TSTP Solution File: SEU226+3 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU226+3 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n022.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 08:47:53 EDT 2022
% Result : Theorem 5.66s 2.01s
% Output : Proof 10.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU226+3 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.33 % Computer : n022.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon Jun 20 09:33:46 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.52/0.59 ____ _
% 0.52/0.59 ___ / __ \_____(_)___ ________ __________
% 0.52/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.52/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.52/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.52/0.59
% 0.52/0.59 A Theorem Prover for First-Order Logic
% 0.52/0.59 (ePrincess v.1.0)
% 0.52/0.59
% 0.52/0.59 (c) Philipp Rümmer, 2009-2015
% 0.52/0.59 (c) Peter Backeman, 2014-2015
% 0.52/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.52/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.52/0.59 Bug reports to peter@backeman.se
% 0.52/0.59
% 0.52/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.52/0.59
% 0.52/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.74/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.62/0.96 Prover 0: Preprocessing ...
% 2.24/1.21 Prover 0: Warning: ignoring some quantifiers
% 2.40/1.24 Prover 0: Constructing countermodel ...
% 3.33/1.50 Prover 0: gave up
% 3.33/1.50 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 3.57/1.54 Prover 1: Preprocessing ...
% 4.11/1.67 Prover 1: Warning: ignoring some quantifiers
% 4.28/1.68 Prover 1: Constructing countermodel ...
% 5.66/2.00 Prover 1: proved (502ms)
% 5.66/2.00
% 5.66/2.00 No countermodel exists, formula is valid
% 5.66/2.01 % SZS status Theorem for theBenchmark
% 5.66/2.01
% 5.66/2.01 Generating proof ... Warning: ignoring some quantifiers
% 10.12/3.02 found it (size 39)
% 10.12/3.02
% 10.12/3.02 % SZS output start Proof for theBenchmark
% 10.12/3.02 Assumed formulas after preprocessing and simplification:
% 10.12/3.02 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ( ~ (v10 = 0) & ~ (v8 = 0) & ~ (v4 = 0) & relation_empty_yielding(v5) = 0 & relation_empty_yielding(empty_set) = 0 & subset(v3, v0) = v4 & relation_inverse_image(v1, v0) = v2 & relation_image(v1, v2) = v3 & one_to_one(v6) = 0 & relation(v14) = 0 & relation(v13) = 0 & relation(v11) = 0 & relation(v9) = 0 & relation(v6) = 0 & relation(v5) = 0 & relation(v1) = 0 & relation(empty_set) = 0 & function(v14) = 0 & function(v11) = 0 & function(v6) = 0 & function(v1) = 0 & empty(v13) = 0 & empty(v12) = 0 & empty(v11) = 0 & empty(v9) = v10 & empty(v7) = v8 & empty(empty_set) = 0 & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v19 = 0 | ~ (powerset(v17) = v18) | ~ (element(v16, v18) = 0) | ~ (element(v15, v17) = v19) | ? [v20] : ( ~ (v20 = 0) & in(v15, v16) = v20)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = 0 | ~ (powerset(v16) = v17) | ~ (element(v15, v17) = v18) | ? [v19] : ( ~ (v19 = 0) & subset(v15, v16) = v19)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (element(v18, v17) = v16) | ~ (element(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (subset(v18, v17) = v16) | ~ (subset(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (relation_inverse_image(v18, v17) = v16) | ~ (relation_inverse_image(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (relation_image(v18, v17) = v16) | ~ (relation_image(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (apply(v18, v17) = v16) | ~ (apply(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (in(v18, v17) = v16) | ~ (in(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (powerset(v17) = v18) | ~ (element(v16, v18) = 0) | ~ (in(v15, v16) = 0) | ? [v19] : ( ~ (v19 = 0) & empty(v17) = v19)) & ! [v15] : ! [v16] : ! [v17] : (v17 = 0 | ~ (element(v15, v16) = v17) | ? [v18] : ( ~ (v18 = 0) & in(v15, v16) = v18)) & ! [v15] : ! [v16] : ! [v17] : (v17 = 0 | ~ (subset(v15, v16) = v17) | ? [v18] : ? [v19] : ( ~ (v19 = 0) & in(v18, v16) = v19 & in(v18, v15) = 0)) & ! [v15] : ! [v16] : ! [v17] : (v16 = v15 | ~ (relation_empty_yielding(v17) = v16) | ~ (relation_empty_yielding(v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : (v16 = v15 | ~ (powerset(v17) = v16) | ~ (powerset(v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : (v16 = v15 | ~ (relation_dom(v17) = v16) | ~ (relation_dom(v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : (v16 = v15 | ~ (one_to_one(v17) = v16) | ~ (one_to_one(v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : (v16 = v15 | ~ (relation(v17) = v16) | ~ (relation(v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : (v16 = v15 | ~ (function(v17) = v16) | ~ (function(v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : (v16 = v15 | ~ (empty(v17) = v16) | ~ (empty(v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (powerset(v16) = v17) | ~ (element(v15, v17) = 0) | subset(v15, v16) = 0) & ! [v15] : ! [v16] : ! [v17] : ( ~ (subset(v15, v16) = 0) | ~ (in(v17, v15) = 0) | in(v17, v16) = 0) & ! [v15] : ! [v16] : (v16 = v15 | ~ (empty(v16) = 0) | ~ (empty(v15) = 0)) & ! [v15] : ! [v16] : (v16 = 0 | ~ (subset(v15, v15) = v16)) & ! [v15] : ! [v16] : (v16 = 0 | ~ (relation(v15) = v16) | ? [v17] : ( ~ (v17 = 0) & empty(v15) = v17)) & ! [v15] : ! [v16] : (v16 = 0 | ~ (function(v15) = v16) | ? [v17] : ( ~ (v17 = 0) & empty(v15) = v17)) & ! [v15] : ! [v16] : ( ~ (powerset(v15) = v16) | ? [v17] : ? [v18] : ? [v19] : ((v18 = 0 & ~ (v19 = 0) & element(v17, v16) = 0 & empty(v17) = v19) | (v17 = 0 & empty(v15) = 0))) & ! [v15] : ! [v16] : ( ~ (powerset(v15) = v16) | ? [v17] : ( ~ (v17 = 0) & empty(v16) = v17)) & ! [v15] : ! [v16] : ( ~ (powerset(v15) = v16) | ? [v17] : (element(v17, v16) = 0 & empty(v17) = 0)) & ! [v15] : ! [v16] : ( ~ (element(v15, v16) = 0) | ? [v17] : ? [v18] : (empty(v16) = v17 & in(v15, v16) = v18 & (v18 = 0 | v17 = 0))) & ! [v15] : ! [v16] : ( ~ (relation_dom(v15) = v16) | ? [v17] : ? [v18] : ? [v19] : (relation(v16) = v19 & empty(v16) = v18 & empty(v15) = v17 & ( ~ (v17 = 0) | (v19 = 0 & v18 = 0)))) & ! [v15] : ! [v16] : ( ~ (relation_dom(v15) = v16) | ? [v17] : ? [v18] : ? [v19] : (relation(v15) = v18 & empty(v16) = v19 & empty(v15) = v17 & ( ~ (v19 = 0) | ~ (v18 = 0) | v17 = 0))) & ! [v15] : ! [v16] : ( ~ (one_to_one(v15) = v16) | ? [v17] : ? [v18] : ? [v19] : (relation(v15) = v17 & function(v15) = v19 & empty(v15) = v18 & ( ~ (v19 = 0) | ~ (v18 = 0) | ~ (v17 = 0) | v16 = 0))) & ! [v15] : ! [v16] : ( ~ (in(v15, v16) = 0) | ? [v17] : ( ~ (v17 = 0) & empty(v16) = v17)) & ! [v15] : ! [v16] : ( ~ (in(v15, v16) = 0) | ? [v17] : ( ~ (v17 = 0) & in(v16, v15) = v17)) & ! [v15] : (v15 = empty_set | ~ (empty(v15) = 0)) & ! [v15] : ( ~ (function(v15) = 0) | ? [v16] : ? [v17] : (relation_dom(v15) = v17 & relation(v15) = v16 & ( ~ (v16 = 0) | ( ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v21 = 0 | ~ (relation_image(v15, v18) = v19) | ~ (in(v22, v17) = 0) | ~ (in(v20, v19) = v21) | ? [v23] : ? [v24] : (apply(v15, v22) = v24 & in(v22, v18) = v23 & ( ~ (v24 = v20) | ~ (v23 = 0)))) & ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_image(v15, v18) = v19) | ~ (in(v20, v19) = 0) | ? [v21] : (apply(v15, v21) = v20 & in(v21, v18) = 0 & in(v21, v17) = 0)) & ? [v18] : ! [v19] : ! [v20] : (v20 = v18 | ~ (relation_image(v15, v19) = v20) | ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : (in(v21, v18) = v22 & ( ~ (v22 = 0) | ! [v27] : ( ~ (in(v27, v17) = 0) | ? [v28] : ? [v29] : (apply(v15, v27) = v29 & in(v27, v19) = v28 & ( ~ (v29 = v21) | ~ (v28 = 0))))) & (v22 = 0 | (v26 = v21 & v25 = 0 & v24 = 0 & apply(v15, v23) = v21 & in(v23, v19) = 0 & in(v23, v17) = 0)))))))) & ! [v15] : ( ~ (function(v15) = 0) | ? [v16] : ? [v17] : (relation_dom(v15) = v17 & relation(v15) = v16 & ( ~ (v16 = 0) | ( ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (relation_inverse_image(v15, v18) = v19) | ~ (apply(v15, v20) = v21) | ~ (in(v21, v18) = v22) | ? [v23] : ? [v24] : (in(v20, v19) = v23 & in(v20, v17) = v24 & ( ~ (v23 = 0) | (v24 = 0 & v22 = 0)))) & ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (relation_inverse_image(v15, v18) = v19) | ~ (apply(v15, v20) = v21) | ~ (in(v21, v18) = 0) | ? [v22] : ? [v23] : (in(v20, v19) = v23 & in(v20, v17) = v22 & ( ~ (v22 = 0) | v23 = 0))) & ? [v18] : ! [v19] : ! [v20] : (v20 = v18 | ~ (relation_inverse_image(v15, v19) = v20) | ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : (apply(v15, v21) = v24 & in(v24, v19) = v25 & in(v21, v18) = v22 & in(v21, v17) = v23 & ( ~ (v25 = 0) | ~ (v23 = 0) | ~ (v22 = 0)) & (v22 = 0 | (v25 = 0 & v23 = 0)))))))) & ? [v15] : ? [v16] : element(v16, v15) = 0)
% 10.39/3.07 | 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 yields:
% 10.39/3.07 | (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 & subset(all_0_11_11, all_0_14_14) = all_0_10_10 & relation_inverse_image(all_0_13_13, all_0_14_14) = all_0_12_12 & relation_image(all_0_13_13, all_0_12_12) = all_0_11_11 & 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_13_13) = 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_13_13) = 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] : (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 | ~ (apply(v3, v2) = v1) | ~ (apply(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] : (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 | ~ (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] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, 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] : ( ~ (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] : ( ~ (function(v0) = 0) | ? [v1] : ? [v2] : (relation_dom(v0) = v2 & relation(v0) = v1 & ( ~ (v1 = 0) | ( ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v6 = 0 | ~ (relation_image(v0, v3) = v4) | ~ (in(v7, v2) = 0) | ~ (in(v5, v4) = v6) | ? [v8] : ? [v9] : (apply(v0, v7) = v9 & in(v7, v3) = v8 & ( ~ (v9 = v5) | ~ (v8 = 0)))) & ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_image(v0, v3) = v4) | ~ (in(v5, v4) = 0) | ? [v6] : (apply(v0, v6) = v5 & in(v6, v3) = 0 & in(v6, v2) = 0)) & ? [v3] : ! [v4] : ! [v5] : (v5 = v3 | ~ (relation_image(v0, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : (in(v6, v3) = v7 & ( ~ (v7 = 0) | ! [v12] : ( ~ (in(v12, v2) = 0) | ? [v13] : ? [v14] : (apply(v0, v12) = v14 & in(v12, v4) = v13 & ( ~ (v14 = v6) | ~ (v13 = 0))))) & (v7 = 0 | (v11 = v6 & v10 = 0 & v9 = 0 & apply(v0, v8) = v6 & in(v8, v4) = 0 & in(v8, v2) = 0)))))))) & ! [v0] : ( ~ (function(v0) = 0) | ? [v1] : ? [v2] : (relation_dom(v0) = v2 & relation(v0) = v1 & ( ~ (v1 = 0) | ( ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (relation_inverse_image(v0, v3) = v4) | ~ (apply(v0, v5) = v6) | ~ (in(v6, v3) = v7) | ? [v8] : ? [v9] : (in(v5, v4) = v8 & in(v5, v2) = v9 & ( ~ (v8 = 0) | (v9 = 0 & v7 = 0)))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (relation_inverse_image(v0, v3) = v4) | ~ (apply(v0, v5) = v6) | ~ (in(v6, v3) = 0) | ? [v7] : ? [v8] : (in(v5, v4) = v8 & in(v5, v2) = v7 & ( ~ (v7 = 0) | v8 = 0))) & ? [v3] : ! [v4] : ! [v5] : (v5 = v3 | ~ (relation_inverse_image(v0, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (apply(v0, v6) = v9 & in(v9, v4) = v10 & in(v6, v3) = v7 & in(v6, v2) = v8 & ( ~ (v10 = 0) | ~ (v8 = 0) | ~ (v7 = 0)) & (v7 = 0 | (v10 = 0 & v8 = 0)))))))) & ? [v0] : ? [v1] : element(v1, v0) = 0
% 10.39/3.09 |
% 10.39/3.09 | Applying alpha-rule on (1) yields:
% 10.39/3.09 | (2) relation(all_0_8_8) = 0
% 10.39/3.09 | (3) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0))
% 10.39/3.09 | (4) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 10.39/3.09 | (5) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | subset(v0, v1) = 0)
% 10.39/3.09 | (6) empty(all_0_1_1) = 0
% 10.39/3.09 | (7) one_to_one(all_0_8_8) = 0
% 10.39/3.09 | (8) function(all_0_13_13) = 0
% 10.39/3.09 | (9) function(all_0_3_3) = 0
% 10.39/3.09 | (10) ! [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))
% 10.39/3.09 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4))
% 10.39/3.09 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0)
% 10.39/3.09 | (13) relation_empty_yielding(all_0_9_9) = 0
% 10.39/3.09 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_inverse_image(v3, v2) = v1) | ~ (relation_inverse_image(v3, v2) = v0))
% 10.39/3.09 | (15) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_empty_yielding(v2) = v1) | ~ (relation_empty_yielding(v2) = v0))
% 10.39/3.09 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0))
% 10.39/3.09 | (17) ~ (all_0_10_10 = 0)
% 10.39/3.09 | (18) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 10.39/3.09 | (19) ~ (all_0_4_4 = 0)
% 10.39/3.09 | (20) relation(empty_set) = 0
% 10.39/3.10 | (21) relation(all_0_9_9) = 0
% 10.39/3.10 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 10.39/3.10 | (23) relation(all_0_0_0) = 0
% 10.39/3.10 | (24) empty(all_0_2_2) = 0
% 10.39/3.10 | (25) function(all_0_0_0) = 0
% 10.39/3.10 | (26) ! [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)))
% 10.39/3.10 | (27) empty(empty_set) = 0
% 10.39/3.10 | (28) empty(all_0_7_7) = all_0_6_6
% 10.39/3.10 | (29) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) = 0 & empty(v2) = 0))
% 10.39/3.10 | (30) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0))
% 10.39/3.10 | (31) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0))
% 10.39/3.10 | (32) relation_image(all_0_13_13, all_0_12_12) = all_0_11_11
% 10.39/3.10 | (33) relation(all_0_3_3) = 0
% 10.39/3.10 | (34) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3))
% 10.39/3.10 | (35) ! [v0] : ( ~ (function(v0) = 0) | ? [v1] : ? [v2] : (relation_dom(v0) = v2 & relation(v0) = v1 & ( ~ (v1 = 0) | ( ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (relation_inverse_image(v0, v3) = v4) | ~ (apply(v0, v5) = v6) | ~ (in(v6, v3) = v7) | ? [v8] : ? [v9] : (in(v5, v4) = v8 & in(v5, v2) = v9 & ( ~ (v8 = 0) | (v9 = 0 & v7 = 0)))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (relation_inverse_image(v0, v3) = v4) | ~ (apply(v0, v5) = v6) | ~ (in(v6, v3) = 0) | ? [v7] : ? [v8] : (in(v5, v4) = v8 & in(v5, v2) = v7 & ( ~ (v7 = 0) | v8 = 0))) & ? [v3] : ! [v4] : ! [v5] : (v5 = v3 | ~ (relation_inverse_image(v0, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (apply(v0, v6) = v9 & in(v9, v4) = v10 & in(v6, v3) = v7 & in(v6, v2) = v8 & ( ~ (v10 = 0) | ~ (v8 = 0) | ~ (v7 = 0)) & (v7 = 0 | (v10 = 0 & v8 = 0))))))))
% 10.39/3.10 | (36) empty(all_0_5_5) = all_0_4_4
% 10.39/3.10 | (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)))
% 10.39/3.10 | (38) ! [v0] : ! [v1] : (v1 = 0 | ~ (function(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2))
% 10.39/3.10 | (39) relation_empty_yielding(empty_set) = 0
% 10.39/3.10 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_image(v3, v2) = v1) | ~ (relation_image(v3, v2) = v0))
% 10.39/3.11 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 10.39/3.11 | (42) relation(all_0_13_13) = 0
% 10.39/3.11 | (43) ! [v0] : ! [v1] : ( ~ (element(v0, v1) = 0) | ? [v2] : ? [v3] : (empty(v1) = v2 & in(v0, v1) = v3 & (v3 = 0 | v2 = 0)))
% 10.39/3.11 | (44) relation(all_0_1_1) = 0
% 10.39/3.11 | (45) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0))
% 10.39/3.11 | (46) relation_inverse_image(all_0_13_13, all_0_14_14) = all_0_12_12
% 10.39/3.11 | (47) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0))
% 10.39/3.11 | (48) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation(v0) = v3 & empty(v1) = v4 & empty(v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2 = 0)))
% 10.39/3.11 | (49) relation(all_0_5_5) = 0
% 10.39/3.11 | (50) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0))
% 10.39/3.11 | (51) ? [v0] : ? [v1] : element(v1, v0) = 0
% 10.39/3.11 | (52) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1))
% 10.39/3.11 | (53) ~ (all_0_6_6 = 0)
% 10.39/3.11 | (54) function(all_0_8_8) = 0
% 10.39/3.11 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0))
% 10.39/3.11 | (56) ! [v0] : ! [v1] : (v1 = 0 | ~ (relation(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2))
% 10.39/3.11 | (57) ! [v0] : ( ~ (function(v0) = 0) | ? [v1] : ? [v2] : (relation_dom(v0) = v2 & relation(v0) = v1 & ( ~ (v1 = 0) | ( ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v6 = 0 | ~ (relation_image(v0, v3) = v4) | ~ (in(v7, v2) = 0) | ~ (in(v5, v4) = v6) | ? [v8] : ? [v9] : (apply(v0, v7) = v9 & in(v7, v3) = v8 & ( ~ (v9 = v5) | ~ (v8 = 0)))) & ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_image(v0, v3) = v4) | ~ (in(v5, v4) = 0) | ? [v6] : (apply(v0, v6) = v5 & in(v6, v3) = 0 & in(v6, v2) = 0)) & ? [v3] : ! [v4] : ! [v5] : (v5 = v3 | ~ (relation_image(v0, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : (in(v6, v3) = v7 & ( ~ (v7 = 0) | ! [v12] : ( ~ (in(v12, v2) = 0) | ? [v13] : ? [v14] : (apply(v0, v12) = v14 & in(v12, v4) = v13 & ( ~ (v14 = v6) | ~ (v13 = 0))))) & (v7 = 0 | (v11 = v6 & v10 = 0 & v9 = 0 & apply(v0, v8) = v6 & in(v8, v4) = 0 & in(v8, v2) = 0))))))))
% 10.39/3.11 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 10.39/3.11 | (59) subset(all_0_11_11, all_0_14_14) = all_0_10_10
% 10.39/3.12 | (60) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation(v1) = v4 & empty(v1) = v3 & empty(v0) = v2 & ( ~ (v2 = 0) | (v4 = 0 & v3 = 0))))
% 10.39/3.12 | (61) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 10.39/3.12 | (62) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 10.39/3.12 | (63) empty(all_0_3_3) = 0
% 10.39/3.12 | (64) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0))
% 10.39/3.12 | (65) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0))
% 10.39/3.12 |
% 10.39/3.12 | Instantiating formula (64) with all_0_10_10, all_0_14_14, all_0_11_11 and discharging atoms subset(all_0_11_11, all_0_14_14) = all_0_10_10, yields:
% 10.39/3.12 | (66) all_0_10_10 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_11_11) = 0 & in(v0, all_0_14_14) = v1)
% 10.39/3.12 |
% 10.39/3.12 | Instantiating formula (57) with all_0_13_13 and discharging atoms function(all_0_13_13) = 0, yields:
% 10.39/3.12 | (67) ? [v0] : ? [v1] : (relation_dom(all_0_13_13) = v1 & relation(all_0_13_13) = v0 & ( ~ (v0 = 0) | ( ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v5 = 0 | ~ (relation_image(all_0_13_13, v2) = v3) | ~ (in(v6, v1) = 0) | ~ (in(v4, v3) = v5) | ? [v7] : ? [v8] : (apply(all_0_13_13, v6) = v8 & in(v6, v2) = v7 & ( ~ (v8 = v4) | ~ (v7 = 0)))) & ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_image(all_0_13_13, v2) = v3) | ~ (in(v4, v3) = 0) | ? [v5] : (apply(all_0_13_13, v5) = v4 & in(v5, v2) = 0 & in(v5, v1) = 0)) & ? [v2] : ! [v3] : ! [v4] : (v4 = v2 | ~ (relation_image(all_0_13_13, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (in(v5, v2) = v6 & ( ~ (v6 = 0) | ! [v11] : ( ~ (in(v11, v1) = 0) | ? [v12] : ? [v13] : (apply(all_0_13_13, v11) = v13 & in(v11, v3) = v12 & ( ~ (v13 = v5) | ~ (v12 = 0))))) & (v6 = 0 | (v10 = v5 & v9 = 0 & v8 = 0 & apply(all_0_13_13, v7) = v5 & in(v7, v3) = 0 & in(v7, v1) = 0)))))))
% 10.39/3.12 |
% 10.39/3.13 | Instantiating formula (35) with all_0_13_13 and discharging atoms function(all_0_13_13) = 0, yields:
% 10.39/3.13 | (68) ? [v0] : ? [v1] : (relation_dom(all_0_13_13) = v1 & relation(all_0_13_13) = v0 & ( ~ (v0 = 0) | ( ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (relation_inverse_image(all_0_13_13, v2) = v3) | ~ (apply(all_0_13_13, v4) = v5) | ~ (in(v5, v2) = v6) | ? [v7] : ? [v8] : (in(v4, v3) = v7 & in(v4, v1) = v8 & ( ~ (v7 = 0) | (v8 = 0 & v6 = 0)))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_inverse_image(all_0_13_13, v2) = v3) | ~ (apply(all_0_13_13, v4) = v5) | ~ (in(v5, v2) = 0) | ? [v6] : ? [v7] : (in(v4, v3) = v7 & in(v4, v1) = v6 & ( ~ (v6 = 0) | v7 = 0))) & ? [v2] : ! [v3] : ! [v4] : (v4 = v2 | ~ (relation_inverse_image(all_0_13_13, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (apply(all_0_13_13, v5) = v8 & in(v8, v3) = v9 & in(v5, v2) = v6 & in(v5, v1) = v7 & ( ~ (v9 = 0) | ~ (v7 = 0) | ~ (v6 = 0)) & (v6 = 0 | (v9 = 0 & v7 = 0)))))))
% 10.39/3.13 |
% 10.39/3.13 | Instantiating (67) with all_24_0_19, all_24_1_20 yields:
% 10.39/3.13 | (69) relation_dom(all_0_13_13) = all_24_0_19 & relation(all_0_13_13) = all_24_1_20 & ( ~ (all_24_1_20 = 0) | ( ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (relation_image(all_0_13_13, v0) = v1) | ~ (in(v4, all_24_0_19) = 0) | ~ (in(v2, v1) = v3) | ? [v5] : ? [v6] : (apply(all_0_13_13, v4) = v6 & in(v4, v0) = v5 & ( ~ (v6 = v2) | ~ (v5 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_image(all_0_13_13, v0) = v1) | ~ (in(v2, v1) = 0) | ? [v3] : (apply(all_0_13_13, v3) = v2 & in(v3, v0) = 0 & in(v3, all_24_0_19) = 0)) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_image(all_0_13_13, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (in(v3, v0) = v4 & ( ~ (v4 = 0) | ! [v9] : ( ~ (in(v9, all_24_0_19) = 0) | ? [v10] : ? [v11] : (apply(all_0_13_13, v9) = v11 & in(v9, v1) = v10 & ( ~ (v11 = v3) | ~ (v10 = 0))))) & (v4 = 0 | (v8 = v3 & v7 = 0 & v6 = 0 & apply(all_0_13_13, v5) = v3 & in(v5, v1) = 0 & in(v5, all_24_0_19) = 0))))))
% 10.39/3.13 |
% 10.39/3.13 | Applying alpha-rule on (69) yields:
% 10.39/3.13 | (70) relation_dom(all_0_13_13) = all_24_0_19
% 10.39/3.13 | (71) relation(all_0_13_13) = all_24_1_20
% 10.39/3.13 | (72) ~ (all_24_1_20 = 0) | ( ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (relation_image(all_0_13_13, v0) = v1) | ~ (in(v4, all_24_0_19) = 0) | ~ (in(v2, v1) = v3) | ? [v5] : ? [v6] : (apply(all_0_13_13, v4) = v6 & in(v4, v0) = v5 & ( ~ (v6 = v2) | ~ (v5 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_image(all_0_13_13, v0) = v1) | ~ (in(v2, v1) = 0) | ? [v3] : (apply(all_0_13_13, v3) = v2 & in(v3, v0) = 0 & in(v3, all_24_0_19) = 0)) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_image(all_0_13_13, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (in(v3, v0) = v4 & ( ~ (v4 = 0) | ! [v9] : ( ~ (in(v9, all_24_0_19) = 0) | ? [v10] : ? [v11] : (apply(all_0_13_13, v9) = v11 & in(v9, v1) = v10 & ( ~ (v11 = v3) | ~ (v10 = 0))))) & (v4 = 0 | (v8 = v3 & v7 = 0 & v6 = 0 & apply(all_0_13_13, v5) = v3 & in(v5, v1) = 0 & in(v5, all_24_0_19) = 0)))))
% 10.39/3.13 |
% 10.39/3.13 | Instantiating (68) with all_30_0_25, all_30_1_26 yields:
% 10.39/3.13 | (73) relation_dom(all_0_13_13) = all_30_0_25 & relation(all_0_13_13) = all_30_1_26 & ( ~ (all_30_1_26 = 0) | ( ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_inverse_image(all_0_13_13, v0) = v1) | ~ (apply(all_0_13_13, v2) = v3) | ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v2, v1) = v5 & in(v2, all_30_0_25) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_inverse_image(all_0_13_13, v0) = v1) | ~ (apply(all_0_13_13, v2) = v3) | ~ (in(v3, v0) = 0) | ? [v4] : ? [v5] : (in(v2, v1) = v5 & in(v2, all_30_0_25) = v4 & ( ~ (v4 = 0) | v5 = 0))) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_inverse_image(all_0_13_13, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (apply(all_0_13_13, v3) = v6 & in(v6, v1) = v7 & in(v3, v0) = v4 & in(v3, all_30_0_25) = v5 & ( ~ (v7 = 0) | ~ (v5 = 0) | ~ (v4 = 0)) & (v4 = 0 | (v7 = 0 & v5 = 0))))))
% 10.39/3.14 |
% 10.39/3.14 | Applying alpha-rule on (73) yields:
% 10.39/3.14 | (74) relation_dom(all_0_13_13) = all_30_0_25
% 10.39/3.14 | (75) relation(all_0_13_13) = all_30_1_26
% 10.39/3.14 | (76) ~ (all_30_1_26 = 0) | ( ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_inverse_image(all_0_13_13, v0) = v1) | ~ (apply(all_0_13_13, v2) = v3) | ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v2, v1) = v5 & in(v2, all_30_0_25) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_inverse_image(all_0_13_13, v0) = v1) | ~ (apply(all_0_13_13, v2) = v3) | ~ (in(v3, v0) = 0) | ? [v4] : ? [v5] : (in(v2, v1) = v5 & in(v2, all_30_0_25) = v4 & ( ~ (v4 = 0) | v5 = 0))) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_inverse_image(all_0_13_13, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (apply(all_0_13_13, v3) = v6 & in(v6, v1) = v7 & in(v3, v0) = v4 & in(v3, all_30_0_25) = v5 & ( ~ (v7 = 0) | ~ (v5 = 0) | ~ (v4 = 0)) & (v4 = 0 | (v7 = 0 & v5 = 0)))))
% 10.39/3.14 |
% 10.39/3.14 +-Applying beta-rule and splitting (66), into two cases.
% 10.39/3.14 |-Branch one:
% 10.39/3.14 | (77) all_0_10_10 = 0
% 10.39/3.14 |
% 10.39/3.14 | Equations (77) can reduce 17 to:
% 10.39/3.14 | (78) $false
% 10.39/3.14 |
% 10.39/3.14 |-The branch is then unsatisfiable
% 10.39/3.14 |-Branch two:
% 10.39/3.14 | (17) ~ (all_0_10_10 = 0)
% 10.39/3.14 | (80) ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_11_11) = 0 & in(v0, all_0_14_14) = v1)
% 10.39/3.14 |
% 10.39/3.14 | Instantiating (80) with all_46_0_38, all_46_1_39 yields:
% 10.39/3.14 | (81) ~ (all_46_0_38 = 0) & in(all_46_1_39, all_0_11_11) = 0 & in(all_46_1_39, all_0_14_14) = all_46_0_38
% 10.39/3.14 |
% 10.39/3.14 | Applying alpha-rule on (81) yields:
% 10.39/3.14 | (82) ~ (all_46_0_38 = 0)
% 10.39/3.14 | (83) in(all_46_1_39, all_0_11_11) = 0
% 10.39/3.14 | (84) in(all_46_1_39, all_0_14_14) = all_46_0_38
% 10.39/3.14 |
% 10.39/3.14 | Instantiating formula (3) with all_0_13_13, all_30_1_26, 0 and discharging atoms relation(all_0_13_13) = all_30_1_26, relation(all_0_13_13) = 0, yields:
% 10.39/3.14 | (85) all_30_1_26 = 0
% 10.39/3.14 |
% 10.39/3.14 | Instantiating formula (3) with all_0_13_13, all_24_1_20, all_30_1_26 and discharging atoms relation(all_0_13_13) = all_30_1_26, relation(all_0_13_13) = all_24_1_20, yields:
% 10.39/3.14 | (86) all_30_1_26 = all_24_1_20
% 10.39/3.14 |
% 10.39/3.14 | Combining equations (86,85) yields a new equation:
% 10.39/3.14 | (87) all_24_1_20 = 0
% 10.39/3.14 |
% 10.39/3.14 | Simplifying 87 yields:
% 10.39/3.14 | (88) all_24_1_20 = 0
% 10.39/3.14 |
% 10.39/3.14 +-Applying beta-rule and splitting (72), into two cases.
% 10.39/3.14 |-Branch one:
% 10.39/3.14 | (89) ~ (all_24_1_20 = 0)
% 10.39/3.14 |
% 10.39/3.14 | Equations (88) can reduce 89 to:
% 10.39/3.14 | (78) $false
% 10.39/3.14 |
% 10.39/3.14 |-The branch is then unsatisfiable
% 10.39/3.14 |-Branch two:
% 10.39/3.14 | (88) all_24_1_20 = 0
% 10.39/3.14 | (92) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (relation_image(all_0_13_13, v0) = v1) | ~ (in(v4, all_24_0_19) = 0) | ~ (in(v2, v1) = v3) | ? [v5] : ? [v6] : (apply(all_0_13_13, v4) = v6 & in(v4, v0) = v5 & ( ~ (v6 = v2) | ~ (v5 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_image(all_0_13_13, v0) = v1) | ~ (in(v2, v1) = 0) | ? [v3] : (apply(all_0_13_13, v3) = v2 & in(v3, v0) = 0 & in(v3, all_24_0_19) = 0)) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_image(all_0_13_13, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (in(v3, v0) = v4 & ( ~ (v4 = 0) | ! [v9] : ( ~ (in(v9, all_24_0_19) = 0) | ? [v10] : ? [v11] : (apply(all_0_13_13, v9) = v11 & in(v9, v1) = v10 & ( ~ (v11 = v3) | ~ (v10 = 0))))) & (v4 = 0 | (v8 = v3 & v7 = 0 & v6 = 0 & apply(all_0_13_13, v5) = v3 & in(v5, v1) = 0 & in(v5, all_24_0_19) = 0))))
% 10.39/3.15 |
% 10.39/3.15 | Applying alpha-rule on (92) yields:
% 10.39/3.15 | (93) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (relation_image(all_0_13_13, v0) = v1) | ~ (in(v4, all_24_0_19) = 0) | ~ (in(v2, v1) = v3) | ? [v5] : ? [v6] : (apply(all_0_13_13, v4) = v6 & in(v4, v0) = v5 & ( ~ (v6 = v2) | ~ (v5 = 0))))
% 10.39/3.15 | (94) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_image(all_0_13_13, v0) = v1) | ~ (in(v2, v1) = 0) | ? [v3] : (apply(all_0_13_13, v3) = v2 & in(v3, v0) = 0 & in(v3, all_24_0_19) = 0))
% 10.39/3.15 | (95) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_image(all_0_13_13, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (in(v3, v0) = v4 & ( ~ (v4 = 0) | ! [v9] : ( ~ (in(v9, all_24_0_19) = 0) | ? [v10] : ? [v11] : (apply(all_0_13_13, v9) = v11 & in(v9, v1) = v10 & ( ~ (v11 = v3) | ~ (v10 = 0))))) & (v4 = 0 | (v8 = v3 & v7 = 0 & v6 = 0 & apply(all_0_13_13, v5) = v3 & in(v5, v1) = 0 & in(v5, all_24_0_19) = 0))))
% 10.39/3.15 |
% 10.39/3.15 +-Applying beta-rule and splitting (76), into two cases.
% 10.39/3.15 |-Branch one:
% 10.39/3.15 | (96) ~ (all_30_1_26 = 0)
% 10.39/3.15 |
% 10.39/3.15 | Equations (85) can reduce 96 to:
% 10.39/3.15 | (78) $false
% 10.39/3.15 |
% 10.39/3.15 |-The branch is then unsatisfiable
% 10.39/3.15 |-Branch two:
% 10.39/3.15 | (85) all_30_1_26 = 0
% 10.39/3.15 | (99) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_inverse_image(all_0_13_13, v0) = v1) | ~ (apply(all_0_13_13, v2) = v3) | ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v2, v1) = v5 & in(v2, all_30_0_25) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_inverse_image(all_0_13_13, v0) = v1) | ~ (apply(all_0_13_13, v2) = v3) | ~ (in(v3, v0) = 0) | ? [v4] : ? [v5] : (in(v2, v1) = v5 & in(v2, all_30_0_25) = v4 & ( ~ (v4 = 0) | v5 = 0))) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_inverse_image(all_0_13_13, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (apply(all_0_13_13, v3) = v6 & in(v6, v1) = v7 & in(v3, v0) = v4 & in(v3, all_30_0_25) = v5 & ( ~ (v7 = 0) | ~ (v5 = 0) | ~ (v4 = 0)) & (v4 = 0 | (v7 = 0 & v5 = 0))))
% 10.39/3.15 |
% 10.39/3.15 | Applying alpha-rule on (99) yields:
% 10.39/3.15 | (100) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_inverse_image(all_0_13_13, v0) = v1) | ~ (apply(all_0_13_13, v2) = v3) | ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v2, v1) = v5 & in(v2, all_30_0_25) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = 0))))
% 10.39/3.15 | (101) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_inverse_image(all_0_13_13, v0) = v1) | ~ (apply(all_0_13_13, v2) = v3) | ~ (in(v3, v0) = 0) | ? [v4] : ? [v5] : (in(v2, v1) = v5 & in(v2, all_30_0_25) = v4 & ( ~ (v4 = 0) | v5 = 0)))
% 10.39/3.15 | (102) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_inverse_image(all_0_13_13, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (apply(all_0_13_13, v3) = v6 & in(v6, v1) = v7 & in(v3, v0) = v4 & in(v3, all_30_0_25) = v5 & ( ~ (v7 = 0) | ~ (v5 = 0) | ~ (v4 = 0)) & (v4 = 0 | (v7 = 0 & v5 = 0))))
% 10.39/3.15 |
% 10.39/3.15 | Instantiating formula (94) with all_46_1_39, all_0_11_11, all_0_12_12 and discharging atoms relation_image(all_0_13_13, all_0_12_12) = all_0_11_11, in(all_46_1_39, all_0_11_11) = 0, yields:
% 10.84/3.15 | (103) ? [v0] : (apply(all_0_13_13, v0) = all_46_1_39 & in(v0, all_24_0_19) = 0 & in(v0, all_0_12_12) = 0)
% 10.84/3.15 |
% 10.84/3.15 | Instantiating (103) with all_110_0_57 yields:
% 10.84/3.15 | (104) apply(all_0_13_13, all_110_0_57) = all_46_1_39 & in(all_110_0_57, all_24_0_19) = 0 & in(all_110_0_57, all_0_12_12) = 0
% 10.84/3.15 |
% 10.84/3.15 | Applying alpha-rule on (104) yields:
% 10.84/3.15 | (105) apply(all_0_13_13, all_110_0_57) = all_46_1_39
% 10.84/3.16 | (106) in(all_110_0_57, all_24_0_19) = 0
% 10.84/3.16 | (107) in(all_110_0_57, all_0_12_12) = 0
% 10.84/3.16 |
% 10.84/3.16 | Instantiating formula (100) with all_46_0_38, all_46_1_39, all_110_0_57, all_0_12_12, all_0_14_14 and discharging atoms relation_inverse_image(all_0_13_13, all_0_14_14) = all_0_12_12, apply(all_0_13_13, all_110_0_57) = all_46_1_39, in(all_46_1_39, all_0_14_14) = all_46_0_38, yields:
% 10.84/3.16 | (108) ? [v0] : ? [v1] : (in(all_110_0_57, all_30_0_25) = v1 & in(all_110_0_57, all_0_12_12) = v0 & ( ~ (v0 = 0) | (v1 = 0 & all_46_0_38 = 0)))
% 10.84/3.16 |
% 10.84/3.16 | Instantiating (108) with all_183_0_86, all_183_1_87 yields:
% 10.84/3.16 | (109) in(all_110_0_57, all_30_0_25) = all_183_0_86 & in(all_110_0_57, all_0_12_12) = all_183_1_87 & ( ~ (all_183_1_87 = 0) | (all_183_0_86 = 0 & all_46_0_38 = 0))
% 10.84/3.16 |
% 10.84/3.16 | Applying alpha-rule on (109) yields:
% 10.84/3.16 | (110) in(all_110_0_57, all_30_0_25) = all_183_0_86
% 10.84/3.16 | (111) in(all_110_0_57, all_0_12_12) = all_183_1_87
% 10.84/3.16 | (112) ~ (all_183_1_87 = 0) | (all_183_0_86 = 0 & all_46_0_38 = 0)
% 10.84/3.16 |
% 10.84/3.16 +-Applying beta-rule and splitting (112), into two cases.
% 10.84/3.16 |-Branch one:
% 10.84/3.16 | (113) ~ (all_183_1_87 = 0)
% 10.84/3.16 |
% 10.84/3.16 | Instantiating formula (22) with all_110_0_57, all_0_12_12, all_183_1_87, 0 and discharging atoms in(all_110_0_57, all_0_12_12) = all_183_1_87, in(all_110_0_57, all_0_12_12) = 0, yields:
% 10.84/3.16 | (114) all_183_1_87 = 0
% 10.84/3.16 |
% 10.84/3.16 | Equations (114) can reduce 113 to:
% 10.84/3.16 | (78) $false
% 10.84/3.16 |
% 10.84/3.16 |-The branch is then unsatisfiable
% 10.84/3.16 |-Branch two:
% 10.84/3.16 | (114) all_183_1_87 = 0
% 10.84/3.16 | (117) all_183_0_86 = 0 & all_46_0_38 = 0
% 10.84/3.16 |
% 10.84/3.16 | Applying alpha-rule on (117) yields:
% 10.84/3.16 | (118) all_183_0_86 = 0
% 10.84/3.16 | (119) all_46_0_38 = 0
% 10.84/3.16 |
% 10.84/3.16 | Equations (119) can reduce 82 to:
% 10.84/3.16 | (78) $false
% 10.84/3.16 |
% 10.84/3.16 |-The branch is then unsatisfiable
% 10.84/3.16 % SZS output end Proof for theBenchmark
% 10.84/3.16
% 10.84/3.16 2557ms
%------------------------------------------------------------------------------