TSTP Solution File: SEU212+2 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU212+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n020.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 08:47:41 EDT 2022
% Result : Theorem 115.28s 70.49s
% Output : Proof 142.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU212+2 : TPTP v8.1.0. Released v3.3.0.
% 0.00/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n020.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 03:34:48 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.58/0.59 ____ _
% 0.58/0.59 ___ / __ \_____(_)___ ________ __________
% 0.58/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.58/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.58/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.58/0.60
% 0.58/0.60 A Theorem Prover for First-Order Logic
% 0.58/0.60 (ePrincess v.1.0)
% 0.58/0.60
% 0.58/0.60 (c) Philipp Rümmer, 2009-2015
% 0.58/0.60 (c) Peter Backeman, 2014-2015
% 0.58/0.60 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.58/0.60 Free software under GNU Lesser General Public License (LGPL).
% 0.58/0.60 Bug reports to peter@backeman.se
% 0.58/0.60
% 0.58/0.60 For more information, visit http://user.uu.se/~petba168/breu/
% 0.58/0.60
% 0.58/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.72/0.67 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.85/1.19 Prover 0: Preprocessing ...
% 6.51/2.00 Prover 0: Warning: ignoring some quantifiers
% 6.51/2.04 Prover 0: Constructing countermodel ...
% 21.29/5.96 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 21.57/6.05 Prover 1: Preprocessing ...
% 23.23/6.43 Prover 1: Warning: ignoring some quantifiers
% 23.23/6.44 Prover 1: Constructing countermodel ...
% 32.11/8.55 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 32.97/8.72 Prover 2: Preprocessing ...
% 34.93/9.19 Prover 2: Warning: ignoring some quantifiers
% 34.93/9.21 Prover 2: Constructing countermodel ...
% 41.54/11.57 Prover 0: stopped
% 42.07/11.77 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 42.49/11.89 Prover 3: Preprocessing ...
% 42.65/12.02 Prover 3: Warning: ignoring some quantifiers
% 43.05/12.02 Prover 3: Constructing countermodel ...
% 90.59/52.71 Prover 3: stopped
% 90.79/52.91 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 91.22/53.08 Prover 4: Preprocessing ...
% 93.07/53.53 Prover 4: Warning: ignoring some quantifiers
% 93.07/53.55 Prover 4: Constructing countermodel ...
% 115.26/70.49 Prover 4: proved (6309ms)
% 115.28/70.49 Prover 2: stopped
% 115.28/70.49 Prover 1: stopped
% 115.28/70.49
% 115.28/70.49 No countermodel exists, formula is valid
% 115.28/70.49 % SZS status Theorem for theBenchmark
% 115.28/70.49
% 115.28/70.49 Generating proof ... Warning: ignoring some quantifiers
% 140.06/84.25 found it (size 722)
% 140.06/84.25
% 140.06/84.25 % SZS output start Proof for theBenchmark
% 140.06/84.25 Assumed formulas after preprocessing and simplification:
% 140.06/84.25 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ( ~ (v13 = 0) & ~ (v11 = 0) & relation_empty_yielding(v9) = 0 & relation_empty_yielding(empty_set) = 0 & relation_rng(empty_set) = empty_set & relation_dom(v2) = v5 & relation_dom(empty_set) = empty_set & apply(v2, v0) = v7 & powerset(empty_set) = v8 & singleton(empty_set) = v8 & ordered_pair(v0, v1) = v3 & relation(v16) = 0 & relation(v15) = 0 & relation(v12) = 0 & relation(v9) = 0 & relation(v2) = 0 & relation(empty_set) = 0 & empty(v15) = 0 & empty(v14) = 0 & empty(v12) = v13 & empty(v10) = v11 & empty(empty_set) = 0 & function(v16) = 0 & function(v2) = 0 & in(v3, v2) = v4 & in(v0, v5) = v6 & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ( ~ (relation_composition(v22, v20) = v23) | ~ (identity_relation(v19) = v22) | ~ (ordered_pair(v17, v18) = v21) | ~ (in(v21, v23) = v24) | ? [v25] : ? [v26] : ? [v27] : (relation(v20) = v25 & in(v21, v20) = v27 & in(v17, v19) = v26 & ( ~ (v25 = 0) | (( ~ (v27 = 0) | ~ (v26 = 0) | v24 = 0) & ( ~ (v24 = 0) | (v27 = 0 & v26 = 0)))))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ( ~ (relation_composition(v17, v18) = v19) | ~ (ordered_pair(v23, v21) = v24) | ~ (ordered_pair(v20, v21) = v22) | ~ (relation(v19) = 0) | ~ (relation(v17) = 0) | ? [v25] : ? [v26] : ? [v27] : ((v25 = 0 & in(v22, v19) = 0) | ( ~ (v25 = 0) & relation(v18) = v25) | (ordered_pair(v20, v23) = v25 & in(v25, v17) = v26 & in(v24, v18) = v27 & ( ~ (v27 = 0) | ~ (v26 = 0))))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ( ~ (relation_composition(v17, v18) = v19) | ~ (ordered_pair(v20, v23) = v24) | ~ (ordered_pair(v20, v21) = v22) | ~ (relation(v19) = 0) | ~ (relation(v17) = 0) | ? [v25] : ? [v26] : ? [v27] : ((v25 = 0 & in(v22, v19) = 0) | ( ~ (v25 = 0) & relation(v18) = v25) | (ordered_pair(v23, v21) = v26 & in(v26, v18) = v27 & in(v24, v17) = v25 & ( ~ (v27 = 0) | ~ (v25 = 0))))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v23 = 0 | ~ (cartesian_product2(v19, v20) = v22) | ~ (ordered_pair(v17, v18) = v21) | ~ (in(v21, v22) = v23) | ? [v24] : ? [v25] : (in(v18, v20) = v25 & in(v17, v19) = v24 & ( ~ (v25 = 0) | ~ (v24 = 0)))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v23 = 0 | ~ (cartesian_product2(v18, v20) = v22) | ~ (cartesian_product2(v17, v19) = v21) | ~ (subset(v21, v22) = v23) | ? [v24] : ? [v25] : (subset(v19, v20) = v25 & subset(v17, v18) = v24 & ( ~ (v25 = 0) | ~ (v24 = 0)))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v21 = 0 | ~ (cartesian_product2(v17, v18) = v19) | ~ (ordered_pair(v22, v23) = v20) | ~ (in(v20, v19) = v21) | ? [v24] : ? [v25] : (in(v23, v18) = v25 & in(v22, v17) = v24 & ( ~ (v25 = 0) | ~ (v24 = 0)))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v21 = 0 | ~ (relation_inverse_image(v17, v18) = v19) | ~ (ordered_pair(v20, v22) = v23) | ~ (relation(v17) = 0) | ~ (in(v20, v19) = v21) | ? [v24] : ? [v25] : (in(v23, v17) = v24 & in(v22, v18) = v25 & ( ~ (v25 = 0) | ~ (v24 = 0)))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v21 = 0 | ~ (relation_image(v17, v18) = v19) | ~ (ordered_pair(v22, v20) = v23) | ~ (relation(v17) = 0) | ~ (in(v20, v19) = v21) | ? [v24] : ? [v25] : (in(v23, v17) = v24 & in(v22, v18) = v25 & ( ~ (v25 = 0) | ~ (v24 = 0)))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v22 = 0 | v17 = empty_set | ~ (subset_complement(v17, v19) = v20) | ~ (powerset(v17) = v18) | ~ (in(v21, v20) = v22) | ? [v23] : ? [v24] : (( ~ (v23 = 0) & element(v19, v18) = v23) | (element(v21, v17) = v23 & in(v21, v19) = v24 & ( ~ (v23 = 0) | v24 = 0)))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v22 = 0 | v17 = empty_set | ~ (subset_complement(v17, v19) = v20) | ~ (powerset(v17) = v18) | ~ (in(v21, v19) = v22) | ? [v23] : ? [v24] : (( ~ (v23 = 0) & element(v19, v18) = v23) | (element(v21, v17) = v23 & in(v21, v20) = v24 & ( ~ (v23 = 0) | v24 = 0)))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v22 = 0 | ~ (set_difference(v18, v20) = v21) | ~ (singleton(v19) = v20) | ~ (subset(v17, v21) = v22) | ? [v23] : ? [v24] : (subset(v17, v18) = v23 & in(v19, v17) = v24 & ( ~ (v23 = 0) | v24 = 0))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v22 = 0 | ~ (set_difference(v18, v19) = v21) | ~ (set_difference(v17, v19) = v20) | ~ (subset(v20, v21) = v22) | ? [v23] : ( ~ (v23 = 0) & subset(v17, v18) = v23)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v22 = 0 | ~ (relation_inverse_image(v19, v18) = v21) | ~ (relation_inverse_image(v19, v17) = v20) | ~ (subset(v20, v21) = v22) | ? [v23] : ? [v24] : (subset(v17, v18) = v24 & relation(v19) = v23 & ( ~ (v24 = 0) | ~ (v23 = 0)))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v22 = 0 | ~ (subset(v20, v21) = v22) | ~ (set_intersection2(v18, v19) = v21) | ~ (set_intersection2(v17, v19) = v20) | ? [v23] : ( ~ (v23 = 0) & subset(v17, v18) = v23)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v21 = 0 | ~ (relation_inverse_image(v17, v18) = v19) | ~ (relation(v17) = 0) | ~ (in(v22, v18) = 0) | ~ (in(v20, v19) = v21) | ? [v23] : ? [v24] : ( ~ (v24 = 0) & ordered_pair(v20, v22) = v23 & in(v23, v17) = v24)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v21 = 0 | ~ (relation_image(v17, v18) = v19) | ~ (relation(v17) = 0) | ~ (in(v22, v18) = 0) | ~ (in(v20, v19) = v21) | ? [v23] : ? [v24] : ( ~ (v24 = 0) & ordered_pair(v22, v20) = v23 & in(v23, v17) = v24)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v20 = 0 | ~ (relation_rng(v17) = v18) | ~ (ordered_pair(v21, v19) = v22) | ~ (in(v19, v18) = v20) | ? [v23] : (( ~ (v23 = 0) & relation(v17) = v23) | ( ~ (v23 = 0) & in(v22, v17) = v23))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v20 = 0 | ~ (relation_dom(v17) = v18) | ~ (ordered_pair(v19, v21) = v22) | ~ (in(v19, v18) = v20) | ? [v23] : (( ~ (v23 = 0) & relation(v17) = v23) | ( ~ (v23 = 0) & in(v22, v17) = v23))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (relation_composition(v17, v18) = v19) | ~ (ordered_pair(v20, v21) = v22) | ~ (relation(v19) = 0) | ~ (relation(v17) = 0) | ? [v23] : ? [v24] : ? [v25] : ? [v26] : ? [v27] : ((v27 = 0 & v25 = 0 & ordered_pair(v23, v21) = v26 & ordered_pair(v20, v23) = v24 & in(v26, v18) = 0 & in(v24, v17) = 0) | ( ~ (v23 = 0) & relation(v18) = v23) | ( ~ (v23 = 0) & in(v22, v19) = v23))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (relation_rng(v20) = v21) | ~ (relation_rng_restriction(v18, v19) = v20) | ~ (in(v17, v21) = v22) | ? [v23] : ? [v24] : ? [v25] : ? [v26] : (relation_rng(v19) = v25 & relation(v19) = v23 & in(v17, v25) = v26 & in(v17, v18) = v24 & ( ~ (v23 = 0) | (( ~ (v26 = 0) | ~ (v24 = 0) | v22 = 0) & ( ~ (v22 = 0) | (v26 = 0 & v24 = 0)))))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (relation_dom(v20) = v21) | ~ (relation_dom_restriction(v19, v18) = v20) | ~ (in(v17, v21) = v22) | ? [v23] : ? [v24] : ? [v25] : ? [v26] : (relation_dom(v19) = v25 & relation(v19) = v23 & in(v17, v25) = v26 & in(v17, v18) = v24 & ( ~ (v23 = 0) | (( ~ (v26 = 0) | ~ (v24 = 0) | v22 = 0) & ( ~ (v22 = 0) | (v26 = 0 & v24 = 0)))))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (cartesian_product2(v19, v20) = v22) | ~ (ordered_pair(v17, v18) = v21) | ~ (in(v21, v22) = 0) | (in(v18, v20) = 0 & in(v17, v19) = 0)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (cartesian_product2(v19, v18) = v21) | ~ (cartesian_product2(v19, v17) = v20) | ~ (subset(v20, v21) = v22) | ? [v23] : ? [v24] : ? [v25] : ? [v26] : (cartesian_product2(v18, v19) = v25 & cartesian_product2(v17, v19) = v24 & subset(v24, v25) = v26 & subset(v17, v18) = v23 & ( ~ (v23 = 0) | (v26 = 0 & v22 = 0)))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (cartesian_product2(v18, v19) = v21) | ~ (cartesian_product2(v17, v19) = v20) | ~ (subset(v20, v21) = v22) | ? [v23] : ? [v24] : ? [v25] : ? [v26] : (cartesian_product2(v19, v18) = v25 & cartesian_product2(v19, v17) = v24 & subset(v24, v25) = v26 & subset(v17, v18) = v23 & ( ~ (v23 = 0) | (v26 = 0 & v22 = 0)))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (relation_rng_restriction(v17, v18) = v19) | ~ (ordered_pair(v20, v21) = v22) | ~ (relation(v19) = 0) | ? [v23] : ? [v24] : ? [v25] : (( ~ (v23 = 0) & relation(v18) = v23) | (in(v22, v19) = v25 & in(v22, v18) = v24 & in(v21, v17) = v23 & ( ~ (v24 = 0) | ~ (v23 = 0) | v25 = 0)))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (relation_rng_restriction(v17, v18) = v19) | ~ (ordered_pair(v20, v21) = v22) | ~ (relation(v19) = 0) | ? [v23] : ? [v24] : ? [v25] : (( ~ (v23 = 0) & relation(v18) = v23) | (in(v22, v19) = v23 & in(v22, v18) = v25 & in(v21, v17) = v24 & ( ~ (v23 = 0) | (v25 = 0 & v24 = 0))))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (relation_dom_restriction(v17, v18) = v19) | ~ (ordered_pair(v20, v21) = v22) | ~ (relation(v19) = 0) | ~ (relation(v17) = 0) | ? [v23] : ? [v24] : ? [v25] : (in(v22, v19) = v25 & in(v22, v17) = v24 & in(v20, v18) = v23 & ( ~ (v24 = 0) | ~ (v23 = 0) | v25 = 0))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (relation_dom_restriction(v17, v18) = v19) | ~ (ordered_pair(v20, v21) = v22) | ~ (relation(v19) = 0) | ~ (relation(v17) = 0) | ? [v23] : ? [v24] : ? [v25] : (in(v22, v19) = v23 & in(v22, v17) = v25 & in(v20, v18) = v24 & ( ~ (v23 = 0) | (v25 = 0 & v24 = 0)))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v21 = 0 | v17 = empty_set | ~ (set_meet(v17) = v18) | ~ (in(v19, v20) = v21) | ~ (in(v19, v18) = 0) | ? [v22] : ( ~ (v22 = 0) & in(v20, v17) = v22)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v21 = 0 | ~ (set_difference(v17, v18) = v19) | ~ (in(v20, v19) = v21) | ? [v22] : ? [v23] : (in(v20, v18) = v23 & in(v20, v17) = v22 & ( ~ (v22 = 0) | v23 = 0))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v21 = 0 | ~ (set_difference(v17, v18) = v19) | ~ (in(v20, v18) = v21) | ? [v22] : ? [v23] : (in(v20, v19) = v23 & in(v20, v17) = v22 & ( ~ (v22 = 0) | v23 = 0))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v21 = 0 | ~ (element(v18, v20) = 0) | ~ (element(v17, v19) = v21) | ~ (powerset(v19) = v20) | ? [v22] : ( ~ (v22 = 0) & in(v17, v18) = v22)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v21 = 0 | ~ (element(v18, v19) = 0) | ~ (powerset(v17) = v19) | ~ (in(v20, v17) = v21) | ? [v22] : ( ~ (v22 = 0) & in(v20, v18) = v22)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v21 = 0 | ~ (subset(v20, v19) = v21) | ~ (unordered_pair(v17, v18) = v20) | ? [v22] : ? [v23] : (in(v18, v19) = v23 & in(v17, v19) = v22 & ( ~ (v23 = 0) | ~ (v22 = 0)))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v21 = 0 | ~ (subset(v20, v18) = v21) | ~ (set_union2(v17, v19) = v20) | ? [v22] : ? [v23] : (subset(v19, v18) = v23 & subset(v17, v18) = v22 & ( ~ (v23 = 0) | ~ (v22 = 0)))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v21 = 0 | ~ (subset(v17, v20) = v21) | ~ (set_intersection2(v18, v19) = v20) | ? [v22] : ? [v23] : (subset(v17, v19) = v23 & subset(v17, v18) = v22 & ( ~ (v23 = 0) | ~ (v22 = 0)))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v21 = 0 | ~ (set_intersection2(v17, v18) = v19) | ~ (in(v20, v19) = v21) | ? [v22] : ? [v23] : (in(v20, v18) = v23 & in(v20, v17) = v22 & ( ~ (v23 = 0) | ~ (v22 = 0)))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v21 = 0 | ~ (set_union2(v17, v18) = v19) | ~ (in(v20, v19) = v21) | ? [v22] : ? [v23] : ( ~ (v23 = 0) & ~ (v22 = 0) & in(v20, v18) = v23 & in(v20, v17) = v22)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v21 = 0 | ~ (set_union2(v17, v18) = v19) | ~ (in(v20, v18) = v21) | ? [v22] : ? [v23] : (in(v20, v19) = v22 & in(v20, v17) = v23 & ( ~ (v22 = 0) | v23 = 0))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v21 = 0 | ~ (set_union2(v17, v18) = v19) | ~ (in(v20, v17) = v21) | ? [v22] : ? [v23] : (in(v20, v19) = v22 & in(v20, v18) = v23 & ( ~ (v22 = 0) | v23 = 0))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v20 = v18 | ~ (ordered_pair(v19, v20) = v21) | ~ (ordered_pair(v17, v18) = v21)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v20 = v17 | v19 = v17 | ~ (unordered_pair(v19, v20) = v21) | ~ (unordered_pair(v17, v18) = v21)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v20 = 0 | ~ (union(v17) = v18) | ~ (in(v21, v17) = 0) | ~ (in(v19, v18) = v20) | ? [v22] : ( ~ (v22 = 0) & in(v19, v21) = v22)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v20 = 0 | ~ (union(v17) = v18) | ~ (in(v19, v21) = 0) | ~ (in(v19, v18) = v20) | ? [v22] : ( ~ (v22 = 0) & in(v21, v17) = v22)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v19 = v17 | ~ (ordered_pair(v19, v20) = v21) | ~ (ordered_pair(v17, v18) = v21)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v18 = v17 | ~ (subset_difference(v21, v20, v19) = v18) | ~ (subset_difference(v21, v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v17 = empty_set | ~ (subset_complement(v17, v19) = v20) | ~ (element(v21, v17) = 0) | ~ (powerset(v17) = v18) | ? [v22] : ? [v23] : (( ~ (v22 = 0) & element(v19, v18) = v22) | (in(v21, v20) = v23 & in(v21, v19) = v22 & (v23 = 0 | v22 = 0)))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (disjoint(v18, v20) = v21) | ~ (element(v18, v19) = 0) | ~ (powerset(v17) = v19) | ? [v22] : ? [v23] : ? [v24] : (subset_complement(v17, v20) = v23 & element(v20, v19) = v22 & subset(v18, v23) = v24 & ( ~ (v22 = 0) | (( ~ (v24 = 0) | v21 = 0) & ( ~ (v21 = 0) | v24 = 0))))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (relation_inverse(v17) = v18) | ~ (ordered_pair(v20, v19) = v21) | ~ (relation(v18) = 0) | ? [v22] : ? [v23] : ? [v24] : (( ~ (v22 = 0) & relation(v17) = v22) | (ordered_pair(v19, v20) = v23 & in(v23, v18) = v24 & in(v21, v17) = v22 & ( ~ (v22 = 0) | v24 = 0)))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (relation_inverse(v17) = v18) | ~ (ordered_pair(v20, v19) = v21) | ~ (relation(v18) = 0) | ? [v22] : ? [v23] : ? [v24] : (( ~ (v22 = 0) & relation(v17) = v22) | (ordered_pair(v19, v20) = v22 & in(v22, v18) = v23 & in(v21, v17) = v24 & ( ~ (v23 = 0) | v24 = 0)))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (relation_inverse(v17) = v18) | ~ (ordered_pair(v19, v20) = v21) | ~ (relation(v18) = 0) | ? [v22] : ? [v23] : ? [v24] : (( ~ (v22 = 0) & relation(v17) = v22) | (ordered_pair(v20, v19) = v23 & in(v23, v17) = v24 & in(v21, v18) = v22 & ( ~ (v22 = 0) | v24 = 0)))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (relation_inverse(v17) = v18) | ~ (ordered_pair(v19, v20) = v21) | ~ (relation(v18) = 0) | ? [v22] : ? [v23] : ? [v24] : (( ~ (v22 = 0) & relation(v17) = v22) | (ordered_pair(v20, v19) = v22 & in(v22, v17) = v23 & in(v21, v18) = v24 & ( ~ (v23 = 0) | v24 = 0)))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (subset_complement(v17, v20) = v21) | ~ (element(v18, v19) = 0) | ~ (powerset(v17) = v19) | ? [v22] : ? [v23] : ? [v24] : (disjoint(v18, v20) = v23 & element(v20, v19) = v22 & subset(v18, v21) = v24 & ( ~ (v22 = 0) | (( ~ (v24 = 0) | v23 = 0) & ( ~ (v23 = 0) | v24 = 0))))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (set_difference(v17, v18) = v19) | ~ (in(v20, v18) = v21) | ? [v22] : ? [v23] : (in(v20, v19) = v22 & in(v20, v17) = v23 & ( ~ (v22 = 0) | (v23 = 0 & ~ (v21 = 0))))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (set_difference(v17, v18) = v19) | ~ (in(v20, v17) = v21) | ? [v22] : ? [v23] : (in(v20, v19) = v22 & in(v20, v18) = v23 & ( ~ (v22 = 0) | (v21 = 0 & ~ (v23 = 0))))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (relation_dom(v17) = v18) | ~ (ordered_pair(v19, v20) = v21) | ? [v22] : ? [v23] : ? [v24] : ((apply(v17, v19) = v23 & in(v21, v17) = v24 & in(v19, v18) = v22 & ( ~ (v22 = 0) | (( ~ (v24 = 0) | v23 = v20) & ( ~ (v23 = v20) | v24 = 0)))) | (relation(v17) = v22 & function(v17) = v23 & ( ~ (v23 = 0) | ~ (v22 = 0))))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (relation_inverse_image(v19, v18) = v20) | ~ (in(v17, v20) = v21) | ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : ? [v27] : ? [v28] : (relation_rng(v19) = v23 & relation(v19) = v22 & ( ~ (v22 = 0) | (( ~ (v21 = 0) | (v28 = 0 & v27 = 0 & v25 = 0 & ordered_pair(v17, v24) = v26 & in(v26, v19) = 0 & in(v24, v23) = 0 & in(v24, v18) = 0)) & (v21 = 0 | ( ! [v29] : ! [v30] : ( ~ (ordered_pair(v17, v29) = v30) | ? [v31] : ? [v32] : ? [v33] : (in(v30, v19) = v32 & in(v29, v23) = v31 & in(v29, v18) = v33 & ( ~ (v33 = 0) | ~ (v32 = 0) | ~ (v31 = 0)))) & ! [v29] : ( ~ (in(v29, v23) = 0) | ? [v30] : ? [v31] : ? [v32] : (ordered_pair(v17, v29) = v30 & in(v30, v19) = v31 & in(v29, v18) = v32 & ( ~ (v32 = 0) | ~ (v31 = 0)))) & ! [v29] : ( ~ (in(v29, v18) = 0) | ? [v30] : ? [v31] : ? [v32] : (ordered_pair(v17, v29) = v31 & in(v31, v19) = v32 & in(v29, v23) = v30 & ( ~ (v32 = 0) | ~ (v30 = 0)))))))))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (relation_image(v19, v18) = v20) | ~ (in(v17, v20) = v21) | ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : ? [v27] : ? [v28] : (relation_dom(v19) = v23 & relation(v19) = v22 & ( ~ (v22 = 0) | (( ~ (v21 = 0) | (v28 = 0 & v27 = 0 & v25 = 0 & ordered_pair(v24, v17) = v26 & in(v26, v19) = 0 & in(v24, v23) = 0 & in(v24, v18) = 0)) & (v21 = 0 | ( ! [v29] : ! [v30] : ( ~ (ordered_pair(v29, v17) = v30) | ? [v31] : ? [v32] : ? [v33] : (in(v30, v19) = v32 & in(v29, v23) = v31 & in(v29, v18) = v33 & ( ~ (v33 = 0) | ~ (v32 = 0) | ~ (v31 = 0)))) & ! [v29] : ( ~ (in(v29, v23) = 0) | ? [v30] : ? [v31] : ? [v32] : (ordered_pair(v29, v17) = v30 & in(v30, v19) = v31 & in(v29, v18) = v32 & ( ~ (v32 = 0) | ~ (v31 = 0)))) & ! [v29] : ( ~ (in(v29, v18) = 0) | ? [v30] : ? [v31] : ? [v32] : (ordered_pair(v29, v17) = v31 & in(v31, v19) = v32 & in(v29, v23) = v30 & ( ~ (v32 = 0) | ~ (v30 = 0)))))))))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (relation_rng_restriction(v17, v20) = v21) | ~ (relation_dom_restriction(v19, v18) = v20) | ? [v22] : ? [v23] : ? [v24] : (relation_rng_restriction(v17, v19) = v23 & relation_dom_restriction(v23, v18) = v24 & relation(v19) = v22 & ( ~ (v22 = 0) | v24 = v21))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (relation_rng_restriction(v17, v19) = v20) | ~ (relation_dom_restriction(v20, v18) = v21) | ? [v22] : ? [v23] : ? [v24] : (relation_rng_restriction(v17, v23) = v24 & relation_dom_restriction(v19, v18) = v23 & relation(v19) = v22 & ( ~ (v22 = 0) | v24 = v21))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (subset(v17, v18) = 0) | ~ (ordered_pair(v19, v20) = v21) | ~ (relation(v17) = 0) | ? [v22] : ? [v23] : (( ~ (v22 = 0) & relation(v18) = v22) | (in(v21, v18) = v23 & in(v21, v17) = v22 & ( ~ (v22 = 0) | v23 = 0)))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (identity_relation(v17) = v18) | ~ (ordered_pair(v19, v20) = v21) | ~ (relation(v18) = 0) | ? [v22] : ? [v23] : (in(v21, v18) = v22 & in(v19, v17) = v23 & ( ~ (v22 = 0) | (v23 = 0 & v20 = v19)))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (set_intersection2(v17, v18) = v19) | ~ (in(v20, v18) = v21) | ? [v22] : ? [v23] : (in(v20, v19) = v22 & in(v20, v17) = v23 & ( ~ (v22 = 0) | (v23 = 0 & v21 = 0)))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (set_intersection2(v17, v18) = v19) | ~ (in(v20, v17) = v21) | ? [v22] : ? [v23] : (in(v20, v19) = v22 & in(v20, v18) = v23 & ( ~ (v22 = 0) | (v23 = 0 & v21 = 0)))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (set_union2(v17, v18) = v19) | ~ (in(v20, v18) = v21) | ? [v22] : ? [v23] : (in(v20, v19) = v23 & in(v20, v17) = v22 & (v23 = 0 | ( ~ (v22 = 0) & ~ (v21 = 0))))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (set_union2(v17, v18) = v19) | ~ (in(v20, v17) = v21) | ? [v22] : ? [v23] : (in(v20, v19) = v23 & in(v20, v18) = v22 & (v23 = 0 | ( ~ (v22 = 0) & ~ (v21 = 0))))) & ? [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v21 = 0 | ~ (relation_dom(v18) = v19) | ~ (in(v20, v19) = v21) | ? [v22] : ? [v23] : ((apply(v18, v20) = v22 & ( ~ (v22 = v17) | v17 = empty_set) & ( ~ (v17 = empty_set) | v22 = empty_set)) | (relation(v18) = v22 & function(v18) = v23 & ( ~ (v23 = 0) | ~ (v22 = 0))))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v20 = v19 | ~ (relation_composition(v17, v18) = v19) | ~ (relation(v20) = 0) | ~ (relation(v17) = 0) | ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : ? [v27] : ? [v28] : ? [v29] : (( ~ (v21 = 0) & relation(v18) = v21) | (ordered_pair(v21, v22) = v23 & in(v23, v20) = v24 & ( ~ (v24 = 0) | ( ! [v30] : ! [v31] : ( ~ (ordered_pair(v30, v22) = v31) | ? [v32] : ? [v33] : ? [v34] : (ordered_pair(v21, v30) = v32 & in(v32, v17) = v33 & in(v31, v18) = v34 & ( ~ (v34 = 0) | ~ (v33 = 0)))) & ! [v30] : ! [v31] : ( ~ (ordered_pair(v21, v30) = v31) | ? [v32] : ? [v33] : ? [v34] : (ordered_pair(v30, v22) = v33 & in(v33, v18) = v34 & in(v31, v17) = v32 & ( ~ (v34 = 0) | ~ (v32 = 0)))))) & (v24 = 0 | (v29 = 0 & v27 = 0 & ordered_pair(v25, v22) = v28 & ordered_pair(v21, v25) = v26 & in(v28, v18) = 0 & in(v26, v17) = 0))))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v20 = v19 | ~ (relation_rng_restriction(v17, v18) = v19) | ~ (relation(v20) = 0) | ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : (( ~ (v21 = 0) & relation(v18) = v21) | (ordered_pair(v21, v22) = v23 & in(v23, v20) = v24 & in(v23, v18) = v26 & in(v22, v17) = v25 & ( ~ (v26 = 0) | ~ (v25 = 0) | ~ (v24 = 0)) & (v24 = 0 | (v26 = 0 & v25 = 0))))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v20 = v19 | ~ (relation_dom_restriction(v17, v18) = v20) | ~ (relation(v19) = 0) | ~ (relation(v17) = 0) | ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : (ordered_pair(v21, v22) = v23 & in(v23, v19) = v24 & in(v23, v17) = v26 & in(v21, v18) = v25 & ( ~ (v26 = 0) | ~ (v25 = 0) | ~ (v24 = 0)) & (v24 = 0 | (v26 = 0 & v25 = 0)))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v20 = v18 | v20 = v17 | ~ (unordered_pair(v17, v18) = v19) | ~ (in(v20, v19) = 0)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v20 = v18 | ~ (singleton(v17) = v19) | ~ (set_union2(v19, v18) = v20) | ? [v21] : ( ~ (v21 = 0) & in(v17, v18) = v21)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v20 = v17 | ~ (set_difference(v17, v19) = v20) | ~ (singleton(v18) = v19) | in(v18, v17) = 0) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v20 = empty_set | ~ (relation_dom(v17) = v18) | ~ (apply(v17, v19) = v20) | ? [v21] : ? [v22] : ((v21 = 0 & in(v19, v18) = 0) | (relation(v17) = v21 & function(v17) = v22 & ( ~ (v22 = 0) | ~ (v21 = 0))))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v20 = 0 | v17 = empty_set | ~ (set_meet(v17) = v18) | ~ (in(v19, v18) = v20) | ? [v21] : ? [v22] : ( ~ (v22 = 0) & in(v21, v17) = 0 & in(v19, v21) = v22)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v20 = 0 | ~ (disjoint(v19, v18) = v20) | ~ (singleton(v17) = v19) | in(v17, v18) = 0) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v20 = 0 | ~ (disjoint(v18, v19) = 0) | ~ (disjoint(v17, v19) = v20) | ? [v21] : ( ~ (v21 = 0) & subset(v17, v18) = v21)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v20 = 0 | ~ (disjoint(v17, v19) = v20) | ~ (subset(v17, v18) = 0) | ? [v21] : ( ~ (v21 = 0) & disjoint(v18, v19) = v21)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v20 = 0 | ~ (union(v18) = v19) | ~ (subset(v17, v19) = v20) | ? [v21] : ( ~ (v21 = 0) & in(v17, v18) = v21)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v20 = 0 | ~ (element(v17, v19) = v20) | ~ (powerset(v18) = v19) | ? [v21] : ? [v22] : ( ~ (v22 = 0) & in(v21, v18) = v22 & in(v21, v17) = 0)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v20 = 0 | ~ (element(v17, v19) = v20) | ~ (powerset(v18) = v19) | ? [v21] : ( ~ (v21 = 0) & subset(v17, v18) = v21)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v20 = 0 | ~ (element(v17, v19) = v20) | ~ (in(v17, v18) = 0) | ? [v21] : ? [v22] : ( ~ (v22 = 0) & element(v18, v21) = v22 & powerset(v19) = v21)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v20 = 0 | ~ (powerset(v17) = v18) | ~ (subset(v19, v17) = v20) | ? [v21] : ( ~ (v21 = 0) & in(v19, v18) = v21)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v20 = 0 | ~ (powerset(v17) = v18) | ~ (in(v19, v18) = v20) | ? [v21] : ( ~ (v21 = 0) & subset(v19, v17) = v21)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v20 = 0 | ~ (singleton(v17) = v19) | ~ (subset(v19, v18) = v20) | ? [v21] : ( ~ (v21 = 0) & in(v17, v18) = v21)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v20 = 0 | ~ (subset(v18, v19) = 0) | ~ (subset(v17, v19) = v20) | ? [v21] : ( ~ (v21 = 0) & subset(v17, v18) = v21)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v20 = 0 | ~ (subset(v17, v19) = v20) | ~ (subset(v17, v18) = 0) | ? [v21] : ( ~ (v21 = 0) & subset(v18, v19) = v21)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v20 = 0 | ~ (subset(v17, v18) = 0) | ~ (in(v19, v18) = v20) | ? [v21] : ( ~ (v21 = 0) & in(v19, v17) = v21)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v20 = 0 | ~ (unordered_pair(v17, v18) = v19) | ~ (in(v18, v19) = v20)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v20 = 0 | ~ (unordered_pair(v17, v18) = v19) | ~ (in(v17, v19) = v20)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v19 = v18 | ~ (singleton(v17) = v20) | ~ (unordered_pair(v18, v19) = v20)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (are_equipotent(v20, v19) = v18) | ~ (are_equipotent(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (meet_of_subsets(v20, v19) = v18) | ~ (meet_of_subsets(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (union_of_subsets(v20, v19) = v18) | ~ (union_of_subsets(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (complements_of_subsets(v20, v19) = v18) | ~ (complements_of_subsets(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (relation_composition(v20, v19) = v18) | ~ (relation_composition(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (disjoint(v20, v19) = v18) | ~ (disjoint(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (subset_complement(v20, v19) = v18) | ~ (subset_complement(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (set_difference(v20, v19) = v18) | ~ (set_difference(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (apply(v20, v19) = v18) | ~ (apply(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (cartesian_product2(v20, v19) = v18) | ~ (cartesian_product2(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (element(v20, v19) = v18) | ~ (element(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (singleton(v18) = v20) | ~ (singleton(v17) = v19) | ~ (subset(v19, v20) = 0)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (singleton(v17) = v20) | ~ (unordered_pair(v18, v19) = v20)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (relation_inverse_image(v20, v19) = v18) | ~ (relation_inverse_image(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (relation_image(v20, v19) = v18) | ~ (relation_image(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (relation_rng_restriction(v20, v19) = v18) | ~ (relation_rng_restriction(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (relation_dom_restriction(v20, v19) = v18) | ~ (relation_dom_restriction(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (subset(v20, v19) = v18) | ~ (subset(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (ordered_pair(v20, v19) = v18) | ~ (ordered_pair(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (set_intersection2(v20, v19) = v18) | ~ (set_intersection2(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (set_union2(v20, v19) = v18) | ~ (set_union2(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (unordered_pair(v20, v19) = v18) | ~ (unordered_pair(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (proper_subset(v20, v19) = v18) | ~ (proper_subset(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (in(v20, v19) = v18) | ~ (in(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = empty_set | ~ (element(v18, v20) = 0) | ~ (powerset(v19) = v20) | ~ (powerset(v17) = v19) | ? [v21] : ? [v22] : ? [v23] : ? [v24] : (subset_difference(v17, v23, v24) = v22 & meet_of_subsets(v17, v18) = v24 & union_of_subsets(v17, v21) = v22 & complements_of_subsets(v17, v18) = v21 & cast_to_subset(v17) = v23)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = empty_set | ~ (element(v18, v20) = 0) | ~ (powerset(v19) = v20) | ~ (powerset(v17) = v19) | ? [v21] : ? [v22] : ? [v23] : ? [v24] : (subset_difference(v17, v21, v22) = v23 & meet_of_subsets(v17, v24) = v23 & union_of_subsets(v17, v18) = v22 & complements_of_subsets(v17, v18) = v24 & cast_to_subset(v17) = v21)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = empty_set | ~ (element(v18, v20) = 0) | ~ (powerset(v19) = v20) | ~ (powerset(v17) = v19) | ? [v21] : ( ~ (v21 = empty_set) & complements_of_subsets(v17, v18) = v21)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v17 = empty_set | ~ (set_meet(v17) = v18) | ~ (in(v20, v17) = 0) | ~ (in(v19, v18) = 0) | in(v19, v20) = 0) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (subset_difference(v17, v18, v19) = v20) | ? [v21] : ? [v22] : ? [v23] : ? [v24] : (set_difference(v18, v19) = v24 & element(v19, v21) = v23 & element(v18, v21) = v22 & powerset(v17) = v21 & ( ~ (v23 = 0) | ~ (v22 = 0) | v24 = v20))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (subset_difference(v17, v18, v19) = v20) | ? [v21] : ? [v22] : ? [v23] : ? [v24] : (element(v20, v21) = v24 & element(v19, v21) = v23 & element(v18, v21) = v22 & powerset(v17) = v21 & ( ~ (v23 = 0) | ~ (v22 = 0) | v24 = 0))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_composition(v19, v18) = v20) | ~ (identity_relation(v17) = v19) | ? [v21] : ? [v22] : (relation_dom_restriction(v18, v17) = v22 & relation(v18) = v21 & ( ~ (v21 = 0) | v22 = v20))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_composition(v17, v19) = v20) | ~ (relation_rng(v17) = v18) | ? [v21] : ? [v22] : ? [v23] : (( ~ (v21 = 0) & relation(v17) = v21) | (relation_rng(v20) = v22 & relation_image(v19, v18) = v23 & relation(v19) = v21 & ( ~ (v21 = 0) | v23 = v22)))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_composition(v17, v19) = v20) | ~ (relation_dom(v17) = v18) | ? [v21] : ? [v22] : ? [v23] : (( ~ (v21 = 0) & relation(v17) = v21) | (relation_dom(v20) = v22 & subset(v22, v18) = v23 & relation(v19) = v21 & ( ~ (v21 = 0) | v23 = 0)))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (subset_complement(v17, v19) = v20) | ~ (in(v18, v20) = 0) | ? [v21] : ? [v22] : ? [v23] : (element(v19, v21) = v22 & powerset(v17) = v21 & in(v18, v19) = v23 & ( ~ (v23 = 0) | ~ (v22 = 0)))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_rng(v18) = v19) | ~ (set_intersection2(v19, v17) = v20) | ? [v21] : ? [v22] : ? [v23] : (relation_rng(v22) = v23 & relation_rng_restriction(v17, v18) = v22 & relation(v18) = v21 & ( ~ (v21 = 0) | v23 = v20))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_rng(v17) = v18) | ~ (relation_image(v19, v18) = v20) | ? [v21] : ? [v22] : ? [v23] : (( ~ (v21 = 0) & relation(v17) = v21) | (relation_composition(v17, v19) = v22 & relation_rng(v22) = v23 & relation(v19) = v21 & ( ~ (v21 = 0) | v23 = v20)))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (set_difference(v17, v18) = v19) | ~ (in(v20, v19) = 0) | ? [v21] : ( ~ (v21 = 0) & in(v20, v18) = v21 & in(v20, v17) = 0)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (set_difference(v17, v18) = v19) | ~ (in(v20, v17) = 0) | ? [v21] : ? [v22] : (in(v20, v19) = v22 & in(v20, v18) = v21 & (v22 = 0 | v21 = 0))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_dom(v18) = v19) | ~ (set_intersection2(v19, v17) = v20) | ? [v21] : ? [v22] : ? [v23] : (relation_dom(v22) = v23 & relation_dom_restriction(v18, v17) = v22 & relation(v18) = v21 & ( ~ (v21 = 0) | v23 = v20))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_dom(v18) = v19) | ~ (set_intersection2(v19, v17) = v20) | ? [v21] : ? [v22] : ? [v23] : (relation_image(v18, v20) = v23 & relation_image(v18, v17) = v22 & relation(v18) = v21 & ( ~ (v21 = 0) | v23 = v22))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (cartesian_product2(v17, v18) = v19) | ~ (in(v20, v19) = 0) | ? [v21] : ? [v22] : (ordered_pair(v21, v22) = v20 & in(v22, v18) = 0 & in(v21, v17) = 0)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (element(v20, v19) = 0) | ~ (element(v18, v19) = 0) | ~ (powerset(v17) = v19) | ? [v21] : ? [v22] : ? [v23] : (disjoint(v18, v20) = v21 & subset_complement(v17, v20) = v22 & subset(v18, v22) = v23 & ( ~ (v23 = 0) | v21 = 0) & ( ~ (v21 = 0) | v23 = 0))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (element(v18, v20) = 0) | ~ (powerset(v19) = v20) | ~ (powerset(v17) = v19) | ? [v21] : (meet_of_subsets(v17, v18) = v21 & element(v21, v19) = 0)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (element(v18, v20) = 0) | ~ (powerset(v19) = v20) | ~ (powerset(v17) = v19) | ? [v21] : (meet_of_subsets(v17, v18) = v21 & set_meet(v18) = v21)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (element(v18, v20) = 0) | ~ (powerset(v19) = v20) | ~ (powerset(v17) = v19) | ? [v21] : (union_of_subsets(v17, v18) = v21 & union(v18) = v21)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (element(v18, v20) = 0) | ~ (powerset(v19) = v20) | ~ (powerset(v17) = v19) | ? [v21] : (union_of_subsets(v17, v18) = v21 & element(v21, v19) = 0)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (element(v18, v20) = 0) | ~ (powerset(v19) = v20) | ~ (powerset(v17) = v19) | ? [v21] : (complements_of_subsets(v17, v21) = v18 & complements_of_subsets(v17, v18) = v21)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (element(v18, v20) = 0) | ~ (powerset(v19) = v20) | ~ (powerset(v17) = v19) | ? [v21] : (complements_of_subsets(v17, v18) = v21 & element(v21, v20) = 0)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (element(v18, v20) = 0) | ~ (powerset(v19) = v20) | ~ (powerset(v17) = v19) | ? [v21] : (complements_of_subsets(v17, v18) = v21 & ! [v22] : ! [v23] : ( ~ (subset_complement(v17, v22) = v23) | ~ (element(v21, v20) = 0) | ? [v24] : ? [v25] : ? [v26] : (element(v22, v19) = v24 & in(v23, v18) = v26 & in(v22, v21) = v25 & ( ~ (v24 = 0) | (( ~ (v26 = 0) | v25 = 0) & ( ~ (v25 = 0) | v26 = 0))))) & ! [v22] : ! [v23] : ( ~ (element(v21, v20) = 0) | ~ (in(v22, v21) = v23) | ? [v24] : ? [v25] : ? [v26] : (subset_complement(v17, v22) = v25 & element(v22, v19) = v24 & in(v25, v18) = v26 & ( ~ (v24 = 0) | (( ~ (v26 = 0) | v23 = 0) & ( ~ (v23 = 0) | v26 = 0))))) & ! [v22] : (v22 = v21 | ~ (element(v22, v20) = 0) | ? [v23] : ? [v24] : ? [v25] : ? [v26] : (subset_complement(v17, v23) = v25 & element(v23, v19) = 0 & in(v25, v18) = v26 & in(v23, v22) = v24 & ( ~ (v26 = 0) | ~ (v24 = 0)) & (v26 = 0 | v24 = 0))) & ! [v22] : ( ~ (element(v22, v19) = 0) | ~ (element(v21, v20) = 0) | ? [v23] : ? [v24] : ? [v25] : (subset_complement(v17, v22) = v24 & in(v24, v18) = v25 & in(v22, v21) = v23 & ( ~ (v25 = 0) | v23 = 0) & ( ~ (v23 = 0) | v25 = 0))))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (element(v18, v20) = 0) | ~ (powerset(v19) = v20) | ~ (in(v17, v18) = 0) | element(v17, v19) = 0) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (element(v18, v20) = 0) | ~ (powerset(v19) = v20) | ~ (in(v17, v18) = 0) | ? [v21] : ( ~ (v21 = 0) & empty(v19) = v21)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (element(v18, v19) = 0) | ~ (powerset(v17) = v19) | ~ (in(v20, v18) = 0) | in(v20, v17) = 0) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_inverse_image(v17, v18) = v19) | ~ (relation(v17) = 0) | ~ (in(v20, v19) = 0) | ? [v21] : ? [v22] : (ordered_pair(v20, v21) = v22 & in(v22, v17) = 0 & in(v21, v18) = 0)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_image(v17, v18) = v19) | ~ (relation(v17) = 0) | ~ (in(v20, v19) = 0) | ? [v21] : ? [v22] : (ordered_pair(v21, v20) = v22 & in(v22, v17) = 0 & in(v21, v18) = 0)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (subset(v20, v19) = 0) | ~ (unordered_pair(v17, v18) = v20) | (in(v18, v19) = 0 & in(v17, v19) = 0)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (identity_relation(v17) = v18) | ~ (ordered_pair(v19, v19) = v20) | ~ (relation(v18) = 0) | ? [v21] : ? [v22] : (in(v20, v18) = v22 & in(v19, v17) = v21 & ( ~ (v21 = 0) | v22 = 0))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (ordered_pair(v18, v19) = v20) | ~ (relation(v17) = 0) | ? [v21] : ? [v22] : (in(v20, v17) = v22 & in(v20, v17) = v21 & ( ~ (v21 = 0) | v22 = 0))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (ordered_pair(v17, v18) = v20) | ~ (in(v20, v19) = 0) | ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : (relation_rng(v19) = v24 & relation_dom(v19) = v22 & relation(v19) = v21 & in(v18, v24) = v25 & in(v17, v22) = v23 & ( ~ (v21 = 0) | (v25 = 0 & v23 = 0)))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (ordered_pair(v17, v18) = v20) | ~ (in(v20, v19) = 0) | ? [v21] : ? [v22] : ? [v23] : ? [v24] : (relation_field(v19) = v22 & relation(v19) = v21 & in(v18, v22) = v24 & in(v17, v22) = v23 & ( ~ (v21 = 0) | (v24 = 0 & v23 = 0)))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (set_intersection2(v17, v18) = v19) | ~ (in(v20, v19) = 0) | ? [v21] : ( ~ (v21 = 0) & disjoint(v17, v18) = v21)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (set_intersection2(v17, v18) = v19) | ~ (in(v20, v19) = 0) | (in(v20, v18) = 0 & in(v20, v17) = 0)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (set_intersection2(v17, v18) = v19) | ~ (in(v20, v18) = 0) | ? [v21] : ? [v22] : (in(v20, v19) = v22 & in(v20, v17) = v21 & ( ~ (v21 = 0) | v22 = 0))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (set_intersection2(v17, v18) = v19) | ~ (in(v20, v17) = 0) | ? [v21] : ? [v22] : (in(v20, v19) = v22 & in(v20, v18) = v21 & ( ~ (v21 = 0) | v22 = 0))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (set_union2(v17, v18) = v19) | ~ (in(v20, v19) = 0) | ? [v21] : ? [v22] : (in(v20, v18) = v22 & in(v20, v17) = v21 & (v22 = 0 | v21 = 0))) & ? [v17] : ! [v18] : ! [v19] : ! [v20] : (v20 = v17 | ~ (set_difference(v18, v19) = v20) | ? [v21] : ? [v22] : ? [v23] : ? [v24] : (in(v21, v19) = v24 & in(v21, v18) = v23 & in(v21, v17) = v22 & ( ~ (v23 = 0) | ~ (v22 = 0) | v24 = 0) & (v22 = 0 | (v23 = 0 & ~ (v24 = 0))))) & ? [v17] : ! [v18] : ! [v19] : ! [v20] : (v20 = v17 | ~ (cartesian_product2(v18, v19) = v20) | ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : ? [v27] : (in(v21, v17) = v22 & ( ~ (v22 = 0) | ! [v28] : ! [v29] : ( ~ (ordered_pair(v28, v29) = v21) | ? [v30] : ? [v31] : (in(v29, v19) = v31 & in(v28, v18) = v30 & ( ~ (v31 = 0) | ~ (v30 = 0))))) & (v22 = 0 | (v27 = v21 & v26 = 0 & v25 = 0 & ordered_pair(v23, v24) = v21 & in(v24, v19) = 0 & in(v23, v18) = 0)))) & ? [v17] : ! [v18] : ! [v19] : ! [v20] : (v20 = v17 | ~ (relation_inverse_image(v18, v19) = v20) | ~ (relation(v18) = 0) | ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : (in(v21, v17) = v22 & ( ~ (v22 = 0) | ( ! [v27] : ! [v28] : ( ~ (ordered_pair(v21, v27) = v28) | ? [v29] : ? [v30] : (in(v28, v18) = v29 & in(v27, v19) = v30 & ( ~ (v30 = 0) | ~ (v29 = 0)))) & ! [v27] : ( ~ (in(v27, v19) = 0) | ? [v28] : ? [v29] : ( ~ (v29 = 0) & ordered_pair(v21, v27) = v28 & in(v28, v18) = v29)))) & (v22 = 0 | (v26 = 0 & v25 = 0 & ordered_pair(v21, v23) = v24 & in(v24, v18) = 0 & in(v23, v19) = 0)))) & ? [v17] : ! [v18] : ! [v19] : ! [v20] : (v20 = v17 | ~ (relation_image(v18, v19) = v20) | ~ (relation(v18) = 0) | ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : (in(v21, v17) = v22 & ( ~ (v22 = 0) | ( ! [v27] : ! [v28] : ( ~ (ordered_pair(v27, v21) = v28) | ? [v29] : ? [v30] : (in(v28, v18) = v29 & in(v27, v19) = v30 & ( ~ (v30 = 0) | ~ (v29 = 0)))) & ! [v27] : ( ~ (in(v27, v19) = 0) | ? [v28] : ? [v29] : ( ~ (v29 = 0) & ordered_pair(v27, v21) = v28 & in(v28, v18) = v29)))) & (v22 = 0 | (v26 = 0 & v25 = 0 & ordered_pair(v23, v21) = v24 & in(v24, v18) = 0 & in(v23, v19) = 0)))) & ? [v17] : ! [v18] : ! [v19] : ! [v20] : (v20 = v17 | ~ (set_intersection2(v18, v19) = v20) | ? [v21] : ? [v22] : ? [v23] : ? [v24] : (in(v21, v19) = v24 & in(v21, v18) = v23 & in(v21, v17) = v22 & ( ~ (v24 = 0) | ~ (v23 = 0) | ~ (v22 = 0)) & (v22 = 0 | (v24 = 0 & v23 = 0)))) & ? [v17] : ! [v18] : ! [v19] : ! [v20] : (v20 = v17 | ~ (set_union2(v18, v19) = v20) | ? [v21] : ? [v22] : ? [v23] : ? [v24] : (in(v21, v19) = v24 & in(v21, v18) = v23 & in(v21, v17) = v22 & ( ~ (v22 = 0) | ( ~ (v24 = 0) & ~ (v23 = 0))) & (v24 = 0 | v23 = 0 | v22 = 0))) & ? [v17] : ! [v18] : ! [v19] : ! [v20] : (v20 = v17 | ~ (unordered_pair(v18, v19) = v20) | ? [v21] : ? [v22] : (in(v21, v17) = v22 & ( ~ (v22 = 0) | ( ~ (v21 = v19) & ~ (v21 = v18))) & (v22 = 0 | v21 = v19 | v21 = v18))) & ! [v17] : ! [v18] : ! [v19] : (v19 = v18 | ~ (relation_inverse(v17) = v18) | ~ (relation(v19) = 0) | ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : (( ~ (v20 = 0) & relation(v17) = v20) | (ordered_pair(v21, v20) = v24 & ordered_pair(v20, v21) = v22 & in(v24, v17) = v25 & in(v22, v19) = v23 & ( ~ (v25 = 0) | ~ (v23 = 0)) & (v25 = 0 | v23 = 0)))) & ! [v17] : ! [v18] : ! [v19] : (v19 = v18 | ~ (identity_relation(v17) = v19) | ~ (relation(v18) = 0) | ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : (ordered_pair(v20, v21) = v22 & in(v22, v18) = v23 & in(v20, v17) = v24 & ( ~ (v24 = 0) | ~ (v23 = 0) | ~ (v21 = v20)) & (v23 = 0 | (v24 = 0 & v21 = v20)))) & ! [v17] : ! [v18] : ! [v19] : (v19 = v18 | ~ (set_union2(v17, v18) = v19) | ? [v20] : ( ~ (v20 = 0) & subset(v17, v18) = v20)) & ! [v17] : ! [v18] : ! [v19] : (v19 = v17 | v17 = empty_set | ~ (singleton(v18) = v19) | ~ (subset(v17, v19) = 0)) & ! [v17] : ! [v18] : ! [v19] : (v19 = v17 | ~ (set_difference(v17, v18) = v19) | ? [v20] : ( ~ (v20 = 0) & disjoint(v17, v18) = v20)) & ! [v17] : ! [v18] : ! [v19] : (v19 = v17 | ~ (singleton(v17) = v18) | ~ (in(v19, v18) = 0)) & ! [v17] : ! [v18] : ! [v19] : (v19 = v17 | ~ (set_intersection2(v17, v18) = v19) | ? [v20] : ( ~ (v20 = 0) & subset(v17, v18) = v20)) & ! [v17] : ! [v18] : ! [v19] : (v19 = empty_set | ~ (set_difference(v17, v18) = v19) | ? [v20] : ( ~ (v20 = 0) & subset(v17, v18) = v20)) & ! [v17] : ! [v18] : ! [v19] : (v19 = empty_set | ~ (set_intersection2(v17, v18) = v19) | ? [v20] : ( ~ (v20 = 0) & disjoint(v17, v18) = v20)) & ! [v17] : ! [v18] : ! [v19] : (v19 = 0 | v18 = v17 | ~ (proper_subset(v17, v18) = v19) | ? [v20] : ( ~ (v20 = 0) & subset(v17, v18) = v20)) & ! [v17] : ! [v18] : ! [v19] : (v19 = 0 | ~ (disjoint(v18, v17) = v19) | ? [v20] : ( ~ (v20 = 0) & disjoint(v17, v18) = v20)) & ! [v17] : ! [v18] : ! [v19] : (v19 = 0 | ~ (disjoint(v17, v18) = v19) | ? [v20] : ? [v21] : (set_intersection2(v17, v18) = v20 & in(v21, v20) = 0)) & ! [v17] : ! [v18] : ! [v19] : (v19 = 0 | ~ (disjoint(v17, v18) = v19) | ? [v20] : ( ~ (v20 = v17) & set_difference(v17, v18) = v20)) & ! [v17] : ! [v18] : ! [v19] : (v19 = 0 | ~ (disjoint(v17, v18) = v19) | ? [v20] : ( ~ (v20 = empty_set) & set_intersection2(v17, v18) = v20)) & ! [v17] : ! [v18] : ! [v19] : (v19 = 0 | ~ (disjoint(v17, v18) = v19) | ? [v20] : (in(v20, v18) = 0 & in(v20, v17) = 0)) & ! [v17] : ! [v18] : ! [v19] : (v19 = 0 | ~ (element(v17, v18) = v19) | ? [v20] : ( ~ (v20 = 0) & in(v17, v18) = v20)) & ! [v17] : ! [v18] : ! [v19] : (v19 = 0 | ~ (singleton(v18) = v17) | ~ (subset(v17, v17) = v19)) & ! [v17] : ! [v18] : ! [v19] : (v19 = 0 | ~ (singleton(v17) = v18) | ~ (subset(empty_set, v18) = v19)) & ! [v17] : ! [v18] : ! [v19] : (v19 = 0 | ~ (singleton(v17) = v18) | ~ (in(v17, v18) = v19)) & ! [v17] : ! [v18] : ! [v19] : (v19 = 0 | ~ (subset(v17, v18) = v19) | ~ (relation(v17) = 0) | ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ((v23 = 0 & ~ (v24 = 0) & ordered_pair(v20, v21) = v22 & in(v22, v18) = v24 & in(v22, v17) = 0) | ( ~ (v20 = 0) & relation(v18) = v20))) & ! [v17] : ! [v18] : ! [v19] : (v19 = 0 | ~ (subset(v17, v18) = v19) | ? [v20] : ? [v21] : ( ~ (v21 = 0) & element(v17, v20) = v21 & powerset(v18) = v20)) & ! [v17] : ! [v18] : ! [v19] : (v19 = 0 | ~ (subset(v17, v18) = v19) | ? [v20] : ? [v21] : ( ~ (v21 = 0) & in(v20, v18) = v21 & in(v20, v17) = 0)) & ! [v17] : ! [v18] : ! [v19] : (v19 = 0 | ~ (subset(v17, v18) = v19) | ? [v20] : ( ~ (v20 = empty_set) & set_difference(v17, v18) = v20)) & ! [v17] : ! [v18] : ! [v19] : (v19 = 0 | ~ (subset(v17, v18) = v19) | ? [v20] : ( ~ (v20 = 0) & proper_subset(v17, v18) = v20)) & ! [v17] : ! [v18] : ! [v19] : (v19 = 0 | ~ (in(v18, v17) = v19) | ? [v20] : (set_difference(v17, v20) = v17 & singleton(v18) = v20)) & ! [v17] : ! [v18] : ! [v19] : (v19 = 0 | ~ (in(v17, v18) = v19) | ? [v20] : ? [v21] : ( ~ (v21 = 0) & singleton(v17) = v20 & subset(v20, v18) = v21)) & ! [v17] : ! [v18] : ! [v19] : (v19 = 0 | ~ (in(v17, v18) = v19) | ? [v20] : ? [v21] : (element(v17, v18) = v20 & empty(v18) = v21 & ( ~ (v20 = 0) | v21 = 0))) & ! [v17] : ! [v18] : ! [v19] : (v19 = 0 | ~ (in(v17, v18) = v19) | ? [v20] : (disjoint(v20, v18) = 0 & singleton(v17) = v20)) & ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (relation_empty_yielding(v19) = v18) | ~ (relation_empty_yielding(v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (relation_inverse(v19) = v18) | ~ (relation_inverse(v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (relation_field(v19) = v18) | ~ (relation_field(v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (relation_rng(v19) = v18) | ~ (relation_rng(v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (union(v19) = v18) | ~ (union(v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (cast_to_subset(v19) = v18) | ~ (cast_to_subset(v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (relation_dom(v19) = v18) | ~ (relation_dom(v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (powerset(v19) = v18) | ~ (powerset(v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (singleton(v19) = v18) | ~ (singleton(v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (set_meet(v19) = v18) | ~ (set_meet(v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (identity_relation(v19) = v18) | ~ (identity_relation(v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (relation(v19) = v18) | ~ (relation(v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (empty(v19) = v18) | ~ (empty(v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (function(v19) = v18) | ~ (function(v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : (v18 = empty_set | ~ (meet_of_subsets(v17, v18) = v19) | ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : (subset_difference(v17, v25, v19) = v26 & union_of_subsets(v17, v23) = v24 & complements_of_subsets(v17, v18) = v23 & cast_to_subset(v17) = v25 & element(v18, v21) = v22 & powerset(v20) = v21 & powerset(v17) = v20 & ( ~ (v22 = 0) | v26 = v24))) & ! [v17] : ! [v18] : ! [v19] : (v18 = empty_set | ~ (union_of_subsets(v17, v18) = v19) | ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : (subset_difference(v17, v23, v19) = v24 & meet_of_subsets(v17, v25) = v26 & complements_of_subsets(v17, v18) = v25 & cast_to_subset(v17) = v23 & element(v18, v21) = v22 & powerset(v20) = v21 & powerset(v17) = v20 & ( ~ (v22 = 0) | v26 = v24))) & ! [v17] : ! [v18] : ! [v19] : (v18 = empty_set | ~ (complements_of_subsets(v17, v18) = v19) | ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : (subset_difference(v17, v24, v25) = v26 & meet_of_subsets(v17, v18) = v25 & union_of_subsets(v17, v19) = v23 & cast_to_subset(v17) = v24 & element(v18, v21) = v22 & powerset(v20) = v21 & powerset(v17) = v20 & ( ~ (v22 = 0) | v26 = v23))) & ! [v17] : ! [v18] : ! [v19] : (v18 = empty_set | ~ (complements_of_subsets(v17, v18) = v19) | ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : (subset_difference(v17, v23, v24) = v25 & meet_of_subsets(v17, v19) = v26 & union_of_subsets(v17, v18) = v24 & cast_to_subset(v17) = v23 & element(v18, v21) = v22 & powerset(v20) = v21 & powerset(v17) = v20 & ( ~ (v22 = 0) | v26 = v25))) & ! [v17] : ! [v18] : ! [v19] : (v17 = empty_set | ~ (relation_rng(v18) = v19) | ~ (subset(v17, v19) = 0) | ? [v20] : ? [v21] : (relation_inverse_image(v18, v17) = v21 & relation(v18) = v20 & ( ~ (v21 = empty_set) | ~ (v20 = 0)))) & ! [v17] : ! [v18] : ! [v19] : (v17 = empty_set | ~ (element(v19, v18) = 0) | ~ (powerset(v17) = v18) | ? [v20] : (subset_complement(v17, v19) = v20 & ! [v21] : ! [v22] : (v22 = 0 | ~ (in(v21, v20) = v22) | ? [v23] : ? [v24] : (element(v21, v17) = v23 & in(v21, v19) = v24 & ( ~ (v23 = 0) | v24 = 0))) & ! [v21] : ! [v22] : (v22 = 0 | ~ (in(v21, v19) = v22) | ? [v23] : ? [v24] : (element(v21, v17) = v23 & in(v21, v20) = v24 & ( ~ (v23 = 0) | v24 = 0))) & ! [v21] : ( ~ (element(v21, v17) = 0) | ? [v22] : ? [v23] : (in(v21, v20) = v23 & in(v21, v19) = v22 & (v23 = 0 | v22 = 0))))) & ! [v17] : ! [v18] : ! [v19] : ( ~ (meet_of_subsets(v17, v18) = v19) | ? [v20] : ? [v21] : ? [v22] : ? [v23] : (element(v19, v20) = v23 & element(v18, v21) = v22 & powerset(v20) = v21 & powerset(v17) = v20 & ( ~ (v22 = 0) | v23 = 0))) & ! [v17] : ! [v18] : ! [v19] : ( ~ (meet_of_subsets(v17, v18) = v19) | ? [v20] : ? [v21] : ? [v22] : ? [v23] : (element(v18, v21) = v22 & powerset(v20) = v21 & powerset(v17) = v20 & set_meet(v18) = v23 & ( ~ (v22 = 0) | v23 = v19))) & ! [v17] : ! [v18] : ! [v19] : ( ~ (union_of_subsets(v17, v18) = v19) | ? [v20] : ? [v21] : ? [v22] : ? [v23] : (union(v18) = v23 & element(v18, v21) = v22 & powerset(v20) = v21 & powerset(v17) = v20 & ( ~ (v22 = 0) | v23 = v19))) & ! [v17] : ! [v18] : ! [v19] : ( ~ (union_of_subsets(v17, v18) = v19) | ? [v20] : ? [v21] : ? [v22] : ? [v23] : (element(v19, v20) = v23 & element(v18, v21) = v22 & powerset(v20) = v21 & powerset(v17) = v20 & ( ~ (v22 = 0) | v23 = 0))) & ! [v17] : ! [v18] : ! [v19] : ( ~ (complements_of_subsets(v17, v18) = v19) | ? [v20] : ? [v21] : ? [v22] : ? [v23] : (complements_of_subsets(v17, v19) = v23 & element(v18, v21) = v22 & powerset(v20) = v21 & powerset(v17) = v20 & ( ~ (v22 = 0) | v23 = v18))) & ! [v17] : ! [v18] : ! [v19] : ( ~ (complements_of_subsets(v17, v18) = v19) | ? [v20] : ? [v21] : ? [v22] : ? [v23] : (element(v19, v21) = v23 & element(v18, v21) = v22 & powerset(v20) = v21 & powerset(v17) = v20 & ( ~ (v22 = 0) | v23 = 0))) & ! [v17] : ! [v18] : ! [v19] : ( ~ (complements_of_subsets(v17, v18) = v19) | ? [v20] : ? [v21] : ? [v22] : (element(v18, v21) = v22 & powerset(v20) = v21 & powerset(v17) = v20 & ( ~ (v22 = 0) | ( ! [v23] : ! [v24] : ( ~ (subset_complement(v17, v23) = v24) | ~ (element(v19, v21) = 0) | ? [v25] : ? [v26] : ? [v27] : (element(v23, v20) = v25 & in(v24, v18) = v27 & in(v23, v19) = v26 & ( ~ (v25 = 0) | (( ~ (v27 = 0) | v26 = 0) & ( ~ (v26 = 0) | v27 = 0))))) & ! [v23] : ! [v24] : ( ~ (element(v19, v21) = 0) | ~ (in(v23, v19) = v24) | ? [v25] : ? [v26] : ? [v27] : (subset_complement(v17, v23) = v26 & element(v23, v20) = v25 & in(v26, v18) = v27 & ( ~ (v25 = 0) | (( ~ (v27 = 0) | v24 = 0) & ( ~ (v24 = 0) | v27 = 0))))) & ! [v23] : (v23 = v19 | ~ (element(v23, v21) = 0) | ? [v24] : ? [v25] : ? [v26] : ? [v27] : (subset_complement(v17, v24) = v26 & element(v24, v20) = 0 & in(v26, v18) = v27 & in(v24, v23) = v25 & ( ~ (v27 = 0) | ~ (v25 = 0)) & (v27 = 0 | v25 = 0))) & ! [v23] : ( ~ (element(v23, v20) = 0) | ~ (element(v19, v21) = 0) | ? [v24] : ? [v25] : ? [v26] : (subset_complement(v17, v23) = v25 & in(v25, v18) = v26 & in(v23, v19) = v24 & ( ~ (v26 = 0) | v24 = 0) & ( ~ (v24 = 0) | v26 = 0))))))) & ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_composition(v18, v17) = v19) | ? [v20] : ? [v21] : ? [v22] : ? [v23] : (relation(v19) = v23 & relation(v18) = v21 & empty(v19) = v22 & empty(v17) = v20 & ( ~ (v21 = 0) | ~ (v20 = 0) | (v23 = 0 & v22 = 0)))) & ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_composition(v17, v18) = v19) | ~ (relation(v17) = 0) | ? [v20] : ? [v21] : ? [v22] : ? [v23] : (relation_rng(v19) = v21 & relation_rng(v18) = v22 & subset(v21, v22) = v23 & relation(v18) = v20 & ( ~ (v20 = 0) | v23 = 0))) & ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_composition(v17, v18) = v19) | ? [v20] : ? [v21] : ? [v22] : ? [v23] : (relation(v19) = v23 & relation(v18) = v21 & empty(v19) = v22 & empty(v17) = v20 & ( ~ (v21 = 0) | ~ (v20 = 0) | (v23 = 0 & v22 = 0)))) & ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_composition(v17, v18) = v19) | ? [v20] : ? [v21] : ? [v22] : (relation(v19) = v22 & relation(v18) = v21 & relation(v17) = v20 & ( ~ (v21 = 0) | ~ (v20 = 0) | v22 = 0))) & ! [v17] : ! [v18] : ! [v19] : ( ~ (disjoint(v19, v18) = 0) | ~ (singleton(v17) = v19) | ? [v20] : ( ~ (v20 = 0) & in(v17, v18) = v20)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (disjoint(v18, v19) = 0) | ~ (subset(v17, v18) = 0) | disjoint(v17, v19) = 0) & ! [v17] : ! [v18] : ! [v19] : ( ~ (disjoint(v17, v18) = 0) | ~ (in(v19, v18) = 0) | ? [v20] : ( ~ (v20 = 0) & in(v19, v17) = v20)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (disjoint(v17, v18) = 0) | ~ (in(v19, v17) = 0) | ? [v20] : ( ~ (v20 = 0) & in(v19, v18) = v20)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (subset_complement(v17, v18) = v19) | ? [v20] : ? [v21] : ? [v22] : (subset_complement(v17, v19) = v22 & element(v18, v20) = v21 & powerset(v17) = v20 & ( ~ (v21 = 0) | v22 = v18))) & ! [v17] : ! [v18] : ! [v19] : ( ~ (subset_complement(v17, v18) = v19) | ? [v20] : ? [v21] : ? [v22] : (set_difference(v17, v18) = v22 & element(v18, v20) = v21 & powerset(v17) = v20 & ( ~ (v21 = 0) | v22 = v19))) & ! [v17] : ! [v18] : ! [v19] : ( ~ (subset_complement(v17, v18) = v19) | ? [v20] : ? [v21] : ? [v22] : (element(v19, v20) = v22 & element(v18, v20) = v21 & powerset(v17) = v20 & ( ~ (v21 = 0) | v22 = 0))) & ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_rng(v18) = v19) | ~ (relation(v17) = 0) | ? [v20] : ? [v21] : ? [v22] : ? [v23] : (relation_composition(v17, v18) = v21 & relation_rng(v21) = v22 & subset(v22, v19) = v23 & relation(v18) = v20 & ( ~ (v20 = 0) | v23 = 0))) & ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_rng(v17) = v18) | ~ (relation(v19) = 0) | ? [v20] : ? [v21] : ? [v22] : ((v22 = v21 & relation_composition(v17, v19) = v20 & relation_rng(v20) = v21 & relation_image(v19, v18) = v21) | ( ~ (v20 = 0) & relation(v17) = v20))) & ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_rng(v17) = v18) | ~ (in(v19, v18) = 0) | ? [v20] : ? [v21] : ? [v22] : ((v22 = 0 & ordered_pair(v20, v19) = v21 & in(v21, v17) = 0) | ( ~ (v20 = 0) & relation(v17) = v20))) & ! [v17] : ! [v18] : ! [v19] : ( ~ (set_difference(v18, v17) = v19) | ? [v20] : ? [v21] : (subset(v17, v18) = v20 & set_union2(v17, v19) = v21 & ( ~ (v20 = 0) | v21 = v18))) & ! [v17] : ! [v18] : ! [v19] : ( ~ (set_difference(v18, v17) = v19) | ? [v20] : (set_union2(v17, v19) = v20 & set_union2(v17, v18) = v20)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (set_difference(v17, v19) = v17) | ~ (singleton(v18) = v19) | ? [v20] : ( ~ (v20 = 0) & in(v18, v17) = v20)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (set_difference(v17, v18) = v19) | subset(v19, v17) = 0) & ! [v17] : ! [v18] : ! [v19] : ( ~ (set_difference(v17, v18) = v19) | ? [v20] : ? [v21] : ? [v22] : (subset_complement(v17, v18) = v22 & element(v18, v20) = v21 & powerset(v17) = v20 & ( ~ (v21 = 0) | v22 = v19))) & ! [v17] : ! [v18] : ! [v19] : ( ~ (set_difference(v17, v18) = v19) | ? [v20] : (set_difference(v20, v18) = v19 & set_union2(v17, v18) = v20)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (set_difference(v17, v18) = v19) | ? [v20] : (set_difference(v17, v19) = v20 & set_intersection2(v17, v18) = v20)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (union(v17) = v18) | ~ (in(v19, v18) = 0) | ? [v20] : (in(v20, v17) = 0 & in(v19, v20) = 0)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_dom(v17) = v18) | ~ (relation(v19) = 0) | ? [v20] : ? [v21] : ? [v22] : ((v22 = 0 & relation_composition(v17, v19) = v20 & relation_dom(v20) = v21 & subset(v21, v18) = 0) | ( ~ (v20 = 0) & relation(v17) = v20))) & ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_dom(v17) = v18) | ~ (in(v19, v18) = 0) | ? [v20] : ? [v21] : ? [v22] : ((v22 = 0 & ordered_pair(v19, v20) = v21 & in(v21, v17) = 0) | ( ~ (v20 = 0) & relation(v17) = v20))) & ! [v17] : ! [v18] : ! [v19] : ( ~ (cartesian_product2(v17, v18) = v19) | ? [v20] : ? [v21] : ? [v22] : (empty(v19) = v22 & empty(v18) = v21 & empty(v17) = v20 & ( ~ (v22 = 0) | v21 = 0 | v20 = 0))) & ! [v17] : ! [v18] : ! [v19] : ( ~ (element(v18, v19) = 0) | ~ (powerset(v17) = v19) | ? [v20] : (subset_complement(v17, v20) = v18 & subset_complement(v17, v18) = v20)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (element(v18, v19) = 0) | ~ (powerset(v17) = v19) | ? [v20] : (subset_complement(v17, v18) = v20 & set_difference(v17, v18) = v20)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (element(v18, v19) = 0) | ~ (powerset(v17) = v19) | ? [v20] : (subset_complement(v17, v18) = v20 & element(v20, v19) = 0)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (element(v18, v17) = v19) | ? [v20] : ? [v21] : (empty(v18) = v21 & empty(v17) = v20 & ( ~ (v20 = 0) | (( ~ (v21 = 0) | v19 = 0) & ( ~ (v19 = 0) | v21 = 0))))) & ! [v17] : ! [v18] : ! [v19] : ( ~ (element(v18, v17) = v19) | ? [v20] : ? [v21] : (empty(v17) = v20 & in(v18, v17) = v21 & (v20 = 0 | (( ~ (v21 = 0) | v19 = 0) & ( ~ (v19 = 0) | v21 = 0))))) & ! [v17] : ! [v18] : ! [v19] : ( ~ (element(v17, v19) = 0) | ~ (powerset(v18) = v19) | subset(v17, v18) = 0) & ! [v17] : ! [v18] : ! [v19] : ( ~ (powerset(v17) = v18) | ~ (subset(v19, v17) = 0) | in(v19, v18) = 0) & ! [v17] : ! [v18] : ! [v19] : ( ~ (powerset(v17) = v18) | ~ (in(v19, v18) = 0) | subset(v19, v17) = 0) & ! [v17] : ! [v18] : ! [v19] : ( ~ (singleton(v17) = v19) | ~ (subset(v19, v18) = 0) | in(v17, v18) = 0) & ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_inverse_image(v18, v17) = v19) | ? [v20] : ? [v21] : ? [v22] : (relation_dom(v18) = v21 & subset(v19, v21) = v22 & relation(v18) = v20 & ( ~ (v20 = 0) | v22 = 0))) & ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_image(v18, v17) = v19) | ? [v20] : ? [v21] : ? [v22] : ? [v23] : (relation_dom(v18) = v21 & relation_image(v18, v22) = v23 & set_intersection2(v21, v17) = v22 & relation(v18) = v20 & ( ~ (v20 = 0) | v23 = v19))) & ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_image(v18, v17) = v19) | ? [v20] : ? [v21] : ? [v22] : (relation_rng(v18) = v21 & subset(v19, v21) = v22 & relation(v18) = v20 & ( ~ (v20 = 0) | v22 = 0))) & ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_rng_restriction(v17, v18) = v19) | ? [v20] : ? [v21] : ? [v22] : ? [v23] : (relation_rng(v19) = v21 & relation_rng(v18) = v22 & subset(v21, v22) = v23 & relation(v18) = v20 & ( ~ (v20 = 0) | v23 = 0))) & ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_rng_restriction(v17, v18) = v19) | ? [v20] : ? [v21] : ? [v22] : ? [v23] : (relation_rng(v19) = v21 & relation_rng(v18) = v22 & set_intersection2(v22, v17) = v23 & relation(v18) = v20 & ( ~ (v20 = 0) | v23 = v21))) & ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_rng_restriction(v17, v18) = v19) | ? [v20] : ? [v21] : ? [v22] : (relation_rng(v19) = v21 & subset(v21, v17) = v22 & relation(v18) = v20 & ( ~ (v20 = 0) | v22 = 0))) & ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_rng_restriction(v17, v18) = v19) | ? [v20] : ? [v21] : (subset(v19, v18) = v21 & relation(v18) = v20 & ( ~ (v20 = 0) | v21 = 0))) & ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_rng_restriction(v17, v18) = v19) | ? [v20] : ? [v21] : (relation(v19) = v21 & relation(v18) = v20 & ( ~ (v20 = 0) | v21 = 0))) & ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_dom_restriction(v18, v17) = v19) | ? [v20] : ? [v21] : ? [v22] : ? [v23] : (relation_rng(v19) = v21 & relation_rng(v18) = v22 & subset(v21, v22) = v23 & relation(v18) = v20 & ( ~ (v20 = 0) | v23 = 0))) & ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_dom_restriction(v18, v17) = v19) | ? [v20] : ? [v21] : ? [v22] : ? [v23] : (relation_dom(v19) = v21 & relation_dom(v18) = v22 & set_intersection2(v22, v17) = v23 & relation(v18) = v20 & ( ~ (v20 = 0) | v23 = v21))) & ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_dom_restriction(v18, v17) = v19) | ? [v20] : ? [v21] : ? [v22] : (relation_composition(v21, v18) = v22 & identity_relation(v17) = v21 & relation(v18) = v20 & ( ~ (v20 = 0) | v22 = v19))) & ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_dom_restriction(v18, v17) = v19) | ? [v20] : ? [v21] : (subset(v19, v18) = v21 & relation(v18) = v20 & ( ~ (v20 = 0) | v21 = 0))) & ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_dom_restriction(v17, v18) = v19) | ? [v20] : ? [v21] : (relation(v19) = v21 & relation(v17) = v20 & ( ~ (v20 = 0) | v21 = 0))) & ! [v17] : ! [v18] : ! [v19] : ( ~ (subset(v18, v19) = 0) | ~ (subset(v17, v18) = 0) | subset(v17, v19) = 0) & ! [v17] : ! [v18] : ! [v19] : ( ~ (subset(v17, v18) = 0) | ~ (in(v19, v17) = 0) | in(v19, v18) = 0) & ! [v17] : ! [v18] : ! [v19] : ( ~ (ordered_pair(v17, v18) = v19) | ? [v20] : ? [v21] : (singleton(v17) = v21 & unordered_pair(v20, v21) = v19 & unordered_pair(v17, v18) = v20)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (ordered_pair(v17, v18) = v19) | ? [v20] : ( ~ (v20 = 0) & empty(v19) = v20)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (set_intersection2(v18, v17) = v19) | set_intersection2(v17, v18) = v19) & ! [v17] : ! [v18] : ! [v19] : ( ~ (set_intersection2(v17, v18) = v19) | subset(v19, v17) = 0) & ! [v17] : ! [v18] : ! [v19] : ( ~ (set_intersection2(v17, v18) = v19) | set_intersection2(v18, v17) = v19) & ! [v17] : ! [v18] : ! [v19] : ( ~ (set_intersection2(v17, v18) = v19) | ? [v20] : ? [v21] : ? [v22] : (relation(v19) = v22 & relation(v18) = v21 & relation(v17) = v20 & ( ~ (v21 = 0) | ~ (v20 = 0) | v22 = 0))) & ! [v17] : ! [v18] : ! [v19] : ( ~ (set_intersection2(v17, v18) = v19) | ? [v20] : ? [v21] : ((v21 = 0 & in(v20, v19) = 0) | (v20 = 0 & disjoint(v17, v18) = 0))) & ! [v17] : ! [v18] : ! [v19] : ( ~ (set_intersection2(v17, v18) = v19) | ? [v20] : (set_difference(v17, v20) = v19 & set_difference(v17, v18) = v20)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (set_union2(v18, v17) = v19) | set_union2(v17, v18) = v19) & ! [v17] : ! [v18] : ! [v19] : ( ~ (set_union2(v18, v17) = v19) | ? [v20] : ? [v21] : (empty(v19) = v21 & empty(v17) = v20 & ( ~ (v21 = 0) | v20 = 0))) & ! [v17] : ! [v18] : ! [v19] : ( ~ (set_union2(v17, v18) = v19) | subset(v17, v19) = 0) & ! [v17] : ! [v18] : ! [v19] : ( ~ (set_union2(v17, v18) = v19) | set_union2(v18, v17) = v19) & ! [v17] : ! [v18] : ! [v19] : ( ~ (set_union2(v17, v18) = v19) | ? [v20] : ? [v21] : ? [v22] : (relation(v19) = v22 & relation(v18) = v21 & relation(v17) = v20 & ( ~ (v21 = 0) | ~ (v20 = 0) | v22 = 0))) & ! [v17] : ! [v18] : ! [v19] : ( ~ (set_union2(v17, v18) = v19) | ? [v20] : ? [v21] : (empty(v19) = v21 & empty(v17) = v20 & ( ~ (v21 = 0) | v20 = 0))) & ! [v17] : ! [v18] : ! [v19] : ( ~ (set_union2(v17, v18) = v19) | ? [v20] : (set_difference(v19, v18) = v20 & set_difference(v17, v18) = v20)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (set_union2(v17, v18) = v19) | ? [v20] : (set_difference(v18, v17) = v20 & set_union2(v17, v20) = v19)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (unordered_pair(v18, v17) = v19) | unordered_pair(v17, v18) = v19) & ! [v17] : ! [v18] : ! [v19] : ( ~ (unordered_pair(v17, v18) = v19) | unordered_pair(v18, v17) = v19) & ! [v17] : ! [v18] : ! [v19] : ( ~ (unordered_pair(v17, v18) = v19) | ? [v20] : ? [v21] : (singleton(v17) = v21 & ordered_pair(v17, v18) = v20 & unordered_pair(v19, v21) = v20)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (unordered_pair(v17, v18) = v19) | ? [v20] : ( ~ (v20 = 0) & empty(v19) = v20)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (empty(v19) = 0) | ~ (in(v17, v18) = 0) | ? [v20] : ? [v21] : ( ~ (v21 = 0) & element(v18, v20) = v21 & powerset(v19) = v20)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (in(v18, v17) = v19) | ? [v20] : ? [v21] : (element(v18, v17) = v21 & empty(v17) = v20 & (v20 = 0 | (( ~ (v21 = 0) | v19 = 0) & ( ~ (v19 = 0) | v21 = 0))))) & ? [v17] : ! [v18] : ! [v19] : (v19 = v17 | v18 = empty_set | ~ (set_meet(v18) = v19) | ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : (in(v20, v17) = v21 & ( ~ (v21 = 0) | (v23 = 0 & ~ (v24 = 0) & in(v22, v18) = 0 & in(v20, v22) = v24)) & (v21 = 0 | ( ! [v25] : ! [v26] : (v26 = 0 | ~ (in(v20, v25) = v26) | ? [v27] : ( ~ (v27 = 0) & in(v25, v18) = v27)) & ! [v25] : ( ~ (in(v25, v18) = 0) | in(v20, v25) = 0))))) & ? [v17] : ! [v18] : ! [v19] : (v19 = v17 | ~ (relation_rng(v18) = v19) | ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : (( ~ (v20 = 0) & relation(v18) = v20) | (in(v20, v17) = v21 & ( ~ (v21 = 0) | ! [v25] : ! [v26] : ( ~ (ordered_pair(v25, v20) = v26) | ? [v27] : ( ~ (v27 = 0) & in(v26, v18) = v27))) & (v21 = 0 | (v24 = 0 & ordered_pair(v22, v20) = v23 & in(v23, v18) = 0))))) & ? [v17] : ! [v18] : ! [v19] : (v19 = v17 | ~ (union(v18) = v19) | ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : (in(v20, v17) = v21 & ( ~ (v21 = 0) | ( ! [v25] : ( ~ (in(v25, v18) = 0) | ? [v26] : ( ~ (v26 = 0) & in(v20, v25) = v26)) & ! [v25] : ( ~ (in(v20, v25) = 0) | ? [v26] : ( ~ (v26 = 0) & in(v25, v18) = v26)))) & (v21 = 0 | (v24 = 0 & v23 = 0 & in(v22, v18) = 0 & in(v20, v22) = 0)))) & ? [v17] : ! [v18] : ! [v19] : (v19 = v17 | ~ (relation_dom(v18) = v19) | ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : (( ~ (v20 = 0) & relation(v18) = v20) | (in(v20, v17) = v21 & ( ~ (v21 = 0) | ! [v25] : ! [v26] : ( ~ (ordered_pair(v20, v25) = v26) | ? [v27] : ( ~ (v27 = 0) & in(v26, v18) = v27))) & (v21 = 0 | (v24 = 0 & ordered_pair(v20, v22) = v23 & in(v23, v18) = 0))))) & ? [v17] : ! [v18] : ! [v19] : (v19 = v17 | ~ (powerset(v18) = v19) | ? [v20] : ? [v21] : ? [v22] : (subset(v20, v18) = v22 & in(v20, v17) = v21 & ( ~ (v22 = 0) | ~ (v21 = 0)) & (v22 = 0 | v21 = 0))) & ? [v17] : ! [v18] : ! [v19] : (v19 = v17 | ~ (singleton(v18) = v19) | ? [v20] : ? [v21] : (in(v20, v17) = v21 & ( ~ (v21 = 0) | ~ (v20 = v18)) & (v21 = 0 | v20 = v18))) & ! [v17] : ! [v18] : (v18 = v17 | ~ (set_difference(v17, empty_set) = v18)) & ! [v17] : ! [v18] : (v18 = v17 | ~ (cast_to_subset(v17) = v18)) & ! [v17] : ! [v18] : (v18 = v17 | ~ (subset(v18, v17) = 0) | ? [v19] : ( ~ (v19 = 0) & subset(v17, v18) = v19)) & ! [v17] : ! [v18] : (v18 = v17 | ~ (subset(v17, v18) = 0) | proper_subset(v17, v18) = 0) & ! [v17] : ! [v18] : (v18 = v17 | ~ (subset(v17, v18) = 0) | ? [v19] : ( ~ (v19 = 0) & subset(v18, v17) = v19)) & ! [v17] : ! [v18] : (v18 = v17 | ~ (set_intersection2(v17, v17) = v18)) & ! [v17] : ! [v18] : (v18 = v17 | ~ (set_union2(v17, v17) = v18)) & ! [v17] : ! [v18] : (v18 = v17 | ~ (set_union2(v17, empty_set) = v18)) & ! [v17] : ! [v18] : (v18 = v17 | ~ (relation(v18) = 0) | ~ (relation(v17) = 0) | ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : (ordered_pair(v19, v20) = v21 & in(v21, v18) = v23 & in(v21, v17) = v22 & ( ~ (v23 = 0) | ~ (v22 = 0)) & (v23 = 0 | v22 = 0))) & ! [v17] : ! [v18] : (v18 = v17 | ~ (empty(v18) = 0) | ~ (empty(v17) = 0)) & ! [v17] : ! [v18] : (v18 = empty_set | ~ (complements_of_subsets(v17, v18) = empty_set) | ? [v19] : ? [v20] : ? [v21] : ( ~ (v21 = 0) & element(v18, v20) = v21 & powerset(v19) = v20 & powerset(v17) = v19)) & ! [v17] : ! [v18] : (v18 = empty_set | ~ (set_difference(empty_set, v17) = v18)) & ! [v17] : ! [v18] : (v18 = empty_set | ~ (set_intersection2(v17, empty_set) = v18)) & ! [v17] : ! [v18] : (v18 = 0 | ~ (subset(v17, v17) = v18)) & ! [v17] : ! [v18] : (v18 = 0 | ~ (subset(empty_set, v17) = v18)) & ! [v17] : ! [v18] : (v18 = 0 | ~ (relation(v17) = v18) | ? [v19] : ( ~ (v19 = 0) & empty(v17) = v19)) & ! [v17] : ! [v18] : (v18 = 0 | ~ (relation(v17) = v18) | ? [v19] : (in(v19, v17) = 0 & ! [v20] : ! [v21] : ~ (ordered_pair(v20, v21) = v19))) & ! [v17] : ! [v18] : (v18 = 0 | ~ (empty(v17) = v18) | ? [v19] : ? [v20] : ? [v21] : ( ~ (v21 = 0) & element(v20, v19) = 0 & powerset(v17) = v19 & empty(v20) = v21)) & ! [v17] : ! [v18] : (v18 = 0 | ~ (empty(v17) = v18) | ? [v19] : ? [v20] : ? [v21] : (relation_rng(v17) = v20 & relation(v17) = v19 & empty(v20) = v21 & ( ~ (v21 = 0) | ~ (v19 = 0)))) & ! [v17] : ! [v18] : (v18 = 0 | ~ (empty(v17) = v18) | ? [v19] : ? [v20] : ? [v21] : (relation_dom(v17) = v20 & relation(v17) = v19 & empty(v20) = v21 & ( ~ (v21 = 0) | ~ (v19 = 0)))) & ! [v17] : ! [v18] : (v18 = 0 | ~ (function(v17) = v18) | ? [v19] : ( ~ (v19 = 0) & empty(v17) = v19)) & ! [v17] : ! [v18] : (v17 = empty_set | ~ (relation_rng(v17) = v18) | ? [v19] : ? [v20] : (relation_dom(v17) = v20 & relation(v17) = v19 & ( ~ (v19 = 0) | ( ~ (v20 = empty_set) & ~ (v18 = empty_set))))) & ! [v17] : ! [v18] : (v17 = empty_set | ~ (relation_dom(v17) = v18) | ? [v19] : ? [v20] : (relation_rng(v17) = v20 & relation(v17) = v19 & ( ~ (v19 = 0) | ( ~ (v20 = empty_set) & ~ (v18 = empty_set))))) & ! [v17] : ! [v18] : (v17 = empty_set | ~ (relation_inverse_image(v18, v17) = empty_set) | ? [v19] : ? [v20] : ? [v21] : (relation_rng(v18) = v20 & subset(v17, v20) = v21 & relation(v18) = v19 & ( ~ (v21 = 0) | ~ (v19 = 0)))) & ! [v17] : ! [v18] : ( ~ (disjoint(v17, v18) = 0) | disjoint(v18, v17) = 0) & ! [v17] : ! [v18] : ( ~ (disjoint(v17, v18) = 0) | set_difference(v17, v18) = v17) & ! [v17] : ! [v18] : ( ~ (disjoint(v17, v18) = 0) | set_intersection2(v17, v18) = empty_set) & ! [v17] : ! [v18] : ( ~ (disjoint(v17, v18) = 0) | ? [v19] : (set_intersection2(v17, v18) = v19 & ! [v20] : ~ (in(v20, v19) = 0))) & ! [v17] : ! [v18] : ( ~ (relation_inverse(v17) = v18) | ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : (relation_rng(v18) = v23 & relation_rng(v17) = v20 & relation_dom(v18) = v21 & relation_dom(v17) = v22 & relation(v17) = v19 & ( ~ (v19 = 0) | (v23 = v22 & v21 = v20)))) & ! [v17] : ! [v18] : ( ~ (relation_inverse(v17) = v18) | ? [v19] : ? [v20] : (relation_inverse(v18) = v20 & relation(v17) = v19 & ( ~ (v19 = 0) | v20 = v17))) & ! [v17] : ! [v18] : ( ~ (relation_inverse(v17) = v18) | ? [v19] : ? [v20] : (relation(v18) = v20 & relation(v17) = v19 & ( ~ (v19 = 0) | v20 = 0))) & ! [v17] : ! [v18] : ( ~ (relation_field(v17) = v18) | ? [v19] : ? [v20] : ? [v21] : ? [v22] : (relation_rng(v17) = v21 & relation_dom(v17) = v20 & set_union2(v20, v21) = v22 & relation(v17) = v19 & ( ~ (v19 = 0) | v22 = v18))) & ! [v17] : ! [v18] : ( ~ (relation_rng(v17) = v18) | ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : (relation_inverse(v17) = v20 & relation_rng(v20) = v23 & relation_dom(v20) = v21 & relation_dom(v17) = v22 & relation(v17) = v19 & ( ~ (v19 = 0) | (v23 = v22 & v21 = v18)))) & ! [v17] : ! [v18] : ( ~ (relation_rng(v17) = v18) | ? [v19] : ? [v20] : ? [v21] : ? [v22] : (relation_field(v17) = v20 & relation_dom(v17) = v21 & set_union2(v21, v18) = v22 & relation(v17) = v19 & ( ~ (v19 = 0) | v22 = v20))) & ! [v17] : ! [v18] : ( ~ (relation_rng(v17) = v18) | ? [v19] : ? [v20] : ? [v21] : ? [v22] : (relation_dom(v17) = v20 & cartesian_product2(v20, v18) = v21 & subset(v17, v21) = v22 & relation(v17) = v19 & ( ~ (v19 = 0) | v22 = 0))) & ! [v17] : ! [v18] : ( ~ (relation_rng(v17) = v18) | ? [v19] : ? [v20] : ? [v21] : (relation_dom(v17) = v20 & relation_image(v17, v20) = v21 & relation(v17) = v19 & ( ~ (v19 = 0) | v21 = v18))) & ! [v17] : ! [v18] : ( ~ (relation_rng(v17) = v18) | ? [v19] : ? [v20] : ? [v21] : (relation(v18) = v21 & empty(v18) = v20 & empty(v17) = v19 & ( ~ (v19 = 0) | (v21 = 0 & v20 = 0)))) & ! [v17] : ! [v18] : ( ~ (relation_rng(v17) = v18) | ? [v19] : ? [v20] : ? [v21] : (relation(v17) = v20 & empty(v18) = v21 & empty(v17) = v19 & ( ~ (v21 = 0) | ~ (v20 = 0) | v19 = 0))) & ! [v17] : ! [v18] : ( ~ (relation_rng(v17) = v18) | ? [v19] : ? [v20] : (relation_dom(v17) = v20 & relation(v17) = v19 & ( ~ (v19 = 0) | ( ! [v21] : ! [v22] : ( ~ (relation_composition(v21, v17) = v22) | ? [v23] : ? [v24] : ? [v25] : ? [v26] : (relation_rng(v22) = v26 & relation_rng(v21) = v24 & subset(v20, v24) = v25 & relation(v21) = v23 & ( ~ (v25 = 0) | ~ (v23 = 0) | v26 = v18))) & ! [v21] : ! [v22] : ( ~ (relation_rng(v21) = v22) | ? [v23] : ? [v24] : ? [v25] : ? [v26] : (relation_composition(v21, v17) = v25 & relation_rng(v25) = v26 & subset(v20, v22) = v24 & relation(v21) = v23 & ( ~ (v24 = 0) | ~ (v23 = 0) | v26 = v18))) & ! [v21] : ( ~ (relation(v21) = 0) | ? [v22] : ? [v23] : ? [v24] : ? [v25] : (relation_composition(v21, v17) = v24 & relation_rng(v24) = v25 & relation_rng(v21) = v22 & subset(v20, v22) = v23 & ( ~ (v23 = 0) | v25 = v18))))))) & ! [v17] : ! [v18] : ( ~ (relation_rng(v17) = v18) | ? [v19] : ? [v20] : (relation_dom(v17) = v20 & relation(v17) = v19 & ( ~ (v19 = 0) | ( ! [v21] : ! [v22] : ( ~ (relation_composition(v17, v21) = v22) | ? [v23] : ? [v24] : ? [v25] : ? [v26] : (relation_dom(v22) = v26 & relation_dom(v21) = v24 & subset(v18, v24) = v25 & relation(v21) = v23 & ( ~ (v25 = 0) | ~ (v23 = 0) | v26 = v20))) & ! [v21] : ! [v22] : ( ~ (relation_dom(v21) = v22) | ? [v23] : ? [v24] : ? [v25] : ? [v26] : (relation_composition(v17, v21) = v25 & relation_dom(v25) = v26 & subset(v18, v22) = v24 & relation(v21) = v23 & ( ~ (v24 = 0) | ~ (v23 = 0) | v26 = v20))) & ! [v21] : ( ~ (relation(v21) = 0) | ? [v22] : ? [v23] : ? [v24] : ? [v25] : (relation_composition(v17, v21) = v24 & relation_dom(v24) = v25 & relation_dom(v21) = v22 & subset(v18, v22) = v23 & ( ~ (v23 = 0) | v25 = v20))))))) & ! [v17] : ! [v18] : ( ~ (relation_rng(v17) = v18) | ? [v19] : ? [v20] : (relation_dom(v17) = v20 & relation(v17) = v19 & ( ~ (v19 = 0) | ( ! [v21] : ! [v22] : ( ~ (relation_rng(v21) = v22) | ? [v23] : ? [v24] : ? [v25] : ? [v26] : ? [v27] : (relation_dom(v21) = v25 & subset(v20, v25) = v26 & subset(v18, v22) = v27 & subset(v17, v21) = v24 & relation(v21) = v23 & ( ~ (v24 = 0) | ~ (v23 = 0) | (v27 = 0 & v26 = 0)))) & ! [v21] : ! [v22] : ( ~ (relation_dom(v21) = v22) | ? [v23] : ? [v24] : ? [v25] : ? [v26] : ? [v27] : (relation_rng(v21) = v26 & subset(v20, v22) = v25 & subset(v18, v26) = v27 & subset(v17, v21) = v24 & relation(v21) = v23 & ( ~ (v24 = 0) | ~ (v23 = 0) | (v27 = 0 & v25 = 0)))) & ! [v21] : ( ~ (subset(v17, v21) = 0) | ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : (relation_rng(v21) = v25 & relation_dom(v21) = v23 & subset(v20, v23) = v24 & subset(v18, v25) = v26 & relation(v21) = v22 & ( ~ (v22 = 0) | (v26 = 0 & v24 = 0)))) & ! [v21] : ( ~ (relation(v21) = 0) | ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : (relation_rng(v21) = v25 & relation_dom(v21) = v23 & subset(v20, v23) = v24 & subset(v18, v25) = v26 & subset(v17, v21) = v22 & ( ~ (v22 = 0) | (v26 = 0 & v24 = 0)))))))) & ! [v17] : ! [v18] : ( ~ (relation_rng(v17) = v18) | ? [v19] : ? [v20] : (relation_dom(v17) = v20 & relation(v17) = v19 & ( ~ (v19 = 0) | (( ~ (v20 = empty_set) | v18 = empty_set) & ( ~ (v18 = empty_set) | v20 = empty_set))))) & ! [v17] : ! [v18] : ( ~ (set_difference(v17, v18) = v17) | disjoint(v17, v18) = 0) & ! [v17] : ! [v18] : ( ~ (set_difference(v17, v18) = empty_set) | subset(v17, v18) = 0) & ! [v17] : ! [v18] : ( ~ (cast_to_subset(v17) = v18) | ? [v19] : (element(v18, v19) = 0 & powerset(v17) = v19)) & ! [v17] : ! [v18] : ( ~ (relation_dom(v17) = v18) | ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : (relation_inverse(v17) = v21 & relation_rng(v21) = v23 & relation_rng(v17) = v20 & relation_dom(v21) = v22 & relation(v17) = v19 & ( ~ (v19 = 0) | (v23 = v18 & v22 = v20)))) & ! [v17] : ! [v18] : ( ~ (relation_dom(v17) = v18) | ? [v19] : ? [v20] : ? [v21] : ? [v22] : (relation_field(v17) = v20 & relation_rng(v17) = v21 & set_union2(v18, v21) = v22 & relation(v17) = v19 & ( ~ (v19 = 0) | v22 = v20))) & ! [v17] : ! [v18] : ( ~ (relation_dom(v17) = v18) | ? [v19] : ? [v20] : ? [v21] : ? [v22] : (relation_rng(v17) = v20 & cartesian_product2(v18, v20) = v21 & subset(v17, v21) = v22 & relation(v17) = v19 & ( ~ (v19 = 0) | v22 = 0))) & ! [v17] : ! [v18] : ( ~ (relation_dom(v17) = v18) | ? [v19] : ? [v20] : ? [v21] : (relation_rng(v17) = v21 & relation_image(v17, v18) = v20 & relation(v17) = v19 & ( ~ (v19 = 0) | v21 = v20))) & ! [v17] : ! [v18] : ( ~ (relation_dom(v17) = v18) | ? [v19] : ? [v20] : ? [v21] : (relation(v18) = v21 & empty(v18) = v20 & empty(v17) = v19 & ( ~ (v19 = 0) | (v21 = 0 & v20 = 0)))) & ! [v17] : ! [v18] : ( ~ (relation_dom(v17) = v18) | ? [v19] : ? [v20] : ? [v21] : (relation(v17) = v20 & empty(v18) = v21 & empty(v17) = v19 & ( ~ (v21 = 0) | ~ (v20 = 0) | v19 = 0))) & ! [v17] : ! [v18] : ( ~ (relation_dom(v17) = v18) | ? [v19] : ? [v20] : (relation_rng(v17) = v20 & relation(v17) = v19 & ( ~ (v19 = 0) | ( ! [v21] : ! [v22] : ( ~ (relation_composition(v21, v17) = v22) | ? [v23] : ? [v24] : ? [v25] : ? [v26] : (relation_rng(v22) = v26 & relation_rng(v21) = v24 & subset(v18, v24) = v25 & relation(v21) = v23 & ( ~ (v25 = 0) | ~ (v23 = 0) | v26 = v20))) & ! [v21] : ! [v22] : ( ~ (relation_rng(v21) = v22) | ? [v23] : ? [v24] : ? [v25] : ? [v26] : (relation_composition(v21, v17) = v25 & relation_rng(v25) = v26 & subset(v18, v22) = v24 & relation(v21) = v23 & ( ~ (v24 = 0) | ~ (v23 = 0) | v26 = v20))) & ! [v21] : ( ~ (relation(v21) = 0) | ? [v22] : ? [v23] : ? [v24] : ? [v25] : (relation_composition(v21, v17) = v24 & relation_rng(v24) = v25 & relation_rng(v21) = v22 & subset(v18, v22) = v23 & ( ~ (v23 = 0) | v25 = v20))))))) & ! [v17] : ! [v18] : ( ~ (relation_dom(v17) = v18) | ? [v19] : ? [v20] : (relation_rng(v17) = v20 & relation(v17) = v19 & ( ~ (v19 = 0) | ( ! [v21] : ! [v22] : ( ~ (relation_composition(v17, v21) = v22) | ? [v23] : ? [v24] : ? [v25] : ? [v26] : (relation_dom(v22) = v26 & relation_dom(v21) = v24 & subset(v20, v24) = v25 & relation(v21) = v23 & ( ~ (v25 = 0) | ~ (v23 = 0) | v26 = v18))) & ! [v21] : ! [v22] : ( ~ (relation_dom(v21) = v22) | ? [v23] : ? [v24] : ? [v25] : ? [v26] : (relation_composition(v17, v21) = v25 & relation_dom(v25) = v26 & subset(v20, v22) = v24 & relation(v21) = v23 & ( ~ (v24 = 0) | ~ (v23 = 0) | v26 = v18))) & ! [v21] : ( ~ (relation(v21) = 0) | ? [v22] : ? [v23] : ? [v24] : ? [v25] : (relation_composition(v17, v21) = v24 & relation_dom(v24) = v25 & relation_dom(v21) = v22 & subset(v20, v22) = v23 & ( ~ (v23 = 0) | v25 = v18))))))) & ! [v17] : ! [v18] : ( ~ (relation_dom(v17) = v18) | ? [v19] : ? [v20] : (relation_rng(v17) = v20 & relation(v17) = v19 & ( ~ (v19 = 0) | ( ! [v21] : ! [v22] : ( ~ (relation_rng(v21) = v22) | ? [v23] : ? [v24] : ? [v25] : ? [v26] : ? [v27] : (relation_dom(v21) = v25 & subset(v20, v22) = v27 & subset(v18, v25) = v26 & subset(v17, v21) = v24 & relation(v21) = v23 & ( ~ (v24 = 0) | ~ (v23 = 0) | (v27 = 0 & v26 = 0)))) & ! [v21] : ! [v22] : ( ~ (relation_dom(v21) = v22) | ? [v23] : ? [v24] : ? [v25] : ? [v26] : ? [v27] : (relation_rng(v21) = v26 & subset(v20, v26) = v27 & subset(v18, v22) = v25 & subset(v17, v21) = v24 & relation(v21) = v23 & ( ~ (v24 = 0) | ~ (v23 = 0) | (v27 = 0 & v25 = 0)))) & ! [v21] : ( ~ (subset(v17, v21) = 0) | ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : (relation_rng(v21) = v25 & relation_dom(v21) = v23 & subset(v20, v25) = v26 & subset(v18, v23) = v24 & relation(v21) = v22 & ( ~ (v22 = 0) | (v26 = 0 & v24 = 0)))) & ! [v21] : ( ~ (relation(v21) = 0) | ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : (relation_rng(v21) = v25 & relation_dom(v21) = v23 & subset(v20, v25) = v26 & subset(v18, v23) = v24 & subset(v17, v21) = v22 & ( ~ (v22 = 0) | (v26 = 0 & v24 = 0)))))))) & ! [v17] : ! [v18] : ( ~ (relation_dom(v17) = v18) | ? [v19] : ? [v20] : (relation_rng(v17) = v20 & relation(v17) = v19 & ( ~ (v19 = 0) | (( ~ (v20 = empty_set) | v18 = empty_set) & ( ~ (v18 = empty_set) | v20 = empty_set))))) & ! [v17] : ! [v18] : ( ~ (element(v17, v18) = 0) | ? [v19] : ? [v20] : (empty(v18) = v19 & in(v17, v18) = v20 & (v20 = 0 | v19 = 0))) & ! [v17] : ! [v18] : ( ~ (powerset(v17) = v18) | union(v18) = v17) & ! [v17] : ! [v18] : ( ~ (powerset(v17) = v18) | ? [v19] : ? [v20] : ? [v21] : ((v20 = 0 & ~ (v21 = 0) & element(v19, v18) = 0 & empty(v19) = v21) | (v19 = 0 & empty(v17) = 0))) & ! [v17] : ! [v18] : ( ~ (powerset(v17) = v18) | ? [v19] : ( ~ (v19 = 0) & empty(v18) = v19)) & ! [v17] : ! [v18] : ( ~ (powerset(v17) = v18) | ? [v19] : (cast_to_subset(v17) = v19 & element(v19, v18) = 0)) & ! [v17] : ! [v18] : ( ~ (powerset(v17) = v18) | ? [v19] : (element(v19, v18) = 0 & empty(v19) = 0)) & ! [v17] : ! [v18] : ( ~ (singleton(v17) = v18) | unordered_pair(v17, v17) = v18) & ! [v17] : ! [v18] : ( ~ (singleton(v17) = v18) | ? [v19] : ( ~ (v19 = 0) & empty(v18) = v19)) & ! [v17] : ! [v18] : ( ~ (subset(v17, v18) = 0) | set_difference(v17, v18) = empty_set) & ! [v17] : ! [v18] : ( ~ (subset(v17, v18) = 0) | set_intersection2(v17, v18) = v17) & ! [v17] : ! [v18] : ( ~ (subset(v17, v18) = 0) | set_union2(v17, v18) = v18) & ! [v17] : ! [v18] : ( ~ (subset(v17, v18) = 0) | ? [v19] : ( ~ (v19 = 0) & proper_subset(v18, v17) = v19)) & ! [v17] : ! [v18] : ( ~ (subset(v17, v18) = 0) | ? [v19] : (set_difference(v18, v17) = v19 & set_union2(v17, v19) = v18)) & ! [v17] : ! [v18] : ( ~ (subset(v17, v18) = 0) | ? [v19] : (element(v17, v19) = 0 & powerset(v18) = v19)) & ! [v17] : ! [v18] : ( ~ (subset(v17, v17) = v18) | ? [v19] : ( ~ (v19 = 0) & proper_subset(v17, v17) = v19)) & ! [v17] : ! [v18] : ( ~ (identity_relation(v17) = v18) | relation_rng(v18) = v17) & ! [v17] : ! [v18] : ( ~ (identity_relation(v17) = v18) | relation_dom(v18) = v17) & ! [v17] : ! [v18] : ( ~ (identity_relation(v17) = v18) | relation(v18) = 0) & ! [v17] : ! [v18] : ( ~ (set_intersection2(v17, v18) = empty_set) | disjoint(v17, v18) = 0) & ! [v17] : ! [v18] : ( ~ (unordered_pair(v17, v17) = v18) | singleton(v17) = v18) & ! [v17] : ! [v18] : ( ~ (relation(v18) = 0) | ~ (relation(v17) = 0) | ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : (subset(v17, v18) = v19 & ( ~ (v19 = 0) | ! [v25] : ! [v26] : ! [v27] : ( ~ (ordered_pair(v25, v26) = v27) | ? [v28] : ? [v29] : (in(v27, v18) = v29 & in(v27, v17) = v28 & ( ~ (v28 = 0) | v29 = 0)))) & (v19 = 0 | (v23 = 0 & ~ (v24 = 0) & ordered_pair(v20, v21) = v22 & in(v22, v18) = v24 & in(v22, v17) = 0)))) & ! [v17] : ! [v18] : ( ~ (relation(v18) = 0) | ~ (relation(v17) = 0) | ? [v19] : ? [v20] : ? [v21] : (relation_composition(v17, v18) = v19 & relation_rng(v19) = v20 & relation_rng(v18) = v21 & subset(v20, v21) = 0)) & ! [v17] : ! [v18] : ( ~ (relation(v18) = 0) | ~ (relation(v17) = 0) | ? [v19] : (relation_composition(v17, v18) = v19 & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ( ~ (ordered_pair(v23, v21) = v24) | ~ (ordered_pair(v20, v21) = v22) | ~ (relation(v19) = 0) | ? [v25] : ? [v26] : ? [v27] : ((v25 = 0 & in(v22, v19) = 0) | (ordered_pair(v20, v23) = v25 & in(v25, v17) = v26 & in(v24, v18) = v27 & ( ~ (v27 = 0) | ~ (v26 = 0))))) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ( ~ (ordered_pair(v20, v23) = v24) | ~ (ordered_pair(v20, v21) = v22) | ~ (relation(v19) = 0) | ? [v25] : ? [v26] : ? [v27] : ((v25 = 0 & in(v22, v19) = 0) | (ordered_pair(v23, v21) = v26 & in(v26, v18) = v27 & in(v24, v17) = v25 & ( ~ (v27 = 0) | ~ (v25 = 0))))) & ! [v20] : ! [v21] : ! [v22] : ( ~ (ordered_pair(v20, v21) = v22) | ~ (relation(v19) = 0) | ? [v23] : ? [v24] : ? [v25] : ? [v26] : ? [v27] : ((v27 = 0 & v25 = 0 & ordered_pair(v23, v21) = v26 & ordered_pair(v20, v23) = v24 & in(v26, v18) = 0 & in(v24, v17) = 0) | ( ~ (v23 = 0) & in(v22, v19) = v23))) & ! [v20] : (v20 = v19 | ~ (relation(v20) = 0) | ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : ? [v27] : ? [v28] : ? [v29] : (ordered_pair(v21, v22) = v23 & in(v23, v20) = v24 & ( ~ (v24 = 0) | ( ! [v30] : ! [v31] : ( ~ (ordered_pair(v30, v22) = v31) | ? [v32] : ? [v33] : ? [v34] : (ordered_pair(v21, v30) = v32 & in(v32, v17) = v33 & in(v31, v18) = v34 & ( ~ (v34 = 0) | ~ (v33 = 0)))) & ! [v30] : ! [v31] : ( ~ (ordered_pair(v21, v30) = v31) | ? [v32] : ? [v33] : ? [v34] : (ordered_pair(v30, v22) = v33 & in(v33, v18) = v34 & in(v31, v17) = v32 & ( ~ (v34 = 0) | ~ (v32 = 0)))))) & (v24 = 0 | (v29 = 0 & v27 = 0 & ordered_pair(v25, v22) = v28 & ordered_pair(v21, v25) = v26 & in(v28, v18) = 0 & in(v26, v17) = 0)))))) & ! [v17] : ! [v18] : ( ~ (relation(v17) = 0) | ~ (in(v18, v17) = 0) | ? [v19] : ? [v20] : ordered_pair(v19, v20) = v18) & ! [v17] : ! [v18] : ( ~ (proper_subset(v18, v17) = 0) | ? [v19] : ( ~ (v19 = 0) & subset(v17, v18) = v19)) & ! [v17] : ! [v18] : ( ~ (proper_subset(v18, v17) = 0) | ? [v19] : ( ~ (v19 = 0) & proper_subset(v17, v18) = v19)) & ! [v17] : ! [v18] : ( ~ (proper_subset(v17, v18) = 0) | subset(v17, v18) = 0) & ! [v17] : ! [v18] : ( ~ (proper_subset(v17, v18) = 0) | ? [v19] : ( ~ (v19 = 0) & proper_subset(v18, v17) = v19)) & ! [v17] : ! [v18] : ( ~ (in(v18, v17) = 0) | ? [v19] : ? [v20] : ( ~ (v20 = v17) & set_difference(v17, v19) = v20 & singleton(v18) = v19)) & ! [v17] : ! [v18] : ( ~ (in(v18, v17) = 0) | ? [v19] : ( ~ (v19 = 0) & in(v17, v18) = v19)) & ! [v17] : ! [v18] : ( ~ (in(v17, v18) = 0) | element(v17, v18) = 0) & ! [v17] : ! [v18] : ( ~ (in(v17, v18) = 0) | ? [v19] : ? [v20] : ( ~ (v20 = 0) & disjoint(v19, v18) = v20 & singleton(v17) = v19)) & ! [v17] : ! [v18] : ( ~ (in(v17, v18) = 0) | ? [v19] : ( ~ (v19 = 0) & empty(v18) = v19)) & ! [v17] : ! [v18] : ( ~ (in(v17, v18) = 0) | ? [v19] : ( ~ (v19 = 0) & in(v18, v17) = v19)) & ! [v17] : ! [v18] : ( ~ (in(v17, v18) = 0) | ? [v19] : (union(v18) = v19 & subset(v17, v19) = 0)) & ! [v17] : ! [v18] : ( ~ (in(v17, v18) = 0) | ? [v19] : (singleton(v17) = v19 & subset(v19, v18) = 0)) & ! [v17] : ! [v18] : ( ~ (in(v17, v18) = 0) | ? [v19] : (singleton(v17) = v19 & set_union2(v19, v18) = v18)) & ! [v17] : (v17 = empty_set | ~ (set_meet(empty_set) = v17)) & ! [v17] : (v17 = empty_set | ~ (subset(v17, empty_set) = 0)) & ! [v17] : (v17 = empty_set | ~ (relation(v17) = 0) | ? [v18] : ? [v19] : ? [v20] : (ordered_pair(v18, v19) = v20 & in(v20, v17) = 0)) & ! [v17] : (v17 = empty_set | ~ (relation(v17) = 0) | ? [v18] : ? [v19] : ( ~ (v19 = empty_set) & ~ (v18 = empty_set) & relation_rng(v17) = v19 & relation_dom(v17) = v18)) & ! [v17] : (v17 = empty_set | ~ (empty(v17) = 0)) & ! [v17] : ~ (singleton(v17) = empty_set) & ! [v17] : ( ~ (relation(v17) = 0) | ? [v18] : ? [v19] : ? [v20] : (relation_inverse(v17) = v19 & relation_rng(v19) = v20 & relation_rng(v17) = v18 & relation_dom(v19) = v18 & relation_dom(v17) = v20)) & ! [v17] : ( ~ (relation(v17) = 0) | ? [v18] : ? [v19] : ? [v20] : (relation_field(v17) = v18 & relation_rng(v17) = v20 & relation_dom(v17) = v19 & set_union2(v19, v20) = v18)) & ! [v17] : ( ~ (relation(v17) = 0) | ? [v18] : ? [v19] : ? [v20] : (relation_rng(v17) = v19 & relation_dom(v17) = v18 & cartesian_product2(v18, v19) = v20 & subset(v17, v20) = 0)) & ! [v17] : ( ~ (relation(v17) = 0) | ? [v18] : ? [v19] : ? [v20] : (relation_rng(v17) = v19 & empty(v19) = v20 & empty(v17) = v18 & ( ~ (v20 = 0) | v18 = 0))) & ! [v17] : ( ~ (relation(v17) = 0) | ? [v18] : ? [v19] : ? [v20] : (relation_dom(v17) = v19 & empty(v19) = v20 & empty(v17) = v18 & ( ~ (v20 = 0) | v18 = 0))) & ! [v17] : ( ~ (relation(v17) = 0) | ? [v18] : ? [v19] : (relation_rng(v17) = v19 & relation_dom(v17) = v18 & relation_image(v17, v18) = v19)) & ! [v17] : ( ~ (relation(v17) = 0) | ? [v18] : ? [v19] : (relation_rng(v17) = v19 & relation_dom(v17) = v18 & ! [v20] : ! [v21] : ( ~ (relation_composition(v20, v17) = v21) | ? [v22] : ? [v23] : ? [v24] : ? [v25] : (relation_rng(v21) = v25 & relation_rng(v20) = v23 & subset(v18, v23) = v24 & relation(v20) = v22 & ( ~ (v24 = 0) | ~ (v22 = 0) | v25 = v19))) & ! [v20] : ! [v21] : ( ~ (relation_rng(v20) = v21) | ? [v22] : ? [v23] : ? [v24] : ? [v25] : (relation_composition(v20, v17) = v24 & relation_rng(v24) = v25 & subset(v18, v21) = v23 & relation(v20) = v22 & ( ~ (v23 = 0) | ~ (v22 = 0) | v25 = v19))) & ! [v20] : ( ~ (relation(v20) = 0) | ? [v21] : ? [v22] : ? [v23] : ? [v24] : (relation_composition(v20, v17) = v23 & relation_rng(v23) = v24 & relation_rng(v20) = v21 & subset(v18, v21) = v22 & ( ~ (v22 = 0) | v24 = v19))))) & ! [v17] : ( ~ (relation(v17) = 0) | ? [v18] : ? [v19] : (relation_rng(v17) = v19 & relation_dom(v17) = v18 & ! [v20] : ! [v21] : ( ~ (relation_rng(v20) = v21) | ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : (relation_dom(v20) = v24 & subset(v19, v21) = v26 & subset(v18, v24) = v25 & subset(v17, v20) = v23 & relation(v20) = v22 & ( ~ (v23 = 0) | ~ (v22 = 0) | (v26 = 0 & v25 = 0)))) & ! [v20] : ! [v21] : ( ~ (relation_dom(v20) = v21) | ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : (relation_rng(v20) = v25 & subset(v19, v25) = v26 & subset(v18, v21) = v24 & subset(v17, v20) = v23 & relation(v20) = v22 & ( ~ (v23 = 0) | ~ (v22 = 0) | (v26 = 0 & v24 = 0)))) & ! [v20] : ( ~ (subset(v17, v20) = 0) | ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : (relation_rng(v20) = v24 & relation_dom(v20) = v22 & subset(v19, v24) = v25 & subset(v18, v22) = v23 & relation(v20) = v21 & ( ~ (v21 = 0) | (v25 = 0 & v23 = 0)))) & ! [v20] : ( ~ (relation(v20) = 0) | ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : (relation_rng(v20) = v24 & relation_dom(v20) = v22 & subset(v19, v24) = v25 & subset(v18, v22) = v23 & subset(v17, v20) = v21 & ( ~ (v21 = 0) | (v25 = 0 & v23 = 0)))))) & ! [v17] : ( ~ (relation(v17) = 0) | ? [v18] : ? [v19] : (relation_rng(v17) = v19 & relation_dom(v17) = v18 & ( ~ (v19 = empty_set) | v18 = empty_set) & ( ~ (v18 = empty_set) | v19 = empty_set))) & ! [v17] : ( ~ (relation(v17) = 0) | ? [v18] : ? [v19] : (relation_rng(v17) = v18 & relation_dom(v17) = v19 & ! [v20] : ! [v21] : ( ~ (relation_composition(v17, v20) = v21) | ? [v22] : ? [v23] : ? [v24] : ? [v25] : (relation_dom(v21) = v25 & relation_dom(v20) = v23 & subset(v18, v23) = v24 & relation(v20) = v22 & ( ~ (v24 = 0) | ~ (v22 = 0) | v25 = v19))) & ! [v20] : ! [v21] : ( ~ (relation_dom(v20) = v21) | ? [v22] : ? [v23] : ? [v24] : ? [v25] : (relation_composition(v17, v20) = v24 & relation_dom(v24) = v25 & subset(v18, v21) = v23 & relation(v20) = v22 & ( ~ (v23 = 0) | ~ (v22 = 0) | v25 = v19))) & ! [v20] : ( ~ (relation(v20) = 0) | ? [v21] : ? [v22] : ? [v23] : ? [v24] : (relation_composition(v17, v20) = v23 & relation_dom(v23) = v24 & relation_dom(v20) = v21 & subset(v18, v21) = v22 & ( ~ (v22 = 0) | v24 = v19))))) & ! [v17] : ( ~ (relation(v17) = 0) | ? [v18] : ? [v19] : (relation_dom(v17) = v19 & function(v17) = v18 & ( ~ (v18 = 0) | ( ! [v20] : ! [v21] : ! [v22] : ( ~ (ordered_pair(v20, v21) = v22) | ? [v23] : ? [v24] : ? [v25] : (apply(v17, v20) = v24 & in(v22, v17) = v25 & in(v20, v19) = v23 & ( ~ (v23 = 0) | (( ~ (v25 = 0) | v24 = v21) & ( ~ (v24 = v21) | v25 = 0))))) & ? [v20] : ! [v21] : ! [v22] : (v22 = 0 | ~ (in(v21, v19) = v22) | ? [v23] : (apply(v17, v21) = v23 & ( ~ (v23 = v20) | v20 = empty_set) & ( ~ (v20 = empty_set) | v23 = empty_set))) & ! [v20] : ! [v21] : (v21 = empty_set | ~ (apply(v17, v20) = v21) | in(v20, v19) = 0))))) & ! [v17] : ( ~ (relation(v17) = 0) | ? [v18] : (relation_inverse(v18) = v17 & relation_inverse(v17) = v18)) & ! [v17] : ( ~ (relation(v17) = 0) | ? [v18] : (relation_inverse(v17) = v18 & relation(v18) = 0)) & ! [v17] : ( ~ (relation(v17) = 0) | ? [v18] : (relation_inverse(v17) = v18 & ! [v19] : ! [v20] : ! [v21] : ( ~ (ordered_pair(v20, v19) = v21) | ~ (relation(v18) = 0) | ? [v22] : ? [v23] : ? [v24] : (ordered_pair(v19, v20) = v23 & in(v23, v18) = v24 & in(v21, v17) = v22 & ( ~ (v22 = 0) | v24 = 0))) & ! [v19] : ! [v20] : ! [v21] : ( ~ (ordered_pair(v20, v19) = v21) | ~ (relation(v18) = 0) | ? [v22] : ? [v23] : ? [v24] : (ordered_pair(v19, v20) = v22 & in(v22, v18) = v23 & in(v21, v17) = v24 & ( ~ (v23 = 0) | v24 = 0))) & ! [v19] : ! [v20] : ! [v21] : ( ~ (ordered_pair(v19, v20) = v21) | ~ (relation(v18) = 0) | ? [v22] : ? [v23] : ? [v24] : (ordered_pair(v20, v19) = v23 & in(v23, v17) = v24 & in(v21, v18) = v22 & ( ~ (v22 = 0) | v24 = 0))) & ! [v19] : ! [v20] : ! [v21] : ( ~ (ordered_pair(v19, v20) = v21) | ~ (relation(v18) = 0) | ? [v22] : ? [v23] : ? [v24] : (ordered_pair(v20, v19) = v22 & in(v22, v17) = v23 & in(v21, v18) = v24 & ( ~ (v23 = 0) | v24 = 0))) & ! [v19] : (v19 = v18 | ~ (relation(v19) = 0) | ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : (ordered_pair(v21, v20) = v24 & ordered_pair(v20, v21) = v22 & in(v24, v17) = v25 & in(v22, v19) = v23 & ( ~ (v25 = 0) | ~ (v23 = 0)) & (v25 = 0 | v23 = 0))))) & ! [v17] : ( ~ (relation(v17) = 0) | ? [v18] : (relation_rng(v17) = v18 & ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v20 = 0 | ~ (ordered_pair(v21, v19) = v22) | ~ (in(v19, v18) = v20) | ? [v23] : ( ~ (v23 = 0) & in(v22, v17) = v23)) & ! [v19] : ( ~ (in(v19, v18) = 0) | ? [v20] : ? [v21] : (ordered_pair(v20, v19) = v21 & in(v21, v17) = 0)) & ? [v19] : (v19 = v18 | ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : (in(v20, v19) = v21 & ( ~ (v21 = 0) | ! [v25] : ! [v26] : ( ~ (ordered_pair(v25, v20) = v26) | ? [v27] : ( ~ (v27 = 0) & in(v26, v17) = v27))) & (v21 = 0 | (v24 = 0 & ordered_pair(v22, v20) = v23 & in(v23, v17) = 0)))))) & ! [v17] : ( ~ (relation(v17) = 0) | ? [v18] : (relation_rng(v17) = v18 & ! [v19] : ! [v20] : ( ~ (relation_composition(v17, v19) = v20) | ? [v21] : ? [v22] : ? [v23] : (relation_rng(v20) = v22 & relation_image(v19, v18) = v23 & relation(v19) = v21 & ( ~ (v21 = 0) | v23 = v22))) & ! [v19] : ! [v20] : ( ~ (relation_image(v19, v18) = v20) | ? [v21] : ? [v22] : ? [v23] : (relation_composition(v17, v19) = v22 & relation_rng(v22) = v23 & relation(v19) = v21 & ( ~ (v21 = 0) | v23 = v20))) & ! [v19] : ( ~ (relation(v19) = 0) | ? [v20] : ? [v21] : (relation_composition(v17, v19) = v20 & relation_rng(v20) = v21 & relation_image(v19, v18) = v21)))) & ! [v17] : ( ~ (relation(v17) = 0) | ? [v18] : (relation_dom(v17) = v18 & ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v20 = 0 | ~ (ordered_pair(v19, v21) = v22) | ~ (in(v19, v18) = v20) | ? [v23] : ( ~ (v23 = 0) & in(v22, v17) = v23)) & ! [v19] : ( ~ (in(v19, v18) = 0) | ? [v20] : ? [v21] : (ordered_pair(v19, v20) = v21 & in(v21, v17) = 0)) & ? [v19] : (v19 = v18 | ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : (in(v20, v19) = v21 & ( ~ (v21 = 0) | ! [v25] : ! [v26] : ( ~ (ordered_pair(v20, v25) = v26) | ? [v27] : ( ~ (v27 = 0) & in(v26, v17) = v27))) & (v21 = 0 | (v24 = 0 & ordered_pair(v20, v22) = v23 & in(v23, v17) = 0)))))) & ! [v17] : ( ~ (relation(v17) = 0) | ? [v18] : (relation_dom(v17) = v18 & ! [v19] : ! [v20] : ( ~ (relation_composition(v17, v19) = v20) | ? [v21] : ? [v22] : ? [v23] : (relation_dom(v20) = v22 & subset(v22, v18) = v23 & relation(v19) = v21 & ( ~ (v21 = 0) | v23 = 0))) & ! [v19] : ( ~ (relation(v19) = 0) | ? [v20] : ? [v21] : (relation_composition(v17, v19) = v20 & relation_dom(v20) = v21 & subset(v21, v18) = 0)))) & ! [v17] : ( ~ (empty(v17) = 0) | relation(v17) = 0) & ! [v17] : ( ~ (empty(v17) = 0) | function(v17) = 0) & ! [v17] : ( ~ (empty(v17) = 0) | ? [v18] : (relation_rng(v17) = v18 & relation(v18) = 0 & empty(v18) = 0)) & ! [v17] : ( ~ (empty(v17) = 0) | ? [v18] : (relation_dom(v17) = v18 & relation(v18) = 0 & empty(v18) = 0)) & ! [v17] : ( ~ (function(v17) = 0) | ? [v18] : ? [v19] : (relation_dom(v17) = v19 & relation(v17) = v18 & ( ~ (v18 = 0) | ( ! [v20] : ! [v21] : ! [v22] : ( ~ (ordered_pair(v20, v21) = v22) | ? [v23] : ? [v24] : ? [v25] : (apply(v17, v20) = v24 & in(v22, v17) = v25 & in(v20, v19) = v23 & ( ~ (v23 = 0) | (( ~ (v25 = 0) | v24 = v21) & ( ~ (v24 = v21) | v25 = 0))))) & ? [v20] : ! [v21] : ! [v22] : (v22 = 0 | ~ (in(v21, v19) = v22) | ? [v23] : (apply(v17, v21) = v23 & ( ~ (v23 = v20) | v20 = empty_set) & ( ~ (v20 = empty_set) | v23 = empty_set))) & ! [v20] : ! [v21] : (v21 = empty_set | ~ (apply(v17, v20) = v21) | in(v20, v19) = 0))))) & ! [v17] : ~ (proper_subset(v17, v17) = 0) & ! [v17] : ~ (in(v17, empty_set) = 0) & ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : (relation_field(v19) = v23 & ordered_pair(v17, v18) = v21 & relation(v19) = v20 & in(v21, v19) = v22 & in(v18, v23) = v25 & in(v17, v23) = v24 & ( ~ (v22 = 0) | ~ (v20 = 0) | (v25 = 0 & v24 = 0))) & ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : (cartesian_product2(v18, v20) = v24 & cartesian_product2(v17, v19) = v23 & subset(v23, v24) = v25 & subset(v19, v20) = v22 & subset(v17, v18) = v21 & ( ~ (v22 = 0) | ~ (v21 = 0) | v25 = 0)) & ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : (subset_difference(v17, v18, v19) = v23 & set_difference(v18, v19) = v24 & element(v19, v20) = v22 & element(v18, v20) = v21 & powerset(v17) = v20 & ( ~ (v22 = 0) | ~ (v21 = 0) | v24 = v23)) & ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : (subset_complement(v17, v19) = v22 & element(v19, v20) = v21 & powerset(v17) = v20 & in(v18, v22) = v23 & in(v18, v19) = v24 & ( ~ (v24 = 0) | ~ (v23 = 0) | ~ (v21 = 0))) & ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : (relation_inverse_image(v19, v18) = v23 & relation_inverse_image(v19, v17) = v22 & subset(v22, v23) = v24 & subset(v17, v18) = v21 & relation(v19) = v20 & ( ~ (v21 = 0) | ~ (v20 = 0) | v24 = 0)) & ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : (relation_rng_restriction(v17, v23) = v24 & relation_rng_restriction(v17, v19) = v21 & relation_dom_restriction(v21, v18) = v22 & relation_dom_restriction(v19, v18) = v23 & relation(v19) = v20 & ( ~ (v20 = 0) | v24 = v22)) & ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : (meet_of_subsets(v17, v18) = v22 & element(v18, v20) = v21 & powerset(v19) = v20 & powerset(v17) = v19 & set_meet(v18) = v23 & ( ~ (v21 = 0) | v23 = v22)) & ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : (union_of_subsets(v17, v18) = v22 & union(v18) = v23 & element(v18, v20) = v21 & powerset(v19) = v20 & powerset(v17) = v19 & ( ~ (v21 = 0) | v23 = v22)) & ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : (complements_of_subsets(v17, v22) = v23 & complements_of_subsets(v17, v18) = v22 & element(v18, v20) = v21 & powerset(v19) = v20 & powerset(v17) = v19 & ( ~ (v21 = 0) | v23 = v18)) & ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : (relation_composition(v17, v18) = v21 & relation(v21) = v23 & relation(v18) = v20 & empty(v21) = v22 & empty(v17) = v19 & ( ~ (v20 = 0) | ~ (v19 = 0) | (v23 = 0 & v22 = 0))) & ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : (relation_inverse(v17) = v20 & relation_rng(v20) = v23 & relation_rng(v17) = v19 & relation_dom(v20) = v21 & relation_dom(v17) = v22 & relation(v17) = v18 & ( ~ (v18 = 0) | (v23 = v22 & v21 = v19))) & ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : (relation_dom(v18) = v21 & relation_image(v18, v22) = v23 & relation_image(v18, v17) = v20 & set_intersection2(v21, v17) = v22 & relation(v18) = v19 & ( ~ (v19 = 0) | v23 = v20)) & ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : (element(v18, v21) = v22 & element(v17, v19) = v23 & powerset(v19) = v21 & in(v17, v18) = v20 & ( ~ (v22 = 0) | ~ (v20 = 0) | v23 = 0)) & ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : (subset(v22, v19) = v23 & unordered_pair(v17, v18) = v22 & in(v18, v19) = v21 & in(v17, v19) = v20 & ( ~ (v21 = 0) | ~ (v20 = 0) | v23 = 0)) & ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : (subset(v22, v18) = v23 & subset(v19, v18) = v21 & subset(v17, v18) = v20 & set_union2(v17, v19) = v22 & ( ~ (v21 = 0) | ~ (v20 = 0) | v23 = 0)) & ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : (relation_composition(v21, v18) = v22 & relation_dom_restriction(v18, v17) = v20 & identity_relation(v17) = v21 & relation(v18) = v19 & ( ~ (v19 = 0) | v22 = v20)) & ? [v17] : ? [v18] : ? [v19] : ? [v20] : (disjoint(v17, v18) = v20 & set_intersection2(v17, v18) = v19 & ( ~ (v20 = 0) | ? [v21] : ? [v22] : ( ~ (v22 = 0) & in(v21, v19) = v22))) & ? [v17] : ? [v18] : ? [v19] : ? [v20] : (relation_dom(v17) = v20 & relation(v17) = v18 & function(v17) = v19 & ( ~ (v19 = 0) | ~ (v18 = 0) | ( ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : (apply(v17, v21) = v24 & ordered_pair(v21, v22) = v25 & in(v25, v17) = v26 & in(v21, v20) = v23 & ( ~ (v23 = 0) | (( ~ (v26 = 0) | v24 = v22) & ( ~ (v24 = v22) | v26 = 0)))) & ? [v21] : ? [v22] : ? [v23] : ? [v24] : (apply(v17, v21) = v24 & in(v21, v20) = v23 & (v23 = 0 | (( ~ (v24 = v22) | v22 = empty_set) & ( ~ (v22 = empty_set) | v24 = empty_set))))))) & ? [v17] : ? [v18] : ? [v19] : ? [v20] : (subset(v17, v18) = v19 & proper_subset(v18, v17) = v20 & ( ~ (v20 = 0) | ~ (v19 = 0))) & ? [v17] : ? [v18] : ? [v19] : (cast_to_subset(v17) = v18 & element(v18, v19) = 0 & powerset(v17) = v19) & ? [v17] : ? [v18] : (v18 = v17 | ? [v19] : ? [v20] : ? [v21] : (in(v19, v18) = v21 & in(v19, v17) = v20 & ( ~ (v21 = 0) | ~ (v20 = 0)) & (v21 = 0 | v20 = 0))) & ? [v17] : ? [v18] : element(v18, v17) = 0 & ? [v17] : ? [v18] : (singleton(v17) = v18 & unordered_pair(v17, v17) = v18) & ? [v17] : ? [v18] : (in(v17, v18) = 0 & ! [v19] : ! [v20] : (v20 = 0 | ~ (are_equipotent(v19, v18) = v20) | ? [v21] : ? [v22] : (subset(v19, v18) = v21 & in(v19, v18) = v22 & ( ~ (v21 = 0) | v22 = 0))) & ! [v19] : ! [v20] : (v20 = 0 | ~ (in(v19, v18) = v20) | ? [v21] : ? [v22] : (are_equipotent(v19, v18) = v22 & subset(v19, v18) = v21 & ( ~ (v21 = 0) | v22 = 0))) & ! [v19] : ! [v20] : ( ~ (powerset(v19) = v20) | ? [v21] : ? [v22] : (in(v20, v18) = v22 & in(v19, v18) = v21 & ( ~ (v21 = 0) | v22 = 0))) & ! [v19] : ! [v20] : ( ~ (subset(v20, v19) = 0) | ? [v21] : ? [v22] : (in(v20, v18) = v22 & in(v19, v18) = v21 & ( ~ (v21 = 0) | v22 = 0))) & ! [v19] : ( ~ (subset(v19, v18) = 0) | ? [v20] : ? [v21] : (are_equipotent(v19, v18) = v20 & in(v19, v18) = v21 & (v21 = 0 | v20 = 0))) & ! [v19] : ( ~ (in(v19, v18) = 0) | ? [v20] : (powerset(v19) = v20 & in(v20, v18) = 0))) & ? [v17] : ? [v18] : (in(v17, v18) = 0 & ! [v19] : ! [v20] : (v20 = 0 | ~ (are_equipotent(v19, v18) = v20) | ? [v21] : ? [v22] : (subset(v19, v18) = v21 & in(v19, v18) = v22 & ( ~ (v21 = 0) | v22 = 0))) & ! [v19] : ! [v20] : (v20 = 0 | ~ (in(v19, v18) = v20) | ? [v21] : ? [v22] : (are_equipotent(v19, v18) = v22 & subset(v19, v18) = v21 & ( ~ (v21 = 0) | v22 = 0))) & ! [v19] : ! [v20] : ( ~ (subset(v20, v19) = 0) | ? [v21] : ? [v22] : (in(v20, v18) = v22 & in(v19, v18) = v21 & ( ~ (v21 = 0) | v22 = 0))) & ! [v19] : ( ~ (subset(v19, v18) = 0) | ? [v20] : ? [v21] : (are_equipotent(v19, v18) = v20 & in(v19, v18) = v21 & (v21 = 0 | v20 = 0))) & ! [v19] : ( ~ (in(v19, v18) = 0) | ? [v20] : (in(v20, v18) = 0 & ! [v21] : ! [v22] : (v22 = 0 | ~ (in(v21, v20) = v22) | ? [v23] : ( ~ (v23 = 0) & subset(v21, v19) = v23)) & ! [v21] : ( ~ (subset(v21, v19) = 0) | in(v21, v20) = 0)))) & ? [v17] : ? [v18] : (in(v17, v18) = 0 & ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : (subset(v20, v19) = v22 & in(v20, v18) = v23 & in(v19, v18) = v21 & ( ~ (v22 = 0) | ~ (v21 = 0) | v23 = 0)) & ? [v19] : ? [v20] : ? [v21] : ? [v22] : (are_equipotent(v19, v18) = v21 & subset(v19, v18) = v20 & in(v19, v18) = v22 & ( ~ (v20 = 0) | v22 = 0 | v21 = 0)) & ? [v19] : ? [v20] : ? [v21] : ? [v22] : (powerset(v19) = v21 & in(v21, v18) = v22 & in(v19, v18) = v20 & ( ~ (v20 = 0) | v22 = 0))) & ? [v17] : ? [v18] : (in(v17, v18) = 0 & ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : (subset(v20, v19) = v22 & in(v20, v18) = v23 & in(v19, v18) = v21 & ( ~ (v22 = 0) | ~ (v21 = 0) | v23 = 0)) & ? [v19] : ? [v20] : ? [v21] : ? [v22] : (are_equipotent(v19, v18) = v21 & subset(v19, v18) = v20 & in(v19, v18) = v22 & ( ~ (v20 = 0) | v22 = 0 | v21 = 0)) & ? [v19] : ? [v20] : ? [v21] : ((v21 = 0 & in(v20, v18) = 0 & ? [v22] : ? [v23] : ? [v24] : (subset(v22, v19) = v23 & in(v22, v20) = v24 & ( ~ (v23 = 0) | v24 = 0))) | ( ~ (v20 = 0) & in(v19, v18) = v20))) & ? [v17] : (v17 = empty_set | ? [v18] : in(v18, v17) = 0) & ((v7 = v1 & v6 = 0 & ~ (v4 = 0)) | (v4 = 0 & ( ~ (v7 = v1) | ~ (v6 = 0)))))
% 141.14/84.45 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9, all_0_10_10, all_0_11_11, all_0_12_12, all_0_13_13, all_0_14_14, all_0_15_15, all_0_16_16 yields:
% 141.14/84.45 | (1) ~ (all_0_3_3 = 0) & ~ (all_0_5_5 = 0) & relation_empty_yielding(all_0_7_7) = 0 & relation_empty_yielding(empty_set) = 0 & relation_rng(empty_set) = empty_set & relation_dom(all_0_14_14) = all_0_11_11 & relation_dom(empty_set) = empty_set & apply(all_0_14_14, all_0_16_16) = all_0_9_9 & powerset(empty_set) = all_0_8_8 & singleton(empty_set) = all_0_8_8 & ordered_pair(all_0_16_16, all_0_15_15) = all_0_13_13 & relation(all_0_0_0) = 0 & relation(all_0_1_1) = 0 & relation(all_0_4_4) = 0 & relation(all_0_7_7) = 0 & relation(all_0_14_14) = 0 & relation(empty_set) = 0 & empty(all_0_1_1) = 0 & empty(all_0_2_2) = 0 & empty(all_0_4_4) = all_0_3_3 & empty(all_0_6_6) = all_0_5_5 & empty(empty_set) = 0 & function(all_0_0_0) = 0 & function(all_0_14_14) = 0 & in(all_0_13_13, all_0_14_14) = all_0_12_12 & in(all_0_16_16, all_0_11_11) = all_0_10_10 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (relation_composition(v5, v3) = v6) | ~ (identity_relation(v2) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ (in(v4, v6) = v7) | ? [v8] : ? [v9] : ? [v10] : (relation(v3) = v8 & in(v4, v3) = v10 & in(v0, v2) = v9 & ( ~ (v8 = 0) | (( ~ (v10 = 0) | ~ (v9 = 0) | v7 = 0) & ( ~ (v7 = 0) | (v10 = 0 & v9 = 0)))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (relation_composition(v0, v1) = v2) | ~ (ordered_pair(v6, v4) = v7) | ~ (ordered_pair(v3, v4) = v5) | ~ (relation(v2) = 0) | ~ (relation(v0) = 0) | ? [v8] : ? [v9] : ? [v10] : ((v8 = 0 & in(v5, v2) = 0) | ( ~ (v8 = 0) & relation(v1) = v8) | (ordered_pair(v3, v6) = v8 & in(v8, v0) = v9 & in(v7, v1) = v10 & ( ~ (v10 = 0) | ~ (v9 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (relation_composition(v0, v1) = v2) | ~ (ordered_pair(v3, v6) = v7) | ~ (ordered_pair(v3, v4) = v5) | ~ (relation(v2) = 0) | ~ (relation(v0) = 0) | ? [v8] : ? [v9] : ? [v10] : ((v8 = 0 & in(v5, v2) = 0) | ( ~ (v8 = 0) & relation(v1) = v8) | (ordered_pair(v6, v4) = v9 & in(v9, v1) = v10 & in(v7, v0) = v8 & ( ~ (v10 = 0) | ~ (v8 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ (in(v4, v5) = v6) | ? [v7] : ? [v8] : (in(v1, v3) = v8 & in(v0, v2) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (cartesian_product2(v1, v3) = v5) | ~ (cartesian_product2(v0, v2) = v4) | ~ (subset(v4, v5) = v6) | ? [v7] : ? [v8] : (subset(v2, v3) = v8 & subset(v0, v1) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = 0 | ~ (cartesian_product2(v0, v1) = v2) | ~ (ordered_pair(v5, v6) = v3) | ~ (in(v3, v2) = v4) | ? [v7] : ? [v8] : (in(v6, v1) = v8 & in(v5, v0) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = 0 | ~ (relation_inverse_image(v0, v1) = v2) | ~ (ordered_pair(v3, v5) = v6) | ~ (relation(v0) = 0) | ~ (in(v3, v2) = v4) | ? [v7] : ? [v8] : (in(v6, v0) = v7 & in(v5, v1) = v8 & ( ~ (v8 = 0) | ~ (v7 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = 0 | ~ (relation_image(v0, v1) = v2) | ~ (ordered_pair(v5, v3) = v6) | ~ (relation(v0) = 0) | ~ (in(v3, v2) = v4) | ? [v7] : ? [v8] : (in(v6, v0) = v7 & in(v5, v1) = v8 & ( ~ (v8 = 0) | ~ (v7 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v0 = empty_set | ~ (subset_complement(v0, v2) = v3) | ~ (powerset(v0) = v1) | ~ (in(v4, v3) = v5) | ? [v6] : ? [v7] : (( ~ (v6 = 0) & element(v2, v1) = v6) | (element(v4, v0) = v6 & in(v4, v2) = v7 & ( ~ (v6 = 0) | v7 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v0 = empty_set | ~ (subset_complement(v0, v2) = v3) | ~ (powerset(v0) = v1) | ~ (in(v4, v2) = v5) | ? [v6] : ? [v7] : (( ~ (v6 = 0) & element(v2, v1) = v6) | (element(v4, v0) = v6 & in(v4, v3) = v7 & ( ~ (v6 = 0) | v7 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (set_difference(v1, v3) = v4) | ~ (singleton(v2) = v3) | ~ (subset(v0, v4) = v5) | ? [v6] : ? [v7] : (subset(v0, v1) = v6 & in(v2, v0) = v7 & ( ~ (v6 = 0) | v7 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (set_difference(v1, v2) = v4) | ~ (set_difference(v0, v2) = v3) | ~ (subset(v3, v4) = v5) | ? [v6] : ( ~ (v6 = 0) & subset(v0, v1) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (relation_inverse_image(v2, v1) = v4) | ~ (relation_inverse_image(v2, v0) = v3) | ~ (subset(v3, v4) = v5) | ? [v6] : ? [v7] : (subset(v0, v1) = v7 & relation(v2) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (subset(v3, v4) = v5) | ~ (set_intersection2(v1, v2) = v4) | ~ (set_intersection2(v0, v2) = v3) | ? [v6] : ( ~ (v6 = 0) & subset(v0, v1) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = 0 | ~ (relation_inverse_image(v0, v1) = v2) | ~ (relation(v0) = 0) | ~ (in(v5, v1) = 0) | ~ (in(v3, v2) = v4) | ? [v6] : ? [v7] : ( ~ (v7 = 0) & ordered_pair(v3, v5) = v6 & in(v6, v0) = v7)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = 0 | ~ (relation_image(v0, v1) = v2) | ~ (relation(v0) = 0) | ~ (in(v5, v1) = 0) | ~ (in(v3, v2) = v4) | ? [v6] : ? [v7] : ( ~ (v7 = 0) & ordered_pair(v5, v3) = v6 & in(v6, v0) = v7)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = 0 | ~ (relation_rng(v0) = v1) | ~ (ordered_pair(v4, v2) = v5) | ~ (in(v2, v1) = v3) | ? [v6] : (( ~ (v6 = 0) & relation(v0) = v6) | ( ~ (v6 = 0) & in(v5, v0) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = 0 | ~ (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v4) = v5) | ~ (in(v2, v1) = v3) | ? [v6] : (( ~ (v6 = 0) & relation(v0) = v6) | ( ~ (v6 = 0) & in(v5, v0) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_composition(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ (relation(v2) = 0) | ~ (relation(v0) = 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) | ( ~ (v6 = 0) & in(v5, v2) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_rng(v3) = v4) | ~ (relation_rng_restriction(v1, v2) = v3) | ~ (in(v0, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (relation_rng(v2) = v8 & relation(v2) = v6 & in(v0, v8) = v9 & in(v0, v1) = v7 & ( ~ (v6 = 0) | (( ~ (v9 = 0) | ~ (v7 = 0) | v5 = 0) & ( ~ (v5 = 0) | (v9 = 0 & v7 = 0)))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_dom(v3) = v4) | ~ (relation_dom_restriction(v2, v1) = v3) | ~ (in(v0, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (relation_dom(v2) = v8 & relation(v2) = v6 & in(v0, v8) = v9 & in(v0, v1) = v7 & ( ~ (v6 = 0) | (( ~ (v9 = 0) | ~ (v7 = 0) | v5 = 0) & ( ~ (v5 = 0) | (v9 = 0 & v7 = 0)))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ (in(v4, v5) = 0) | (in(v1, v3) = 0 & in(v0, v2) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v1) = v4) | ~ (cartesian_product2(v2, v0) = v3) | ~ (subset(v3, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (cartesian_product2(v1, v2) = v8 & cartesian_product2(v0, v2) = v7 & subset(v7, v8) = v9 & subset(v0, v1) = v6 & ( ~ (v6 = 0) | (v9 = 0 & v5 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v1, v2) = v4) | ~ (cartesian_product2(v0, v2) = v3) | ~ (subset(v3, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (cartesian_product2(v2, v1) = v8 & cartesian_product2(v2, v0) = v7 & subset(v7, v8) = v9 & subset(v0, v1) = v6 & ( ~ (v6 = 0) | (v9 = 0 & v5 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ (relation(v2) = 0) | ? [v6] : ? [v7] : ? [v8] : (( ~ (v6 = 0) & relation(v1) = v6) | (in(v5, v2) = v8 & in(v5, v1) = v7 & in(v4, v0) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v8 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ (relation(v2) = 0) | ? [v6] : ? [v7] : ? [v8] : (( ~ (v6 = 0) & relation(v1) = v6) | (in(v5, v2) = v6 & in(v5, v1) = v8 & in(v4, v0) = v7 & ( ~ (v6 = 0) | (v8 = 0 & v7 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ (relation(v2) = 0) | ~ (relation(v0) = 0) | ? [v6] : ? [v7] : ? [v8] : (in(v5, v2) = v8 & in(v5, v0) = v7 & in(v3, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v8 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ (relation(v2) = 0) | ~ (relation(v0) = 0) | ? [v6] : ? [v7] : ? [v8] : (in(v5, v2) = v6 & in(v5, v0) = v8 & in(v3, v1) = v7 & ( ~ (v6 = 0) | (v8 = 0 & v7 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v0 = empty_set | ~ (set_meet(v0) = v1) | ~ (in(v2, v3) = v4) | ~ (in(v2, v1) = 0) | ? [v5] : ( ~ (v5 = 0) & in(v3, v0) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v2) = v4) | ? [v5] : ? [v6] : (in(v3, v1) = v6 & in(v3, v0) = v5 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v6 & in(v3, v0) = v5 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (element(v1, v3) = 0) | ~ (element(v0, v2) = v4) | ~ (powerset(v2) = v3) | ? [v5] : ( ~ (v5 = 0) & in(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (element(v1, v2) = 0) | ~ (powerset(v0) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ( ~ (v5 = 0) & in(v3, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (subset(v3, v2) = v4) | ~ (unordered_pair(v0, v1) = v3) | ? [v5] : ? [v6] : (in(v1, v2) = v6 & in(v0, v2) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (subset(v3, v1) = v4) | ~ (set_union2(v0, v2) = v3) | ? [v5] : ? [v6] : (subset(v2, v1) = v6 & subset(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (subset(v0, v3) = v4) | ~ (set_intersection2(v1, v2) = v3) | ? [v5] : ? [v6] : (subset(v0, v2) = v6 & subset(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v2) = v4) | ? [v5] : ? [v6] : (in(v3, v1) = v6 & in(v3, v0) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v2) = v4) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & ~ (v5 = 0) & in(v3, v1) = v6 & in(v3, v0) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v5 & in(v3, v0) = v6 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v1 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v0 | v2 = v0 | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (union(v0) = v1) | ~ (in(v4, v0) = 0) | ~ (in(v2, v1) = v3) | ? [v5] : ( ~ (v5 = 0) & in(v2, v4) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (union(v0) = v1) | ~ (in(v2, v4) = 0) | ~ (in(v2, v1) = v3) | ? [v5] : ( ~ (v5 = 0) & in(v4, v0) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v0 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (subset_difference(v4, v3, v2) = v1) | ~ (subset_difference(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v0 = empty_set | ~ (subset_complement(v0, v2) = v3) | ~ (element(v4, v0) = 0) | ~ (powerset(v0) = v1) | ? [v5] : ? [v6] : (( ~ (v5 = 0) & element(v2, v1) = v5) | (in(v4, v3) = v6 & in(v4, v2) = v5 & (v6 = 0 | v5 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (disjoint(v1, v3) = v4) | ~ (element(v1, v2) = 0) | ~ (powerset(v0) = v2) | ? [v5] : ? [v6] : ? [v7] : (subset_complement(v0, v3) = v6 & element(v3, v2) = v5 & subset(v1, v6) = v7 & ( ~ (v5 = 0) | (( ~ (v7 = 0) | v4 = 0) & ( ~ (v4 = 0) | v7 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_inverse(v0) = v1) | ~ (ordered_pair(v3, v2) = v4) | ~ (relation(v1) = 0) | ? [v5] : ? [v6] : ? [v7] : (( ~ (v5 = 0) & relation(v0) = v5) | (ordered_pair(v2, v3) = v6 & in(v6, v1) = v7 & in(v4, v0) = v5 & ( ~ (v5 = 0) | v7 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_inverse(v0) = v1) | ~ (ordered_pair(v3, v2) = v4) | ~ (relation(v1) = 0) | ? [v5] : ? [v6] : ? [v7] : (( ~ (v5 = 0) & relation(v0) = v5) | (ordered_pair(v2, v3) = v5 & in(v5, v1) = v6 & in(v4, v0) = v7 & ( ~ (v6 = 0) | v7 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_inverse(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ (relation(v1) = 0) | ? [v5] : ? [v6] : ? [v7] : (( ~ (v5 = 0) & relation(v0) = v5) | (ordered_pair(v3, v2) = v6 & in(v6, v0) = v7 & in(v4, v1) = v5 & ( ~ (v5 = 0) | v7 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_inverse(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ (relation(v1) = 0) | ? [v5] : ? [v6] : ? [v7] : (( ~ (v5 = 0) & relation(v0) = v5) | (ordered_pair(v3, v2) = v5 & in(v5, v0) = v6 & in(v4, v1) = v7 & ( ~ (v6 = 0) | v7 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (subset_complement(v0, v3) = v4) | ~ (element(v1, v2) = 0) | ~ (powerset(v0) = v2) | ? [v5] : ? [v6] : ? [v7] : (disjoint(v1, v3) = v6 & element(v3, v2) = v5 & subset(v1, v4) = v7 & ( ~ (v5 = 0) | (( ~ (v7 = 0) | v6 = 0) & ( ~ (v6 = 0) | v7 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v5 & in(v3, v0) = v6 & ( ~ (v5 = 0) | (v6 = 0 & ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | (v4 = 0 & ~ (v6 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ((apply(v0, v2) = v6 & in(v4, v0) = v7 & in(v2, v1) = v5 & ( ~ (v5 = 0) | (( ~ (v7 = 0) | v6 = v3) & ( ~ (v6 = v3) | v7 = 0)))) | (relation(v0) = v5 & function(v0) = v6 & ( ~ (v6 = 0) | ~ (v5 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_inverse_image(v2, v1) = v3) | ~ (in(v0, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : (relation_rng(v2) = v6 & relation(v2) = v5 & ( ~ (v5 = 0) | (( ~ (v4 = 0) | (v11 = 0 & v10 = 0 & v8 = 0 & ordered_pair(v0, v7) = v9 & in(v9, v2) = 0 & in(v7, v6) = 0 & in(v7, v1) = 0)) & (v4 = 0 | ( ! [v12] : ! [v13] : ( ~ (ordered_pair(v0, v12) = v13) | ? [v14] : ? [v15] : ? [v16] : (in(v13, v2) = v15 & in(v12, v6) = v14 & in(v12, v1) = v16 & ( ~ (v16 = 0) | ~ (v15 = 0) | ~ (v14 = 0)))) & ! [v12] : ( ~ (in(v12, v6) = 0) | ? [v13] : ? [v14] : ? [v15] : (ordered_pair(v0, v12) = v13 & in(v13, v2) = v14 & in(v12, v1) = v15 & ( ~ (v15 = 0) | ~ (v14 = 0)))) & ! [v12] : ( ~ (in(v12, v1) = 0) | ? [v13] : ? [v14] : ? [v15] : (ordered_pair(v0, v12) = v14 & in(v14, v2) = v15 & in(v12, v6) = v13 & ( ~ (v15 = 0) | ~ (v13 = 0)))))))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_image(v2, v1) = v3) | ~ (in(v0, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : (relation_dom(v2) = v6 & relation(v2) = v5 & ( ~ (v5 = 0) | (( ~ (v4 = 0) | (v11 = 0 & v10 = 0 & v8 = 0 & ordered_pair(v7, v0) = v9 & in(v9, v2) = 0 & in(v7, v6) = 0 & in(v7, v1) = 0)) & (v4 = 0 | ( ! [v12] : ! [v13] : ( ~ (ordered_pair(v12, v0) = v13) | ? [v14] : ? [v15] : ? [v16] : (in(v13, v2) = v15 & in(v12, v6) = v14 & in(v12, v1) = v16 & ( ~ (v16 = 0) | ~ (v15 = 0) | ~ (v14 = 0)))) & ! [v12] : ( ~ (in(v12, v6) = 0) | ? [v13] : ? [v14] : ? [v15] : (ordered_pair(v12, v0) = v13 & in(v13, v2) = v14 & in(v12, v1) = v15 & ( ~ (v15 = 0) | ~ (v14 = 0)))) & ! [v12] : ( ~ (in(v12, v1) = 0) | ? [v13] : ? [v14] : ? [v15] : (ordered_pair(v12, v0) = v14 & in(v14, v2) = v15 & in(v12, v6) = v13 & ( ~ (v15 = 0) | ~ (v13 = 0)))))))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_rng_restriction(v0, v3) = v4) | ~ (relation_dom_restriction(v2, v1) = v3) | ? [v5] : ? [v6] : ? [v7] : (relation_rng_restriction(v0, v2) = v6 & relation_dom_restriction(v6, v1) = v7 & relation(v2) = v5 & ( ~ (v5 = 0) | v7 = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_rng_restriction(v0, v2) = v3) | ~ (relation_dom_restriction(v3, v1) = v4) | ? [v5] : ? [v6] : ? [v7] : (relation_rng_restriction(v0, v6) = v7 & relation_dom_restriction(v2, v1) = v6 & relation(v2) = v5 & ( ~ (v5 = 0) | v7 = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (subset(v0, v1) = 0) | ~ (ordered_pair(v2, v3) = v4) | ~ (relation(v0) = 0) | ? [v5] : ? [v6] : (( ~ (v5 = 0) & relation(v1) = v5) | (in(v4, v1) = v6 & in(v4, v0) = v5 & ( ~ (v5 = 0) | v6 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (identity_relation(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ (relation(v1) = 0) | ? [v5] : ? [v6] : (in(v4, v1) = v5 & in(v2, v0) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v3 = v2)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v5 & in(v3, v0) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v6 & in(v3, v0) = v5 & (v6 = 0 | ( ~ (v5 = 0) & ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v6 & in(v3, v1) = v5 & (v6 = 0 | ( ~ (v5 = 0) & ~ (v4 = 0))))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (relation_dom(v1) = v2) | ~ (in(v3, v2) = v4) | ? [v5] : ? [v6] : ((apply(v1, v3) = v5 & ( ~ (v5 = v0) | v0 = empty_set) & ( ~ (v0 = empty_set) | v5 = empty_set)) | (relation(v1) = v5 & function(v1) = v6 & ( ~ (v6 = 0) | ~ (v5 = 0))))) & ! [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(v13, v5) = v14) | ? [v15] : ? [v16] : ? [v17] : (ordered_pair(v4, v13) = v15 & in(v15, v0) = v16 & in(v14, v1) = v17 & ( ~ (v17 = 0) | ~ (v16 = 0)))) & ! [v13] : ! [v14] : ( ~ (ordered_pair(v4, v13) = v14) | ? [v15] : ? [v16] : ? [v17] : (ordered_pair(v13, v5) = v16 & in(v16, v1) = v17 & in(v14, v0) = v15 & ( ~ (v17 = 0) | ~ (v15 = 0)))))) & (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 = v2 | ~ (relation_rng_restriction(v0, v1) = v2) | ~ (relation(v3) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (( ~ (v4 = 0) & relation(v1) = v4) | (ordered_pair(v4, v5) = v6 & in(v6, v3) = v7 & in(v6, v1) = v9 & in(v5, v0) = v8 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0)) & (v7 = 0 | (v9 = 0 & v8 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (relation_dom_restriction(v0, v1) = v3) | ~ (relation(v2) = 0) | ~ (relation(v0) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (ordered_pair(v4, v5) = v6 & in(v6, v2) = v7 & in(v6, v0) = v9 & in(v4, v1) = v8 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0)) & (v7 = 0 | (v9 = 0 & v8 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v3 = v0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v3, v2) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (singleton(v0) = v2) | ~ (set_union2(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_difference(v0, v2) = v3) | ~ (singleton(v1) = v2) | in(v1, v0) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = empty_set | ~ (relation_dom(v0) = v1) | ~ (apply(v0, v2) = v3) | ? [v4] : ? [v5] : ((v4 = 0 & in(v2, v1) = 0) | (relation(v0) = v4 & function(v0) = v5 & ( ~ (v5 = 0) | ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | v0 = empty_set | ~ (set_meet(v0) = v1) | ~ (in(v2, v1) = v3) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & in(v4, v0) = 0 & in(v2, v4) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (disjoint(v2, v1) = v3) | ~ (singleton(v0) = v2) | in(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (disjoint(v1, v2) = 0) | ~ (disjoint(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (disjoint(v0, v2) = v3) | ~ (subset(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & disjoint(v1, v2) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (union(v1) = v2) | ~ (subset(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (element(v0, v2) = v3) | ~ (powerset(v1) = v2) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & in(v4, v1) = v5 & in(v4, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (element(v0, v2) = v3) | ~ (powerset(v1) = v2) | ? [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) & element(v1, v4) = v5 & powerset(v2) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v0) = v1) | ~ (subset(v2, v0) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v2, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v0) = v1) | ~ (in(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v2, v0) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (singleton(v0) = v2) | ~ (subset(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v1, v2) = 0) | ~ (subset(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v2) = v3) | ~ (subset(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & subset(v1, v2) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v2, v0) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v1, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v0, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (are_equipotent(v3, v2) = v1) | ~ (are_equipotent(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (meet_of_subsets(v3, v2) = v1) | ~ (meet_of_subsets(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union_of_subsets(v3, v2) = v1) | ~ (union_of_subsets(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (complements_of_subsets(v3, v2) = v1) | ~ (complements_of_subsets(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 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset_complement(v3, v2) = v1) | ~ (subset_complement(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (singleton(v1) = v3) | ~ (singleton(v0) = v2) | ~ (subset(v2, v3) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_inverse_image(v3, v2) = v1) | ~ (relation_inverse_image(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_image(v3, v2) = v1) | ~ (relation_image(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_rng_restriction(v3, v2) = v1) | ~ (relation_rng_restriction(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_dom_restriction(v3, v2) = v1) | ~ (relation_dom_restriction(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(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 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(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 | ~ (proper_subset(v3, v2) = v1) | ~ (proper_subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = empty_set | ~ (element(v1, v3) = 0) | ~ (powerset(v2) = v3) | ~ (powerset(v0) = v2) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (subset_difference(v0, v6, v7) = v5 & meet_of_subsets(v0, v1) = v7 & union_of_subsets(v0, v4) = v5 & complements_of_subsets(v0, v1) = v4 & cast_to_subset(v0) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = empty_set | ~ (element(v1, v3) = 0) | ~ (powerset(v2) = v3) | ~ (powerset(v0) = v2) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (subset_difference(v0, v4, v5) = v6 & meet_of_subsets(v0, v7) = v6 & union_of_subsets(v0, v1) = v5 & complements_of_subsets(v0, v1) = v7 & cast_to_subset(v0) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = empty_set | ~ (element(v1, v3) = 0) | ~ (powerset(v2) = v3) | ~ (powerset(v0) = v2) | ? [v4] : ( ~ (v4 = empty_set) & complements_of_subsets(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = empty_set | ~ (set_meet(v0) = v1) | ~ (in(v3, v0) = 0) | ~ (in(v2, v1) = 0) | in(v2, v3) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_difference(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (set_difference(v1, v2) = v7 & element(v2, v4) = v6 & element(v1, v4) = v5 & powerset(v0) = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | v7 = v3))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_difference(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (element(v3, v4) = v7 & element(v2, v4) = v6 & element(v1, v4) = v5 & powerset(v0) = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | v7 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_composition(v2, v1) = v3) | ~ (identity_relation(v0) = v2) | ? [v4] : ? [v5] : (relation_dom_restriction(v1, v0) = v5 & relation(v1) = v4 & ( ~ (v4 = 0) | v5 = v3))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_composition(v0, v2) = v3) | ~ (relation_rng(v0) = v1) | ? [v4] : ? [v5] : ? [v6] : (( ~ (v4 = 0) & relation(v0) = v4) | (relation_rng(v3) = v5 & relation_image(v2, v1) = v6 & relation(v2) = v4 & ( ~ (v4 = 0) | v6 = v5)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_composition(v0, v2) = v3) | ~ (relation_dom(v0) = v1) | ? [v4] : ? [v5] : ? [v6] : (( ~ (v4 = 0) & relation(v0) = v4) | (relation_dom(v3) = v5 & subset(v5, v1) = v6 & relation(v2) = v4 & ( ~ (v4 = 0) | v6 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_complement(v0, v2) = v3) | ~ (in(v1, v3) = 0) | ? [v4] : ? [v5] : ? [v6] : (element(v2, v4) = v5 & powerset(v0) = v4 & in(v1, v2) = v6 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng(v1) = v2) | ~ (set_intersection2(v2, v0) = v3) | ? [v4] : ? [v5] : ? [v6] : (relation_rng(v5) = v6 & relation_rng_restriction(v0, v1) = v5 & relation(v1) = v4 & ( ~ (v4 = 0) | v6 = v3))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng(v0) = v1) | ~ (relation_image(v2, v1) = v3) | ? [v4] : ? [v5] : ? [v6] : (( ~ (v4 = 0) & relation(v0) = v4) | (relation_composition(v0, v2) = v5 & relation_rng(v5) = v6 & relation(v2) = v4 & ( ~ (v4 = 0) | v6 = v3)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v0) = 0) | ? [v4] : ? [v5] : (in(v3, v2) = v5 & in(v3, v1) = v4 & (v5 = 0 | v4 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom(v1) = v2) | ~ (set_intersection2(v2, v0) = v3) | ? [v4] : ? [v5] : ? [v6] : (relation_dom(v5) = v6 & relation_dom_restriction(v1, v0) = v5 & relation(v1) = v4 & ( ~ (v4 = 0) | v6 = v3))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom(v1) = v2) | ~ (set_intersection2(v2, v0) = v3) | ? [v4] : ? [v5] : ? [v6] : (relation_image(v1, v3) = v6 & relation_image(v1, v0) = v5 & relation(v1) = v4 & ( ~ (v4 = 0) | v6 = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cartesian_product2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ? [v4] : ? [v5] : (ordered_pair(v4, v5) = v3 & in(v5, v1) = 0 & in(v4, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (element(v3, v2) = 0) | ~ (element(v1, v2) = 0) | ~ (powerset(v0) = v2) | ? [v4] : ? [v5] : ? [v6] : (disjoint(v1, v3) = v4 & subset_complement(v0, v3) = v5 & subset(v1, v5) = v6 & ( ~ (v6 = 0) | v4 = 0) & ( ~ (v4 = 0) | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (element(v1, v3) = 0) | ~ (powerset(v2) = v3) | ~ (powerset(v0) = v2) | ? [v4] : (meet_of_subsets(v0, v1) = v4 & element(v4, v2) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (element(v1, v3) = 0) | ~ (powerset(v2) = v3) | ~ (powerset(v0) = v2) | ? [v4] : (meet_of_subsets(v0, v1) = v4 & set_meet(v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (element(v1, v3) = 0) | ~ (powerset(v2) = v3) | ~ (powerset(v0) = v2) | ? [v4] : (union_of_subsets(v0, v1) = v4 & union(v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (element(v1, v3) = 0) | ~ (powerset(v2) = v3) | ~ (powerset(v0) = v2) | ? [v4] : (union_of_subsets(v0, v1) = v4 & element(v4, v2) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (element(v1, v3) = 0) | ~ (powerset(v2) = v3) | ~ (powerset(v0) = v2) | ? [v4] : (complements_of_subsets(v0, v4) = v1 & complements_of_subsets(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (element(v1, v3) = 0) | ~ (powerset(v2) = v3) | ~ (powerset(v0) = v2) | ? [v4] : (complements_of_subsets(v0, v1) = v4 & element(v4, v3) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (element(v1, v3) = 0) | ~ (powerset(v2) = v3) | ~ (powerset(v0) = v2) | ? [v4] : (complements_of_subsets(v0, v1) = v4 & ! [v5] : ! [v6] : ( ~ (subset_complement(v0, v5) = v6) | ~ (element(v4, v3) = 0) | ? [v7] : ? [v8] : ? [v9] : (element(v5, v2) = v7 & in(v6, v1) = v9 & in(v5, v4) = v8 & ( ~ (v7 = 0) | (( ~ (v9 = 0) | v8 = 0) & ( ~ (v8 = 0) | v9 = 0))))) & ! [v5] : ! [v6] : ( ~ (element(v4, v3) = 0) | ~ (in(v5, v4) = v6) | ? [v7] : ? [v8] : ? [v9] : (subset_complement(v0, v5) = v8 & element(v5, v2) = v7 & in(v8, v1) = v9 & ( ~ (v7 = 0) | (( ~ (v9 = 0) | v6 = 0) & ( ~ (v6 = 0) | v9 = 0))))) & ! [v5] : (v5 = v4 | ~ (element(v5, v3) = 0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (subset_complement(v0, v6) = v8 & element(v6, v2) = 0 & in(v8, v1) = v9 & in(v6, v5) = v7 & ( ~ (v9 = 0) | ~ (v7 = 0)) & (v9 = 0 | v7 = 0))) & ! [v5] : ( ~ (element(v5, v2) = 0) | ~ (element(v4, v3) = 0) | ? [v6] : ? [v7] : ? [v8] : (subset_complement(v0, v5) = v7 & in(v7, v1) = v8 & in(v5, v4) = v6 & ( ~ (v8 = 0) | v6 = 0) & ( ~ (v6 = 0) | v8 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (element(v1, v3) = 0) | ~ (powerset(v2) = v3) | ~ (in(v0, v1) = 0) | element(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (element(v1, v3) = 0) | ~ (powerset(v2) = v3) | ~ (in(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (element(v1, v2) = 0) | ~ (powerset(v0) = v2) | ~ (in(v3, v1) = 0) | in(v3, v0) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_inverse_image(v0, v1) = v2) | ~ (relation(v0) = 0) | ~ (in(v3, v2) = 0) | ? [v4] : ? [v5] : (ordered_pair(v3, v4) = v5 & in(v5, v0) = 0 & in(v4, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_image(v0, v1) = v2) | ~ (relation(v0) = 0) | ~ (in(v3, v2) = 0) | ? [v4] : ? [v5] : (ordered_pair(v4, v3) = v5 & in(v5, v0) = 0 & in(v4, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset(v3, v2) = 0) | ~ (unordered_pair(v0, v1) = v3) | (in(v1, v2) = 0 & in(v0, v2) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (identity_relation(v0) = v1) | ~ (ordered_pair(v2, v2) = v3) | ~ (relation(v1) = 0) | ? [v4] : ? [v5] : (in(v3, v1) = v5 & in(v2, v0) = v4 & ( ~ (v4 = 0) | v5 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (ordered_pair(v1, v2) = v3) | ~ (relation(v0) = 0) | ? [v4] : ? [v5] : (in(v3, v0) = v5 & in(v3, v0) = v4 & ( ~ (v4 = 0) | v5 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (ordered_pair(v0, v1) = v3) | ~ (in(v3, v2) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (relation_rng(v2) = v7 & relation_dom(v2) = v5 & relation(v2) = v4 & in(v1, v7) = v8 & in(v0, v5) = v6 & ( ~ (v4 = 0) | (v8 = 0 & v6 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (ordered_pair(v0, v1) = v3) | ~ (in(v3, v2) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (relation_field(v2) = v5 & relation(v2) = v4 & in(v1, v5) = v7 & in(v0, v5) = v6 & ( ~ (v4 = 0) | (v7 = 0 & v6 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ? [v4] : ( ~ (v4 = 0) & disjoint(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | (in(v3, v1) = 0 & in(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v1) = 0) | ? [v4] : ? [v5] : (in(v3, v2) = v5 & in(v3, v0) = v4 & ( ~ (v4 = 0) | v5 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v0) = 0) | ? [v4] : ? [v5] : (in(v3, v2) = v5 & in(v3, v1) = v4 & ( ~ (v4 = 0) | v5 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ? [v4] : ? [v5] : (in(v3, v1) = v5 & in(v3, v0) = v4 & (v5 = 0 | v4 = 0))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_difference(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | v7 = 0) & (v5 = 0 | (v6 = 0 & ~ (v7 = 0))))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (cartesian_product2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (in(v4, v0) = v5 & ( ~ (v5 = 0) | ! [v11] : ! [v12] : ( ~ (ordered_pair(v11, v12) = v4) | ? [v13] : ? [v14] : (in(v12, v2) = v14 & in(v11, v1) = v13 & ( ~ (v14 = 0) | ~ (v13 = 0))))) & (v5 = 0 | (v10 = v4 & v9 = 0 & v8 = 0 & ordered_pair(v6, v7) = v4 & in(v7, v2) = 0 & in(v6, v1) = 0)))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (relation_inverse_image(v1, v2) = v3) | ~ (relation(v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (in(v4, v0) = v5 & ( ~ (v5 = 0) | ( ! [v10] : ! [v11] : ( ~ (ordered_pair(v4, v10) = v11) | ? [v12] : ? [v13] : (in(v11, v1) = v12 & in(v10, v2) = v13 & ( ~ (v13 = 0) | ~ (v12 = 0)))) & ! [v10] : ( ~ (in(v10, v2) = 0) | ? [v11] : ? [v12] : ( ~ (v12 = 0) & ordered_pair(v4, v10) = v11 & in(v11, v1) = v12)))) & (v5 = 0 | (v9 = 0 & v8 = 0 & ordered_pair(v4, v6) = v7 & in(v7, v1) = 0 & in(v6, v2) = 0)))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (relation_image(v1, v2) = v3) | ~ (relation(v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (in(v4, v0) = v5 & ( ~ (v5 = 0) | ( ! [v10] : ! [v11] : ( ~ (ordered_pair(v10, v4) = v11) | ? [v12] : ? [v13] : (in(v11, v1) = v12 & in(v10, v2) = v13 & ( ~ (v13 = 0) | ~ (v12 = 0)))) & ! [v10] : ( ~ (in(v10, v2) = 0) | ? [v11] : ? [v12] : ( ~ (v12 = 0) & ordered_pair(v10, v4) = v11 & in(v11, v1) = v12)))) & (v5 = 0 | (v9 = 0 & v8 = 0 & ordered_pair(v6, v4) = v7 & in(v7, v1) = 0 & in(v6, v2) = 0)))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_intersection2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0)) & (v5 = 0 | (v7 = 0 & v6 = 0)))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_union2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & ( ~ (v5 = 0) | ( ~ (v7 = 0) & ~ (v6 = 0))) & (v7 = 0 | v6 = 0 | v5 = 0))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (unordered_pair(v1, v2) = v3) | ? [v4] : ? [v5] : (in(v4, v0) = v5 & ( ~ (v5 = 0) | ( ~ (v4 = v2) & ~ (v4 = v1))) & (v5 = 0 | v4 = v2 | v4 = v1))) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (relation_inverse(v0) = v1) | ~ (relation(v2) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (( ~ (v3 = 0) & relation(v0) = v3) | (ordered_pair(v4, v3) = v7 & ordered_pair(v3, v4) = v5 & in(v7, v0) = v8 & in(v5, v2) = v6 & ( ~ (v8 = 0) | ~ (v6 = 0)) & (v8 = 0 | v6 = 0)))) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (identity_relation(v0) = v2) | ~ (relation(v1) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (ordered_pair(v3, v4) = v5 & in(v5, v1) = v6 & in(v3, v0) = v7 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v4 = v3)) & (v6 = 0 | (v7 = 0 & v4 = v3)))) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (set_union2(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | v0 = empty_set | ~ (singleton(v1) = v2) | ~ (subset(v0, v2) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_difference(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & disjoint(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ (in(v2, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_intersection2(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_difference(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_intersection2(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & disjoint(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (proper_subset(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & disjoint(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ? [v4] : (set_intersection2(v0, v1) = v3 & in(v4, v3) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ( ~ (v3 = v0) & set_difference(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ( ~ (v3 = empty_set) & set_intersection2(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : (in(v3, v1) = 0 & in(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v1) = v0) | ~ (subset(v0, v0) = v2)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (subset(empty_set, v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (in(v0, v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ (relation(v0) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v6 = 0 & ~ (v7 = 0) & ordered_pair(v3, v4) = v5 & in(v5, v1) = v7 & in(v5, v0) = 0) | ( ~ (v3 = 0) & relation(v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & element(v0, v3) = v4 & powerset(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] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ( ~ (v3 = empty_set) & set_difference(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & proper_subset(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v1, v0) = v2) | ? [v3] : (set_difference(v0, v3) = v0 & singleton(v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & singleton(v0) = v3 & subset(v3, v1) = 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] : (v2 = 0 | ~ (in(v0, v1) = v2) | ? [v3] : (disjoint(v3, v1) = 0 & singleton(v0) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_empty_yielding(v2) = v1) | ~ (relation_empty_yielding(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_inverse(v2) = v1) | ~ (relation_inverse(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_field(v2) = v1) | ~ (relation_field(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cast_to_subset(v2) = v1) | ~ (cast_to_subset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (set_meet(v2) = v1) | ~ (set_meet(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (identity_relation(v2) = v1) | ~ (identity_relation(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = empty_set | ~ (meet_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (subset_difference(v0, v8, v2) = v9 & union_of_subsets(v0, v6) = v7 & complements_of_subsets(v0, v1) = v6 & cast_to_subset(v0) = v8 & element(v1, v4) = v5 & powerset(v3) = v4 & powerset(v0) = v3 & ( ~ (v5 = 0) | v9 = v7))) & ! [v0] : ! [v1] : ! [v2] : (v1 = empty_set | ~ (union_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (subset_difference(v0, v6, v2) = v7 & meet_of_subsets(v0, v8) = v9 & complements_of_subsets(v0, v1) = v8 & cast_to_subset(v0) = v6 & element(v1, v4) = v5 & powerset(v3) = v4 & powerset(v0) = v3 & ( ~ (v5 = 0) | v9 = v7))) & ! [v0] : ! [v1] : ! [v2] : (v1 = empty_set | ~ (complements_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (subset_difference(v0, v7, v8) = v9 & meet_of_subsets(v0, v1) = v8 & union_of_subsets(v0, v2) = v6 & cast_to_subset(v0) = v7 & element(v1, v4) = v5 & powerset(v3) = v4 & powerset(v0) = v3 & ( ~ (v5 = 0) | v9 = v6))) & ! [v0] : ! [v1] : ! [v2] : (v1 = empty_set | ~ (complements_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (subset_difference(v0, v6, v7) = v8 & meet_of_subsets(v0, v2) = v9 & union_of_subsets(v0, v1) = v7 & cast_to_subset(v0) = v6 & element(v1, v4) = v5 & powerset(v3) = v4 & powerset(v0) = v3 & ( ~ (v5 = 0) | v9 = v8))) & ! [v0] : ! [v1] : ! [v2] : (v0 = empty_set | ~ (relation_rng(v1) = v2) | ~ (subset(v0, v2) = 0) | ? [v3] : ? [v4] : (relation_inverse_image(v1, v0) = v4 & relation(v1) = v3 & ( ~ (v4 = empty_set) | ~ (v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : (v0 = empty_set | ~ (element(v2, v1) = 0) | ~ (powerset(v0) = v1) | ? [v3] : (subset_complement(v0, v2) = v3 & ! [v4] : ! [v5] : (v5 = 0 | ~ (in(v4, v3) = v5) | ? [v6] : ? [v7] : (element(v4, v0) = v6 & in(v4, v2) = v7 & ( ~ (v6 = 0) | v7 = 0))) & ! [v4] : ! [v5] : (v5 = 0 | ~ (in(v4, v2) = v5) | ? [v6] : ? [v7] : (element(v4, v0) = v6 & in(v4, v3) = v7 & ( ~ (v6 = 0) | v7 = 0))) & ! [v4] : ( ~ (element(v4, v0) = 0) | ? [v5] : ? [v6] : (in(v4, v3) = v6 & in(v4, v2) = v5 & (v6 = 0 | v5 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (meet_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (element(v2, v3) = v6 & element(v1, v4) = v5 & powerset(v3) = v4 & powerset(v0) = v3 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (meet_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (element(v1, v4) = v5 & powerset(v3) = v4 & powerset(v0) = v3 & set_meet(v1) = v6 & ( ~ (v5 = 0) | v6 = v2))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (union_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (union(v1) = v6 & element(v1, v4) = v5 & powerset(v3) = v4 & powerset(v0) = v3 & ( ~ (v5 = 0) | v6 = v2))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (union_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (element(v2, v3) = v6 & element(v1, v4) = v5 & powerset(v3) = v4 & powerset(v0) = v3 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (complements_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (complements_of_subsets(v0, v2) = v6 & element(v1, v4) = v5 & powerset(v3) = v4 & powerset(v0) = v3 & ( ~ (v5 = 0) | v6 = v1))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (complements_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (element(v2, v4) = v6 & element(v1, v4) = v5 & powerset(v3) = v4 & powerset(v0) = v3 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (complements_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (element(v1, v4) = v5 & powerset(v3) = v4 & powerset(v0) = v3 & ( ~ (v5 = 0) | ( ! [v6] : ! [v7] : ( ~ (subset_complement(v0, v6) = v7) | ~ (element(v2, v4) = 0) | ? [v8] : ? [v9] : ? [v10] : (element(v6, v3) = v8 & in(v7, v1) = v10 & in(v6, v2) = v9 & ( ~ (v8 = 0) | (( ~ (v10 = 0) | v9 = 0) & ( ~ (v9 = 0) | v10 = 0))))) & ! [v6] : ! [v7] : ( ~ (element(v2, v4) = 0) | ~ (in(v6, v2) = v7) | ? [v8] : ? [v9] : ? [v10] : (subset_complement(v0, v6) = v9 & element(v6, v3) = v8 & in(v9, v1) = v10 & ( ~ (v8 = 0) | (( ~ (v10 = 0) | v7 = 0) & ( ~ (v7 = 0) | v10 = 0))))) & ! [v6] : (v6 = v2 | ~ (element(v6, v4) = 0) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : (subset_complement(v0, v7) = v9 & element(v7, v3) = 0 & in(v9, v1) = v10 & in(v7, v6) = v8 & ( ~ (v10 = 0) | ~ (v8 = 0)) & (v10 = 0 | v8 = 0))) & ! [v6] : ( ~ (element(v6, v3) = 0) | ~ (element(v2, v4) = 0) | ? [v7] : ? [v8] : ? [v9] : (subset_complement(v0, v6) = v8 & in(v8, v1) = v9 & in(v6, v2) = v7 & ( ~ (v9 = 0) | v7 = 0) & ( ~ (v7 = 0) | v9 = 0))))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v1, v0) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation(v2) = v6 & relation(v1) = v4 & empty(v2) = v5 & empty(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | (v6 = 0 & v5 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ (relation(v0) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_rng(v2) = v4 & relation_rng(v1) = v5 & subset(v4, v5) = v6 & relation(v1) = v3 & ( ~ (v3 = 0) | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation(v2) = v6 & relation(v1) = v4 & empty(v2) = v5 & empty(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | (v6 = 0 & v5 = 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] : ( ~ (disjoint(v2, v1) = 0) | ~ (singleton(v0) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v1, v2) = 0) | ~ (subset(v0, v1) = 0) | disjoint(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v0, v1) = 0) | ~ (in(v2, v1) = 0) | ? [v3] : ( ~ (v3 = 0) & in(v2, v0) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v0, v1) = 0) | ~ (in(v2, v0) = 0) | ? [v3] : ( ~ (v3 = 0) & in(v2, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_complement(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (subset_complement(v0, v2) = v5 & element(v1, v3) = v4 & powerset(v0) = v3 & ( ~ (v4 = 0) | v5 = v1))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_complement(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (set_difference(v0, v1) = v5 & element(v1, v3) = v4 & powerset(v0) = v3 & ( ~ (v4 = 0) | v5 = v2))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_complement(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (element(v2, v3) = v5 & element(v1, v3) = v4 & powerset(v0) = v3 & ( ~ (v4 = 0) | v5 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng(v1) = v2) | ~ (relation(v0) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_composition(v0, v1) = v4 & relation_rng(v4) = v5 & subset(v5, v2) = v6 & relation(v1) = v3 & ( ~ (v3 = 0) | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng(v0) = v1) | ~ (relation(v2) = 0) | ? [v3] : ? [v4] : ? [v5] : ((v5 = v4 & relation_composition(v0, v2) = v3 & relation_rng(v3) = v4 & relation_image(v2, v1) = v4) | ( ~ (v3 = 0) & relation(v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng(v0) = v1) | ~ (in(v2, v1) = 0) | ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & ordered_pair(v3, v2) = v4 & in(v4, v0) = 0) | ( ~ (v3 = 0) & relation(v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v1, v0) = v2) | ? [v3] : ? [v4] : (subset(v0, v1) = v3 & set_union2(v0, v2) = v4 & ( ~ (v3 = 0) | v4 = v1))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v1, v0) = v2) | ? [v3] : (set_union2(v0, v2) = v3 & set_union2(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v2) = v0) | ~ (singleton(v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v1, v0) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | subset(v2, v0) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (subset_complement(v0, v1) = v5 & element(v1, v3) = v4 & powerset(v0) = v3 & ( ~ (v4 = 0) | v5 = v2))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ? [v3] : (set_difference(v3, v1) = v2 & set_union2(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ? [v3] : (set_difference(v0, v2) = v3 & set_intersection2(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0) = v1) | ~ (in(v2, v1) = 0) | ? [v3] : (in(v3, v0) = 0 & in(v2, v3) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom(v0) = v1) | ~ (relation(v2) = 0) | ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & relation_composition(v0, v2) = v3 & relation_dom(v3) = v4 & subset(v4, v1) = 0) | ( ~ (v3 = 0) & relation(v0) = v3))) & ! [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] : ( ~ (cartesian_product2(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (empty(v2) = v5 & empty(v1) = v4 & empty(v0) = v3 & ( ~ (v5 = 0) | v4 = 0 | v3 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (element(v1, v2) = 0) | ~ (powerset(v0) = v2) | ? [v3] : (subset_complement(v0, v3) = v1 & subset_complement(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (element(v1, v2) = 0) | ~ (powerset(v0) = v2) | ? [v3] : (subset_complement(v0, v1) = v3 & set_difference(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (element(v1, v2) = 0) | ~ (powerset(v0) = v2) | ? [v3] : (subset_complement(v0, v1) = v3 & element(v3, v2) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (element(v1, v0) = v2) | ? [v3] : ? [v4] : (empty(v1) = v4 & empty(v0) = v3 & ( ~ (v3 = 0) | (( ~ (v4 = 0) | v2 = 0) & ( ~ (v2 = 0) | v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (element(v1, v0) = v2) | ? [v3] : ? [v4] : (empty(v0) = v3 & in(v1, v0) = v4 & (v3 = 0 | (( ~ (v4 = 0) | v2 = 0) & ( ~ (v2 = 0) | v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (element(v0, v2) = 0) | ~ (powerset(v1) = v2) | subset(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ (subset(v2, v0) = 0) | in(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ (in(v2, v1) = 0) | subset(v2, v0) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ (subset(v2, v1) = 0) | in(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_inverse_image(v1, v0) = v2) | ? [v3] : ? [v4] : ? [v5] : (relation_dom(v1) = v4 & subset(v2, v4) = v5 & relation(v1) = v3 & ( ~ (v3 = 0) | v5 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_image(v1, v0) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_dom(v1) = v4 & relation_image(v1, v5) = v6 & set_intersection2(v4, v0) = v5 & relation(v1) = v3 & ( ~ (v3 = 0) | v6 = v2))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_image(v1, v0) = v2) | ? [v3] : ? [v4] : ? [v5] : (relation_rng(v1) = v4 & subset(v2, v4) = v5 & relation(v1) = v3 & ( ~ (v3 = 0) | v5 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_rng(v2) = v4 & relation_rng(v1) = v5 & subset(v4, v5) = v6 & relation(v1) = v3 & ( ~ (v3 = 0) | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_rng(v2) = v4 & relation_rng(v1) = v5 & set_intersection2(v5, v0) = v6 & relation(v1) = v3 & ( ~ (v3 = 0) | v6 = v4))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (relation_rng(v2) = v4 & subset(v4, v0) = v5 & relation(v1) = v3 & ( ~ (v3 = 0) | v5 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ? [v3] : ? [v4] : (subset(v2, v1) = v4 & relation(v1) = v3 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ? [v3] : ? [v4] : (relation(v2) = v4 & relation(v1) = v3 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v1, v0) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_rng(v2) = v4 & relation_rng(v1) = v5 & subset(v4, v5) = v6 & relation(v1) = v3 & ( ~ (v3 = 0) | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v1, v0) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_dom(v2) = v4 & relation_dom(v1) = v5 & set_intersection2(v5, v0) = v6 & relation(v1) = v3 & ( ~ (v3 = 0) | v6 = v4))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v1, v0) = v2) | ? [v3] : ? [v4] : ? [v5] : (relation_composition(v4, v1) = v5 & identity_relation(v0) = v4 & relation(v1) = v3 & ( ~ (v3 = 0) | v5 = v2))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v1, v0) = v2) | ? [v3] : ? [v4] : (subset(v2, v1) = v4 & relation(v1) = v3 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ? [v3] : ? [v4] : (relation(v2) = v4 & relation(v0) = v3 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v1, v2) = 0) | ~ (subset(v0, v1) = 0) | subset(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | subset(v2, v0) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (relation(v2) = v5 & relation(v1) = v4 & relation(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ? [v3] : ? [v4] : ((v4 = 0 & in(v3, v2) = 0) | (v3 = 0 & disjoint(v0, v1) = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ? [v3] : (set_difference(v0, v3) = v2 & set_difference(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ? [v3] : ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | subset(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (relation(v2) = v5 & relation(v1) = v4 & relation(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : (set_difference(v2, v1) = v3 & set_difference(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : (set_difference(v1, v0) = v3 & set_union2(v0, v3) = v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & ordered_pair(v0, v1) = v3 & unordered_pair(v2, v4) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (empty(v2) = 0) | ~ (in(v0, v1) = 0) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & element(v1, v3) = v4 & powerset(v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (in(v1, v0) = v2) | ? [v3] : ? [v4] : (element(v1, v0) = v4 & empty(v0) = v3 & (v3 = 0 | (( ~ (v4 = 0) | v2 = 0) & ( ~ (v2 = 0) | v4 = 0))))) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | v1 = empty_set | ~ (set_meet(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (in(v3, v0) = v4 & ( ~ (v4 = 0) | (v6 = 0 & ~ (v7 = 0) & in(v5, v1) = 0 & in(v3, v5) = v7)) & (v4 = 0 | ( ! [v8] : ! [v9] : (v9 = 0 | ~ (in(v3, v8) = v9) | ? [v10] : ( ~ (v10 = 0) & in(v8, v1) = v10)) & ! [v8] : ( ~ (in(v8, v1) = 0) | in(v3, v8) = 0))))) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_rng(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (( ~ (v3 = 0) & relation(v1) = v3) | (in(v3, v0) = v4 & ( ~ (v4 = 0) | ! [v8] : ! [v9] : ( ~ (ordered_pair(v8, v3) = v9) | ? [v10] : ( ~ (v10 = 0) & in(v9, v1) = v10))) & (v4 = 0 | (v7 = 0 & ordered_pair(v5, v3) = v6 & in(v6, v1) = 0))))) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (union(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (in(v3, v0) = v4 & ( ~ (v4 = 0) | ( ! [v8] : ( ~ (in(v8, v1) = 0) | ? [v9] : ( ~ (v9 = 0) & in(v3, v8) = v9)) & ! [v8] : ( ~ (in(v3, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & in(v8, v1) = v9)))) & (v4 = 0 | (v7 = 0 & v6 = 0 & in(v5, v1) = 0 & in(v3, v5) = 0)))) & ? [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) | ? [v10] : ( ~ (v10 = 0) & in(v9, v1) = v10))) & (v4 = 0 | (v7 = 0 & ordered_pair(v3, v5) = v6 & in(v6, v1) = 0))))) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (powerset(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (subset(v3, v1) = v5 & in(v3, v0) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)) & (v5 = 0 | v4 = 0))) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : ? [v4] : (in(v3, v0) = v4 & ( ~ (v4 = 0) | ~ (v3 = v1)) & (v4 = 0 | v3 = v1))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_difference(v0, empty_set) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (cast_to_subset(v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (subset(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v0, v1) = v2)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (subset(v0, v1) = 0) | proper_subset(v0, v1) = 0) & ! [v0] : ! [v1] : (v1 = v0 | ~ (subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v1, v0) = v2)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (relation(v1) = 0) | ~ (relation(v0) = 0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (ordered_pair(v2, v3) = v4 & in(v4, v1) = v6 & in(v4, v0) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)) & (v6 = 0 | v5 = 0))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)) & ! [v0] : ! [v1] : (v1 = empty_set | ~ (complements_of_subsets(v0, v1) = empty_set) | ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & element(v1, v3) = v4 & powerset(v2) = v3 & powerset(v0) = v2)) & ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_difference(empty_set, v0) = v1)) & ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(empty_set, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (relation(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (relation(v0) = v1) | ? [v2] : (in(v2, v0) = 0 & ! [v3] : ! [v4] : ~ (ordered_pair(v3, v4) = v2))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (empty(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & element(v3, v2) = 0 & powerset(v0) = v2 & empty(v3) = v4)) & ! [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] : ? [v3] : ? [v4] : (relation_dom(v0) = v3 & relation(v0) = v2 & empty(v3) = v4 & ( ~ (v4 = 0) | ~ (v2 = 0)))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (function(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2)) & ! [v0] : ! [v1] : (v0 = empty_set | ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : (relation_dom(v0) = v3 & relation(v0) = v2 & ( ~ (v2 = 0) | ( ~ (v3 = empty_set) & ~ (v1 = empty_set))))) & ! [v0] : ! [v1] : (v0 = empty_set | ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : (relation_rng(v0) = v3 & relation(v0) = v2 & ( ~ (v2 = 0) | ( ~ (v3 = empty_set) & ~ (v1 = empty_set))))) & ! [v0] : ! [v1] : (v0 = empty_set | ~ (relation_inverse_image(v1, v0) = empty_set) | ? [v2] : ? [v3] : ? [v4] : (relation_rng(v1) = v3 & subset(v0, v3) = v4 & relation(v1) = v2 & ( ~ (v4 = 0) | ~ (v2 = 0)))) & ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | disjoint(v1, v0) = 0) & ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | set_difference(v0, v1) = v0) & ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | set_intersection2(v0, v1) = empty_set) & ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | ? [v2] : (set_intersection2(v0, v1) = v2 & ! [v3] : ~ (in(v3, v2) = 0))) & ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_rng(v1) = v6 & relation_rng(v0) = v3 & relation_dom(v1) = v4 & relation_dom(v0) = v5 & relation(v0) = v2 & ( ~ (v2 = 0) | (v6 = v5 & v4 = v3)))) & ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ? [v2] : ? [v3] : (relation_inverse(v1) = v3 & relation(v0) = v2 & ( ~ (v2 = 0) | v3 = v0))) & ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ? [v2] : ? [v3] : (relation(v1) = v3 & relation(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_rng(v0) = v4 & relation_dom(v0) = v3 & set_union2(v3, v4) = v5 & relation(v0) = v2 & ( ~ (v2 = 0) | v5 = v1))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_inverse(v0) = v3 & relation_rng(v3) = v6 & relation_dom(v3) = v4 & relation_dom(v0) = v5 & relation(v0) = v2 & ( ~ (v2 = 0) | (v6 = v5 & v4 = v1)))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_field(v0) = v3 & relation_dom(v0) = v4 & set_union2(v4, v1) = v5 & relation(v0) = v2 & ( ~ (v2 = 0) | v5 = v3))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_dom(v0) = v3 & cartesian_product2(v3, v1) = v4 & subset(v0, v4) = v5 & relation(v0) = v2 & ( ~ (v2 = 0) | v5 = 0))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation_dom(v0) = v3 & relation_image(v0, v3) = v4 & relation(v0) = v2 & ( ~ (v2 = 0) | v4 = v1))) & ! [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] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : (relation_dom(v0) = v3 & relation(v0) = v2 & ( ~ (v2 = 0) | ( ! [v4] : ! [v5] : ( ~ (relation_composition(v4, v0) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (relation_rng(v5) = v9 & relation_rng(v4) = v7 & subset(v3, v7) = v8 & relation(v4) = v6 & ( ~ (v8 = 0) | ~ (v6 = 0) | v9 = v1))) & ! [v4] : ! [v5] : ( ~ (relation_rng(v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (relation_composition(v4, v0) = v8 & relation_rng(v8) = v9 & subset(v3, v5) = v7 & relation(v4) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = v1))) & ! [v4] : ( ~ (relation(v4) = 0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (relation_composition(v4, v0) = v7 & relation_rng(v7) = v8 & relation_rng(v4) = v5 & subset(v3, v5) = v6 & ( ~ (v6 = 0) | v8 = v1))))))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : (relation_dom(v0) = v3 & relation(v0) = v2 & ( ~ (v2 = 0) | ( ! [v4] : ! [v5] : ( ~ (relation_composition(v0, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (relation_dom(v5) = v9 & relation_dom(v4) = v7 & subset(v1, v7) = v8 & relation(v4) = v6 & ( ~ (v8 = 0) | ~ (v6 = 0) | v9 = v3))) & ! [v4] : ! [v5] : ( ~ (relation_dom(v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (relation_composition(v0, v4) = v8 & relation_dom(v8) = v9 & subset(v1, v5) = v7 & relation(v4) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = v3))) & ! [v4] : ( ~ (relation(v4) = 0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (relation_composition(v0, v4) = v7 & relation_dom(v7) = v8 & relation_dom(v4) = v5 & subset(v1, v5) = v6 & ( ~ (v6 = 0) | v8 = v3))))))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : (relation_dom(v0) = v3 & relation(v0) = v2 & ( ~ (v2 = 0) | ( ! [v4] : ! [v5] : ( ~ (relation_rng(v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (relation_dom(v4) = v8 & subset(v3, v8) = v9 & subset(v1, v5) = v10 & subset(v0, v4) = v7 & relation(v4) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | (v10 = 0 & v9 = 0)))) & ! [v4] : ! [v5] : ( ~ (relation_dom(v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (relation_rng(v4) = v9 & subset(v3, v5) = v8 & subset(v1, v9) = v10 & subset(v0, v4) = v7 & relation(v4) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | (v10 = 0 & v8 = 0)))) & ! [v4] : ( ~ (subset(v0, v4) = 0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (relation_rng(v4) = v8 & relation_dom(v4) = v6 & subset(v3, v6) = v7 & subset(v1, v8) = v9 & relation(v4) = v5 & ( ~ (v5 = 0) | (v9 = 0 & v7 = 0)))) & ! [v4] : ( ~ (relation(v4) = 0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (relation_rng(v4) = v8 & relation_dom(v4) = v6 & subset(v3, v6) = v7 & subset(v1, v8) = v9 & subset(v0, v4) = v5 & ( ~ (v5 = 0) | (v9 = 0 & v7 = 0)))))))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : (relation_dom(v0) = v3 & relation(v0) = v2 & ( ~ (v2 = 0) | (( ~ (v3 = empty_set) | v1 = empty_set) & ( ~ (v1 = empty_set) | v3 = empty_set))))) & ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = v0) | disjoint(v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = empty_set) | subset(v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (cast_to_subset(v0) = v1) | ? [v2] : (element(v1, v2) = 0 & powerset(v0) = v2)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_inverse(v0) = v4 & relation_rng(v4) = v6 & relation_rng(v0) = v3 & relation_dom(v4) = v5 & relation(v0) = v2 & ( ~ (v2 = 0) | (v6 = v1 & v5 = v3)))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_field(v0) = v3 & relation_rng(v0) = v4 & set_union2(v1, v4) = v5 & relation(v0) = v2 & ( ~ (v2 = 0) | v5 = v3))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_rng(v0) = v3 & cartesian_product2(v1, v3) = v4 & subset(v0, v4) = v5 & relation(v0) = v2 & ( ~ (v2 = 0) | v5 = 0))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation_rng(v0) = v4 & relation_image(v0, v1) = v3 & relation(v0) = v2 & ( ~ (v2 = 0) | v4 = v3))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation(v1) = v4 & empty(v1) = v3 & empty(v0) = v2 & ( ~ (v2 = 0) | (v4 = 0 & v3 = 0)))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation(v0) = v3 & empty(v1) = v4 & empty(v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2 = 0))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : (relation_rng(v0) = v3 & relation(v0) = v2 & ( ~ (v2 = 0) | ( ! [v4] : ! [v5] : ( ~ (relation_composition(v4, v0) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (relation_rng(v5) = v9 & relation_rng(v4) = v7 & subset(v1, v7) = v8 & relation(v4) = v6 & ( ~ (v8 = 0) | ~ (v6 = 0) | v9 = v3))) & ! [v4] : ! [v5] : ( ~ (relation_rng(v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (relation_composition(v4, v0) = v8 & relation_rng(v8) = v9 & subset(v1, v5) = v7 & relation(v4) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = v3))) & ! [v4] : ( ~ (relation(v4) = 0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (relation_composition(v4, v0) = v7 & relation_rng(v7) = v8 & relation_rng(v4) = v5 & subset(v1, v5) = v6 & ( ~ (v6 = 0) | v8 = v3))))))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : (relation_rng(v0) = v3 & relation(v0) = v2 & ( ~ (v2 = 0) | ( ! [v4] : ! [v5] : ( ~ (relation_composition(v0, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (relation_dom(v5) = v9 & relation_dom(v4) = v7 & subset(v3, v7) = v8 & relation(v4) = v6 & ( ~ (v8 = 0) | ~ (v6 = 0) | v9 = v1))) & ! [v4] : ! [v5] : ( ~ (relation_dom(v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (relation_composition(v0, v4) = v8 & relation_dom(v8) = v9 & subset(v3, v5) = v7 & relation(v4) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = v1))) & ! [v4] : ( ~ (relation(v4) = 0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (relation_composition(v0, v4) = v7 & relation_dom(v7) = v8 & relation_dom(v4) = v5 & subset(v3, v5) = v6 & ( ~ (v6 = 0) | v8 = v1))))))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : (relation_rng(v0) = v3 & relation(v0) = v2 & ( ~ (v2 = 0) | ( ! [v4] : ! [v5] : ( ~ (relation_rng(v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (relation_dom(v4) = v8 & subset(v3, v5) = v10 & subset(v1, v8) = v9 & subset(v0, v4) = v7 & relation(v4) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | (v10 = 0 & v9 = 0)))) & ! [v4] : ! [v5] : ( ~ (relation_dom(v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (relation_rng(v4) = v9 & subset(v3, v9) = v10 & subset(v1, v5) = v8 & subset(v0, v4) = v7 & relation(v4) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | (v10 = 0 & v8 = 0)))) & ! [v4] : ( ~ (subset(v0, v4) = 0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (relation_rng(v4) = v8 & relation_dom(v4) = v6 & subset(v3, v8) = v9 & subset(v1, v6) = v7 & relation(v4) = v5 & ( ~ (v5 = 0) | (v9 = 0 & v7 = 0)))) & ! [v4] : ( ~ (relation(v4) = 0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (relation_rng(v4) = v8 & relation_dom(v4) = v6 & subset(v3, v8) = v9 & subset(v1, v6) = v7 & subset(v0, v4) = v5 & ( ~ (v5 = 0) | (v9 = 0 & v7 = 0)))))))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : (relation_rng(v0) = v3 & relation(v0) = v2 & ( ~ (v2 = 0) | (( ~ (v3 = empty_set) | v1 = empty_set) & ( ~ (v1 = empty_set) | v3 = empty_set))))) & ! [v0] : ! [v1] : ( ~ (element(v0, v1) = 0) | ? [v2] : ? [v3] : (empty(v1) = v2 & in(v0, v1) = v3 & (v3 = 0 | v2 = 0))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | union(v1) = v0) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v3 = 0 & ~ (v4 = 0) & element(v2, v1) = 0 & empty(v2) = v4) | (v2 = 0 & empty(v0) = 0))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (cast_to_subset(v0) = v2 & element(v2, v1) = 0)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) = 0 & empty(v2) = 0)) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | unordered_pair(v0, v0) = v1) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | set_difference(v0, v1) = empty_set) & ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | set_intersection2(v0, v1) = v0) & ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | set_union2(v0, v1) = v1) & ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & proper_subset(v1, v0) = v2)) & ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (set_difference(v1, v0) = v2 & set_union2(v0, v2) = v1)) & ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (element(v0, v2) = 0 & powerset(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (subset(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & proper_subset(v0, v0) = v2)) & ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation_rng(v1) = v0) & ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation_dom(v1) = v0) & ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation(v1) = 0) & ! [v0] : ! [v1] : ( ~ (set_intersection2(v0, v1) = empty_set) | disjoint(v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (unordered_pair(v0, v0) = v1) | singleton(v0) = v1) & ! [v0] : ! [v1] : ( ~ (relation(v1) = 0) | ~ (relation(v0) = 0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (subset(v0, v1) = v2 & ( ~ (v2 = 0) | ! [v8] : ! [v9] : ! [v10] : ( ~ (ordered_pair(v8, v9) = v10) | ? [v11] : ? [v12] : (in(v10, v1) = v12 & in(v10, v0) = v11 & ( ~ (v11 = 0) | v12 = 0)))) & (v2 = 0 | (v6 = 0 & ~ (v7 = 0) & ordered_pair(v3, v4) = v5 & in(v5, v1) = v7 & in(v5, v0) = 0)))) & ! [v0] : ! [v1] : ( ~ (relation(v1) = 0) | ~ (relation(v0) = 0) | ? [v2] : ? [v3] : ? [v4] : (relation_composition(v0, v1) = v2 & relation_rng(v2) = v3 & relation_rng(v1) = v4 & subset(v3, v4) = 0)) & ! [v0] : ! [v1] : ( ~ (relation(v1) = 0) | ~ (relation(v0) = 0) | ? [v2] : (relation_composition(v0, v1) = v2 & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (ordered_pair(v6, v4) = v7) | ~ (ordered_pair(v3, v4) = v5) | ~ (relation(v2) = 0) | ? [v8] : ? [v9] : ? [v10] : ((v8 = 0 & in(v5, v2) = 0) | (ordered_pair(v3, v6) = v8 & in(v8, v0) = v9 & in(v7, v1) = v10 & ( ~ (v10 = 0) | ~ (v9 = 0))))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (ordered_pair(v3, v6) = v7) | ~ (ordered_pair(v3, v4) = v5) | ~ (relation(v2) = 0) | ? [v8] : ? [v9] : ? [v10] : ((v8 = 0 & in(v5, v2) = 0) | (ordered_pair(v6, v4) = v9 & in(v9, v1) = v10 & in(v7, v0) = v8 & ( ~ (v10 = 0) | ~ (v8 = 0))))) & ! [v3] : ! [v4] : ! [v5] : ( ~ (ordered_pair(v3, v4) = v5) | ~ (relation(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) & in(v5, v2) = v6))) & ! [v3] : (v3 = v2 | ~ (relation(v3) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : (ordered_pair(v4, v5) = v6 & in(v6, v3) = v7 & ( ~ (v7 = 0) | ( ! [v13] : ! [v14] : ( ~ (ordered_pair(v13, v5) = v14) | ? [v15] : ? [v16] : ? [v17] : (ordered_pair(v4, v13) = v15 & in(v15, v0) = v16 & in(v14, v1) = v17 & ( ~ (v17 = 0) | ~ (v16 = 0)))) & ! [v13] : ! [v14] : ( ~ (ordered_pair(v4, v13) = v14) | ? [v15] : ? [v16] : ? [v17] : (ordered_pair(v13, v5) = v16 & in(v16, v1) = v17 & in(v14, v0) = v15 & ( ~ (v17 = 0) | ~ (v15 = 0)))))) & (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] : ( ~ (relation(v0) = 0) | ~ (in(v1, v0) = 0) | ? [v2] : ? [v3] : ordered_pair(v2, v3) = v1) & ! [v0] : ! [v1] : ( ~ (proper_subset(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (proper_subset(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & proper_subset(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (proper_subset(v0, v1) = 0) | subset(v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (proper_subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & proper_subset(v1, v0) = v2)) & ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = v0) & set_difference(v0, v2) = v3 & singleton(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | element(v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & disjoint(v2, v1) = v3 & singleton(v0) = 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] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : (union(v1) = v2 & subset(v0, v2) = 0)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : (singleton(v0) = v2 & subset(v2, v1) = 0)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : (singleton(v0) = v2 & set_union2(v2, v1) = v1)) & ! [v0] : (v0 = empty_set | ~ (set_meet(empty_set) = v0)) & ! [v0] : (v0 = empty_set | ~ (subset(v0, empty_set) = 0)) & ! [v0] : (v0 = empty_set | ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (ordered_pair(v1, v2) = v3 & in(v3, v0) = 0)) & ! [v0] : (v0 = empty_set | ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ( ~ (v2 = empty_set) & ~ (v1 = empty_set) & relation_rng(v0) = v2 & relation_dom(v0) = v1)) & ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0)) & ! [v0] : ~ (singleton(v0) = empty_set) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (relation_inverse(v0) = v2 & relation_rng(v2) = v3 & relation_rng(v0) = v1 & relation_dom(v2) = v1 & relation_dom(v0) = v3)) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (relation_field(v0) = v1 & relation_rng(v0) = v3 & relation_dom(v0) = v2 & set_union2(v2, v3) = v1)) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (relation_rng(v0) = v2 & relation_dom(v0) = v1 & cartesian_product2(v1, v2) = v3 & subset(v0, v3) = 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] : (relation_dom(v0) = v2 & empty(v2) = v3 & empty(v0) = v1 & ( ~ (v3 = 0) | v1 = 0))) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : (relation_rng(v0) = v2 & relation_dom(v0) = v1 & relation_image(v0, v1) = v2)) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : (relation_rng(v0) = v2 & relation_dom(v0) = v1 & ! [v3] : ! [v4] : ( ~ (relation_composition(v3, v0) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (relation_rng(v4) = v8 & relation_rng(v3) = v6 & subset(v1, v6) = v7 & relation(v3) = v5 & ( ~ (v7 = 0) | ~ (v5 = 0) | v8 = v2))) & ! [v3] : ! [v4] : ( ~ (relation_rng(v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (relation_composition(v3, v0) = v7 & relation_rng(v7) = v8 & subset(v1, v4) = v6 & relation(v3) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | v8 = v2))) & ! [v3] : ( ~ (relation(v3) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (relation_composition(v3, v0) = v6 & relation_rng(v6) = v7 & relation_rng(v3) = v4 & subset(v1, v4) = v5 & ( ~ (v5 = 0) | v7 = v2))))) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : (relation_rng(v0) = v2 & relation_dom(v0) = v1 & ! [v3] : ! [v4] : ( ~ (relation_rng(v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (relation_dom(v3) = v7 & subset(v2, v4) = v9 & subset(v1, v7) = v8 & subset(v0, v3) = v6 & relation(v3) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | (v9 = 0 & v8 = 0)))) & ! [v3] : ! [v4] : ( ~ (relation_dom(v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (relation_rng(v3) = v8 & subset(v2, v8) = v9 & subset(v1, v4) = v7 & subset(v0, v3) = v6 & relation(v3) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | (v9 = 0 & v7 = 0)))) & ! [v3] : ( ~ (subset(v0, v3) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (relation_rng(v3) = v7 & relation_dom(v3) = v5 & subset(v2, v7) = v8 & subset(v1, v5) = v6 & relation(v3) = v4 & ( ~ (v4 = 0) | (v8 = 0 & v6 = 0)))) & ! [v3] : ( ~ (relation(v3) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (relation_rng(v3) = v7 & relation_dom(v3) = v5 & subset(v2, v7) = v8 & subset(v1, v5) = v6 & subset(v0, v3) = v4 & ( ~ (v4 = 0) | (v8 = 0 & v6 = 0)))))) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : (relation_rng(v0) = v2 & relation_dom(v0) = v1 & ( ~ (v2 = empty_set) | v1 = empty_set) & ( ~ (v1 = empty_set) | v2 = empty_set))) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : (relation_rng(v0) = v1 & relation_dom(v0) = v2 & ! [v3] : ! [v4] : ( ~ (relation_composition(v0, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (relation_dom(v4) = v8 & relation_dom(v3) = v6 & subset(v1, v6) = v7 & relation(v3) = v5 & ( ~ (v7 = 0) | ~ (v5 = 0) | v8 = v2))) & ! [v3] : ! [v4] : ( ~ (relation_dom(v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (relation_composition(v0, v3) = v7 & relation_dom(v7) = v8 & subset(v1, v4) = v6 & relation(v3) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | v8 = v2))) & ! [v3] : ( ~ (relation(v3) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (relation_composition(v0, v3) = v6 & relation_dom(v6) = v7 & relation_dom(v3) = v4 & subset(v1, v4) = v5 & ( ~ (v5 = 0) | v7 = v2))))) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : (relation_dom(v0) = v2 & function(v0) = v1 & ( ~ (v1 = 0) | ( ! [v3] : ! [v4] : ! [v5] : ( ~ (ordered_pair(v3, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : (apply(v0, v3) = v7 & in(v5, v0) = v8 & in(v3, v2) = v6 & ( ~ (v6 = 0) | (( ~ (v8 = 0) | v7 = v4) & ( ~ (v7 = v4) | v8 = 0))))) & ? [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (in(v4, v2) = v5) | ? [v6] : (apply(v0, v4) = v6 & ( ~ (v6 = v3) | v3 = empty_set) & ( ~ (v3 = empty_set) | v6 = empty_set))) & ! [v3] : ! [v4] : (v4 = empty_set | ~ (apply(v0, v3) = v4) | in(v3, v2) = 0))))) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : (relation_inverse(v1) = v0 & relation_inverse(v0) = v1)) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : (relation_inverse(v0) = v1 & relation(v1) = 0)) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : (relation_inverse(v0) = v1 & ! [v2] : ! [v3] : ! [v4] : ( ~ (ordered_pair(v3, v2) = v4) | ~ (relation(v1) = 0) | ? [v5] : ? [v6] : ? [v7] : (ordered_pair(v2, v3) = v6 & in(v6, v1) = v7 & in(v4, v0) = v5 & ( ~ (v5 = 0) | v7 = 0))) & ! [v2] : ! [v3] : ! [v4] : ( ~ (ordered_pair(v3, v2) = v4) | ~ (relation(v1) = 0) | ? [v5] : ? [v6] : ? [v7] : (ordered_pair(v2, v3) = v5 & in(v5, v1) = v6 & in(v4, v0) = v7 & ( ~ (v6 = 0) | v7 = 0))) & ! [v2] : ! [v3] : ! [v4] : ( ~ (ordered_pair(v2, v3) = v4) | ~ (relation(v1) = 0) | ? [v5] : ? [v6] : ? [v7] : (ordered_pair(v3, v2) = v6 & in(v6, v0) = v7 & in(v4, v1) = v5 & ( ~ (v5 = 0) | v7 = 0))) & ! [v2] : ! [v3] : ! [v4] : ( ~ (ordered_pair(v2, v3) = v4) | ~ (relation(v1) = 0) | ? [v5] : ? [v6] : ? [v7] : (ordered_pair(v3, v2) = v5 & in(v5, v0) = v6 & in(v4, v1) = v7 & ( ~ (v6 = 0) | v7 = 0))) & ! [v2] : (v2 = v1 | ~ (relation(v2) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (ordered_pair(v4, v3) = v7 & ordered_pair(v3, v4) = v5 & in(v7, v0) = v8 & in(v5, v2) = v6 & ( ~ (v8 = 0) | ~ (v6 = 0)) & (v8 = 0 | v6 = 0))))) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : (relation_rng(v0) = v1 & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = 0 | ~ (ordered_pair(v4, v2) = v5) | ~ (in(v2, v1) = v3) | ? [v6] : ( ~ (v6 = 0) & in(v5, v0) = v6)) & ! [v2] : ( ~ (in(v2, v1) = 0) | ? [v3] : ? [v4] : (ordered_pair(v3, v2) = v4 & in(v4, v0) = 0)) & ? [v2] : (v2 = v1 | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (in(v3, v2) = v4 & ( ~ (v4 = 0) | ! [v8] : ! [v9] : ( ~ (ordered_pair(v8, v3) = v9) | ? [v10] : ( ~ (v10 = 0) & in(v9, v0) = v10))) & (v4 = 0 | (v7 = 0 & ordered_pair(v5, v3) = v6 & in(v6, v0) = 0)))))) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : (relation_rng(v0) = v1 & ! [v2] : ! [v3] : ( ~ (relation_composition(v0, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : (relation_rng(v3) = v5 & relation_image(v2, v1) = v6 & relation(v2) = v4 & ( ~ (v4 = 0) | v6 = v5))) & ! [v2] : ! [v3] : ( ~ (relation_image(v2, v1) = v3) | ? [v4] : ? [v5] : ? [v6] : (relation_composition(v0, v2) = v5 & relation_rng(v5) = v6 & relation(v2) = v4 & ( ~ (v4 = 0) | v6 = v3))) & ! [v2] : ( ~ (relation(v2) = 0) | ? [v3] : ? [v4] : (relation_composition(v0, v2) = v3 & relation_rng(v3) = v4 & relation_image(v2, v1) = v4)))) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : (relation_dom(v0) = v1 & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = 0 | ~ (ordered_pair(v2, v4) = v5) | ~ (in(v2, v1) = v3) | ? [v6] : ( ~ (v6 = 0) & in(v5, v0) = v6)) & ! [v2] : ( ~ (in(v2, v1) = 0) | ? [v3] : ? [v4] : (ordered_pair(v2, v3) = v4 & in(v4, v0) = 0)) & ? [v2] : (v2 = v1 | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (in(v3, v2) = v4 & ( ~ (v4 = 0) | ! [v8] : ! [v9] : ( ~ (ordered_pair(v3, v8) = v9) | ? [v10] : ( ~ (v10 = 0) & in(v9, v0) = v10))) & (v4 = 0 | (v7 = 0 & ordered_pair(v3, v5) = v6 & in(v6, v0) = 0)))))) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : (relation_dom(v0) = v1 & ! [v2] : ! [v3] : ( ~ (relation_composition(v0, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : (relation_dom(v3) = v5 & subset(v5, v1) = v6 & relation(v2) = v4 & ( ~ (v4 = 0) | v6 = 0))) & ! [v2] : ( ~ (relation(v2) = 0) | ? [v3] : ? [v4] : (relation_composition(v0, v2) = v3 & relation_dom(v3) = v4 & subset(v4, v1) = 0)))) & ! [v0] : ( ~ (empty(v0) = 0) | relation(v0) = 0) & ! [v0] : ( ~ (empty(v0) = 0) | function(v0) = 0) & ! [v0] : ( ~ (empty(v0) = 0) | ? [v1] : (relation_rng(v0) = v1 & relation(v1) = 0 & empty(v1) = 0)) & ! [v0] : ( ~ (empty(v0) = 0) | ? [v1] : (relation_dom(v0) = v1 & relation(v1) = 0 & empty(v1) = 0)) & ! [v0] : ( ~ (function(v0) = 0) | ? [v1] : ? [v2] : (relation_dom(v0) = v2 & relation(v0) = v1 & ( ~ (v1 = 0) | ( ! [v3] : ! [v4] : ! [v5] : ( ~ (ordered_pair(v3, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : (apply(v0, v3) = v7 & in(v5, v0) = v8 & in(v3, v2) = v6 & ( ~ (v6 = 0) | (( ~ (v8 = 0) | v7 = v4) & ( ~ (v7 = v4) | v8 = 0))))) & ? [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (in(v4, v2) = v5) | ? [v6] : (apply(v0, v4) = v6 & ( ~ (v6 = v3) | v3 = empty_set) & ( ~ (v3 = empty_set) | v6 = empty_set))) & ! [v3] : ! [v4] : (v4 = empty_set | ~ (apply(v0, v3) = v4) | in(v3, v2) = 0))))) & ! [v0] : ~ (proper_subset(v0, v0) = 0) & ! [v0] : ~ (in(v0, empty_set) = 0) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (relation_field(v2) = v6 & ordered_pair(v0, v1) = v4 & relation(v2) = v3 & in(v4, v2) = v5 & in(v1, v6) = v8 & in(v0, v6) = v7 & ( ~ (v5 = 0) | ~ (v3 = 0) | (v8 = 0 & v7 = 0))) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (cartesian_product2(v1, v3) = v7 & cartesian_product2(v0, v2) = v6 & subset(v6, v7) = v8 & subset(v2, v3) = v5 & subset(v0, v1) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0) | v8 = 0)) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (subset_difference(v0, v1, v2) = v6 & set_difference(v1, v2) = v7 & element(v2, v3) = v5 & element(v1, v3) = v4 & powerset(v0) = v3 & ( ~ (v5 = 0) | ~ (v4 = 0) | v7 = v6)) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (subset_complement(v0, v2) = v5 & element(v2, v3) = v4 & powerset(v0) = v3 & in(v1, v5) = v6 & in(v1, v2) = v7 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v4 = 0))) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (relation_inverse_image(v2, v1) = v6 & relation_inverse_image(v2, v0) = v5 & subset(v5, v6) = v7 & subset(v0, v1) = v4 & relation(v2) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v7 = 0)) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (relation_rng_restriction(v0, v6) = v7 & relation_rng_restriction(v0, v2) = v4 & relation_dom_restriction(v4, v1) = v5 & relation_dom_restriction(v2, v1) = v6 & relation(v2) = v3 & ( ~ (v3 = 0) | v7 = v5)) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (meet_of_subsets(v0, v1) = v5 & element(v1, v3) = v4 & powerset(v2) = v3 & powerset(v0) = v2 & set_meet(v1) = v6 & ( ~ (v4 = 0) | v6 = v5)) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (union_of_subsets(v0, v1) = v5 & union(v1) = v6 & element(v1, v3) = v4 & powerset(v2) = v3 & powerset(v0) = v2 & ( ~ (v4 = 0) | v6 = v5)) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (complements_of_subsets(v0, v5) = v6 & complements_of_subsets(v0, v1) = v5 & element(v1, v3) = v4 & powerset(v2) = v3 & powerset(v0) = v2 & ( ~ (v4 = 0) | v6 = v1)) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_composition(v0, v1) = v4 & relation(v4) = v6 & relation(v1) = v3 & empty(v4) = v5 & empty(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | (v6 = 0 & v5 = 0))) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_inverse(v0) = v3 & relation_rng(v3) = v6 & relation_rng(v0) = v2 & relation_dom(v3) = v4 & relation_dom(v0) = v5 & relation(v0) = v1 & ( ~ (v1 = 0) | (v6 = v5 & v4 = v2))) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_dom(v1) = v4 & relation_image(v1, v5) = v6 & relation_image(v1, v0) = v3 & set_intersection2(v4, v0) = v5 & relation(v1) = v2 & ( ~ (v2 = 0) | v6 = v3)) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (element(v1, v4) = v5 & element(v0, v2) = v6 & powerset(v2) = v4 & in(v0, v1) = v3 & ( ~ (v5 = 0) | ~ (v3 = 0) | v6 = 0)) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (subset(v5, v2) = v6 & unordered_pair(v0, v1) = v5 & in(v1, v2) = v4 & in(v0, v2) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v6 = 0)) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (subset(v5, v1) = v6 & subset(v2, v1) = v4 & subset(v0, v1) = v3 & set_union2(v0, v2) = v5 & ( ~ (v4 = 0) | ~ (v3 = 0) | v6 = 0)) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_composition(v4, v1) = v5 & relation_dom_restriction(v1, v0) = v3 & identity_relation(v0) = v4 & relation(v1) = v2 & ( ~ (v2 = 0) | v5 = v3)) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : (disjoint(v0, v1) = v3 & set_intersection2(v0, v1) = v2 & ( ~ (v3 = 0) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & in(v4, v2) = v5))) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : (relation_dom(v0) = v3 & relation(v0) = v1 & function(v0) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | ( ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (apply(v0, v4) = v7 & ordered_pair(v4, v5) = v8 & in(v8, v0) = v9 & in(v4, v3) = v6 & ( ~ (v6 = 0) | (( ~ (v9 = 0) | v7 = v5) & ( ~ (v7 = v5) | v9 = 0)))) & ? [v4] : ? [v5] : ? [v6] : ? [v7] : (apply(v0, v4) = v7 & in(v4, v3) = v6 & (v6 = 0 | (( ~ (v7 = v5) | v5 = empty_set) & ( ~ (v5 = empty_set) | v7 = empty_set))))))) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : (subset(v0, v1) = v2 & proper_subset(v1, v0) = v3 & ( ~ (v3 = 0) | ~ (v2 = 0))) & ? [v0] : ? [v1] : ? [v2] : (cast_to_subset(v0) = v1 & element(v1, v2) = 0 & powerset(v0) = v2) & ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : ? [v3] : ? [v4] : (in(v2, v1) = v4 & in(v2, v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)) & (v4 = 0 | v3 = 0))) & ? [v0] : ? [v1] : element(v1, v0) = 0 & ? [v0] : ? [v1] : (singleton(v0) = v1 & unordered_pair(v0, v0) = v1) & ? [v0] : ? [v1] : (in(v0, v1) = 0 & ! [v2] : ! [v3] : (v3 = 0 | ~ (are_equipotent(v2, v1) = v3) | ? [v4] : ? [v5] : (subset(v2, v1) = v4 & in(v2, v1) = v5 & ( ~ (v4 = 0) | v5 = 0))) & ! [v2] : ! [v3] : (v3 = 0 | ~ (in(v2, v1) = v3) | ? [v4] : ? [v5] : (are_equipotent(v2, v1) = v5 & subset(v2, v1) = v4 & ( ~ (v4 = 0) | v5 = 0))) & ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ? [v4] : ? [v5] : (in(v3, v1) = v5 & in(v2, v1) = v4 & ( ~ (v4 = 0) | v5 = 0))) & ! [v2] : ! [v3] : ( ~ (subset(v3, v2) = 0) | ? [v4] : ? [v5] : (in(v3, v1) = v5 & in(v2, v1) = v4 & ( ~ (v4 = 0) | v5 = 0))) & ! [v2] : ( ~ (subset(v2, v1) = 0) | ? [v3] : ? [v4] : (are_equipotent(v2, v1) = v3 & in(v2, v1) = v4 & (v4 = 0 | v3 = 0))) & ! [v2] : ( ~ (in(v2, v1) = 0) | ? [v3] : (powerset(v2) = v3 & in(v3, v1) = 0))) & ? [v0] : ? [v1] : (in(v0, v1) = 0 & ! [v2] : ! [v3] : (v3 = 0 | ~ (are_equipotent(v2, v1) = v3) | ? [v4] : ? [v5] : (subset(v2, v1) = v4 & in(v2, v1) = v5 & ( ~ (v4 = 0) | v5 = 0))) & ! [v2] : ! [v3] : (v3 = 0 | ~ (in(v2, v1) = v3) | ? [v4] : ? [v5] : (are_equipotent(v2, v1) = v5 & subset(v2, v1) = v4 & ( ~ (v4 = 0) | v5 = 0))) & ! [v2] : ! [v3] : ( ~ (subset(v3, v2) = 0) | ? [v4] : ? [v5] : (in(v3, v1) = v5 & in(v2, v1) = v4 & ( ~ (v4 = 0) | v5 = 0))) & ! [v2] : ( ~ (subset(v2, v1) = 0) | ? [v3] : ? [v4] : (are_equipotent(v2, v1) = v3 & in(v2, v1) = v4 & (v4 = 0 | v3 = 0))) & ! [v2] : ( ~ (in(v2, v1) = 0) | ? [v3] : (in(v3, v1) = 0 & ! [v4] : ! [v5] : (v5 = 0 | ~ (in(v4, v3) = v5) | ? [v6] : ( ~ (v6 = 0) & subset(v4, v2) = v6)) & ! [v4] : ( ~ (subset(v4, v2) = 0) | in(v4, v3) = 0)))) & ? [v0] : ? [v1] : (in(v0, v1) = 0 & ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (subset(v3, v2) = v5 & in(v3, v1) = v6 & in(v2, v1) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0) | v6 = 0)) & ? [v2] : ? [v3] : ? [v4] : ? [v5] : (are_equipotent(v2, v1) = v4 & subset(v2, v1) = v3 & in(v2, v1) = v5 & ( ~ (v3 = 0) | v5 = 0 | v4 = 0)) & ? [v2] : ? [v3] : ? [v4] : ? [v5] : (powerset(v2) = v4 & in(v4, v1) = v5 & in(v2, v1) = v3 & ( ~ (v3 = 0) | v5 = 0))) & ? [v0] : ? [v1] : (in(v0, v1) = 0 & ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (subset(v3, v2) = v5 & in(v3, v1) = v6 & in(v2, v1) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0) | v6 = 0)) & ? [v2] : ? [v3] : ? [v4] : ? [v5] : (are_equipotent(v2, v1) = v4 & subset(v2, v1) = v3 & in(v2, v1) = v5 & ( ~ (v3 = 0) | v5 = 0 | v4 = 0)) & ? [v2] : ? [v3] : ? [v4] : ((v4 = 0 & in(v3, v1) = 0 & ? [v5] : ? [v6] : ? [v7] : (subset(v5, v2) = v6 & in(v5, v3) = v7 & ( ~ (v6 = 0) | v7 = 0))) | ( ~ (v3 = 0) & in(v2, v1) = v3))) & ? [v0] : (v0 = empty_set | ? [v1] : in(v1, v0) = 0) & ((all_0_9_9 = all_0_15_15 & all_0_10_10 = 0 & ~ (all_0_12_12 = 0)) | (all_0_12_12 = 0 & ( ~ (all_0_9_9 = all_0_15_15) | ~ (all_0_10_10 = 0))))
% 141.36/84.53 |
% 141.36/84.53 | Applying alpha-rule on (1) yields:
% 141.36/84.53 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_image(v3, v2) = v1) | ~ (relation_image(v3, v2) = v0))
% 141.36/84.53 | (3) relation_dom(all_0_14_14) = all_0_11_11
% 141.36/84.53 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ? [v3] : ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0)))
% 141.36/84.53 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (element(v0, v2) = v3) | ~ (in(v0, v1) = 0) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & element(v1, v4) = v5 & powerset(v2) = v4))
% 141.36/84.53 | (6) empty(all_0_4_4) = all_0_3_3
% 141.36/84.53 | (7) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0))
% 141.36/84.53 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_dom_restriction(v3, v2) = v1) | ~ (relation_dom_restriction(v3, v2) = v0))
% 141.36/84.53 | (9) ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v2, v1) = 0) | ~ (singleton(v0) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3))
% 141.36/84.53 | (10) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (subset_difference(v0, v1, v2) = v6 & set_difference(v1, v2) = v7 & element(v2, v3) = v5 & element(v1, v3) = v4 & powerset(v0) = v3 & ( ~ (v5 = 0) | ~ (v4 = 0) | v7 = v6))
% 141.36/84.53 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_inverse_image(v2, v1) = v3) | ~ (in(v0, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : (relation_rng(v2) = v6 & relation(v2) = v5 & ( ~ (v5 = 0) | (( ~ (v4 = 0) | (v11 = 0 & v10 = 0 & v8 = 0 & ordered_pair(v0, v7) = v9 & in(v9, v2) = 0 & in(v7, v6) = 0 & in(v7, v1) = 0)) & (v4 = 0 | ( ! [v12] : ! [v13] : ( ~ (ordered_pair(v0, v12) = v13) | ? [v14] : ? [v15] : ? [v16] : (in(v13, v2) = v15 & in(v12, v6) = v14 & in(v12, v1) = v16 & ( ~ (v16 = 0) | ~ (v15 = 0) | ~ (v14 = 0)))) & ! [v12] : ( ~ (in(v12, v6) = 0) | ? [v13] : ? [v14] : ? [v15] : (ordered_pair(v0, v12) = v13 & in(v13, v2) = v14 & in(v12, v1) = v15 & ( ~ (v15 = 0) | ~ (v14 = 0)))) & ! [v12] : ( ~ (in(v12, v1) = 0) | ? [v13] : ? [v14] : ? [v15] : (ordered_pair(v0, v12) = v14 & in(v14, v2) = v15 & in(v12, v6) = v13 & ( ~ (v15 = 0) | ~ (v13 = 0))))))))))
% 141.36/84.53 | (12) ! [v0] : ( ~ (empty(v0) = 0) | ? [v1] : (relation_dom(v0) = v1 & relation(v1) = 0 & empty(v1) = 0))
% 141.36/84.53 | (13) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (relation(v2) = v5 & relation(v1) = v4 & relation(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0)))
% 141.36/84.53 | (14) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : (relation_rng(v0) = v3 & relation(v0) = v2 & ( ~ (v2 = 0) | (( ~ (v3 = empty_set) | v1 = empty_set) & ( ~ (v1 = empty_set) | v3 = empty_set)))))
% 141.36/84.53 | (15) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_composition(v0, v1) = v4 & relation(v4) = v6 & relation(v1) = v3 & empty(v4) = v5 & empty(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | (v6 = 0 & v5 = 0)))
% 141.36/84.53 | (16) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_difference(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | v7 = 0) & (v5 = 0 | (v6 = 0 & ~ (v7 = 0)))))
% 141.36/84.53 | (17) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (subset(v0, v1) = v2 & proper_subset(v1, v0) = v3 & ( ~ (v3 = 0) | ~ (v2 = 0)))
% 141.36/84.53 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (disjoint(v0, v2) = v3) | ~ (subset(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & disjoint(v1, v2) = v4))
% 141.36/84.53 | (19) ! [v0] : ! [v1] : (v1 = empty_set | ~ (complements_of_subsets(v0, v1) = empty_set) | ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & element(v1, v3) = v4 & powerset(v2) = v3 & powerset(v0) = v2))
% 141.36/84.53 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cartesian_product2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ? [v4] : ? [v5] : (ordered_pair(v4, v5) = v3 & in(v5, v1) = 0 & in(v4, v0) = 0))
% 141.36/84.53 | (21) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (relation_field(v2) = v6 & ordered_pair(v0, v1) = v4 & relation(v2) = v3 & in(v4, v2) = v5 & in(v1, v6) = v8 & in(v0, v6) = v7 & ( ~ (v5 = 0) | ~ (v3 = 0) | (v8 = 0 & v7 = 0)))
% 141.36/84.53 | (22) ! [v0] : ! [v1] : ! [v2] : ( ~ (cartesian_product2(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (empty(v2) = v5 & empty(v1) = v4 & empty(v0) = v3 & ( ~ (v5 = 0) | v4 = 0 | v3 = 0)))
% 141.36/84.54 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_image(v0, v1) = v2) | ~ (relation(v0) = 0) | ~ (in(v3, v2) = 0) | ? [v4] : ? [v5] : (ordered_pair(v4, v3) = v5 & in(v5, v0) = 0 & in(v4, v1) = 0))
% 141.36/84.54 | (24) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & singleton(v0) = v3 & subset(v3, v1) = v4))
% 141.36/84.54 | (25) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (relation_dom(v0) = v3 & relation(v0) = v1 & function(v0) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | ( ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (apply(v0, v4) = v7 & ordered_pair(v4, v5) = v8 & in(v8, v0) = v9 & in(v4, v3) = v6 & ( ~ (v6 = 0) | (( ~ (v9 = 0) | v7 = v5) & ( ~ (v7 = v5) | v9 = 0)))) & ? [v4] : ? [v5] : ? [v6] : ? [v7] : (apply(v0, v4) = v7 & in(v4, v3) = v6 & (v6 = 0 | (( ~ (v7 = v5) | v5 = empty_set) & ( ~ (v5 = empty_set) | v7 = empty_set)))))))
% 141.36/84.54 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (element(v1, v3) = 0) | ~ (powerset(v2) = v3) | ~ (in(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4))
% 141.36/84.54 | (27) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | set_intersection2(v0, v1) = v0)
% 141.36/84.54 | (28) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | set_difference(v0, v1) = empty_set)
% 141.36/84.54 | (29) ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = empty_set) | subset(v0, v1) = 0)
% 141.36/84.54 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0))
% 141.36/84.54 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (relation_composition(v0, v1) = v2) | ~ (ordered_pair(v3, v6) = v7) | ~ (ordered_pair(v3, v4) = v5) | ~ (relation(v2) = 0) | ~ (relation(v0) = 0) | ? [v8] : ? [v9] : ? [v10] : ((v8 = 0 & in(v5, v2) = 0) | ( ~ (v8 = 0) & relation(v1) = v8) | (ordered_pair(v6, v4) = v9 & in(v9, v1) = v10 & in(v7, v0) = v8 & ( ~ (v10 = 0) | ~ (v8 = 0)))))
% 141.36/84.54 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng(v1) = v2) | ~ (set_intersection2(v2, v0) = v3) | ? [v4] : ? [v5] : ? [v6] : (relation_rng(v5) = v6 & relation_rng_restriction(v0, v1) = v5 & relation(v1) = v4 & ( ~ (v4 = 0) | v6 = v3)))
% 141.36/84.54 | (33) relation(empty_set) = 0
% 141.36/84.54 | (34) ? [v0] : ? [v1] : (in(v0, v1) = 0 & ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (subset(v3, v2) = v5 & in(v3, v1) = v6 & in(v2, v1) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0) | v6 = 0)) & ? [v2] : ? [v3] : ? [v4] : ? [v5] : (are_equipotent(v2, v1) = v4 & subset(v2, v1) = v3 & in(v2, v1) = v5 & ( ~ (v3 = 0) | v5 = 0 | v4 = 0)) & ? [v2] : ? [v3] : ? [v4] : ((v4 = 0 & in(v3, v1) = 0 & ? [v5] : ? [v6] : ? [v7] : (subset(v5, v2) = v6 & in(v5, v3) = v7 & ( ~ (v6 = 0) | v7 = 0))) | ( ~ (v3 = 0) & in(v2, v1) = v3)))
% 141.36/84.54 | (35) ! [v0] : ! [v1] : ( ~ (proper_subset(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & proper_subset(v0, v1) = v2))
% 141.36/84.54 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 141.36/84.54 | (37) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : (in(v3, v1) = 0 & in(v3, v0) = 0))
% 141.36/84.54 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = 0 | ~ (relation_inverse_image(v0, v1) = v2) | ~ (relation(v0) = 0) | ~ (in(v5, v1) = 0) | ~ (in(v3, v2) = v4) | ? [v6] : ? [v7] : ( ~ (v7 = 0) & ordered_pair(v3, v5) = v6 & in(v6, v0) = v7))
% 141.36/84.54 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (cartesian_product2(v1, v3) = v5) | ~ (cartesian_product2(v0, v2) = v4) | ~ (subset(v4, v5) = v6) | ? [v7] : ? [v8] : (subset(v2, v3) = v8 & subset(v0, v1) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0))))
% 141.36/84.54 | (40) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom(v0) = v1) | ~ (relation(v2) = 0) | ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & relation_composition(v0, v2) = v3 & relation_dom(v3) = v4 & subset(v4, v1) = 0) | ( ~ (v3 = 0) & relation(v0) = v3)))
% 141.36/84.54 | (41) ! [v0] : ! [v1] : ! [v2] : ( ~ (complements_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (element(v1, v4) = v5 & powerset(v3) = v4 & powerset(v0) = v3 & ( ~ (v5 = 0) | ( ! [v6] : ! [v7] : ( ~ (subset_complement(v0, v6) = v7) | ~ (element(v2, v4) = 0) | ? [v8] : ? [v9] : ? [v10] : (element(v6, v3) = v8 & in(v7, v1) = v10 & in(v6, v2) = v9 & ( ~ (v8 = 0) | (( ~ (v10 = 0) | v9 = 0) & ( ~ (v9 = 0) | v10 = 0))))) & ! [v6] : ! [v7] : ( ~ (element(v2, v4) = 0) | ~ (in(v6, v2) = v7) | ? [v8] : ? [v9] : ? [v10] : (subset_complement(v0, v6) = v9 & element(v6, v3) = v8 & in(v9, v1) = v10 & ( ~ (v8 = 0) | (( ~ (v10 = 0) | v7 = 0) & ( ~ (v7 = 0) | v10 = 0))))) & ! [v6] : (v6 = v2 | ~ (element(v6, v4) = 0) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : (subset_complement(v0, v7) = v9 & element(v7, v3) = 0 & in(v9, v1) = v10 & in(v7, v6) = v8 & ( ~ (v10 = 0) | ~ (v8 = 0)) & (v10 = 0 | v8 = 0))) & ! [v6] : ( ~ (element(v6, v3) = 0) | ~ (element(v2, v4) = 0) | ? [v7] : ? [v8] : ? [v9] : (subset_complement(v0, v6) = v8 & in(v8, v1) = v9 & in(v6, v2) = v7 & ( ~ (v9 = 0) | v7 = 0) & ( ~ (v7 = 0) | v9 = 0)))))))
% 141.36/84.54 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_inverse(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ (relation(v1) = 0) | ? [v5] : ? [v6] : ? [v7] : (( ~ (v5 = 0) & relation(v0) = v5) | (ordered_pair(v3, v2) = v6 & in(v6, v0) = v7 & in(v4, v1) = v5 & ( ~ (v5 = 0) | v7 = 0))))
% 141.36/84.54 | (43) ? [v0] : ? [v1] : (singleton(v0) = v1 & unordered_pair(v0, v0) = v1)
% 141.36/84.54 | (44) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (relation_image(v1, v2) = v3) | ~ (relation(v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (in(v4, v0) = v5 & ( ~ (v5 = 0) | ( ! [v10] : ! [v11] : ( ~ (ordered_pair(v10, v4) = v11) | ? [v12] : ? [v13] : (in(v11, v1) = v12 & in(v10, v2) = v13 & ( ~ (v13 = 0) | ~ (v12 = 0)))) & ! [v10] : ( ~ (in(v10, v2) = 0) | ? [v11] : ? [v12] : ( ~ (v12 = 0) & ordered_pair(v10, v4) = v11 & in(v11, v1) = v12)))) & (v5 = 0 | (v9 = 0 & v8 = 0 & ordered_pair(v6, v4) = v7 & in(v7, v1) = 0 & in(v6, v2) = 0))))
% 141.36/84.54 | (45) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0))
% 141.36/84.54 | (46) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : (relation_dom(v0) = v3 & relation(v0) = v2 & ( ~ (v2 = 0) | ( ! [v4] : ! [v5] : ( ~ (relation_composition(v4, v0) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (relation_rng(v5) = v9 & relation_rng(v4) = v7 & subset(v3, v7) = v8 & relation(v4) = v6 & ( ~ (v8 = 0) | ~ (v6 = 0) | v9 = v1))) & ! [v4] : ! [v5] : ( ~ (relation_rng(v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (relation_composition(v4, v0) = v8 & relation_rng(v8) = v9 & subset(v3, v5) = v7 & relation(v4) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = v1))) & ! [v4] : ( ~ (relation(v4) = 0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (relation_composition(v4, v0) = v7 & relation_rng(v7) = v8 & relation_rng(v4) = v5 & subset(v3, v5) = v6 & ( ~ (v6 = 0) | v8 = v1)))))))
% 141.36/84.54 | (47) ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v0, v1) = 0) | ~ (in(v2, v0) = 0) | ? [v3] : ( ~ (v3 = 0) & in(v2, v1) = v3))
% 141.36/84.54 | (48) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (relation_dom(v0) = v2 & empty(v2) = v3 & empty(v0) = v1 & ( ~ (v3 = 0) | v1 = 0)))
% 141.36/84.54 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0))
% 141.36/84.54 | (50) ! [v0] : ! [v1] : (v1 = 0 | ~ (relation(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2))
% 141.36/84.54 | (51) empty(all_0_2_2) = 0
% 141.36/84.54 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_difference(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (set_difference(v1, v2) = v7 & element(v2, v4) = v6 & element(v1, v4) = v5 & powerset(v0) = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | v7 = v3)))
% 141.36/84.54 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng(v0) = v1) | ~ (relation_image(v2, v1) = v3) | ? [v4] : ? [v5] : ? [v6] : (( ~ (v4 = 0) & relation(v0) = v4) | (relation_composition(v0, v2) = v5 & relation_rng(v5) = v6 & relation(v2) = v4 & ( ~ (v4 = 0) | v6 = v3))))
% 141.36/84.54 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_inverse(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ (relation(v1) = 0) | ? [v5] : ? [v6] : ? [v7] : (( ~ (v5 = 0) & relation(v0) = v5) | (ordered_pair(v3, v2) = v5 & in(v5, v0) = v6 & in(v4, v1) = v7 & ( ~ (v6 = 0) | v7 = 0))))
% 141.36/84.54 | (55) ! [v0] : ! [v1] : ( ~ (unordered_pair(v0, v0) = v1) | singleton(v0) = v1)
% 141.36/84.54 | (56) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | unordered_pair(v0, v0) = v1)
% 141.36/84.54 | (57) ! [v0] : ! [v1] : (v1 = 0 | ~ (empty(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & element(v3, v2) = 0 & powerset(v0) = v2 & empty(v3) = v4))
% 141.36/84.54 | (58) ! [v0] : ! [v1] : ! [v2] : (v0 = empty_set | ~ (element(v2, v1) = 0) | ~ (powerset(v0) = v1) | ? [v3] : (subset_complement(v0, v2) = v3 & ! [v4] : ! [v5] : (v5 = 0 | ~ (in(v4, v3) = v5) | ? [v6] : ? [v7] : (element(v4, v0) = v6 & in(v4, v2) = v7 & ( ~ (v6 = 0) | v7 = 0))) & ! [v4] : ! [v5] : (v5 = 0 | ~ (in(v4, v2) = v5) | ? [v6] : ? [v7] : (element(v4, v0) = v6 & in(v4, v3) = v7 & ( ~ (v6 = 0) | v7 = 0))) & ! [v4] : ( ~ (element(v4, v0) = 0) | ? [v5] : ? [v6] : (in(v4, v3) = v6 & in(v4, v2) = v5 & (v6 = 0 | v5 = 0)))))
% 141.36/84.55 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | v0 = empty_set | ~ (set_meet(v0) = v1) | ~ (in(v2, v1) = v3) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & in(v4, v0) = 0 & in(v2, v4) = v5))
% 141.36/84.55 | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = 0 | ~ (relation_image(v0, v1) = v2) | ~ (ordered_pair(v5, v3) = v6) | ~ (relation(v0) = 0) | ~ (in(v3, v2) = v4) | ? [v7] : ? [v8] : (in(v6, v0) = v7 & in(v5, v1) = v8 & ( ~ (v8 = 0) | ~ (v7 = 0))))
% 141.36/84.55 | (61) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_field(v0) = v3 & relation_rng(v0) = v4 & set_union2(v1, v4) = v5 & relation(v0) = v2 & ( ~ (v2 = 0) | v5 = v3)))
% 141.36/84.55 | (62) ! [v0] : ! [v1] : ! [v2] : ( ~ (in(v1, v0) = v2) | ? [v3] : ? [v4] : (element(v1, v0) = v4 & empty(v0) = v3 & (v3 = 0 | (( ~ (v4 = 0) | v2 = 0) & ( ~ (v2 = 0) | v4 = 0)))))
% 141.36/84.55 | (63) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (element(v1, v3) = 0) | ~ (element(v0, v2) = v4) | ~ (powerset(v2) = v3) | ? [v5] : ( ~ (v5 = 0) & in(v0, v1) = v5))
% 141.36/84.55 | (64) empty(all_0_6_6) = all_0_5_5
% 141.36/84.55 | (65) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : (relation_rng(v0) = v3 & relation(v0) = v2 & ( ~ (v2 = 0) | ( ! [v4] : ! [v5] : ( ~ (relation_rng(v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (relation_dom(v4) = v8 & subset(v3, v5) = v10 & subset(v1, v8) = v9 & subset(v0, v4) = v7 & relation(v4) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | (v10 = 0 & v9 = 0)))) & ! [v4] : ! [v5] : ( ~ (relation_dom(v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (relation_rng(v4) = v9 & subset(v3, v9) = v10 & subset(v1, v5) = v8 & subset(v0, v4) = v7 & relation(v4) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | (v10 = 0 & v8 = 0)))) & ! [v4] : ( ~ (subset(v0, v4) = 0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (relation_rng(v4) = v8 & relation_dom(v4) = v6 & subset(v3, v8) = v9 & subset(v1, v6) = v7 & relation(v4) = v5 & ( ~ (v5 = 0) | (v9 = 0 & v7 = 0)))) & ! [v4] : ( ~ (relation(v4) = 0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (relation_rng(v4) = v8 & relation_dom(v4) = v6 & subset(v3, v8) = v9 & subset(v1, v6) = v7 & subset(v0, v4) = v5 & ( ~ (v5 = 0) | (v9 = 0 & v7 = 0))))))))
% 141.36/84.55 | (66) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1))
% 141.36/84.55 | (67) ? [v0] : ? [v1] : ? [v2] : (cast_to_subset(v0) = v1 & element(v1, v2) = 0 & powerset(v0) = v2)
% 141.36/84.55 | (68) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v2) = v4) | ? [v5] : ? [v6] : (in(v3, v1) = v6 & in(v3, v0) = v5 & ( ~ (v5 = 0) | v6 = 0)))
% 141.36/84.55 | (69) ! [v0] : ! [v1] : (v1 = 0 | ~ (empty(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation_rng(v0) = v3 & relation(v0) = v2 & empty(v3) = v4 & ( ~ (v4 = 0) | ~ (v2 = 0))))
% 141.36/84.55 | (70) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 141.36/84.55 | (71) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_difference(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (element(v3, v4) = v7 & element(v2, v4) = v6 & element(v1, v4) = v5 & powerset(v0) = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | v7 = 0)))
% 141.36/84.55 | (72) relation_dom(empty_set) = empty_set
% 141.36/84.55 | (73) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng(v1) = v2) | ~ (relation(v0) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_composition(v0, v1) = v4 & relation_rng(v4) = v5 & subset(v5, v2) = v6 & relation(v1) = v3 & ( ~ (v3 = 0) | v6 = 0)))
% 141.36/84.55 | (74) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation(v0) = v3 & empty(v1) = v4 & empty(v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2 = 0)))
% 141.36/84.55 | (75) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v5 & in(v3, v0) = v6 & ( ~ (v5 = 0) | v6 = 0)))
% 141.36/84.55 | (76) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_field(v0) = v3 & relation_dom(v0) = v4 & set_union2(v4, v1) = v5 & relation(v0) = v2 & ( ~ (v2 = 0) | v5 = v3)))
% 141.36/84.55 | (77) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = 0 | ~ (relation_image(v0, v1) = v2) | ~ (relation(v0) = 0) | ~ (in(v5, v1) = 0) | ~ (in(v3, v2) = v4) | ? [v6] : ? [v7] : ( ~ (v7 = 0) & ordered_pair(v5, v3) = v6 & in(v6, v0) = v7))
% 141.36/84.55 | (78) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation(v1) = v4 & empty(v1) = v3 & empty(v0) = v2 & ( ~ (v2 = 0) | (v4 = 0 & v3 = 0))))
% 141.36/84.55 | (79) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (relation_inverse(v0) = v1) | ~ (relation(v2) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (( ~ (v3 = 0) & relation(v0) = v3) | (ordered_pair(v4, v3) = v7 & ordered_pair(v3, v4) = v5 & in(v7, v0) = v8 & in(v5, v2) = v6 & ( ~ (v8 = 0) | ~ (v6 = 0)) & (v8 = 0 | v6 = 0))))
% 141.36/84.55 | (80) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation(v0) = v3 & empty(v1) = v4 & empty(v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2 = 0)))
% 141.36/84.55 | (81) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (unordered_pair(v1, v2) = v3) | ? [v4] : ? [v5] : (in(v4, v0) = v5 & ( ~ (v5 = 0) | ( ~ (v4 = v2) & ~ (v4 = v1))) & (v5 = 0 | v4 = v2 | v4 = v1)))
% 141.36/84.55 | (82) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (relation_rng(v0) = v2 & relation_dom(v0) = v1 & cartesian_product2(v1, v2) = v3 & subset(v0, v3) = 0))
% 141.58/84.55 | (83) ! [v0] : ! [v1] : (v1 = v0 | ~ (relation(v1) = 0) | ~ (relation(v0) = 0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (ordered_pair(v2, v3) = v4 & in(v4, v1) = v6 & in(v4, v0) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)) & (v6 = 0 | v5 = 0)))
% 141.58/84.55 | (84) powerset(empty_set) = all_0_8_8
% 141.58/84.55 | (85) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (relation_inverse_image(v2, v1) = v4) | ~ (relation_inverse_image(v2, v0) = v3) | ~ (subset(v3, v4) = v5) | ? [v6] : ? [v7] : (subset(v0, v1) = v7 & relation(v2) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0))))
% 141.58/84.55 | (86) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_complement(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (set_difference(v0, v1) = v5 & element(v1, v3) = v4 & powerset(v0) = v3 & ( ~ (v4 = 0) | v5 = v2)))
% 141.58/84.55 | (87) ? [v0] : (v0 = empty_set | ? [v1] : in(v1, v0) = 0)
% 141.58/84.55 | (88) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = v0))
% 141.58/84.55 | (89) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2)
% 141.58/84.55 | (90) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2)
% 141.58/84.55 | (91) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v1, v2) = v3))
% 141.58/84.55 | (92) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0))
% 141.58/84.55 | (93) ! [v0] : ! [v1] : (v0 = empty_set | ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : (relation_rng(v0) = v3 & relation(v0) = v2 & ( ~ (v2 = 0) | ( ~ (v3 = empty_set) & ~ (v1 = empty_set)))))
% 141.58/84.55 | (94) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (element(v1, v2) = 0) | ~ (powerset(v0) = v2) | ~ (in(v3, v1) = 0) | in(v3, v0) = 0)
% 141.58/84.55 | (95) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ (relation(v0) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_rng(v2) = v4 & relation_rng(v1) = v5 & subset(v4, v5) = v6 & relation(v1) = v3 & ( ~ (v3 = 0) | v6 = 0)))
% 141.58/84.55 | (96) ! [v0] : ! [v1] : ! [v2] : (v1 = empty_set | ~ (union_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (subset_difference(v0, v6, v2) = v7 & meet_of_subsets(v0, v8) = v9 & complements_of_subsets(v0, v1) = v8 & cast_to_subset(v0) = v6 & element(v1, v4) = v5 & powerset(v3) = v4 & powerset(v0) = v3 & ( ~ (v5 = 0) | v9 = v7)))
% 141.58/84.56 | (97) ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_rng(v0) = v4 & relation_dom(v0) = v3 & set_union2(v3, v4) = v5 & relation(v0) = v2 & ( ~ (v2 = 0) | v5 = v1)))
% 141.58/84.56 | (98) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_difference(v0, v2) = v3) | ~ (singleton(v1) = v2) | in(v1, v0) = 0)
% 141.58/84.56 | (99) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (element(v1, v2) = 0) | ~ (powerset(v0) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ( ~ (v5 = 0) & in(v3, v1) = v5))
% 141.58/84.56 | (100) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = empty_set | ~ (set_meet(v0) = v1) | ~ (in(v3, v0) = 0) | ~ (in(v2, v1) = 0) | in(v2, v3) = 0)
% 141.58/84.56 | (101) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : (set_difference(v1, v0) = v3 & set_union2(v0, v3) = v2))
% 141.58/84.56 | (102) singleton(empty_set) = all_0_8_8
% 141.58/84.56 | (103) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (element(v1, v3) = 0) | ~ (powerset(v2) = v3) | ~ (powerset(v0) = v2) | ? [v4] : (union_of_subsets(v0, v1) = v4 & element(v4, v2) = 0))
% 141.58/84.56 | (104) ! [v0] : ! [v1] : ! [v2] : ( ~ (complements_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (complements_of_subsets(v0, v2) = v6 & element(v1, v4) = v5 & powerset(v3) = v4 & powerset(v0) = v3 & ( ~ (v5 = 0) | v6 = v1)))
% 141.58/84.56 | (105) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ? [v3] : ? [v4] : (subset(v2, v1) = v4 & relation(v1) = v3 & ( ~ (v3 = 0) | v4 = 0)))
% 141.58/84.56 | (106) ? [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (relation_dom(v1) = v2) | ~ (in(v3, v2) = v4) | ? [v5] : ? [v6] : ((apply(v1, v3) = v5 & ( ~ (v5 = v0) | v0 = empty_set) & ( ~ (v0 = empty_set) | v5 = empty_set)) | (relation(v1) = v5 & function(v1) = v6 & ( ~ (v6 = 0) | ~ (v5 = 0)))))
% 141.58/84.56 | (107) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0))
% 141.58/84.56 | (108) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v1, v0) = v2) | ? [v3] : ? [v4] : ? [v5] : (relation_composition(v4, v1) = v5 & identity_relation(v0) = v4 & relation(v1) = v3 & ( ~ (v3 = 0) | v5 = v2)))
% 141.58/84.56 | (109) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (element(v1, v3) = 0) | ~ (powerset(v2) = v3) | ~ (powerset(v0) = v2) | ? [v4] : (union_of_subsets(v0, v1) = v4 & union(v1) = v4))
% 141.58/84.56 | (110) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v0) = v1) | ~ (subset(v2, v0) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v2, v1) = v4))
% 141.58/84.56 | (111) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(empty_set, v0) = v1))
% 141.58/84.56 | (112) ! [v0] : ! [v1] : ! [v2] : ( ~ (empty(v2) = 0) | ~ (in(v0, v1) = 0) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & element(v1, v3) = v4 & powerset(v2) = v3))
% 141.58/84.56 | (113) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v0 | v2 = v0 | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v4))
% 141.58/84.56 | (114) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0))
% 141.58/84.56 | (115) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v2) = v4) | ? [v5] : ? [v6] : (in(v3, v1) = v6 & in(v3, v0) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0))))
% 141.58/84.56 | (116) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | subset(v0, v2) = 0)
% 141.58/84.56 | (117) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (ordered_pair(v0, v1) = v3) | ~ (in(v3, v2) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (relation_field(v2) = v5 & relation(v2) = v4 & in(v1, v5) = v7 & in(v0, v5) = v6 & ( ~ (v4 = 0) | (v7 = 0 & v6 = 0))))
% 141.58/84.56 | (118) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | (v4 = 0 & ~ (v6 = 0)))))
% 141.58/84.56 | (119) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : (singleton(v0) = v2 & subset(v2, v1) = 0))
% 141.58/84.56 | (120) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (element(v1, v3) = 0) | ~ (powerset(v2) = v3) | ~ (powerset(v0) = v2) | ? [v4] : (meet_of_subsets(v0, v1) = v4 & element(v4, v2) = 0))
% 141.58/84.56 | (121) ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v0, v1) = 0) | ~ (in(v2, v1) = 0) | ? [v3] : ( ~ (v3 = 0) & in(v2, v0) = v3))
% 141.58/84.56 | (122) ! [v0] : ( ~ (empty(v0) = 0) | function(v0) = 0)
% 141.58/84.56 | (123) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3))
% 141.58/84.56 | (124) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (singleton(v1) = v3) | ~ (singleton(v0) = v2) | ~ (subset(v2, v3) = 0))
% 141.58/84.56 | (125) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & proper_subset(v0, v1) = v3))
% 141.58/84.56 | (126) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v1) = v4) | ~ (cartesian_product2(v2, v0) = v3) | ~ (subset(v3, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (cartesian_product2(v1, v2) = v8 & cartesian_product2(v0, v2) = v7 & subset(v7, v8) = v9 & subset(v0, v1) = v6 & ( ~ (v6 = 0) | (v9 = 0 & v5 = 0))))
% 141.58/84.56 | (127) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_dom(v0) = v3 & cartesian_product2(v3, v1) = v4 & subset(v0, v4) = v5 & relation(v0) = v2 & ( ~ (v2 = 0) | v5 = 0)))
% 141.58/84.56 | (128) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (element(v1, v3) = 0) | ~ (powerset(v2) = v3) | ~ (powerset(v0) = v2) | ? [v4] : (complements_of_subsets(v0, v1) = v4 & element(v4, v3) = 0))
% 141.58/84.56 | (129) in(all_0_16_16, all_0_11_11) = all_0_10_10
% 141.58/84.56 | (130) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 141.58/84.56 | (131) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v1, v0) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_dom(v2) = v4 & relation_dom(v1) = v5 & set_intersection2(v5, v0) = v6 & relation(v1) = v3 & ( ~ (v3 = 0) | v6 = v4)))
% 141.58/84.56 | (132) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_complement(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (subset_complement(v0, v2) = v5 & element(v1, v3) = v4 & powerset(v0) = v3 & ( ~ (v4 = 0) | v5 = v1)))
% 141.58/84.56 | (133) ! [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)))
% 141.58/84.56 | (134) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3))
% 141.58/84.56 | (135) ! [v0] : ! [v1] : ( ~ (subset(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & proper_subset(v0, v0) = v2))
% 141.58/84.56 | (136) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1))
% 141.58/84.56 | (137) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation(v1) = v4 & empty(v1) = v3 & empty(v0) = v2 & ( ~ (v2 = 0) | (v4 = 0 & v3 = 0))))
% 141.58/84.56 | (138) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1))
% 141.58/84.56 | (139) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = empty_set | ~ (element(v1, v3) = 0) | ~ (powerset(v2) = v3) | ~ (powerset(v0) = v2) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (subset_difference(v0, v4, v5) = v6 & meet_of_subsets(v0, v7) = v6 & union_of_subsets(v0, v1) = v5 & complements_of_subsets(v0, v1) = v7 & cast_to_subset(v0) = v4))
% 141.58/84.56 | (140) ! [v0] : ! [v1] : (v1 = 0 | ~ (function(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2))
% 141.58/84.56 | (141) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (subset(v3, v2) = v4) | ~ (unordered_pair(v0, v1) = v3) | ? [v5] : ? [v6] : (in(v1, v2) = v6 & in(v0, v2) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0))))
% 141.58/84.56 | (142) ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : ? [v3] : ? [v4] : (in(v2, v1) = v4 & in(v2, v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)) & (v4 = 0 | v3 = 0)))
% 141.58/84.56 | (143) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1))
% 141.58/84.56 | (144) ! [v0] : ! [v1] : ! [v2] : ( ~ (meet_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (element(v2, v3) = v6 & element(v1, v4) = v5 & powerset(v3) = v4 & powerset(v0) = v3 & ( ~ (v5 = 0) | v6 = 0)))
% 141.58/84.56 | (145) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (subset_complement(v0, v3) = v4) | ~ (element(v1, v2) = 0) | ~ (powerset(v0) = v2) | ? [v5] : ? [v6] : ? [v7] : (disjoint(v1, v3) = v6 & element(v3, v2) = v5 & subset(v1, v4) = v7 & ( ~ (v5 = 0) | (( ~ (v7 = 0) | v6 = 0) & ( ~ (v6 = 0) | v7 = 0)))))
% 141.58/84.57 | (146) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0)))
% 141.58/84.57 | (147) ! [v0] : (v0 = empty_set | ~ (set_meet(empty_set) = v0))
% 141.58/84.57 | (148) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (element(v1, v3) = 0) | ~ (powerset(v2) = v3) | ~ (powerset(v0) = v2) | ? [v4] : (meet_of_subsets(v0, v1) = v4 & set_meet(v1) = v4))
% 141.58/84.57 | (149) ! [v0] : ! [v1] : ! [v2] : ( ~ (meet_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (element(v1, v4) = v5 & powerset(v3) = v4 & powerset(v0) = v3 & set_meet(v1) = v6 & ( ~ (v5 = 0) | v6 = v2)))
% 141.58/84.57 | (150) relation_empty_yielding(all_0_7_7) = 0
% 141.58/84.57 | (151) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng(v0) = v1) | ~ (in(v2, v1) = 0) | ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & ordered_pair(v3, v2) = v4 & in(v4, v0) = 0) | ( ~ (v3 = 0) & relation(v0) = v3)))
% 141.58/84.57 | (152) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_intersection2(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3))
% 141.58/84.57 | (153) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (subset(v0, v1) = 0) | ~ (ordered_pair(v2, v3) = v4) | ~ (relation(v0) = 0) | ? [v5] : ? [v6] : (( ~ (v5 = 0) & relation(v1) = v5) | (in(v4, v1) = v6 & in(v4, v0) = v5 & ( ~ (v5 = 0) | v6 = 0))))
% 141.58/84.57 | (154) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_composition(v3, v2) = v1) | ~ (relation_composition(v3, v2) = v0))
% 141.58/84.57 | (155) relation_empty_yielding(empty_set) = 0
% 141.58/84.57 | (156) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_dom(v3) = v4) | ~ (relation_dom_restriction(v2, v1) = v3) | ~ (in(v0, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (relation_dom(v2) = v8 & relation(v2) = v6 & in(v0, v8) = v9 & in(v0, v1) = v7 & ( ~ (v6 = 0) | (( ~ (v9 = 0) | ~ (v7 = 0) | v5 = 0) & ( ~ (v5 = 0) | (v9 = 0 & v7 = 0))))))
% 141.58/84.57 | (157) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = empty_set | ~ (element(v1, v3) = 0) | ~ (powerset(v2) = v3) | ~ (powerset(v0) = v2) | ? [v4] : ( ~ (v4 = empty_set) & complements_of_subsets(v0, v1) = v4))
% 141.58/84.57 | (158) ! [v0] : ! [v1] : ! [v2] : (v1 = empty_set | ~ (complements_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (subset_difference(v0, v6, v7) = v8 & meet_of_subsets(v0, v2) = v9 & union_of_subsets(v0, v1) = v7 & cast_to_subset(v0) = v6 & element(v1, v4) = v5 & powerset(v3) = v4 & powerset(v0) = v3 & ( ~ (v5 = 0) | v9 = v8)))
% 141.58/84.57 | (159) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation_rng(v0) = v4 & relation_image(v0, v1) = v3 & relation(v0) = v2 & ( ~ (v2 = 0) | v4 = v3)))
% 141.58/84.57 | (160) ! [v0] : (v0 = empty_set | ~ (subset(v0, empty_set) = 0))
% 141.58/84.57 | (161) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_rng_restriction(v0, v2) = v3) | ~ (relation_dom_restriction(v3, v1) = v4) | ? [v5] : ? [v6] : ? [v7] : (relation_rng_restriction(v0, v6) = v7 & relation_dom_restriction(v2, v1) = v6 & relation(v2) = v5 & ( ~ (v5 = 0) | v7 = v4)))
% 141.58/84.57 | (162) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (meet_of_subsets(v0, v1) = v5 & element(v1, v3) = v4 & powerset(v2) = v3 & powerset(v0) = v2 & set_meet(v1) = v6 & ( ~ (v4 = 0) | v6 = v5))
% 141.58/84.57 | (163) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v6 & in(v3, v1) = v5 & (v6 = 0 | ( ~ (v5 = 0) & ~ (v4 = 0)))))
% 141.58/84.57 | (164) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (subset(v5, v1) = v6 & subset(v2, v1) = v4 & subset(v0, v1) = v3 & set_union2(v0, v2) = v5 & ( ~ (v4 = 0) | ~ (v3 = 0) | v6 = 0))
% 141.58/84.57 | (165) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : (relation_rng(v0) = v2 & relation_dom(v0) = v1 & ! [v3] : ! [v4] : ( ~ (relation_composition(v3, v0) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (relation_rng(v4) = v8 & relation_rng(v3) = v6 & subset(v1, v6) = v7 & relation(v3) = v5 & ( ~ (v7 = 0) | ~ (v5 = 0) | v8 = v2))) & ! [v3] : ! [v4] : ( ~ (relation_rng(v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (relation_composition(v3, v0) = v7 & relation_rng(v7) = v8 & subset(v1, v4) = v6 & relation(v3) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | v8 = v2))) & ! [v3] : ( ~ (relation(v3) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (relation_composition(v3, v0) = v6 & relation_rng(v6) = v7 & relation_rng(v3) = v4 & subset(v1, v4) = v5 & ( ~ (v5 = 0) | v7 = v2)))))
% 141.58/84.57 | (166) ! [v0] : ! [v1] : ( ~ (proper_subset(v0, v1) = 0) | subset(v0, v1) = 0)
% 141.58/84.57 | (167) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v1, v2) = v4) | ~ (cartesian_product2(v0, v2) = v3) | ~ (subset(v3, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (cartesian_product2(v2, v1) = v8 & cartesian_product2(v2, v0) = v7 & subset(v7, v8) = v9 & subset(v0, v1) = v6 & ( ~ (v6 = 0) | (v9 = 0 & v5 = 0))))
% 141.58/84.57 | (168) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (union(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (in(v3, v0) = v4 & ( ~ (v4 = 0) | ( ! [v8] : ( ~ (in(v8, v1) = 0) | ? [v9] : ( ~ (v9 = 0) & in(v3, v8) = v9)) & ! [v8] : ( ~ (in(v3, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & in(v8, v1) = v9)))) & (v4 = 0 | (v7 = 0 & v6 = 0 & in(v5, v1) = 0 & in(v3, v5) = 0))))
% 141.58/84.57 | (169) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v1, v0) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation(v2) = v6 & relation(v1) = v4 & empty(v2) = v5 & empty(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | (v6 = 0 & v5 = 0))))
% 141.58/84.57 | (170) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0))
% 141.58/84.57 | (171) ! [v0] : ! [v1] : (v1 = v0 | ~ (subset(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v0, v1) = v2))
% 141.58/84.57 | (172) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (relation_composition(v5, v3) = v6) | ~ (identity_relation(v2) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ (in(v4, v6) = v7) | ? [v8] : ? [v9] : ? [v10] : (relation(v3) = v8 & in(v4, v3) = v10 & in(v0, v2) = v9 & ( ~ (v8 = 0) | (( ~ (v10 = 0) | ~ (v9 = 0) | v7 = 0) & ( ~ (v7 = 0) | (v10 = 0 & v9 = 0))))))
% 141.58/84.57 | (173) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_inverse(v0) = v1) | ~ (ordered_pair(v3, v2) = v4) | ~ (relation(v1) = 0) | ? [v5] : ? [v6] : ? [v7] : (( ~ (v5 = 0) & relation(v0) = v5) | (ordered_pair(v2, v3) = v5 & in(v5, v1) = v6 & in(v4, v0) = v7 & ( ~ (v6 = 0) | v7 = 0))))
% 141.58/84.57 | (174) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_rng_restriction(v0, v3) = v4) | ~ (relation_dom_restriction(v2, v1) = v3) | ? [v5] : ? [v6] : ? [v7] : (relation_rng_restriction(v0, v2) = v6 & relation_dom_restriction(v6, v1) = v7 & relation(v2) = v5 & ( ~ (v5 = 0) | v7 = v4)))
% 141.58/84.57 | (175) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = 0 | ~ (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v4) = v5) | ~ (in(v2, v1) = v3) | ? [v6] : (( ~ (v6 = 0) & relation(v0) = v6) | ( ~ (v6 = 0) & in(v5, v0) = v6)))
% 141.58/84.57 | (176) ! [v0] : ! [v1] : ( ~ (cast_to_subset(v0) = v1) | ? [v2] : (element(v1, v2) = 0 & powerset(v0) = v2))
% 141.58/84.57 | (177) relation(all_0_4_4) = 0
% 141.58/84.57 | (178) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (subset(v3, v1) = v4) | ~ (set_union2(v0, v2) = v3) | ? [v5] : ? [v6] : (subset(v2, v1) = v6 & subset(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0))))
% 141.58/84.57 | (179) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_field(v2) = v1) | ~ (relation_field(v2) = v0))
% 141.58/84.57 | (180) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 141.58/84.57 | (181) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (ordered_pair(v1, v2) = v3) | ~ (relation(v0) = 0) | ? [v4] : ? [v5] : (in(v3, v0) = v5 & in(v3, v0) = v4 & ( ~ (v4 = 0) | v5 = 0)))
% 141.58/84.57 | (182) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cast_to_subset(v2) = v1) | ~ (cast_to_subset(v2) = v0))
% 141.58/84.57 | (183) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (complements_of_subsets(v3, v2) = v1) | ~ (complements_of_subsets(v3, v2) = v0))
% 141.58/84.57 | (184) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_difference(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & disjoint(v0, v1) = v3))
% 141.58/84.57 | (185) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ (relation(v2) = 0) | ~ (relation(v0) = 0) | ? [v6] : ? [v7] : ? [v8] : (in(v5, v2) = v8 & in(v5, v0) = v7 & in(v3, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v8 = 0)))
% 141.58/84.57 | (186) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : (relation_dom(v0) = v1 & ! [v2] : ! [v3] : ( ~ (relation_composition(v0, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : (relation_dom(v3) = v5 & subset(v5, v1) = v6 & relation(v2) = v4 & ( ~ (v4 = 0) | v6 = 0))) & ! [v2] : ( ~ (relation(v2) = 0) | ? [v3] : ? [v4] : (relation_composition(v0, v2) = v3 & relation_dom(v3) = v4 & subset(v4, v1) = 0))))
% 141.58/84.57 | (187) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_image(v1, v0) = v2) | ? [v3] : ? [v4] : ? [v5] : (relation_rng(v1) = v4 & subset(v2, v4) = v5 & relation(v1) = v3 & ( ~ (v3 = 0) | v5 = 0)))
% 141.58/84.57 | (188) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (subset(v3, v4) = v5) | ~ (set_intersection2(v1, v2) = v4) | ~ (set_intersection2(v0, v2) = v3) | ? [v6] : ( ~ (v6 = 0) & subset(v0, v1) = v6))
% 141.58/84.58 | (189) ! [v0] : ! [v1] : ! [v2] : ( ~ (union_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (element(v2, v3) = v6 & element(v1, v4) = v5 & powerset(v3) = v4 & powerset(v0) = v3 & ( ~ (v5 = 0) | v6 = 0)))
% 141.58/84.58 | (190) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2)
% 141.58/84.58 | (191) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2)
% 141.58/84.58 | (192) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v0, v2) = v3))
% 141.58/84.58 | (193) ! [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)))
% 141.58/84.58 | (194) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_inverse(v0) = v3 & relation_rng(v3) = v6 & relation_dom(v3) = v4 & relation_dom(v0) = v5 & relation(v0) = v2 & ( ~ (v2 = 0) | (v6 = v5 & v4 = v1))))
% 141.58/84.58 | (195) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (proper_subset(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3))
% 141.58/84.58 | (196) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation_dom(v0) = v3 & relation_image(v0, v3) = v4 & relation(v0) = v2 & ( ~ (v2 = 0) | v4 = v1)))
% 141.58/84.58 | (197) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (disjoint(v1, v2) = 0) | ~ (disjoint(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 141.58/84.58 | (198) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : ? [v4] : (in(v3, v0) = v4 & ( ~ (v4 = 0) | ~ (v3 = v1)) & (v4 = 0 | v3 = v1)))
% 141.58/84.58 | (199) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & ordered_pair(v0, v1) = v3 & unordered_pair(v2, v4) = v3))
% 141.58/84.58 | (200) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (set_meet(v2) = v1) | ~ (set_meet(v2) = v0))
% 141.58/84.58 | (201) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v2) = v3) | ~ (subset(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & subset(v1, v2) = v4))
% 141.58/84.58 | (202) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_inverse_image(v0, v1) = v2) | ~ (relation(v0) = 0) | ~ (in(v3, v2) = 0) | ? [v4] : ? [v5] : (ordered_pair(v3, v4) = v5 & in(v5, v0) = 0 & in(v4, v1) = 0))
% 141.58/84.58 | (203) (all_0_9_9 = all_0_15_15 & all_0_10_10 = 0 & ~ (all_0_12_12 = 0)) | (all_0_12_12 = 0 & ( ~ (all_0_9_9 = all_0_15_15) | ~ (all_0_10_10 = 0)))
% 141.58/84.58 | (204) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (element(v1, v3) = 0) | ~ (powerset(v2) = v3) | ~ (in(v0, v1) = 0) | element(v0, v2) = 0)
% 141.58/84.58 | (205) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v0) = v1) | ~ (in(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v2, v0) = v4))
% 141.58/84.58 | (206) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ( ~ (v3 = empty_set) & set_difference(v0, v1) = v3))
% 141.58/84.58 | (207) ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_difference(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3))
% 141.58/84.58 | (208) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3))
% 141.58/84.58 | (209) ? [v0] : ? [v1] : (in(v0, v1) = 0 & ! [v2] : ! [v3] : (v3 = 0 | ~ (are_equipotent(v2, v1) = v3) | ? [v4] : ? [v5] : (subset(v2, v1) = v4 & in(v2, v1) = v5 & ( ~ (v4 = 0) | v5 = 0))) & ! [v2] : ! [v3] : (v3 = 0 | ~ (in(v2, v1) = v3) | ? [v4] : ? [v5] : (are_equipotent(v2, v1) = v5 & subset(v2, v1) = v4 & ( ~ (v4 = 0) | v5 = 0))) & ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ? [v4] : ? [v5] : (in(v3, v1) = v5 & in(v2, v1) = v4 & ( ~ (v4 = 0) | v5 = 0))) & ! [v2] : ! [v3] : ( ~ (subset(v3, v2) = 0) | ? [v4] : ? [v5] : (in(v3, v1) = v5 & in(v2, v1) = v4 & ( ~ (v4 = 0) | v5 = 0))) & ! [v2] : ( ~ (subset(v2, v1) = 0) | ? [v3] : ? [v4] : (are_equipotent(v2, v1) = v3 & in(v2, v1) = v4 & (v4 = 0 | v3 = 0))) & ! [v2] : ( ~ (in(v2, v1) = 0) | ? [v3] : (powerset(v2) = v3 & in(v3, v1) = 0)))
% 141.58/84.58 | (210) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (relation_inverse_image(v1, v2) = v3) | ~ (relation(v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (in(v4, v0) = v5 & ( ~ (v5 = 0) | ( ! [v10] : ! [v11] : ( ~ (ordered_pair(v4, v10) = v11) | ? [v12] : ? [v13] : (in(v11, v1) = v12 & in(v10, v2) = v13 & ( ~ (v13 = 0) | ~ (v12 = 0)))) & ! [v10] : ( ~ (in(v10, v2) = 0) | ? [v11] : ? [v12] : ( ~ (v12 = 0) & ordered_pair(v4, v10) = v11 & in(v11, v1) = v12)))) & (v5 = 0 | (v9 = 0 & v8 = 0 & ordered_pair(v4, v6) = v7 & in(v7, v1) = 0 & in(v6, v2) = 0))))
% 141.58/84.58 | (211) ! [v0] : ! [v1] : ( ~ (set_intersection2(v0, v1) = empty_set) | disjoint(v0, v1) = 0)
% 141.58/84.58 | (212) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | set_intersection2(v0, v1) = empty_set)
% 141.58/84.58 | (213) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : (relation_inverse(v1) = v0 & relation_inverse(v0) = v1))
% 141.58/84.58 | (214) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v5 & in(v3, v0) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = 0))))
% 141.58/84.58 | (215) ! [v0] : ! [v1] : (v0 = empty_set | ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : (relation_dom(v0) = v3 & relation(v0) = v2 & ( ~ (v2 = 0) | ( ~ (v3 = empty_set) & ~ (v1 = empty_set)))))
% 141.58/84.58 | (216) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : (relation_dom(v0) = v3 & relation(v0) = v2 & ( ~ (v2 = 0) | ( ! [v4] : ! [v5] : ( ~ (relation_composition(v0, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (relation_dom(v5) = v9 & relation_dom(v4) = v7 & subset(v1, v7) = v8 & relation(v4) = v6 & ( ~ (v8 = 0) | ~ (v6 = 0) | v9 = v3))) & ! [v4] : ! [v5] : ( ~ (relation_dom(v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (relation_composition(v0, v4) = v8 & relation_dom(v8) = v9 & subset(v1, v5) = v7 & relation(v4) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = v3))) & ! [v4] : ( ~ (relation(v4) = 0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (relation_composition(v0, v4) = v7 & relation_dom(v7) = v8 & relation_dom(v4) = v5 & subset(v1, v5) = v6 & ( ~ (v6 = 0) | v8 = v3)))))))
% 141.58/84.58 | (217) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (disjoint(v2, v1) = v3) | ~ (singleton(v0) = v2) | in(v0, v1) = 0)
% 141.58/84.58 | (218) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ (in(v4, v5) = 0) | (in(v1, v3) = 0 & in(v0, v2) = 0))
% 141.58/84.58 | (219) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v0 = empty_set | ~ (subset_complement(v0, v2) = v3) | ~ (powerset(v0) = v1) | ~ (in(v4, v2) = v5) | ? [v6] : ? [v7] : (( ~ (v6 = 0) & element(v2, v1) = v6) | (element(v4, v0) = v6 & in(v4, v3) = v7 & ( ~ (v6 = 0) | v7 = 0))))
% 141.58/84.58 | (220) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0))
% 141.58/84.58 | (221) function(all_0_14_14) = 0
% 141.58/84.58 | (222) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_inverse_image(v1, v0) = v2) | ? [v3] : ? [v4] : ? [v5] : (relation_dom(v1) = v4 & subset(v2, v4) = v5 & relation(v1) = v3 & ( ~ (v3 = 0) | v5 = 0)))
% 141.58/84.58 | (223) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 141.58/84.58 | (224) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v0, v1) = v2) | ? [v3] : (disjoint(v3, v1) = 0 & singleton(v0) = v3))
% 141.58/84.58 | (225) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : (relation_dom(v0) = v3 & relation(v0) = v2 & ( ~ (v2 = 0) | ( ! [v4] : ! [v5] : ( ~ (relation_rng(v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (relation_dom(v4) = v8 & subset(v3, v8) = v9 & subset(v1, v5) = v10 & subset(v0, v4) = v7 & relation(v4) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | (v10 = 0 & v9 = 0)))) & ! [v4] : ! [v5] : ( ~ (relation_dom(v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (relation_rng(v4) = v9 & subset(v3, v5) = v8 & subset(v1, v9) = v10 & subset(v0, v4) = v7 & relation(v4) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | (v10 = 0 & v8 = 0)))) & ! [v4] : ( ~ (subset(v0, v4) = 0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (relation_rng(v4) = v8 & relation_dom(v4) = v6 & subset(v3, v6) = v7 & subset(v1, v8) = v9 & relation(v4) = v5 & ( ~ (v5 = 0) | (v9 = 0 & v7 = 0)))) & ! [v4] : ( ~ (relation(v4) = 0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (relation_rng(v4) = v8 & relation_dom(v4) = v6 & subset(v3, v6) = v7 & subset(v1, v8) = v9 & subset(v0, v4) = v5 & ( ~ (v5 = 0) | (v9 = 0 & v7 = 0))))))))
% 141.58/84.58 | (226) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (relation_rng_restriction(v0, v1) = v2) | ~ (relation(v3) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (( ~ (v4 = 0) & relation(v1) = v4) | (ordered_pair(v4, v5) = v6 & in(v6, v3) = v7 & in(v6, v1) = v9 & in(v5, v0) = v8 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0)) & (v7 = 0 | (v9 = 0 & v8 = 0)))))
% 141.58/84.59 | (227) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : (relation_rng(v0) = v2 & relation_dom(v0) = v1 & ( ~ (v2 = empty_set) | v1 = empty_set) & ( ~ (v1 = empty_set) | v2 = empty_set)))
% 141.58/84.59 | (228) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v2, v0) = v4))
% 141.58/84.59 | (229) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 141.58/84.59 | (230) ! [v0] : ! [v1] : (v1 = v0 | ~ (cast_to_subset(v0) = v1))
% 141.58/84.59 | (231) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng(v0) = v1) | ~ (relation(v2) = 0) | ? [v3] : ? [v4] : ? [v5] : ((v5 = v4 & relation_composition(v0, v2) = v3 & relation_rng(v3) = v4 & relation_image(v2, v1) = v4) | ( ~ (v3 = 0) & relation(v0) = v3)))
% 141.58/84.59 | (232) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v5 & in(v3, v0) = v6 & ( ~ (v5 = 0) | (v6 = 0 & ~ (v4 = 0)))))
% 141.58/84.59 | (233) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_composition(v4, v1) = v5 & relation_dom_restriction(v1, v0) = v3 & identity_relation(v0) = v4 & relation(v1) = v2 & ( ~ (v2 = 0) | v5 = v3))
% 141.58/84.59 | (234) ? [v0] : ? [v1] : element(v1, v0) = 0
% 141.58/84.59 | (235) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v0 = empty_set | ~ (subset_complement(v0, v2) = v3) | ~ (powerset(v0) = v1) | ~ (in(v4, v3) = v5) | ? [v6] : ? [v7] : (( ~ (v6 = 0) & element(v2, v1) = v6) | (element(v4, v0) = v6 & in(v4, v2) = v7 & ( ~ (v6 = 0) | v7 = 0))))
% 141.58/84.59 | (236) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ (relation(v2) = 0) | ~ (relation(v0) = 0) | ? [v6] : ? [v7] : ? [v8] : (in(v5, v2) = v6 & in(v5, v0) = v8 & in(v3, v1) = v7 & ( ~ (v6 = 0) | (v8 = 0 & v7 = 0))))
% 141.58/84.59 | (237) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ? [v2] : ? [v3] : (relation_inverse(v1) = v3 & relation(v0) = v2 & ( ~ (v2 = 0) | v3 = v0)))
% 141.58/84.59 | (238) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ((apply(v0, v2) = v6 & in(v4, v0) = v7 & in(v2, v1) = v5 & ( ~ (v5 = 0) | (( ~ (v7 = 0) | v6 = v3) & ( ~ (v6 = v3) | v7 = 0)))) | (relation(v0) = v5 & function(v0) = v6 & ( ~ (v6 = 0) | ~ (v5 = 0)))))
% 141.58/84.59 | (239) function(all_0_0_0) = 0
% 141.58/84.59 | (240) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v1, v2) = 0) | ~ (subset(v0, v1) = 0) | subset(v0, v2) = 0)
% 141.58/84.59 | (241) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ? [v3] : ? [v4] : (relation(v2) = v4 & relation(v1) = v3 & ( ~ (v3 = 0) | v4 = 0)))
% 141.58/84.59 | (242) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ? [v4] : ? [v5] : (in(v3, v1) = v5 & in(v3, v0) = v4 & (v5 = 0 | v4 = 0)))
% 141.58/84.59 | (243) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : (set_difference(v2, v1) = v3 & set_difference(v0, v1) = v3))
% 141.58/84.59 | (244) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (ordered_pair(v0, v1) = v3) | ~ (in(v3, v2) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (relation_rng(v2) = v7 & relation_dom(v2) = v5 & relation(v2) = v4 & in(v1, v7) = v8 & in(v0, v5) = v6 & ( ~ (v4 = 0) | (v8 = 0 & v6 = 0))))
% 141.58/84.59 | (245) ! [v0] : ! [v1] : ! [v2] : ( ~ (element(v1, v0) = v2) | ? [v3] : ? [v4] : (empty(v1) = v4 & empty(v0) = v3 & ( ~ (v3 = 0) | (( ~ (v4 = 0) | v2 = 0) & ( ~ (v2 = 0) | v4 = 0)))))
% 141.58/84.59 | (246) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : (relation_dom(v0) = v1 & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = 0 | ~ (ordered_pair(v2, v4) = v5) | ~ (in(v2, v1) = v3) | ? [v6] : ( ~ (v6 = 0) & in(v5, v0) = v6)) & ! [v2] : ( ~ (in(v2, v1) = 0) | ? [v3] : ? [v4] : (ordered_pair(v2, v3) = v4 & in(v4, v0) = 0)) & ? [v2] : (v2 = v1 | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (in(v3, v2) = v4 & ( ~ (v4 = 0) | ! [v8] : ! [v9] : ( ~ (ordered_pair(v3, v8) = v9) | ? [v10] : ( ~ (v10 = 0) & in(v9, v0) = v10))) & (v4 = 0 | (v7 = 0 & ordered_pair(v3, v5) = v6 & in(v6, v0) = 0))))))
% 141.58/84.59 | (247) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_rng(v3) = v4) | ~ (relation_rng_restriction(v1, v2) = v3) | ~ (in(v0, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (relation_rng(v2) = v8 & relation(v2) = v6 & in(v0, v8) = v9 & in(v0, v1) = v7 & ( ~ (v6 = 0) | (( ~ (v9 = 0) | ~ (v7 = 0) | v5 = 0) & ( ~ (v5 = 0) | (v9 = 0 & v7 = 0))))))
% 141.58/84.59 | (248) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v1 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4))
% 141.58/84.59 | (249) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0))
% 141.58/84.59 | (250) ! [v0] : ! [v1] : ! [v2] : ( ~ (complements_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (element(v2, v4) = v6 & element(v1, v4) = v5 & powerset(v3) = v4 & powerset(v0) = v3 & ( ~ (v5 = 0) | v6 = 0)))
% 141.58/84.59 | (251) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ (relation(v0) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v6 = 0 & ~ (v7 = 0) & ordered_pair(v3, v4) = v5 & in(v5, v1) = v7 & in(v5, v0) = 0) | ( ~ (v3 = 0) & relation(v1) = v3)))
% 141.58/84.59 | (252) ! [v0] : (v0 = empty_set | ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ( ~ (v2 = empty_set) & ~ (v1 = empty_set) & relation_rng(v0) = v2 & relation_dom(v0) = v1))
% 141.58/84.59 | (253) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : (relation_rng(v0) = v2 & relation_dom(v0) = v1 & relation_image(v0, v1) = v2))
% 141.58/84.59 | (254) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (relation_inverse(v0) = v2 & relation_rng(v2) = v3 & relation_rng(v0) = v1 & relation_dom(v2) = v1 & relation_dom(v0) = v3))
% 141.58/84.59 | (255) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_difference(empty_set, v0) = v1))
% 141.58/84.59 | (256) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & disjoint(v2, v1) = v3 & singleton(v0) = v2))
% 141.58/84.59 | (257) ! [v0] : ! [v1] : ( ~ (relation(v0) = 0) | ~ (in(v1, v0) = 0) | ? [v2] : ? [v3] : ordered_pair(v2, v3) = v1)
% 141.58/84.59 | (258) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = 0 | ~ (cartesian_product2(v0, v1) = v2) | ~ (ordered_pair(v5, v6) = v3) | ~ (in(v3, v2) = v4) | ? [v7] : ? [v8] : (in(v6, v1) = v8 & in(v5, v0) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0))))
% 141.58/84.59 | (259) ! [v0] : ! [v1] : ! [v2] : (v1 = empty_set | ~ (meet_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (subset_difference(v0, v8, v2) = v9 & union_of_subsets(v0, v6) = v7 & complements_of_subsets(v0, v1) = v6 & cast_to_subset(v0) = v8 & element(v1, v4) = v5 & powerset(v3) = v4 & powerset(v0) = v3 & ( ~ (v5 = 0) | v9 = v7)))
% 141.58/84.59 | (260) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_inverse(v0) = v1) | ~ (ordered_pair(v3, v2) = v4) | ~ (relation(v1) = 0) | ? [v5] : ? [v6] : ? [v7] : (( ~ (v5 = 0) & relation(v0) = v5) | (ordered_pair(v2, v3) = v6 & in(v6, v1) = v7 & in(v4, v0) = v5 & ( ~ (v5 = 0) | v7 = 0))))
% 141.58/84.59 | (261) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (in(v0, v1) = v2))
% 141.58/84.59 | (262) in(all_0_13_13, all_0_14_14) = all_0_12_12
% 141.58/84.59 | (263) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v0 = empty_set | ~ (subset_complement(v0, v2) = v3) | ~ (element(v4, v0) = 0) | ~ (powerset(v0) = v1) | ? [v5] : ? [v6] : (( ~ (v5 = 0) & element(v2, v1) = v5) | (in(v4, v3) = v6 & in(v4, v2) = v5 & (v6 = 0 | v5 = 0))))
% 141.58/84.59 | (264) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (cartesian_product2(v1, v3) = v7 & cartesian_product2(v0, v2) = v6 & subset(v6, v7) = v8 & subset(v2, v3) = v5 & subset(v0, v1) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0) | v8 = 0))
% 141.58/84.59 | (265) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (are_equipotent(v3, v2) = v1) | ~ (are_equipotent(v3, v2) = v0))
% 141.58/84.59 | (266) ! [v0] : (v0 = empty_set | ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (ordered_pair(v1, v2) = v3 & in(v3, v0) = 0))
% 141.58/84.59 | (267) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v1, v0) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_rng(v2) = v4 & relation_rng(v1) = v5 & subset(v4, v5) = v6 & relation(v1) = v3 & ( ~ (v3 = 0) | v6 = 0)))
% 141.58/84.59 | (268) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v2) = v4) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & ~ (v5 = 0) & in(v3, v1) = v6 & in(v3, v0) = v5))
% 141.58/84.60 | (269) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0))
% 141.58/84.60 | (270) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (meet_of_subsets(v3, v2) = v1) | ~ (meet_of_subsets(v3, v2) = v0))
% 141.58/84.60 | (271) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v6 & in(v3, v0) = v5 & (v6 = 0 | ( ~ (v5 = 0) & ~ (v4 = 0)))))
% 141.58/84.60 | (272) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (set_union2(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3))
% 141.58/84.60 | (273) ! [v0] : ! [v1] : ! [v2] : ( ~ (union_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (union(v1) = v6 & element(v1, v4) = v5 & powerset(v3) = v4 & powerset(v0) = v3 & ( ~ (v5 = 0) | v6 = v2)))
% 141.58/84.60 | (274) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | v1 = empty_set | ~ (set_meet(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (in(v3, v0) = v4 & ( ~ (v4 = 0) | (v6 = 0 & ~ (v7 = 0) & in(v5, v1) = 0 & in(v3, v5) = v7)) & (v4 = 0 | ( ! [v8] : ! [v9] : (v9 = 0 | ~ (in(v3, v8) = v9) | ? [v10] : ( ~ (v10 = 0) & in(v8, v1) = v10)) & ! [v8] : ( ~ (in(v8, v1) = 0) | in(v3, v8) = 0)))))
% 141.58/84.60 | (275) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | set_union2(v0, v1) = v1)
% 141.58/84.60 | (276) ! [v0] : ! [v1] : (v1 = 0 | ~ (empty(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation_dom(v0) = v3 & relation(v0) = v2 & empty(v3) = v4 & ( ~ (v4 = 0) | ~ (v2 = 0))))
% 141.58/84.60 | (277) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (relation_composition(v0, v1) = v2) | ~ (ordered_pair(v6, v4) = v7) | ~ (ordered_pair(v3, v4) = v5) | ~ (relation(v2) = 0) | ~ (relation(v0) = 0) | ? [v8] : ? [v9] : ? [v10] : ((v8 = 0 & in(v5, v2) = 0) | ( ~ (v8 = 0) & relation(v1) = v8) | (ordered_pair(v3, v6) = v8 & in(v8, v0) = v9 & in(v7, v1) = v10 & ( ~ (v10 = 0) | ~ (v9 = 0)))))
% 141.58/84.60 | (278) ! [v0] : ! [v1] : (v1 = v0 | ~ (subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v1, v0) = v2))
% 141.58/84.60 | (279) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (set_difference(v1, v3) = v4) | ~ (singleton(v2) = v3) | ~ (subset(v0, v4) = v5) | ? [v6] : ? [v7] : (subset(v0, v1) = v6 & in(v2, v0) = v7 & ( ~ (v6 = 0) | v7 = 0)))
% 141.58/84.60 | (280) ! [v0] : ( ~ (empty(v0) = 0) | relation(v0) = 0)
% 141.58/84.60 | (281) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3))
% 141.58/84.60 | (282) ! [v0] : ! [v1] : (v1 = 0 | ~ (relation(v0) = v1) | ? [v2] : (in(v2, v0) = 0 & ! [v3] : ! [v4] : ~ (ordered_pair(v3, v4) = v2)))
% 141.58/84.60 | (283) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0)
% 141.58/84.60 | (284) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (disjoint(v0, v1) = v3 & set_intersection2(v0, v1) = v2 & ( ~ (v3 = 0) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & in(v4, v2) = v5)))
% 141.58/84.60 | (285) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_dom(v1) = v4 & relation_image(v1, v5) = v6 & relation_image(v1, v0) = v3 & set_intersection2(v4, v0) = v5 & relation(v1) = v2 & ( ~ (v2 = 0) | v6 = v3))
% 141.58/84.60 | (286) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | (in(v3, v1) = 0 & in(v3, v0) = 0))
% 141.58/84.60 | (287) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (cartesian_product2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (in(v4, v0) = v5 & ( ~ (v5 = 0) | ! [v11] : ! [v12] : ( ~ (ordered_pair(v11, v12) = v4) | ? [v13] : ? [v14] : (in(v12, v2) = v14 & in(v11, v1) = v13 & ( ~ (v14 = 0) | ~ (v13 = 0))))) & (v5 = 0 | (v10 = v4 & v9 = 0 & v8 = 0 & ordered_pair(v6, v7) = v4 & in(v7, v2) = 0 & in(v6, v1) = 0))))
% 141.58/84.60 | (288) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_image(v1, v0) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_dom(v1) = v4 & relation_image(v1, v5) = v6 & set_intersection2(v4, v0) = v5 & relation(v1) = v3 & ( ~ (v3 = 0) | v6 = v2)))
% 141.58/84.60 | (289) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) = 0 & empty(v2) = 0))
% 141.58/84.60 | (290) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (subset(v5, v2) = v6 & unordered_pair(v0, v1) = v5 & in(v1, v2) = v4 & in(v0, v2) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v6 = 0))
% 141.58/84.60 | (291) ! [v0] : ! [v1] : ! [v2] : (v0 = empty_set | ~ (relation_rng(v1) = v2) | ~ (subset(v0, v2) = 0) | ? [v3] : ? [v4] : (relation_inverse_image(v1, v0) = v4 & relation(v1) = v3 & ( ~ (v4 = empty_set) | ~ (v3 = 0))))
% 141.58/84.60 | (292) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = 0))))
% 141.58/84.60 | (293) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0))
% 141.58/84.60 | (294) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_union2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & ( ~ (v5 = 0) | ( ~ (v7 = 0) & ~ (v6 = 0))) & (v7 = 0 | v6 = 0 | v5 = 0)))
% 141.58/84.60 | (295) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (relation_dom_restriction(v0, v1) = v3) | ~ (relation(v2) = 0) | ~ (relation(v0) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (ordered_pair(v4, v5) = v6 & in(v6, v2) = v7 & in(v6, v0) = v9 & in(v4, v1) = v8 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0)) & (v7 = 0 | (v9 = 0 & v8 = 0))))
% 141.58/84.60 | (296) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_inverse(v0) = v4 & relation_rng(v4) = v6 & relation_rng(v0) = v3 & relation_dom(v4) = v5 & relation(v0) = v2 & ( ~ (v2 = 0) | (v6 = v1 & v5 = v3))))
% 141.58/84.60 | (297) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 141.58/84.60 | (298) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : (relation_rng(v0) = v1 & ! [v2] : ! [v3] : ( ~ (relation_composition(v0, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : (relation_rng(v3) = v5 & relation_image(v2, v1) = v6 & relation(v2) = v4 & ( ~ (v4 = 0) | v6 = v5))) & ! [v2] : ! [v3] : ( ~ (relation_image(v2, v1) = v3) | ? [v4] : ? [v5] : ? [v6] : (relation_composition(v0, v2) = v5 & relation_rng(v5) = v6 & relation(v2) = v4 & ( ~ (v4 = 0) | v6 = v3))) & ! [v2] : ( ~ (relation(v2) = 0) | ? [v3] : ? [v4] : (relation_composition(v0, v2) = v3 & relation_rng(v3) = v4 & relation_image(v2, v1) = v4))))
% 141.58/84.60 | (299) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : (relation_inverse(v0) = v1 & ! [v2] : ! [v3] : ! [v4] : ( ~ (ordered_pair(v3, v2) = v4) | ~ (relation(v1) = 0) | ? [v5] : ? [v6] : ? [v7] : (ordered_pair(v2, v3) = v6 & in(v6, v1) = v7 & in(v4, v0) = v5 & ( ~ (v5 = 0) | v7 = 0))) & ! [v2] : ! [v3] : ! [v4] : ( ~ (ordered_pair(v3, v2) = v4) | ~ (relation(v1) = 0) | ? [v5] : ? [v6] : ? [v7] : (ordered_pair(v2, v3) = v5 & in(v5, v1) = v6 & in(v4, v0) = v7 & ( ~ (v6 = 0) | v7 = 0))) & ! [v2] : ! [v3] : ! [v4] : ( ~ (ordered_pair(v2, v3) = v4) | ~ (relation(v1) = 0) | ? [v5] : ? [v6] : ? [v7] : (ordered_pair(v3, v2) = v6 & in(v6, v0) = v7 & in(v4, v1) = v5 & ( ~ (v5 = 0) | v7 = 0))) & ! [v2] : ! [v3] : ! [v4] : ( ~ (ordered_pair(v2, v3) = v4) | ~ (relation(v1) = 0) | ? [v5] : ? [v6] : ? [v7] : (ordered_pair(v3, v2) = v5 & in(v5, v0) = v6 & in(v4, v1) = v7 & ( ~ (v6 = 0) | v7 = 0))) & ! [v2] : (v2 = v1 | ~ (relation(v2) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (ordered_pair(v4, v3) = v7 & ordered_pair(v3, v4) = v5 & in(v7, v0) = v8 & in(v5, v2) = v6 & ( ~ (v8 = 0) | ~ (v6 = 0)) & (v8 = 0 | v6 = 0)))))
% 141.58/84.60 | (300) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & disjoint(v0, v1) = v3))
% 141.58/84.60 | (301) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ? [v3] : ? [v4] : ((v4 = 0 & in(v3, v2) = 0) | (v3 = 0 & disjoint(v0, v1) = 0)))
% 141.58/84.60 | (302) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_rng(v1) = v6 & relation_rng(v0) = v3 & relation_dom(v1) = v4 & relation_dom(v0) = v5 & relation(v0) = v2 & ( ~ (v2 = 0) | (v6 = v5 & v4 = v3))))
% 141.58/84.60 | (303) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_rng(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (( ~ (v3 = 0) & relation(v1) = v3) | (in(v3, v0) = v4 & ( ~ (v4 = 0) | ! [v8] : ! [v9] : ( ~ (ordered_pair(v8, v3) = v9) | ? [v10] : ( ~ (v10 = 0) & in(v9, v1) = v10))) & (v4 = 0 | (v7 = 0 & ordered_pair(v5, v3) = v6 & in(v6, v1) = 0)))))
% 141.58/84.61 | (304) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (relation_field(v0) = v1 & relation_rng(v0) = v3 & relation_dom(v0) = v2 & set_union2(v2, v3) = v1))
% 141.58/84.61 | (305) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2)
% 141.58/84.61 | (306) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2)
% 141.58/84.61 | (307) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | v6 = 0)))
% 141.58/84.61 | (308) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ (in(v2, v1) = 0))
% 141.58/84.61 | (309) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ (relation(v2) = 0) | ? [v6] : ? [v7] : ? [v8] : (( ~ (v6 = 0) & relation(v1) = v6) | (in(v5, v2) = v8 & in(v5, v1) = v7 & in(v4, v0) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v8 = 0))))
% 141.58/84.61 | (310) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (cast_to_subset(v0) = v2 & element(v2, v1) = 0))
% 141.58/84.61 | (311) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (singleton(v0) = v2) | ~ (set_union2(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v0, v1) = v4))
% 141.58/84.61 | (312) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (disjoint(v1, v3) = v4) | ~ (element(v1, v2) = 0) | ~ (powerset(v0) = v2) | ? [v5] : ? [v6] : ? [v7] : (subset_complement(v0, v3) = v6 & element(v3, v2) = v5 & subset(v1, v6) = v7 & ( ~ (v5 = 0) | (( ~ (v7 = 0) | v4 = 0) & ( ~ (v4 = 0) | v7 = 0)))))
% 141.58/84.61 | (313) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = 0 | ~ (relation_rng(v0) = v1) | ~ (ordered_pair(v4, v2) = v5) | ~ (in(v2, v1) = v3) | ? [v6] : (( ~ (v6 = 0) & relation(v0) = v6) | ( ~ (v6 = 0) & in(v5, v0) = v6)))
% 141.58/84.61 | (314) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (relation(v2) = v5 & relation(v1) = v4 & relation(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0)))
% 141.58/84.61 | (315) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ (in(v2, v1) = 0) | subset(v2, v0) = 0)
% 141.58/84.61 | (316) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ (subset(v2, v0) = 0) | in(v2, v1) = 0)
% 141.58/84.61 | (317) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (set_difference(v1, v0) = v2 & set_union2(v0, v2) = v1))
% 141.58/84.61 | (318) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ? [v3] : (set_difference(v3, v1) = v2 & set_union2(v0, v1) = v3))
% 141.58/84.61 | (319) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v3 = 0 & ~ (v4 = 0) & element(v2, v1) = 0 & empty(v2) = v4) | (v2 = 0 & empty(v0) = 0)))
% 141.58/84.61 | (320) relation(all_0_7_7) = 0
% 141.58/84.61 | (321) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (element(v1, v4) = v5 & element(v0, v2) = v6 & powerset(v2) = v4 & in(v0, v1) = v3 & ( ~ (v5 = 0) | ~ (v3 = 0) | v6 = 0))
% 141.58/84.61 | (322) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (subset_difference(v4, v3, v2) = v1) | ~ (subset_difference(v4, v3, v2) = v0))
% 141.58/84.61 | (323) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | subset(v2, v0) = 0)
% 141.58/84.61 | (324) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_composition(v2, v1) = v3) | ~ (identity_relation(v0) = v2) | ? [v4] : ? [v5] : (relation_dom_restriction(v1, v0) = v5 & relation(v1) = v4 & ( ~ (v4 = 0) | v5 = v3)))
% 141.58/84.61 | (325) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ? [v2] : ? [v3] : (relation(v1) = v3 & relation(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 141.58/84.61 | (326) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = empty_set | ~ (element(v1, v3) = 0) | ~ (powerset(v2) = v3) | ~ (powerset(v0) = v2) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (subset_difference(v0, v6, v7) = v5 & meet_of_subsets(v0, v1) = v7 & union_of_subsets(v0, v4) = v5 & complements_of_subsets(v0, v1) = v4 & cast_to_subset(v0) = v6))
% 141.58/84.61 | (327) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & element(v0, v3) = v4 & powerset(v1) = v3))
% 141.58/84.61 | (328) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom(v1) = v2) | ~ (set_intersection2(v2, v0) = v3) | ? [v4] : ? [v5] : ? [v6] : (relation_dom(v5) = v6 & relation_dom_restriction(v1, v0) = v5 & relation(v1) = v4 & ( ~ (v4 = 0) | v6 = v3)))
% 141.58/84.61 | (329) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 141.58/84.61 | (330) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v0 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4))
% 141.58/84.61 | (331) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (element(v0, v2) = v3) | ~ (powerset(v1) = v2) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & in(v4, v1) = v5 & in(v4, v0) = 0))
% 141.58/84.61 | (332) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v0) = 0) | ? [v4] : ? [v5] : (in(v3, v2) = v5 & in(v3, v1) = v4 & (v5 = 0 | v4 = 0)))
% 141.58/84.61 | (333) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (element(v3, v2) = 0) | ~ (element(v1, v2) = 0) | ~ (powerset(v0) = v2) | ? [v4] : ? [v5] : ? [v6] : (disjoint(v1, v3) = v4 & subset_complement(v0, v3) = v5 & subset(v1, v5) = v6 & ( ~ (v6 = 0) | v4 = 0) & ( ~ (v4 = 0) | v6 = 0)))
% 141.58/84.61 | (334) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (element(v0, v2) = v3) | ~ (powerset(v1) = v2) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 141.58/84.61 | (335) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_inverse_image(v3, v2) = v1) | ~ (relation_inverse_image(v3, v2) = v0))
% 141.58/84.61 | (336) ? [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) | ? [v10] : ( ~ (v10 = 0) & in(v9, v1) = v10))) & (v4 = 0 | (v7 = 0 & ordered_pair(v3, v5) = v6 & in(v6, v1) = 0)))))
% 141.58/84.61 | (337) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union_of_subsets(v3, v2) = v1) | ~ (union_of_subsets(v3, v2) = v0))
% 141.58/84.61 | (338) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ? [v4] : (set_intersection2(v0, v1) = v3 & in(v4, v3) = 0))
% 141.58/84.61 | (339) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_complement(v0, v2) = v3) | ~ (in(v1, v3) = 0) | ? [v4] : ? [v5] : ? [v6] : (element(v2, v4) = v5 & powerset(v0) = v4 & in(v1, v2) = v6 & ( ~ (v6 = 0) | ~ (v5 = 0))))
% 141.58/84.61 | (340) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (element(v1, v3) = 0) | ~ (powerset(v2) = v3) | ~ (powerset(v0) = v2) | ? [v4] : (complements_of_subsets(v0, v4) = v1 & complements_of_subsets(v0, v1) = v4))
% 141.58/84.61 | (341) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_rng(v0) = v3 & cartesian_product2(v1, v3) = v4 & subset(v0, v4) = v5 & relation(v0) = v2 & ( ~ (v2 = 0) | v5 = 0)))
% 141.58/84.61 | (342) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_empty_yielding(v2) = v1) | ~ (relation_empty_yielding(v2) = v0))
% 141.58/84.61 | (343) ~ (all_0_3_3 = 0)
% 141.58/84.61 | (344) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0))
% 141.58/84.61 | (345) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ( ~ (v3 = v0) & set_difference(v0, v1) = v3))
% 141.58/84.61 | (346) ! [v0] : ! [v1] : ( ~ (element(v0, v1) = 0) | ? [v2] : ? [v3] : (empty(v1) = v2 & in(v0, v1) = v3 & (v3 = 0 | v2 = 0)))
% 141.58/84.61 | (347) ! [v0] : ~ (singleton(v0) = empty_set)
% 141.58/84.61 | (348) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom(v1) = v2) | ~ (set_intersection2(v2, v0) = v3) | ? [v4] : ? [v5] : ? [v6] : (relation_image(v1, v3) = v6 & relation_image(v1, v0) = v5 & relation(v1) = v4 & ( ~ (v4 = 0) | v6 = v5)))
% 141.58/84.61 | (349) ~ (all_0_5_5 = 0)
% 141.58/84.61 | (350) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ( ~ (v3 = empty_set) & set_intersection2(v0, v1) = v3))
% 141.58/84.61 | (351) ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_intersection2(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & disjoint(v0, v1) = v3))
% 141.58/84.61 | (352) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (element(v1, v3) = 0) | ~ (powerset(v2) = v3) | ~ (powerset(v0) = v2) | ? [v4] : (complements_of_subsets(v0, v1) = v4 & ! [v5] : ! [v6] : ( ~ (subset_complement(v0, v5) = v6) | ~ (element(v4, v3) = 0) | ? [v7] : ? [v8] : ? [v9] : (element(v5, v2) = v7 & in(v6, v1) = v9 & in(v5, v4) = v8 & ( ~ (v7 = 0) | (( ~ (v9 = 0) | v8 = 0) & ( ~ (v8 = 0) | v9 = 0))))) & ! [v5] : ! [v6] : ( ~ (element(v4, v3) = 0) | ~ (in(v5, v4) = v6) | ? [v7] : ? [v8] : ? [v9] : (subset_complement(v0, v5) = v8 & element(v5, v2) = v7 & in(v8, v1) = v9 & ( ~ (v7 = 0) | (( ~ (v9 = 0) | v6 = 0) & ( ~ (v6 = 0) | v9 = 0))))) & ! [v5] : (v5 = v4 | ~ (element(v5, v3) = 0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (subset_complement(v0, v6) = v8 & element(v6, v2) = 0 & in(v8, v1) = v9 & in(v6, v5) = v7 & ( ~ (v9 = 0) | ~ (v7 = 0)) & (v9 = 0 | v7 = 0))) & ! [v5] : ( ~ (element(v5, v2) = 0) | ~ (element(v4, v3) = 0) | ? [v6] : ? [v7] : ? [v8] : (subset_complement(v0, v5) = v7 & in(v7, v1) = v8 & in(v5, v4) = v6 & ( ~ (v8 = 0) | v6 = 0) & ( ~ (v6 = 0) | v8 = 0)))))
% 141.58/84.62 | (353) ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2))
% 141.58/84.62 | (354) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (identity_relation(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ (relation(v1) = 0) | ? [v5] : ? [v6] : (in(v4, v1) = v5 & in(v2, v0) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v3 = v2))))
% 141.58/84.62 | (355) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_difference(v0, empty_set) = v1))
% 141.58/84.62 | (356) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (proper_subset(v3, v2) = v1) | ~ (proper_subset(v3, v2) = v0))
% 141.58/84.62 | (357) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ? [v3] : (set_difference(v0, v2) = v3 & set_intersection2(v0, v1) = v3))
% 141.58/84.62 | (358) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v0 = empty_set | ~ (set_meet(v0) = v1) | ~ (in(v2, v3) = v4) | ~ (in(v2, v1) = 0) | ? [v5] : ( ~ (v5 = 0) & in(v3, v0) = v5))
% 141.58/84.62 | (359) empty(all_0_1_1) = 0
% 141.58/84.62 | (360) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : (relation_rng(v0) = v1 & relation_dom(v0) = v2 & ! [v3] : ! [v4] : ( ~ (relation_composition(v0, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (relation_dom(v4) = v8 & relation_dom(v3) = v6 & subset(v1, v6) = v7 & relation(v3) = v5 & ( ~ (v7 = 0) | ~ (v5 = 0) | v8 = v2))) & ! [v3] : ! [v4] : ( ~ (relation_dom(v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (relation_composition(v0, v3) = v7 & relation_dom(v7) = v8 & subset(v1, v4) = v6 & relation(v3) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | v8 = v2))) & ! [v3] : ( ~ (relation(v3) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (relation_composition(v0, v3) = v6 & relation_dom(v6) = v7 & relation_dom(v3) = v4 & subset(v1, v4) = v5 & ( ~ (v5 = 0) | v7 = v2)))))
% 141.58/84.62 | (361) ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = v0) | disjoint(v0, v1) = 0)
% 141.58/84.62 | (362) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | set_difference(v0, v1) = v0)
% 141.58/84.62 | (363) ! [v0] : ( ~ (function(v0) = 0) | ? [v1] : ? [v2] : (relation_dom(v0) = v2 & relation(v0) = v1 & ( ~ (v1 = 0) | ( ! [v3] : ! [v4] : ! [v5] : ( ~ (ordered_pair(v3, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : (apply(v0, v3) = v7 & in(v5, v0) = v8 & in(v3, v2) = v6 & ( ~ (v6 = 0) | (( ~ (v8 = 0) | v7 = v4) & ( ~ (v7 = v4) | v8 = 0))))) & ? [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (in(v4, v2) = v5) | ? [v6] : (apply(v0, v4) = v6 & ( ~ (v6 = v3) | v3 = empty_set) & ( ~ (v3 = empty_set) | v6 = empty_set))) & ! [v3] : ! [v4] : (v4 = empty_set | ~ (apply(v0, v3) = v4) | in(v3, v2) = 0)))))
% 141.58/84.62 | (364) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : (relation_dom(v0) = v2 & function(v0) = v1 & ( ~ (v1 = 0) | ( ! [v3] : ! [v4] : ! [v5] : ( ~ (ordered_pair(v3, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : (apply(v0, v3) = v7 & in(v5, v0) = v8 & in(v3, v2) = v6 & ( ~ (v6 = 0) | (( ~ (v8 = 0) | v7 = v4) & ( ~ (v7 = v4) | v8 = 0))))) & ? [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (in(v4, v2) = v5) | ? [v6] : (apply(v0, v4) = v6 & ( ~ (v6 = v3) | v3 = empty_set) & ( ~ (v3 = empty_set) | v6 = empty_set))) & ! [v3] : ! [v4] : (v4 = empty_set | ~ (apply(v0, v3) = v4) | in(v3, v2) = 0)))))
% 141.58/84.62 | (365) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v0, v1) = v2) | ? [v3] : ? [v4] : (element(v0, v1) = v3 & empty(v1) = v4 & ( ~ (v3 = 0) | v4 = 0)))
% 141.58/84.62 | (366) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (subset(v0, v3) = v4) | ~ (set_intersection2(v1, v2) = v3) | ? [v5] : ? [v6] : (subset(v0, v2) = v6 & subset(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0))))
% 141.58/84.62 | (367) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_rng(v2) = v4 & relation_rng(v1) = v5 & set_intersection2(v5, v0) = v6 & relation(v1) = v3 & ( ~ (v3 = 0) | v6 = v4)))
% 141.58/84.62 | (368) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (identity_relation(v0) = v2) | ~ (relation(v1) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (ordered_pair(v3, v4) = v5 & in(v5, v1) = v6 & in(v3, v0) = v7 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v4 = v3)) & (v6 = 0 | (v7 = 0 & v4 = v3))))
% 141.58/84.62 | (369) relation(all_0_14_14) = 0
% 141.58/84.62 | (370) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | union(v1) = v0)
% 141.58/84.62 | (371) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | v0 = empty_set | ~ (singleton(v1) = v2) | ~ (subset(v0, v2) = 0))
% 141.58/84.62 | (372) apply(all_0_14_14, all_0_16_16) = all_0_9_9
% 141.58/84.62 | (373) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0))
% 141.58/84.62 | (374) ! [v0] : ! [v1] : ! [v2] : ( ~ (element(v0, v2) = 0) | ~ (powerset(v1) = v2) | subset(v0, v1) = 0)
% 141.58/84.62 | (375) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (identity_relation(v2) = v1) | ~ (identity_relation(v2) = v0))
% 141.58/84.62 | (376) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0))
% 141.58/84.62 | (377) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation_dom(v1) = v0)
% 141.58/84.62 | (378) ! [v0] : ! [v1] : ! [v2] : ( ~ (element(v1, v2) = 0) | ~ (powerset(v0) = v2) | ? [v3] : (subset_complement(v0, v3) = v1 & subset_complement(v0, v1) = v3))
% 141.58/84.62 | (379) ! [v0] : ( ~ (empty(v0) = 0) | ? [v1] : (relation_rng(v0) = v1 & relation(v1) = 0 & empty(v1) = 0))
% 141.58/84.62 | (380) relation_rng(empty_set) = empty_set
% 141.58/84.62 | (381) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_inverse(v0) = v3 & relation_rng(v3) = v6 & relation_rng(v0) = v2 & relation_dom(v3) = v4 & relation_dom(v0) = v5 & relation(v0) = v1 & ( ~ (v1 = 0) | (v6 = v5 & v4 = v2)))
% 141.58/84.62 | (382) ! [v0] : ! [v1] : (v0 = empty_set | ~ (relation_inverse_image(v1, v0) = empty_set) | ? [v2] : ? [v3] : ? [v4] : (relation_rng(v1) = v3 & subset(v0, v3) = v4 & relation(v1) = v2 & ( ~ (v4 = 0) | ~ (v2 = 0))))
% 141.58/84.62 | (383) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (element(v0, v2) = 0 & powerset(v1) = v2))
% 141.58/84.62 | (384) ! [v0] : ! [v1] : ( ~ (proper_subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & proper_subset(v1, v0) = v2))
% 141.58/84.62 | (385) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0) = v1) | ~ (in(v2, v1) = 0) | ? [v3] : (in(v3, v0) = 0 & in(v2, v3) = 0))
% 141.58/84.62 | (386) ! [v0] : ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = v0) & set_difference(v0, v2) = v3 & singleton(v1) = v2))
% 141.58/84.62 | (387) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (subset(empty_set, v1) = v2))
% 141.58/84.62 | (388) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (complements_of_subsets(v0, v5) = v6 & complements_of_subsets(v0, v1) = v5 & element(v1, v3) = v4 & powerset(v2) = v3 & powerset(v0) = v2 & ( ~ (v4 = 0) | v6 = v1))
% 141.58/84.62 | (389) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : (relation_rng(v0) = v3 & relation(v0) = v2 & ( ~ (v2 = 0) | ( ! [v4] : ! [v5] : ( ~ (relation_composition(v4, v0) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (relation_rng(v5) = v9 & relation_rng(v4) = v7 & subset(v1, v7) = v8 & relation(v4) = v6 & ( ~ (v8 = 0) | ~ (v6 = 0) | v9 = v3))) & ! [v4] : ! [v5] : ( ~ (relation_rng(v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (relation_composition(v4, v0) = v8 & relation_rng(v8) = v9 & subset(v1, v5) = v7 & relation(v4) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = v3))) & ! [v4] : ( ~ (relation(v4) = 0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (relation_composition(v4, v0) = v7 & relation_rng(v7) = v8 & relation_rng(v4) = v5 & subset(v1, v5) = v6 & ( ~ (v6 = 0) | v8 = v3)))))))
% 141.58/84.62 | (390) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_inverse(v2) = v1) | ~ (relation_inverse(v2) = v0))
% 141.58/84.62 | (391) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (relation_rng(v2) = v4 & subset(v4, v0) = v5 & relation(v1) = v3 & ( ~ (v3 = 0) | v5 = 0)))
% 141.58/84.62 | (392) ! [v0] : ! [v1] : ! [v2] : ( ~ (element(v1, v0) = v2) | ? [v3] : ? [v4] : (empty(v0) = v3 & in(v1, v0) = v4 & (v3 = 0 | (( ~ (v4 = 0) | v2 = 0) & ( ~ (v2 = 0) | v4 = 0)))))
% 141.58/84.62 | (393) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (subset_complement(v0, v1) = v5 & element(v1, v3) = v4 & powerset(v0) = v3 & ( ~ (v4 = 0) | v5 = v2)))
% 141.58/84.62 | (394) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation(v2) = v6 & relation(v1) = v4 & empty(v2) = v5 & empty(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | (v6 = 0 & v5 = 0))))
% 141.58/84.62 | (395) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_composition(v0, v2) = v3) | ~ (relation_rng(v0) = v1) | ? [v4] : ? [v5] : ? [v6] : (( ~ (v4 = 0) & relation(v0) = v4) | (relation_rng(v3) = v5 & relation_image(v2, v1) = v6 & relation(v2) = v4 & ( ~ (v4 = 0) | v6 = v5))))
% 141.58/84.62 | (396) relation(all_0_0_0) = 0
% 141.58/84.63 | (397) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0))
% 141.58/84.63 | (398) ordered_pair(all_0_16_16, all_0_15_15) = all_0_13_13
% 141.58/84.63 | (399) ! [v0] : ! [v1] : (v1 = v0 | ~ (subset(v0, v1) = 0) | proper_subset(v0, v1) = 0)
% 141.58/84.63 | (400) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (union(v0) = v1) | ~ (in(v4, v0) = 0) | ~ (in(v2, v1) = v3) | ? [v5] : ( ~ (v5 = 0) & in(v2, v4) = v5))
% 141.58/84.63 | (401) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & proper_subset(v1, v0) = v2))
% 141.58/84.63 | (402) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (union(v0) = v1) | ~ (in(v2, v4) = 0) | ~ (in(v2, v1) = v3) | ? [v5] : ( ~ (v5 = 0) & in(v4, v0) = v5))
% 141.58/84.63 | (403) empty(empty_set) = 0
% 141.58/84.63 | (404) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v1) = v0) | ~ (subset(v0, v0) = v2))
% 141.58/84.63 | (405) ! [v0] : ! [v1] : ( ~ (relation(v1) = 0) | ~ (relation(v0) = 0) | ? [v2] : (relation_composition(v0, v1) = v2 & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (ordered_pair(v6, v4) = v7) | ~ (ordered_pair(v3, v4) = v5) | ~ (relation(v2) = 0) | ? [v8] : ? [v9] : ? [v10] : ((v8 = 0 & in(v5, v2) = 0) | (ordered_pair(v3, v6) = v8 & in(v8, v0) = v9 & in(v7, v1) = v10 & ( ~ (v10 = 0) | ~ (v9 = 0))))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (ordered_pair(v3, v6) = v7) | ~ (ordered_pair(v3, v4) = v5) | ~ (relation(v2) = 0) | ? [v8] : ? [v9] : ? [v10] : ((v8 = 0 & in(v5, v2) = 0) | (ordered_pair(v6, v4) = v9 & in(v9, v1) = v10 & in(v7, v0) = v8 & ( ~ (v10 = 0) | ~ (v8 = 0))))) & ! [v3] : ! [v4] : ! [v5] : ( ~ (ordered_pair(v3, v4) = v5) | ~ (relation(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) & in(v5, v2) = v6))) & ! [v3] : (v3 = v2 | ~ (relation(v3) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : (ordered_pair(v4, v5) = v6 & in(v6, v3) = v7 & ( ~ (v7 = 0) | ( ! [v13] : ! [v14] : ( ~ (ordered_pair(v13, v5) = v14) | ? [v15] : ? [v16] : ? [v17] : (ordered_pair(v4, v13) = v15 & in(v15, v0) = v16 & in(v14, v1) = v17 & ( ~ (v17 = 0) | ~ (v16 = 0)))) & ! [v13] : ! [v14] : ( ~ (ordered_pair(v4, v13) = v14) | ? [v15] : ? [v16] : ? [v17] : (ordered_pair(v13, v5) = v16 & in(v16, v1) = v17 & in(v14, v0) = v15 & ( ~ (v17 = 0) | ~ (v15 = 0)))))) & (v7 = 0 | (v12 = 0 & v10 = 0 & ordered_pair(v8, v5) = v11 & ordered_pair(v4, v8) = v9 & in(v11, v1) = 0 & in(v9, v0) = 0))))))
% 141.58/84.63 | (406) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (relation_inverse_image(v2, v1) = v6 & relation_inverse_image(v2, v0) = v5 & subset(v5, v6) = v7 & subset(v0, v1) = v4 & relation(v2) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v7 = 0))
% 141.58/84.63 | (407) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ? [v3] : (set_difference(v0, v3) = v2 & set_difference(v0, v1) = v3))
% 141.58/84.63 | (408) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation_rng(v1) = v0)
% 141.58/84.63 | (409) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_image(v2, v1) = v3) | ~ (in(v0, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : (relation_dom(v2) = v6 & relation(v2) = v5 & ( ~ (v5 = 0) | (( ~ (v4 = 0) | (v11 = 0 & v10 = 0 & v8 = 0 & ordered_pair(v7, v0) = v9 & in(v9, v2) = 0 & in(v7, v6) = 0 & in(v7, v1) = 0)) & (v4 = 0 | ( ! [v12] : ! [v13] : ( ~ (ordered_pair(v12, v0) = v13) | ? [v14] : ? [v15] : ? [v16] : (in(v13, v2) = v15 & in(v12, v6) = v14 & in(v12, v1) = v16 & ( ~ (v16 = 0) | ~ (v15 = 0) | ~ (v14 = 0)))) & ! [v12] : ( ~ (in(v12, v6) = 0) | ? [v13] : ? [v14] : ? [v15] : (ordered_pair(v12, v0) = v13 & in(v13, v2) = v14 & in(v12, v1) = v15 & ( ~ (v15 = 0) | ~ (v14 = 0)))) & ! [v12] : ( ~ (in(v12, v1) = 0) | ? [v13] : ? [v14] : ? [v15] : (ordered_pair(v12, v0) = v14 & in(v14, v2) = v15 & in(v12, v6) = v13 & ( ~ (v15 = 0) | ~ (v13 = 0))))))))))
% 141.58/84.63 | (410) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1))
% 141.58/84.63 | (411) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v1, v0) = v2) | ? [v3] : ? [v4] : (subset(v2, v1) = v4 & relation(v1) = v3 & ( ~ (v3 = 0) | v4 = 0)))
% 141.58/84.63 | (412) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0))
% 141.58/84.63 | (413) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v1, v0) = v2) | ? [v3] : ? [v4] : (subset(v0, v1) = v3 & set_union2(v0, v2) = v4 & ( ~ (v3 = 0) | v4 = v1)))
% 141.58/84.63 | (414) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = empty_set | ~ (relation_dom(v0) = v1) | ~ (apply(v0, v2) = v3) | ? [v4] : ? [v5] : ((v4 = 0 & in(v2, v1) = 0) | (relation(v0) = v4 & function(v0) = v5 & ( ~ (v5 = 0) | ~ (v4 = 0)))))
% 141.58/84.63 | (415) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation(v1) = 0)
% 141.58/84.63 | (416) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (set_difference(v1, v2) = v4) | ~ (set_difference(v0, v2) = v3) | ~ (subset(v3, v4) = v5) | ? [v6] : ( ~ (v6 = 0) & subset(v0, v1) = v6))
% 141.58/84.63 | (417) ! [v0] : ! [v1] : ! [v2] : ( ~ (element(v1, v2) = 0) | ~ (powerset(v0) = v2) | ? [v3] : (subset_complement(v0, v1) = v3 & set_difference(v0, v1) = v3))
% 141.58/84.63 | (418) ! [v0] : ! [v1] : ! [v2] : ( ~ (element(v1, v2) = 0) | ~ (powerset(v0) = v2) | ? [v3] : (subset_complement(v0, v1) = v3 & element(v3, v2) = 0))
% 141.58/84.63 | (419) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : (relation_inverse(v0) = v1 & relation(v1) = 0))
% 141.58/84.63 | (420) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3))
% 141.58/84.63 | (421) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (powerset(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (subset(v3, v1) = v5 & in(v3, v0) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)) & (v5 = 0 | v4 = 0)))
% 141.58/84.63 | (422) ? [v0] : ? [v1] : (in(v0, v1) = 0 & ! [v2] : ! [v3] : (v3 = 0 | ~ (are_equipotent(v2, v1) = v3) | ? [v4] : ? [v5] : (subset(v2, v1) = v4 & in(v2, v1) = v5 & ( ~ (v4 = 0) | v5 = 0))) & ! [v2] : ! [v3] : (v3 = 0 | ~ (in(v2, v1) = v3) | ? [v4] : ? [v5] : (are_equipotent(v2, v1) = v5 & subset(v2, v1) = v4 & ( ~ (v4 = 0) | v5 = 0))) & ! [v2] : ! [v3] : ( ~ (subset(v3, v2) = 0) | ? [v4] : ? [v5] : (in(v3, v1) = v5 & in(v2, v1) = v4 & ( ~ (v4 = 0) | v5 = 0))) & ! [v2] : ( ~ (subset(v2, v1) = 0) | ? [v3] : ? [v4] : (are_equipotent(v2, v1) = v3 & in(v2, v1) = v4 & (v4 = 0 | v3 = 0))) & ! [v2] : ( ~ (in(v2, v1) = 0) | ? [v3] : (in(v3, v1) = 0 & ! [v4] : ! [v5] : (v5 = 0 | ~ (in(v4, v3) = v5) | ? [v6] : ( ~ (v6 = 0) & subset(v4, v2) = v6)) & ! [v4] : ( ~ (subset(v4, v2) = 0) | in(v4, v3) = 0))))
% 141.58/84.63 | (423) ! [v0] : ! [v1] : ( ~ (proper_subset(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v0, v1) = v2))
% 141.58/84.63 | (424) ! [v0] : ! [v1] : ( ~ (relation(v1) = 0) | ~ (relation(v0) = 0) | ? [v2] : ? [v3] : ? [v4] : (relation_composition(v0, v1) = v2 & relation_rng(v2) = v3 & relation_rng(v1) = v4 & subset(v3, v4) = 0))
% 141.58/84.63 | (425) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_rng_restriction(v3, v2) = v1) | ~ (relation_rng_restriction(v3, v2) = v0))
% 141.58/84.63 | (426) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = 0 | ~ (relation_inverse_image(v0, v1) = v2) | ~ (ordered_pair(v3, v5) = v6) | ~ (relation(v0) = 0) | ~ (in(v3, v2) = v4) | ? [v7] : ? [v8] : (in(v6, v0) = v7 & in(v5, v1) = v8 & ( ~ (v8 = 0) | ~ (v7 = 0))))
% 141.58/84.63 | (427) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (union_of_subsets(v0, v1) = v5 & union(v1) = v6 & element(v1, v3) = v4 & powerset(v2) = v3 & powerset(v0) = v2 & ( ~ (v4 = 0) | v6 = v5))
% 141.58/84.63 | (428) ! [v0] : ! [v1] : ! [v2] : (v1 = empty_set | ~ (complements_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (subset_difference(v0, v7, v8) = v9 & meet_of_subsets(v0, v1) = v8 & union_of_subsets(v0, v2) = v6 & cast_to_subset(v0) = v7 & element(v1, v4) = v5 & powerset(v3) = v4 & powerset(v0) = v3 & ( ~ (v5 = 0) | v9 = v6)))
% 141.58/84.63 | (429) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v6 & in(v3, v0) = v5 & ( ~ (v5 = 0) | v6 = 0)))
% 141.58/84.63 | (430) relation(all_0_1_1) = 0
% 141.58/84.63 | (431) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v1, v2) = 0) | ~ (subset(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 141.58/84.63 | (432) ! [v0] : ~ (proper_subset(v0, v0) = 0)
% 141.58/84.63 | (433) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | element(v0, v1) = 0)
% 141.58/84.63 | (434) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_composition(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ (relation(v2) = 0) | ~ (relation(v0) = 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) | ( ~ (v6 = 0) & in(v5, v2) = v6)))
% 141.58/84.63 | (435) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (subset_complement(v0, v2) = v5 & element(v2, v3) = v4 & powerset(v0) = v3 & in(v1, v5) = v6 & in(v1, v2) = v7 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v4 = 0)))
% 141.58/84.63 | (436) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_composition(v0, v2) = v3) | ~ (relation_dom(v0) = v1) | ? [v4] : ? [v5] : ? [v6] : (( ~ (v4 = 0) & relation(v0) = v4) | (relation_dom(v3) = v5 & subset(v5, v1) = v6 & relation(v2) = v4 & ( ~ (v4 = 0) | v6 = 0))))
% 141.58/84.64 | (437) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v1, v0) = v2) | ? [v3] : (set_union2(v0, v2) = v3 & set_union2(v0, v1) = v3))
% 141.58/84.64 | (438) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (identity_relation(v0) = v1) | ~ (ordered_pair(v2, v2) = v3) | ~ (relation(v1) = 0) | ? [v4] : ? [v5] : (in(v3, v1) = v5 & in(v2, v0) = v4 & ( ~ (v4 = 0) | v5 = 0)))
% 141.58/84.64 | (439) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v0) = 0) | ? [v4] : ? [v5] : (in(v3, v2) = v5 & in(v3, v1) = v4 & ( ~ (v4 = 0) | v5 = 0)))
% 141.58/84.64 | (440) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (relation_rng(v0) = v2 & empty(v2) = v3 & empty(v0) = v1 & ( ~ (v3 = 0) | v1 = 0)))
% 141.58/84.64 | (441) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : (relation_rng(v0) = v3 & relation(v0) = v2 & ( ~ (v2 = 0) | ( ! [v4] : ! [v5] : ( ~ (relation_composition(v0, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (relation_dom(v5) = v9 & relation_dom(v4) = v7 & subset(v3, v7) = v8 & relation(v4) = v6 & ( ~ (v8 = 0) | ~ (v6 = 0) | v9 = v1))) & ! [v4] : ! [v5] : ( ~ (relation_dom(v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (relation_composition(v0, v4) = v8 & relation_dom(v8) = v9 & subset(v3, v5) = v7 & relation(v4) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = v1))) & ! [v4] : ( ~ (relation(v4) = 0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (relation_composition(v0, v4) = v7 & relation_dom(v7) = v8 & relation_dom(v4) = v5 & subset(v3, v5) = v6 & ( ~ (v6 = 0) | v8 = v1)))))))
% 141.58/84.64 | (442) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : (singleton(v0) = v2 & set_union2(v2, v1) = v1))
% 141.58/84.64 | (443) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 141.58/84.64 | (444) ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ (subset(v2, v1) = 0) | in(v0, v1) = 0)
% 141.58/84.64 | (445) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | disjoint(v1, v0) = 0)
% 141.58/84.64 | (446) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ? [v4] : ( ~ (v4 = 0) & disjoint(v0, v1) = v4))
% 141.58/84.64 | (447) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (relation_rng_restriction(v0, v6) = v7 & relation_rng_restriction(v0, v2) = v4 & relation_dom_restriction(v4, v1) = v5 & relation_dom_restriction(v2, v1) = v6 & relation(v2) = v3 & ( ~ (v3 = 0) | v7 = v5))
% 141.58/84.64 | (448) ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v1, v2) = 0) | ~ (subset(v0, v1) = 0) | disjoint(v0, v2) = 0)
% 141.58/84.64 | (449) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v2) = v0) | ~ (singleton(v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v1, v0) = v3))
% 141.58/84.64 | (450) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ? [v3] : ? [v4] : (relation(v2) = v4 & relation(v0) = v3 & ( ~ (v3 = 0) | v4 = 0)))
% 141.58/84.64 | (451) ! [v0] : ~ (in(v0, empty_set) = 0)
% 141.58/84.64 | (452) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : (relation_rng(v0) = v2 & relation_dom(v0) = v1 & ! [v3] : ! [v4] : ( ~ (relation_rng(v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (relation_dom(v3) = v7 & subset(v2, v4) = v9 & subset(v1, v7) = v8 & subset(v0, v3) = v6 & relation(v3) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | (v9 = 0 & v8 = 0)))) & ! [v3] : ! [v4] : ( ~ (relation_dom(v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (relation_rng(v3) = v8 & subset(v2, v8) = v9 & subset(v1, v4) = v7 & subset(v0, v3) = v6 & relation(v3) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | (v9 = 0 & v7 = 0)))) & ! [v3] : ( ~ (subset(v0, v3) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (relation_rng(v3) = v7 & relation_dom(v3) = v5 & subset(v2, v7) = v8 & subset(v1, v5) = v6 & relation(v3) = v4 & ( ~ (v4 = 0) | (v8 = 0 & v6 = 0)))) & ! [v3] : ( ~ (relation(v3) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (relation_rng(v3) = v7 & relation_dom(v3) = v5 & subset(v2, v7) = v8 & subset(v1, v5) = v6 & subset(v0, v3) = v4 & ( ~ (v4 = 0) | (v8 = 0 & v6 = 0))))))
% 141.58/84.64 | (453) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : (union(v1) = v2 & subset(v0, v2) = 0))
% 141.58/84.64 | (454) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | ? [v2] : (set_intersection2(v0, v1) = v2 & ! [v3] : ~ (in(v3, v2) = 0)))
% 141.58/84.64 | (455) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : (relation_dom(v0) = v3 & relation(v0) = v2 & ( ~ (v2 = 0) | (( ~ (v3 = empty_set) | v1 = empty_set) & ( ~ (v1 = empty_set) | v3 = empty_set)))))
% 141.58/84.64 | (456) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ (in(v4, v5) = v6) | ? [v7] : ? [v8] : (in(v1, v3) = v8 & in(v0, v2) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0))))
% 141.58/84.64 | (457) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3))
% 141.58/84.64 | (458) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_rng(v2) = v4 & relation_rng(v1) = v5 & subset(v4, v5) = v6 & relation(v1) = v3 & ( ~ (v3 = 0) | v6 = 0)))
% 141.58/84.64 | (459) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (singleton(v0) = v2) | ~ (subset(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v0, v1) = v4))
% 141.58/84.64 | (460) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (union(v1) = v2) | ~ (subset(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v0, v1) = v4))
% 141.58/84.64 | (461) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v3 = v0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v3, v2) = 0))
% 141.58/84.64 | (462) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : (relation_rng(v0) = v1 & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = 0 | ~ (ordered_pair(v4, v2) = v5) | ~ (in(v2, v1) = v3) | ? [v6] : ( ~ (v6 = 0) & in(v5, v0) = v6)) & ! [v2] : ( ~ (in(v2, v1) = 0) | ? [v3] : ? [v4] : (ordered_pair(v3, v2) = v4 & in(v4, v0) = 0)) & ? [v2] : (v2 = v1 | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (in(v3, v2) = v4 & ( ~ (v4 = 0) | ! [v8] : ! [v9] : ( ~ (ordered_pair(v8, v3) = v9) | ? [v10] : ( ~ (v10 = 0) & in(v9, v0) = v10))) & (v4 = 0 | (v7 = 0 & ordered_pair(v5, v3) = v6 & in(v6, v0) = 0))))))
% 141.58/84.64 | (463) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ (relation(v2) = 0) | ? [v6] : ? [v7] : ? [v8] : (( ~ (v6 = 0) & relation(v1) = v6) | (in(v5, v2) = v6 & in(v5, v1) = v8 & in(v4, v0) = v7 & ( ~ (v6 = 0) | (v8 = 0 & v7 = 0)))))
% 141.58/84.64 | (464) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_complement(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (element(v2, v3) = v5 & element(v1, v3) = v4 & powerset(v0) = v3 & ( ~ (v4 = 0) | v5 = 0)))
% 141.58/84.64 | (465) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset(v3, v2) = 0) | ~ (unordered_pair(v0, v1) = v3) | (in(v1, v2) = 0 & in(v0, v2) = 0))
% 141.58/84.64 | (466) ! [v0] : ! [v1] : ( ~ (relation(v1) = 0) | ~ (relation(v0) = 0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (subset(v0, v1) = v2 & ( ~ (v2 = 0) | ! [v8] : ! [v9] : ! [v10] : ( ~ (ordered_pair(v8, v9) = v10) | ? [v11] : ? [v12] : (in(v10, v1) = v12 & in(v10, v0) = v11 & ( ~ (v11 = 0) | v12 = 0)))) & (v2 = 0 | (v6 = 0 & ~ (v7 = 0) & ordered_pair(v3, v4) = v5 & in(v5, v1) = v7 & in(v5, v0) = 0))))
% 141.58/84.64 | (467) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v1, v0) = v2) | ? [v3] : (set_difference(v0, v3) = v0 & singleton(v1) = v3))
% 141.58/84.64 | (468) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v1) = 0) | ? [v4] : ? [v5] : (in(v3, v2) = v5 & in(v3, v0) = v4 & ( ~ (v4 = 0) | v5 = 0)))
% 141.58/84.64 | (469) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset_complement(v3, v2) = v1) | ~ (subset_complement(v3, v2) = v0))
% 141.58/84.64 | (470) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_intersection2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0)) & (v5 = 0 | (v7 = 0 & v6 = 0))))
% 141.58/84.64 | (471) ? [v0] : ? [v1] : (in(v0, v1) = 0 & ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (subset(v3, v2) = v5 & in(v3, v1) = v6 & in(v2, v1) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0) | v6 = 0)) & ? [v2] : ? [v3] : ? [v4] : ? [v5] : (are_equipotent(v2, v1) = v4 & subset(v2, v1) = v3 & in(v2, v1) = v5 & ( ~ (v3 = 0) | v5 = 0 | v4 = 0)) & ? [v2] : ? [v3] : ? [v4] : ? [v5] : (powerset(v2) = v4 & in(v4, v1) = v5 & in(v2, v1) = v3 & ( ~ (v3 = 0) | v5 = 0)))
% 141.58/84.64 | (472) ! [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(v13, v5) = v14) | ? [v15] : ? [v16] : ? [v17] : (ordered_pair(v4, v13) = v15 & in(v15, v0) = v16 & in(v14, v1) = v17 & ( ~ (v17 = 0) | ~ (v16 = 0)))) & ! [v13] : ! [v14] : ( ~ (ordered_pair(v4, v13) = v14) | ? [v15] : ? [v16] : ? [v17] : (ordered_pair(v13, v5) = v16 & in(v16, v1) = v17 & in(v14, v0) = v15 & ( ~ (v17 = 0) | ~ (v15 = 0)))))) & (v7 = 0 | (v12 = 0 & v10 = 0 & ordered_pair(v8, v5) = v11 & ordered_pair(v4, v8) = v9 & in(v11, v1) = 0 & in(v9, v0) = 0)))))
% 141.58/84.64 | (473) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | subset(v2, v0) = 0)
% 141.58/84.64 |
% 141.58/84.64 | Instantiating formula (376) with all_0_2_2, all_0_1_1 and discharging atoms empty(all_0_1_1) = 0, empty(all_0_2_2) = 0, yields:
% 141.58/84.64 | (474) all_0_1_1 = all_0_2_2
% 141.58/84.64 |
% 141.58/84.64 | Instantiating formula (376) with empty_set, all_0_1_1 and discharging atoms empty(all_0_1_1) = 0, empty(empty_set) = 0, yields:
% 141.58/84.64 | (475) all_0_1_1 = empty_set
% 141.58/84.64 |
% 141.58/84.65 | Combining equations (475,474) yields a new equation:
% 141.58/84.65 | (476) all_0_2_2 = empty_set
% 141.58/84.65 |
% 141.58/84.65 | Combining equations (476,474) yields a new equation:
% 141.58/84.65 | (475) all_0_1_1 = empty_set
% 141.58/84.65 |
% 141.58/84.65 | From (475) and (430) follows:
% 141.58/84.65 | (33) relation(empty_set) = 0
% 141.58/84.65 |
% 141.58/84.65 | Instantiating formula (194) with empty_set, empty_set and discharging atoms relation_rng(empty_set) = empty_set, yields:
% 141.58/84.65 | (479) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (relation_inverse(empty_set) = v1 & relation_rng(v1) = v4 & relation_dom(v1) = v2 & relation_dom(empty_set) = v3 & relation(empty_set) = v0 & ( ~ (v0 = 0) | (v4 = v3 & v2 = empty_set)))
% 141.58/84.65 |
% 141.58/84.65 | Instantiating formula (76) with empty_set, empty_set and discharging atoms relation_rng(empty_set) = empty_set, yields:
% 141.58/84.65 | (480) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (relation_field(empty_set) = v1 & relation_dom(empty_set) = v2 & set_union2(v2, empty_set) = v3 & relation(empty_set) = v0 & ( ~ (v0 = 0) | v3 = v1))
% 141.58/84.65 |
% 141.58/84.65 | Instantiating formula (127) with empty_set, empty_set and discharging atoms relation_rng(empty_set) = empty_set, yields:
% 141.58/84.65 | (481) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (relation_dom(empty_set) = v1 & cartesian_product2(v1, empty_set) = v2 & subset(empty_set, v2) = v3 & relation(empty_set) = v0 & ( ~ (v0 = 0) | v3 = 0))
% 141.58/84.65 |
% 141.58/84.65 | Instantiating formula (196) with empty_set, empty_set and discharging atoms relation_rng(empty_set) = empty_set, yields:
% 141.58/84.65 | (482) ? [v0] : ? [v1] : ? [v2] : (relation_dom(empty_set) = v1 & relation_image(empty_set, v1) = v2 & relation(empty_set) = v0 & ( ~ (v0 = 0) | v2 = empty_set))
% 141.58/84.65 |
% 141.58/84.65 | Instantiating formula (46) with empty_set, empty_set and discharging atoms relation_rng(empty_set) = empty_set, yields:
% 141.58/84.65 | (483) ? [v0] : ? [v1] : (relation_dom(empty_set) = v1 & relation(empty_set) = v0 & ( ~ (v0 = 0) | ( ! [v2] : ! [v3] : ( ~ (relation_composition(v2, empty_set) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (relation_rng(v3) = v7 & relation_rng(v2) = v5 & subset(v1, v5) = v6 & relation(v2) = v4 & ( ~ (v6 = 0) | ~ (v4 = 0) | v7 = empty_set))) & ! [v2] : ! [v3] : ( ~ (relation_rng(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (relation_composition(v2, empty_set) = v6 & relation_rng(v6) = v7 & subset(v1, v3) = v5 & relation(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0) | v7 = empty_set))) & ! [v2] : ( ~ (relation(v2) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_composition(v2, empty_set) = v5 & relation_rng(v5) = v6 & relation_rng(v2) = v3 & subset(v1, v3) = v4 & ( ~ (v4 = 0) | v6 = empty_set))))))
% 141.58/84.65 |
% 141.58/84.65 | Instantiating formula (216) with empty_set, empty_set and discharging atoms relation_rng(empty_set) = empty_set, yields:
% 141.58/84.65 | (484) ? [v0] : ? [v1] : (relation_dom(empty_set) = v1 & relation(empty_set) = v0 & ( ~ (v0 = 0) | ( ! [v2] : ! [v3] : ( ~ (relation_composition(empty_set, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (relation_dom(v3) = v7 & relation_dom(v2) = v5 & subset(empty_set, v5) = v6 & relation(v2) = v4 & ( ~ (v6 = 0) | ~ (v4 = 0) | v7 = v1))) & ! [v2] : ! [v3] : ( ~ (relation_dom(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (relation_composition(empty_set, v2) = v6 & relation_dom(v6) = v7 & subset(empty_set, v3) = v5 & relation(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0) | v7 = v1))) & ! [v2] : ( ~ (relation(v2) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_composition(empty_set, v2) = v5 & relation_dom(v5) = v6 & relation_dom(v2) = v3 & subset(empty_set, v3) = v4 & ( ~ (v4 = 0) | v6 = v1))))))
% 141.58/84.65 |
% 141.58/84.65 | Instantiating formula (225) with empty_set, empty_set and discharging atoms relation_rng(empty_set) = empty_set, yields:
% 141.58/84.65 | (485) ? [v0] : ? [v1] : (relation_dom(empty_set) = v1 & relation(empty_set) = v0 & ( ~ (v0 = 0) | ( ! [v2] : ! [v3] : ( ~ (relation_rng(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (relation_dom(v2) = v6 & subset(v1, v6) = v7 & subset(empty_set, v3) = v8 & subset(empty_set, v2) = v5 & relation(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0) | (v8 = 0 & v7 = 0)))) & ! [v2] : ! [v3] : ( ~ (relation_dom(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (relation_rng(v2) = v7 & subset(v1, v3) = v6 & subset(empty_set, v7) = v8 & subset(empty_set, v2) = v5 & relation(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0) | (v8 = 0 & v6 = 0)))) & ! [v2] : ( ~ (subset(empty_set, v2) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (relation_rng(v2) = v6 & relation_dom(v2) = v4 & subset(v1, v4) = v5 & subset(empty_set, v6) = v7 & relation(v2) = v3 & ( ~ (v3 = 0) | (v7 = 0 & v5 = 0)))) & ! [v2] : ( ~ (relation(v2) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (relation_rng(v2) = v6 & relation_dom(v2) = v4 & subset(v1, v4) = v5 & subset(empty_set, v6) = v7 & subset(empty_set, v2) = v3 & ( ~ (v3 = 0) | (v7 = 0 & v5 = 0)))))))
% 141.58/84.65 |
% 141.58/84.65 | Instantiating formula (296) with all_0_11_11, all_0_14_14 and discharging atoms relation_dom(all_0_14_14) = all_0_11_11, yields:
% 141.58/84.65 | (486) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (relation_inverse(all_0_14_14) = v2 & relation_rng(v2) = v4 & relation_rng(all_0_14_14) = v1 & relation_dom(v2) = v3 & relation(all_0_14_14) = v0 & ( ~ (v0 = 0) | (v4 = all_0_11_11 & v3 = v1)))
% 141.58/84.65 |
% 141.58/84.65 | Instantiating formula (61) with all_0_11_11, all_0_14_14 and discharging atoms relation_dom(all_0_14_14) = all_0_11_11, yields:
% 141.58/84.65 | (487) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (relation_field(all_0_14_14) = v1 & relation_rng(all_0_14_14) = v2 & set_union2(all_0_11_11, v2) = v3 & relation(all_0_14_14) = v0 & ( ~ (v0 = 0) | v3 = v1))
% 141.58/84.65 |
% 141.58/84.65 | Instantiating formula (341) with all_0_11_11, all_0_14_14 and discharging atoms relation_dom(all_0_14_14) = all_0_11_11, yields:
% 141.58/84.65 | (488) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (relation_rng(all_0_14_14) = v1 & cartesian_product2(all_0_11_11, v1) = v2 & subset(all_0_14_14, v2) = v3 & relation(all_0_14_14) = v0 & ( ~ (v0 = 0) | v3 = 0))
% 141.58/84.65 |
% 141.58/84.65 | Instantiating formula (159) with all_0_11_11, all_0_14_14 and discharging atoms relation_dom(all_0_14_14) = all_0_11_11, yields:
% 141.58/84.65 | (489) ? [v0] : ? [v1] : ? [v2] : (relation_rng(all_0_14_14) = v2 & relation_image(all_0_14_14, all_0_11_11) = v1 & relation(all_0_14_14) = v0 & ( ~ (v0 = 0) | v2 = v1))
% 141.98/84.65 |
% 141.98/84.65 | Instantiating formula (80) with all_0_11_11, all_0_14_14 and discharging atoms relation_dom(all_0_14_14) = all_0_11_11, yields:
% 141.98/84.65 | (490) ? [v0] : ? [v1] : ? [v2] : (relation(all_0_14_14) = v1 & empty(all_0_11_11) = v2 & empty(all_0_14_14) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | v0 = 0))
% 141.98/84.65 |
% 141.98/84.65 | Instantiating formula (389) with all_0_11_11, all_0_14_14 and discharging atoms relation_dom(all_0_14_14) = all_0_11_11, yields:
% 141.98/84.65 | (491) ? [v0] : ? [v1] : (relation_rng(all_0_14_14) = v1 & relation(all_0_14_14) = v0 & ( ~ (v0 = 0) | ( ! [v2] : ! [v3] : ( ~ (relation_composition(v2, all_0_14_14) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (relation_rng(v3) = v7 & relation_rng(v2) = v5 & subset(all_0_11_11, v5) = v6 & relation(v2) = v4 & ( ~ (v6 = 0) | ~ (v4 = 0) | v7 = v1))) & ! [v2] : ! [v3] : ( ~ (relation_rng(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (relation_composition(v2, all_0_14_14) = v6 & relation_rng(v6) = v7 & subset(all_0_11_11, v3) = v5 & relation(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0) | v7 = v1))) & ! [v2] : ( ~ (relation(v2) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_composition(v2, all_0_14_14) = v5 & relation_rng(v5) = v6 & relation_rng(v2) = v3 & subset(all_0_11_11, v3) = v4 & ( ~ (v4 = 0) | v6 = v1))))))
% 141.98/84.65 |
% 141.98/84.65 | Instantiating formula (441) with all_0_11_11, all_0_14_14 and discharging atoms relation_dom(all_0_14_14) = all_0_11_11, yields:
% 141.98/84.65 | (492) ? [v0] : ? [v1] : (relation_rng(all_0_14_14) = v1 & relation(all_0_14_14) = v0 & ( ~ (v0 = 0) | ( ! [v2] : ! [v3] : ( ~ (relation_composition(all_0_14_14, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (relation_dom(v3) = v7 & relation_dom(v2) = v5 & subset(v1, v5) = v6 & relation(v2) = v4 & ( ~ (v6 = 0) | ~ (v4 = 0) | v7 = all_0_11_11))) & ! [v2] : ! [v3] : ( ~ (relation_dom(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (relation_composition(all_0_14_14, v2) = v6 & relation_dom(v6) = v7 & subset(v1, v3) = v5 & relation(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0) | v7 = all_0_11_11))) & ! [v2] : ( ~ (relation(v2) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_composition(all_0_14_14, v2) = v5 & relation_dom(v5) = v6 & relation_dom(v2) = v3 & subset(v1, v3) = v4 & ( ~ (v4 = 0) | v6 = all_0_11_11))))))
% 141.98/84.65 |
% 141.98/84.65 | Instantiating formula (65) with all_0_11_11, all_0_14_14 and discharging atoms relation_dom(all_0_14_14) = all_0_11_11, yields:
% 141.98/84.65 | (493) ? [v0] : ? [v1] : (relation_rng(all_0_14_14) = v1 & relation(all_0_14_14) = v0 & ( ~ (v0 = 0) | ( ! [v2] : ! [v3] : ( ~ (relation_rng(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (relation_dom(v2) = v6 & subset(v1, v3) = v8 & subset(all_0_11_11, v6) = v7 & subset(all_0_14_14, v2) = v5 & relation(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0) | (v8 = 0 & v7 = 0)))) & ! [v2] : ! [v3] : ( ~ (relation_dom(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (relation_rng(v2) = v7 & subset(v1, v7) = v8 & subset(all_0_11_11, v3) = v6 & subset(all_0_14_14, v2) = v5 & relation(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0) | (v8 = 0 & v6 = 0)))) & ! [v2] : ( ~ (subset(all_0_14_14, v2) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (relation_rng(v2) = v6 & relation_dom(v2) = v4 & subset(v1, v6) = v7 & subset(all_0_11_11, v4) = v5 & relation(v2) = v3 & ( ~ (v3 = 0) | (v7 = 0 & v5 = 0)))) & ! [v2] : ( ~ (relation(v2) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (relation_rng(v2) = v6 & relation_dom(v2) = v4 & subset(v1, v6) = v7 & subset(all_0_11_11, v4) = v5 & subset(all_0_14_14, v2) = v3 & ( ~ (v3 = 0) | (v7 = 0 & v5 = 0)))))))
% 141.98/84.65 |
% 141.98/84.65 | Instantiating formula (14) with all_0_11_11, all_0_14_14 and discharging atoms relation_dom(all_0_14_14) = all_0_11_11, yields:
% 141.98/84.65 | (494) ? [v0] : ? [v1] : (relation_rng(all_0_14_14) = v1 & relation(all_0_14_14) = v0 & ( ~ (v0 = 0) | (( ~ (v1 = empty_set) | all_0_11_11 = empty_set) & ( ~ (all_0_11_11 = empty_set) | v1 = empty_set))))
% 141.98/84.65 |
% 141.98/84.65 | Instantiating formula (296) with empty_set, empty_set and discharging atoms relation_dom(empty_set) = empty_set, yields:
% 141.98/84.65 | (495) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (relation_inverse(empty_set) = v2 & relation_rng(v2) = v4 & relation_rng(empty_set) = v1 & relation_dom(v2) = v3 & relation(empty_set) = v0 & ( ~ (v0 = 0) | (v4 = empty_set & v3 = v1)))
% 141.98/84.65 |
% 141.98/84.65 | Instantiating formula (61) with empty_set, empty_set and discharging atoms relation_dom(empty_set) = empty_set, yields:
% 141.98/84.65 | (496) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (relation_field(empty_set) = v1 & relation_rng(empty_set) = v2 & set_union2(empty_set, v2) = v3 & relation(empty_set) = v0 & ( ~ (v0 = 0) | v3 = v1))
% 141.98/84.65 |
% 141.98/84.65 | Instantiating formula (341) with empty_set, empty_set and discharging atoms relation_dom(empty_set) = empty_set, yields:
% 141.98/84.65 | (497) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (relation_rng(empty_set) = v1 & cartesian_product2(empty_set, v1) = v2 & subset(empty_set, v2) = v3 & relation(empty_set) = v0 & ( ~ (v0 = 0) | v3 = 0))
% 141.98/84.65 |
% 141.98/84.65 | Instantiating formula (159) with empty_set, empty_set and discharging atoms relation_dom(empty_set) = empty_set, yields:
% 141.98/84.65 | (498) ? [v0] : ? [v1] : ? [v2] : (relation_rng(empty_set) = v2 & relation_image(empty_set, empty_set) = v1 & relation(empty_set) = v0 & ( ~ (v0 = 0) | v2 = v1))
% 141.98/84.65 |
% 141.98/84.65 | Instantiating formula (389) with empty_set, empty_set and discharging atoms relation_dom(empty_set) = empty_set, yields:
% 141.98/84.65 | (499) ? [v0] : ? [v1] : (relation_rng(empty_set) = v1 & relation(empty_set) = v0 & ( ~ (v0 = 0) | ( ! [v2] : ! [v3] : ( ~ (relation_composition(v2, empty_set) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (relation_rng(v3) = v7 & relation_rng(v2) = v5 & subset(empty_set, v5) = v6 & relation(v2) = v4 & ( ~ (v6 = 0) | ~ (v4 = 0) | v7 = v1))) & ! [v2] : ! [v3] : ( ~ (relation_rng(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (relation_composition(v2, empty_set) = v6 & relation_rng(v6) = v7 & subset(empty_set, v3) = v5 & relation(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0) | v7 = v1))) & ! [v2] : ( ~ (relation(v2) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_composition(v2, empty_set) = v5 & relation_rng(v5) = v6 & relation_rng(v2) = v3 & subset(empty_set, v3) = v4 & ( ~ (v4 = 0) | v6 = v1))))))
% 141.98/84.66 |
% 141.98/84.66 | Instantiating formula (441) with empty_set, empty_set and discharging atoms relation_dom(empty_set) = empty_set, yields:
% 141.98/84.66 | (500) ? [v0] : ? [v1] : (relation_rng(empty_set) = v1 & relation(empty_set) = v0 & ( ~ (v0 = 0) | ( ! [v2] : ! [v3] : ( ~ (relation_composition(empty_set, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (relation_dom(v3) = v7 & relation_dom(v2) = v5 & subset(v1, v5) = v6 & relation(v2) = v4 & ( ~ (v6 = 0) | ~ (v4 = 0) | v7 = empty_set))) & ! [v2] : ! [v3] : ( ~ (relation_dom(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (relation_composition(empty_set, v2) = v6 & relation_dom(v6) = v7 & subset(v1, v3) = v5 & relation(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0) | v7 = empty_set))) & ! [v2] : ( ~ (relation(v2) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_composition(empty_set, v2) = v5 & relation_dom(v5) = v6 & relation_dom(v2) = v3 & subset(v1, v3) = v4 & ( ~ (v4 = 0) | v6 = empty_set))))))
% 141.98/84.66 |
% 141.98/84.66 | Instantiating formula (65) with empty_set, empty_set and discharging atoms relation_dom(empty_set) = empty_set, yields:
% 141.98/84.66 | (501) ? [v0] : ? [v1] : (relation_rng(empty_set) = v1 & relation(empty_set) = v0 & ( ~ (v0 = 0) | ( ! [v2] : ! [v3] : ( ~ (relation_rng(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (relation_dom(v2) = v6 & subset(v1, v3) = v8 & subset(empty_set, v6) = v7 & subset(empty_set, v2) = v5 & relation(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0) | (v8 = 0 & v7 = 0)))) & ! [v2] : ! [v3] : ( ~ (relation_dom(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (relation_rng(v2) = v7 & subset(v1, v7) = v8 & subset(empty_set, v3) = v6 & subset(empty_set, v2) = v5 & relation(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0) | (v8 = 0 & v6 = 0)))) & ! [v2] : ( ~ (subset(empty_set, v2) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (relation_rng(v2) = v6 & relation_dom(v2) = v4 & subset(v1, v6) = v7 & subset(empty_set, v4) = v5 & relation(v2) = v3 & ( ~ (v3 = 0) | (v7 = 0 & v5 = 0)))) & ! [v2] : ( ~ (relation(v2) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (relation_rng(v2) = v6 & relation_dom(v2) = v4 & subset(v1, v6) = v7 & subset(empty_set, v4) = v5 & subset(empty_set, v2) = v3 & ( ~ (v3 = 0) | (v7 = 0 & v5 = 0)))))))
% 141.98/84.66 |
% 141.98/84.66 | Instantiating formula (238) with all_0_13_13, all_0_15_15, all_0_16_16, all_0_11_11, all_0_14_14 and discharging atoms relation_dom(all_0_14_14) = all_0_11_11, ordered_pair(all_0_16_16, all_0_15_15) = all_0_13_13, yields:
% 141.98/84.66 | (502) ? [v0] : ? [v1] : ? [v2] : ((apply(all_0_14_14, all_0_16_16) = v1 & in(all_0_13_13, all_0_14_14) = v2 & in(all_0_16_16, all_0_11_11) = v0 & ( ~ (v0 = 0) | (( ~ (v2 = 0) | v1 = all_0_15_15) & ( ~ (v1 = all_0_15_15) | v2 = 0)))) | (relation(all_0_14_14) = v0 & function(all_0_14_14) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 141.98/84.66 |
% 141.98/84.66 | Instantiating formula (73) with empty_set, empty_set, all_0_0_0 and discharging atoms relation_rng(empty_set) = empty_set, relation(all_0_0_0) = 0, yields:
% 141.98/84.66 | (503) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (relation_composition(all_0_0_0, empty_set) = v1 & relation_rng(v1) = v2 & subset(v2, empty_set) = v3 & relation(empty_set) = v0 & ( ~ (v0 = 0) | v3 = 0))
% 141.98/84.66 |
% 141.98/84.66 | Instantiating formula (165) with all_0_0_0 and discharging atoms relation(all_0_0_0) = 0, yields:
% 141.98/84.66 | (504) ? [v0] : ? [v1] : (relation_rng(all_0_0_0) = v1 & relation_dom(all_0_0_0) = v0 & ! [v2] : ! [v3] : ( ~ (relation_composition(v2, all_0_0_0) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (relation_rng(v3) = v7 & relation_rng(v2) = v5 & subset(v0, v5) = v6 & relation(v2) = v4 & ( ~ (v6 = 0) | ~ (v4 = 0) | v7 = v1))) & ! [v2] : ! [v3] : ( ~ (relation_rng(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (relation_composition(v2, all_0_0_0) = v6 & relation_rng(v6) = v7 & subset(v0, v3) = v5 & relation(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0) | v7 = v1))) & ! [v2] : ( ~ (relation(v2) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_composition(v2, all_0_0_0) = v5 & relation_rng(v5) = v6 & relation_rng(v2) = v3 & subset(v0, v3) = v4 & ( ~ (v4 = 0) | v6 = v1))))
% 141.98/84.66 |
% 141.98/84.66 | Instantiating formula (452) with all_0_0_0 and discharging atoms relation(all_0_0_0) = 0, yields:
% 141.98/84.66 | (505) ? [v0] : ? [v1] : (relation_rng(all_0_0_0) = v1 & relation_dom(all_0_0_0) = v0 & ! [v2] : ! [v3] : ( ~ (relation_rng(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (relation_dom(v2) = v6 & subset(v1, v3) = v8 & subset(v0, v6) = v7 & subset(all_0_0_0, v2) = v5 & relation(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0) | (v8 = 0 & v7 = 0)))) & ! [v2] : ! [v3] : ( ~ (relation_dom(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (relation_rng(v2) = v7 & subset(v1, v7) = v8 & subset(v0, v3) = v6 & subset(all_0_0_0, v2) = v5 & relation(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0) | (v8 = 0 & v6 = 0)))) & ! [v2] : ( ~ (subset(all_0_0_0, v2) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (relation_rng(v2) = v6 & relation_dom(v2) = v4 & subset(v1, v6) = v7 & subset(v0, v4) = v5 & relation(v2) = v3 & ( ~ (v3 = 0) | (v7 = 0 & v5 = 0)))) & ! [v2] : ( ~ (relation(v2) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (relation_rng(v2) = v6 & relation_dom(v2) = v4 & subset(v1, v6) = v7 & subset(v0, v4) = v5 & subset(all_0_0_0, v2) = v3 & ( ~ (v3 = 0) | (v7 = 0 & v5 = 0)))))
% 141.98/84.66 |
% 141.98/84.66 | Instantiating formula (360) with all_0_0_0 and discharging atoms relation(all_0_0_0) = 0, yields:
% 141.98/84.66 | (506) ? [v0] : ? [v1] : (relation_rng(all_0_0_0) = v0 & relation_dom(all_0_0_0) = v1 & ! [v2] : ! [v3] : ( ~ (relation_composition(all_0_0_0, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (relation_dom(v3) = v7 & relation_dom(v2) = v5 & subset(v0, v5) = v6 & relation(v2) = v4 & ( ~ (v6 = 0) | ~ (v4 = 0) | v7 = v1))) & ! [v2] : ! [v3] : ( ~ (relation_dom(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (relation_composition(all_0_0_0, v2) = v6 & relation_dom(v6) = v7 & subset(v0, v3) = v5 & relation(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0) | v7 = v1))) & ! [v2] : ( ~ (relation(v2) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_composition(all_0_0_0, v2) = v5 & relation_dom(v5) = v6 & relation_dom(v2) = v3 & subset(v0, v3) = v4 & ( ~ (v4 = 0) | v6 = v1))))
% 141.98/84.66 |
% 141.98/84.66 | Instantiating formula (73) with empty_set, empty_set, all_0_4_4 and discharging atoms relation_rng(empty_set) = empty_set, relation(all_0_4_4) = 0, yields:
% 141.98/84.66 | (507) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (relation_composition(all_0_4_4, empty_set) = v1 & relation_rng(v1) = v2 & subset(v2, empty_set) = v3 & relation(empty_set) = v0 & ( ~ (v0 = 0) | v3 = 0))
% 141.98/84.66 |
% 141.98/84.66 | Instantiating formula (165) with all_0_4_4 and discharging atoms relation(all_0_4_4) = 0, yields:
% 141.98/84.66 | (508) ? [v0] : ? [v1] : (relation_rng(all_0_4_4) = v1 & relation_dom(all_0_4_4) = v0 & ! [v2] : ! [v3] : ( ~ (relation_composition(v2, all_0_4_4) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (relation_rng(v3) = v7 & relation_rng(v2) = v5 & subset(v0, v5) = v6 & relation(v2) = v4 & ( ~ (v6 = 0) | ~ (v4 = 0) | v7 = v1))) & ! [v2] : ! [v3] : ( ~ (relation_rng(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (relation_composition(v2, all_0_4_4) = v6 & relation_rng(v6) = v7 & subset(v0, v3) = v5 & relation(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0) | v7 = v1))) & ! [v2] : ( ~ (relation(v2) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_composition(v2, all_0_4_4) = v5 & relation_rng(v5) = v6 & relation_rng(v2) = v3 & subset(v0, v3) = v4 & ( ~ (v4 = 0) | v6 = v1))))
% 141.98/84.66 |
% 141.98/84.66 | Instantiating formula (452) with all_0_4_4 and discharging atoms relation(all_0_4_4) = 0, yields:
% 141.98/84.66 | (509) ? [v0] : ? [v1] : (relation_rng(all_0_4_4) = v1 & relation_dom(all_0_4_4) = v0 & ! [v2] : ! [v3] : ( ~ (relation_rng(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (relation_dom(v2) = v6 & subset(v1, v3) = v8 & subset(v0, v6) = v7 & subset(all_0_4_4, v2) = v5 & relation(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0) | (v8 = 0 & v7 = 0)))) & ! [v2] : ! [v3] : ( ~ (relation_dom(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (relation_rng(v2) = v7 & subset(v1, v7) = v8 & subset(v0, v3) = v6 & subset(all_0_4_4, v2) = v5 & relation(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0) | (v8 = 0 & v6 = 0)))) & ! [v2] : ( ~ (subset(all_0_4_4, v2) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (relation_rng(v2) = v6 & relation_dom(v2) = v4 & subset(v1, v6) = v7 & subset(v0, v4) = v5 & relation(v2) = v3 & ( ~ (v3 = 0) | (v7 = 0 & v5 = 0)))) & ! [v2] : ( ~ (relation(v2) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (relation_rng(v2) = v6 & relation_dom(v2) = v4 & subset(v1, v6) = v7 & subset(v0, v4) = v5 & subset(all_0_4_4, v2) = v3 & ( ~ (v3 = 0) | (v7 = 0 & v5 = 0)))))
% 141.98/84.66 |
% 141.98/84.66 | Instantiating formula (360) with all_0_4_4 and discharging atoms relation(all_0_4_4) = 0, yields:
% 141.98/84.66 | (510) ? [v0] : ? [v1] : (relation_rng(all_0_4_4) = v0 & relation_dom(all_0_4_4) = v1 & ! [v2] : ! [v3] : ( ~ (relation_composition(all_0_4_4, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (relation_dom(v3) = v7 & relation_dom(v2) = v5 & subset(v0, v5) = v6 & relation(v2) = v4 & ( ~ (v6 = 0) | ~ (v4 = 0) | v7 = v1))) & ! [v2] : ! [v3] : ( ~ (relation_dom(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (relation_composition(all_0_4_4, v2) = v6 & relation_dom(v6) = v7 & subset(v0, v3) = v5 & relation(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0) | v7 = v1))) & ! [v2] : ( ~ (relation(v2) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_composition(all_0_4_4, v2) = v5 & relation_dom(v5) = v6 & relation_dom(v2) = v3 & subset(v0, v3) = v4 & ( ~ (v4 = 0) | v6 = v1))))
% 141.98/84.66 |
% 141.98/84.66 | Instantiating formula (73) with empty_set, empty_set, all_0_7_7 and discharging atoms relation_rng(empty_set) = empty_set, relation(all_0_7_7) = 0, yields:
% 141.98/84.66 | (511) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (relation_composition(all_0_7_7, empty_set) = v1 & relation_rng(v1) = v2 & subset(v2, empty_set) = v3 & relation(empty_set) = v0 & ( ~ (v0 = 0) | v3 = 0))
% 141.98/84.66 |
% 141.98/84.66 | Instantiating formula (165) with all_0_7_7 and discharging atoms relation(all_0_7_7) = 0, yields:
% 141.98/84.66 | (512) ? [v0] : ? [v1] : (relation_rng(all_0_7_7) = v1 & relation_dom(all_0_7_7) = v0 & ! [v2] : ! [v3] : ( ~ (relation_composition(v2, all_0_7_7) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (relation_rng(v3) = v7 & relation_rng(v2) = v5 & subset(v0, v5) = v6 & relation(v2) = v4 & ( ~ (v6 = 0) | ~ (v4 = 0) | v7 = v1))) & ! [v2] : ! [v3] : ( ~ (relation_rng(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (relation_composition(v2, all_0_7_7) = v6 & relation_rng(v6) = v7 & subset(v0, v3) = v5 & relation(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0) | v7 = v1))) & ! [v2] : ( ~ (relation(v2) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_composition(v2, all_0_7_7) = v5 & relation_rng(v5) = v6 & relation_rng(v2) = v3 & subset(v0, v3) = v4 & ( ~ (v4 = 0) | v6 = v1))))
% 141.98/84.66 |
% 141.98/84.66 | Instantiating formula (452) with all_0_7_7 and discharging atoms relation(all_0_7_7) = 0, yields:
% 141.98/84.66 | (513) ? [v0] : ? [v1] : (relation_rng(all_0_7_7) = v1 & relation_dom(all_0_7_7) = v0 & ! [v2] : ! [v3] : ( ~ (relation_rng(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (relation_dom(v2) = v6 & subset(v1, v3) = v8 & subset(v0, v6) = v7 & subset(all_0_7_7, v2) = v5 & relation(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0) | (v8 = 0 & v7 = 0)))) & ! [v2] : ! [v3] : ( ~ (relation_dom(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (relation_rng(v2) = v7 & subset(v1, v7) = v8 & subset(v0, v3) = v6 & subset(all_0_7_7, v2) = v5 & relation(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0) | (v8 = 0 & v6 = 0)))) & ! [v2] : ( ~ (subset(all_0_7_7, v2) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (relation_rng(v2) = v6 & relation_dom(v2) = v4 & subset(v1, v6) = v7 & subset(v0, v4) = v5 & relation(v2) = v3 & ( ~ (v3 = 0) | (v7 = 0 & v5 = 0)))) & ! [v2] : ( ~ (relation(v2) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (relation_rng(v2) = v6 & relation_dom(v2) = v4 & subset(v1, v6) = v7 & subset(v0, v4) = v5 & subset(all_0_7_7, v2) = v3 & ( ~ (v3 = 0) | (v7 = 0 & v5 = 0)))))
% 141.98/84.67 |
% 141.98/84.67 | Instantiating formula (360) with all_0_7_7 and discharging atoms relation(all_0_7_7) = 0, yields:
% 141.98/84.67 | (514) ? [v0] : ? [v1] : (relation_rng(all_0_7_7) = v0 & relation_dom(all_0_7_7) = v1 & ! [v2] : ! [v3] : ( ~ (relation_composition(all_0_7_7, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (relation_dom(v3) = v7 & relation_dom(v2) = v5 & subset(v0, v5) = v6 & relation(v2) = v4 & ( ~ (v6 = 0) | ~ (v4 = 0) | v7 = v1))) & ! [v2] : ! [v3] : ( ~ (relation_dom(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (relation_composition(all_0_7_7, v2) = v6 & relation_dom(v6) = v7 & subset(v0, v3) = v5 & relation(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0) | v7 = v1))) & ! [v2] : ( ~ (relation(v2) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_composition(all_0_7_7, v2) = v5 & relation_dom(v5) = v6 & relation_dom(v2) = v3 & subset(v0, v3) = v4 & ( ~ (v4 = 0) | v6 = v1))))
% 141.98/84.67 |
% 141.98/84.67 | Instantiating formula (254) with all_0_14_14 and discharging atoms relation(all_0_14_14) = 0, yields:
% 141.98/84.67 | (515) ? [v0] : ? [v1] : ? [v2] : (relation_inverse(all_0_14_14) = v1 & relation_rng(v1) = v2 & relation_rng(all_0_14_14) = v0 & relation_dom(v1) = v0 & relation_dom(all_0_14_14) = v2)
% 141.98/84.67 |
% 141.98/84.67 | Instantiating formula (304) with all_0_14_14 and discharging atoms relation(all_0_14_14) = 0, yields:
% 141.98/84.67 | (516) ? [v0] : ? [v1] : ? [v2] : (relation_field(all_0_14_14) = v0 & relation_rng(all_0_14_14) = v2 & relation_dom(all_0_14_14) = v1 & set_union2(v1, v2) = v0)
% 141.98/84.67 |
% 141.98/84.67 | Instantiating formula (82) with all_0_14_14 and discharging atoms relation(all_0_14_14) = 0, yields:
% 141.98/84.67 | (517) ? [v0] : ? [v1] : ? [v2] : (relation_rng(all_0_14_14) = v1 & relation_dom(all_0_14_14) = v0 & cartesian_product2(v0, v1) = v2 & subset(all_0_14_14, v2) = 0)
% 141.98/84.67 |
% 141.98/84.67 | Instantiating formula (48) with all_0_14_14 and discharging atoms relation(all_0_14_14) = 0, yields:
% 141.98/84.67 | (518) ? [v0] : ? [v1] : ? [v2] : (relation_dom(all_0_14_14) = v1 & empty(v1) = v2 & empty(all_0_14_14) = v0 & ( ~ (v2 = 0) | v0 = 0))
% 141.98/84.67 |
% 141.98/84.67 | Instantiating formula (253) with all_0_14_14 and discharging atoms relation(all_0_14_14) = 0, yields:
% 141.98/84.67 | (519) ? [v0] : ? [v1] : (relation_rng(all_0_14_14) = v1 & relation_dom(all_0_14_14) = v0 & relation_image(all_0_14_14, v0) = v1)
% 141.98/84.67 |
% 141.98/84.67 | Instantiating formula (165) with all_0_14_14 and discharging atoms relation(all_0_14_14) = 0, yields:
% 141.98/84.67 | (520) ? [v0] : ? [v1] : (relation_rng(all_0_14_14) = v1 & relation_dom(all_0_14_14) = v0 & ! [v2] : ! [v3] : ( ~ (relation_composition(v2, all_0_14_14) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (relation_rng(v3) = v7 & relation_rng(v2) = v5 & subset(v0, v5) = v6 & relation(v2) = v4 & ( ~ (v6 = 0) | ~ (v4 = 0) | v7 = v1))) & ! [v2] : ! [v3] : ( ~ (relation_rng(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (relation_composition(v2, all_0_14_14) = v6 & relation_rng(v6) = v7 & subset(v0, v3) = v5 & relation(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0) | v7 = v1))) & ! [v2] : ( ~ (relation(v2) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_composition(v2, all_0_14_14) = v5 & relation_rng(v5) = v6 & relation_rng(v2) = v3 & subset(v0, v3) = v4 & ( ~ (v4 = 0) | v6 = v1))))
% 141.98/84.67 |
% 141.98/84.67 | Instantiating formula (452) with all_0_14_14 and discharging atoms relation(all_0_14_14) = 0, yields:
% 141.98/84.67 | (521) ? [v0] : ? [v1] : (relation_rng(all_0_14_14) = v1 & relation_dom(all_0_14_14) = v0 & ! [v2] : ! [v3] : ( ~ (relation_rng(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (relation_dom(v2) = v6 & subset(v1, v3) = v8 & subset(v0, v6) = v7 & subset(all_0_14_14, v2) = v5 & relation(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0) | (v8 = 0 & v7 = 0)))) & ! [v2] : ! [v3] : ( ~ (relation_dom(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (relation_rng(v2) = v7 & subset(v1, v7) = v8 & subset(v0, v3) = v6 & subset(all_0_14_14, v2) = v5 & relation(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0) | (v8 = 0 & v6 = 0)))) & ! [v2] : ( ~ (subset(all_0_14_14, v2) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (relation_rng(v2) = v6 & relation_dom(v2) = v4 & subset(v1, v6) = v7 & subset(v0, v4) = v5 & relation(v2) = v3 & ( ~ (v3 = 0) | (v7 = 0 & v5 = 0)))) & ! [v2] : ( ~ (relation(v2) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (relation_rng(v2) = v6 & relation_dom(v2) = v4 & subset(v1, v6) = v7 & subset(v0, v4) = v5 & subset(all_0_14_14, v2) = v3 & ( ~ (v3 = 0) | (v7 = 0 & v5 = 0)))))
% 141.98/84.67 |
% 141.98/84.67 | Instantiating formula (227) with all_0_14_14 and discharging atoms relation(all_0_14_14) = 0, yields:
% 141.98/84.67 | (522) ? [v0] : ? [v1] : (relation_rng(all_0_14_14) = v1 & relation_dom(all_0_14_14) = v0 & ( ~ (v1 = empty_set) | v0 = empty_set) & ( ~ (v0 = empty_set) | v1 = empty_set))
% 141.98/84.67 |
% 141.98/84.67 | Instantiating formula (360) with all_0_14_14 and discharging atoms relation(all_0_14_14) = 0, yields:
% 141.98/84.67 | (523) ? [v0] : ? [v1] : (relation_rng(all_0_14_14) = v0 & relation_dom(all_0_14_14) = v1 & ! [v2] : ! [v3] : ( ~ (relation_composition(all_0_14_14, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (relation_dom(v3) = v7 & relation_dom(v2) = v5 & subset(v0, v5) = v6 & relation(v2) = v4 & ( ~ (v6 = 0) | ~ (v4 = 0) | v7 = v1))) & ! [v2] : ! [v3] : ( ~ (relation_dom(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (relation_composition(all_0_14_14, v2) = v6 & relation_dom(v6) = v7 & subset(v0, v3) = v5 & relation(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0) | v7 = v1))) & ! [v2] : ( ~ (relation(v2) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_composition(all_0_14_14, v2) = v5 & relation_dom(v5) = v6 & relation_dom(v2) = v3 & subset(v0, v3) = v4 & ( ~ (v4 = 0) | v6 = v1))))
% 141.98/84.67 |
% 141.98/84.67 | Instantiating formula (364) with all_0_14_14 and discharging atoms relation(all_0_14_14) = 0, yields:
% 141.98/84.67 | (524) ? [v0] : ? [v1] : (relation_dom(all_0_14_14) = v1 & function(all_0_14_14) = v0 & ( ~ (v0 = 0) | ( ! [v2] : ! [v3] : ! [v4] : ( ~ (ordered_pair(v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : (apply(all_0_14_14, v2) = v6 & in(v4, all_0_14_14) = v7 & in(v2, v1) = v5 & ( ~ (v5 = 0) | (( ~ (v7 = 0) | v6 = v3) & ( ~ (v6 = v3) | v7 = 0))))) & ? [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (in(v3, v1) = v4) | ? [v5] : (apply(all_0_14_14, v3) = v5 & ( ~ (v5 = v2) | v2 = empty_set) & ( ~ (v2 = empty_set) | v5 = empty_set))) & ! [v2] : ! [v3] : (v3 = empty_set | ~ (apply(all_0_14_14, v2) = v3) | in(v2, v1) = 0))))
% 141.98/84.67 |
% 141.98/84.67 | Instantiating formula (246) with all_0_14_14 and discharging atoms relation(all_0_14_14) = 0, yields:
% 141.98/84.67 | (525) ? [v0] : (relation_dom(all_0_14_14) = v0 & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = 0 | ~ (ordered_pair(v1, v3) = v4) | ~ (in(v1, v0) = v2) | ? [v5] : ( ~ (v5 = 0) & in(v4, all_0_14_14) = v5)) & ! [v1] : ( ~ (in(v1, v0) = 0) | ? [v2] : ? [v3] : (ordered_pair(v1, v2) = v3 & in(v3, all_0_14_14) = 0)) & ? [v1] : (v1 = v0 | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (in(v2, v1) = v3 & ( ~ (v3 = 0) | ! [v7] : ! [v8] : ( ~ (ordered_pair(v2, v7) = v8) | ? [v9] : ( ~ (v9 = 0) & in(v8, all_0_14_14) = v9))) & (v3 = 0 | (v6 = 0 & ordered_pair(v2, v4) = v5 & in(v5, all_0_14_14) = 0)))))
% 141.98/84.67 |
% 141.98/84.67 | Instantiating formula (186) with all_0_14_14 and discharging atoms relation(all_0_14_14) = 0, yields:
% 141.98/84.67 | (526) ? [v0] : (relation_dom(all_0_14_14) = v0 & ! [v1] : ! [v2] : ( ~ (relation_composition(all_0_14_14, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (relation_dom(v2) = v4 & subset(v4, v0) = v5 & relation(v1) = v3 & ( ~ (v3 = 0) | v5 = 0))) & ! [v1] : ( ~ (relation(v1) = 0) | ? [v2] : ? [v3] : (relation_composition(all_0_14_14, v1) = v2 & relation_dom(v2) = v3 & subset(v3, v0) = 0)))
% 141.98/84.67 |
% 141.98/84.67 | Instantiating formula (73) with empty_set, empty_set, empty_set and discharging atoms relation_rng(empty_set) = empty_set, relation(empty_set) = 0, yields:
% 141.98/84.67 | (527) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (relation_composition(empty_set, empty_set) = v1 & relation_rng(v1) = v2 & subset(v2, empty_set) = v3 & relation(empty_set) = v0 & ( ~ (v0 = 0) | v3 = 0))
% 141.98/84.67 |
% 141.98/84.67 | Instantiating formula (466) with all_0_14_14, empty_set and discharging atoms relation(all_0_14_14) = 0, relation(empty_set) = 0, yields:
% 141.98/84.67 | (528) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (subset(empty_set, all_0_14_14) = v0 & ( ~ (v0 = 0) | ! [v6] : ! [v7] : ! [v8] : ( ~ (ordered_pair(v6, v7) = v8) | ? [v9] : ? [v10] : (in(v8, all_0_14_14) = v10 & in(v8, empty_set) = v9 & ( ~ (v9 = 0) | v10 = 0)))) & (v0 = 0 | (v4 = 0 & ~ (v5 = 0) & ordered_pair(v1, v2) = v3 & in(v3, all_0_14_14) = v5 & in(v3, empty_set) = 0)))
% 141.98/84.67 |
% 141.98/84.67 | Instantiating formula (165) with empty_set and discharging atoms relation(empty_set) = 0, yields:
% 141.98/84.67 | (529) ? [v0] : ? [v1] : (relation_rng(empty_set) = v1 & relation_dom(empty_set) = v0 & ! [v2] : ! [v3] : ( ~ (relation_composition(v2, empty_set) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (relation_rng(v3) = v7 & relation_rng(v2) = v5 & subset(v0, v5) = v6 & relation(v2) = v4 & ( ~ (v6 = 0) | ~ (v4 = 0) | v7 = v1))) & ! [v2] : ! [v3] : ( ~ (relation_rng(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (relation_composition(v2, empty_set) = v6 & relation_rng(v6) = v7 & subset(v0, v3) = v5 & relation(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0) | v7 = v1))) & ! [v2] : ( ~ (relation(v2) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_composition(v2, empty_set) = v5 & relation_rng(v5) = v6 & relation_rng(v2) = v3 & subset(v0, v3) = v4 & ( ~ (v4 = 0) | v6 = v1))))
% 141.98/84.67 |
% 141.98/84.67 | Instantiating formula (452) with empty_set and discharging atoms relation(empty_set) = 0, yields:
% 141.98/84.67 | (530) ? [v0] : ? [v1] : (relation_rng(empty_set) = v1 & relation_dom(empty_set) = v0 & ! [v2] : ! [v3] : ( ~ (relation_rng(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (relation_dom(v2) = v6 & subset(v1, v3) = v8 & subset(v0, v6) = v7 & subset(empty_set, v2) = v5 & relation(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0) | (v8 = 0 & v7 = 0)))) & ! [v2] : ! [v3] : ( ~ (relation_dom(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (relation_rng(v2) = v7 & subset(v1, v7) = v8 & subset(v0, v3) = v6 & subset(empty_set, v2) = v5 & relation(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0) | (v8 = 0 & v6 = 0)))) & ! [v2] : ( ~ (subset(empty_set, v2) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (relation_rng(v2) = v6 & relation_dom(v2) = v4 & subset(v1, v6) = v7 & subset(v0, v4) = v5 & relation(v2) = v3 & ( ~ (v3 = 0) | (v7 = 0 & v5 = 0)))) & ! [v2] : ( ~ (relation(v2) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (relation_rng(v2) = v6 & relation_dom(v2) = v4 & subset(v1, v6) = v7 & subset(v0, v4) = v5 & subset(empty_set, v2) = v3 & ( ~ (v3 = 0) | (v7 = 0 & v5 = 0)))))
% 141.98/84.67 |
% 141.98/84.67 | Instantiating formula (360) with empty_set and discharging atoms relation(empty_set) = 0, yields:
% 141.98/84.67 | (531) ? [v0] : ? [v1] : (relation_rng(empty_set) = v0 & relation_dom(empty_set) = v1 & ! [v2] : ! [v3] : ( ~ (relation_composition(empty_set, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (relation_dom(v3) = v7 & relation_dom(v2) = v5 & subset(v0, v5) = v6 & relation(v2) = v4 & ( ~ (v6 = 0) | ~ (v4 = 0) | v7 = v1))) & ! [v2] : ! [v3] : ( ~ (relation_dom(v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (relation_composition(empty_set, v2) = v6 & relation_dom(v6) = v7 & subset(v0, v3) = v5 & relation(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0) | v7 = v1))) & ! [v2] : ( ~ (relation(v2) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_composition(empty_set, v2) = v5 & relation_dom(v5) = v6 & relation_dom(v2) = v3 & subset(v0, v3) = v4 & ( ~ (v4 = 0) | v6 = v1))))
% 141.98/84.68 |
% 141.98/84.68 | Instantiating formula (363) with all_0_14_14 and discharging atoms function(all_0_14_14) = 0, yields:
% 141.98/84.68 | (532) ? [v0] : ? [v1] : (relation_dom(all_0_14_14) = v1 & relation(all_0_14_14) = v0 & ( ~ (v0 = 0) | ( ! [v2] : ! [v3] : ! [v4] : ( ~ (ordered_pair(v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : (apply(all_0_14_14, v2) = v6 & in(v4, all_0_14_14) = v7 & in(v2, v1) = v5 & ( ~ (v5 = 0) | (( ~ (v7 = 0) | v6 = v3) & ( ~ (v6 = v3) | v7 = 0))))) & ? [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (in(v3, v1) = v4) | ? [v5] : (apply(all_0_14_14, v3) = v5 & ( ~ (v5 = v2) | v2 = empty_set) & ( ~ (v2 = empty_set) | v5 = empty_set))) & ! [v2] : ! [v3] : (v3 = empty_set | ~ (apply(all_0_14_14, v2) = v3) | in(v2, v1) = 0))))
% 141.98/84.68 |
% 141.98/84.68 | Instantiating formula (175) with all_0_13_13, all_0_15_15, all_0_10_10, all_0_16_16, all_0_11_11, all_0_14_14 and discharging atoms relation_dom(all_0_14_14) = all_0_11_11, ordered_pair(all_0_16_16, all_0_15_15) = all_0_13_13, in(all_0_16_16, all_0_11_11) = all_0_10_10, yields:
% 141.98/84.68 | (533) all_0_10_10 = 0 | ? [v0] : (( ~ (v0 = 0) & relation(all_0_14_14) = v0) | ( ~ (v0 = 0) & in(all_0_13_13, all_0_14_14) = v0))
% 141.98/84.68 |
% 141.98/84.68 | Instantiating (531) with all_206_0_315, all_206_1_316 yields:
% 141.98/84.68 | (534) relation_rng(empty_set) = all_206_1_316 & relation_dom(empty_set) = all_206_0_315 & ! [v0] : ! [v1] : ( ~ (relation_composition(empty_set, v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_dom(v1) = v5 & relation_dom(v0) = v3 & subset(all_206_1_316, v3) = v4 & relation(v0) = v2 & ( ~ (v4 = 0) | ~ (v2 = 0) | v5 = all_206_0_315))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_composition(empty_set, v0) = v4 & relation_dom(v4) = v5 & subset(all_206_1_316, v1) = v3 & relation(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | v5 = all_206_0_315))) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : (relation_composition(empty_set, v0) = v3 & relation_dom(v3) = v4 & relation_dom(v0) = v1 & subset(all_206_1_316, v1) = v2 & ( ~ (v2 = 0) | v4 = all_206_0_315)))
% 141.98/84.68 |
% 141.98/84.68 | Applying alpha-rule on (534) yields:
% 141.98/84.68 | (535) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : (relation_composition(empty_set, v0) = v3 & relation_dom(v3) = v4 & relation_dom(v0) = v1 & subset(all_206_1_316, v1) = v2 & ( ~ (v2 = 0) | v4 = all_206_0_315)))
% 141.98/84.68 | (536) ! [v0] : ! [v1] : ( ~ (relation_composition(empty_set, v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_dom(v1) = v5 & relation_dom(v0) = v3 & subset(all_206_1_316, v3) = v4 & relation(v0) = v2 & ( ~ (v4 = 0) | ~ (v2 = 0) | v5 = all_206_0_315)))
% 141.98/84.68 | (537) relation_rng(empty_set) = all_206_1_316
% 141.98/84.68 | (538) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_composition(empty_set, v0) = v4 & relation_dom(v4) = v5 & subset(all_206_1_316, v1) = v3 & relation(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | v5 = all_206_0_315)))
% 141.98/84.68 | (539) relation_dom(empty_set) = all_206_0_315
% 141.98/84.68 |
% 141.98/84.68 | Instantiating formula (538) with all_0_11_11, all_0_14_14 and discharging atoms relation_dom(all_0_14_14) = all_0_11_11, yields:
% 141.98/84.68 | (540) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (relation_composition(empty_set, all_0_14_14) = v2 & relation_dom(v2) = v3 & subset(all_206_1_316, all_0_11_11) = v1 & relation(all_0_14_14) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = all_206_0_315))
% 141.98/84.68 |
% 141.98/84.68 | Instantiating formula (538) with empty_set, empty_set and discharging atoms relation_dom(empty_set) = empty_set, yields:
% 141.98/84.68 | (541) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (relation_composition(empty_set, empty_set) = v2 & relation_dom(v2) = v3 & subset(all_206_1_316, empty_set) = v1 & relation(empty_set) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = all_206_0_315))
% 141.98/84.68 |
% 141.98/84.68 | Instantiating formula (535) with all_0_14_14 and discharging atoms relation(all_0_14_14) = 0, yields:
% 141.98/84.68 | (542) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (relation_composition(empty_set, all_0_14_14) = v2 & relation_dom(v2) = v3 & relation_dom(all_0_14_14) = v0 & subset(all_206_1_316, v0) = v1 & ( ~ (v1 = 0) | v3 = all_206_0_315))
% 141.98/84.68 |
% 141.98/84.68 | Instantiating (530) with all_209_0_317, all_209_1_318 yields:
% 141.98/84.68 | (543) relation_rng(empty_set) = all_209_0_317 & relation_dom(empty_set) = all_209_1_318 & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_dom(v0) = v4 & subset(all_209_0_317, v1) = v6 & subset(all_209_1_318, v4) = v5 & subset(empty_set, v0) = v3 & relation(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | (v6 = 0 & v5 = 0)))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_rng(v0) = v5 & subset(all_209_0_317, v5) = v6 & subset(all_209_1_318, v1) = v4 & subset(empty_set, v0) = v3 & relation(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | (v6 = 0 & v4 = 0)))) & ! [v0] : ( ~ (subset(empty_set, v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_rng(v0) = v4 & relation_dom(v0) = v2 & subset(all_209_0_317, v4) = v5 & subset(all_209_1_318, v2) = v3 & relation(v0) = v1 & ( ~ (v1 = 0) | (v5 = 0 & v3 = 0)))) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_rng(v0) = v4 & relation_dom(v0) = v2 & subset(all_209_0_317, v4) = v5 & subset(all_209_1_318, v2) = v3 & subset(empty_set, v0) = v1 & ( ~ (v1 = 0) | (v5 = 0 & v3 = 0))))
% 141.98/84.68 |
% 141.98/84.68 | Applying alpha-rule on (543) yields:
% 141.98/84.68 | (544) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_rng(v0) = v5 & subset(all_209_0_317, v5) = v6 & subset(all_209_1_318, v1) = v4 & subset(empty_set, v0) = v3 & relation(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | (v6 = 0 & v4 = 0))))
% 141.98/84.68 | (545) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_rng(v0) = v4 & relation_dom(v0) = v2 & subset(all_209_0_317, v4) = v5 & subset(all_209_1_318, v2) = v3 & subset(empty_set, v0) = v1 & ( ~ (v1 = 0) | (v5 = 0 & v3 = 0))))
% 141.98/84.68 | (546) ! [v0] : ( ~ (subset(empty_set, v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_rng(v0) = v4 & relation_dom(v0) = v2 & subset(all_209_0_317, v4) = v5 & subset(all_209_1_318, v2) = v3 & relation(v0) = v1 & ( ~ (v1 = 0) | (v5 = 0 & v3 = 0))))
% 141.98/84.68 | (547) relation_dom(empty_set) = all_209_1_318
% 141.98/84.68 | (548) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_dom(v0) = v4 & subset(all_209_0_317, v1) = v6 & subset(all_209_1_318, v4) = v5 & subset(empty_set, v0) = v3 & relation(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | (v6 = 0 & v5 = 0))))
% 141.98/84.68 | (549) relation_rng(empty_set) = all_209_0_317
% 141.98/84.68 |
% 141.98/84.68 | Instantiating formula (548) with empty_set, empty_set and discharging atoms relation_rng(empty_set) = empty_set, yields:
% 141.98/84.68 | (550) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (relation_dom(empty_set) = v2 & subset(all_209_0_317, empty_set) = v4 & subset(all_209_1_318, v2) = v3 & subset(empty_set, empty_set) = v1 & relation(empty_set) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | (v4 = 0 & v3 = 0)))
% 141.98/84.68 |
% 141.98/84.68 | Instantiating formula (544) with all_0_11_11, all_0_14_14 and discharging atoms relation_dom(all_0_14_14) = all_0_11_11, yields:
% 141.98/84.68 | (551) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (relation_rng(all_0_14_14) = v3 & subset(all_209_0_317, v3) = v4 & subset(all_209_1_318, all_0_11_11) = v2 & subset(empty_set, all_0_14_14) = v1 & relation(all_0_14_14) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | (v4 = 0 & v2 = 0)))
% 141.98/84.68 |
% 141.98/84.68 | Instantiating formula (544) with empty_set, empty_set and discharging atoms relation_dom(empty_set) = empty_set, yields:
% 141.98/84.68 | (552) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (relation_rng(empty_set) = v3 & subset(all_209_0_317, v3) = v4 & subset(all_209_1_318, empty_set) = v2 & subset(empty_set, empty_set) = v1 & relation(empty_set) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | (v4 = 0 & v2 = 0)))
% 141.98/84.68 |
% 141.98/84.68 | Instantiating formula (545) with all_0_14_14 and discharging atoms relation(all_0_14_14) = 0, yields:
% 141.98/84.68 | (553) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (relation_rng(all_0_14_14) = v3 & relation_dom(all_0_14_14) = v1 & subset(all_209_0_317, v3) = v4 & subset(all_209_1_318, v1) = v2 & subset(empty_set, all_0_14_14) = v0 & ( ~ (v0 = 0) | (v4 = 0 & v2 = 0)))
% 141.98/84.68 |
% 141.98/84.68 | Instantiating (523) with all_227_0_339, all_227_1_340 yields:
% 141.98/84.68 | (554) relation_rng(all_0_14_14) = all_227_1_340 & relation_dom(all_0_14_14) = all_227_0_339 & ! [v0] : ! [v1] : ( ~ (relation_composition(all_0_14_14, v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_dom(v1) = v5 & relation_dom(v0) = v3 & subset(all_227_1_340, v3) = v4 & relation(v0) = v2 & ( ~ (v4 = 0) | ~ (v2 = 0) | v5 = all_227_0_339))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_composition(all_0_14_14, v0) = v4 & relation_dom(v4) = v5 & subset(all_227_1_340, v1) = v3 & relation(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | v5 = all_227_0_339))) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : (relation_composition(all_0_14_14, v0) = v3 & relation_dom(v3) = v4 & relation_dom(v0) = v1 & subset(all_227_1_340, v1) = v2 & ( ~ (v2 = 0) | v4 = all_227_0_339)))
% 141.98/84.68 |
% 141.98/84.68 | Applying alpha-rule on (554) yields:
% 141.98/84.68 | (555) ! [v0] : ! [v1] : ( ~ (relation_composition(all_0_14_14, v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_dom(v1) = v5 & relation_dom(v0) = v3 & subset(all_227_1_340, v3) = v4 & relation(v0) = v2 & ( ~ (v4 = 0) | ~ (v2 = 0) | v5 = all_227_0_339)))
% 141.98/84.68 | (556) relation_dom(all_0_14_14) = all_227_0_339
% 141.98/84.68 | (557) relation_rng(all_0_14_14) = all_227_1_340
% 141.98/84.68 | (558) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : (relation_composition(all_0_14_14, v0) = v3 & relation_dom(v3) = v4 & relation_dom(v0) = v1 & subset(all_227_1_340, v1) = v2 & ( ~ (v2 = 0) | v4 = all_227_0_339)))
% 141.98/84.68 | (559) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_composition(all_0_14_14, v0) = v4 & relation_dom(v4) = v5 & subset(all_227_1_340, v1) = v3 & relation(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | v5 = all_227_0_339)))
% 141.98/84.68 |
% 141.98/84.68 | Instantiating formula (559) with all_0_11_11, all_0_14_14 and discharging atoms relation_dom(all_0_14_14) = all_0_11_11, yields:
% 141.98/84.68 | (560) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (relation_composition(all_0_14_14, all_0_14_14) = v2 & relation_dom(v2) = v3 & subset(all_227_1_340, all_0_11_11) = v1 & relation(all_0_14_14) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = all_227_0_339))
% 141.98/84.68 |
% 141.98/84.68 | Instantiating formula (559) with empty_set, empty_set and discharging atoms relation_dom(empty_set) = empty_set, yields:
% 141.98/84.68 | (561) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (relation_composition(all_0_14_14, empty_set) = v2 & relation_dom(v2) = v3 & subset(all_227_1_340, empty_set) = v1 & relation(empty_set) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = all_227_0_339))
% 141.98/84.68 |
% 141.98/84.68 | Instantiating formula (558) with all_0_14_14 and discharging atoms relation(all_0_14_14) = 0, yields:
% 141.98/84.68 | (562) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (relation_composition(all_0_14_14, all_0_14_14) = v2 & relation_dom(v2) = v3 & relation_dom(all_0_14_14) = v0 & subset(all_227_1_340, v0) = v1 & ( ~ (v1 = 0) | v3 = all_227_0_339))
% 141.98/84.68 |
% 141.98/84.68 | Instantiating (522) with all_230_0_341, all_230_1_342 yields:
% 141.98/84.68 | (563) relation_rng(all_0_14_14) = all_230_0_341 & relation_dom(all_0_14_14) = all_230_1_342 & ( ~ (all_230_0_341 = empty_set) | all_230_1_342 = empty_set) & ( ~ (all_230_1_342 = empty_set) | all_230_0_341 = empty_set)
% 141.98/84.68 |
% 141.98/84.68 | Applying alpha-rule on (563) yields:
% 141.98/84.68 | (564) relation_rng(all_0_14_14) = all_230_0_341
% 141.98/84.68 | (565) relation_dom(all_0_14_14) = all_230_1_342
% 141.98/84.68 | (566) ~ (all_230_0_341 = empty_set) | all_230_1_342 = empty_set
% 141.98/84.68 | (567) ~ (all_230_1_342 = empty_set) | all_230_0_341 = empty_set
% 141.98/84.68 |
% 141.98/84.68 | Instantiating (524) with all_232_0_343, all_232_1_344 yields:
% 141.98/84.68 | (568) relation_dom(all_0_14_14) = all_232_0_343 & function(all_0_14_14) = all_232_1_344 & ( ~ (all_232_1_344 = 0) | ( ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (apply(all_0_14_14, v0) = v4 & in(v2, all_0_14_14) = v5 & in(v0, all_232_0_343) = v3 & ( ~ (v3 = 0) | (( ~ (v5 = 0) | v4 = v1) & ( ~ (v4 = v1) | v5 = 0))))) & ? [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v1, all_232_0_343) = v2) | ? [v3] : (apply(all_0_14_14, v1) = v3 & ( ~ (v3 = v0) | v0 = empty_set) & ( ~ (v0 = empty_set) | v3 = empty_set))) & ! [v0] : ! [v1] : (v1 = empty_set | ~ (apply(all_0_14_14, v0) = v1) | in(v0, all_232_0_343) = 0)))
% 141.98/84.69 |
% 141.98/84.69 | Applying alpha-rule on (568) yields:
% 141.98/84.69 | (569) relation_dom(all_0_14_14) = all_232_0_343
% 141.98/84.69 | (570) function(all_0_14_14) = all_232_1_344
% 141.98/84.69 | (571) ~ (all_232_1_344 = 0) | ( ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (apply(all_0_14_14, v0) = v4 & in(v2, all_0_14_14) = v5 & in(v0, all_232_0_343) = v3 & ( ~ (v3 = 0) | (( ~ (v5 = 0) | v4 = v1) & ( ~ (v4 = v1) | v5 = 0))))) & ? [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v1, all_232_0_343) = v2) | ? [v3] : (apply(all_0_14_14, v1) = v3 & ( ~ (v3 = v0) | v0 = empty_set) & ( ~ (v0 = empty_set) | v3 = empty_set))) & ! [v0] : ! [v1] : (v1 = empty_set | ~ (apply(all_0_14_14, v0) = v1) | in(v0, all_232_0_343) = 0))
% 141.98/84.69 |
% 141.98/84.69 | Instantiating (529) with all_234_0_345, all_234_1_346 yields:
% 141.98/84.69 | (572) relation_rng(empty_set) = all_234_0_345 & relation_dom(empty_set) = all_234_1_346 & ! [v0] : ! [v1] : ( ~ (relation_composition(v0, empty_set) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_rng(v1) = v5 & relation_rng(v0) = v3 & subset(all_234_1_346, v3) = v4 & relation(v0) = v2 & ( ~ (v4 = 0) | ~ (v2 = 0) | v5 = all_234_0_345))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_composition(v0, empty_set) = v4 & relation_rng(v4) = v5 & subset(all_234_1_346, v1) = v3 & relation(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | v5 = all_234_0_345))) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : (relation_composition(v0, empty_set) = v3 & relation_rng(v3) = v4 & relation_rng(v0) = v1 & subset(all_234_1_346, v1) = v2 & ( ~ (v2 = 0) | v4 = all_234_0_345)))
% 141.98/84.69 |
% 141.98/84.69 | Applying alpha-rule on (572) yields:
% 141.98/84.69 | (573) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : (relation_composition(v0, empty_set) = v3 & relation_rng(v3) = v4 & relation_rng(v0) = v1 & subset(all_234_1_346, v1) = v2 & ( ~ (v2 = 0) | v4 = all_234_0_345)))
% 141.98/84.69 | (574) relation_rng(empty_set) = all_234_0_345
% 141.98/84.69 | (575) ! [v0] : ! [v1] : ( ~ (relation_composition(v0, empty_set) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_rng(v1) = v5 & relation_rng(v0) = v3 & subset(all_234_1_346, v3) = v4 & relation(v0) = v2 & ( ~ (v4 = 0) | ~ (v2 = 0) | v5 = all_234_0_345)))
% 141.98/84.69 | (576) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_composition(v0, empty_set) = v4 & relation_rng(v4) = v5 & subset(all_234_1_346, v1) = v3 & relation(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | v5 = all_234_0_345)))
% 141.98/84.69 | (577) relation_dom(empty_set) = all_234_1_346
% 141.98/84.69 |
% 141.98/84.69 | Instantiating formula (576) with empty_set, empty_set and discharging atoms relation_rng(empty_set) = empty_set, yields:
% 141.98/84.69 | (578) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (relation_composition(empty_set, empty_set) = v2 & relation_rng(v2) = v3 & subset(all_234_1_346, empty_set) = v1 & relation(empty_set) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = all_234_0_345))
% 141.98/84.69 |
% 141.98/84.69 | Instantiating (528) with all_261_0_378, all_261_1_379, all_261_2_380, all_261_3_381, all_261_4_382, all_261_5_383 yields:
% 141.98/84.69 | (579) subset(empty_set, all_0_14_14) = all_261_5_383 & ( ~ (all_261_5_383 = 0) | ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (in(v2, all_0_14_14) = v4 & in(v2, empty_set) = v3 & ( ~ (v3 = 0) | v4 = 0)))) & (all_261_5_383 = 0 | (all_261_1_379 = 0 & ~ (all_261_0_378 = 0) & ordered_pair(all_261_4_382, all_261_3_381) = all_261_2_380 & in(all_261_2_380, all_0_14_14) = all_261_0_378 & in(all_261_2_380, empty_set) = 0))
% 141.98/84.69 |
% 141.98/84.69 | Applying alpha-rule on (579) yields:
% 141.98/84.69 | (580) subset(empty_set, all_0_14_14) = all_261_5_383
% 141.98/84.69 | (581) ~ (all_261_5_383 = 0) | ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (in(v2, all_0_14_14) = v4 & in(v2, empty_set) = v3 & ( ~ (v3 = 0) | v4 = 0)))
% 141.98/84.69 | (582) all_261_5_383 = 0 | (all_261_1_379 = 0 & ~ (all_261_0_378 = 0) & ordered_pair(all_261_4_382, all_261_3_381) = all_261_2_380 & in(all_261_2_380, all_0_14_14) = all_261_0_378 & in(all_261_2_380, empty_set) = 0)
% 141.98/84.69 |
% 141.98/84.69 | Instantiating (514) with all_269_0_391, all_269_1_392 yields:
% 141.98/84.69 | (583) relation_rng(all_0_7_7) = all_269_1_392 & relation_dom(all_0_7_7) = all_269_0_391 & ! [v0] : ! [v1] : ( ~ (relation_composition(all_0_7_7, v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_dom(v1) = v5 & relation_dom(v0) = v3 & subset(all_269_1_392, v3) = v4 & relation(v0) = v2 & ( ~ (v4 = 0) | ~ (v2 = 0) | v5 = all_269_0_391))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_composition(all_0_7_7, v0) = v4 & relation_dom(v4) = v5 & subset(all_269_1_392, v1) = v3 & relation(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | v5 = all_269_0_391))) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : (relation_composition(all_0_7_7, v0) = v3 & relation_dom(v3) = v4 & relation_dom(v0) = v1 & subset(all_269_1_392, v1) = v2 & ( ~ (v2 = 0) | v4 = all_269_0_391)))
% 141.98/84.69 |
% 141.98/84.69 | Applying alpha-rule on (583) yields:
% 141.98/84.69 | (584) relation_dom(all_0_7_7) = all_269_0_391
% 141.98/84.69 | (585) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : (relation_composition(all_0_7_7, v0) = v3 & relation_dom(v3) = v4 & relation_dom(v0) = v1 & subset(all_269_1_392, v1) = v2 & ( ~ (v2 = 0) | v4 = all_269_0_391)))
% 141.98/84.69 | (586) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_composition(all_0_7_7, v0) = v4 & relation_dom(v4) = v5 & subset(all_269_1_392, v1) = v3 & relation(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | v5 = all_269_0_391)))
% 141.98/84.69 | (587) ! [v0] : ! [v1] : ( ~ (relation_composition(all_0_7_7, v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_dom(v1) = v5 & relation_dom(v0) = v3 & subset(all_269_1_392, v3) = v4 & relation(v0) = v2 & ( ~ (v4 = 0) | ~ (v2 = 0) | v5 = all_269_0_391)))
% 141.98/84.69 | (588) relation_rng(all_0_7_7) = all_269_1_392
% 141.98/84.69 |
% 141.98/84.69 | Instantiating formula (586) with all_0_11_11, all_0_14_14 and discharging atoms relation_dom(all_0_14_14) = all_0_11_11, yields:
% 141.98/84.69 | (589) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (relation_composition(all_0_7_7, all_0_14_14) = v2 & relation_dom(v2) = v3 & subset(all_269_1_392, all_0_11_11) = v1 & relation(all_0_14_14) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = all_269_0_391))
% 141.98/84.69 |
% 141.98/84.69 | Instantiating formula (586) with empty_set, empty_set and discharging atoms relation_dom(empty_set) = empty_set, yields:
% 141.98/84.69 | (590) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (relation_composition(all_0_7_7, empty_set) = v2 & relation_dom(v2) = v3 & subset(all_269_1_392, empty_set) = v1 & relation(empty_set) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = all_269_0_391))
% 141.98/84.69 |
% 141.98/84.69 | Instantiating formula (585) with all_0_14_14 and discharging atoms relation(all_0_14_14) = 0, yields:
% 141.98/84.69 | (591) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (relation_composition(all_0_7_7, all_0_14_14) = v2 & relation_dom(v2) = v3 & relation_dom(all_0_14_14) = v0 & subset(all_269_1_392, v0) = v1 & ( ~ (v1 = 0) | v3 = all_269_0_391))
% 141.98/84.69 |
% 141.98/84.69 | Instantiating (507) with all_289_0_412, all_289_1_413, all_289_2_414, all_289_3_415 yields:
% 141.98/84.69 | (592) relation_composition(all_0_4_4, empty_set) = all_289_2_414 & relation_rng(all_289_2_414) = all_289_1_413 & subset(all_289_1_413, empty_set) = all_289_0_412 & relation(empty_set) = all_289_3_415 & ( ~ (all_289_3_415 = 0) | all_289_0_412 = 0)
% 141.98/84.69 |
% 141.98/84.69 | Applying alpha-rule on (592) yields:
% 141.98/84.69 | (593) relation_composition(all_0_4_4, empty_set) = all_289_2_414
% 141.98/84.69 | (594) relation_rng(all_289_2_414) = all_289_1_413
% 141.98/84.69 | (595) ~ (all_289_3_415 = 0) | all_289_0_412 = 0
% 141.98/84.69 | (596) subset(all_289_1_413, empty_set) = all_289_0_412
% 141.98/84.69 | (597) relation(empty_set) = all_289_3_415
% 141.98/84.69 |
% 141.98/84.69 | Instantiating (509) with all_293_0_418, all_293_1_419 yields:
% 141.98/84.69 | (598) relation_rng(all_0_4_4) = all_293_0_418 & relation_dom(all_0_4_4) = all_293_1_419 & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_dom(v0) = v4 & subset(all_293_0_418, v1) = v6 & subset(all_293_1_419, v4) = v5 & subset(all_0_4_4, v0) = v3 & relation(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | (v6 = 0 & v5 = 0)))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_rng(v0) = v5 & subset(all_293_0_418, v5) = v6 & subset(all_293_1_419, v1) = v4 & subset(all_0_4_4, v0) = v3 & relation(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | (v6 = 0 & v4 = 0)))) & ! [v0] : ( ~ (subset(all_0_4_4, v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_rng(v0) = v4 & relation_dom(v0) = v2 & subset(all_293_0_418, v4) = v5 & subset(all_293_1_419, v2) = v3 & relation(v0) = v1 & ( ~ (v1 = 0) | (v5 = 0 & v3 = 0)))) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_rng(v0) = v4 & relation_dom(v0) = v2 & subset(all_293_0_418, v4) = v5 & subset(all_293_1_419, v2) = v3 & subset(all_0_4_4, v0) = v1 & ( ~ (v1 = 0) | (v5 = 0 & v3 = 0))))
% 141.98/84.69 |
% 141.98/84.69 | Applying alpha-rule on (598) yields:
% 141.98/84.69 | (599) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_rng(v0) = v4 & relation_dom(v0) = v2 & subset(all_293_0_418, v4) = v5 & subset(all_293_1_419, v2) = v3 & subset(all_0_4_4, v0) = v1 & ( ~ (v1 = 0) | (v5 = 0 & v3 = 0))))
% 141.98/84.69 | (600) ! [v0] : ( ~ (subset(all_0_4_4, v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_rng(v0) = v4 & relation_dom(v0) = v2 & subset(all_293_0_418, v4) = v5 & subset(all_293_1_419, v2) = v3 & relation(v0) = v1 & ( ~ (v1 = 0) | (v5 = 0 & v3 = 0))))
% 141.98/84.69 | (601) relation_rng(all_0_4_4) = all_293_0_418
% 141.98/84.69 | (602) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_rng(v0) = v5 & subset(all_293_0_418, v5) = v6 & subset(all_293_1_419, v1) = v4 & subset(all_0_4_4, v0) = v3 & relation(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | (v6 = 0 & v4 = 0))))
% 141.98/84.69 | (603) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_dom(v0) = v4 & subset(all_293_0_418, v1) = v6 & subset(all_293_1_419, v4) = v5 & subset(all_0_4_4, v0) = v3 & relation(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | (v6 = 0 & v5 = 0))))
% 141.98/84.69 | (604) relation_dom(all_0_4_4) = all_293_1_419
% 141.98/84.69 |
% 141.98/84.69 | Instantiating formula (603) with empty_set, empty_set and discharging atoms relation_rng(empty_set) = empty_set, yields:
% 141.98/84.69 | (605) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (relation_dom(empty_set) = v2 & subset(all_293_0_418, empty_set) = v4 & subset(all_293_1_419, v2) = v3 & subset(all_0_4_4, empty_set) = v1 & relation(empty_set) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | (v4 = 0 & v3 = 0)))
% 141.98/84.69 |
% 141.98/84.69 | Instantiating formula (602) with all_0_11_11, all_0_14_14 and discharging atoms relation_dom(all_0_14_14) = all_0_11_11, yields:
% 141.98/84.69 | (606) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (relation_rng(all_0_14_14) = v3 & subset(all_293_0_418, v3) = v4 & subset(all_293_1_419, all_0_11_11) = v2 & subset(all_0_4_4, all_0_14_14) = v1 & relation(all_0_14_14) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | (v4 = 0 & v2 = 0)))
% 141.98/84.69 |
% 141.98/84.69 | Instantiating formula (602) with empty_set, empty_set and discharging atoms relation_dom(empty_set) = empty_set, yields:
% 141.98/84.69 | (607) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (relation_rng(empty_set) = v3 & subset(all_293_0_418, v3) = v4 & subset(all_293_1_419, empty_set) = v2 & subset(all_0_4_4, empty_set) = v1 & relation(empty_set) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | (v4 = 0 & v2 = 0)))
% 141.98/84.69 |
% 141.98/84.69 | Instantiating formula (599) with all_0_14_14 and discharging atoms relation(all_0_14_14) = 0, yields:
% 141.98/84.69 | (608) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (relation_rng(all_0_14_14) = v3 & relation_dom(all_0_14_14) = v1 & subset(all_293_0_418, v3) = v4 & subset(all_293_1_419, v1) = v2 & subset(all_0_4_4, all_0_14_14) = v0 & ( ~ (v0 = 0) | (v4 = 0 & v2 = 0)))
% 141.98/84.69 |
% 141.98/84.69 | Instantiating (508) with all_296_0_420, all_296_1_421 yields:
% 141.98/84.69 | (609) relation_rng(all_0_4_4) = all_296_0_420 & relation_dom(all_0_4_4) = all_296_1_421 & ! [v0] : ! [v1] : ( ~ (relation_composition(v0, all_0_4_4) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_rng(v1) = v5 & relation_rng(v0) = v3 & subset(all_296_1_421, v3) = v4 & relation(v0) = v2 & ( ~ (v4 = 0) | ~ (v2 = 0) | v5 = all_296_0_420))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_composition(v0, all_0_4_4) = v4 & relation_rng(v4) = v5 & subset(all_296_1_421, v1) = v3 & relation(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | v5 = all_296_0_420))) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : (relation_composition(v0, all_0_4_4) = v3 & relation_rng(v3) = v4 & relation_rng(v0) = v1 & subset(all_296_1_421, v1) = v2 & ( ~ (v2 = 0) | v4 = all_296_0_420)))
% 141.98/84.69 |
% 141.98/84.69 | Applying alpha-rule on (609) yields:
% 141.98/84.69 | (610) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : (relation_composition(v0, all_0_4_4) = v3 & relation_rng(v3) = v4 & relation_rng(v0) = v1 & subset(all_296_1_421, v1) = v2 & ( ~ (v2 = 0) | v4 = all_296_0_420)))
% 141.98/84.69 | (611) relation_rng(all_0_4_4) = all_296_0_420
% 141.98/84.70 | (612) relation_dom(all_0_4_4) = all_296_1_421
% 141.98/84.70 | (613) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_composition(v0, all_0_4_4) = v4 & relation_rng(v4) = v5 & subset(all_296_1_421, v1) = v3 & relation(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | v5 = all_296_0_420)))
% 141.98/84.70 | (614) ! [v0] : ! [v1] : ( ~ (relation_composition(v0, all_0_4_4) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_rng(v1) = v5 & relation_rng(v0) = v3 & subset(all_296_1_421, v3) = v4 & relation(v0) = v2 & ( ~ (v4 = 0) | ~ (v2 = 0) | v5 = all_296_0_420)))
% 142.16/84.70 |
% 142.16/84.70 | Instantiating formula (613) with empty_set, empty_set and discharging atoms relation_rng(empty_set) = empty_set, yields:
% 142.16/84.70 | (615) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (relation_composition(empty_set, all_0_4_4) = v2 & relation_rng(v2) = v3 & subset(all_296_1_421, empty_set) = v1 & relation(empty_set) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = all_296_0_420))
% 142.16/84.70 |
% 142.16/84.70 | Instantiating (510) with all_301_0_424, all_301_1_425 yields:
% 142.16/84.70 | (616) relation_rng(all_0_4_4) = all_301_1_425 & relation_dom(all_0_4_4) = all_301_0_424 & ! [v0] : ! [v1] : ( ~ (relation_composition(all_0_4_4, v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_dom(v1) = v5 & relation_dom(v0) = v3 & subset(all_301_1_425, v3) = v4 & relation(v0) = v2 & ( ~ (v4 = 0) | ~ (v2 = 0) | v5 = all_301_0_424))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_composition(all_0_4_4, v0) = v4 & relation_dom(v4) = v5 & subset(all_301_1_425, v1) = v3 & relation(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | v5 = all_301_0_424))) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : (relation_composition(all_0_4_4, v0) = v3 & relation_dom(v3) = v4 & relation_dom(v0) = v1 & subset(all_301_1_425, v1) = v2 & ( ~ (v2 = 0) | v4 = all_301_0_424)))
% 142.16/84.70 |
% 142.16/84.70 | Applying alpha-rule on (616) yields:
% 142.16/84.70 | (617) relation_rng(all_0_4_4) = all_301_1_425
% 142.16/84.70 | (618) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_composition(all_0_4_4, v0) = v4 & relation_dom(v4) = v5 & subset(all_301_1_425, v1) = v3 & relation(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | v5 = all_301_0_424)))
% 142.16/84.70 | (619) relation_dom(all_0_4_4) = all_301_0_424
% 142.16/84.70 | (620) ! [v0] : ! [v1] : ( ~ (relation_composition(all_0_4_4, v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_dom(v1) = v5 & relation_dom(v0) = v3 & subset(all_301_1_425, v3) = v4 & relation(v0) = v2 & ( ~ (v4 = 0) | ~ (v2 = 0) | v5 = all_301_0_424)))
% 142.16/84.70 | (621) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : (relation_composition(all_0_4_4, v0) = v3 & relation_dom(v3) = v4 & relation_dom(v0) = v1 & subset(all_301_1_425, v1) = v2 & ( ~ (v2 = 0) | v4 = all_301_0_424)))
% 142.16/84.70 |
% 142.16/84.70 | Instantiating formula (618) with all_0_11_11, all_0_14_14 and discharging atoms relation_dom(all_0_14_14) = all_0_11_11, yields:
% 142.16/84.70 | (622) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (relation_composition(all_0_4_4, all_0_14_14) = v2 & relation_dom(v2) = v3 & subset(all_301_1_425, all_0_11_11) = v1 & relation(all_0_14_14) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = all_301_0_424))
% 142.16/84.70 |
% 142.16/84.70 | Instantiating formula (618) with empty_set, empty_set and discharging atoms relation_dom(empty_set) = empty_set, yields:
% 142.16/84.70 | (623) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (relation_composition(all_0_4_4, empty_set) = v2 & relation_dom(v2) = v3 & subset(all_301_1_425, empty_set) = v1 & relation(empty_set) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = all_301_0_424))
% 142.16/84.70 |
% 142.16/84.70 | Instantiating formula (621) with all_0_14_14 and discharging atoms relation(all_0_14_14) = 0, yields:
% 142.16/84.70 | (624) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (relation_composition(all_0_4_4, all_0_14_14) = v2 & relation_dom(v2) = v3 & relation_dom(all_0_14_14) = v0 & subset(all_301_1_425, v0) = v1 & ( ~ (v1 = 0) | v3 = all_301_0_424))
% 142.16/84.70 |
% 142.16/84.70 | Instantiating (513) with all_348_0_474, all_348_1_475 yields:
% 142.16/84.70 | (625) relation_rng(all_0_7_7) = all_348_0_474 & relation_dom(all_0_7_7) = all_348_1_475 & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_dom(v0) = v4 & subset(all_348_0_474, v1) = v6 & subset(all_348_1_475, v4) = v5 & subset(all_0_7_7, v0) = v3 & relation(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | (v6 = 0 & v5 = 0)))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_rng(v0) = v5 & subset(all_348_0_474, v5) = v6 & subset(all_348_1_475, v1) = v4 & subset(all_0_7_7, v0) = v3 & relation(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | (v6 = 0 & v4 = 0)))) & ! [v0] : ( ~ (subset(all_0_7_7, v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_rng(v0) = v4 & relation_dom(v0) = v2 & subset(all_348_0_474, v4) = v5 & subset(all_348_1_475, v2) = v3 & relation(v0) = v1 & ( ~ (v1 = 0) | (v5 = 0 & v3 = 0)))) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_rng(v0) = v4 & relation_dom(v0) = v2 & subset(all_348_0_474, v4) = v5 & subset(all_348_1_475, v2) = v3 & subset(all_0_7_7, v0) = v1 & ( ~ (v1 = 0) | (v5 = 0 & v3 = 0))))
% 142.16/84.70 |
% 142.16/84.70 | Applying alpha-rule on (625) yields:
% 142.16/84.70 | (626) relation_rng(all_0_7_7) = all_348_0_474
% 142.16/84.70 | (627) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_rng(v0) = v5 & subset(all_348_0_474, v5) = v6 & subset(all_348_1_475, v1) = v4 & subset(all_0_7_7, v0) = v3 & relation(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | (v6 = 0 & v4 = 0))))
% 142.16/84.70 | (628) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_rng(v0) = v4 & relation_dom(v0) = v2 & subset(all_348_0_474, v4) = v5 & subset(all_348_1_475, v2) = v3 & subset(all_0_7_7, v0) = v1 & ( ~ (v1 = 0) | (v5 = 0 & v3 = 0))))
% 142.16/84.70 | (629) ! [v0] : ( ~ (subset(all_0_7_7, v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_rng(v0) = v4 & relation_dom(v0) = v2 & subset(all_348_0_474, v4) = v5 & subset(all_348_1_475, v2) = v3 & relation(v0) = v1 & ( ~ (v1 = 0) | (v5 = 0 & v3 = 0))))
% 142.16/84.70 | (630) relation_dom(all_0_7_7) = all_348_1_475
% 142.16/84.70 | (631) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_dom(v0) = v4 & subset(all_348_0_474, v1) = v6 & subset(all_348_1_475, v4) = v5 & subset(all_0_7_7, v0) = v3 & relation(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | (v6 = 0 & v5 = 0))))
% 142.16/84.70 |
% 142.16/84.70 | Instantiating formula (631) with empty_set, empty_set and discharging atoms relation_rng(empty_set) = empty_set, yields:
% 142.16/84.70 | (632) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (relation_dom(empty_set) = v2 & subset(all_348_0_474, empty_set) = v4 & subset(all_348_1_475, v2) = v3 & subset(all_0_7_7, empty_set) = v1 & relation(empty_set) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | (v4 = 0 & v3 = 0)))
% 142.16/84.70 |
% 142.16/84.70 | Instantiating formula (627) with all_0_11_11, all_0_14_14 and discharging atoms relation_dom(all_0_14_14) = all_0_11_11, yields:
% 142.16/84.70 | (633) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (relation_rng(all_0_14_14) = v3 & subset(all_348_0_474, v3) = v4 & subset(all_348_1_475, all_0_11_11) = v2 & subset(all_0_7_7, all_0_14_14) = v1 & relation(all_0_14_14) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | (v4 = 0 & v2 = 0)))
% 142.16/84.70 |
% 142.16/84.70 | Instantiating formula (627) with empty_set, empty_set and discharging atoms relation_dom(empty_set) = empty_set, yields:
% 142.16/84.70 | (634) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (relation_rng(empty_set) = v3 & subset(all_348_0_474, v3) = v4 & subset(all_348_1_475, empty_set) = v2 & subset(all_0_7_7, empty_set) = v1 & relation(empty_set) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | (v4 = 0 & v2 = 0)))
% 142.16/84.70 |
% 142.16/84.70 | Instantiating formula (628) with all_0_14_14 and discharging atoms relation(all_0_14_14) = 0, yields:
% 142.16/84.70 | (635) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (relation_rng(all_0_14_14) = v3 & relation_dom(all_0_14_14) = v1 & subset(all_348_0_474, v3) = v4 & subset(all_348_1_475, v1) = v2 & subset(all_0_7_7, all_0_14_14) = v0 & ( ~ (v0 = 0) | (v4 = 0 & v2 = 0)))
% 142.16/84.70 |
% 142.16/84.70 | Instantiating (512) with all_355_0_481, all_355_1_482 yields:
% 142.16/84.70 | (636) relation_rng(all_0_7_7) = all_355_0_481 & relation_dom(all_0_7_7) = all_355_1_482 & ! [v0] : ! [v1] : ( ~ (relation_composition(v0, all_0_7_7) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_rng(v1) = v5 & relation_rng(v0) = v3 & subset(all_355_1_482, v3) = v4 & relation(v0) = v2 & ( ~ (v4 = 0) | ~ (v2 = 0) | v5 = all_355_0_481))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_composition(v0, all_0_7_7) = v4 & relation_rng(v4) = v5 & subset(all_355_1_482, v1) = v3 & relation(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | v5 = all_355_0_481))) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : (relation_composition(v0, all_0_7_7) = v3 & relation_rng(v3) = v4 & relation_rng(v0) = v1 & subset(all_355_1_482, v1) = v2 & ( ~ (v2 = 0) | v4 = all_355_0_481)))
% 142.16/84.70 |
% 142.16/84.70 | Applying alpha-rule on (636) yields:
% 142.16/84.70 | (637) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_composition(v0, all_0_7_7) = v4 & relation_rng(v4) = v5 & subset(all_355_1_482, v1) = v3 & relation(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | v5 = all_355_0_481)))
% 142.16/84.70 | (638) ! [v0] : ! [v1] : ( ~ (relation_composition(v0, all_0_7_7) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_rng(v1) = v5 & relation_rng(v0) = v3 & subset(all_355_1_482, v3) = v4 & relation(v0) = v2 & ( ~ (v4 = 0) | ~ (v2 = 0) | v5 = all_355_0_481)))
% 142.16/84.70 | (639) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : (relation_composition(v0, all_0_7_7) = v3 & relation_rng(v3) = v4 & relation_rng(v0) = v1 & subset(all_355_1_482, v1) = v2 & ( ~ (v2 = 0) | v4 = all_355_0_481)))
% 142.16/84.70 | (640) relation_rng(all_0_7_7) = all_355_0_481
% 142.16/84.70 | (641) relation_dom(all_0_7_7) = all_355_1_482
% 142.16/84.70 |
% 142.16/84.70 | Instantiating formula (637) with empty_set, empty_set and discharging atoms relation_rng(empty_set) = empty_set, yields:
% 142.16/84.70 | (642) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (relation_composition(empty_set, all_0_7_7) = v2 & relation_rng(v2) = v3 & subset(all_355_1_482, empty_set) = v1 & relation(empty_set) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = all_355_0_481))
% 142.16/84.70 |
% 142.16/84.70 | Instantiating (521) with all_358_0_483, all_358_1_484 yields:
% 142.16/84.70 | (643) relation_rng(all_0_14_14) = all_358_0_483 & relation_dom(all_0_14_14) = all_358_1_484 & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_dom(v0) = v4 & subset(all_358_0_483, v1) = v6 & subset(all_358_1_484, v4) = v5 & subset(all_0_14_14, v0) = v3 & relation(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | (v6 = 0 & v5 = 0)))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_rng(v0) = v5 & subset(all_358_0_483, v5) = v6 & subset(all_358_1_484, v1) = v4 & subset(all_0_14_14, v0) = v3 & relation(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | (v6 = 0 & v4 = 0)))) & ! [v0] : ( ~ (subset(all_0_14_14, v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_rng(v0) = v4 & relation_dom(v0) = v2 & subset(all_358_0_483, v4) = v5 & subset(all_358_1_484, v2) = v3 & relation(v0) = v1 & ( ~ (v1 = 0) | (v5 = 0 & v3 = 0)))) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_rng(v0) = v4 & relation_dom(v0) = v2 & subset(all_358_0_483, v4) = v5 & subset(all_358_1_484, v2) = v3 & subset(all_0_14_14, v0) = v1 & ( ~ (v1 = 0) | (v5 = 0 & v3 = 0))))
% 142.16/84.70 |
% 142.16/84.70 | Applying alpha-rule on (643) yields:
% 142.16/84.70 | (644) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_rng(v0) = v4 & relation_dom(v0) = v2 & subset(all_358_0_483, v4) = v5 & subset(all_358_1_484, v2) = v3 & subset(all_0_14_14, v0) = v1 & ( ~ (v1 = 0) | (v5 = 0 & v3 = 0))))
% 142.16/84.70 | (645) ! [v0] : ( ~ (subset(all_0_14_14, v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_rng(v0) = v4 & relation_dom(v0) = v2 & subset(all_358_0_483, v4) = v5 & subset(all_358_1_484, v2) = v3 & relation(v0) = v1 & ( ~ (v1 = 0) | (v5 = 0 & v3 = 0))))
% 142.16/84.70 | (646) relation_dom(all_0_14_14) = all_358_1_484
% 142.16/84.70 | (647) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_dom(v0) = v4 & subset(all_358_0_483, v1) = v6 & subset(all_358_1_484, v4) = v5 & subset(all_0_14_14, v0) = v3 & relation(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | (v6 = 0 & v5 = 0))))
% 142.16/84.70 | (648) relation_rng(all_0_14_14) = all_358_0_483
% 142.16/84.70 | (649) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_rng(v0) = v5 & subset(all_358_0_483, v5) = v6 & subset(all_358_1_484, v1) = v4 & subset(all_0_14_14, v0) = v3 & relation(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | (v6 = 0 & v4 = 0))))
% 142.16/84.70 |
% 142.16/84.70 | Instantiating formula (647) with empty_set, empty_set and discharging atoms relation_rng(empty_set) = empty_set, yields:
% 142.16/84.70 | (650) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (relation_dom(empty_set) = v2 & subset(all_358_0_483, empty_set) = v4 & subset(all_358_1_484, v2) = v3 & subset(all_0_14_14, empty_set) = v1 & relation(empty_set) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | (v4 = 0 & v3 = 0)))
% 142.16/84.71 |
% 142.16/84.71 | Instantiating formula (649) with all_0_11_11, all_0_14_14 and discharging atoms relation_dom(all_0_14_14) = all_0_11_11, yields:
% 142.16/84.71 | (651) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (relation_rng(all_0_14_14) = v3 & subset(all_358_0_483, v3) = v4 & subset(all_358_1_484, all_0_11_11) = v2 & subset(all_0_14_14, all_0_14_14) = v1 & relation(all_0_14_14) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | (v4 = 0 & v2 = 0)))
% 142.16/84.71 |
% 142.16/84.71 | Instantiating formula (649) with empty_set, empty_set and discharging atoms relation_dom(empty_set) = empty_set, yields:
% 142.16/84.71 | (652) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (relation_rng(empty_set) = v3 & subset(all_358_0_483, v3) = v4 & subset(all_358_1_484, empty_set) = v2 & subset(all_0_14_14, empty_set) = v1 & relation(empty_set) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | (v4 = 0 & v2 = 0)))
% 142.16/84.71 |
% 142.16/84.71 | Instantiating formula (644) with all_0_14_14 and discharging atoms relation(all_0_14_14) = 0, yields:
% 142.16/84.71 | (653) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (relation_rng(all_0_14_14) = v3 & relation_dom(all_0_14_14) = v1 & subset(all_358_0_483, v3) = v4 & subset(all_358_1_484, v1) = v2 & subset(all_0_14_14, all_0_14_14) = v0 & ( ~ (v0 = 0) | (v4 = 0 & v2 = 0)))
% 142.16/84.71 |
% 142.16/84.71 | Instantiating (520) with all_361_0_485, all_361_1_486 yields:
% 142.16/84.71 | (654) relation_rng(all_0_14_14) = all_361_0_485 & relation_dom(all_0_14_14) = all_361_1_486 & ! [v0] : ! [v1] : ( ~ (relation_composition(v0, all_0_14_14) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_rng(v1) = v5 & relation_rng(v0) = v3 & subset(all_361_1_486, v3) = v4 & relation(v0) = v2 & ( ~ (v4 = 0) | ~ (v2 = 0) | v5 = all_361_0_485))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_composition(v0, all_0_14_14) = v4 & relation_rng(v4) = v5 & subset(all_361_1_486, v1) = v3 & relation(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | v5 = all_361_0_485))) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : (relation_composition(v0, all_0_14_14) = v3 & relation_rng(v3) = v4 & relation_rng(v0) = v1 & subset(all_361_1_486, v1) = v2 & ( ~ (v2 = 0) | v4 = all_361_0_485)))
% 142.16/84.71 |
% 142.16/84.71 | Applying alpha-rule on (654) yields:
% 142.16/84.71 | (655) relation_rng(all_0_14_14) = all_361_0_485
% 142.16/84.71 | (656) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : (relation_composition(v0, all_0_14_14) = v3 & relation_rng(v3) = v4 & relation_rng(v0) = v1 & subset(all_361_1_486, v1) = v2 & ( ~ (v2 = 0) | v4 = all_361_0_485)))
% 142.16/84.71 | (657) ! [v0] : ! [v1] : ( ~ (relation_composition(v0, all_0_14_14) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_rng(v1) = v5 & relation_rng(v0) = v3 & subset(all_361_1_486, v3) = v4 & relation(v0) = v2 & ( ~ (v4 = 0) | ~ (v2 = 0) | v5 = all_361_0_485)))
% 142.16/84.71 | (658) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_composition(v0, all_0_14_14) = v4 & relation_rng(v4) = v5 & subset(all_361_1_486, v1) = v3 & relation(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | v5 = all_361_0_485)))
% 142.16/84.71 | (659) relation_dom(all_0_14_14) = all_361_1_486
% 142.16/84.71 |
% 142.16/84.71 | Instantiating formula (658) with empty_set, empty_set and discharging atoms relation_rng(empty_set) = empty_set, yields:
% 142.16/84.71 | (660) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (relation_composition(empty_set, all_0_14_14) = v2 & relation_rng(v2) = v3 & subset(all_361_1_486, empty_set) = v1 & relation(empty_set) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = all_361_0_485))
% 142.16/84.71 |
% 142.16/84.71 | Instantiating (503) with all_393_0_530, all_393_1_531, all_393_2_532, all_393_3_533 yields:
% 142.16/84.71 | (661) relation_composition(all_0_0_0, empty_set) = all_393_2_532 & relation_rng(all_393_2_532) = all_393_1_531 & subset(all_393_1_531, empty_set) = all_393_0_530 & relation(empty_set) = all_393_3_533 & ( ~ (all_393_3_533 = 0) | all_393_0_530 = 0)
% 142.16/84.71 |
% 142.16/84.71 | Applying alpha-rule on (661) yields:
% 142.16/84.71 | (662) relation_composition(all_0_0_0, empty_set) = all_393_2_532
% 142.16/84.71 | (663) subset(all_393_1_531, empty_set) = all_393_0_530
% 142.16/84.71 | (664) relation_rng(all_393_2_532) = all_393_1_531
% 142.16/84.71 | (665) relation(empty_set) = all_393_3_533
% 142.16/84.71 | (666) ~ (all_393_3_533 = 0) | all_393_0_530 = 0
% 142.16/84.71 |
% 142.16/84.71 | Instantiating (502) with all_497_0_627, all_497_1_628, all_497_2_629 yields:
% 142.16/84.71 | (667) (apply(all_0_14_14, all_0_16_16) = all_497_1_628 & in(all_0_13_13, all_0_14_14) = all_497_0_627 & in(all_0_16_16, all_0_11_11) = all_497_2_629 & ( ~ (all_497_2_629 = 0) | (( ~ (all_497_0_627 = 0) | all_497_1_628 = all_0_15_15) & ( ~ (all_497_1_628 = all_0_15_15) | all_497_0_627 = 0)))) | (relation(all_0_14_14) = all_497_2_629 & function(all_0_14_14) = all_497_1_628 & ( ~ (all_497_1_628 = 0) | ~ (all_497_2_629 = 0)))
% 142.16/84.71 |
% 142.16/84.71 | Instantiating (532) with all_554_0_701, all_554_1_702 yields:
% 142.16/84.71 | (668) relation_dom(all_0_14_14) = all_554_0_701 & relation(all_0_14_14) = all_554_1_702 & ( ~ (all_554_1_702 = 0) | ( ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (apply(all_0_14_14, v0) = v4 & in(v2, all_0_14_14) = v5 & in(v0, all_554_0_701) = v3 & ( ~ (v3 = 0) | (( ~ (v5 = 0) | v4 = v1) & ( ~ (v4 = v1) | v5 = 0))))) & ? [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v1, all_554_0_701) = v2) | ? [v3] : (apply(all_0_14_14, v1) = v3 & ( ~ (v3 = v0) | v0 = empty_set) & ( ~ (v0 = empty_set) | v3 = empty_set))) & ! [v0] : ! [v1] : (v1 = empty_set | ~ (apply(all_0_14_14, v0) = v1) | in(v0, all_554_0_701) = 0)))
% 142.16/84.71 |
% 142.16/84.71 | Applying alpha-rule on (668) yields:
% 142.16/84.71 | (669) relation_dom(all_0_14_14) = all_554_0_701
% 142.16/84.71 | (670) relation(all_0_14_14) = all_554_1_702
% 142.16/84.71 | (671) ~ (all_554_1_702 = 0) | ( ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (apply(all_0_14_14, v0) = v4 & in(v2, all_0_14_14) = v5 & in(v0, all_554_0_701) = v3 & ( ~ (v3 = 0) | (( ~ (v5 = 0) | v4 = v1) & ( ~ (v4 = v1) | v5 = 0))))) & ? [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v1, all_554_0_701) = v2) | ? [v3] : (apply(all_0_14_14, v1) = v3 & ( ~ (v3 = v0) | v0 = empty_set) & ( ~ (v0 = empty_set) | v3 = empty_set))) & ! [v0] : ! [v1] : (v1 = empty_set | ~ (apply(all_0_14_14, v0) = v1) | in(v0, all_554_0_701) = 0))
% 142.16/84.71 |
% 142.16/84.71 | Instantiating (527) with all_582_0_727, all_582_1_728, all_582_2_729, all_582_3_730 yields:
% 142.16/84.71 | (672) relation_composition(empty_set, empty_set) = all_582_2_729 & relation_rng(all_582_2_729) = all_582_1_728 & subset(all_582_1_728, empty_set) = all_582_0_727 & relation(empty_set) = all_582_3_730 & ( ~ (all_582_3_730 = 0) | all_582_0_727 = 0)
% 142.16/84.71 |
% 142.16/84.71 | Applying alpha-rule on (672) yields:
% 142.16/84.71 | (673) relation_composition(empty_set, empty_set) = all_582_2_729
% 142.16/84.71 | (674) relation(empty_set) = all_582_3_730
% 142.16/84.71 | (675) relation_rng(all_582_2_729) = all_582_1_728
% 142.16/84.71 | (676) ~ (all_582_3_730 = 0) | all_582_0_727 = 0
% 142.16/84.71 | (677) subset(all_582_1_728, empty_set) = all_582_0_727
% 142.16/84.71 |
% 142.16/84.71 | Instantiating (481) with all_662_0_839, all_662_1_840, all_662_2_841, all_662_3_842 yields:
% 142.16/84.71 | (678) relation_dom(empty_set) = all_662_2_841 & cartesian_product2(all_662_2_841, empty_set) = all_662_1_840 & subset(empty_set, all_662_1_840) = all_662_0_839 & relation(empty_set) = all_662_3_842 & ( ~ (all_662_3_842 = 0) | all_662_0_839 = 0)
% 142.16/84.71 |
% 142.16/84.71 | Applying alpha-rule on (678) yields:
% 142.16/84.71 | (679) cartesian_product2(all_662_2_841, empty_set) = all_662_1_840
% 142.16/84.71 | (680) ~ (all_662_3_842 = 0) | all_662_0_839 = 0
% 142.16/84.71 | (681) relation(empty_set) = all_662_3_842
% 142.16/84.71 | (682) relation_dom(empty_set) = all_662_2_841
% 142.16/84.71 | (683) subset(empty_set, all_662_1_840) = all_662_0_839
% 142.16/84.71 |
% 142.16/84.71 | Instantiating (479) with all_664_0_843, all_664_1_844, all_664_2_845, all_664_3_846, all_664_4_847 yields:
% 142.16/84.71 | (684) relation_inverse(empty_set) = all_664_3_846 & relation_rng(all_664_3_846) = all_664_0_843 & relation_dom(all_664_3_846) = all_664_2_845 & relation_dom(empty_set) = all_664_1_844 & relation(empty_set) = all_664_4_847 & ( ~ (all_664_4_847 = 0) | (all_664_0_843 = all_664_1_844 & all_664_2_845 = empty_set))
% 142.16/84.71 |
% 142.16/84.71 | Applying alpha-rule on (684) yields:
% 142.16/84.71 | (685) ~ (all_664_4_847 = 0) | (all_664_0_843 = all_664_1_844 & all_664_2_845 = empty_set)
% 142.16/84.71 | (686) relation_dom(empty_set) = all_664_1_844
% 142.16/84.71 | (687) relation_dom(all_664_3_846) = all_664_2_845
% 142.16/84.71 | (688) relation_inverse(empty_set) = all_664_3_846
% 142.16/84.71 | (689) relation_rng(all_664_3_846) = all_664_0_843
% 142.16/84.71 | (690) relation(empty_set) = all_664_4_847
% 142.16/84.71 |
% 142.16/84.71 | Instantiating (485) with all_668_0_850, all_668_1_851 yields:
% 142.16/84.71 | (691) relation_dom(empty_set) = all_668_0_850 & relation(empty_set) = all_668_1_851 & ( ~ (all_668_1_851 = 0) | ( ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_dom(v0) = v4 & subset(all_668_0_850, v4) = v5 & subset(empty_set, v1) = v6 & subset(empty_set, v0) = v3 & relation(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | (v6 = 0 & v5 = 0)))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_rng(v0) = v5 & subset(all_668_0_850, v1) = v4 & subset(empty_set, v5) = v6 & subset(empty_set, v0) = v3 & relation(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | (v6 = 0 & v4 = 0)))) & ! [v0] : ( ~ (subset(empty_set, v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_rng(v0) = v4 & relation_dom(v0) = v2 & subset(all_668_0_850, v2) = v3 & subset(empty_set, v4) = v5 & relation(v0) = v1 & ( ~ (v1 = 0) | (v5 = 0 & v3 = 0)))) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_rng(v0) = v4 & relation_dom(v0) = v2 & subset(all_668_0_850, v2) = v3 & subset(empty_set, v4) = v5 & subset(empty_set, v0) = v1 & ( ~ (v1 = 0) | (v5 = 0 & v3 = 0))))))
% 142.16/84.71 |
% 142.16/84.71 | Applying alpha-rule on (691) yields:
% 142.16/84.71 | (692) relation_dom(empty_set) = all_668_0_850
% 142.16/84.71 | (693) relation(empty_set) = all_668_1_851
% 142.16/84.71 | (694) ~ (all_668_1_851 = 0) | ( ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_dom(v0) = v4 & subset(all_668_0_850, v4) = v5 & subset(empty_set, v1) = v6 & subset(empty_set, v0) = v3 & relation(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | (v6 = 0 & v5 = 0)))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_rng(v0) = v5 & subset(all_668_0_850, v1) = v4 & subset(empty_set, v5) = v6 & subset(empty_set, v0) = v3 & relation(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | (v6 = 0 & v4 = 0)))) & ! [v0] : ( ~ (subset(empty_set, v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_rng(v0) = v4 & relation_dom(v0) = v2 & subset(all_668_0_850, v2) = v3 & subset(empty_set, v4) = v5 & relation(v0) = v1 & ( ~ (v1 = 0) | (v5 = 0 & v3 = 0)))) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_rng(v0) = v4 & relation_dom(v0) = v2 & subset(all_668_0_850, v2) = v3 & subset(empty_set, v4) = v5 & subset(empty_set, v0) = v1 & ( ~ (v1 = 0) | (v5 = 0 & v3 = 0)))))
% 142.16/84.71 |
% 142.16/84.71 | Instantiating (484) with all_670_0_852, all_670_1_853 yields:
% 142.16/84.71 | (695) relation_dom(empty_set) = all_670_0_852 & relation(empty_set) = all_670_1_853 & ( ~ (all_670_1_853 = 0) | ( ! [v0] : ! [v1] : ( ~ (relation_composition(empty_set, v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_dom(v1) = v5 & relation_dom(v0) = v3 & subset(empty_set, v3) = v4 & relation(v0) = v2 & ( ~ (v4 = 0) | ~ (v2 = 0) | v5 = all_670_0_852))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_composition(empty_set, v0) = v4 & relation_dom(v4) = v5 & subset(empty_set, v1) = v3 & relation(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | v5 = all_670_0_852))) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : (relation_composition(empty_set, v0) = v3 & relation_dom(v3) = v4 & relation_dom(v0) = v1 & subset(empty_set, v1) = v2 & ( ~ (v2 = 0) | v4 = all_670_0_852)))))
% 142.16/84.71 |
% 142.16/84.71 | Applying alpha-rule on (695) yields:
% 142.16/84.71 | (696) relation_dom(empty_set) = all_670_0_852
% 142.16/84.71 | (697) relation(empty_set) = all_670_1_853
% 142.16/84.71 | (698) ~ (all_670_1_853 = 0) | ( ! [v0] : ! [v1] : ( ~ (relation_composition(empty_set, v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_dom(v1) = v5 & relation_dom(v0) = v3 & subset(empty_set, v3) = v4 & relation(v0) = v2 & ( ~ (v4 = 0) | ~ (v2 = 0) | v5 = all_670_0_852))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_composition(empty_set, v0) = v4 & relation_dom(v4) = v5 & subset(empty_set, v1) = v3 & relation(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | v5 = all_670_0_852))) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : (relation_composition(empty_set, v0) = v3 & relation_dom(v3) = v4 & relation_dom(v0) = v1 & subset(empty_set, v1) = v2 & ( ~ (v2 = 0) | v4 = all_670_0_852))))
% 142.16/84.71 |
% 142.16/84.71 | Instantiating (483) with all_724_0_920, all_724_1_921 yields:
% 142.16/84.71 | (699) relation_dom(empty_set) = all_724_0_920 & relation(empty_set) = all_724_1_921 & ( ~ (all_724_1_921 = 0) | ( ! [v0] : ! [v1] : ( ~ (relation_composition(v0, empty_set) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_rng(v1) = v5 & relation_rng(v0) = v3 & subset(all_724_0_920, v3) = v4 & relation(v0) = v2 & ( ~ (v4 = 0) | ~ (v2 = 0) | v5 = empty_set))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_composition(v0, empty_set) = v4 & relation_rng(v4) = v5 & subset(all_724_0_920, v1) = v3 & relation(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | v5 = empty_set))) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : (relation_composition(v0, empty_set) = v3 & relation_rng(v3) = v4 & relation_rng(v0) = v1 & subset(all_724_0_920, v1) = v2 & ( ~ (v2 = 0) | v4 = empty_set)))))
% 142.16/84.72 |
% 142.16/84.72 | Applying alpha-rule on (699) yields:
% 142.16/84.72 | (700) relation_dom(empty_set) = all_724_0_920
% 142.16/84.72 | (701) relation(empty_set) = all_724_1_921
% 142.16/84.72 | (702) ~ (all_724_1_921 = 0) | ( ! [v0] : ! [v1] : ( ~ (relation_composition(v0, empty_set) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_rng(v1) = v5 & relation_rng(v0) = v3 & subset(all_724_0_920, v3) = v4 & relation(v0) = v2 & ( ~ (v4 = 0) | ~ (v2 = 0) | v5 = empty_set))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_composition(v0, empty_set) = v4 & relation_rng(v4) = v5 & subset(all_724_0_920, v1) = v3 & relation(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | v5 = empty_set))) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : (relation_composition(v0, empty_set) = v3 & relation_rng(v3) = v4 & relation_rng(v0) = v1 & subset(all_724_0_920, v1) = v2 & ( ~ (v2 = 0) | v4 = empty_set))))
% 142.16/84.72 |
% 142.16/84.72 | Instantiating (482) with all_738_0_937, all_738_1_938, all_738_2_939 yields:
% 142.16/84.72 | (703) relation_dom(empty_set) = all_738_1_938 & relation_image(empty_set, all_738_1_938) = all_738_0_937 & relation(empty_set) = all_738_2_939 & ( ~ (all_738_2_939 = 0) | all_738_0_937 = empty_set)
% 142.16/84.72 |
% 142.16/84.72 | Applying alpha-rule on (703) yields:
% 142.16/84.72 | (704) relation_dom(empty_set) = all_738_1_938
% 142.16/84.72 | (705) relation_image(empty_set, all_738_1_938) = all_738_0_937
% 142.16/84.72 | (706) relation(empty_set) = all_738_2_939
% 142.16/84.72 | (707) ~ (all_738_2_939 = 0) | all_738_0_937 = empty_set
% 142.16/84.72 |
% 142.16/84.72 | Instantiating (480) with all_744_0_946, all_744_1_947, all_744_2_948, all_744_3_949 yields:
% 142.16/84.72 | (708) relation_field(empty_set) = all_744_2_948 & relation_dom(empty_set) = all_744_1_947 & set_union2(all_744_1_947, empty_set) = all_744_0_946 & relation(empty_set) = all_744_3_949 & ( ~ (all_744_3_949 = 0) | all_744_0_946 = all_744_2_948)
% 142.16/84.72 |
% 142.16/84.72 | Applying alpha-rule on (708) yields:
% 142.16/84.72 | (709) ~ (all_744_3_949 = 0) | all_744_0_946 = all_744_2_948
% 142.16/84.72 | (710) relation(empty_set) = all_744_3_949
% 142.16/84.72 | (711) relation_dom(empty_set) = all_744_1_947
% 142.16/84.72 | (712) relation_field(empty_set) = all_744_2_948
% 142.16/84.72 | (713) set_union2(all_744_1_947, empty_set) = all_744_0_946
% 142.16/84.72 |
% 142.16/84.72 | Instantiating (519) with all_863_0_1107, all_863_1_1108 yields:
% 142.16/84.72 | (714) relation_rng(all_0_14_14) = all_863_0_1107 & relation_dom(all_0_14_14) = all_863_1_1108 & relation_image(all_0_14_14, all_863_1_1108) = all_863_0_1107
% 142.16/84.72 |
% 142.16/84.72 | Applying alpha-rule on (714) yields:
% 142.16/84.72 | (715) relation_rng(all_0_14_14) = all_863_0_1107
% 142.16/84.72 | (716) relation_dom(all_0_14_14) = all_863_1_1108
% 142.16/84.72 | (717) relation_image(all_0_14_14, all_863_1_1108) = all_863_0_1107
% 142.16/84.72 |
% 142.16/84.72 | Instantiating (518) with all_904_0_1142, all_904_1_1143, all_904_2_1144 yields:
% 142.16/84.72 | (718) relation_dom(all_0_14_14) = all_904_1_1143 & empty(all_904_1_1143) = all_904_0_1142 & empty(all_0_14_14) = all_904_2_1144 & ( ~ (all_904_0_1142 = 0) | all_904_2_1144 = 0)
% 142.16/84.72 |
% 142.16/84.72 | Applying alpha-rule on (718) yields:
% 142.16/84.72 | (719) relation_dom(all_0_14_14) = all_904_1_1143
% 142.16/84.72 | (720) empty(all_904_1_1143) = all_904_0_1142
% 142.16/84.72 | (721) empty(all_0_14_14) = all_904_2_1144
% 142.16/84.72 | (722) ~ (all_904_0_1142 = 0) | all_904_2_1144 = 0
% 142.16/84.72 |
% 142.16/84.72 | Instantiating (501) with all_920_0_1163, all_920_1_1164 yields:
% 142.16/84.72 | (723) relation_rng(empty_set) = all_920_0_1163 & relation(empty_set) = all_920_1_1164 & ( ~ (all_920_1_1164 = 0) | ( ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_dom(v0) = v4 & subset(all_920_0_1163, v1) = v6 & subset(empty_set, v4) = v5 & subset(empty_set, v0) = v3 & relation(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | (v6 = 0 & v5 = 0)))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_rng(v0) = v5 & subset(all_920_0_1163, v5) = v6 & subset(empty_set, v1) = v4 & subset(empty_set, v0) = v3 & relation(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | (v6 = 0 & v4 = 0)))) & ! [v0] : ( ~ (subset(empty_set, v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_rng(v0) = v4 & relation_dom(v0) = v2 & subset(all_920_0_1163, v4) = v5 & subset(empty_set, v2) = v3 & relation(v0) = v1 & ( ~ (v1 = 0) | (v5 = 0 & v3 = 0)))) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_rng(v0) = v4 & relation_dom(v0) = v2 & subset(all_920_0_1163, v4) = v5 & subset(empty_set, v2) = v3 & subset(empty_set, v0) = v1 & ( ~ (v1 = 0) | (v5 = 0 & v3 = 0))))))
% 142.16/84.72 |
% 142.16/84.72 | Applying alpha-rule on (723) yields:
% 142.16/84.72 | (724) relation_rng(empty_set) = all_920_0_1163
% 142.16/84.72 | (725) relation(empty_set) = all_920_1_1164
% 142.16/84.72 | (726) ~ (all_920_1_1164 = 0) | ( ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_dom(v0) = v4 & subset(all_920_0_1163, v1) = v6 & subset(empty_set, v4) = v5 & subset(empty_set, v0) = v3 & relation(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | (v6 = 0 & v5 = 0)))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_rng(v0) = v5 & subset(all_920_0_1163, v5) = v6 & subset(empty_set, v1) = v4 & subset(empty_set, v0) = v3 & relation(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | (v6 = 0 & v4 = 0)))) & ! [v0] : ( ~ (subset(empty_set, v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_rng(v0) = v4 & relation_dom(v0) = v2 & subset(all_920_0_1163, v4) = v5 & subset(empty_set, v2) = v3 & relation(v0) = v1 & ( ~ (v1 = 0) | (v5 = 0 & v3 = 0)))) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_rng(v0) = v4 & relation_dom(v0) = v2 & subset(all_920_0_1163, v4) = v5 & subset(empty_set, v2) = v3 & subset(empty_set, v0) = v1 & ( ~ (v1 = 0) | (v5 = 0 & v3 = 0)))))
% 142.16/84.72 |
% 142.16/84.72 | Instantiating (500) with all_922_0_1165, all_922_1_1166 yields:
% 142.16/84.72 | (727) relation_rng(empty_set) = all_922_0_1165 & relation(empty_set) = all_922_1_1166 & ( ~ (all_922_1_1166 = 0) | ( ! [v0] : ! [v1] : ( ~ (relation_composition(empty_set, v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_dom(v1) = v5 & relation_dom(v0) = v3 & subset(all_922_0_1165, v3) = v4 & relation(v0) = v2 & ( ~ (v4 = 0) | ~ (v2 = 0) | v5 = empty_set))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_composition(empty_set, v0) = v4 & relation_dom(v4) = v5 & subset(all_922_0_1165, v1) = v3 & relation(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | v5 = empty_set))) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : (relation_composition(empty_set, v0) = v3 & relation_dom(v3) = v4 & relation_dom(v0) = v1 & subset(all_922_0_1165, v1) = v2 & ( ~ (v2 = 0) | v4 = empty_set)))))
% 142.16/84.72 |
% 142.16/84.72 | Applying alpha-rule on (727) yields:
% 142.16/84.72 | (728) relation_rng(empty_set) = all_922_0_1165
% 142.16/84.72 | (729) relation(empty_set) = all_922_1_1166
% 142.16/84.72 | (730) ~ (all_922_1_1166 = 0) | ( ! [v0] : ! [v1] : ( ~ (relation_composition(empty_set, v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_dom(v1) = v5 & relation_dom(v0) = v3 & subset(all_922_0_1165, v3) = v4 & relation(v0) = v2 & ( ~ (v4 = 0) | ~ (v2 = 0) | v5 = empty_set))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_composition(empty_set, v0) = v4 & relation_dom(v4) = v5 & subset(all_922_0_1165, v1) = v3 & relation(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | v5 = empty_set))) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : (relation_composition(empty_set, v0) = v3 & relation_dom(v3) = v4 & relation_dom(v0) = v1 & subset(all_922_0_1165, v1) = v2 & ( ~ (v2 = 0) | v4 = empty_set))))
% 142.16/84.72 |
% 142.16/84.72 | Instantiating (526) with all_986_0_1249 yields:
% 142.16/84.72 | (731) relation_dom(all_0_14_14) = all_986_0_1249 & ! [v0] : ! [v1] : ( ~ (relation_composition(all_0_14_14, v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation_dom(v1) = v3 & subset(v3, all_986_0_1249) = v4 & relation(v0) = v2 & ( ~ (v2 = 0) | v4 = 0))) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : (relation_composition(all_0_14_14, v0) = v1 & relation_dom(v1) = v2 & subset(v2, all_986_0_1249) = 0))
% 142.16/84.72 |
% 142.16/84.72 | Applying alpha-rule on (731) yields:
% 142.16/84.72 | (732) relation_dom(all_0_14_14) = all_986_0_1249
% 142.16/84.72 | (733) ! [v0] : ! [v1] : ( ~ (relation_composition(all_0_14_14, v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation_dom(v1) = v3 & subset(v3, all_986_0_1249) = v4 & relation(v0) = v2 & ( ~ (v2 = 0) | v4 = 0)))
% 142.16/84.72 | (734) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : (relation_composition(all_0_14_14, v0) = v1 & relation_dom(v1) = v2 & subset(v2, all_986_0_1249) = 0))
% 142.16/84.72 |
% 142.16/84.72 | Instantiating (516) with all_991_0_1253, all_991_1_1254, all_991_2_1255 yields:
% 142.16/84.72 | (735) relation_field(all_0_14_14) = all_991_2_1255 & relation_rng(all_0_14_14) = all_991_0_1253 & relation_dom(all_0_14_14) = all_991_1_1254 & set_union2(all_991_1_1254, all_991_0_1253) = all_991_2_1255
% 142.16/84.72 |
% 142.16/84.72 | Applying alpha-rule on (735) yields:
% 142.16/84.72 | (736) relation_field(all_0_14_14) = all_991_2_1255
% 142.16/84.72 | (737) relation_rng(all_0_14_14) = all_991_0_1253
% 142.16/84.72 | (738) relation_dom(all_0_14_14) = all_991_1_1254
% 142.16/84.72 | (739) set_union2(all_991_1_1254, all_991_0_1253) = all_991_2_1255
% 142.16/84.72 |
% 142.16/84.72 | Instantiating (515) with all_993_0_1256, all_993_1_1257, all_993_2_1258 yields:
% 142.16/84.72 | (740) relation_inverse(all_0_14_14) = all_993_1_1257 & relation_rng(all_993_1_1257) = all_993_0_1256 & relation_rng(all_0_14_14) = all_993_2_1258 & relation_dom(all_993_1_1257) = all_993_2_1258 & relation_dom(all_0_14_14) = all_993_0_1256
% 142.16/84.72 |
% 142.16/84.72 | Applying alpha-rule on (740) yields:
% 142.16/84.72 | (741) relation_inverse(all_0_14_14) = all_993_1_1257
% 142.16/84.72 | (742) relation_dom(all_993_1_1257) = all_993_2_1258
% 142.16/84.72 | (743) relation_rng(all_993_1_1257) = all_993_0_1256
% 142.16/84.72 | (744) relation_dom(all_0_14_14) = all_993_0_1256
% 142.16/84.72 | (745) relation_rng(all_0_14_14) = all_993_2_1258
% 142.16/84.72 |
% 142.16/84.72 | Instantiating (525) with all_995_0_1259 yields:
% 142.16/84.72 | (746) relation_dom(all_0_14_14) = all_995_0_1259 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = 0 | ~ (ordered_pair(v0, v2) = v3) | ~ (in(v0, all_995_0_1259) = v1) | ? [v4] : ( ~ (v4 = 0) & in(v3, all_0_14_14) = v4)) & ! [v0] : ( ~ (in(v0, all_995_0_1259) = 0) | ? [v1] : ? [v2] : (ordered_pair(v0, v1) = v2 & in(v2, all_0_14_14) = 0)) & ? [v0] : (v0 = all_995_0_1259 | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (in(v1, v0) = v2 & ( ~ (v2 = 0) | ! [v6] : ! [v7] : ( ~ (ordered_pair(v1, v6) = v7) | ? [v8] : ( ~ (v8 = 0) & in(v7, all_0_14_14) = v8))) & (v2 = 0 | (v5 = 0 & ordered_pair(v1, v3) = v4 & in(v4, all_0_14_14) = 0))))
% 142.16/84.72 |
% 142.16/84.72 | Applying alpha-rule on (746) yields:
% 142.16/84.72 | (747) relation_dom(all_0_14_14) = all_995_0_1259
% 142.16/84.72 | (748) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = 0 | ~ (ordered_pair(v0, v2) = v3) | ~ (in(v0, all_995_0_1259) = v1) | ? [v4] : ( ~ (v4 = 0) & in(v3, all_0_14_14) = v4))
% 142.16/84.72 | (749) ! [v0] : ( ~ (in(v0, all_995_0_1259) = 0) | ? [v1] : ? [v2] : (ordered_pair(v0, v1) = v2 & in(v2, all_0_14_14) = 0))
% 142.16/84.72 | (750) ? [v0] : (v0 = all_995_0_1259 | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (in(v1, v0) = v2 & ( ~ (v2 = 0) | ! [v6] : ! [v7] : ( ~ (ordered_pair(v1, v6) = v7) | ? [v8] : ( ~ (v8 = 0) & in(v7, all_0_14_14) = v8))) & (v2 = 0 | (v5 = 0 & ordered_pair(v1, v3) = v4 & in(v4, all_0_14_14) = 0))))
% 142.16/84.72 |
% 142.16/84.72 | Instantiating (511) with all_1035_0_1308, all_1035_1_1309, all_1035_2_1310, all_1035_3_1311 yields:
% 142.16/84.72 | (751) relation_composition(all_0_7_7, empty_set) = all_1035_2_1310 & relation_rng(all_1035_2_1310) = all_1035_1_1309 & subset(all_1035_1_1309, empty_set) = all_1035_0_1308 & relation(empty_set) = all_1035_3_1311 & ( ~ (all_1035_3_1311 = 0) | all_1035_0_1308 = 0)
% 142.16/84.72 |
% 142.16/84.72 | Applying alpha-rule on (751) yields:
% 142.16/84.72 | (752) relation_composition(all_0_7_7, empty_set) = all_1035_2_1310
% 142.16/84.72 | (753) ~ (all_1035_3_1311 = 0) | all_1035_0_1308 = 0
% 142.16/84.72 | (754) relation(empty_set) = all_1035_3_1311
% 142.16/84.72 | (755) relation_rng(all_1035_2_1310) = all_1035_1_1309
% 142.16/84.72 | (756) subset(all_1035_1_1309, empty_set) = all_1035_0_1308
% 142.16/84.72 |
% 142.16/84.72 | Instantiating (506) with all_1076_0_1379, all_1076_1_1380 yields:
% 142.16/84.72 | (757) relation_rng(all_0_0_0) = all_1076_1_1380 & relation_dom(all_0_0_0) = all_1076_0_1379 & ! [v0] : ! [v1] : ( ~ (relation_composition(all_0_0_0, v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_dom(v1) = v5 & relation_dom(v0) = v3 & subset(all_1076_1_1380, v3) = v4 & relation(v0) = v2 & ( ~ (v4 = 0) | ~ (v2 = 0) | v5 = all_1076_0_1379))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_composition(all_0_0_0, v0) = v4 & relation_dom(v4) = v5 & subset(all_1076_1_1380, v1) = v3 & relation(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | v5 = all_1076_0_1379))) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : (relation_composition(all_0_0_0, v0) = v3 & relation_dom(v3) = v4 & relation_dom(v0) = v1 & subset(all_1076_1_1380, v1) = v2 & ( ~ (v2 = 0) | v4 = all_1076_0_1379)))
% 142.16/84.73 |
% 142.16/84.73 | Applying alpha-rule on (757) yields:
% 142.16/84.73 | (758) relation_dom(all_0_0_0) = all_1076_0_1379
% 142.16/84.73 | (759) relation_rng(all_0_0_0) = all_1076_1_1380
% 142.16/84.73 | (760) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_composition(all_0_0_0, v0) = v4 & relation_dom(v4) = v5 & subset(all_1076_1_1380, v1) = v3 & relation(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | v5 = all_1076_0_1379)))
% 142.16/84.73 | (761) ! [v0] : ! [v1] : ( ~ (relation_composition(all_0_0_0, v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_dom(v1) = v5 & relation_dom(v0) = v3 & subset(all_1076_1_1380, v3) = v4 & relation(v0) = v2 & ( ~ (v4 = 0) | ~ (v2 = 0) | v5 = all_1076_0_1379)))
% 142.16/84.73 | (762) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : (relation_composition(all_0_0_0, v0) = v3 & relation_dom(v3) = v4 & relation_dom(v0) = v1 & subset(all_1076_1_1380, v1) = v2 & ( ~ (v2 = 0) | v4 = all_1076_0_1379)))
% 142.16/84.73 |
% 142.16/84.73 | Instantiating formula (760) with all_0_11_11, all_0_14_14 and discharging atoms relation_dom(all_0_14_14) = all_0_11_11, yields:
% 142.16/84.73 | (763) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (relation_composition(all_0_0_0, all_0_14_14) = v2 & relation_dom(v2) = v3 & subset(all_1076_1_1380, all_0_11_11) = v1 & relation(all_0_14_14) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = all_1076_0_1379))
% 142.16/84.73 |
% 142.16/84.73 | Instantiating formula (760) with empty_set, empty_set and discharging atoms relation_dom(empty_set) = empty_set, yields:
% 142.16/84.73 | (764) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (relation_composition(all_0_0_0, empty_set) = v2 & relation_dom(v2) = v3 & subset(all_1076_1_1380, empty_set) = v1 & relation(empty_set) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = all_1076_0_1379))
% 142.16/84.73 |
% 142.16/84.73 | Instantiating formula (762) with all_0_14_14 and discharging atoms relation(all_0_14_14) = 0, yields:
% 142.16/84.73 | (765) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (relation_composition(all_0_0_0, all_0_14_14) = v2 & relation_dom(v2) = v3 & relation_dom(all_0_14_14) = v0 & subset(all_1076_1_1380, v0) = v1 & ( ~ (v1 = 0) | v3 = all_1076_0_1379))
% 142.16/84.73 |
% 142.16/84.73 | Instantiating (505) with all_1081_0_1383, all_1081_1_1384 yields:
% 142.16/84.73 | (766) relation_rng(all_0_0_0) = all_1081_0_1383 & relation_dom(all_0_0_0) = all_1081_1_1384 & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_dom(v0) = v4 & subset(all_1081_0_1383, v1) = v6 & subset(all_1081_1_1384, v4) = v5 & subset(all_0_0_0, v0) = v3 & relation(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | (v6 = 0 & v5 = 0)))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_rng(v0) = v5 & subset(all_1081_0_1383, v5) = v6 & subset(all_1081_1_1384, v1) = v4 & subset(all_0_0_0, v0) = v3 & relation(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | (v6 = 0 & v4 = 0)))) & ! [v0] : ( ~ (subset(all_0_0_0, v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_rng(v0) = v4 & relation_dom(v0) = v2 & subset(all_1081_0_1383, v4) = v5 & subset(all_1081_1_1384, v2) = v3 & relation(v0) = v1 & ( ~ (v1 = 0) | (v5 = 0 & v3 = 0)))) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_rng(v0) = v4 & relation_dom(v0) = v2 & subset(all_1081_0_1383, v4) = v5 & subset(all_1081_1_1384, v2) = v3 & subset(all_0_0_0, v0) = v1 & ( ~ (v1 = 0) | (v5 = 0 & v3 = 0))))
% 142.16/84.73 |
% 142.16/84.73 | Applying alpha-rule on (766) yields:
% 142.16/84.73 | (767) relation_dom(all_0_0_0) = all_1081_1_1384
% 142.16/84.73 | (768) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_dom(v0) = v4 & subset(all_1081_0_1383, v1) = v6 & subset(all_1081_1_1384, v4) = v5 & subset(all_0_0_0, v0) = v3 & relation(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | (v6 = 0 & v5 = 0))))
% 142.16/84.73 | (769) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_rng(v0) = v4 & relation_dom(v0) = v2 & subset(all_1081_0_1383, v4) = v5 & subset(all_1081_1_1384, v2) = v3 & subset(all_0_0_0, v0) = v1 & ( ~ (v1 = 0) | (v5 = 0 & v3 = 0))))
% 142.16/84.73 | (770) ! [v0] : ( ~ (subset(all_0_0_0, v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_rng(v0) = v4 & relation_dom(v0) = v2 & subset(all_1081_0_1383, v4) = v5 & subset(all_1081_1_1384, v2) = v3 & relation(v0) = v1 & ( ~ (v1 = 0) | (v5 = 0 & v3 = 0))))
% 142.16/84.73 | (771) relation_rng(all_0_0_0) = all_1081_0_1383
% 142.16/84.73 | (772) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_rng(v0) = v5 & subset(all_1081_0_1383, v5) = v6 & subset(all_1081_1_1384, v1) = v4 & subset(all_0_0_0, v0) = v3 & relation(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | (v6 = 0 & v4 = 0))))
% 142.16/84.73 |
% 142.16/84.73 | Instantiating formula (768) with empty_set, empty_set and discharging atoms relation_rng(empty_set) = empty_set, yields:
% 142.16/84.73 | (773) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (relation_dom(empty_set) = v2 & subset(all_1081_0_1383, empty_set) = v4 & subset(all_1081_1_1384, v2) = v3 & subset(all_0_0_0, empty_set) = v1 & relation(empty_set) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | (v4 = 0 & v3 = 0)))
% 142.16/84.73 |
% 142.16/84.73 | Instantiating formula (772) with all_0_11_11, all_0_14_14 and discharging atoms relation_dom(all_0_14_14) = all_0_11_11, yields:
% 142.16/84.73 | (774) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (relation_rng(all_0_14_14) = v3 & subset(all_1081_0_1383, v3) = v4 & subset(all_1081_1_1384, all_0_11_11) = v2 & subset(all_0_0_0, all_0_14_14) = v1 & relation(all_0_14_14) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | (v4 = 0 & v2 = 0)))
% 142.16/84.73 |
% 142.16/84.73 | Instantiating formula (772) with empty_set, empty_set and discharging atoms relation_dom(empty_set) = empty_set, yields:
% 142.16/84.73 | (775) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (relation_rng(empty_set) = v3 & subset(all_1081_0_1383, v3) = v4 & subset(all_1081_1_1384, empty_set) = v2 & subset(all_0_0_0, empty_set) = v1 & relation(empty_set) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | (v4 = 0 & v2 = 0)))
% 142.16/84.73 |
% 142.16/84.73 | Instantiating formula (769) with all_0_14_14 and discharging atoms relation(all_0_14_14) = 0, yields:
% 142.16/84.73 | (776) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (relation_rng(all_0_14_14) = v3 & relation_dom(all_0_14_14) = v1 & subset(all_1081_0_1383, v3) = v4 & subset(all_1081_1_1384, v1) = v2 & subset(all_0_0_0, all_0_14_14) = v0 & ( ~ (v0 = 0) | (v4 = 0 & v2 = 0)))
% 142.16/84.73 |
% 142.16/84.73 | Instantiating (504) with all_1084_0_1385, all_1084_1_1386 yields:
% 142.16/84.73 | (777) relation_rng(all_0_0_0) = all_1084_0_1385 & relation_dom(all_0_0_0) = all_1084_1_1386 & ! [v0] : ! [v1] : ( ~ (relation_composition(v0, all_0_0_0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_rng(v1) = v5 & relation_rng(v0) = v3 & subset(all_1084_1_1386, v3) = v4 & relation(v0) = v2 & ( ~ (v4 = 0) | ~ (v2 = 0) | v5 = all_1084_0_1385))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_composition(v0, all_0_0_0) = v4 & relation_rng(v4) = v5 & subset(all_1084_1_1386, v1) = v3 & relation(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | v5 = all_1084_0_1385))) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : (relation_composition(v0, all_0_0_0) = v3 & relation_rng(v3) = v4 & relation_rng(v0) = v1 & subset(all_1084_1_1386, v1) = v2 & ( ~ (v2 = 0) | v4 = all_1084_0_1385)))
% 142.16/84.73 |
% 142.16/84.73 | Applying alpha-rule on (777) yields:
% 142.16/84.73 | (778) relation_rng(all_0_0_0) = all_1084_0_1385
% 142.16/84.73 | (779) relation_dom(all_0_0_0) = all_1084_1_1386
% 142.16/84.73 | (780) ! [v0] : ! [v1] : ( ~ (relation_composition(v0, all_0_0_0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_rng(v1) = v5 & relation_rng(v0) = v3 & subset(all_1084_1_1386, v3) = v4 & relation(v0) = v2 & ( ~ (v4 = 0) | ~ (v2 = 0) | v5 = all_1084_0_1385)))
% 142.16/84.73 | (781) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_composition(v0, all_0_0_0) = v4 & relation_rng(v4) = v5 & subset(all_1084_1_1386, v1) = v3 & relation(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | v5 = all_1084_0_1385)))
% 142.16/84.73 | (782) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : (relation_composition(v0, all_0_0_0) = v3 & relation_rng(v3) = v4 & relation_rng(v0) = v1 & subset(all_1084_1_1386, v1) = v2 & ( ~ (v2 = 0) | v4 = all_1084_0_1385)))
% 142.16/84.73 |
% 142.16/84.73 | Instantiating formula (781) with empty_set, empty_set and discharging atoms relation_rng(empty_set) = empty_set, yields:
% 142.16/84.73 | (783) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (relation_composition(empty_set, all_0_0_0) = v2 & relation_rng(v2) = v3 & subset(all_1084_1_1386, empty_set) = v1 & relation(empty_set) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = all_1084_0_1385))
% 142.16/84.73 |
% 142.16/84.73 | Instantiating (517) with all_1111_0_1418, all_1111_1_1419, all_1111_2_1420 yields:
% 142.16/84.73 | (784) relation_rng(all_0_14_14) = all_1111_1_1419 & relation_dom(all_0_14_14) = all_1111_2_1420 & cartesian_product2(all_1111_2_1420, all_1111_1_1419) = all_1111_0_1418 & subset(all_0_14_14, all_1111_0_1418) = 0
% 142.16/84.73 |
% 142.16/84.73 | Applying alpha-rule on (784) yields:
% 142.16/84.73 | (785) relation_rng(all_0_14_14) = all_1111_1_1419
% 142.16/84.73 | (786) relation_dom(all_0_14_14) = all_1111_2_1420
% 142.16/84.73 | (787) cartesian_product2(all_1111_2_1420, all_1111_1_1419) = all_1111_0_1418
% 142.16/84.73 | (788) subset(all_0_14_14, all_1111_0_1418) = 0
% 142.16/84.73 |
% 142.16/84.73 | Instantiating (499) with all_1115_0_1427, all_1115_1_1428 yields:
% 142.16/84.73 | (789) relation_rng(empty_set) = all_1115_0_1427 & relation(empty_set) = all_1115_1_1428 & ( ~ (all_1115_1_1428 = 0) | ( ! [v0] : ! [v1] : ( ~ (relation_composition(v0, empty_set) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_rng(v1) = v5 & relation_rng(v0) = v3 & subset(empty_set, v3) = v4 & relation(v0) = v2 & ( ~ (v4 = 0) | ~ (v2 = 0) | v5 = all_1115_0_1427))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_composition(v0, empty_set) = v4 & relation_rng(v4) = v5 & subset(empty_set, v1) = v3 & relation(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | v5 = all_1115_0_1427))) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : (relation_composition(v0, empty_set) = v3 & relation_rng(v3) = v4 & relation_rng(v0) = v1 & subset(empty_set, v1) = v2 & ( ~ (v2 = 0) | v4 = all_1115_0_1427)))))
% 142.16/84.73 |
% 142.16/84.73 | Applying alpha-rule on (789) yields:
% 142.16/84.73 | (790) relation_rng(empty_set) = all_1115_0_1427
% 142.16/84.73 | (791) relation(empty_set) = all_1115_1_1428
% 142.16/84.73 | (792) ~ (all_1115_1_1428 = 0) | ( ! [v0] : ! [v1] : ( ~ (relation_composition(v0, empty_set) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_rng(v1) = v5 & relation_rng(v0) = v3 & subset(empty_set, v3) = v4 & relation(v0) = v2 & ( ~ (v4 = 0) | ~ (v2 = 0) | v5 = all_1115_0_1427))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_composition(v0, empty_set) = v4 & relation_rng(v4) = v5 & subset(empty_set, v1) = v3 & relation(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | v5 = all_1115_0_1427))) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : (relation_composition(v0, empty_set) = v3 & relation_rng(v3) = v4 & relation_rng(v0) = v1 & subset(empty_set, v1) = v2 & ( ~ (v2 = 0) | v4 = all_1115_0_1427))))
% 142.16/84.73 |
% 142.16/84.73 | Instantiating (498) with all_1117_0_1429, all_1117_1_1430, all_1117_2_1431 yields:
% 142.16/84.73 | (793) relation_rng(empty_set) = all_1117_0_1429 & relation_image(empty_set, empty_set) = all_1117_1_1430 & relation(empty_set) = all_1117_2_1431 & ( ~ (all_1117_2_1431 = 0) | all_1117_0_1429 = all_1117_1_1430)
% 142.16/84.74 |
% 142.16/84.74 | Applying alpha-rule on (793) yields:
% 142.16/84.74 | (794) relation_rng(empty_set) = all_1117_0_1429
% 142.16/84.74 | (795) relation_image(empty_set, empty_set) = all_1117_1_1430
% 142.16/84.74 | (796) relation(empty_set) = all_1117_2_1431
% 142.16/84.74 | (797) ~ (all_1117_2_1431 = 0) | all_1117_0_1429 = all_1117_1_1430
% 142.16/84.74 |
% 142.16/84.74 | Instantiating (495) with all_1119_0_1432, all_1119_1_1433, all_1119_2_1434, all_1119_3_1435, all_1119_4_1436 yields:
% 142.16/84.74 | (798) relation_inverse(empty_set) = all_1119_2_1434 & relation_rng(all_1119_2_1434) = all_1119_0_1432 & relation_rng(empty_set) = all_1119_3_1435 & relation_dom(all_1119_2_1434) = all_1119_1_1433 & relation(empty_set) = all_1119_4_1436 & ( ~ (all_1119_4_1436 = 0) | (all_1119_0_1432 = empty_set & all_1119_1_1433 = all_1119_3_1435))
% 142.16/84.74 |
% 142.16/84.74 | Applying alpha-rule on (798) yields:
% 142.16/84.74 | (799) relation_dom(all_1119_2_1434) = all_1119_1_1433
% 142.16/84.74 | (800) relation_inverse(empty_set) = all_1119_2_1434
% 142.16/84.74 | (801) ~ (all_1119_4_1436 = 0) | (all_1119_0_1432 = empty_set & all_1119_1_1433 = all_1119_3_1435)
% 142.16/84.74 | (802) relation_rng(all_1119_2_1434) = all_1119_0_1432
% 142.16/84.74 | (803) relation_rng(empty_set) = all_1119_3_1435
% 142.16/84.74 | (804) relation(empty_set) = all_1119_4_1436
% 142.16/84.74 |
% 142.16/84.74 | Instantiating (494) with all_1133_0_1457, all_1133_1_1458 yields:
% 142.16/84.74 | (805) relation_rng(all_0_14_14) = all_1133_0_1457 & relation(all_0_14_14) = all_1133_1_1458 & ( ~ (all_1133_1_1458 = 0) | (( ~ (all_1133_0_1457 = empty_set) | all_0_11_11 = empty_set) & ( ~ (all_0_11_11 = empty_set) | all_1133_0_1457 = empty_set)))
% 142.16/84.74 |
% 142.16/84.74 | Applying alpha-rule on (805) yields:
% 142.16/84.74 | (806) relation_rng(all_0_14_14) = all_1133_0_1457
% 142.16/84.74 | (807) relation(all_0_14_14) = all_1133_1_1458
% 142.16/84.74 | (808) ~ (all_1133_1_1458 = 0) | (( ~ (all_1133_0_1457 = empty_set) | all_0_11_11 = empty_set) & ( ~ (all_0_11_11 = empty_set) | all_1133_0_1457 = empty_set))
% 142.16/84.74 |
% 142.16/84.74 | Instantiating (497) with all_1135_0_1459, all_1135_1_1460, all_1135_2_1461, all_1135_3_1462 yields:
% 142.16/84.74 | (809) relation_rng(empty_set) = all_1135_2_1461 & cartesian_product2(empty_set, all_1135_2_1461) = all_1135_1_1460 & subset(empty_set, all_1135_1_1460) = all_1135_0_1459 & relation(empty_set) = all_1135_3_1462 & ( ~ (all_1135_3_1462 = 0) | all_1135_0_1459 = 0)
% 142.16/84.74 |
% 142.16/84.74 | Applying alpha-rule on (809) yields:
% 142.16/84.74 | (810) cartesian_product2(empty_set, all_1135_2_1461) = all_1135_1_1460
% 142.16/84.74 | (811) ~ (all_1135_3_1462 = 0) | all_1135_0_1459 = 0
% 142.16/84.74 | (812) relation_rng(empty_set) = all_1135_2_1461
% 142.16/84.74 | (813) subset(empty_set, all_1135_1_1460) = all_1135_0_1459
% 142.16/84.74 | (814) relation(empty_set) = all_1135_3_1462
% 142.16/84.74 |
% 142.16/84.74 | Instantiating (496) with all_1137_0_1463, all_1137_1_1464, all_1137_2_1465, all_1137_3_1466 yields:
% 142.16/84.74 | (815) relation_field(empty_set) = all_1137_2_1465 & relation_rng(empty_set) = all_1137_1_1464 & set_union2(empty_set, all_1137_1_1464) = all_1137_0_1463 & relation(empty_set) = all_1137_3_1466 & ( ~ (all_1137_3_1466 = 0) | all_1137_0_1463 = all_1137_2_1465)
% 142.16/84.74 |
% 142.16/84.74 | Applying alpha-rule on (815) yields:
% 142.16/84.74 | (816) relation_rng(empty_set) = all_1137_1_1464
% 142.16/84.74 | (817) relation(empty_set) = all_1137_3_1466
% 142.16/84.74 | (818) set_union2(empty_set, all_1137_1_1464) = all_1137_0_1463
% 142.16/84.74 | (819) relation_field(empty_set) = all_1137_2_1465
% 142.16/84.74 | (820) ~ (all_1137_3_1466 = 0) | all_1137_0_1463 = all_1137_2_1465
% 142.16/84.74 |
% 142.16/84.74 | Instantiating (492) with all_1139_0_1467, all_1139_1_1468 yields:
% 142.16/84.74 | (821) relation_rng(all_0_14_14) = all_1139_0_1467 & relation(all_0_14_14) = all_1139_1_1468 & ( ~ (all_1139_1_1468 = 0) | ( ! [v0] : ! [v1] : ( ~ (relation_composition(all_0_14_14, v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_dom(v1) = v5 & relation_dom(v0) = v3 & subset(all_1139_0_1467, v3) = v4 & relation(v0) = v2 & ( ~ (v4 = 0) | ~ (v2 = 0) | v5 = all_0_11_11))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_composition(all_0_14_14, v0) = v4 & relation_dom(v4) = v5 & subset(all_1139_0_1467, v1) = v3 & relation(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | v5 = all_0_11_11))) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : (relation_composition(all_0_14_14, v0) = v3 & relation_dom(v3) = v4 & relation_dom(v0) = v1 & subset(all_1139_0_1467, v1) = v2 & ( ~ (v2 = 0) | v4 = all_0_11_11)))))
% 142.16/84.74 |
% 142.16/84.74 | Applying alpha-rule on (821) yields:
% 142.16/84.74 | (822) relation_rng(all_0_14_14) = all_1139_0_1467
% 142.16/84.74 | (823) relation(all_0_14_14) = all_1139_1_1468
% 142.16/84.74 | (824) ~ (all_1139_1_1468 = 0) | ( ! [v0] : ! [v1] : ( ~ (relation_composition(all_0_14_14, v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_dom(v1) = v5 & relation_dom(v0) = v3 & subset(all_1139_0_1467, v3) = v4 & relation(v0) = v2 & ( ~ (v4 = 0) | ~ (v2 = 0) | v5 = all_0_11_11))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_composition(all_0_14_14, v0) = v4 & relation_dom(v4) = v5 & subset(all_1139_0_1467, v1) = v3 & relation(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | v5 = all_0_11_11))) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : (relation_composition(all_0_14_14, v0) = v3 & relation_dom(v3) = v4 & relation_dom(v0) = v1 & subset(all_1139_0_1467, v1) = v2 & ( ~ (v2 = 0) | v4 = all_0_11_11))))
% 142.16/84.74 |
% 142.16/84.74 | Instantiating (490) with all_1141_0_1469, all_1141_1_1470, all_1141_2_1471 yields:
% 142.16/84.74 | (825) relation(all_0_14_14) = all_1141_1_1470 & empty(all_0_11_11) = all_1141_0_1469 & empty(all_0_14_14) = all_1141_2_1471 & ( ~ (all_1141_0_1469 = 0) | ~ (all_1141_1_1470 = 0) | all_1141_2_1471 = 0)
% 142.16/84.74 |
% 142.16/84.74 | Applying alpha-rule on (825) yields:
% 142.16/84.74 | (826) relation(all_0_14_14) = all_1141_1_1470
% 142.16/84.74 | (827) empty(all_0_11_11) = all_1141_0_1469
% 142.16/84.74 | (828) empty(all_0_14_14) = all_1141_2_1471
% 142.16/84.74 | (829) ~ (all_1141_0_1469 = 0) | ~ (all_1141_1_1470 = 0) | all_1141_2_1471 = 0
% 142.16/84.74 |
% 142.16/84.74 | Instantiating (493) with all_1143_0_1472, all_1143_1_1473 yields:
% 142.16/84.74 | (830) relation_rng(all_0_14_14) = all_1143_0_1472 & relation(all_0_14_14) = all_1143_1_1473 & ( ~ (all_1143_1_1473 = 0) | ( ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_dom(v0) = v4 & subset(all_1143_0_1472, v1) = v6 & subset(all_0_11_11, v4) = v5 & subset(all_0_14_14, v0) = v3 & relation(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | (v6 = 0 & v5 = 0)))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_rng(v0) = v5 & subset(all_1143_0_1472, v5) = v6 & subset(all_0_11_11, v1) = v4 & subset(all_0_14_14, v0) = v3 & relation(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | (v6 = 0 & v4 = 0)))) & ! [v0] : ( ~ (subset(all_0_14_14, v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_rng(v0) = v4 & relation_dom(v0) = v2 & subset(all_1143_0_1472, v4) = v5 & subset(all_0_11_11, v2) = v3 & relation(v0) = v1 & ( ~ (v1 = 0) | (v5 = 0 & v3 = 0)))) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_rng(v0) = v4 & relation_dom(v0) = v2 & subset(all_1143_0_1472, v4) = v5 & subset(all_0_11_11, v2) = v3 & subset(all_0_14_14, v0) = v1 & ( ~ (v1 = 0) | (v5 = 0 & v3 = 0))))))
% 142.16/84.74 |
% 142.16/84.74 | Applying alpha-rule on (830) yields:
% 142.16/84.74 | (831) relation_rng(all_0_14_14) = all_1143_0_1472
% 142.16/84.74 | (832) relation(all_0_14_14) = all_1143_1_1473
% 142.16/84.74 | (833) ~ (all_1143_1_1473 = 0) | ( ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_dom(v0) = v4 & subset(all_1143_0_1472, v1) = v6 & subset(all_0_11_11, v4) = v5 & subset(all_0_14_14, v0) = v3 & relation(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | (v6 = 0 & v5 = 0)))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_rng(v0) = v5 & subset(all_1143_0_1472, v5) = v6 & subset(all_0_11_11, v1) = v4 & subset(all_0_14_14, v0) = v3 & relation(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | (v6 = 0 & v4 = 0)))) & ! [v0] : ( ~ (subset(all_0_14_14, v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_rng(v0) = v4 & relation_dom(v0) = v2 & subset(all_1143_0_1472, v4) = v5 & subset(all_0_11_11, v2) = v3 & relation(v0) = v1 & ( ~ (v1 = 0) | (v5 = 0 & v3 = 0)))) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_rng(v0) = v4 & relation_dom(v0) = v2 & subset(all_1143_0_1472, v4) = v5 & subset(all_0_11_11, v2) = v3 & subset(all_0_14_14, v0) = v1 & ( ~ (v1 = 0) | (v5 = 0 & v3 = 0)))))
% 142.32/84.74 |
% 142.32/84.74 | Instantiating (491) with all_1156_0_1490, all_1156_1_1491 yields:
% 142.32/84.74 | (834) relation_rng(all_0_14_14) = all_1156_0_1490 & relation(all_0_14_14) = all_1156_1_1491 & ( ~ (all_1156_1_1491 = 0) | ( ! [v0] : ! [v1] : ( ~ (relation_composition(v0, all_0_14_14) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_rng(v1) = v5 & relation_rng(v0) = v3 & subset(all_0_11_11, v3) = v4 & relation(v0) = v2 & ( ~ (v4 = 0) | ~ (v2 = 0) | v5 = all_1156_0_1490))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_composition(v0, all_0_14_14) = v4 & relation_rng(v4) = v5 & subset(all_0_11_11, v1) = v3 & relation(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | v5 = all_1156_0_1490))) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : (relation_composition(v0, all_0_14_14) = v3 & relation_rng(v3) = v4 & relation_rng(v0) = v1 & subset(all_0_11_11, v1) = v2 & ( ~ (v2 = 0) | v4 = all_1156_0_1490)))))
% 142.32/84.74 |
% 142.32/84.74 | Applying alpha-rule on (834) yields:
% 142.32/84.74 | (835) relation_rng(all_0_14_14) = all_1156_0_1490
% 142.32/84.74 | (836) relation(all_0_14_14) = all_1156_1_1491
% 142.32/84.74 | (837) ~ (all_1156_1_1491 = 0) | ( ! [v0] : ! [v1] : ( ~ (relation_composition(v0, all_0_14_14) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_rng(v1) = v5 & relation_rng(v0) = v3 & subset(all_0_11_11, v3) = v4 & relation(v0) = v2 & ( ~ (v4 = 0) | ~ (v2 = 0) | v5 = all_1156_0_1490))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_composition(v0, all_0_14_14) = v4 & relation_rng(v4) = v5 & subset(all_0_11_11, v1) = v3 & relation(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | v5 = all_1156_0_1490))) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : (relation_composition(v0, all_0_14_14) = v3 & relation_rng(v3) = v4 & relation_rng(v0) = v1 & subset(all_0_11_11, v1) = v2 & ( ~ (v2 = 0) | v4 = all_1156_0_1490))))
% 142.33/84.74 |
% 142.33/84.74 | Instantiating (489) with all_1158_0_1492, all_1158_1_1493, all_1158_2_1494 yields:
% 142.33/84.74 | (838) relation_rng(all_0_14_14) = all_1158_0_1492 & relation_image(all_0_14_14, all_0_11_11) = all_1158_1_1493 & relation(all_0_14_14) = all_1158_2_1494 & ( ~ (all_1158_2_1494 = 0) | all_1158_0_1492 = all_1158_1_1493)
% 142.33/84.74 |
% 142.33/84.74 | Applying alpha-rule on (838) yields:
% 142.33/84.74 | (839) relation_rng(all_0_14_14) = all_1158_0_1492
% 142.33/84.74 | (840) relation_image(all_0_14_14, all_0_11_11) = all_1158_1_1493
% 142.33/84.74 | (841) relation(all_0_14_14) = all_1158_2_1494
% 142.33/84.74 | (842) ~ (all_1158_2_1494 = 0) | all_1158_0_1492 = all_1158_1_1493
% 142.33/84.74 |
% 142.33/84.74 | Instantiating (487) with all_1160_0_1495, all_1160_1_1496, all_1160_2_1497, all_1160_3_1498 yields:
% 142.33/84.74 | (843) relation_field(all_0_14_14) = all_1160_2_1497 & relation_rng(all_0_14_14) = all_1160_1_1496 & set_union2(all_0_11_11, all_1160_1_1496) = all_1160_0_1495 & relation(all_0_14_14) = all_1160_3_1498 & ( ~ (all_1160_3_1498 = 0) | all_1160_0_1495 = all_1160_2_1497)
% 142.33/84.74 |
% 142.33/84.74 | Applying alpha-rule on (843) yields:
% 142.33/84.74 | (844) relation(all_0_14_14) = all_1160_3_1498
% 142.33/84.74 | (845) relation_rng(all_0_14_14) = all_1160_1_1496
% 142.33/84.74 | (846) set_union2(all_0_11_11, all_1160_1_1496) = all_1160_0_1495
% 142.33/84.74 | (847) relation_field(all_0_14_14) = all_1160_2_1497
% 142.33/84.74 | (848) ~ (all_1160_3_1498 = 0) | all_1160_0_1495 = all_1160_2_1497
% 142.33/84.74 |
% 142.33/84.74 | Instantiating (486) with all_1162_0_1499, all_1162_1_1500, all_1162_2_1501, all_1162_3_1502, all_1162_4_1503 yields:
% 142.33/84.74 | (849) relation_inverse(all_0_14_14) = all_1162_2_1501 & relation_rng(all_1162_2_1501) = all_1162_0_1499 & relation_rng(all_0_14_14) = all_1162_3_1502 & relation_dom(all_1162_2_1501) = all_1162_1_1500 & relation(all_0_14_14) = all_1162_4_1503 & ( ~ (all_1162_4_1503 = 0) | (all_1162_0_1499 = all_0_11_11 & all_1162_1_1500 = all_1162_3_1502))
% 142.33/84.74 |
% 142.33/84.74 | Applying alpha-rule on (849) yields:
% 142.33/84.74 | (850) relation_inverse(all_0_14_14) = all_1162_2_1501
% 142.33/84.74 | (851) relation_rng(all_0_14_14) = all_1162_3_1502
% 142.33/84.74 | (852) relation_dom(all_1162_2_1501) = all_1162_1_1500
% 142.33/84.74 | (853) relation_rng(all_1162_2_1501) = all_1162_0_1499
% 142.33/84.74 | (854) ~ (all_1162_4_1503 = 0) | (all_1162_0_1499 = all_0_11_11 & all_1162_1_1500 = all_1162_3_1502)
% 142.33/84.74 | (855) relation(all_0_14_14) = all_1162_4_1503
% 142.33/84.74 |
% 142.33/84.74 | Instantiating (488) with all_1168_0_1516, all_1168_1_1517, all_1168_2_1518, all_1168_3_1519 yields:
% 142.33/84.74 | (856) relation_rng(all_0_14_14) = all_1168_2_1518 & cartesian_product2(all_0_11_11, all_1168_2_1518) = all_1168_1_1517 & subset(all_0_14_14, all_1168_1_1517) = all_1168_0_1516 & relation(all_0_14_14) = all_1168_3_1519 & ( ~ (all_1168_3_1519 = 0) | all_1168_0_1516 = 0)
% 142.33/84.75 |
% 142.33/84.75 | Applying alpha-rule on (856) yields:
% 142.33/84.75 | (857) ~ (all_1168_3_1519 = 0) | all_1168_0_1516 = 0
% 142.33/84.75 | (858) relation_rng(all_0_14_14) = all_1168_2_1518
% 142.33/84.75 | (859) subset(all_0_14_14, all_1168_1_1517) = all_1168_0_1516
% 142.33/84.75 | (860) relation(all_0_14_14) = all_1168_3_1519
% 142.33/84.75 | (861) cartesian_product2(all_0_11_11, all_1168_2_1518) = all_1168_1_1517
% 142.33/84.75 |
% 142.33/84.75 | Instantiating (542) with all_1236_0_1626, all_1236_1_1627, all_1236_2_1628, all_1236_3_1629 yields:
% 142.33/84.75 | (862) relation_composition(empty_set, all_0_14_14) = all_1236_1_1627 & relation_dom(all_1236_1_1627) = all_1236_0_1626 & relation_dom(all_0_14_14) = all_1236_3_1629 & subset(all_206_1_316, all_1236_3_1629) = all_1236_2_1628 & ( ~ (all_1236_2_1628 = 0) | all_1236_0_1626 = all_206_0_315)
% 142.33/84.75 |
% 142.33/84.75 | Applying alpha-rule on (862) yields:
% 142.33/84.75 | (863) relation_composition(empty_set, all_0_14_14) = all_1236_1_1627
% 142.33/84.75 | (864) subset(all_206_1_316, all_1236_3_1629) = all_1236_2_1628
% 142.33/84.75 | (865) ~ (all_1236_2_1628 = 0) | all_1236_0_1626 = all_206_0_315
% 142.33/84.75 | (866) relation_dom(all_0_14_14) = all_1236_3_1629
% 142.33/84.75 | (867) relation_dom(all_1236_1_1627) = all_1236_0_1626
% 142.33/84.75 |
% 142.33/84.75 | Instantiating (541) with all_1242_0_1638, all_1242_1_1639, all_1242_2_1640, all_1242_3_1641 yields:
% 142.33/84.75 | (868) relation_composition(empty_set, empty_set) = all_1242_1_1639 & relation_dom(all_1242_1_1639) = all_1242_0_1638 & subset(all_206_1_316, empty_set) = all_1242_2_1640 & relation(empty_set) = all_1242_3_1641 & ( ~ (all_1242_2_1640 = 0) | ~ (all_1242_3_1641 = 0) | all_1242_0_1638 = all_206_0_315)
% 142.33/84.75 |
% 142.33/84.75 | Applying alpha-rule on (868) yields:
% 142.33/84.75 | (869) relation_dom(all_1242_1_1639) = all_1242_0_1638
% 142.33/84.75 | (870) ~ (all_1242_2_1640 = 0) | ~ (all_1242_3_1641 = 0) | all_1242_0_1638 = all_206_0_315
% 142.33/84.75 | (871) subset(all_206_1_316, empty_set) = all_1242_2_1640
% 142.33/84.75 | (872) relation_composition(empty_set, empty_set) = all_1242_1_1639
% 142.33/84.75 | (873) relation(empty_set) = all_1242_3_1641
% 142.33/84.75 |
% 142.33/84.75 | Instantiating (540) with all_1244_0_1642, all_1244_1_1643, all_1244_2_1644, all_1244_3_1645 yields:
% 142.33/84.75 | (874) relation_composition(empty_set, all_0_14_14) = all_1244_1_1643 & relation_dom(all_1244_1_1643) = all_1244_0_1642 & subset(all_206_1_316, all_0_11_11) = all_1244_2_1644 & relation(all_0_14_14) = all_1244_3_1645 & ( ~ (all_1244_2_1644 = 0) | ~ (all_1244_3_1645 = 0) | all_1244_0_1642 = all_206_0_315)
% 142.33/84.75 |
% 142.33/84.75 | Applying alpha-rule on (874) yields:
% 142.33/84.75 | (875) relation(all_0_14_14) = all_1244_3_1645
% 142.33/84.75 | (876) ~ (all_1244_2_1644 = 0) | ~ (all_1244_3_1645 = 0) | all_1244_0_1642 = all_206_0_315
% 142.33/84.75 | (877) relation_dom(all_1244_1_1643) = all_1244_0_1642
% 142.33/84.75 | (878) relation_composition(empty_set, all_0_14_14) = all_1244_1_1643
% 142.33/84.75 | (879) subset(all_206_1_316, all_0_11_11) = all_1244_2_1644
% 142.33/84.75 |
% 142.33/84.75 | Instantiating (553) with all_1258_0_1671, all_1258_1_1672, all_1258_2_1673, all_1258_3_1674, all_1258_4_1675 yields:
% 142.33/84.75 | (880) relation_rng(all_0_14_14) = all_1258_1_1672 & relation_dom(all_0_14_14) = all_1258_3_1674 & subset(all_209_0_317, all_1258_1_1672) = all_1258_0_1671 & subset(all_209_1_318, all_1258_3_1674) = all_1258_2_1673 & subset(empty_set, all_0_14_14) = all_1258_4_1675 & ( ~ (all_1258_4_1675 = 0) | (all_1258_0_1671 = 0 & all_1258_2_1673 = 0))
% 142.33/84.75 |
% 142.33/84.75 | Applying alpha-rule on (880) yields:
% 142.33/84.75 | (881) subset(all_209_1_318, all_1258_3_1674) = all_1258_2_1673
% 142.33/84.75 | (882) relation_rng(all_0_14_14) = all_1258_1_1672
% 142.33/84.75 | (883) relation_dom(all_0_14_14) = all_1258_3_1674
% 142.33/84.75 | (884) subset(all_209_0_317, all_1258_1_1672) = all_1258_0_1671
% 142.33/84.75 | (885) ~ (all_1258_4_1675 = 0) | (all_1258_0_1671 = 0 & all_1258_2_1673 = 0)
% 142.33/84.75 | (886) subset(empty_set, all_0_14_14) = all_1258_4_1675
% 142.33/84.75 |
% 142.33/84.75 | Instantiating (551) with all_1260_0_1676, all_1260_1_1677, all_1260_2_1678, all_1260_3_1679, all_1260_4_1680 yields:
% 142.33/84.75 | (887) relation_rng(all_0_14_14) = all_1260_1_1677 & subset(all_209_0_317, all_1260_1_1677) = all_1260_0_1676 & subset(all_209_1_318, all_0_11_11) = all_1260_2_1678 & subset(empty_set, all_0_14_14) = all_1260_3_1679 & relation(all_0_14_14) = all_1260_4_1680 & ( ~ (all_1260_3_1679 = 0) | ~ (all_1260_4_1680 = 0) | (all_1260_0_1676 = 0 & all_1260_2_1678 = 0))
% 142.33/84.75 |
% 142.33/84.75 | Applying alpha-rule on (887) yields:
% 142.33/84.75 | (888) subset(all_209_0_317, all_1260_1_1677) = all_1260_0_1676
% 142.33/84.75 | (889) relation_rng(all_0_14_14) = all_1260_1_1677
% 142.33/84.75 | (890) subset(all_209_1_318, all_0_11_11) = all_1260_2_1678
% 142.33/84.75 | (891) relation(all_0_14_14) = all_1260_4_1680
% 142.33/84.75 | (892) ~ (all_1260_3_1679 = 0) | ~ (all_1260_4_1680 = 0) | (all_1260_0_1676 = 0 & all_1260_2_1678 = 0)
% 142.33/84.75 | (893) subset(empty_set, all_0_14_14) = all_1260_3_1679
% 142.33/84.75 |
% 142.33/84.75 | Instantiating (550) with all_1278_0_1721, all_1278_1_1722, all_1278_2_1723, all_1278_3_1724, all_1278_4_1725 yields:
% 142.33/84.75 | (894) relation_dom(empty_set) = all_1278_2_1723 & subset(all_209_0_317, empty_set) = all_1278_0_1721 & subset(all_209_1_318, all_1278_2_1723) = all_1278_1_1722 & subset(empty_set, empty_set) = all_1278_3_1724 & relation(empty_set) = all_1278_4_1725 & ( ~ (all_1278_3_1724 = 0) | ~ (all_1278_4_1725 = 0) | (all_1278_0_1721 = 0 & all_1278_1_1722 = 0))
% 142.33/84.75 |
% 142.33/84.75 | Applying alpha-rule on (894) yields:
% 142.33/84.75 | (895) subset(empty_set, empty_set) = all_1278_3_1724
% 142.33/84.75 | (896) ~ (all_1278_3_1724 = 0) | ~ (all_1278_4_1725 = 0) | (all_1278_0_1721 = 0 & all_1278_1_1722 = 0)
% 142.33/84.75 | (897) subset(all_209_1_318, all_1278_2_1723) = all_1278_1_1722
% 142.33/84.75 | (898) relation(empty_set) = all_1278_4_1725
% 142.33/84.75 | (899) relation_dom(empty_set) = all_1278_2_1723
% 142.33/84.75 | (900) subset(all_209_0_317, empty_set) = all_1278_0_1721
% 142.33/84.75 |
% 142.33/84.75 | Instantiating (552) with all_1280_0_1726, all_1280_1_1727, all_1280_2_1728, all_1280_3_1729, all_1280_4_1730 yields:
% 142.33/84.75 | (901) relation_rng(empty_set) = all_1280_1_1727 & subset(all_209_0_317, all_1280_1_1727) = all_1280_0_1726 & subset(all_209_1_318, empty_set) = all_1280_2_1728 & subset(empty_set, empty_set) = all_1280_3_1729 & relation(empty_set) = all_1280_4_1730 & ( ~ (all_1280_3_1729 = 0) | ~ (all_1280_4_1730 = 0) | (all_1280_0_1726 = 0 & all_1280_2_1728 = 0))
% 142.33/84.75 |
% 142.33/84.75 | Applying alpha-rule on (901) yields:
% 142.33/84.75 | (902) subset(empty_set, empty_set) = all_1280_3_1729
% 142.33/84.75 | (903) ~ (all_1280_3_1729 = 0) | ~ (all_1280_4_1730 = 0) | (all_1280_0_1726 = 0 & all_1280_2_1728 = 0)
% 142.33/84.75 | (904) relation(empty_set) = all_1280_4_1730
% 142.33/84.75 | (905) relation_rng(empty_set) = all_1280_1_1727
% 142.33/84.75 | (906) subset(all_209_0_317, all_1280_1_1727) = all_1280_0_1726
% 142.33/84.75 | (907) subset(all_209_1_318, empty_set) = all_1280_2_1728
% 142.33/84.75 |
% 142.33/84.75 | Instantiating (562) with all_1287_0_1741, all_1287_1_1742, all_1287_2_1743, all_1287_3_1744 yields:
% 142.33/84.75 | (908) relation_composition(all_0_14_14, all_0_14_14) = all_1287_1_1742 & relation_dom(all_1287_1_1742) = all_1287_0_1741 & relation_dom(all_0_14_14) = all_1287_3_1744 & subset(all_227_1_340, all_1287_3_1744) = all_1287_2_1743 & ( ~ (all_1287_2_1743 = 0) | all_1287_0_1741 = all_227_0_339)
% 142.33/84.75 |
% 142.33/84.75 | Applying alpha-rule on (908) yields:
% 142.33/84.75 | (909) ~ (all_1287_2_1743 = 0) | all_1287_0_1741 = all_227_0_339
% 142.33/84.75 | (910) subset(all_227_1_340, all_1287_3_1744) = all_1287_2_1743
% 142.33/84.75 | (911) relation_composition(all_0_14_14, all_0_14_14) = all_1287_1_1742
% 142.33/84.75 | (912) relation_dom(all_1287_1_1742) = all_1287_0_1741
% 142.33/84.75 | (913) relation_dom(all_0_14_14) = all_1287_3_1744
% 142.33/84.75 |
% 142.33/84.75 | Instantiating (561) with all_1293_0_1753, all_1293_1_1754, all_1293_2_1755, all_1293_3_1756 yields:
% 142.33/84.75 | (914) relation_composition(all_0_14_14, empty_set) = all_1293_1_1754 & relation_dom(all_1293_1_1754) = all_1293_0_1753 & subset(all_227_1_340, empty_set) = all_1293_2_1755 & relation(empty_set) = all_1293_3_1756 & ( ~ (all_1293_2_1755 = 0) | ~ (all_1293_3_1756 = 0) | all_1293_0_1753 = all_227_0_339)
% 142.33/84.75 |
% 142.33/84.75 | Applying alpha-rule on (914) yields:
% 142.33/84.75 | (915) subset(all_227_1_340, empty_set) = all_1293_2_1755
% 142.33/84.75 | (916) relation_composition(all_0_14_14, empty_set) = all_1293_1_1754
% 142.33/84.75 | (917) relation(empty_set) = all_1293_3_1756
% 142.33/84.75 | (918) ~ (all_1293_2_1755 = 0) | ~ (all_1293_3_1756 = 0) | all_1293_0_1753 = all_227_0_339
% 142.33/84.75 | (919) relation_dom(all_1293_1_1754) = all_1293_0_1753
% 142.33/84.75 |
% 142.33/84.75 | Instantiating (560) with all_1295_0_1757, all_1295_1_1758, all_1295_2_1759, all_1295_3_1760 yields:
% 142.33/84.75 | (920) relation_composition(all_0_14_14, all_0_14_14) = all_1295_1_1758 & relation_dom(all_1295_1_1758) = all_1295_0_1757 & subset(all_227_1_340, all_0_11_11) = all_1295_2_1759 & relation(all_0_14_14) = all_1295_3_1760 & ( ~ (all_1295_2_1759 = 0) | ~ (all_1295_3_1760 = 0) | all_1295_0_1757 = all_227_0_339)
% 142.33/84.75 |
% 142.33/84.75 | Applying alpha-rule on (920) yields:
% 142.33/84.75 | (921) relation_composition(all_0_14_14, all_0_14_14) = all_1295_1_1758
% 142.33/84.75 | (922) subset(all_227_1_340, all_0_11_11) = all_1295_2_1759
% 142.33/84.75 | (923) relation_dom(all_1295_1_1758) = all_1295_0_1757
% 142.33/84.75 | (924) ~ (all_1295_2_1759 = 0) | ~ (all_1295_3_1760 = 0) | all_1295_0_1757 = all_227_0_339
% 142.33/84.75 | (925) relation(all_0_14_14) = all_1295_3_1760
% 142.33/84.75 |
% 142.33/84.75 | Instantiating (578) with all_1317_0_1801, all_1317_1_1802, all_1317_2_1803, all_1317_3_1804 yields:
% 142.33/84.75 | (926) relation_composition(empty_set, empty_set) = all_1317_1_1802 & relation_rng(all_1317_1_1802) = all_1317_0_1801 & subset(all_234_1_346, empty_set) = all_1317_2_1803 & relation(empty_set) = all_1317_3_1804 & ( ~ (all_1317_2_1803 = 0) | ~ (all_1317_3_1804 = 0) | all_1317_0_1801 = all_234_0_345)
% 142.33/84.75 |
% 142.33/84.75 | Applying alpha-rule on (926) yields:
% 142.33/84.75 | (927) relation(empty_set) = all_1317_3_1804
% 142.33/84.75 | (928) relation_composition(empty_set, empty_set) = all_1317_1_1802
% 142.33/84.75 | (929) ~ (all_1317_2_1803 = 0) | ~ (all_1317_3_1804 = 0) | all_1317_0_1801 = all_234_0_345
% 142.33/84.75 | (930) subset(all_234_1_346, empty_set) = all_1317_2_1803
% 142.33/84.75 | (931) relation_rng(all_1317_1_1802) = all_1317_0_1801
% 142.33/84.75 |
% 142.33/84.75 | Instantiating (591) with all_1325_0_1817, all_1325_1_1818, all_1325_2_1819, all_1325_3_1820 yields:
% 142.33/84.75 | (932) relation_composition(all_0_7_7, all_0_14_14) = all_1325_1_1818 & relation_dom(all_1325_1_1818) = all_1325_0_1817 & relation_dom(all_0_14_14) = all_1325_3_1820 & subset(all_269_1_392, all_1325_3_1820) = all_1325_2_1819 & ( ~ (all_1325_2_1819 = 0) | all_1325_0_1817 = all_269_0_391)
% 142.33/84.75 |
% 142.33/84.75 | Applying alpha-rule on (932) yields:
% 142.33/84.75 | (933) subset(all_269_1_392, all_1325_3_1820) = all_1325_2_1819
% 142.33/84.75 | (934) relation_dom(all_0_14_14) = all_1325_3_1820
% 142.33/84.75 | (935) ~ (all_1325_2_1819 = 0) | all_1325_0_1817 = all_269_0_391
% 142.33/84.75 | (936) relation_dom(all_1325_1_1818) = all_1325_0_1817
% 142.33/84.75 | (937) relation_composition(all_0_7_7, all_0_14_14) = all_1325_1_1818
% 142.33/84.75 |
% 142.33/84.75 | Instantiating (590) with all_1331_0_1829, all_1331_1_1830, all_1331_2_1831, all_1331_3_1832 yields:
% 142.33/84.75 | (938) relation_composition(all_0_7_7, empty_set) = all_1331_1_1830 & relation_dom(all_1331_1_1830) = all_1331_0_1829 & subset(all_269_1_392, empty_set) = all_1331_2_1831 & relation(empty_set) = all_1331_3_1832 & ( ~ (all_1331_2_1831 = 0) | ~ (all_1331_3_1832 = 0) | all_1331_0_1829 = all_269_0_391)
% 142.33/84.75 |
% 142.33/84.75 | Applying alpha-rule on (938) yields:
% 142.33/84.75 | (939) relation_dom(all_1331_1_1830) = all_1331_0_1829
% 142.33/84.75 | (940) ~ (all_1331_2_1831 = 0) | ~ (all_1331_3_1832 = 0) | all_1331_0_1829 = all_269_0_391
% 142.33/84.75 | (941) subset(all_269_1_392, empty_set) = all_1331_2_1831
% 142.33/84.75 | (942) relation_composition(all_0_7_7, empty_set) = all_1331_1_1830
% 142.33/84.75 | (943) relation(empty_set) = all_1331_3_1832
% 142.33/84.75 |
% 142.33/84.75 | Instantiating (589) with all_1333_0_1833, all_1333_1_1834, all_1333_2_1835, all_1333_3_1836 yields:
% 142.33/84.75 | (944) relation_composition(all_0_7_7, all_0_14_14) = all_1333_1_1834 & relation_dom(all_1333_1_1834) = all_1333_0_1833 & subset(all_269_1_392, all_0_11_11) = all_1333_2_1835 & relation(all_0_14_14) = all_1333_3_1836 & ( ~ (all_1333_2_1835 = 0) | ~ (all_1333_3_1836 = 0) | all_1333_0_1833 = all_269_0_391)
% 142.33/84.75 |
% 142.33/84.75 | Applying alpha-rule on (944) yields:
% 142.33/84.75 | (945) ~ (all_1333_2_1835 = 0) | ~ (all_1333_3_1836 = 0) | all_1333_0_1833 = all_269_0_391
% 142.33/84.75 | (946) relation_composition(all_0_7_7, all_0_14_14) = all_1333_1_1834
% 142.33/84.75 | (947) subset(all_269_1_392, all_0_11_11) = all_1333_2_1835
% 142.33/84.75 | (948) relation(all_0_14_14) = all_1333_3_1836
% 142.33/84.75 | (949) relation_dom(all_1333_1_1834) = all_1333_0_1833
% 142.33/84.75 |
% 142.33/84.75 | Instantiating (608) with all_1373_0_1897, all_1373_1_1898, all_1373_2_1899, all_1373_3_1900, all_1373_4_1901 yields:
% 142.33/84.75 | (950) relation_rng(all_0_14_14) = all_1373_1_1898 & relation_dom(all_0_14_14) = all_1373_3_1900 & subset(all_293_0_418, all_1373_1_1898) = all_1373_0_1897 & subset(all_293_1_419, all_1373_3_1900) = all_1373_2_1899 & subset(all_0_4_4, all_0_14_14) = all_1373_4_1901 & ( ~ (all_1373_4_1901 = 0) | (all_1373_0_1897 = 0 & all_1373_2_1899 = 0))
% 142.33/84.75 |
% 142.33/84.75 | Applying alpha-rule on (950) yields:
% 142.33/84.75 | (951) subset(all_0_4_4, all_0_14_14) = all_1373_4_1901
% 142.33/84.75 | (952) subset(all_293_0_418, all_1373_1_1898) = all_1373_0_1897
% 142.33/84.75 | (953) subset(all_293_1_419, all_1373_3_1900) = all_1373_2_1899
% 142.33/84.75 | (954) relation_dom(all_0_14_14) = all_1373_3_1900
% 142.33/84.75 | (955) ~ (all_1373_4_1901 = 0) | (all_1373_0_1897 = 0 & all_1373_2_1899 = 0)
% 142.33/84.75 | (956) relation_rng(all_0_14_14) = all_1373_1_1898
% 142.33/84.75 |
% 142.33/84.75 | Instantiating (606) with all_1375_0_1902, all_1375_1_1903, all_1375_2_1904, all_1375_3_1905, all_1375_4_1906 yields:
% 142.33/84.75 | (957) relation_rng(all_0_14_14) = all_1375_1_1903 & subset(all_293_0_418, all_1375_1_1903) = all_1375_0_1902 & subset(all_293_1_419, all_0_11_11) = all_1375_2_1904 & subset(all_0_4_4, all_0_14_14) = all_1375_3_1905 & relation(all_0_14_14) = all_1375_4_1906 & ( ~ (all_1375_3_1905 = 0) | ~ (all_1375_4_1906 = 0) | (all_1375_0_1902 = 0 & all_1375_2_1904 = 0))
% 142.33/84.75 |
% 142.33/84.75 | Applying alpha-rule on (957) yields:
% 142.33/84.76 | (958) subset(all_0_4_4, all_0_14_14) = all_1375_3_1905
% 142.33/84.76 | (959) subset(all_293_1_419, all_0_11_11) = all_1375_2_1904
% 142.33/84.76 | (960) subset(all_293_0_418, all_1375_1_1903) = all_1375_0_1902
% 142.33/84.76 | (961) relation_rng(all_0_14_14) = all_1375_1_1903
% 142.33/84.76 | (962) ~ (all_1375_3_1905 = 0) | ~ (all_1375_4_1906 = 0) | (all_1375_0_1902 = 0 & all_1375_2_1904 = 0)
% 142.33/84.76 | (963) relation(all_0_14_14) = all_1375_4_1906
% 142.33/84.76 |
% 142.33/84.76 | Instantiating (607) with all_1379_0_1912, all_1379_1_1913, all_1379_2_1914, all_1379_3_1915, all_1379_4_1916 yields:
% 142.33/84.76 | (964) relation_rng(empty_set) = all_1379_1_1913 & subset(all_293_0_418, all_1379_1_1913) = all_1379_0_1912 & subset(all_293_1_419, empty_set) = all_1379_2_1914 & subset(all_0_4_4, empty_set) = all_1379_3_1915 & relation(empty_set) = all_1379_4_1916 & ( ~ (all_1379_3_1915 = 0) | ~ (all_1379_4_1916 = 0) | (all_1379_0_1912 = 0 & all_1379_2_1914 = 0))
% 142.33/84.76 |
% 142.33/84.76 | Applying alpha-rule on (964) yields:
% 142.33/84.76 | (965) subset(all_0_4_4, empty_set) = all_1379_3_1915
% 142.33/84.76 | (966) ~ (all_1379_3_1915 = 0) | ~ (all_1379_4_1916 = 0) | (all_1379_0_1912 = 0 & all_1379_2_1914 = 0)
% 142.33/84.76 | (967) relation(empty_set) = all_1379_4_1916
% 142.33/84.76 | (968) subset(all_293_0_418, all_1379_1_1913) = all_1379_0_1912
% 142.33/84.76 | (969) subset(all_293_1_419, empty_set) = all_1379_2_1914
% 142.33/84.76 | (970) relation_rng(empty_set) = all_1379_1_1913
% 142.33/84.76 |
% 142.33/84.76 | Instantiating (605) with all_1391_0_1942, all_1391_1_1943, all_1391_2_1944, all_1391_3_1945, all_1391_4_1946 yields:
% 142.33/84.76 | (971) relation_dom(empty_set) = all_1391_2_1944 & subset(all_293_0_418, empty_set) = all_1391_0_1942 & subset(all_293_1_419, all_1391_2_1944) = all_1391_1_1943 & subset(all_0_4_4, empty_set) = all_1391_3_1945 & relation(empty_set) = all_1391_4_1946 & ( ~ (all_1391_3_1945 = 0) | ~ (all_1391_4_1946 = 0) | (all_1391_0_1942 = 0 & all_1391_1_1943 = 0))
% 142.33/84.76 |
% 142.33/84.76 | Applying alpha-rule on (971) yields:
% 142.33/84.76 | (972) subset(all_293_0_418, empty_set) = all_1391_0_1942
% 142.33/84.76 | (973) relation_dom(empty_set) = all_1391_2_1944
% 142.33/84.76 | (974) subset(all_0_4_4, empty_set) = all_1391_3_1945
% 142.33/84.76 | (975) subset(all_293_1_419, all_1391_2_1944) = all_1391_1_1943
% 142.33/84.76 | (976) relation(empty_set) = all_1391_4_1946
% 142.33/84.76 | (977) ~ (all_1391_3_1945 = 0) | ~ (all_1391_4_1946 = 0) | (all_1391_0_1942 = 0 & all_1391_1_1943 = 0)
% 142.33/84.76 |
% 142.33/84.76 | Instantiating (615) with all_1407_0_1975, all_1407_1_1976, all_1407_2_1977, all_1407_3_1978 yields:
% 142.33/84.76 | (978) relation_composition(empty_set, all_0_4_4) = all_1407_1_1976 & relation_rng(all_1407_1_1976) = all_1407_0_1975 & subset(all_296_1_421, empty_set) = all_1407_2_1977 & relation(empty_set) = all_1407_3_1978 & ( ~ (all_1407_2_1977 = 0) | ~ (all_1407_3_1978 = 0) | all_1407_0_1975 = all_296_0_420)
% 142.33/84.76 |
% 142.33/84.76 | Applying alpha-rule on (978) yields:
% 142.33/84.76 | (979) relation_composition(empty_set, all_0_4_4) = all_1407_1_1976
% 142.33/84.76 | (980) subset(all_296_1_421, empty_set) = all_1407_2_1977
% 142.33/84.76 | (981) relation_rng(all_1407_1_1976) = all_1407_0_1975
% 142.33/84.76 | (982) relation(empty_set) = all_1407_3_1978
% 142.33/84.76 | (983) ~ (all_1407_2_1977 = 0) | ~ (all_1407_3_1978 = 0) | all_1407_0_1975 = all_296_0_420
% 142.33/84.76 |
% 142.33/84.76 | Instantiating (623) with all_1413_0_1987, all_1413_1_1988, all_1413_2_1989, all_1413_3_1990 yields:
% 142.33/84.76 | (984) relation_composition(all_0_4_4, empty_set) = all_1413_1_1988 & relation_dom(all_1413_1_1988) = all_1413_0_1987 & subset(all_301_1_425, empty_set) = all_1413_2_1989 & relation(empty_set) = all_1413_3_1990 & ( ~ (all_1413_2_1989 = 0) | ~ (all_1413_3_1990 = 0) | all_1413_0_1987 = all_301_0_424)
% 142.33/84.76 |
% 142.33/84.76 | Applying alpha-rule on (984) yields:
% 142.33/84.76 | (985) relation_dom(all_1413_1_1988) = all_1413_0_1987
% 142.33/84.76 | (986) ~ (all_1413_2_1989 = 0) | ~ (all_1413_3_1990 = 0) | all_1413_0_1987 = all_301_0_424
% 142.33/84.76 | (987) subset(all_301_1_425, empty_set) = all_1413_2_1989
% 142.33/84.76 | (988) relation_composition(all_0_4_4, empty_set) = all_1413_1_1988
% 142.33/84.76 | (989) relation(empty_set) = all_1413_3_1990
% 142.33/84.76 |
% 142.33/84.76 | Instantiating (624) with all_1415_0_1991, all_1415_1_1992, all_1415_2_1993, all_1415_3_1994 yields:
% 142.33/84.76 | (990) relation_composition(all_0_4_4, all_0_14_14) = all_1415_1_1992 & relation_dom(all_1415_1_1992) = all_1415_0_1991 & relation_dom(all_0_14_14) = all_1415_3_1994 & subset(all_301_1_425, all_1415_3_1994) = all_1415_2_1993 & ( ~ (all_1415_2_1993 = 0) | all_1415_0_1991 = all_301_0_424)
% 142.33/84.76 |
% 142.33/84.76 | Applying alpha-rule on (990) yields:
% 142.33/84.76 | (991) ~ (all_1415_2_1993 = 0) | all_1415_0_1991 = all_301_0_424
% 142.33/84.76 | (992) relation_dom(all_0_14_14) = all_1415_3_1994
% 142.33/84.76 | (993) subset(all_301_1_425, all_1415_3_1994) = all_1415_2_1993
% 142.33/84.76 | (994) relation_composition(all_0_4_4, all_0_14_14) = all_1415_1_1992
% 142.33/84.76 | (995) relation_dom(all_1415_1_1992) = all_1415_0_1991
% 142.33/84.76 |
% 142.33/84.76 | Instantiating (622) with all_1419_0_1999, all_1419_1_2000, all_1419_2_2001, all_1419_3_2002 yields:
% 142.33/84.76 | (996) relation_composition(all_0_4_4, all_0_14_14) = all_1419_1_2000 & relation_dom(all_1419_1_2000) = all_1419_0_1999 & subset(all_301_1_425, all_0_11_11) = all_1419_2_2001 & relation(all_0_14_14) = all_1419_3_2002 & ( ~ (all_1419_2_2001 = 0) | ~ (all_1419_3_2002 = 0) | all_1419_0_1999 = all_301_0_424)
% 142.33/84.76 |
% 142.33/84.76 | Applying alpha-rule on (996) yields:
% 142.33/84.76 | (997) relation_composition(all_0_4_4, all_0_14_14) = all_1419_1_2000
% 142.33/84.76 | (998) ~ (all_1419_2_2001 = 0) | ~ (all_1419_3_2002 = 0) | all_1419_0_1999 = all_301_0_424
% 142.33/84.76 | (999) relation_dom(all_1419_1_2000) = all_1419_0_1999
% 142.33/84.76 | (1000) subset(all_301_1_425, all_0_11_11) = all_1419_2_2001
% 142.33/84.76 | (1001) relation(all_0_14_14) = all_1419_3_2002
% 142.33/84.76 |
% 142.33/84.76 | Instantiating (635) with all_1446_0_2041, all_1446_1_2042, all_1446_2_2043, all_1446_3_2044, all_1446_4_2045 yields:
% 142.33/84.76 | (1002) relation_rng(all_0_14_14) = all_1446_1_2042 & relation_dom(all_0_14_14) = all_1446_3_2044 & subset(all_348_0_474, all_1446_1_2042) = all_1446_0_2041 & subset(all_348_1_475, all_1446_3_2044) = all_1446_2_2043 & subset(all_0_7_7, all_0_14_14) = all_1446_4_2045 & ( ~ (all_1446_4_2045 = 0) | (all_1446_0_2041 = 0 & all_1446_2_2043 = 0))
% 142.33/84.76 |
% 142.33/84.76 | Applying alpha-rule on (1002) yields:
% 142.33/84.76 | (1003) ~ (all_1446_4_2045 = 0) | (all_1446_0_2041 = 0 & all_1446_2_2043 = 0)
% 142.33/84.76 | (1004) subset(all_0_7_7, all_0_14_14) = all_1446_4_2045
% 142.33/84.76 | (1005) relation_dom(all_0_14_14) = all_1446_3_2044
% 142.33/84.76 | (1006) subset(all_348_0_474, all_1446_1_2042) = all_1446_0_2041
% 142.33/84.76 | (1007) subset(all_348_1_475, all_1446_3_2044) = all_1446_2_2043
% 142.33/84.76 | (1008) relation_rng(all_0_14_14) = all_1446_1_2042
% 142.33/84.76 |
% 142.33/84.76 | Instantiating (634) with all_1454_0_2061, all_1454_1_2062, all_1454_2_2063, all_1454_3_2064, all_1454_4_2065 yields:
% 142.33/84.76 | (1009) relation_rng(empty_set) = all_1454_1_2062 & subset(all_348_0_474, all_1454_1_2062) = all_1454_0_2061 & subset(all_348_1_475, empty_set) = all_1454_2_2063 & subset(all_0_7_7, empty_set) = all_1454_3_2064 & relation(empty_set) = all_1454_4_2065 & ( ~ (all_1454_3_2064 = 0) | ~ (all_1454_4_2065 = 0) | (all_1454_0_2061 = 0 & all_1454_2_2063 = 0))
% 142.33/84.76 |
% 142.33/84.76 | Applying alpha-rule on (1009) yields:
% 142.33/84.76 | (1010) ~ (all_1454_3_2064 = 0) | ~ (all_1454_4_2065 = 0) | (all_1454_0_2061 = 0 & all_1454_2_2063 = 0)
% 142.33/84.76 | (1011) relation(empty_set) = all_1454_4_2065
% 142.33/84.76 | (1012) subset(all_0_7_7, empty_set) = all_1454_3_2064
% 142.33/84.76 | (1013) subset(all_348_1_475, empty_set) = all_1454_2_2063
% 142.33/84.76 | (1014) relation_rng(empty_set) = all_1454_1_2062
% 142.33/84.76 | (1015) subset(all_348_0_474, all_1454_1_2062) = all_1454_0_2061
% 142.33/84.76 |
% 142.33/84.76 | Instantiating (633) with all_1456_0_2066, all_1456_1_2067, all_1456_2_2068, all_1456_3_2069, all_1456_4_2070 yields:
% 142.33/84.76 | (1016) relation_rng(all_0_14_14) = all_1456_1_2067 & subset(all_348_0_474, all_1456_1_2067) = all_1456_0_2066 & subset(all_348_1_475, all_0_11_11) = all_1456_2_2068 & subset(all_0_7_7, all_0_14_14) = all_1456_3_2069 & relation(all_0_14_14) = all_1456_4_2070 & ( ~ (all_1456_3_2069 = 0) | ~ (all_1456_4_2070 = 0) | (all_1456_0_2066 = 0 & all_1456_2_2068 = 0))
% 142.33/84.76 |
% 142.33/84.76 | Applying alpha-rule on (1016) yields:
% 142.33/84.76 | (1017) relation_rng(all_0_14_14) = all_1456_1_2067
% 142.33/84.76 | (1018) subset(all_348_0_474, all_1456_1_2067) = all_1456_0_2066
% 142.33/84.76 | (1019) subset(all_348_1_475, all_0_11_11) = all_1456_2_2068
% 142.33/84.76 | (1020) subset(all_0_7_7, all_0_14_14) = all_1456_3_2069
% 142.33/84.76 | (1021) ~ (all_1456_3_2069 = 0) | ~ (all_1456_4_2070 = 0) | (all_1456_0_2066 = 0 & all_1456_2_2068 = 0)
% 142.33/84.76 | (1022) relation(all_0_14_14) = all_1456_4_2070
% 142.33/84.76 |
% 142.33/84.76 | Instantiating (632) with all_1466_0_2091, all_1466_1_2092, all_1466_2_2093, all_1466_3_2094, all_1466_4_2095 yields:
% 142.33/84.76 | (1023) relation_dom(empty_set) = all_1466_2_2093 & subset(all_348_0_474, empty_set) = all_1466_0_2091 & subset(all_348_1_475, all_1466_2_2093) = all_1466_1_2092 & subset(all_0_7_7, empty_set) = all_1466_3_2094 & relation(empty_set) = all_1466_4_2095 & ( ~ (all_1466_3_2094 = 0) | ~ (all_1466_4_2095 = 0) | (all_1466_0_2091 = 0 & all_1466_1_2092 = 0))
% 142.33/84.76 |
% 142.33/84.76 | Applying alpha-rule on (1023) yields:
% 142.33/84.76 | (1024) ~ (all_1466_3_2094 = 0) | ~ (all_1466_4_2095 = 0) | (all_1466_0_2091 = 0 & all_1466_1_2092 = 0)
% 142.33/84.76 | (1025) subset(all_348_1_475, all_1466_2_2093) = all_1466_1_2092
% 142.33/84.76 | (1026) relation_dom(empty_set) = all_1466_2_2093
% 142.33/84.76 | (1027) subset(all_348_0_474, empty_set) = all_1466_0_2091
% 142.33/84.76 | (1028) relation(empty_set) = all_1466_4_2095
% 142.33/84.76 | (1029) subset(all_0_7_7, empty_set) = all_1466_3_2094
% 142.33/84.76 |
% 142.33/84.76 | Instantiating (642) with all_1480_0_2122, all_1480_1_2123, all_1480_2_2124, all_1480_3_2125 yields:
% 142.33/84.76 | (1030) relation_composition(empty_set, all_0_7_7) = all_1480_1_2123 & relation_rng(all_1480_1_2123) = all_1480_0_2122 & subset(all_355_1_482, empty_set) = all_1480_2_2124 & relation(empty_set) = all_1480_3_2125 & ( ~ (all_1480_2_2124 = 0) | ~ (all_1480_3_2125 = 0) | all_1480_0_2122 = all_355_0_481)
% 142.33/84.76 |
% 142.33/84.76 | Applying alpha-rule on (1030) yields:
% 142.33/84.76 | (1031) relation(empty_set) = all_1480_3_2125
% 142.33/84.76 | (1032) relation_composition(empty_set, all_0_7_7) = all_1480_1_2123
% 142.33/84.76 | (1033) ~ (all_1480_2_2124 = 0) | ~ (all_1480_3_2125 = 0) | all_1480_0_2122 = all_355_0_481
% 142.33/84.76 | (1034) subset(all_355_1_482, empty_set) = all_1480_2_2124
% 142.33/84.76 | (1035) relation_rng(all_1480_1_2123) = all_1480_0_2122
% 142.33/84.76 |
% 142.33/84.76 | Instantiating (653) with all_1490_0_2143, all_1490_1_2144, all_1490_2_2145, all_1490_3_2146, all_1490_4_2147 yields:
% 142.33/84.76 | (1036) relation_rng(all_0_14_14) = all_1490_1_2144 & relation_dom(all_0_14_14) = all_1490_3_2146 & subset(all_358_0_483, all_1490_1_2144) = all_1490_0_2143 & subset(all_358_1_484, all_1490_3_2146) = all_1490_2_2145 & subset(all_0_14_14, all_0_14_14) = all_1490_4_2147 & ( ~ (all_1490_4_2147 = 0) | (all_1490_0_2143 = 0 & all_1490_2_2145 = 0))
% 142.33/84.76 |
% 142.33/84.76 | Applying alpha-rule on (1036) yields:
% 142.33/84.76 | (1037) relation_dom(all_0_14_14) = all_1490_3_2146
% 142.33/84.76 | (1038) relation_rng(all_0_14_14) = all_1490_1_2144
% 142.33/84.76 | (1039) subset(all_358_0_483, all_1490_1_2144) = all_1490_0_2143
% 142.33/84.76 | (1040) subset(all_358_1_484, all_1490_3_2146) = all_1490_2_2145
% 142.33/84.76 | (1041) subset(all_0_14_14, all_0_14_14) = all_1490_4_2147
% 142.33/84.76 | (1042) ~ (all_1490_4_2147 = 0) | (all_1490_0_2143 = 0 & all_1490_2_2145 = 0)
% 142.33/84.76 |
% 142.33/84.76 | Instantiating (651) with all_1492_0_2148, all_1492_1_2149, all_1492_2_2150, all_1492_3_2151, all_1492_4_2152 yields:
% 142.33/84.76 | (1043) relation_rng(all_0_14_14) = all_1492_1_2149 & subset(all_358_0_483, all_1492_1_2149) = all_1492_0_2148 & subset(all_358_1_484, all_0_11_11) = all_1492_2_2150 & subset(all_0_14_14, all_0_14_14) = all_1492_3_2151 & relation(all_0_14_14) = all_1492_4_2152 & ( ~ (all_1492_3_2151 = 0) | ~ (all_1492_4_2152 = 0) | (all_1492_0_2148 = 0 & all_1492_2_2150 = 0))
% 142.33/84.76 |
% 142.33/84.76 | Applying alpha-rule on (1043) yields:
% 142.33/84.76 | (1044) subset(all_358_0_483, all_1492_1_2149) = all_1492_0_2148
% 142.33/84.76 | (1045) relation_rng(all_0_14_14) = all_1492_1_2149
% 142.33/84.76 | (1046) subset(all_0_14_14, all_0_14_14) = all_1492_3_2151
% 142.33/84.76 | (1047) relation(all_0_14_14) = all_1492_4_2152
% 142.33/84.76 | (1048) subset(all_358_1_484, all_0_11_11) = all_1492_2_2150
% 142.33/84.76 | (1049) ~ (all_1492_3_2151 = 0) | ~ (all_1492_4_2152 = 0) | (all_1492_0_2148 = 0 & all_1492_2_2150 = 0)
% 142.33/84.76 |
% 142.33/84.76 | Instantiating (650) with all_1500_0_2168, all_1500_1_2169, all_1500_2_2170, all_1500_3_2171, all_1500_4_2172 yields:
% 142.33/84.76 | (1050) relation_dom(empty_set) = all_1500_2_2170 & subset(all_358_0_483, empty_set) = all_1500_0_2168 & subset(all_358_1_484, all_1500_2_2170) = all_1500_1_2169 & subset(all_0_14_14, empty_set) = all_1500_3_2171 & relation(empty_set) = all_1500_4_2172 & ( ~ (all_1500_3_2171 = 0) | ~ (all_1500_4_2172 = 0) | (all_1500_0_2168 = 0 & all_1500_1_2169 = 0))
% 142.33/84.76 |
% 142.33/84.76 | Applying alpha-rule on (1050) yields:
% 142.33/84.76 | (1051) ~ (all_1500_3_2171 = 0) | ~ (all_1500_4_2172 = 0) | (all_1500_0_2168 = 0 & all_1500_1_2169 = 0)
% 142.33/84.76 | (1052) relation(empty_set) = all_1500_4_2172
% 142.33/84.76 | (1053) relation_dom(empty_set) = all_1500_2_2170
% 142.33/84.76 | (1054) subset(all_358_0_483, empty_set) = all_1500_0_2168
% 142.33/84.76 | (1055) subset(all_0_14_14, empty_set) = all_1500_3_2171
% 142.33/84.77 | (1056) subset(all_358_1_484, all_1500_2_2170) = all_1500_1_2169
% 142.33/84.77 |
% 142.33/84.77 | Instantiating (652) with all_1506_0_2183, all_1506_1_2184, all_1506_2_2185, all_1506_3_2186, all_1506_4_2187 yields:
% 142.33/84.77 | (1057) relation_rng(empty_set) = all_1506_1_2184 & subset(all_358_0_483, all_1506_1_2184) = all_1506_0_2183 & subset(all_358_1_484, empty_set) = all_1506_2_2185 & subset(all_0_14_14, empty_set) = all_1506_3_2186 & relation(empty_set) = all_1506_4_2187 & ( ~ (all_1506_3_2186 = 0) | ~ (all_1506_4_2187 = 0) | (all_1506_0_2183 = 0 & all_1506_2_2185 = 0))
% 142.33/84.77 |
% 142.33/84.77 | Applying alpha-rule on (1057) yields:
% 142.33/84.77 | (1058) relation_rng(empty_set) = all_1506_1_2184
% 142.33/84.77 | (1059) ~ (all_1506_3_2186 = 0) | ~ (all_1506_4_2187 = 0) | (all_1506_0_2183 = 0 & all_1506_2_2185 = 0)
% 142.33/84.77 | (1060) relation(empty_set) = all_1506_4_2187
% 142.33/84.77 | (1061) subset(all_358_0_483, all_1506_1_2184) = all_1506_0_2183
% 142.33/84.77 | (1062) subset(all_358_1_484, empty_set) = all_1506_2_2185
% 142.33/84.77 | (1063) subset(all_0_14_14, empty_set) = all_1506_3_2186
% 142.33/84.77 |
% 142.33/84.77 | Instantiating (660) with all_1526_0_2228, all_1526_1_2229, all_1526_2_2230, all_1526_3_2231 yields:
% 142.33/84.77 | (1064) relation_composition(empty_set, all_0_14_14) = all_1526_1_2229 & relation_rng(all_1526_1_2229) = all_1526_0_2228 & subset(all_361_1_486, empty_set) = all_1526_2_2230 & relation(empty_set) = all_1526_3_2231 & ( ~ (all_1526_2_2230 = 0) | ~ (all_1526_3_2231 = 0) | all_1526_0_2228 = all_361_0_485)
% 142.33/84.77 |
% 142.33/84.77 | Applying alpha-rule on (1064) yields:
% 142.33/84.77 | (1065) relation_composition(empty_set, all_0_14_14) = all_1526_1_2229
% 142.33/84.77 | (1066) relation_rng(all_1526_1_2229) = all_1526_0_2228
% 142.33/84.77 | (1067) subset(all_361_1_486, empty_set) = all_1526_2_2230
% 142.33/84.77 | (1068) relation(empty_set) = all_1526_3_2231
% 142.33/84.77 | (1069) ~ (all_1526_2_2230 = 0) | ~ (all_1526_3_2231 = 0) | all_1526_0_2228 = all_361_0_485
% 142.33/84.77 |
% 142.33/84.77 | Instantiating (765) with all_1578_0_2288, all_1578_1_2289, all_1578_2_2290, all_1578_3_2291 yields:
% 142.33/84.77 | (1070) relation_composition(all_0_0_0, all_0_14_14) = all_1578_1_2289 & relation_dom(all_1578_1_2289) = all_1578_0_2288 & relation_dom(all_0_14_14) = all_1578_3_2291 & subset(all_1076_1_1380, all_1578_3_2291) = all_1578_2_2290 & ( ~ (all_1578_2_2290 = 0) | all_1578_0_2288 = all_1076_0_1379)
% 142.33/84.77 |
% 142.33/84.77 | Applying alpha-rule on (1070) yields:
% 142.33/84.77 | (1071) subset(all_1076_1_1380, all_1578_3_2291) = all_1578_2_2290
% 142.33/84.77 | (1072) relation_composition(all_0_0_0, all_0_14_14) = all_1578_1_2289
% 142.33/84.77 | (1073) relation_dom(all_0_14_14) = all_1578_3_2291
% 142.33/84.77 | (1074) ~ (all_1578_2_2290 = 0) | all_1578_0_2288 = all_1076_0_1379
% 142.33/84.77 | (1075) relation_dom(all_1578_1_2289) = all_1578_0_2288
% 142.33/84.77 |
% 142.33/84.77 | Instantiating (764) with all_1584_0_2300, all_1584_1_2301, all_1584_2_2302, all_1584_3_2303 yields:
% 142.33/84.77 | (1076) relation_composition(all_0_0_0, empty_set) = all_1584_1_2301 & relation_dom(all_1584_1_2301) = all_1584_0_2300 & subset(all_1076_1_1380, empty_set) = all_1584_2_2302 & relation(empty_set) = all_1584_3_2303 & ( ~ (all_1584_2_2302 = 0) | ~ (all_1584_3_2303 = 0) | all_1584_0_2300 = all_1076_0_1379)
% 142.33/84.77 |
% 142.33/84.77 | Applying alpha-rule on (1076) yields:
% 142.33/84.77 | (1077) ~ (all_1584_2_2302 = 0) | ~ (all_1584_3_2303 = 0) | all_1584_0_2300 = all_1076_0_1379
% 142.33/84.77 | (1078) relation_dom(all_1584_1_2301) = all_1584_0_2300
% 142.33/84.77 | (1079) relation_composition(all_0_0_0, empty_set) = all_1584_1_2301
% 142.33/84.77 | (1080) subset(all_1076_1_1380, empty_set) = all_1584_2_2302
% 142.33/84.77 | (1081) relation(empty_set) = all_1584_3_2303
% 142.33/84.77 |
% 142.33/84.77 | Instantiating (763) with all_1596_0_2324, all_1596_1_2325, all_1596_2_2326, all_1596_3_2327 yields:
% 142.33/84.77 | (1082) relation_composition(all_0_0_0, all_0_14_14) = all_1596_1_2325 & relation_dom(all_1596_1_2325) = all_1596_0_2324 & subset(all_1076_1_1380, all_0_11_11) = all_1596_2_2326 & relation(all_0_14_14) = all_1596_3_2327 & ( ~ (all_1596_2_2326 = 0) | ~ (all_1596_3_2327 = 0) | all_1596_0_2324 = all_1076_0_1379)
% 142.33/84.77 |
% 142.33/84.77 | Applying alpha-rule on (1082) yields:
% 142.33/84.77 | (1083) relation_dom(all_1596_1_2325) = all_1596_0_2324
% 142.33/84.77 | (1084) subset(all_1076_1_1380, all_0_11_11) = all_1596_2_2326
% 142.33/84.77 | (1085) relation(all_0_14_14) = all_1596_3_2327
% 142.33/84.77 | (1086) ~ (all_1596_2_2326 = 0) | ~ (all_1596_3_2327 = 0) | all_1596_0_2324 = all_1076_0_1379
% 142.33/84.77 | (1087) relation_composition(all_0_0_0, all_0_14_14) = all_1596_1_2325
% 142.33/84.77 |
% 142.33/84.77 | Instantiating (776) with all_1600_0_2333, all_1600_1_2334, all_1600_2_2335, all_1600_3_2336, all_1600_4_2337 yields:
% 142.33/84.77 | (1088) relation_rng(all_0_14_14) = all_1600_1_2334 & relation_dom(all_0_14_14) = all_1600_3_2336 & subset(all_1081_0_1383, all_1600_1_2334) = all_1600_0_2333 & subset(all_1081_1_1384, all_1600_3_2336) = all_1600_2_2335 & subset(all_0_0_0, all_0_14_14) = all_1600_4_2337 & ( ~ (all_1600_4_2337 = 0) | (all_1600_0_2333 = 0 & all_1600_2_2335 = 0))
% 142.33/84.77 |
% 142.33/84.77 | Applying alpha-rule on (1088) yields:
% 142.33/84.77 | (1089) subset(all_1081_1_1384, all_1600_3_2336) = all_1600_2_2335
% 142.33/84.77 | (1090) relation_rng(all_0_14_14) = all_1600_1_2334
% 142.33/84.77 | (1091) ~ (all_1600_4_2337 = 0) | (all_1600_0_2333 = 0 & all_1600_2_2335 = 0)
% 142.33/84.77 | (1092) subset(all_1081_0_1383, all_1600_1_2334) = all_1600_0_2333
% 142.33/84.77 | (1093) subset(all_0_0_0, all_0_14_14) = all_1600_4_2337
% 142.33/84.77 | (1094) relation_dom(all_0_14_14) = all_1600_3_2336
% 142.33/84.77 |
% 142.33/84.77 | Instantiating (774) with all_1608_0_2353, all_1608_1_2354, all_1608_2_2355, all_1608_3_2356, all_1608_4_2357 yields:
% 142.33/84.77 | (1095) relation_rng(all_0_14_14) = all_1608_1_2354 & subset(all_1081_0_1383, all_1608_1_2354) = all_1608_0_2353 & subset(all_1081_1_1384, all_0_11_11) = all_1608_2_2355 & subset(all_0_0_0, all_0_14_14) = all_1608_3_2356 & relation(all_0_14_14) = all_1608_4_2357 & ( ~ (all_1608_3_2356 = 0) | ~ (all_1608_4_2357 = 0) | (all_1608_0_2353 = 0 & all_1608_2_2355 = 0))
% 142.33/84.77 |
% 142.33/84.77 | Applying alpha-rule on (1095) yields:
% 142.33/84.77 | (1096) subset(all_1081_1_1384, all_0_11_11) = all_1608_2_2355
% 142.33/84.77 | (1097) relation_rng(all_0_14_14) = all_1608_1_2354
% 142.33/84.77 | (1098) ~ (all_1608_3_2356 = 0) | ~ (all_1608_4_2357 = 0) | (all_1608_0_2353 = 0 & all_1608_2_2355 = 0)
% 142.33/84.77 | (1099) subset(all_0_0_0, all_0_14_14) = all_1608_3_2356
% 142.33/84.77 | (1100) subset(all_1081_0_1383, all_1608_1_2354) = all_1608_0_2353
% 142.33/84.77 | (1101) relation(all_0_14_14) = all_1608_4_2357
% 142.33/84.77 |
% 142.33/84.77 | Instantiating (775) with all_1614_0_2368, all_1614_1_2369, all_1614_2_2370, all_1614_3_2371, all_1614_4_2372 yields:
% 142.33/84.77 | (1102) relation_rng(empty_set) = all_1614_1_2369 & subset(all_1081_0_1383, all_1614_1_2369) = all_1614_0_2368 & subset(all_1081_1_1384, empty_set) = all_1614_2_2370 & subset(all_0_0_0, empty_set) = all_1614_3_2371 & relation(empty_set) = all_1614_4_2372 & ( ~ (all_1614_3_2371 = 0) | ~ (all_1614_4_2372 = 0) | (all_1614_0_2368 = 0 & all_1614_2_2370 = 0))
% 142.33/84.77 |
% 142.33/84.77 | Applying alpha-rule on (1102) yields:
% 142.33/84.77 | (1103) subset(all_1081_1_1384, empty_set) = all_1614_2_2370
% 142.33/84.77 | (1104) subset(all_1081_0_1383, all_1614_1_2369) = all_1614_0_2368
% 142.33/84.77 | (1105) subset(all_0_0_0, empty_set) = all_1614_3_2371
% 142.33/84.77 | (1106) relation_rng(empty_set) = all_1614_1_2369
% 142.33/84.77 | (1107) relation(empty_set) = all_1614_4_2372
% 142.33/84.77 | (1108) ~ (all_1614_3_2371 = 0) | ~ (all_1614_4_2372 = 0) | (all_1614_0_2368 = 0 & all_1614_2_2370 = 0)
% 142.33/84.77 |
% 142.33/84.77 | Instantiating (773) with all_1620_0_2383, all_1620_1_2384, all_1620_2_2385, all_1620_3_2386, all_1620_4_2387 yields:
% 142.33/84.77 | (1109) relation_dom(empty_set) = all_1620_2_2385 & subset(all_1081_0_1383, empty_set) = all_1620_0_2383 & subset(all_1081_1_1384, all_1620_2_2385) = all_1620_1_2384 & subset(all_0_0_0, empty_set) = all_1620_3_2386 & relation(empty_set) = all_1620_4_2387 & ( ~ (all_1620_3_2386 = 0) | ~ (all_1620_4_2387 = 0) | (all_1620_0_2383 = 0 & all_1620_1_2384 = 0))
% 142.33/84.77 |
% 142.33/84.77 | Applying alpha-rule on (1109) yields:
% 142.33/84.77 | (1110) subset(all_0_0_0, empty_set) = all_1620_3_2386
% 142.33/84.77 | (1111) relation_dom(empty_set) = all_1620_2_2385
% 142.33/84.77 | (1112) ~ (all_1620_3_2386 = 0) | ~ (all_1620_4_2387 = 0) | (all_1620_0_2383 = 0 & all_1620_1_2384 = 0)
% 142.33/84.77 | (1113) relation(empty_set) = all_1620_4_2387
% 142.33/84.77 | (1114) subset(all_1081_0_1383, empty_set) = all_1620_0_2383
% 142.33/84.77 | (1115) subset(all_1081_1_1384, all_1620_2_2385) = all_1620_1_2384
% 142.33/84.77 |
% 142.33/84.77 | Instantiating (783) with all_1636_0_2418, all_1636_1_2419, all_1636_2_2420, all_1636_3_2421 yields:
% 142.33/84.77 | (1116) relation_composition(empty_set, all_0_0_0) = all_1636_1_2419 & relation_rng(all_1636_1_2419) = all_1636_0_2418 & subset(all_1084_1_1386, empty_set) = all_1636_2_2420 & relation(empty_set) = all_1636_3_2421 & ( ~ (all_1636_2_2420 = 0) | ~ (all_1636_3_2421 = 0) | all_1636_0_2418 = all_1084_0_1385)
% 142.33/84.77 |
% 142.33/84.77 | Applying alpha-rule on (1116) yields:
% 142.33/84.77 | (1117) relation(empty_set) = all_1636_3_2421
% 142.33/84.77 | (1118) relation_rng(all_1636_1_2419) = all_1636_0_2418
% 142.33/84.77 | (1119) ~ (all_1636_2_2420 = 0) | ~ (all_1636_3_2421 = 0) | all_1636_0_2418 = all_1084_0_1385
% 142.33/84.77 | (1120) subset(all_1084_1_1386, empty_set) = all_1636_2_2420
% 142.33/84.77 | (1121) relation_composition(empty_set, all_0_0_0) = all_1636_1_2419
% 142.33/84.77 |
% 142.33/84.77 | Instantiating formula (249) with all_0_14_14, all_1578_3_2291, all_1600_3_2336 and discharging atoms relation_dom(all_0_14_14) = all_1600_3_2336, relation_dom(all_0_14_14) = all_1578_3_2291, yields:
% 142.33/84.77 | (1122) all_1600_3_2336 = all_1578_3_2291
% 142.33/84.77 |
% 142.33/84.77 | Instantiating formula (249) with all_0_14_14, all_1446_3_2044, all_1490_3_2146 and discharging atoms relation_dom(all_0_14_14) = all_1490_3_2146, relation_dom(all_0_14_14) = all_1446_3_2044, yields:
% 142.33/84.77 | (1123) all_1490_3_2146 = all_1446_3_2044
% 142.33/84.77 |
% 142.33/84.77 | Instantiating formula (249) with all_0_14_14, all_1373_3_1900, all_1415_3_1994 and discharging atoms relation_dom(all_0_14_14) = all_1415_3_1994, relation_dom(all_0_14_14) = all_1373_3_1900, yields:
% 142.33/84.77 | (1124) all_1415_3_1994 = all_1373_3_1900
% 142.33/84.77 |
% 142.33/84.77 | Instantiating formula (249) with all_0_14_14, all_1325_3_1820, all_1373_3_1900 and discharging atoms relation_dom(all_0_14_14) = all_1373_3_1900, relation_dom(all_0_14_14) = all_1325_3_1820, yields:
% 142.33/84.77 | (1125) all_1373_3_1900 = all_1325_3_1820
% 142.33/84.77 |
% 142.33/84.77 | Instantiating formula (249) with all_0_14_14, all_1287_3_1744, all_1325_3_1820 and discharging atoms relation_dom(all_0_14_14) = all_1325_3_1820, relation_dom(all_0_14_14) = all_1287_3_1744, yields:
% 142.33/84.77 | (1126) all_1325_3_1820 = all_1287_3_1744
% 142.33/84.77 |
% 142.33/84.77 | Instantiating formula (249) with all_0_14_14, all_1258_3_1674, all_1600_3_2336 and discharging atoms relation_dom(all_0_14_14) = all_1600_3_2336, relation_dom(all_0_14_14) = all_1258_3_1674, yields:
% 142.33/84.77 | (1127) all_1600_3_2336 = all_1258_3_1674
% 142.33/84.77 |
% 142.33/84.77 | Instantiating formula (249) with all_0_14_14, all_1258_3_1674, all_1287_3_1744 and discharging atoms relation_dom(all_0_14_14) = all_1287_3_1744, relation_dom(all_0_14_14) = all_1258_3_1674, yields:
% 142.33/84.77 | (1128) all_1287_3_1744 = all_1258_3_1674
% 142.33/84.77 |
% 142.33/84.77 | Instantiating formula (249) with all_0_14_14, all_1236_3_1629, all_1600_3_2336 and discharging atoms relation_dom(all_0_14_14) = all_1600_3_2336, relation_dom(all_0_14_14) = all_1236_3_1629, yields:
% 142.33/84.77 | (1129) all_1600_3_2336 = all_1236_3_1629
% 142.33/84.77 |
% 142.33/84.77 | Instantiating formula (249) with all_0_14_14, all_1111_2_1420, all_1578_3_2291 and discharging atoms relation_dom(all_0_14_14) = all_1578_3_2291, relation_dom(all_0_14_14) = all_1111_2_1420, yields:
% 142.33/84.77 | (1130) all_1578_3_2291 = all_1111_2_1420
% 142.33/84.77 |
% 142.33/84.77 | Instantiating formula (249) with all_0_14_14, all_995_0_1259, all_1446_3_2044 and discharging atoms relation_dom(all_0_14_14) = all_1446_3_2044, relation_dom(all_0_14_14) = all_995_0_1259, yields:
% 142.33/84.77 | (1131) all_1446_3_2044 = all_995_0_1259
% 142.33/84.77 |
% 142.33/84.77 | Instantiating formula (249) with all_0_14_14, all_993_0_1256, all_1415_3_1994 and discharging atoms relation_dom(all_0_14_14) = all_1415_3_1994, relation_dom(all_0_14_14) = all_993_0_1256, yields:
% 142.33/84.77 | (1132) all_1415_3_1994 = all_993_0_1256
% 142.33/84.77 |
% 142.33/84.77 | Instantiating formula (249) with all_0_14_14, all_986_0_1249, all_1578_3_2291 and discharging atoms relation_dom(all_0_14_14) = all_1578_3_2291, relation_dom(all_0_14_14) = all_986_0_1249, yields:
% 142.33/84.77 | (1133) all_1578_3_2291 = all_986_0_1249
% 142.33/84.77 |
% 142.33/84.77 | Instantiating formula (249) with all_0_14_14, all_986_0_1249, all_995_0_1259 and discharging atoms relation_dom(all_0_14_14) = all_995_0_1259, relation_dom(all_0_14_14) = all_986_0_1249, yields:
% 142.33/84.77 | (1134) all_995_0_1259 = all_986_0_1249
% 142.33/84.77 |
% 142.33/84.77 | Instantiating formula (249) with all_0_14_14, all_904_1_1143, all_1578_3_2291 and discharging atoms relation_dom(all_0_14_14) = all_1578_3_2291, relation_dom(all_0_14_14) = all_904_1_1143, yields:
% 142.33/84.77 | (1135) all_1578_3_2291 = all_904_1_1143
% 142.33/84.77 |
% 142.33/84.77 | Instantiating formula (249) with all_0_14_14, all_863_1_1108, all_1578_3_2291 and discharging atoms relation_dom(all_0_14_14) = all_1578_3_2291, relation_dom(all_0_14_14) = all_863_1_1108, yields:
% 142.33/84.77 | (1136) all_1578_3_2291 = all_863_1_1108
% 142.33/84.77 |
% 142.33/84.77 | Instantiating formula (249) with all_0_14_14, all_554_0_701, all_0_11_11 and discharging atoms relation_dom(all_0_14_14) = all_554_0_701, relation_dom(all_0_14_14) = all_0_11_11, yields:
% 142.33/84.77 | (1137) all_554_0_701 = all_0_11_11
% 142.33/84.77 |
% 142.33/84.77 | Instantiating formula (249) with all_0_14_14, all_554_0_701, all_991_1_1254 and discharging atoms relation_dom(all_0_14_14) = all_991_1_1254, relation_dom(all_0_14_14) = all_554_0_701, yields:
% 142.33/84.77 | (1138) all_991_1_1254 = all_554_0_701
% 142.33/84.77 |
% 142.33/84.77 | Instantiating formula (249) with all_0_14_14, all_361_1_486, all_863_1_1108 and discharging atoms relation_dom(all_0_14_14) = all_863_1_1108, relation_dom(all_0_14_14) = all_361_1_486, yields:
% 142.33/84.77 | (1139) all_863_1_1108 = all_361_1_486
% 142.33/84.77 |
% 142.33/84.77 | Instantiating formula (249) with all_0_14_14, all_358_1_484, all_554_0_701 and discharging atoms relation_dom(all_0_14_14) = all_554_0_701, relation_dom(all_0_14_14) = all_358_1_484, yields:
% 142.33/84.77 | (1140) all_554_0_701 = all_358_1_484
% 142.33/84.77 |
% 142.33/84.77 | Instantiating formula (249) with all_0_14_14, all_358_1_484, all_361_1_486 and discharging atoms relation_dom(all_0_14_14) = all_361_1_486, relation_dom(all_0_14_14) = all_358_1_484, yields:
% 142.33/84.77 | (1141) all_361_1_486 = all_358_1_484
% 142.33/84.77 |
% 142.33/84.77 | Instantiating formula (249) with all_0_14_14, all_232_0_343, all_991_1_1254 and discharging atoms relation_dom(all_0_14_14) = all_991_1_1254, relation_dom(all_0_14_14) = all_232_0_343, yields:
% 142.33/84.77 | (1142) all_991_1_1254 = all_232_0_343
% 142.33/84.77 |
% 142.33/84.77 | Instantiating formula (249) with all_0_14_14, all_230_1_342, all_1490_3_2146 and discharging atoms relation_dom(all_0_14_14) = all_1490_3_2146, relation_dom(all_0_14_14) = all_230_1_342, yields:
% 142.33/84.77 | (1143) all_1490_3_2146 = all_230_1_342
% 142.33/84.77 |
% 142.33/84.77 | Instantiating formula (249) with all_0_14_14, all_227_0_339, all_554_0_701 and discharging atoms relation_dom(all_0_14_14) = all_554_0_701, relation_dom(all_0_14_14) = all_227_0_339, yields:
% 142.33/84.77 | (1144) all_554_0_701 = all_227_0_339
% 142.33/84.77 |
% 142.33/84.77 | Instantiating formula (329) with empty_set, all_0_14_14, all_1258_4_1675, all_1260_3_1679 and discharging atoms subset(empty_set, all_0_14_14) = all_1260_3_1679, subset(empty_set, all_0_14_14) = all_1258_4_1675, yields:
% 142.33/84.78 | (1145) all_1260_3_1679 = all_1258_4_1675
% 142.33/84.78 |
% 142.33/84.78 | Instantiating formula (111) with all_1258_4_1675, all_0_14_14 and discharging atoms subset(empty_set, all_0_14_14) = all_1258_4_1675, yields:
% 142.33/84.78 | (1146) all_1258_4_1675 = 0
% 142.33/84.78 |
% 142.33/84.78 | Instantiating formula (329) with empty_set, all_0_14_14, all_261_5_383, all_1260_3_1679 and discharging atoms subset(empty_set, all_0_14_14) = all_1260_3_1679, subset(empty_set, all_0_14_14) = all_261_5_383, yields:
% 142.33/84.78 | (1147) all_1260_3_1679 = all_261_5_383
% 142.33/84.78 |
% 142.33/84.78 | Instantiating formula (7) with all_0_14_14, all_1492_4_2152, all_1596_3_2327 and discharging atoms relation(all_0_14_14) = all_1596_3_2327, relation(all_0_14_14) = all_1492_4_2152, yields:
% 142.33/84.78 | (1148) all_1596_3_2327 = all_1492_4_2152
% 142.33/84.78 |
% 142.33/84.78 | Instantiating formula (7) with all_0_14_14, all_1456_4_2070, all_1608_4_2357 and discharging atoms relation(all_0_14_14) = all_1608_4_2357, relation(all_0_14_14) = all_1456_4_2070, yields:
% 142.33/84.78 | (1149) all_1608_4_2357 = all_1456_4_2070
% 142.33/84.78 |
% 142.33/84.78 | Instantiating formula (7) with all_0_14_14, all_1419_3_2002, all_1492_4_2152 and discharging atoms relation(all_0_14_14) = all_1492_4_2152, relation(all_0_14_14) = all_1419_3_2002, yields:
% 142.33/84.78 | (1150) all_1492_4_2152 = all_1419_3_2002
% 142.33/84.78 |
% 142.33/84.78 | Instantiating formula (7) with all_0_14_14, all_1375_4_1906, all_1492_4_2152 and discharging atoms relation(all_0_14_14) = all_1492_4_2152, relation(all_0_14_14) = all_1375_4_1906, yields:
% 142.33/84.78 | (1151) all_1492_4_2152 = all_1375_4_1906
% 142.33/84.78 |
% 142.33/84.78 | Instantiating formula (7) with all_0_14_14, all_1333_3_1836, all_1375_4_1906 and discharging atoms relation(all_0_14_14) = all_1375_4_1906, relation(all_0_14_14) = all_1333_3_1836, yields:
% 142.33/84.78 | (1152) all_1375_4_1906 = all_1333_3_1836
% 142.33/84.78 |
% 142.33/84.78 | Instantiating formula (7) with all_0_14_14, all_1295_3_1760, all_1333_3_1836 and discharging atoms relation(all_0_14_14) = all_1333_3_1836, relation(all_0_14_14) = all_1295_3_1760, yields:
% 142.33/84.78 | (1153) all_1333_3_1836 = all_1295_3_1760
% 142.33/84.78 |
% 142.33/84.78 | Instantiating formula (7) with all_0_14_14, all_1260_4_1680, all_1295_3_1760 and discharging atoms relation(all_0_14_14) = all_1295_3_1760, relation(all_0_14_14) = all_1260_4_1680, yields:
% 142.33/84.78 | (1154) all_1295_3_1760 = all_1260_4_1680
% 142.33/84.78 |
% 142.33/84.78 | Instantiating formula (7) with all_0_14_14, all_1244_3_1645, all_1260_4_1680 and discharging atoms relation(all_0_14_14) = all_1260_4_1680, relation(all_0_14_14) = all_1244_3_1645, yields:
% 142.33/84.78 | (1155) all_1260_4_1680 = all_1244_3_1645
% 142.33/84.78 |
% 142.33/84.78 | Instantiating formula (7) with all_0_14_14, all_1168_3_1519, all_1456_4_2070 and discharging atoms relation(all_0_14_14) = all_1456_4_2070, relation(all_0_14_14) = all_1168_3_1519, yields:
% 142.33/84.78 | (1156) all_1456_4_2070 = all_1168_3_1519
% 142.33/84.78 |
% 142.33/84.78 | Instantiating formula (7) with all_0_14_14, all_1162_4_1503, all_1608_4_2357 and discharging atoms relation(all_0_14_14) = all_1608_4_2357, relation(all_0_14_14) = all_1162_4_1503, yields:
% 142.33/84.78 | (1157) all_1608_4_2357 = all_1162_4_1503
% 142.33/84.78 |
% 142.33/84.78 | Instantiating formula (7) with all_0_14_14, all_1160_3_1498, all_1244_3_1645 and discharging atoms relation(all_0_14_14) = all_1244_3_1645, relation(all_0_14_14) = all_1160_3_1498, yields:
% 142.33/84.78 | (1158) all_1244_3_1645 = all_1160_3_1498
% 142.33/84.78 |
% 142.33/84.78 | Instantiating formula (7) with all_0_14_14, all_1160_3_1498, all_1168_3_1519 and discharging atoms relation(all_0_14_14) = all_1168_3_1519, relation(all_0_14_14) = all_1160_3_1498, yields:
% 142.33/84.78 | (1159) all_1168_3_1519 = all_1160_3_1498
% 142.33/84.78 |
% 142.33/84.78 | Instantiating formula (7) with all_0_14_14, all_1158_2_1494, all_1168_3_1519 and discharging atoms relation(all_0_14_14) = all_1168_3_1519, relation(all_0_14_14) = all_1158_2_1494, yields:
% 142.33/84.78 | (1160) all_1168_3_1519 = all_1158_2_1494
% 142.33/84.78 |
% 142.33/84.78 | Instantiating formula (7) with all_0_14_14, all_1156_1_1491, all_1596_3_2327 and discharging atoms relation(all_0_14_14) = all_1596_3_2327, relation(all_0_14_14) = all_1156_1_1491, yields:
% 142.33/84.78 | (1161) all_1596_3_2327 = all_1156_1_1491
% 142.33/84.78 |
% 142.33/84.78 | Instantiating formula (7) with all_0_14_14, all_1143_1_1473, all_1168_3_1519 and discharging atoms relation(all_0_14_14) = all_1168_3_1519, relation(all_0_14_14) = all_1143_1_1473, yields:
% 142.33/84.78 | (1162) all_1168_3_1519 = all_1143_1_1473
% 142.33/84.78 |
% 142.33/84.78 | Instantiating formula (7) with all_0_14_14, all_1141_1_1470, 0 and discharging atoms relation(all_0_14_14) = all_1141_1_1470, relation(all_0_14_14) = 0, yields:
% 142.33/84.78 | (1163) all_1141_1_1470 = 0
% 142.33/84.78 |
% 142.33/84.78 | Instantiating formula (7) with all_0_14_14, all_1139_1_1468, all_1168_3_1519 and discharging atoms relation(all_0_14_14) = all_1168_3_1519, relation(all_0_14_14) = all_1139_1_1468, yields:
% 142.33/84.78 | (1164) all_1168_3_1519 = all_1139_1_1468
% 142.33/84.78 |
% 142.33/84.78 | Instantiating formula (7) with all_0_14_14, all_1133_1_1458, all_1143_1_1473 and discharging atoms relation(all_0_14_14) = all_1143_1_1473, relation(all_0_14_14) = all_1133_1_1458, yields:
% 142.33/84.78 | (1165) all_1143_1_1473 = all_1133_1_1458
% 142.33/84.78 |
% 142.33/84.78 | Instantiating formula (7) with all_0_14_14, all_1133_1_1458, all_1141_1_1470 and discharging atoms relation(all_0_14_14) = all_1141_1_1470, relation(all_0_14_14) = all_1133_1_1458, yields:
% 142.33/84.78 | (1166) all_1141_1_1470 = all_1133_1_1458
% 142.33/84.78 |
% 142.33/84.78 | Instantiating formula (7) with all_0_14_14, all_554_1_702, all_1143_1_1473 and discharging atoms relation(all_0_14_14) = all_1143_1_1473, relation(all_0_14_14) = all_554_1_702, yields:
% 142.33/84.78 | (1167) all_1143_1_1473 = all_554_1_702
% 142.33/84.78 |
% 142.33/84.78 | Instantiating formula (7) with empty_set, all_1620_4_2387, all_1636_3_2421 and discharging atoms relation(empty_set) = all_1636_3_2421, relation(empty_set) = all_1620_4_2387, yields:
% 142.33/84.78 | (1168) all_1636_3_2421 = all_1620_4_2387
% 142.33/84.78 |
% 142.33/84.78 | Instantiating formula (7) with empty_set, all_1614_4_2372, all_1620_4_2387 and discharging atoms relation(empty_set) = all_1620_4_2387, relation(empty_set) = all_1614_4_2372, yields:
% 142.33/84.78 | (1169) all_1620_4_2387 = all_1614_4_2372
% 142.33/84.78 |
% 142.33/84.78 | Instantiating formula (7) with empty_set, all_1584_3_2303, all_1614_4_2372 and discharging atoms relation(empty_set) = all_1614_4_2372, relation(empty_set) = all_1584_3_2303, yields:
% 142.33/84.78 | (1170) all_1614_4_2372 = all_1584_3_2303
% 142.33/84.78 |
% 142.33/84.78 | Instantiating formula (7) with empty_set, all_1506_4_2187, all_1526_3_2231 and discharging atoms relation(empty_set) = all_1526_3_2231, relation(empty_set) = all_1506_4_2187, yields:
% 142.33/84.78 | (1171) all_1526_3_2231 = all_1506_4_2187
% 142.33/84.78 |
% 142.33/84.78 | Instantiating formula (7) with empty_set, all_1500_4_2172, all_1584_3_2303 and discharging atoms relation(empty_set) = all_1584_3_2303, relation(empty_set) = all_1500_4_2172, yields:
% 142.33/84.78 | (1172) all_1584_3_2303 = all_1500_4_2172
% 142.33/84.78 |
% 142.33/84.78 | Instantiating formula (7) with empty_set, all_1480_3_2125, all_1506_4_2187 and discharging atoms relation(empty_set) = all_1506_4_2187, relation(empty_set) = all_1480_3_2125, yields:
% 142.33/84.78 | (1173) all_1506_4_2187 = all_1480_3_2125
% 142.33/84.78 |
% 142.33/84.78 | Instantiating formula (7) with empty_set, all_1466_4_2095, all_1480_3_2125 and discharging atoms relation(empty_set) = all_1480_3_2125, relation(empty_set) = all_1466_4_2095, yields:
% 142.33/84.78 | (1174) all_1480_3_2125 = all_1466_4_2095
% 142.33/84.78 |
% 142.33/84.78 | Instantiating formula (7) with empty_set, all_1413_3_1990, all_1500_4_2172 and discharging atoms relation(empty_set) = all_1500_4_2172, relation(empty_set) = all_1413_3_1990, yields:
% 142.33/84.78 | (1175) all_1500_4_2172 = all_1413_3_1990
% 142.33/84.78 |
% 142.33/84.78 | Instantiating formula (7) with empty_set, all_1407_3_1978, all_1466_4_2095 and discharging atoms relation(empty_set) = all_1466_4_2095, relation(empty_set) = all_1407_3_1978, yields:
% 142.33/84.78 | (1176) all_1466_4_2095 = all_1407_3_1978
% 142.33/84.78 |
% 142.33/84.78 | Instantiating formula (7) with empty_set, all_1379_4_1916, all_1391_4_1946 and discharging atoms relation(empty_set) = all_1391_4_1946, relation(empty_set) = all_1379_4_1916, yields:
% 142.33/84.78 | (1177) all_1391_4_1946 = all_1379_4_1916
% 142.33/84.78 |
% 142.33/84.78 | Instantiating formula (7) with empty_set, all_1331_3_1832, all_1379_4_1916 and discharging atoms relation(empty_set) = all_1379_4_1916, relation(empty_set) = all_1331_3_1832, yields:
% 142.33/84.78 | (1178) all_1379_4_1916 = all_1331_3_1832
% 142.33/84.78 |
% 142.33/84.78 | Instantiating formula (7) with empty_set, all_1317_3_1804, all_1331_3_1832 and discharging atoms relation(empty_set) = all_1331_3_1832, relation(empty_set) = all_1317_3_1804, yields:
% 142.33/84.78 | (1179) all_1331_3_1832 = all_1317_3_1804
% 142.33/84.78 |
% 142.33/84.78 | Instantiating formula (7) with empty_set, all_1293_3_1756, all_1317_3_1804 and discharging atoms relation(empty_set) = all_1317_3_1804, relation(empty_set) = all_1293_3_1756, yields:
% 142.33/84.78 | (1180) all_1317_3_1804 = all_1293_3_1756
% 142.33/84.78 |
% 142.33/84.78 | Instantiating formula (7) with empty_set, all_1280_4_1730, all_1413_3_1990 and discharging atoms relation(empty_set) = all_1413_3_1990, relation(empty_set) = all_1280_4_1730, yields:
% 142.33/84.78 | (1181) all_1413_3_1990 = all_1280_4_1730
% 142.33/84.78 |
% 142.33/84.78 | Instantiating formula (7) with empty_set, all_1242_3_1641, all_1280_4_1730 and discharging atoms relation(empty_set) = all_1280_4_1730, relation(empty_set) = all_1242_3_1641, yields:
% 142.33/84.78 | (1182) all_1280_4_1730 = all_1242_3_1641
% 142.33/84.78 |
% 142.33/84.78 | Instantiating formula (7) with empty_set, all_1137_3_1466, all_1407_3_1978 and discharging atoms relation(empty_set) = all_1407_3_1978, relation(empty_set) = all_1137_3_1466, yields:
% 142.33/84.78 | (1183) all_1407_3_1978 = all_1137_3_1466
% 142.33/84.78 |
% 142.33/84.78 | Instantiating formula (7) with empty_set, all_1135_3_1462, all_1278_4_1725 and discharging atoms relation(empty_set) = all_1278_4_1725, relation(empty_set) = all_1135_3_1462, yields:
% 142.33/84.78 | (1184) all_1278_4_1725 = all_1135_3_1462
% 142.33/84.78 |
% 142.33/84.78 | Instantiating formula (7) with empty_set, all_1135_3_1462, all_1137_3_1466 and discharging atoms relation(empty_set) = all_1137_3_1466, relation(empty_set) = all_1135_3_1462, yields:
% 142.33/84.78 | (1185) all_1137_3_1466 = all_1135_3_1462
% 142.33/84.78 |
% 142.33/84.78 | Instantiating formula (7) with empty_set, all_1119_4_1436, all_1242_3_1641 and discharging atoms relation(empty_set) = all_1242_3_1641, relation(empty_set) = all_1119_4_1436, yields:
% 142.33/84.78 | (1186) all_1242_3_1641 = all_1119_4_1436
% 142.33/84.78 |
% 142.33/84.78 | Instantiating formula (7) with empty_set, all_1115_1_1428, all_1526_3_2231 and discharging atoms relation(empty_set) = all_1526_3_2231, relation(empty_set) = all_1115_1_1428, yields:
% 142.33/84.78 | (1187) all_1526_3_2231 = all_1115_1_1428
% 142.33/84.78 |
% 142.33/84.78 | Instantiating formula (7) with empty_set, all_1035_3_1311, all_1137_3_1466 and discharging atoms relation(empty_set) = all_1137_3_1466, relation(empty_set) = all_1035_3_1311, yields:
% 142.33/84.78 | (1188) all_1137_3_1466 = all_1035_3_1311
% 142.33/84.78 |
% 142.33/84.78 | Instantiating formula (7) with empty_set, all_922_1_1166, all_1119_4_1436 and discharging atoms relation(empty_set) = all_1119_4_1436, relation(empty_set) = all_922_1_1166, yields:
% 142.33/84.78 | (1189) all_1119_4_1436 = all_922_1_1166
% 142.33/84.78 |
% 142.33/84.78 | Instantiating formula (7) with empty_set, all_922_1_1166, all_1117_2_1431 and discharging atoms relation(empty_set) = all_1117_2_1431, relation(empty_set) = all_922_1_1166, yields:
% 142.33/84.78 | (1190) all_1117_2_1431 = all_922_1_1166
% 142.33/84.78 |
% 142.33/84.78 | Instantiating formula (7) with empty_set, all_920_1_1164, all_1454_4_2065 and discharging atoms relation(empty_set) = all_1454_4_2065, relation(empty_set) = all_920_1_1164, yields:
% 142.33/84.78 | (1191) all_1454_4_2065 = all_920_1_1164
% 142.33/84.78 |
% 142.33/84.78 | Instantiating formula (7) with empty_set, all_920_1_1164, all_1035_3_1311 and discharging atoms relation(empty_set) = all_1035_3_1311, relation(empty_set) = all_920_1_1164, yields:
% 142.33/84.78 | (1192) all_1035_3_1311 = all_920_1_1164
% 142.33/84.78 |
% 142.33/84.78 | Instantiating formula (7) with empty_set, all_744_3_949, all_1117_2_1431 and discharging atoms relation(empty_set) = all_1117_2_1431, relation(empty_set) = all_744_3_949, yields:
% 142.33/84.78 | (1193) all_1117_2_1431 = all_744_3_949
% 142.33/84.78 |
% 142.33/84.78 | Instantiating formula (7) with empty_set, all_738_2_939, all_1454_4_2065 and discharging atoms relation(empty_set) = all_1454_4_2065, relation(empty_set) = all_738_2_939, yields:
% 142.33/84.78 | (1194) all_1454_4_2065 = all_738_2_939
% 142.33/84.78 |
% 142.33/84.78 | Instantiating formula (7) with empty_set, all_724_1_921, all_1117_2_1431 and discharging atoms relation(empty_set) = all_1117_2_1431, relation(empty_set) = all_724_1_921, yields:
% 142.33/84.78 | (1195) all_1117_2_1431 = all_724_1_921
% 142.33/84.78 |
% 142.33/84.78 | Instantiating formula (7) with empty_set, all_670_1_853, all_1293_3_1756 and discharging atoms relation(empty_set) = all_1293_3_1756, relation(empty_set) = all_670_1_853, yields:
% 142.33/84.78 | (1196) all_1293_3_1756 = all_670_1_853
% 142.33/84.78 |
% 142.33/84.78 | Instantiating formula (7) with empty_set, all_670_1_853, all_920_1_1164 and discharging atoms relation(empty_set) = all_920_1_1164, relation(empty_set) = all_670_1_853, yields:
% 142.33/84.78 | (1197) all_920_1_1164 = all_670_1_853
% 142.33/84.78 |
% 142.33/84.78 | Instantiating formula (7) with empty_set, all_668_1_851, 0 and discharging atoms relation(empty_set) = all_668_1_851, relation(empty_set) = 0, yields:
% 142.33/84.78 | (1198) all_668_1_851 = 0
% 142.33/84.78 |
% 142.33/84.78 | Instantiating formula (7) with empty_set, all_668_1_851, all_724_1_921 and discharging atoms relation(empty_set) = all_724_1_921, relation(empty_set) = all_668_1_851, yields:
% 142.33/84.78 | (1199) all_724_1_921 = all_668_1_851
% 142.33/84.78 |
% 142.33/84.78 | Instantiating formula (7) with empty_set, all_668_1_851, all_670_1_853 and discharging atoms relation(empty_set) = all_670_1_853, relation(empty_set) = all_668_1_851, yields:
% 142.33/84.78 | (1200) all_670_1_853 = all_668_1_851
% 142.33/84.78 |
% 142.33/84.78 | Instantiating formula (7) with empty_set, all_664_4_847, all_1278_4_1725 and discharging atoms relation(empty_set) = all_1278_4_1725, relation(empty_set) = all_664_4_847, yields:
% 142.33/84.78 | (1201) all_1278_4_1725 = all_664_4_847
% 142.33/84.78 |
% 142.33/84.78 | Instantiating formula (7) with empty_set, all_662_3_842, all_670_1_853 and discharging atoms relation(empty_set) = all_670_1_853, relation(empty_set) = all_662_3_842, yields:
% 142.33/84.78 | (1202) all_670_1_853 = all_662_3_842
% 142.33/84.78 |
% 142.33/84.78 | Instantiating formula (7) with empty_set, all_582_3_730, all_1391_4_1946 and discharging atoms relation(empty_set) = all_1391_4_1946, relation(empty_set) = all_582_3_730, yields:
% 142.33/84.78 | (1203) all_1391_4_1946 = all_582_3_730
% 142.33/84.78 |
% 142.33/84.78 | Instantiating formula (7) with empty_set, all_393_3_533, all_1636_3_2421 and discharging atoms relation(empty_set) = all_1636_3_2421, relation(empty_set) = all_393_3_533, yields:
% 142.33/84.78 | (1204) all_1636_3_2421 = all_393_3_533
% 142.33/84.78 |
% 142.33/84.78 | Instantiating formula (7) with empty_set, all_289_3_415, all_1454_4_2065 and discharging atoms relation(empty_set) = all_1454_4_2065, relation(empty_set) = all_289_3_415, yields:
% 142.33/84.78 | (1205) all_1454_4_2065 = all_289_3_415
% 142.33/84.78 |
% 142.33/84.78 | Instantiating formula (92) with all_0_14_14, all_232_1_344, 0 and discharging atoms function(all_0_14_14) = all_232_1_344, function(all_0_14_14) = 0, yields:
% 142.33/84.78 | (1206) all_232_1_344 = 0
% 142.33/84.78 |
% 142.33/84.78 | Combining equations (1168,1204) yields a new equation:
% 142.33/84.78 | (1207) all_1620_4_2387 = all_393_3_533
% 142.33/84.78 |
% 142.33/84.78 | Simplifying 1207 yields:
% 142.33/84.78 | (1208) all_1620_4_2387 = all_393_3_533
% 142.33/84.78 |
% 142.33/84.78 | Combining equations (1169,1208) yields a new equation:
% 142.33/84.78 | (1209) all_1614_4_2372 = all_393_3_533
% 142.33/84.78 |
% 142.33/84.78 | Simplifying 1209 yields:
% 142.33/84.78 | (1210) all_1614_4_2372 = all_393_3_533
% 142.33/84.78 |
% 142.33/84.78 | Combining equations (1170,1210) yields a new equation:
% 142.33/84.78 | (1211) all_1584_3_2303 = all_393_3_533
% 142.33/84.78 |
% 142.33/84.78 | Simplifying 1211 yields:
% 142.33/84.78 | (1212) all_1584_3_2303 = all_393_3_533
% 142.33/84.78 |
% 142.33/84.78 | Combining equations (1149,1157) yields a new equation:
% 142.33/84.78 | (1213) all_1456_4_2070 = all_1162_4_1503
% 142.33/84.78 |
% 142.33/84.78 | Simplifying 1213 yields:
% 142.33/84.78 | (1214) all_1456_4_2070 = all_1162_4_1503
% 142.33/84.78 |
% 142.33/84.78 | Combining equations (1127,1129) yields a new equation:
% 142.33/84.78 | (1215) all_1258_3_1674 = all_1236_3_1629
% 142.33/84.78 |
% 142.33/84.78 | Simplifying 1215 yields:
% 142.33/84.78 | (1216) all_1258_3_1674 = all_1236_3_1629
% 142.33/84.78 |
% 142.33/84.78 | Combining equations (1122,1129) yields a new equation:
% 142.33/84.78 | (1217) all_1578_3_2291 = all_1236_3_1629
% 142.33/84.78 |
% 142.33/84.78 | Simplifying 1217 yields:
% 142.33/84.78 | (1218) all_1578_3_2291 = all_1236_3_1629
% 142.33/84.78 |
% 142.33/84.78 | Combining equations (1148,1161) yields a new equation:
% 142.33/84.78 | (1219) all_1492_4_2152 = all_1156_1_1491
% 142.33/84.78 |
% 142.33/84.78 | Simplifying 1219 yields:
% 142.33/84.78 | (1220) all_1492_4_2152 = all_1156_1_1491
% 142.33/84.78 |
% 142.33/84.78 | Combining equations (1172,1212) yields a new equation:
% 142.33/84.78 | (1221) all_1500_4_2172 = all_393_3_533
% 142.33/84.78 |
% 142.33/84.78 | Simplifying 1221 yields:
% 142.33/84.78 | (1222) all_1500_4_2172 = all_393_3_533
% 142.33/84.78 |
% 142.33/84.78 | Combining equations (1133,1130) yields a new equation:
% 142.33/84.78 | (1223) all_1111_2_1420 = all_986_0_1249
% 142.33/84.78 |
% 142.33/84.78 | Combining equations (1135,1130) yields a new equation:
% 142.33/84.78 | (1224) all_1111_2_1420 = all_904_1_1143
% 142.33/84.78 |
% 142.33/84.78 | Combining equations (1218,1130) yields a new equation:
% 142.33/84.78 | (1225) all_1236_3_1629 = all_1111_2_1420
% 142.33/84.78 |
% 142.33/84.78 | Simplifying 1225 yields:
% 142.33/84.78 | (1226) all_1236_3_1629 = all_1111_2_1420
% 142.33/84.78 |
% 142.33/84.78 | Combining equations (1136,1130) yields a new equation:
% 142.33/84.78 | (1227) all_1111_2_1420 = all_863_1_1108
% 142.33/84.78 |
% 142.33/84.78 | Combining equations (1171,1187) yields a new equation:
% 142.33/84.78 | (1228) all_1506_4_2187 = all_1115_1_1428
% 142.33/84.78 |
% 142.33/84.78 | Simplifying 1228 yields:
% 142.33/84.78 | (1229) all_1506_4_2187 = all_1115_1_1428
% 142.33/84.79 |
% 142.33/84.79 | Combining equations (1173,1229) yields a new equation:
% 142.33/84.79 | (1230) all_1480_3_2125 = all_1115_1_1428
% 142.33/84.79 |
% 142.33/84.79 | Simplifying 1230 yields:
% 142.33/84.79 | (1231) all_1480_3_2125 = all_1115_1_1428
% 142.33/84.79 |
% 142.33/84.79 | Combining equations (1175,1222) yields a new equation:
% 142.33/84.79 | (1232) all_1413_3_1990 = all_393_3_533
% 142.33/84.79 |
% 142.33/84.79 | Simplifying 1232 yields:
% 142.33/84.79 | (1233) all_1413_3_1990 = all_393_3_533
% 142.33/84.79 |
% 142.33/84.79 | Combining equations (1151,1150) yields a new equation:
% 142.33/84.79 | (1234) all_1419_3_2002 = all_1375_4_1906
% 142.33/84.79 |
% 142.33/84.79 | Combining equations (1220,1150) yields a new equation:
% 142.33/84.79 | (1235) all_1419_3_2002 = all_1156_1_1491
% 142.33/84.79 |
% 142.33/84.79 | Combining equations (1123,1143) yields a new equation:
% 142.33/84.79 | (1236) all_1446_3_2044 = all_230_1_342
% 142.33/84.79 |
% 142.33/84.79 | Simplifying 1236 yields:
% 142.33/84.79 | (1237) all_1446_3_2044 = all_230_1_342
% 142.33/84.79 |
% 142.33/84.79 | Combining equations (1174,1231) yields a new equation:
% 142.33/84.79 | (1238) all_1466_4_2095 = all_1115_1_1428
% 142.33/84.79 |
% 142.33/84.79 | Simplifying 1238 yields:
% 142.33/84.79 | (1239) all_1466_4_2095 = all_1115_1_1428
% 142.33/84.79 |
% 142.33/84.79 | Combining equations (1176,1239) yields a new equation:
% 142.33/84.79 | (1240) all_1407_3_1978 = all_1115_1_1428
% 142.33/84.79 |
% 142.33/84.79 | Simplifying 1240 yields:
% 142.33/84.79 | (1241) all_1407_3_1978 = all_1115_1_1428
% 142.33/84.79 |
% 142.33/84.79 | Combining equations (1156,1214) yields a new equation:
% 142.33/84.79 | (1242) all_1168_3_1519 = all_1162_4_1503
% 142.33/84.79 |
% 142.33/84.79 | Simplifying 1242 yields:
% 142.33/84.79 | (1243) all_1168_3_1519 = all_1162_4_1503
% 142.33/84.79 |
% 142.33/84.79 | Combining equations (1191,1194) yields a new equation:
% 142.33/84.79 | (1244) all_920_1_1164 = all_738_2_939
% 142.33/84.79 |
% 142.33/84.79 | Simplifying 1244 yields:
% 142.33/84.79 | (1245) all_920_1_1164 = all_738_2_939
% 142.33/84.79 |
% 142.33/84.79 | Combining equations (1205,1194) yields a new equation:
% 142.33/84.79 | (1246) all_738_2_939 = all_289_3_415
% 142.33/84.79 |
% 142.33/84.79 | Combining equations (1131,1237) yields a new equation:
% 142.33/84.79 | (1247) all_995_0_1259 = all_230_1_342
% 142.33/84.79 |
% 142.33/84.79 | Simplifying 1247 yields:
% 142.33/84.79 | (1248) all_995_0_1259 = all_230_1_342
% 142.33/84.79 |
% 142.33/84.79 | Combining equations (1234,1235) yields a new equation:
% 142.33/84.79 | (1249) all_1375_4_1906 = all_1156_1_1491
% 142.33/84.79 |
% 142.33/84.79 | Simplifying 1249 yields:
% 142.33/84.79 | (1250) all_1375_4_1906 = all_1156_1_1491
% 142.33/84.79 |
% 142.33/84.79 | Combining equations (1124,1132) yields a new equation:
% 142.33/84.79 | (1251) all_1373_3_1900 = all_993_0_1256
% 142.33/84.79 |
% 142.33/84.79 | Simplifying 1251 yields:
% 142.33/84.79 | (1252) all_1373_3_1900 = all_993_0_1256
% 142.33/84.79 |
% 142.33/84.79 | Combining equations (1181,1233) yields a new equation:
% 142.33/84.79 | (1253) all_1280_4_1730 = all_393_3_533
% 142.33/84.79 |
% 142.33/84.79 | Simplifying 1253 yields:
% 142.33/84.79 | (1254) all_1280_4_1730 = all_393_3_533
% 142.33/84.79 |
% 142.33/84.79 | Combining equations (1183,1241) yields a new equation:
% 142.33/84.79 | (1255) all_1137_3_1466 = all_1115_1_1428
% 142.33/84.79 |
% 142.33/84.79 | Simplifying 1255 yields:
% 142.33/84.79 | (1256) all_1137_3_1466 = all_1115_1_1428
% 142.33/84.79 |
% 142.33/84.79 | Combining equations (1177,1203) yields a new equation:
% 142.33/84.79 | (1257) all_1379_4_1916 = all_582_3_730
% 142.33/84.79 |
% 142.33/84.79 | Simplifying 1257 yields:
% 142.33/84.79 | (1258) all_1379_4_1916 = all_582_3_730
% 142.33/84.79 |
% 142.33/84.79 | Combining equations (1178,1258) yields a new equation:
% 142.33/84.79 | (1259) all_1331_3_1832 = all_582_3_730
% 142.33/84.79 |
% 142.33/84.79 | Simplifying 1259 yields:
% 142.33/84.79 | (1260) all_1331_3_1832 = all_582_3_730
% 142.33/84.79 |
% 142.33/84.79 | Combining equations (1152,1250) yields a new equation:
% 142.33/84.79 | (1261) all_1333_3_1836 = all_1156_1_1491
% 142.33/84.79 |
% 142.33/84.79 | Simplifying 1261 yields:
% 142.33/84.79 | (1262) all_1333_3_1836 = all_1156_1_1491
% 142.33/84.79 |
% 142.33/84.79 | Combining equations (1125,1252) yields a new equation:
% 142.33/84.79 | (1263) all_1325_3_1820 = all_993_0_1256
% 142.33/84.79 |
% 142.33/84.79 | Simplifying 1263 yields:
% 142.33/84.79 | (1264) all_1325_3_1820 = all_993_0_1256
% 142.33/84.79 |
% 142.33/84.79 | Combining equations (1153,1262) yields a new equation:
% 142.33/84.79 | (1265) all_1295_3_1760 = all_1156_1_1491
% 142.33/84.79 |
% 142.33/84.79 | Simplifying 1265 yields:
% 142.33/84.79 | (1266) all_1295_3_1760 = all_1156_1_1491
% 142.33/84.79 |
% 142.33/84.79 | Combining equations (1179,1260) yields a new equation:
% 142.33/84.79 | (1267) all_1317_3_1804 = all_582_3_730
% 142.33/84.79 |
% 142.33/84.79 | Simplifying 1267 yields:
% 142.33/84.79 | (1268) all_1317_3_1804 = all_582_3_730
% 142.33/84.79 |
% 142.33/84.79 | Combining equations (1126,1264) yields a new equation:
% 142.33/84.79 | (1269) all_1287_3_1744 = all_993_0_1256
% 142.33/84.79 |
% 142.33/84.79 | Simplifying 1269 yields:
% 142.33/84.79 | (1270) all_1287_3_1744 = all_993_0_1256
% 142.33/84.79 |
% 142.33/84.79 | Combining equations (1180,1268) yields a new equation:
% 142.33/84.79 | (1271) all_1293_3_1756 = all_582_3_730
% 142.33/84.79 |
% 142.33/84.79 | Simplifying 1271 yields:
% 142.33/84.79 | (1272) all_1293_3_1756 = all_582_3_730
% 142.33/84.79 |
% 142.33/84.79 | Combining equations (1154,1266) yields a new equation:
% 142.33/84.79 | (1273) all_1260_4_1680 = all_1156_1_1491
% 142.33/84.79 |
% 142.33/84.79 | Simplifying 1273 yields:
% 142.33/84.79 | (1274) all_1260_4_1680 = all_1156_1_1491
% 142.33/84.79 |
% 142.33/84.79 | Combining equations (1196,1272) yields a new equation:
% 142.33/84.79 | (1275) all_670_1_853 = all_582_3_730
% 142.33/84.79 |
% 142.33/84.79 | Simplifying 1275 yields:
% 142.33/84.79 | (1276) all_670_1_853 = all_582_3_730
% 142.33/84.79 |
% 142.33/84.79 | Combining equations (1128,1270) yields a new equation:
% 142.33/84.79 | (1277) all_1258_3_1674 = all_993_0_1256
% 142.33/84.79 |
% 142.33/84.79 | Simplifying 1277 yields:
% 142.33/84.79 | (1278) all_1258_3_1674 = all_993_0_1256
% 142.33/84.79 |
% 142.33/84.79 | Combining equations (1182,1254) yields a new equation:
% 142.33/84.79 | (1279) all_1242_3_1641 = all_393_3_533
% 142.33/84.79 |
% 142.33/84.79 | Simplifying 1279 yields:
% 142.33/84.79 | (1280) all_1242_3_1641 = all_393_3_533
% 142.33/84.79 |
% 142.33/84.79 | Combining equations (1184,1201) yields a new equation:
% 142.33/84.79 | (1281) all_1135_3_1462 = all_664_4_847
% 142.33/84.79 |
% 142.33/84.79 | Simplifying 1281 yields:
% 142.33/84.79 | (1282) all_1135_3_1462 = all_664_4_847
% 142.33/84.79 |
% 142.33/84.79 | Combining equations (1145,1147) yields a new equation:
% 142.33/84.79 | (1283) all_1258_4_1675 = all_261_5_383
% 142.33/84.79 |
% 142.33/84.79 | Simplifying 1283 yields:
% 142.33/84.79 | (1284) all_1258_4_1675 = all_261_5_383
% 142.33/84.79 |
% 142.33/84.79 | Combining equations (1155,1274) yields a new equation:
% 142.33/84.79 | (1285) all_1244_3_1645 = all_1156_1_1491
% 142.33/84.79 |
% 142.33/84.79 | Simplifying 1285 yields:
% 142.33/84.79 | (1286) all_1244_3_1645 = all_1156_1_1491
% 142.33/84.79 |
% 142.33/84.79 | Combining equations (1216,1278) yields a new equation:
% 142.33/84.79 | (1287) all_1236_3_1629 = all_993_0_1256
% 142.33/84.79 |
% 142.33/84.79 | Simplifying 1287 yields:
% 142.33/84.79 | (1288) all_1236_3_1629 = all_993_0_1256
% 142.33/84.79 |
% 142.33/84.79 | Combining equations (1146,1284) yields a new equation:
% 142.33/84.79 | (1289) all_261_5_383 = 0
% 142.33/84.79 |
% 142.33/84.79 | Combining equations (1158,1286) yields a new equation:
% 142.33/84.79 | (1290) all_1160_3_1498 = all_1156_1_1491
% 142.33/84.79 |
% 142.33/84.79 | Simplifying 1290 yields:
% 142.33/84.79 | (1291) all_1160_3_1498 = all_1156_1_1491
% 142.33/84.79 |
% 142.33/84.79 | Combining equations (1186,1280) yields a new equation:
% 142.33/84.79 | (1292) all_1119_4_1436 = all_393_3_533
% 142.33/84.79 |
% 142.33/84.79 | Simplifying 1292 yields:
% 142.33/84.79 | (1293) all_1119_4_1436 = all_393_3_533
% 142.33/84.79 |
% 142.33/84.79 | Combining equations (1226,1288) yields a new equation:
% 142.33/84.79 | (1294) all_1111_2_1420 = all_993_0_1256
% 142.33/84.79 |
% 142.33/84.79 | Simplifying 1294 yields:
% 142.33/84.79 | (1295) all_1111_2_1420 = all_993_0_1256
% 142.33/84.79 |
% 142.33/84.79 | Combining equations (1160,1243) yields a new equation:
% 142.33/84.79 | (1296) all_1162_4_1503 = all_1158_2_1494
% 142.33/84.79 |
% 142.33/84.79 | Combining equations (1159,1243) yields a new equation:
% 142.33/84.79 | (1297) all_1162_4_1503 = all_1160_3_1498
% 142.33/84.79 |
% 142.33/84.79 | Combining equations (1162,1243) yields a new equation:
% 142.33/84.79 | (1298) all_1162_4_1503 = all_1143_1_1473
% 142.33/84.79 |
% 142.33/84.79 | Combining equations (1164,1243) yields a new equation:
% 142.33/84.79 | (1299) all_1162_4_1503 = all_1139_1_1468
% 142.33/84.79 |
% 142.33/84.79 | Combining equations (1297,1296) yields a new equation:
% 142.33/84.79 | (1300) all_1160_3_1498 = all_1158_2_1494
% 142.33/84.79 |
% 142.33/84.79 | Simplifying 1300 yields:
% 142.33/84.79 | (1301) all_1160_3_1498 = all_1158_2_1494
% 142.33/84.79 |
% 142.33/84.79 | Combining equations (1298,1296) yields a new equation:
% 142.33/84.79 | (1302) all_1158_2_1494 = all_1143_1_1473
% 142.33/84.79 |
% 142.33/84.79 | Combining equations (1299,1296) yields a new equation:
% 142.33/84.79 | (1303) all_1158_2_1494 = all_1139_1_1468
% 142.33/84.79 |
% 142.33/84.79 | Combining equations (1301,1291) yields a new equation:
% 142.33/84.79 | (1304) all_1158_2_1494 = all_1156_1_1491
% 142.33/84.79 |
% 142.33/84.79 | Simplifying 1304 yields:
% 142.33/84.79 | (1305) all_1158_2_1494 = all_1156_1_1491
% 142.33/84.79 |
% 142.33/84.79 | Combining equations (1303,1305) yields a new equation:
% 142.33/84.79 | (1306) all_1156_1_1491 = all_1139_1_1468
% 142.33/84.79 |
% 142.33/84.79 | Combining equations (1302,1305) yields a new equation:
% 142.33/84.79 | (1307) all_1156_1_1491 = all_1143_1_1473
% 142.33/84.79 |
% 142.33/84.79 | Combining equations (1307,1306) yields a new equation:
% 142.33/84.79 | (1308) all_1143_1_1473 = all_1139_1_1468
% 142.33/84.79 |
% 142.33/84.79 | Simplifying 1308 yields:
% 142.33/84.79 | (1309) all_1143_1_1473 = all_1139_1_1468
% 142.33/84.79 |
% 142.33/84.79 | Combining equations (1167,1309) yields a new equation:
% 142.33/84.79 | (1310) all_1139_1_1468 = all_554_1_702
% 142.33/84.79 |
% 142.33/84.79 | Combining equations (1165,1309) yields a new equation:
% 142.33/84.79 | (1311) all_1139_1_1468 = all_1133_1_1458
% 142.33/84.79 |
% 142.33/84.79 | Combining equations (1166,1163) yields a new equation:
% 142.33/84.79 | (1312) all_1133_1_1458 = 0
% 142.33/84.79 |
% 142.33/84.79 | Simplifying 1312 yields:
% 142.33/84.79 | (1313) all_1133_1_1458 = 0
% 142.33/84.79 |
% 142.33/84.79 | Combining equations (1311,1310) yields a new equation:
% 142.33/84.79 | (1314) all_1133_1_1458 = all_554_1_702
% 142.33/84.79 |
% 142.33/84.79 | Simplifying 1314 yields:
% 142.33/84.79 | (1315) all_1133_1_1458 = all_554_1_702
% 142.33/84.79 |
% 142.33/84.79 | Combining equations (1188,1256) yields a new equation:
% 142.33/84.79 | (1316) all_1115_1_1428 = all_1035_3_1311
% 142.33/84.79 |
% 142.33/84.79 | Combining equations (1185,1256) yields a new equation:
% 142.33/84.79 | (1317) all_1135_3_1462 = all_1115_1_1428
% 142.33/84.79 |
% 142.33/84.79 | Simplifying 1317 yields:
% 142.33/84.79 | (1318) all_1135_3_1462 = all_1115_1_1428
% 142.33/84.79 |
% 142.33/84.79 | Combining equations (1318,1282) yields a new equation:
% 142.33/84.79 | (1319) all_1115_1_1428 = all_664_4_847
% 142.33/84.79 |
% 142.33/84.79 | Simplifying 1319 yields:
% 142.33/84.79 | (1320) all_1115_1_1428 = all_664_4_847
% 142.33/84.79 |
% 142.33/84.79 | Combining equations (1313,1315) yields a new equation:
% 142.33/84.79 | (1321) all_554_1_702 = 0
% 142.33/84.79 |
% 142.33/84.79 | Combining equations (1189,1293) yields a new equation:
% 142.33/84.79 | (1322) all_922_1_1166 = all_393_3_533
% 142.33/84.79 |
% 142.33/84.79 | Simplifying 1322 yields:
% 142.33/84.79 | (1323) all_922_1_1166 = all_393_3_533
% 142.33/84.79 |
% 142.33/84.79 | Combining equations (1190,1193) yields a new equation:
% 142.33/84.79 | (1324) all_922_1_1166 = all_744_3_949
% 142.33/84.79 |
% 142.33/84.79 | Simplifying 1324 yields:
% 142.33/84.79 | (1325) all_922_1_1166 = all_744_3_949
% 142.33/84.79 |
% 142.33/84.79 | Combining equations (1195,1193) yields a new equation:
% 142.33/84.80 | (1326) all_744_3_949 = all_724_1_921
% 142.33/84.80 |
% 142.33/84.80 | Combining equations (1316,1320) yields a new equation:
% 142.33/84.80 | (1327) all_1035_3_1311 = all_664_4_847
% 142.33/84.80 |
% 142.33/84.80 | Simplifying 1327 yields:
% 142.33/84.80 | (1328) all_1035_3_1311 = all_664_4_847
% 142.33/84.80 |
% 142.33/84.80 | Combining equations (1227,1295) yields a new equation:
% 142.33/84.80 | (1329) all_993_0_1256 = all_863_1_1108
% 142.33/84.80 |
% 142.33/84.80 | Combining equations (1224,1295) yields a new equation:
% 142.33/84.80 | (1330) all_993_0_1256 = all_904_1_1143
% 142.33/84.80 |
% 142.33/84.80 | Combining equations (1223,1295) yields a new equation:
% 142.33/84.80 | (1331) all_993_0_1256 = all_986_0_1249
% 142.33/84.80 |
% 142.33/84.80 | Combining equations (1192,1328) yields a new equation:
% 142.33/84.80 | (1332) all_920_1_1164 = all_664_4_847
% 142.33/84.80 |
% 142.33/84.80 | Simplifying 1332 yields:
% 142.33/84.80 | (1333) all_920_1_1164 = all_664_4_847
% 142.33/84.80 |
% 142.33/84.80 | Combining equations (1134,1248) yields a new equation:
% 142.33/84.80 | (1334) all_986_0_1249 = all_230_1_342
% 142.33/84.80 |
% 142.33/84.80 | Simplifying 1334 yields:
% 142.33/84.80 | (1335) all_986_0_1249 = all_230_1_342
% 142.33/84.80 |
% 142.33/84.80 | Combining equations (1329,1330) yields a new equation:
% 142.33/84.80 | (1336) all_904_1_1143 = all_863_1_1108
% 142.33/84.80 |
% 142.33/84.80 | Combining equations (1331,1330) yields a new equation:
% 142.33/84.80 | (1337) all_986_0_1249 = all_904_1_1143
% 142.33/84.80 |
% 142.33/84.80 | Simplifying 1337 yields:
% 142.33/84.80 | (1338) all_986_0_1249 = all_904_1_1143
% 142.33/84.80 |
% 142.33/84.80 | Combining equations (1138,1142) yields a new equation:
% 142.33/84.80 | (1339) all_554_0_701 = all_232_0_343
% 142.33/84.80 |
% 142.33/84.80 | Simplifying 1339 yields:
% 142.33/84.80 | (1340) all_554_0_701 = all_232_0_343
% 142.33/84.80 |
% 142.33/84.80 | Combining equations (1338,1335) yields a new equation:
% 142.33/84.80 | (1341) all_904_1_1143 = all_230_1_342
% 142.33/84.80 |
% 142.33/84.80 | Simplifying 1341 yields:
% 142.33/84.80 | (1342) all_904_1_1143 = all_230_1_342
% 142.33/84.80 |
% 142.33/84.80 | Combining equations (1325,1323) yields a new equation:
% 142.33/84.80 | (1343) all_744_3_949 = all_393_3_533
% 142.33/84.80 |
% 142.33/84.80 | Simplifying 1343 yields:
% 142.33/84.80 | (1344) all_744_3_949 = all_393_3_533
% 142.33/84.80 |
% 142.33/84.80 | Combining equations (1197,1333) yields a new equation:
% 142.33/84.80 | (1345) all_670_1_853 = all_664_4_847
% 142.33/84.80 |
% 142.33/84.80 | Simplifying 1345 yields:
% 142.33/84.80 | (1346) all_670_1_853 = all_664_4_847
% 142.33/84.80 |
% 142.33/84.80 | Combining equations (1245,1333) yields a new equation:
% 142.33/84.80 | (1347) all_738_2_939 = all_664_4_847
% 142.33/84.80 |
% 142.33/84.80 | Simplifying 1347 yields:
% 142.33/84.80 | (1348) all_738_2_939 = all_664_4_847
% 142.33/84.80 |
% 142.33/84.80 | Combining equations (1336,1342) yields a new equation:
% 142.33/84.80 | (1349) all_863_1_1108 = all_230_1_342
% 142.33/84.80 |
% 142.33/84.80 | Simplifying 1349 yields:
% 142.33/84.80 | (1350) all_863_1_1108 = all_230_1_342
% 142.33/84.80 |
% 142.33/84.80 | Combining equations (1139,1350) yields a new equation:
% 142.33/84.80 | (1351) all_361_1_486 = all_230_1_342
% 142.33/84.80 |
% 142.33/84.80 | Simplifying 1351 yields:
% 142.33/84.80 | (1352) all_361_1_486 = all_230_1_342
% 142.33/84.80 |
% 142.33/84.80 | Combining equations (1326,1344) yields a new equation:
% 142.33/84.80 | (1353) all_724_1_921 = all_393_3_533
% 142.33/84.80 |
% 142.33/84.80 | Simplifying 1353 yields:
% 142.33/84.80 | (1354) all_724_1_921 = all_393_3_533
% 142.33/84.80 |
% 142.33/84.80 | Combining equations (1348,1246) yields a new equation:
% 142.33/84.80 | (1355) all_664_4_847 = all_289_3_415
% 142.33/84.80 |
% 142.56/84.80 | Simplifying 1355 yields:
% 142.56/84.80 | (1356) all_664_4_847 = all_289_3_415
% 142.56/84.80 |
% 142.56/84.80 | Combining equations (1199,1354) yields a new equation:
% 142.56/84.80 | (1357) all_668_1_851 = all_393_3_533
% 142.56/84.80 |
% 142.56/84.80 | Simplifying 1357 yields:
% 142.56/84.80 | (1358) all_668_1_851 = all_393_3_533
% 142.56/84.80 |
% 142.56/84.80 | Combining equations (1200,1202) yields a new equation:
% 142.56/84.80 | (1359) all_668_1_851 = all_662_3_842
% 142.56/84.80 |
% 142.56/84.80 | Simplifying 1359 yields:
% 142.56/84.80 | (1360) all_668_1_851 = all_662_3_842
% 142.56/84.80 |
% 142.56/84.80 | Combining equations (1346,1202) yields a new equation:
% 142.56/84.80 | (1361) all_664_4_847 = all_662_3_842
% 142.56/84.80 |
% 142.56/84.80 | Simplifying 1361 yields:
% 142.56/84.80 | (1362) all_664_4_847 = all_662_3_842
% 142.56/84.80 |
% 142.56/84.80 | Combining equations (1276,1202) yields a new equation:
% 142.56/84.80 | (1363) all_662_3_842 = all_582_3_730
% 142.56/84.80 |
% 142.56/84.80 | Combining equations (1198,1358) yields a new equation:
% 142.56/84.80 | (1364) all_393_3_533 = 0
% 142.56/84.80 |
% 142.56/84.80 | Combining equations (1360,1358) yields a new equation:
% 142.56/84.80 | (1365) all_662_3_842 = all_393_3_533
% 142.56/84.80 |
% 142.56/84.80 | Simplifying 1365 yields:
% 142.56/84.80 | (1366) all_662_3_842 = all_393_3_533
% 142.56/84.80 |
% 142.56/84.80 | Combining equations (1362,1356) yields a new equation:
% 142.56/84.80 | (1367) all_662_3_842 = all_289_3_415
% 142.56/84.80 |
% 142.56/84.80 | Simplifying 1367 yields:
% 142.56/84.80 | (1368) all_662_3_842 = all_289_3_415
% 142.56/84.80 |
% 142.56/84.80 | Combining equations (1368,1363) yields a new equation:
% 142.56/84.80 | (1369) all_582_3_730 = all_289_3_415
% 142.56/84.80 |
% 142.56/84.80 | Combining equations (1366,1363) yields a new equation:
% 142.56/84.80 | (1370) all_582_3_730 = all_393_3_533
% 142.56/84.80 |
% 142.56/84.80 | Combining equations (1370,1369) yields a new equation:
% 142.56/84.80 | (1371) all_393_3_533 = all_289_3_415
% 142.56/84.80 |
% 142.56/84.80 | Simplifying 1371 yields:
% 142.56/84.80 | (1372) all_393_3_533 = all_289_3_415
% 142.56/84.80 |
% 142.56/84.80 | Combining equations (1137,1340) yields a new equation:
% 142.56/84.80 | (1373) all_232_0_343 = all_0_11_11
% 142.56/84.80 |
% 142.56/84.80 | Combining equations (1140,1340) yields a new equation:
% 142.56/84.80 | (1374) all_358_1_484 = all_232_0_343
% 142.56/84.80 |
% 142.56/84.80 | Simplifying 1374 yields:
% 142.56/84.80 | (1375) all_358_1_484 = all_232_0_343
% 142.56/84.80 |
% 142.56/84.80 | Combining equations (1144,1340) yields a new equation:
% 142.56/84.80 | (1376) all_232_0_343 = all_227_0_339
% 142.56/84.80 |
% 142.56/84.80 | Combining equations (1364,1372) yields a new equation:
% 142.56/84.80 | (1377) all_289_3_415 = 0
% 142.56/84.80 |
% 142.56/84.80 | Combining equations (1141,1352) yields a new equation:
% 142.56/84.80 | (1378) all_358_1_484 = all_230_1_342
% 142.56/84.80 |
% 142.56/84.80 | Simplifying 1378 yields:
% 142.56/84.80 | (1379) all_358_1_484 = all_230_1_342
% 142.56/84.80 |
% 142.56/84.80 | Combining equations (1375,1379) yields a new equation:
% 142.56/84.80 | (1380) all_232_0_343 = all_230_1_342
% 142.56/84.80 |
% 142.56/84.80 | Simplifying 1380 yields:
% 142.56/84.80 | (1381) all_232_0_343 = all_230_1_342
% 142.56/84.80 |
% 142.56/84.80 | Combining equations (1373,1381) yields a new equation:
% 142.56/84.80 | (1382) all_230_1_342 = all_0_11_11
% 142.56/84.80 |
% 142.56/84.80 | Combining equations (1376,1381) yields a new equation:
% 142.56/84.80 | (1383) all_230_1_342 = all_227_0_339
% 142.56/84.80 |
% 142.56/84.80 | Combining equations (1383,1382) yields a new equation:
% 142.56/84.80 | (1384) all_227_0_339 = all_0_11_11
% 142.56/84.80 |
% 142.56/84.80 | Simplifying 1384 yields:
% 142.56/84.80 | (1385) all_227_0_339 = all_0_11_11
% 142.56/84.80 |
% 142.56/84.80 | Combining equations (1382,1381) yields a new equation:
% 142.56/84.80 | (1373) all_232_0_343 = all_0_11_11
% 142.56/84.80 |
% 142.56/84.80 | Combining equations (1377,1372) yields a new equation:
% 142.56/84.80 | (1364) all_393_3_533 = 0
% 142.56/84.80 |
% 142.56/84.80 | Combining equations (1373,1340) yields a new equation:
% 142.56/84.80 | (1137) all_554_0_701 = all_0_11_11
% 142.56/84.80 |
% 142.56/84.80 | Combining equations (1377,1369) yields a new equation:
% 142.56/84.80 | (1389) all_582_3_730 = 0
% 142.56/84.80 |
% 142.56/84.80 | Combining equations (1389,1363) yields a new equation:
% 142.56/84.80 | (1390) all_662_3_842 = 0
% 142.56/84.80 |
% 142.56/84.80 | Combining equations (1377,1356) yields a new equation:
% 142.56/84.80 | (1391) all_664_4_847 = 0
% 142.56/84.80 |
% 142.56/84.80 | Combining equations (1364,1358) yields a new equation:
% 142.56/84.80 | (1198) all_668_1_851 = 0
% 142.56/84.80 |
% 142.56/84.80 | Combining equations (1390,1202) yields a new equation:
% 142.56/84.80 | (1393) all_670_1_853 = 0
% 142.56/84.80 |
% 142.56/84.80 | Combining equations (1391,1333) yields a new equation:
% 142.56/84.80 | (1394) all_920_1_1164 = 0
% 142.56/84.80 |
% 142.56/84.80 | Combining equations (1364,1323) yields a new equation:
% 142.56/84.80 | (1395) all_922_1_1166 = 0
% 142.56/84.80 |
% 142.56/84.80 | Combining equations (1321,1310) yields a new equation:
% 142.56/84.80 | (1396) all_1139_1_1468 = 0
% 142.56/84.80 |
% 142.56/84.80 | Combining equations (1396,1309) yields a new equation:
% 142.56/84.80 | (1397) all_1143_1_1473 = 0
% 142.56/84.80 |
% 142.56/84.80 | From (1385) and (556) follows:
% 142.56/84.80 | (3) relation_dom(all_0_14_14) = all_0_11_11
% 142.56/84.80 |
% 142.56/84.80 | From (1321) and (670) follows:
% 142.56/84.80 | (369) relation(all_0_14_14) = 0
% 142.56/84.80 |
% 142.56/84.80 | From (1206) and (570) follows:
% 142.56/84.80 | (221) function(all_0_14_14) = 0
% 142.56/84.80 |
% 142.56/84.80 +-Applying beta-rule and splitting (671), into two cases.
% 142.56/84.80 |-Branch one:
% 142.56/84.80 | (1401) ~ (all_554_1_702 = 0)
% 142.56/84.80 |
% 142.56/84.80 | Equations (1321) can reduce 1401 to:
% 142.56/84.80 | (1402) $false
% 142.56/84.80 |
% 142.56/84.80 |-The branch is then unsatisfiable
% 142.56/84.80 |-Branch two:
% 142.56/84.80 | (1321) all_554_1_702 = 0
% 142.56/84.80 | (1404) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (apply(all_0_14_14, v0) = v4 & in(v2, all_0_14_14) = v5 & in(v0, all_554_0_701) = v3 & ( ~ (v3 = 0) | (( ~ (v5 = 0) | v4 = v1) & ( ~ (v4 = v1) | v5 = 0))))) & ? [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v1, all_554_0_701) = v2) | ? [v3] : (apply(all_0_14_14, v1) = v3 & ( ~ (v3 = v0) | v0 = empty_set) & ( ~ (v0 = empty_set) | v3 = empty_set))) & ! [v0] : ! [v1] : (v1 = empty_set | ~ (apply(all_0_14_14, v0) = v1) | in(v0, all_554_0_701) = 0)
% 142.56/84.81 |
% 142.56/84.81 | Applying alpha-rule on (1404) yields:
% 142.56/84.81 | (1405) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (apply(all_0_14_14, v0) = v4 & in(v2, all_0_14_14) = v5 & in(v0, all_554_0_701) = v3 & ( ~ (v3 = 0) | (( ~ (v5 = 0) | v4 = v1) & ( ~ (v4 = v1) | v5 = 0)))))
% 142.56/84.81 | (1406) ? [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v1, all_554_0_701) = v2) | ? [v3] : (apply(all_0_14_14, v1) = v3 & ( ~ (v3 = v0) | v0 = empty_set) & ( ~ (v0 = empty_set) | v3 = empty_set)))
% 142.56/84.81 | (1407) ! [v0] : ! [v1] : (v1 = empty_set | ~ (apply(all_0_14_14, v0) = v1) | in(v0, all_554_0_701) = 0)
% 142.56/84.81 |
% 142.56/84.81 | Instantiating formula (1405) with all_0_13_13, all_0_15_15, all_0_16_16 and discharging atoms ordered_pair(all_0_16_16, all_0_15_15) = all_0_13_13, yields:
% 142.56/84.81 | (1408) ? [v0] : ? [v1] : ? [v2] : (apply(all_0_14_14, all_0_16_16) = v1 & in(all_0_13_13, all_0_14_14) = v2 & in(all_0_16_16, all_554_0_701) = v0 & ( ~ (v0 = 0) | (( ~ (v2 = 0) | v1 = all_0_15_15) & ( ~ (v1 = all_0_15_15) | v2 = 0))))
% 142.56/84.81 |
% 142.56/84.81 +-Applying beta-rule and splitting (694), into two cases.
% 142.56/84.81 |-Branch one:
% 142.56/84.81 | (1409) ~ (all_668_1_851 = 0)
% 142.56/84.81 |
% 142.56/84.81 | Equations (1198) can reduce 1409 to:
% 142.56/84.81 | (1402) $false
% 142.56/84.81 |
% 142.56/84.81 |-The branch is then unsatisfiable
% 142.56/84.81 |-Branch two:
% 142.56/84.81 | (1198) all_668_1_851 = 0
% 142.56/84.81 | (1412) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_dom(v0) = v4 & subset(all_668_0_850, v4) = v5 & subset(empty_set, v1) = v6 & subset(empty_set, v0) = v3 & relation(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | (v6 = 0 & v5 = 0)))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_rng(v0) = v5 & subset(all_668_0_850, v1) = v4 & subset(empty_set, v5) = v6 & subset(empty_set, v0) = v3 & relation(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | (v6 = 0 & v4 = 0)))) & ! [v0] : ( ~ (subset(empty_set, v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_rng(v0) = v4 & relation_dom(v0) = v2 & subset(all_668_0_850, v2) = v3 & subset(empty_set, v4) = v5 & relation(v0) = v1 & ( ~ (v1 = 0) | (v5 = 0 & v3 = 0)))) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_rng(v0) = v4 & relation_dom(v0) = v2 & subset(all_668_0_850, v2) = v3 & subset(empty_set, v4) = v5 & subset(empty_set, v0) = v1 & ( ~ (v1 = 0) | (v5 = 0 & v3 = 0))))
% 142.56/84.81 |
% 142.56/84.81 | Applying alpha-rule on (1412) yields:
% 142.56/84.81 | (1413) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_dom(v0) = v4 & subset(all_668_0_850, v4) = v5 & subset(empty_set, v1) = v6 & subset(empty_set, v0) = v3 & relation(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | (v6 = 0 & v5 = 0))))
% 142.56/84.81 | (1414) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_rng(v0) = v5 & subset(all_668_0_850, v1) = v4 & subset(empty_set, v5) = v6 & subset(empty_set, v0) = v3 & relation(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | (v6 = 0 & v4 = 0))))
% 142.56/84.81 | (1415) ! [v0] : ( ~ (subset(empty_set, v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_rng(v0) = v4 & relation_dom(v0) = v2 & subset(all_668_0_850, v2) = v3 & subset(empty_set, v4) = v5 & relation(v0) = v1 & ( ~ (v1 = 0) | (v5 = 0 & v3 = 0))))
% 142.56/84.81 | (1416) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_rng(v0) = v4 & relation_dom(v0) = v2 & subset(all_668_0_850, v2) = v3 & subset(empty_set, v4) = v5 & subset(empty_set, v0) = v1 & ( ~ (v1 = 0) | (v5 = 0 & v3 = 0))))
% 142.56/84.81 |
% 142.56/84.81 | Instantiating formula (1414) with all_0_11_11, all_0_14_14 and discharging atoms relation_dom(all_0_14_14) = all_0_11_11, yields:
% 142.56/84.81 | (1417) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (relation_rng(all_0_14_14) = v3 & subset(all_668_0_850, all_0_11_11) = v2 & subset(empty_set, v3) = v4 & subset(empty_set, all_0_14_14) = v1 & relation(all_0_14_14) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | (v4 = 0 & v2 = 0)))
% 142.56/84.81 |
% 142.56/84.81 | Instantiating (1408) with all_1783_0_2529, all_1783_1_2530, all_1783_2_2531 yields:
% 142.56/84.81 | (1418) apply(all_0_14_14, all_0_16_16) = all_1783_1_2530 & in(all_0_13_13, all_0_14_14) = all_1783_0_2529 & in(all_0_16_16, all_554_0_701) = all_1783_2_2531 & ( ~ (all_1783_2_2531 = 0) | (( ~ (all_1783_0_2529 = 0) | all_1783_1_2530 = all_0_15_15) & ( ~ (all_1783_1_2530 = all_0_15_15) | all_1783_0_2529 = 0)))
% 142.56/84.81 |
% 142.56/84.81 | Applying alpha-rule on (1418) yields:
% 142.56/84.81 | (1419) apply(all_0_14_14, all_0_16_16) = all_1783_1_2530
% 142.56/84.81 | (1420) in(all_0_13_13, all_0_14_14) = all_1783_0_2529
% 142.56/84.81 | (1421) in(all_0_16_16, all_554_0_701) = all_1783_2_2531
% 142.56/84.81 | (1422) ~ (all_1783_2_2531 = 0) | (( ~ (all_1783_0_2529 = 0) | all_1783_1_2530 = all_0_15_15) & ( ~ (all_1783_1_2530 = all_0_15_15) | all_1783_0_2529 = 0))
% 142.56/84.81 |
% 142.56/84.81 | Instantiating (1417) with all_1799_0_2565, all_1799_1_2566, all_1799_2_2567, all_1799_3_2568, all_1799_4_2569 yields:
% 142.56/84.81 | (1423) relation_rng(all_0_14_14) = all_1799_1_2566 & subset(all_668_0_850, all_0_11_11) = all_1799_2_2567 & subset(empty_set, all_1799_1_2566) = all_1799_0_2565 & subset(empty_set, all_0_14_14) = all_1799_3_2568 & relation(all_0_14_14) = all_1799_4_2569 & ( ~ (all_1799_3_2568 = 0) | ~ (all_1799_4_2569 = 0) | (all_1799_0_2565 = 0 & all_1799_2_2567 = 0))
% 142.56/84.81 |
% 142.56/84.81 | Applying alpha-rule on (1423) yields:
% 142.56/84.81 | (1424) subset(all_668_0_850, all_0_11_11) = all_1799_2_2567
% 142.56/84.81 | (1425) relation(all_0_14_14) = all_1799_4_2569
% 142.56/84.81 | (1426) subset(empty_set, all_1799_1_2566) = all_1799_0_2565
% 142.56/84.81 | (1427) relation_rng(all_0_14_14) = all_1799_1_2566
% 142.56/84.81 | (1428) subset(empty_set, all_0_14_14) = all_1799_3_2568
% 142.56/84.81 | (1429) ~ (all_1799_3_2568 = 0) | ~ (all_1799_4_2569 = 0) | (all_1799_0_2565 = 0 & all_1799_2_2567 = 0)
% 142.56/84.81 |
% 142.56/84.81 | From (1137) and (1421) follows:
% 142.56/84.81 | (1430) in(all_0_16_16, all_0_11_11) = all_1783_2_2531
% 142.56/84.81 |
% 142.56/84.81 +-Applying beta-rule and splitting (581), into two cases.
% 142.56/84.81 |-Branch one:
% 142.56/84.81 | (1431) ~ (all_261_5_383 = 0)
% 142.56/84.81 |
% 142.56/84.81 | Equations (1289) can reduce 1431 to:
% 142.56/84.81 | (1402) $false
% 142.56/84.81 |
% 142.56/84.81 |-The branch is then unsatisfiable
% 142.56/84.81 |-Branch two:
% 142.56/84.81 | (1289) all_261_5_383 = 0
% 142.56/84.81 | (1434) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (in(v2, all_0_14_14) = v4 & in(v2, empty_set) = v3 & ( ~ (v3 = 0) | v4 = 0)))
% 142.56/84.81 |
% 142.56/84.81 | Instantiating formula (1434) with all_0_13_13, all_0_15_15, all_0_16_16 and discharging atoms ordered_pair(all_0_16_16, all_0_15_15) = all_0_13_13, yields:
% 142.56/84.81 | (1435) ? [v0] : ? [v1] : (in(all_0_13_13, all_0_14_14) = v1 & in(all_0_13_13, empty_set) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 142.56/84.81 |
% 142.56/84.81 | Instantiating (1435) with all_1867_0_2637, all_1867_1_2638 yields:
% 142.56/84.81 | (1436) in(all_0_13_13, all_0_14_14) = all_1867_0_2637 & in(all_0_13_13, empty_set) = all_1867_1_2638 & ( ~ (all_1867_1_2638 = 0) | all_1867_0_2637 = 0)
% 142.56/84.81 |
% 142.56/84.81 | Applying alpha-rule on (1436) yields:
% 142.56/84.81 | (1437) in(all_0_13_13, all_0_14_14) = all_1867_0_2637
% 142.56/84.81 | (1438) in(all_0_13_13, empty_set) = all_1867_1_2638
% 142.56/84.82 | (1439) ~ (all_1867_1_2638 = 0) | all_1867_0_2637 = 0
% 142.56/84.82 |
% 142.56/84.82 +-Applying beta-rule and splitting (571), into two cases.
% 142.56/84.82 |-Branch one:
% 142.56/84.82 | (1440) ~ (all_232_1_344 = 0)
% 142.56/84.82 |
% 142.56/84.82 | Equations (1206) can reduce 1440 to:
% 142.56/84.82 | (1402) $false
% 142.56/84.82 |
% 142.56/84.82 |-The branch is then unsatisfiable
% 142.56/84.82 |-Branch two:
% 142.56/84.82 | (1206) all_232_1_344 = 0
% 142.56/84.82 | (1443) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (apply(all_0_14_14, v0) = v4 & in(v2, all_0_14_14) = v5 & in(v0, all_232_0_343) = v3 & ( ~ (v3 = 0) | (( ~ (v5 = 0) | v4 = v1) & ( ~ (v4 = v1) | v5 = 0))))) & ? [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v1, all_232_0_343) = v2) | ? [v3] : (apply(all_0_14_14, v1) = v3 & ( ~ (v3 = v0) | v0 = empty_set) & ( ~ (v0 = empty_set) | v3 = empty_set))) & ! [v0] : ! [v1] : (v1 = empty_set | ~ (apply(all_0_14_14, v0) = v1) | in(v0, all_232_0_343) = 0)
% 142.56/84.82 |
% 142.56/84.82 | Applying alpha-rule on (1443) yields:
% 142.56/84.82 | (1444) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (apply(all_0_14_14, v0) = v4 & in(v2, all_0_14_14) = v5 & in(v0, all_232_0_343) = v3 & ( ~ (v3 = 0) | (( ~ (v5 = 0) | v4 = v1) & ( ~ (v4 = v1) | v5 = 0)))))
% 142.56/84.82 | (1445) ? [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v1, all_232_0_343) = v2) | ? [v3] : (apply(all_0_14_14, v1) = v3 & ( ~ (v3 = v0) | v0 = empty_set) & ( ~ (v0 = empty_set) | v3 = empty_set)))
% 142.56/84.82 | (1446) ! [v0] : ! [v1] : (v1 = empty_set | ~ (apply(all_0_14_14, v0) = v1) | in(v0, all_232_0_343) = 0)
% 142.56/84.82 |
% 142.56/84.82 | Instantiating formula (1444) with all_0_13_13, all_0_15_15, all_0_16_16 and discharging atoms ordered_pair(all_0_16_16, all_0_15_15) = all_0_13_13, yields:
% 142.56/84.82 | (1447) ? [v0] : ? [v1] : ? [v2] : (apply(all_0_14_14, all_0_16_16) = v1 & in(all_0_13_13, all_0_14_14) = v2 & in(all_0_16_16, all_232_0_343) = v0 & ( ~ (v0 = 0) | (( ~ (v2 = 0) | v1 = all_0_15_15) & ( ~ (v1 = all_0_15_15) | v2 = 0))))
% 142.56/84.82 |
% 142.56/84.82 | Instantiating (1447) with all_1881_0_2642, all_1881_1_2643, all_1881_2_2644 yields:
% 142.56/84.82 | (1448) apply(all_0_14_14, all_0_16_16) = all_1881_1_2643 & in(all_0_13_13, all_0_14_14) = all_1881_0_2642 & in(all_0_16_16, all_232_0_343) = all_1881_2_2644 & ( ~ (all_1881_2_2644 = 0) | (( ~ (all_1881_0_2642 = 0) | all_1881_1_2643 = all_0_15_15) & ( ~ (all_1881_1_2643 = all_0_15_15) | all_1881_0_2642 = 0)))
% 142.56/84.82 |
% 142.56/84.82 | Applying alpha-rule on (1448) yields:
% 142.56/84.82 | (1449) apply(all_0_14_14, all_0_16_16) = all_1881_1_2643
% 142.56/84.82 | (1450) in(all_0_13_13, all_0_14_14) = all_1881_0_2642
% 142.56/84.82 | (1451) in(all_0_16_16, all_232_0_343) = all_1881_2_2644
% 142.56/84.82 | (1452) ~ (all_1881_2_2644 = 0) | (( ~ (all_1881_0_2642 = 0) | all_1881_1_2643 = all_0_15_15) & ( ~ (all_1881_1_2643 = all_0_15_15) | all_1881_0_2642 = 0))
% 142.56/84.82 |
% 142.56/84.82 | From (1373) and (1451) follows:
% 142.56/84.82 | (1453) in(all_0_16_16, all_0_11_11) = all_1881_2_2644
% 142.56/84.82 |
% 142.56/84.82 +-Applying beta-rule and splitting (824), into two cases.
% 142.56/84.82 |-Branch one:
% 142.56/84.82 | (1454) ~ (all_1139_1_1468 = 0)
% 142.56/84.82 |
% 142.56/84.82 | Equations (1396) can reduce 1454 to:
% 142.56/84.82 | (1402) $false
% 142.56/84.82 |
% 142.56/84.82 |-The branch is then unsatisfiable
% 142.56/84.82 |-Branch two:
% 142.56/84.82 | (1396) all_1139_1_1468 = 0
% 142.56/84.82 | (1457) ! [v0] : ! [v1] : ( ~ (relation_composition(all_0_14_14, v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_dom(v1) = v5 & relation_dom(v0) = v3 & subset(all_1139_0_1467, v3) = v4 & relation(v0) = v2 & ( ~ (v4 = 0) | ~ (v2 = 0) | v5 = all_0_11_11))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_composition(all_0_14_14, v0) = v4 & relation_dom(v4) = v5 & subset(all_1139_0_1467, v1) = v3 & relation(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | v5 = all_0_11_11))) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : (relation_composition(all_0_14_14, v0) = v3 & relation_dom(v3) = v4 & relation_dom(v0) = v1 & subset(all_1139_0_1467, v1) = v2 & ( ~ (v2 = 0) | v4 = all_0_11_11)))
% 142.56/84.82 |
% 142.56/84.82 | Applying alpha-rule on (1457) yields:
% 142.56/84.82 | (1458) ! [v0] : ! [v1] : ( ~ (relation_composition(all_0_14_14, v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_dom(v1) = v5 & relation_dom(v0) = v3 & subset(all_1139_0_1467, v3) = v4 & relation(v0) = v2 & ( ~ (v4 = 0) | ~ (v2 = 0) | v5 = all_0_11_11)))
% 142.56/84.82 | (1459) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_composition(all_0_14_14, v0) = v4 & relation_dom(v4) = v5 & subset(all_1139_0_1467, v1) = v3 & relation(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | v5 = all_0_11_11)))
% 142.56/84.82 | (1460) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : (relation_composition(all_0_14_14, v0) = v3 & relation_dom(v3) = v4 & relation_dom(v0) = v1 & subset(all_1139_0_1467, v1) = v2 & ( ~ (v2 = 0) | v4 = all_0_11_11)))
% 142.56/84.82 |
% 142.56/84.82 | Instantiating formula (1459) with all_0_11_11, all_0_14_14 and discharging atoms relation_dom(all_0_14_14) = all_0_11_11, yields:
% 142.56/84.82 | (1461) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (relation_composition(all_0_14_14, all_0_14_14) = v2 & relation_dom(v2) = v3 & subset(all_1139_0_1467, all_0_11_11) = v1 & relation(all_0_14_14) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = all_0_11_11))
% 142.56/84.82 |
% 142.56/84.82 +-Applying beta-rule and splitting (833), into two cases.
% 142.56/84.82 |-Branch one:
% 142.56/84.82 | (1462) ~ (all_1143_1_1473 = 0)
% 142.56/84.82 |
% 142.56/84.82 | Equations (1397) can reduce 1462 to:
% 142.56/84.82 | (1402) $false
% 142.56/84.82 |
% 142.56/84.82 |-The branch is then unsatisfiable
% 142.56/84.82 |-Branch two:
% 142.56/84.82 | (1397) all_1143_1_1473 = 0
% 142.56/84.82 | (1465) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_dom(v0) = v4 & subset(all_1143_0_1472, v1) = v6 & subset(all_0_11_11, v4) = v5 & subset(all_0_14_14, v0) = v3 & relation(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | (v6 = 0 & v5 = 0)))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_rng(v0) = v5 & subset(all_1143_0_1472, v5) = v6 & subset(all_0_11_11, v1) = v4 & subset(all_0_14_14, v0) = v3 & relation(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | (v6 = 0 & v4 = 0)))) & ! [v0] : ( ~ (subset(all_0_14_14, v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_rng(v0) = v4 & relation_dom(v0) = v2 & subset(all_1143_0_1472, v4) = v5 & subset(all_0_11_11, v2) = v3 & relation(v0) = v1 & ( ~ (v1 = 0) | (v5 = 0 & v3 = 0)))) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_rng(v0) = v4 & relation_dom(v0) = v2 & subset(all_1143_0_1472, v4) = v5 & subset(all_0_11_11, v2) = v3 & subset(all_0_14_14, v0) = v1 & ( ~ (v1 = 0) | (v5 = 0 & v3 = 0))))
% 142.56/84.82 |
% 142.56/84.82 | Applying alpha-rule on (1465) yields:
% 142.56/84.82 | (1466) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_dom(v0) = v4 & subset(all_1143_0_1472, v1) = v6 & subset(all_0_11_11, v4) = v5 & subset(all_0_14_14, v0) = v3 & relation(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | (v6 = 0 & v5 = 0))))
% 142.56/84.82 | (1467) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_rng(v0) = v5 & subset(all_1143_0_1472, v5) = v6 & subset(all_0_11_11, v1) = v4 & subset(all_0_14_14, v0) = v3 & relation(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | (v6 = 0 & v4 = 0))))
% 142.56/84.83 | (1468) ! [v0] : ( ~ (subset(all_0_14_14, v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_rng(v0) = v4 & relation_dom(v0) = v2 & subset(all_1143_0_1472, v4) = v5 & subset(all_0_11_11, v2) = v3 & relation(v0) = v1 & ( ~ (v1 = 0) | (v5 = 0 & v3 = 0))))
% 142.56/84.83 | (1469) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_rng(v0) = v4 & relation_dom(v0) = v2 & subset(all_1143_0_1472, v4) = v5 & subset(all_0_11_11, v2) = v3 & subset(all_0_14_14, v0) = v1 & ( ~ (v1 = 0) | (v5 = 0 & v3 = 0))))
% 142.56/84.83 |
% 142.56/84.83 | Instantiating formula (1467) with all_0_11_11, all_0_14_14 and discharging atoms relation_dom(all_0_14_14) = all_0_11_11, yields:
% 142.56/84.83 | (1470) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (relation_rng(all_0_14_14) = v3 & subset(all_1143_0_1472, v3) = v4 & subset(all_0_11_11, all_0_11_11) = v2 & subset(all_0_14_14, all_0_14_14) = v1 & relation(all_0_14_14) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | (v4 = 0 & v2 = 0)))
% 142.56/84.83 |
% 142.56/84.83 | Instantiating (1461) with all_1939_0_2720, all_1939_1_2721, all_1939_2_2722, all_1939_3_2723 yields:
% 142.56/84.83 | (1471) relation_composition(all_0_14_14, all_0_14_14) = all_1939_1_2721 & relation_dom(all_1939_1_2721) = all_1939_0_2720 & subset(all_1139_0_1467, all_0_11_11) = all_1939_2_2722 & relation(all_0_14_14) = all_1939_3_2723 & ( ~ (all_1939_2_2722 = 0) | ~ (all_1939_3_2723 = 0) | all_1939_0_2720 = all_0_11_11)
% 142.56/84.83 |
% 142.56/84.83 | Applying alpha-rule on (1471) yields:
% 142.56/84.83 | (1472) relation_composition(all_0_14_14, all_0_14_14) = all_1939_1_2721
% 142.56/84.83 | (1473) relation(all_0_14_14) = all_1939_3_2723
% 142.56/84.83 | (1474) ~ (all_1939_2_2722 = 0) | ~ (all_1939_3_2723 = 0) | all_1939_0_2720 = all_0_11_11
% 142.56/84.83 | (1475) subset(all_1139_0_1467, all_0_11_11) = all_1939_2_2722
% 142.56/84.83 | (1476) relation_dom(all_1939_1_2721) = all_1939_0_2720
% 142.56/84.83 |
% 142.56/84.83 | Instantiating (1470) with all_1955_0_2754, all_1955_1_2755, all_1955_2_2756, all_1955_3_2757, all_1955_4_2758 yields:
% 142.56/84.83 | (1477) relation_rng(all_0_14_14) = all_1955_1_2755 & subset(all_1143_0_1472, all_1955_1_2755) = all_1955_0_2754 & subset(all_0_11_11, all_0_11_11) = all_1955_2_2756 & subset(all_0_14_14, all_0_14_14) = all_1955_3_2757 & relation(all_0_14_14) = all_1955_4_2758 & ( ~ (all_1955_3_2757 = 0) | ~ (all_1955_4_2758 = 0) | (all_1955_0_2754 = 0 & all_1955_2_2756 = 0))
% 142.56/84.83 |
% 142.56/84.83 | Applying alpha-rule on (1477) yields:
% 142.56/84.83 | (1478) relation(all_0_14_14) = all_1955_4_2758
% 142.56/84.83 | (1479) relation_rng(all_0_14_14) = all_1955_1_2755
% 142.56/84.83 | (1480) subset(all_0_11_11, all_0_11_11) = all_1955_2_2756
% 142.56/84.83 | (1481) ~ (all_1955_3_2757 = 0) | ~ (all_1955_4_2758 = 0) | (all_1955_0_2754 = 0 & all_1955_2_2756 = 0)
% 142.56/84.83 | (1482) subset(all_1143_0_1472, all_1955_1_2755) = all_1955_0_2754
% 142.56/84.83 | (1483) subset(all_0_14_14, all_0_14_14) = all_1955_3_2757
% 142.56/84.83 |
% 142.56/84.83 +-Applying beta-rule and splitting (726), into two cases.
% 142.56/84.83 |-Branch one:
% 142.56/84.83 | (1484) ~ (all_920_1_1164 = 0)
% 142.56/84.83 |
% 142.56/84.83 | Equations (1394) can reduce 1484 to:
% 142.56/84.83 | (1402) $false
% 142.56/84.83 |
% 142.56/84.83 |-The branch is then unsatisfiable
% 142.56/84.83 |-Branch two:
% 142.56/84.83 | (1394) all_920_1_1164 = 0
% 142.56/84.83 | (1487) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_dom(v0) = v4 & subset(all_920_0_1163, v1) = v6 & subset(empty_set, v4) = v5 & subset(empty_set, v0) = v3 & relation(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | (v6 = 0 & v5 = 0)))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_rng(v0) = v5 & subset(all_920_0_1163, v5) = v6 & subset(empty_set, v1) = v4 & subset(empty_set, v0) = v3 & relation(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | (v6 = 0 & v4 = 0)))) & ! [v0] : ( ~ (subset(empty_set, v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_rng(v0) = v4 & relation_dom(v0) = v2 & subset(all_920_0_1163, v4) = v5 & subset(empty_set, v2) = v3 & relation(v0) = v1 & ( ~ (v1 = 0) | (v5 = 0 & v3 = 0)))) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_rng(v0) = v4 & relation_dom(v0) = v2 & subset(all_920_0_1163, v4) = v5 & subset(empty_set, v2) = v3 & subset(empty_set, v0) = v1 & ( ~ (v1 = 0) | (v5 = 0 & v3 = 0))))
% 142.56/84.83 |
% 142.56/84.83 | Applying alpha-rule on (1487) yields:
% 142.56/84.83 | (1488) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_dom(v0) = v4 & subset(all_920_0_1163, v1) = v6 & subset(empty_set, v4) = v5 & subset(empty_set, v0) = v3 & relation(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | (v6 = 0 & v5 = 0))))
% 142.56/84.83 | (1489) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_rng(v0) = v5 & subset(all_920_0_1163, v5) = v6 & subset(empty_set, v1) = v4 & subset(empty_set, v0) = v3 & relation(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | (v6 = 0 & v4 = 0))))
% 142.56/84.83 | (1490) ! [v0] : ( ~ (subset(empty_set, v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_rng(v0) = v4 & relation_dom(v0) = v2 & subset(all_920_0_1163, v4) = v5 & subset(empty_set, v2) = v3 & relation(v0) = v1 & ( ~ (v1 = 0) | (v5 = 0 & v3 = 0))))
% 142.56/84.83 | (1491) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_rng(v0) = v4 & relation_dom(v0) = v2 & subset(all_920_0_1163, v4) = v5 & subset(empty_set, v2) = v3 & subset(empty_set, v0) = v1 & ( ~ (v1 = 0) | (v5 = 0 & v3 = 0))))
% 142.56/84.83 |
% 142.56/84.83 | Instantiating formula (1489) with all_0_11_11, all_0_14_14 and discharging atoms relation_dom(all_0_14_14) = all_0_11_11, yields:
% 142.56/84.83 | (1492) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (relation_rng(all_0_14_14) = v3 & subset(all_920_0_1163, v3) = v4 & subset(empty_set, all_0_11_11) = v2 & subset(empty_set, all_0_14_14) = v1 & relation(all_0_14_14) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | (v4 = 0 & v2 = 0)))
% 142.56/84.83 |
% 142.56/84.83 | Instantiating (1492) with all_1995_0_2824, all_1995_1_2825, all_1995_2_2826, all_1995_3_2827, all_1995_4_2828 yields:
% 142.56/84.83 | (1493) relation_rng(all_0_14_14) = all_1995_1_2825 & subset(all_920_0_1163, all_1995_1_2825) = all_1995_0_2824 & subset(empty_set, all_0_11_11) = all_1995_2_2826 & subset(empty_set, all_0_14_14) = all_1995_3_2827 & relation(all_0_14_14) = all_1995_4_2828 & ( ~ (all_1995_3_2827 = 0) | ~ (all_1995_4_2828 = 0) | (all_1995_0_2824 = 0 & all_1995_2_2826 = 0))
% 142.56/84.83 |
% 142.56/84.83 | Applying alpha-rule on (1493) yields:
% 142.56/84.83 | (1494) subset(empty_set, all_0_14_14) = all_1995_3_2827
% 142.56/84.83 | (1495) subset(empty_set, all_0_11_11) = all_1995_2_2826
% 142.56/84.83 | (1496) subset(all_920_0_1163, all_1995_1_2825) = all_1995_0_2824
% 142.56/84.83 | (1497) ~ (all_1995_3_2827 = 0) | ~ (all_1995_4_2828 = 0) | (all_1995_0_2824 = 0 & all_1995_2_2826 = 0)
% 142.56/84.83 | (1498) relation(all_0_14_14) = all_1995_4_2828
% 142.56/84.83 | (1499) relation_rng(all_0_14_14) = all_1995_1_2825
% 142.56/84.83 |
% 142.56/84.83 +-Applying beta-rule and splitting (698), into two cases.
% 142.56/84.83 |-Branch one:
% 142.56/84.83 | (1500) ~ (all_670_1_853 = 0)
% 142.56/84.83 |
% 142.56/84.83 | Equations (1393) can reduce 1500 to:
% 142.56/84.83 | (1402) $false
% 142.56/84.83 |
% 142.56/84.83 |-The branch is then unsatisfiable
% 142.56/84.83 |-Branch two:
% 142.56/84.83 | (1393) all_670_1_853 = 0
% 142.56/84.83 | (1503) ! [v0] : ! [v1] : ( ~ (relation_composition(empty_set, v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_dom(v1) = v5 & relation_dom(v0) = v3 & subset(empty_set, v3) = v4 & relation(v0) = v2 & ( ~ (v4 = 0) | ~ (v2 = 0) | v5 = all_670_0_852))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_composition(empty_set, v0) = v4 & relation_dom(v4) = v5 & subset(empty_set, v1) = v3 & relation(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | v5 = all_670_0_852))) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : (relation_composition(empty_set, v0) = v3 & relation_dom(v3) = v4 & relation_dom(v0) = v1 & subset(empty_set, v1) = v2 & ( ~ (v2 = 0) | v4 = all_670_0_852)))
% 142.56/84.83 |
% 142.56/84.83 | Applying alpha-rule on (1503) yields:
% 142.56/84.83 | (1504) ! [v0] : ! [v1] : ( ~ (relation_composition(empty_set, v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_dom(v1) = v5 & relation_dom(v0) = v3 & subset(empty_set, v3) = v4 & relation(v0) = v2 & ( ~ (v4 = 0) | ~ (v2 = 0) | v5 = all_670_0_852)))
% 142.56/84.83 | (1505) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_composition(empty_set, v0) = v4 & relation_dom(v4) = v5 & subset(empty_set, v1) = v3 & relation(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | v5 = all_670_0_852)))
% 142.56/84.84 | (1506) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : (relation_composition(empty_set, v0) = v3 & relation_dom(v3) = v4 & relation_dom(v0) = v1 & subset(empty_set, v1) = v2 & ( ~ (v2 = 0) | v4 = all_670_0_852)))
% 142.56/84.84 |
% 142.56/84.84 | Instantiating formula (1505) with all_0_11_11, all_0_14_14 and discharging atoms relation_dom(all_0_14_14) = all_0_11_11, yields:
% 142.56/84.84 | (1507) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (relation_composition(empty_set, all_0_14_14) = v2 & relation_dom(v2) = v3 & subset(empty_set, all_0_11_11) = v1 & relation(all_0_14_14) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = all_670_0_852))
% 142.56/84.84 |
% 142.56/84.84 | Instantiating (1507) with all_2141_0_2987, all_2141_1_2988, all_2141_2_2989, all_2141_3_2990 yields:
% 142.56/84.84 | (1508) relation_composition(empty_set, all_0_14_14) = all_2141_1_2988 & relation_dom(all_2141_1_2988) = all_2141_0_2987 & subset(empty_set, all_0_11_11) = all_2141_2_2989 & relation(all_0_14_14) = all_2141_3_2990 & ( ~ (all_2141_2_2989 = 0) | ~ (all_2141_3_2990 = 0) | all_2141_0_2987 = all_670_0_852)
% 142.56/84.84 |
% 142.56/84.84 | Applying alpha-rule on (1508) yields:
% 142.56/84.84 | (1509) ~ (all_2141_2_2989 = 0) | ~ (all_2141_3_2990 = 0) | all_2141_0_2987 = all_670_0_852
% 142.56/84.84 | (1510) relation_dom(all_2141_1_2988) = all_2141_0_2987
% 142.56/84.84 | (1511) relation_composition(empty_set, all_0_14_14) = all_2141_1_2988
% 142.56/84.84 | (1512) subset(empty_set, all_0_11_11) = all_2141_2_2989
% 142.56/84.84 | (1513) relation(all_0_14_14) = all_2141_3_2990
% 142.56/84.84 |
% 142.56/84.84 +-Applying beta-rule and splitting (730), into two cases.
% 142.56/84.84 |-Branch one:
% 142.56/84.84 | (1514) ~ (all_922_1_1166 = 0)
% 142.56/84.84 |
% 142.56/84.84 | Equations (1395) can reduce 1514 to:
% 142.56/84.84 | (1402) $false
% 142.56/84.84 |
% 142.56/84.84 |-The branch is then unsatisfiable
% 142.56/84.84 |-Branch two:
% 142.56/84.84 | (1395) all_922_1_1166 = 0
% 142.56/84.84 | (1517) ! [v0] : ! [v1] : ( ~ (relation_composition(empty_set, v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_dom(v1) = v5 & relation_dom(v0) = v3 & subset(all_922_0_1165, v3) = v4 & relation(v0) = v2 & ( ~ (v4 = 0) | ~ (v2 = 0) | v5 = empty_set))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_composition(empty_set, v0) = v4 & relation_dom(v4) = v5 & subset(all_922_0_1165, v1) = v3 & relation(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | v5 = empty_set))) & ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : (relation_composition(empty_set, v0) = v3 & relation_dom(v3) = v4 & relation_dom(v0) = v1 & subset(all_922_0_1165, v1) = v2 & ( ~ (v2 = 0) | v4 = empty_set)))
% 142.56/84.84 |
% 142.56/84.84 | Applying alpha-rule on (1517) yields:
% 142.56/84.84 | (1518) ! [v0] : ! [v1] : ( ~ (relation_composition(empty_set, v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_dom(v1) = v5 & relation_dom(v0) = v3 & subset(all_922_0_1165, v3) = v4 & relation(v0) = v2 & ( ~ (v4 = 0) | ~ (v2 = 0) | v5 = empty_set)))
% 142.56/84.84 | (1519) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_composition(empty_set, v0) = v4 & relation_dom(v4) = v5 & subset(all_922_0_1165, v1) = v3 & relation(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | v5 = empty_set)))
% 142.56/84.84 | (1520) ! [v0] : ( ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : (relation_composition(empty_set, v0) = v3 & relation_dom(v3) = v4 & relation_dom(v0) = v1 & subset(all_922_0_1165, v1) = v2 & ( ~ (v2 = 0) | v4 = empty_set)))
% 142.56/84.84 |
% 142.56/84.84 | Instantiating formula (1519) with all_0_11_11, all_0_14_14 and discharging atoms relation_dom(all_0_14_14) = all_0_11_11, yields:
% 142.56/84.84 | (1521) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (relation_composition(empty_set, all_0_14_14) = v2 & relation_dom(v2) = v3 & subset(all_922_0_1165, all_0_11_11) = v1 & relation(all_0_14_14) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = empty_set))
% 142.56/84.84 |
% 142.56/84.84 | Instantiating (1521) with all_2171_0_3031, all_2171_1_3032, all_2171_2_3033, all_2171_3_3034 yields:
% 142.56/84.84 | (1522) relation_composition(empty_set, all_0_14_14) = all_2171_1_3032 & relation_dom(all_2171_1_3032) = all_2171_0_3031 & subset(all_922_0_1165, all_0_11_11) = all_2171_2_3033 & relation(all_0_14_14) = all_2171_3_3034 & ( ~ (all_2171_2_3033 = 0) | ~ (all_2171_3_3034 = 0) | all_2171_0_3031 = empty_set)
% 142.56/84.84 |
% 142.56/84.84 | Applying alpha-rule on (1522) yields:
% 142.56/84.84 | (1523) subset(all_922_0_1165, all_0_11_11) = all_2171_2_3033
% 142.56/84.84 | (1524) ~ (all_2171_2_3033 = 0) | ~ (all_2171_3_3034 = 0) | all_2171_0_3031 = empty_set
% 142.56/84.84 | (1525) relation(all_0_14_14) = all_2171_3_3034
% 142.56/84.84 | (1526) relation_composition(empty_set, all_0_14_14) = all_2171_1_3032
% 142.56/84.84 | (1527) relation_dom(all_2171_1_3032) = all_2171_0_3031
% 142.56/84.84 |
% 142.56/84.84 | Instantiating formula (220) with all_0_14_14, all_0_16_16, all_1881_1_2643, all_0_9_9 and discharging atoms apply(all_0_14_14, all_0_16_16) = all_1881_1_2643, apply(all_0_14_14, all_0_16_16) = all_0_9_9, yields:
% 142.56/84.84 | (1528) all_1881_1_2643 = all_0_9_9
% 142.56/84.84 |
% 142.56/84.84 | Instantiating formula (220) with all_0_14_14, all_0_16_16, all_1783_1_2530, all_1881_1_2643 and discharging atoms apply(all_0_14_14, all_0_16_16) = all_1881_1_2643, apply(all_0_14_14, all_0_16_16) = all_1783_1_2530, yields:
% 142.56/84.84 | (1529) all_1881_1_2643 = all_1783_1_2530
% 142.56/84.84 |
% 142.56/84.84 | Instantiating formula (7) with all_0_14_14, all_2171_3_3034, 0 and discharging atoms relation(all_0_14_14) = all_2171_3_3034, relation(all_0_14_14) = 0, yields:
% 142.56/84.84 | (1530) all_2171_3_3034 = 0
% 142.56/84.84 |
% 142.56/84.84 | Instantiating formula (7) with all_0_14_14, all_2141_3_2990, all_2171_3_3034 and discharging atoms relation(all_0_14_14) = all_2171_3_3034, relation(all_0_14_14) = all_2141_3_2990, yields:
% 142.56/84.84 | (1531) all_2171_3_3034 = all_2141_3_2990
% 142.56/84.84 |
% 142.56/84.84 | Instantiating formula (7) with all_0_14_14, all_1955_4_2758, all_2141_3_2990 and discharging atoms relation(all_0_14_14) = all_2141_3_2990, relation(all_0_14_14) = all_1955_4_2758, yields:
% 142.56/84.84 | (1532) all_2141_3_2990 = all_1955_4_2758
% 142.56/84.84 |
% 142.56/84.84 | Instantiating formula (7) with all_0_14_14, all_1955_4_2758, all_1995_4_2828 and discharging atoms relation(all_0_14_14) = all_1995_4_2828, relation(all_0_14_14) = all_1955_4_2758, yields:
% 142.56/84.84 | (1533) all_1995_4_2828 = all_1955_4_2758
% 142.56/84.84 |
% 142.56/84.84 | Instantiating formula (7) with all_0_14_14, all_1939_3_2723, all_1995_4_2828 and discharging atoms relation(all_0_14_14) = all_1995_4_2828, relation(all_0_14_14) = all_1939_3_2723, yields:
% 142.56/84.84 | (1534) all_1995_4_2828 = all_1939_3_2723
% 142.56/84.84 |
% 142.56/84.84 | Instantiating formula (7) with all_0_14_14, all_1799_4_2569, all_1995_4_2828 and discharging atoms relation(all_0_14_14) = all_1995_4_2828, relation(all_0_14_14) = all_1799_4_2569, yields:
% 142.56/84.84 | (1535) all_1995_4_2828 = all_1799_4_2569
% 142.56/84.84 |
% 142.56/84.84 | Instantiating formula (36) with all_0_13_13, all_0_14_14, all_1881_0_2642, all_0_12_12 and discharging atoms in(all_0_13_13, all_0_14_14) = all_1881_0_2642, in(all_0_13_13, all_0_14_14) = all_0_12_12, yields:
% 142.56/84.84 | (1536) all_1881_0_2642 = all_0_12_12
% 142.56/84.84 |
% 142.56/84.84 | Instantiating formula (36) with all_0_13_13, all_0_14_14, all_1867_0_2637, all_1881_0_2642 and discharging atoms in(all_0_13_13, all_0_14_14) = all_1881_0_2642, in(all_0_13_13, all_0_14_14) = all_1867_0_2637, yields:
% 142.56/84.84 | (1537) all_1881_0_2642 = all_1867_0_2637
% 142.56/84.84 |
% 142.56/84.84 | Instantiating formula (36) with all_0_13_13, all_0_14_14, all_1783_0_2529, all_1881_0_2642 and discharging atoms in(all_0_13_13, all_0_14_14) = all_1881_0_2642, in(all_0_13_13, all_0_14_14) = all_1783_0_2529, yields:
% 142.56/84.84 | (1538) all_1881_0_2642 = all_1783_0_2529
% 142.56/84.84 |
% 142.56/84.84 | Instantiating formula (36) with all_0_16_16, all_0_11_11, all_1881_2_2644, all_0_10_10 and discharging atoms in(all_0_16_16, all_0_11_11) = all_1881_2_2644, in(all_0_16_16, all_0_11_11) = all_0_10_10, yields:
% 142.56/84.84 | (1539) all_1881_2_2644 = all_0_10_10
% 142.56/84.84 |
% 142.56/84.84 | Instantiating formula (36) with all_0_16_16, all_0_11_11, all_1783_2_2531, all_1881_2_2644 and discharging atoms in(all_0_16_16, all_0_11_11) = all_1881_2_2644, in(all_0_16_16, all_0_11_11) = all_1783_2_2531, yields:
% 142.56/84.84 | (1540) all_1881_2_2644 = all_1783_2_2531
% 142.56/84.84 |
% 142.56/84.84 | Combining equations (1531,1530) yields a new equation:
% 142.56/84.84 | (1541) all_2141_3_2990 = 0
% 142.56/84.84 |
% 142.56/84.84 | Simplifying 1541 yields:
% 142.56/84.84 | (1542) all_2141_3_2990 = 0
% 142.56/84.84 |
% 142.56/84.84 | Combining equations (1532,1542) yields a new equation:
% 142.56/84.84 | (1543) all_1955_4_2758 = 0
% 142.56/84.84 |
% 142.56/84.84 | Simplifying 1543 yields:
% 142.56/84.84 | (1544) all_1955_4_2758 = 0
% 142.56/84.84 |
% 142.56/84.84 | Combining equations (1533,1534) yields a new equation:
% 142.56/84.84 | (1545) all_1955_4_2758 = all_1939_3_2723
% 142.56/84.84 |
% 142.56/84.84 | Simplifying 1545 yields:
% 142.56/84.84 | (1546) all_1955_4_2758 = all_1939_3_2723
% 142.56/84.84 |
% 142.56/84.84 | Combining equations (1535,1534) yields a new equation:
% 142.56/84.84 | (1547) all_1939_3_2723 = all_1799_4_2569
% 142.56/84.84 |
% 142.56/84.84 | Combining equations (1546,1544) yields a new equation:
% 142.56/84.84 | (1548) all_1939_3_2723 = 0
% 142.56/84.84 |
% 142.56/84.84 | Simplifying 1548 yields:
% 142.56/84.84 | (1549) all_1939_3_2723 = 0
% 142.56/84.84 |
% 142.56/84.84 | Combining equations (1547,1549) yields a new equation:
% 142.56/84.84 | (1550) all_1799_4_2569 = 0
% 142.56/84.84 |
% 142.56/84.84 | Simplifying 1550 yields:
% 142.56/84.84 | (1551) all_1799_4_2569 = 0
% 142.56/84.84 |
% 142.56/84.84 | Combining equations (1538,1537) yields a new equation:
% 142.56/84.84 | (1552) all_1867_0_2637 = all_1783_0_2529
% 142.56/84.84 |
% 142.56/84.84 | Combining equations (1536,1537) yields a new equation:
% 142.56/84.84 | (1553) all_1867_0_2637 = all_0_12_12
% 142.56/84.84 |
% 142.56/84.84 | Combining equations (1528,1529) yields a new equation:
% 142.56/84.84 | (1554) all_1783_1_2530 = all_0_9_9
% 142.56/84.84 |
% 142.56/84.84 | Combining equations (1539,1540) yields a new equation:
% 142.56/84.84 | (1555) all_1783_2_2531 = all_0_10_10
% 142.56/84.84 |
% 142.56/84.84 | Combining equations (1552,1553) yields a new equation:
% 142.56/84.84 | (1556) all_1783_0_2529 = all_0_12_12
% 142.56/84.84 |
% 142.56/84.84 | Simplifying 1556 yields:
% 142.56/84.84 | (1557) all_1783_0_2529 = all_0_12_12
% 142.56/84.84 |
% 142.56/84.84 | From (1554) and (1419) follows:
% 142.56/84.84 | (372) apply(all_0_14_14, all_0_16_16) = all_0_9_9
% 142.56/84.84 |
% 142.56/84.84 | From (1551) and (1425) follows:
% 142.56/84.85 | (369) relation(all_0_14_14) = 0
% 142.56/84.85 |
% 142.56/84.85 | From (1557) and (1420) follows:
% 142.56/84.85 | (262) in(all_0_13_13, all_0_14_14) = all_0_12_12
% 142.56/84.85 |
% 142.56/84.85 | From (1555) and (1430) follows:
% 142.56/84.85 | (129) in(all_0_16_16, all_0_11_11) = all_0_10_10
% 142.56/84.85 |
% 142.56/84.85 +-Applying beta-rule and splitting (667), into two cases.
% 142.56/84.85 |-Branch one:
% 142.56/84.85 | (1562) apply(all_0_14_14, all_0_16_16) = all_497_1_628 & in(all_0_13_13, all_0_14_14) = all_497_0_627 & in(all_0_16_16, all_0_11_11) = all_497_2_629 & ( ~ (all_497_2_629 = 0) | (( ~ (all_497_0_627 = 0) | all_497_1_628 = all_0_15_15) & ( ~ (all_497_1_628 = all_0_15_15) | all_497_0_627 = 0)))
% 142.56/84.85 |
% 142.56/84.85 | Applying alpha-rule on (1562) yields:
% 142.56/84.85 | (1563) apply(all_0_14_14, all_0_16_16) = all_497_1_628
% 142.56/84.85 | (1564) in(all_0_13_13, all_0_14_14) = all_497_0_627
% 142.56/84.85 | (1565) in(all_0_16_16, all_0_11_11) = all_497_2_629
% 142.56/84.85 | (1566) ~ (all_497_2_629 = 0) | (( ~ (all_497_0_627 = 0) | all_497_1_628 = all_0_15_15) & ( ~ (all_497_1_628 = all_0_15_15) | all_497_0_627 = 0))
% 142.56/84.85 |
% 142.56/84.85 | Instantiating formula (220) with all_0_14_14, all_0_16_16, all_497_1_628, all_0_9_9 and discharging atoms apply(all_0_14_14, all_0_16_16) = all_497_1_628, apply(all_0_14_14, all_0_16_16) = all_0_9_9, yields:
% 142.56/84.85 | (1567) all_497_1_628 = all_0_9_9
% 142.56/84.85 |
% 142.56/84.85 | Instantiating formula (36) with all_0_13_13, all_0_14_14, all_497_0_627, all_0_12_12 and discharging atoms in(all_0_13_13, all_0_14_14) = all_497_0_627, in(all_0_13_13, all_0_14_14) = all_0_12_12, yields:
% 142.56/84.85 | (1568) all_497_0_627 = all_0_12_12
% 142.56/84.85 |
% 142.56/84.85 | Instantiating formula (36) with all_0_16_16, all_0_11_11, all_497_2_629, all_0_10_10 and discharging atoms in(all_0_16_16, all_0_11_11) = all_497_2_629, in(all_0_16_16, all_0_11_11) = all_0_10_10, yields:
% 142.56/84.85 | (1569) all_497_2_629 = all_0_10_10
% 142.56/84.85 |
% 142.56/84.85 | From (1568) and (1564) follows:
% 142.56/84.85 | (262) in(all_0_13_13, all_0_14_14) = all_0_12_12
% 142.56/84.85 |
% 142.56/84.85 +-Applying beta-rule and splitting (203), into two cases.
% 142.56/84.85 |-Branch one:
% 142.56/84.85 | (1571) all_0_9_9 = all_0_15_15 & all_0_10_10 = 0 & ~ (all_0_12_12 = 0)
% 142.56/84.85 |
% 142.56/84.85 | Applying alpha-rule on (1571) yields:
% 142.56/84.85 | (1572) all_0_9_9 = all_0_15_15
% 142.56/84.85 | (1573) all_0_10_10 = 0
% 142.56/84.85 | (1574) ~ (all_0_12_12 = 0)
% 142.56/84.85 |
% 142.56/84.85 | Combining equations (1573,1569) yields a new equation:
% 142.56/84.85 | (1575) all_497_2_629 = 0
% 142.56/84.85 |
% 142.56/84.85 | Combining equations (1572,1567) yields a new equation:
% 142.56/84.85 | (1576) all_497_1_628 = all_0_15_15
% 142.56/84.85 |
% 142.56/84.85 +-Applying beta-rule and splitting (1566), into two cases.
% 142.56/84.85 |-Branch one:
% 142.56/84.85 | (1577) ~ (all_497_2_629 = 0)
% 142.56/84.85 |
% 142.56/84.85 | Equations (1575) can reduce 1577 to:
% 142.56/84.85 | (1402) $false
% 142.56/84.85 |
% 142.56/84.85 |-The branch is then unsatisfiable
% 142.56/84.85 |-Branch two:
% 142.56/84.85 | (1575) all_497_2_629 = 0
% 142.56/84.85 | (1580) ( ~ (all_497_0_627 = 0) | all_497_1_628 = all_0_15_15) & ( ~ (all_497_1_628 = all_0_15_15) | all_497_0_627 = 0)
% 142.56/84.85 |
% 142.56/84.85 | Applying alpha-rule on (1580) yields:
% 142.56/84.85 | (1581) ~ (all_497_0_627 = 0) | all_497_1_628 = all_0_15_15
% 142.56/84.85 | (1582) ~ (all_497_1_628 = all_0_15_15) | all_497_0_627 = 0
% 142.56/84.85 |
% 142.56/84.85 +-Applying beta-rule and splitting (1582), into two cases.
% 142.56/84.85 |-Branch one:
% 142.56/84.85 | (1583) ~ (all_497_1_628 = all_0_15_15)
% 142.56/84.85 |
% 142.56/84.85 | Equations (1576) can reduce 1583 to:
% 142.56/84.85 | (1402) $false
% 142.56/84.85 |
% 142.56/84.85 |-The branch is then unsatisfiable
% 142.56/84.85 |-Branch two:
% 142.56/84.85 | (1576) all_497_1_628 = all_0_15_15
% 142.56/84.85 | (1586) all_497_0_627 = 0
% 142.56/84.85 |
% 142.56/84.85 | Combining equations (1586,1568) yields a new equation:
% 142.56/84.85 | (1587) all_0_12_12 = 0
% 142.56/84.85 |
% 142.56/84.85 | Equations (1587) can reduce 1574 to:
% 142.56/84.85 | (1402) $false
% 142.56/84.85 |
% 142.56/84.85 |-The branch is then unsatisfiable
% 142.56/84.85 |-Branch two:
% 142.56/84.85 | (1589) all_0_12_12 = 0 & ( ~ (all_0_9_9 = all_0_15_15) | ~ (all_0_10_10 = 0))
% 142.56/84.85 |
% 142.56/84.85 | Applying alpha-rule on (1589) yields:
% 142.56/84.85 | (1587) all_0_12_12 = 0
% 142.56/84.85 | (1591) ~ (all_0_9_9 = all_0_15_15) | ~ (all_0_10_10 = 0)
% 142.56/84.85 |
% 142.56/84.85 | Combining equations (1587,1557) yields a new equation:
% 142.56/84.85 | (1592) all_1783_0_2529 = 0
% 142.56/84.85 |
% 142.56/84.85 | From (1587) and (262) follows:
% 142.56/84.85 | (1593) in(all_0_13_13, all_0_14_14) = 0
% 142.56/84.85 |
% 142.56/84.85 +-Applying beta-rule and splitting (533), into two cases.
% 142.56/84.85 |-Branch one:
% 142.56/84.85 | (1573) all_0_10_10 = 0
% 142.56/84.85 |
% 142.56/84.85 | Combining equations (1573,1555) yields a new equation:
% 142.56/84.85 | (1595) all_1783_2_2531 = 0
% 142.56/84.85 |
% 142.56/84.85 +-Applying beta-rule and splitting (1422), into two cases.
% 142.56/84.85 |-Branch one:
% 142.56/84.85 | (1596) ~ (all_1783_2_2531 = 0)
% 142.56/84.85 |
% 142.56/84.85 | Equations (1595) can reduce 1596 to:
% 142.56/84.85 | (1402) $false
% 142.56/84.85 |
% 142.56/84.85 |-The branch is then unsatisfiable
% 142.56/84.85 |-Branch two:
% 142.56/84.85 | (1595) all_1783_2_2531 = 0
% 142.56/84.85 | (1599) ( ~ (all_1783_0_2529 = 0) | all_1783_1_2530 = all_0_15_15) & ( ~ (all_1783_1_2530 = all_0_15_15) | all_1783_0_2529 = 0)
% 142.56/84.85 |
% 142.56/84.85 | Applying alpha-rule on (1599) yields:
% 142.56/84.85 | (1600) ~ (all_1783_0_2529 = 0) | all_1783_1_2530 = all_0_15_15
% 142.56/84.85 | (1601) ~ (all_1783_1_2530 = all_0_15_15) | all_1783_0_2529 = 0
% 142.56/84.85 |
% 142.56/84.85 +-Applying beta-rule and splitting (1591), into two cases.
% 142.56/84.85 |-Branch one:
% 142.56/84.85 | (1602) ~ (all_0_10_10 = 0)
% 142.56/84.85 |
% 142.56/84.85 | Equations (1573) can reduce 1602 to:
% 142.56/84.85 | (1402) $false
% 142.56/84.85 |
% 142.56/84.85 |-The branch is then unsatisfiable
% 142.56/84.85 |-Branch two:
% 142.56/84.85 | (1573) all_0_10_10 = 0
% 142.56/84.85 | (1605) ~ (all_0_9_9 = all_0_15_15)
% 142.56/84.85 |
% 142.56/84.85 +-Applying beta-rule and splitting (1600), into two cases.
% 142.56/84.85 |-Branch one:
% 142.56/84.85 | (1606) ~ (all_1783_0_2529 = 0)
% 142.56/84.85 |
% 142.56/84.85 | Equations (1592) can reduce 1606 to:
% 142.56/84.85 | (1402) $false
% 142.56/84.85 |
% 142.56/84.85 |-The branch is then unsatisfiable
% 142.56/84.85 |-Branch two:
% 142.56/84.85 | (1592) all_1783_0_2529 = 0
% 142.56/84.85 | (1609) all_1783_1_2530 = all_0_15_15
% 142.56/84.85 |
% 142.56/84.85 | Combining equations (1609,1554) yields a new equation:
% 142.56/84.85 | (1572) all_0_9_9 = all_0_15_15
% 142.56/84.85 |
% 142.56/84.85 | Equations (1572) can reduce 1605 to:
% 142.56/84.85 | (1402) $false
% 142.56/84.85 |
% 142.56/84.85 |-The branch is then unsatisfiable
% 142.56/84.85 |-Branch two:
% 142.56/84.85 | (1602) ~ (all_0_10_10 = 0)
% 142.56/84.85 | (1613) ? [v0] : (( ~ (v0 = 0) & relation(all_0_14_14) = v0) | ( ~ (v0 = 0) & in(all_0_13_13, all_0_14_14) = v0))
% 142.56/84.85 |
% 142.56/84.85 | Instantiating (1613) with all_2435_0_3047 yields:
% 142.56/84.85 | (1614) ( ~ (all_2435_0_3047 = 0) & relation(all_0_14_14) = all_2435_0_3047) | ( ~ (all_2435_0_3047 = 0) & in(all_0_13_13, all_0_14_14) = all_2435_0_3047)
% 142.56/84.85 |
% 142.56/84.85 +-Applying beta-rule and splitting (1614), into two cases.
% 142.56/84.85 |-Branch one:
% 142.56/84.85 | (1615) ~ (all_2435_0_3047 = 0) & relation(all_0_14_14) = all_2435_0_3047
% 142.56/84.85 |
% 142.56/84.85 | Applying alpha-rule on (1615) yields:
% 142.56/84.85 | (1616) ~ (all_2435_0_3047 = 0)
% 142.56/84.85 | (1617) relation(all_0_14_14) = all_2435_0_3047
% 142.56/84.85 |
% 142.56/84.85 | Instantiating formula (7) with all_0_14_14, all_2435_0_3047, 0 and discharging atoms relation(all_0_14_14) = all_2435_0_3047, relation(all_0_14_14) = 0, yields:
% 142.56/84.85 | (1618) all_2435_0_3047 = 0
% 142.56/84.85 |
% 142.56/84.85 | Equations (1618) can reduce 1616 to:
% 142.56/84.85 | (1402) $false
% 142.56/84.85 |
% 142.56/84.85 |-The branch is then unsatisfiable
% 142.56/84.85 |-Branch two:
% 142.56/84.85 | (1620) ~ (all_2435_0_3047 = 0) & in(all_0_13_13, all_0_14_14) = all_2435_0_3047
% 142.56/84.85 |
% 142.56/84.85 | Applying alpha-rule on (1620) yields:
% 142.56/84.85 | (1616) ~ (all_2435_0_3047 = 0)
% 142.56/84.85 | (1622) in(all_0_13_13, all_0_14_14) = all_2435_0_3047
% 142.56/84.85 |
% 142.56/84.85 | Instantiating formula (36) with all_0_13_13, all_0_14_14, 0, all_2435_0_3047 and discharging atoms in(all_0_13_13, all_0_14_14) = all_2435_0_3047, in(all_0_13_13, all_0_14_14) = 0, yields:
% 142.56/84.85 | (1618) all_2435_0_3047 = 0
% 142.56/84.85 |
% 142.56/84.85 | Equations (1618) can reduce 1616 to:
% 142.56/84.85 | (1402) $false
% 142.56/84.85 |
% 142.56/84.85 |-The branch is then unsatisfiable
% 142.56/84.85 |-Branch two:
% 142.56/84.85 | (1625) relation(all_0_14_14) = all_497_2_629 & function(all_0_14_14) = all_497_1_628 & ( ~ (all_497_1_628 = 0) | ~ (all_497_2_629 = 0))
% 142.56/84.85 |
% 142.56/84.85 | Applying alpha-rule on (1625) yields:
% 142.56/84.85 | (1626) relation(all_0_14_14) = all_497_2_629
% 142.56/84.86 | (1627) function(all_0_14_14) = all_497_1_628
% 142.56/84.86 | (1628) ~ (all_497_1_628 = 0) | ~ (all_497_2_629 = 0)
% 142.56/84.86 |
% 142.56/84.86 | Instantiating formula (7) with all_0_14_14, all_497_2_629, 0 and discharging atoms relation(all_0_14_14) = all_497_2_629, relation(all_0_14_14) = 0, yields:
% 142.56/84.86 | (1575) all_497_2_629 = 0
% 142.56/84.86 |
% 142.56/84.86 | Instantiating formula (92) with all_0_14_14, all_497_1_628, 0 and discharging atoms function(all_0_14_14) = all_497_1_628, function(all_0_14_14) = 0, yields:
% 142.56/84.86 | (1630) all_497_1_628 = 0
% 142.56/84.86 |
% 142.56/84.86 +-Applying beta-rule and splitting (1628), into two cases.
% 142.56/84.86 |-Branch one:
% 142.56/84.86 | (1631) ~ (all_497_1_628 = 0)
% 142.56/84.86 |
% 142.56/84.86 | Equations (1630) can reduce 1631 to:
% 142.56/84.86 | (1402) $false
% 142.56/84.86 |
% 142.56/84.86 |-The branch is then unsatisfiable
% 142.56/84.86 |-Branch two:
% 142.56/84.86 | (1630) all_497_1_628 = 0
% 142.56/84.86 | (1577) ~ (all_497_2_629 = 0)
% 142.56/84.86 |
% 142.56/84.86 | Equations (1575) can reduce 1577 to:
% 142.56/84.86 | (1402) $false
% 142.56/84.86 |
% 142.56/84.86 |-The branch is then unsatisfiable
% 142.56/84.86 % SZS output end Proof for theBenchmark
% 142.56/84.86
% 142.56/84.86 84243ms
%------------------------------------------------------------------------------