TSTP Solution File: NUM383+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : NUM383+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n007.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 : Mon Jul 18 08:44:04 EDT 2022
% Result : Theorem 4.61s 1.78s
% Output : Proof 6.32s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM383+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n007.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 : Thu Jul 7 00:22:29 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.48/0.57 ____ _
% 0.48/0.57 ___ / __ \_____(_)___ ________ __________
% 0.48/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.48/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.48/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.48/0.57
% 0.48/0.57 A Theorem Prover for First-Order Logic
% 0.48/0.57 (ePrincess v.1.0)
% 0.48/0.57
% 0.48/0.57 (c) Philipp Rümmer, 2009-2015
% 0.48/0.57 (c) Peter Backeman, 2014-2015
% 0.48/0.57 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.48/0.57 Free software under GNU Lesser General Public License (LGPL).
% 0.48/0.57 Bug reports to peter@backeman.se
% 0.48/0.57
% 0.48/0.57 For more information, visit http://user.uu.se/~petba168/breu/
% 0.48/0.57
% 0.48/0.57 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.48/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.35/0.92 Prover 0: Preprocessing ...
% 1.75/1.05 Prover 0: Warning: ignoring some quantifiers
% 1.93/1.07 Prover 0: Constructing countermodel ...
% 2.48/1.24 Prover 0: gave up
% 2.48/1.24 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.48/1.26 Prover 1: Preprocessing ...
% 2.92/1.36 Prover 1: Warning: ignoring some quantifiers
% 3.00/1.37 Prover 1: Constructing countermodel ...
% 3.58/1.56 Prover 1: gave up
% 3.58/1.56 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 3.78/1.58 Prover 2: Preprocessing ...
% 4.18/1.67 Prover 2: Warning: ignoring some quantifiers
% 4.18/1.67 Prover 2: Constructing countermodel ...
% 4.61/1.78 Prover 2: proved (213ms)
% 4.61/1.78
% 4.61/1.78 No countermodel exists, formula is valid
% 4.61/1.78 % SZS status Theorem for theBenchmark
% 4.61/1.78
% 4.61/1.78 Generating proof ... Warning: ignoring some quantifiers
% 6.00/2.05 found it (size 23)
% 6.00/2.05
% 6.00/2.05 % SZS output start Proof for theBenchmark
% 6.00/2.05 Assumed formulas after preprocessing and simplification:
% 6.00/2.05 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ( ~ (v9 = 0) & ~ (v7 = 0) & subset(v1, v0) = 0 & relation_non_empty(v2) = 0 & relation_empty_yielding(v4) = 0 & relation_empty_yielding(v3) = 0 & relation_empty_yielding(empty_set) = 0 & one_to_one(v5) = 0 & relation(v13) = 0 & relation(v12) = 0 & relation(v10) = 0 & relation(v8) = 0 & relation(v5) = 0 & relation(v4) = 0 & relation(v3) = 0 & relation(v2) = 0 & relation(empty_set) = 0 & function(v13) = 0 & function(v10) = 0 & function(v5) = 0 & function(v3) = 0 & function(v2) = 0 & empty(v12) = 0 & empty(v11) = 0 & empty(v10) = 0 & empty(v8) = v9 & empty(v6) = v7 & empty(empty_set) = 0 & in(v0, v1) = 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] : (v15 = v14 | ~ (subset(v17, v16) = v15) | ~ (subset(v17, v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v15 = v14 | ~ (element(v17, v16) = v15) | ~ (element(v17, v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v15 = v14 | ~ (in(v17, v16) = v15) | ~ (in(v17, v16) = v14)) & ! [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 | ~ (subset(v14, v15) = v16) | ? [v17] : ? [v18] : ( ~ (v18 = 0) & powerset(v15) = v17 & element(v14, v17) = v18)) & ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (element(v14, v15) = v16) | ? [v17] : ( ~ (v17 = 0) & in(v14, v15) = v17)) & ! [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 | ~ (powerset(v16) = v15) | ~ (powerset(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (relation_non_empty(v16) = v15) | ~ (relation_non_empty(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (relation_empty_yielding(v16) = v15) | ~ (relation_empty_yielding(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] : ( ~ (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] : ( ~ (subset(v14, v15) = 0) | ? [v16] : (powerset(v15) = v16 & element(v14, v16) = 0)) & ! [v14] : ! [v15] : ( ~ (element(v14, v15) = 0) | ? [v16] : ((v16 = 0 & empty(v15) = 0) | (v16 = 0 & in(v14, v15) = 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] : ( ~ (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] : ? [v15] : ? [v16] : subset(v15, v14) = v16 & ? [v14] : ? [v15] : ? [v16] : element(v15, v14) = v16 & ? [v14] : ? [v15] : ? [v16] : in(v15, v14) = v16 & ? [v14] : ? [v15] : powerset(v14) = v15 & ? [v14] : ? [v15] : relation_non_empty(v14) = v15 & ? [v14] : ? [v15] : relation_empty_yielding(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)
% 6.00/2.09 | 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:
% 6.00/2.09 | (1) ~ (all_0_4_4 = 0) & ~ (all_0_6_6 = 0) & subset(all_0_12_12, all_0_13_13) = 0 & relation_non_empty(all_0_11_11) = 0 & relation_empty_yielding(all_0_9_9) = 0 & relation_empty_yielding(all_0_10_10) = 0 & relation_empty_yielding(empty_set) = 0 & 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_10_10) = 0 & relation(all_0_11_11) = 0 & relation(empty_set) = 0 & function(all_0_0_0) = 0 & function(all_0_3_3) = 0 & function(all_0_8_8) = 0 & function(all_0_10_10) = 0 & function(all_0_11_11) = 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 & in(all_0_13_13, all_0_12_12) = 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] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | element(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v1) = v3 & element(v0, v3) = v4)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v0, v1) = v2) | ? [v3] : ((v3 = 0 & empty(v1) = 0) | ( ~ (v3 = 0) & element(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_non_empty(v2) = v1) | ~ (relation_non_empty(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_empty_yielding(v2) = v1) | ~ (relation_empty_yielding(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] : ( ~ (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] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (powerset(v1) = v2 & element(v0, v2) = 0)) & ! [v0] : ! [v1] : ( ~ (element(v0, v1) = 0) | ? [v2] : ((v2 = 0 & empty(v1) = 0) | (v2 = 0 & in(v0, v1) = 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) | 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] : ? [v1] : ? [v2] : subset(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : element(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2 & ? [v0] : ? [v1] : powerset(v0) = v1 & ? [v0] : ? [v1] : relation_non_empty(v0) = v1 & ? [v0] : ? [v1] : relation_empty_yielding(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
% 6.00/2.10 |
% 6.00/2.10 | Applying alpha-rule on (1) yields:
% 6.00/2.11 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0))
% 6.00/2.11 | (3) ? [v0] : ? [v1] : ? [v2] : in(v1, v0) = v2
% 6.00/2.11 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 6.00/2.11 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 6.00/2.11 | (6) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | subset(v0, v1) = 0)
% 6.00/2.11 | (7) relation(all_0_1_1) = 0
% 6.00/2.11 | (8) relation(all_0_8_8) = 0
% 6.00/2.11 | (9) ! [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)))
% 6.00/2.11 | (10) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3))
% 6.00/2.11 | (11) in(all_0_13_13, all_0_12_12) = 0
% 6.00/2.11 | (12) relation_empty_yielding(all_0_10_10) = 0
% 6.00/2.11 | (13) ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2
% 6.00/2.11 | (14) ! [v0] : ! [v1] : ! [v2] : ( ~ (empty(v2) = 0) | ~ (in(v0, v1) = 0) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v2) = v3 & element(v1, v3) = v4))
% 6.00/2.11 | (15) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_empty_yielding(v2) = v1) | ~ (relation_empty_yielding(v2) = v0))
% 6.00/2.11 | (16) relation_empty_yielding(all_0_9_9) = 0
% 6.00/2.11 | (17) ? [v0] : ? [v1] : relation_non_empty(v0) = v1
% 6.00/2.11 | (18) ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2))
% 6.00/2.11 | (19) relation(all_0_9_9) = 0
% 6.00/2.11 | (20) ? [v0] : ? [v1] : powerset(v0) = v1
% 6.00/2.11 | (21) function(all_0_0_0) = 0
% 6.00/2.11 | (22) ? [v0] : ? [v1] : ? [v2] : element(v1, v0) = v2
% 6.00/2.11 | (23) ! [v0] : ! [v1] : (v1 = 0 | ~ (function(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2))
% 6.00/2.11 | (24) ? [v0] : ? [v1] : function(v0) = v1
% 6.00/2.11 | (25) ! [v0] : ( ~ (empty(v0) = 0) | relation(v0) = 0)
% 6.00/2.11 | (26) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 6.00/2.11 | (27) ! [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))
% 6.00/2.11 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 6.00/2.11 | (29) ? [v0] : ? [v1] : one_to_one(v0) = v1
% 6.00/2.11 | (30) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0))
% 6.00/2.11 | (31) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0))
% 6.00/2.11 | (32) relation(all_0_0_0) = 0
% 6.00/2.11 | (33) ! [v0] : ! [v1] : (v1 = 0 | ~ (relation(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2))
% 6.00/2.11 | (34) ! [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)))
% 6.00/2.11 | (35) relation(empty_set) = 0
% 6.32/2.11 | (36) ~ (all_0_4_4 = 0)
% 6.32/2.11 | (37) relation(all_0_10_10) = 0
% 6.32/2.12 | (38) empty(all_0_2_2) = 0
% 6.32/2.12 | (39) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 6.32/2.12 | (40) ! [v0] : ( ~ (empty(v0) = 0) | function(v0) = 0)
% 6.32/2.12 | (41) function(all_0_11_11) = 0
% 6.32/2.12 | (42) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 6.32/2.12 | (43) function(all_0_8_8) = 0
% 6.32/2.12 | (44) ? [v0] : ? [v1] : relation_empty_yielding(v0) = v1
% 6.32/2.12 | (45) empty(all_0_1_1) = 0
% 6.32/2.12 | (46) relation(all_0_5_5) = 0
% 6.32/2.12 | (47) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0))
% 6.32/2.12 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | element(v0, v2) = 0)
% 6.32/2.12 | (49) ? [v0] : ? [v1] : element(v1, v0) = 0
% 6.32/2.12 | (50) ! [v0] : ! [v1] : ( ~ (element(v0, v1) = 0) | ? [v2] : ((v2 = 0 & empty(v1) = 0) | (v2 = 0 & in(v0, v1) = 0)))
% 6.32/2.12 | (51) empty(all_0_3_3) = 0
% 6.32/2.12 | (52) empty(empty_set) = 0
% 6.32/2.12 | (53) relation(all_0_11_11) = 0
% 6.32/2.12 | (54) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | element(v0, v1) = 0)
% 6.32/2.12 | (55) empty(all_0_5_5) = all_0_4_4
% 6.32/2.12 | (56) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v0, v1) = v2) | ? [v3] : ((v3 = 0 & empty(v1) = 0) | ( ~ (v3 = 0) & element(v0, v1) = v3)))
% 6.32/2.12 | (57) ! [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)))
% 6.32/2.12 | (58) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (powerset(v1) = v2 & element(v0, v2) = 0))
% 6.32/2.12 | (59) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_non_empty(v2) = v1) | ~ (relation_non_empty(v2) = v0))
% 6.32/2.12 | (60) ! [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))
% 6.32/2.12 | (61) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1))
% 6.32/2.12 | (62) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0))
% 6.32/2.12 | (63) function(all_0_10_10) = 0
% 6.32/2.12 | (64) ? [v0] : ? [v1] : relation(v0) = v1
% 6.32/2.12 | (65) empty(all_0_7_7) = all_0_6_6
% 6.32/2.12 | (66) ! [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)))
% 6.32/2.12 | (67) ~ (all_0_6_6 = 0)
% 6.32/2.12 | (68) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4))
% 6.32/2.12 | (69) one_to_one(all_0_8_8) = 0
% 6.32/2.12 | (70) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0))
% 6.32/2.12 | (71) subset(all_0_12_12, all_0_13_13) = 0
% 6.32/2.12 | (72) relation_non_empty(all_0_11_11) = 0
% 6.32/2.13 | (73) ? [v0] : ? [v1] : empty(v0) = v1
% 6.32/2.13 | (74) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0))
% 6.32/2.13 | (75) relation(all_0_3_3) = 0
% 6.32/2.13 | (76) function(all_0_3_3) = 0
% 6.32/2.13 | (77) relation_empty_yielding(empty_set) = 0
% 6.32/2.13 | (78) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v1) = v3 & element(v0, v3) = v4))
% 6.32/2.13 |
% 6.32/2.13 | Instantiating formula (58) with all_0_13_13, all_0_12_12 and discharging atoms subset(all_0_12_12, all_0_13_13) = 0, yields:
% 6.32/2.13 | (79) ? [v0] : (powerset(all_0_13_13) = v0 & element(all_0_12_12, v0) = 0)
% 6.32/2.13 |
% 6.32/2.13 | Instantiating (79) with all_56_0_73 yields:
% 6.32/2.13 | (80) powerset(all_0_13_13) = all_56_0_73 & element(all_0_12_12, all_56_0_73) = 0
% 6.32/2.13 |
% 6.32/2.13 | Applying alpha-rule on (80) yields:
% 6.32/2.13 | (81) powerset(all_0_13_13) = all_56_0_73
% 6.32/2.13 | (82) element(all_0_12_12, all_56_0_73) = 0
% 6.32/2.13 |
% 6.32/2.13 | Instantiating formula (48) with all_56_0_73, all_0_13_13, all_0_12_12, all_0_13_13 and discharging atoms powerset(all_0_13_13) = all_56_0_73, element(all_0_12_12, all_56_0_73) = 0, in(all_0_13_13, all_0_12_12) = 0, yields:
% 6.32/2.13 | (83) element(all_0_13_13, all_0_13_13) = 0
% 6.32/2.13 |
% 6.32/2.13 | Instantiating formula (68) with all_56_0_73, all_0_13_13, all_0_12_12, all_0_13_13 and discharging atoms powerset(all_0_13_13) = all_56_0_73, element(all_0_12_12, all_56_0_73) = 0, in(all_0_13_13, all_0_12_12) = 0, yields:
% 6.32/2.13 | (84) ? [v0] : ( ~ (v0 = 0) & empty(all_0_13_13) = v0)
% 6.32/2.13 |
% 6.32/2.13 | Instantiating (84) with all_77_0_75 yields:
% 6.32/2.13 | (85) ~ (all_77_0_75 = 0) & empty(all_0_13_13) = all_77_0_75
% 6.32/2.13 |
% 6.32/2.13 | Applying alpha-rule on (85) yields:
% 6.32/2.13 | (86) ~ (all_77_0_75 = 0)
% 6.32/2.13 | (87) empty(all_0_13_13) = all_77_0_75
% 6.32/2.13 |
% 6.32/2.13 | Instantiating formula (50) with all_0_13_13, all_0_13_13 and discharging atoms element(all_0_13_13, all_0_13_13) = 0, yields:
% 6.32/2.13 | (88) ? [v0] : ((v0 = 0 & empty(all_0_13_13) = 0) | (v0 = 0 & in(all_0_13_13, all_0_13_13) = 0))
% 6.32/2.13 |
% 6.32/2.13 | Instantiating (88) with all_103_0_79 yields:
% 6.32/2.13 | (89) (all_103_0_79 = 0 & empty(all_0_13_13) = 0) | (all_103_0_79 = 0 & in(all_0_13_13, all_0_13_13) = 0)
% 6.32/2.13 |
% 6.32/2.13 +-Applying beta-rule and splitting (89), into two cases.
% 6.32/2.13 |-Branch one:
% 6.32/2.13 | (90) all_103_0_79 = 0 & empty(all_0_13_13) = 0
% 6.32/2.13 |
% 6.32/2.13 | Applying alpha-rule on (90) yields:
% 6.32/2.13 | (91) all_103_0_79 = 0
% 6.32/2.13 | (92) empty(all_0_13_13) = 0
% 6.32/2.13 |
% 6.32/2.13 | Instantiating formula (42) with all_0_13_13, 0, all_77_0_75 and discharging atoms empty(all_0_13_13) = all_77_0_75, empty(all_0_13_13) = 0, yields:
% 6.32/2.13 | (93) all_77_0_75 = 0
% 6.32/2.13 |
% 6.32/2.13 | Equations (93) can reduce 86 to:
% 6.32/2.13 | (94) $false
% 6.32/2.13 |
% 6.32/2.13 |-The branch is then unsatisfiable
% 6.32/2.13 |-Branch two:
% 6.32/2.13 | (95) all_103_0_79 = 0 & in(all_0_13_13, all_0_13_13) = 0
% 6.32/2.13 |
% 6.32/2.13 | Applying alpha-rule on (95) yields:
% 6.32/2.13 | (91) all_103_0_79 = 0
% 6.32/2.13 | (97) in(all_0_13_13, all_0_13_13) = 0
% 6.32/2.13 |
% 6.32/2.13 | Instantiating formula (18) with all_0_13_13, all_0_13_13 and discharging atoms in(all_0_13_13, all_0_13_13) = 0, yields:
% 6.32/2.13 | (98) ? [v0] : ( ~ (v0 = 0) & in(all_0_13_13, all_0_13_13) = v0)
% 6.32/2.13 |
% 6.32/2.13 | Instantiating (98) with all_124_0_84 yields:
% 6.32/2.13 | (99) ~ (all_124_0_84 = 0) & in(all_0_13_13, all_0_13_13) = all_124_0_84
% 6.32/2.14 |
% 6.32/2.14 | Applying alpha-rule on (99) yields:
% 6.32/2.14 | (100) ~ (all_124_0_84 = 0)
% 6.32/2.14 | (101) in(all_0_13_13, all_0_13_13) = all_124_0_84
% 6.32/2.14 |
% 6.32/2.14 | Instantiating formula (28) with all_0_13_13, all_0_13_13, all_124_0_84, 0 and discharging atoms in(all_0_13_13, all_0_13_13) = all_124_0_84, in(all_0_13_13, all_0_13_13) = 0, yields:
% 6.32/2.14 | (102) all_124_0_84 = 0
% 6.32/2.14 |
% 6.32/2.14 | Equations (102) can reduce 100 to:
% 6.32/2.14 | (94) $false
% 6.32/2.14 |
% 6.32/2.14 |-The branch is then unsatisfiable
% 6.32/2.14 % SZS output end Proof for theBenchmark
% 6.32/2.14
% 6.32/2.14 1553ms
%------------------------------------------------------------------------------