 = 0 & v22 = 0 & v21 = 0 & v19 = 0 & ~ (v20 = 0) & empty_carrier(v18) = v20 & join_commutative(v18) = 0 & join_associative(v18) = 0 & meet_commutative(v18) = 0 & meet_associative(v18) = 0 & join_absorbing(v18) = 0) | (v20 = 0 & empty_carrier(v18) = 0) | ( ~ (v20 = 0) & lattice(v18) = v20) | ( ~ (v20 = 0) & latt_str(v18) = v20))) & ! [v18] : ! [v19] : ( ~ (join_absorbing(v18) = v19) | ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ((v25 = 0 & v24 = 0 & v23 = 0 & v22 = 0 & v21 = 0 & v19 = 0 & ~ (v20 = 0) & empty_carrier(v18) = v20 & join_commutative(v18) = 0 & join_associative(v18) = 0 & meet_commutative(v18) = 0 & meet_associative(v18) = 0 & meet_absorbing(v18) = 0) | (v20 = 0 & empty_carrier(v18) = 0) | ( ~ (v20 = 0) & lattice(v18) = v20) | ( ~ (v20 = 0) & latt_str(v18) = v20))) & ! [v18] : ! [v19] : ( ~ (in(v19, v18) = 0) | ? [v20] : ( ~ (v20 = 0) & in(v18, v19) = v20)) & ! [v18] : ! [v19] : ( ~ (in(v18, v19) = 0) | element(v18, v19) = 0) & ! [v18] : ! [v19] : ( ~ (in(v18, v19) = 0) | ? [v20] : ( ~ (v20 = 0) & empty(v19) = v20)) & ! [v18] : ! [v19] : ( ~ (in(v18, v19) = 0) | ? [v20] : ( ~ (v20 = 0) & in(v19, v18) = v20)) & ! [v18] : (v18 = empty_set | ~ (empty(v18) = 0)) & ! [v18] : ( ~ (join_semilatt_str(v18) = 0) | one_sorted_str(v18) = 0) & ! [v18] : ( ~ (one_sorted_str(v18) = 0) | ? [v19] : ? [v20] : ((v19 = 0 & empty_carrier(v18) = 0) | ( ~ (v20 = 0) & the_carrier(v18) = v19 & empty(v19) = v20))) & ! [v18] : ( ~ (meet_semilatt_str(v18) = 0) | one_sorted_str(v18) = 0) & ! [v18] : ( ~ (lattice(v18) = 0) | ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ((v25 = 0 & v24 = 0 & v23 = 0 & v22 = 0 & v21 = 0 & v20 = 0 & ~ (v19 = 0) & empty_carrier(v18) = v19 & join_commutative(v18) = 0 & join_associative(v18) = 0 & meet_commutative(v18) = 0 & meet_associative(v18) = 0 & meet_absorbing(v18) = 0 & join_absorbing(v18) = 0) | (v19 = 0 & empty_carrier(v18) = 0) | ( ~ (v19 = 0) & latt_str(v18) = v19))) & ! [v18] : ( ~ (lattice(v18) = 0) | ? [v19] : ? [v20] : ((v20 = v19 & relation_of_lattice(v18) = v19 & a_1_0_filter_1(v18) = v19) | (v19 = 0 & empty_carrier(v18) = 0) | ( ~ (v19 = 0) & latt_str(v18) = v19))) & ! [v18] : ( ~ (lattice(v18) = 0) | ? [v19] : ? [v20] : ((v20 = 0 & relation(v19) = 0 & relation_of_lattice(v18) = v19) | (v19 = 0 & empty_carrier(v18) = 0) | ( ~ (v19 = 0) & latt_str(v18) = v19))) & ! [v18] : ( ~ (latt_str(v18) = 0) | ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ((v25 = 0 & v24 = 0 & v23 = 0 & v22 = 0 & v21 = 0 & v20 = 0 & ~ (v19 = 0) & empty_carrier(v18) = v19 & join_commutative(v18) = 0 & join_associative(v18) = 0 & meet_commutative(v18) = 0 & meet_associative(v18) = 0 & meet_absorbing(v18) = 0 & join_absorbing(v18) = 0) | (v19 = 0 & empty_carrier(v18) = 0) | ( ~ (v19 = 0) & lattice(v18) = v19))) & ! [v18] : ( ~ (latt_str(v18) = 0) | ? [v19] : ? [v20] : ((v20 = v19 & relation_of_lattice(v18) = v19 & a_1_0_filter_1(v18) = v19) | (v19 = 0 & empty_carrier(v18) = 0) | ( ~ (v19 = 0) & lattice(v18) = v19))) & ! [v18] : ( ~ (latt_str(v18) = 0) | ? [v19] : ? [v20] : ((v20 = 0 & ~ (v19 = 0) & lattice(v18) = 0 & empty_carrier(v18) = v19) | (v19 = 0 & empty_carrier(v18) = 0) | ( ~ (v19 = 0) & join_commutative(v18) = v19) | ( ~ (v19 = 0) & join_associative(v18) = v19) | ( ~ (v19 = 0) & meet_commutative(v18) = v19) | ( ~ (v19 = 0) & meet_associative(v18) = v19) | ( ~ (v19 = 0) & meet_absorbing(v18) = v19) | ( ~ (v19 = 0) & join_absorbing(v18) = v19))) & ! [v18] : ( ~ (latt_str(v18) = 0) | ? [v19] : ? [v20] : ((v20 = 0 & relation(v19) = 0 & relation_of_lattice(v18) = v19) | (v19 = 0 & empty_carrier(v18) = 0) | ( ~ (v19 = 0) & lattice(v18) = v19))) & ! [v18] : ( ~ (latt_str(v18) = 0) | (join_semilatt_str(v18) = 0 & meet_semilatt_str(v18) = 0)) & ! [v18] : ( ~ (join_commutative(v18) = 0) | ? [v19] : ? [v20] : ((v20 = 0 & ~ (v19 = 0) & lattice(v18) = 0 & empty_carrier(v18) = v19) | (v19 = 0 & empty_carrier(v18) = 0) | ( ~ (v19 = 0) & latt_str(v18) = v19) | ( ~ (v19 = 0) & join_associative(v18) = v19) | ( ~ (v19 = 0) & meet_commutative(v18) = v19) | ( ~ (v19 = 0) & meet_associative(v18) = v19) | ( ~ (v19 = 0) & meet_absorbing(v18) = v19) | ( ~ (v19 = 0) & join_absorbing(v18) = v19))) & ! [v18] : ( ~ (join_associative(v18) = 0) | ? [v19] : ? [v20] : ((v20 = 0 & ~ (v19 = 0) & lattice(v18) = 0 & empty_carrier(v18) = v19) | (v19 = 0 & empty_carrier(v18) = 0) | ( ~ (v19 = 0) & latt_str(v18) = v19) | ( ~ (v19 = 0) & join_commutative(v18) = v19) | ( ~ (v19 = 0) & meet_commutative(v18) = v19) | ( ~ (v19 = 0) & meet_associative(v18) = v19) | ( ~ (v19 = 0) & meet_absorbing(v18) = v19) | ( ~ (v19 = 0) & join_absorbing(v18) = v19))) & ! [v18] : ( ~ (meet_commutative(v18) = 0) | ? [v19] : ? [v20] : ((v20 = 0 & ~ (v19 = 0) & lattice(v18) = 0 & empty_carrier(v18) = v19) | (v19 = 0 & empty_carrier(v18) = 0) | ( ~ (v19 = 0) & latt_str(v18) = v19) | ( ~ (v19 = 0) & join_commutative(v18) = v19) | ( ~ (v19 = 0) & join_associative(v18) = v19) | ( ~ (v19 = 0) & meet_associative(v18) = v19) | ( ~ (v19 = 0) & meet_absorbing(v18) = v19) | ( ~ (v19 = 0) & join_absorbing(v18) = v19))) & ! [v18] : ( ~ (meet_associative(v18) = 0) | ? [v19] : ? [v20] : ((v20 = 0 & ~ (v19 = 0) & lattice(v18) = 0 & empty_carrier(v18) = v19) | (v19 = 0 & empty_carrier(v18) = 0) | ( ~ (v19 = 0) & latt_str(v18) = v19) | ( ~ (v19 = 0) & join_commutative(v18) = v19) | ( ~ (v19 = 0) & join_associative(v18) = v19) | ( ~ (v19 = 0) & meet_commutative(v18) = v19) | ( ~ (v19 = 0) & meet_absorbing(v18) = v19) | ( ~ (v19 = 0) & join_absorbing(v18) = v19))) & ! [v18] : ( ~ (meet_absorbing(v18) = 0) | ? [v19] : ? [v20] : ((v20 = 0 & ~ (v19 = 0) & lattice(v18) = 0 & empty_carrier(v18) = v19) | (v19 = 0 & empty_carrier(v18) = 0) | ( ~ (v19 = 0) & latt_str(v18) = v19) | ( ~ (v19 = 0) & join_commutative(v18) = v19) | ( ~ (v19 = 0) & join_associative(v18) = v19) | ( ~ (v19 = 0) & meet_commutative(v18) = v19) | ( ~ (v19 = 0) & meet_associative(v18) = v19) | ( ~ (v19 = 0) & join_absorbing(v18) = v19))) & ! [v18] : ( ~ (join_absorbing(v18) = 0) | ? [v19] : ? [v20] : ((v20 = 0 & ~ (v19 = 0) & lattice(v18) = 0 & empty_carrier(v18) = v19) | (v19 = 0 & empty_carrier(v18) = 0) | ( ~ (v19 = 0) & latt_str(v18) = v19) | ( ~ (v19 = 0) & join_commutative(v18) = v19) | ( ~ (v19 = 0) & join_associative(v18) = v19) | ( ~ (v19 = 0) & meet_commutative(v18) = v19) | ( ~ (v19 = 0) & meet_associative(v18) = v19) | ( ~ (v19 = 0) & meet_absorbing(v18) = v19))) & ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ordered_pair_as_product_element(v21, v20, v19, v18) = v22 & ? [v18] : ? [v19] : ? [v20] : ? [v21] : below(v20, v19, v18) = v21 & ? [v18] : ? [v19] : ? [v20] : ? [v21] : below_refl(v20, v19, v18) = v21 & ? [v18] : ? [v19] : ? [v20] : cartesian_product2(v19, v18) = v20 & ? [v18] : ? [v19] : ? [v20] : element(v19, v18) = v20 & ? [v18] : ? [v19] : ? [v20] : ordered_pair(v19, v18) = v20 & ? [v18] : ? [v19] : ? [v20] : unordered_pair(v19, v18) = v20 & ? [v18] : ? [v19] : ? [v20] : in(v19, v18) = v20 & ? [v18] : ? [v19] : (v19 = v18 | ? [v20] : ? [v21] : ? [v22] : (((v22 = 0 & in(v20, v19) = 0) | (v21 = 0 & in(v20, v18) = 0)) & (( ~ (v22 = 0) & in(v20, v19) = v22) | ( ~ (v21 = 0) & in(v20, v18) = v21)))) & ? [v18] : ? [v19] : the_carrier(v18) = v19 & ? [v18] : ? [v19] : join_semilatt_str(v18) = v19 & ? [v18] : ? [v19] : one_sorted_str(v18) = v19 & ? [v18] : ? [v19] : meet_semilatt_str(v18) = v19 & ? [v18] : ? [v19] : relation(v18) = v19 & ? [v18] : ? [v19] : empty(v18) = v19 & ? [v18] : ? [v19] : element(v19, v18) = 0 & ? [v18] : ? [v19] : relation_of_lattice(v18) = v19 & ? [v18] : ? [v19] : a_1_0_filter_1(v18) = v19 & ? [v18] : ? [v19] : singleton(v18) = v19 & ? [v18] : ? [v19] : lattice(v18) = v19 & ? [v18] : ? [v19] : latt_str(v18) = v19 & ? [v18] : ? [v19] : empty_carrier(v18) = v19 & ? [v18] : ? [v19] : join_commutative(v18) = v19 & ? [v18] : ? [v19] : join_associative(v18) = v19 & ? [v18] : ? [v19] : meet_commutative(v18) = v19 & ? [v18] : ? [v19] : meet_associative(v18) = v19 & ? [v18] : ? [v19] : meet_absorbing(v18) = v19 & ? [v18] : ? [v19] : join_absorbing(v18) = v19 & ((v8 = 0 & ~ (v7 = 0)) | (v7 = 0 & ~ (v8 = 0)))) % 21.51/5.67 | 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: % 21.51/5.67 | (1) ~ (all_0_5_5 = 0) & ~ (all_0_7_7 = 0) & ~ (all_0_16_16 = 0) & below_refl(all_0_17_17, all_0_13_13, all_0_12_12) = all_0_9_9 & the_carrier(all_0_17_17) = all_0_15_15 & join_semilatt_str(all_0_2_2) = 0 & one_sorted_str(all_0_1_1) = 0 & one_sorted_str(all_0_8_8) = 0 & meet_semilatt_str(all_0_0_0) = 0 & ordered_pair_as_product_element(all_0_15_15, all_0_15_15, all_0_13_13, all_0_12_12) = all_0_11_11 & empty(all_0_4_4) = 0 & empty(all_0_6_6) = all_0_5_5 & empty(empty_set) = 0 & element(all_0_12_12, all_0_15_15) = 0 & element(all_0_13_13, all_0_15_15) = 0 & relation_of_lattice(all_0_17_17) = all_0_14_14 & lattice(all_0_17_17) = 0 & latt_str(all_0_3_3) = 0 & latt_str(all_0_17_17) = 0 & empty_carrier(all_0_8_8) = all_0_7_7 & empty_carrier(all_0_17_17) = all_0_16_16 & in(all_0_11_11, all_0_14_14) = all_0_10_10 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (ordered_pair_as_product_element(v5, v4, v3, v2) = v1) | ~ (ordered_pair_as_product_element(v5, v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (below_refl(v0, v1, v1) = v4) | ~ (the_carrier(v0) = v3) | ~ (element(v2, v3) = 0) | ? [v5] : ((v5 = 0 & empty_carrier(v0) = 0) | ( ~ (v5 = 0) & element(v1, v3) = v5) | ( ~ (v5 = 0) & latt_str(v0) = v5) | ( ~ (v5 = 0) & meet_commutative(v0) = v5) | ( ~ (v5 = 0) & meet_absorbing(v0) = v5) | ( ~ (v5 = 0) & join_absorbing(v0) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v1 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v0 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (below(v4, v3, v2) = v1) | ~ (below(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (below_refl(v4, v3, v2) = v1) | ~ (below_refl(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (ordered_pair_as_product_element(v0, v1, v2, v3) = v4) | ? [v5] : ? [v6] : ((v6 = 0 & cartesian_product2(v0, v1) = v5 & element(v4, v5) = 0) | (v5 = 0 & empty(v1) = 0) | (v5 = 0 & empty(v0) = 0) | ( ~ (v5 = 0) & element(v3, v1) = v5) | ( ~ (v5 = 0) & element(v2, v0) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (ordered_pair_as_product_element(v0, v1, v2, v3) = v4) | ? [v5] : ((v5 = v4 & ordered_pair(v2, v3) = v4) | (v5 = 0 & empty(v1) = 0) | (v5 = 0 & empty(v0) = 0) | ( ~ (v5 = 0) & element(v3, v1) = v5) | ( ~ (v5 = 0) & element(v2, v0) = v5))) & ! [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 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (below(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ((v4 = 0 & empty_carrier(v0) = 0) | ( ~ (v5 = 0) & the_carrier(v0) = v4 & element(v2, v4) = v5) | ( ~ (v5 = 0) & the_carrier(v0) = v4 & element(v1, v4) = v5) | ( ~ (v4 = 0) & latt_str(v0) = v4) | ( ~ (v4 = 0) & meet_commutative(v0) = v4) | ( ~ (v4 = 0) & meet_absorbing(v0) = v4) | ( ~ (v4 = 0) & join_absorbing(v0) = v4) | (( ~ (v3 = 0) | (v4 = 0 & below_refl(v0, v1, v2) = 0)) & (v3 = 0 | ( ~ (v4 = 0) & below_refl(v0, v1, v2) = v4))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (below_refl(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ((v4 = 0 & empty_carrier(v0) = 0) | ( ~ (v5 = 0) & the_carrier(v0) = v4 & element(v2, v4) = v5) | ( ~ (v5 = 0) & the_carrier(v0) = v4 & element(v1, v4) = v5) | ( ~ (v4 = 0) & latt_str(v0) = v4) | ( ~ (v4 = 0) & meet_commutative(v0) = v4) | ( ~ (v4 = 0) & meet_absorbing(v0) = v4) | ( ~ (v4 = 0) & join_absorbing(v0) = v4) | (( ~ (v3 = 0) | (v4 = 0 & below(v0, v1, v2) = 0)) & (v3 = 0 | ( ~ (v4 = 0) & below(v0, v1, v2) = v4))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (the_carrier(v0) = v3) | ~ (element(v2, v3) = 0) | ~ (element(v1, v3) = 0) | ? [v4] : ((v4 = 0 & below_refl(v0, v1, v1) = 0) | (v4 = 0 & empty_carrier(v0) = 0) | ( ~ (v4 = 0) & latt_str(v0) = v4) | ( ~ (v4 = 0) & meet_commutative(v0) = v4) | ( ~ (v4 = 0) & meet_absorbing(v0) = v4) | ( ~ (v4 = 0) & join_absorbing(v0) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (a_1_0_filter_1(v1) = v2) | ~ (in(v0, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ((v4 = 0 & empty_carrier(v1) = 0) | ( ~ (v4 = 0) & lattice(v1) = v4) | ( ~ (v4 = 0) & latt_str(v1) = v4) | (( ~ (v3 = 0) | (v10 = 0 & v9 = v0 & v8 = 0 & v7 = 0 & below_refl(v1, v5, v6) = 0 & the_carrier(v1) = v4 & ordered_pair_as_product_element(v4, v4, v5, v6) = v0 & element(v6, v4) = 0 & element(v5, v4) = 0)) & (v3 = 0 | (the_carrier(v1) = v4 & ! [v11] : ! [v12] : ( ~ (below_refl(v1, v11, v12) = 0) | ? [v13] : (( ~ (v13 = v0) & ordered_pair_as_product_element(v4, v4, v11, v12) = v13) | ( ~ (v13 = 0) & element(v12, v4) = v13) | ( ~ (v13 = 0) & element(v11, v4) = v13))) & ! [v11] : ! [v12] : ( ~ (ordered_pair_as_product_element(v4, v4, v11, v12) = v0) | ? [v13] : (( ~ (v13 = 0) & below_refl(v1, v11, v12) = v13) | ( ~ (v13 = 0) & element(v12, v4) = v13) | ( ~ (v13 = 0) & element(v11, v4) = v13)))))))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v0, v1) = v2) | ? [v3] : ((v3 = 0 & empty(v1) = 0) | ( ~ (v3 = 0) & element(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (the_carrier(v2) = v1) | ~ (the_carrier(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (join_semilatt_str(v2) = v1) | ~ (join_semilatt_str(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (one_sorted_str(v2) = v1) | ~ (one_sorted_str(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (meet_semilatt_str(v2) = v1) | ~ (meet_semilatt_str(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_of_lattice(v2) = v1) | ~ (relation_of_lattice(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (a_1_0_filter_1(v2) = v1) | ~ (a_1_0_filter_1(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (lattice(v2) = v1) | ~ (lattice(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (latt_str(v2) = v1) | ~ (latt_str(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_associative(v2) = v1) | ~ (join_associative(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (meet_commutative(v2) = v1) | ~ (meet_commutative(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (meet_associative(v2) = v1) | ~ (meet_associative(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (meet_absorbing(v2) = v1) | ~ (meet_absorbing(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (join_absorbing(v2) = v1) | ~ (join_absorbing(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (cartesian_product2(v0, v1) = v2) | ? [v3] : ((v3 = 0 & empty(v1) = 0) | (v3 = 0 & empty(v0) = 0) | ( ~ (v3 = 0) & empty(v2) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (ordered_pair(v0, v1) = v3 & singleton(v0) = v4 & unordered_pair(v2, v4) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (one_sorted_str(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & join_semilatt_str(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (one_sorted_str(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & meet_semilatt_str(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (empty_carrier(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & v2 = 0 & join_commutative(v0) = 0 & join_associative(v0) = 0 & meet_commutative(v0) = 0 & meet_associative(v0) = 0 & meet_absorbing(v0) = 0 & join_absorbing(v0) = 0) | ( ~ (v2 = 0) & lattice(v0) = v2) | ( ~ (v2 = 0) & latt_str(v0) = v2))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (empty_carrier(v0) = v1) | ? [v2] : ? [v3] : ((v3 = v2 & relation_of_lattice(v0) = v2 & a_1_0_filter_1(v0) = v2) | ( ~ (v2 = 0) & lattice(v0) = v2) | ( ~ (v2 = 0) & latt_str(v0) = v2))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (empty_carrier(v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & relation(v2) = 0 & relation_of_lattice(v0) = v2) | ( ~ (v2 = 0) & lattice(v0) = v2) | ( ~ (v2 = 0) & latt_str(v0) = v2))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (empty_carrier(v0) = v1) | ? [v2] : ? [v3] : (( ~ (v3 = 0) & the_carrier(v0) = v2 & empty(v2) = v3) | ( ~ (v2 = 0) & one_sorted_str(v0) = v2))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (empty_carrier(v0) = v1) | ? [v2] : ((v2 = 0 & lattice(v0) = 0) | ( ~ (v2 = 0) & latt_str(v0) = v2) | ( ~ (v2 = 0) & join_commutative(v0) = v2) | ( ~ (v2 = 0) & join_associative(v0) = v2) | ( ~ (v2 = 0) & meet_commutative(v0) = v2) | ( ~ (v2 = 0) & meet_associative(v0) = v2) | ( ~ (v2 = 0) & meet_absorbing(v0) = v2) | ( ~ (v2 = 0) & join_absorbing(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ? [v2] : ((v2 = 0 & empty_carrier(v0) = 0) | ( ~ (v2 = 0) & one_sorted_str(v0) = v2) | ( ~ (v2 = 0) & empty(v1) = v2))) & ! [v0] : ! [v1] : ( ~ (join_semilatt_str(v0) = v1) | ? [v2] : ((v2 = 0 & v1 = 0 & meet_semilatt_str(v0) = 0) | ( ~ (v2 = 0) & latt_str(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (meet_semilatt_str(v0) = v1) | ? [v2] : ((v2 = 0 & v1 = 0 & join_semilatt_str(v0) = 0) | ( ~ (v2 = 0) & latt_str(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (element(v0, v1) = 0) | ? [v2] : ((v2 = 0 & empty(v1) = 0) | (v2 = 0 & in(v0, v1) = 0))) & ! [v0] : ! [v1] : ( ~ (relation_of_lattice(v0) = v1) | ? [v2] : ((v2 = v1 & a_1_0_filter_1(v0) = v1) | (v2 = 0 & empty_carrier(v0) = 0) | ( ~ (v2 = 0) & lattice(v0) = v2) | ( ~ (v2 = 0) & latt_str(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (relation_of_lattice(v0) = v1) | ? [v2] : ((v2 = 0 & relation(v1) = 0) | (v2 = 0 & empty_carrier(v0) = 0) | ( ~ (v2 = 0) & lattice(v0) = v2) | ( ~ (v2 = 0) & latt_str(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (a_1_0_filter_1(v0) = v1) | ? [v2] : ((v2 = v1 & relation_of_lattice(v0) = v1) | (v2 = 0 & empty_carrier(v0) = 0) | ( ~ (v2 = 0) & lattice(v0) = v2) | ( ~ (v2 = 0) & latt_str(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (lattice(v0) = v1) | ? [v2] : ((v2 = 0 & empty_carrier(v0) = 0) | (v1 = 0 & ~ (v2 = 0) & empty_carrier(v0) = v2) | ( ~ (v2 = 0) & latt_str(v0) = v2) | ( ~ (v2 = 0) & join_commutative(v0) = v2) | ( ~ (v2 = 0) & join_associative(v0) = v2) | ( ~ (v2 = 0) & meet_commutative(v0) = v2) | ( ~ (v2 = 0) & meet_associative(v0) = v2) | ( ~ (v2 = 0) & meet_absorbing(v0) = v2) | ( ~ (v2 = 0) & join_absorbing(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (join_commutative(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & v1 = 0 & ~ (v2 = 0) & empty_carrier(v0) = v2 & join_associative(v0) = 0 & meet_commutative(v0) = 0 & meet_associative(v0) = 0 & meet_absorbing(v0) = 0 & join_absorbing(v0) = 0) | (v2 = 0 & empty_carrier(v0) = 0) | ( ~ (v2 = 0) & lattice(v0) = v2) | ( ~ (v2 = 0) & latt_str(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (join_associative(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & v1 = 0 & ~ (v2 = 0) & empty_carrier(v0) = v2 & join_commutative(v0) = 0 & meet_commutative(v0) = 0 & meet_associative(v0) = 0 & meet_absorbing(v0) = 0 & join_absorbing(v0) = 0) | (v2 = 0 & empty_carrier(v0) = 0) | ( ~ (v2 = 0) & lattice(v0) = v2) | ( ~ (v2 = 0) & latt_str(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (meet_commutative(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & v1 = 0 & ~ (v2 = 0) & empty_carrier(v0) = v2 & join_commutative(v0) = 0 & join_associative(v0) = 0 & meet_associative(v0) = 0 & meet_absorbing(v0) = 0 & join_absorbing(v0) = 0) | (v2 = 0 & empty_carrier(v0) = 0) | ( ~ (v2 = 0) & lattice(v0) = v2) | ( ~ (v2 = 0) & latt_str(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (meet_associative(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & v1 = 0 & ~ (v2 = 0) & empty_carrier(v0) = v2 & join_commutative(v0) = 0 & join_associative(v0) = 0 & meet_commutative(v0) = 0 & meet_absorbing(v0) = 0 & join_absorbing(v0) = 0) | (v2 = 0 & empty_carrier(v0) = 0) | ( ~ (v2 = 0) & lattice(v0) = v2) | ( ~ (v2 = 0) & latt_str(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (meet_absorbing(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & v1 = 0 & ~ (v2 = 0) & empty_carrier(v0) = v2 & join_commutative(v0) = 0 & join_associative(v0) = 0 & meet_commutative(v0) = 0 & meet_associative(v0) = 0 & join_absorbing(v0) = 0) | (v2 = 0 & empty_carrier(v0) = 0) | ( ~ (v2 = 0) & lattice(v0) = v2) | ( ~ (v2 = 0) & latt_str(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (join_absorbing(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & v1 = 0 & ~ (v2 = 0) & empty_carrier(v0) = v2 & join_commutative(v0) = 0 & join_associative(v0) = 0 & meet_commutative(v0) = 0 & meet_associative(v0) = 0 & meet_absorbing(v0) = 0) | (v2 = 0 & empty_carrier(v0) = 0) | ( ~ (v2 = 0) & lattice(v0) = v2) | ( ~ (v2 = 0) & latt_str(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | element(v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) & ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0)) & ! [v0] : ( ~ (join_semilatt_str(v0) = 0) | one_sorted_str(v0) = 0) & ! [v0] : ( ~ (one_sorted_str(v0) = 0) | ? [v1] : ? [v2] : ((v1 = 0 & empty_carrier(v0) = 0) | ( ~ (v2 = 0) & the_carrier(v0) = v1 & empty(v1) = v2))) & ! [v0] : ( ~ (meet_semilatt_str(v0) = 0) | one_sorted_str(v0) = 0) & ! [v0] : ( ~ (lattice(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & v2 = 0 & ~ (v1 = 0) & empty_carrier(v0) = v1 & join_commutative(v0) = 0 & join_associative(v0) = 0 & meet_commutative(v0) = 0 & meet_associative(v0) = 0 & meet_absorbing(v0) = 0 & join_absorbing(v0) = 0) | (v1 = 0 & empty_carrier(v0) = 0) | ( ~ (v1 = 0) & latt_str(v0) = v1))) & ! [v0] : ( ~ (lattice(v0) = 0) | ? [v1] : ? [v2] : ((v2 = v1 & relation_of_lattice(v0) = v1 & a_1_0_filter_1(v0) = v1) | (v1 = 0 & empty_carrier(v0) = 0) | ( ~ (v1 = 0) & latt_str(v0) = v1))) & ! [v0] : ( ~ (lattice(v0) = 0) | ? [v1] : ? [v2] : ((v2 = 0 & relation(v1) = 0 & relation_of_lattice(v0) = v1) | (v1 = 0 & empty_carrier(v0) = 0) | ( ~ (v1 = 0) & latt_str(v0) = v1))) & ! [v0] : ( ~ (latt_str(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & v2 = 0 & ~ (v1 = 0) & empty_carrier(v0) = v1 & join_commutative(v0) = 0 & join_associative(v0) = 0 & meet_commutative(v0) = 0 & meet_associative(v0) = 0 & meet_absorbing(v0) = 0 & join_absorbing(v0) = 0) | (v1 = 0 & empty_carrier(v0) = 0) | ( ~ (v1 = 0) & lattice(v0) = v1))) & ! [v0] : ( ~ (latt_str(v0) = 0) | ? [v1] : ? [v2] : ((v2 = v1 & relation_of_lattice(v0) = v1 & a_1_0_filter_1(v0) = v1) | (v1 = 0 & empty_carrier(v0) = 0) | ( ~ (v1 = 0) & lattice(v0) = v1))) & ! [v0] : ( ~ (latt_str(v0) = 0) | ? [v1] : ? [v2] : ((v2 = 0 & ~ (v1 = 0) & lattice(v0) = 0 & empty_carrier(v0) = v1) | (v1 = 0 & empty_carrier(v0) = 0) | ( ~ (v1 = 0) & join_commutative(v0) = v1) | ( ~ (v1 = 0) & join_associative(v0) = v1) | ( ~ (v1 = 0) & meet_commutative(v0) = v1) | ( ~ (v1 = 0) & meet_associative(v0) = v1) | ( ~ (v1 = 0) & meet_absorbing(v0) = v1) | ( ~ (v1 = 0) & join_absorbing(v0) = v1))) & ! [v0] : ( ~ (latt_str(v0) = 0) | ? [v1] : ? [v2] : ((v2 = 0 & relation(v1) = 0 & relation_of_lattice(v0) = v1) | (v1 = 0 & empty_carrier(v0) = 0) | ( ~ (v1 = 0) & lattice(v0) = v1))) & ! [v0] : ( ~ (latt_str(v0) = 0) | (join_semilatt_str(v0) = 0 & meet_semilatt_str(v0) = 0)) & ! [v0] : ( ~ (join_commutative(v0) = 0) | ? [v1] : ? [v2] : ((v2 = 0 & ~ (v1 = 0) & lattice(v0) = 0 & empty_carrier(v0) = v1) | (v1 = 0 & empty_carrier(v0) = 0) | ( ~ (v1 = 0) & latt_str(v0) = v1) | ( ~ (v1 = 0) & join_associative(v0) = v1) | ( ~ (v1 = 0) & meet_commutative(v0) = v1) | ( ~ (v1 = 0) & meet_associative(v0) = v1) | ( ~ (v1 = 0) & meet_absorbing(v0) = v1) | ( ~ (v1 = 0) & join_absorbing(v0) = v1))) & ! [v0] : ( ~ (join_associative(v0) = 0) | ? [v1] : ? [v2] : ((v2 = 0 & ~ (v1 = 0) & lattice(v0) = 0 & empty_carrier(v0) = v1) | (v1 = 0 & empty_carrier(v0) = 0) | ( ~ (v1 = 0) & latt_str(v0) = v1) | ( ~ (v1 = 0) & join_commutative(v0) = v1) | ( ~ (v1 = 0) & meet_commutative(v0) = v1) | ( ~ (v1 = 0) & meet_associative(v0) = v1) | ( ~ (v1 = 0) & meet_absorbing(v0) = v1) | ( ~ (v1 = 0) & join_absorbing(v0) = v1))) & ! [v0] : ( ~ (meet_commutative(v0) = 0) | ? [v1] : ? [v2] : ((v2 = 0 & ~ (v1 = 0) & lattice(v0) = 0 & empty_carrier(v0) = v1) | (v1 = 0 & empty_carrier(v0) = 0) | ( ~ (v1 = 0) & latt_str(v0) = v1) | ( ~ (v1 = 0) & join_commutative(v0) = v1) | ( ~ (v1 = 0) & join_associative(v0) = v1) | ( ~ (v1 = 0) & meet_associative(v0) = v1) | ( ~ (v1 = 0) & meet_absorbing(v0) = v1) | ( ~ (v1 = 0) & join_absorbing(v0) = v1))) & ! [v0] : ( ~ (meet_associative(v0) = 0) | ? [v1] : ? [v2] : ((v2 = 0 & ~ (v1 = 0) & lattice(v0) = 0 & empty_carrier(v0) = v1) | (v1 = 0 & empty_carrier(v0) = 0) | ( ~ (v1 = 0) & latt_str(v0) = v1) | ( ~ (v1 = 0) & join_commutative(v0) = v1) | ( ~ (v1 = 0) & join_associative(v0) = v1) | ( ~ (v1 = 0) & meet_commutative(v0) = v1) | ( ~ (v1 = 0) & meet_absorbing(v0) = v1) | ( ~ (v1 = 0) & join_absorbing(v0) = v1))) & ! [v0] : ( ~ (meet_absorbing(v0) = 0) | ? [v1] : ? [v2] : ((v2 = 0 & ~ (v1 = 0) & lattice(v0) = 0 & empty_carrier(v0) = v1) | (v1 = 0 & empty_carrier(v0) = 0) | ( ~ (v1 = 0) & latt_str(v0) = v1) | ( ~ (v1 = 0) & join_commutative(v0) = v1) | ( ~ (v1 = 0) & join_associative(v0) = v1) | ( ~ (v1 = 0) & meet_commutative(v0) = v1) | ( ~ (v1 = 0) & meet_associative(v0) = v1) | ( ~ (v1 = 0) & join_absorbing(v0) = v1))) & ! [v0] : ( ~ (join_absorbing(v0) = 0) | ? [v1] : ? [v2] : ((v2 = 0 & ~ (v1 = 0) & lattice(v0) = 0 & empty_carrier(v0) = v1) | (v1 = 0 & empty_carrier(v0) = 0) | ( ~ (v1 = 0) & latt_str(v0) = v1) | ( ~ (v1 = 0) & join_commutative(v0) = v1) | ( ~ (v1 = 0) & join_associative(v0) = v1) | ( ~ (v1 = 0) & meet_commutative(v0) = v1) | ( ~ (v1 = 0) & meet_associative(v0) = v1) | ( ~ (v1 = 0) & meet_absorbing(v0) = v1))) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ordered_pair_as_product_element(v3, v2, v1, v0) = v4 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : below(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : below_refl(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : cartesian_product2(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : element(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : ordered_pair(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : unordered_pair(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2 & ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : ? [v3] : ? [v4] : (((v4 = 0 & in(v2, v1) = 0) | (v3 = 0 & in(v2, v0) = 0)) & (( ~ (v4 = 0) & in(v2, v1) = v4) | ( ~ (v3 = 0) & in(v2, v0) = v3)))) & ? [v0] : ? [v1] : the_carrier(v0) = v1 & ? [v0] : ? [v1] : join_semilatt_str(v0) = v1 & ? [v0] : ? [v1] : one_sorted_str(v0) = v1 & ? [v0] : ? [v1] : meet_semilatt_str(v0) = v1 & ? [v0] : ? [v1] : relation(v0) = v1 & ? [v0] : ? [v1] : empty(v0) = v1 & ? [v0] : ? [v1] : element(v1, v0) = 0 & ? [v0] : ? [v1] : relation_of_lattice(v0) = v1 & ? [v0] : ? [v1] : a_1_0_filter_1(v0) = v1 & ? [v0] : ? [v1] : singleton(v0) = v1 & ? [v0] : ? [v1] : lattice(v0) = v1 & ? [v0] : ? [v1] : latt_str(v0) = v1 & ? [v0] : ? [v1] : empty_carrier(v0) = v1 & ? [v0] : ? [v1] : join_commutative(v0) = v1 & ? [v0] : ? [v1] : join_associative(v0) = v1 & ? [v0] : ? [v1] : meet_commutative(v0) = v1 & ? [v0] : ? [v1] : meet_associative(v0) = v1 & ? [v0] : ? [v1] : meet_absorbing(v0) = v1 & ? [v0] : ? [v1] : join_absorbing(v0) = v1 & ((all_0_9_9 = 0 & ~ (all_0_10_10 = 0)) | (all_0_10_10 = 0 & ~ (all_0_9_9 = 0))) % 21.69/5.71 | % 21.69/5.71 | Applying alpha-rule on (1) yields: % 21.69/5.71 | (2) ? [v0] : ? [v1] : join_semilatt_str(v0) = v1 % 21.69/5.71 | (3) ! [v0] : ! [v1] : (v1 = 0 | ~ (empty_carrier(v0) = v1) | ? [v2] : ? [v3] : (( ~ (v3 = 0) & the_carrier(v0) = v2 & empty(v2) = v3) | ( ~ (v2 = 0) & one_sorted_str(v0) = v2))) % 21.69/5.71 | (4) ! [v0] : ( ~ (one_sorted_str(v0) = 0) | ? [v1] : ? [v2] : ((v1 = 0 & empty_carrier(v0) = 0) | ( ~ (v2 = 0) & the_carrier(v0) = v1 & empty(v1) = v2))) % 21.69/5.71 | (5) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (join_absorbing(v2) = v1) | ~ (join_absorbing(v2) = v0)) % 21.69/5.71 | (6) meet_semilatt_str(all_0_0_0) = 0 % 21.69/5.71 | (7) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0)) % 21.69/5.71 | (8) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (meet_absorbing(v2) = v1) | ~ (meet_absorbing(v2) = v0)) % 21.69/5.71 | (9) empty_carrier(all_0_17_17) = all_0_16_16 % 21.69/5.71 | (10) ! [v0] : ( ~ (join_associative(v0) = 0) | ? [v1] : ? [v2] : ((v2 = 0 & ~ (v1 = 0) & lattice(v0) = 0 & empty_carrier(v0) = v1) | (v1 = 0 & empty_carrier(v0) = 0) | ( ~ (v1 = 0) & latt_str(v0) = v1) | ( ~ (v1 = 0) & join_commutative(v0) = v1) | ( ~ (v1 = 0) & meet_commutative(v0) = v1) | ( ~ (v1 = 0) & meet_associative(v0) = v1) | ( ~ (v1 = 0) & meet_absorbing(v0) = v1) | ( ~ (v1 = 0) & join_absorbing(v0) = v1))) % 21.69/5.71 | (11) lattice(all_0_17_17) = 0 % 21.69/5.71 | (12) ? [v0] : ? [v1] : empty(v0) = v1 % 21.69/5.71 | (13) ! [v0] : ( ~ (meet_associative(v0) = 0) | ? [v1] : ? [v2] : ((v2 = 0 & ~ (v1 = 0) & lattice(v0) = 0 & empty_carrier(v0) = v1) | (v1 = 0 & empty_carrier(v0) = 0) | ( ~ (v1 = 0) & latt_str(v0) = v1) | ( ~ (v1 = 0) & join_commutative(v0) = v1) | ( ~ (v1 = 0) & join_associative(v0) = v1) | ( ~ (v1 = 0) & meet_commutative(v0) = v1) | ( ~ (v1 = 0) & meet_absorbing(v0) = v1) | ( ~ (v1 = 0) & join_absorbing(v0) = v1))) % 21.69/5.72 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (below(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ((v4 = 0 & empty_carrier(v0) = 0) | ( ~ (v5 = 0) & the_carrier(v0) = v4 & element(v2, v4) = v5) | ( ~ (v5 = 0) & the_carrier(v0) = v4 & element(v1, v4) = v5) | ( ~ (v4 = 0) & latt_str(v0) = v4) | ( ~ (v4 = 0) & meet_commutative(v0) = v4) | ( ~ (v4 = 0) & meet_absorbing(v0) = v4) | ( ~ (v4 = 0) & join_absorbing(v0) = v4) | (( ~ (v3 = 0) | (v4 = 0 & below_refl(v0, v1, v2) = 0)) & (v3 = 0 | ( ~ (v4 = 0) & below_refl(v0, v1, v2) = v4))))) % 21.69/5.72 | (15) ordered_pair_as_product_element(all_0_15_15, all_0_15_15, all_0_13_13, all_0_12_12) = all_0_11_11 % 21.69/5.72 | (16) ! [v0] : ! [v1] : ( ~ (meet_absorbing(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & v1 = 0 & ~ (v2 = 0) & empty_carrier(v0) = v2 & join_commutative(v0) = 0 & join_associative(v0) = 0 & meet_commutative(v0) = 0 & meet_associative(v0) = 0 & join_absorbing(v0) = 0) | (v2 = 0 & empty_carrier(v0) = 0) | ( ~ (v2 = 0) & lattice(v0) = v2) | ( ~ (v2 = 0) & latt_str(v0) = v2))) % 21.69/5.72 | (17) ! [v0] : ( ~ (latt_str(v0) = 0) | ? [v1] : ? [v2] : ((v2 = v1 & relation_of_lattice(v0) = v1 & a_1_0_filter_1(v0) = v1) | (v1 = 0 & empty_carrier(v0) = 0) | ( ~ (v1 = 0) & lattice(v0) = v1))) % 21.69/5.72 | (18) ! [v0] : ( ~ (lattice(v0) = 0) | ? [v1] : ? [v2] : ((v2 = v1 & relation_of_lattice(v0) = v1 & a_1_0_filter_1(v0) = v1) | (v1 = 0 & empty_carrier(v0) = 0) | ( ~ (v1 = 0) & latt_str(v0) = v1))) % 21.69/5.72 | (19) ! [v0] : ! [v1] : ( ~ (join_absorbing(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & v1 = 0 & ~ (v2 = 0) & empty_carrier(v0) = v2 & join_commutative(v0) = 0 & join_associative(v0) = 0 & meet_commutative(v0) = 0 & meet_associative(v0) = 0 & meet_absorbing(v0) = 0) | (v2 = 0 & empty_carrier(v0) = 0) | ( ~ (v2 = 0) & lattice(v0) = v2) | ( ~ (v2 = 0) & latt_str(v0) = v2))) % 21.69/5.72 | (20) ! [v0] : ( ~ (latt_str(v0) = 0) | ? [v1] : ? [v2] : ((v2 = 0 & ~ (v1 = 0) & lattice(v0) = 0 & empty_carrier(v0) = v1) | (v1 = 0 & empty_carrier(v0) = 0) | ( ~ (v1 = 0) & join_commutative(v0) = v1) | ( ~ (v1 = 0) & join_associative(v0) = v1) | ( ~ (v1 = 0) & meet_commutative(v0) = v1) | ( ~ (v1 = 0) & meet_associative(v0) = v1) | ( ~ (v1 = 0) & meet_absorbing(v0) = v1) | ( ~ (v1 = 0) & join_absorbing(v0) = v1))) % 21.69/5.72 | (21) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | element(v0, v1) = 0) % 21.69/5.72 | (22) ! [v0] : ! [v1] : ! [v2] : ( ~ (cartesian_product2(v0, v1) = v2) | ? [v3] : ((v3 = 0 & empty(v1) = 0) | (v3 = 0 & empty(v0) = 0) | ( ~ (v3 = 0) & empty(v2) = v3))) % 21.69/5.72 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) % 21.69/5.72 | (24) element(all_0_12_12, all_0_15_15) = 0 % 21.69/5.72 | (25) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3)) % 21.69/5.72 | (26) ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2)) % 21.69/5.72 | (27) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) % 21.69/5.72 | (28) ? [v0] : ? [v1] : lattice(v0) = v1 % 21.69/5.72 | (29) empty(all_0_6_6) = all_0_5_5 % 21.69/5.72 | (30) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (meet_semilatt_str(v2) = v1) | ~ (meet_semilatt_str(v2) = v0)) % 21.69/5.72 | (31) (all_0_9_9 = 0 & ~ (all_0_10_10 = 0)) | (all_0_10_10 = 0 & ~ (all_0_9_9 = 0)) % 21.69/5.72 | (32) empty_carrier(all_0_8_8) = all_0_7_7 % 21.69/5.72 | (33) relation_of_lattice(all_0_17_17) = all_0_14_14 % 21.69/5.72 | (34) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (lattice(v2) = v1) | ~ (lattice(v2) = v0)) % 21.69/5.72 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) % 21.69/5.72 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v1 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4)) % 21.69/5.72 | (37) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (ordered_pair(v0, v1) = v3 & singleton(v0) = v4 & unordered_pair(v2, v4) = v3)) % 21.69/5.72 | (38) element(all_0_13_13, all_0_15_15) = 0 % 21.69/5.72 | (39) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3)) % 21.69/5.72 | (40) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) % 21.69/5.72 | (41) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) % 21.69/5.72 | (42) ! [v0] : ( ~ (latt_str(v0) = 0) | (join_semilatt_str(v0) = 0 & meet_semilatt_str(v0) = 0)) % 21.69/5.72 | (43) ! [v0] : ! [v1] : ( ~ (element(v0, v1) = 0) | ? [v2] : ((v2 = 0 & empty(v1) = 0) | (v2 = 0 & in(v0, v1) = 0))) % 21.69/5.72 | (44) ? [v0] : ? [v1] : meet_associative(v0) = v1 % 21.69/5.72 | (45) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)) % 21.69/5.72 | (46) ! [v0] : ! [v1] : ( ~ (relation_of_lattice(v0) = v1) | ? [v2] : ((v2 = 0 & relation(v1) = 0) | (v2 = 0 & empty_carrier(v0) = 0) | ( ~ (v2 = 0) & lattice(v0) = v2) | ( ~ (v2 = 0) & latt_str(v0) = v2))) % 21.69/5.72 | (47) ? [v0] : ? [v1] : ? [v2] : ? [v3] : below(v2, v1, v0) = v3 % 21.69/5.72 | (48) ! [v0] : ( ~ (latt_str(v0) = 0) | ? [v1] : ? [v2] : ((v2 = 0 & relation(v1) = 0 & relation_of_lattice(v0) = v1) | (v1 = 0 & empty_carrier(v0) = 0) | ( ~ (v1 = 0) & lattice(v0) = v1))) % 21.69/5.72 | (49) ! [v0] : ( ~ (lattice(v0) = 0) | ? [v1] : ? [v2] : ((v2 = 0 & relation(v1) = 0 & relation_of_lattice(v0) = v1) | (v1 = 0 & empty_carrier(v0) = 0) | ( ~ (v1 = 0) & latt_str(v0) = v1))) % 21.69/5.72 | (50) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (latt_str(v2) = v1) | ~ (latt_str(v2) = v0)) % 21.69/5.72 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) % 21.69/5.72 | (52) ! [v0] : ! [v1] : ( ~ (join_associative(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & v1 = 0 & ~ (v2 = 0) & empty_carrier(v0) = v2 & join_commutative(v0) = 0 & meet_commutative(v0) = 0 & meet_associative(v0) = 0 & meet_absorbing(v0) = 0 & join_absorbing(v0) = 0) | (v2 = 0 & empty_carrier(v0) = 0) | ( ~ (v2 = 0) & lattice(v0) = v2) | ( ~ (v2 = 0) & latt_str(v0) = v2))) % 21.69/5.72 | (53) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_of_lattice(v2) = v1) | ~ (relation_of_lattice(v2) = v0)) % 21.69/5.73 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (below_refl(v4, v3, v2) = v1) | ~ (below_refl(v4, v3, v2) = v0)) % 21.69/5.73 | (55) ? [v0] : ? [v1] : ? [v2] : cartesian_product2(v1, v0) = v2 % 21.69/5.73 | (56) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) % 21.69/5.73 | (57) ? [v0] : ? [v1] : the_carrier(v0) = v1 % 21.69/5.73 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (below_refl(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ((v4 = 0 & empty_carrier(v0) = 0) | ( ~ (v5 = 0) & the_carrier(v0) = v4 & element(v2, v4) = v5) | ( ~ (v5 = 0) & the_carrier(v0) = v4 & element(v1, v4) = v5) | ( ~ (v4 = 0) & latt_str(v0) = v4) | ( ~ (v4 = 0) & meet_commutative(v0) = v4) | ( ~ (v4 = 0) & meet_absorbing(v0) = v4) | ( ~ (v4 = 0) & join_absorbing(v0) = v4) | (( ~ (v3 = 0) | (v4 = 0 & below(v0, v1, v2) = 0)) & (v3 = 0 | ( ~ (v4 = 0) & below(v0, v1, v2) = v4))))) % 21.69/5.73 | (59) ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2 % 21.69/5.73 | (60) ! [v0] : ( ~ (join_absorbing(v0) = 0) | ? [v1] : ? [v2] : ((v2 = 0 & ~ (v1 = 0) & lattice(v0) = 0 & empty_carrier(v0) = v1) | (v1 = 0 & empty_carrier(v0) = 0) | ( ~ (v1 = 0) & latt_str(v0) = v1) | ( ~ (v1 = 0) & join_commutative(v0) = v1) | ( ~ (v1 = 0) & join_associative(v0) = v1) | ( ~ (v1 = 0) & meet_commutative(v0) = v1) | ( ~ (v1 = 0) & meet_associative(v0) = v1) | ( ~ (v1 = 0) & meet_absorbing(v0) = v1))) % 21.69/5.73 | (61) ! [v0] : ( ~ (meet_absorbing(v0) = 0) | ? [v1] : ? [v2] : ((v2 = 0 & ~ (v1 = 0) & lattice(v0) = 0 & empty_carrier(v0) = v1) | (v1 = 0 & empty_carrier(v0) = 0) | ( ~ (v1 = 0) & latt_str(v0) = v1) | ( ~ (v1 = 0) & join_commutative(v0) = v1) | ( ~ (v1 = 0) & join_associative(v0) = v1) | ( ~ (v1 = 0) & meet_commutative(v0) = v1) | ( ~ (v1 = 0) & meet_associative(v0) = v1) | ( ~ (v1 = 0) & join_absorbing(v0) = v1))) % 21.69/5.73 | (62) ? [v0] : ? [v1] : ? [v2] : ? [v3] : below_refl(v2, v1, v0) = v3 % 21.69/5.73 | (63) latt_str(all_0_3_3) = 0 % 21.69/5.73 | (64) ! [v0] : ! [v1] : ( ~ (meet_associative(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & v1 = 0 & ~ (v2 = 0) & empty_carrier(v0) = v2 & join_commutative(v0) = 0 & join_associative(v0) = 0 & meet_commutative(v0) = 0 & meet_absorbing(v0) = 0 & join_absorbing(v0) = 0) | (v2 = 0 & empty_carrier(v0) = 0) | ( ~ (v2 = 0) & lattice(v0) = v2) | ( ~ (v2 = 0) & latt_str(v0) = v2))) % 21.69/5.73 | (65) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v0 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4)) % 21.69/5.73 | (66) ? [v0] : ? [v1] : join_associative(v0) = v1 % 21.69/5.73 | (67) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) % 21.69/5.73 | (68) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2) % 21.69/5.73 | (69) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) % 21.69/5.73 | (70) ! [v0] : ( ~ (join_commutative(v0) = 0) | ? [v1] : ? [v2] : ((v2 = 0 & ~ (v1 = 0) & lattice(v0) = 0 & empty_carrier(v0) = v1) | (v1 = 0 & empty_carrier(v0) = 0) | ( ~ (v1 = 0) & latt_str(v0) = v1) | ( ~ (v1 = 0) & join_associative(v0) = v1) | ( ~ (v1 = 0) & meet_commutative(v0) = v1) | ( ~ (v1 = 0) & meet_associative(v0) = v1) | ( ~ (v1 = 0) & meet_absorbing(v0) = v1) | ( ~ (v1 = 0) & join_absorbing(v0) = v1))) % 21.69/5.73 | (71) ? [v0] : ? [v1] : ? [v2] : ordered_pair(v1, v0) = v2 % 21.69/5.73 | (72) ? [v0] : ? [v1] : a_1_0_filter_1(v0) = v1 % 21.69/5.73 | (73) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty_carrier(v2) = v1) | ~ (empty_carrier(v2) = v0)) % 21.69/5.73 | (74) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (a_1_0_filter_1(v1) = v2) | ~ (in(v0, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ((v4 = 0 & empty_carrier(v1) = 0) | ( ~ (v4 = 0) & lattice(v1) = v4) | ( ~ (v4 = 0) & latt_str(v1) = v4) | (( ~ (v3 = 0) | (v10 = 0 & v9 = v0 & v8 = 0 & v7 = 0 & below_refl(v1, v5, v6) = 0 & the_carrier(v1) = v4 & ordered_pair_as_product_element(v4, v4, v5, v6) = v0 & element(v6, v4) = 0 & element(v5, v4) = 0)) & (v3 = 0 | (the_carrier(v1) = v4 & ! [v11] : ! [v12] : ( ~ (below_refl(v1, v11, v12) = 0) | ? [v13] : (( ~ (v13 = v0) & ordered_pair_as_product_element(v4, v4, v11, v12) = v13) | ( ~ (v13 = 0) & element(v12, v4) = v13) | ( ~ (v13 = 0) & element(v11, v4) = v13))) & ! [v11] : ! [v12] : ( ~ (ordered_pair_as_product_element(v4, v4, v11, v12) = v0) | ? [v13] : (( ~ (v13 = 0) & below_refl(v1, v11, v12) = v13) | ( ~ (v13 = 0) & element(v12, v4) = v13) | ( ~ (v13 = 0) & element(v11, v4) = v13)))))))) % 21.69/5.73 | (75) join_semilatt_str(all_0_2_2) = 0 % 21.69/5.73 | (76) ? [v0] : ? [v1] : one_sorted_str(v0) = v1 % 21.69/5.73 | (77) latt_str(all_0_17_17) = 0 % 21.69/5.73 | (78) ? [v0] : ? [v1] : meet_absorbing(v0) = v1 % 21.69/5.73 | (79) ! [v0] : ! [v1] : ( ~ (relation_of_lattice(v0) = v1) | ? [v2] : ((v2 = v1 & a_1_0_filter_1(v0) = v1) | (v2 = 0 & empty_carrier(v0) = 0) | ( ~ (v2 = 0) & lattice(v0) = v2) | ( ~ (v2 = 0) & latt_str(v0) = v2))) % 21.69/5.73 | (80) ~ (all_0_5_5 = 0) % 21.69/5.73 | (81) ! [v0] : ! [v1] : (v1 = 0 | ~ (empty_carrier(v0) = v1) | ? [v2] : ((v2 = 0 & lattice(v0) = 0) | ( ~ (v2 = 0) & latt_str(v0) = v2) | ( ~ (v2 = 0) & join_commutative(v0) = v2) | ( ~ (v2 = 0) & join_associative(v0) = v2) | ( ~ (v2 = 0) & meet_commutative(v0) = v2) | ( ~ (v2 = 0) & meet_associative(v0) = v2) | ( ~ (v2 = 0) & meet_absorbing(v0) = v2) | ( ~ (v2 = 0) & join_absorbing(v0) = v2))) % 21.69/5.73 | (82) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (join_commutative(v2) = v1) | ~ (join_commutative(v2) = v0)) % 21.69/5.73 | (83) ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ? [v2] : ((v2 = 0 & empty_carrier(v0) = 0) | ( ~ (v2 = 0) & one_sorted_str(v0) = v2) | ( ~ (v2 = 0) & empty(v1) = v2))) % 21.69/5.73 | (84) ! [v0] : ! [v1] : (v1 = 0 | ~ (one_sorted_str(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & join_semilatt_str(v0) = v2)) % 21.69/5.73 | (85) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (ordered_pair_as_product_element(v0, v1, v2, v3) = v4) | ? [v5] : ((v5 = v4 & ordered_pair(v2, v3) = v4) | (v5 = 0 & empty(v1) = 0) | (v5 = 0 & empty(v0) = 0) | ( ~ (v5 = 0) & element(v3, v1) = v5) | ( ~ (v5 = 0) & element(v2, v0) = v5))) % 21.69/5.73 | (86) ? [v0] : ? [v1] : relation_of_lattice(v0) = v1 % 21.69/5.73 | (87) ? [v0] : ? [v1] : element(v1, v0) = 0 % 21.69/5.73 | (88) one_sorted_str(all_0_8_8) = 0 % 21.69/5.73 | (89) ! [v0] : ! [v1] : (v1 = 0 | ~ (empty_carrier(v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & relation(v2) = 0 & relation_of_lattice(v0) = v2) | ( ~ (v2 = 0) & lattice(v0) = v2) | ( ~ (v2 = 0) & latt_str(v0) = v2))) % 21.69/5.73 | (90) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (ordered_pair_as_product_element(v0, v1, v2, v3) = v4) | ? [v5] : ? [v6] : ((v6 = 0 & cartesian_product2(v0, v1) = v5 & element(v4, v5) = 0) | (v5 = 0 & empty(v1) = 0) | (v5 = 0 & empty(v0) = 0) | ( ~ (v5 = 0) & element(v3, v1) = v5) | ( ~ (v5 = 0) & element(v2, v0) = v5))) % 21.69/5.73 | (91) ? [v0] : ? [v1] : join_absorbing(v0) = v1 % 21.90/5.74 | (92) ! [v0] : ( ~ (meet_commutative(v0) = 0) | ? [v1] : ? [v2] : ((v2 = 0 & ~ (v1 = 0) & lattice(v0) = 0 & empty_carrier(v0) = v1) | (v1 = 0 & empty_carrier(v0) = 0) | ( ~ (v1 = 0) & latt_str(v0) = v1) | ( ~ (v1 = 0) & join_commutative(v0) = v1) | ( ~ (v1 = 0) & join_associative(v0) = v1) | ( ~ (v1 = 0) & meet_associative(v0) = v1) | ( ~ (v1 = 0) & meet_absorbing(v0) = v1) | ( ~ (v1 = 0) & join_absorbing(v0) = v1))) % 21.90/5.74 | (93) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (the_carrier(v0) = v3) | ~ (element(v2, v3) = 0) | ~ (element(v1, v3) = 0) | ? [v4] : ((v4 = 0 & below_refl(v0, v1, v1) = 0) | (v4 = 0 & empty_carrier(v0) = 0) | ( ~ (v4 = 0) & latt_str(v0) = v4) | ( ~ (v4 = 0) & meet_commutative(v0) = v4) | ( ~ (v4 = 0) & meet_absorbing(v0) = v4) | ( ~ (v4 = 0) & join_absorbing(v0) = v4))) % 21.90/5.74 | (94) below_refl(all_0_17_17, all_0_13_13, all_0_12_12) = all_0_9_9 % 21.90/5.74 | (95) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 21.90/5.74 | (96) ! [v0] : ! [v1] : ( ~ (meet_semilatt_str(v0) = v1) | ? [v2] : ((v2 = 0 & v1 = 0 & join_semilatt_str(v0) = 0) | ( ~ (v2 = 0) & latt_str(v0) = v2))) % 21.90/5.74 | (97) ! [v0] : ( ~ (join_semilatt_str(v0) = 0) | one_sorted_str(v0) = 0) % 21.90/5.74 | (98) ~ (all_0_16_16 = 0) % 21.90/5.74 | (99) ? [v0] : ? [v1] : ? [v2] : unordered_pair(v1, v0) = v2 % 21.90/5.74 | (100) ? [v0] : ? [v1] : ? [v2] : element(v1, v0) = v2 % 21.90/5.74 | (101) in(all_0_11_11, all_0_14_14) = all_0_10_10 % 21.90/5.74 | (102) ? [v0] : ? [v1] : meet_commutative(v0) = v1 % 21.90/5.74 | (103) ? [v0] : ? [v1] : latt_str(v0) = v1 % 21.90/5.74 | (104) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (one_sorted_str(v2) = v1) | ~ (one_sorted_str(v2) = v0)) % 21.90/5.74 | (105) ! [v0] : ! [v1] : ( ~ (meet_commutative(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & v1 = 0 & ~ (v2 = 0) & empty_carrier(v0) = v2 & join_commutative(v0) = 0 & join_associative(v0) = 0 & meet_associative(v0) = 0 & meet_absorbing(v0) = 0 & join_absorbing(v0) = 0) | (v2 = 0 & empty_carrier(v0) = 0) | ( ~ (v2 = 0) & lattice(v0) = v2) | ( ~ (v2 = 0) & latt_str(v0) = v2))) % 21.90/5.74 | (106) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (meet_associative(v2) = v1) | ~ (meet_associative(v2) = v0)) % 21.90/5.74 | (107) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (meet_commutative(v2) = v1) | ~ (meet_commutative(v2) = v0)) % 21.90/5.74 | (108) ? [v0] : ? [v1] : relation(v0) = v1 % 21.90/5.74 | (109) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (join_associative(v2) = v1) | ~ (join_associative(v2) = v0)) % 21.90/5.74 | (110) ! [v0] : ! [v1] : ( ~ (join_commutative(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & v1 = 0 & ~ (v2 = 0) & empty_carrier(v0) = v2 & join_associative(v0) = 0 & meet_commutative(v0) = 0 & meet_associative(v0) = 0 & meet_absorbing(v0) = 0 & join_absorbing(v0) = 0) | (v2 = 0 & empty_carrier(v0) = 0) | ( ~ (v2 = 0) & lattice(v0) = v2) | ( ~ (v2 = 0) & latt_str(v0) = v2))) % 21.90/5.74 | (111) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (a_1_0_filter_1(v2) = v1) | ~ (a_1_0_filter_1(v2) = v0)) % 21.90/5.74 | (112) empty(empty_set) = 0 % 21.90/5.74 | (113) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (ordered_pair_as_product_element(v5, v4, v3, v2) = v1) | ~ (ordered_pair_as_product_element(v5, v4, v3, v2) = v0)) % 21.90/5.74 | (114) ! [v0] : ! [v1] : (v1 = 0 | ~ (one_sorted_str(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & meet_semilatt_str(v0) = v2)) % 21.90/5.74 | (115) ! [v0] : ! [v1] : ( ~ (lattice(v0) = v1) | ? [v2] : ((v2 = 0 & empty_carrier(v0) = 0) | (v1 = 0 & ~ (v2 = 0) & empty_carrier(v0) = v2) | ( ~ (v2 = 0) & latt_str(v0) = v2) | ( ~ (v2 = 0) & join_commutative(v0) = v2) | ( ~ (v2 = 0) & join_associative(v0) = v2) | ( ~ (v2 = 0) & meet_commutative(v0) = v2) | ( ~ (v2 = 0) & meet_associative(v0) = v2) | ( ~ (v2 = 0) & meet_absorbing(v0) = v2) | ( ~ (v2 = 0) & join_absorbing(v0) = v2))) % 21.90/5.74 | (116) ! [v0] : ( ~ (meet_semilatt_str(v0) = 0) | one_sorted_str(v0) = 0) % 21.90/5.74 | (117) empty(all_0_4_4) = 0 % 21.90/5.74 | (118) ? [v0] : ? [v1] : meet_semilatt_str(v0) = v1 % 21.90/5.74 | (119) one_sorted_str(all_0_1_1) = 0 % 21.90/5.74 | (120) ! [v0] : ( ~ (latt_str(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & v2 = 0 & ~ (v1 = 0) & empty_carrier(v0) = v1 & join_commutative(v0) = 0 & join_associative(v0) = 0 & meet_commutative(v0) = 0 & meet_associative(v0) = 0 & meet_absorbing(v0) = 0 & join_absorbing(v0) = 0) | (v1 = 0 & empty_carrier(v0) = 0) | ( ~ (v1 = 0) & lattice(v0) = v1))) % 21.90/5.74 | (121) ! [v0] : ( ~ (lattice(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & v2 = 0 & ~ (v1 = 0) & empty_carrier(v0) = v1 & join_commutative(v0) = 0 & join_associative(v0) = 0 & meet_commutative(v0) = 0 & meet_associative(v0) = 0 & meet_absorbing(v0) = 0 & join_absorbing(v0) = 0) | (v1 = 0 & empty_carrier(v0) = 0) | ( ~ (v1 = 0) & latt_str(v0) = v1))) % 21.90/5.74 | (122) ! [v0] : ! [v1] : (v1 = 0 | ~ (empty_carrier(v0) = v1) | ? [v2] : ? [v3] : ((v3 = v2 & relation_of_lattice(v0) = v2 & a_1_0_filter_1(v0) = v2) | ( ~ (v2 = 0) & lattice(v0) = v2) | ( ~ (v2 = 0) & latt_str(v0) = v2))) % 21.90/5.74 | (123) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) % 21.90/5.74 | (124) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (the_carrier(v2) = v1) | ~ (the_carrier(v2) = v0)) % 21.90/5.74 | (125) ! [v0] : ! [v1] : (v1 = 0 | ~ (empty_carrier(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & v2 = 0 & join_commutative(v0) = 0 & join_associative(v0) = 0 & meet_commutative(v0) = 0 & meet_associative(v0) = 0 & meet_absorbing(v0) = 0 & join_absorbing(v0) = 0) | ( ~ (v2 = 0) & lattice(v0) = v2) | ( ~ (v2 = 0) & latt_str(v0) = v2))) % 21.90/5.74 | (126) ~ (all_0_7_7 = 0) % 21.94/5.74 | (127) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ordered_pair_as_product_element(v3, v2, v1, v0) = v4 % 21.94/5.74 | (128) ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : ? [v3] : ? [v4] : (((v4 = 0 & in(v2, v1) = 0) | (v3 = 0 & in(v2, v0) = 0)) & (( ~ (v4 = 0) & in(v2, v1) = v4) | ( ~ (v3 = 0) & in(v2, v0) = v3)))) % 21.94/5.74 | (129) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3)) % 21.94/5.75 | (130) ! [v0] : ! [v1] : ( ~ (join_semilatt_str(v0) = v1) | ? [v2] : ((v2 = 0 & v1 = 0 & meet_semilatt_str(v0) = 0) | ( ~ (v2 = 0) & latt_str(v0) = v2))) % 21.94/5.75 | (131) ! [v0] : ! [v1] : ( ~ (a_1_0_filter_1(v0) = v1) | ? [v2] : ((v2 = v1 & relation_of_lattice(v0) = v1) | (v2 = 0 & empty_carrier(v0) = 0) | ( ~ (v2 = 0) & lattice(v0) = v2) | ( ~ (v2 = 0) & latt_str(v0) = v2))) % 21.94/5.75 | (132) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (below(v4, v3, v2) = v1) | ~ (below(v4, v3, v2) = v0)) % 21.94/5.75 | (133) the_carrier(all_0_17_17) = all_0_15_15 % 21.94/5.75 | (134) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v0, v1) = v2) | ? [v3] : ((v3 = 0 & empty(v1) = 0) | ( ~ (v3 = 0) & element(v0, v1) = v3))) % 21.94/5.75 | (135) ? [v0] : ? [v1] : empty_carrier(v0) = v1 % 21.94/5.75 | (136) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (join_semilatt_str(v2) = v1) | ~ (join_semilatt_str(v2) = v0)) % 21.94/5.75 | (137) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 21.94/5.75 | (138) ? [v0] : ? [v1] : join_commutative(v0) = v1 % 21.94/5.75 | (139) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (below_refl(v0, v1, v1) = v4) | ~ (the_carrier(v0) = v3) | ~ (element(v2, v3) = 0) | ? [v5] : ((v5 = 0 & empty_carrier(v0) = 0) | ( ~ (v5 = 0) & element(v1, v3) = v5) | ( ~ (v5 = 0) & latt_str(v0) = v5) | ( ~ (v5 = 0) & meet_commutative(v0) = v5) | ( ~ (v5 = 0) & meet_absorbing(v0) = v5) | ( ~ (v5 = 0) & join_absorbing(v0) = v5))) % 21.94/5.75 | (140) ? [v0] : ? [v1] : singleton(v0) = v1 % 21.94/5.75 | % 21.94/5.75 | Instantiating formula (58) with all_0_9_9, all_0_12_12, all_0_13_13, all_0_17_17 and discharging atoms below_refl(all_0_17_17, all_0_13_13, all_0_12_12) = all_0_9_9, yields: % 21.94/5.75 | (141) ? [v0] : ? [v1] : ((v0 = 0 & empty_carrier(all_0_17_17) = 0) | ( ~ (v1 = 0) & the_carrier(all_0_17_17) = v0 & element(all_0_12_12, v0) = v1) | ( ~ (v1 = 0) & the_carrier(all_0_17_17) = v0 & element(all_0_13_13, v0) = v1) | ( ~ (v0 = 0) & latt_str(all_0_17_17) = v0) | ( ~ (v0 = 0) & meet_commutative(all_0_17_17) = v0) | ( ~ (v0 = 0) & meet_absorbing(all_0_17_17) = v0) | ( ~ (v0 = 0) & join_absorbing(all_0_17_17) = v0) | (( ~ (all_0_9_9 = 0) | (v0 = 0 & below(all_0_17_17, all_0_13_13, all_0_12_12) = 0)) & (all_0_9_9 = 0 | ( ~ (v0 = 0) & below(all_0_17_17, all_0_13_13, all_0_12_12) = v0)))) % 21.94/5.75 | % 21.94/5.75 | Instantiating formula (83) with all_0_15_15, all_0_17_17 and discharging atoms the_carrier(all_0_17_17) = all_0_15_15, yields: % 21.94/5.75 | (142) ? [v0] : ((v0 = 0 & empty_carrier(all_0_17_17) = 0) | ( ~ (v0 = 0) & one_sorted_str(all_0_17_17) = v0) | ( ~ (v0 = 0) & empty(all_0_15_15) = v0)) % 21.94/5.75 | % 21.94/5.75 | Instantiating formula (85) with all_0_11_11, all_0_12_12, all_0_13_13, all_0_15_15, all_0_15_15 and discharging atoms ordered_pair_as_product_element(all_0_15_15, all_0_15_15, all_0_13_13, all_0_12_12) = all_0_11_11, yields: % 21.94/5.75 | (143) ? [v0] : ((v0 = all_0_11_11 & ordered_pair(all_0_13_13, all_0_12_12) = all_0_11_11) | (v0 = 0 & empty(all_0_15_15) = 0) | ( ~ (v0 = 0) & element(all_0_12_12, all_0_15_15) = v0) | ( ~ (v0 = 0) & element(all_0_13_13, all_0_15_15) = v0)) % 21.94/5.75 | % 21.94/5.75 | Instantiating formula (121) with all_0_17_17 and discharging atoms lattice(all_0_17_17) = 0, yields: % 21.94/5.75 | (144) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & v2 = 0 & v1 = 0 & ~ (v0 = 0) & empty_carrier(all_0_17_17) = v0 & join_commutative(all_0_17_17) = 0 & join_associative(all_0_17_17) = 0 & meet_commutative(all_0_17_17) = 0 & meet_associative(all_0_17_17) = 0 & meet_absorbing(all_0_17_17) = 0 & join_absorbing(all_0_17_17) = 0) | (v0 = 0 & empty_carrier(all_0_17_17) = 0) | ( ~ (v0 = 0) & latt_str(all_0_17_17) = v0)) % 21.94/5.75 | % 21.94/5.75 | Instantiating formula (18) with all_0_17_17 and discharging atoms lattice(all_0_17_17) = 0, yields: % 21.94/5.75 | (145) ? [v0] : ? [v1] : ((v1 = v0 & relation_of_lattice(all_0_17_17) = v0 & a_1_0_filter_1(all_0_17_17) = v0) | (v0 = 0 & empty_carrier(all_0_17_17) = 0) | ( ~ (v0 = 0) & latt_str(all_0_17_17) = v0)) % 21.94/5.75 | % 21.94/5.75 | Instantiating formula (49) with all_0_17_17 and discharging atoms lattice(all_0_17_17) = 0, yields: % 21.94/5.75 | (146) ? [v0] : ? [v1] : ((v1 = 0 & relation(v0) = 0 & relation_of_lattice(all_0_17_17) = v0) | (v0 = 0 & empty_carrier(all_0_17_17) = 0) | ( ~ (v0 = 0) & latt_str(all_0_17_17) = v0)) % 21.94/5.75 | % 21.94/5.75 | Instantiating formula (115) with 0, all_0_17_17 and discharging atoms lattice(all_0_17_17) = 0, yields: % 21.94/5.75 | (147) ? [v0] : ((v0 = 0 & empty_carrier(all_0_17_17) = 0) | ( ~ (v0 = 0) & latt_str(all_0_17_17) = v0) | ( ~ (v0 = 0) & empty_carrier(all_0_17_17) = v0) | ( ~ (v0 = 0) & join_commutative(all_0_17_17) = v0) | ( ~ (v0 = 0) & join_associative(all_0_17_17) = v0) | ( ~ (v0 = 0) & meet_commutative(all_0_17_17) = v0) | ( ~ (v0 = 0) & meet_associative(all_0_17_17) = v0) | ( ~ (v0 = 0) & meet_absorbing(all_0_17_17) = v0) | ( ~ (v0 = 0) & join_absorbing(all_0_17_17) = v0)) % 21.94/5.75 | % 21.94/5.75 | Instantiating formula (120) with all_0_17_17 and discharging atoms latt_str(all_0_17_17) = 0, yields: % 21.94/5.75 | (148) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & v2 = 0 & v1 = 0 & ~ (v0 = 0) & empty_carrier(all_0_17_17) = v0 & join_commutative(all_0_17_17) = 0 & join_associative(all_0_17_17) = 0 & meet_commutative(all_0_17_17) = 0 & meet_associative(all_0_17_17) = 0 & meet_absorbing(all_0_17_17) = 0 & join_absorbing(all_0_17_17) = 0) | (v0 = 0 & empty_carrier(all_0_17_17) = 0) | ( ~ (v0 = 0) & lattice(all_0_17_17) = v0)) % 21.94/5.75 | % 21.94/5.75 | Instantiating formula (17) with all_0_17_17 and discharging atoms latt_str(all_0_17_17) = 0, yields: % 21.94/5.75 | (149) ? [v0] : ? [v1] : ((v1 = v0 & relation_of_lattice(all_0_17_17) = v0 & a_1_0_filter_1(all_0_17_17) = v0) | (v0 = 0 & empty_carrier(all_0_17_17) = 0) | ( ~ (v0 = 0) & lattice(all_0_17_17) = v0)) % 21.94/5.75 | % 21.94/5.75 | Instantiating formula (20) with all_0_17_17 and discharging atoms latt_str(all_0_17_17) = 0, yields: % 21.94/5.75 | (150) ? [v0] : ? [v1] : ((v1 = 0 & ~ (v0 = 0) & lattice(all_0_17_17) = 0 & empty_carrier(all_0_17_17) = v0) | (v0 = 0 & empty_carrier(all_0_17_17) = 0) | ( ~ (v0 = 0) & join_commutative(all_0_17_17) = v0) | ( ~ (v0 = 0) & join_associative(all_0_17_17) = v0) | ( ~ (v0 = 0) & meet_commutative(all_0_17_17) = v0) | ( ~ (v0 = 0) & meet_associative(all_0_17_17) = v0) | ( ~ (v0 = 0) & meet_absorbing(all_0_17_17) = v0) | ( ~ (v0 = 0) & join_absorbing(all_0_17_17) = v0)) % 21.94/5.75 | % 21.94/5.75 | Instantiating formula (42) with all_0_17_17 and discharging atoms latt_str(all_0_17_17) = 0, yields: % 21.94/5.75 | (151) join_semilatt_str(all_0_17_17) = 0 & meet_semilatt_str(all_0_17_17) = 0 % 21.94/5.75 | % 21.94/5.75 | Applying alpha-rule on (151) yields: % 21.94/5.75 | (152) join_semilatt_str(all_0_17_17) = 0 % 21.94/5.75 | (153) meet_semilatt_str(all_0_17_17) = 0 % 21.94/5.75 | % 21.94/5.75 | Instantiating formula (125) with all_0_16_16, all_0_17_17 and discharging atoms empty_carrier(all_0_17_17) = all_0_16_16, yields: % 21.94/5.75 | (154) all_0_16_16 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & v3 = 0 & v2 = 0 & v1 = 0 & v0 = 0 & join_commutative(all_0_17_17) = 0 & join_associative(all_0_17_17) = 0 & meet_commutative(all_0_17_17) = 0 & meet_associative(all_0_17_17) = 0 & meet_absorbing(all_0_17_17) = 0 & join_absorbing(all_0_17_17) = 0) | ( ~ (v0 = 0) & lattice(all_0_17_17) = v0) | ( ~ (v0 = 0) & latt_str(all_0_17_17) = v0)) % 21.94/5.75 | % 21.94/5.75 | Instantiating formula (122) with all_0_16_16, all_0_17_17 and discharging atoms empty_carrier(all_0_17_17) = all_0_16_16, yields: % 21.94/5.76 | (155) all_0_16_16 = 0 | ? [v0] : ? [v1] : ((v1 = v0 & relation_of_lattice(all_0_17_17) = v0 & a_1_0_filter_1(all_0_17_17) = v0) | ( ~ (v0 = 0) & lattice(all_0_17_17) = v0) | ( ~ (v0 = 0) & latt_str(all_0_17_17) = v0)) % 21.94/5.76 | % 21.94/5.76 | Instantiating formula (89) with all_0_16_16, all_0_17_17 and discharging atoms empty_carrier(all_0_17_17) = all_0_16_16, yields: % 21.94/5.76 | (156) all_0_16_16 = 0 | ? [v0] : ? [v1] : ((v1 = 0 & relation(v0) = 0 & relation_of_lattice(all_0_17_17) = v0) | ( ~ (v0 = 0) & lattice(all_0_17_17) = v0) | ( ~ (v0 = 0) & latt_str(all_0_17_17) = v0)) % 21.94/5.76 | % 21.94/5.76 | Instantiating formula (3) with all_0_16_16, all_0_17_17 and discharging atoms empty_carrier(all_0_17_17) = all_0_16_16, yields: % 21.94/5.76 | (157) all_0_16_16 = 0 | ? [v0] : ? [v1] : (( ~ (v1 = 0) & the_carrier(all_0_17_17) = v0 & empty(v0) = v1) | ( ~ (v0 = 0) & one_sorted_str(all_0_17_17) = v0)) % 21.94/5.76 | % 21.94/5.76 | Instantiating formula (81) with all_0_16_16, all_0_17_17 and discharging atoms empty_carrier(all_0_17_17) = all_0_16_16, yields: % 21.94/5.76 | (158) all_0_16_16 = 0 | ? [v0] : ((v0 = 0 & lattice(all_0_17_17) = 0) | ( ~ (v0 = 0) & latt_str(all_0_17_17) = v0) | ( ~ (v0 = 0) & join_commutative(all_0_17_17) = v0) | ( ~ (v0 = 0) & join_associative(all_0_17_17) = v0) | ( ~ (v0 = 0) & meet_commutative(all_0_17_17) = v0) | ( ~ (v0 = 0) & meet_associative(all_0_17_17) = v0) | ( ~ (v0 = 0) & meet_absorbing(all_0_17_17) = v0) | ( ~ (v0 = 0) & join_absorbing(all_0_17_17) = v0)) % 21.94/5.76 | % 21.94/5.76 | Instantiating formula (134) with all_0_10_10, all_0_14_14, all_0_11_11 and discharging atoms in(all_0_11_11, all_0_14_14) = all_0_10_10, yields: % 21.94/5.76 | (159) all_0_10_10 = 0 | ? [v0] : ((v0 = 0 & empty(all_0_14_14) = 0) | ( ~ (v0 = 0) & element(all_0_11_11, all_0_14_14) = v0)) % 21.94/5.76 | % 21.94/5.76 | Instantiating (147) with all_70_0_95 yields: % 21.94/5.76 | (160) (all_70_0_95 = 0 & empty_carrier(all_0_17_17) = 0) | ( ~ (all_70_0_95 = 0) & latt_str(all_0_17_17) = all_70_0_95) | ( ~ (all_70_0_95 = 0) & empty_carrier(all_0_17_17) = all_70_0_95) | ( ~ (all_70_0_95 = 0) & join_commutative(all_0_17_17) = all_70_0_95) | ( ~ (all_70_0_95 = 0) & join_associative(all_0_17_17) = all_70_0_95) | ( ~ (all_70_0_95 = 0) & meet_commutative(all_0_17_17) = all_70_0_95) | ( ~ (all_70_0_95 = 0) & meet_associative(all_0_17_17) = all_70_0_95) | ( ~ (all_70_0_95 = 0) & meet_absorbing(all_0_17_17) = all_70_0_95) | ( ~ (all_70_0_95 = 0) & join_absorbing(all_0_17_17) = all_70_0_95) % 21.94/5.76 | % 21.94/5.76 | Instantiating (143) with all_71_0_96 yields: % 21.94/5.76 | (161) (all_71_0_96 = all_0_11_11 & ordered_pair(all_0_13_13, all_0_12_12) = all_0_11_11) | (all_71_0_96 = 0 & empty(all_0_15_15) = 0) | ( ~ (all_71_0_96 = 0) & element(all_0_12_12, all_0_15_15) = all_71_0_96) | ( ~ (all_71_0_96 = 0) & element(all_0_13_13, all_0_15_15) = all_71_0_96) % 21.94/5.76 | % 21.94/5.76 | Instantiating (150) with all_74_0_101, all_74_1_102 yields: % 21.94/5.76 | (162) (all_74_0_101 = 0 & ~ (all_74_1_102 = 0) & lattice(all_0_17_17) = 0 & empty_carrier(all_0_17_17) = all_74_1_102) | (all_74_1_102 = 0 & empty_carrier(all_0_17_17) = 0) | ( ~ (all_74_1_102 = 0) & join_commutative(all_0_17_17) = all_74_1_102) | ( ~ (all_74_1_102 = 0) & join_associative(all_0_17_17) = all_74_1_102) | ( ~ (all_74_1_102 = 0) & meet_commutative(all_0_17_17) = all_74_1_102) | ( ~ (all_74_1_102 = 0) & meet_associative(all_0_17_17) = all_74_1_102) | ( ~ (all_74_1_102 = 0) & meet_absorbing(all_0_17_17) = all_74_1_102) | ( ~ (all_74_1_102 = 0) & join_absorbing(all_0_17_17) = all_74_1_102) % 21.94/5.76 | % 21.94/5.76 | Instantiating (149) with all_78_0_109, all_78_1_110 yields: % 21.94/5.76 | (163) (all_78_0_109 = all_78_1_110 & relation_of_lattice(all_0_17_17) = all_78_1_110 & a_1_0_filter_1(all_0_17_17) = all_78_1_110) | (all_78_1_110 = 0 & empty_carrier(all_0_17_17) = 0) | ( ~ (all_78_1_110 = 0) & lattice(all_0_17_17) = all_78_1_110) % 21.94/5.76 | % 21.94/5.76 | Instantiating (148) with all_79_0_111, all_79_1_112, all_79_2_113, all_79_3_114, all_79_4_115, all_79_5_116, all_79_6_117 yields: % 21.94/5.76 | (164) (all_79_0_111 = 0 & all_79_1_112 = 0 & all_79_2_113 = 0 & all_79_3_114 = 0 & all_79_4_115 = 0 & all_79_5_116 = 0 & ~ (all_79_6_117 = 0) & empty_carrier(all_0_17_17) = all_79_6_117 & join_commutative(all_0_17_17) = 0 & join_associative(all_0_17_17) = 0 & meet_commutative(all_0_17_17) = 0 & meet_associative(all_0_17_17) = 0 & meet_absorbing(all_0_17_17) = 0 & join_absorbing(all_0_17_17) = 0) | (all_79_6_117 = 0 & empty_carrier(all_0_17_17) = 0) | ( ~ (all_79_6_117 = 0) & lattice(all_0_17_17) = all_79_6_117) % 21.94/5.76 | % 21.94/5.76 | Instantiating (144) with all_80_0_118, all_80_1_119, all_80_2_120, all_80_3_121, all_80_4_122, all_80_5_123, all_80_6_124 yields: % 21.94/5.76 | (165) (all_80_0_118 = 0 & all_80_1_119 = 0 & all_80_2_120 = 0 & all_80_3_121 = 0 & all_80_4_122 = 0 & all_80_5_123 = 0 & ~ (all_80_6_124 = 0) & empty_carrier(all_0_17_17) = all_80_6_124 & join_commutative(all_0_17_17) = 0 & join_associative(all_0_17_17) = 0 & meet_commutative(all_0_17_17) = 0 & meet_associative(all_0_17_17) = 0 & meet_absorbing(all_0_17_17) = 0 & join_absorbing(all_0_17_17) = 0) | (all_80_6_124 = 0 & empty_carrier(all_0_17_17) = 0) | ( ~ (all_80_6_124 = 0) & latt_str(all_0_17_17) = all_80_6_124) % 21.94/5.76 | % 21.94/5.76 | Instantiating (146) with all_82_0_126, all_82_1_127 yields: % 21.94/5.76 | (166) (all_82_0_126 = 0 & relation(all_82_1_127) = 0 & relation_of_lattice(all_0_17_17) = all_82_1_127) | (all_82_1_127 = 0 & empty_carrier(all_0_17_17) = 0) | ( ~ (all_82_1_127 = 0) & latt_str(all_0_17_17) = all_82_1_127) % 21.94/5.76 | % 21.94/5.76 | Instantiating (142) with all_85_0_130 yields: % 21.94/5.76 | (167) (all_85_0_130 = 0 & empty_carrier(all_0_17_17) = 0) | ( ~ (all_85_0_130 = 0) & one_sorted_str(all_0_17_17) = all_85_0_130) | ( ~ (all_85_0_130 = 0) & empty(all_0_15_15) = all_85_0_130) % 21.94/5.76 | % 21.94/5.76 | Instantiating (141) with all_86_0_131, all_86_1_132 yields: % 21.94/5.76 | (168) (all_86_1_132 = 0 & empty_carrier(all_0_17_17) = 0) | ( ~ (all_86_0_131 = 0) & the_carrier(all_0_17_17) = all_86_1_132 & element(all_0_12_12, all_86_1_132) = all_86_0_131) | ( ~ (all_86_0_131 = 0) & the_carrier(all_0_17_17) = all_86_1_132 & element(all_0_13_13, all_86_1_132) = all_86_0_131) | ( ~ (all_86_1_132 = 0) & latt_str(all_0_17_17) = all_86_1_132) | ( ~ (all_86_1_132 = 0) & meet_commutative(all_0_17_17) = all_86_1_132) | ( ~ (all_86_1_132 = 0) & meet_absorbing(all_0_17_17) = all_86_1_132) | ( ~ (all_86_1_132 = 0) & join_absorbing(all_0_17_17) = all_86_1_132) | (( ~ (all_0_9_9 = 0) | (all_86_1_132 = 0 & below(all_0_17_17, all_0_13_13, all_0_12_12) = 0)) & (all_0_9_9 = 0 | ( ~ (all_86_1_132 = 0) & below(all_0_17_17, all_0_13_13, all_0_12_12) = all_86_1_132))) % 21.94/5.76 | % 21.94/5.76 | Instantiating (145) with all_87_0_133, all_87_1_134 yields: % 21.94/5.76 | (169) (all_87_0_133 = all_87_1_134 & relation_of_lattice(all_0_17_17) = all_87_1_134 & a_1_0_filter_1(all_0_17_17) = all_87_1_134) | (all_87_1_134 = 0 & empty_carrier(all_0_17_17) = 0) | ( ~ (all_87_1_134 = 0) & latt_str(all_0_17_17) = all_87_1_134) % 21.94/5.76 | % 21.94/5.76 +-Applying beta-rule and splitting (163), into two cases. % 21.94/5.76 |-Branch one: % 21.94/5.76 | (170) (all_78_0_109 = all_78_1_110 & relation_of_lattice(all_0_17_17) = all_78_1_110 & a_1_0_filter_1(all_0_17_17) = all_78_1_110) | (all_78_1_110 = 0 & empty_carrier(all_0_17_17) = 0) % 21.94/5.76 | % 21.94/5.76 +-Applying beta-rule and splitting (170), into two cases. % 21.94/5.76 |-Branch one: % 21.94/5.76 | (171) all_78_0_109 = all_78_1_110 & relation_of_lattice(all_0_17_17) = all_78_1_110 & a_1_0_filter_1(all_0_17_17) = all_78_1_110 % 21.94/5.76 | % 21.94/5.76 | Applying alpha-rule on (171) yields: % 21.94/5.76 | (172) all_78_0_109 = all_78_1_110 % 21.94/5.76 | (173) relation_of_lattice(all_0_17_17) = all_78_1_110 % 21.94/5.76 | (174) a_1_0_filter_1(all_0_17_17) = all_78_1_110 % 21.94/5.76 | % 21.94/5.76 +-Applying beta-rule and splitting (164), into two cases. % 21.94/5.76 |-Branch one: % 21.94/5.76 | (175) (all_79_0_111 = 0 & all_79_1_112 = 0 & all_79_2_113 = 0 & all_79_3_114 = 0 & all_79_4_115 = 0 & all_79_5_116 = 0 & ~ (all_79_6_117 = 0) & empty_carrier(all_0_17_17) = all_79_6_117 & join_commutative(all_0_17_17) = 0 & join_associative(all_0_17_17) = 0 & meet_commutative(all_0_17_17) = 0 & meet_associative(all_0_17_17) = 0 & meet_absorbing(all_0_17_17) = 0 & join_absorbing(all_0_17_17) = 0) | (all_79_6_117 = 0 & empty_carrier(all_0_17_17) = 0) % 21.94/5.76 | % 21.94/5.76 +-Applying beta-rule and splitting (175), into two cases. % 21.94/5.76 |-Branch one: % 21.94/5.76 | (176) all_79_0_111 = 0 & all_79_1_112 = 0 & all_79_2_113 = 0 & all_79_3_114 = 0 & all_79_4_115 = 0 & all_79_5_116 = 0 & ~ (all_79_6_117 = 0) & empty_carrier(all_0_17_17) = all_79_6_117 & join_commutative(all_0_17_17) = 0 & join_associative(all_0_17_17) = 0 & meet_commutative(all_0_17_17) = 0 & meet_associative(all_0_17_17) = 0 & meet_absorbing(all_0_17_17) = 0 & join_absorbing(all_0_17_17) = 0 % 21.94/5.76 | % 21.94/5.76 | Applying alpha-rule on (176) yields: % 21.94/5.76 | (177) all_79_3_114 = 0 % 21.94/5.76 | (178) join_associative(all_0_17_17) = 0 % 21.94/5.76 | (179) all_79_2_113 = 0 % 21.94/5.76 | (180) meet_absorbing(all_0_17_17) = 0 % 21.94/5.76 | (181) join_absorbing(all_0_17_17) = 0 % 21.94/5.76 | (182) meet_associative(all_0_17_17) = 0 % 21.94/5.76 | (183) all_79_0_111 = 0 % 21.94/5.76 | (184) all_79_4_115 = 0 % 21.94/5.76 | (185) empty_carrier(all_0_17_17) = all_79_6_117 % 21.94/5.76 | (186) ~ (all_79_6_117 = 0) % 21.94/5.76 | (187) join_commutative(all_0_17_17) = 0 % 21.94/5.76 | (188) all_79_5_116 = 0 % 21.94/5.76 | (189) meet_commutative(all_0_17_17) = 0 % 21.94/5.76 | (190) all_79_1_112 = 0 % 21.94/5.76 | % 21.94/5.76 +-Applying beta-rule and splitting (166), into two cases. % 21.94/5.76 |-Branch one: % 21.94/5.76 | (191) (all_82_0_126 = 0 & relation(all_82_1_127) = 0 & relation_of_lattice(all_0_17_17) = all_82_1_127) | (all_82_1_127 = 0 & empty_carrier(all_0_17_17) = 0) % 21.94/5.76 | % 21.94/5.76 +-Applying beta-rule and splitting (191), into two cases. % 21.94/5.76 |-Branch one: % 21.94/5.76 | (192) all_82_0_126 = 0 & relation(all_82_1_127) = 0 & relation_of_lattice(all_0_17_17) = all_82_1_127 % 21.94/5.76 | % 21.94/5.76 | Applying alpha-rule on (192) yields: % 21.94/5.76 | (193) all_82_0_126 = 0 % 21.94/5.76 | (194) relation(all_82_1_127) = 0 % 21.94/5.76 | (195) relation_of_lattice(all_0_17_17) = all_82_1_127 % 21.94/5.76 | % 21.94/5.76 +-Applying beta-rule and splitting (165), into two cases. % 21.94/5.76 |-Branch one: % 21.94/5.76 | (196) (all_80_0_118 = 0 & all_80_1_119 = 0 & all_80_2_120 = 0 & all_80_3_121 = 0 & all_80_4_122 = 0 & all_80_5_123 = 0 & ~ (all_80_6_124 = 0) & empty_carrier(all_0_17_17) = all_80_6_124 & join_commutative(all_0_17_17) = 0 & join_associative(all_0_17_17) = 0 & meet_commutative(all_0_17_17) = 0 & meet_associative(all_0_17_17) = 0 & meet_absorbing(all_0_17_17) = 0 & join_absorbing(all_0_17_17) = 0) | (all_80_6_124 = 0 & empty_carrier(all_0_17_17) = 0) % 21.94/5.76 | % 21.94/5.76 +-Applying beta-rule and splitting (196), into two cases. % 21.94/5.76 |-Branch one: % 21.94/5.77 | (197) all_80_0_118 = 0 & all_80_1_119 = 0 & all_80_2_120 = 0 & all_80_3_121 = 0 & all_80_4_122 = 0 & all_80_5_123 = 0 & ~ (all_80_6_124 = 0) & empty_carrier(all_0_17_17) = all_80_6_124 & join_commutative(all_0_17_17) = 0 & join_associative(all_0_17_17) = 0 & meet_commutative(all_0_17_17) = 0 & meet_associative(all_0_17_17) = 0 & meet_absorbing(all_0_17_17) = 0 & join_absorbing(all_0_17_17) = 0 % 21.94/5.77 | % 21.94/5.77 | Applying alpha-rule on (197) yields: % 21.94/5.77 | (178) join_associative(all_0_17_17) = 0 % 21.94/5.77 | (199) all_80_1_119 = 0 % 21.94/5.77 | (200) all_80_4_122 = 0 % 21.94/5.77 | (180) meet_absorbing(all_0_17_17) = 0 % 21.94/5.77 | (202) empty_carrier(all_0_17_17) = all_80_6_124 % 21.94/5.77 | (203) all_80_0_118 = 0 % 21.94/5.77 | (204) all_80_5_123 = 0 % 21.94/5.77 | (181) join_absorbing(all_0_17_17) = 0 % 21.94/5.77 | (182) meet_associative(all_0_17_17) = 0 % 21.94/5.77 | (207) all_80_3_121 = 0 % 21.94/5.77 | (208) ~ (all_80_6_124 = 0) % 21.94/5.77 | (187) join_commutative(all_0_17_17) = 0 % 21.94/5.77 | (189) meet_commutative(all_0_17_17) = 0 % 21.94/5.77 | (211) all_80_2_120 = 0 % 21.94/5.77 | % 21.94/5.77 +-Applying beta-rule and splitting (157), into two cases. % 21.94/5.77 |-Branch one: % 21.94/5.77 | (212) all_0_16_16 = 0 % 21.94/5.77 | % 21.94/5.77 | Equations (212) can reduce 98 to: % 21.94/5.77 | (213) $false % 21.94/5.77 | % 21.94/5.77 |-The branch is then unsatisfiable % 21.94/5.77 |-Branch two: % 21.94/5.77 | (98) ~ (all_0_16_16 = 0) % 21.94/5.77 | (215) ? [v0] : ? [v1] : (( ~ (v1 = 0) & the_carrier(all_0_17_17) = v0 & empty(v0) = v1) | ( ~ (v0 = 0) & one_sorted_str(all_0_17_17) = v0)) % 21.94/5.77 | % 21.94/5.77 | Instantiating (215) with all_146_0_162, all_146_1_163 yields: % 21.94/5.77 | (216) ( ~ (all_146_0_162 = 0) & the_carrier(all_0_17_17) = all_146_1_163 & empty(all_146_1_163) = all_146_0_162) | ( ~ (all_146_1_163 = 0) & one_sorted_str(all_0_17_17) = all_146_1_163) % 21.94/5.77 | % 21.94/5.77 +-Applying beta-rule and splitting (162), into two cases. % 21.94/5.77 |-Branch one: % 21.94/5.77 | (217) (all_74_0_101 = 0 & ~ (all_74_1_102 = 0) & lattice(all_0_17_17) = 0 & empty_carrier(all_0_17_17) = all_74_1_102) | (all_74_1_102 = 0 & empty_carrier(all_0_17_17) = 0) | ( ~ (all_74_1_102 = 0) & join_commutative(all_0_17_17) = all_74_1_102) | ( ~ (all_74_1_102 = 0) & join_associative(all_0_17_17) = all_74_1_102) | ( ~ (all_74_1_102 = 0) & meet_commutative(all_0_17_17) = all_74_1_102) | ( ~ (all_74_1_102 = 0) & meet_associative(all_0_17_17) = all_74_1_102) | ( ~ (all_74_1_102 = 0) & meet_absorbing(all_0_17_17) = all_74_1_102) % 21.94/5.77 | % 21.94/5.77 +-Applying beta-rule and splitting (217), into two cases. % 21.94/5.77 |-Branch one: % 21.94/5.77 | (218) (all_74_0_101 = 0 & ~ (all_74_1_102 = 0) & lattice(all_0_17_17) = 0 & empty_carrier(all_0_17_17) = all_74_1_102) | (all_74_1_102 = 0 & empty_carrier(all_0_17_17) = 0) | ( ~ (all_74_1_102 = 0) & join_commutative(all_0_17_17) = all_74_1_102) | ( ~ (all_74_1_102 = 0) & join_associative(all_0_17_17) = all_74_1_102) | ( ~ (all_74_1_102 = 0) & meet_commutative(all_0_17_17) = all_74_1_102) | ( ~ (all_74_1_102 = 0) & meet_associative(all_0_17_17) = all_74_1_102) % 21.94/5.77 | % 21.94/5.77 +-Applying beta-rule and splitting (218), into two cases. % 21.94/5.77 |-Branch one: % 21.94/5.77 | (219) (all_74_0_101 = 0 & ~ (all_74_1_102 = 0) & lattice(all_0_17_17) = 0 & empty_carrier(all_0_17_17) = all_74_1_102) | (all_74_1_102 = 0 & empty_carrier(all_0_17_17) = 0) | ( ~ (all_74_1_102 = 0) & join_commutative(all_0_17_17) = all_74_1_102) | ( ~ (all_74_1_102 = 0) & join_associative(all_0_17_17) = all_74_1_102) | ( ~ (all_74_1_102 = 0) & meet_commutative(all_0_17_17) = all_74_1_102) % 21.94/5.77 | % 21.94/5.77 +-Applying beta-rule and splitting (219), into two cases. % 21.94/5.77 |-Branch one: % 21.94/5.77 | (220) (all_74_0_101 = 0 & ~ (all_74_1_102 = 0) & lattice(all_0_17_17) = 0 & empty_carrier(all_0_17_17) = all_74_1_102) | (all_74_1_102 = 0 & empty_carrier(all_0_17_17) = 0) | ( ~ (all_74_1_102 = 0) & join_commutative(all_0_17_17) = all_74_1_102) | ( ~ (all_74_1_102 = 0) & join_associative(all_0_17_17) = all_74_1_102) % 21.94/5.77 | % 21.94/5.77 +-Applying beta-rule and splitting (220), into two cases. % 21.94/5.77 |-Branch one: % 21.94/5.77 | (221) (all_74_0_101 = 0 & ~ (all_74_1_102 = 0) & lattice(all_0_17_17) = 0 & empty_carrier(all_0_17_17) = all_74_1_102) | (all_74_1_102 = 0 & empty_carrier(all_0_17_17) = 0) | ( ~ (all_74_1_102 = 0) & join_commutative(all_0_17_17) = all_74_1_102) % 21.94/5.77 | % 21.94/5.77 +-Applying beta-rule and splitting (221), into two cases. % 21.94/5.77 |-Branch one: % 21.94/5.77 | (222) (all_74_0_101 = 0 & ~ (all_74_1_102 = 0) & lattice(all_0_17_17) = 0 & empty_carrier(all_0_17_17) = all_74_1_102) | (all_74_1_102 = 0 & empty_carrier(all_0_17_17) = 0) % 21.94/5.77 | % 21.94/5.77 +-Applying beta-rule and splitting (222), into two cases. % 21.94/5.77 |-Branch one: % 21.94/5.77 | (223) all_74_0_101 = 0 & ~ (all_74_1_102 = 0) & lattice(all_0_17_17) = 0 & empty_carrier(all_0_17_17) = all_74_1_102 % 21.94/5.77 | % 21.94/5.77 | Applying alpha-rule on (223) yields: % 21.94/5.77 | (224) all_74_0_101 = 0 % 21.94/5.77 | (225) ~ (all_74_1_102 = 0) % 21.94/5.77 | (11) lattice(all_0_17_17) = 0 % 21.94/5.77 | (227) empty_carrier(all_0_17_17) = all_74_1_102 % 21.94/5.77 | % 21.94/5.77 +-Applying beta-rule and splitting (169), into two cases. % 21.94/5.77 |-Branch one: % 21.94/5.77 | (228) (all_87_0_133 = all_87_1_134 & relation_of_lattice(all_0_17_17) = all_87_1_134 & a_1_0_filter_1(all_0_17_17) = all_87_1_134) | (all_87_1_134 = 0 & empty_carrier(all_0_17_17) = 0) % 21.94/5.77 | % 21.94/5.77 +-Applying beta-rule and splitting (228), into two cases. % 21.94/5.77 |-Branch one: % 21.94/5.77 | (229) all_87_0_133 = all_87_1_134 & relation_of_lattice(all_0_17_17) = all_87_1_134 & a_1_0_filter_1(all_0_17_17) = all_87_1_134 % 21.94/5.77 | % 21.94/5.77 | Applying alpha-rule on (229) yields: % 21.94/5.77 | (230) all_87_0_133 = all_87_1_134 % 21.94/5.77 | (231) relation_of_lattice(all_0_17_17) = all_87_1_134 % 21.94/5.77 | (232) a_1_0_filter_1(all_0_17_17) = all_87_1_134 % 21.94/5.77 | % 21.94/5.77 +-Applying beta-rule and splitting (160), into two cases. % 21.94/5.77 |-Branch one: % 21.94/5.77 | (233) (all_70_0_95 = 0 & empty_carrier(all_0_17_17) = 0) | ( ~ (all_70_0_95 = 0) & latt_str(all_0_17_17) = all_70_0_95) | ( ~ (all_70_0_95 = 0) & empty_carrier(all_0_17_17) = all_70_0_95) | ( ~ (all_70_0_95 = 0) & join_commutative(all_0_17_17) = all_70_0_95) | ( ~ (all_70_0_95 = 0) & join_associative(all_0_17_17) = all_70_0_95) | ( ~ (all_70_0_95 = 0) & meet_commutative(all_0_17_17) = all_70_0_95) | ( ~ (all_70_0_95 = 0) & meet_associative(all_0_17_17) = all_70_0_95) | ( ~ (all_70_0_95 = 0) & meet_absorbing(all_0_17_17) = all_70_0_95) % 21.94/5.77 | % 21.94/5.77 +-Applying beta-rule and splitting (233), into two cases. % 21.94/5.77 |-Branch one: % 21.94/5.77 | (234) (all_70_0_95 = 0 & empty_carrier(all_0_17_17) = 0) | ( ~ (all_70_0_95 = 0) & latt_str(all_0_17_17) = all_70_0_95) | ( ~ (all_70_0_95 = 0) & empty_carrier(all_0_17_17) = all_70_0_95) | ( ~ (all_70_0_95 = 0) & join_commutative(all_0_17_17) = all_70_0_95) | ( ~ (all_70_0_95 = 0) & join_associative(all_0_17_17) = all_70_0_95) | ( ~ (all_70_0_95 = 0) & meet_commutative(all_0_17_17) = all_70_0_95) | ( ~ (all_70_0_95 = 0) & meet_associative(all_0_17_17) = all_70_0_95) % 21.94/5.77 | % 21.94/5.77 +-Applying beta-rule and splitting (234), into two cases. % 21.94/5.77 |-Branch one: % 21.94/5.77 | (235) (all_70_0_95 = 0 & empty_carrier(all_0_17_17) = 0) | ( ~ (all_70_0_95 = 0) & latt_str(all_0_17_17) = all_70_0_95) | ( ~ (all_70_0_95 = 0) & empty_carrier(all_0_17_17) = all_70_0_95) | ( ~ (all_70_0_95 = 0) & join_commutative(all_0_17_17) = all_70_0_95) | ( ~ (all_70_0_95 = 0) & join_associative(all_0_17_17) = all_70_0_95) | ( ~ (all_70_0_95 = 0) & meet_commutative(all_0_17_17) = all_70_0_95) % 21.94/5.77 | % 21.94/5.77 +-Applying beta-rule and splitting (235), into two cases. % 21.94/5.77 |-Branch one: % 21.94/5.77 | (236) (all_70_0_95 = 0 & empty_carrier(all_0_17_17) = 0) | ( ~ (all_70_0_95 = 0) & latt_str(all_0_17_17) = all_70_0_95) | ( ~ (all_70_0_95 = 0) & empty_carrier(all_0_17_17) = all_70_0_95) | ( ~ (all_70_0_95 = 0) & join_commutative(all_0_17_17) = all_70_0_95) | ( ~ (all_70_0_95 = 0) & join_associative(all_0_17_17) = all_70_0_95) % 21.94/5.77 | % 21.94/5.77 +-Applying beta-rule and splitting (236), into two cases. % 21.94/5.77 |-Branch one: % 21.94/5.77 | (237) (all_70_0_95 = 0 & empty_carrier(all_0_17_17) = 0) | ( ~ (all_70_0_95 = 0) & latt_str(all_0_17_17) = all_70_0_95) | ( ~ (all_70_0_95 = 0) & empty_carrier(all_0_17_17) = all_70_0_95) | ( ~ (all_70_0_95 = 0) & join_commutative(all_0_17_17) = all_70_0_95) % 21.94/5.77 | % 21.94/5.77 +-Applying beta-rule and splitting (237), into two cases. % 21.94/5.77 |-Branch one: % 21.94/5.77 | (238) (all_70_0_95 = 0 & empty_carrier(all_0_17_17) = 0) | ( ~ (all_70_0_95 = 0) & latt_str(all_0_17_17) = all_70_0_95) | ( ~ (all_70_0_95 = 0) & empty_carrier(all_0_17_17) = all_70_0_95) % 21.94/5.77 | % 21.94/5.77 +-Applying beta-rule and splitting (238), into two cases. % 21.94/5.77 |-Branch one: % 21.94/5.77 | (239) (all_70_0_95 = 0 & empty_carrier(all_0_17_17) = 0) | ( ~ (all_70_0_95 = 0) & latt_str(all_0_17_17) = all_70_0_95) % 21.94/5.77 | % 21.94/5.77 +-Applying beta-rule and splitting (239), into two cases. % 21.94/5.77 |-Branch one: % 21.94/5.77 | (240) all_70_0_95 = 0 & empty_carrier(all_0_17_17) = 0 % 21.94/5.77 | % 21.94/5.77 | Applying alpha-rule on (240) yields: % 21.94/5.77 | (241) all_70_0_95 = 0 % 21.94/5.77 | (242) empty_carrier(all_0_17_17) = 0 % 21.94/5.77 | % 21.94/5.77 | Instantiating formula (73) with all_0_17_17, all_80_6_124, all_0_16_16 and discharging atoms empty_carrier(all_0_17_17) = all_80_6_124, empty_carrier(all_0_17_17) = all_0_16_16, yields: % 21.94/5.77 | (243) all_80_6_124 = all_0_16_16 % 21.94/5.77 | % 21.94/5.77 | Instantiating formula (73) with all_0_17_17, all_79_6_117, all_80_6_124 and discharging atoms empty_carrier(all_0_17_17) = all_80_6_124, empty_carrier(all_0_17_17) = all_79_6_117, yields: % 21.94/5.77 | (244) all_80_6_124 = all_79_6_117 % 21.94/5.77 | % 21.94/5.77 | Instantiating formula (73) with all_0_17_17, all_74_1_102, all_80_6_124 and discharging atoms empty_carrier(all_0_17_17) = all_80_6_124, empty_carrier(all_0_17_17) = all_74_1_102, yields: % 21.94/5.77 | (245) all_80_6_124 = all_74_1_102 % 21.94/5.77 | % 21.94/5.77 | Instantiating formula (73) with all_0_17_17, 0, all_74_1_102 and discharging atoms empty_carrier(all_0_17_17) = all_74_1_102, empty_carrier(all_0_17_17) = 0, yields: % 21.94/5.77 | (246) all_74_1_102 = 0 % 21.94/5.77 | % 21.94/5.78 | Combining equations (245,244) yields a new equation: % 21.94/5.78 | (247) all_79_6_117 = all_74_1_102 % 21.94/5.78 | % 21.94/5.78 | Combining equations (243,244) yields a new equation: % 21.94/5.78 | (248) all_79_6_117 = all_0_16_16 % 21.94/5.78 | % 21.94/5.78 | Combining equations (247,248) yields a new equation: % 21.94/5.78 | (249) all_74_1_102 = all_0_16_16 % 21.94/5.78 | % 21.94/5.78 | Simplifying 249 yields: % 21.94/5.78 | (250) all_74_1_102 = all_0_16_16 % 21.94/5.78 | % 21.94/5.78 | Combining equations (250,246) yields a new equation: % 21.94/5.78 | (251) all_0_16_16 = 0 % 21.94/5.78 | % 21.94/5.78 | Simplifying 251 yields: % 21.94/5.78 | (212) all_0_16_16 = 0 % 21.94/5.78 | % 21.94/5.78 | Equations (212) can reduce 98 to: % 21.94/5.78 | (213) $false % 21.94/5.78 | % 21.94/5.78 |-The branch is then unsatisfiable % 21.94/5.78 |-Branch two: % 21.94/5.78 | (254) ~ (all_70_0_95 = 0) & latt_str(all_0_17_17) = all_70_0_95 % 21.94/5.78 | % 21.94/5.78 | Applying alpha-rule on (254) yields: % 21.94/5.78 | (255) ~ (all_70_0_95 = 0) % 21.94/5.78 | (256) latt_str(all_0_17_17) = all_70_0_95 % 21.94/5.78 | % 21.94/5.78 | Instantiating formula (50) with all_0_17_17, all_70_0_95, 0 and discharging atoms latt_str(all_0_17_17) = all_70_0_95, latt_str(all_0_17_17) = 0, yields: % 21.94/5.78 | (241) all_70_0_95 = 0 % 21.94/5.78 | % 21.94/5.78 | Equations (241) can reduce 255 to: % 21.94/5.78 | (213) $false % 21.94/5.78 | % 21.94/5.78 |-The branch is then unsatisfiable % 21.94/5.78 |-Branch two: % 21.94/5.78 | (259) ~ (all_70_0_95 = 0) & empty_carrier(all_0_17_17) = all_70_0_95 % 21.94/5.78 | % 21.94/5.78 | Applying alpha-rule on (259) yields: % 21.94/5.78 | (255) ~ (all_70_0_95 = 0) % 21.94/5.78 | (261) empty_carrier(all_0_17_17) = all_70_0_95 % 21.94/5.78 | % 21.94/5.78 | Instantiating formula (53) with all_0_17_17, all_82_1_127, all_0_14_14 and discharging atoms relation_of_lattice(all_0_17_17) = all_82_1_127, relation_of_lattice(all_0_17_17) = all_0_14_14, yields: % 21.94/5.78 | (262) all_82_1_127 = all_0_14_14 % 21.94/5.78 | % 21.94/5.78 | Instantiating formula (53) with all_0_17_17, all_82_1_127, all_87_1_134 and discharging atoms relation_of_lattice(all_0_17_17) = all_87_1_134, relation_of_lattice(all_0_17_17) = all_82_1_127, yields: % 21.94/5.78 | (263) all_87_1_134 = all_82_1_127 % 21.94/5.78 | % 21.94/5.78 | Instantiating formula (111) with all_0_17_17, all_78_1_110, all_87_1_134 and discharging atoms a_1_0_filter_1(all_0_17_17) = all_87_1_134, a_1_0_filter_1(all_0_17_17) = all_78_1_110, yields: % 21.94/5.78 | (264) all_87_1_134 = all_78_1_110 % 21.94/5.78 | % 21.94/5.78 | Instantiating formula (73) with all_0_17_17, all_80_6_124, all_0_16_16 and discharging atoms empty_carrier(all_0_17_17) = all_80_6_124, empty_carrier(all_0_17_17) = all_0_16_16, yields: % 21.94/5.78 | (243) all_80_6_124 = all_0_16_16 % 21.94/5.78 | % 21.94/5.78 | Instantiating formula (73) with all_0_17_17, all_79_6_117, all_80_6_124 and discharging atoms empty_carrier(all_0_17_17) = all_80_6_124, empty_carrier(all_0_17_17) = all_79_6_117, yields: % 21.94/5.78 | (244) all_80_6_124 = all_79_6_117 % 21.94/5.78 | % 21.94/5.78 | Instantiating formula (73) with all_0_17_17, all_74_1_102, all_80_6_124 and discharging atoms empty_carrier(all_0_17_17) = all_80_6_124, empty_carrier(all_0_17_17) = all_74_1_102, yields: % 21.94/5.78 | (245) all_80_6_124 = all_74_1_102 % 21.94/5.78 | % 21.94/5.78 | Instantiating formula (73) with all_0_17_17, all_70_0_95, all_74_1_102 and discharging atoms empty_carrier(all_0_17_17) = all_74_1_102, empty_carrier(all_0_17_17) = all_70_0_95, yields: % 21.94/5.78 | (268) all_74_1_102 = all_70_0_95 % 21.94/5.78 | % 21.94/5.78 | Combining equations (263,264) yields a new equation: % 21.94/5.78 | (269) all_82_1_127 = all_78_1_110 % 21.94/5.78 | % 21.94/5.78 | Simplifying 269 yields: % 21.94/5.78 | (270) all_82_1_127 = all_78_1_110 % 21.94/5.78 | % 21.94/5.78 | Combining equations (262,270) yields a new equation: % 21.94/5.78 | (271) all_78_1_110 = all_0_14_14 % 21.94/5.78 | % 21.94/5.78 | Combining equations (245,244) yields a new equation: % 21.94/5.78 | (247) all_79_6_117 = all_74_1_102 % 21.94/5.78 | % 21.94/5.78 | Combining equations (243,244) yields a new equation: % 21.94/5.78 | (248) all_79_6_117 = all_0_16_16 % 21.94/5.78 | % 21.94/5.78 | Combining equations (247,248) yields a new equation: % 21.94/5.78 | (249) all_74_1_102 = all_0_16_16 % 21.94/5.78 | % 21.94/5.78 | Simplifying 249 yields: % 21.94/5.78 | (250) all_74_1_102 = all_0_16_16 % 21.94/5.78 | % 21.94/5.78 | Combining equations (268,250) yields a new equation: % 21.94/5.78 | (276) all_70_0_95 = all_0_16_16 % 21.94/5.78 | % 21.94/5.78 | Simplifying 276 yields: % 21.94/5.78 | (277) all_70_0_95 = all_0_16_16 % 21.94/5.78 | % 21.94/5.78 | Equations (277) can reduce 255 to: % 21.94/5.78 | (98) ~ (all_0_16_16 = 0) % 21.94/5.78 | % 21.94/5.78 | From (271) and (174) follows: % 21.94/5.78 | (279) a_1_0_filter_1(all_0_17_17) = all_0_14_14 % 21.94/5.78 | % 21.94/5.78 | From (277) and (261) follows: % 21.94/5.78 | (9) empty_carrier(all_0_17_17) = all_0_16_16 % 21.94/5.78 | % 21.94/5.78 | Instantiating formula (116) with all_0_17_17 and discharging atoms meet_semilatt_str(all_0_17_17) = 0, yields: % 21.94/5.78 | (281) one_sorted_str(all_0_17_17) = 0 % 21.94/5.78 | % 21.94/5.78 | Instantiating formula (74) with all_0_10_10, all_0_14_14, all_0_17_17, all_0_11_11 and discharging atoms a_1_0_filter_1(all_0_17_17) = all_0_14_14, in(all_0_11_11, all_0_14_14) = all_0_10_10, yields: % 21.94/5.78 | (282) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ((v0 = 0 & empty_carrier(all_0_17_17) = 0) | ( ~ (v0 = 0) & lattice(all_0_17_17) = v0) | ( ~ (v0 = 0) & latt_str(all_0_17_17) = v0) | (( ~ (all_0_10_10 = 0) | (v6 = 0 & v5 = all_0_11_11 & v4 = 0 & v3 = 0 & below_refl(all_0_17_17, v1, v2) = 0 & the_carrier(all_0_17_17) = v0 & ordered_pair_as_product_element(v0, v0, v1, v2) = all_0_11_11 & element(v2, v0) = 0 & element(v1, v0) = 0)) & (all_0_10_10 = 0 | (the_carrier(all_0_17_17) = v0 & ! [v7] : ! [v8] : ( ~ (below_refl(all_0_17_17, v7, v8) = 0) | ? [v9] : (( ~ (v9 = all_0_11_11) & ordered_pair_as_product_element(v0, v0, v7, v8) = v9) | ( ~ (v9 = 0) & element(v8, v0) = v9) | ( ~ (v9 = 0) & element(v7, v0) = v9))) & ! [v7] : ! [v8] : ( ~ (ordered_pair_as_product_element(v0, v0, v7, v8) = all_0_11_11) | ? [v9] : (( ~ (v9 = 0) & below_refl(all_0_17_17, v7, v8) = v9) | ( ~ (v9 = 0) & element(v8, v0) = v9) | ( ~ (v9 = 0) & element(v7, v0) = v9))))))) % 21.94/5.78 | % 21.94/5.78 | Instantiating (282) with all_191_0_168, all_191_1_169, all_191_2_170, all_191_3_171, all_191_4_172, all_191_5_173, all_191_6_174 yields: % 21.94/5.78 | (283) (all_191_6_174 = 0 & empty_carrier(all_0_17_17) = 0) | ( ~ (all_191_6_174 = 0) & lattice(all_0_17_17) = all_191_6_174) | ( ~ (all_191_6_174 = 0) & latt_str(all_0_17_17) = all_191_6_174) | (( ~ (all_0_10_10 = 0) | (all_191_0_168 = 0 & all_191_1_169 = all_0_11_11 & all_191_2_170 = 0 & all_191_3_171 = 0 & below_refl(all_0_17_17, all_191_5_173, all_191_4_172) = 0 & the_carrier(all_0_17_17) = all_191_6_174 & ordered_pair_as_product_element(all_191_6_174, all_191_6_174, all_191_5_173, all_191_4_172) = all_0_11_11 & element(all_191_4_172, all_191_6_174) = 0 & element(all_191_5_173, all_191_6_174) = 0)) & (all_0_10_10 = 0 | (the_carrier(all_0_17_17) = all_191_6_174 & ! [v0] : ! [v1] : ( ~ (below_refl(all_0_17_17, v0, v1) = 0) | ? [v2] : (( ~ (v2 = all_0_11_11) & ordered_pair_as_product_element(all_191_6_174, all_191_6_174, v0, v1) = v2) | ( ~ (v2 = 0) & element(v1, all_191_6_174) = v2) | ( ~ (v2 = 0) & element(v0, all_191_6_174) = v2))) & ! [v0] : ! [v1] : ( ~ (ordered_pair_as_product_element(all_191_6_174, all_191_6_174, v0, v1) = all_0_11_11) | ? [v2] : (( ~ (v2 = 0) & below_refl(all_0_17_17, v0, v1) = v2) | ( ~ (v2 = 0) & element(v1, all_191_6_174) = v2) | ( ~ (v2 = 0) & element(v0, all_191_6_174) = v2)))))) % 21.94/5.78 | % 21.94/5.78 +-Applying beta-rule and splitting (167), into two cases. % 21.94/5.78 |-Branch one: % 21.94/5.78 | (284) (all_85_0_130 = 0 & empty_carrier(all_0_17_17) = 0) | ( ~ (all_85_0_130 = 0) & one_sorted_str(all_0_17_17) = all_85_0_130) % 21.94/5.78 | % 21.94/5.78 +-Applying beta-rule and splitting (284), into two cases. % 21.94/5.78 |-Branch one: % 21.94/5.78 | (285) all_85_0_130 = 0 & empty_carrier(all_0_17_17) = 0 % 21.94/5.78 | % 21.94/5.78 | Applying alpha-rule on (285) yields: % 21.94/5.78 | (286) all_85_0_130 = 0 % 21.94/5.78 | (242) empty_carrier(all_0_17_17) = 0 % 21.94/5.78 | % 21.94/5.78 | Instantiating formula (73) with all_0_17_17, 0, all_0_16_16 and discharging atoms empty_carrier(all_0_17_17) = all_0_16_16, empty_carrier(all_0_17_17) = 0, yields: % 21.94/5.78 | (212) all_0_16_16 = 0 % 21.94/5.78 | % 21.94/5.78 | Equations (212) can reduce 98 to: % 21.94/5.78 | (213) $false % 21.94/5.78 | % 21.94/5.78 |-The branch is then unsatisfiable % 21.94/5.78 |-Branch two: % 21.94/5.78 | (290) ~ (all_85_0_130 = 0) & one_sorted_str(all_0_17_17) = all_85_0_130 % 21.94/5.78 | % 21.94/5.78 | Applying alpha-rule on (290) yields: % 21.94/5.78 | (291) ~ (all_85_0_130 = 0) % 21.94/5.78 | (292) one_sorted_str(all_0_17_17) = all_85_0_130 % 21.94/5.78 | % 21.94/5.78 | Instantiating formula (104) with all_0_17_17, 0, all_85_0_130 and discharging atoms one_sorted_str(all_0_17_17) = all_85_0_130, one_sorted_str(all_0_17_17) = 0, yields: % 21.94/5.78 | (286) all_85_0_130 = 0 % 21.94/5.78 | % 21.94/5.78 | Equations (286) can reduce 291 to: % 21.94/5.78 | (213) $false % 21.94/5.78 | % 21.94/5.78 |-The branch is then unsatisfiable % 21.94/5.78 |-Branch two: % 21.94/5.78 | (295) ~ (all_85_0_130 = 0) & empty(all_0_15_15) = all_85_0_130 % 21.94/5.78 | % 21.94/5.78 | Applying alpha-rule on (295) yields: % 21.94/5.78 | (291) ~ (all_85_0_130 = 0) % 21.94/5.78 | (297) empty(all_0_15_15) = all_85_0_130 % 21.94/5.78 | % 21.94/5.78 +-Applying beta-rule and splitting (161), into two cases. % 21.94/5.78 |-Branch one: % 21.94/5.78 | (298) (all_71_0_96 = all_0_11_11 & ordered_pair(all_0_13_13, all_0_12_12) = all_0_11_11) | (all_71_0_96 = 0 & empty(all_0_15_15) = 0) | ( ~ (all_71_0_96 = 0) & element(all_0_12_12, all_0_15_15) = all_71_0_96) % 21.94/5.78 | % 21.94/5.78 +-Applying beta-rule and splitting (298), into two cases. % 21.94/5.78 |-Branch one: % 21.94/5.78 | (299) (all_71_0_96 = all_0_11_11 & ordered_pair(all_0_13_13, all_0_12_12) = all_0_11_11) | (all_71_0_96 = 0 & empty(all_0_15_15) = 0) % 21.94/5.78 | % 21.94/5.78 +-Applying beta-rule and splitting (299), into two cases. % 21.94/5.78 |-Branch one: % 21.94/5.78 | (300) all_71_0_96 = all_0_11_11 & ordered_pair(all_0_13_13, all_0_12_12) = all_0_11_11 % 21.94/5.78 | % 21.94/5.78 | Applying alpha-rule on (300) yields: % 21.94/5.78 | (301) all_71_0_96 = all_0_11_11 % 21.94/5.78 | (302) ordered_pair(all_0_13_13, all_0_12_12) = all_0_11_11 % 21.94/5.78 | % 21.94/5.78 +-Applying beta-rule and splitting (216), into two cases. % 21.94/5.78 |-Branch one: % 21.94/5.78 | (303) ~ (all_146_0_162 = 0) & the_carrier(all_0_17_17) = all_146_1_163 & empty(all_146_1_163) = all_146_0_162 % 21.94/5.78 | % 21.94/5.78 | Applying alpha-rule on (303) yields: % 21.94/5.78 | (304) ~ (all_146_0_162 = 0) % 21.94/5.78 | (305) the_carrier(all_0_17_17) = all_146_1_163 % 21.94/5.78 | (306) empty(all_146_1_163) = all_146_0_162 % 21.94/5.78 | % 21.94/5.78 | Instantiating formula (124) with all_0_17_17, all_146_1_163, all_0_15_15 and discharging atoms the_carrier(all_0_17_17) = all_146_1_163, the_carrier(all_0_17_17) = all_0_15_15, yields: % 21.94/5.78 | (307) all_146_1_163 = all_0_15_15 % 21.94/5.78 | % 21.94/5.78 | From (307) and (305) follows: % 21.94/5.78 | (133) the_carrier(all_0_17_17) = all_0_15_15 % 21.94/5.78 | % 21.94/5.78 | From (307) and (306) follows: % 21.94/5.79 | (309) empty(all_0_15_15) = all_146_0_162 % 21.94/5.79 | % 21.94/5.79 | Instantiating formula (123) with all_0_15_15, all_146_0_162, all_85_0_130 and discharging atoms empty(all_0_15_15) = all_146_0_162, empty(all_0_15_15) = all_85_0_130, yields: % 21.94/5.79 | (310) all_146_0_162 = all_85_0_130 % 21.94/5.79 | % 21.94/5.79 | Equations (310) can reduce 304 to: % 21.94/5.79 | (291) ~ (all_85_0_130 = 0) % 21.94/5.79 | % 21.94/5.79 | From (310) and (309) follows: % 21.94/5.79 | (297) empty(all_0_15_15) = all_85_0_130 % 21.94/5.79 | % 21.94/5.79 +-Applying beta-rule and splitting (31), into two cases. % 21.94/5.79 |-Branch one: % 21.94/5.79 | (313) all_0_9_9 = 0 & ~ (all_0_10_10 = 0) % 21.94/5.79 | % 21.94/5.79 | Applying alpha-rule on (313) yields: % 21.94/5.79 | (314) all_0_9_9 = 0 % 21.94/5.79 | (315) ~ (all_0_10_10 = 0) % 21.94/5.79 | % 21.94/5.79 | From (314) and (94) follows: % 21.94/5.79 | (316) below_refl(all_0_17_17, all_0_13_13, all_0_12_12) = 0 % 21.94/5.79 | % 21.94/5.79 +-Applying beta-rule and splitting (283), into two cases. % 21.94/5.79 |-Branch one: % 21.94/5.79 | (317) (all_191_6_174 = 0 & empty_carrier(all_0_17_17) = 0) | ( ~ (all_191_6_174 = 0) & lattice(all_0_17_17) = all_191_6_174) | ( ~ (all_191_6_174 = 0) & latt_str(all_0_17_17) = all_191_6_174) % 21.94/5.79 | % 21.94/5.79 +-Applying beta-rule and splitting (317), into two cases. % 21.94/5.79 |-Branch one: % 21.94/5.79 | (318) (all_191_6_174 = 0 & empty_carrier(all_0_17_17) = 0) | ( ~ (all_191_6_174 = 0) & lattice(all_0_17_17) = all_191_6_174) % 21.94/5.79 | % 21.94/5.79 +-Applying beta-rule and splitting (318), into two cases. % 21.94/5.79 |-Branch one: % 21.94/5.79 | (319) all_191_6_174 = 0 & empty_carrier(all_0_17_17) = 0 % 21.94/5.79 | % 21.94/5.79 | Applying alpha-rule on (319) yields: % 21.94/5.79 | (320) all_191_6_174 = 0 % 21.94/5.79 | (242) empty_carrier(all_0_17_17) = 0 % 21.94/5.79 | % 21.94/5.79 | Instantiating formula (73) with all_0_17_17, 0, all_0_16_16 and discharging atoms empty_carrier(all_0_17_17) = all_0_16_16, empty_carrier(all_0_17_17) = 0, yields: % 21.94/5.79 | (212) all_0_16_16 = 0 % 21.94/5.79 | % 21.94/5.79 | Equations (212) can reduce 98 to: % 21.94/5.79 | (213) $false % 21.94/5.79 | % 21.94/5.79 |-The branch is then unsatisfiable % 21.94/5.79 |-Branch two: % 21.94/5.79 | (324) ~ (all_191_6_174 = 0) & lattice(all_0_17_17) = all_191_6_174 % 21.94/5.79 | % 21.94/5.79 | Applying alpha-rule on (324) yields: % 21.94/5.79 | (325) ~ (all_191_6_174 = 0) % 21.94/5.79 | (326) lattice(all_0_17_17) = all_191_6_174 % 21.94/5.79 | % 21.94/5.79 | Instantiating formula (34) with all_0_17_17, all_191_6_174, 0 and discharging atoms lattice(all_0_17_17) = all_191_6_174, lattice(all_0_17_17) = 0, yields: % 21.94/5.79 | (320) all_191_6_174 = 0 % 21.94/5.79 | % 21.94/5.79 | Equations (320) can reduce 325 to: % 21.94/5.79 | (213) $false % 21.94/5.79 | % 21.94/5.79 |-The branch is then unsatisfiable % 21.94/5.79 |-Branch two: % 21.94/5.79 | (329) ~ (all_191_6_174 = 0) & latt_str(all_0_17_17) = all_191_6_174 % 21.94/5.79 | % 21.94/5.79 | Applying alpha-rule on (329) yields: % 21.94/5.79 | (325) ~ (all_191_6_174 = 0) % 21.94/5.79 | (331) latt_str(all_0_17_17) = all_191_6_174 % 21.94/5.79 | % 21.94/5.79 | Instantiating formula (50) with all_0_17_17, all_191_6_174, 0 and discharging atoms latt_str(all_0_17_17) = all_191_6_174, latt_str(all_0_17_17) = 0, yields: % 21.94/5.79 | (320) all_191_6_174 = 0 % 21.94/5.79 | % 21.94/5.79 | Equations (320) can reduce 325 to: % 21.94/5.79 | (213) $false % 21.94/5.79 | % 21.94/5.79 |-The branch is then unsatisfiable % 21.94/5.79 |-Branch two: % 21.94/5.79 | (334) ( ~ (all_0_10_10 = 0) | (all_191_0_168 = 0 & all_191_1_169 = all_0_11_11 & all_191_2_170 = 0 & all_191_3_171 = 0 & below_refl(all_0_17_17, all_191_5_173, all_191_4_172) = 0 & the_carrier(all_0_17_17) = all_191_6_174 & ordered_pair_as_product_element(all_191_6_174, all_191_6_174, all_191_5_173, all_191_4_172) = all_0_11_11 & element(all_191_4_172, all_191_6_174) = 0 & element(all_191_5_173, all_191_6_174) = 0)) & (all_0_10_10 = 0 | (the_carrier(all_0_17_17) = all_191_6_174 & ! [v0] : ! [v1] : ( ~ (below_refl(all_0_17_17, v0, v1) = 0) | ? [v2] : (( ~ (v2 = all_0_11_11) & ordered_pair_as_product_element(all_191_6_174, all_191_6_174, v0, v1) = v2) | ( ~ (v2 = 0) & element(v1, all_191_6_174) = v2) | ( ~ (v2 = 0) & element(v0, all_191_6_174) = v2))) & ! [v0] : ! [v1] : ( ~ (ordered_pair_as_product_element(all_191_6_174, all_191_6_174, v0, v1) = all_0_11_11) | ? [v2] : (( ~ (v2 = 0) & below_refl(all_0_17_17, v0, v1) = v2) | ( ~ (v2 = 0) & element(v1, all_191_6_174) = v2) | ( ~ (v2 = 0) & element(v0, all_191_6_174) = v2))))) % 21.94/5.79 | % 21.94/5.79 | Applying alpha-rule on (334) yields: % 21.94/5.79 | (335) ~ (all_0_10_10 = 0) | (all_191_0_168 = 0 & all_191_1_169 = all_0_11_11 & all_191_2_170 = 0 & all_191_3_171 = 0 & below_refl(all_0_17_17, all_191_5_173, all_191_4_172) = 0 & the_carrier(all_0_17_17) = all_191_6_174 & ordered_pair_as_product_element(all_191_6_174, all_191_6_174, all_191_5_173, all_191_4_172) = all_0_11_11 & element(all_191_4_172, all_191_6_174) = 0 & element(all_191_5_173, all_191_6_174) = 0) % 21.94/5.79 | (336) all_0_10_10 = 0 | (the_carrier(all_0_17_17) = all_191_6_174 & ! [v0] : ! [v1] : ( ~ (below_refl(all_0_17_17, v0, v1) = 0) | ? [v2] : (( ~ (v2 = all_0_11_11) & ordered_pair_as_product_element(all_191_6_174, all_191_6_174, v0, v1) = v2) | ( ~ (v2 = 0) & element(v1, all_191_6_174) = v2) | ( ~ (v2 = 0) & element(v0, all_191_6_174) = v2))) & ! [v0] : ! [v1] : ( ~ (ordered_pair_as_product_element(all_191_6_174, all_191_6_174, v0, v1) = all_0_11_11) | ? [v2] : (( ~ (v2 = 0) & below_refl(all_0_17_17, v0, v1) = v2) | ( ~ (v2 = 0) & element(v1, all_191_6_174) = v2) | ( ~ (v2 = 0) & element(v0, all_191_6_174) = v2)))) % 21.94/5.79 | % 21.94/5.79 +-Applying beta-rule and splitting (159), into two cases. % 21.94/5.79 |-Branch one: % 21.94/5.79 | (337) all_0_10_10 = 0 % 21.94/5.79 | % 21.94/5.79 | Equations (337) can reduce 315 to: % 21.94/5.79 | (213) $false % 21.94/5.79 | % 21.94/5.79 |-The branch is then unsatisfiable % 21.94/5.79 |-Branch two: % 21.94/5.79 | (315) ~ (all_0_10_10 = 0) % 21.94/5.79 | (340) ? [v0] : ((v0 = 0 & empty(all_0_14_14) = 0) | ( ~ (v0 = 0) & element(all_0_11_11, all_0_14_14) = v0)) % 21.94/5.79 | % 21.94/5.79 +-Applying beta-rule and splitting (336), into two cases. % 21.94/5.79 |-Branch one: % 21.94/5.79 | (337) all_0_10_10 = 0 % 21.94/5.79 | % 21.94/5.79 | Equations (337) can reduce 315 to: % 21.94/5.79 | (213) $false % 21.94/5.79 | % 21.94/5.79 |-The branch is then unsatisfiable % 21.94/5.79 |-Branch two: % 21.94/5.79 | (315) ~ (all_0_10_10 = 0) % 21.94/5.79 | (344) the_carrier(all_0_17_17) = all_191_6_174 & ! [v0] : ! [v1] : ( ~ (below_refl(all_0_17_17, v0, v1) = 0) | ? [v2] : (( ~ (v2 = all_0_11_11) & ordered_pair_as_product_element(all_191_6_174, all_191_6_174, v0, v1) = v2) | ( ~ (v2 = 0) & element(v1, all_191_6_174) = v2) | ( ~ (v2 = 0) & element(v0, all_191_6_174) = v2))) & ! [v0] : ! [v1] : ( ~ (ordered_pair_as_product_element(all_191_6_174, all_191_6_174, v0, v1) = all_0_11_11) | ? [v2] : (( ~ (v2 = 0) & below_refl(all_0_17_17, v0, v1) = v2) | ( ~ (v2 = 0) & element(v1, all_191_6_174) = v2) | ( ~ (v2 = 0) & element(v0, all_191_6_174) = v2))) % 21.94/5.79 | % 21.94/5.79 | Applying alpha-rule on (344) yields: % 21.94/5.79 | (345) the_carrier(all_0_17_17) = all_191_6_174 % 21.94/5.79 | (346) ! [v0] : ! [v1] : ( ~ (below_refl(all_0_17_17, v0, v1) = 0) | ? [v2] : (( ~ (v2 = all_0_11_11) & ordered_pair_as_product_element(all_191_6_174, all_191_6_174, v0, v1) = v2) | ( ~ (v2 = 0) & element(v1, all_191_6_174) = v2) | ( ~ (v2 = 0) & element(v0, all_191_6_174) = v2))) % 21.94/5.79 | (347) ! [v0] : ! [v1] : ( ~ (ordered_pair_as_product_element(all_191_6_174, all_191_6_174, v0, v1) = all_0_11_11) | ? [v2] : (( ~ (v2 = 0) & below_refl(all_0_17_17, v0, v1) = v2) | ( ~ (v2 = 0) & element(v1, all_191_6_174) = v2) | ( ~ (v2 = 0) & element(v0, all_191_6_174) = v2))) % 21.94/5.79 | % 21.94/5.79 | Instantiating formula (124) with all_0_17_17, all_191_6_174, all_0_15_15 and discharging atoms the_carrier(all_0_17_17) = all_191_6_174, the_carrier(all_0_17_17) = all_0_15_15, yields: % 21.94/5.79 | (348) all_191_6_174 = all_0_15_15 % 21.94/5.79 | % 21.94/5.79 | Instantiating formula (346) with all_0_12_12, all_0_13_13 and discharging atoms below_refl(all_0_17_17, all_0_13_13, all_0_12_12) = 0, yields: % 21.94/5.79 | (349) ? [v0] : (( ~ (v0 = all_0_11_11) & ordered_pair_as_product_element(all_191_6_174, all_191_6_174, all_0_13_13, all_0_12_12) = v0) | ( ~ (v0 = 0) & element(all_0_12_12, all_191_6_174) = v0) | ( ~ (v0 = 0) & element(all_0_13_13, all_191_6_174) = v0)) % 21.94/5.79 | % 21.94/5.79 | Instantiating (349) with all_330_0_223 yields: % 21.94/5.79 | (350) ( ~ (all_330_0_223 = all_0_11_11) & ordered_pair_as_product_element(all_191_6_174, all_191_6_174, all_0_13_13, all_0_12_12) = all_330_0_223) | ( ~ (all_330_0_223 = 0) & element(all_0_12_12, all_191_6_174) = all_330_0_223) | ( ~ (all_330_0_223 = 0) & element(all_0_13_13, all_191_6_174) = all_330_0_223) % 21.94/5.79 | % 21.94/5.79 +-Applying beta-rule and splitting (350), into two cases. % 21.94/5.79 |-Branch one: % 21.94/5.79 | (351) ( ~ (all_330_0_223 = all_0_11_11) & ordered_pair_as_product_element(all_191_6_174, all_191_6_174, all_0_13_13, all_0_12_12) = all_330_0_223) | ( ~ (all_330_0_223 = 0) & element(all_0_12_12, all_191_6_174) = all_330_0_223) % 21.94/5.79 | % 21.94/5.79 +-Applying beta-rule and splitting (351), into two cases. % 21.94/5.79 |-Branch one: % 21.94/5.79 | (352) ~ (all_330_0_223 = all_0_11_11) & ordered_pair_as_product_element(all_191_6_174, all_191_6_174, all_0_13_13, all_0_12_12) = all_330_0_223 % 21.94/5.79 | % 21.94/5.79 | Applying alpha-rule on (352) yields: % 21.94/5.79 | (353) ~ (all_330_0_223 = all_0_11_11) % 21.94/5.79 | (354) ordered_pair_as_product_element(all_191_6_174, all_191_6_174, all_0_13_13, all_0_12_12) = all_330_0_223 % 21.94/5.79 | % 21.94/5.79 | From (348)(348) and (354) follows: % 21.94/5.79 | (355) ordered_pair_as_product_element(all_0_15_15, all_0_15_15, all_0_13_13, all_0_12_12) = all_330_0_223 % 21.94/5.79 | % 21.94/5.79 | Instantiating formula (113) with all_0_15_15, all_0_15_15, all_0_13_13, all_0_12_12, all_330_0_223, all_0_11_11 and discharging atoms ordered_pair_as_product_element(all_0_15_15, all_0_15_15, all_0_13_13, all_0_12_12) = all_330_0_223, ordered_pair_as_product_element(all_0_15_15, all_0_15_15, all_0_13_13, all_0_12_12) = all_0_11_11, yields: % 21.94/5.79 | (356) all_330_0_223 = all_0_11_11 % 21.94/5.79 | % 21.94/5.79 | Equations (356) can reduce 353 to: % 21.94/5.79 | (213) $false % 21.94/5.79 | % 21.94/5.79 |-The branch is then unsatisfiable % 21.94/5.79 |-Branch two: % 21.94/5.79 | (358) ~ (all_330_0_223 = 0) & element(all_0_12_12, all_191_6_174) = all_330_0_223 % 21.94/5.79 | % 21.94/5.79 | Applying alpha-rule on (358) yields: % 21.94/5.79 | (359) ~ (all_330_0_223 = 0) % 21.94/5.79 | (360) element(all_0_12_12, all_191_6_174) = all_330_0_223 % 21.94/5.79 | % 21.94/5.79 | From (348) and (360) follows: % 21.94/5.79 | (361) element(all_0_12_12, all_0_15_15) = all_330_0_223 % 21.94/5.79 | % 21.94/5.79 | Instantiating formula (23) with all_0_12_12, all_0_15_15, all_330_0_223, 0 and discharging atoms element(all_0_12_12, all_0_15_15) = all_330_0_223, element(all_0_12_12, all_0_15_15) = 0, yields: % 21.94/5.79 | (362) all_330_0_223 = 0 % 21.94/5.79 | % 21.94/5.79 | Equations (362) can reduce 359 to: % 21.94/5.79 | (213) $false % 21.94/5.79 | % 21.94/5.79 |-The branch is then unsatisfiable % 21.94/5.79 |-Branch two: % 21.94/5.79 | (364) ~ (all_330_0_223 = 0) & element(all_0_13_13, all_191_6_174) = all_330_0_223 % 21.94/5.79 | % 21.94/5.79 | Applying alpha-rule on (364) yields: % 21.94/5.79 | (359) ~ (all_330_0_223 = 0) % 21.94/5.79 | (366) element(all_0_13_13, all_191_6_174) = all_330_0_223 % 21.94/5.79 | % 21.94/5.79 | From (348) and (366) follows: % 21.94/5.80 | (367) element(all_0_13_13, all_0_15_15) = all_330_0_223 % 21.94/5.80 | % 21.94/5.80 | Instantiating formula (23) with all_0_13_13, all_0_15_15, all_330_0_223, 0 and discharging atoms element(all_0_13_13, all_0_15_15) = all_330_0_223, element(all_0_13_13, all_0_15_15) = 0, yields: % 21.94/5.80 | (362) all_330_0_223 = 0 % 21.94/5.80 | % 21.94/5.80 | Equations (362) can reduce 359 to: % 21.94/5.80 | (213) $false % 21.94/5.80 | % 21.94/5.80 |-The branch is then unsatisfiable % 21.94/5.80 |-Branch two: % 21.94/5.80 | (370) all_0_10_10 = 0 & ~ (all_0_9_9 = 0) % 21.94/5.80 | % 21.94/5.80 | Applying alpha-rule on (370) yields: % 21.94/5.80 | (337) all_0_10_10 = 0 % 21.94/5.80 | (372) ~ (all_0_9_9 = 0) % 21.94/5.80 | % 21.94/5.80 +-Applying beta-rule and splitting (283), into two cases. % 21.94/5.80 |-Branch one: % 21.94/5.80 | (317) (all_191_6_174 = 0 & empty_carrier(all_0_17_17) = 0) | ( ~ (all_191_6_174 = 0) & lattice(all_0_17_17) = all_191_6_174) | ( ~ (all_191_6_174 = 0) & latt_str(all_0_17_17) = all_191_6_174) % 21.94/5.80 | % 21.94/5.80 +-Applying beta-rule and splitting (317), into two cases. % 21.94/5.80 |-Branch one: % 21.94/5.80 | (318) (all_191_6_174 = 0 & empty_carrier(all_0_17_17) = 0) | ( ~ (all_191_6_174 = 0) & lattice(all_0_17_17) = all_191_6_174) % 21.94/5.80 | % 21.94/5.80 +-Applying beta-rule and splitting (318), into two cases. % 21.94/5.80 |-Branch one: % 21.94/5.80 | (319) all_191_6_174 = 0 & empty_carrier(all_0_17_17) = 0 % 21.94/5.80 | % 21.94/5.80 | Applying alpha-rule on (319) yields: % 21.94/5.80 | (320) all_191_6_174 = 0 % 21.94/5.80 | (242) empty_carrier(all_0_17_17) = 0 % 21.94/5.80 | % 21.94/5.80 | Instantiating formula (73) with all_0_17_17, 0, all_0_16_16 and discharging atoms empty_carrier(all_0_17_17) = all_0_16_16, empty_carrier(all_0_17_17) = 0, yields: % 21.94/5.80 | (212) all_0_16_16 = 0 % 21.94/5.80 | % 21.94/5.80 | Equations (212) can reduce 98 to: % 21.94/5.80 | (213) $false % 21.94/5.80 | % 21.94/5.80 |-The branch is then unsatisfiable % 21.94/5.80 |-Branch two: % 21.94/5.80 | (324) ~ (all_191_6_174 = 0) & lattice(all_0_17_17) = all_191_6_174 % 21.94/5.80 | % 21.94/5.80 | Applying alpha-rule on (324) yields: % 21.94/5.80 | (325) ~ (all_191_6_174 = 0) % 21.94/5.80 | (326) lattice(all_0_17_17) = all_191_6_174 % 21.94/5.80 | % 21.94/5.80 | Instantiating formula (34) with all_0_17_17, all_191_6_174, 0 and discharging atoms lattice(all_0_17_17) = all_191_6_174, lattice(all_0_17_17) = 0, yields: % 21.94/5.80 | (320) all_191_6_174 = 0 % 21.94/5.80 | % 21.94/5.80 | Equations (320) can reduce 325 to: % 21.94/5.80 | (213) $false % 21.94/5.80 | % 21.94/5.80 |-The branch is then unsatisfiable % 21.94/5.80 |-Branch two: % 21.94/5.80 | (329) ~ (all_191_6_174 = 0) & latt_str(all_0_17_17) = all_191_6_174 % 21.94/5.80 | % 21.94/5.80 | Applying alpha-rule on (329) yields: % 21.94/5.80 | (325) ~ (all_191_6_174 = 0) % 21.94/5.80 | (331) latt_str(all_0_17_17) = all_191_6_174 % 21.94/5.80 | % 21.94/5.80 | Instantiating formula (50) with all_0_17_17, all_191_6_174, 0 and discharging atoms latt_str(all_0_17_17) = all_191_6_174, latt_str(all_0_17_17) = 0, yields: % 21.94/5.80 | (320) all_191_6_174 = 0 % 21.94/5.80 | % 21.94/5.80 | Equations (320) can reduce 325 to: % 21.94/5.80 | (213) $false % 21.94/5.80 | % 21.94/5.80 |-The branch is then unsatisfiable % 21.94/5.80 |-Branch two: % 21.94/5.80 | (334) ( ~ (all_0_10_10 = 0) | (all_191_0_168 = 0 & all_191_1_169 = all_0_11_11 & all_191_2_170 = 0 & all_191_3_171 = 0 & below_refl(all_0_17_17, all_191_5_173, all_191_4_172) = 0 & the_carrier(all_0_17_17) = all_191_6_174 & ordered_pair_as_product_element(all_191_6_174, all_191_6_174, all_191_5_173, all_191_4_172) = all_0_11_11 & element(all_191_4_172, all_191_6_174) = 0 & element(all_191_5_173, all_191_6_174) = 0)) & (all_0_10_10 = 0 | (the_carrier(all_0_17_17) = all_191_6_174 & ! [v0] : ! [v1] : ( ~ (below_refl(all_0_17_17, v0, v1) = 0) | ? [v2] : (( ~ (v2 = all_0_11_11) & ordered_pair_as_product_element(all_191_6_174, all_191_6_174, v0, v1) = v2) | ( ~ (v2 = 0) & element(v1, all_191_6_174) = v2) | ( ~ (v2 = 0) & element(v0, all_191_6_174) = v2))) & ! [v0] : ! [v1] : ( ~ (ordered_pair_as_product_element(all_191_6_174, all_191_6_174, v0, v1) = all_0_11_11) | ? [v2] : (( ~ (v2 = 0) & below_refl(all_0_17_17, v0, v1) = v2) | ( ~ (v2 = 0) & element(v1, all_191_6_174) = v2) | ( ~ (v2 = 0) & element(v0, all_191_6_174) = v2))))) % 21.94/5.80 | % 21.94/5.80 | Applying alpha-rule on (334) yields: % 21.94/5.80 | (335) ~ (all_0_10_10 = 0) | (all_191_0_168 = 0 & all_191_1_169 = all_0_11_11 & all_191_2_170 = 0 & all_191_3_171 = 0 & below_refl(all_0_17_17, all_191_5_173, all_191_4_172) = 0 & the_carrier(all_0_17_17) = all_191_6_174 & ordered_pair_as_product_element(all_191_6_174, all_191_6_174, all_191_5_173, all_191_4_172) = all_0_11_11 & element(all_191_4_172, all_191_6_174) = 0 & element(all_191_5_173, all_191_6_174) = 0) % 21.94/5.80 | (336) all_0_10_10 = 0 | (the_carrier(all_0_17_17) = all_191_6_174 & ! [v0] : ! [v1] : ( ~ (below_refl(all_0_17_17, v0, v1) = 0) | ? [v2] : (( ~ (v2 = all_0_11_11) & ordered_pair_as_product_element(all_191_6_174, all_191_6_174, v0, v1) = v2) | ( ~ (v2 = 0) & element(v1, all_191_6_174) = v2) | ( ~ (v2 = 0) & element(v0, all_191_6_174) = v2))) & ! [v0] : ! [v1] : ( ~ (ordered_pair_as_product_element(all_191_6_174, all_191_6_174, v0, v1) = all_0_11_11) | ? [v2] : (( ~ (v2 = 0) & below_refl(all_0_17_17, v0, v1) = v2) | ( ~ (v2 = 0) & element(v1, all_191_6_174) = v2) | ( ~ (v2 = 0) & element(v0, all_191_6_174) = v2)))) % 21.94/5.80 | % 21.94/5.80 +-Applying beta-rule and splitting (168), into two cases. % 21.94/5.80 |-Branch one: % 21.94/5.80 | (393) (all_86_1_132 = 0 & empty_carrier(all_0_17_17) = 0) | ( ~ (all_86_0_131 = 0) & the_carrier(all_0_17_17) = all_86_1_132 & element(all_0_12_12, all_86_1_132) = all_86_0_131) | ( ~ (all_86_0_131 = 0) & the_carrier(all_0_17_17) = all_86_1_132 & element(all_0_13_13, all_86_1_132) = all_86_0_131) | ( ~ (all_86_1_132 = 0) & latt_str(all_0_17_17) = all_86_1_132) | ( ~ (all_86_1_132 = 0) & meet_commutative(all_0_17_17) = all_86_1_132) | ( ~ (all_86_1_132 = 0) & meet_absorbing(all_0_17_17) = all_86_1_132) | ( ~ (all_86_1_132 = 0) & join_absorbing(all_0_17_17) = all_86_1_132) % 21.94/5.80 | % 21.94/5.80 +-Applying beta-rule and splitting (393), into two cases. % 21.94/5.80 |-Branch one: % 21.94/5.80 | (394) (all_86_1_132 = 0 & empty_carrier(all_0_17_17) = 0) | ( ~ (all_86_0_131 = 0) & the_carrier(all_0_17_17) = all_86_1_132 & element(all_0_12_12, all_86_1_132) = all_86_0_131) | ( ~ (all_86_0_131 = 0) & the_carrier(all_0_17_17) = all_86_1_132 & element(all_0_13_13, all_86_1_132) = all_86_0_131) | ( ~ (all_86_1_132 = 0) & latt_str(all_0_17_17) = all_86_1_132) | ( ~ (all_86_1_132 = 0) & meet_commutative(all_0_17_17) = all_86_1_132) | ( ~ (all_86_1_132 = 0) & meet_absorbing(all_0_17_17) = all_86_1_132) % 21.94/5.80 | % 21.94/5.80 +-Applying beta-rule and splitting (394), into two cases. % 21.94/5.80 |-Branch one: % 21.94/5.80 | (395) (all_86_1_132 = 0 & empty_carrier(all_0_17_17) = 0) | ( ~ (all_86_0_131 = 0) & the_carrier(all_0_17_17) = all_86_1_132 & element(all_0_12_12, all_86_1_132) = all_86_0_131) | ( ~ (all_86_0_131 = 0) & the_carrier(all_0_17_17) = all_86_1_132 & element(all_0_13_13, all_86_1_132) = all_86_0_131) | ( ~ (all_86_1_132 = 0) & latt_str(all_0_17_17) = all_86_1_132) | ( ~ (all_86_1_132 = 0) & meet_commutative(all_0_17_17) = all_86_1_132) % 21.94/5.80 | % 21.94/5.80 +-Applying beta-rule and splitting (395), into two cases. % 21.94/5.80 |-Branch one: % 21.94/5.80 | (396) (all_86_1_132 = 0 & empty_carrier(all_0_17_17) = 0) | ( ~ (all_86_0_131 = 0) & the_carrier(all_0_17_17) = all_86_1_132 & element(all_0_12_12, all_86_1_132) = all_86_0_131) | ( ~ (all_86_0_131 = 0) & the_carrier(all_0_17_17) = all_86_1_132 & element(all_0_13_13, all_86_1_132) = all_86_0_131) | ( ~ (all_86_1_132 = 0) & latt_str(all_0_17_17) = all_86_1_132) % 21.94/5.80 | % 21.94/5.80 +-Applying beta-rule and splitting (396), into two cases. % 21.94/5.80 |-Branch one: % 21.94/5.80 | (397) (all_86_1_132 = 0 & empty_carrier(all_0_17_17) = 0) | ( ~ (all_86_0_131 = 0) & the_carrier(all_0_17_17) = all_86_1_132 & element(all_0_12_12, all_86_1_132) = all_86_0_131) | ( ~ (all_86_0_131 = 0) & the_carrier(all_0_17_17) = all_86_1_132 & element(all_0_13_13, all_86_1_132) = all_86_0_131) % 21.94/5.80 | % 21.94/5.80 +-Applying beta-rule and splitting (397), into two cases. % 21.94/5.80 |-Branch one: % 21.94/5.80 | (398) (all_86_1_132 = 0 & empty_carrier(all_0_17_17) = 0) | ( ~ (all_86_0_131 = 0) & the_carrier(all_0_17_17) = all_86_1_132 & element(all_0_12_12, all_86_1_132) = all_86_0_131) % 21.94/5.80 | % 21.94/5.80 +-Applying beta-rule and splitting (398), into two cases. % 21.94/5.80 |-Branch one: % 21.94/5.80 | (399) all_86_1_132 = 0 & empty_carrier(all_0_17_17) = 0 % 21.94/5.80 | % 21.94/5.80 | Applying alpha-rule on (399) yields: % 21.94/5.80 | (400) all_86_1_132 = 0 % 21.94/5.80 | (242) empty_carrier(all_0_17_17) = 0 % 21.94/5.80 | % 21.94/5.80 | Instantiating formula (73) with all_0_17_17, 0, all_0_16_16 and discharging atoms empty_carrier(all_0_17_17) = all_0_16_16, empty_carrier(all_0_17_17) = 0, yields: % 21.94/5.80 | (212) all_0_16_16 = 0 % 21.94/5.80 | % 21.94/5.80 | Equations (212) can reduce 98 to: % 21.94/5.80 | (213) $false % 21.94/5.80 | % 21.94/5.80 |-The branch is then unsatisfiable % 21.94/5.80 |-Branch two: % 21.94/5.80 | (404) ~ (all_86_0_131 = 0) & the_carrier(all_0_17_17) = all_86_1_132 & element(all_0_12_12, all_86_1_132) = all_86_0_131 % 21.94/5.80 | % 21.94/5.80 | Applying alpha-rule on (404) yields: % 21.94/5.80 | (405) ~ (all_86_0_131 = 0) % 21.94/5.80 | (406) the_carrier(all_0_17_17) = all_86_1_132 % 21.94/5.80 | (407) element(all_0_12_12, all_86_1_132) = all_86_0_131 % 21.94/5.80 | % 21.94/5.80 +-Applying beta-rule and splitting (335), into two cases. % 21.94/5.80 |-Branch one: % 21.94/5.80 | (315) ~ (all_0_10_10 = 0) % 21.94/5.80 | % 21.94/5.80 | Equations (337) can reduce 315 to: % 21.94/5.80 | (213) $false % 21.94/5.80 | % 21.94/5.80 |-The branch is then unsatisfiable % 21.94/5.80 |-Branch two: % 21.94/5.80 | (337) all_0_10_10 = 0 % 21.94/5.80 | (411) all_191_0_168 = 0 & all_191_1_169 = all_0_11_11 & all_191_2_170 = 0 & all_191_3_171 = 0 & below_refl(all_0_17_17, all_191_5_173, all_191_4_172) = 0 & the_carrier(all_0_17_17) = all_191_6_174 & ordered_pair_as_product_element(all_191_6_174, all_191_6_174, all_191_5_173, all_191_4_172) = all_0_11_11 & element(all_191_4_172, all_191_6_174) = 0 & element(all_191_5_173, all_191_6_174) = 0 % 21.94/5.80 | % 21.94/5.80 | Applying alpha-rule on (411) yields: % 21.94/5.80 | (412) all_191_3_171 = 0 % 21.94/5.80 | (413) all_191_0_168 = 0 % 21.94/5.80 | (414) all_191_1_169 = all_0_11_11 % 21.94/5.80 | (415) all_191_2_170 = 0 % 21.94/5.80 | (416) ordered_pair_as_product_element(all_191_6_174, all_191_6_174, all_191_5_173, all_191_4_172) = all_0_11_11 % 21.94/5.80 | (345) the_carrier(all_0_17_17) = all_191_6_174 % 21.94/5.80 | (418) below_refl(all_0_17_17, all_191_5_173, all_191_4_172) = 0 % 21.94/5.80 | (419) element(all_191_4_172, all_191_6_174) = 0 % 21.94/5.80 | (420) element(all_191_5_173, all_191_6_174) = 0 % 21.94/5.80 | % 21.94/5.80 | Instantiating formula (124) with all_0_17_17, all_191_6_174, all_0_15_15 and discharging atoms the_carrier(all_0_17_17) = all_191_6_174, the_carrier(all_0_17_17) = all_0_15_15, yields: % 21.94/5.80 | (348) all_191_6_174 = all_0_15_15 % 21.94/5.80 | % 21.94/5.80 | Instantiating formula (124) with all_0_17_17, all_86_1_132, all_191_6_174 and discharging atoms the_carrier(all_0_17_17) = all_191_6_174, the_carrier(all_0_17_17) = all_86_1_132, yields: % 21.94/5.80 | (422) all_191_6_174 = all_86_1_132 % 21.94/5.80 | % 21.94/5.80 | Combining equations (422,348) yields a new equation: % 21.94/5.80 | (423) all_86_1_132 = all_0_15_15 % 21.94/5.80 | % 21.94/5.80 | Simplifying 423 yields: % 21.94/5.80 | (424) all_86_1_132 = all_0_15_15 % 21.94/5.80 | % 21.94/5.80 | From (424) and (407) follows: % 21.94/5.80 | (425) element(all_0_12_12, all_0_15_15) = all_86_0_131 % 21.94/5.81 | % 21.94/5.81 | Instantiating formula (23) with all_0_12_12, all_0_15_15, all_86_0_131, 0 and discharging atoms element(all_0_12_12, all_0_15_15) = all_86_0_131, element(all_0_12_12, all_0_15_15) = 0, yields: % 21.94/5.81 | (426) all_86_0_131 = 0 % 21.94/5.81 | % 21.94/5.81 | Equations (426) can reduce 405 to: % 21.94/5.81 | (213) $false % 21.94/5.81 | % 21.94/5.81 |-The branch is then unsatisfiable % 21.94/5.81 |-Branch two: % 21.94/5.81 | (428) ~ (all_86_0_131 = 0) & the_carrier(all_0_17_17) = all_86_1_132 & element(all_0_13_13, all_86_1_132) = all_86_0_131 % 21.94/5.81 | % 21.94/5.81 | Applying alpha-rule on (428) yields: % 21.94/5.81 | (405) ~ (all_86_0_131 = 0) % 21.94/5.81 | (406) the_carrier(all_0_17_17) = all_86_1_132 % 21.94/5.81 | (431) element(all_0_13_13, all_86_1_132) = all_86_0_131 % 21.94/5.81 | % 21.94/5.81 +-Applying beta-rule and splitting (335), into two cases. % 21.94/5.81 |-Branch one: % 21.94/5.81 | (315) ~ (all_0_10_10 = 0) % 21.94/5.81 | % 21.94/5.81 | Equations (337) can reduce 315 to: % 21.94/5.81 | (213) $false % 21.94/5.81 | % 21.94/5.81 |-The branch is then unsatisfiable % 21.94/5.81 |-Branch two: % 22.23/5.81 | (337) all_0_10_10 = 0 % 22.23/5.81 | (411) all_191_0_168 = 0 & all_191_1_169 = all_0_11_11 & all_191_2_170 = 0 & all_191_3_171 = 0 & below_refl(all_0_17_17, all_191_5_173, all_191_4_172) = 0 & the_carrier(all_0_17_17) = all_191_6_174 & ordered_pair_as_product_element(all_191_6_174, all_191_6_174, all_191_5_173, all_191_4_172) = all_0_11_11 & element(all_191_4_172, all_191_6_174) = 0 & element(all_191_5_173, all_191_6_174) = 0 % 22.23/5.81 | % 22.23/5.81 | Applying alpha-rule on (411) yields: % 22.23/5.81 | (412) all_191_3_171 = 0 % 22.23/5.81 | (413) all_191_0_168 = 0 % 22.23/5.81 | (414) all_191_1_169 = all_0_11_11 % 22.23/5.81 | (415) all_191_2_170 = 0 % 22.23/5.81 | (416) ordered_pair_as_product_element(all_191_6_174, all_191_6_174, all_191_5_173, all_191_4_172) = all_0_11_11 % 22.23/5.81 | (345) the_carrier(all_0_17_17) = all_191_6_174 % 22.23/5.81 | (418) below_refl(all_0_17_17, all_191_5_173, all_191_4_172) = 0 % 22.23/5.81 | (419) element(all_191_4_172, all_191_6_174) = 0 % 22.23/5.81 | (420) element(all_191_5_173, all_191_6_174) = 0 % 22.23/5.81 | % 22.23/5.81 | Instantiating formula (124) with all_0_17_17, all_191_6_174, all_0_15_15 and discharging atoms the_carrier(all_0_17_17) = all_191_6_174, the_carrier(all_0_17_17) = all_0_15_15, yields: % 22.23/5.81 | (348) all_191_6_174 = all_0_15_15 % 22.23/5.81 | % 22.23/5.81 | Instantiating formula (124) with all_0_17_17, all_86_1_132, all_191_6_174 and discharging atoms the_carrier(all_0_17_17) = all_191_6_174, the_carrier(all_0_17_17) = all_86_1_132, yields: % 22.23/5.81 | (422) all_191_6_174 = all_86_1_132 % 22.23/5.81 | % 22.23/5.81 | Combining equations (422,348) yields a new equation: % 22.23/5.81 | (423) all_86_1_132 = all_0_15_15 % 22.23/5.81 | % 22.23/5.81 | Simplifying 423 yields: % 22.23/5.81 | (424) all_86_1_132 = all_0_15_15 % 22.23/5.81 | % 22.23/5.81 | From (424) and (431) follows: % 22.23/5.81 | (449) element(all_0_13_13, all_0_15_15) = all_86_0_131 % 22.23/5.81 | % 22.23/5.81 | Instantiating formula (23) with all_0_13_13, all_0_15_15, all_86_0_131, 0 and discharging atoms element(all_0_13_13, all_0_15_15) = all_86_0_131, element(all_0_13_13, all_0_15_15) = 0, yields: % 22.23/5.81 | (426) all_86_0_131 = 0 % 22.23/5.81 | % 22.23/5.81 | Equations (426) can reduce 405 to: % 22.23/5.81 | (213) $false % 22.23/5.81 | % 22.23/5.81 |-The branch is then unsatisfiable % 22.23/5.81 |-Branch two: % 22.23/5.81 | (452) ~ (all_86_1_132 = 0) & latt_str(all_0_17_17) = all_86_1_132 % 22.23/5.81 | % 22.23/5.81 | Applying alpha-rule on (452) yields: % 22.23/5.81 | (453) ~ (all_86_1_132 = 0) % 22.23/5.81 | (454) latt_str(all_0_17_17) = all_86_1_132 % 22.23/5.81 | % 22.23/5.81 | Instantiating formula (50) with all_0_17_17, all_86_1_132, 0 and discharging atoms latt_str(all_0_17_17) = all_86_1_132, latt_str(all_0_17_17) = 0, yields: % 22.23/5.81 | (400) all_86_1_132 = 0 % 22.23/5.81 | % 22.23/5.81 | Equations (400) can reduce 453 to: % 22.23/5.81 | (213) $false % 22.23/5.81 | % 22.23/5.81 |-The branch is then unsatisfiable % 22.23/5.81 |-Branch two: % 22.23/5.81 | (457) ~ (all_86_1_132 = 0) & meet_commutative(all_0_17_17) = all_86_1_132 % 22.23/5.81 | % 22.23/5.81 | Applying alpha-rule on (457) yields: % 22.23/5.81 | (453) ~ (all_86_1_132 = 0) % 22.23/5.81 | (459) meet_commutative(all_0_17_17) = all_86_1_132 % 22.23/5.81 | % 22.23/5.81 | Instantiating formula (107) with all_0_17_17, all_86_1_132, 0 and discharging atoms meet_commutative(all_0_17_17) = all_86_1_132, meet_commutative(all_0_17_17) = 0, yields: % 22.23/5.81 | (400) all_86_1_132 = 0 % 22.23/5.81 | % 22.23/5.81 | Equations (400) can reduce 453 to: % 22.23/5.81 | (213) $false % 22.23/5.81 | % 22.23/5.81 |-The branch is then unsatisfiable % 22.23/5.81 |-Branch two: % 22.23/5.81 | (462) ~ (all_86_1_132 = 0) & meet_absorbing(all_0_17_17) = all_86_1_132 % 22.23/5.81 | % 22.23/5.81 | Applying alpha-rule on (462) yields: % 22.23/5.81 | (453) ~ (all_86_1_132 = 0) % 22.23/5.81 | (464) meet_absorbing(all_0_17_17) = all_86_1_132 % 22.23/5.81 | % 22.23/5.81 | Instantiating formula (8) with all_0_17_17, all_86_1_132, 0 and discharging atoms meet_absorbing(all_0_17_17) = all_86_1_132, meet_absorbing(all_0_17_17) = 0, yields: % 22.23/5.81 | (400) all_86_1_132 = 0 % 22.23/5.81 | % 22.23/5.81 | Equations (400) can reduce 453 to: % 22.23/5.81 | (213) $false % 22.23/5.81 | % 22.23/5.81 |-The branch is then unsatisfiable % 22.23/5.81 |-Branch two: % 22.23/5.81 | (467) ~ (all_86_1_132 = 0) & join_absorbing(all_0_17_17) = all_86_1_132 % 22.23/5.81 | % 22.23/5.81 | Applying alpha-rule on (467) yields: % 22.23/5.81 | (453) ~ (all_86_1_132 = 0) % 22.23/5.81 | (469) join_absorbing(all_0_17_17) = all_86_1_132 % 22.23/5.81 | % 22.23/5.81 | Instantiating formula (5) with all_0_17_17, all_86_1_132, 0 and discharging atoms join_absorbing(all_0_17_17) = all_86_1_132, join_absorbing(all_0_17_17) = 0, yields: % 22.23/5.81 | (400) all_86_1_132 = 0 % 22.23/5.81 | % 22.23/5.81 | Equations (400) can reduce 453 to: % 22.23/5.81 | (213) $false % 22.23/5.81 | % 22.23/5.81 |-The branch is then unsatisfiable % 22.23/5.81 |-Branch two: % 22.23/5.81 | (472) ( ~ (all_0_9_9 = 0) | (all_86_1_132 = 0 & below(all_0_17_17, all_0_13_13, all_0_12_12) = 0)) & (all_0_9_9 = 0 | ( ~ (all_86_1_132 = 0) & below(all_0_17_17, all_0_13_13, all_0_12_12) = all_86_1_132)) % 22.23/5.81 | % 22.23/5.81 | Applying alpha-rule on (472) yields: % 22.23/5.81 | (473) ~ (all_0_9_9 = 0) | (all_86_1_132 = 0 & below(all_0_17_17, all_0_13_13, all_0_12_12) = 0) % 22.23/5.81 | (474) all_0_9_9 = 0 | ( ~ (all_86_1_132 = 0) & below(all_0_17_17, all_0_13_13, all_0_12_12) = all_86_1_132) % 22.23/5.81 | % 22.23/5.81 +-Applying beta-rule and splitting (335), into two cases. % 22.23/5.81 |-Branch one: % 22.23/5.81 | (315) ~ (all_0_10_10 = 0) % 22.23/5.81 | % 22.23/5.81 | Equations (337) can reduce 315 to: % 22.23/5.81 | (213) $false % 22.23/5.81 | % 22.23/5.81 |-The branch is then unsatisfiable % 22.23/5.81 |-Branch two: % 22.23/5.81 | (337) all_0_10_10 = 0 % 22.23/5.81 | (411) all_191_0_168 = 0 & all_191_1_169 = all_0_11_11 & all_191_2_170 = 0 & all_191_3_171 = 0 & below_refl(all_0_17_17, all_191_5_173, all_191_4_172) = 0 & the_carrier(all_0_17_17) = all_191_6_174 & ordered_pair_as_product_element(all_191_6_174, all_191_6_174, all_191_5_173, all_191_4_172) = all_0_11_11 & element(all_191_4_172, all_191_6_174) = 0 & element(all_191_5_173, all_191_6_174) = 0 % 22.23/5.81 | % 22.23/5.81 | Applying alpha-rule on (411) yields: % 22.23/5.81 | (412) all_191_3_171 = 0 % 22.23/5.81 | (413) all_191_0_168 = 0 % 22.23/5.81 | (414) all_191_1_169 = all_0_11_11 % 22.23/5.81 | (415) all_191_2_170 = 0 % 22.23/5.81 | (416) ordered_pair_as_product_element(all_191_6_174, all_191_6_174, all_191_5_173, all_191_4_172) = all_0_11_11 % 22.23/5.81 | (345) the_carrier(all_0_17_17) = all_191_6_174 % 22.23/5.81 | (418) below_refl(all_0_17_17, all_191_5_173, all_191_4_172) = 0 % 22.23/5.81 | (419) element(all_191_4_172, all_191_6_174) = 0 % 22.23/5.81 | (420) element(all_191_5_173, all_191_6_174) = 0 % 22.23/5.81 | % 22.23/5.81 +-Applying beta-rule and splitting (474), into two cases. % 22.23/5.81 |-Branch one: % 22.23/5.81 | (314) all_0_9_9 = 0 % 22.23/5.81 | % 22.23/5.81 | Equations (314) can reduce 372 to: % 22.23/5.81 | (213) $false % 22.23/5.81 | % 22.23/5.81 |-The branch is then unsatisfiable % 22.23/5.81 |-Branch two: % 22.23/5.81 | (372) ~ (all_0_9_9 = 0) % 22.23/5.81 | (491) ~ (all_86_1_132 = 0) & below(all_0_17_17, all_0_13_13, all_0_12_12) = all_86_1_132 % 22.23/5.81 | % 22.23/5.81 | Instantiating formula (124) with all_0_17_17, all_191_6_174, all_0_15_15 and discharging atoms the_carrier(all_0_17_17) = all_191_6_174, the_carrier(all_0_17_17) = all_0_15_15, yields: % 22.23/5.81 | (348) all_191_6_174 = all_0_15_15 % 22.23/5.81 | % 22.23/5.81 | From (348)(348) and (416) follows: % 22.23/5.81 | (493) ordered_pair_as_product_element(all_0_15_15, all_0_15_15, all_191_5_173, all_191_4_172) = all_0_11_11 % 22.23/5.81 | % 22.23/5.81 | From (348) and (419) follows: % 22.23/5.81 | (494) element(all_191_4_172, all_0_15_15) = 0 % 22.23/5.81 | % 22.23/5.81 | From (348) and (420) follows: % 22.23/5.81 | (495) element(all_191_5_173, all_0_15_15) = 0 % 22.23/5.81 | % 22.23/5.81 | Instantiating formula (85) with all_0_11_11, all_191_4_172, all_191_5_173, all_0_15_15, all_0_15_15 and discharging atoms ordered_pair_as_product_element(all_0_15_15, all_0_15_15, all_191_5_173, all_191_4_172) = all_0_11_11, yields: % 22.23/5.81 | (496) ? [v0] : ((v0 = all_0_11_11 & ordered_pair(all_191_5_173, all_191_4_172) = all_0_11_11) | (v0 = 0 & empty(all_0_15_15) = 0) | ( ~ (v0 = 0) & element(all_191_4_172, all_0_15_15) = v0) | ( ~ (v0 = 0) & element(all_191_5_173, all_0_15_15) = v0)) % 22.23/5.81 | % 22.23/5.81 | Instantiating (496) with all_318_0_242 yields: % 22.23/5.81 | (497) (all_318_0_242 = all_0_11_11 & ordered_pair(all_191_5_173, all_191_4_172) = all_0_11_11) | (all_318_0_242 = 0 & empty(all_0_15_15) = 0) | ( ~ (all_318_0_242 = 0) & element(all_191_4_172, all_0_15_15) = all_318_0_242) | ( ~ (all_318_0_242 = 0) & element(all_191_5_173, all_0_15_15) = all_318_0_242) % 22.23/5.82 | % 22.23/5.82 +-Applying beta-rule and splitting (497), into two cases. % 22.23/5.82 |-Branch one: % 22.23/5.82 | (498) (all_318_0_242 = all_0_11_11 & ordered_pair(all_191_5_173, all_191_4_172) = all_0_11_11) | (all_318_0_242 = 0 & empty(all_0_15_15) = 0) | ( ~ (all_318_0_242 = 0) & element(all_191_4_172, all_0_15_15) = all_318_0_242) % 22.23/5.82 | % 22.23/5.82 +-Applying beta-rule and splitting (498), into two cases. % 22.23/5.82 |-Branch one: % 22.23/5.82 | (499) (all_318_0_242 = all_0_11_11 & ordered_pair(all_191_5_173, all_191_4_172) = all_0_11_11) | (all_318_0_242 = 0 & empty(all_0_15_15) = 0) % 22.23/5.82 | % 22.23/5.82 +-Applying beta-rule and splitting (499), into two cases. % 22.23/5.82 |-Branch one: % 22.23/5.82 | (500) all_318_0_242 = all_0_11_11 & ordered_pair(all_191_5_173, all_191_4_172) = all_0_11_11 % 22.23/5.82 | % 22.23/5.82 | Applying alpha-rule on (500) yields: % 22.23/5.82 | (501) all_318_0_242 = all_0_11_11 % 22.23/5.82 | (502) ordered_pair(all_191_5_173, all_191_4_172) = all_0_11_11 % 22.23/5.82 | % 22.23/5.82 | Instantiating formula (36) with all_0_11_11, all_191_4_172, all_191_5_173, all_0_12_12, all_0_13_13 and discharging atoms ordered_pair(all_191_5_173, all_191_4_172) = all_0_11_11, ordered_pair(all_0_13_13, all_0_12_12) = all_0_11_11, yields: % 22.23/5.82 | (503) all_191_4_172 = all_0_12_12 % 22.23/5.82 | % 22.23/5.82 | Instantiating formula (65) with all_0_11_11, all_191_4_172, all_191_5_173, all_0_12_12, all_0_13_13 and discharging atoms ordered_pair(all_191_5_173, all_191_4_172) = all_0_11_11, ordered_pair(all_0_13_13, all_0_12_12) = all_0_11_11, yields: % 22.23/5.82 | (504) all_191_5_173 = all_0_13_13 % 22.23/5.82 | % 22.23/5.82 | From (504)(503) and (418) follows: % 22.23/5.82 | (316) below_refl(all_0_17_17, all_0_13_13, all_0_12_12) = 0 % 22.23/5.82 | % 22.23/5.82 | Instantiating formula (54) with all_0_17_17, all_0_13_13, all_0_12_12, 0, all_0_9_9 and discharging atoms below_refl(all_0_17_17, all_0_13_13, all_0_12_12) = all_0_9_9, below_refl(all_0_17_17, all_0_13_13, all_0_12_12) = 0, yields: % 22.23/5.82 | (314) all_0_9_9 = 0 % 22.23/5.82 | % 22.23/5.82 | Equations (314) can reduce 372 to: % 22.23/5.82 | (213) $false % 22.23/5.82 | % 22.23/5.82 |-The branch is then unsatisfiable % 22.23/5.82 |-Branch two: % 22.23/5.82 | (508) all_318_0_242 = 0 & empty(all_0_15_15) = 0 % 22.23/5.82 | % 22.23/5.82 | Applying alpha-rule on (508) yields: % 22.23/5.82 | (509) all_318_0_242 = 0 % 22.23/5.82 | (510) empty(all_0_15_15) = 0 % 22.23/5.82 | % 22.23/5.82 | Instantiating formula (123) with all_0_15_15, 0, all_85_0_130 and discharging atoms empty(all_0_15_15) = all_85_0_130, empty(all_0_15_15) = 0, yields: % 22.23/5.82 | (286) all_85_0_130 = 0 % 22.23/5.82 | % 22.23/5.82 | Equations (286) can reduce 291 to: % 22.23/5.82 | (213) $false % 22.23/5.82 | % 22.23/5.82 |-The branch is then unsatisfiable % 22.23/5.82 |-Branch two: % 22.23/5.82 | (513) ~ (all_318_0_242 = 0) & element(all_191_4_172, all_0_15_15) = all_318_0_242 % 22.23/5.82 | % 22.23/5.82 | Applying alpha-rule on (513) yields: % 22.23/5.82 | (514) ~ (all_318_0_242 = 0) % 22.23/5.82 | (515) element(all_191_4_172, all_0_15_15) = all_318_0_242 % 22.23/5.82 | % 22.23/5.82 | Instantiating formula (23) with all_191_4_172, all_0_15_15, all_318_0_242, 0 and discharging atoms element(all_191_4_172, all_0_15_15) = all_318_0_242, element(all_191_4_172, all_0_15_15) = 0, yields: % 22.23/5.82 | (509) all_318_0_242 = 0 % 22.23/5.82 | % 22.23/5.82 | Equations (509) can reduce 514 to: % 22.23/5.82 | (213) $false % 22.23/5.82 | % 22.23/5.82 |-The branch is then unsatisfiable % 22.23/5.82 |-Branch two: % 22.23/5.82 | (518) ~ (all_318_0_242 = 0) & element(all_191_5_173, all_0_15_15) = all_318_0_242 % 22.23/5.82 | % 22.23/5.82 | Applying alpha-rule on (518) yields: % 22.23/5.82 | (514) ~ (all_318_0_242 = 0) % 22.23/5.82 | (520) element(all_191_5_173, all_0_15_15) = all_318_0_242 % 22.23/5.82 | % 22.23/5.82 | Instantiating formula (23) with all_191_5_173, all_0_15_15, all_318_0_242, 0 and discharging atoms element(all_191_5_173, all_0_15_15) = all_318_0_242, element(all_191_5_173, all_0_15_15) = 0, yields: % 22.23/5.82 | (509) all_318_0_242 = 0 % 22.23/5.82 | % 22.23/5.82 | Equations (509) can reduce 514 to: % 22.23/5.82 | (213) $false % 22.23/5.82 | % 22.23/5.82 |-The branch is then unsatisfiable % 22.23/5.82 |-Branch two: % 22.23/5.82 | (523) ~ (all_146_1_163 = 0) & one_sorted_str(all_0_17_17) = all_146_1_163 % 22.23/5.82 | % 22.23/5.82 | Applying alpha-rule on (523) yields: % 22.23/5.82 | (524) ~ (all_146_1_163 = 0) % 22.23/5.82 | (525) one_sorted_str(all_0_17_17) = all_146_1_163 % 22.23/5.82 | % 22.23/5.82 | Instantiating formula (104) with all_0_17_17, 0, all_146_1_163 and discharging atoms one_sorted_str(all_0_17_17) = all_146_1_163, one_sorted_str(all_0_17_17) = 0, yields: % 22.23/5.82 | (526) all_146_1_163 = 0 % 22.23/5.82 | % 22.23/5.82 | Equations (526) can reduce 524 to: % 22.23/5.82 | (213) $false % 22.23/5.82 | % 22.23/5.82 |-The branch is then unsatisfiable % 22.23/5.82 |-Branch two: % 22.23/5.82 | (528) all_71_0_96 = 0 & empty(all_0_15_15) = 0 % 22.23/5.82 | % 22.23/5.82 | Applying alpha-rule on (528) yields: % 22.23/5.82 | (529) all_71_0_96 = 0 % 22.23/5.82 | (510) empty(all_0_15_15) = 0 % 22.23/5.82 | % 22.23/5.82 | Instantiating formula (123) with all_0_15_15, 0, all_85_0_130 and discharging atoms empty(all_0_15_15) = all_85_0_130, empty(all_0_15_15) = 0, yields: % 22.23/5.82 | (286) all_85_0_130 = 0 % 22.23/5.82 | % 22.23/5.82 | Equations (286) can reduce 291 to: % 22.23/5.82 | (213) $false % 22.23/5.82 | % 22.23/5.82 |-The branch is then unsatisfiable % 22.23/5.82 |-Branch two: % 22.23/5.82 | (533) ~ (all_71_0_96 = 0) & element(all_0_12_12, all_0_15_15) = all_71_0_96 % 22.23/5.82 | % 22.23/5.82 | Applying alpha-rule on (533) yields: % 22.23/5.82 | (534) ~ (all_71_0_96 = 0) % 22.23/5.82 | (535) element(all_0_12_12, all_0_15_15) = all_71_0_96 % 22.23/5.82 | % 22.23/5.82 | Instantiating formula (23) with all_0_12_12, all_0_15_15, all_71_0_96, 0 and discharging atoms element(all_0_12_12, all_0_15_15) = all_71_0_96, element(all_0_12_12, all_0_15_15) = 0, yields: % 22.23/5.82 | (529) all_71_0_96 = 0 % 22.23/5.82 | % 22.23/5.82 | Equations (529) can reduce 534 to: % 22.23/5.82 | (213) $false % 22.23/5.82 | % 22.23/5.82 |-The branch is then unsatisfiable % 22.23/5.82 |-Branch two: % 22.23/5.82 | (538) ~ (all_71_0_96 = 0) & element(all_0_13_13, all_0_15_15) = all_71_0_96 % 22.23/5.82 | % 22.23/5.82 | Applying alpha-rule on (538) yields: % 22.23/5.82 | (534) ~ (all_71_0_96 = 0) % 22.23/5.82 | (540) element(all_0_13_13, all_0_15_15) = all_71_0_96 % 22.23/5.82 | % 22.23/5.82 | Instantiating formula (23) with all_0_13_13, all_0_15_15, all_71_0_96, 0 and discharging atoms element(all_0_13_13, all_0_15_15) = all_71_0_96, element(all_0_13_13, all_0_15_15) = 0, yields: % 22.23/5.82 | (529) all_71_0_96 = 0 % 22.23/5.82 | % 22.23/5.82 | Equations (529) can reduce 534 to: % 22.23/5.82 | (213) $false % 22.23/5.82 | % 22.23/5.82 |-The branch is then unsatisfiable % 22.23/5.82 |-Branch two: % 22.23/5.82 | (543) ~ (all_70_0_95 = 0) & join_commutative(all_0_17_17) = all_70_0_95 % 22.23/5.82 | % 22.23/5.82 | Applying alpha-rule on (543) yields: % 22.23/5.82 | (255) ~ (all_70_0_95 = 0) % 22.23/5.82 | (545) join_commutative(all_0_17_17) = all_70_0_95 % 22.23/5.82 | % 22.23/5.82 | Instantiating formula (82) with all_0_17_17, 0, all_70_0_95 and discharging atoms join_commutative(all_0_17_17) = all_70_0_95, join_commutative(all_0_17_17) = 0, yields: % 22.23/5.82 | (241) all_70_0_95 = 0 % 22.23/5.82 | % 22.23/5.82 | Equations (241) can reduce 255 to: % 22.23/5.82 | (213) $false % 22.23/5.82 | % 22.23/5.82 |-The branch is then unsatisfiable % 22.23/5.82 |-Branch two: % 22.23/5.82 | (548) ~ (all_70_0_95 = 0) & join_associative(all_0_17_17) = all_70_0_95 % 22.23/5.82 | % 22.23/5.82 | Applying alpha-rule on (548) yields: % 22.23/5.82 | (255) ~ (all_70_0_95 = 0) % 22.23/5.82 | (550) join_associative(all_0_17_17) = all_70_0_95 % 22.23/5.82 | % 22.23/5.82 | Instantiating formula (109) with all_0_17_17, 0, all_70_0_95 and discharging atoms join_associative(all_0_17_17) = all_70_0_95, join_associative(all_0_17_17) = 0, yields: % 22.23/5.82 | (241) all_70_0_95 = 0 % 22.23/5.82 | % 22.23/5.82 | Equations (241) can reduce 255 to: % 22.23/5.82 | (213) $false % 22.23/5.82 | % 22.23/5.82 |-The branch is then unsatisfiable % 22.23/5.82 |-Branch two: % 22.23/5.82 | (553) ~ (all_70_0_95 = 0) & meet_commutative(all_0_17_17) = all_70_0_95 % 22.23/5.82 | % 22.23/5.82 | Applying alpha-rule on (553) yields: % 22.23/5.82 | (255) ~ (all_70_0_95 = 0) % 22.23/5.82 | (555) meet_commutative(all_0_17_17) = all_70_0_95 % 22.23/5.82 | % 22.23/5.82 | Instantiating formula (107) with all_0_17_17, 0, all_70_0_95 and discharging atoms meet_commutative(all_0_17_17) = all_70_0_95, meet_commutative(all_0_17_17) = 0, yields: % 22.23/5.82 | (241) all_70_0_95 = 0 % 22.23/5.82 | % 22.23/5.82 | Equations (241) can reduce 255 to: % 22.23/5.82 | (213) $false % 22.23/5.83 | % 22.23/5.83 |-The branch is then unsatisfiable % 22.23/5.83 |-Branch two: % 22.23/5.83 | (558) ~ (all_70_0_95 = 0) & meet_associative(all_0_17_17) = all_70_0_95 % 22.23/5.83 | % 22.23/5.83 | Applying alpha-rule on (558) yields: % 22.23/5.83 | (255) ~ (all_70_0_95 = 0) % 22.23/5.83 | (560) meet_associative(all_0_17_17) = all_70_0_95 % 22.23/5.83 | % 22.23/5.83 | Instantiating formula (106) with all_0_17_17, 0, all_70_0_95 and discharging atoms meet_associative(all_0_17_17) = all_70_0_95, meet_associative(all_0_17_17) = 0, yields: % 22.23/5.83 | (241) all_70_0_95 = 0 % 22.23/5.83 | % 22.23/5.83 | Equations (241) can reduce 255 to: % 22.23/5.83 | (213) $false % 22.23/5.83 | % 22.23/5.83 |-The branch is then unsatisfiable % 22.23/5.83 |-Branch two: % 22.23/5.83 | (563) ~ (all_70_0_95 = 0) & meet_absorbing(all_0_17_17) = all_70_0_95 % 22.23/5.83 | % 22.23/5.83 | Applying alpha-rule on (563) yields: % 22.23/5.83 | (255) ~ (all_70_0_95 = 0) % 22.23/5.83 | (565) meet_absorbing(all_0_17_17) = all_70_0_95 % 22.23/5.83 | % 22.23/5.83 | Instantiating formula (8) with all_0_17_17, 0, all_70_0_95 and discharging atoms meet_absorbing(all_0_17_17) = all_70_0_95, meet_absorbing(all_0_17_17) = 0, yields: % 22.23/5.83 | (241) all_70_0_95 = 0 % 22.23/5.83 | % 22.23/5.83 | Equations (241) can reduce 255 to: % 22.23/5.83 | (213) $false % 22.23/5.83 | % 22.23/5.83 |-The branch is then unsatisfiable % 22.23/5.83 |-Branch two: % 22.23/5.83 | (568) ~ (all_70_0_95 = 0) & join_absorbing(all_0_17_17) = all_70_0_95 % 22.23/5.83 | % 22.23/5.83 | Applying alpha-rule on (568) yields: % 22.23/5.83 | (255) ~ (all_70_0_95 = 0) % 22.23/5.83 | (570) join_absorbing(all_0_17_17) = all_70_0_95 % 22.23/5.83 | % 22.23/5.83 | Instantiating formula (5) with all_0_17_17, 0, all_70_0_95 and discharging atoms join_absorbing(all_0_17_17) = all_70_0_95, join_absorbing(all_0_17_17) = 0, yields: % 22.23/5.83 | (241) all_70_0_95 = 0 % 22.23/5.83 | % 22.23/5.83 | Equations (241) can reduce 255 to: % 22.23/5.83 | (213) $false % 22.23/5.83 | % 22.23/5.83 |-The branch is then unsatisfiable % 22.23/5.83 |-Branch two: % 22.23/5.83 | (573) all_87_1_134 = 0 & empty_carrier(all_0_17_17) = 0 % 22.23/5.83 | % 22.23/5.83 | Applying alpha-rule on (573) yields: % 22.23/5.83 | (574) all_87_1_134 = 0 % 22.23/5.83 | (242) empty_carrier(all_0_17_17) = 0 % 22.23/5.83 | % 22.23/5.83 | Instantiating formula (73) with all_0_17_17, all_79_6_117, all_0_16_16 and discharging atoms empty_carrier(all_0_17_17) = all_79_6_117, empty_carrier(all_0_17_17) = all_0_16_16, yields: % 22.23/5.83 | (248) all_79_6_117 = all_0_16_16 % 22.23/5.83 | % 22.23/5.83 | Instantiating formula (73) with all_0_17_17, all_79_6_117, all_80_6_124 and discharging atoms empty_carrier(all_0_17_17) = all_80_6_124, empty_carrier(all_0_17_17) = all_79_6_117, yields: % 22.23/5.83 | (244) all_80_6_124 = all_79_6_117 % 22.23/5.83 | % 22.23/5.83 | Instantiating formula (73) with all_0_17_17, all_74_1_102, all_79_6_117 and discharging atoms empty_carrier(all_0_17_17) = all_79_6_117, empty_carrier(all_0_17_17) = all_74_1_102, yields: % 22.23/5.83 | (247) all_79_6_117 = all_74_1_102 % 22.23/5.83 | % 22.23/5.83 | Instantiating formula (73) with all_0_17_17, 0, all_80_6_124 and discharging atoms empty_carrier(all_0_17_17) = all_80_6_124, empty_carrier(all_0_17_17) = 0, yields: % 22.23/5.83 | (579) all_80_6_124 = 0 % 22.23/5.83 | % 22.23/5.83 | Combining equations (244,579) yields a new equation: % 22.23/5.83 | (580) all_79_6_117 = 0 % 22.23/5.83 | % 22.23/5.83 | Simplifying 580 yields: % 22.23/5.83 | (581) all_79_6_117 = 0 % 22.23/5.83 | % 22.23/5.83 | Combining equations (248,247) yields a new equation: % 22.23/5.83 | (250) all_74_1_102 = all_0_16_16 % 22.23/5.83 | % 22.23/5.83 | Combining equations (581,247) yields a new equation: % 22.23/5.83 | (246) all_74_1_102 = 0 % 22.23/5.83 | % 22.23/5.83 | Combining equations (250,246) yields a new equation: % 22.23/5.83 | (251) all_0_16_16 = 0 % 22.23/5.83 | % 22.23/5.83 | Simplifying 251 yields: % 22.23/5.83 | (212) all_0_16_16 = 0 % 22.23/5.83 | % 22.23/5.83 | Equations (212) can reduce 98 to: % 22.23/5.83 | (213) $false % 22.23/5.83 | % 22.23/5.83 |-The branch is then unsatisfiable % 22.23/5.83 |-Branch two: % 22.23/5.83 | (587) ~ (all_87_1_134 = 0) & latt_str(all_0_17_17) = all_87_1_134 % 22.23/5.83 | % 22.23/5.83 | Applying alpha-rule on (587) yields: % 22.23/5.83 | (588) ~ (all_87_1_134 = 0) % 22.23/5.83 | (589) latt_str(all_0_17_17) = all_87_1_134 % 22.23/5.83 | % 22.23/5.83 | Instantiating formula (50) with all_0_17_17, all_87_1_134, 0 and discharging atoms latt_str(all_0_17_17) = all_87_1_134, latt_str(all_0_17_17) = 0, yields: % 22.23/5.83 | (574) all_87_1_134 = 0 % 22.23/5.83 | % 22.23/5.83 | Equations (574) can reduce 588 to: % 22.23/5.83 | (213) $false % 22.23/5.83 | % 22.23/5.83 |-The branch is then unsatisfiable % 22.23/5.83 |-Branch two: % 22.23/5.83 | (592) all_74_1_102 = 0 & empty_carrier(all_0_17_17) = 0 % 22.23/5.83 | % 22.23/5.83 | Applying alpha-rule on (592) yields: % 22.23/5.83 | (246) all_74_1_102 = 0 % 22.23/5.83 | (242) empty_carrier(all_0_17_17) = 0 % 22.23/5.83 | % 22.23/5.83 | Instantiating formula (73) with all_0_17_17, all_79_6_117, all_0_16_16 and discharging atoms empty_carrier(all_0_17_17) = all_79_6_117, empty_carrier(all_0_17_17) = all_0_16_16, yields: % 22.23/5.83 | (248) all_79_6_117 = all_0_16_16 % 22.23/5.83 | % 22.23/5.83 | Instantiating formula (73) with all_0_17_17, all_79_6_117, all_80_6_124 and discharging atoms empty_carrier(all_0_17_17) = all_80_6_124, empty_carrier(all_0_17_17) = all_79_6_117, yields: % 22.23/5.83 | (244) all_80_6_124 = all_79_6_117 % 22.23/5.83 | % 22.23/5.83 | Instantiating formula (73) with all_0_17_17, 0, all_80_6_124 and discharging atoms empty_carrier(all_0_17_17) = all_80_6_124, empty_carrier(all_0_17_17) = 0, yields: % 22.23/5.83 | (579) all_80_6_124 = 0 % 22.23/5.83 | % 22.23/5.83 | Combining equations (244,579) yields a new equation: % 22.23/5.83 | (580) all_79_6_117 = 0 % 22.23/5.83 | % 22.23/5.83 | Simplifying 580 yields: % 22.23/5.83 | (581) all_79_6_117 = 0 % 22.23/5.83 | % 22.23/5.83 | Combining equations (248,581) yields a new equation: % 22.23/5.83 | (251) all_0_16_16 = 0 % 22.23/5.83 | % 22.23/5.83 | Simplifying 251 yields: % 22.23/5.83 | (212) all_0_16_16 = 0 % 22.23/5.83 | % 22.23/5.83 | Equations (212) can reduce 98 to: % 22.23/5.83 | (213) $false % 22.23/5.83 | % 22.23/5.83 |-The branch is then unsatisfiable % 22.23/5.83 |-Branch two: % 22.23/5.83 | (603) ~ (all_74_1_102 = 0) & join_commutative(all_0_17_17) = all_74_1_102 % 22.23/5.83 | % 22.23/5.83 | Applying alpha-rule on (603) yields: % 22.23/5.83 | (225) ~ (all_74_1_102 = 0) % 22.23/5.83 | (605) join_commutative(all_0_17_17) = all_74_1_102 % 22.23/5.83 | % 22.23/5.83 | Instantiating formula (82) with all_0_17_17, 0, all_74_1_102 and discharging atoms join_commutative(all_0_17_17) = all_74_1_102, join_commutative(all_0_17_17) = 0, yields: % 22.23/5.83 | (246) all_74_1_102 = 0 % 22.23/5.83 | % 22.23/5.83 | Equations (246) can reduce 225 to: % 22.23/5.83 | (213) $false % 22.23/5.83 | % 22.23/5.83 |-The branch is then unsatisfiable % 22.23/5.83 |-Branch two: % 22.23/5.83 | (608) ~ (all_74_1_102 = 0) & join_associative(all_0_17_17) = all_74_1_102 % 22.23/5.83 | % 22.23/5.83 | Applying alpha-rule on (608) yields: % 22.23/5.83 | (225) ~ (all_74_1_102 = 0) % 22.23/5.83 | (610) join_associative(all_0_17_17) = all_74_1_102 % 22.23/5.83 | % 22.23/5.83 | Instantiating formula (109) with all_0_17_17, 0, all_74_1_102 and discharging atoms join_associative(all_0_17_17) = all_74_1_102, join_associative(all_0_17_17) = 0, yields: % 22.23/5.83 | (246) all_74_1_102 = 0 % 22.23/5.83 | % 22.23/5.83 | Equations (246) can reduce 225 to: % 22.23/5.83 | (213) $false % 22.23/5.83 | % 22.23/5.83 |-The branch is then unsatisfiable % 22.23/5.83 |-Branch two: % 22.23/5.83 | (613) ~ (all_74_1_102 = 0) & meet_commutative(all_0_17_17) = all_74_1_102 % 22.23/5.83 | % 22.23/5.83 | Applying alpha-rule on (613) yields: % 22.23/5.83 | (225) ~ (all_74_1_102 = 0) % 22.23/5.83 | (615) meet_commutative(all_0_17_17) = all_74_1_102 % 22.23/5.83 | % 22.23/5.83 | Instantiating formula (107) with all_0_17_17, 0, all_74_1_102 and discharging atoms meet_commutative(all_0_17_17) = all_74_1_102, meet_commutative(all_0_17_17) = 0, yields: % 22.23/5.83 | (246) all_74_1_102 = 0 % 22.23/5.83 | % 22.23/5.83 | Equations (246) can reduce 225 to: % 22.23/5.83 | (213) $false % 22.23/5.83 | % 22.23/5.83 |-The branch is then unsatisfiable % 22.23/5.83 |-Branch two: % 22.23/5.83 | (618) ~ (all_74_1_102 = 0) & meet_associative(all_0_17_17) = all_74_1_102 % 22.23/5.83 | % 22.23/5.83 | Applying alpha-rule on (618) yields: % 22.23/5.83 | (225) ~ (all_74_1_102 = 0) % 22.23/5.83 | (620) meet_associative(all_0_17_17) = all_74_1_102 % 22.23/5.83 | % 22.23/5.83 | Instantiating formula (106) with all_0_17_17, 0, all_74_1_102 and discharging atoms meet_associative(all_0_17_17) = all_74_1_102, meet_associative(all_0_17_17) = 0, yields: % 22.23/5.83 | (246) all_74_1_102 = 0 % 22.23/5.83 | % 22.23/5.83 | Equations (246) can reduce 225 to: % 22.23/5.83 | (213) $false % 22.23/5.83 | % 22.23/5.83 |-The branch is then unsatisfiable % 22.23/5.83 |-Branch two: % 22.23/5.83 | (623) ~ (all_74_1_102 = 0) & meet_absorbing(all_0_17_17) = all_74_1_102 % 22.23/5.83 | % 22.23/5.83 | Applying alpha-rule on (623) yields: % 22.23/5.83 | (225) ~ (all_74_1_102 = 0) % 22.23/5.83 | (625) meet_absorbing(all_0_17_17) = all_74_1_102 % 22.23/5.83 | % 22.23/5.83 | Instantiating formula (8) with all_0_17_17, 0, all_74_1_102 and discharging atoms meet_absorbing(all_0_17_17) = all_74_1_102, meet_absorbing(all_0_17_17) = 0, yields: % 22.23/5.83 | (246) all_74_1_102 = 0 % 22.23/5.83 | % 22.23/5.83 | Equations (246) can reduce 225 to: % 22.23/5.83 | (213) $false % 22.23/5.83 | % 22.23/5.83 |-The branch is then unsatisfiable % 22.23/5.83 |-Branch two: % 22.23/5.83 | (628) ~ (all_74_1_102 = 0) & join_absorbing(all_0_17_17) = all_74_1_102 % 22.23/5.83 | % 22.23/5.84 | Applying alpha-rule on (628) yields: % 22.23/5.84 | (225) ~ (all_74_1_102 = 0) % 22.23/5.84 | (630) join_absorbing(all_0_17_17) = all_74_1_102 % 22.23/5.84 | % 22.23/5.84 | Instantiating formula (5) with all_0_17_17, 0, all_74_1_102 and discharging atoms join_absorbing(all_0_17_17) = all_74_1_102, join_absorbing(all_0_17_17) = 0, yields: % 22.23/5.84 | (246) all_74_1_102 = 0 % 22.23/5.84 | % 22.23/5.84 | Equations (246) can reduce 225 to: % 22.23/5.84 | (213) $false % 22.23/5.84 | % 22.23/5.84 |-The branch is then unsatisfiable % 22.23/5.84 |-Branch two: % 22.23/5.84 | (633) all_80_6_124 = 0 & empty_carrier(all_0_17_17) = 0 % 22.23/5.84 | % 22.23/5.84 | Applying alpha-rule on (633) yields: % 22.23/5.84 | (579) all_80_6_124 = 0 % 22.23/5.84 | (242) empty_carrier(all_0_17_17) = 0 % 22.23/5.84 | % 22.23/5.84 +-Applying beta-rule and splitting (157), into two cases. % 22.23/5.84 |-Branch one: % 22.23/5.84 | (212) all_0_16_16 = 0 % 22.23/5.84 | % 22.23/5.84 | Equations (212) can reduce 98 to: % 22.23/5.84 | (213) $false % 22.23/5.84 | % 22.23/5.84 |-The branch is then unsatisfiable % 22.23/5.84 |-Branch two: % 22.23/5.84 | (98) ~ (all_0_16_16 = 0) % 22.23/5.84 | (215) ? [v0] : ? [v1] : (( ~ (v1 = 0) & the_carrier(all_0_17_17) = v0 & empty(v0) = v1) | ( ~ (v0 = 0) & one_sorted_str(all_0_17_17) = v0)) % 22.23/5.84 | % 22.23/5.84 | Instantiating formula (73) with all_0_17_17, all_79_6_117, all_0_16_16 and discharging atoms empty_carrier(all_0_17_17) = all_79_6_117, empty_carrier(all_0_17_17) = all_0_16_16, yields: % 22.23/5.84 | (248) all_79_6_117 = all_0_16_16 % 22.23/5.84 | % 22.23/5.84 | Instantiating formula (73) with all_0_17_17, 0, all_79_6_117 and discharging atoms empty_carrier(all_0_17_17) = all_79_6_117, empty_carrier(all_0_17_17) = 0, yields: % 22.23/5.84 | (581) all_79_6_117 = 0 % 22.23/5.84 | % 22.23/5.84 | Combining equations (581,248) yields a new equation: % 22.23/5.84 | (212) all_0_16_16 = 0 % 22.23/5.84 | % 22.23/5.84 | Equations (212) can reduce 98 to: % 22.23/5.84 | (213) $false % 22.23/5.84 | % 22.23/5.84 |-The branch is then unsatisfiable % 22.23/5.84 |-Branch two: % 22.23/5.84 | (644) ~ (all_80_6_124 = 0) & latt_str(all_0_17_17) = all_80_6_124 % 22.23/5.84 | % 22.23/5.84 | Applying alpha-rule on (644) yields: % 22.23/5.84 | (208) ~ (all_80_6_124 = 0) % 22.23/5.84 | (646) latt_str(all_0_17_17) = all_80_6_124 % 22.23/5.84 | % 22.23/5.84 | Instantiating formula (50) with all_0_17_17, all_80_6_124, 0 and discharging atoms latt_str(all_0_17_17) = all_80_6_124, latt_str(all_0_17_17) = 0, yields: % 22.23/5.84 | (579) all_80_6_124 = 0 % 22.23/5.84 | % 22.23/5.84 | Equations (579) can reduce 208 to: % 22.23/5.84 | (213) $false % 22.23/5.84 | % 22.23/5.84 |-The branch is then unsatisfiable % 22.23/5.84 |-Branch two: % 22.23/5.84 | (649) all_82_1_127 = 0 & empty_carrier(all_0_17_17) = 0 % 22.23/5.84 | % 22.23/5.84 | Applying alpha-rule on (649) yields: % 22.23/5.84 | (650) all_82_1_127 = 0 % 22.23/5.84 | (242) empty_carrier(all_0_17_17) = 0 % 22.23/5.84 | % 22.23/5.84 +-Applying beta-rule and splitting (156), into two cases. % 22.23/5.84 |-Branch one: % 22.23/5.84 | (212) all_0_16_16 = 0 % 22.23/5.84 | % 22.23/5.84 | Equations (212) can reduce 98 to: % 22.23/5.84 | (213) $false % 22.23/5.84 | % 22.23/5.84 |-The branch is then unsatisfiable % 22.23/5.84 |-Branch two: % 22.23/5.84 | (98) ~ (all_0_16_16 = 0) % 22.23/5.84 | (655) ? [v0] : ? [v1] : ((v1 = 0 & relation(v0) = 0 & relation_of_lattice(all_0_17_17) = v0) | ( ~ (v0 = 0) & lattice(all_0_17_17) = v0) | ( ~ (v0 = 0) & latt_str(all_0_17_17) = v0)) % 22.23/5.84 | % 22.23/5.84 +-Applying beta-rule and splitting (157), into two cases. % 22.23/5.84 |-Branch one: % 22.23/5.84 | (212) all_0_16_16 = 0 % 22.23/5.84 | % 22.23/5.84 | Equations (212) can reduce 98 to: % 22.23/5.84 | (213) $false % 22.23/5.84 | % 22.23/5.84 |-The branch is then unsatisfiable % 22.23/5.84 |-Branch two: % 22.23/5.84 | (98) ~ (all_0_16_16 = 0) % 22.23/5.84 | (215) ? [v0] : ? [v1] : (( ~ (v1 = 0) & the_carrier(all_0_17_17) = v0 & empty(v0) = v1) | ( ~ (v0 = 0) & one_sorted_str(all_0_17_17) = v0)) % 22.23/5.84 | % 22.23/5.84 | Instantiating formula (73) with all_0_17_17, all_79_6_117, all_0_16_16 and discharging atoms empty_carrier(all_0_17_17) = all_79_6_117, empty_carrier(all_0_17_17) = all_0_16_16, yields: % 22.23/5.84 | (248) all_79_6_117 = all_0_16_16 % 22.23/5.84 | % 22.23/5.84 | Instantiating formula (73) with all_0_17_17, 0, all_79_6_117 and discharging atoms empty_carrier(all_0_17_17) = all_79_6_117, empty_carrier(all_0_17_17) = 0, yields: % 22.23/5.84 | (581) all_79_6_117 = 0 % 22.23/5.84 | % 22.23/5.84 | Combining equations (581,248) yields a new equation: % 22.23/5.84 | (212) all_0_16_16 = 0 % 22.23/5.84 | % 22.23/5.84 | Equations (212) can reduce 98 to: % 22.23/5.84 | (213) $false % 22.23/5.84 | % 22.23/5.84 |-The branch is then unsatisfiable % 22.23/5.84 |-Branch two: % 22.23/5.84 | (664) ~ (all_82_1_127 = 0) & latt_str(all_0_17_17) = all_82_1_127 % 22.23/5.84 | % 22.23/5.84 | Applying alpha-rule on (664) yields: % 22.23/5.84 | (665) ~ (all_82_1_127 = 0) % 22.23/5.84 | (666) latt_str(all_0_17_17) = all_82_1_127 % 22.23/5.84 | % 22.23/5.84 | Instantiating formula (50) with all_0_17_17, all_82_1_127, 0 and discharging atoms latt_str(all_0_17_17) = all_82_1_127, latt_str(all_0_17_17) = 0, yields: % 22.23/5.84 | (650) all_82_1_127 = 0 % 22.23/5.84 | % 22.23/5.84 | Equations (650) can reduce 665 to: % 22.23/5.84 | (213) $false % 22.23/5.84 | % 22.23/5.84 |-The branch is then unsatisfiable % 22.23/5.84 |-Branch two: % 22.23/5.84 | (669) all_79_6_117 = 0 & empty_carrier(all_0_17_17) = 0 % 22.23/5.84 | % 22.23/5.84 | Applying alpha-rule on (669) yields: % 22.23/5.84 | (581) all_79_6_117 = 0 % 22.23/5.84 | (242) empty_carrier(all_0_17_17) = 0 % 22.23/5.84 | % 22.23/5.84 +-Applying beta-rule and splitting (154), into two cases. % 22.23/5.84 |-Branch one: % 22.23/5.84 | (212) all_0_16_16 = 0 % 22.23/5.84 | % 22.23/5.84 | Equations (212) can reduce 98 to: % 22.23/5.84 | (213) $false % 22.23/5.84 | % 22.23/5.84 |-The branch is then unsatisfiable % 22.23/5.84 |-Branch two: % 22.23/5.84 | (98) ~ (all_0_16_16 = 0) % 22.23/5.84 | (675) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & v3 = 0 & v2 = 0 & v1 = 0 & v0 = 0 & join_commutative(all_0_17_17) = 0 & join_associative(all_0_17_17) = 0 & meet_commutative(all_0_17_17) = 0 & meet_associative(all_0_17_17) = 0 & meet_absorbing(all_0_17_17) = 0 & join_absorbing(all_0_17_17) = 0) | ( ~ (v0 = 0) & lattice(all_0_17_17) = v0) | ( ~ (v0 = 0) & latt_str(all_0_17_17) = v0)) % 22.23/5.84 | % 22.23/5.84 +-Applying beta-rule and splitting (156), into two cases. % 22.23/5.84 |-Branch one: % 22.23/5.84 | (212) all_0_16_16 = 0 % 22.23/5.84 | % 22.23/5.84 | Equations (212) can reduce 98 to: % 22.23/5.84 | (213) $false % 22.23/5.84 | % 22.23/5.84 |-The branch is then unsatisfiable % 22.23/5.84 |-Branch two: % 22.23/5.84 | (98) ~ (all_0_16_16 = 0) % 22.23/5.84 | (655) ? [v0] : ? [v1] : ((v1 = 0 & relation(v0) = 0 & relation_of_lattice(all_0_17_17) = v0) | ( ~ (v0 = 0) & lattice(all_0_17_17) = v0) | ( ~ (v0 = 0) & latt_str(all_0_17_17) = v0)) % 22.23/5.84 | % 22.23/5.84 +-Applying beta-rule and splitting (157), into two cases. % 22.23/5.84 |-Branch one: % 22.23/5.84 | (212) all_0_16_16 = 0 % 22.23/5.84 | % 22.23/5.84 | Equations (212) can reduce 98 to: % 22.23/5.84 | (213) $false % 22.23/5.84 | % 22.23/5.84 |-The branch is then unsatisfiable % 22.23/5.84 |-Branch two: % 22.23/5.84 | (98) ~ (all_0_16_16 = 0) % 22.23/5.84 | (215) ? [v0] : ? [v1] : (( ~ (v1 = 0) & the_carrier(all_0_17_17) = v0 & empty(v0) = v1) | ( ~ (v0 = 0) & one_sorted_str(all_0_17_17) = v0)) % 22.23/5.84 | % 22.23/5.84 | Instantiating formula (73) with all_0_17_17, 0, all_0_16_16 and discharging atoms empty_carrier(all_0_17_17) = all_0_16_16, empty_carrier(all_0_17_17) = 0, yields: % 22.23/5.84 | (212) all_0_16_16 = 0 % 22.23/5.84 | % 22.23/5.84 | Equations (212) can reduce 98 to: % 22.23/5.84 | (213) $false % 22.23/5.84 | % 22.23/5.84 |-The branch is then unsatisfiable % 22.23/5.84 |-Branch two: % 22.23/5.84 | (686) ~ (all_79_6_117 = 0) & lattice(all_0_17_17) = all_79_6_117 % 22.23/5.84 | % 22.23/5.84 | Applying alpha-rule on (686) yields: % 22.23/5.84 | (186) ~ (all_79_6_117 = 0) % 22.23/5.84 | (688) lattice(all_0_17_17) = all_79_6_117 % 22.23/5.84 | % 22.23/5.84 | Instantiating formula (34) with all_0_17_17, all_79_6_117, 0 and discharging atoms lattice(all_0_17_17) = all_79_6_117, lattice(all_0_17_17) = 0, yields: % 22.23/5.84 | (581) all_79_6_117 = 0 % 22.23/5.84 | % 22.23/5.84 | Equations (581) can reduce 186 to: % 22.23/5.84 | (213) $false % 22.23/5.84 | % 22.23/5.84 |-The branch is then unsatisfiable % 22.23/5.84 |-Branch two: % 22.23/5.84 | (691) all_78_1_110 = 0 & empty_carrier(all_0_17_17) = 0 % 22.23/5.84 | % 22.23/5.84 | Applying alpha-rule on (691) yields: % 22.23/5.84 | (692) all_78_1_110 = 0 % 22.23/5.84 | (242) empty_carrier(all_0_17_17) = 0 % 22.23/5.84 | % 22.23/5.84 +-Applying beta-rule and splitting (155), into two cases. % 22.23/5.84 |-Branch one: % 22.23/5.84 | (212) all_0_16_16 = 0 % 22.23/5.84 | % 22.23/5.84 | Equations (212) can reduce 98 to: % 22.23/5.84 | (213) $false % 22.23/5.84 | % 22.23/5.84 |-The branch is then unsatisfiable % 22.23/5.84 |-Branch two: % 22.23/5.84 | (98) ~ (all_0_16_16 = 0) % 22.23/5.84 | (697) ? [v0] : ? [v1] : ((v1 = v0 & relation_of_lattice(all_0_17_17) = v0 & a_1_0_filter_1(all_0_17_17) = v0) | ( ~ (v0 = 0) & lattice(all_0_17_17) = v0) | ( ~ (v0 = 0) & latt_str(all_0_17_17) = v0)) % 22.23/5.85 | % 22.23/5.85 +-Applying beta-rule and splitting (154), into two cases. % 22.23/5.85 |-Branch one: % 22.23/5.85 | (212) all_0_16_16 = 0 % 22.23/5.85 | % 22.23/5.85 | Equations (212) can reduce 98 to: % 22.23/5.85 | (213) $false % 22.23/5.85 | % 22.23/5.85 |-The branch is then unsatisfiable % 22.23/5.85 |-Branch two: % 22.23/5.85 | (98) ~ (all_0_16_16 = 0) % 22.23/5.85 | (675) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & v3 = 0 & v2 = 0 & v1 = 0 & v0 = 0 & join_commutative(all_0_17_17) = 0 & join_associative(all_0_17_17) = 0 & meet_commutative(all_0_17_17) = 0 & meet_associative(all_0_17_17) = 0 & meet_absorbing(all_0_17_17) = 0 & join_absorbing(all_0_17_17) = 0) | ( ~ (v0 = 0) & lattice(all_0_17_17) = v0) | ( ~ (v0 = 0) & latt_str(all_0_17_17) = v0)) % 22.23/5.85 | % 22.23/5.85 +-Applying beta-rule and splitting (158), into two cases. % 22.23/5.85 |-Branch one: % 22.23/5.85 | (212) all_0_16_16 = 0 % 22.23/5.85 | % 22.23/5.85 | Equations (212) can reduce 98 to: % 22.23/5.85 | (213) $false % 22.23/5.85 | % 22.23/5.85 |-The branch is then unsatisfiable % 22.23/5.85 |-Branch two: % 22.23/5.85 | (98) ~ (all_0_16_16 = 0) % 22.23/5.85 | (705) ? [v0] : ((v0 = 0 & lattice(all_0_17_17) = 0) | ( ~ (v0 = 0) & latt_str(all_0_17_17) = v0) | ( ~ (v0 = 0) & join_commutative(all_0_17_17) = v0) | ( ~ (v0 = 0) & join_associative(all_0_17_17) = v0) | ( ~ (v0 = 0) & meet_commutative(all_0_17_17) = v0) | ( ~ (v0 = 0) & meet_associative(all_0_17_17) = v0) | ( ~ (v0 = 0) & meet_absorbing(all_0_17_17) = v0) | ( ~ (v0 = 0) & join_absorbing(all_0_17_17) = v0)) % 22.23/5.85 | % 22.23/5.85 +-Applying beta-rule and splitting (156), into two cases. % 22.23/5.85 |-Branch one: % 22.23/5.85 | (212) all_0_16_16 = 0 % 22.23/5.85 | % 22.23/5.85 | Equations (212) can reduce 98 to: % 22.23/5.85 | (213) $false % 22.23/5.85 | % 22.23/5.85 |-The branch is then unsatisfiable % 22.23/5.85 |-Branch two: % 22.23/5.85 | (98) ~ (all_0_16_16 = 0) % 22.23/5.85 | (655) ? [v0] : ? [v1] : ((v1 = 0 & relation(v0) = 0 & relation_of_lattice(all_0_17_17) = v0) | ( ~ (v0 = 0) & lattice(all_0_17_17) = v0) | ( ~ (v0 = 0) & latt_str(all_0_17_17) = v0)) % 22.23/5.85 | % 22.23/5.85 +-Applying beta-rule and splitting (157), into two cases. % 22.23/5.85 |-Branch one: % 22.23/5.85 | (212) all_0_16_16 = 0 % 22.23/5.85 | % 22.23/5.85 | Equations (212) can reduce 98 to: % 22.23/5.85 | (213) $false % 22.23/5.85 | % 22.23/5.85 |-The branch is then unsatisfiable % 22.23/5.85 |-Branch two: % 22.23/5.85 | (98) ~ (all_0_16_16 = 0) % 22.23/5.85 | (215) ? [v0] : ? [v1] : (( ~ (v1 = 0) & the_carrier(all_0_17_17) = v0 & empty(v0) = v1) | ( ~ (v0 = 0) & one_sorted_str(all_0_17_17) = v0)) % 22.23/5.85 | % 22.23/5.85 | Instantiating formula (73) with all_0_17_17, 0, all_0_16_16 and discharging atoms empty_carrier(all_0_17_17) = all_0_16_16, empty_carrier(all_0_17_17) = 0, yields: % 22.23/5.85 | (212) all_0_16_16 = 0 % 22.23/5.85 | % 22.23/5.85 | Equations (212) can reduce 98 to: % 22.23/5.85 | (213) $false % 22.23/5.85 | % 22.23/5.85 |-The branch is then unsatisfiable % 22.23/5.85 |-Branch two: % 22.23/5.85 | (716) ~ (all_78_1_110 = 0) & lattice(all_0_17_17) = all_78_1_110 % 22.23/5.85 | % 22.23/5.85 | Applying alpha-rule on (716) yields: % 22.23/5.85 | (717) ~ (all_78_1_110 = 0) % 22.23/5.85 | (718) lattice(all_0_17_17) = all_78_1_110 % 22.23/5.85 | % 22.23/5.85 | Instantiating formula (34) with all_0_17_17, all_78_1_110, 0 and discharging atoms lattice(all_0_17_17) = all_78_1_110, lattice(all_0_17_17) = 0, yields: % 22.23/5.85 | (692) all_78_1_110 = 0 % 22.23/5.85 | % 22.23/5.85 | Equations (692) can reduce 717 to: % 22.23/5.85 | (213) $false % 22.23/5.85 | % 22.23/5.85 |-The branch is then unsatisfiable % 22.23/5.85 % SZS output end Proof for theBenchmark % 22.23/5.85 % 22.23/5.85 5255ms %------------------------------------------------------------------------------