TSTP Solution File: SEU251+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU251+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n026.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 08:48:09 EDT 2022
% Result : Theorem 7.03s 2.31s
% Output : Proof 9.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SEU251+1 : TPTP v8.1.0. Released v3.3.0.
% 0.10/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n026.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 20 05:11:26 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.58 ____ _
% 0.18/0.58 ___ / __ \_____(_)___ ________ __________
% 0.18/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.18/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.18/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.18/0.58
% 0.18/0.58 A Theorem Prover for First-Order Logic
% 0.18/0.58 (ePrincess v.1.0)
% 0.18/0.58
% 0.18/0.58 (c) Philipp Rümmer, 2009-2015
% 0.18/0.58 (c) Peter Backeman, 2014-2015
% 0.18/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.18/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.18/0.58 Bug reports to peter@backeman.se
% 0.18/0.58
% 0.18/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.18/0.58
% 0.18/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.74/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.62/0.95 Prover 0: Preprocessing ...
% 2.29/1.22 Prover 0: Warning: ignoring some quantifiers
% 2.36/1.25 Prover 0: Constructing countermodel ...
% 3.53/1.61 Prover 0: gave up
% 3.53/1.61 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 3.97/1.64 Prover 1: Preprocessing ...
% 4.28/1.74 Prover 1: Warning: ignoring some quantifiers
% 4.28/1.75 Prover 1: Constructing countermodel ...
% 6.03/2.08 Prover 1: gave up
% 6.03/2.08 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 6.03/2.11 Prover 2: Preprocessing ...
% 6.28/2.20 Prover 2: Warning: ignoring some quantifiers
% 6.28/2.20 Prover 2: Constructing countermodel ...
% 7.03/2.31 Prover 2: proved (226ms)
% 7.03/2.31
% 7.03/2.31 No countermodel exists, formula is valid
% 7.03/2.31 % SZS status Theorem for theBenchmark
% 7.03/2.31
% 7.03/2.31 Generating proof ... Warning: ignoring some quantifiers
% 9.30/2.85 found it (size 57)
% 9.30/2.85
% 9.30/2.85 % SZS output start Proof for theBenchmark
% 9.30/2.85 Assumed formulas after preprocessing and simplification:
% 9.30/2.85 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ( ~ (v9 = 0) & ~ (v6 = 0) & relation_restriction(v2, v0) = v3 & subset(v4, v5) = v6 & fiber(v3, v1) = v4 & fiber(v2, v1) = v5 & one_to_one(v7) = 0 & relation(v12) = 0 & relation(v10) = 0 & relation(v7) = 0 & relation(v2) = 0 & function(v12) = 0 & function(v10) = 0 & function(v7) = 0 & empty(v11) = 0 & empty(v10) = 0 & empty(v8) = v9 & empty(empty_set) = 0 & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v17 = 0 | v16 = v14 | ~ (fiber(v13, v14) = v15) | ~ (relation(v13) = 0) | ~ (in(v16, v15) = v17) | ? [v18] : ? [v19] : ( ~ (v19 = 0) & ordered_pair(v16, v14) = v18 & in(v18, v13) = v19)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v17 = 0 | ~ (powerset(v15) = v16) | ~ (element(v14, v16) = 0) | ~ (element(v13, v15) = v17) | ? [v18] : ( ~ (v18 = 0) & in(v13, v14) = v18)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v16 = v14 | ~ (fiber(v13, v14) = v15) | ~ (ordered_pair(v16, v14) = v17) | ~ (relation(v13) = 0) | ? [v18] : ((v18 = 0 & in(v16, v15) = 0) | ( ~ (v18 = 0) & in(v17, v13) = v18))) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_restriction(v15, v14) = v16) | ~ (in(v13, v16) = v17) | ? [v18] : ? [v19] : ? [v20] : (( ~ (v18 = 0) & relation(v15) = v18) | (( ~ (v17 = 0) | (v20 = 0 & v18 = 0 & cartesian_product2(v14, v14) = v19 & in(v13, v19) = 0 & in(v13, v15) = 0)) & (v17 = 0 | ( ~ (v20 = 0) & cartesian_product2(v14, v14) = v19 & in(v13, v19) = v20) | ( ~ (v18 = 0) & in(v13, v15) = v18))))) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (fiber(v13, v14) = v15) | ~ (ordered_pair(v16, v14) = v17) | ~ (relation(v13) = 0) | ? [v18] : ((v18 = 0 & ~ (v16 = v14) & in(v17, v13) = 0) | ( ~ (v18 = 0) & in(v16, v15) = v18))) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (powerset(v14) = v15) | ~ (element(v13, v15) = v16) | ? [v17] : ( ~ (v17 = 0) & subset(v13, v14) = v17)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (element(v13, v15) = v16) | ~ (in(v13, v14) = 0) | ? [v17] : ? [v18] : ( ~ (v18 = 0) & powerset(v15) = v17 & element(v14, v17) = v18)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (subset(v13, v14) = 0) | ~ (in(v15, v14) = v16) | ? [v17] : ( ~ (v17 = 0) & in(v15, v13) = v17)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v14 = v13 | ~ (element(v16, v15) = v14) | ~ (element(v16, v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v14 = v13 | ~ (cartesian_product2(v16, v15) = v14) | ~ (cartesian_product2(v16, v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v14 = v13 | ~ (relation_restriction(v16, v15) = v14) | ~ (relation_restriction(v16, v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v14 = v13 | ~ (subset(v16, v15) = v14) | ~ (subset(v16, v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v14 = v13 | ~ (fiber(v16, v15) = v14) | ~ (fiber(v16, v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v14 = v13 | ~ (ordered_pair(v16, v15) = v14) | ~ (ordered_pair(v16, v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v14 = v13 | ~ (set_intersection2(v16, v15) = v14) | ~ (set_intersection2(v16, v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v14 = v13 | ~ (unordered_pair(v16, v15) = v14) | ~ (unordered_pair(v16, v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v14 = v13 | ~ (in(v16, v15) = v14) | ~ (in(v16, v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (powerset(v15) = v16) | ~ (element(v14, v16) = 0) | ~ (in(v13, v14) = 0) | element(v13, v15) = 0) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (powerset(v15) = v16) | ~ (element(v14, v16) = 0) | ~ (in(v13, v14) = 0) | ? [v17] : ( ~ (v17 = 0) & empty(v15) = v17)) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (fiber(v13, v14) = v15) | ~ (relation(v13) = 0) | ~ (in(v16, v15) = 0) | ? [v17] : (ordered_pair(v16, v14) = v17 & in(v17, v13) = 0)) & ? [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = v13 | ~ (fiber(v14, v15) = v16) | ~ (relation(v14) = 0) | ? [v17] : ? [v18] : ? [v19] : ? [v20] : ((v17 = v15 | ( ~ (v20 = 0) & ordered_pair(v17, v15) = v19 & in(v19, v14) = v20) | ( ~ (v18 = 0) & in(v17, v13) = v18)) & ((v20 = 0 & ~ (v17 = v15) & ordered_pair(v17, v15) = v19 & in(v19, v14) = 0) | (v18 = 0 & in(v17, v13) = 0)))) & ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (element(v13, v14) = v15) | ? [v16] : ( ~ (v16 = 0) & in(v13, v14) = v16)) & ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (subset(v13, v14) = v15) | ? [v16] : ? [v17] : ( ~ (v17 = 0) & powerset(v14) = v16 & element(v13, v16) = v17)) & ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (subset(v13, v14) = v15) | ? [v16] : ? [v17] : ( ~ (v17 = 0) & in(v16, v14) = v17 & in(v16, v13) = 0)) & ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (in(v13, v14) = v15) | ? [v16] : ((v16 = 0 & empty(v14) = 0) | ( ~ (v16 = 0) & element(v13, v14) = v16))) & ! [v13] : ! [v14] : ! [v15] : (v14 = v13 | ~ (powerset(v15) = v14) | ~ (powerset(v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : (v14 = v13 | ~ (singleton(v15) = v14) | ~ (singleton(v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : (v14 = v13 | ~ (one_to_one(v15) = v14) | ~ (one_to_one(v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : (v14 = v13 | ~ (relation(v15) = v14) | ~ (relation(v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : (v14 = v13 | ~ (function(v15) = v14) | ~ (function(v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : (v14 = v13 | ~ (empty(v15) = v14) | ~ (empty(v15) = v13)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (powerset(v14) = v15) | ~ (element(v13, v15) = 0) | subset(v13, v14) = 0) & ! [v13] : ! [v14] : ! [v15] : ( ~ (cartesian_product2(v14, v14) = v15) | ~ (relation(v13) = 0) | ? [v16] : (relation_restriction(v13, v14) = v16 & set_intersection2(v13, v15) = v16)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (relation_restriction(v13, v14) = v15) | ~ (relation(v13) = 0) | ? [v16] : (cartesian_product2(v14, v14) = v16 & set_intersection2(v13, v16) = v15)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (relation_restriction(v13, v14) = v15) | ? [v16] : ((v16 = 0 & relation(v15) = 0) | ( ~ (v16 = 0) & relation(v13) = v16))) & ! [v13] : ! [v14] : ! [v15] : ( ~ (subset(v13, v14) = 0) | ~ (in(v15, v13) = 0) | in(v15, v14) = 0) & ! [v13] : ! [v14] : ! [v15] : ( ~ (fiber(v13, v14) = v15) | ~ (relation(v13) = 0) | ~ (in(v14, v15) = 0)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (ordered_pair(v13, v14) = v15) | ? [v16] : ? [v17] : (singleton(v13) = v17 & unordered_pair(v16, v17) = v15 & unordered_pair(v13, v14) = v16)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (ordered_pair(v13, v14) = v15) | ? [v16] : ( ~ (v16 = 0) & empty(v15) = v16)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (set_intersection2(v14, v13) = v15) | set_intersection2(v13, v14) = v15) & ! [v13] : ! [v14] : ! [v15] : ( ~ (set_intersection2(v13, v14) = v15) | set_intersection2(v14, v13) = v15) & ! [v13] : ! [v14] : ! [v15] : ( ~ (unordered_pair(v14, v13) = v15) | unordered_pair(v13, v14) = v15) & ! [v13] : ! [v14] : ! [v15] : ( ~ (unordered_pair(v13, v14) = v15) | unordered_pair(v14, v13) = v15) & ! [v13] : ! [v14] : ! [v15] : ( ~ (unordered_pair(v13, v14) = v15) | ? [v16] : ? [v17] : (singleton(v13) = v17 & ordered_pair(v13, v14) = v16 & unordered_pair(v15, v17) = v16)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (empty(v15) = 0) | ~ (in(v13, v14) = 0) | ? [v16] : ? [v17] : ( ~ (v17 = 0) & powerset(v15) = v16 & element(v14, v16) = v17)) & ! [v13] : ! [v14] : (v14 = v13 | ~ (set_intersection2(v13, v13) = v14)) & ! [v13] : ! [v14] : (v14 = v13 | ~ (empty(v14) = 0) | ~ (empty(v13) = 0)) & ! [v13] : ! [v14] : (v14 = empty_set | ~ (set_intersection2(v13, empty_set) = v14)) & ! [v13] : ! [v14] : (v14 = 0 | ~ (subset(v13, v13) = v14)) & ! [v13] : ! [v14] : (v14 = 0 | ~ (function(v13) = v14) | ? [v15] : ( ~ (v15 = 0) & empty(v13) = v15)) & ! [v13] : ! [v14] : ( ~ (element(v13, v14) = 0) | ? [v15] : ((v15 = 0 & empty(v14) = 0) | (v15 = 0 & in(v13, v14) = 0))) & ! [v13] : ! [v14] : ( ~ (subset(v13, v14) = 0) | ? [v15] : (powerset(v14) = v15 & element(v13, v15) = 0)) & ! [v13] : ! [v14] : ( ~ (one_to_one(v13) = v14) | ? [v15] : ? [v16] : ((v16 = 0 & v15 = 0 & v14 = 0 & relation(v13) = 0 & function(v13) = 0) | ( ~ (v15 = 0) & relation(v13) = v15) | ( ~ (v15 = 0) & function(v13) = v15) | ( ~ (v15 = 0) & empty(v13) = v15))) & ! [v13] : ! [v14] : ( ~ (in(v14, v13) = 0) | ? [v15] : ( ~ (v15 = 0) & in(v13, v14) = v15)) & ! [v13] : ! [v14] : ( ~ (in(v13, v14) = 0) | element(v13, v14) = 0) & ! [v13] : ! [v14] : ( ~ (in(v13, v14) = 0) | ? [v15] : ( ~ (v15 = 0) & empty(v14) = v15)) & ! [v13] : ! [v14] : ( ~ (in(v13, v14) = 0) | ? [v15] : ( ~ (v15 = 0) & in(v14, v13) = v15)) & ! [v13] : (v13 = empty_set | ~ (empty(v13) = 0)) & ! [v13] : ( ~ (relation(v13) = 0) | ? [v14] : ? [v15] : ((v15 = 0 & v14 = 0 & one_to_one(v13) = 0 & function(v13) = 0) | ( ~ (v14 = 0) & function(v13) = v14) | ( ~ (v14 = 0) & empty(v13) = v14))) & ! [v13] : ( ~ (function(v13) = 0) | ? [v14] : ? [v15] : ((v15 = 0 & v14 = 0 & one_to_one(v13) = 0 & relation(v13) = 0) | ( ~ (v14 = 0) & relation(v13) = v14) | ( ~ (v14 = 0) & empty(v13) = v14))) & ! [v13] : ( ~ (empty(v13) = 0) | function(v13) = 0) & ! [v13] : ( ~ (empty(v13) = 0) | ? [v14] : ? [v15] : ? [v16] : ((v16 = 0 & v15 = 0 & v14 = 0 & one_to_one(v13) = 0 & relation(v13) = 0 & function(v13) = 0) | ( ~ (v14 = 0) & relation(v13) = v14) | ( ~ (v14 = 0) & function(v13) = v14))) & ? [v13] : ? [v14] : ? [v15] : element(v14, v13) = v15 & ? [v13] : ? [v14] : ? [v15] : cartesian_product2(v14, v13) = v15 & ? [v13] : ? [v14] : ? [v15] : relation_restriction(v14, v13) = v15 & ? [v13] : ? [v14] : ? [v15] : subset(v14, v13) = v15 & ? [v13] : ? [v14] : ? [v15] : fiber(v14, v13) = v15 & ? [v13] : ? [v14] : ? [v15] : ordered_pair(v14, v13) = v15 & ? [v13] : ? [v14] : ? [v15] : set_intersection2(v14, v13) = v15 & ? [v13] : ? [v14] : ? [v15] : unordered_pair(v14, v13) = v15 & ? [v13] : ? [v14] : ? [v15] : in(v14, v13) = v15 & ? [v13] : ? [v14] : powerset(v13) = v14 & ? [v13] : ? [v14] : element(v14, v13) = 0 & ? [v13] : ? [v14] : singleton(v13) = v14 & ? [v13] : ? [v14] : one_to_one(v13) = v14 & ? [v13] : ? [v14] : relation(v13) = v14 & ? [v13] : ? [v14] : function(v13) = v14 & ? [v13] : ? [v14] : empty(v13) = v14)
% 9.30/2.89 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9, all_0_10_10, all_0_11_11, all_0_12_12 yields:
% 9.30/2.89 | (1) ~ (all_0_3_3 = 0) & ~ (all_0_6_6 = 0) & relation_restriction(all_0_10_10, all_0_12_12) = all_0_9_9 & subset(all_0_8_8, all_0_7_7) = all_0_6_6 & fiber(all_0_9_9, all_0_11_11) = all_0_8_8 & fiber(all_0_10_10, all_0_11_11) = 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_10_10) = 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 | v3 = v1 | ~ (fiber(v0, v1) = v2) | ~ (relation(v0) = 0) | ~ (in(v3, v2) = v4) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & ordered_pair(v3, v1) = v5 & in(v5, v0) = v6)) & ! [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] : ! [v4] : (v3 = v1 | ~ (fiber(v0, v1) = v2) | ~ (ordered_pair(v3, v1) = v4) | ~ (relation(v0) = 0) | ? [v5] : ((v5 = 0 & in(v3, v2) = 0) | ( ~ (v5 = 0) & in(v4, v0) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_restriction(v2, v1) = v3) | ~ (in(v0, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : (( ~ (v5 = 0) & relation(v2) = v5) | (( ~ (v4 = 0) | (v7 = 0 & v5 = 0 & cartesian_product2(v1, v1) = v6 & in(v0, v6) = 0 & in(v0, v2) = 0)) & (v4 = 0 | ( ~ (v7 = 0) & cartesian_product2(v1, v1) = v6 & in(v0, v6) = v7) | ( ~ (v5 = 0) & in(v0, v2) = v5))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (fiber(v0, v1) = v2) | ~ (ordered_pair(v3, v1) = v4) | ~ (relation(v0) = 0) | ? [v5] : ((v5 = 0 & ~ (v3 = v1) & in(v4, v0) = 0) | ( ~ (v5 = 0) & in(v3, v2) = 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] : (v3 = 0 | ~ (element(v0, v2) = v3) | ~ (in(v0, v1) = 0) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & powerset(v2) = v4 & element(v1, v4) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v2, v0) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_restriction(v3, v2) = v1) | ~ (relation_restriction(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 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | element(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (fiber(v0, v1) = v2) | ~ (relation(v0) = 0) | ~ (in(v3, v2) = 0) | ? [v4] : (ordered_pair(v3, v1) = v4 & in(v4, v0) = 0)) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (fiber(v1, v2) = v3) | ~ (relation(v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v4 = v2 | ( ~ (v7 = 0) & ordered_pair(v4, v2) = v6 & in(v6, v1) = v7) | ( ~ (v5 = 0) & in(v4, v0) = v5)) & ((v7 = 0 & ~ (v4 = v2) & ordered_pair(v4, v2) = v6 & in(v6, v1) = 0) | (v5 = 0 & in(v4, v0) = 0)))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v1) = v3 & element(v0, v3) = v4)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v0, v1) = v2) | ? [v3] : ((v3 = 0 & empty(v1) = 0) | ( ~ (v3 = 0) & element(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(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] : ( ~ (cartesian_product2(v1, v1) = v2) | ~ (relation(v0) = 0) | ? [v3] : (relation_restriction(v0, v1) = v3 & set_intersection2(v0, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_restriction(v0, v1) = v2) | ~ (relation(v0) = 0) | ? [v3] : (cartesian_product2(v1, v1) = v3 & set_intersection2(v0, v3) = v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_restriction(v0, v1) = v2) | ? [v3] : ((v3 = 0 & relation(v2) = 0) | ( ~ (v3 = 0) & relation(v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (fiber(v0, v1) = v2) | ~ (relation(v0) = 0) | ~ (in(v1, v2) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & ordered_pair(v0, v1) = v3 & unordered_pair(v2, v4) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (empty(v2) = 0) | ~ (in(v0, v1) = 0) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v2) = v3 & element(v1, v3) = v4)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)) & ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1)) & ! [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] : ((v2 = 0 & empty(v1) = 0) | (v2 = 0 & in(v0, v1) = 0))) & ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (powerset(v1) = v2 & element(v0, v2) = 0)) & ! [v0] : ! [v1] : ( ~ (one_to_one(v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & relation(v0) = 0 & function(v0) = 0) | ( ~ (v2 = 0) & relation(v0) = v2) | ( ~ (v2 = 0) & function(v0) = v2) | ( ~ (v2 = 0) & empty(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | element(v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) & ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0)) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ((v2 = 0 & v1 = 0 & one_to_one(v0) = 0 & function(v0) = 0) | ( ~ (v1 = 0) & function(v0) = v1) | ( ~ (v1 = 0) & empty(v0) = v1))) & ! [v0] : ( ~ (function(v0) = 0) | ? [v1] : ? [v2] : ((v2 = 0 & v1 = 0 & one_to_one(v0) = 0 & relation(v0) = 0) | ( ~ (v1 = 0) & relation(v0) = v1) | ( ~ (v1 = 0) & empty(v0) = v1))) & ! [v0] : ( ~ (empty(v0) = 0) | function(v0) = 0) & ! [v0] : ( ~ (empty(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & one_to_one(v0) = 0 & relation(v0) = 0 & function(v0) = 0) | ( ~ (v1 = 0) & relation(v0) = v1) | ( ~ (v1 = 0) & function(v0) = v1))) & ? [v0] : ? [v1] : ? [v2] : element(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : cartesian_product2(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : relation_restriction(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : fiber(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : ordered_pair(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : set_intersection2(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : unordered_pair(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2 & ? [v0] : ? [v1] : powerset(v0) = v1 & ? [v0] : ? [v1] : element(v1, v0) = 0 & ? [v0] : ? [v1] : singleton(v0) = v1 & ? [v0] : ? [v1] : one_to_one(v0) = v1 & ? [v0] : ? [v1] : relation(v0) = v1 & ? [v0] : ? [v1] : function(v0) = v1 & ? [v0] : ? [v1] : empty(v0) = v1
% 9.72/2.91 |
% 9.72/2.91 | Applying alpha-rule on (1) yields:
% 9.72/2.91 | (2) ? [v0] : ? [v1] : ? [v2] : element(v1, v0) = v2
% 9.72/2.91 | (3) ? [v0] : ? [v1] : powerset(v0) = v1
% 9.72/2.91 | (4) ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2))
% 9.72/2.91 | (5) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 9.72/2.91 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_restriction(v2, v1) = v3) | ~ (in(v0, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : (( ~ (v5 = 0) & relation(v2) = v5) | (( ~ (v4 = 0) | (v7 = 0 & v5 = 0 & cartesian_product2(v1, v1) = v6 & in(v0, v6) = 0 & in(v0, v2) = 0)) & (v4 = 0 | ( ~ (v7 = 0) & cartesian_product2(v1, v1) = v6 & in(v0, v6) = v7) | ( ~ (v5 = 0) & in(v0, v2) = v5)))))
% 9.72/2.91 | (7) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3))
% 9.72/2.91 | (8) empty(all_0_4_4) = all_0_3_3
% 9.72/2.92 | (9) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2)
% 9.72/2.92 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2)
% 9.72/2.92 | (11) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v1) = v3 & element(v0, v3) = v4))
% 9.72/2.92 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (fiber(v0, v1) = v2) | ~ (relation(v0) = 0) | ~ (in(v3, v2) = 0) | ? [v4] : (ordered_pair(v3, v1) = v4 & in(v4, v0) = 0))
% 9.72/2.92 | (13) ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2
% 9.72/2.92 | (14) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3))
% 9.72/2.92 | (15) ? [v0] : ? [v1] : function(v0) = v1
% 9.72/2.92 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v1 | ~ (fiber(v0, v1) = v2) | ~ (ordered_pair(v3, v1) = v4) | ~ (relation(v0) = 0) | ? [v5] : ((v5 = 0 & in(v3, v2) = 0) | ( ~ (v5 = 0) & in(v4, v0) = v5)))
% 9.72/2.92 | (17) ! [v0] : ( ~ (empty(v0) = 0) | function(v0) = 0)
% 9.72/2.92 | (18) ? [v0] : ? [v1] : ? [v2] : unordered_pair(v1, v0) = v2
% 9.72/2.92 | (19) empty(all_0_2_2) = 0
% 9.72/2.92 | (20) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1))
% 9.72/2.92 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 9.72/2.92 | (22) relation_restriction(all_0_10_10, all_0_12_12) = all_0_9_9
% 9.72/2.92 | (23) empty(empty_set) = 0
% 9.72/2.92 | (24) relation(all_0_2_2) = 0
% 9.72/2.92 | (25) relation(all_0_5_5) = 0
% 9.72/2.92 | (26) relation(all_0_10_10) = 0
% 9.72/2.92 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_restriction(v3, v2) = v1) | ~ (relation_restriction(v3, v2) = v0))
% 9.72/2.92 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0))
% 9.72/2.92 | (29) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0))
% 9.72/2.92 | (30) ! [v0] : ! [v1] : ! [v2] : ( ~ (empty(v2) = 0) | ~ (in(v0, v1) = 0) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v2) = v3 & element(v1, v3) = v4))
% 9.72/2.92 | (31) ! [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))
% 9.72/2.92 | (32) ? [v0] : ? [v1] : one_to_one(v0) = v1
% 9.72/2.92 | (33) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0))
% 9.72/2.92 | (34) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | subset(v0, v1) = 0)
% 9.72/2.92 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v2, v0) = v4))
% 9.72/2.92 | (36) ? [v0] : ? [v1] : empty(v0) = v1
% 9.72/2.92 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 9.72/2.92 | (38) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 9.72/2.92 | (39) ? [v0] : ? [v1] : ? [v2] : set_intersection2(v1, v0) = v2
% 9.72/2.92 | (40) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ((v2 = 0 & v1 = 0 & one_to_one(v0) = 0 & function(v0) = 0) | ( ~ (v1 = 0) & function(v0) = v1) | ( ~ (v1 = 0) & empty(v0) = v1)))
% 9.72/2.92 | (41) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1))
% 9.72/2.92 | (42) ? [v0] : ? [v1] : element(v1, v0) = 0
% 9.72/2.92 | (43) ! [v0] : ! [v1] : ! [v2] : ( ~ (cartesian_product2(v1, v1) = v2) | ~ (relation(v0) = 0) | ? [v3] : (relation_restriction(v0, v1) = v3 & set_intersection2(v0, v2) = v3))
% 9.72/2.92 | (44) relation(all_0_0_0) = 0
% 9.72/2.92 | (45) ! [v0] : ! [v1] : ( ~ (one_to_one(v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & relation(v0) = 0 & function(v0) = 0) | ( ~ (v2 = 0) & relation(v0) = v2) | ( ~ (v2 = 0) & function(v0) = v2) | ( ~ (v2 = 0) & empty(v0) = v2)))
% 9.72/2.92 | (46) function(all_0_2_2) = 0
% 9.72/2.93 | (47) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0))
% 9.72/2.93 | (48) empty(all_0_1_1) = 0
% 9.72/2.93 | (49) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (powerset(v1) = v2 & element(v0, v2) = 0))
% 9.72/2.93 | (50) function(all_0_0_0) = 0
% 9.72/2.93 | (51) function(all_0_5_5) = 0
% 9.72/2.93 | (52) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0))
% 9.72/2.93 | (53) ? [v0] : ? [v1] : ? [v2] : cartesian_product2(v1, v0) = v2
% 9.72/2.93 | (54) ! [v0] : ! [v1] : ! [v2] : ( ~ (fiber(v0, v1) = v2) | ~ (relation(v0) = 0) | ~ (in(v1, v2) = 0))
% 9.72/2.93 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | element(v0, v2) = 0)
% 9.72/2.93 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = v1 | ~ (fiber(v0, v1) = v2) | ~ (relation(v0) = 0) | ~ (in(v3, v2) = v4) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & ordered_pair(v3, v1) = v5 & in(v5, v0) = v6))
% 9.72/2.93 | (57) ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2
% 9.72/2.93 | (58) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0))
% 9.72/2.93 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 9.72/2.93 | (60) ! [v0] : ! [v1] : ( ~ (element(v0, v1) = 0) | ? [v2] : ((v2 = 0 & empty(v1) = 0) | (v2 = 0 & in(v0, v1) = 0)))
% 9.72/2.93 | (61) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4))
% 9.72/2.93 | (62) ? [v0] : ? [v1] : ? [v2] : relation_restriction(v1, v0) = v2
% 9.72/2.93 | (63) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 9.72/2.93 | (64) ? [v0] : ? [v1] : ? [v2] : ordered_pair(v1, v0) = v2
% 9.72/2.93 | (65) fiber(all_0_10_10, all_0_11_11) = all_0_7_7
% 9.72/2.93 | (66) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | element(v0, v1) = 0)
% 9.72/2.93 | (67) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (fiber(v0, v1) = v2) | ~ (ordered_pair(v3, v1) = v4) | ~ (relation(v0) = 0) | ? [v5] : ((v5 = 0 & ~ (v3 = v1) & in(v4, v0) = 0) | ( ~ (v5 = 0) & in(v3, v2) = v5)))
% 9.72/2.93 | (68) ? [v0] : ? [v1] : relation(v0) = v1
% 9.72/2.93 | (69) ~ (all_0_6_6 = 0)
% 9.72/2.93 | (70) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0))
% 9.72/2.93 | (71) fiber(all_0_9_9, all_0_11_11) = all_0_8_8
% 9.72/2.93 | (72) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0))
% 9.72/2.93 | (73) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & ordered_pair(v0, v1) = v3 & unordered_pair(v2, v4) = v3))
% 9.72/2.93 | (74) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0))
% 9.72/2.93 | (75) ! [v0] : ( ~ (function(v0) = 0) | ? [v1] : ? [v2] : ((v2 = 0 & v1 = 0 & one_to_one(v0) = 0 & relation(v0) = 0) | ( ~ (v1 = 0) & relation(v0) = v1) | ( ~ (v1 = 0) & empty(v0) = v1)))
% 9.72/2.93 | (76) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2)
% 9.72/2.93 | (77) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2)
% 9.72/2.93 | (78) ! [v0] : ! [v1] : (v1 = 0 | ~ (function(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2))
% 9.72/2.93 | (79) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0)
% 9.72/2.93 | (80) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 9.72/2.93 | (81) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1))
% 9.72/2.93 | (82) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0))
% 9.72/2.93 | (83) subset(all_0_8_8, all_0_7_7) = all_0_6_6
% 9.72/2.93 | (84) ~ (all_0_3_3 = 0)
% 9.72/2.93 | (85) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_restriction(v0, v1) = v2) | ~ (relation(v0) = 0) | ? [v3] : (cartesian_product2(v1, v1) = v3 & set_intersection2(v0, v3) = v2))
% 9.72/2.93 | (86) ? [v0] : ? [v1] : ? [v2] : fiber(v1, v0) = v2
% 9.72/2.93 | (87) one_to_one(all_0_5_5) = 0
% 9.72/2.93 | (88) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (element(v0, v2) = v3) | ~ (in(v0, v1) = 0) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & powerset(v2) = v4 & element(v1, v4) = v5))
% 9.72/2.93 | (89) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_restriction(v0, v1) = v2) | ? [v3] : ((v3 = 0 & relation(v2) = 0) | ( ~ (v3 = 0) & relation(v0) = v3)))
% 9.72/2.94 | (90) ! [v0] : ( ~ (empty(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & v1 = 0 & one_to_one(v0) = 0 & relation(v0) = 0 & function(v0) = 0) | ( ~ (v1 = 0) & relation(v0) = v1) | ( ~ (v1 = 0) & function(v0) = v1)))
% 9.72/2.94 | (91) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v0, v1) = v2) | ? [v3] : ((v3 = 0 & empty(v1) = 0) | ( ~ (v3 = 0) & element(v0, v1) = v3)))
% 9.72/2.94 | (92) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (fiber(v3, v2) = v1) | ~ (fiber(v3, v2) = v0))
% 9.72/2.94 | (93) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (fiber(v1, v2) = v3) | ~ (relation(v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v4 = v2 | ( ~ (v7 = 0) & ordered_pair(v4, v2) = v6 & in(v6, v1) = v7) | ( ~ (v5 = 0) & in(v4, v0) = v5)) & ((v7 = 0 & ~ (v4 = v2) & ordered_pair(v4, v2) = v6 & in(v6, v1) = 0) | (v5 = 0 & in(v4, v0) = 0))))
% 9.72/2.94 | (94) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3))
% 9.72/2.94 | (95) ? [v0] : ? [v1] : singleton(v0) = v1
% 9.72/2.94 | (96) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0))
% 9.72/2.94 | (97) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 9.72/2.94 |
% 9.72/2.94 | Instantiating formula (89) with all_0_9_9, all_0_12_12, all_0_10_10 and discharging atoms relation_restriction(all_0_10_10, all_0_12_12) = all_0_9_9, yields:
% 9.72/2.94 | (98) ? [v0] : ((v0 = 0 & relation(all_0_9_9) = 0) | ( ~ (v0 = 0) & relation(all_0_10_10) = v0))
% 9.72/2.94 |
% 9.72/2.94 | Instantiating formula (72) with all_0_6_6, all_0_7_7, all_0_8_8 and discharging atoms subset(all_0_8_8, all_0_7_7) = all_0_6_6, yields:
% 9.72/2.94 | (99) all_0_6_6 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_7_7) = v1 & in(v0, all_0_8_8) = 0)
% 9.72/2.94 |
% 9.72/2.94 | Instantiating (98) with all_51_0_66 yields:
% 9.72/2.94 | (100) (all_51_0_66 = 0 & relation(all_0_9_9) = 0) | ( ~ (all_51_0_66 = 0) & relation(all_0_10_10) = all_51_0_66)
% 9.72/2.94 |
% 9.72/2.94 +-Applying beta-rule and splitting (99), into two cases.
% 9.72/2.94 |-Branch one:
% 9.72/2.94 | (101) all_0_6_6 = 0
% 9.72/2.94 |
% 9.72/2.94 | Equations (101) can reduce 69 to:
% 9.72/2.94 | (102) $false
% 9.72/2.94 |
% 9.72/2.94 |-The branch is then unsatisfiable
% 9.72/2.94 |-Branch two:
% 9.72/2.94 | (69) ~ (all_0_6_6 = 0)
% 9.72/2.94 | (104) ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_7_7) = v1 & in(v0, all_0_8_8) = 0)
% 9.72/2.94 |
% 9.72/2.94 | Instantiating (104) with all_66_0_77, all_66_1_78 yields:
% 9.72/2.94 | (105) ~ (all_66_0_77 = 0) & in(all_66_1_78, all_0_7_7) = all_66_0_77 & in(all_66_1_78, all_0_8_8) = 0
% 9.72/2.94 |
% 9.72/2.94 | Applying alpha-rule on (105) yields:
% 9.72/2.94 | (106) ~ (all_66_0_77 = 0)
% 9.72/2.94 | (107) in(all_66_1_78, all_0_7_7) = all_66_0_77
% 9.72/2.94 | (108) in(all_66_1_78, all_0_8_8) = 0
% 9.72/2.94 |
% 9.72/2.94 +-Applying beta-rule and splitting (100), into two cases.
% 9.72/2.94 |-Branch one:
% 9.72/2.94 | (109) all_51_0_66 = 0 & relation(all_0_9_9) = 0
% 9.72/2.94 |
% 9.72/2.94 | Applying alpha-rule on (109) yields:
% 9.72/2.94 | (110) all_51_0_66 = 0
% 9.72/2.94 | (111) relation(all_0_9_9) = 0
% 9.72/2.94 |
% 9.72/2.94 | Instantiating formula (56) with all_66_0_77, all_66_1_78, all_0_7_7, all_0_11_11, all_0_10_10 and discharging atoms fiber(all_0_10_10, all_0_11_11) = all_0_7_7, relation(all_0_10_10) = 0, in(all_66_1_78, all_0_7_7) = all_66_0_77, yields:
% 9.72/2.94 | (112) all_66_0_77 = 0 | all_66_1_78 = all_0_11_11 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & ordered_pair(all_66_1_78, all_0_11_11) = v0 & in(v0, all_0_10_10) = v1)
% 9.72/2.94 |
% 9.72/2.94 | Instantiating formula (91) with all_66_0_77, all_0_7_7, all_66_1_78 and discharging atoms in(all_66_1_78, all_0_7_7) = all_66_0_77, yields:
% 9.72/2.94 | (113) all_66_0_77 = 0 | ? [v0] : ((v0 = 0 & empty(all_0_7_7) = 0) | ( ~ (v0 = 0) & element(all_66_1_78, all_0_7_7) = v0))
% 9.72/2.94 |
% 9.72/2.94 | Instantiating formula (12) with all_66_1_78, all_0_8_8, all_0_11_11, all_0_9_9 and discharging atoms fiber(all_0_9_9, all_0_11_11) = all_0_8_8, relation(all_0_9_9) = 0, in(all_66_1_78, all_0_8_8) = 0, yields:
% 9.72/2.94 | (114) ? [v0] : (ordered_pair(all_66_1_78, all_0_11_11) = v0 & in(v0, all_0_9_9) = 0)
% 9.72/2.94 |
% 9.72/2.94 | Instantiating (114) with all_100_0_88 yields:
% 9.72/2.94 | (115) ordered_pair(all_66_1_78, all_0_11_11) = all_100_0_88 & in(all_100_0_88, all_0_9_9) = 0
% 9.72/2.94 |
% 9.72/2.94 | Applying alpha-rule on (115) yields:
% 9.72/2.94 | (116) ordered_pair(all_66_1_78, all_0_11_11) = all_100_0_88
% 9.72/2.94 | (117) in(all_100_0_88, all_0_9_9) = 0
% 9.72/2.94 |
% 9.72/2.94 +-Applying beta-rule and splitting (113), into two cases.
% 9.72/2.94 |-Branch one:
% 9.72/2.94 | (118) all_66_0_77 = 0
% 9.72/2.94 |
% 9.72/2.94 | Equations (118) can reduce 106 to:
% 9.72/2.94 | (102) $false
% 9.72/2.94 |
% 9.72/2.94 |-The branch is then unsatisfiable
% 9.72/2.94 |-Branch two:
% 9.72/2.94 | (106) ~ (all_66_0_77 = 0)
% 9.72/2.94 | (121) ? [v0] : ((v0 = 0 & empty(all_0_7_7) = 0) | ( ~ (v0 = 0) & element(all_66_1_78, all_0_7_7) = v0))
% 9.72/2.94 |
% 9.72/2.94 | Instantiating formula (67) with all_100_0_88, all_66_1_78, all_0_8_8, all_0_11_11, all_0_9_9 and discharging atoms fiber(all_0_9_9, all_0_11_11) = all_0_8_8, ordered_pair(all_66_1_78, all_0_11_11) = all_100_0_88, relation(all_0_9_9) = 0, yields:
% 9.72/2.95 | (122) ? [v0] : ((v0 = 0 & ~ (all_66_1_78 = all_0_11_11) & in(all_100_0_88, all_0_9_9) = 0) | ( ~ (v0 = 0) & in(all_66_1_78, all_0_8_8) = v0))
% 9.72/2.95 |
% 9.72/2.95 | Instantiating formula (16) with all_100_0_88, all_66_1_78, all_0_7_7, all_0_11_11, all_0_10_10 and discharging atoms fiber(all_0_10_10, all_0_11_11) = all_0_7_7, ordered_pair(all_66_1_78, all_0_11_11) = all_100_0_88, relation(all_0_10_10) = 0, yields:
% 9.72/2.95 | (123) all_66_1_78 = all_0_11_11 | ? [v0] : ((v0 = 0 & in(all_66_1_78, all_0_7_7) = 0) | ( ~ (v0 = 0) & in(all_100_0_88, all_0_10_10) = v0))
% 9.72/2.95 |
% 9.72/2.95 | Instantiating formula (6) with 0, all_0_9_9, all_0_10_10, all_0_12_12, all_100_0_88 and discharging atoms relation_restriction(all_0_10_10, all_0_12_12) = all_0_9_9, in(all_100_0_88, all_0_9_9) = 0, yields:
% 9.72/2.95 | (124) ? [v0] : ? [v1] : ? [v2] : ((v2 = 0 & v0 = 0 & cartesian_product2(all_0_12_12, all_0_12_12) = v1 & in(all_100_0_88, v1) = 0 & in(all_100_0_88, all_0_10_10) = 0) | ( ~ (v0 = 0) & relation(all_0_10_10) = v0))
% 9.72/2.95 |
% 9.72/2.95 | Instantiating (122) with all_124_0_94 yields:
% 9.72/2.95 | (125) (all_124_0_94 = 0 & ~ (all_66_1_78 = all_0_11_11) & in(all_100_0_88, all_0_9_9) = 0) | ( ~ (all_124_0_94 = 0) & in(all_66_1_78, all_0_8_8) = all_124_0_94)
% 9.72/2.95 |
% 9.72/2.95 | Instantiating (124) with all_136_0_105, all_136_1_106, all_136_2_107 yields:
% 9.72/2.95 | (126) (all_136_0_105 = 0 & all_136_2_107 = 0 & cartesian_product2(all_0_12_12, all_0_12_12) = all_136_1_106 & in(all_100_0_88, all_136_1_106) = 0 & in(all_100_0_88, all_0_10_10) = 0) | ( ~ (all_136_2_107 = 0) & relation(all_0_10_10) = all_136_2_107)
% 9.72/2.95 |
% 9.72/2.95 +-Applying beta-rule and splitting (126), into two cases.
% 9.72/2.95 |-Branch one:
% 9.72/2.95 | (127) all_136_0_105 = 0 & all_136_2_107 = 0 & cartesian_product2(all_0_12_12, all_0_12_12) = all_136_1_106 & in(all_100_0_88, all_136_1_106) = 0 & in(all_100_0_88, all_0_10_10) = 0
% 9.72/2.95 |
% 9.72/2.95 | Applying alpha-rule on (127) yields:
% 9.72/2.95 | (128) all_136_0_105 = 0
% 9.72/2.95 | (129) in(all_100_0_88, all_0_10_10) = 0
% 9.72/2.95 | (130) cartesian_product2(all_0_12_12, all_0_12_12) = all_136_1_106
% 9.72/2.95 | (131) in(all_100_0_88, all_136_1_106) = 0
% 9.72/2.95 | (132) all_136_2_107 = 0
% 9.72/2.95 |
% 9.72/2.95 +-Applying beta-rule and splitting (112), into two cases.
% 9.72/2.95 |-Branch one:
% 9.72/2.95 | (118) all_66_0_77 = 0
% 9.72/2.95 |
% 9.72/2.95 | Equations (118) can reduce 106 to:
% 9.72/2.95 | (102) $false
% 9.72/2.95 |
% 9.72/2.95 |-The branch is then unsatisfiable
% 9.72/2.95 |-Branch two:
% 9.72/2.95 | (106) ~ (all_66_0_77 = 0)
% 9.72/2.95 | (136) all_66_1_78 = all_0_11_11 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & ordered_pair(all_66_1_78, all_0_11_11) = v0 & in(v0, all_0_10_10) = v1)
% 9.72/2.95 |
% 9.72/2.95 +-Applying beta-rule and splitting (125), into two cases.
% 9.72/2.95 |-Branch one:
% 9.72/2.95 | (137) all_124_0_94 = 0 & ~ (all_66_1_78 = all_0_11_11) & in(all_100_0_88, all_0_9_9) = 0
% 9.72/2.95 |
% 9.72/2.95 | Applying alpha-rule on (137) yields:
% 9.72/2.95 | (138) all_124_0_94 = 0
% 9.72/2.95 | (139) ~ (all_66_1_78 = all_0_11_11)
% 9.72/2.95 | (117) in(all_100_0_88, all_0_9_9) = 0
% 9.72/2.95 |
% 9.72/2.95 +-Applying beta-rule and splitting (123), into two cases.
% 9.72/2.95 |-Branch one:
% 9.72/2.95 | (141) all_66_1_78 = all_0_11_11
% 9.72/2.95 |
% 9.72/2.95 | Equations (141) can reduce 139 to:
% 9.72/2.95 | (102) $false
% 9.72/2.95 |
% 9.72/2.95 |-The branch is then unsatisfiable
% 9.72/2.95 |-Branch two:
% 9.72/2.95 | (139) ~ (all_66_1_78 = all_0_11_11)
% 9.72/2.95 | (144) ? [v0] : ((v0 = 0 & in(all_66_1_78, all_0_7_7) = 0) | ( ~ (v0 = 0) & in(all_100_0_88, all_0_10_10) = v0))
% 9.72/2.95 |
% 9.72/2.95 | Instantiating (144) with all_183_0_112 yields:
% 9.72/2.95 | (145) (all_183_0_112 = 0 & in(all_66_1_78, all_0_7_7) = 0) | ( ~ (all_183_0_112 = 0) & in(all_100_0_88, all_0_10_10) = all_183_0_112)
% 9.72/2.95 |
% 9.72/2.95 +-Applying beta-rule and splitting (145), into two cases.
% 9.72/2.95 |-Branch one:
% 9.72/2.95 | (146) all_183_0_112 = 0 & in(all_66_1_78, all_0_7_7) = 0
% 9.72/2.95 |
% 9.72/2.95 | Applying alpha-rule on (146) yields:
% 9.72/2.95 | (147) all_183_0_112 = 0
% 9.72/2.95 | (148) in(all_66_1_78, all_0_7_7) = 0
% 9.72/2.95 |
% 9.72/2.95 | Instantiating formula (21) with all_66_1_78, all_0_7_7, 0, all_66_0_77 and discharging atoms in(all_66_1_78, all_0_7_7) = all_66_0_77, in(all_66_1_78, all_0_7_7) = 0, yields:
% 9.72/2.95 | (118) all_66_0_77 = 0
% 9.72/2.95 |
% 9.72/2.95 | Equations (118) can reduce 106 to:
% 9.72/2.95 | (102) $false
% 9.72/2.95 |
% 9.72/2.95 |-The branch is then unsatisfiable
% 9.72/2.95 |-Branch two:
% 9.72/2.95 | (151) ~ (all_183_0_112 = 0) & in(all_100_0_88, all_0_10_10) = all_183_0_112
% 9.72/2.95 |
% 9.72/2.95 | Applying alpha-rule on (151) yields:
% 9.72/2.95 | (152) ~ (all_183_0_112 = 0)
% 9.72/2.95 | (153) in(all_100_0_88, all_0_10_10) = all_183_0_112
% 9.72/2.95 |
% 9.72/2.95 | Instantiating formula (21) with all_100_0_88, all_0_10_10, 0, all_183_0_112 and discharging atoms in(all_100_0_88, all_0_10_10) = all_183_0_112, in(all_100_0_88, all_0_10_10) = 0, yields:
% 9.72/2.95 | (147) all_183_0_112 = 0
% 9.72/2.95 |
% 9.72/2.95 | Equations (147) can reduce 152 to:
% 9.72/2.95 | (102) $false
% 9.72/2.95 |
% 9.72/2.95 |-The branch is then unsatisfiable
% 9.72/2.95 |-Branch two:
% 9.72/2.95 | (156) ~ (all_124_0_94 = 0) & in(all_66_1_78, all_0_8_8) = all_124_0_94
% 9.72/2.95 |
% 9.72/2.95 | Applying alpha-rule on (156) yields:
% 9.72/2.95 | (157) ~ (all_124_0_94 = 0)
% 9.72/2.95 | (158) in(all_66_1_78, all_0_8_8) = all_124_0_94
% 9.72/2.95 |
% 9.72/2.95 | Instantiating formula (21) with all_66_1_78, all_0_8_8, all_124_0_94, 0 and discharging atoms in(all_66_1_78, all_0_8_8) = all_124_0_94, in(all_66_1_78, all_0_8_8) = 0, yields:
% 9.72/2.95 | (138) all_124_0_94 = 0
% 9.72/2.95 |
% 9.72/2.95 | Equations (138) can reduce 157 to:
% 9.72/2.95 | (102) $false
% 9.72/2.95 |
% 9.72/2.95 |-The branch is then unsatisfiable
% 9.72/2.95 |-Branch two:
% 9.72/2.95 | (161) ~ (all_136_2_107 = 0) & relation(all_0_10_10) = all_136_2_107
% 9.72/2.95 |
% 9.72/2.95 | Applying alpha-rule on (161) yields:
% 9.72/2.95 | (162) ~ (all_136_2_107 = 0)
% 9.72/2.95 | (163) relation(all_0_10_10) = all_136_2_107
% 9.72/2.95 |
% 9.72/2.95 | Instantiating formula (29) with all_0_10_10, all_136_2_107, 0 and discharging atoms relation(all_0_10_10) = all_136_2_107, relation(all_0_10_10) = 0, yields:
% 9.72/2.95 | (132) all_136_2_107 = 0
% 9.72/2.95 |
% 9.72/2.95 | Equations (132) can reduce 162 to:
% 9.72/2.95 | (102) $false
% 9.72/2.95 |
% 9.72/2.95 |-The branch is then unsatisfiable
% 9.72/2.95 |-Branch two:
% 9.72/2.95 | (166) ~ (all_51_0_66 = 0) & relation(all_0_10_10) = all_51_0_66
% 9.72/2.95 |
% 9.72/2.95 | Applying alpha-rule on (166) yields:
% 9.72/2.95 | (167) ~ (all_51_0_66 = 0)
% 9.72/2.95 | (168) relation(all_0_10_10) = all_51_0_66
% 9.72/2.95 |
% 9.72/2.95 | Instantiating formula (29) with all_0_10_10, all_51_0_66, 0 and discharging atoms relation(all_0_10_10) = all_51_0_66, relation(all_0_10_10) = 0, yields:
% 9.72/2.95 | (110) all_51_0_66 = 0
% 9.72/2.95 |
% 9.72/2.95 | Equations (110) can reduce 167 to:
% 9.72/2.95 | (102) $false
% 9.72/2.95 |
% 9.72/2.95 |-The branch is then unsatisfiable
% 9.72/2.95 % SZS output end Proof for theBenchmark
% 9.72/2.95
% 9.72/2.95 2366ms
%------------------------------------------------------------------------------