TSTP Solution File: SEU227+3 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU227+3 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 08:47:54 EDT 2022
% Result : Theorem 7.22s 2.46s
% Output : Proof 10.78s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU227+3 : TPTP v8.1.0. Released v3.2.0.
% 0.00/0.09 % Command : ePrincess-casc -timeout=%d %s
% 0.09/0.29 % Computer : n021.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 600
% 0.09/0.29 % DateTime : Mon Jun 20 01:11:33 EDT 2022
% 0.09/0.29 % CPUTime :
% 0.14/0.53 ____ _
% 0.14/0.53 ___ / __ \_____(_)___ ________ __________
% 0.14/0.53 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.14/0.53 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.14/0.53 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.14/0.53
% 0.14/0.53 A Theorem Prover for First-Order Logic
% 0.14/0.53 (ePrincess v.1.0)
% 0.14/0.53
% 0.14/0.53 (c) Philipp Rümmer, 2009-2015
% 0.14/0.53 (c) Peter Backeman, 2014-2015
% 0.14/0.53 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.14/0.53 Free software under GNU Lesser General Public License (LGPL).
% 0.14/0.53 Bug reports to peter@backeman.se
% 0.14/0.53
% 0.14/0.53 For more information, visit http://user.uu.se/~petba168/breu/
% 0.14/0.53
% 0.14/0.53 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.65/0.59 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.63/0.96 Prover 0: Preprocessing ...
% 2.69/1.34 Prover 0: Warning: ignoring some quantifiers
% 2.69/1.38 Prover 0: Constructing countermodel ...
% 4.94/1.98 Prover 0: gave up
% 4.94/1.98 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 5.33/2.03 Prover 1: Preprocessing ...
% 6.35/2.23 Prover 1: Warning: ignoring some quantifiers
% 6.35/2.24 Prover 1: Constructing countermodel ...
% 7.22/2.46 Prover 1: proved (484ms)
% 7.22/2.46
% 7.22/2.46 No countermodel exists, formula is valid
% 7.22/2.46 % SZS status Theorem for theBenchmark
% 7.22/2.46
% 7.22/2.46 Generating proof ... Warning: ignoring some quantifiers
% 10.38/3.12 found it (size 37)
% 10.38/3.12
% 10.38/3.12 % SZS output start Proof for theBenchmark
% 10.38/3.12 Assumed formulas after preprocessing and simplification:
% 10.38/3.12 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ( ~ (v11 = 0) & ~ (v9 = 0) & ~ (v5 = 0) & relation_empty_yielding(v6) = 0 & relation_empty_yielding(empty_set) = 0 & relation_dom(v1) = v2 & subset(v0, v4) = v5 & subset(v0, v2) = 0 & relation_inverse_image(v1, v3) = v4 & relation_image(v1, v0) = v3 & one_to_one(v7) = 0 & relation(v15) = 0 & relation(v14) = 0 & relation(v12) = 0 & relation(v10) = 0 & relation(v7) = 0 & relation(v6) = 0 & relation(v1) = 0 & relation(empty_set) = 0 & function(v15) = 0 & function(v12) = 0 & function(v7) = 0 & empty(v14) = 0 & empty(v13) = 0 & empty(v12) = 0 & empty(v10) = v11 & empty(v8) = v9 & empty(empty_set) = 0 & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v20 = 0 | ~ (relation_inverse_image(v16, v17) = v18) | ~ (ordered_pair(v19, v21) = v22) | ~ (relation(v16) = 0) | ~ (in(v22, v16) = 0) | ~ (in(v19, v18) = v20) | ? [v23] : ( ~ (v23 = 0) & in(v21, v17) = v23)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v20 = 0 | ~ (relation_image(v16, v17) = v18) | ~ (ordered_pair(v21, v19) = v22) | ~ (relation(v16) = 0) | ~ (in(v22, v16) = 0) | ~ (in(v19, v18) = v20) | ? [v23] : ( ~ (v23 = 0) & in(v21, v17) = v23)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v19 = 0 | ~ (relation_dom(v16) = v17) | ~ (ordered_pair(v18, v20) = v21) | ~ (in(v21, v16) = 0) | ~ (in(v18, v17) = v19) | ? [v22] : ( ~ (v22 = 0) & relation(v16) = v22)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v20 = 0 | ~ (powerset(v18) = v19) | ~ (element(v17, v19) = 0) | ~ (element(v16, v18) = v20) | ? [v21] : ( ~ (v21 = 0) & in(v16, v17) = v21)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (singleton(v16) = v19) | ~ (unordered_pair(v18, v19) = v20) | ~ (unordered_pair(v16, v17) = v18) | ordered_pair(v16, v17) = v20) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v19 = 0 | ~ (powerset(v17) = v18) | ~ (element(v16, v18) = v19) | ? [v20] : ( ~ (v20 = 0) & subset(v16, v17) = v20)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v17 = v16 | ~ (element(v19, v18) = v17) | ~ (element(v19, v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v17 = v16 | ~ (subset(v19, v18) = v17) | ~ (subset(v19, v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v17 = v16 | ~ (relation_inverse_image(v19, v18) = v17) | ~ (relation_inverse_image(v19, v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v17 = v16 | ~ (relation_image(v19, v18) = v17) | ~ (relation_image(v19, v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v17 = v16 | ~ (ordered_pair(v19, v18) = v17) | ~ (ordered_pair(v19, v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v17 = v16 | ~ (unordered_pair(v19, v18) = v17) | ~ (unordered_pair(v19, v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v17 = v16 | ~ (in(v19, v18) = v17) | ~ (in(v19, v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (powerset(v18) = v19) | ~ (element(v17, v19) = 0) | ~ (in(v16, v17) = 0) | ? [v20] : ( ~ (v20 = 0) & empty(v18) = v20)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_inverse_image(v16, v17) = v18) | ~ (relation(v16) = 0) | ~ (in(v19, v18) = 0) | ? [v20] : ? [v21] : (ordered_pair(v19, v20) = v21 & in(v21, v16) = 0 & in(v20, v17) = 0)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_image(v16, v17) = v18) | ~ (relation(v16) = 0) | ~ (in(v19, v18) = 0) | ? [v20] : ? [v21] : (ordered_pair(v20, v19) = v21 & in(v21, v16) = 0 & in(v20, v17) = 0)) & ? [v16] : ! [v17] : ! [v18] : ! [v19] : (v19 = v16 | ~ (relation_inverse_image(v17, v18) = v19) | ~ (relation(v17) = 0) | ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : (in(v20, v16) = v21 & ( ~ (v21 = 0) | ! [v26] : ! [v27] : ( ~ (ordered_pair(v20, v26) = v27) | ~ (in(v27, v17) = 0) | ? [v28] : ( ~ (v28 = 0) & in(v26, v18) = v28))) & (v21 = 0 | (v25 = 0 & v24 = 0 & ordered_pair(v20, v22) = v23 & in(v23, v17) = 0 & in(v22, v18) = 0)))) & ? [v16] : ! [v17] : ! [v18] : ! [v19] : (v19 = v16 | ~ (relation_image(v17, v18) = v19) | ~ (relation(v17) = 0) | ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : (in(v20, v16) = v21 & ( ~ (v21 = 0) | ! [v26] : ! [v27] : ( ~ (ordered_pair(v26, v20) = v27) | ~ (in(v27, v17) = 0) | ? [v28] : ( ~ (v28 = 0) & in(v26, v18) = v28))) & (v21 = 0 | (v25 = 0 & v24 = 0 & ordered_pair(v22, v20) = v23 & in(v23, v17) = 0 & in(v22, v18) = 0)))) & ! [v16] : ! [v17] : ! [v18] : (v18 = 0 | ~ (element(v16, v17) = v18) | ? [v19] : ( ~ (v19 = 0) & in(v16, v17) = v19)) & ! [v16] : ! [v17] : ! [v18] : (v18 = 0 | ~ (subset(v16, v17) = v18) | ? [v19] : ? [v20] : ( ~ (v20 = 0) & in(v19, v17) = v20 & in(v19, v16) = 0)) & ! [v16] : ! [v17] : ! [v18] : (v17 = v16 | ~ (relation_empty_yielding(v18) = v17) | ~ (relation_empty_yielding(v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : (v17 = v16 | ~ (powerset(v18) = v17) | ~ (powerset(v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : (v17 = v16 | ~ (singleton(v18) = v17) | ~ (singleton(v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : (v17 = v16 | ~ (relation_dom(v18) = v17) | ~ (relation_dom(v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : (v17 = v16 | ~ (one_to_one(v18) = v17) | ~ (one_to_one(v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : (v17 = v16 | ~ (relation(v18) = v17) | ~ (relation(v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : (v17 = v16 | ~ (function(v18) = v17) | ~ (function(v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : (v17 = v16 | ~ (empty(v18) = v17) | ~ (empty(v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (powerset(v17) = v18) | ~ (element(v16, v18) = 0) | subset(v16, v17) = 0) & ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_dom(v16) = v17) | ~ (in(v18, v17) = 0) | ? [v19] : ? [v20] : ? [v21] : ((v21 = 0 & ordered_pair(v18, v19) = v20 & in(v20, v16) = 0) | ( ~ (v19 = 0) & relation(v16) = v19))) & ! [v16] : ! [v17] : ! [v18] : ( ~ (subset(v16, v17) = 0) | ~ (in(v18, v16) = 0) | in(v18, v17) = 0) & ! [v16] : ! [v17] : ! [v18] : ( ~ (ordered_pair(v16, v17) = v18) | ? [v19] : ( ~ (v19 = 0) & empty(v18) = v19)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (unordered_pair(v16, v17) = v18) | unordered_pair(v17, v16) = v18) & ! [v16] : ! [v17] : ! [v18] : ( ~ (unordered_pair(v16, v17) = v18) | ? [v19] : ( ~ (v19 = 0) & empty(v18) = v19)) & ? [v16] : ! [v17] : ! [v18] : (v18 = v16 | ~ (relation_dom(v17) = v18) | ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : (( ~ (v19 = 0) & relation(v17) = v19) | (in(v19, v16) = v20 & ( ~ (v20 = 0) | ! [v24] : ! [v25] : ( ~ (ordered_pair(v19, v24) = v25) | ~ (in(v25, v17) = 0))) & (v20 = 0 | (v23 = 0 & ordered_pair(v19, v21) = v22 & in(v22, v17) = 0))))) & ! [v16] : ! [v17] : (v17 = v16 | ~ (empty(v17) = 0) | ~ (empty(v16) = 0)) & ! [v16] : ! [v17] : (v17 = 0 | ~ (subset(v16, v16) = v17)) & ! [v16] : ! [v17] : (v17 = 0 | ~ (relation(v16) = v17) | ? [v18] : ( ~ (v18 = 0) & empty(v16) = v18)) & ! [v16] : ! [v17] : (v17 = 0 | ~ (function(v16) = v17) | ? [v18] : ( ~ (v18 = 0) & empty(v16) = v18)) & ! [v16] : ! [v17] : ( ~ (powerset(v16) = v17) | ? [v18] : ? [v19] : ? [v20] : ((v19 = 0 & ~ (v20 = 0) & element(v18, v17) = 0 & empty(v18) = v20) | (v18 = 0 & empty(v16) = 0))) & ! [v16] : ! [v17] : ( ~ (powerset(v16) = v17) | ? [v18] : ( ~ (v18 = 0) & empty(v17) = v18)) & ! [v16] : ! [v17] : ( ~ (powerset(v16) = v17) | ? [v18] : (element(v18, v17) = 0 & empty(v18) = 0)) & ! [v16] : ! [v17] : ( ~ (element(v16, v17) = 0) | ? [v18] : ? [v19] : (empty(v17) = v18 & in(v16, v17) = v19 & (v19 = 0 | v18 = 0))) & ! [v16] : ! [v17] : ( ~ (singleton(v16) = v17) | ? [v18] : ( ~ (v18 = 0) & empty(v17) = v18)) & ! [v16] : ! [v17] : ( ~ (relation_dom(v16) = v17) | ? [v18] : ? [v19] : ? [v20] : (relation(v17) = v20 & empty(v17) = v19 & empty(v16) = v18 & ( ~ (v18 = 0) | (v20 = 0 & v19 = 0)))) & ! [v16] : ! [v17] : ( ~ (relation_dom(v16) = v17) | ? [v18] : ? [v19] : ? [v20] : (relation(v16) = v19 & empty(v17) = v20 & empty(v16) = v18 & ( ~ (v20 = 0) | ~ (v19 = 0) | v18 = 0))) & ! [v16] : ! [v17] : ( ~ (one_to_one(v16) = v17) | ? [v18] : ? [v19] : ? [v20] : (relation(v16) = v18 & function(v16) = v20 & empty(v16) = v19 & ( ~ (v20 = 0) | ~ (v19 = 0) | ~ (v18 = 0) | v17 = 0))) & ! [v16] : ! [v17] : ( ~ (in(v16, v17) = 0) | ? [v18] : ( ~ (v18 = 0) & empty(v17) = v18)) & ! [v16] : ! [v17] : ( ~ (in(v16, v17) = 0) | ? [v18] : ( ~ (v18 = 0) & in(v17, v16) = v18)) & ! [v16] : (v16 = empty_set | ~ (empty(v16) = 0)) & ? [v16] : ? [v17] : element(v17, v16) = 0)
% 10.78/3.19 | 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, all_0_14_14, all_0_15_15 yields:
% 10.78/3.19 | (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_dom(all_0_14_14) = all_0_13_13 & subset(all_0_15_15, all_0_11_11) = all_0_10_10 & subset(all_0_15_15, all_0_13_13) = 0 & relation_inverse_image(all_0_14_14, all_0_12_12) = all_0_11_11 & relation_image(all_0_14_14, all_0_15_15) = all_0_12_12 & 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_14_14) = 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] : ! [v5] : ! [v6] : (v4 = 0 | ~ (relation_inverse_image(v0, v1) = v2) | ~ (ordered_pair(v3, v5) = v6) | ~ (relation(v0) = 0) | ~ (in(v6, v0) = 0) | ~ (in(v3, v2) = v4) | ? [v7] : ( ~ (v7 = 0) & in(v5, v1) = v7)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = 0 | ~ (relation_image(v0, v1) = v2) | ~ (ordered_pair(v5, v3) = v6) | ~ (relation(v0) = 0) | ~ (in(v6, v0) = 0) | ~ (in(v3, v2) = v4) | ? [v7] : ( ~ (v7 = 0) & in(v5, v1) = v7)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = 0 | ~ (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v4) = v5) | ~ (in(v5, v0) = 0) | ~ (in(v2, v1) = v3) | ? [v6] : ( ~ (v6 = 0) & relation(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] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_inverse_image(v3, v2) = v1) | ~ (relation_inverse_image(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_image(v3, v2) = v1) | ~ (relation_image(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 | ~ (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) | ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_inverse_image(v0, v1) = v2) | ~ (relation(v0) = 0) | ~ (in(v3, v2) = 0) | ? [v4] : ? [v5] : (ordered_pair(v3, v4) = v5 & in(v5, v0) = 0 & in(v4, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_image(v0, v1) = v2) | ~ (relation(v0) = 0) | ~ (in(v3, v2) = 0) | ? [v4] : ? [v5] : (ordered_pair(v4, v3) = v5 & in(v5, v0) = 0 & in(v4, v1) = 0)) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (relation_inverse_image(v1, v2) = v3) | ~ (relation(v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (in(v4, v0) = v5 & ( ~ (v5 = 0) | ! [v10] : ! [v11] : ( ~ (ordered_pair(v4, v10) = v11) | ~ (in(v11, v1) = 0) | ? [v12] : ( ~ (v12 = 0) & in(v10, v2) = v12))) & (v5 = 0 | (v9 = 0 & v8 = 0 & ordered_pair(v4, v6) = v7 & in(v7, v1) = 0 & in(v6, v2) = 0)))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (relation_image(v1, v2) = v3) | ~ (relation(v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (in(v4, v0) = v5 & ( ~ (v5 = 0) | ! [v10] : ! [v11] : ( ~ (ordered_pair(v10, v4) = v11) | ~ (in(v11, v1) = 0) | ? [v12] : ( ~ (v12 = 0) & in(v10, v2) = v12))) & (v5 = 0 | (v9 = 0 & v8 = 0 & ordered_pair(v6, v4) = v7 & in(v7, v1) = 0 & in(v6, v2) = 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) & in(v3, v1) = v4 & in(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_empty_yielding(v2) = v1) | ~ (relation_empty_yielding(v2) = v0)) & ! [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 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(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] : ( ~ (relation_dom(v0) = v1) | ~ (in(v2, v1) = 0) | ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & ordered_pair(v2, v3) = v4 & in(v4, v0) = 0) | ( ~ (v3 = 0) & relation(v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3)) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_dom(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (( ~ (v3 = 0) & relation(v1) = v3) | (in(v3, v0) = v4 & ( ~ (v4 = 0) | ! [v8] : ! [v9] : ( ~ (ordered_pair(v3, v8) = v9) | ~ (in(v9, v1) = 0))) & (v4 = 0 | (v7 = 0 & ordered_pair(v3, v5) = v6 & in(v6, v1) = 0))))) & ! [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] : ( ~ (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] : ? [v3] : (empty(v1) = v2 & in(v0, v1) = v3 & (v3 = 0 | v2 = 0))) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation(v1) = v4 & empty(v1) = v3 & empty(v0) = v2 & ( ~ (v2 = 0) | (v4 = 0 & v3 = 0)))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation(v0) = v3 & empty(v1) = v4 & empty(v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2 = 0))) & ! [v0] : ! [v1] : ( ~ (one_to_one(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation(v0) = v2 & function(v0) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | v1 = 0))) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) & ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0)) & ? [v0] : ? [v1] : element(v1, v0) = 0
% 10.78/3.21 |
% 10.78/3.21 | Applying alpha-rule on (1) yields:
% 10.78/3.21 | (2) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0)
% 10.78/3.21 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 10.78/3.21 | (4) relation(all_0_8_8) = 0
% 10.78/3.21 | (5) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (relation_inverse_image(v1, v2) = v3) | ~ (relation(v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (in(v4, v0) = v5 & ( ~ (v5 = 0) | ! [v10] : ! [v11] : ( ~ (ordered_pair(v4, v10) = v11) | ~ (in(v11, v1) = 0) | ? [v12] : ( ~ (v12 = 0) & in(v10, v2) = v12))) & (v5 = 0 | (v9 = 0 & v8 = 0 & ordered_pair(v4, v6) = v7 & in(v7, v1) = 0 & in(v6, v2) = 0))))
% 10.78/3.21 | (6) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom(v0) = v1) | ~ (in(v2, v1) = 0) | ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & ordered_pair(v2, v3) = v4 & in(v4, v0) = 0) | ( ~ (v3 = 0) & relation(v0) = v3)))
% 10.78/3.22 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_inverse_image(v3, v2) = v1) | ~ (relation_inverse_image(v3, v2) = v0))
% 10.78/3.22 | (8) ~ (all_0_6_6 = 0)
% 10.78/3.22 | (9) empty(all_0_7_7) = all_0_6_6
% 10.78/3.22 | (10) relation(empty_set) = 0
% 10.78/3.22 | (11) one_to_one(all_0_8_8) = 0
% 10.78/3.22 | (12) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_dom(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (( ~ (v3 = 0) & relation(v1) = v3) | (in(v3, v0) = v4 & ( ~ (v4 = 0) | ! [v8] : ! [v9] : ( ~ (ordered_pair(v3, v8) = v9) | ~ (in(v9, v1) = 0))) & (v4 = 0 | (v7 = 0 & ordered_pair(v3, v5) = v6 & in(v6, v1) = 0)))))
% 10.78/3.22 | (13) relation_empty_yielding(all_0_9_9) = 0
% 10.78/3.22 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0))
% 10.78/3.22 | (15) function(all_0_8_8) = 0
% 10.78/3.22 | (16) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 10.78/3.22 | (17) empty(all_0_5_5) = all_0_4_4
% 10.78/3.22 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = 0 | ~ (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v4) = v5) | ~ (in(v5, v0) = 0) | ~ (in(v2, v1) = v3) | ? [v6] : ( ~ (v6 = 0) & relation(v0) = v6))
% 10.78/3.22 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_image(v0, v1) = v2) | ~ (relation(v0) = 0) | ~ (in(v3, v2) = 0) | ? [v4] : ? [v5] : (ordered_pair(v4, v3) = v5 & in(v5, v0) = 0 & in(v4, v1) = 0))
% 10.78/3.22 | (20) ! [v0] : ! [v1] : (v1 = 0 | ~ (function(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2))
% 10.78/3.22 | (21) subset(all_0_15_15, all_0_11_11) = all_0_10_10
% 10.78/3.22 | (22) ? [v0] : ? [v1] : element(v1, v0) = 0
% 10.78/3.22 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = 0 | ~ (relation_inverse_image(v0, v1) = v2) | ~ (ordered_pair(v3, v5) = v6) | ~ (relation(v0) = 0) | ~ (in(v6, v0) = 0) | ~ (in(v3, v2) = v4) | ? [v7] : ( ~ (v7 = 0) & in(v5, v1) = v7))
% 10.78/3.22 | (24) subset(all_0_15_15, all_0_13_13) = 0
% 10.78/3.22 | (25) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0))
% 10.78/3.22 | (26) relation(all_0_9_9) = 0
% 10.78/3.22 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0))
% 10.78/3.22 | (28) empty(all_0_2_2) = 0
% 10.78/3.22 | (29) ! [v0] : ! [v1] : ( ~ (element(v0, v1) = 0) | ? [v2] : ? [v3] : (empty(v1) = v2 & in(v0, v1) = v3 & (v3 = 0 | v2 = 0)))
% 10.78/3.22 | (30) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v3 = 0 & ~ (v4 = 0) & element(v2, v1) = 0 & empty(v2) = v4) | (v2 = 0 & empty(v0) = 0)))
% 10.78/3.23 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 10.78/3.23 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 10.78/3.23 | (33) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0))
% 10.78/3.23 | (34) ! [v0] : ! [v1] : ( ~ (one_to_one(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation(v0) = v2 & function(v0) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | v1 = 0)))
% 10.78/3.23 | (35) function(all_0_0_0) = 0
% 10.78/3.23 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4)
% 10.78/3.23 | (37) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 10.78/3.23 | (38) relation_image(all_0_14_14, all_0_15_15) = all_0_12_12
% 10.78/3.23 | (39) relation(all_0_0_0) = 0
% 10.78/3.23 | (40) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 10.78/3.23 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = 0 | ~ (relation_image(v0, v1) = v2) | ~ (ordered_pair(v5, v3) = v6) | ~ (relation(v0) = 0) | ~ (in(v6, v0) = 0) | ~ (in(v3, v2) = v4) | ? [v7] : ( ~ (v7 = 0) & in(v5, v1) = v7))
% 10.78/3.23 | (42) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 10.78/3.23 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_image(v3, v2) = v1) | ~ (relation_image(v3, v2) = v0))
% 10.78/3.23 | (44) empty(empty_set) = 0
% 10.78/3.23 | (45) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3))
% 10.78/3.23 | (46) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3))
% 10.78/3.23 | (47) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0))
% 10.78/3.23 | (48) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0))
% 10.78/3.23 | (49) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (relation_image(v1, v2) = v3) | ~ (relation(v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (in(v4, v0) = v5 & ( ~ (v5 = 0) | ! [v10] : ! [v11] : ( ~ (ordered_pair(v10, v4) = v11) | ~ (in(v11, v1) = 0) | ? [v12] : ( ~ (v12 = 0) & in(v10, v2) = v12))) & (v5 = 0 | (v9 = 0 & v8 = 0 & ordered_pair(v6, v4) = v7 & in(v7, v1) = 0 & in(v6, v2) = 0))))
% 10.78/3.24 | (50) relation_empty_yielding(empty_set) = 0
% 10.78/3.24 | (51) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation(v1) = v4 & empty(v1) = v3 & empty(v0) = v2 & ( ~ (v2 = 0) | (v4 = 0 & v3 = 0))))
% 10.78/3.24 | (52) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) = 0 & empty(v2) = 0))
% 10.78/3.24 | (53) ! [v0] : ! [v1] : (v1 = 0 | ~ (relation(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2))
% 10.78/3.24 | (54) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation(v0) = v3 & empty(v1) = v4 & empty(v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2 = 0)))
% 10.78/3.24 | (55) relation(all_0_5_5) = 0
% 10.78/3.24 | (56) relation(all_0_14_14) = 0
% 10.78/3.24 | (57) relation_dom(all_0_14_14) = all_0_13_13
% 10.78/3.24 | (58) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0))
% 10.78/3.24 | (59) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3))
% 10.78/3.24 | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4))
% 10.78/3.24 | (61) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1))
% 10.78/3.24 | (62) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 10.78/3.24 | (63) empty(all_0_3_3) = 0
% 10.78/3.24 | (64) empty(all_0_1_1) = 0
% 10.78/3.24 | (65) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 10.78/3.24 | (66) ~ (all_0_4_4 = 0)
% 10.78/3.24 | (67) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0))
% 10.78/3.24 | (68) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_empty_yielding(v2) = v1) | ~ (relation_empty_yielding(v2) = v0))
% 10.78/3.24 | (69) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0))
% 10.78/3.24 | (70) function(all_0_3_3) = 0
% 10.78/3.24 | (71) ~ (all_0_10_10 = 0)
% 10.78/3.24 | (72) ! [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))
% 10.78/3.24 | (73) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_inverse_image(v0, v1) = v2) | ~ (relation(v0) = 0) | ~ (in(v3, v2) = 0) | ? [v4] : ? [v5] : (ordered_pair(v3, v4) = v5 & in(v5, v0) = 0 & in(v4, v1) = 0))
% 10.78/3.24 | (74) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 10.78/3.24 | (75) relation(all_0_1_1) = 0
% 10.78/3.24 | (76) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0))
% 10.78/3.24 | (77) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2)
% 10.78/3.24 | (78) relation_inverse_image(all_0_14_14, all_0_12_12) = all_0_11_11
% 10.78/3.24 | (79) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | subset(v0, v1) = 0)
% 10.78/3.24 | (80) relation(all_0_3_3) = 0
% 10.78/3.24 |
% 10.78/3.25 | Instantiating formula (54) with all_0_13_13, all_0_14_14 and discharging atoms relation_dom(all_0_14_14) = all_0_13_13, yields:
% 10.78/3.25 | (81) ? [v0] : ? [v1] : ? [v2] : (relation(all_0_14_14) = v1 & empty(all_0_13_13) = v2 & empty(all_0_14_14) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | v0 = 0))
% 10.78/3.25 |
% 10.78/3.25 | Instantiating formula (69) with all_0_10_10, all_0_11_11, all_0_15_15 and discharging atoms subset(all_0_15_15, all_0_11_11) = all_0_10_10, yields:
% 10.78/3.25 | (82) all_0_10_10 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_11_11) = v1 & in(v0, all_0_15_15) = 0)
% 10.78/3.25 |
% 10.78/3.25 | Instantiating (81) with all_30_0_24, all_30_1_25, all_30_2_26 yields:
% 10.78/3.25 | (83) relation(all_0_14_14) = all_30_1_25 & empty(all_0_13_13) = all_30_0_24 & empty(all_0_14_14) = all_30_2_26 & ( ~ (all_30_0_24 = 0) | ~ (all_30_1_25 = 0) | all_30_2_26 = 0)
% 10.78/3.25 |
% 10.78/3.25 | Applying alpha-rule on (83) yields:
% 10.78/3.25 | (84) relation(all_0_14_14) = all_30_1_25
% 10.78/3.25 | (85) empty(all_0_13_13) = all_30_0_24
% 10.78/3.25 | (86) empty(all_0_14_14) = all_30_2_26
% 10.78/3.25 | (87) ~ (all_30_0_24 = 0) | ~ (all_30_1_25 = 0) | all_30_2_26 = 0
% 10.78/3.25 |
% 10.78/3.25 +-Applying beta-rule and splitting (82), into two cases.
% 10.78/3.25 |-Branch one:
% 10.78/3.25 | (88) all_0_10_10 = 0
% 10.78/3.25 |
% 10.78/3.25 | Equations (88) can reduce 71 to:
% 10.78/3.25 | (89) $false
% 10.78/3.25 |
% 10.78/3.25 |-The branch is then unsatisfiable
% 10.78/3.25 |-Branch two:
% 10.78/3.25 | (71) ~ (all_0_10_10 = 0)
% 10.78/3.25 | (91) ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_11_11) = v1 & in(v0, all_0_15_15) = 0)
% 10.78/3.25 |
% 10.78/3.25 | Instantiating (91) with all_40_0_32, all_40_1_33 yields:
% 10.78/3.25 | (92) ~ (all_40_0_32 = 0) & in(all_40_1_33, all_0_11_11) = all_40_0_32 & in(all_40_1_33, all_0_15_15) = 0
% 10.78/3.25 |
% 10.78/3.25 | Applying alpha-rule on (92) yields:
% 10.78/3.25 | (93) ~ (all_40_0_32 = 0)
% 10.78/3.25 | (94) in(all_40_1_33, all_0_11_11) = all_40_0_32
% 10.78/3.25 | (95) in(all_40_1_33, all_0_15_15) = 0
% 10.78/3.25 |
% 10.78/3.25 | Instantiating formula (47) with all_0_14_14, all_30_1_25, 0 and discharging atoms relation(all_0_14_14) = all_30_1_25, relation(all_0_14_14) = 0, yields:
% 10.78/3.25 | (96) all_30_1_25 = 0
% 10.78/3.25 |
% 10.78/3.25 | From (96) and (84) follows:
% 10.78/3.25 | (56) relation(all_0_14_14) = 0
% 10.78/3.25 |
% 10.78/3.25 | Instantiating formula (2) with all_40_1_33, all_0_13_13, all_0_15_15 and discharging atoms subset(all_0_15_15, all_0_13_13) = 0, in(all_40_1_33, all_0_15_15) = 0, yields:
% 10.78/3.25 | (98) in(all_40_1_33, all_0_13_13) = 0
% 10.78/3.25 |
% 10.78/3.25 | Instantiating formula (6) with all_40_1_33, all_0_13_13, all_0_14_14 and discharging atoms relation_dom(all_0_14_14) = all_0_13_13, in(all_40_1_33, all_0_13_13) = 0, yields:
% 10.78/3.25 | (99) ? [v0] : ? [v1] : ? [v2] : ((v2 = 0 & ordered_pair(all_40_1_33, v0) = v1 & in(v1, all_0_14_14) = 0) | ( ~ (v0 = 0) & relation(all_0_14_14) = v0))
% 10.78/3.25 |
% 10.78/3.25 | Instantiating (99) with all_65_0_38, all_65_1_39, all_65_2_40 yields:
% 10.78/3.25 | (100) (all_65_0_38 = 0 & ordered_pair(all_40_1_33, all_65_2_40) = all_65_1_39 & in(all_65_1_39, all_0_14_14) = 0) | ( ~ (all_65_2_40 = 0) & relation(all_0_14_14) = all_65_2_40)
% 10.78/3.25 |
% 10.78/3.25 +-Applying beta-rule and splitting (100), into two cases.
% 10.78/3.25 |-Branch one:
% 10.78/3.25 | (101) all_65_0_38 = 0 & ordered_pair(all_40_1_33, all_65_2_40) = all_65_1_39 & in(all_65_1_39, all_0_14_14) = 0
% 10.78/3.25 |
% 10.78/3.25 | Applying alpha-rule on (101) yields:
% 10.78/3.25 | (102) all_65_0_38 = 0
% 10.78/3.25 | (103) ordered_pair(all_40_1_33, all_65_2_40) = all_65_1_39
% 10.78/3.25 | (104) in(all_65_1_39, all_0_14_14) = 0
% 10.78/3.25 |
% 10.78/3.25 | Instantiating formula (23) with all_65_1_39, all_65_2_40, all_40_0_32, all_40_1_33, all_0_11_11, all_0_12_12, all_0_14_14 and discharging atoms relation_inverse_image(all_0_14_14, all_0_12_12) = all_0_11_11, ordered_pair(all_40_1_33, all_65_2_40) = all_65_1_39, relation(all_0_14_14) = 0, in(all_65_1_39, all_0_14_14) = 0, in(all_40_1_33, all_0_11_11) = all_40_0_32, yields:
% 10.78/3.26 | (105) all_40_0_32 = 0 | ? [v0] : ( ~ (v0 = 0) & in(all_65_2_40, all_0_12_12) = v0)
% 10.78/3.26 |
% 10.78/3.26 +-Applying beta-rule and splitting (105), into two cases.
% 10.78/3.26 |-Branch one:
% 10.78/3.26 | (106) all_40_0_32 = 0
% 10.78/3.26 |
% 10.78/3.26 | Equations (106) can reduce 93 to:
% 10.78/3.26 | (89) $false
% 10.78/3.26 |
% 10.78/3.26 |-The branch is then unsatisfiable
% 10.78/3.26 |-Branch two:
% 10.78/3.26 | (93) ~ (all_40_0_32 = 0)
% 10.78/3.26 | (109) ? [v0] : ( ~ (v0 = 0) & in(all_65_2_40, all_0_12_12) = v0)
% 10.78/3.26 |
% 10.78/3.26 | Instantiating (109) with all_91_0_43 yields:
% 10.78/3.26 | (110) ~ (all_91_0_43 = 0) & in(all_65_2_40, all_0_12_12) = all_91_0_43
% 10.78/3.26 |
% 10.78/3.26 | Applying alpha-rule on (110) yields:
% 10.78/3.26 | (111) ~ (all_91_0_43 = 0)
% 10.78/3.26 | (112) in(all_65_2_40, all_0_12_12) = all_91_0_43
% 10.78/3.26 |
% 10.78/3.26 | Instantiating formula (41) with all_65_1_39, all_40_1_33, all_91_0_43, all_65_2_40, all_0_12_12, all_0_15_15, all_0_14_14 and discharging atoms relation_image(all_0_14_14, all_0_15_15) = all_0_12_12, ordered_pair(all_40_1_33, all_65_2_40) = all_65_1_39, relation(all_0_14_14) = 0, in(all_65_1_39, all_0_14_14) = 0, in(all_65_2_40, all_0_12_12) = all_91_0_43, yields:
% 10.78/3.26 | (113) all_91_0_43 = 0 | ? [v0] : ( ~ (v0 = 0) & in(all_40_1_33, all_0_15_15) = v0)
% 10.78/3.26 |
% 10.78/3.26 +-Applying beta-rule and splitting (113), into two cases.
% 10.78/3.26 |-Branch one:
% 10.78/3.26 | (114) all_91_0_43 = 0
% 10.78/3.26 |
% 10.78/3.26 | Equations (114) can reduce 111 to:
% 10.78/3.26 | (89) $false
% 10.78/3.26 |
% 10.78/3.26 |-The branch is then unsatisfiable
% 10.78/3.26 |-Branch two:
% 10.78/3.26 | (111) ~ (all_91_0_43 = 0)
% 10.78/3.26 | (117) ? [v0] : ( ~ (v0 = 0) & in(all_40_1_33, all_0_15_15) = v0)
% 10.78/3.26 |
% 10.78/3.26 | Instantiating (117) with all_104_0_44 yields:
% 10.78/3.26 | (118) ~ (all_104_0_44 = 0) & in(all_40_1_33, all_0_15_15) = all_104_0_44
% 10.78/3.26 |
% 10.78/3.26 | Applying alpha-rule on (118) yields:
% 10.78/3.26 | (119) ~ (all_104_0_44 = 0)
% 10.78/3.26 | (120) in(all_40_1_33, all_0_15_15) = all_104_0_44
% 10.78/3.26 |
% 10.78/3.26 | Instantiating formula (31) with all_40_1_33, all_0_15_15, all_104_0_44, 0 and discharging atoms in(all_40_1_33, all_0_15_15) = all_104_0_44, in(all_40_1_33, all_0_15_15) = 0, yields:
% 10.78/3.26 | (121) all_104_0_44 = 0
% 10.78/3.26 |
% 10.78/3.26 | Equations (121) can reduce 119 to:
% 10.78/3.26 | (89) $false
% 10.78/3.26 |
% 10.78/3.26 |-The branch is then unsatisfiable
% 10.78/3.26 |-Branch two:
% 10.78/3.26 | (123) ~ (all_65_2_40 = 0) & relation(all_0_14_14) = all_65_2_40
% 10.78/3.26 |
% 10.78/3.26 | Applying alpha-rule on (123) yields:
% 10.78/3.26 | (124) ~ (all_65_2_40 = 0)
% 10.78/3.26 | (125) relation(all_0_14_14) = all_65_2_40
% 10.78/3.26 |
% 10.78/3.26 | Instantiating formula (47) with all_0_14_14, all_65_2_40, 0 and discharging atoms relation(all_0_14_14) = all_65_2_40, relation(all_0_14_14) = 0, yields:
% 10.78/3.26 | (126) all_65_2_40 = 0
% 10.78/3.26 |
% 10.78/3.26 | Equations (126) can reduce 124 to:
% 10.78/3.26 | (89) $false
% 10.78/3.26 |
% 10.78/3.26 |-The branch is then unsatisfiable
% 10.78/3.26 % SZS output end Proof for theBenchmark
% 10.78/3.26
% 10.78/3.26 2716ms
%------------------------------------------------------------------------------