TSTP Solution File: SEU243+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU243+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 08:48:05 EDT 2022
% Result : Theorem 4.62s 1.75s
% Output : Proof 6.88s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU243+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.33 % Computer : n025.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jun 19 20:25:59 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.54/0.57 ____ _
% 0.54/0.57 ___ / __ \_____(_)___ ________ __________
% 0.54/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.54/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.54/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.54/0.57
% 0.54/0.57 A Theorem Prover for First-Order Logic
% 0.54/0.57 (ePrincess v.1.0)
% 0.54/0.57
% 0.54/0.57 (c) Philipp Rümmer, 2009-2015
% 0.54/0.57 (c) Peter Backeman, 2014-2015
% 0.54/0.57 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.54/0.57 Free software under GNU Lesser General Public License (LGPL).
% 0.54/0.57 Bug reports to peter@backeman.se
% 0.54/0.57
% 0.54/0.57 For more information, visit http://user.uu.se/~petba168/breu/
% 0.54/0.57
% 0.54/0.57 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.54/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.40/0.93 Prover 0: Preprocessing ...
% 1.93/1.14 Prover 0: Warning: ignoring some quantifiers
% 2.10/1.16 Prover 0: Constructing countermodel ...
% 3.63/1.54 Prover 0: gave up
% 3.63/1.54 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 3.73/1.56 Prover 1: Preprocessing ...
% 4.06/1.66 Prover 1: Warning: ignoring some quantifiers
% 4.06/1.66 Prover 1: Constructing countermodel ...
% 4.62/1.75 Prover 1: proved (216ms)
% 4.62/1.75
% 4.62/1.75 No countermodel exists, formula is valid
% 4.62/1.75 % SZS status Theorem for theBenchmark
% 4.62/1.75
% 4.62/1.75 Generating proof ... Warning: ignoring some quantifiers
% 6.34/2.16 found it (size 62)
% 6.34/2.16
% 6.34/2.16 % SZS output start Proof for theBenchmark
% 6.34/2.16 Assumed formulas after preprocessing and simplification:
% 6.34/2.16 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ( ~ (v6 = 0) & is_well_founded_in(v0, v2) = v3 & well_founded_relation(v0) = v1 & relation_field(v0) = v2 & one_to_one(v4) = 0 & relation(v9) = 0 & relation(v7) = 0 & relation(v4) = 0 & relation(v0) = 0 & function(v9) = 0 & function(v7) = 0 & function(v4) = 0 & empty(v8) = 0 & empty(v7) = 0 & empty(v5) = v6 & empty(empty_set) = 0 & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (powerset(v12) = v13) | ~ (element(v11, v13) = 0) | ~ (element(v10, v12) = v14) | ? [v15] : ( ~ (v15 = 0) & in(v10, v11) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (powerset(v11) = v12) | ~ (element(v10, v12) = v13) | ? [v14] : ( ~ (v14 = 0) & subset(v10, v11) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (element(v13, v12) = v11) | ~ (element(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (is_well_founded_in(v13, v12) = v11) | ~ (is_well_founded_in(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (subset(v13, v12) = v11) | ~ (subset(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (fiber(v13, v12) = v11) | ~ (fiber(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (disjoint(v13, v12) = v11) | ~ (disjoint(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (set_union2(v13, v12) = v11) | ~ (set_union2(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (in(v13, v12) = v11) | ~ (in(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (powerset(v12) = v13) | ~ (element(v11, v13) = 0) | ~ (in(v10, v11) = 0) | ? [v14] : ( ~ (v14 = 0) & empty(v12) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (relation_dom(v10) = v11) | ~ (relation_rng(v10) = v12) | ~ (set_union2(v11, v12) = v13) | ? [v14] : ? [v15] : (relation_field(v10) = v15 & relation(v10) = v14 & ( ~ (v14 = 0) | v15 = v13))) & ! [v10] : ! [v11] : ! [v12] : (v12 = empty_set | ~ (is_well_founded_in(v10, v11) = 0) | ~ (subset(v12, v11) = 0) | ~ (relation(v10) = 0) | ? [v13] : ? [v14] : (fiber(v10, v13) = v14 & disjoint(v14, v12) = 0 & in(v13, v12) = 0)) & ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (element(v10, v11) = v12) | ? [v13] : ( ~ (v13 = 0) & in(v10, v11) = v13)) & ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (is_well_founded_in(v10, v11) = v12) | ~ (relation(v10) = 0) | ? [v13] : ( ~ (v13 = empty_set) & subset(v13, v11) = 0 & ! [v14] : ! [v15] : ( ~ (fiber(v10, v14) = v15) | ~ (disjoint(v15, v13) = 0) | ? [v16] : ( ~ (v16 = 0) & in(v14, v13) = v16)))) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (powerset(v12) = v11) | ~ (powerset(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (relation_dom(v12) = v11) | ~ (relation_dom(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (relation_rng(v12) = v11) | ~ (relation_rng(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (well_founded_relation(v12) = v11) | ~ (well_founded_relation(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (relation_field(v12) = v11) | ~ (relation_field(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (one_to_one(v12) = v11) | ~ (one_to_one(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (relation(v12) = v11) | ~ (relation(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (function(v12) = v11) | ~ (function(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (empty(v12) = v11) | ~ (empty(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (powerset(v11) = v12) | ~ (element(v10, v12) = 0) | subset(v10, v11) = 0) & ! [v10] : ! [v11] : ! [v12] : ( ~ (set_union2(v11, v10) = v12) | ? [v13] : ? [v14] : (empty(v12) = v14 & empty(v10) = v13 & ( ~ (v14 = 0) | v13 = 0))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (set_union2(v10, v11) = v12) | set_union2(v11, v10) = v12) & ! [v10] : ! [v11] : ! [v12] : ( ~ (set_union2(v10, v11) = v12) | ? [v13] : ? [v14] : (empty(v12) = v14 & empty(v10) = v13 & ( ~ (v14 = 0) | v13 = 0))) & ! [v10] : ! [v11] : (v11 = v10 | ~ (set_union2(v10, v10) = v11)) & ! [v10] : ! [v11] : (v11 = v10 | ~ (set_union2(v10, empty_set) = v11)) & ! [v10] : ! [v11] : (v11 = v10 | ~ (empty(v11) = 0) | ~ (empty(v10) = 0)) & ! [v10] : ! [v11] : (v11 = 0 | ~ (subset(v10, v10) = v11)) & ! [v10] : ! [v11] : (v11 = 0 | ~ (function(v10) = v11) | ? [v12] : ( ~ (v12 = 0) & empty(v10) = v12)) & ! [v10] : ! [v11] : ( ~ (element(v10, v11) = 0) | ? [v12] : ? [v13] : (empty(v11) = v12 & in(v10, v11) = v13 & (v13 = 0 | v12 = 0))) & ! [v10] : ! [v11] : ( ~ (well_founded_relation(v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : (relation_field(v10) = v13 & relation(v10) = v12 & ( ~ (v12 = 0) | (( ~ (v11 = 0) | ! [v16] : (v16 = empty_set | ~ (subset(v16, v13) = 0) | ? [v17] : ? [v18] : (fiber(v10, v17) = v18 & disjoint(v18, v16) = 0 & in(v17, v16) = 0))) & (v11 = 0 | (v15 = 0 & ~ (v14 = empty_set) & subset(v14, v13) = 0 & ! [v16] : ! [v17] : ( ~ (fiber(v10, v16) = v17) | ~ (disjoint(v17, v14) = 0) | ? [v18] : ( ~ (v18 = 0) & in(v16, v14) = v18)))))))) & ! [v10] : ! [v11] : ( ~ (disjoint(v10, v11) = 0) | disjoint(v11, v10) = 0) & ! [v10] : ! [v11] : ( ~ (one_to_one(v10) = v11) | ? [v12] : ? [v13] : ? [v14] : (relation(v10) = v12 & function(v10) = v14 & empty(v10) = v13 & ( ~ (v14 = 0) | ~ (v13 = 0) | ~ (v12 = 0) | v11 = 0))) & ! [v10] : ! [v11] : ( ~ (in(v10, v11) = 0) | ? [v12] : ( ~ (v12 = 0) & empty(v11) = v12)) & ! [v10] : ! [v11] : ( ~ (in(v10, v11) = 0) | ? [v12] : ( ~ (v12 = 0) & in(v11, v10) = v12)) & ! [v10] : (v10 = empty_set | ~ (empty(v10) = 0)) & ? [v10] : ? [v11] : element(v11, v10) = 0 & ((v3 = 0 & ~ (v1 = 0)) | (v1 = 0 & ~ (v3 = 0))))
% 6.50/2.20 | 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 yields:
% 6.50/2.20 | (1) ~ (all_0_3_3 = 0) & is_well_founded_in(all_0_9_9, all_0_7_7) = all_0_6_6 & well_founded_relation(all_0_9_9) = all_0_8_8 & relation_field(all_0_9_9) = all_0_7_7 & one_to_one(all_0_5_5) = 0 & relation(all_0_0_0) = 0 & relation(all_0_2_2) = 0 & relation(all_0_5_5) = 0 & relation(all_0_9_9) = 0 & function(all_0_0_0) = 0 & function(all_0_2_2) = 0 & function(all_0_5_5) = 0 & empty(all_0_1_1) = 0 & empty(all_0_2_2) = 0 & empty(all_0_4_4) = all_0_3_3 & empty(empty_set) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (element(v0, v2) = v4) | ? [v5] : ( ~ (v5 = 0) & in(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (is_well_founded_in(v3, v2) = v1) | ~ (is_well_founded_in(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (fiber(v3, v2) = v1) | ~ (fiber(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom(v0) = v1) | ~ (relation_rng(v0) = v2) | ~ (set_union2(v1, v2) = v3) | ? [v4] : ? [v5] : (relation_field(v0) = v5 & relation(v0) = v4 & ( ~ (v4 = 0) | v5 = v3))) & ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (is_well_founded_in(v0, v1) = 0) | ~ (subset(v2, v1) = 0) | ~ (relation(v0) = 0) | ? [v3] : ? [v4] : (fiber(v0, v3) = v4 & disjoint(v4, v2) = 0 & in(v3, v2) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (is_well_founded_in(v0, v1) = v2) | ~ (relation(v0) = 0) | ? [v3] : ( ~ (v3 = empty_set) & subset(v3, v1) = 0 & ! [v4] : ! [v5] : ( ~ (fiber(v0, v4) = v5) | ~ (disjoint(v5, v3) = 0) | ? [v6] : ( ~ (v6 = 0) & in(v4, v3) = v6)))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (well_founded_relation(v2) = v1) | ~ (well_founded_relation(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_field(v2) = v1) | ~ (relation_field(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | subset(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ? [v3] : ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (function(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2)) & ! [v0] : ! [v1] : ( ~ (element(v0, v1) = 0) | ? [v2] : ? [v3] : (empty(v1) = v2 & in(v0, v1) = v3 & (v3 = 0 | v2 = 0))) & ! [v0] : ! [v1] : ( ~ (well_founded_relation(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_field(v0) = v3 & relation(v0) = v2 & ( ~ (v2 = 0) | (( ~ (v1 = 0) | ! [v6] : (v6 = empty_set | ~ (subset(v6, v3) = 0) | ? [v7] : ? [v8] : (fiber(v0, v7) = v8 & disjoint(v8, v6) = 0 & in(v7, v6) = 0))) & (v1 = 0 | (v5 = 0 & ~ (v4 = empty_set) & subset(v4, v3) = 0 & ! [v6] : ! [v7] : ( ~ (fiber(v0, v6) = v7) | ~ (disjoint(v7, v4) = 0) | ? [v8] : ( ~ (v8 = 0) & in(v6, v4) = v8)))))))) & ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | disjoint(v1, v0) = 0) & ! [v0] : ! [v1] : ( ~ (one_to_one(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation(v0) = v2 & function(v0) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | 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] : ? [v1] : element(v1, v0) = 0 & ((all_0_6_6 = 0 & ~ (all_0_8_8 = 0)) | (all_0_8_8 = 0 & ~ (all_0_6_6 = 0)))
% 6.50/2.21 |
% 6.50/2.21 | Applying alpha-rule on (1) yields:
% 6.50/2.21 | (2) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (well_founded_relation(v2) = v1) | ~ (well_founded_relation(v2) = v0))
% 6.50/2.21 | (3) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (is_well_founded_in(v0, v1) = v2) | ~ (relation(v0) = 0) | ? [v3] : ( ~ (v3 = empty_set) & subset(v3, v1) = 0 & ! [v4] : ! [v5] : ( ~ (fiber(v0, v4) = v5) | ~ (disjoint(v5, v3) = 0) | ? [v6] : ( ~ (v6 = 0) & in(v4, v3) = v6))))
% 6.50/2.21 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (is_well_founded_in(v3, v2) = v1) | ~ (is_well_founded_in(v3, v2) = v0))
% 6.50/2.21 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (element(v0, v2) = v4) | ? [v5] : ( ~ (v5 = 0) & in(v0, v1) = v5))
% 6.50/2.21 | (6) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 6.50/2.21 | (7) relation(all_0_9_9) = 0
% 6.50/2.21 | (8) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0))
% 6.50/2.21 | (9) empty(all_0_2_2) = 0
% 6.50/2.21 | (10) function(all_0_2_2) = 0
% 6.50/2.21 | (11) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0))
% 6.50/2.21 | (12) well_founded_relation(all_0_9_9) = all_0_8_8
% 6.50/2.21 | (13) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0))
% 6.50/2.21 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 6.50/2.21 | (15) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0)))
% 6.50/2.22 | (16) relation(all_0_5_5) = 0
% 6.50/2.22 | (17) ! [v0] : ! [v1] : ( ~ (well_founded_relation(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_field(v0) = v3 & relation(v0) = v2 & ( ~ (v2 = 0) | (( ~ (v1 = 0) | ! [v6] : (v6 = empty_set | ~ (subset(v6, v3) = 0) | ? [v7] : ? [v8] : (fiber(v0, v7) = v8 & disjoint(v8, v6) = 0 & in(v7, v6) = 0))) & (v1 = 0 | (v5 = 0 & ~ (v4 = empty_set) & subset(v4, v3) = 0 & ! [v6] : ! [v7] : ( ~ (fiber(v0, v6) = v7) | ~ (disjoint(v7, v4) = 0) | ? [v8] : ( ~ (v8 = 0) & in(v6, v4) = v8))))))))
% 6.50/2.22 | (18) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0))
% 6.50/2.22 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0))
% 6.50/2.22 | (20) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 6.50/2.22 | (21) empty(all_0_4_4) = all_0_3_3
% 6.50/2.22 | (22) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0))
% 6.50/2.22 | (23) ? [v0] : ? [v1] : element(v1, v0) = 0
% 6.50/2.22 | (24) empty(empty_set) = 0
% 6.50/2.22 | (25) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_field(v2) = v1) | ~ (relation_field(v2) = v0))
% 6.50/2.22 | (26) ! [v0] : ! [v1] : ( ~ (element(v0, v1) = 0) | ? [v2] : ? [v3] : (empty(v1) = v2 & in(v0, v1) = v3 & (v3 = 0 | v2 = 0)))
% 6.50/2.22 | (27) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | subset(v0, v1) = 0)
% 6.50/2.22 | (28) ~ (all_0_3_3 = 0)
% 6.50/2.22 | (29) ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (is_well_founded_in(v0, v1) = 0) | ~ (subset(v2, v1) = 0) | ~ (relation(v0) = 0) | ? [v3] : ? [v4] : (fiber(v0, v3) = v4 & disjoint(v4, v2) = 0 & in(v3, v2) = 0))
% 6.50/2.22 | (30) ! [v0] : ! [v1] : (v1 = 0 | ~ (function(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2))
% 6.50/2.22 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0))
% 6.50/2.22 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0))
% 6.50/2.22 | (33) (all_0_6_6 = 0 & ~ (all_0_8_8 = 0)) | (all_0_8_8 = 0 & ~ (all_0_6_6 = 0))
% 6.50/2.22 | (34) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3))
% 6.50/2.22 | (35) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | disjoint(v1, v0) = 0)
% 6.50/2.22 | (36) relation(all_0_2_2) = 0
% 6.50/2.22 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 6.50/2.22 | (38) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1))
% 6.50/2.22 | (39) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0))
% 6.50/2.22 | (40) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 6.50/2.22 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom(v0) = v1) | ~ (relation_rng(v0) = v2) | ~ (set_union2(v1, v2) = v3) | ? [v4] : ? [v5] : (relation_field(v0) = v5 & relation(v0) = v4 & ( ~ (v4 = 0) | v5 = v3)))
% 6.50/2.22 | (42) function(all_0_5_5) = 0
% 6.50/2.22 | (43) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2)
% 6.50/2.22 | (44) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0))
% 6.50/2.22 | (45) function(all_0_0_0) = 0
% 6.50/2.22 | (46) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1))
% 6.50/2.22 | (47) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1))
% 6.50/2.22 | (48) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ? [v3] : ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0)))
% 6.50/2.23 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 6.50/2.23 | (50) is_well_founded_in(all_0_9_9, all_0_7_7) = all_0_6_6
% 6.50/2.23 | (51) relation(all_0_0_0) = 0
% 6.50/2.23 | (52) one_to_one(all_0_5_5) = 0
% 6.50/2.23 | (53) empty(all_0_1_1) = 0
% 6.50/2.23 | (54) relation_field(all_0_9_9) = all_0_7_7
% 6.50/2.23 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (fiber(v3, v2) = v1) | ~ (fiber(v3, v2) = v0))
% 6.50/2.23 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4))
% 6.50/2.23 | (57) ! [v0] : ! [v1] : ( ~ (one_to_one(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation(v0) = v2 & function(v0) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | v1 = 0)))
% 6.50/2.23 | (58) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0))
% 6.50/2.23 |
% 6.50/2.23 | Instantiating formula (17) with all_0_8_8, all_0_9_9 and discharging atoms well_founded_relation(all_0_9_9) = all_0_8_8, yields:
% 6.50/2.23 | (59) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (relation_field(all_0_9_9) = v1 & relation(all_0_9_9) = v0 & ( ~ (v0 = 0) | (( ~ (all_0_8_8 = 0) | ! [v4] : (v4 = empty_set | ~ (subset(v4, v1) = 0) | ? [v5] : ? [v6] : (fiber(all_0_9_9, v5) = v6 & disjoint(v6, v4) = 0 & in(v5, v4) = 0))) & (all_0_8_8 = 0 | (v3 = 0 & ~ (v2 = empty_set) & subset(v2, v1) = 0 & ! [v4] : ! [v5] : ( ~ (fiber(all_0_9_9, v4) = v5) | ~ (disjoint(v5, v2) = 0) | ? [v6] : ( ~ (v6 = 0) & in(v4, v2) = v6)))))))
% 6.50/2.23 |
% 6.50/2.23 | Instantiating formula (3) with all_0_6_6, all_0_7_7, all_0_9_9 and discharging atoms is_well_founded_in(all_0_9_9, all_0_7_7) = all_0_6_6, relation(all_0_9_9) = 0, yields:
% 6.50/2.23 | (60) all_0_6_6 = 0 | ? [v0] : ( ~ (v0 = empty_set) & subset(v0, all_0_7_7) = 0 & ! [v1] : ! [v2] : ( ~ (fiber(all_0_9_9, v1) = v2) | ~ (disjoint(v2, v0) = 0) | ? [v3] : ( ~ (v3 = 0) & in(v1, v0) = v3)))
% 6.50/2.23 |
% 6.50/2.23 | Instantiating (59) with all_16_0_15, all_16_1_16, all_16_2_17, all_16_3_18 yields:
% 6.50/2.23 | (61) relation_field(all_0_9_9) = all_16_2_17 & relation(all_0_9_9) = all_16_3_18 & ( ~ (all_16_3_18 = 0) | (( ~ (all_0_8_8 = 0) | ! [v0] : (v0 = empty_set | ~ (subset(v0, all_16_2_17) = 0) | ? [v1] : ? [v2] : (fiber(all_0_9_9, v1) = v2 & disjoint(v2, v0) = 0 & in(v1, v0) = 0))) & (all_0_8_8 = 0 | (all_16_0_15 = 0 & ~ (all_16_1_16 = empty_set) & subset(all_16_1_16, all_16_2_17) = 0 & ! [v0] : ! [v1] : ( ~ (fiber(all_0_9_9, v0) = v1) | ~ (disjoint(v1, all_16_1_16) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, all_16_1_16) = v2))))))
% 6.50/2.23 |
% 6.50/2.23 | Applying alpha-rule on (61) yields:
% 6.50/2.23 | (62) relation_field(all_0_9_9) = all_16_2_17
% 6.50/2.23 | (63) relation(all_0_9_9) = all_16_3_18
% 6.50/2.23 | (64) ~ (all_16_3_18 = 0) | (( ~ (all_0_8_8 = 0) | ! [v0] : (v0 = empty_set | ~ (subset(v0, all_16_2_17) = 0) | ? [v1] : ? [v2] : (fiber(all_0_9_9, v1) = v2 & disjoint(v2, v0) = 0 & in(v1, v0) = 0))) & (all_0_8_8 = 0 | (all_16_0_15 = 0 & ~ (all_16_1_16 = empty_set) & subset(all_16_1_16, all_16_2_17) = 0 & ! [v0] : ! [v1] : ( ~ (fiber(all_0_9_9, v0) = v1) | ~ (disjoint(v1, all_16_1_16) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, all_16_1_16) = v2)))))
% 6.50/2.23 |
% 6.50/2.23 | Instantiating formula (25) with all_0_9_9, all_16_2_17, all_0_7_7 and discharging atoms relation_field(all_0_9_9) = all_16_2_17, relation_field(all_0_9_9) = all_0_7_7, yields:
% 6.50/2.23 | (65) all_16_2_17 = all_0_7_7
% 6.50/2.23 |
% 6.50/2.23 | Instantiating formula (58) with all_0_9_9, all_16_3_18, 0 and discharging atoms relation(all_0_9_9) = all_16_3_18, relation(all_0_9_9) = 0, yields:
% 6.50/2.23 | (66) all_16_3_18 = 0
% 6.50/2.23 |
% 6.50/2.24 | From (66) and (63) follows:
% 6.88/2.24 | (7) relation(all_0_9_9) = 0
% 6.88/2.24 |
% 6.88/2.24 +-Applying beta-rule and splitting (33), into two cases.
% 6.88/2.24 |-Branch one:
% 6.88/2.24 | (68) all_0_6_6 = 0 & ~ (all_0_8_8 = 0)
% 6.88/2.24 |
% 6.88/2.24 | Applying alpha-rule on (68) yields:
% 6.88/2.24 | (69) all_0_6_6 = 0
% 6.88/2.24 | (70) ~ (all_0_8_8 = 0)
% 6.88/2.24 |
% 6.88/2.24 | From (69) and (50) follows:
% 6.88/2.24 | (71) is_well_founded_in(all_0_9_9, all_0_7_7) = 0
% 6.88/2.24 |
% 6.88/2.24 +-Applying beta-rule and splitting (64), into two cases.
% 6.88/2.24 |-Branch one:
% 6.88/2.24 | (72) ~ (all_16_3_18 = 0)
% 6.88/2.24 |
% 6.88/2.24 | Equations (66) can reduce 72 to:
% 6.88/2.24 | (73) $false
% 6.88/2.24 |
% 6.88/2.24 |-The branch is then unsatisfiable
% 6.88/2.24 |-Branch two:
% 6.88/2.24 | (66) all_16_3_18 = 0
% 6.88/2.24 | (75) ( ~ (all_0_8_8 = 0) | ! [v0] : (v0 = empty_set | ~ (subset(v0, all_16_2_17) = 0) | ? [v1] : ? [v2] : (fiber(all_0_9_9, v1) = v2 & disjoint(v2, v0) = 0 & in(v1, v0) = 0))) & (all_0_8_8 = 0 | (all_16_0_15 = 0 & ~ (all_16_1_16 = empty_set) & subset(all_16_1_16, all_16_2_17) = 0 & ! [v0] : ! [v1] : ( ~ (fiber(all_0_9_9, v0) = v1) | ~ (disjoint(v1, all_16_1_16) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, all_16_1_16) = v2))))
% 6.88/2.24 |
% 6.88/2.24 | Applying alpha-rule on (75) yields:
% 6.88/2.24 | (76) ~ (all_0_8_8 = 0) | ! [v0] : (v0 = empty_set | ~ (subset(v0, all_16_2_17) = 0) | ? [v1] : ? [v2] : (fiber(all_0_9_9, v1) = v2 & disjoint(v2, v0) = 0 & in(v1, v0) = 0))
% 6.88/2.24 | (77) all_0_8_8 = 0 | (all_16_0_15 = 0 & ~ (all_16_1_16 = empty_set) & subset(all_16_1_16, all_16_2_17) = 0 & ! [v0] : ! [v1] : ( ~ (fiber(all_0_9_9, v0) = v1) | ~ (disjoint(v1, all_16_1_16) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, all_16_1_16) = v2)))
% 6.88/2.24 |
% 6.88/2.24 +-Applying beta-rule and splitting (77), into two cases.
% 6.88/2.24 |-Branch one:
% 6.88/2.24 | (78) all_0_8_8 = 0
% 6.88/2.24 |
% 6.88/2.24 | Equations (78) can reduce 70 to:
% 6.88/2.24 | (73) $false
% 6.88/2.24 |
% 6.88/2.24 |-The branch is then unsatisfiable
% 6.88/2.24 |-Branch two:
% 6.88/2.24 | (70) ~ (all_0_8_8 = 0)
% 6.88/2.24 | (81) all_16_0_15 = 0 & ~ (all_16_1_16 = empty_set) & subset(all_16_1_16, all_16_2_17) = 0 & ! [v0] : ! [v1] : ( ~ (fiber(all_0_9_9, v0) = v1) | ~ (disjoint(v1, all_16_1_16) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, all_16_1_16) = v2))
% 6.88/2.24 |
% 6.88/2.24 | Applying alpha-rule on (81) yields:
% 6.88/2.24 | (82) all_16_0_15 = 0
% 6.88/2.24 | (83) ~ (all_16_1_16 = empty_set)
% 6.88/2.24 | (84) subset(all_16_1_16, all_16_2_17) = 0
% 6.88/2.24 | (85) ! [v0] : ! [v1] : ( ~ (fiber(all_0_9_9, v0) = v1) | ~ (disjoint(v1, all_16_1_16) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, all_16_1_16) = v2))
% 6.88/2.24 |
% 6.88/2.24 | From (65) and (84) follows:
% 6.88/2.24 | (86) subset(all_16_1_16, all_0_7_7) = 0
% 6.88/2.24 |
% 6.88/2.24 | Instantiating formula (29) with all_16_1_16, all_0_7_7, all_0_9_9 and discharging atoms is_well_founded_in(all_0_9_9, all_0_7_7) = 0, subset(all_16_1_16, all_0_7_7) = 0, relation(all_0_9_9) = 0, yields:
% 6.88/2.24 | (87) all_16_1_16 = empty_set | ? [v0] : ? [v1] : (fiber(all_0_9_9, v0) = v1 & disjoint(v1, all_16_1_16) = 0 & in(v0, all_16_1_16) = 0)
% 6.88/2.24 |
% 6.88/2.24 +-Applying beta-rule and splitting (87), into two cases.
% 6.88/2.24 |-Branch one:
% 6.88/2.24 | (88) all_16_1_16 = empty_set
% 6.88/2.24 |
% 6.88/2.24 | Equations (88) can reduce 83 to:
% 6.88/2.24 | (73) $false
% 6.88/2.24 |
% 6.88/2.24 |-The branch is then unsatisfiable
% 6.88/2.24 |-Branch two:
% 6.88/2.24 | (83) ~ (all_16_1_16 = empty_set)
% 6.88/2.24 | (91) ? [v0] : ? [v1] : (fiber(all_0_9_9, v0) = v1 & disjoint(v1, all_16_1_16) = 0 & in(v0, all_16_1_16) = 0)
% 6.88/2.24 |
% 6.88/2.24 | Instantiating (91) with all_69_0_21, all_69_1_22 yields:
% 6.88/2.24 | (92) fiber(all_0_9_9, all_69_1_22) = all_69_0_21 & disjoint(all_69_0_21, all_16_1_16) = 0 & in(all_69_1_22, all_16_1_16) = 0
% 6.88/2.25 |
% 6.88/2.25 | Applying alpha-rule on (92) yields:
% 6.88/2.25 | (93) fiber(all_0_9_9, all_69_1_22) = all_69_0_21
% 6.88/2.25 | (94) disjoint(all_69_0_21, all_16_1_16) = 0
% 6.88/2.25 | (95) in(all_69_1_22, all_16_1_16) = 0
% 6.88/2.25 |
% 6.88/2.25 | Instantiating formula (85) with all_69_0_21, all_69_1_22 and discharging atoms fiber(all_0_9_9, all_69_1_22) = all_69_0_21, disjoint(all_69_0_21, all_16_1_16) = 0, yields:
% 6.88/2.25 | (96) ? [v0] : ( ~ (v0 = 0) & in(all_69_1_22, all_16_1_16) = v0)
% 6.88/2.25 |
% 6.88/2.25 | Instantiating (96) with all_81_0_23 yields:
% 6.88/2.25 | (97) ~ (all_81_0_23 = 0) & in(all_69_1_22, all_16_1_16) = all_81_0_23
% 6.88/2.25 |
% 6.88/2.25 | Applying alpha-rule on (97) yields:
% 6.88/2.25 | (98) ~ (all_81_0_23 = 0)
% 6.88/2.25 | (99) in(all_69_1_22, all_16_1_16) = all_81_0_23
% 6.88/2.25 |
% 6.88/2.25 | Instantiating formula (49) with all_69_1_22, all_16_1_16, all_81_0_23, 0 and discharging atoms in(all_69_1_22, all_16_1_16) = all_81_0_23, in(all_69_1_22, all_16_1_16) = 0, yields:
% 6.88/2.25 | (100) all_81_0_23 = 0
% 6.88/2.25 |
% 6.88/2.25 | Equations (100) can reduce 98 to:
% 6.88/2.25 | (73) $false
% 6.88/2.25 |
% 6.88/2.25 |-The branch is then unsatisfiable
% 6.88/2.25 |-Branch two:
% 6.88/2.25 | (102) all_0_8_8 = 0 & ~ (all_0_6_6 = 0)
% 6.88/2.25 |
% 6.88/2.25 | Applying alpha-rule on (102) yields:
% 6.88/2.25 | (78) all_0_8_8 = 0
% 6.88/2.25 | (104) ~ (all_0_6_6 = 0)
% 6.88/2.25 |
% 6.88/2.25 +-Applying beta-rule and splitting (64), into two cases.
% 6.88/2.25 |-Branch one:
% 6.88/2.25 | (72) ~ (all_16_3_18 = 0)
% 6.88/2.25 |
% 6.88/2.25 | Equations (66) can reduce 72 to:
% 6.88/2.25 | (73) $false
% 6.88/2.25 |
% 6.88/2.25 |-The branch is then unsatisfiable
% 6.88/2.25 |-Branch two:
% 6.88/2.25 | (66) all_16_3_18 = 0
% 6.88/2.25 | (75) ( ~ (all_0_8_8 = 0) | ! [v0] : (v0 = empty_set | ~ (subset(v0, all_16_2_17) = 0) | ? [v1] : ? [v2] : (fiber(all_0_9_9, v1) = v2 & disjoint(v2, v0) = 0 & in(v1, v0) = 0))) & (all_0_8_8 = 0 | (all_16_0_15 = 0 & ~ (all_16_1_16 = empty_set) & subset(all_16_1_16, all_16_2_17) = 0 & ! [v0] : ! [v1] : ( ~ (fiber(all_0_9_9, v0) = v1) | ~ (disjoint(v1, all_16_1_16) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, all_16_1_16) = v2))))
% 6.88/2.25 |
% 6.88/2.25 | Applying alpha-rule on (75) yields:
% 6.88/2.25 | (76) ~ (all_0_8_8 = 0) | ! [v0] : (v0 = empty_set | ~ (subset(v0, all_16_2_17) = 0) | ? [v1] : ? [v2] : (fiber(all_0_9_9, v1) = v2 & disjoint(v2, v0) = 0 & in(v1, v0) = 0))
% 6.88/2.25 | (77) all_0_8_8 = 0 | (all_16_0_15 = 0 & ~ (all_16_1_16 = empty_set) & subset(all_16_1_16, all_16_2_17) = 0 & ! [v0] : ! [v1] : ( ~ (fiber(all_0_9_9, v0) = v1) | ~ (disjoint(v1, all_16_1_16) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, all_16_1_16) = v2)))
% 6.88/2.25 |
% 6.88/2.25 +-Applying beta-rule and splitting (60), into two cases.
% 6.88/2.25 |-Branch one:
% 6.88/2.25 | (69) all_0_6_6 = 0
% 6.88/2.25 |
% 6.88/2.25 | Equations (69) can reduce 104 to:
% 6.88/2.25 | (73) $false
% 6.88/2.25 |
% 6.88/2.25 |-The branch is then unsatisfiable
% 6.88/2.25 |-Branch two:
% 6.88/2.25 | (104) ~ (all_0_6_6 = 0)
% 6.88/2.25 | (114) ? [v0] : ( ~ (v0 = empty_set) & subset(v0, all_0_7_7) = 0 & ! [v1] : ! [v2] : ( ~ (fiber(all_0_9_9, v1) = v2) | ~ (disjoint(v2, v0) = 0) | ? [v3] : ( ~ (v3 = 0) & in(v1, v0) = v3)))
% 6.88/2.25 |
% 6.88/2.25 | Instantiating (114) with all_56_0_26 yields:
% 6.88/2.25 | (115) ~ (all_56_0_26 = empty_set) & subset(all_56_0_26, all_0_7_7) = 0 & ! [v0] : ! [v1] : ( ~ (fiber(all_0_9_9, v0) = v1) | ~ (disjoint(v1, all_56_0_26) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, all_56_0_26) = v2))
% 6.88/2.25 |
% 6.88/2.25 | Applying alpha-rule on (115) yields:
% 6.88/2.25 | (116) ~ (all_56_0_26 = empty_set)
% 6.88/2.25 | (117) subset(all_56_0_26, all_0_7_7) = 0
% 6.88/2.25 | (118) ! [v0] : ! [v1] : ( ~ (fiber(all_0_9_9, v0) = v1) | ~ (disjoint(v1, all_56_0_26) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, all_56_0_26) = v2))
% 6.88/2.25 |
% 6.88/2.25 +-Applying beta-rule and splitting (76), into two cases.
% 6.88/2.25 |-Branch one:
% 6.88/2.25 | (70) ~ (all_0_8_8 = 0)
% 6.88/2.25 |
% 6.88/2.25 | Equations (78) can reduce 70 to:
% 6.88/2.25 | (73) $false
% 6.88/2.26 |
% 6.88/2.26 |-The branch is then unsatisfiable
% 6.88/2.26 |-Branch two:
% 6.88/2.26 | (78) all_0_8_8 = 0
% 6.88/2.26 | (122) ! [v0] : (v0 = empty_set | ~ (subset(v0, all_16_2_17) = 0) | ? [v1] : ? [v2] : (fiber(all_0_9_9, v1) = v2 & disjoint(v2, v0) = 0 & in(v1, v0) = 0))
% 6.88/2.26 |
% 6.88/2.26 | Instantiating formula (122) with all_56_0_26 yields:
% 6.88/2.26 | (123) all_56_0_26 = empty_set | ~ (subset(all_56_0_26, all_16_2_17) = 0) | ? [v0] : ? [v1] : (fiber(all_0_9_9, v0) = v1 & disjoint(v1, all_56_0_26) = 0 & in(v0, all_56_0_26) = 0)
% 6.88/2.26 |
% 6.88/2.26 +-Applying beta-rule and splitting (123), into two cases.
% 6.88/2.26 |-Branch one:
% 6.88/2.26 | (124) ~ (subset(all_56_0_26, all_16_2_17) = 0)
% 6.88/2.26 |
% 6.88/2.26 | From (65) and (124) follows:
% 6.88/2.26 | (125) ~ (subset(all_56_0_26, all_0_7_7) = 0)
% 6.88/2.26 |
% 6.88/2.26 | Using (117) and (125) yields:
% 6.88/2.26 | (126) $false
% 6.88/2.26 |
% 6.88/2.26 |-The branch is then unsatisfiable
% 6.88/2.26 |-Branch two:
% 6.88/2.26 | (127) subset(all_56_0_26, all_16_2_17) = 0
% 6.88/2.26 | (128) all_56_0_26 = empty_set | ? [v0] : ? [v1] : (fiber(all_0_9_9, v0) = v1 & disjoint(v1, all_56_0_26) = 0 & in(v0, all_56_0_26) = 0)
% 6.88/2.26 |
% 6.88/2.26 +-Applying beta-rule and splitting (128), into two cases.
% 6.88/2.26 |-Branch one:
% 6.88/2.26 | (129) all_56_0_26 = empty_set
% 6.88/2.26 |
% 6.88/2.26 | Equations (129) can reduce 116 to:
% 6.88/2.26 | (73) $false
% 6.88/2.26 |
% 6.88/2.26 |-The branch is then unsatisfiable
% 6.88/2.26 |-Branch two:
% 6.88/2.26 | (116) ~ (all_56_0_26 = empty_set)
% 6.88/2.26 | (132) ? [v0] : ? [v1] : (fiber(all_0_9_9, v0) = v1 & disjoint(v1, all_56_0_26) = 0 & in(v0, all_56_0_26) = 0)
% 6.88/2.26 |
% 6.88/2.26 | Instantiating (132) with all_79_0_29, all_79_1_30 yields:
% 6.88/2.26 | (133) fiber(all_0_9_9, all_79_1_30) = all_79_0_29 & disjoint(all_79_0_29, all_56_0_26) = 0 & in(all_79_1_30, all_56_0_26) = 0
% 6.88/2.26 |
% 6.88/2.26 | Applying alpha-rule on (133) yields:
% 6.88/2.26 | (134) fiber(all_0_9_9, all_79_1_30) = all_79_0_29
% 6.88/2.26 | (135) disjoint(all_79_0_29, all_56_0_26) = 0
% 6.88/2.26 | (136) in(all_79_1_30, all_56_0_26) = 0
% 6.88/2.26 |
% 6.88/2.26 | Instantiating formula (118) with all_79_0_29, all_79_1_30 and discharging atoms fiber(all_0_9_9, all_79_1_30) = all_79_0_29, disjoint(all_79_0_29, all_56_0_26) = 0, yields:
% 6.88/2.26 | (137) ? [v0] : ( ~ (v0 = 0) & in(all_79_1_30, all_56_0_26) = v0)
% 6.88/2.26 |
% 6.88/2.26 | Instantiating (137) with all_112_0_36 yields:
% 6.88/2.26 | (138) ~ (all_112_0_36 = 0) & in(all_79_1_30, all_56_0_26) = all_112_0_36
% 6.88/2.26 |
% 6.88/2.26 | Applying alpha-rule on (138) yields:
% 6.88/2.26 | (139) ~ (all_112_0_36 = 0)
% 6.88/2.26 | (140) in(all_79_1_30, all_56_0_26) = all_112_0_36
% 6.88/2.26 |
% 6.88/2.26 | Instantiating formula (49) with all_79_1_30, all_56_0_26, all_112_0_36, 0 and discharging atoms in(all_79_1_30, all_56_0_26) = all_112_0_36, in(all_79_1_30, all_56_0_26) = 0, yields:
% 6.88/2.26 | (141) all_112_0_36 = 0
% 6.88/2.26 |
% 6.88/2.26 | Equations (141) can reduce 139 to:
% 6.88/2.26 | (73) $false
% 6.88/2.26 |
% 6.88/2.26 |-The branch is then unsatisfiable
% 6.88/2.26 % SZS output end Proof for theBenchmark
% 6.88/2.26
% 6.88/2.26 1682ms
%------------------------------------------------------------------------------