TSTP Solution File: SEU080+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU080+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 08:46:30 EDT 2022
% Result : Theorem 21.77s 5.91s
% Output : Proof 29.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU080+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n025.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 20 02:06:30 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.48/0.60 ____ _
% 0.48/0.60 ___ / __ \_____(_)___ ________ __________
% 0.48/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.48/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.48/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.48/0.60
% 0.48/0.60 A Theorem Prover for First-Order Logic
% 0.48/0.60 (ePrincess v.1.0)
% 0.48/0.60
% 0.48/0.60 (c) Philipp Rümmer, 2009-2015
% 0.48/0.60 (c) Peter Backeman, 2014-2015
% 0.48/0.60 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.48/0.60 Free software under GNU Lesser General Public License (LGPL).
% 0.48/0.60 Bug reports to peter@backeman.se
% 0.48/0.60
% 0.48/0.60 For more information, visit http://user.uu.se/~petba168/breu/
% 0.48/0.60
% 0.48/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.68/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.54/0.95 Prover 0: Preprocessing ...
% 2.06/1.14 Prover 0: Warning: ignoring some quantifiers
% 2.12/1.16 Prover 0: Constructing countermodel ...
% 4.51/1.80 Prover 0: gave up
% 4.51/1.80 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 4.77/1.84 Prover 1: Preprocessing ...
% 4.99/1.91 Prover 1: Warning: ignoring some quantifiers
% 4.99/1.92 Prover 1: Constructing countermodel ...
% 5.87/2.05 Prover 1: gave up
% 5.87/2.05 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 5.87/2.08 Prover 2: Preprocessing ...
% 6.14/2.15 Prover 2: Warning: ignoring some quantifiers
% 6.14/2.16 Prover 2: Constructing countermodel ...
% 14.88/4.24 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 14.88/4.27 Prover 3: Preprocessing ...
% 14.88/4.31 Prover 3: Warning: ignoring some quantifiers
% 14.88/4.31 Prover 3: Constructing countermodel ...
% 16.52/4.66 Prover 3: gave up
% 16.52/4.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 16.52/4.68 Prover 4: Preprocessing ...
% 16.76/4.75 Prover 4: Warning: ignoring some quantifiers
% 16.76/4.75 Prover 4: Constructing countermodel ...
% 20.86/5.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 20.86/5.69 Prover 5: Preprocessing ...
% 21.18/5.77 Prover 5: Warning: ignoring some quantifiers
% 21.18/5.78 Prover 5: Constructing countermodel ...
% 21.77/5.90 Prover 5: proved (241ms)
% 21.77/5.90 Prover 4: stopped
% 21.77/5.90 Prover 2: stopped
% 21.77/5.91
% 21.77/5.91 No countermodel exists, formula is valid
% 21.77/5.91 % SZS status Theorem for theBenchmark
% 21.77/5.91
% 21.77/5.91 Generating proof ... Warning: ignoring some quantifiers
% 28.49/7.49 found it (size 175)
% 28.49/7.49
% 28.49/7.49 % SZS output start Proof for theBenchmark
% 28.49/7.49 Assumed formulas after preprocessing and simplification:
% 28.49/7.49 | (0) relation_empty_yielding(empty_set) = 0 & relation(empty_set) = 0 & empty(empty_set) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (relation_inverse_image(v2, v1) = v3) | ~ (subset(v0, v1) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (relation_inverse_image(v2, v0) = v7 & relation_rng(v2) = v9 & subset(v7, v3) = v8 & subset(v0, v9) = v10 & relation(v2) = v5 & function(v2) = v6 & ( ~ (v10 = 0) | ~ (v8 = 0) | ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (relation_inverse_image(v2, v0) = v3) | ~ (subset(v0, v1) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (relation_inverse_image(v2, v1) = v7 & relation_rng(v2) = v9 & subset(v3, v7) = v8 & subset(v0, v9) = v10 & relation(v2) = v5 & function(v2) = v6 & ( ~ (v10 = 0) | ~ (v8 = 0) | ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (relation_rng(v2) = v3) | ~ (subset(v0, v1) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (relation_inverse_image(v2, v1) = v8 & relation_inverse_image(v2, v0) = v7 & subset(v7, v8) = v9 & subset(v0, v3) = v10 & relation(v2) = v5 & function(v2) = v6 & ( ~ (v10 = 0) | ~ (v9 = 0) | ~ (v6 = 0) | ~ (v5 = 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] : ! [v4] : ( ~ (relation_inverse_image(v2, v1) = v4) | ~ (relation_inverse_image(v2, v0) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (relation_rng(v2) = v8 & subset(v3, v4) = v7 & subset(v0, v8) = v9 & subset(v0, v1) = v10 & relation(v2) = v5 & function(v2) = v6 & ( ~ (v9 = 0) | ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | v10 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_inverse_image(v2, v1) = v3) | ~ (relation_rng(v2) = v4) | ~ (subset(v0, v4) = 0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (relation_inverse_image(v2, v0) = v7 & subset(v7, v3) = v8 & subset(v0, v1) = v9 & relation(v2) = v5 & function(v2) = v6 & ( ~ (v8 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | v9 = 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] : (v3 = 0 | ~ (element(v0, v2) = v3) | ~ (in(v0, v1) = 0) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & powerset(v2) = v4 & element(v1, v4) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v1) = v3) | ~ (relation(v2) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (relation_inverse_image(v2, v1) = v6 & relation_inverse_image(v2, v0) = v5 & relation_rng(v2) = v8 & subset(v5, v6) = v7 & subset(v0, v8) = v9 & function(v2) = v4 & ( ~ (v9 = 0) | ~ (v7 = 0) | ~ (v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v1) = v3) | ~ (function(v2) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (relation_inverse_image(v2, v1) = v6 & relation_inverse_image(v2, v0) = v5 & relation_rng(v2) = v8 & subset(v5, v6) = v7 & subset(v0, v8) = v9 & relation(v2) = v4 & ( ~ (v9 = 0) | ~ (v7 = 0) | ~ (v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_inverse_image(v3, v2) = v1) | ~ (relation_inverse_image(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (in(v0, v1) = 0) | ? [v4] : ? [v5] : (element(v1, v3) = v4 & element(v0, v2) = v5 & ( ~ (v4 = 0) | v5 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (in(v0, v1) = 0) | ? [v4] : ? [v5] : (element(v1, v3) = v4 & empty(v2) = v5 & ( ~ (v5 = 0) | ~ (v4 = 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) & powerset(v1) = v3 & element(v0, v3) = v4)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v0, v1) = v2) | ? [v3] : ? [v4] : (element(v0, v1) = v3 & empty(v1) = v4 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_empty_yielding(v2) = v1) | ~ (relation_empty_yielding(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | subset(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (empty(v2) = 0) | ~ (in(v0, v1) = 0) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v2) = v3 & element(v1, v3) = v4)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (subset(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v0, v1) = v2)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v1, v0) = v2)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (relation(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (function(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (empty(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation_rng(v0) = v3 & relation(v0) = v2 & empty(v3) = v4 & ( ~ (v4 = 0) | ~ (v2 = 0)))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (empty(v0) = v1) | ? [v2] : (powerset(v0) = v2 & ? [v3] : ? [v4] : ( ~ (v4 = 0) & element(v3, v2) = 0 & empty(v3) = v4))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation(v1) = v4 & empty(v1) = v3 & empty(v0) = v2 & ( ~ (v2 = 0) | (v4 = 0 & v3 = 0)))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation(v0) = v3 & empty(v1) = v4 & empty(v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2 = 0))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) = 0 | ? [v2] : ? [v3] : ( ~ (v3 = 0) & element(v2, v1) = 0 & empty(v2) = v3)) & ! [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] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (powerset(v1) = v2 & element(v0, 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(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | element(v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) & ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0)) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (relation_rng(v0) = v2 & empty(v2) = v3 & empty(v0) = v1 & ( ~ (v3 = 0) | v1 = 0))) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (one_to_one(v0) = v3 & function(v0) = v2 & empty(v0) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0))) & ! [v0] : ( ~ (function(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (one_to_one(v0) = v3 & relation(v0) = v1 & empty(v0) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0))) & ! [v0] : ( ~ (empty(v0) = 0) | relation(v0) = 0) & ! [v0] : ( ~ (empty(v0) = 0) | function(v0) = 0) & ! [v0] : ( ~ (empty(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (one_to_one(v0) = v3 & relation(v0) = v1 & function(v0) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0))) & ! [v0] : ( ~ (empty(v0) = 0) | ? [v1] : (relation_rng(v0) = v1 & relation(v1) = 0 & empty(v1) = 0)) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ( ~ (v1 = v0) & relation_inverse_image(v2, v1) = v3 & relation_inverse_image(v2, v0) = v3 & relation_rng(v2) = v4 & subset(v1, v4) = 0 & subset(v0, v4) = 0 & relation(v2) = 0 & function(v2) = 0) & ? [v0] : ? [v1] : element(v1, v0) = 0 & ? [v0] : ? [v1] : ( ~ (v1 = 0) & relation(v0) = 0 & empty(v0) = v1) & ? [v0] : ? [v1] : ( ~ (v1 = 0) & empty(v0) = v1) & ? [v0] : empty(v0) = 0 & ? [v0] : (relation_empty_yielding(v0) = 0 & relation(v0) = 0) & ? [v0] : (one_to_one(v0) = 0 & relation(v0) = 0 & function(v0) = 0) & ? [v0] : (relation(v0) = 0 & function(v0) = 0 & empty(v0) = 0) & ? [v0] : (relation(v0) = 0 & function(v0) = 0) & ? [v0] : (relation(v0) = 0 & empty(v0) = 0)
% 28.49/7.54 | Applying alpha-rule on (0) yields:
% 28.49/7.54 | (1) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v1) = v3 & element(v0, v3) = v4))
% 28.49/7.54 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_inverse_image(v2, v1) = v4) | ~ (relation_inverse_image(v2, v0) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (relation_rng(v2) = v8 & subset(v3, v4) = v7 & subset(v0, v8) = v9 & subset(v0, v1) = v10 & relation(v2) = v5 & function(v2) = v6 & ( ~ (v9 = 0) | ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | v10 = 0)))
% 28.49/7.54 | (3) ? [v0] : ? [v1] : ( ~ (v1 = 0) & relation(v0) = 0 & empty(v0) = v1)
% 28.49/7.54 | (4) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0))
% 28.49/7.54 | (5) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 28.49/7.54 | (6) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation(v0) = v3 & empty(v1) = v4 & empty(v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2 = 0)))
% 28.49/7.54 | (7) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0))
% 28.49/7.54 | (8) ! [v0] : ( ~ (empty(v0) = 0) | ? [v1] : (relation_rng(v0) = v1 & relation(v1) = 0 & empty(v1) = 0))
% 28.49/7.54 | (9) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | element(v0, v1) = 0)
% 28.49/7.54 | (10) ! [v0] : ( ~ (empty(v0) = 0) | function(v0) = 0)
% 28.49/7.54 | (11) ? [v0] : (relation_empty_yielding(v0) = 0 & relation(v0) = 0)
% 28.49/7.54 | (12) ! [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)))
% 28.49/7.54 | (13) ! [v0] : ! [v1] : (v1 = v0 | ~ (subset(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v0, v1) = v2))
% 28.49/7.54 | (14) ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2))
% 28.49/7.54 | (15) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) = 0 & empty(v2) = 0))
% 28.49/7.54 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 28.49/7.54 | (17) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0))
% 28.49/7.54 | (18) ! [v0] : ! [v1] : (v1 = 0 | ~ (function(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2))
% 28.49/7.54 | (19) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0))
% 28.49/7.54 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v1) = v3) | ~ (function(v2) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (relation_inverse_image(v2, v1) = v6 & relation_inverse_image(v2, v0) = v5 & relation_rng(v2) = v8 & subset(v5, v6) = v7 & subset(v0, v8) = v9 & relation(v2) = v4 & ( ~ (v9 = 0) | ~ (v7 = 0) | ~ (v4 = 0))))
% 28.49/7.54 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v1) = v3) | ~ (relation(v2) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (relation_inverse_image(v2, v1) = v6 & relation_inverse_image(v2, v0) = v5 & relation_rng(v2) = v8 & subset(v5, v6) = v7 & subset(v0, v8) = v9 & function(v2) = v4 & ( ~ (v9 = 0) | ~ (v7 = 0) | ~ (v4 = 0))))
% 28.49/7.55 | (22) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation(v1) = v4 & empty(v1) = v3 & empty(v0) = v2 & ( ~ (v2 = 0) | (v4 = 0 & v3 = 0))))
% 28.49/7.55 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (relation_inverse_image(v2, v0) = v3) | ~ (subset(v0, v1) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (relation_inverse_image(v2, v1) = v7 & relation_rng(v2) = v9 & subset(v3, v7) = v8 & subset(v0, v9) = v10 & relation(v2) = v5 & function(v2) = v6 & ( ~ (v10 = 0) | ~ (v8 = 0) | ~ (v6 = 0) | ~ (v5 = 0))))
% 28.49/7.55 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (in(v0, v1) = 0) | ? [v4] : ? [v5] : (element(v1, v3) = v4 & element(v0, v2) = v5 & ( ~ (v4 = 0) | v5 = 0)))
% 28.49/7.55 | (25) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (relation_rng(v0) = v2 & empty(v2) = v3 & empty(v0) = v1 & ( ~ (v3 = 0) | v1 = 0)))
% 28.49/7.55 | (26) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0))
% 28.49/7.55 | (27) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ( ~ (v1 = v0) & relation_inverse_image(v2, v1) = v3 & relation_inverse_image(v2, v0) = v3 & relation_rng(v2) = v4 & subset(v1, v4) = 0 & subset(v0, v4) = 0 & relation(v2) = 0 & function(v2) = 0)
% 28.49/7.55 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (element(v0, v2) = v3) | ~ (in(v0, v1) = 0) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & powerset(v2) = v4 & element(v1, v4) = v5))
% 28.49/7.55 | (29) ! [v0] : ! [v1] : ( ~ (element(v0, v1) = 0) | ? [v2] : ? [v3] : (empty(v1) = v2 & in(v0, v1) = v3 & (v3 = 0 | v2 = 0)))
% 28.49/7.55 | (30) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1))
% 28.49/7.55 | (31) ! [v0] : ( ~ (empty(v0) = 0) | relation(v0) = 0)
% 28.49/7.55 | (32) ? [v0] : (relation(v0) = 0 & function(v0) = 0)
% 28.49/7.55 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (relation_inverse_image(v2, v1) = v3) | ~ (subset(v0, v1) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (relation_inverse_image(v2, v0) = v7 & relation_rng(v2) = v9 & subset(v7, v3) = v8 & subset(v0, v9) = v10 & relation(v2) = v5 & function(v2) = v6 & ( ~ (v10 = 0) | ~ (v8 = 0) | ~ (v6 = 0) | ~ (v5 = 0))))
% 28.49/7.55 | (34) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) = 0 | ? [v2] : ? [v3] : ( ~ (v3 = 0) & element(v2, v1) = 0 & empty(v2) = v3))
% 28.49/7.55 | (35) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0))
% 28.49/7.55 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 28.49/7.55 | (37) relation(empty_set) = 0
% 28.49/7.55 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_inverse_image(v2, v1) = v3) | ~ (relation_rng(v2) = v4) | ~ (subset(v0, v4) = 0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (relation_inverse_image(v2, v0) = v7 & subset(v7, v3) = v8 & subset(v0, v1) = v9 & relation(v2) = v5 & function(v2) = v6 & ( ~ (v8 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | v9 = 0)))
% 28.49/7.55 | (39) ? [v0] : empty(v0) = 0
% 28.49/7.55 | (40) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_empty_yielding(v2) = v1) | ~ (relation_empty_yielding(v2) = v0))
% 28.49/7.55 | (41) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | subset(v0, v1) = 0)
% 28.49/7.55 | (42) ! [v0] : ! [v1] : (v1 = 0 | ~ (relation(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2))
% 28.49/7.55 | (43) ? [v0] : (relation(v0) = 0 & empty(v0) = 0)
% 28.49/7.55 | (44) ! [v0] : ! [v1] : (v1 = v0 | ~ (subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v1, v0) = v2))
% 28.49/7.55 | (45) ? [v0] : (one_to_one(v0) = 0 & relation(v0) = 0 & function(v0) = 0)
% 28.49/7.55 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (relation_rng(v2) = v3) | ~ (subset(v0, v1) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (relation_inverse_image(v2, v1) = v8 & relation_inverse_image(v2, v0) = v7 & subset(v7, v8) = v9 & subset(v0, v3) = v10 & relation(v2) = v5 & function(v2) = v6 & ( ~ (v10 = 0) | ~ (v9 = 0) | ~ (v6 = 0) | ~ (v5 = 0))))
% 28.49/7.55 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_inverse_image(v3, v2) = v1) | ~ (relation_inverse_image(v3, v2) = v0))
% 28.49/7.55 | (48) ! [v0] : ! [v1] : (v1 = 0 | ~ (empty(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation_rng(v0) = v3 & relation(v0) = v2 & empty(v3) = v4 & ( ~ (v4 = 0) | ~ (v2 = 0))))
% 28.49/7.56 | (49) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 28.49/7.56 | (50) ! [v0] : ( ~ (empty(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (one_to_one(v0) = v3 & relation(v0) = v1 & function(v0) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0)))
% 28.49/7.56 | (51) ! [v0] : ( ~ (function(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (one_to_one(v0) = v3 & relation(v0) = v1 & empty(v0) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0)))
% 28.49/7.56 | (52) ! [v0] : ! [v1] : (v1 = 0 | ~ (empty(v0) = v1) | ? [v2] : (powerset(v0) = v2 & ? [v3] : ? [v4] : ( ~ (v4 = 0) & element(v3, v2) = 0 & empty(v3) = v4)))
% 28.49/7.56 | (53) ? [v0] : (relation(v0) = 0 & function(v0) = 0 & empty(v0) = 0)
% 28.49/7.56 | (54) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 28.49/7.56 | (55) empty(empty_set) = 0
% 28.49/7.56 | (56) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 28.49/7.56 | (57) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (one_to_one(v0) = v3 & function(v0) = v2 & empty(v0) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0)))
% 28.49/7.56 | (58) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3))
% 28.49/7.56 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 28.49/7.56 | (60) ? [v0] : ? [v1] : ( ~ (v1 = 0) & empty(v0) = v1)
% 28.49/7.56 | (61) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0))
% 28.49/7.56 | (62) relation_empty_yielding(empty_set) = 0
% 28.95/7.56 | (63) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v0, v1) = v2) | ? [v3] : ? [v4] : (element(v0, v1) = v3 & empty(v1) = v4 & ( ~ (v3 = 0) | v4 = 0)))
% 28.95/7.56 | (64) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (powerset(v1) = v2 & element(v0, v2) = 0))
% 28.95/7.56 | (65) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ (in(v0, v1) = 0) | ? [v4] : ? [v5] : (element(v1, v3) = v4 & empty(v2) = v5 & ( ~ (v5 = 0) | ~ (v4 = 0))))
% 28.95/7.56 | (66) ? [v0] : ? [v1] : element(v1, v0) = 0
% 28.95/7.56 | (67) ! [v0] : ! [v1] : ! [v2] : ( ~ (empty(v2) = 0) | ~ (in(v0, v1) = 0) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & powerset(v2) = v3 & element(v1, v3) = v4))
% 28.95/7.56 | (68) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0))
% 28.95/7.56 | (69) ! [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))
% 28.95/7.56 |
% 28.95/7.56 | Instantiating (27) with all_20_0_12, all_20_1_13, all_20_2_14, all_20_3_15, all_20_4_16 yields:
% 28.95/7.56 | (70) ~ (all_20_3_15 = all_20_4_16) & relation_inverse_image(all_20_2_14, all_20_3_15) = all_20_1_13 & relation_inverse_image(all_20_2_14, all_20_4_16) = all_20_1_13 & relation_rng(all_20_2_14) = all_20_0_12 & subset(all_20_3_15, all_20_0_12) = 0 & subset(all_20_4_16, all_20_0_12) = 0 & relation(all_20_2_14) = 0 & function(all_20_2_14) = 0
% 28.95/7.56 |
% 28.95/7.56 | Applying alpha-rule on (70) yields:
% 28.95/7.56 | (71) relation_inverse_image(all_20_2_14, all_20_4_16) = all_20_1_13
% 28.95/7.56 | (72) ~ (all_20_3_15 = all_20_4_16)
% 28.95/7.56 | (73) relation_inverse_image(all_20_2_14, all_20_3_15) = all_20_1_13
% 28.95/7.56 | (74) relation(all_20_2_14) = 0
% 28.95/7.56 | (75) subset(all_20_4_16, all_20_0_12) = 0
% 28.95/7.56 | (76) relation_rng(all_20_2_14) = all_20_0_12
% 28.95/7.56 | (77) subset(all_20_3_15, all_20_0_12) = 0
% 28.95/7.56 | (78) function(all_20_2_14) = 0
% 28.95/7.56 |
% 28.95/7.56 | Instantiating formula (2) with all_20_1_13, all_20_1_13, all_20_2_14, all_20_3_15, all_20_3_15 and discharging atoms relation_inverse_image(all_20_2_14, all_20_3_15) = all_20_1_13, yields:
% 28.95/7.56 | (79) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_rng(all_20_2_14) = v3 & subset(all_20_1_13, all_20_1_13) = v2 & subset(all_20_3_15, v3) = v4 & subset(all_20_3_15, all_20_3_15) = v5 & relation(all_20_2_14) = v0 & function(all_20_2_14) = v1 & ( ~ (v4 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v5 = 0))
% 28.95/7.56 |
% 28.95/7.56 | Instantiating formula (2) with all_20_1_13, all_20_1_13, all_20_2_14, all_20_4_16, all_20_3_15 and discharging atoms relation_inverse_image(all_20_2_14, all_20_3_15) = all_20_1_13, relation_inverse_image(all_20_2_14, all_20_4_16) = all_20_1_13, yields:
% 28.95/7.57 | (80) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_rng(all_20_2_14) = v3 & subset(all_20_1_13, all_20_1_13) = v2 & subset(all_20_3_15, v3) = v4 & subset(all_20_3_15, all_20_4_16) = v5 & relation(all_20_2_14) = v0 & function(all_20_2_14) = v1 & ( ~ (v4 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v5 = 0))
% 28.95/7.57 |
% 28.95/7.57 | Instantiating formula (2) with all_20_1_13, all_20_1_13, all_20_2_14, all_20_3_15, all_20_4_16 and discharging atoms relation_inverse_image(all_20_2_14, all_20_3_15) = all_20_1_13, relation_inverse_image(all_20_2_14, all_20_4_16) = all_20_1_13, yields:
% 28.95/7.57 | (81) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_rng(all_20_2_14) = v3 & subset(all_20_1_13, all_20_1_13) = v2 & subset(all_20_4_16, v3) = v4 & subset(all_20_4_16, all_20_3_15) = v5 & relation(all_20_2_14) = v0 & function(all_20_2_14) = v1 & ( ~ (v4 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v5 = 0))
% 28.95/7.57 |
% 28.95/7.57 | Instantiating formula (2) with all_20_1_13, all_20_1_13, all_20_2_14, all_20_4_16, all_20_4_16 and discharging atoms relation_inverse_image(all_20_2_14, all_20_4_16) = all_20_1_13, yields:
% 28.95/7.57 | (82) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_rng(all_20_2_14) = v3 & subset(all_20_1_13, all_20_1_13) = v2 & subset(all_20_4_16, v3) = v4 & subset(all_20_4_16, all_20_4_16) = v5 & relation(all_20_2_14) = v0 & function(all_20_2_14) = v1 & ( ~ (v4 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v5 = 0))
% 28.95/7.57 |
% 28.95/7.57 | Instantiating formula (6) with all_20_0_12, all_20_2_14 and discharging atoms relation_rng(all_20_2_14) = all_20_0_12, yields:
% 28.95/7.57 | (83) ? [v0] : ? [v1] : ? [v2] : (relation(all_20_2_14) = v1 & empty(all_20_0_12) = v2 & empty(all_20_2_14) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | v0 = 0))
% 28.95/7.57 |
% 28.95/7.57 | Instantiating formula (38) with all_20_0_12, all_20_1_13, all_20_2_14, all_20_3_15, all_20_3_15 and discharging atoms relation_inverse_image(all_20_2_14, all_20_3_15) = all_20_1_13, relation_rng(all_20_2_14) = all_20_0_12, subset(all_20_3_15, all_20_0_12) = 0, yields:
% 28.95/7.57 | (84) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (relation_inverse_image(all_20_2_14, all_20_3_15) = v2 & subset(v2, all_20_1_13) = v3 & subset(all_20_3_15, all_20_3_15) = v4 & relation(all_20_2_14) = v0 & function(all_20_2_14) = v1 & ( ~ (v3 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = 0))
% 28.95/7.57 |
% 28.95/7.57 | Instantiating formula (38) with all_20_0_12, all_20_1_13, all_20_2_14, all_20_4_16, all_20_3_15 and discharging atoms relation_inverse_image(all_20_2_14, all_20_4_16) = all_20_1_13, relation_rng(all_20_2_14) = all_20_0_12, subset(all_20_3_15, all_20_0_12) = 0, yields:
% 28.95/7.57 | (85) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (relation_inverse_image(all_20_2_14, all_20_3_15) = v2 & subset(v2, all_20_1_13) = v3 & subset(all_20_3_15, all_20_4_16) = v4 & relation(all_20_2_14) = v0 & function(all_20_2_14) = v1 & ( ~ (v3 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = 0))
% 28.95/7.57 |
% 28.95/7.57 | Instantiating formula (38) with all_20_0_12, all_20_1_13, all_20_2_14, all_20_3_15, all_20_4_16 and discharging atoms relation_inverse_image(all_20_2_14, all_20_3_15) = all_20_1_13, relation_rng(all_20_2_14) = all_20_0_12, subset(all_20_4_16, all_20_0_12) = 0, yields:
% 28.95/7.57 | (86) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (relation_inverse_image(all_20_2_14, all_20_4_16) = v2 & subset(v2, all_20_1_13) = v3 & subset(all_20_4_16, all_20_3_15) = v4 & relation(all_20_2_14) = v0 & function(all_20_2_14) = v1 & ( ~ (v3 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = 0))
% 28.95/7.57 |
% 28.95/7.57 | Instantiating formula (38) with all_20_0_12, all_20_1_13, all_20_2_14, all_20_4_16, all_20_4_16 and discharging atoms relation_inverse_image(all_20_2_14, all_20_4_16) = all_20_1_13, relation_rng(all_20_2_14) = all_20_0_12, subset(all_20_4_16, all_20_0_12) = 0, yields:
% 28.95/7.57 | (87) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (relation_inverse_image(all_20_2_14, all_20_4_16) = v2 & subset(v2, all_20_1_13) = v3 & subset(all_20_4_16, all_20_4_16) = v4 & relation(all_20_2_14) = v0 & function(all_20_2_14) = v1 & ( ~ (v3 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 = 0))
% 28.95/7.57 |
% 28.95/7.57 | Instantiating formula (57) with all_20_2_14 and discharging atoms relation(all_20_2_14) = 0, yields:
% 28.95/7.57 | (88) ? [v0] : ? [v1] : ? [v2] : (one_to_one(all_20_2_14) = v2 & function(all_20_2_14) = v1 & empty(all_20_2_14) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 28.95/7.57 |
% 28.95/7.57 | Instantiating formula (51) with all_20_2_14 and discharging atoms function(all_20_2_14) = 0, yields:
% 28.95/7.57 | (89) ? [v0] : ? [v1] : ? [v2] : (one_to_one(all_20_2_14) = v2 & relation(all_20_2_14) = v0 & empty(all_20_2_14) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 28.95/7.57 |
% 28.95/7.57 | Instantiating (87) with all_39_0_25, all_39_1_26, all_39_2_27, all_39_3_28, all_39_4_29 yields:
% 28.95/7.57 | (90) relation_inverse_image(all_20_2_14, all_20_4_16) = all_39_2_27 & subset(all_39_2_27, all_20_1_13) = all_39_1_26 & subset(all_20_4_16, all_20_4_16) = all_39_0_25 & relation(all_20_2_14) = all_39_4_29 & function(all_20_2_14) = all_39_3_28 & ( ~ (all_39_1_26 = 0) | ~ (all_39_3_28 = 0) | ~ (all_39_4_29 = 0) | all_39_0_25 = 0)
% 28.95/7.57 |
% 28.95/7.57 | Applying alpha-rule on (90) yields:
% 28.95/7.57 | (91) relation_inverse_image(all_20_2_14, all_20_4_16) = all_39_2_27
% 28.95/7.57 | (92) ~ (all_39_1_26 = 0) | ~ (all_39_3_28 = 0) | ~ (all_39_4_29 = 0) | all_39_0_25 = 0
% 28.95/7.57 | (93) function(all_20_2_14) = all_39_3_28
% 28.95/7.57 | (94) relation(all_20_2_14) = all_39_4_29
% 28.95/7.57 | (95) subset(all_39_2_27, all_20_1_13) = all_39_1_26
% 28.95/7.57 | (96) subset(all_20_4_16, all_20_4_16) = all_39_0_25
% 28.95/7.57 |
% 28.95/7.57 | Instantiating (84) with all_41_0_30, all_41_1_31, all_41_2_32, all_41_3_33, all_41_4_34 yields:
% 28.95/7.57 | (97) relation_inverse_image(all_20_2_14, all_20_3_15) = all_41_2_32 & subset(all_41_2_32, all_20_1_13) = all_41_1_31 & subset(all_20_3_15, all_20_3_15) = all_41_0_30 & relation(all_20_2_14) = all_41_4_34 & function(all_20_2_14) = all_41_3_33 & ( ~ (all_41_1_31 = 0) | ~ (all_41_3_33 = 0) | ~ (all_41_4_34 = 0) | all_41_0_30 = 0)
% 28.95/7.57 |
% 28.95/7.57 | Applying alpha-rule on (97) yields:
% 28.95/7.57 | (98) relation_inverse_image(all_20_2_14, all_20_3_15) = all_41_2_32
% 28.95/7.57 | (99) subset(all_41_2_32, all_20_1_13) = all_41_1_31
% 28.95/7.57 | (100) ~ (all_41_1_31 = 0) | ~ (all_41_3_33 = 0) | ~ (all_41_4_34 = 0) | all_41_0_30 = 0
% 28.95/7.57 | (101) relation(all_20_2_14) = all_41_4_34
% 28.95/7.57 | (102) function(all_20_2_14) = all_41_3_33
% 28.95/7.57 | (103) subset(all_20_3_15, all_20_3_15) = all_41_0_30
% 28.95/7.57 |
% 28.95/7.57 | Instantiating (83) with all_43_0_35, all_43_1_36, all_43_2_37 yields:
% 28.95/7.57 | (104) relation(all_20_2_14) = all_43_1_36 & empty(all_20_0_12) = all_43_0_35 & empty(all_20_2_14) = all_43_2_37 & ( ~ (all_43_0_35 = 0) | ~ (all_43_1_36 = 0) | all_43_2_37 = 0)
% 28.95/7.58 |
% 28.95/7.58 | Applying alpha-rule on (104) yields:
% 28.95/7.58 | (105) relation(all_20_2_14) = all_43_1_36
% 28.95/7.58 | (106) empty(all_20_0_12) = all_43_0_35
% 28.95/7.58 | (107) empty(all_20_2_14) = all_43_2_37
% 28.95/7.58 | (108) ~ (all_43_0_35 = 0) | ~ (all_43_1_36 = 0) | all_43_2_37 = 0
% 28.95/7.58 |
% 28.95/7.58 | Instantiating (82) with all_47_0_40, all_47_1_41, all_47_2_42, all_47_3_43, all_47_4_44, all_47_5_45 yields:
% 28.95/7.58 | (109) relation_rng(all_20_2_14) = all_47_2_42 & subset(all_20_1_13, all_20_1_13) = all_47_3_43 & subset(all_20_4_16, all_47_2_42) = all_47_1_41 & subset(all_20_4_16, all_20_4_16) = all_47_0_40 & relation(all_20_2_14) = all_47_5_45 & function(all_20_2_14) = all_47_4_44 & ( ~ (all_47_1_41 = 0) | ~ (all_47_3_43 = 0) | ~ (all_47_4_44 = 0) | ~ (all_47_5_45 = 0) | all_47_0_40 = 0)
% 28.95/7.58 |
% 28.95/7.58 | Applying alpha-rule on (109) yields:
% 28.95/7.58 | (110) subset(all_20_4_16, all_20_4_16) = all_47_0_40
% 28.95/7.58 | (111) subset(all_20_4_16, all_47_2_42) = all_47_1_41
% 28.95/7.58 | (112) relation_rng(all_20_2_14) = all_47_2_42
% 28.95/7.58 | (113) function(all_20_2_14) = all_47_4_44
% 28.95/7.58 | (114) relation(all_20_2_14) = all_47_5_45
% 28.95/7.58 | (115) ~ (all_47_1_41 = 0) | ~ (all_47_3_43 = 0) | ~ (all_47_4_44 = 0) | ~ (all_47_5_45 = 0) | all_47_0_40 = 0
% 28.95/7.58 | (116) subset(all_20_1_13, all_20_1_13) = all_47_3_43
% 28.95/7.58 |
% 28.95/7.58 | Instantiating (81) with all_49_0_46, all_49_1_47, all_49_2_48, all_49_3_49, all_49_4_50, all_49_5_51 yields:
% 28.95/7.58 | (117) relation_rng(all_20_2_14) = all_49_2_48 & subset(all_20_1_13, all_20_1_13) = all_49_3_49 & subset(all_20_4_16, all_49_2_48) = all_49_1_47 & subset(all_20_4_16, all_20_3_15) = all_49_0_46 & relation(all_20_2_14) = all_49_5_51 & function(all_20_2_14) = all_49_4_50 & ( ~ (all_49_1_47 = 0) | ~ (all_49_3_49 = 0) | ~ (all_49_4_50 = 0) | ~ (all_49_5_51 = 0) | all_49_0_46 = 0)
% 28.95/7.58 |
% 28.95/7.58 | Applying alpha-rule on (117) yields:
% 28.95/7.58 | (118) subset(all_20_4_16, all_20_3_15) = all_49_0_46
% 28.95/7.58 | (119) subset(all_20_1_13, all_20_1_13) = all_49_3_49
% 28.95/7.58 | (120) function(all_20_2_14) = all_49_4_50
% 28.95/7.58 | (121) subset(all_20_4_16, all_49_2_48) = all_49_1_47
% 28.95/7.58 | (122) ~ (all_49_1_47 = 0) | ~ (all_49_3_49 = 0) | ~ (all_49_4_50 = 0) | ~ (all_49_5_51 = 0) | all_49_0_46 = 0
% 28.95/7.58 | (123) relation(all_20_2_14) = all_49_5_51
% 28.95/7.58 | (124) relation_rng(all_20_2_14) = all_49_2_48
% 28.95/7.58 |
% 28.95/7.58 | Instantiating (86) with all_51_0_52, all_51_1_53, all_51_2_54, all_51_3_55, all_51_4_56 yields:
% 28.95/7.58 | (125) relation_inverse_image(all_20_2_14, all_20_4_16) = all_51_2_54 & subset(all_51_2_54, all_20_1_13) = all_51_1_53 & subset(all_20_4_16, all_20_3_15) = all_51_0_52 & relation(all_20_2_14) = all_51_4_56 & function(all_20_2_14) = all_51_3_55 & ( ~ (all_51_1_53 = 0) | ~ (all_51_3_55 = 0) | ~ (all_51_4_56 = 0) | all_51_0_52 = 0)
% 28.95/7.58 |
% 28.95/7.58 | Applying alpha-rule on (125) yields:
% 28.95/7.58 | (126) subset(all_20_4_16, all_20_3_15) = all_51_0_52
% 28.95/7.58 | (127) function(all_20_2_14) = all_51_3_55
% 28.95/7.58 | (128) ~ (all_51_1_53 = 0) | ~ (all_51_3_55 = 0) | ~ (all_51_4_56 = 0) | all_51_0_52 = 0
% 28.95/7.58 | (129) relation_inverse_image(all_20_2_14, all_20_4_16) = all_51_2_54
% 28.95/7.58 | (130) subset(all_51_2_54, all_20_1_13) = all_51_1_53
% 28.95/7.58 | (131) relation(all_20_2_14) = all_51_4_56
% 28.95/7.58 |
% 28.95/7.58 | Instantiating (85) with all_53_0_57, all_53_1_58, all_53_2_59, all_53_3_60, all_53_4_61 yields:
% 28.95/7.58 | (132) relation_inverse_image(all_20_2_14, all_20_3_15) = all_53_2_59 & subset(all_53_2_59, all_20_1_13) = all_53_1_58 & subset(all_20_3_15, all_20_4_16) = all_53_0_57 & relation(all_20_2_14) = all_53_4_61 & function(all_20_2_14) = all_53_3_60 & ( ~ (all_53_1_58 = 0) | ~ (all_53_3_60 = 0) | ~ (all_53_4_61 = 0) | all_53_0_57 = 0)
% 28.95/7.58 |
% 28.95/7.58 | Applying alpha-rule on (132) yields:
% 28.95/7.58 | (133) ~ (all_53_1_58 = 0) | ~ (all_53_3_60 = 0) | ~ (all_53_4_61 = 0) | all_53_0_57 = 0
% 28.95/7.58 | (134) relation_inverse_image(all_20_2_14, all_20_3_15) = all_53_2_59
% 28.95/7.58 | (135) relation(all_20_2_14) = all_53_4_61
% 28.95/7.58 | (136) subset(all_20_3_15, all_20_4_16) = all_53_0_57
% 28.95/7.58 | (137) function(all_20_2_14) = all_53_3_60
% 28.95/7.58 | (138) subset(all_53_2_59, all_20_1_13) = all_53_1_58
% 28.95/7.58 |
% 28.95/7.58 | Instantiating (80) with all_55_0_62, all_55_1_63, all_55_2_64, all_55_3_65, all_55_4_66, all_55_5_67 yields:
% 28.95/7.58 | (139) relation_rng(all_20_2_14) = all_55_2_64 & subset(all_20_1_13, all_20_1_13) = all_55_3_65 & subset(all_20_3_15, all_55_2_64) = all_55_1_63 & subset(all_20_3_15, all_20_4_16) = all_55_0_62 & relation(all_20_2_14) = all_55_5_67 & function(all_20_2_14) = all_55_4_66 & ( ~ (all_55_1_63 = 0) | ~ (all_55_3_65 = 0) | ~ (all_55_4_66 = 0) | ~ (all_55_5_67 = 0) | all_55_0_62 = 0)
% 28.95/7.58 |
% 28.95/7.58 | Applying alpha-rule on (139) yields:
% 28.95/7.58 | (140) function(all_20_2_14) = all_55_4_66
% 28.95/7.58 | (141) relation(all_20_2_14) = all_55_5_67
% 28.95/7.58 | (142) subset(all_20_1_13, all_20_1_13) = all_55_3_65
% 28.95/7.58 | (143) ~ (all_55_1_63 = 0) | ~ (all_55_3_65 = 0) | ~ (all_55_4_66 = 0) | ~ (all_55_5_67 = 0) | all_55_0_62 = 0
% 28.95/7.58 | (144) subset(all_20_3_15, all_55_2_64) = all_55_1_63
% 28.95/7.58 | (145) relation_rng(all_20_2_14) = all_55_2_64
% 28.95/7.58 | (146) subset(all_20_3_15, all_20_4_16) = all_55_0_62
% 28.95/7.58 |
% 28.95/7.58 | Instantiating (79) with all_57_0_68, all_57_1_69, all_57_2_70, all_57_3_71, all_57_4_72, all_57_5_73 yields:
% 28.95/7.58 | (147) relation_rng(all_20_2_14) = all_57_2_70 & subset(all_20_1_13, all_20_1_13) = all_57_3_71 & subset(all_20_3_15, all_57_2_70) = all_57_1_69 & subset(all_20_3_15, all_20_3_15) = all_57_0_68 & relation(all_20_2_14) = all_57_5_73 & function(all_20_2_14) = all_57_4_72 & ( ~ (all_57_1_69 = 0) | ~ (all_57_3_71 = 0) | ~ (all_57_4_72 = 0) | ~ (all_57_5_73 = 0) | all_57_0_68 = 0)
% 28.95/7.58 |
% 28.95/7.58 | Applying alpha-rule on (147) yields:
% 28.95/7.58 | (148) ~ (all_57_1_69 = 0) | ~ (all_57_3_71 = 0) | ~ (all_57_4_72 = 0) | ~ (all_57_5_73 = 0) | all_57_0_68 = 0
% 28.95/7.58 | (149) subset(all_20_1_13, all_20_1_13) = all_57_3_71
% 28.95/7.58 | (150) relation(all_20_2_14) = all_57_5_73
% 28.95/7.58 | (151) subset(all_20_3_15, all_57_2_70) = all_57_1_69
% 28.95/7.58 | (152) function(all_20_2_14) = all_57_4_72
% 28.95/7.58 | (153) relation_rng(all_20_2_14) = all_57_2_70
% 28.95/7.58 | (154) subset(all_20_3_15, all_20_3_15) = all_57_0_68
% 28.95/7.59 |
% 28.95/7.59 | Instantiating (89) with all_65_0_83, all_65_1_84, all_65_2_85 yields:
% 28.95/7.59 | (155) one_to_one(all_20_2_14) = all_65_0_83 & relation(all_20_2_14) = all_65_2_85 & empty(all_20_2_14) = all_65_1_84 & ( ~ (all_65_1_84 = 0) | ~ (all_65_2_85 = 0) | all_65_0_83 = 0)
% 28.95/7.59 |
% 28.95/7.59 | Applying alpha-rule on (155) yields:
% 28.95/7.59 | (156) one_to_one(all_20_2_14) = all_65_0_83
% 28.95/7.59 | (157) relation(all_20_2_14) = all_65_2_85
% 28.95/7.59 | (158) empty(all_20_2_14) = all_65_1_84
% 28.95/7.59 | (159) ~ (all_65_1_84 = 0) | ~ (all_65_2_85 = 0) | all_65_0_83 = 0
% 28.95/7.59 |
% 28.95/7.59 | Instantiating (88) with all_91_0_120, all_91_1_121, all_91_2_122 yields:
% 28.95/7.59 | (160) one_to_one(all_20_2_14) = all_91_0_120 & function(all_20_2_14) = all_91_1_121 & empty(all_20_2_14) = all_91_2_122 & ( ~ (all_91_1_121 = 0) | ~ (all_91_2_122 = 0) | all_91_0_120 = 0)
% 28.95/7.59 |
% 28.95/7.59 | Applying alpha-rule on (160) yields:
% 28.95/7.59 | (161) one_to_one(all_20_2_14) = all_91_0_120
% 28.95/7.59 | (162) function(all_20_2_14) = all_91_1_121
% 28.95/7.59 | (163) empty(all_20_2_14) = all_91_2_122
% 28.95/7.59 | (164) ~ (all_91_1_121 = 0) | ~ (all_91_2_122 = 0) | all_91_0_120 = 0
% 28.95/7.59 |
% 28.95/7.59 | Instantiating formula (47) with all_20_2_14, all_20_3_15, all_53_2_59, all_20_1_13 and discharging atoms relation_inverse_image(all_20_2_14, all_20_3_15) = all_53_2_59, relation_inverse_image(all_20_2_14, all_20_3_15) = all_20_1_13, yields:
% 28.95/7.59 | (165) all_53_2_59 = all_20_1_13
% 28.95/7.59 |
% 28.95/7.59 | Instantiating formula (47) with all_20_2_14, all_20_3_15, all_41_2_32, all_53_2_59 and discharging atoms relation_inverse_image(all_20_2_14, all_20_3_15) = all_53_2_59, relation_inverse_image(all_20_2_14, all_20_3_15) = all_41_2_32, yields:
% 28.95/7.59 | (166) all_53_2_59 = all_41_2_32
% 28.95/7.59 |
% 28.95/7.59 | Instantiating formula (47) with all_20_2_14, all_20_4_16, all_51_2_54, all_20_1_13 and discharging atoms relation_inverse_image(all_20_2_14, all_20_4_16) = all_51_2_54, relation_inverse_image(all_20_2_14, all_20_4_16) = all_20_1_13, yields:
% 28.95/7.59 | (167) all_51_2_54 = all_20_1_13
% 28.95/7.59 |
% 28.95/7.59 | Instantiating formula (47) with all_20_2_14, all_20_4_16, all_39_2_27, all_51_2_54 and discharging atoms relation_inverse_image(all_20_2_14, all_20_4_16) = all_51_2_54, relation_inverse_image(all_20_2_14, all_20_4_16) = all_39_2_27, yields:
% 28.95/7.59 | (168) all_51_2_54 = all_39_2_27
% 28.95/7.59 |
% 28.95/7.59 | Instantiating formula (30) with all_57_3_71, all_20_1_13 and discharging atoms subset(all_20_1_13, all_20_1_13) = all_57_3_71, yields:
% 28.95/7.59 | (169) all_57_3_71 = 0
% 28.95/7.59 |
% 28.95/7.59 | Instantiating formula (16) with all_20_1_13, all_20_1_13, all_55_3_65, all_57_3_71 and discharging atoms subset(all_20_1_13, all_20_1_13) = all_57_3_71, subset(all_20_1_13, all_20_1_13) = all_55_3_65, yields:
% 28.95/7.59 | (170) all_57_3_71 = all_55_3_65
% 28.95/7.59 |
% 28.95/7.59 | Instantiating formula (16) with all_20_1_13, all_20_1_13, all_49_3_49, all_55_3_65 and discharging atoms subset(all_20_1_13, all_20_1_13) = all_55_3_65, subset(all_20_1_13, all_20_1_13) = all_49_3_49, yields:
% 28.95/7.59 | (171) all_55_3_65 = all_49_3_49
% 28.95/7.59 |
% 28.95/7.59 | Instantiating formula (16) with all_20_1_13, all_20_1_13, all_47_3_43, all_53_1_58 and discharging atoms subset(all_20_1_13, all_20_1_13) = all_47_3_43, yields:
% 28.95/7.59 | (172) all_53_1_58 = all_47_3_43 | ~ (subset(all_20_1_13, all_20_1_13) = all_53_1_58)
% 28.95/7.59 |
% 28.95/7.59 | Instantiating formula (16) with all_20_1_13, all_20_1_13, all_47_3_43, all_51_1_53 and discharging atoms subset(all_20_1_13, all_20_1_13) = all_47_3_43, yields:
% 28.95/7.59 | (173) all_51_1_53 = all_47_3_43 | ~ (subset(all_20_1_13, all_20_1_13) = all_51_1_53)
% 28.95/7.59 |
% 28.95/7.59 | Instantiating formula (16) with all_20_1_13, all_20_1_13, all_47_3_43, all_41_1_31 and discharging atoms subset(all_20_1_13, all_20_1_13) = all_47_3_43, yields:
% 28.95/7.59 | (174) all_47_3_43 = all_41_1_31 | ~ (subset(all_20_1_13, all_20_1_13) = all_41_1_31)
% 28.95/7.59 |
% 28.95/7.59 | Instantiating formula (16) with all_20_1_13, all_20_1_13, all_47_3_43, all_39_1_26 and discharging atoms subset(all_20_1_13, all_20_1_13) = all_47_3_43, yields:
% 28.95/7.59 | (175) all_47_3_43 = all_39_1_26 | ~ (subset(all_20_1_13, all_20_1_13) = all_39_1_26)
% 28.95/7.59 |
% 28.95/7.59 | Instantiating formula (16) with all_20_1_13, all_20_1_13, all_47_3_43, all_49_3_49 and discharging atoms subset(all_20_1_13, all_20_1_13) = all_49_3_49, subset(all_20_1_13, all_20_1_13) = all_47_3_43, yields:
% 29.10/7.59 | (176) all_49_3_49 = all_47_3_43
% 29.10/7.59 |
% 29.10/7.59 | Instantiating formula (16) with all_20_3_15, all_20_4_16, all_53_0_57, all_55_0_62 and discharging atoms subset(all_20_3_15, all_20_4_16) = all_55_0_62, subset(all_20_3_15, all_20_4_16) = all_53_0_57, yields:
% 29.10/7.59 | (177) all_55_0_62 = all_53_0_57
% 29.10/7.59 |
% 29.10/7.59 | Instantiating formula (16) with all_20_4_16, all_20_3_15, all_49_0_46, all_51_0_52 and discharging atoms subset(all_20_4_16, all_20_3_15) = all_51_0_52, subset(all_20_4_16, all_20_3_15) = all_49_0_46, yields:
% 29.10/7.59 | (178) all_51_0_52 = all_49_0_46
% 29.10/7.59 |
% 29.10/7.59 | Instantiating formula (17) with all_20_2_14, all_57_5_73, 0 and discharging atoms relation(all_20_2_14) = all_57_5_73, relation(all_20_2_14) = 0, yields:
% 29.10/7.59 | (179) all_57_5_73 = 0
% 29.10/7.59 |
% 29.10/7.59 | Instantiating formula (17) with all_20_2_14, all_57_5_73, all_65_2_85 and discharging atoms relation(all_20_2_14) = all_65_2_85, relation(all_20_2_14) = all_57_5_73, yields:
% 29.10/7.59 | (180) all_65_2_85 = all_57_5_73
% 29.10/7.59 |
% 29.10/7.59 | Instantiating formula (17) with all_20_2_14, all_53_4_61, all_55_5_67 and discharging atoms relation(all_20_2_14) = all_55_5_67, relation(all_20_2_14) = all_53_4_61, yields:
% 29.10/7.59 | (181) all_55_5_67 = all_53_4_61
% 29.10/7.59 |
% 29.10/7.59 | Instantiating formula (17) with all_20_2_14, all_51_4_56, all_57_5_73 and discharging atoms relation(all_20_2_14) = all_57_5_73, relation(all_20_2_14) = all_51_4_56, yields:
% 29.10/7.59 | (182) all_57_5_73 = all_51_4_56
% 29.10/7.59 |
% 29.10/7.59 | Instantiating formula (17) with all_20_2_14, all_51_4_56, all_53_4_61 and discharging atoms relation(all_20_2_14) = all_53_4_61, relation(all_20_2_14) = all_51_4_56, yields:
% 29.10/7.59 | (183) all_53_4_61 = all_51_4_56
% 29.10/7.59 |
% 29.10/7.59 | Instantiating formula (17) with all_20_2_14, all_49_5_51, all_55_5_67 and discharging atoms relation(all_20_2_14) = all_55_5_67, relation(all_20_2_14) = all_49_5_51, yields:
% 29.10/7.59 | (184) all_55_5_67 = all_49_5_51
% 29.10/7.59 |
% 29.10/7.59 | Instantiating formula (17) with all_20_2_14, all_47_5_45, all_51_4_56 and discharging atoms relation(all_20_2_14) = all_51_4_56, relation(all_20_2_14) = all_47_5_45, yields:
% 29.10/7.59 | (185) all_51_4_56 = all_47_5_45
% 29.10/7.59 |
% 29.10/7.59 | Instantiating formula (17) with all_20_2_14, all_43_1_36, all_57_5_73 and discharging atoms relation(all_20_2_14) = all_57_5_73, relation(all_20_2_14) = all_43_1_36, yields:
% 29.10/7.59 | (186) all_57_5_73 = all_43_1_36
% 29.10/7.59 |
% 29.10/7.59 | Instantiating formula (17) with all_20_2_14, all_41_4_34, all_65_2_85 and discharging atoms relation(all_20_2_14) = all_65_2_85, relation(all_20_2_14) = all_41_4_34, yields:
% 29.10/7.59 | (187) all_65_2_85 = all_41_4_34
% 29.10/7.59 |
% 29.10/7.59 | Instantiating formula (17) with all_20_2_14, all_39_4_29, all_51_4_56 and discharging atoms relation(all_20_2_14) = all_51_4_56, relation(all_20_2_14) = all_39_4_29, yields:
% 29.10/7.59 | (188) all_51_4_56 = all_39_4_29
% 29.10/7.59 |
% 29.10/7.59 | Instantiating formula (4) with all_20_2_14, all_57_4_72, 0 and discharging atoms function(all_20_2_14) = all_57_4_72, function(all_20_2_14) = 0, yields:
% 29.10/7.59 | (189) all_57_4_72 = 0
% 29.10/7.60 |
% 29.10/7.60 | Instantiating formula (4) with all_20_2_14, all_55_4_66, all_91_1_121 and discharging atoms function(all_20_2_14) = all_91_1_121, function(all_20_2_14) = all_55_4_66, yields:
% 29.10/7.60 | (190) all_91_1_121 = all_55_4_66
% 29.10/7.60 |
% 29.10/7.60 | Instantiating formula (4) with all_20_2_14, all_53_3_60, all_55_4_66 and discharging atoms function(all_20_2_14) = all_55_4_66, function(all_20_2_14) = all_53_3_60, yields:
% 29.10/7.60 | (191) all_55_4_66 = all_53_3_60
% 29.10/7.60 |
% 29.10/7.60 | Instantiating formula (4) with all_20_2_14, all_51_3_55, all_53_3_60 and discharging atoms function(all_20_2_14) = all_53_3_60, function(all_20_2_14) = all_51_3_55, yields:
% 29.10/7.60 | (192) all_53_3_60 = all_51_3_55
% 29.10/7.60 |
% 29.10/7.60 | Instantiating formula (4) with all_20_2_14, all_49_4_50, all_51_3_55 and discharging atoms function(all_20_2_14) = all_51_3_55, function(all_20_2_14) = all_49_4_50, yields:
% 29.10/7.60 | (193) all_51_3_55 = all_49_4_50
% 29.10/7.60 |
% 29.10/7.60 | Instantiating formula (4) with all_20_2_14, all_47_4_44, all_49_4_50 and discharging atoms function(all_20_2_14) = all_49_4_50, function(all_20_2_14) = all_47_4_44, yields:
% 29.10/7.60 | (194) all_49_4_50 = all_47_4_44
% 29.10/7.60 |
% 29.10/7.60 | Instantiating formula (4) with all_20_2_14, all_41_3_33, all_57_4_72 and discharging atoms function(all_20_2_14) = all_57_4_72, function(all_20_2_14) = all_41_3_33, yields:
% 29.10/7.60 | (195) all_57_4_72 = all_41_3_33
% 29.10/7.60 |
% 29.10/7.60 | Instantiating formula (4) with all_20_2_14, all_41_3_33, all_49_4_50 and discharging atoms function(all_20_2_14) = all_49_4_50, function(all_20_2_14) = all_41_3_33, yields:
% 29.10/7.60 | (196) all_49_4_50 = all_41_3_33
% 29.10/7.60 |
% 29.10/7.60 | Instantiating formula (4) with all_20_2_14, all_39_3_28, all_91_1_121 and discharging atoms function(all_20_2_14) = all_91_1_121, function(all_20_2_14) = all_39_3_28, yields:
% 29.10/7.60 | (197) all_91_1_121 = all_39_3_28
% 29.10/7.60 |
% 29.10/7.60 | Combining equations (190,197) yields a new equation:
% 29.10/7.60 | (198) all_55_4_66 = all_39_3_28
% 29.10/7.60 |
% 29.10/7.60 | Simplifying 198 yields:
% 29.10/7.60 | (199) all_55_4_66 = all_39_3_28
% 29.10/7.60 |
% 29.10/7.60 | Combining equations (180,187) yields a new equation:
% 29.10/7.60 | (200) all_57_5_73 = all_41_4_34
% 29.10/7.60 |
% 29.10/7.60 | Simplifying 200 yields:
% 29.10/7.60 | (201) all_57_5_73 = all_41_4_34
% 29.10/7.60 |
% 29.10/7.60 | Combining equations (170,169) yields a new equation:
% 29.10/7.60 | (202) all_55_3_65 = 0
% 29.10/7.60 |
% 29.10/7.60 | Simplifying 202 yields:
% 29.10/7.60 | (203) all_55_3_65 = 0
% 29.10/7.60 |
% 29.10/7.60 | Combining equations (195,189) yields a new equation:
% 29.10/7.60 | (204) all_41_3_33 = 0
% 29.10/7.60 |
% 29.10/7.60 | Simplifying 204 yields:
% 29.10/7.60 | (205) all_41_3_33 = 0
% 29.10/7.60 |
% 29.10/7.60 | Combining equations (201,186) yields a new equation:
% 29.10/7.60 | (206) all_43_1_36 = all_41_4_34
% 29.10/7.60 |
% 29.10/7.60 | Combining equations (179,186) yields a new equation:
% 29.10/7.60 | (207) all_43_1_36 = 0
% 29.10/7.60 |
% 29.10/7.60 | Combining equations (182,186) yields a new equation:
% 29.10/7.60 | (208) all_51_4_56 = all_43_1_36
% 29.10/7.60 |
% 29.10/7.60 | Simplifying 208 yields:
% 29.10/7.60 | (209) all_51_4_56 = all_43_1_36
% 29.10/7.60 |
% 29.10/7.60 | Combining equations (171,203) yields a new equation:
% 29.10/7.60 | (210) all_49_3_49 = 0
% 29.10/7.60 |
% 29.10/7.60 | Simplifying 210 yields:
% 29.10/7.60 | (211) all_49_3_49 = 0
% 29.10/7.60 |
% 29.10/7.60 | Combining equations (191,199) yields a new equation:
% 29.10/7.60 | (212) all_53_3_60 = all_39_3_28
% 29.10/7.60 |
% 29.10/7.60 | Simplifying 212 yields:
% 29.10/7.60 | (213) all_53_3_60 = all_39_3_28
% 29.10/7.60 |
% 29.10/7.60 | Combining equations (181,184) yields a new equation:
% 29.10/7.60 | (214) all_53_4_61 = all_49_5_51
% 29.10/7.60 |
% 29.10/7.60 | Simplifying 214 yields:
% 29.10/7.60 | (215) all_53_4_61 = all_49_5_51
% 29.10/7.60 |
% 29.10/7.60 | Combining equations (166,165) yields a new equation:
% 29.10/7.60 | (216) all_41_2_32 = all_20_1_13
% 29.10/7.60 |
% 29.10/7.60 | Simplifying 216 yields:
% 29.10/7.60 | (217) all_41_2_32 = all_20_1_13
% 29.10/7.60 |
% 29.10/7.60 | Combining equations (192,213) yields a new equation:
% 29.10/7.60 | (218) all_51_3_55 = all_39_3_28
% 29.10/7.60 |
% 29.10/7.60 | Simplifying 218 yields:
% 29.10/7.60 | (219) all_51_3_55 = all_39_3_28
% 29.10/7.60 |
% 29.10/7.60 | Combining equations (183,215) yields a new equation:
% 29.10/7.60 | (220) all_51_4_56 = all_49_5_51
% 29.10/7.60 |
% 29.10/7.60 | Simplifying 220 yields:
% 29.10/7.60 | (221) all_51_4_56 = all_49_5_51
% 29.10/7.60 |
% 29.10/7.60 | Combining equations (168,167) yields a new equation:
% 29.10/7.60 | (222) all_39_2_27 = all_20_1_13
% 29.10/7.60 |
% 29.10/7.60 | Simplifying 222 yields:
% 29.10/7.60 | (223) all_39_2_27 = all_20_1_13
% 29.10/7.60 |
% 29.10/7.60 | Combining equations (193,219) yields a new equation:
% 29.10/7.60 | (224) all_49_4_50 = all_39_3_28
% 29.10/7.60 |
% 29.10/7.60 | Simplifying 224 yields:
% 29.10/7.60 | (225) all_49_4_50 = all_39_3_28
% 29.10/7.60 |
% 29.10/7.60 | Combining equations (209,221) yields a new equation:
% 29.10/7.60 | (226) all_49_5_51 = all_43_1_36
% 29.10/7.60 |
% 29.10/7.60 | Combining equations (185,221) yields a new equation:
% 29.10/7.60 | (227) all_49_5_51 = all_47_5_45
% 29.10/7.60 |
% 29.10/7.60 | Combining equations (188,221) yields a new equation:
% 29.10/7.60 | (228) all_49_5_51 = all_39_4_29
% 29.10/7.60 |
% 29.10/7.60 | Combining equations (176,211) yields a new equation:
% 29.10/7.60 | (229) all_47_3_43 = 0
% 29.10/7.60 |
% 29.10/7.60 | Simplifying 229 yields:
% 29.10/7.60 | (230) all_47_3_43 = 0
% 29.10/7.60 |
% 29.10/7.60 | Combining equations (196,194) yields a new equation:
% 29.10/7.60 | (231) all_47_4_44 = all_41_3_33
% 29.10/7.60 |
% 29.10/7.60 | Combining equations (225,194) yields a new equation:
% 29.10/7.60 | (232) all_47_4_44 = all_39_3_28
% 29.10/7.60 |
% 29.10/7.60 | Combining equations (226,227) yields a new equation:
% 29.10/7.60 | (233) all_47_5_45 = all_43_1_36
% 29.10/7.60 |
% 29.10/7.60 | Combining equations (228,227) yields a new equation:
% 29.10/7.60 | (234) all_47_5_45 = all_39_4_29
% 29.10/7.60 |
% 29.10/7.60 | Combining equations (231,232) yields a new equation:
% 29.10/7.60 | (235) all_41_3_33 = all_39_3_28
% 29.10/7.60 |
% 29.10/7.60 | Simplifying 235 yields:
% 29.10/7.61 | (236) all_41_3_33 = all_39_3_28
% 29.10/7.61 |
% 29.10/7.61 | Combining equations (233,234) yields a new equation:
% 29.10/7.61 | (237) all_43_1_36 = all_39_4_29
% 29.10/7.61 |
% 29.10/7.61 | Simplifying 237 yields:
% 29.10/7.61 | (238) all_43_1_36 = all_39_4_29
% 29.10/7.61 |
% 29.10/7.61 | Combining equations (207,206) yields a new equation:
% 29.10/7.61 | (239) all_41_4_34 = 0
% 29.10/7.61 |
% 29.10/7.61 | Combining equations (238,206) yields a new equation:
% 29.10/7.61 | (240) all_41_4_34 = all_39_4_29
% 29.10/7.61 |
% 29.10/7.61 | Combining equations (205,236) yields a new equation:
% 29.10/7.61 | (241) all_39_3_28 = 0
% 29.10/7.61 |
% 29.10/7.61 | Combining equations (239,240) yields a new equation:
% 29.10/7.61 | (242) all_39_4_29 = 0
% 29.10/7.61 |
% 29.10/7.61 | Combining equations (242,234) yields a new equation:
% 29.10/7.61 | (243) all_47_5_45 = 0
% 29.10/7.61 |
% 29.10/7.61 | Combining equations (243,227) yields a new equation:
% 29.10/7.61 | (244) all_49_5_51 = 0
% 29.10/7.61 |
% 29.10/7.61 | Combining equations (244,221) yields a new equation:
% 29.10/7.61 | (245) all_51_4_56 = 0
% 29.10/7.61 |
% 29.10/7.61 | Combining equations (241,219) yields a new equation:
% 29.10/7.61 | (246) all_51_3_55 = 0
% 29.10/7.61 |
% 29.10/7.61 | Combining equations (244,215) yields a new equation:
% 29.10/7.61 | (247) all_53_4_61 = 0
% 29.10/7.61 |
% 29.10/7.61 | Combining equations (241,213) yields a new equation:
% 29.10/7.61 | (248) all_53_3_60 = 0
% 29.10/7.61 |
% 29.10/7.61 | From (165) and (138) follows:
% 29.10/7.61 | (249) subset(all_20_1_13, all_20_1_13) = all_53_1_58
% 29.10/7.61 |
% 29.10/7.61 | From (167) and (130) follows:
% 29.10/7.61 | (250) subset(all_20_1_13, all_20_1_13) = all_51_1_53
% 29.10/7.61 |
% 29.10/7.61 | From (217) and (99) follows:
% 29.10/7.61 | (251) subset(all_20_1_13, all_20_1_13) = all_41_1_31
% 29.10/7.61 |
% 29.10/7.61 | From (223) and (95) follows:
% 29.10/7.61 | (252) subset(all_20_1_13, all_20_1_13) = all_39_1_26
% 29.10/7.61 |
% 29.10/7.61 | From (177) and (146) follows:
% 29.10/7.61 | (136) subset(all_20_3_15, all_20_4_16) = all_53_0_57
% 29.10/7.61 |
% 29.10/7.61 | From (178) and (126) follows:
% 29.10/7.61 | (118) subset(all_20_4_16, all_20_3_15) = all_49_0_46
% 29.10/7.61 |
% 29.10/7.61 +-Applying beta-rule and splitting (175), into two cases.
% 29.10/7.61 |-Branch one:
% 29.10/7.61 | (255) ~ (subset(all_20_1_13, all_20_1_13) = all_39_1_26)
% 29.10/7.61 |
% 29.10/7.61 | Using (252) and (255) yields:
% 29.10/7.61 | (256) $false
% 29.10/7.61 |
% 29.10/7.61 |-The branch is then unsatisfiable
% 29.10/7.61 |-Branch two:
% 29.10/7.61 | (252) subset(all_20_1_13, all_20_1_13) = all_39_1_26
% 29.10/7.61 | (258) all_47_3_43 = all_39_1_26
% 29.10/7.61 |
% 29.10/7.61 | Combining equations (230,258) yields a new equation:
% 29.10/7.61 | (259) all_39_1_26 = 0
% 29.10/7.61 |
% 29.10/7.61 | Combining equations (259,258) yields a new equation:
% 29.10/7.61 | (230) all_47_3_43 = 0
% 29.10/7.61 |
% 29.10/7.61 +-Applying beta-rule and splitting (172), into two cases.
% 29.10/7.61 |-Branch one:
% 29.10/7.61 | (261) ~ (subset(all_20_1_13, all_20_1_13) = all_53_1_58)
% 29.10/7.61 |
% 29.10/7.61 | Using (249) and (261) yields:
% 29.10/7.61 | (256) $false
% 29.10/7.61 |
% 29.10/7.61 |-The branch is then unsatisfiable
% 29.10/7.61 |-Branch two:
% 29.10/7.61 | (249) subset(all_20_1_13, all_20_1_13) = all_53_1_58
% 29.10/7.61 | (264) all_53_1_58 = all_47_3_43
% 29.10/7.61 |
% 29.10/7.61 | Combining equations (230,264) yields a new equation:
% 29.10/7.61 | (265) all_53_1_58 = 0
% 29.10/7.61 |
% 29.10/7.61 +-Applying beta-rule and splitting (133), into two cases.
% 29.10/7.61 |-Branch one:
% 29.10/7.61 | (266) ~ (all_53_1_58 = 0)
% 29.10/7.61 |
% 29.10/7.61 | Equations (265) can reduce 266 to:
% 29.10/7.61 | (267) $false
% 29.10/7.61 |
% 29.10/7.61 |-The branch is then unsatisfiable
% 29.10/7.61 |-Branch two:
% 29.10/7.61 | (265) all_53_1_58 = 0
% 29.10/7.61 | (269) ~ (all_53_3_60 = 0) | ~ (all_53_4_61 = 0) | all_53_0_57 = 0
% 29.10/7.61 |
% 29.10/7.61 +-Applying beta-rule and splitting (174), into two cases.
% 29.10/7.61 |-Branch one:
% 29.10/7.61 | (270) ~ (subset(all_20_1_13, all_20_1_13) = all_41_1_31)
% 29.10/7.61 |
% 29.10/7.61 | Using (251) and (270) yields:
% 29.10/7.61 | (256) $false
% 29.10/7.61 |
% 29.10/7.61 |-The branch is then unsatisfiable
% 29.10/7.61 |-Branch two:
% 29.10/7.61 | (251) subset(all_20_1_13, all_20_1_13) = all_41_1_31
% 29.10/7.61 | (273) all_47_3_43 = all_41_1_31
% 29.10/7.61 |
% 29.10/7.61 | Combining equations (230,273) yields a new equation:
% 29.10/7.61 | (274) all_41_1_31 = 0
% 29.10/7.61 |
% 29.10/7.61 | Combining equations (274,273) yields a new equation:
% 29.10/7.61 | (230) all_47_3_43 = 0
% 29.10/7.61 |
% 29.10/7.61 +-Applying beta-rule and splitting (173), into two cases.
% 29.10/7.61 |-Branch one:
% 29.10/7.61 | (276) ~ (subset(all_20_1_13, all_20_1_13) = all_51_1_53)
% 29.10/7.61 |
% 29.10/7.61 | Using (250) and (276) yields:
% 29.10/7.61 | (256) $false
% 29.10/7.61 |
% 29.10/7.61 |-The branch is then unsatisfiable
% 29.10/7.61 |-Branch two:
% 29.10/7.61 | (250) subset(all_20_1_13, all_20_1_13) = all_51_1_53
% 29.10/7.61 | (279) all_51_1_53 = all_47_3_43
% 29.10/7.61 |
% 29.10/7.61 | Combining equations (230,279) yields a new equation:
% 29.10/7.61 | (280) all_51_1_53 = 0
% 29.10/7.61 |
% 29.10/7.61 +-Applying beta-rule and splitting (269), into two cases.
% 29.10/7.61 |-Branch one:
% 29.10/7.61 | (281) ~ (all_53_3_60 = 0)
% 29.10/7.61 |
% 29.10/7.62 | Equations (248) can reduce 281 to:
% 29.10/7.62 | (267) $false
% 29.10/7.62 |
% 29.10/7.62 |-The branch is then unsatisfiable
% 29.10/7.62 |-Branch two:
% 29.10/7.62 | (248) all_53_3_60 = 0
% 29.10/7.62 | (284) ~ (all_53_4_61 = 0) | all_53_0_57 = 0
% 29.10/7.62 |
% 29.10/7.62 +-Applying beta-rule and splitting (128), into two cases.
% 29.10/7.62 |-Branch one:
% 29.10/7.62 | (285) ~ (all_51_1_53 = 0)
% 29.10/7.62 |
% 29.10/7.62 | Equations (280) can reduce 285 to:
% 29.10/7.62 | (267) $false
% 29.10/7.62 |
% 29.10/7.62 |-The branch is then unsatisfiable
% 29.10/7.62 |-Branch two:
% 29.10/7.62 | (280) all_51_1_53 = 0
% 29.10/7.62 | (288) ~ (all_51_3_55 = 0) | ~ (all_51_4_56 = 0) | all_51_0_52 = 0
% 29.10/7.62 |
% 29.10/7.62 +-Applying beta-rule and splitting (288), into two cases.
% 29.10/7.62 |-Branch one:
% 29.10/7.62 | (289) ~ (all_51_3_55 = 0)
% 29.10/7.62 |
% 29.10/7.62 | Equations (246) can reduce 289 to:
% 29.10/7.62 | (267) $false
% 29.10/7.62 |
% 29.10/7.62 |-The branch is then unsatisfiable
% 29.10/7.62 |-Branch two:
% 29.10/7.62 | (246) all_51_3_55 = 0
% 29.10/7.62 | (292) ~ (all_51_4_56 = 0) | all_51_0_52 = 0
% 29.10/7.62 |
% 29.10/7.62 +-Applying beta-rule and splitting (292), into two cases.
% 29.10/7.62 |-Branch one:
% 29.10/7.62 | (293) ~ (all_51_4_56 = 0)
% 29.10/7.62 |
% 29.10/7.62 | Equations (245) can reduce 293 to:
% 29.10/7.62 | (267) $false
% 29.10/7.62 |
% 29.10/7.62 |-The branch is then unsatisfiable
% 29.10/7.62 |-Branch two:
% 29.10/7.62 | (245) all_51_4_56 = 0
% 29.10/7.62 | (296) all_51_0_52 = 0
% 29.10/7.62 |
% 29.10/7.62 | Combining equations (178,296) yields a new equation:
% 29.10/7.62 | (297) all_49_0_46 = 0
% 29.10/7.62 |
% 29.10/7.62 | Simplifying 297 yields:
% 29.10/7.62 | (298) all_49_0_46 = 0
% 29.10/7.62 |
% 29.10/7.62 | From (298) and (118) follows:
% 29.10/7.62 | (299) subset(all_20_4_16, all_20_3_15) = 0
% 29.10/7.62 |
% 29.10/7.62 +-Applying beta-rule and splitting (284), into two cases.
% 29.10/7.62 |-Branch one:
% 29.10/7.62 | (300) ~ (all_53_4_61 = 0)
% 29.10/7.62 |
% 29.10/7.62 | Equations (247) can reduce 300 to:
% 29.10/7.62 | (267) $false
% 29.10/7.62 |
% 29.10/7.62 |-The branch is then unsatisfiable
% 29.10/7.62 |-Branch two:
% 29.10/7.62 | (247) all_53_4_61 = 0
% 29.10/7.62 | (303) all_53_0_57 = 0
% 29.10/7.62 |
% 29.10/7.62 | From (303) and (136) follows:
% 29.10/7.62 | (304) subset(all_20_3_15, all_20_4_16) = 0
% 29.10/7.62 |
% 29.10/7.62 | Instantiating formula (13) with all_20_3_15, all_20_4_16 and discharging atoms subset(all_20_3_15, all_20_4_16) = 0, yields:
% 29.10/7.62 | (305) all_20_3_15 = all_20_4_16 | ? [v0] : ( ~ (v0 = 0) & subset(all_20_4_16, all_20_3_15) = v0)
% 29.10/7.62 |
% 29.10/7.62 +-Applying beta-rule and splitting (305), into two cases.
% 29.10/7.62 |-Branch one:
% 29.10/7.62 | (306) all_20_3_15 = all_20_4_16
% 29.10/7.62 |
% 29.10/7.62 | Equations (306) can reduce 72 to:
% 29.10/7.62 | (267) $false
% 29.10/7.62 |
% 29.10/7.62 |-The branch is then unsatisfiable
% 29.10/7.62 |-Branch two:
% 29.10/7.62 | (72) ~ (all_20_3_15 = all_20_4_16)
% 29.10/7.62 | (309) ? [v0] : ( ~ (v0 = 0) & subset(all_20_4_16, all_20_3_15) = v0)
% 29.10/7.62 |
% 29.10/7.62 | Instantiating (309) with all_288_0_193 yields:
% 29.10/7.62 | (310) ~ (all_288_0_193 = 0) & subset(all_20_4_16, all_20_3_15) = all_288_0_193
% 29.10/7.62 |
% 29.10/7.62 | Applying alpha-rule on (310) yields:
% 29.10/7.62 | (311) ~ (all_288_0_193 = 0)
% 29.10/7.62 | (312) subset(all_20_4_16, all_20_3_15) = all_288_0_193
% 29.10/7.62 |
% 29.10/7.62 | Instantiating formula (16) with all_20_4_16, all_20_3_15, all_288_0_193, 0 and discharging atoms subset(all_20_4_16, all_20_3_15) = all_288_0_193, subset(all_20_4_16, all_20_3_15) = 0, yields:
% 29.10/7.62 | (313) all_288_0_193 = 0
% 29.10/7.62 |
% 29.10/7.62 | Equations (313) can reduce 311 to:
% 29.10/7.62 | (267) $false
% 29.10/7.62 |
% 29.10/7.62 |-The branch is then unsatisfiable
% 29.10/7.62 % SZS output end Proof for theBenchmark
% 29.10/7.62
% 29.10/7.62 7010ms
%------------------------------------------------------------------------------