TSTP Solution File: SEU341+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU341+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n021.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 08:49:00 EDT 2022
% Result : Theorem 6.77s 2.24s
% Output : Proof 10.40s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SEU341+1 : TPTP v8.1.0. Released v3.3.0.
% 0.04/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.34 % Computer : n021.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jun 19 10:36:17 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.56/0.59 ____ _
% 0.56/0.59 ___ / __ \_____(_)___ ________ __________
% 0.56/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.56/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.56/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.56/0.59
% 0.56/0.59 A Theorem Prover for First-Order Logic
% 0.56/0.59 (ePrincess v.1.0)
% 0.56/0.59
% 0.56/0.59 (c) Philipp Rümmer, 2009-2015
% 0.56/0.59 (c) Peter Backeman, 2014-2015
% 0.56/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.56/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.56/0.59 Bug reports to peter@backeman.se
% 0.56/0.59
% 0.56/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.56/0.59
% 0.56/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.72/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.70/0.99 Prover 0: Preprocessing ...
% 2.51/1.27 Prover 0: Warning: ignoring some quantifiers
% 2.72/1.30 Prover 0: Constructing countermodel ...
% 5.33/1.94 Prover 0: gave up
% 5.33/1.95 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 5.67/2.00 Prover 1: Preprocessing ...
% 6.32/2.13 Prover 1: Warning: ignoring some quantifiers
% 6.39/2.14 Prover 1: Constructing countermodel ...
% 6.77/2.24 Prover 1: proved (297ms)
% 6.77/2.24
% 6.77/2.24 No countermodel exists, formula is valid
% 6.77/2.24 % SZS status Theorem for theBenchmark
% 6.77/2.24
% 6.77/2.24 Generating proof ... Warning: ignoring some quantifiers
% 9.74/2.95 found it (size 124)
% 9.74/2.95
% 9.74/2.95 % SZS output start Proof for theBenchmark
% 9.74/2.95 Assumed formulas after preprocessing and simplification:
% 9.74/2.95 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ( ~ (v8 = 0) & ~ (v6 = 0) & ~ (v1 = 0) & open_subset(v4, v0) = 0 & one_sorted_str(v9) = 0 & empty_carrier(v0) = v1 & topological_space(v0) = 0 & top_str(v10) = 0 & top_str(v0) = 0 & the_carrier(v0) = v2 & point_neighbourhood(v4, v0, v5) = v6 & powerset(v2) = v3 & empty(v7) = v8 & empty(empty_set) = 0 & v5_membered(v7) = 0 & v5_membered(empty_set) = 0 & v4_membered(v7) = 0 & v4_membered(empty_set) = 0 & v3_membered(v7) = 0 & v3_membered(empty_set) = 0 & v2_membered(v7) = 0 & v2_membered(empty_set) = 0 & v1_membered(v7) = 0 & v1_membered(empty_set) = 0 & element(v5, v2) = 0 & element(v4, v3) = 0 & in(v5, v4) = 0 & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (the_carrier(v11) = v13) | ~ (interior(v11, v12) = v15) | ~ (powerset(v13) = v14) | ~ (element(v15, v14) = v16) | ? [v17] : ? [v18] : (top_str(v11) = v17 & element(v12, v14) = v18 & ( ~ (v18 = 0) | ~ (v17 = 0)))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v12 = v11 | ~ (point_neighbourhood(v15, v14, v13) = v12) | ~ (point_neighbourhood(v15, v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (powerset(v12) = v13) | ~ (element(v11, v13) = v14) | ? [v15] : ( ~ (v15 = 0) & subset(v11, v12) = v15)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (open_subset(v14, v13) = v12) | ~ (open_subset(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (subset(v14, v13) = v12) | ~ (subset(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (interior(v14, v13) = v12) | ~ (interior(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (element(v14, v13) = v12) | ~ (element(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (in(v14, v13) = v12) | ~ (in(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (powerset(v13) = v14) | ~ (element(v12, v14) = 0) | ~ (in(v11, v12) = 0) | element(v11, v13) = 0) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (powerset(v13) = v14) | ~ (element(v12, v14) = 0) | ~ (in(v11, v12) = 0) | ? [v15] : ( ~ (v15 = 0) & empty(v13) = v15)) & ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (v1_membered(v11) = 0) | ~ (v1_xcmplx_0(v12) = v13) | ? [v14] : ( ~ (v14 = 0) & element(v12, v11) = v14)) & ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (in(v11, v12) = v13) | ? [v14] : ? [v15] : (empty(v12) = v15 & element(v11, v12) = v14 & ( ~ (v14 = 0) | v15 = 0))) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (one_sorted_str(v13) = v12) | ~ (one_sorted_str(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (empty_carrier(v13) = v12) | ~ (empty_carrier(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (topological_space(v13) = v12) | ~ (topological_space(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (top_str(v13) = v12) | ~ (top_str(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (the_carrier(v13) = v12) | ~ (the_carrier(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (powerset(v13) = v12) | ~ (powerset(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (empty(v13) = v12) | ~ (empty(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (v5_membered(v13) = v12) | ~ (v5_membered(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (natural(v13) = v12) | ~ (natural(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (v4_membered(v13) = v12) | ~ (v4_membered(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (v1_int_1(v13) = v12) | ~ (v1_int_1(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (v3_membered(v13) = v12) | ~ (v3_membered(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (v1_rat_1(v13) = v12) | ~ (v1_rat_1(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (v2_membered(v13) = v12) | ~ (v2_membered(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (v1_xreal_0(v13) = v12) | ~ (v1_xreal_0(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (v1_membered(v13) = v12) | ~ (v1_membered(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (v1_xcmplx_0(v13) = v12) | ~ (v1_xcmplx_0(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (the_carrier(v11) = v13) | ~ (element(v12, v13) = 0) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : (empty_carrier(v11) = v14 & topological_space(v11) = v15 & top_str(v11) = v16 & powerset(v13) = v17 & ( ~ (v16 = 0) | ~ (v15 = 0) | v14 = 0 | ! [v18] : ! [v19] : (v19 = 0 | ~ (element(v18, v17) = v19) | ? [v20] : ( ~ (v20 = 0) & point_neighbourhood(v18, v11, v12) = v20))))) & ! [v11] : ! [v12] : ! [v13] : ( ~ (the_carrier(v11) = v13) | ~ (element(v12, v13) = 0) | ? [v14] : ? [v15] : ? [v16] : ((v15 = 0 & point_neighbourhood(v14, v11, v12) = 0) | (empty_carrier(v11) = v14 & topological_space(v11) = v15 & top_str(v11) = v16 & ( ~ (v16 = 0) | ~ (v15 = 0) | v14 = 0)))) & ! [v11] : ! [v12] : ! [v13] : ( ~ (powerset(v12) = v13) | ~ (element(v11, v13) = 0) | subset(v11, v12) = 0) & ! [v11] : ! [v12] : ! [v13] : ( ~ (v5_membered(v11) = 0) | ~ (natural(v12) = v13) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : (v1_int_1(v12) = v17 & v1_rat_1(v12) = v18 & v1_xreal_0(v12) = v16 & v1_xcmplx_0(v12) = v15 & element(v12, v11) = v14 & ( ~ (v14 = 0) | (v18 = 0 & v17 = 0 & v16 = 0 & v15 = 0 & v13 = 0)))) & ! [v11] : ! [v12] : ! [v13] : ( ~ (v4_membered(v11) = 0) | ~ (v1_int_1(v12) = v13) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : (v1_rat_1(v12) = v17 & v1_xreal_0(v12) = v16 & v1_xcmplx_0(v12) = v15 & element(v12, v11) = v14 & ( ~ (v14 = 0) | (v17 = 0 & v16 = 0 & v15 = 0 & v13 = 0)))) & ! [v11] : ! [v12] : ! [v13] : ( ~ (v3_membered(v11) = 0) | ~ (v1_rat_1(v12) = v13) | ? [v14] : ? [v15] : ? [v16] : (v1_xreal_0(v12) = v16 & v1_xcmplx_0(v12) = v15 & element(v12, v11) = v14 & ( ~ (v14 = 0) | (v16 = 0 & v15 = 0 & v13 = 0)))) & ! [v11] : ! [v12] : ! [v13] : ( ~ (v2_membered(v11) = 0) | ~ (v1_xreal_0(v12) = v13) | ? [v14] : ? [v15] : (v1_xcmplx_0(v12) = v15 & element(v12, v11) = v14 & ( ~ (v14 = 0) | (v15 = 0 & v13 = 0)))) & ! [v11] : ! [v12] : (v12 = v11 | ~ (empty(v12) = 0) | ~ (empty(v11) = 0)) & ! [v11] : ! [v12] : (v12 = 0 | ~ (subset(v11, v11) = v12)) & ! [v11] : ! [v12] : (v12 = 0 | ~ (one_sorted_str(v11) = v12) | ? [v13] : ( ~ (v13 = 0) & top_str(v11) = v13)) & ! [v11] : ! [v12] : (v12 = 0 | ~ (empty_carrier(v11) = v12) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : (topological_space(v11) = v13 & top_str(v11) = v14 & the_carrier(v11) = v15 & powerset(v15) = v16 & ( ~ (v14 = 0) | ~ (v13 = 0) | ! [v17] : ! [v18] : ( ~ (element(v18, v16) = 0) | ~ (element(v17, v15) = 0) | ? [v19] : ? [v20] : ? [v21] : (point_neighbourhood(v18, v11, v17) = v19 & interior(v11, v18) = v20 & in(v17, v20) = v21 & ( ~ (v21 = 0) | v19 = 0) & ( ~ (v19 = 0) | v21 = 0)))))) & ! [v11] : ! [v12] : (v12 = 0 | ~ (empty(v11) = v12) | ? [v13] : ? [v14] : ? [v15] : ( ~ (v15 = 0) & powerset(v11) = v13 & empty(v14) = v15 & element(v14, v13) = 0)) & ! [v11] : ! [v12] : ( ~ (powerset(v11) = v12) | ? [v13] : ( ~ (v13 = 0) & empty(v12) = v13)) & ! [v11] : ! [v12] : ( ~ (powerset(v11) = v12) | ? [v13] : (empty(v13) = 0 & element(v13, v12) = 0)) & ! [v11] : ! [v12] : ( ~ (v5_membered(v11) = v12) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : (empty(v11) = v13 & v4_membered(v11) = v17 & v3_membered(v11) = v16 & v2_membered(v11) = v15 & v1_membered(v11) = v14 & ( ~ (v13 = 0) | (v17 = 0 & v16 = 0 & v15 = 0 & v14 = 0 & v12 = 0)))) & ! [v11] : ! [v12] : ( ~ (in(v11, v12) = 0) | element(v11, v12) = 0) & ! [v11] : ! [v12] : ( ~ (in(v11, v12) = 0) | ? [v13] : ( ~ (v13 = 0) & empty(v12) = v13)) & ! [v11] : ! [v12] : ( ~ (in(v11, v12) = 0) | ? [v13] : ( ~ (v13 = 0) & in(v12, v11) = v13)) & ! [v11] : (v11 = empty_set | ~ (empty(v11) = 0)) & ! [v11] : ( ~ (topological_space(v11) = 0) | ? [v12] : ? [v13] : ? [v14] : (top_str(v11) = v12 & the_carrier(v11) = v13 & powerset(v13) = v14 & ( ~ (v12 = 0) | ! [v15] : ( ~ (top_str(v15) = 0) | ? [v16] : ? [v17] : (the_carrier(v15) = v16 & powerset(v16) = v17 & ! [v18] : ( ~ (element(v18, v14) = 0) | ? [v19] : ? [v20] : (open_subset(v18, v11) = v20 & interior(v11, v18) = v19 & ! [v21] : ( ~ (v19 = v18) | v20 = 0 | ~ (element(v21, v17) = 0)) & ! [v21] : ( ~ (element(v21, v17) = 0) | ? [v22] : ? [v23] : (open_subset(v21, v15) = v22 & interior(v15, v21) = v23 & ( ~ (v22 = 0) | v23 = v21)))))))))) & ! [v11] : ( ~ (v5_membered(v11) = 0) | v4_membered(v11) = 0) & ! [v11] : ( ~ (v5_membered(v11) = 0) | ? [v12] : (powerset(v11) = v12 & ! [v13] : ( ~ (element(v13, v12) = 0) | (v5_membered(v13) = 0 & v4_membered(v13) = 0 & v3_membered(v13) = 0 & v2_membered(v13) = 0 & v1_membered(v13) = 0)))) & ! [v11] : ( ~ (v4_membered(v11) = 0) | v3_membered(v11) = 0) & ! [v11] : ( ~ (v4_membered(v11) = 0) | ? [v12] : (powerset(v11) = v12 & ! [v13] : ( ~ (element(v13, v12) = 0) | (v4_membered(v13) = 0 & v3_membered(v13) = 0 & v2_membered(v13) = 0 & v1_membered(v13) = 0)))) & ! [v11] : ( ~ (v3_membered(v11) = 0) | v2_membered(v11) = 0) & ! [v11] : ( ~ (v3_membered(v11) = 0) | ? [v12] : (powerset(v11) = v12 & ! [v13] : ( ~ (element(v13, v12) = 0) | (v3_membered(v13) = 0 & v2_membered(v13) = 0 & v1_membered(v13) = 0)))) & ! [v11] : ( ~ (v2_membered(v11) = 0) | v1_membered(v11) = 0) & ! [v11] : ( ~ (v2_membered(v11) = 0) | ? [v12] : (powerset(v11) = v12 & ! [v13] : ( ~ (element(v13, v12) = 0) | (v2_membered(v13) = 0 & v1_membered(v13) = 0)))) & ! [v11] : ( ~ (v1_membered(v11) = 0) | ? [v12] : (powerset(v11) = v12 & ! [v13] : ( ~ (element(v13, v12) = 0) | v1_membered(v13) = 0))) & ? [v11] : ? [v12] : element(v12, v11) = 0)
% 10.21/3.00 | 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 yields:
% 10.21/3.00 | (1) ~ (all_0_2_2 = 0) & ~ (all_0_4_4 = 0) & ~ (all_0_9_9 = 0) & open_subset(all_0_6_6, all_0_10_10) = 0 & one_sorted_str(all_0_1_1) = 0 & empty_carrier(all_0_10_10) = all_0_9_9 & topological_space(all_0_10_10) = 0 & top_str(all_0_0_0) = 0 & top_str(all_0_10_10) = 0 & the_carrier(all_0_10_10) = all_0_8_8 & point_neighbourhood(all_0_6_6, all_0_10_10, all_0_5_5) = all_0_4_4 & powerset(all_0_8_8) = all_0_7_7 & empty(all_0_3_3) = all_0_2_2 & empty(empty_set) = 0 & v5_membered(all_0_3_3) = 0 & v5_membered(empty_set) = 0 & v4_membered(all_0_3_3) = 0 & v4_membered(empty_set) = 0 & v3_membered(all_0_3_3) = 0 & v3_membered(empty_set) = 0 & v2_membered(all_0_3_3) = 0 & v2_membered(empty_set) = 0 & v1_membered(all_0_3_3) = 0 & v1_membered(empty_set) = 0 & element(all_0_5_5, all_0_8_8) = 0 & element(all_0_6_6, all_0_7_7) = 0 & in(all_0_5_5, all_0_6_6) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (the_carrier(v0) = v2) | ~ (interior(v0, v1) = v4) | ~ (powerset(v2) = v3) | ~ (element(v4, v3) = v5) | ? [v6] : ? [v7] : (top_str(v0) = v6 & element(v1, v3) = v7 & ( ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (point_neighbourhood(v4, v3, v2) = v1) | ~ (point_neighbourhood(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (open_subset(v3, v2) = v1) | ~ (open_subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (interior(v3, v2) = v1) | ~ (interior(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | element(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (v1_membered(v0) = 0) | ~ (v1_xcmplx_0(v1) = v2) | ? [v3] : ( ~ (v3 = 0) & element(v1, v0) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v0, v1) = v2) | ? [v3] : ? [v4] : (empty(v1) = v4 & element(v0, v1) = v3 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (one_sorted_str(v2) = v1) | ~ (one_sorted_str(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty_carrier(v2) = v1) | ~ (empty_carrier(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (topological_space(v2) = v1) | ~ (topological_space(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (top_str(v2) = v1) | ~ (top_str(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (the_carrier(v2) = v1) | ~ (the_carrier(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (v5_membered(v2) = v1) | ~ (v5_membered(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (natural(v2) = v1) | ~ (natural(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (v4_membered(v2) = v1) | ~ (v4_membered(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (v1_int_1(v2) = v1) | ~ (v1_int_1(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (v3_membered(v2) = v1) | ~ (v3_membered(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (v1_rat_1(v2) = v1) | ~ (v1_rat_1(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (v2_membered(v2) = v1) | ~ (v2_membered(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (v1_xreal_0(v2) = v1) | ~ (v1_xreal_0(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (v1_membered(v2) = v1) | ~ (v1_membered(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (v1_xcmplx_0(v2) = v1) | ~ (v1_xcmplx_0(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (the_carrier(v0) = v2) | ~ (element(v1, v2) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (empty_carrier(v0) = v3 & topological_space(v0) = v4 & top_str(v0) = v5 & powerset(v2) = v6 & ( ~ (v5 = 0) | ~ (v4 = 0) | v3 = 0 | ! [v7] : ! [v8] : (v8 = 0 | ~ (element(v7, v6) = v8) | ? [v9] : ( ~ (v9 = 0) & point_neighbourhood(v7, v0, v1) = v9))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (the_carrier(v0) = v2) | ~ (element(v1, v2) = 0) | ? [v3] : ? [v4] : ? [v5] : ((v4 = 0 & point_neighbourhood(v3, v0, v1) = 0) | (empty_carrier(v0) = v3 & topological_space(v0) = v4 & top_str(v0) = v5 & ( ~ (v5 = 0) | ~ (v4 = 0) | v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | subset(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (v5_membered(v0) = 0) | ~ (natural(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (v1_int_1(v1) = v6 & v1_rat_1(v1) = v7 & v1_xreal_0(v1) = v5 & v1_xcmplx_0(v1) = v4 & element(v1, v0) = v3 & ( ~ (v3 = 0) | (v7 = 0 & v6 = 0 & v5 = 0 & v4 = 0 & v2 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (v4_membered(v0) = 0) | ~ (v1_int_1(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (v1_rat_1(v1) = v6 & v1_xreal_0(v1) = v5 & v1_xcmplx_0(v1) = v4 & element(v1, v0) = v3 & ( ~ (v3 = 0) | (v6 = 0 & v5 = 0 & v4 = 0 & v2 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (v3_membered(v0) = 0) | ~ (v1_rat_1(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (v1_xreal_0(v1) = v5 & v1_xcmplx_0(v1) = v4 & element(v1, v0) = v3 & ( ~ (v3 = 0) | (v5 = 0 & v4 = 0 & v2 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (v2_membered(v0) = 0) | ~ (v1_xreal_0(v1) = v2) | ? [v3] : ? [v4] : (v1_xcmplx_0(v1) = v4 & element(v1, v0) = v3 & ( ~ (v3 = 0) | (v4 = 0 & v2 = 0)))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (one_sorted_str(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & top_str(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (empty_carrier(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (topological_space(v0) = v2 & top_str(v0) = v3 & the_carrier(v0) = v4 & powerset(v4) = v5 & ( ~ (v3 = 0) | ~ (v2 = 0) | ! [v6] : ! [v7] : ( ~ (element(v7, v5) = 0) | ~ (element(v6, v4) = 0) | ? [v8] : ? [v9] : ? [v10] : (point_neighbourhood(v7, v0, v6) = v8 & interior(v0, v7) = v9 & in(v6, v9) = v10 & ( ~ (v10 = 0) | v8 = 0) & ( ~ (v8 = 0) | v10 = 0)))))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (empty(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v0) = v2 & empty(v3) = v4 & element(v3, v2) = 0)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (empty(v2) = 0 & element(v2, v1) = 0)) & ! [v0] : ! [v1] : ( ~ (v5_membered(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (empty(v0) = v2 & v4_membered(v0) = v6 & v3_membered(v0) = v5 & v2_membered(v0) = v4 & v1_membered(v0) = v3 & ( ~ (v2 = 0) | (v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & v1 = 0)))) & ! [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] : ( ~ (topological_space(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (top_str(v0) = v1 & the_carrier(v0) = v2 & powerset(v2) = v3 & ( ~ (v1 = 0) | ! [v4] : ( ~ (top_str(v4) = 0) | ? [v5] : ? [v6] : (the_carrier(v4) = v5 & powerset(v5) = v6 & ! [v7] : ( ~ (element(v7, v3) = 0) | ? [v8] : ? [v9] : (open_subset(v7, v0) = v9 & interior(v0, v7) = v8 & ! [v10] : ( ~ (v8 = v7) | v9 = 0 | ~ (element(v10, v6) = 0)) & ! [v10] : ( ~ (element(v10, v6) = 0) | ? [v11] : ? [v12] : (open_subset(v10, v4) = v11 & interior(v4, v10) = v12 & ( ~ (v11 = 0) | v12 = v10)))))))))) & ! [v0] : ( ~ (v5_membered(v0) = 0) | v4_membered(v0) = 0) & ! [v0] : ( ~ (v5_membered(v0) = 0) | ? [v1] : (powerset(v0) = v1 & ! [v2] : ( ~ (element(v2, v1) = 0) | (v5_membered(v2) = 0 & v4_membered(v2) = 0 & v3_membered(v2) = 0 & v2_membered(v2) = 0 & v1_membered(v2) = 0)))) & ! [v0] : ( ~ (v4_membered(v0) = 0) | v3_membered(v0) = 0) & ! [v0] : ( ~ (v4_membered(v0) = 0) | ? [v1] : (powerset(v0) = v1 & ! [v2] : ( ~ (element(v2, v1) = 0) | (v4_membered(v2) = 0 & v3_membered(v2) = 0 & v2_membered(v2) = 0 & v1_membered(v2) = 0)))) & ! [v0] : ( ~ (v3_membered(v0) = 0) | v2_membered(v0) = 0) & ! [v0] : ( ~ (v3_membered(v0) = 0) | ? [v1] : (powerset(v0) = v1 & ! [v2] : ( ~ (element(v2, v1) = 0) | (v3_membered(v2) = 0 & v2_membered(v2) = 0 & v1_membered(v2) = 0)))) & ! [v0] : ( ~ (v2_membered(v0) = 0) | v1_membered(v0) = 0) & ! [v0] : ( ~ (v2_membered(v0) = 0) | ? [v1] : (powerset(v0) = v1 & ! [v2] : ( ~ (element(v2, v1) = 0) | (v2_membered(v2) = 0 & v1_membered(v2) = 0)))) & ! [v0] : ( ~ (v1_membered(v0) = 0) | ? [v1] : (powerset(v0) = v1 & ! [v2] : ( ~ (element(v2, v1) = 0) | v1_membered(v2) = 0))) & ? [v0] : ? [v1] : element(v1, v0) = 0
% 10.21/3.02 |
% 10.21/3.02 | Applying alpha-rule on (1) yields:
% 10.21/3.02 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (open_subset(v3, v2) = v1) | ~ (open_subset(v3, v2) = v0))
% 10.21/3.02 | (3) the_carrier(all_0_10_10) = all_0_8_8
% 10.21/3.02 | (4) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 10.21/3.02 | (5) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (v2_membered(v2) = v1) | ~ (v2_membered(v2) = v0))
% 10.21/3.02 | (6) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (v1_membered(v2) = v1) | ~ (v1_membered(v2) = v0))
% 10.21/3.02 | (7) ! [v0] : ( ~ (v5_membered(v0) = 0) | v4_membered(v0) = 0)
% 10.21/3.02 | (8) open_subset(all_0_6_6, all_0_10_10) = 0
% 10.21/3.02 | (9) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (v1_membered(v0) = 0) | ~ (v1_xcmplx_0(v1) = v2) | ? [v3] : ( ~ (v3 = 0) & element(v1, v0) = v3))
% 10.21/3.02 | (10) top_str(all_0_0_0) = 0
% 10.21/3.02 | (11) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0))
% 10.21/3.02 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (the_carrier(v0) = v2) | ~ (element(v1, v2) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (empty_carrier(v0) = v3 & topological_space(v0) = v4 & top_str(v0) = v5 & powerset(v2) = v6 & ( ~ (v5 = 0) | ~ (v4 = 0) | v3 = 0 | ! [v7] : ! [v8] : (v8 = 0 | ~ (element(v7, v6) = v8) | ? [v9] : ( ~ (v9 = 0) & point_neighbourhood(v7, v0, v1) = v9)))))
% 10.21/3.02 | (13) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (the_carrier(v2) = v1) | ~ (the_carrier(v2) = v0))
% 10.21/3.02 | (14) empty(empty_set) = 0
% 10.21/3.02 | (15) ! [v0] : ! [v1] : ! [v2] : ( ~ (the_carrier(v0) = v2) | ~ (element(v1, v2) = 0) | ? [v3] : ? [v4] : ? [v5] : ((v4 = 0 & point_neighbourhood(v3, v0, v1) = 0) | (empty_carrier(v0) = v3 & topological_space(v0) = v4 & top_str(v0) = v5 & ( ~ (v5 = 0) | ~ (v4 = 0) | v3 = 0))))
% 10.21/3.02 | (16) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | element(v0, v1) = 0)
% 10.21/3.02 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 10.21/3.02 | (18) ! [v0] : ! [v1] : ( ~ (v5_membered(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (empty(v0) = v2 & v4_membered(v0) = v6 & v3_membered(v0) = v5 & v2_membered(v0) = v4 & v1_membered(v0) = v3 & ( ~ (v2 = 0) | (v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & v1 = 0))))
% 10.21/3.02 | (19) v2_membered(empty_set) = 0
% 10.21/3.02 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (interior(v3, v2) = v1) | ~ (interior(v3, v2) = v0))
% 10.21/3.02 | (21) ~ (all_0_9_9 = 0)
% 10.21/3.02 | (22) ! [v0] : ! [v1] : (v1 = 0 | ~ (one_sorted_str(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & top_str(v0) = v2))
% 10.21/3.02 | (23) powerset(all_0_8_8) = all_0_7_7
% 10.21/3.02 | (24) ! [v0] : ! [v1] : (v1 = 0 | ~ (empty(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v0) = v2 & empty(v3) = v4 & element(v3, v2) = 0))
% 10.21/3.02 | (25) ! [v0] : ( ~ (v5_membered(v0) = 0) | ? [v1] : (powerset(v0) = v1 & ! [v2] : ( ~ (element(v2, v1) = 0) | (v5_membered(v2) = 0 & v4_membered(v2) = 0 & v3_membered(v2) = 0 & v2_membered(v2) = 0 & v1_membered(v2) = 0))))
% 10.21/3.02 | (26) point_neighbourhood(all_0_6_6, all_0_10_10, all_0_5_5) = all_0_4_4
% 10.21/3.02 | (27) ! [v0] : ( ~ (v1_membered(v0) = 0) | ? [v1] : (powerset(v0) = v1 & ! [v2] : ( ~ (element(v2, v1) = 0) | v1_membered(v2) = 0)))
% 10.21/3.02 | (28) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v0, v1) = v2) | ? [v3] : ? [v4] : (empty(v1) = v4 & element(v0, v1) = v3 & ( ~ (v3 = 0) | v4 = 0)))
% 10.21/3.03 | (29) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (one_sorted_str(v2) = v1) | ~ (one_sorted_str(v2) = v0))
% 10.21/3.03 | (30) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (v4_membered(v2) = v1) | ~ (v4_membered(v2) = v0))
% 10.21/3.03 | (31) ! [v0] : ( ~ (v3_membered(v0) = 0) | ? [v1] : (powerset(v0) = v1 & ! [v2] : ( ~ (element(v2, v1) = 0) | (v3_membered(v2) = 0 & v2_membered(v2) = 0 & v1_membered(v2) = 0))))
% 10.21/3.03 | (32) ! [v0] : ! [v1] : ! [v2] : ( ~ (v5_membered(v0) = 0) | ~ (natural(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (v1_int_1(v1) = v6 & v1_rat_1(v1) = v7 & v1_xreal_0(v1) = v5 & v1_xcmplx_0(v1) = v4 & element(v1, v0) = v3 & ( ~ (v3 = 0) | (v7 = 0 & v6 = 0 & v5 = 0 & v4 = 0 & v2 = 0))))
% 10.21/3.03 | (33) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0))
% 10.21/3.03 | (34) ~ (all_0_4_4 = 0)
% 10.21/3.03 | (35) ~ (all_0_2_2 = 0)
% 10.21/3.03 | (36) empty_carrier(all_0_10_10) = all_0_9_9
% 10.21/3.03 | (37) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1))
% 10.21/3.03 | (38) one_sorted_str(all_0_1_1) = 0
% 10.21/3.03 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (point_neighbourhood(v4, v3, v2) = v1) | ~ (point_neighbourhood(v4, v3, v2) = v0))
% 10.21/3.03 | (40) v3_membered(all_0_3_3) = 0
% 10.21/3.03 | (41) ! [v0] : ( ~ (v2_membered(v0) = 0) | v1_membered(v0) = 0)
% 10.21/3.03 | (42) element(all_0_5_5, all_0_8_8) = 0
% 10.21/3.03 | (43) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (v1_xcmplx_0(v2) = v1) | ~ (v1_xcmplx_0(v2) = v0))
% 10.21/3.03 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0))
% 10.21/3.03 | (45) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (v1_rat_1(v2) = v1) | ~ (v1_rat_1(v2) = v0))
% 10.21/3.03 | (46) ! [v0] : ( ~ (v2_membered(v0) = 0) | ? [v1] : (powerset(v0) = v1 & ! [v2] : ( ~ (element(v2, v1) = 0) | (v2_membered(v2) = 0 & v1_membered(v2) = 0))))
% 10.21/3.03 | (47) ! [v0] : ! [v1] : ! [v2] : ( ~ (v4_membered(v0) = 0) | ~ (v1_int_1(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (v1_rat_1(v1) = v6 & v1_xreal_0(v1) = v5 & v1_xcmplx_0(v1) = v4 & element(v1, v0) = v3 & ( ~ (v3 = 0) | (v6 = 0 & v5 = 0 & v4 = 0 & v2 = 0))))
% 10.21/3.03 | (48) v4_membered(all_0_3_3) = 0
% 10.21/3.03 | (49) ! [v0] : ! [v1] : ! [v2] : ( ~ (v3_membered(v0) = 0) | ~ (v1_rat_1(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (v1_xreal_0(v1) = v5 & v1_xcmplx_0(v1) = v4 & element(v1, v0) = v3 & ( ~ (v3 = 0) | (v5 = 0 & v4 = 0 & v2 = 0))))
% 10.21/3.03 | (50) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | element(v0, v2) = 0)
% 10.21/3.03 | (51) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (v1_int_1(v2) = v1) | ~ (v1_int_1(v2) = v0))
% 10.21/3.03 | (52) ! [v0] : ! [v1] : ! [v2] : ( ~ (v2_membered(v0) = 0) | ~ (v1_xreal_0(v1) = v2) | ? [v3] : ? [v4] : (v1_xcmplx_0(v1) = v4 & element(v1, v0) = v3 & ( ~ (v3 = 0) | (v4 = 0 & v2 = 0))))
% 10.21/3.03 | (53) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (empty(v2) = 0 & element(v2, v1) = 0))
% 10.21/3.03 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4))
% 10.21/3.03 | (55) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (v3_membered(v2) = v1) | ~ (v3_membered(v2) = v0))
% 10.21/3.03 | (56) topological_space(all_0_10_10) = 0
% 10.21/3.03 | (57) v1_membered(all_0_3_3) = 0
% 10.21/3.03 | (58) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 10.21/3.03 | (59) element(all_0_6_6, all_0_7_7) = 0
% 10.21/3.03 | (60) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 10.21/3.03 | (61) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (top_str(v2) = v1) | ~ (top_str(v2) = v0))
% 10.21/3.03 | (62) v5_membered(empty_set) = 0
% 10.21/3.03 | (63) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | subset(v0, v1) = 0)
% 10.21/3.03 | (64) in(all_0_5_5, all_0_6_6) = 0
% 10.21/3.04 | (65) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (topological_space(v2) = v1) | ~ (topological_space(v2) = v0))
% 10.21/3.04 | (66) ! [v0] : ( ~ (topological_space(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (top_str(v0) = v1 & the_carrier(v0) = v2 & powerset(v2) = v3 & ( ~ (v1 = 0) | ! [v4] : ( ~ (top_str(v4) = 0) | ? [v5] : ? [v6] : (the_carrier(v4) = v5 & powerset(v5) = v6 & ! [v7] : ( ~ (element(v7, v3) = 0) | ? [v8] : ? [v9] : (open_subset(v7, v0) = v9 & interior(v0, v7) = v8 & ! [v10] : ( ~ (v8 = v7) | v9 = 0 | ~ (element(v10, v6) = 0)) & ! [v10] : ( ~ (element(v10, v6) = 0) | ? [v11] : ? [v12] : (open_subset(v10, v4) = v11 & interior(v4, v10) = v12 & ( ~ (v11 = 0) | v12 = v10))))))))))
% 10.40/3.04 | (67) ! [v0] : ( ~ (v4_membered(v0) = 0) | ? [v1] : (powerset(v0) = v1 & ! [v2] : ( ~ (element(v2, v1) = 0) | (v4_membered(v2) = 0 & v3_membered(v2) = 0 & v2_membered(v2) = 0 & v1_membered(v2) = 0))))
% 10.40/3.04 | (68) top_str(all_0_10_10) = 0
% 10.40/3.04 | (69) v2_membered(all_0_3_3) = 0
% 10.40/3.04 | (70) ! [v0] : ( ~ (v3_membered(v0) = 0) | v2_membered(v0) = 0)
% 10.40/3.04 | (71) v1_membered(empty_set) = 0
% 10.40/3.04 | (72) ! [v0] : ! [v1] : (v1 = 0 | ~ (empty_carrier(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (topological_space(v0) = v2 & top_str(v0) = v3 & the_carrier(v0) = v4 & powerset(v4) = v5 & ( ~ (v3 = 0) | ~ (v2 = 0) | ! [v6] : ! [v7] : ( ~ (element(v7, v5) = 0) | ~ (element(v6, v4) = 0) | ? [v8] : ? [v9] : ? [v10] : (point_neighbourhood(v7, v0, v6) = v8 & interior(v0, v7) = v9 & in(v6, v9) = v10 & ( ~ (v10 = 0) | v8 = 0) & ( ~ (v8 = 0) | v10 = 0))))))
% 10.40/3.04 | (73) v4_membered(empty_set) = 0
% 10.40/3.04 | (74) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 10.40/3.04 | (75) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 10.40/3.04 | (76) empty(all_0_3_3) = all_0_2_2
% 10.40/3.04 | (77) v5_membered(all_0_3_3) = 0
% 10.40/3.04 | (78) ? [v0] : ? [v1] : element(v1, v0) = 0
% 10.40/3.04 | (79) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 10.40/3.04 | (80) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (natural(v2) = v1) | ~ (natural(v2) = v0))
% 10.40/3.04 | (81) ! [v0] : ( ~ (v4_membered(v0) = 0) | v3_membered(v0) = 0)
% 10.40/3.04 | (82) v3_membered(empty_set) = 0
% 10.40/3.04 | (83) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (v5_membered(v2) = v1) | ~ (v5_membered(v2) = v0))
% 10.40/3.04 | (84) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (the_carrier(v0) = v2) | ~ (interior(v0, v1) = v4) | ~ (powerset(v2) = v3) | ~ (element(v4, v3) = v5) | ? [v6] : ? [v7] : (top_str(v0) = v6 & element(v1, v3) = v7 & ( ~ (v7 = 0) | ~ (v6 = 0))))
% 10.40/3.04 | (85) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty_carrier(v2) = v1) | ~ (empty_carrier(v2) = v0))
% 10.40/3.04 | (86) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (v1_xreal_0(v2) = v1) | ~ (v1_xreal_0(v2) = v0))
% 10.40/3.04 | (87) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0))
% 10.40/3.04 |
% 10.40/3.04 | Instantiating formula (72) with all_0_9_9, all_0_10_10 and discharging atoms empty_carrier(all_0_10_10) = all_0_9_9, yields:
% 10.40/3.04 | (88) all_0_9_9 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (topological_space(all_0_10_10) = v0 & top_str(all_0_10_10) = v1 & the_carrier(all_0_10_10) = v2 & powerset(v2) = v3 & ( ~ (v1 = 0) | ~ (v0 = 0) | ! [v4] : ! [v5] : ( ~ (element(v5, v3) = 0) | ~ (element(v4, v2) = 0) | ? [v6] : ? [v7] : ? [v8] : (point_neighbourhood(v5, all_0_10_10, v4) = v6 & interior(all_0_10_10, v5) = v7 & in(v4, v7) = v8 & ( ~ (v8 = 0) | v6 = 0) & ( ~ (v6 = 0) | v8 = 0)))))
% 10.40/3.05 |
% 10.40/3.05 | Instantiating formula (66) with all_0_10_10 and discharging atoms topological_space(all_0_10_10) = 0, yields:
% 10.40/3.05 | (89) ? [v0] : ? [v1] : ? [v2] : (top_str(all_0_10_10) = v0 & the_carrier(all_0_10_10) = v1 & powerset(v1) = v2 & ( ~ (v0 = 0) | ! [v3] : ( ~ (top_str(v3) = 0) | ? [v4] : ? [v5] : (the_carrier(v3) = v4 & powerset(v4) = v5 & ! [v6] : ( ~ (element(v6, v2) = 0) | ? [v7] : ? [v8] : (open_subset(v6, all_0_10_10) = v8 & interior(all_0_10_10, v6) = v7 & ! [v9] : ( ~ (v7 = v6) | v8 = 0 | ~ (element(v9, v5) = 0)) & ! [v9] : ( ~ (element(v9, v5) = 0) | ? [v10] : ? [v11] : (open_subset(v9, v3) = v10 & interior(v3, v9) = v11 & ( ~ (v10 = 0) | v11 = v9)))))))))
% 10.40/3.05 |
% 10.40/3.05 | Instantiating formula (12) with all_0_8_8, all_0_5_5, all_0_10_10 and discharging atoms the_carrier(all_0_10_10) = all_0_8_8, element(all_0_5_5, all_0_8_8) = 0, yields:
% 10.40/3.05 | (90) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (empty_carrier(all_0_10_10) = v0 & topological_space(all_0_10_10) = v1 & top_str(all_0_10_10) = v2 & powerset(all_0_8_8) = v3 & ( ~ (v2 = 0) | ~ (v1 = 0) | v0 = 0 | ! [v4] : ! [v5] : (v5 = 0 | ~ (element(v4, v3) = v5) | ? [v6] : ( ~ (v6 = 0) & point_neighbourhood(v4, all_0_10_10, all_0_5_5) = v6))))
% 10.40/3.05 |
% 10.40/3.05 | Instantiating (90) with all_52_0_31, all_52_1_32, all_52_2_33, all_52_3_34 yields:
% 10.40/3.05 | (91) empty_carrier(all_0_10_10) = all_52_3_34 & topological_space(all_0_10_10) = all_52_2_33 & top_str(all_0_10_10) = all_52_1_32 & powerset(all_0_8_8) = all_52_0_31 & ( ~ (all_52_1_32 = 0) | ~ (all_52_2_33 = 0) | all_52_3_34 = 0 | ! [v0] : ! [v1] : (v1 = 0 | ~ (element(v0, all_52_0_31) = v1) | ? [v2] : ( ~ (v2 = 0) & point_neighbourhood(v0, all_0_10_10, all_0_5_5) = v2)))
% 10.40/3.05 |
% 10.40/3.05 | Applying alpha-rule on (91) yields:
% 10.40/3.05 | (92) top_str(all_0_10_10) = all_52_1_32
% 10.40/3.05 | (93) ~ (all_52_1_32 = 0) | ~ (all_52_2_33 = 0) | all_52_3_34 = 0 | ! [v0] : ! [v1] : (v1 = 0 | ~ (element(v0, all_52_0_31) = v1) | ? [v2] : ( ~ (v2 = 0) & point_neighbourhood(v0, all_0_10_10, all_0_5_5) = v2))
% 10.40/3.05 | (94) empty_carrier(all_0_10_10) = all_52_3_34
% 10.40/3.05 | (95) topological_space(all_0_10_10) = all_52_2_33
% 10.40/3.05 | (96) powerset(all_0_8_8) = all_52_0_31
% 10.40/3.05 |
% 10.40/3.05 | Instantiating (89) with all_54_0_35, all_54_1_36, all_54_2_37 yields:
% 10.40/3.05 | (97) top_str(all_0_10_10) = all_54_2_37 & the_carrier(all_0_10_10) = all_54_1_36 & powerset(all_54_1_36) = all_54_0_35 & ( ~ (all_54_2_37 = 0) | ! [v0] : ( ~ (top_str(v0) = 0) | ? [v1] : ? [v2] : (the_carrier(v0) = v1 & powerset(v1) = v2 & ! [v3] : ( ~ (element(v3, all_54_0_35) = 0) | ? [v4] : ? [v5] : (open_subset(v3, all_0_10_10) = v5 & interior(all_0_10_10, v3) = v4 & ! [v6] : ( ~ (v4 = v3) | v5 = 0 | ~ (element(v6, v2) = 0)) & ! [v6] : ( ~ (element(v6, v2) = 0) | ? [v7] : ? [v8] : (open_subset(v6, v0) = v7 & interior(v0, v6) = v8 & ( ~ (v7 = 0) | v8 = v6))))))))
% 10.40/3.05 |
% 10.40/3.05 | Applying alpha-rule on (97) yields:
% 10.40/3.05 | (98) top_str(all_0_10_10) = all_54_2_37
% 10.40/3.05 | (99) the_carrier(all_0_10_10) = all_54_1_36
% 10.40/3.05 | (100) powerset(all_54_1_36) = all_54_0_35
% 10.40/3.05 | (101) ~ (all_54_2_37 = 0) | ! [v0] : ( ~ (top_str(v0) = 0) | ? [v1] : ? [v2] : (the_carrier(v0) = v1 & powerset(v1) = v2 & ! [v3] : ( ~ (element(v3, all_54_0_35) = 0) | ? [v4] : ? [v5] : (open_subset(v3, all_0_10_10) = v5 & interior(all_0_10_10, v3) = v4 & ! [v6] : ( ~ (v4 = v3) | v5 = 0 | ~ (element(v6, v2) = 0)) & ! [v6] : ( ~ (element(v6, v2) = 0) | ? [v7] : ? [v8] : (open_subset(v6, v0) = v7 & interior(v0, v6) = v8 & ( ~ (v7 = 0) | v8 = v6)))))))
% 10.40/3.05 |
% 10.40/3.05 | Instantiating formula (65) with all_0_10_10, all_52_2_33, 0 and discharging atoms topological_space(all_0_10_10) = all_52_2_33, topological_space(all_0_10_10) = 0, yields:
% 10.40/3.05 | (102) all_52_2_33 = 0
% 10.40/3.05 |
% 10.40/3.05 | Instantiating formula (61) with all_0_10_10, all_54_2_37, 0 and discharging atoms top_str(all_0_10_10) = all_54_2_37, top_str(all_0_10_10) = 0, yields:
% 10.40/3.05 | (103) all_54_2_37 = 0
% 10.40/3.05 |
% 10.40/3.05 | Instantiating formula (61) with all_0_10_10, all_52_1_32, all_54_2_37 and discharging atoms top_str(all_0_10_10) = all_54_2_37, top_str(all_0_10_10) = all_52_1_32, yields:
% 10.40/3.05 | (104) all_54_2_37 = all_52_1_32
% 10.40/3.05 |
% 10.40/3.05 | Instantiating formula (13) with all_0_10_10, all_54_1_36, all_0_8_8 and discharging atoms the_carrier(all_0_10_10) = all_54_1_36, the_carrier(all_0_10_10) = all_0_8_8, yields:
% 10.40/3.05 | (105) all_54_1_36 = all_0_8_8
% 10.40/3.05 |
% 10.40/3.05 | Instantiating formula (33) with all_0_8_8, all_54_0_35, all_0_7_7 and discharging atoms powerset(all_0_8_8) = all_0_7_7, yields:
% 10.40/3.05 | (106) all_54_0_35 = all_0_7_7 | ~ (powerset(all_0_8_8) = all_54_0_35)
% 10.40/3.05 |
% 10.40/3.05 | Combining equations (104,103) yields a new equation:
% 10.40/3.05 | (107) all_52_1_32 = 0
% 10.40/3.05 |
% 10.40/3.05 | Simplifying 107 yields:
% 10.40/3.05 | (108) all_52_1_32 = 0
% 10.40/3.05 |
% 10.40/3.05 | From (102) and (95) follows:
% 10.40/3.05 | (56) topological_space(all_0_10_10) = 0
% 10.40/3.05 |
% 10.40/3.05 | From (108) and (92) follows:
% 10.40/3.05 | (68) top_str(all_0_10_10) = 0
% 10.40/3.05 |
% 10.40/3.05 | From (105) and (99) follows:
% 10.40/3.05 | (3) the_carrier(all_0_10_10) = all_0_8_8
% 10.40/3.05 |
% 10.40/3.05 | From (105) and (100) follows:
% 10.40/3.06 | (112) powerset(all_0_8_8) = all_54_0_35
% 10.40/3.06 |
% 10.40/3.06 +-Applying beta-rule and splitting (101), into two cases.
% 10.40/3.06 |-Branch one:
% 10.40/3.06 | (113) ~ (all_54_2_37 = 0)
% 10.40/3.06 |
% 10.40/3.06 | Equations (103) can reduce 113 to:
% 10.40/3.06 | (114) $false
% 10.40/3.06 |
% 10.40/3.06 |-The branch is then unsatisfiable
% 10.40/3.06 |-Branch two:
% 10.40/3.06 | (103) all_54_2_37 = 0
% 10.40/3.06 | (116) ! [v0] : ( ~ (top_str(v0) = 0) | ? [v1] : ? [v2] : (the_carrier(v0) = v1 & powerset(v1) = v2 & ! [v3] : ( ~ (element(v3, all_54_0_35) = 0) | ? [v4] : ? [v5] : (open_subset(v3, all_0_10_10) = v5 & interior(all_0_10_10, v3) = v4 & ! [v6] : ( ~ (v4 = v3) | v5 = 0 | ~ (element(v6, v2) = 0)) & ! [v6] : ( ~ (element(v6, v2) = 0) | ? [v7] : ? [v8] : (open_subset(v6, v0) = v7 & interior(v0, v6) = v8 & ( ~ (v7 = 0) | v8 = v6)))))))
% 10.40/3.06 |
% 10.40/3.06 | Instantiating formula (116) with all_0_0_0 and discharging atoms top_str(all_0_0_0) = 0, yields:
% 10.40/3.06 | (117) ? [v0] : ? [v1] : (the_carrier(all_0_0_0) = v0 & powerset(v0) = v1 & ! [v2] : ( ~ (element(v2, all_54_0_35) = 0) | ? [v3] : ? [v4] : (open_subset(v2, all_0_10_10) = v4 & interior(all_0_10_10, v2) = v3 & ! [v5] : ( ~ (v3 = v2) | v4 = 0 | ~ (element(v5, v1) = 0)) & ! [v5] : ( ~ (element(v5, v1) = 0) | ? [v6] : ? [v7] : (open_subset(v5, all_0_0_0) = v6 & interior(all_0_0_0, v5) = v7 & ( ~ (v6 = 0) | v7 = v5))))))
% 10.40/3.06 |
% 10.40/3.06 | Instantiating formula (116) with all_0_10_10 and discharging atoms top_str(all_0_10_10) = 0, yields:
% 10.40/3.06 | (118) ? [v0] : ? [v1] : (the_carrier(all_0_10_10) = v0 & powerset(v0) = v1 & ! [v2] : ( ~ (element(v2, all_54_0_35) = 0) | ? [v3] : ? [v4] : (open_subset(v2, all_0_10_10) = v4 & interior(all_0_10_10, v2) = v3 & ! [v5] : ( ~ (v3 = v2) | v4 = 0 | ~ (element(v5, v1) = 0)) & ! [v5] : ( ~ (element(v5, v1) = 0) | ? [v6] : ? [v7] : (open_subset(v5, all_0_10_10) = v6 & interior(all_0_10_10, v5) = v7 & ( ~ (v6 = 0) | v7 = v5))))))
% 10.40/3.06 |
% 10.40/3.06 | Instantiating (118) with all_77_0_45, all_77_1_46 yields:
% 10.40/3.06 | (119) the_carrier(all_0_10_10) = all_77_1_46 & powerset(all_77_1_46) = all_77_0_45 & ! [v0] : ( ~ (element(v0, all_54_0_35) = 0) | ? [v1] : ? [v2] : (open_subset(v0, all_0_10_10) = v2 & interior(all_0_10_10, v0) = v1 & ! [v3] : ( ~ (v1 = v0) | v2 = 0 | ~ (element(v3, all_77_0_45) = 0)) & ! [v3] : ( ~ (element(v3, all_77_0_45) = 0) | ? [v4] : ? [v5] : (open_subset(v3, all_0_10_10) = v4 & interior(all_0_10_10, v3) = v5 & ( ~ (v4 = 0) | v5 = v3)))))
% 10.40/3.06 |
% 10.40/3.06 | Applying alpha-rule on (119) yields:
% 10.40/3.06 | (120) the_carrier(all_0_10_10) = all_77_1_46
% 10.40/3.06 | (121) powerset(all_77_1_46) = all_77_0_45
% 10.40/3.06 | (122) ! [v0] : ( ~ (element(v0, all_54_0_35) = 0) | ? [v1] : ? [v2] : (open_subset(v0, all_0_10_10) = v2 & interior(all_0_10_10, v0) = v1 & ! [v3] : ( ~ (v1 = v0) | v2 = 0 | ~ (element(v3, all_77_0_45) = 0)) & ! [v3] : ( ~ (element(v3, all_77_0_45) = 0) | ? [v4] : ? [v5] : (open_subset(v3, all_0_10_10) = v4 & interior(all_0_10_10, v3) = v5 & ( ~ (v4 = 0) | v5 = v3)))))
% 10.40/3.06 |
% 10.40/3.06 | Instantiating formula (122) with all_0_6_6 yields:
% 10.40/3.06 | (123) ~ (element(all_0_6_6, all_54_0_35) = 0) | ? [v0] : ? [v1] : (open_subset(all_0_6_6, all_0_10_10) = v1 & interior(all_0_10_10, all_0_6_6) = v0 & ! [v2] : ( ~ (v0 = all_0_6_6) | v1 = 0 | ~ (element(v2, all_77_0_45) = 0)) & ! [v2] : ( ~ (element(v2, all_77_0_45) = 0) | ? [v3] : ? [v4] : (open_subset(v2, all_0_10_10) = v3 & interior(all_0_10_10, v2) = v4 & ( ~ (v3 = 0) | v4 = v2))))
% 10.40/3.06 |
% 10.40/3.06 | Instantiating (117) with all_80_0_47, all_80_1_48 yields:
% 10.40/3.06 | (124) the_carrier(all_0_0_0) = all_80_1_48 & powerset(all_80_1_48) = all_80_0_47 & ! [v0] : ( ~ (element(v0, all_54_0_35) = 0) | ? [v1] : ? [v2] : (open_subset(v0, all_0_10_10) = v2 & interior(all_0_10_10, v0) = v1 & ! [v3] : ( ~ (v1 = v0) | v2 = 0 | ~ (element(v3, all_80_0_47) = 0)) & ! [v3] : ( ~ (element(v3, all_80_0_47) = 0) | ? [v4] : ? [v5] : (open_subset(v3, all_0_0_0) = v4 & interior(all_0_0_0, v3) = v5 & ( ~ (v4 = 0) | v5 = v3)))))
% 10.40/3.06 |
% 10.40/3.06 | Applying alpha-rule on (124) yields:
% 10.40/3.06 | (125) the_carrier(all_0_0_0) = all_80_1_48
% 10.40/3.06 | (126) powerset(all_80_1_48) = all_80_0_47
% 10.40/3.06 | (127) ! [v0] : ( ~ (element(v0, all_54_0_35) = 0) | ? [v1] : ? [v2] : (open_subset(v0, all_0_10_10) = v2 & interior(all_0_10_10, v0) = v1 & ! [v3] : ( ~ (v1 = v0) | v2 = 0 | ~ (element(v3, all_80_0_47) = 0)) & ! [v3] : ( ~ (element(v3, all_80_0_47) = 0) | ? [v4] : ? [v5] : (open_subset(v3, all_0_0_0) = v4 & interior(all_0_0_0, v3) = v5 & ( ~ (v4 = 0) | v5 = v3)))))
% 10.40/3.06 |
% 10.40/3.06 | Instantiating formula (127) with all_0_6_6 yields:
% 10.40/3.06 | (128) ~ (element(all_0_6_6, all_54_0_35) = 0) | ? [v0] : ? [v1] : (open_subset(all_0_6_6, all_0_10_10) = v1 & interior(all_0_10_10, all_0_6_6) = v0 & ! [v2] : ( ~ (v0 = all_0_6_6) | v1 = 0 | ~ (element(v2, all_80_0_47) = 0)) & ! [v2] : ( ~ (element(v2, all_80_0_47) = 0) | ? [v3] : ? [v4] : (open_subset(v2, all_0_0_0) = v3 & interior(all_0_0_0, v2) = v4 & ( ~ (v3 = 0) | v4 = v2))))
% 10.40/3.06 |
% 10.40/3.06 +-Applying beta-rule and splitting (106), into two cases.
% 10.40/3.06 |-Branch one:
% 10.40/3.06 | (129) ~ (powerset(all_0_8_8) = all_54_0_35)
% 10.40/3.06 |
% 10.40/3.07 | Using (112) and (129) yields:
% 10.40/3.07 | (130) $false
% 10.40/3.07 |
% 10.40/3.07 |-The branch is then unsatisfiable
% 10.40/3.07 |-Branch two:
% 10.40/3.07 | (112) powerset(all_0_8_8) = all_54_0_35
% 10.40/3.07 | (132) all_54_0_35 = all_0_7_7
% 10.40/3.07 |
% 10.40/3.07 | From (132) and (112) follows:
% 10.40/3.07 | (23) powerset(all_0_8_8) = all_0_7_7
% 10.40/3.07 |
% 10.40/3.07 +-Applying beta-rule and splitting (88), into two cases.
% 10.40/3.07 |-Branch one:
% 10.40/3.07 | (134) all_0_9_9 = 0
% 10.40/3.07 |
% 10.40/3.07 | Equations (134) can reduce 21 to:
% 10.40/3.07 | (114) $false
% 10.40/3.07 |
% 10.40/3.07 |-The branch is then unsatisfiable
% 10.40/3.07 |-Branch two:
% 10.40/3.07 | (21) ~ (all_0_9_9 = 0)
% 10.40/3.07 | (137) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (topological_space(all_0_10_10) = v0 & top_str(all_0_10_10) = v1 & the_carrier(all_0_10_10) = v2 & powerset(v2) = v3 & ( ~ (v1 = 0) | ~ (v0 = 0) | ! [v4] : ! [v5] : ( ~ (element(v5, v3) = 0) | ~ (element(v4, v2) = 0) | ? [v6] : ? [v7] : ? [v8] : (point_neighbourhood(v5, all_0_10_10, v4) = v6 & interior(all_0_10_10, v5) = v7 & in(v4, v7) = v8 & ( ~ (v8 = 0) | v6 = 0) & ( ~ (v6 = 0) | v8 = 0)))))
% 10.40/3.07 |
% 10.40/3.07 | Instantiating (137) with all_93_0_53, all_93_1_54, all_93_2_55, all_93_3_56 yields:
% 10.40/3.07 | (138) topological_space(all_0_10_10) = all_93_3_56 & top_str(all_0_10_10) = all_93_2_55 & the_carrier(all_0_10_10) = all_93_1_54 & powerset(all_93_1_54) = all_93_0_53 & ( ~ (all_93_2_55 = 0) | ~ (all_93_3_56 = 0) | ! [v0] : ! [v1] : ( ~ (element(v1, all_93_0_53) = 0) | ~ (element(v0, all_93_1_54) = 0) | ? [v2] : ? [v3] : ? [v4] : (point_neighbourhood(v1, all_0_10_10, v0) = v2 & interior(all_0_10_10, v1) = v3 & in(v0, v3) = v4 & ( ~ (v4 = 0) | v2 = 0) & ( ~ (v2 = 0) | v4 = 0))))
% 10.40/3.07 |
% 10.40/3.07 | Applying alpha-rule on (138) yields:
% 10.40/3.07 | (139) the_carrier(all_0_10_10) = all_93_1_54
% 10.40/3.07 | (140) topological_space(all_0_10_10) = all_93_3_56
% 10.40/3.07 | (141) top_str(all_0_10_10) = all_93_2_55
% 10.40/3.07 | (142) powerset(all_93_1_54) = all_93_0_53
% 10.40/3.07 | (143) ~ (all_93_2_55 = 0) | ~ (all_93_3_56 = 0) | ! [v0] : ! [v1] : ( ~ (element(v1, all_93_0_53) = 0) | ~ (element(v0, all_93_1_54) = 0) | ? [v2] : ? [v3] : ? [v4] : (point_neighbourhood(v1, all_0_10_10, v0) = v2 & interior(all_0_10_10, v1) = v3 & in(v0, v3) = v4 & ( ~ (v4 = 0) | v2 = 0) & ( ~ (v2 = 0) | v4 = 0)))
% 10.40/3.07 |
% 10.40/3.07 +-Applying beta-rule and splitting (123), into two cases.
% 10.40/3.07 |-Branch one:
% 10.40/3.07 | (144) ~ (element(all_0_6_6, all_54_0_35) = 0)
% 10.40/3.07 |
% 10.40/3.07 | From (132) and (144) follows:
% 10.40/3.07 | (145) ~ (element(all_0_6_6, all_0_7_7) = 0)
% 10.40/3.07 |
% 10.40/3.07 | Using (59) and (145) yields:
% 10.40/3.07 | (130) $false
% 10.40/3.07 |
% 10.40/3.07 |-The branch is then unsatisfiable
% 10.40/3.07 |-Branch two:
% 10.40/3.07 | (147) element(all_0_6_6, all_54_0_35) = 0
% 10.40/3.07 | (148) ? [v0] : ? [v1] : (open_subset(all_0_6_6, all_0_10_10) = v1 & interior(all_0_10_10, all_0_6_6) = v0 & ! [v2] : ( ~ (v0 = all_0_6_6) | v1 = 0 | ~ (element(v2, all_77_0_45) = 0)) & ! [v2] : ( ~ (element(v2, all_77_0_45) = 0) | ? [v3] : ? [v4] : (open_subset(v2, all_0_10_10) = v3 & interior(all_0_10_10, v2) = v4 & ( ~ (v3 = 0) | v4 = v2))))
% 10.40/3.07 |
% 10.40/3.07 | Instantiating (148) with all_103_0_57, all_103_1_58 yields:
% 10.40/3.07 | (149) open_subset(all_0_6_6, all_0_10_10) = all_103_0_57 & interior(all_0_10_10, all_0_6_6) = all_103_1_58 & ! [v0] : ( ~ (all_103_1_58 = all_0_6_6) | all_103_0_57 = 0 | ~ (element(v0, all_77_0_45) = 0)) & ! [v0] : ( ~ (element(v0, all_77_0_45) = 0) | ? [v1] : ? [v2] : (open_subset(v0, all_0_10_10) = v1 & interior(all_0_10_10, v0) = v2 & ( ~ (v1 = 0) | v2 = v0)))
% 10.40/3.07 |
% 10.40/3.07 | Applying alpha-rule on (149) yields:
% 10.40/3.07 | (150) open_subset(all_0_6_6, all_0_10_10) = all_103_0_57
% 10.40/3.07 | (151) interior(all_0_10_10, all_0_6_6) = all_103_1_58
% 10.40/3.07 | (152) ! [v0] : ( ~ (all_103_1_58 = all_0_6_6) | all_103_0_57 = 0 | ~ (element(v0, all_77_0_45) = 0))
% 10.40/3.07 | (153) ! [v0] : ( ~ (element(v0, all_77_0_45) = 0) | ? [v1] : ? [v2] : (open_subset(v0, all_0_10_10) = v1 & interior(all_0_10_10, v0) = v2 & ( ~ (v1 = 0) | v2 = v0)))
% 10.40/3.07 |
% 10.40/3.07 | Instantiating formula (153) with all_0_6_6 yields:
% 10.40/3.07 | (154) ~ (element(all_0_6_6, all_77_0_45) = 0) | ? [v0] : ? [v1] : (open_subset(all_0_6_6, all_0_10_10) = v0 & interior(all_0_10_10, all_0_6_6) = v1 & ( ~ (v0 = 0) | v1 = all_0_6_6))
% 10.40/3.07 |
% 10.40/3.07 | From (132) and (147) follows:
% 10.40/3.07 | (59) element(all_0_6_6, all_0_7_7) = 0
% 10.40/3.07 |
% 10.40/3.07 +-Applying beta-rule and splitting (128), into two cases.
% 10.40/3.07 |-Branch one:
% 10.40/3.07 | (144) ~ (element(all_0_6_6, all_54_0_35) = 0)
% 10.40/3.07 |
% 10.40/3.07 | From (132) and (144) follows:
% 10.40/3.07 | (145) ~ (element(all_0_6_6, all_0_7_7) = 0)
% 10.40/3.07 |
% 10.40/3.07 | Using (59) and (145) yields:
% 10.40/3.07 | (130) $false
% 10.40/3.07 |
% 10.40/3.07 |-The branch is then unsatisfiable
% 10.40/3.07 |-Branch two:
% 10.40/3.07 | (147) element(all_0_6_6, all_54_0_35) = 0
% 10.40/3.07 | (160) ? [v0] : ? [v1] : (open_subset(all_0_6_6, all_0_10_10) = v1 & interior(all_0_10_10, all_0_6_6) = v0 & ! [v2] : ( ~ (v0 = all_0_6_6) | v1 = 0 | ~ (element(v2, all_80_0_47) = 0)) & ! [v2] : ( ~ (element(v2, all_80_0_47) = 0) | ? [v3] : ? [v4] : (open_subset(v2, all_0_0_0) = v3 & interior(all_0_0_0, v2) = v4 & ( ~ (v3 = 0) | v4 = v2))))
% 10.40/3.07 |
% 10.40/3.07 | Instantiating (160) with all_109_0_59, all_109_1_60 yields:
% 10.40/3.07 | (161) open_subset(all_0_6_6, all_0_10_10) = all_109_0_59 & interior(all_0_10_10, all_0_6_6) = all_109_1_60 & ! [v0] : ( ~ (all_109_1_60 = all_0_6_6) | all_109_0_59 = 0 | ~ (element(v0, all_80_0_47) = 0)) & ! [v0] : ( ~ (element(v0, all_80_0_47) = 0) | ? [v1] : ? [v2] : (open_subset(v0, all_0_0_0) = v1 & interior(all_0_0_0, v0) = v2 & ( ~ (v1 = 0) | v2 = v0)))
% 10.40/3.07 |
% 10.40/3.07 | Applying alpha-rule on (161) yields:
% 10.40/3.07 | (162) open_subset(all_0_6_6, all_0_10_10) = all_109_0_59
% 10.40/3.07 | (163) interior(all_0_10_10, all_0_6_6) = all_109_1_60
% 10.40/3.07 | (164) ! [v0] : ( ~ (all_109_1_60 = all_0_6_6) | all_109_0_59 = 0 | ~ (element(v0, all_80_0_47) = 0))
% 10.40/3.07 | (165) ! [v0] : ( ~ (element(v0, all_80_0_47) = 0) | ? [v1] : ? [v2] : (open_subset(v0, all_0_0_0) = v1 & interior(all_0_0_0, v0) = v2 & ( ~ (v1 = 0) | v2 = v0)))
% 10.40/3.07 |
% 10.40/3.07 | From (132) and (147) follows:
% 10.40/3.07 | (59) element(all_0_6_6, all_0_7_7) = 0
% 10.40/3.07 |
% 10.40/3.07 | Instantiating formula (2) with all_0_6_6, all_0_10_10, all_109_0_59, 0 and discharging atoms open_subset(all_0_6_6, all_0_10_10) = all_109_0_59, open_subset(all_0_6_6, all_0_10_10) = 0, yields:
% 10.40/3.08 | (167) all_109_0_59 = 0
% 10.40/3.08 |
% 10.40/3.08 | Instantiating formula (2) with all_0_6_6, all_0_10_10, all_103_0_57, all_109_0_59 and discharging atoms open_subset(all_0_6_6, all_0_10_10) = all_109_0_59, open_subset(all_0_6_6, all_0_10_10) = all_103_0_57, yields:
% 10.40/3.08 | (168) all_109_0_59 = all_103_0_57
% 10.40/3.08 |
% 10.40/3.08 | Instantiating formula (65) with all_0_10_10, all_93_3_56, 0 and discharging atoms topological_space(all_0_10_10) = all_93_3_56, topological_space(all_0_10_10) = 0, yields:
% 10.40/3.08 | (169) all_93_3_56 = 0
% 10.40/3.08 |
% 10.40/3.08 | Instantiating formula (61) with all_0_10_10, all_93_2_55, 0 and discharging atoms top_str(all_0_10_10) = all_93_2_55, top_str(all_0_10_10) = 0, yields:
% 10.40/3.08 | (170) all_93_2_55 = 0
% 10.40/3.08 |
% 10.40/3.08 | Instantiating formula (13) with all_0_10_10, all_93_1_54, all_0_8_8 and discharging atoms the_carrier(all_0_10_10) = all_93_1_54, the_carrier(all_0_10_10) = all_0_8_8, yields:
% 10.40/3.08 | (171) all_93_1_54 = all_0_8_8
% 10.40/3.08 |
% 10.40/3.08 | Instantiating formula (13) with all_0_10_10, all_77_1_46, all_93_1_54 and discharging atoms the_carrier(all_0_10_10) = all_93_1_54, the_carrier(all_0_10_10) = all_77_1_46, yields:
% 10.40/3.08 | (172) all_93_1_54 = all_77_1_46
% 10.40/3.08 |
% 10.40/3.08 | Instantiating formula (20) with all_0_10_10, all_0_6_6, all_103_1_58, all_109_1_60 and discharging atoms interior(all_0_10_10, all_0_6_6) = all_109_1_60, interior(all_0_10_10, all_0_6_6) = all_103_1_58, yields:
% 10.40/3.08 | (173) all_109_1_60 = all_103_1_58
% 10.40/3.08 |
% 10.40/3.08 | Instantiating formula (33) with all_0_8_8, all_93_0_53, all_0_7_7 and discharging atoms powerset(all_0_8_8) = all_0_7_7, yields:
% 10.40/3.08 | (174) all_93_0_53 = all_0_7_7 | ~ (powerset(all_0_8_8) = all_93_0_53)
% 10.40/3.08 |
% 10.40/3.08 | Instantiating formula (33) with all_0_8_8, all_77_0_45, all_0_7_7 and discharging atoms powerset(all_0_8_8) = all_0_7_7, yields:
% 10.40/3.08 | (175) all_77_0_45 = all_0_7_7 | ~ (powerset(all_0_8_8) = all_77_0_45)
% 10.40/3.08 |
% 10.40/3.08 | Combining equations (167,168) yields a new equation:
% 10.40/3.08 | (176) all_103_0_57 = 0
% 10.40/3.08 |
% 10.40/3.08 | Combining equations (171,172) yields a new equation:
% 10.40/3.08 | (177) all_77_1_46 = all_0_8_8
% 10.40/3.08 |
% 10.40/3.08 | Combining equations (177,172) yields a new equation:
% 10.40/3.08 | (171) all_93_1_54 = all_0_8_8
% 10.40/3.08 |
% 10.40/3.08 | From (176) and (150) follows:
% 10.40/3.08 | (8) open_subset(all_0_6_6, all_0_10_10) = 0
% 10.40/3.08 |
% 10.40/3.08 | From (173) and (163) follows:
% 10.40/3.08 | (151) interior(all_0_10_10, all_0_6_6) = all_103_1_58
% 10.40/3.08 |
% 10.40/3.08 | From (171) and (142) follows:
% 10.40/3.08 | (181) powerset(all_0_8_8) = all_93_0_53
% 10.40/3.08 |
% 10.40/3.08 | From (177) and (121) follows:
% 10.40/3.08 | (182) powerset(all_0_8_8) = all_77_0_45
% 10.40/3.08 |
% 10.40/3.08 +-Applying beta-rule and splitting (175), into two cases.
% 10.40/3.08 |-Branch one:
% 10.40/3.08 | (183) ~ (powerset(all_0_8_8) = all_77_0_45)
% 10.40/3.08 |
% 10.40/3.08 | Using (182) and (183) yields:
% 10.40/3.08 | (130) $false
% 10.40/3.08 |
% 10.40/3.08 |-The branch is then unsatisfiable
% 10.40/3.08 |-Branch two:
% 10.40/3.08 | (182) powerset(all_0_8_8) = all_77_0_45
% 10.40/3.08 | (186) all_77_0_45 = all_0_7_7
% 10.40/3.08 |
% 10.40/3.08 +-Applying beta-rule and splitting (143), into two cases.
% 10.40/3.08 |-Branch one:
% 10.40/3.08 | (187) ~ (all_93_2_55 = 0)
% 10.40/3.08 |
% 10.40/3.08 | Equations (170) can reduce 187 to:
% 10.40/3.08 | (114) $false
% 10.40/3.08 |
% 10.40/3.08 |-The branch is then unsatisfiable
% 10.40/3.08 |-Branch two:
% 10.40/3.08 | (170) all_93_2_55 = 0
% 10.40/3.08 | (190) ~ (all_93_3_56 = 0) | ! [v0] : ! [v1] : ( ~ (element(v1, all_93_0_53) = 0) | ~ (element(v0, all_93_1_54) = 0) | ? [v2] : ? [v3] : ? [v4] : (point_neighbourhood(v1, all_0_10_10, v0) = v2 & interior(all_0_10_10, v1) = v3 & in(v0, v3) = v4 & ( ~ (v4 = 0) | v2 = 0) & ( ~ (v2 = 0) | v4 = 0)))
% 10.40/3.08 |
% 10.40/3.08 +-Applying beta-rule and splitting (174), into two cases.
% 10.40/3.08 |-Branch one:
% 10.40/3.08 | (191) ~ (powerset(all_0_8_8) = all_93_0_53)
% 10.40/3.08 |
% 10.40/3.08 | Using (181) and (191) yields:
% 10.40/3.08 | (130) $false
% 10.40/3.08 |
% 10.40/3.08 |-The branch is then unsatisfiable
% 10.40/3.08 |-Branch two:
% 10.40/3.08 | (181) powerset(all_0_8_8) = all_93_0_53
% 10.40/3.08 | (194) all_93_0_53 = all_0_7_7
% 10.40/3.08 |
% 10.40/3.08 +-Applying beta-rule and splitting (154), into two cases.
% 10.40/3.08 |-Branch one:
% 10.40/3.08 | (195) ~ (element(all_0_6_6, all_77_0_45) = 0)
% 10.40/3.08 |
% 10.40/3.08 | From (186) and (195) follows:
% 10.40/3.08 | (145) ~ (element(all_0_6_6, all_0_7_7) = 0)
% 10.40/3.08 |
% 10.40/3.08 | Using (59) and (145) yields:
% 10.40/3.08 | (130) $false
% 10.40/3.08 |
% 10.40/3.08 |-The branch is then unsatisfiable
% 10.40/3.08 |-Branch two:
% 10.40/3.08 | (198) element(all_0_6_6, all_77_0_45) = 0
% 10.40/3.08 | (199) ? [v0] : ? [v1] : (open_subset(all_0_6_6, all_0_10_10) = v0 & interior(all_0_10_10, all_0_6_6) = v1 & ( ~ (v0 = 0) | v1 = all_0_6_6))
% 10.40/3.08 |
% 10.40/3.08 | Instantiating (199) with all_131_0_61, all_131_1_62 yields:
% 10.40/3.08 | (200) open_subset(all_0_6_6, all_0_10_10) = all_131_1_62 & interior(all_0_10_10, all_0_6_6) = all_131_0_61 & ( ~ (all_131_1_62 = 0) | all_131_0_61 = all_0_6_6)
% 10.40/3.08 |
% 10.40/3.08 | Applying alpha-rule on (200) yields:
% 10.40/3.08 | (201) open_subset(all_0_6_6, all_0_10_10) = all_131_1_62
% 10.40/3.08 | (202) interior(all_0_10_10, all_0_6_6) = all_131_0_61
% 10.40/3.08 | (203) ~ (all_131_1_62 = 0) | all_131_0_61 = all_0_6_6
% 10.40/3.08 |
% 10.40/3.08 | From (186) and (198) follows:
% 10.40/3.08 | (59) element(all_0_6_6, all_0_7_7) = 0
% 10.40/3.08 |
% 10.40/3.08 +-Applying beta-rule and splitting (190), into two cases.
% 10.40/3.08 |-Branch one:
% 10.40/3.08 | (205) ~ (all_93_3_56 = 0)
% 10.40/3.08 |
% 10.40/3.08 | Equations (169) can reduce 205 to:
% 10.40/3.08 | (114) $false
% 10.40/3.08 |
% 10.40/3.08 |-The branch is then unsatisfiable
% 10.40/3.08 |-Branch two:
% 10.40/3.08 | (169) all_93_3_56 = 0
% 10.40/3.08 | (208) ! [v0] : ! [v1] : ( ~ (element(v1, all_93_0_53) = 0) | ~ (element(v0, all_93_1_54) = 0) | ? [v2] : ? [v3] : ? [v4] : (point_neighbourhood(v1, all_0_10_10, v0) = v2 & interior(all_0_10_10, v1) = v3 & in(v0, v3) = v4 & ( ~ (v4 = 0) | v2 = 0) & ( ~ (v2 = 0) | v4 = 0)))
% 10.40/3.08 |
% 10.40/3.08 | Instantiating formula (208) with all_0_6_6, all_0_5_5 yields:
% 10.40/3.08 | (209) ~ (element(all_0_5_5, all_93_1_54) = 0) | ~ (element(all_0_6_6, all_93_0_53) = 0) | ? [v0] : ? [v1] : ? [v2] : (point_neighbourhood(all_0_6_6, all_0_10_10, all_0_5_5) = v0 & interior(all_0_10_10, all_0_6_6) = v1 & in(all_0_5_5, v1) = v2 & ( ~ (v2 = 0) | v0 = 0) & ( ~ (v0 = 0) | v2 = 0))
% 10.40/3.09 |
% 10.40/3.09 +-Applying beta-rule and splitting (209), into two cases.
% 10.40/3.09 |-Branch one:
% 10.40/3.09 | (210) ~ (element(all_0_5_5, all_93_1_54) = 0)
% 10.40/3.09 |
% 10.40/3.09 | From (171) and (210) follows:
% 10.40/3.09 | (211) ~ (element(all_0_5_5, all_0_8_8) = 0)
% 10.40/3.09 |
% 10.40/3.09 | Using (42) and (211) yields:
% 10.40/3.09 | (130) $false
% 10.40/3.09 |
% 10.40/3.09 |-The branch is then unsatisfiable
% 10.40/3.09 |-Branch two:
% 10.40/3.09 | (213) element(all_0_5_5, all_93_1_54) = 0
% 10.40/3.09 | (214) ~ (element(all_0_6_6, all_93_0_53) = 0) | ? [v0] : ? [v1] : ? [v2] : (point_neighbourhood(all_0_6_6, all_0_10_10, all_0_5_5) = v0 & interior(all_0_10_10, all_0_6_6) = v1 & in(all_0_5_5, v1) = v2 & ( ~ (v2 = 0) | v0 = 0) & ( ~ (v0 = 0) | v2 = 0))
% 10.40/3.09 |
% 10.40/3.09 +-Applying beta-rule and splitting (214), into two cases.
% 10.40/3.09 |-Branch one:
% 10.40/3.09 | (215) ~ (element(all_0_6_6, all_93_0_53) = 0)
% 10.40/3.09 |
% 10.40/3.09 | From (194) and (215) follows:
% 10.40/3.09 | (145) ~ (element(all_0_6_6, all_0_7_7) = 0)
% 10.40/3.09 |
% 10.40/3.09 | Using (59) and (145) yields:
% 10.40/3.09 | (130) $false
% 10.40/3.09 |
% 10.40/3.09 |-The branch is then unsatisfiable
% 10.40/3.09 |-Branch two:
% 10.40/3.09 | (218) element(all_0_6_6, all_93_0_53) = 0
% 10.40/3.09 | (219) ? [v0] : ? [v1] : ? [v2] : (point_neighbourhood(all_0_6_6, all_0_10_10, all_0_5_5) = v0 & interior(all_0_10_10, all_0_6_6) = v1 & in(all_0_5_5, v1) = v2 & ( ~ (v2 = 0) | v0 = 0) & ( ~ (v0 = 0) | v2 = 0))
% 10.40/3.09 |
% 10.40/3.09 | Instantiating (219) with all_146_0_63, all_146_1_64, all_146_2_65 yields:
% 10.40/3.09 | (220) point_neighbourhood(all_0_6_6, all_0_10_10, all_0_5_5) = all_146_2_65 & interior(all_0_10_10, all_0_6_6) = all_146_1_64 & in(all_0_5_5, all_146_1_64) = all_146_0_63 & ( ~ (all_146_0_63 = 0) | all_146_2_65 = 0) & ( ~ (all_146_2_65 = 0) | all_146_0_63 = 0)
% 10.40/3.09 |
% 10.40/3.09 | Applying alpha-rule on (220) yields:
% 10.40/3.09 | (221) point_neighbourhood(all_0_6_6, all_0_10_10, all_0_5_5) = all_146_2_65
% 10.40/3.09 | (222) ~ (all_146_2_65 = 0) | all_146_0_63 = 0
% 10.40/3.09 | (223) ~ (all_146_0_63 = 0) | all_146_2_65 = 0
% 10.40/3.09 | (224) in(all_0_5_5, all_146_1_64) = all_146_0_63
% 10.40/3.09 | (225) interior(all_0_10_10, all_0_6_6) = all_146_1_64
% 10.40/3.09 |
% 10.40/3.09 | Instantiating formula (2) with all_0_6_6, all_0_10_10, all_131_1_62, 0 and discharging atoms open_subset(all_0_6_6, all_0_10_10) = all_131_1_62, open_subset(all_0_6_6, all_0_10_10) = 0, yields:
% 10.40/3.09 | (226) all_131_1_62 = 0
% 10.40/3.09 |
% 10.40/3.09 | Instantiating formula (39) with all_0_6_6, all_0_10_10, all_0_5_5, all_146_2_65, all_0_4_4 and discharging atoms point_neighbourhood(all_0_6_6, all_0_10_10, all_0_5_5) = all_146_2_65, point_neighbourhood(all_0_6_6, all_0_10_10, all_0_5_5) = all_0_4_4, yields:
% 10.40/3.09 | (227) all_146_2_65 = all_0_4_4
% 10.40/3.09 |
% 10.40/3.09 | Instantiating formula (20) with all_0_10_10, all_0_6_6, all_146_1_64, all_103_1_58 and discharging atoms interior(all_0_10_10, all_0_6_6) = all_146_1_64, interior(all_0_10_10, all_0_6_6) = all_103_1_58, yields:
% 10.40/3.09 | (228) all_146_1_64 = all_103_1_58
% 10.40/3.09 |
% 10.40/3.09 | Instantiating formula (20) with all_0_10_10, all_0_6_6, all_131_0_61, all_146_1_64 and discharging atoms interior(all_0_10_10, all_0_6_6) = all_146_1_64, interior(all_0_10_10, all_0_6_6) = all_131_0_61, yields:
% 10.40/3.09 | (229) all_146_1_64 = all_131_0_61
% 10.40/3.09 |
% 10.40/3.09 | Instantiating formula (75) with all_0_5_5, all_0_6_6, all_146_0_63, 0 and discharging atoms in(all_0_5_5, all_0_6_6) = 0, yields:
% 10.40/3.09 | (230) all_146_0_63 = 0 | ~ (in(all_0_5_5, all_0_6_6) = all_146_0_63)
% 10.40/3.09 |
% 10.40/3.09 | Combining equations (228,229) yields a new equation:
% 10.40/3.09 | (231) all_131_0_61 = all_103_1_58
% 10.40/3.09 |
% 10.40/3.09 | Combining equations (231,229) yields a new equation:
% 10.40/3.09 | (228) all_146_1_64 = all_103_1_58
% 10.40/3.09 |
% 10.40/3.09 | From (228) and (224) follows:
% 10.40/3.09 | (233) in(all_0_5_5, all_103_1_58) = all_146_0_63
% 10.40/3.09 |
% 10.40/3.09 +-Applying beta-rule and splitting (223), into two cases.
% 10.40/3.09 |-Branch one:
% 10.40/3.09 | (234) ~ (all_146_0_63 = 0)
% 10.40/3.09 |
% 10.40/3.09 +-Applying beta-rule and splitting (203), into two cases.
% 10.40/3.09 |-Branch one:
% 10.40/3.09 | (235) ~ (all_131_1_62 = 0)
% 10.40/3.09 |
% 10.40/3.09 | Equations (226) can reduce 235 to:
% 10.40/3.09 | (114) $false
% 10.40/3.09 |
% 10.40/3.09 |-The branch is then unsatisfiable
% 10.40/3.09 |-Branch two:
% 10.40/3.09 | (226) all_131_1_62 = 0
% 10.40/3.09 | (238) all_131_0_61 = all_0_6_6
% 10.40/3.09 |
% 10.40/3.09 | Combining equations (231,238) yields a new equation:
% 10.40/3.09 | (239) all_103_1_58 = all_0_6_6
% 10.40/3.09 |
% 10.40/3.09 | Simplifying 239 yields:
% 10.40/3.09 | (240) all_103_1_58 = all_0_6_6
% 10.40/3.09 |
% 10.40/3.09 | From (240) and (233) follows:
% 10.40/3.09 | (241) in(all_0_5_5, all_0_6_6) = all_146_0_63
% 10.40/3.09 |
% 10.40/3.09 +-Applying beta-rule and splitting (230), into two cases.
% 10.40/3.09 |-Branch one:
% 10.40/3.09 | (242) ~ (in(all_0_5_5, all_0_6_6) = all_146_0_63)
% 10.40/3.09 |
% 10.40/3.09 | Using (241) and (242) yields:
% 10.40/3.09 | (130) $false
% 10.40/3.09 |
% 10.40/3.09 |-The branch is then unsatisfiable
% 10.40/3.09 |-Branch two:
% 10.40/3.09 | (241) in(all_0_5_5, all_0_6_6) = all_146_0_63
% 10.40/3.09 | (245) all_146_0_63 = 0
% 10.40/3.09 |
% 10.40/3.09 | Equations (245) can reduce 234 to:
% 10.40/3.09 | (114) $false
% 10.40/3.09 |
% 10.40/3.09 |-The branch is then unsatisfiable
% 10.40/3.09 |-Branch two:
% 10.40/3.09 | (245) all_146_0_63 = 0
% 10.40/3.09 | (248) all_146_2_65 = 0
% 10.40/3.09 |
% 10.40/3.09 | Combining equations (248,227) yields a new equation:
% 10.40/3.09 | (249) all_0_4_4 = 0
% 10.40/3.09 |
% 10.40/3.09 | Equations (249) can reduce 34 to:
% 10.40/3.10 | (114) $false
% 10.40/3.10 |
% 10.40/3.10 |-The branch is then unsatisfiable
% 10.40/3.10 % SZS output end Proof for theBenchmark
% 10.40/3.10
% 10.40/3.10 2494ms
%------------------------------------------------------------------------------