TSTP Solution File: SEU182+1 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU182+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n028.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 08:47:23 EDT 2022
% Result : Theorem 5.25s 1.96s
% Output : Proof 8.01s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU182+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.33 % Computer : n028.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 : Sun Jun 19 07:22:30 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.59/0.59 ____ _
% 0.59/0.59 ___ / __ \_____(_)___ ________ __________
% 0.59/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.59/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.59/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.59/0.59
% 0.59/0.59 A Theorem Prover for First-Order Logic
% 0.59/0.59 (ePrincess v.1.0)
% 0.59/0.59
% 0.59/0.59 (c) Philipp Rümmer, 2009-2015
% 0.59/0.59 (c) Peter Backeman, 2014-2015
% 0.59/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.59/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.59/0.59 Bug reports to peter@backeman.se
% 0.59/0.59
% 0.59/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.59/0.59
% 0.59/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.76/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.64/0.95 Prover 0: Preprocessing ...
% 2.30/1.22 Prover 0: Warning: ignoring some quantifiers
% 2.42/1.25 Prover 0: Constructing countermodel ...
% 3.61/1.58 Prover 0: gave up
% 3.61/1.58 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 3.61/1.61 Prover 1: Preprocessing ...
% 4.22/1.72 Prover 1: Warning: ignoring some quantifiers
% 4.22/1.73 Prover 1: Constructing countermodel ...
% 5.25/1.96 Prover 1: proved (376ms)
% 5.25/1.96
% 5.25/1.96 No countermodel exists, formula is valid
% 5.25/1.96 % SZS status Theorem for theBenchmark
% 5.25/1.96
% 5.25/1.96 Generating proof ... Warning: ignoring some quantifiers
% 7.56/2.48 found it (size 47)
% 7.56/2.48
% 7.56/2.48 % SZS output start Proof for theBenchmark
% 7.56/2.48 Assumed formulas after preprocessing and simplification:
% 7.56/2.48 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ( ~ (v7 = 0) & ~ (v5 = 0) & empty(v9) = 0 & empty(v8) = 0 & empty(v6) = v7 & empty(empty_set) = 0 & relation_composition(v0, v2) = v3 & relation_dom(v3) = v4 & relation_dom(v0) = v1 & relation(v9) = 0 & relation(v2) = 0 & relation(v0) = 0 & subset(v4, v1) = v5 & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = 0 | ~ (relation_composition(v10, v11) = v12) | ~ (relation(v12) = 0) | ~ (relation(v10) = 0) | ~ (ordered_pair(v13, v17) = v18) | ~ (ordered_pair(v13, v14) = v15) | ~ (in(v18, v10) = 0) | ~ (in(v15, v12) = v16) | ? [v19] : ? [v20] : (( ~ (v20 = 0) & ordered_pair(v17, v14) = v19 & in(v19, v11) = v20) | ( ~ (v19 = 0) & relation(v11) = v19))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = 0 | ~ (relation_dom(v10) = v11) | ~ (ordered_pair(v12, v14) = v15) | ~ (in(v15, v10) = 0) | ~ (in(v12, v11) = v13) | ? [v16] : ( ~ (v16 = 0) & relation(v10) = v16)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (relation_composition(v10, v11) = v12) | ~ (relation(v12) = 0) | ~ (relation(v10) = 0) | ~ (ordered_pair(v13, v14) = v15) | ~ (in(v15, v12) = 0) | ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ((v20 = 0 & v18 = 0 & ordered_pair(v16, v14) = v19 & ordered_pair(v13, v16) = v17 & in(v19, v11) = 0 & in(v17, v10) = 0) | ( ~ (v16 = 0) & relation(v11) = v16))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (powerset(v12) = v13) | ~ (element(v11, v13) = 0) | ~ (element(v10, v12) = v14) | ? [v15] : ( ~ (v15 = 0) & in(v10, v11) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (singleton(v10) = v13) | ~ (unordered_pair(v12, v13) = v14) | ~ (unordered_pair(v10, v11) = v12) | ordered_pair(v10, v11) = v14) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v12 | ~ (relation_composition(v10, v11) = v12) | ~ (relation(v13) = 0) | ~ (relation(v10) = 0) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : (( ~ (v14 = 0) & relation(v11) = v14) | (ordered_pair(v14, v15) = v16 & in(v16, v13) = v17 & ( ~ (v17 = 0) | ! [v23] : ! [v24] : ( ~ (ordered_pair(v14, v23) = v24) | ~ (in(v24, v10) = 0) | ? [v25] : ? [v26] : ( ~ (v26 = 0) & ordered_pair(v23, v15) = v25 & in(v25, v11) = v26))) & (v17 = 0 | (v22 = 0 & v20 = 0 & ordered_pair(v18, v15) = v21 & ordered_pair(v14, v18) = v19 & in(v21, v11) = 0 & in(v19, v10) = 0))))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (powerset(v11) = v12) | ~ (element(v10, v12) = v13) | ? [v14] : ( ~ (v14 = 0) & subset(v10, v11) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (element(v13, v12) = v11) | ~ (element(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (relation_composition(v13, v12) = v11) | ~ (relation_composition(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (ordered_pair(v13, v12) = v11) | ~ (ordered_pair(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (subset(v13, v12) = v11) | ~ (subset(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (unordered_pair(v13, v12) = v11) | ~ (unordered_pair(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (in(v13, v12) = v11) | ~ (in(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (powerset(v12) = v13) | ~ (element(v11, v13) = 0) | ~ (in(v10, v11) = 0) | ? [v14] : ( ~ (v14 = 0) & empty(v12) = v14)) & ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (element(v10, v11) = v12) | ? [v13] : ( ~ (v13 = 0) & in(v10, v11) = v13)) & ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (subset(v10, v11) = v12) | ? [v13] : ? [v14] : ( ~ (v14 = 0) & in(v13, v11) = v14 & in(v13, v10) = 0)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (powerset(v12) = v11) | ~ (powerset(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (empty(v12) = v11) | ~ (empty(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (singleton(v12) = v11) | ~ (singleton(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (relation_dom(v12) = v11) | ~ (relation_dom(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (relation(v12) = v11) | ~ (relation(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (powerset(v11) = v12) | ~ (element(v10, v12) = 0) | subset(v10, v11) = 0) & ! [v10] : ! [v11] : ! [v12] : ( ~ (relation_composition(v10, v11) = v12) | ? [v13] : ? [v14] : ? [v15] : (relation(v12) = v15 & relation(v11) = v14 & relation(v10) = v13 & ( ~ (v14 = 0) | ~ (v13 = 0) | v15 = 0))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (relation_dom(v10) = v11) | ~ (in(v12, v11) = 0) | ? [v13] : ? [v14] : ? [v15] : ((v15 = 0 & ordered_pair(v12, v13) = v14 & in(v14, v10) = 0) | ( ~ (v13 = 0) & relation(v10) = v13))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (ordered_pair(v10, v11) = v12) | ? [v13] : ( ~ (v13 = 0) & empty(v12) = v13)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (subset(v10, v11) = 0) | ~ (in(v12, v10) = 0) | in(v12, v11) = 0) & ! [v10] : ! [v11] : ! [v12] : ( ~ (unordered_pair(v10, v11) = v12) | unordered_pair(v11, v10) = v12) & ! [v10] : ! [v11] : ! [v12] : ( ~ (unordered_pair(v10, v11) = v12) | ? [v13] : ( ~ (v13 = 0) & empty(v12) = v13)) & ? [v10] : ! [v11] : ! [v12] : (v12 = v10 | ~ (relation_dom(v11) = v12) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : (( ~ (v13 = 0) & relation(v11) = v13) | (in(v13, v10) = v14 & ( ~ (v14 = 0) | ! [v18] : ! [v19] : ( ~ (ordered_pair(v13, v18) = v19) | ~ (in(v19, v11) = 0))) & (v14 = 0 | (v17 = 0 & ordered_pair(v13, v15) = v16 & in(v16, v11) = 0))))) & ! [v10] : ! [v11] : (v11 = v10 | ~ (empty(v11) = 0) | ~ (empty(v10) = 0)) & ! [v10] : ! [v11] : (v11 = 0 | ~ (subset(v10, v10) = v11)) & ! [v10] : ! [v11] : ( ~ (powerset(v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ((v13 = 0 & ~ (v14 = 0) & empty(v12) = v14 & element(v12, v11) = 0) | (v12 = 0 & empty(v10) = 0))) & ! [v10] : ! [v11] : ( ~ (powerset(v10) = v11) | ? [v12] : ( ~ (v12 = 0) & empty(v11) = v12)) & ! [v10] : ! [v11] : ( ~ (powerset(v10) = v11) | ? [v12] : (empty(v12) = 0 & element(v12, v11) = 0)) & ! [v10] : ! [v11] : ( ~ (element(v10, v11) = 0) | ? [v12] : ? [v13] : (empty(v11) = v12 & in(v10, v11) = v13 & (v13 = 0 | v12 = 0))) & ! [v10] : ! [v11] : ( ~ (singleton(v10) = v11) | ? [v12] : ( ~ (v12 = 0) & empty(v11) = v12)) & ! [v10] : ! [v11] : ( ~ (in(v10, v11) = 0) | ? [v12] : ( ~ (v12 = 0) & empty(v11) = v12)) & ! [v10] : ! [v11] : ( ~ (in(v10, v11) = 0) | ? [v12] : ( ~ (v12 = 0) & in(v11, v10) = v12)) & ! [v10] : (v10 = empty_set | ~ (empty(v10) = 0)) & ? [v10] : ? [v11] : element(v11, v10) = 0)
% 8.01/2.52 | 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 yields:
% 8.01/2.52 | (1) ~ (all_0_2_2 = 0) & ~ (all_0_4_4 = 0) & empty(all_0_0_0) = 0 & empty(all_0_1_1) = 0 & empty(all_0_3_3) = all_0_2_2 & empty(empty_set) = 0 & relation_composition(all_0_9_9, all_0_7_7) = all_0_6_6 & relation_dom(all_0_6_6) = all_0_5_5 & relation_dom(all_0_9_9) = all_0_8_8 & relation(all_0_0_0) = 0 & relation(all_0_7_7) = 0 & relation(all_0_9_9) = 0 & subset(all_0_5_5, all_0_8_8) = all_0_4_4 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = 0 | ~ (relation_composition(v0, v1) = v2) | ~ (relation(v2) = 0) | ~ (relation(v0) = 0) | ~ (ordered_pair(v3, v7) = v8) | ~ (ordered_pair(v3, v4) = v5) | ~ (in(v8, v0) = 0) | ~ (in(v5, v2) = v6) | ? [v9] : ? [v10] : (( ~ (v10 = 0) & ordered_pair(v7, v4) = v9 & in(v9, v1) = v10) | ( ~ (v9 = 0) & relation(v1) = v9))) & ! [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] : ! [v5] : ( ~ (relation_composition(v0, v1) = v2) | ~ (relation(v2) = 0) | ~ (relation(v0) = 0) | ~ (ordered_pair(v3, v4) = v5) | ~ (in(v5, v2) = 0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ((v10 = 0 & v8 = 0 & ordered_pair(v6, v4) = v9 & ordered_pair(v3, v6) = v7 & in(v9, v1) = 0 & in(v7, v0) = 0) | ( ~ (v6 = 0) & relation(v1) = 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 = v2 | ~ (relation_composition(v0, v1) = v2) | ~ (relation(v3) = 0) | ~ (relation(v0) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : (( ~ (v4 = 0) & relation(v1) = v4) | (ordered_pair(v4, v5) = v6 & in(v6, v3) = v7 & ( ~ (v7 = 0) | ! [v13] : ! [v14] : ( ~ (ordered_pair(v4, v13) = v14) | ~ (in(v14, v0) = 0) | ? [v15] : ? [v16] : ( ~ (v16 = 0) & ordered_pair(v13, v5) = v15 & in(v15, v1) = v16))) & (v7 = 0 | (v12 = 0 & v10 = 0 & ordered_pair(v8, v5) = v11 & ordered_pair(v4, v8) = v9 & in(v11, v1) = 0 & in(v9, v0) = 0))))) & ! [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 | ~ (relation_composition(v3, v2) = v1) | ~ (relation_composition(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 | ~ (subset(v3, v2) = v1) | ~ (subset(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] : (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 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(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 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | subset(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (relation(v2) = v5 & relation(v1) = v4 & relation(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 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] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0) & ! [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] : ( ~ (powerset(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v3 = 0 & ~ (v4 = 0) & empty(v2) = v4 & element(v2, v1) = 0) | (v2 = 0 & empty(v0) = 0))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (empty(v2) = 0 & element(v2, v1) = 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] : ( ~ (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
% 8.01/2.53 |
% 8.01/2.53 | Applying alpha-rule on (1) yields:
% 8.01/2.53 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 8.01/2.53 | (3) relation(all_0_9_9) = 0
% 8.01/2.53 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4))
% 8.01/2.53 | (5) empty(all_0_1_1) = 0
% 8.01/2.53 | (6) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0))
% 8.01/2.53 | (7) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 8.01/2.53 | (8) relation_dom(all_0_6_6) = all_0_5_5
% 8.01/2.53 | (9) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 8.01/2.53 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (relation(v2) = v5 & relation(v1) = v4 & relation(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0)))
% 8.01/2.54 | (11) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 8.01/2.54 | (12) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 8.01/2.54 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 8.01/2.54 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 8.01/2.54 | (15) relation(all_0_7_7) = 0
% 8.01/2.54 | (16) relation_dom(all_0_9_9) = all_0_8_8
% 8.01/2.54 | (17) relation(all_0_0_0) = 0
% 8.01/2.54 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4)
% 8.01/2.54 | (19) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0))
% 8.01/2.54 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (relation_composition(v0, v1) = v2) | ~ (relation(v3) = 0) | ~ (relation(v0) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : (( ~ (v4 = 0) & relation(v1) = v4) | (ordered_pair(v4, v5) = v6 & in(v6, v3) = v7 & ( ~ (v7 = 0) | ! [v13] : ! [v14] : ( ~ (ordered_pair(v4, v13) = v14) | ~ (in(v14, v0) = 0) | ? [v15] : ? [v16] : ( ~ (v16 = 0) & ordered_pair(v13, v5) = v15 & in(v15, v1) = v16))) & (v7 = 0 | (v12 = 0 & v10 = 0 & ordered_pair(v8, v5) = v11 & ordered_pair(v4, v8) = v9 & in(v11, v1) = 0 & in(v9, v0) = 0)))))
% 8.01/2.54 | (21) ! [v0] : ! [v1] : ( ~ (element(v0, v1) = 0) | ? [v2] : ? [v3] : (empty(v1) = v2 & in(v0, v1) = v3 & (v3 = 0 | v2 = 0)))
% 8.01/2.54 | (22) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | subset(v0, v1) = 0)
% 8.01/2.54 | (23) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0))
% 8.01/2.54 | (24) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3))
% 8.01/2.54 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_composition(v0, v1) = v2) | ~ (relation(v2) = 0) | ~ (relation(v0) = 0) | ~ (ordered_pair(v3, v4) = v5) | ~ (in(v5, v2) = 0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ((v10 = 0 & v8 = 0 & ordered_pair(v6, v4) = v9 & ordered_pair(v3, v6) = v7 & in(v9, v1) = 0 & in(v7, v0) = 0) | ( ~ (v6 = 0) & relation(v1) = v6)))
% 8.01/2.54 | (26) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (empty(v2) = 0 & element(v2, v1) = 0))
% 8.01/2.54 | (27) empty(empty_set) = 0
% 8.01/2.54 | (28) empty(all_0_0_0) = 0
% 8.01/2.54 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0))
% 8.01/2.54 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 8.01/2.54 | (31) ? [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)))))
% 8.01/2.54 | (32) ~ (all_0_4_4 = 0)
% 8.01/2.54 | (33) subset(all_0_5_5, all_0_8_8) = all_0_4_4
% 8.01/2.54 | (34) empty(all_0_3_3) = all_0_2_2
% 8.01/2.54 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = 0 | ~ (relation_composition(v0, v1) = v2) | ~ (relation(v2) = 0) | ~ (relation(v0) = 0) | ~ (ordered_pair(v3, v7) = v8) | ~ (ordered_pair(v3, v4) = v5) | ~ (in(v8, v0) = 0) | ~ (in(v5, v2) = v6) | ? [v9] : ? [v10] : (( ~ (v10 = 0) & ordered_pair(v7, v4) = v9 & in(v9, v1) = v10) | ( ~ (v9 = 0) & relation(v1) = v9)))
% 8.01/2.54 | (36) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0))
% 8.01/2.54 | (37) ! [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))
% 8.01/2.54 | (38) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0))
% 8.01/2.54 | (39) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0)
% 8.01/2.54 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (element(v0, v2) = v4) | ? [v5] : ( ~ (v5 = 0) & in(v0, v1) = v5))
% 8.01/2.54 | (41) ? [v0] : ? [v1] : element(v1, v0) = 0
% 8.01/2.54 | (42) ! [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)))
% 8.01/2.54 | (43) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3))
% 8.01/2.54 | (44) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3))
% 8.01/2.55 | (45) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 8.01/2.55 | (46) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1))
% 8.01/2.55 | (47) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v3 = 0 & ~ (v4 = 0) & empty(v2) = v4 & element(v2, v1) = 0) | (v2 = 0 & empty(v0) = 0)))
% 8.01/2.55 | (48) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0))
% 8.01/2.55 | (49) relation_composition(all_0_9_9, all_0_7_7) = all_0_6_6
% 8.01/2.55 | (50) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0))
% 8.01/2.55 | (51) ~ (all_0_2_2 = 0)
% 8.01/2.55 | (52) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2)
% 8.01/2.55 | (53) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 8.01/2.55 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_composition(v3, v2) = v1) | ~ (relation_composition(v3, v2) = v0))
% 8.01/2.55 |
% 8.01/2.55 | Instantiating formula (10) with all_0_6_6, all_0_7_7, all_0_9_9 and discharging atoms relation_composition(all_0_9_9, all_0_7_7) = all_0_6_6, yields:
% 8.01/2.55 | (55) ? [v0] : ? [v1] : ? [v2] : (relation(all_0_6_6) = v2 & relation(all_0_7_7) = v1 & relation(all_0_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 8.01/2.55 |
% 8.01/2.55 | Instantiating formula (48) with all_0_4_4, all_0_8_8, all_0_5_5 and discharging atoms subset(all_0_5_5, all_0_8_8) = all_0_4_4, yields:
% 8.01/2.55 | (56) all_0_4_4 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_5_5) = 0 & in(v0, all_0_8_8) = v1)
% 8.01/2.55 |
% 8.01/2.55 | Instantiating (55) with all_24_0_13, all_24_1_14, all_24_2_15 yields:
% 8.01/2.55 | (57) relation(all_0_6_6) = all_24_0_13 & relation(all_0_7_7) = all_24_1_14 & relation(all_0_9_9) = all_24_2_15 & ( ~ (all_24_1_14 = 0) | ~ (all_24_2_15 = 0) | all_24_0_13 = 0)
% 8.01/2.55 |
% 8.01/2.55 | Applying alpha-rule on (57) yields:
% 8.01/2.55 | (58) relation(all_0_6_6) = all_24_0_13
% 8.01/2.55 | (59) relation(all_0_7_7) = all_24_1_14
% 8.01/2.55 | (60) relation(all_0_9_9) = all_24_2_15
% 8.01/2.55 | (61) ~ (all_24_1_14 = 0) | ~ (all_24_2_15 = 0) | all_24_0_13 = 0
% 8.01/2.55 |
% 8.01/2.55 +-Applying beta-rule and splitting (56), into two cases.
% 8.01/2.55 |-Branch one:
% 8.01/2.55 | (62) all_0_4_4 = 0
% 8.01/2.55 |
% 8.01/2.55 | Equations (62) can reduce 32 to:
% 8.01/2.55 | (63) $false
% 8.01/2.55 |
% 8.01/2.55 |-The branch is then unsatisfiable
% 8.01/2.55 |-Branch two:
% 8.01/2.55 | (32) ~ (all_0_4_4 = 0)
% 8.01/2.55 | (65) ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_5_5) = 0 & in(v0, all_0_8_8) = v1)
% 8.01/2.55 |
% 8.01/2.55 | Instantiating (65) with all_32_0_18, all_32_1_19 yields:
% 8.01/2.55 | (66) ~ (all_32_0_18 = 0) & in(all_32_1_19, all_0_5_5) = 0 & in(all_32_1_19, all_0_8_8) = all_32_0_18
% 8.01/2.55 |
% 8.01/2.55 | Applying alpha-rule on (66) yields:
% 8.01/2.55 | (67) ~ (all_32_0_18 = 0)
% 8.01/2.55 | (68) in(all_32_1_19, all_0_5_5) = 0
% 8.01/2.55 | (69) in(all_32_1_19, all_0_8_8) = all_32_0_18
% 8.01/2.55 |
% 8.01/2.55 | Instantiating formula (36) with all_0_7_7, all_24_1_14, 0 and discharging atoms relation(all_0_7_7) = all_24_1_14, relation(all_0_7_7) = 0, yields:
% 8.01/2.55 | (70) all_24_1_14 = 0
% 8.01/2.55 |
% 8.01/2.55 | Instantiating formula (36) with all_0_9_9, all_24_2_15, 0 and discharging atoms relation(all_0_9_9) = all_24_2_15, relation(all_0_9_9) = 0, yields:
% 8.01/2.55 | (71) all_24_2_15 = 0
% 8.01/2.55 |
% 8.01/2.55 | From (70) and (59) follows:
% 8.01/2.55 | (15) relation(all_0_7_7) = 0
% 8.01/2.55 |
% 8.01/2.55 | From (71) and (60) follows:
% 8.01/2.55 | (3) relation(all_0_9_9) = 0
% 8.01/2.55 |
% 8.01/2.55 +-Applying beta-rule and splitting (61), into two cases.
% 8.01/2.55 |-Branch one:
% 8.01/2.55 | (74) ~ (all_24_1_14 = 0)
% 8.01/2.55 |
% 8.01/2.55 | Equations (70) can reduce 74 to:
% 8.01/2.55 | (63) $false
% 8.01/2.55 |
% 8.01/2.55 |-The branch is then unsatisfiable
% 8.01/2.55 |-Branch two:
% 8.01/2.55 | (70) all_24_1_14 = 0
% 8.01/2.55 | (77) ~ (all_24_2_15 = 0) | all_24_0_13 = 0
% 8.01/2.55 |
% 8.01/2.55 +-Applying beta-rule and splitting (77), into two cases.
% 8.01/2.55 |-Branch one:
% 8.01/2.55 | (78) ~ (all_24_2_15 = 0)
% 8.01/2.56 |
% 8.01/2.56 | Equations (71) can reduce 78 to:
% 8.01/2.56 | (63) $false
% 8.01/2.56 |
% 8.01/2.56 |-The branch is then unsatisfiable
% 8.01/2.56 |-Branch two:
% 8.01/2.56 | (71) all_24_2_15 = 0
% 8.01/2.56 | (81) all_24_0_13 = 0
% 8.01/2.56 |
% 8.01/2.56 | From (81) and (58) follows:
% 8.01/2.56 | (82) relation(all_0_6_6) = 0
% 8.01/2.56 |
% 8.01/2.56 | Instantiating formula (42) with all_32_1_19, all_0_5_5, all_0_6_6 and discharging atoms relation_dom(all_0_6_6) = all_0_5_5, in(all_32_1_19, all_0_5_5) = 0, yields:
% 8.01/2.56 | (83) ? [v0] : ? [v1] : ? [v2] : ((v2 = 0 & ordered_pair(all_32_1_19, v0) = v1 & in(v1, all_0_6_6) = 0) | ( ~ (v0 = 0) & relation(all_0_6_6) = v0))
% 8.01/2.56 |
% 8.01/2.56 | Instantiating (83) with all_55_0_22, all_55_1_23, all_55_2_24 yields:
% 8.01/2.56 | (84) (all_55_0_22 = 0 & ordered_pair(all_32_1_19, all_55_2_24) = all_55_1_23 & in(all_55_1_23, all_0_6_6) = 0) | ( ~ (all_55_2_24 = 0) & relation(all_0_6_6) = all_55_2_24)
% 8.01/2.56 |
% 8.01/2.56 +-Applying beta-rule and splitting (84), into two cases.
% 8.01/2.56 |-Branch one:
% 8.01/2.56 | (85) all_55_0_22 = 0 & ordered_pair(all_32_1_19, all_55_2_24) = all_55_1_23 & in(all_55_1_23, all_0_6_6) = 0
% 8.01/2.56 |
% 8.01/2.56 | Applying alpha-rule on (85) yields:
% 8.01/2.56 | (86) all_55_0_22 = 0
% 8.01/2.56 | (87) ordered_pair(all_32_1_19, all_55_2_24) = all_55_1_23
% 8.01/2.56 | (88) in(all_55_1_23, all_0_6_6) = 0
% 8.01/2.56 |
% 8.01/2.56 | Instantiating formula (25) with all_55_1_23, all_55_2_24, all_32_1_19, all_0_6_6, all_0_7_7, all_0_9_9 and discharging atoms relation_composition(all_0_9_9, all_0_7_7) = all_0_6_6, relation(all_0_6_6) = 0, relation(all_0_9_9) = 0, ordered_pair(all_32_1_19, all_55_2_24) = all_55_1_23, in(all_55_1_23, all_0_6_6) = 0, yields:
% 8.01/2.56 | (89) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ((v4 = 0 & v2 = 0 & ordered_pair(v0, all_55_2_24) = v3 & ordered_pair(all_32_1_19, v0) = v1 & in(v3, all_0_7_7) = 0 & in(v1, all_0_9_9) = 0) | ( ~ (v0 = 0) & relation(all_0_7_7) = v0))
% 8.01/2.56 |
% 8.01/2.56 | Instantiating (89) with all_67_0_26, all_67_1_27, all_67_2_28, all_67_3_29, all_67_4_30 yields:
% 8.01/2.56 | (90) (all_67_0_26 = 0 & all_67_2_28 = 0 & ordered_pair(all_67_4_30, all_55_2_24) = all_67_1_27 & ordered_pair(all_32_1_19, all_67_4_30) = all_67_3_29 & in(all_67_1_27, all_0_7_7) = 0 & in(all_67_3_29, all_0_9_9) = 0) | ( ~ (all_67_4_30 = 0) & relation(all_0_7_7) = all_67_4_30)
% 8.01/2.56 |
% 8.01/2.56 +-Applying beta-rule and splitting (90), into two cases.
% 8.01/2.56 |-Branch one:
% 8.01/2.56 | (91) all_67_0_26 = 0 & all_67_2_28 = 0 & ordered_pair(all_67_4_30, all_55_2_24) = all_67_1_27 & ordered_pair(all_32_1_19, all_67_4_30) = all_67_3_29 & in(all_67_1_27, all_0_7_7) = 0 & in(all_67_3_29, all_0_9_9) = 0
% 8.01/2.56 |
% 8.01/2.56 | Applying alpha-rule on (91) yields:
% 8.01/2.56 | (92) in(all_67_1_27, all_0_7_7) = 0
% 8.01/2.56 | (93) ordered_pair(all_67_4_30, all_55_2_24) = all_67_1_27
% 8.01/2.56 | (94) all_67_0_26 = 0
% 8.01/2.56 | (95) all_67_2_28 = 0
% 8.01/2.56 | (96) ordered_pair(all_32_1_19, all_67_4_30) = all_67_3_29
% 8.01/2.56 | (97) in(all_67_3_29, all_0_9_9) = 0
% 8.01/2.56 |
% 8.01/2.56 | Instantiating formula (37) with all_67_3_29, all_67_4_30, all_32_0_18, all_32_1_19, all_0_8_8, all_0_9_9 and discharging atoms relation_dom(all_0_9_9) = all_0_8_8, ordered_pair(all_32_1_19, all_67_4_30) = all_67_3_29, in(all_67_3_29, all_0_9_9) = 0, in(all_32_1_19, all_0_8_8) = all_32_0_18, yields:
% 8.01/2.56 | (98) all_32_0_18 = 0 | ? [v0] : ( ~ (v0 = 0) & relation(all_0_9_9) = v0)
% 8.01/2.56 |
% 8.01/2.56 +-Applying beta-rule and splitting (98), into two cases.
% 8.01/2.56 |-Branch one:
% 8.01/2.56 | (99) all_32_0_18 = 0
% 8.01/2.56 |
% 8.01/2.56 | Equations (99) can reduce 67 to:
% 8.01/2.56 | (63) $false
% 8.01/2.56 |
% 8.01/2.56 |-The branch is then unsatisfiable
% 8.01/2.56 |-Branch two:
% 8.01/2.56 | (67) ~ (all_32_0_18 = 0)
% 8.01/2.56 | (102) ? [v0] : ( ~ (v0 = 0) & relation(all_0_9_9) = v0)
% 8.01/2.56 |
% 8.01/2.56 | Instantiating (102) with all_116_0_49 yields:
% 8.01/2.56 | (103) ~ (all_116_0_49 = 0) & relation(all_0_9_9) = all_116_0_49
% 8.01/2.56 |
% 8.01/2.56 | Applying alpha-rule on (103) yields:
% 8.01/2.56 | (104) ~ (all_116_0_49 = 0)
% 8.01/2.56 | (105) relation(all_0_9_9) = all_116_0_49
% 8.01/2.56 |
% 8.01/2.56 | Instantiating formula (36) with all_0_9_9, all_116_0_49, 0 and discharging atoms relation(all_0_9_9) = all_116_0_49, relation(all_0_9_9) = 0, yields:
% 8.01/2.56 | (106) all_116_0_49 = 0
% 8.01/2.56 |
% 8.01/2.56 | Equations (106) can reduce 104 to:
% 8.01/2.56 | (63) $false
% 8.01/2.56 |
% 8.01/2.56 |-The branch is then unsatisfiable
% 8.01/2.56 |-Branch two:
% 8.01/2.56 | (108) ~ (all_67_4_30 = 0) & relation(all_0_7_7) = all_67_4_30
% 8.01/2.56 |
% 8.01/2.56 | Applying alpha-rule on (108) yields:
% 8.01/2.56 | (109) ~ (all_67_4_30 = 0)
% 8.01/2.56 | (110) relation(all_0_7_7) = all_67_4_30
% 8.01/2.56 |
% 8.01/2.56 | Instantiating formula (36) with all_0_7_7, all_67_4_30, 0 and discharging atoms relation(all_0_7_7) = all_67_4_30, relation(all_0_7_7) = 0, yields:
% 8.01/2.56 | (111) all_67_4_30 = 0
% 8.01/2.56 |
% 8.01/2.56 | Equations (111) can reduce 109 to:
% 8.01/2.56 | (63) $false
% 8.01/2.56 |
% 8.01/2.56 |-The branch is then unsatisfiable
% 8.01/2.56 |-Branch two:
% 8.01/2.56 | (113) ~ (all_55_2_24 = 0) & relation(all_0_6_6) = all_55_2_24
% 8.01/2.56 |
% 8.01/2.56 | Applying alpha-rule on (113) yields:
% 8.01/2.56 | (114) ~ (all_55_2_24 = 0)
% 8.01/2.56 | (115) relation(all_0_6_6) = all_55_2_24
% 8.01/2.56 |
% 8.01/2.56 | Instantiating formula (36) with all_0_6_6, all_55_2_24, 0 and discharging atoms relation(all_0_6_6) = all_55_2_24, relation(all_0_6_6) = 0, yields:
% 8.01/2.56 | (116) all_55_2_24 = 0
% 8.01/2.56 |
% 8.01/2.56 | Equations (116) can reduce 114 to:
% 8.01/2.56 | (63) $false
% 8.01/2.56 |
% 8.01/2.56 |-The branch is then unsatisfiable
% 8.01/2.56 % SZS output end Proof for theBenchmark
% 8.01/2.56
% 8.01/2.56 1965ms
%------------------------------------------------------------------------------