TSTP Solution File: SEU062+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU062+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n027.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 08:46:25 EDT 2022
% Result : Theorem 5.78s 1.99s
% Output : Proof 8.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU062+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.34 % Computer : n027.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 : Mon Jun 20 01:42:09 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.59 ____ _
% 0.19/0.59 ___ / __ \_____(_)___ ________ __________
% 0.19/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.19/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.19/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.19/0.59
% 0.19/0.59 A Theorem Prover for First-Order Logic
% 0.19/0.59 (ePrincess v.1.0)
% 0.19/0.59
% 0.19/0.59 (c) Philipp Rümmer, 2009-2015
% 0.19/0.59 (c) Peter Backeman, 2014-2015
% 0.19/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.19/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.19/0.59 Bug reports to peter@backeman.se
% 0.19/0.59
% 0.19/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.19/0.59
% 0.19/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.72/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.56/0.95 Prover 0: Preprocessing ...
% 1.97/1.13 Prover 0: Warning: ignoring some quantifiers
% 1.97/1.15 Prover 0: Constructing countermodel ...
% 2.75/1.37 Prover 0: gave up
% 2.75/1.37 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.95/1.40 Prover 1: Preprocessing ...
% 3.54/1.51 Prover 1: Warning: ignoring some quantifiers
% 3.54/1.52 Prover 1: Constructing countermodel ...
% 4.42/1.76 Prover 1: gave up
% 4.42/1.76 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 4.85/1.78 Prover 2: Preprocessing ...
% 5.07/1.87 Prover 2: Warning: ignoring some quantifiers
% 5.07/1.87 Prover 2: Constructing countermodel ...
% 5.78/1.99 Prover 2: proved (226ms)
% 5.78/1.99
% 5.78/1.99 No countermodel exists, formula is valid
% 5.78/1.99 % SZS status Theorem for theBenchmark
% 5.78/1.99
% 5.78/1.99 Generating proof ... Warning: ignoring some quantifiers
% 8.04/2.54 found it (size 32)
% 8.04/2.54
% 8.04/2.54 % SZS output start Proof for theBenchmark
% 8.04/2.54 Assumed formulas after preprocessing and simplification:
% 8.04/2.54 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ( ~ (v9 = 0) & ~ (v7 = 0) & ~ (v3 = 0) & relation_empty_yielding(v4) = 0 & relation_empty_yielding(empty_set) = 0 & relation_rng(v1) = v2 & subset(v0, v2) = v3 & one_to_one(v5) = 0 & relation(v13) = 0 & relation(v12) = 0 & relation(v10) = 0 & relation(v8) = 0 & relation(v5) = 0 & relation(v4) = 0 & relation(v1) = 0 & relation(empty_set) = 0 & function(v13) = 0 & function(v10) = 0 & function(v5) = 0 & empty(v12) = 0 & empty(v11) = 0 & empty(v10) = 0 & empty(v8) = v9 & empty(v6) = v7 & empty(empty_set) = 0 & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = 0 | ~ (powerset(v16) = v17) | ~ (element(v15, v17) = 0) | ~ (element(v14, v16) = v18) | ? [v19] : ( ~ (v19 = 0) & in(v14, v15) = v19)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v17 = 0 | ~ (powerset(v15) = v16) | ~ (element(v14, v16) = v17) | ? [v18] : ( ~ (v18 = 0) & subset(v14, v15) = v18)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v17 = 0 | ~ (element(v14, v16) = v17) | ~ (in(v14, v15) = 0) | ? [v18] : ? [v19] : ( ~ (v19 = 0) & powerset(v16) = v18 & element(v15, v18) = v19)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v17 = 0 | ~ (subset(v14, v15) = 0) | ~ (in(v16, v15) = v17) | ? [v18] : ( ~ (v18 = 0) & in(v16, v14) = v18)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v15 = v14 | ~ (relation_inverse_image(v17, v16) = v15) | ~ (relation_inverse_image(v17, v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v15 = v14 | ~ (element(v17, v16) = v15) | ~ (element(v17, v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v15 = v14 | ~ (subset(v17, v16) = v15) | ~ (subset(v17, v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v15 = v14 | ~ (in(v17, v16) = v15) | ~ (in(v17, v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_inverse_image(v15, v16) = v17) | ~ (singleton(v14) = v16) | ? [v18] : ? [v19] : (( ~ (v18 = 0) & relation(v15) = v18) | (( ~ (v17 = empty_set) | ( ~ (v19 = 0) & relation_rng(v15) = v18 & in(v14, v18) = v19)) & (v17 = empty_set | (v19 = 0 & relation_rng(v15) = v18 & in(v14, v18) = 0))))) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_rng(v15) = v16) | ~ (in(v14, v16) = v17) | ? [v18] : ? [v19] : (( ~ (v18 = 0) & relation(v15) = v18) | (( ~ (v17 = 0) | ( ~ (v19 = empty_set) & relation_inverse_image(v15, v18) = v19 & singleton(v14) = v18)) & (v17 = 0 | (v19 = empty_set & relation_inverse_image(v15, v18) = empty_set & singleton(v14) = v18))))) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (powerset(v16) = v17) | ~ (element(v15, v17) = 0) | ~ (in(v14, v15) = 0) | element(v14, v16) = 0) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (powerset(v16) = v17) | ~ (element(v15, v17) = 0) | ~ (in(v14, v15) = 0) | ? [v18] : ( ~ (v18 = 0) & empty(v16) = v18)) & ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (element(v14, v15) = v16) | ? [v17] : ( ~ (v17 = 0) & in(v14, v15) = v17)) & ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (subset(v14, v15) = v16) | ? [v17] : ? [v18] : ( ~ (v18 = 0) & powerset(v15) = v17 & element(v14, v17) = v18)) & ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (subset(v14, v15) = v16) | ? [v17] : ? [v18] : ( ~ (v18 = 0) & in(v17, v15) = v18 & in(v17, v14) = 0)) & ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (in(v14, v15) = v16) | ? [v17] : ((v17 = 0 & empty(v15) = 0) | ( ~ (v17 = 0) & element(v14, v15) = v17))) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (relation_empty_yielding(v16) = v15) | ~ (relation_empty_yielding(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (relation_rng(v16) = v15) | ~ (relation_rng(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (singleton(v16) = v15) | ~ (singleton(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (powerset(v16) = v15) | ~ (powerset(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (one_to_one(v16) = v15) | ~ (one_to_one(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (relation(v16) = v15) | ~ (relation(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (function(v16) = v15) | ~ (function(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (empty(v16) = v15) | ~ (empty(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : ( ~ (powerset(v15) = v16) | ~ (element(v14, v16) = 0) | subset(v14, v15) = 0) & ! [v14] : ! [v15] : ! [v16] : ( ~ (subset(v14, v15) = 0) | ~ (in(v16, v14) = 0) | in(v16, v15) = 0) & ! [v14] : ! [v15] : ! [v16] : ( ~ (empty(v16) = 0) | ~ (in(v14, v15) = 0) | ? [v17] : ? [v18] : ( ~ (v18 = 0) & powerset(v16) = v17 & element(v15, v17) = v18)) & ! [v14] : ! [v15] : (v15 = v14 | ~ (empty(v15) = 0) | ~ (empty(v14) = 0)) & ! [v14] : ! [v15] : (v15 = 0 | ~ (subset(v14, v14) = v15)) & ! [v14] : ! [v15] : (v15 = 0 | ~ (relation(v14) = v15) | ? [v16] : ( ~ (v16 = 0) & empty(v14) = v16)) & ! [v14] : ! [v15] : (v15 = 0 | ~ (function(v14) = v15) | ? [v16] : ( ~ (v16 = 0) & empty(v14) = v16)) & ! [v14] : ! [v15] : (v15 = 0 | ~ (empty(v14) = v15) | ? [v16] : ? [v17] : ? [v18] : ( ~ (v18 = 0) & powerset(v14) = v16 & element(v17, v16) = 0 & empty(v17) = v18)) & ! [v14] : ! [v15] : (v15 = 0 | ~ (empty(v14) = v15) | ? [v16] : ? [v17] : (( ~ (v17 = 0) & relation_rng(v14) = v16 & empty(v16) = v17) | ( ~ (v16 = 0) & relation(v14) = v16))) & ! [v14] : ! [v15] : ( ~ (relation_rng(v14) = v15) | ? [v16] : ? [v17] : ((v17 = 0 & v16 = 0 & relation(v15) = 0 & empty(v15) = 0) | ( ~ (v16 = 0) & empty(v14) = v16))) & ! [v14] : ! [v15] : ( ~ (relation_rng(v14) = v15) | ? [v16] : ((v16 = 0 & empty(v14) = 0) | ( ~ (v16 = 0) & relation(v14) = v16) | ( ~ (v16 = 0) & empty(v15) = v16))) & ! [v14] : ! [v15] : ( ~ (singleton(v14) = v15) | ? [v16] : ( ~ (v16 = 0) & empty(v15) = v16)) & ! [v14] : ! [v15] : ( ~ (singleton(v14) = v15) | ? [v16] : (( ~ (v16 = empty_set) & relation_inverse_image(v1, v15) = v16) | ( ~ (v16 = 0) & in(v14, v0) = v16))) & ! [v14] : ! [v15] : ( ~ (powerset(v14) = v15) | ? [v16] : ? [v17] : ? [v18] : ((v17 = 0 & ~ (v18 = 0) & element(v16, v15) = 0 & empty(v16) = v18) | (v16 = 0 & empty(v14) = 0))) & ! [v14] : ! [v15] : ( ~ (powerset(v14) = v15) | ? [v16] : ( ~ (v16 = 0) & empty(v15) = v16)) & ! [v14] : ! [v15] : ( ~ (powerset(v14) = v15) | ? [v16] : (element(v16, v15) = 0 & empty(v16) = 0)) & ! [v14] : ! [v15] : ( ~ (element(v14, v15) = 0) | ? [v16] : ((v16 = 0 & empty(v15) = 0) | (v16 = 0 & in(v14, v15) = 0))) & ! [v14] : ! [v15] : ( ~ (subset(v14, v15) = 0) | ? [v16] : (powerset(v15) = v16 & element(v14, v16) = 0)) & ! [v14] : ! [v15] : ( ~ (one_to_one(v14) = v15) | ? [v16] : ? [v17] : ((v17 = 0 & v16 = 0 & v15 = 0 & relation(v14) = 0 & function(v14) = 0) | ( ~ (v16 = 0) & relation(v14) = v16) | ( ~ (v16 = 0) & function(v14) = v16) | ( ~ (v16 = 0) & empty(v14) = v16))) & ! [v14] : ! [v15] : ( ~ (in(v15, v14) = 0) | ? [v16] : ( ~ (v16 = 0) & in(v14, v15) = v16)) & ! [v14] : ! [v15] : ( ~ (in(v14, v15) = 0) | element(v14, v15) = 0) & ! [v14] : ! [v15] : ( ~ (in(v14, v15) = 0) | ? [v16] : ( ~ (v16 = 0) & empty(v15) = v16)) & ! [v14] : ! [v15] : ( ~ (in(v14, v15) = 0) | ? [v16] : ( ~ (v16 = 0) & in(v15, v14) = v16)) & ! [v14] : (v14 = empty_set | ~ (empty(v14) = 0)) & ! [v14] : ( ~ (relation(v14) = 0) | ? [v15] : ? [v16] : ((v16 = 0 & v15 = 0 & one_to_one(v14) = 0 & function(v14) = 0) | ( ~ (v15 = 0) & function(v14) = v15) | ( ~ (v15 = 0) & empty(v14) = v15))) & ! [v14] : ( ~ (relation(v14) = 0) | ? [v15] : ? [v16] : ((v15 = 0 & empty(v14) = 0) | ( ~ (v16 = 0) & relation_rng(v14) = v15 & empty(v15) = v16))) & ! [v14] : ( ~ (function(v14) = 0) | ? [v15] : ? [v16] : ((v16 = 0 & v15 = 0 & one_to_one(v14) = 0 & relation(v14) = 0) | ( ~ (v15 = 0) & relation(v14) = v15) | ( ~ (v15 = 0) & empty(v14) = v15))) & ! [v14] : ( ~ (empty(v14) = 0) | relation(v14) = 0) & ! [v14] : ( ~ (empty(v14) = 0) | function(v14) = 0) & ! [v14] : ( ~ (empty(v14) = 0) | ? [v15] : ? [v16] : ? [v17] : ((v17 = 0 & v16 = 0 & v15 = 0 & one_to_one(v14) = 0 & relation(v14) = 0 & function(v14) = 0) | ( ~ (v15 = 0) & relation(v14) = v15) | ( ~ (v15 = 0) & function(v14) = v15))) & ! [v14] : ( ~ (empty(v14) = 0) | ? [v15] : (relation_rng(v14) = v15 & relation(v15) = 0 & empty(v15) = 0)) & ! [v14] : ( ~ (in(v14, v0) = 0) | ? [v15] : ? [v16] : ( ~ (v16 = empty_set) & relation_inverse_image(v1, v15) = v16 & singleton(v14) = v15)) & ? [v14] : ? [v15] : ? [v16] : relation_inverse_image(v15, v14) = v16 & ? [v14] : ? [v15] : ? [v16] : element(v15, v14) = v16 & ? [v14] : ? [v15] : ? [v16] : subset(v15, v14) = v16 & ? [v14] : ? [v15] : ? [v16] : in(v15, v14) = v16 & ? [v14] : ? [v15] : relation_empty_yielding(v14) = v15 & ? [v14] : ? [v15] : relation_rng(v14) = v15 & ? [v14] : ? [v15] : singleton(v14) = v15 & ? [v14] : ? [v15] : powerset(v14) = v15 & ? [v14] : ? [v15] : element(v15, v14) = 0 & ? [v14] : ? [v15] : one_to_one(v14) = v15 & ? [v14] : ? [v15] : relation(v14) = v15 & ? [v14] : ? [v15] : function(v14) = v15 & ? [v14] : ? [v15] : empty(v14) = v15)
% 8.43/2.59 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9, all_0_10_10, all_0_11_11, all_0_12_12, all_0_13_13 yields:
% 8.43/2.59 | (1) ~ (all_0_4_4 = 0) & ~ (all_0_6_6 = 0) & ~ (all_0_10_10 = 0) & relation_empty_yielding(all_0_9_9) = 0 & relation_empty_yielding(empty_set) = 0 & relation_rng(all_0_12_12) = all_0_11_11 & subset(all_0_13_13, all_0_11_11) = all_0_10_10 & one_to_one(all_0_8_8) = 0 & relation(all_0_0_0) = 0 & relation(all_0_1_1) = 0 & relation(all_0_3_3) = 0 & relation(all_0_5_5) = 0 & relation(all_0_8_8) = 0 & relation(all_0_9_9) = 0 & relation(all_0_12_12) = 0 & relation(empty_set) = 0 & function(all_0_0_0) = 0 & function(all_0_3_3) = 0 & function(all_0_8_8) = 0 & empty(all_0_1_1) = 0 & empty(all_0_2_2) = 0 & empty(all_0_3_3) = 0 & empty(all_0_5_5) = all_0_4_4 & empty(all_0_7_7) = all_0_6_6 & 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] : (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 | ~ (relation_inverse_image(v3, v2) = v1) | ~ (relation_inverse_image(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_inverse_image(v1, v2) = v3) | ~ (singleton(v0) = v2) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & relation(v1) = v4) | (( ~ (v3 = empty_set) | ( ~ (v5 = 0) & relation_rng(v1) = v4 & in(v0, v4) = v5)) & (v3 = empty_set | (v5 = 0 & relation_rng(v1) = v4 & in(v0, v4) = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng(v1) = v2) | ~ (in(v0, v2) = v3) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & relation(v1) = v4) | (( ~ (v3 = 0) | ( ~ (v5 = empty_set) & relation_inverse_image(v1, v4) = v5 & singleton(v0) = v4)) & (v3 = 0 | (v5 = empty_set & relation_inverse_image(v1, v4) = empty_set & singleton(v0) = v4))))) & ! [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 | ~ (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 | ~ (relation_empty_yielding(v2) = v1) | ~ (relation_empty_yielding(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(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] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0) & ! [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 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (relation(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (function(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (empty(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v0) = v2 & element(v3, v2) = 0 & empty(v3) = v4)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (empty(v0) = v1) | ? [v2] : ? [v3] : (( ~ (v3 = 0) & relation_rng(v0) = v2 & empty(v2) = v3) | ( ~ (v2 = 0) & relation(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & relation(v1) = 0 & empty(v1) = 0) | ( ~ (v2 = 0) & empty(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ((v2 = 0 & empty(v0) = 0) | ( ~ (v2 = 0) & relation(v0) = v2) | ( ~ (v2 = 0) & empty(v1) = v2))) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ? [v2] : (( ~ (v2 = empty_set) & relation_inverse_image(all_0_12_12, v1) = v2) | ( ~ (v2 = 0) & in(v0, all_0_13_13) = v2))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v3 = 0 & ~ (v4 = 0) & element(v2, v1) = 0 & empty(v2) = v4) | (v2 = 0 & empty(v0) = 0))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) = 0 & empty(v2) = 0)) & ! [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] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ((v1 = 0 & empty(v0) = 0) | ( ~ (v2 = 0) & relation_rng(v0) = v1 & empty(v1) = v2))) & ! [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) | relation(v0) = 0) & ! [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] : ( ~ (empty(v0) = 0) | ? [v1] : (relation_rng(v0) = v1 & relation(v1) = 0 & empty(v1) = 0)) & ! [v0] : ( ~ (in(v0, all_0_13_13) = 0) | ? [v1] : ? [v2] : ( ~ (v2 = empty_set) & relation_inverse_image(all_0_12_12, v1) = v2 & singleton(v0) = v1)) & ? [v0] : ? [v1] : ? [v2] : relation_inverse_image(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : element(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2 & ? [v0] : ? [v1] : relation_empty_yielding(v0) = v1 & ? [v0] : ? [v1] : relation_rng(v0) = v1 & ? [v0] : ? [v1] : singleton(v0) = v1 & ? [v0] : ? [v1] : powerset(v0) = v1 & ? [v0] : ? [v1] : element(v1, v0) = 0 & ? [v0] : ? [v1] : one_to_one(v0) = v1 & ? [v0] : ? [v1] : relation(v0) = v1 & ? [v0] : ? [v1] : function(v0) = v1 & ? [v0] : ? [v1] : empty(v0) = v1
% 8.43/2.61 |
% 8.43/2.61 | Applying alpha-rule on (1) yields:
% 8.43/2.61 | (2) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ? [v2] : (( ~ (v2 = empty_set) & relation_inverse_image(all_0_12_12, v1) = v2) | ( ~ (v2 = 0) & in(v0, all_0_13_13) = v2)))
% 8.43/2.61 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4))
% 8.43/2.61 | (4) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0))
% 8.43/2.61 | (5) function(all_0_0_0) = 0
% 8.43/2.61 | (6) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3))
% 8.43/2.61 | (7) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 8.43/2.61 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0)
% 8.43/2.61 | (9) ! [v0] : ( ~ (empty(v0) = 0) | ? [v1] : (relation_rng(v0) = v1 & relation(v1) = 0 & empty(v1) = 0))
% 8.43/2.61 | (10) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1))
% 8.43/2.61 | (11) relation_rng(all_0_12_12) = all_0_11_11
% 8.43/2.61 | (12) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ((v1 = 0 & empty(v0) = 0) | ( ~ (v2 = 0) & relation_rng(v0) = v1 & empty(v1) = v2)))
% 8.43/2.61 | (13) ! [v0] : ( ~ (empty(v0) = 0) | relation(v0) = 0)
% 8.43/2.61 | (14) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0))
% 8.43/2.61 | (15) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ((v2 = 0 & empty(v0) = 0) | ( ~ (v2 = 0) & relation(v0) = v2) | ( ~ (v2 = 0) & empty(v1) = v2)))
% 8.43/2.61 | (16) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 8.43/2.61 | (17) ? [v0] : ? [v1] : relation(v0) = v1
% 8.43/2.61 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | element(v0, v2) = 0)
% 8.43/2.61 | (19) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0))
% 8.43/2.61 | (20) ! [v0] : ! [v1] : (v1 = 0 | ~ (empty(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v0) = v2 & element(v3, v2) = 0 & empty(v3) = v4))
% 8.43/2.61 | (21) relation(empty_set) = 0
% 8.43/2.61 | (22) ! [v0] : ! [v1] : (v1 = 0 | ~ (function(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2))
% 8.43/2.61 | (23) ! [v0] : ! [v1] : ( ~ (element(v0, v1) = 0) | ? [v2] : ((v2 = 0 & empty(v1) = 0) | (v2 = 0 & in(v0, v1) = 0)))
% 8.43/2.61 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng(v1) = v2) | ~ (in(v0, v2) = v3) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & relation(v1) = v4) | (( ~ (v3 = 0) | ( ~ (v5 = empty_set) & relation_inverse_image(v1, v4) = v5 & singleton(v0) = v4)) & (v3 = 0 | (v5 = empty_set & relation_inverse_image(v1, v4) = empty_set & singleton(v0) = v4)))))
% 8.43/2.61 | (25) relation_empty_yielding(empty_set) = 0
% 8.43/2.61 | (26) empty(all_0_1_1) = 0
% 8.43/2.61 | (27) ! [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)))
% 8.43/2.61 | (28) ? [v0] : ? [v1] : one_to_one(v0) = v1
% 8.43/2.61 | (29) ! [v0] : ! [v1] : ! [v2] : ( ~ (empty(v2) = 0) | ~ (in(v0, v1) = 0) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v2) = v3 & element(v1, v3) = v4))
% 8.43/2.62 | (30) ? [v0] : ? [v1] : relation_rng(v0) = v1
% 8.43/2.62 | (31) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & relation(v1) = 0 & empty(v1) = 0) | ( ~ (v2 = 0) & empty(v0) = v2)))
% 8.43/2.62 | (32) ! [v0] : ( ~ (in(v0, all_0_13_13) = 0) | ? [v1] : ? [v2] : ( ~ (v2 = empty_set) & relation_inverse_image(all_0_12_12, v1) = v2 & singleton(v0) = v1))
% 8.43/2.62 | (33) empty(empty_set) = 0
% 8.43/2.62 | (34) ~ (all_0_4_4 = 0)
% 8.43/2.62 | (35) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0))
% 8.43/2.62 | (36) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | subset(v0, v1) = 0)
% 8.43/2.62 | (37) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v3 = 0 & ~ (v4 = 0) & element(v2, v1) = 0 & empty(v2) = v4) | (v2 = 0 & empty(v0) = 0)))
% 8.43/2.62 | (38) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0))
% 8.43/2.62 | (39) ? [v0] : ? [v1] : relation_empty_yielding(v0) = v1
% 8.43/2.62 | (40) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0))
% 8.43/2.62 | (41) relation(all_0_12_12) = 0
% 8.43/2.62 | (42) ~ (all_0_6_6 = 0)
% 8.43/2.62 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 8.43/2.62 | (44) ? [v0] : ? [v1] : powerset(v0) = v1
% 8.43/2.62 | (45) ? [v0] : ? [v1] : ? [v2] : relation_inverse_image(v1, v0) = v2
% 8.43/2.62 | (46) ~ (all_0_10_10 = 0)
% 8.43/2.62 | (47) ! [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))
% 8.43/2.62 | (48) ? [v0] : ? [v1] : empty(v0) = v1
% 8.43/2.62 | (49) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 8.43/2.62 | (50) empty(all_0_5_5) = all_0_4_4
% 8.43/2.62 | (51) relation(all_0_9_9) = 0
% 8.43/2.62 | (52) empty(all_0_2_2) = 0
% 8.43/2.62 | (53) ! [v0] : ! [v1] : (v1 = 0 | ~ (relation(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2))
% 8.43/2.62 | (54) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) = 0 & empty(v2) = 0))
% 8.43/2.62 | (55) ? [v0] : ? [v1] : ? [v2] : element(v1, v0) = v2
% 8.43/2.62 | (56) ? [v0] : ? [v1] : singleton(v0) = v1
% 8.43/2.62 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_inverse_image(v1, v2) = v3) | ~ (singleton(v0) = v2) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & relation(v1) = v4) | (( ~ (v3 = empty_set) | ( ~ (v5 = 0) & relation_rng(v1) = v4 & in(v0, v4) = v5)) & (v3 = empty_set | (v5 = 0 & relation_rng(v1) = v4 & in(v0, v4) = 0)))))
% 8.43/2.62 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0))
% 8.43/2.62 | (59) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0))
% 8.43/2.62 | (60) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_empty_yielding(v2) = v1) | ~ (relation_empty_yielding(v2) = v0))
% 8.43/2.62 | (61) ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2
% 8.43/2.62 | (62) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 8.43/2.62 | (63) relation(all_0_3_3) = 0
% 8.43/2.62 | (64) ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2
% 8.43/2.62 | (65) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 8.43/2.62 | (66) ! [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)))
% 8.43/2.63 | (67) relation(all_0_8_8) = 0
% 8.43/2.63 | (68) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_inverse_image(v3, v2) = v1) | ~ (relation_inverse_image(v3, v2) = v0))
% 8.43/2.63 | (69) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v0, v1) = v2) | ? [v3] : ((v3 = 0 & empty(v1) = 0) | ( ~ (v3 = 0) & element(v0, v1) = v3)))
% 8.43/2.63 | (70) relation(all_0_5_5) = 0
% 8.43/2.63 | (71) relation_empty_yielding(all_0_9_9) = 0
% 8.43/2.63 | (72) ! [v0] : ( ~ (empty(v0) = 0) | function(v0) = 0)
% 8.43/2.63 | (73) relation(all_0_1_1) = 0
% 8.43/2.63 | (74) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v2, v0) = v4))
% 8.43/2.63 | (75) ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2))
% 8.43/2.63 | (76) ! [v0] : ! [v1] : (v1 = 0 | ~ (empty(v0) = v1) | ? [v2] : ? [v3] : (( ~ (v3 = 0) & relation_rng(v0) = v2 & empty(v2) = v3) | ( ~ (v2 = 0) & relation(v0) = v2)))
% 8.43/2.63 | (77) relation(all_0_0_0) = 0
% 8.43/2.63 | (78) ? [v0] : ? [v1] : function(v0) = v1
% 8.43/2.63 | (79) empty(all_0_3_3) = 0
% 8.43/2.63 | (80) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (powerset(v1) = v2 & element(v0, v2) = 0))
% 8.43/2.63 | (81) function(all_0_8_8) = 0
% 8.43/2.63 | (82) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0))
% 8.43/2.63 | (83) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 8.43/2.63 | (84) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 8.43/2.63 | (85) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v1) = v3 & element(v0, v3) = v4))
% 8.43/2.63 | (86) ! [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)))
% 8.43/2.63 | (87) ? [v0] : ? [v1] : element(v1, v0) = 0
% 8.43/2.63 | (88) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 8.43/2.63 | (89) ! [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)))
% 8.43/2.63 | (90) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | element(v0, v1) = 0)
% 8.43/2.63 | (91) ! [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))
% 8.43/2.63 | (92) one_to_one(all_0_8_8) = 0
% 8.43/2.63 | (93) function(all_0_3_3) = 0
% 8.43/2.63 | (94) subset(all_0_13_13, all_0_11_11) = all_0_10_10
% 8.43/2.63 | (95) empty(all_0_7_7) = all_0_6_6
% 8.43/2.63 |
% 8.43/2.63 | Instantiating formula (35) with all_0_10_10, all_0_11_11, all_0_13_13 and discharging atoms subset(all_0_13_13, all_0_11_11) = all_0_10_10, yields:
% 8.43/2.63 | (96) all_0_10_10 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_11_11) = v1 & in(v0, all_0_13_13) = 0)
% 8.43/2.64 |
% 8.43/2.64 +-Applying beta-rule and splitting (96), into two cases.
% 8.43/2.64 |-Branch one:
% 8.43/2.64 | (97) all_0_10_10 = 0
% 8.43/2.64 |
% 8.43/2.64 | Equations (97) can reduce 46 to:
% 8.43/2.64 | (98) $false
% 8.43/2.64 |
% 8.43/2.64 |-The branch is then unsatisfiable
% 8.43/2.64 |-Branch two:
% 8.43/2.64 | (46) ~ (all_0_10_10 = 0)
% 8.43/2.64 | (100) ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_11_11) = v1 & in(v0, all_0_13_13) = 0)
% 8.43/2.64 |
% 8.43/2.64 | Instantiating (100) with all_67_0_84, all_67_1_85 yields:
% 8.43/2.64 | (101) ~ (all_67_0_84 = 0) & in(all_67_1_85, all_0_11_11) = all_67_0_84 & in(all_67_1_85, all_0_13_13) = 0
% 8.43/2.64 |
% 8.43/2.64 | Applying alpha-rule on (101) yields:
% 8.43/2.64 | (102) ~ (all_67_0_84 = 0)
% 8.43/2.64 | (103) in(all_67_1_85, all_0_11_11) = all_67_0_84
% 8.43/2.64 | (104) in(all_67_1_85, all_0_13_13) = 0
% 8.43/2.64 |
% 8.43/2.64 | Instantiating formula (24) with all_67_0_84, all_0_11_11, all_0_12_12, all_67_1_85 and discharging atoms relation_rng(all_0_12_12) = all_0_11_11, in(all_67_1_85, all_0_11_11) = all_67_0_84, yields:
% 8.43/2.64 | (105) ? [v0] : ? [v1] : (( ~ (v0 = 0) & relation(all_0_12_12) = v0) | (( ~ (all_67_0_84 = 0) | ( ~ (v1 = empty_set) & relation_inverse_image(all_0_12_12, v0) = v1 & singleton(all_67_1_85) = v0)) & (all_67_0_84 = 0 | (v1 = empty_set & relation_inverse_image(all_0_12_12, v0) = empty_set & singleton(all_67_1_85) = v0))))
% 8.43/2.64 |
% 8.43/2.64 | Instantiating formula (69) with all_67_0_84, all_0_11_11, all_67_1_85 and discharging atoms in(all_67_1_85, all_0_11_11) = all_67_0_84, yields:
% 8.43/2.64 | (106) all_67_0_84 = 0 | ? [v0] : ((v0 = 0 & empty(all_0_11_11) = 0) | ( ~ (v0 = 0) & element(all_67_1_85, all_0_11_11) = v0))
% 8.43/2.64 |
% 8.43/2.64 | Instantiating formula (32) with all_67_1_85 and discharging atoms in(all_67_1_85, all_0_13_13) = 0, yields:
% 8.43/2.64 | (107) ? [v0] : ? [v1] : ( ~ (v1 = empty_set) & relation_inverse_image(all_0_12_12, v0) = v1 & singleton(all_67_1_85) = v0)
% 8.43/2.64 |
% 8.43/2.64 | Instantiating (107) with all_140_0_111, all_140_1_112 yields:
% 8.43/2.64 | (108) ~ (all_140_0_111 = empty_set) & relation_inverse_image(all_0_12_12, all_140_1_112) = all_140_0_111 & singleton(all_67_1_85) = all_140_1_112
% 8.43/2.64 |
% 8.43/2.64 | Applying alpha-rule on (108) yields:
% 8.43/2.64 | (109) ~ (all_140_0_111 = empty_set)
% 8.43/2.64 | (110) relation_inverse_image(all_0_12_12, all_140_1_112) = all_140_0_111
% 8.43/2.64 | (111) singleton(all_67_1_85) = all_140_1_112
% 8.43/2.64 |
% 8.43/2.64 | Instantiating (105) with all_142_0_113, all_142_1_114 yields:
% 8.43/2.64 | (112) ( ~ (all_142_1_114 = 0) & relation(all_0_12_12) = all_142_1_114) | (( ~ (all_67_0_84 = 0) | ( ~ (all_142_0_113 = empty_set) & relation_inverse_image(all_0_12_12, all_142_1_114) = all_142_0_113 & singleton(all_67_1_85) = all_142_1_114)) & (all_67_0_84 = 0 | (all_142_0_113 = empty_set & relation_inverse_image(all_0_12_12, all_142_1_114) = empty_set & singleton(all_67_1_85) = all_142_1_114)))
% 8.43/2.64 |
% 8.43/2.64 +-Applying beta-rule and splitting (112), into two cases.
% 8.43/2.64 |-Branch one:
% 8.43/2.64 | (113) ~ (all_142_1_114 = 0) & relation(all_0_12_12) = all_142_1_114
% 8.43/2.64 |
% 8.43/2.64 | Applying alpha-rule on (113) yields:
% 8.43/2.64 | (114) ~ (all_142_1_114 = 0)
% 8.43/2.64 | (115) relation(all_0_12_12) = all_142_1_114
% 8.43/2.64 |
% 8.43/2.64 | Instantiating formula (19) with all_0_12_12, all_142_1_114, 0 and discharging atoms relation(all_0_12_12) = all_142_1_114, relation(all_0_12_12) = 0, yields:
% 8.43/2.64 | (116) all_142_1_114 = 0
% 8.43/2.64 |
% 8.43/2.64 | Equations (116) can reduce 114 to:
% 8.43/2.64 | (98) $false
% 8.43/2.64 |
% 8.43/2.64 |-The branch is then unsatisfiable
% 8.43/2.64 |-Branch two:
% 8.43/2.64 | (118) ( ~ (all_67_0_84 = 0) | ( ~ (all_142_0_113 = empty_set) & relation_inverse_image(all_0_12_12, all_142_1_114) = all_142_0_113 & singleton(all_67_1_85) = all_142_1_114)) & (all_67_0_84 = 0 | (all_142_0_113 = empty_set & relation_inverse_image(all_0_12_12, all_142_1_114) = empty_set & singleton(all_67_1_85) = all_142_1_114))
% 8.43/2.64 |
% 8.43/2.64 | Applying alpha-rule on (118) yields:
% 8.43/2.64 | (119) ~ (all_67_0_84 = 0) | ( ~ (all_142_0_113 = empty_set) & relation_inverse_image(all_0_12_12, all_142_1_114) = all_142_0_113 & singleton(all_67_1_85) = all_142_1_114)
% 8.43/2.64 | (120) all_67_0_84 = 0 | (all_142_0_113 = empty_set & relation_inverse_image(all_0_12_12, all_142_1_114) = empty_set & singleton(all_67_1_85) = all_142_1_114)
% 8.43/2.64 |
% 8.43/2.64 +-Applying beta-rule and splitting (106), into two cases.
% 8.43/2.64 |-Branch one:
% 8.43/2.64 | (121) all_67_0_84 = 0
% 8.43/2.64 |
% 8.43/2.64 | Equations (121) can reduce 102 to:
% 8.43/2.64 | (98) $false
% 8.43/2.64 |
% 8.43/2.64 |-The branch is then unsatisfiable
% 8.43/2.64 |-Branch two:
% 8.43/2.64 | (102) ~ (all_67_0_84 = 0)
% 8.43/2.64 | (124) ? [v0] : ((v0 = 0 & empty(all_0_11_11) = 0) | ( ~ (v0 = 0) & element(all_67_1_85, all_0_11_11) = v0))
% 8.43/2.64 |
% 8.43/2.64 +-Applying beta-rule and splitting (120), into two cases.
% 8.43/2.64 |-Branch one:
% 8.43/2.64 | (121) all_67_0_84 = 0
% 8.43/2.64 |
% 8.43/2.64 | Equations (121) can reduce 102 to:
% 8.43/2.64 | (98) $false
% 8.43/2.64 |
% 8.43/2.64 |-The branch is then unsatisfiable
% 8.43/2.64 |-Branch two:
% 8.43/2.64 | (102) ~ (all_67_0_84 = 0)
% 8.43/2.64 | (128) all_142_0_113 = empty_set & relation_inverse_image(all_0_12_12, all_142_1_114) = empty_set & singleton(all_67_1_85) = all_142_1_114
% 8.43/2.64 |
% 8.43/2.64 | Applying alpha-rule on (128) yields:
% 8.43/2.64 | (129) all_142_0_113 = empty_set
% 8.43/2.64 | (130) relation_inverse_image(all_0_12_12, all_142_1_114) = empty_set
% 8.43/2.64 | (131) singleton(all_67_1_85) = all_142_1_114
% 8.43/2.64 |
% 8.43/2.64 | Instantiating formula (7) with all_67_1_85, all_140_1_112, all_142_1_114 and discharging atoms singleton(all_67_1_85) = all_142_1_114, singleton(all_67_1_85) = all_140_1_112, yields:
% 8.43/2.65 | (132) all_142_1_114 = all_140_1_112
% 8.43/2.65 |
% 8.43/2.65 | From (132) and (130) follows:
% 8.43/2.65 | (133) relation_inverse_image(all_0_12_12, all_140_1_112) = empty_set
% 8.43/2.65 |
% 8.43/2.65 | Instantiating formula (68) with all_0_12_12, all_140_1_112, empty_set, all_140_0_111 and discharging atoms relation_inverse_image(all_0_12_12, all_140_1_112) = all_140_0_111, relation_inverse_image(all_0_12_12, all_140_1_112) = empty_set, yields:
% 8.43/2.65 | (134) all_140_0_111 = empty_set
% 8.43/2.65 |
% 8.43/2.65 | Equations (134) can reduce 109 to:
% 8.43/2.65 | (98) $false
% 8.43/2.65 |
% 8.43/2.65 |-The branch is then unsatisfiable
% 8.43/2.65 % SZS output end Proof for theBenchmark
% 8.43/2.65
% 8.43/2.65 2045ms
%------------------------------------------------------------------------------